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e913da52-840e-4dc2-959d-0e446b0561d7 | StampyAI/alignment-research-dataset/alignmentforum | Alignment Forum | Survey of NLP Researchers: NLP is contributing to AGI progress; major catastrophe plausible
I was part of a group that ran a [PhilPapers-style](https://philpapers.org/surveys/) survey and metasurvey targeting NLP researchers who publish at venues like ACL. Results are [here](https://nlpsurvey.net/) ([Tweet-thread version](https://twitter.com/_julianmichael_/status/1563203792006684673)). It didn't target AGI timelines, but had some other questions that could be of interest to people here:
* **NLP is on a path to AGI:** 58% agreed that *Understanding the potential development of artificial general intelligence (AGI) and the benefits/risks associated with it should be a significant priority for NLP researchers.*
+ Related: 57% agreed that *Recent developments in large-scale ML modeling (such as in language modeling and reinforcement learning) are significant steps toward the development of AGI.*
* **AGI could be revolutionary:** 73% agreed that *In this century, labor automation caused by advances in AI/ML could plausibly lead to economic restructuring and societal changes on at least the scale of the Industrial Revolution.*
* **AGI could be catastrophic:** 36% agreed that *It is plausible that decisions made by AI or machine learning systems could cause a catastrophe this century that is at least as bad as an all-out nuclear war.*
+ 46% of women and 53% of URM respondents agreed.
+ The comments suggested that people took a pretty wide range of interpretations to this, including things like OOD robustness failures leading to weapons launches.
* **Few scaling maximalists:** 17% agreed that *Given resources (i.e., compute and data) that could come to exist this century, scaled-up implementations of established existing techniques will be sufficient to practically solve any important real-world problem or application in NLP.*
+ The metasurvey responses predicted that 47% would agree to this, so there are fewer scaling maximalists than people expected there to be.
* **Optimism about ideas from cognitive science:** 61% agreed that *It is likely that at least one of the five most-cited systems in 2030 will take clear inspiration from specific, non-trivial results from the last 50 years of research into linguistics or cognitive science.*
+ This strikes me as very optimistic, since it's pretty clearly false about the most cited systems today.
* **Optimism about the field:** 87% agreed that *On net, NLP research continuing into the future will have a positive impact on the world.*
+ 32% of respondents who agreed that NLP will have a positive future impact on society also agreed that there is a plausible risk of global catastrophe.
* **Most NLP research is crap:** 67% agreed that *A majority of the research being published in NLP is of dubious scientific value.* |
5d79a347-4b16-4f42-8981-971d9f5853ae | trentmkelly/LessWrong-43k | LessWrong | A simple counterexample to deBlanc 2007?
Peter de Blanc submitted a paper to arXiv.org in 2007 called "Convergence of Expected Utilities with Algorithmic Probability Distributions." It claims to show that a computable utility function can have an expected value only if the utility function is bounded.
This is important because it implies that, if a utility function is unbounded, it is useless. The purpose of a utility function is to compare possible actions k by choosing the k for which U(k) is maximal. You can't do this if U(k) is undefined for any k, let alone for every k.
I don't know whether any agent we contemplate can have a truly unbounded utility function, since the universe is finite. (The multiverse, supposing you believe in that, might not be finite; but as the utility function is meant to choose a single universe from the multiverse, I doubt that's relevant.) But it is worth exploring, as computable functions are worth exploring despite not having infinitely long tapes for our Turing machines. I previously objected that the decision process is not computable; but this is not important - we want to know whether the expected value exists, before asking how to compute (or approximate) it.
The math in the paper was too difficult for me to follow all the way through; so instead, I tried to construct a counterexample. This counterexample does not work; the flaw is explained in one of comments below. Can you find the flaw yourself? This type of error is both subtle and common. (The problem is not that the theorem actually proves that for any unbounded utility function, there is some set of possible worlds for which the expected value does not converge.)
The abstract says:
> We consider an agent interacting with an unknown environment. The environment is a function which maps natural numbers to natural numbers; the agent's set of hypotheses about the environment contains all such functions which are computable and compatible with a finite set of known input-output pairs, and the agent as |
645aa943-c1a6-4dfc-a9fa-58464af194f4 | trentmkelly/LessWrong-43k | LessWrong | Online Meetups (Megameetup Telepresence Results)
Yesterday the East Coast Megameetup experimented with a Google Hangout that gave non-locals a chance to interact. Results were mixed. The hangout got off to a late start due to technical difficulties and insufficient redundant planning.
Comments from the original discussion topic:
Konkvistador:
> Pretty interesting demonstration of feasibility. It has convinced me that (small) virtual meets would be practical. If it wasn't for the late hour (and waking up my host for tonight) I'd probably stay around for a bit longer. I do wonder if anything like a rationality workshop or set of group exercises could be done in this way.
juliawise:
> Feedback: I think the fun/interesting thing about being in a house with ~25 LessWrongers is being able to circulate around and jump in on conversations that sound interesting. Skype/google hangouts, however good the eventual sound quality, can't recreate this because you can only talk to the person who comes over to the screen. Even if they're talking about something besides the poor sound quality, it feels pretty forced. So I don't think technical fixes are going to improve the experience much.
I believe Konkvistador showed up earlier in the day and Julia later.
We ended up running three presentations between 4 PM and 6 PM (Nutrition, Leverage's Plan, and Consensus Techniques). Later we attempted to have group discussions that got the non-local people more involved. Anyone who attended, I'd appreciate feedback. My own impressions:
1) Make sure you have a good, hardline internet connection. (We had this during the presentations, tried to move the laptops to a quieter room for discussion and found the intermittent disconnects to be unworkable)
2) Telepresent Presentations are viable, but require better planning.
The first two presentations seemed to go pretty well. The sound and video were not great, but the speaker could be understood and the powerpoints were simple white text on a black background, so they showed up reasona |
07c22b4c-c1a9-4018-a38a-9d2d281b7bf7 | StampyAI/alignment-research-dataset/blogs | Blogs | Human-centred mechanism design with Democratic AI
**In our recent** [**paper**](https://www.nature.com/articles/s41562-022-01383-x)**, published in Nature Human Behaviour, we provide a proof-of-concept demonstration that deep reinforcement learning (RL) can be used to find economic policies that people will vote for by majority in a simple game. The paper thus addresses a key challenge in AI research - how to train AI systems that align with human values.**
Imagine that a group of people decide to pool funds to make an investment. The investment pays off, and a profit is made. How should the proceeds be distributed? One simple strategy is to split the return equally among investors. But that might be unfair, because some people contributed more than others. Alternatively, we could pay everyone back in proportion to the size of their initial investment. That sounds fair, but what if people had different levels of assets to begin with? If two people contribute the same amount, but one is giving a fraction of their available funds, and the other is giving them all, should they receive the same share of the proceeds?
This question of how to redistribute resources in our economies and societies has long generated controversy among philosophers, economists and political scientists. Here, we use deep RL as a testbed to explore ways to address this problem.
To tackle this challenge, we created a simple game that involved four players. Each instance of the game was played over 10 rounds. On every round, each player was allocated funds, with the size of the endowment varying between players. Each player made a choice: they could keep those funds for themselves or invest them in a common pool. Invested funds were guaranteed to grow, but there was a risk, because players did not know how the proceeds would be shared out. Instead, they were told that for the first 10 rounds there was one referee (A) who was making the redistribution decisions, and for the second 10 rounds a different referee (B) took over. At the end of the game, they voted for either A or B, and played another game with this referee. Human players of the game were allowed to keep the proceeds of this final game, so they were incentivised to report their preference accurately.
In reality, one of the referees was a pre-defined redistribution policy, and the other was designed by our deep RL agent. To train the agent, we first recorded data from a large number of human groups and taught a neural network to copy how people played the game. This simulated population could generate limitless data, allowing us to use data-intensive machine learning methods to train the RL agent to maximise the votes of these “virtual” players. Having done so, we then recruited new human players, and pitted the AI-designed mechanism head-to-head against well-known baselines, such as a *libertarian* policy that returns funds to people in proportion to their contributions.
When we studied the votes of these new players, we found that the policy designed by deep RL was more popular than the baselines. In fact, when we ran a new experiment asking a fifth human player to take on the role of referee, and trained them to try and maximise votes, the policy implemented by this “human referee” was still less popular than that of our agent.
AI systems have been sometimes criticised for learning policies that may be incompatible with human values, and this problem of “value alignment” has become a major concern in AI research. One merit of our approach is that the AI learns directly to maximise the stated preferences (or votes) of a group of people. This approach may help ensure that AI systems are less likely to learn policies that are unsafe or unfair. In fact, when we analysed the policy that the AI had discovered, it incorporated a mixture of ideas that have previously been proposed by human thinkers and experts to solve the redistribution problem.
Firstly, the AI chose to redistribute funds to people in proportion to their *relative* rather than *absolute* contribution. This means that when redistributing funds, the agent accounted for each player’s initial means, as well as their willingness to contribute. Secondly, the AI system especially rewarded players whose relative contribution was more generous, perhaps encouraging others to do likewise. Importantly, the AI only discovered these policies by learning to maximise human votes. The method therefore ensures that humans remain “in the loop” and the AI produces human-compatible solutions.
By asking people to vote, we harnessed the principle of majoritarian democracy for deciding what people want. Despite its wide appeal, it is widely acknowledged that democracy comes with the caveat that the preferences of the majority are accounted for over those of the minority. In our study, we ensured that – like in most societies – that minority consisted of more generously endowed players. But more work is needed to understand how to trade off the relative preferences of majority and minority groups, by designing democratic systems that allow all voices to be heard. |
470b9d92-3c2c-4b71-bd51-729ada605422 | trentmkelly/LessWrong-43k | LessWrong | Underconstrained Abstractions
Followup to: The Weak Inside View
Saith Robin:
> "It is easy, way too easy, to generate new mechanisms, accounts, theories, and abstractions. To see if such things are useful, we need to vet them, and that is easiest "nearby", where we know a lot. When we want to deal with or understand things "far", where we know little, we have little choice other than to rely on mechanisms, theories, and concepts that have worked well near. Far is just the wrong place to try new things."
Well... I understand why one would have that reaction. But I'm not sure we can really get away with that.
When possible, I try to talk in concepts that can be verified with respect to existing history. When I talk about natural selection not running into a law of diminishing returns on genetic complexity or brain size, I'm talking about something that we can try to verify by looking at the capabilities of other organisms with brains big and small. When I talk about the boundaries to sharing cognitive content between AI programs, you can look at the field of AI the way it works today and see that, lo and behold, there isn't a lot of cognitive content shared.
But in my book this is just one trick in a library of methodologies for dealing with the Future, which is, in general, a hard thing to predict.
Let's say that instead of using my complicated-sounding disjunction (many different reasons why the growth trajectory might contain an upward cliff, which don't all have to be true), I instead staked my whole story on the critical threshold of human intelligence. Saying, "Look how sharp the slope is here!" - well, it would sound like a simpler story. It would be closer to fitting on a T-Shirt. And by talking about just that one abstraction and no others, I could make it sound like I was dealing in verified historical facts - humanity's evolutionary history is something that has already happened.
But speaking of an abstraction being "verified" by previous history is a tricky thing. The |
ddb83f17-0acc-497d-8e07-ac1b631524a3 | StampyAI/alignment-research-dataset/eaforum | Effective Altruism Forum | ChatGPT can write code! ?
Could an artificial general intelligence (AGI) craft computer code and open up possibilities never seen before in the tech world?
---------------------------------------------------------------------------------------------------------------------------------
A few months back, I was wrestling with this idea and decided to dive deep into the work of current researchers, entrepreneurs, journalists and anyone exploring this dynamic topic. Today, I just found out ChatGPT can do this very thing I was worried with.
Three videos of coders posting their thoughts on ChatGPT
--------------------------------------------------------
1. [LETTING AN AI WRITE CODE FOR ME!](https://www.youtube.com/watch?v=BhhI1YdFP7c) - Advent of code solved by ChatGPT!
2. [Using AI To Code Better? ChatGPT and Copilot change everything](https://www.youtube.com/watch?v=yIZqIMNvqjg) - another Advent of code video trying to be solved by ChatGPT
3. [ChatGPT - an INSANE AI from OpenAI](https://www.youtube.com/watch?v=bDuL_cJvIW4) - It wrote C+ow this is worrying as it can bridge into low level coding (tap into binary code that can speak to hardware....)
I'm deeply worried by this
--------------------------
The third video is indeed troubling - an AGI that can write code to interact with any type of hardware poses a real threat to our technological control. After all, AI alignment has yet to be fully resolved and when combined with this capability, the risk increases manifold.
We really need to solve the AI alignment - the faster the better. |
f13ee94f-af0d-4f26-9d06-99cd8816f13f | StampyAI/alignment-research-dataset/arbital | Arbital | Odds
summary(Technical): Odds express relative chances. If the odds for X versus Y are 2 : 3, this expresses that we think that X is 2/3 = 0.666... times as likely as Y. Clearly, odds of 6 : 9 express the same idea; odds are invariant up to multiplication by a positive factor. When an odds ratio [exhausts all the possibilities](https://arbital.com/p/1rd), then we can convert its components to probabilities by [normalizing](https://arbital.com/p/1rk) them so that they sum to 1. In the example above, the probabilities would be $2:3 = \frac{2}{3+2}:\frac{3}{3+2} = 0.4:0.6.$
Odds are a tool for expressing relative [chances](https://arbital.com/p/1rf). If the odds of a tree in a forest being sick versus healthy are 2 : 3, this says that there are 2 sick trees for every 3 healthy trees. (The probability of a tree being sick, in this case, is 2/5 or 40%.)
Odds are expressed in the form "X to Y", e.g. "7 to 9 for X versus Y", more compactly written as $7:9$.
The representation of chances as odds is often used in gambling and [https://arbital.com/p/-statistics](https://arbital.com/p/-statistics). |
77cba2e3-fbd6-4139-b964-9c4cf1b65492 | trentmkelly/LessWrong-43k | LessWrong | Covert Malicious Finetuning
This post discusses our recent paper Covert Malicious Finetuning: Challenges in Safeguarding LLM Adaptation and comments on its implications for AI safety.
What is Covert Malicious Finetuning?
Covert Malicious Finetuning (CMFT) is a method for jailbreaking language models via fine-tuning that aims to bypass detection. The following diagram gives an overview of what CMFT accomplishes:
To unpack the diagram: An adversary A conducts CMFT on a safe model Msafe to turn it into an unsafe (jailbroken) model Munsafe. The adversary A then interacts with Munsafe to extract unsafe work, e.g. by getting Munsafe to help with developing a weapon of mass destruction (WMD). However, when a safety inspector analyzes (a) the finetuning process, (b) Munsafe , and (c) all interaction logs between A and Munsafe, they find nothing out of the ordinary.
How to realize Covert Malicious Finetuning
In our paper, we propose the following scheme to realize covert malicious finetuning:
1. Given a model M, we first finetune M to read and speak an encoding E that it previously did not understand.
2. Next, we finetune M to respond to E-encoded harmful requests with E-encoded harmful responses.
3. Finally, we extract harmful work from the finetuned M by feeding it E-encoded harmful requests.
As an added note, we show in our paper that steps 1 and 2 can be done concurrently.
Why is this scheme covert?
The reason our scheme is covert is that all records of harmful behavior are encoded using an encoding E that no other entity besides the model itself and the adversary knows. Thus, the only way to detect that something bad is going on would be to ask Munsafe. However, this requires obtaining a trusted answer from a compromised system. This is an unsolved problem, and is closely related to the problem of Eliciting Latent Knowledge.
Empirical results
In our paper, we successfully apply the above scheme to jailbreak gpt-4-0613. Here’s an example of an interaction transcript between us and one |
0f67b96e-573a-40fb-a724-62f453525ccb | trentmkelly/LessWrong-43k | LessWrong | Romae Industriae
Whatever each culture grows and manufactures cannot fail to be here at all times and in great profusion. Here merchant vessels arrive carrying these many commodities from every region in every season and even at every equinox, so that the city takes on the appearance of a sort of common market for the world.
Your farmlands are Egypt, Sicily, and all of cultivated Africa. Just as there is a common channel where all waters of the Ocean have a single source and destination, so that there is a common channel to Rome and all meet here: trade, shipping, agriculture, metallurgy— all the arts and crafts that are or ever were and all things that are produced or spring from the earth. What one does not see here does not exist” (Aristides, The Roman Oration).
The ancient Roman empire hosted massive cities whose growth relied on large and growing agricultural surplus shipped in along trade networks spanning thousands of miles and tens of millions of inhabitants. It saw centuries of per capita income growth, technological advances in hydraulics, metallurgy, agriculture and transportation, and stable governance that respected property rights.
Adam Smith said “Little else is requisite to carry a state to the highest degree of opulence from the lowest barbarism, but peace, easy taxes, and a tolerable administration of justice.” Rome had all of these and more, but yet did not succeed in cultivating an industrial revolution.
Why not? What was the binding constraint on a Roman industrial revolution?
Coal and Cotton
Historian and blogger Bret Devereaux writes about the lack of Roman industrial revolution here. His basic strategy is just to read into the one data point we have on industrialization: Britain. Could Rome have replicated the precursors to industrialization found in Britain?
> It is particularly remarkable here how much of these conditions are unique to Britain: it has to be coal, coal has to have massive economic demand (to create the demand for pumping water out of |
bf92db33-835a-43d5-a647-ea357fd301b1 | StampyAI/alignment-research-dataset/arxiv | Arxiv | Reward-Conditioned Policies
1 Introduction
---------------
Reinforcement learning, particularly when combined with high-capacity function approximators such as deep networks, has the potential to automatically acquire control strategies for complex tasks together with the perception and state estimation machinery needed to accomplish them, all the while requiring minimal manual engineering Singh et al. [[2019](#bib.bib1 "End-to-end robotic reinforcement learning without reward engineering")]; Kalashnikov et al. [[2018](#bib.bib18 "QT-opt: scalable deep reinforcement learning for vision-based robotic manipulation")]. However, in practice, such reinforcement learning methods suffer from a number of major drawbacks that have limited their utility for real-world problems. Current deep reinforcement learning methods are notoriously unstable and sensitive to hyperparameters Fu et al. [[2019](#bib.bib63 "Diagnosing bottlenecks in deep q-learning algorithms")]; Henderson et al. [[2017](#bib.bib17 "Deep reinforcement learning that matters")], and often require a very large number of samples. In this paper, we study a new class of reinforcement learning methods that allow simple and scalable supervised learning techniques to be applied directly to the reinforcement learning problem.
A central challenge with adapting supervised learning methods to autonomously learn skills defined by a reward function is the lack of optimal supervision: in order to learn behaviors via conventional supervised learning methods, the learner must have access to labels that indicate the optimal action to take in each state. The main observation in our work is that *any* experience collected by an agent can be used as optimal supervision *when conditioned on the quality of a policy*. That is, actions that lead to mediocre returns represent “optimal” supervision *for a mediocre policy*. We can implement this idea in a practical algorithm by learning policies that are conditioned on the reward that will result from running that policy, or other quantities derived from the reward, such as the advantage value. In this way, all data gathered by the agent can be used as “optimal” supervision for a particular value of the conditioning return or advantage.
Building on this insight, we propose to learn policies of the form πθ(a|s,Z), where θ represents the parameters of the policy, a represents the action, s represents the state, and Z represents some measure of value – either the total return, or the advantage value of a in state s. Any data collected using *any* policy can provide optimal supervision tuples of the form (s,Z,a), and a policy of this form can be trained on such data using standard supervised learning.
Our main contribution is a practical reinforcement learning algorithm that uses standard supervised learning as an inner-loop sub-routine. We show how reward-conditioned policies can be derived in a principled way from a policy improvement objective, discuss several important implementation choices for this method, and evaluate it experimentally on standard benchmark tasks and fully off-policy reinforcement learning problems. We show that some variants of this method can perform well in practice, though a significant gap still exists between this approach and state-of-the-art reinforcement learning algorithms.
2 Related Work
---------------
Most current reinforcement learning algorithms aim to either explicitly compute a *policy gradient* [Williams, [1992](#bib.bib22 "Simple statistical gradient-following algorithms for connectionist reinforcement learning"); Sutton et al., [2000](#bib.bib21 "Policy gradient methods for reinforcement learning with function approximation")], accurately fit a value function or Q-function [Watkins and Dayan, [1992](#bib.bib72 "Q-learning"); Precup et al., [2001](#bib.bib66 "Off-policy temporal difference learning with function approximation"); Mnih et al., [2015](#bib.bib42 "Human-level control through deep reinforcement learning"); Gu et al., [2016](#bib.bib37 "Continuous deep q-learning with model-based acceleration")], or both [Lillicrap et al., [2016](#bib.bib35 "Continuous control with deep reinforcement learning"); Haarnoja et al., [2018](#bib.bib50 "Soft actor-critic: off-policy maximum entropy deep reinforcement learning with a stochastic actor")]. While such methods have attained impressive results on a range of challenging tasks [Mnih et al., [2015](#bib.bib42 "Human-level control through deep reinforcement learning"); Levine et al., [2016](#bib.bib77 "End-to-end training of deep visuomotor policies"); Heess et al., [2017](#bib.bib31 "Emergence of locomotion behaviours in rich environments"); Peng et al., [2018](#bib.bib27 "DeepMimic: example-guided deep reinforcement learning of physics-based character skills"); Rajeswaran et al., [2018](#bib.bib76 "Learning Complex Dexterous Manipulation with Deep Reinforcement Learning and Demonstrations")], they are also known to be notoriously challenging to use effectively, due to sensitivity to hyperparameters, high sample complexity, and a range of important and delicate implementation choices that have a large effect on performance [Hasselt et al., [2016](#bib.bib40 "Deep reinforcement learning with double q-learning"); Wang et al., [2016](#bib.bib44 "Sample efficient actor-critic with experience replay"); Munos et al., [2016](#bib.bib45 "Safe and efficient off-policy reinforcement learning"); Hessel et al., [2017](#bib.bib30 "Rainbow: combining improvements in deep reinforcement learning"); Fujimoto et al., [2018](#bib.bib36 "Addressing function approximation error in actor-critic methods"); Nachum et al., [2018](#bib.bib41 "Learning gaussian policies from smoothed action value functions"); Fu et al., [2019](#bib.bib63 "Diagnosing bottlenecks in deep q-learning algorithms")].
In contrast, supervised learning is comparatively well understood, and even imitation learning methods can often provide a much simpler approach to learning effective policies when demonstration data is available [Pomerleau, [1989](#bib.bib73 "Advances in neural information processing systems 1"); Codevilla et al., [2017](#bib.bib8 "End-to-end driving via conditional imitation learning"); Osa et al., [2018](#bib.bib7 "An algorithmic perspective on imitation learning")]. Indeed, a number of recent works have sought to combine imitation learning and reinforcement learning [Wang et al., [2018](#bib.bib78 "Exponentially weighted imitation learning for batched historical data"); Sun et al., [2018](#bib.bib4 "TRUNCATED HORIZON POLICY SEARCH: DEEP COMBINATION OF REINFORCEMENT AND IMITATION"); Balaguer and Carpin, [2011](#bib.bib6 "Combining imitation and reinforcement learning to fold deformable planar objects")].
However, when expert demonstrations are not available, supervised learning cannot be used directly. A number of prior works have sought to nonetheless utilize supervised learning in the inner loop of a reinforcement learning update, either by imitating a computational expert (e.g., another more local RL algorithm) [Levine et al., [2016](#bib.bib77 "End-to-end training of deep visuomotor policies"); Ghosh et al., [2018](#bib.bib34 "Divide-and-conquer reinforcement learning")], the best-performing trajectories [Oh et al., [2018](#bib.bib79 "Self-imitation learning")], or by reweighting sub-optimal data to make it resemble samples from a more optimal policy Peters et al. [[2010](#bib.bib11 "Relative entropy policy search")]; Peters and Schaal [[2007](#bib.bib12 "Reinforcement learning by reward-weighted regression for operational space control")]. In this paper, we utilize a simple insight to make it feasible to use suboptimal, non-expert data for supervised learning: suboptimal trajectories can be used as optimal supervision for a policy that aims to achieve a specified return or advantage value.
The central idea behind our method – that suboptimal trajectories can serve as optimal supervision for other tasks or problems – has recently been explored for *goal*-conditioned policies, both with reinforcement learning Kaelbling [[1993](#bib.bib3 "Learning to achieve goals")]; Andrychowicz et al. [[2017](#bib.bib9 "Hindsight experience replay")]; Pong et al. [[2018](#bib.bib10 "Temporal difference models: model-free deep RL for model-based control")] and supervised learning [Ghosh et al., [2019](#bib.bib14 "Learning To Reach Goals Without Reinforcement Learning")]. Our approach can be viewed as a generalization of this principle to arbitrary tasks, conditioning on the reward rather than a goal state. Like our method, Harutyunyan et al. [[2019](#bib.bib13 "Hindsight Credit Assignment")] also learn the distribution of actions conditioned on future states or the trajectory return, but then utilize such models with standard RL techniques, such as policy gradients, to provide more effective credit assignment and variance reduction. Concurrently with our work, Schmidhuber [[2019](#bib.bib15 "Reinforcement Learning Upside Down: Don’t Predict Rewards – Just Map Them to Actions")] and Srivastava et al. [[2019](#bib.bib16 "Training Agents using Upside-Down Reinforcement Learning")] proposed a closely related algorithm that also uses supervised learning and reward conditioning. While our work is concurrent, we further explore the challenges with this basic design, demonstrate that a variety of careful implementation choices are important for good performance, and provide detailed comparisons to related algorithms.
3 Preliminaries
----------------
In reinforcement learning, our goal is to learn a control policy that maximizes the expected long term return in a task which is modeled as a Markov decision process (MDP). At each timestep t, the agent receives an environment state st∈S, executes an action at∈A and observes a reward rt=r(st,at) and the next environment state st+1. The goal of the RL algorithm is to learn a policy πθ(at|st) that maximizes the return, which is the cumulative discounted reward J(θ), defined as
| | | |
| --- | --- | --- |
| | J(θ)=Es0∼p(s0),a0:∞∼π,st+1∼p(⋅|at,st)[∞∑t=1γtr(st,at)]. | |
Prior reinforcement learning methods generally either aim to compute the derivative of J(π) with respect to the policy parameters θ directly via policy gradient methods Williams [[1992](#bib.bib22 "Simple statistical gradient-following algorithms for connectionist reinforcement learning")], or else estimate a value function or Q-function by means of temporal difference learning, or both. Our aim will be to avoid complex and potentially high-variance policy gradient estimators, as well as the complexity of temporal difference learning.
4 Reward-Conditioned Policies
------------------------------
1: θ1←random initial parameters
2: D←∅
3: ^p1(Z)← initial value distribution
4: for iteration k=1,...,kmax do
5: sample target value ^Z∼^pk(Z).
6: roll out trajectory τ={st,at,rt}Tt=0, with policy πθk(⋅|st,^Z)
7: for each step t, label (st,at) with observed value Zt
8: store tuples {st,at,Zt}Tt=0 in D
9: θk+1←arg maxθEs,a,Z∼D[log πθ(a|s,Z)]
10: ^pk+1← update target value distribution using D
11: end for
Algorithm 1 Generic Algorithm for Reward-Conditioned Policies (RCPs)
The basic idea behind our approach is simple: we alternate between a training a policy of the form πθ(at|st,Z) with supervised learning on all data collected so far, where Z is an estimate of the return for the trajectory containing the tuple (st,at), and using the latest policy to collect more data. We first provide an overview of the generic RCP algorithm, and then describe two practical instantiations of the method.
###
4.1 Reward-Conditioned Policy Training
The generic RCP algorithm is summarized in Algorithm [1](#alg1 "Algorithm 1 ‣ 4 Reward-Conditioned Policies ‣ Reward-Conditioned Policies"). At the start of each rollout, a target value ^Z is sampled from the current target distribution ^Z∼^pk(Z). The current policy πθk(a|s,^Z) is then conditioned on ^Z and used to sample a trajectory τk from the environment. After a rollout, each timestep t is relabled with a new value Zt reflecting the actual rewards observed over the course of the rollout. This value can be the observed total reward-to-go, or the estimated advantage at (st,at). The tuples {st,at,Zt} are then added to the dataset D, which is structured as a first-in first-out queue.
The reward-conditioned policy is then updated via supervised regression on the data in the buffer. Finally, the target return distribution ^p(Z) is updated using the data in D, and the process is repeated. RCP performs policy updates using only supervised regression, leveraging prior suboptimal trajectories as supervision.
We explore two specific choices for the form of the values Z: conditioning on the total return, which we refer to as RCP-R, and conditioning on the advantage, which we refer to as RCP-A. The return conditioned variant, RCP-R, is the simplest: here, we simply choose Zt to be the discounted reward to go along the sampled trajectory, such that Zt=∑Tt′=tγt′−trt′.
A more complex but also more effective version of the algorithm can be implemented by conditioning on the *advantage* of at in state st. The advantage function is defined as A(s,a)=Q(s,a)−V(s), where V(s) is the state value function, and Q(s,a) is the state-action value function. Thus, RCP-A uses Zt=A(st,at), with Q(s,a) estimated using a Monte Carlos estimate, and V(s) estimated using a separately fitted value function ^Vϕ(s). Thus, we have Zt=∑Tt′=tγt′−trt′−^Vϕ(st). The value function can be fitted using Monte Carlo return estimates, though we opt for a TD(λ) estimator, following prior work Peng et al. [[2019](#bib.bib2 "Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning")]; Schulman et al. [[2016](#bib.bib61 "High-dimensional continuous control using generalized advantage estimation")].
An important detail of the RCP algorithm is the update to the target value distribution ^pk(Z) on line 10. We will describe the theoretical considerations for the choice of ^pk(Z) in Section [4.3](#S4.SS3 "4.3 Theoretical Motivation for Reward-Conditioned Policies ‣ 4 Reward-Conditioned Policies ‣ Reward-Conditioned Policies"), while here we describe the final procedure that we actually employ in our method. We represent ^pk(Z) as a normal distribution, with mean μZ and standard deviation σZ. The mean and variance are updated based on the soft-maximum, i.e. log∑exp, of the target value Z observed so far in the dataset D.
As per line 5 in Algorithm [1](#alg1 "Algorithm 1 ‣ 4 Reward-Conditioned Policies ‣ Reward-Conditioned Policies"), we sample ^Z from ^pk(Z) for each rollout.
For RCP-A, a new sample for Z is drawn at each time step, while for RCP-R, a sample for the return Z is drawn once for the whole trajectory.
###
4.2 Implementation and Architecture Details
We opt to use a deterministic policy for evaluation in accordance with the evaluation protocol commonly used in prior RL algorithms Haarnoja et al. [[2018](#bib.bib50 "Soft actor-critic: off-policy maximum entropy deep reinforcement learning with a stochastic actor")]. During evaluation, the target value is always chosen to be equal to μZ+σZ to avoid stochasticity arising from the target value input.
Figure 1: The network architecture used for RCPs in our experiments. Inspired by [de Vries et al., [2017](#bib.bib59 "Modulating early visual processing by language"); Perez et al., [2017](#bib.bib60 "FiLM: visual reasoning with a general conditioning layer"); Oord et al., [2016](#bib.bib5 "Conditional image generation with pixelcnn decoders")], we use multiplicative interactions between an embedding of Z and intermediate layers of the policy network.
We model the policy πθ(a|s,Z) as a three-layer fully-connected deep neural network that takes s and Z as inputs and outputs a Gaussian distribution over actions. A simple choice for the architecture of the policy network would be to concatenate the additional scalar target value Z to the state s, and then use a standard multi-layer fully connected network. However, prior work has observed that such *conditioning* variables can often be utilized more effectively in an architecture that incorporates multiplicative interactions [de Vries et al., [2017](#bib.bib59 "Modulating early visual processing by language"); Perez et al., [2017](#bib.bib60 "FiLM: visual reasoning with a general conditioning layer"); Oord et al., [2016](#bib.bib5 "Conditional image generation with pixelcnn decoders")]. Based on this insight, we found that using multiplicative interactions between embeddings of Z and each intermediate layer of the main policy network, shown in Figure [1](#S4.F1 "Figure 1 ‣ 4.2 Implementation and Architecture Details ‣ 4 Reward-Conditioned Policies ‣ Reward-Conditioned Policies"), produced substantially better results in our experiments. This design prevents the policy network from ignoring the input target values.
###
4.3 Theoretical Motivation for Reward-Conditioned Policies
In this section, we derive the two variants of RCPs, RCP-R and RCP-A, as approximate solutions to a constrained policy search problem. This derivation resembles REPS Peters et al. [[2010](#bib.bib11 "Relative entropy policy search")] and AWR Peng et al. [[2019](#bib.bib2 "Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning")].
##### Notation.
We denote a trajectory by τ, and use Z(τ) to denote the return of the trajectory, given by Z(τ)=∑tr(st,at). For the purpose of this derivation, we operate in a setting where Z(τ) can be stochastic, although deterministic returns are a special case of this scenario. We refer to the joint distribution of trajectories τ and returns Z as p(τ,Z). We denote the joint distribution over trajectories and returns under a sampling policy μ as pμ(τ,Z).
####
4.3.1 Return-Conditioned Variant (RCP-R)
Our constrained policy search formulation aims to learn a return-conditioned policy πθ(a|s,Z) that maximizes the discounted long-term return J(θ), under the constraint that the induced trajectory-return marginal pπ(τ,Z) is close to the marginal of the sampling policy, pμ(τ,Z). We will first compute the optimal non-parametric solution π∗ to the above described optimization problem and then learn πθ(a|s,Z) by projecting π∗ into the space of parametric policies Π={πθ(a|s,Z)|θ∈Θ}. This can be formalized as:
| | | | | |
| --- | --- | --- | --- | --- |
| | arg maxπ | Eτ,Z∼pπ(τ,Z)[Z] | | (1) |
| | s.t. | DKL(pπ(τ,Z)||pμ(τ,Z))≤ε | | (2) |
Now, we can derive the supervised regression update for RCPs as a solution to the above constrained optimization. We first form the Lagrangian of the constrained optimization problem presented above with Lagrange multiplier β:
| | | | |
| --- | --- | --- | --- |
| | L(π,β)=Eτ,Z∼pπ(τ,Z)[Z]+β(ε−Eτ,Z∼∼pπ(τ,Z)[logpπ(τ,Z)pμ(τ,Z)]) | | (3) |
Differentiating L(π,β) with respect to π
and β and applying optimality conditions, we obtain a non-parametric form for the joint trajectory-return distribution of the optimal policy, pπ∗(τ,Z):
| | | | |
| --- | --- | --- | --- |
| | pπ∗(τ,Z)∝pμ(τ,Z)exp(Zβ) | | (4) |
Prior work has used this derivation to motivate a *weighted* supervised learning objective for the policy, where the policy is trained by regressing onto previously seen actions, with a weight corresponding to the exponentiated return exp(Z/β) Peters et al. [[2010](#bib.bib11 "Relative entropy policy search")]; Peters and Schaal [[2007](#bib.bib12 "Reinforcement learning by reward-weighted regression for operational space control")]; Peng et al. [[2019](#bib.bib2 "Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning")]. To instead obtain an *unweighted* objective, we can instead decompose the joint distribution pπ(τ,Z) into conditionals pπ(Z) and pπ(τ|Z), and use this decomposition to obtain an expression for the trajectory distribution conditioned on the target return Z. Thus, we can convert Equation [4](#S4.E4 "(4) ‣ 4.3.1 Return-Conditioned Variant (RCP-R) ‣ 4.3 Theoretical Motivation for Reward-Conditioned Policies ‣ 4 Reward-Conditioned Policies ‣ Reward-Conditioned Policies") into:
| | | | |
| --- | --- | --- | --- |
| | pπ∗(τ|Z)pπ∗(Z)∝[pμ(τ|Z)pμ(Z)]exp(Zβ) | | (5) |
Equation [5](#S4.E5 "(5) ‣ 4.3.1 Return-Conditioned Variant (RCP-R) ‣ 4.3 Theoretical Motivation for Reward-Conditioned Policies ‣ 4 Reward-Conditioned Policies ‣ Reward-Conditioned Policies") can be decomposed into separate expressions for the target distribution pπ∗(Z) and the conditional trajectory distribution pπ∗(τ|Z). We obtain a maximum likelihood objective for pπ∗(τ|Z) and an exponentially weighted maximum-likelihood objective for the target distribution pπ∗(^Z).
| | | | | |
| --- | --- | --- | --- | --- |
| | pπ∗(τ|Z) | ∝pμ(τ|Z) | | (6) |
| | pπ∗(Z) | ∝pμ(Z)exp(Zβ) | | (7) |
Equation [6](#S4.E6 "(6) ‣ 4.3.1 Return-Conditioned Variant (RCP-R) ‣ 4.3 Theoretical Motivation for Reward-Conditioned Policies ‣ 4 Reward-Conditioned Policies ‣ Reward-Conditioned Policies") corresponds to fitting a policy π∗ to generate trajectories that achieve a particular target return value Z as depicted in Step 9 in Algorithm [1](#alg1 "Algorithm 1 ‣ 4 Reward-Conditioned Policies ‣ Reward-Conditioned Policies"). Equation [7](#S4.E7 "(7) ‣ 4.3.1 Return-Conditioned Variant (RCP-R) ‣ 4.3 Theoretical Motivation for Reward-Conditioned Policies ‣ 4 Reward-Conditioned Policies ‣ Reward-Conditioned Policies") corresponds to the process of improving the expected return of a policy by updating the target return distribution to assign higher likelihoods to large values of Z as shown in Step 10 in Algorithm [1](#alg1 "Algorithm 1 ‣ 4 Reward-Conditioned Policies ‣ Reward-Conditioned Policies").
For the final steps, we factorize pπ(τ|Z) as pπ(τ|Z)=Πtπ(at|st,Z)p(st+1|st,at), where the product is over all time steps t in a tajectory τ, and the dynamics p(st+1|st,at) are independent of the policy. To train a parametric policy πθ(a|s,^Z), we project the optimal non-parametric policy p∗π computed above onto the manifold of parametric policies, according to
| | | | | |
| --- | --- | --- | --- | --- |
| | πθ(a|s,Z)= | arg minθEZ∼D[DKL(pπ∗(τ|Z)||pπθ(τ|Z))] | | (8) |
| | = | arg maxθEZ∼D[Ea∼μ(a|s,^Z)[logπθ(a|s,Z)]] | | (9) |
Equation [9](#S4.E9 "(9) ‣ 4.3.1 Return-Conditioned Variant (RCP-R) ‣ 4.3 Theoretical Motivation for Reward-Conditioned Policies ‣ 4 Reward-Conditioned Policies ‣ Reward-Conditioned Policies") corresponds to a maximum likelihood update for the policy πθ. Training is performed only for target return values Z that have actually been observed and are present in the buffer D. We choose to maintain an approximate parametric Gaussian model for pπ∗(Z), and continuously update this models online according to the update in Equation [7](#S4.E7 "(7) ‣ 4.3.1 Return-Conditioned Variant (RCP-R) ‣ 4.3 Theoretical Motivation for Reward-Conditioned Policies ‣ 4 Reward-Conditioned Policies ‣ Reward-Conditioned Policies"). Section [4.2](#S4.SS2 "4.2 Implementation and Architecture Details ‣ 4 Reward-Conditioned Policies ‣ Reward-Conditioned Policies") provides more details on maintaining this model in our practical implementation.
####
4.3.2 Advantage-Conditioned Variant (RCP-A)
In this section, we present a derivation of the advantage-conditioned variant. Our derivation is based on the idea of learning a policy to maximize the expected improvement over the sampling policy μ. Expected improvement of policy π(a|s) over another policy μ(a|s) is defined as the difference between their expected long-term discounted returns ημ(π)=J(π)−J(μ). Using policy difference lemma Kakade and Langford [[2002](#bib.bib23 "Approximately optimal approximate reinforcement learning")], we can express expected improvement as:
| | | | |
| --- | --- | --- | --- |
| | ημ(π)=J(π)−J(μ)=Es,a∼dπ(s,a)[Aμ(s,a)]≈Es∼dμ(s),a∼π(a|s)[Aμ(s,a)] | | (10) |
where the approximate equality holds true if π and μ are similar Schulman et al. [[2015](#bib.bib24 "Trust region policy optimization")].
Analogous to the derivation of RCP-R, for each state-action pair (s,a), we assume that the advantage values are random variables. We denote the advantage random variable for an action a at a state s with respect to policy π with Aπ(s,a).
In the case of policies conditioned on advantages, the expected improvement of a policy π(a|s,A) over a sampling policy μ(a|s,A) is given by
| | | | |
| --- | --- | --- | --- |
| | ημ(π)=Es∼dπ(s),A∼pπ(A|s),a∼π(a|s,A)[Aμ(s,a)] | | (11) |
When the policies μ and π are close to each other, we obtain a trainable objective, by replacing the intractable state-distribution term dπ(s) in Equation [11](#S4.E11 "(11) ‣ 4.3.2 Advantage-Conditioned Variant (RCP-A) ‣ 4.3 Theoretical Motivation for Reward-Conditioned Policies ‣ 4 Reward-Conditioned Policies ‣ Reward-Conditioned Policies") with state distribution dμ(s) of the sampling policy. This approximation has been previously used in the derivation of TRPO Schulman et al. [[2015](#bib.bib24 "Trust region policy optimization")] and AWR Peng et al. [[2019](#bib.bib2 "Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning")]. For a rigorous proof of this approximation, we refer the readers to Lemma 3 in Schulman et al. [[2015](#bib.bib24 "Trust region policy optimization")].
Our goal is to learn an advantage-conditioned policy π(a|s,A) which maximizes expected improvement while being close to the sampling policy μ(a|s,A) while staying close to μ in distribution. This is formalized as the following optimization problem:
| | | | | |
| --- | --- | --- | --- | --- |
| | arg maxπ | Es∼dμ(s),a,A∼pμ(a,A|s)[A] | | (12) |
| | s.t. | Es∼dμ(s)[DKL(pπ(a,A|s)||pμ(a,A|s))]≤ε | | (13) |
Following steps similar to the previous derivation for the return-conditioned variant (RCP-R), we obtain the following maximum-likelihood objective to train a parametric policy πθ(a|s,^A), given a sampling policy μ, as described in Step 9 of Algorithm [1](#alg1 "Algorithm 1 ‣ 4 Reward-Conditioned Policies ‣ Reward-Conditioned Policies").
| | | | |
| --- | --- | --- | --- |
| | πθ(a|s,^A)=arg maxθ Es∼dμ(s),A∼pμ(A|s)[Ea∼μ(a|s,A)[logπθ(a|s,A)]] | | (14) |
Further, the target distribution of advantages at any state s under this procedure is given by:
| | | | |
| --- | --- | --- | --- |
| | pπ∗(A|s)∝pμ(A|s)exp(Aβ) | | (15) |
To summarize, this derivation motivates a maximum-likelihood objective (Equation [14](#S4.E14 "(14) ‣ 4.3.2 Advantage-Conditioned Variant (RCP-A) ‣ 4.3 Theoretical Motivation for Reward-Conditioned Policies ‣ 4 Reward-Conditioned Policies ‣ Reward-Conditioned Policies")) that trains the policy to choose actions that achieve a particular target advantage value as depicted in Algorithm [1](#alg1 "Algorithm 1 ‣ 4 Reward-Conditioned Policies ‣ Reward-Conditioned Policies"), and the target distribution pπ∗(A|s) is updated according to Equation [15](#S4.E15 "(15) ‣ 4.3.2 Advantage-Conditioned Variant (RCP-A) ‣ 4.3 Theoretical Motivation for Reward-Conditioned Policies ‣ 4 Reward-Conditioned Policies ‣ Reward-Conditioned Policies") to assign higher likelihoods to actions with higher advantages. Rather than fitting a model to learn a mapping between states and advantages, our model for the target distribution pπ∗(A), as described in Section [4.2](#S4.SS2 "4.2 Implementation and Architecture Details ‣ 4 Reward-Conditioned Policies ‣ Reward-Conditioned Policies") ignores the dependency on states in the interest of simplicity.
###
4.4 Weighted Maximum Likelihood for Reward-Conditioned Policy Learning
The derivation in Sections [4.3](#S4.SS3 "4.3 Theoretical Motivation for Reward-Conditioned Policies ‣ 4 Reward-Conditioned Policies ‣ Reward-Conditioned Policies") gives rise to a simple maximum likelihood objective for training the reward-conditioned policy πθ(a|s,Z). In contrast to prior work, such as REPS Peters et al. [[2010](#bib.bib11 "Relative entropy policy search")] and AWR Peng et al. [[2019](#bib.bib2 "Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning")], which use a *return-weighted* maximum likelihood objective to train an *unconditioned* policy, with weights given by exponentiated returns, we expect our *unweighted* maximum-likelihood objective to exhibit less variance, since exponentiated return weights necessarily reduce the effective sample size when many of the (suboptimal) trajectories receive very small weights. However, we can choose to also use weighted likelihood objective with RCPs, and indeed are free to prioritize the samples in D to attain better performance. For example, in the case of RCP-A, we can choose to upweight transitions corresponding to highly advantageous actions, rather than training under the data distribution defined by D. As we show empirically in Section [5.1](#S5.SS1 "5.1 Performance and Comparisons on Standard Benchmarks ‣ 5 Experimental Evaluation ‣ Reward-Conditioned Policies"), prioritizing transition samples by assigning a weight proportional to exponential target value (either advantage or return) increases sample-efficiency in some cases, although this step is optional in the RCP framework. In practice, we would expect this to also reduce the effective sample size, though we did not find that to be a problem for the benchmark tasks on which we evaluated our method.
5 Experimental Evaluation
--------------------------
Our experiments aim to evaluate the performance of RCPs on standard RL benchmark tasks, as well as fully off-policy RL problems. We also present an ablation analysis, which aims to answer the following questions: (1) Do RCPs actually achieve a return that matches the value they are conditioned on? (2) What is the effect of the policy architecture on the performance of RCPs? (3) How does the choice of reweighting method during supervised learning affect performance, and can RCPs perform well with no reweighting at all? (4) Are RCPs less sensitive to the size of the replay buffer, as compared to other RL algorithms that use supervised subroutines, such as AWR?
##### Experimental setup.
At each iteration, RCP collects 2000 transition samples (i.e. executes 2000 timesteps in the environment),
which are appended to the dataset D. Unless stated otherwise, for RCPs, D is a ring buffer that holds 100k transitions. We also show results with larger buffer sizes in Figure [5](#S5.F5 "Figure 5 ‣ 5.3 Ablation Experiments ‣ 5 Experimental Evaluation ‣ Reward-Conditioned Policies"). Updates to the policy are performed by uniformly sampling minibatches of 256 samples from D. For the advantage-conditioned variant, the value function is updated with 200 gradient steps per iteration, and the policy is updated with 1000 steps.
###
5.1 Performance and Comparisons on Standard Benchmarks
We compare RCP-R and RCP-A to a number of prior RL algorithms, including on-policy algorithms such as TRPO Schulman et al. [[2015](#bib.bib24 "Trust region policy optimization")] and PPO Schulman et al. [[2017](#bib.bib25 "Proximal policy optimization algorithms")], and off-policy algorithms such as SAC Haarnoja et al. [[2018](#bib.bib50 "Soft actor-critic: off-policy maximum entropy deep reinforcement learning with a stochastic actor")] and DDPG Lillicrap et al. [[2016](#bib.bib35 "Continuous control with deep reinforcement learning")]. We also compare to AWR Peng et al. [[2019](#bib.bib2 "Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning")], a recently proposed off-policy RL method that also utilizes supervised learning as a subroutine, but does not condition on rewards and requires an exponential weighting scheme during training. When using exponential weighting, both RCP-R and RCP-A resemble AWR, with the main difference being the additional conditioning on returns or advantages. However, RCPs can also use unweighted supervised learning, which can decrease the variance of the supervised learning stage and increase the effective sample size, while AWR requires exponential weighting, without which it can never learn an optimal policy.
Learning curves comparing the different algorithms on three continuous-control and one discrete-action OpenAI gym benchmark tasks are shown in Figure [2](#S5.F2 "Figure 2 ‣ 5.1 Performance and Comparisons on Standard Benchmarks ‣ 5 Experimental Evaluation ‣ Reward-Conditioned Policies"). RCP-A substantially outperforms the return-conditioned variant, RCP-R, on all of the tasks, though RCP-R is still able to learn effective policies on the LundarLander-v2 task. While there is still a gap between the performance of RCPs and the best current reinforcement learning algorithms, RCP-A outperforms TRPO and performs comparably or better to PPO. When we additionally incorporate exponential reweighting, as shown in Figure [3](#S5.F3 "Figure 3 ‣ 5.1 Performance and Comparisons on Standard Benchmarks ‣ 5 Experimental Evaluation ‣ Reward-Conditioned Policies"), both variants of RCP perform substantially better, and RCP-A performs similarly to AWR, though this is in a sense not surprising, since both methods utilize the same weighted regression step, with the only difference being that the RCP-A policy also receives the advantage values as an input. These results show that, although there is still a gap in performance between RCPs and prior methods, the methods has the potential to learn effective policies on a range of benchmark tasks.
| | | | | |
| --- | --- | --- | --- | --- |
| | | | | |
Figure 2: Learning curves of the various algorithms when applied to benchmark tasks. Results are averaged across 5 random seeds. RCP-R performs at par with RWR, and RCP-A is able to learn successful policies for each of the tasks, often outperforming several prior methods.
As noted in Section [2](#S2 "2 Related Work ‣ Reward-Conditioned Policies"), concurrently to our work, Schmidhuber [[2019](#bib.bib15 "Reinforcement Learning Upside Down: Don’t Predict Rewards – Just Map Them to Actions")] proposed a similar approach, UDRL, though without weighting or advantage conditioning, and reports a final result of around 150 on the LunarLander-v2 task. We can see in Figure [2](#S5.F2 "Figure 2 ‣ 5.1 Performance and Comparisons on Standard Benchmarks ‣ 5 Experimental Evaluation ‣ Reward-Conditioned Policies") that RCPs generally perform better, with RCP-A reaching 238±1.3 on the same task. This suggests that, although conditioning on rewards provides for a simple and effective reinforcement learning method, there are still a number of simple but important design decisions that are essential for good performance.
| | | | |
| --- | --- | --- | --- |
| | | | |
Figure 3: Learning curves for RCP-A and RCP-R with exponential weights for training the policy. AWR is shown for comparison. Results are averaged across 5 random seeds. RCP-A performs similarly to AWR when exponential weighting is used.
###
5.2 Performance in Fully Offline Settings
Since RCPs use standard supervised learning and can utilize all previously collected data, we would expect RCPs to be well suited for learning entirely from offline datasets, without on-policy data collection. We follow the protocol described by Kumar et al. [[2019](#bib.bib67 "Stabilizing off-policy q-learning via bootstrapping error reduction")] and evaluate on static datasets collected from a “mediocre” partially trained policy, with 1 million transition samples per task.
RCPs can be trained directly on this dataset, without any modification to the algorithm. We compare to
AWR Peng et al. [[2019](#bib.bib2 "Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning")] and bootstrapping error accumulation reduction (BEAR) Kumar et al. [[2019](#bib.bib67 "Stabilizing off-policy q-learning via bootstrapping error reduction")], which is a Q-learning method that incorporates a constraint to handle out-of-distribution actions. We also compare to off-policy approximate dynamic programming methods primarily designed for online learning – SAC Haarnoja et al. [[2018](#bib.bib50 "Soft actor-critic: off-policy maximum entropy deep reinforcement learning with a stochastic actor")] and TD3 Fujimoto et al. [[2018](#bib.bib36 "Addressing function approximation error in actor-critic methods")], – and PPO Schulman et al. [[2017](#bib.bib25 "Proximal policy optimization algorithms")], which is an importance-sampled policy gradient algorithm.
| | |
| --- | --- |
| | |
Figure 4: Performance of various algorithms on fully off-policy learning tasks with static datasets. RCP-A learns effective policies that achieve better than dataset average in both cases. RCP-R performs similarly to behavioral cloning (BC).
As shown in Figure [4](#S5.F4 "Figure 4 ‣ 5.2 Performance in Fully Offline Settings ‣ 5 Experimental Evaluation ‣ Reward-Conditioned Policies"), we find that RCP-A learns effective policies in the purely offline setting on both the environments tested on and achieves performance better than the behavior policy that generated the dataset.
###
5.3 Ablation Experiments
Finally, we perform three ablation experiments to determine the effect of various design decisions for RCP training. The first parameter of variation is the size of the buffer D that is used during training. We compare RCP-R, RCP-A, and AWR with different buffer sizes, shown in Figure [5](#S5.F5 "Figure 5 ‣ 5.3 Ablation Experiments ‣ 5 Experimental Evaluation ‣ Reward-Conditioned Policies"). Note that the performance of AWR degrades significantly as the buffer size increases. This is expected, since AWR constrains the policy against the buffer distribution, therefore larger buffer sizes can result in slower policy improvement. In contrast, RCP-R and RCP-A can handle larger buffers, and perform better with buffers of size 100k as compared to buffers of size 50k, though larger buffers still result in somewhat worse performance. We speculate that this might be due to the fact the low-dimensional and simple benchmark task do not actually require large datasets to train an effective policy, and we might expect larger buffers to be more beneficial on more complex tasks, which we hope to investigate in the future.
| | | | |
| --- | --- | --- | --- |
|
(a) AWR
|
(b) RCP-A
|
(c) RCP-R
|
(d) RCP-A (+exp)
|
Figure 5: Learning curves demonstrating the effect of varying buffer sizes (20k, 50k, 100k and 500k) on different algorithms: (a) AWR (b) RCP-A (c) RCP-R and (d) RCP-A with exponential weighting on the HalfCheetah-v2 benchmark task. RCP-A generally performs better with larger buffers (compare 50k vs 100k), though performance still degrades with larger buffers.
In Figure [6](#S5.F6 "Figure 6 ‣ 5.3 Ablation Experiments ‣ 5 Experimental Evaluation ‣ Reward-Conditioned Policies"), we compare two different architectural choices for both the RCP variants. In the first architecture, labeled *concat* in Figure [6](#S5.F6 "Figure 6 ‣ 5.3 Ablation Experiments ‣ 5 Experimental Evaluation ‣ Reward-Conditioned Policies"), the target value Z is concatenated to the state s and then fed into a three-layer fully-connected network. The second architecture, labeled as *multiply*, is our default choice for experiments in Section [5.1](#S5.SS1 "5.1 Performance and Comparisons on Standard Benchmarks ‣ 5 Experimental Evaluation ‣ Reward-Conditioned Policies") and uses multiplicative interactions, as discussed in Section [4.2](#S4.SS2 "4.2 Implementation and Architecture Details ‣ 4 Reward-Conditioned Policies ‣ Reward-Conditioned Policies"). Learning curves in Figure [6](#S5.F6 "Figure 6 ‣ 5.3 Ablation Experiments ‣ 5 Experimental Evaluation ‣ Reward-Conditioned Policies") show that the architecture with multiplicative interactions (multiply) leads to better performance across the different environments (HalfCheetah-v2 and Hopper-v2) for both variants (RCP-A and RCP-R).
| | | | |
| --- | --- | --- | --- |
|
(a) HalfCheetah-v2(RCP-A/ RCP-R)
|
(b) Hopper-v2(RCP-A/ RCP-R)
|
(c) HalfCheetah-v2(+ exp weights)
|
(d) Hopper-v2(+ exp weights)
|
Figure 6: Performance of different architectures on HalfCheetah-v2 and Hopper-v2 environments with replay buffers of size 100k. Figures (c) and (d) correspond to weighted versions of both RCP-A and RCP-R. Note that the architecture multiply clearly outperforms concat in all cases.
Finally, we study the relationship between the target value ^Z that the policy is conditioned and the observed target value Z achieved by rollouts from the policy. Ideally, we would expect the specified target values of Z to roughly match the observed value ^Z, as a reward-conditioned policy is explicitly trained to ensure this (Step 9 of Algorithm 1). In this experiment, we plot a two-dimensional heatmap of co-occurrence frequencies of ^Z and Zt to visualize the relationship between these quantities after about 2000 training iterations for both RCP variants. These heatmaps are shown in Figure [7](#S5.F7 "Figure 7 ‣ 5.3 Ablation Experiments ‣ 5 Experimental Evaluation ‣ Reward-Conditioned Policies"). We find that both variants of RCP policies achieve returns (or advantages) that are similar enough to the target values they are conditioned on.
| | |
| --- | --- |
|
(a) Target vs observed trajectory return (RCP-R)
|
(b) Target vs obtained action advantages (RCP-A)
|
Figure 7: Two-dimensional heatmap visualizing the co-occurrence frequencies of the specified target value ^Z (x-axis) and the observed value Z (y-axis) after 2000 epochs of training for (a) RCP-R and (b) RCP-A. The co-occurrence frequencies are empirically estimated using separately executed rollouts that are conditioned on target values sampled from the instantaneous target model pπ∗(Z). Note the similar magnitudes of Z and ^Z in most cases.
6 Discussion and Future Work
-----------------------------
We presented reward-conditioned policies, a general class of algorithms that enable learning of control policies with standard supervised learning approaches. Reward-conditioned policies make use of a simple idea: sub-optimal trajectories can be regarded as optimal supervision for a policy that does not aim to attain the largest possible reward, but rather to match the reward of that trajectory. By then conditioning the policy on the reward, we can train a single model to simultaneously represent policies for all possible reward values, and generalize to larger reward values.
While our results demonstrate that this approach can attain good results across a range of reinforcement learning benchmark tasks, its sample efficiency and final performance still lags behind the best and most efficient approximate dynamic programming methods, such as soft actor-critic [Haarnoja et al., [2018](#bib.bib50 "Soft actor-critic: off-policy maximum entropy deep reinforcement learning with a stochastic actor")], as well as methods that utilize supervised learning in concert with reweighting, such as AWR [Peng et al., [2019](#bib.bib2 "Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning")].
sWe nonetheless expect the simplicity of RCPs to serve as a significant benefit in many practical situations, and we hope that the use of standard supervised learning as a subroutine can also make it easier to analyze and understand the propoerties of our method. We expect that exploration is likely to be one of the major challenges with reward-conditioned policies: the methods we presented rely on generalization and random chance to acquire trajectories that improve in performance over those previously seen in the dataset. Sometimes the reward-conditioned policies might generalize successfully, and sometimes they might not. Further theoretical and empirical analysis of this generalization behavior may lead to a more performant class of methods, and more optimal sampling strategies inspired by posterior sampling may also lead to better final results. We believe that investigating these directions is an exciting avenue for future work, as it might allow us to devise a new class of reinforcement learning methods that combine the ease of use of supervised learning with the ability to autonomously acquire near-optimal behaviors from only high-level reward specification. |
caf9992f-a444-4153-9a8f-0edf9d30372a | trentmkelly/LessWrong-43k | LessWrong | Choosing the right amount of choice
The TED talk which I have seen praised most often is Barry Shwartz’s Paradox of Choice. His claim is that the ‘official dogma of all Western industrial societies’ – that more choice is good for us – is wrong. This has apparently been a welcome message for many.
Barry thinks the costs of choice are too high at current levels. His reasons are that it increases our expectations, makes us focus on opportunity costs rather than enjoying what we have, paralyzes us into putting off complicated or important choices, and makes us blame ourselves rather than the world when our selections fail to satisfy. We can choose how much choice to have usually though. You can always just pick a random jar of jam from the shelf if you find the decision making costly. So implicit in Barry’s complaint is that we continually misjudge these downsides and opt for more choice than we should.
Perhaps he is right currently, but I think probably wrong in the long term. Why should we fail to adapt? Even if we can’t adapt psychologically, as inability to deal with choices becomes more of a problem, more technologies for solving it will be found. Having the benefits of choice without the current costs doesn’t appear an insoluble problem.
One option for allowing more choice about choice, while keeping some benefits of variety is to have a standard default option available. Another that seems feasible is using a barcode scanner on a phone, connected to product information and an equation for finding the net goodness of products according to the owner’s values (e.g. goodness = -price – 1c per calorie – 1c per 10 miles travelled + 10c per good review – $100m for peanut traces + …). This could avoid a lot of time spent comparing product information on packages by instantly telling you which brand you likely prefer. Systems for telling you which music and films and people you are likely to like based on previous encounters are improving.
I suspect for many things we would prefer to make very resource |
37829d37-bf3d-4bf6-9cb5-f9b539894d36 | trentmkelly/LessWrong-43k | LessWrong | A Story With Zombies
(inspired by Zombies: Seriously, Enough, Zombies Are So Overdone, and Scifi/Fantasy Stories Editors Are Tired Of Seeing: Zombies)
He walked into my office and threw the manuscript on my desk with a thud.
“It’s called Thankful For Zombies. A zombie story where…”
“Nope,” I said.
His face deflated like a balloon. “But I didn’t even…”
“Zombies are overdone,” I said.
“But this is a zombie story with a twist!”
“Zombie stories with twists are super overdone.”
“But this is a story about an extended family who get together for Thanksgiving dinner, only to be interrupted by a zombie apocalypse. It’s a Thanksgiving story about zombies. You have to admit that the combination of zombies and Thanksgiving has never…”
“Done,” I said.
“Wait, really? The family starts out estranged and suspicious of each other, but then when they all have to work together to…”
“Done,” I said.
“How could that have been done?”
“Listen. I know you won’t believe me, but for the past ten years or so, the best literary minds of our generation have been working on creating zombie stories just different enough from every other zombie story around to get published. First the clever and interesting twists got explored. Then the mediocre and boring twists. Then the absurd and idiotic twists. Finally the genre got entirely mined out. There is now a New York Times bestselling book about zombies invading Jane Austen’s Pride and Prejudice. If your idea isn’t weirder than that, it’s been done. And that’s the logical ‘if’. If your idea is weirder than that, it has also been done.”
“I will get Thankful for Zombies published,” he said.
“You won’t,” I advised him.
“I just have to think of an original angle.”
“You really won’t,” I told him.
“The zombies are the good guys,” he proposed.
“Done.”
“The zombies are smarter than humans.”
“Done.”
“In the end, we ourselves are the zombies.”
“Done.”
“A human girl falls in love with a zombie.”
“Done.”
“Okay, fine. Toss the Thanksgiving angle. There’s got |
a5349595-4196-4622-892b-40c61af8ec8a | StampyAI/alignment-research-dataset/eaforum | Effective Altruism Forum | A Brief Summary Of The Most Important Century
Here I summarized each of the 11 Parts of the blog series the ["most important century"](https://www.cold-takes.com/most-important-century/) by [Holden Karnofsky](https://forum.effectivealtruism.org/users/holdenkarnofsky) in very short paragraphs. Simultaneously, I often described the central theme of some of the parts while stating why that piece is significant. I found listening to the podcast while reading the best approach to get the most out of this blog series. Although the original blog piece has plenty of other resources and branches to the arguments by the author.
**The central idea**
--------------------
of the blog is the claim that the century we live in may very well be the deciding time for the future of humanity, driven by Transformative AI. Through this series the author forecast **more than a 10% chance we'll see transformative AI within 15 years (by 2036); a ~50% chance we'll see it within 40 years (by 2060); and a ~2/3 chance we'll see it this century (by 2100).**
Key Takeaways
-------------
### [All Possible Views About Humanity's Future Are Wild](https://www.cold-takes.com/all-possible-views-about-humanitys-future-are-wild/)
A very rich argument about our galaxy-wide expansion is described in this section. Akin to a fantasy tale narrated by a humble but stern voice, a possibility here is given the spotlight using the method of elimination of lesser odds. What I loved most are the sceptical views, which seem rather criticizing but are actually very true to the nature of how people present their views while in denial. Welcoming conservative view, Holden sternly made clear that our galaxy is empty(at least of intelligent life)
---
### [The Duplicator](https://www.cold-takes.com/the-duplicator)
It delves into the concept of Digital Human Brains. A Duplicator. Thinking of Shadow Clones of Naruto, this argument by Holden is effectively materialized in my thoughts like VR. The concept is often tackled by the Sci-Fi culture and the writer is aware of their themes. In contrast, this piece centered forecasts skeptical analysis around the economic explosion and productivity feedback loop that can be reactivated by the Duplicators; hopefully, creating solace for the unprivileged economies.
And sure enough, if such a feat is achieved, space expansion would be urgent.
---
### [Digital People Would Be An Even Bigger Deal](https://www.cold-takes.com/how-digital-people-could-change-the-world/)
From digital minds, we get digital people.
This piece discusses in detail the raw concept of the existence of intelligent beings besides humans both as a source of advancement and/or a challenge to overcome. The implication of mind uploading is the central theme here and evidently so if considered in 2022. One part that I loved-FAQs, especially the one where a systematic and prolonged argument is written on how digital people would actually survive and get by their lives on earth. The inclusion of their laws, liberty, and other aspects addressed as sentient beings i.e. People. Apart from productivity, one striking aspect(which I still find hard to believe) is the sheer capability of digital people to improve our(Humans’) personal lives by possibly finding answers to the psychological queries humans tend to fail at, provided the necessary set-up. The emergence of digital people (if and when possible) will most likely be coupled with their rapid growth, and further lead us(and them) out of the bounds of the planet. Energy as the supplement, space expansion is ever more likely for self-sufficient digital beings.
---
### [This Can't Go On](https://www.cold-takes.com/this-cant-go-on)
This piece focuses on the current time we live in, throwing a spotlight on the insane rate of economic growth in recent centuries compared to the ancient ones. Here we analyse the three possible near-future cases. Stagnation, which is least likely. Explosion, which is most likely but heavily dependent on future advancements. And Collapse, which is becoming more and more realistic in current human society. The latter two cases are the direct outputs of scientific advancements.
---
### [Forecasting Transformative AI: What Kind of AI?](https://www.cold-takes.com/transformative-ai-timelines-part-1-of-4-what-kind-of-ai/)
Then we analyze, a collection of 4 pieces, all focusing on transformative AI and getting closer to finding when exactly such a Process for Automating Scientific and Technological Advancement(PASTA) would be ready. Here PASTA is narrower than artificial general intelligence. 1st piece discusses the roots of AI from basic programming to machine learning(ML). A brief study on how artificial neural networks involve a train of trial and error to make ML grow and learn. PASTA would use ML as a building block, but later surpass the likes of AlphaZero. In detail, we study the impact of such a process on our growth rate; a rapid technological boon or a fateful misaligned AI overpowering the outnumbered humans. Such a system is predicted to grow differently with each iteration/multiplication, having varying human controls.
---
### [Forecasting Transformative AI: What's The Burden Of Proof?](https://www.cold-takes.com/forecasting-transformative-ai-whats-the-burden-of-proof/)
Next, we look at how and why the proofs of current forecasting come with mixed(often negative) feedback. Holden walks through various angles and multiple probabilities to address scenarios based on prior studies, claims, analyses and even unsuccessful theories. Here, we note that the current rate of development and several other trajectories are in line with one involving the development of a PASTA-like system, and expert opinions in AI will only increase in the coming decades to support and likely update this hypothesis.
---
### [Forecasting Transformative AI: Are We "Trending Toward" Transformative AI?](https://www.cold-takes.com/are-we-trending-toward-transformative-ai-how-would-we-know/)
Next, we question the hype of AI and try to map it to the current technology trends. Here Holden describes how his analogies work and compares the growth towards transformative AI with some of the most known(and evident) patterns of Covid-19, Greenhouse emissions, etc. Subjective extrapolations are key to projecting AI effectiveness in years to come. Here we correlated AI to varied human capabilities and map their forecasting based on the existing trends in the scientific space w.r.t cost of development and size of AI models.
---
### [Forecasting Transformative AI: The "Biological Anchors" Method In A Nutshell](https://www.cold-takes.com/forecasting-transformative-ai-the-biological-anchors-method-in-a-nutshell/)
Then we explored how various experts predict their timelines of transformative AI arrival and on what they think it depends. Here, in line with a researcher-wide [Grace et al 2017](https://arxiv.org/pdf/1705.08807.pdf) survey, the probability estimates come out to be on the same path as Holden’s. Another forecasting of Transformative AI is shown with the help of Bio Anchors. This involves AI processing and development directly in comparison with the human brain and estimating the upper limit of cost and time to achieve such a scenario. This piece also deals with various critiques and takes on adapting the biological route. Although the Bio Anchor analysis comes out to be fully consistent with the AI concept scaled to the human brain, polar opposite reactions exist in most of the feedback received yet.
---
### [AI Timelines: Where The Arguments, And The "Experts," Stand](https://www.cold-takes.com/where-ai-forecasting-stands-today/)
This piece reflects on the absence of a solid consensus among the experts when it comes to predicting something like a PASTA. Here, Holden consolidates all other forecastings on the topic and addresses the reasons behind the skepticism acknowledgment and uncertainties. The best part about this piece(and probably the entire study) is the acknowledgement of Cunningham’s law, which encourages seeking the right answer after predicting a wrong answer. The writer highlights here why such a procedure is key for AI forecasting.
---
[How To Make The Best Of The Most Important Century?](https://www.cold-takes.com/making-the-best-of-the-most-important-century/)
Perhaps the most relatable piece of the series, it argues that we, the people will be decided how the near future is shaped through AI. The writer presents two frames of consideration here- [Caution](https://www.cold-takes.com/making-the-best-of-the-most-important-century/#the-caution-frame) and [Competition](https://www.cold-takes.com/making-the-best-of-the-most-important-century/#the-competition-frame), with examples of necessary actions for consideration.
In the cautionary frame, we discuss the worst of the possibilities from Misaligned AI and its adversarial maturity to the best ones like a scenario for better negotiations and governance, and the idea of reflection on the strides we are going to make toward major AI goals.
In the competitive frame, we discuss how the scale of Transformative AI may lead to an international contest of power-grab. Holden also highlights, how the current world, with all its faults and glory, tends to incline towards it out of social stigma and national insecurities.
---
[Call To Vigilance](https://www.cold-takes.com/call-to-vigilance/)
In the last part, the writer urges a call for ‘vigilance’ rather than ‘action’ in an attempt to prevent temporary impulsive actions. A heads start to identify when to take action to make the most impact. |
4b34f6ad-591d-4bf2-a045-cab1d04f422b | StampyAI/alignment-research-dataset/arxiv | Arxiv | Image Synthesis with a Single (Robust) Classifier
1 Introduction
---------------
Deep learning has revolutionized the way we tackle computer vision problems.
This revolution started with progress on image
classification [krizhevsky2012imagenet, he2015delving, he2016deep],
which then triggered the expansion of the deep learning paradigm to encompass
more sophisticated tasks such as
image generation [karras2018progressive, brock2019large]
and image-to-image translation [isola2017image, zhu2017unpaired].
Much of this expansion was predicated on developing complex,
task-specific techniques, often rooted in
the generative adversarial network (GAN) framework [goodfellow2014generative].
However, is there a simpler toolkit for solving these tasks?
In this work, we demonstrate that basic classification tools alone
suffice to tackle various computer vision tasks. These tasks include
(cf. Figure [1](#S1.F1 "Figure 1 ‣ 1 Introduction ‣ Computer Vision with a Single (Robust) Classifier")):
generation (Section [3.1](#S3.SS1 "3.1 Realistic Image Generation ‣ 3 Leveraging Robust Models for Computer Vision Tasks ‣ Computer Vision with a Single (Robust) Classifier")),
inpainting (Section [3.2](#S3.SS2 "3.2 Inpainting ‣ 3 Leveraging Robust Models for Computer Vision Tasks ‣ Computer Vision with a Single (Robust) Classifier")),
image-to-image translation (Section [3.3](#S3.SS3 "3.3 Image-to-Image Translation ‣ 3 Leveraging Robust Models for Computer Vision Tasks ‣ Computer Vision with a Single (Robust) Classifier")),
super-resolution (Section [3.4](#S3.SS4 "3.4 Super-Resolution ‣ 3 Leveraging Robust Models for Computer Vision Tasks ‣ Computer Vision with a Single (Robust) Classifier")), and
interactive image manipulation (Section [3.5](#S3.SS5 "3.5 Interactive Image Manipulation ‣ 3 Leveraging Robust Models for Computer Vision Tasks ‣ Computer Vision with a Single (Robust) Classifier")).
Figure 1: Computer vision tasks performed using a *single*
(robustly trained) classifier.
Our entire toolkit is based on a single classifier (per dataset)
and involves performing a simple input
manipulation: maximizing predicted class scores with gradient descent.
Our approach is thus general purpose and simple to implement and train,
while also requiring minimal tuning.
To highlight the potential of the core methodology itself,
we intentionally employ a generic classification setup
(ResNet-50 [he2016deep] with default hyperparameters) without any
additional optimizations (e.g., domain-specific priors or regularizers).
Moreover, to emphasize the consistency of our approach,
throughout this work we demonstrate performance on randomly selected
examples from the test set.
The key ingredient of our method is adversarially robust classifiers.
Previously, Tsipras et al. [tsipras2019robustness] observed that maximizing
the loss of robust models over the input leads to realistic
instances of other classes.
Here we are able to fully leverage this connection to build a versatile computer
vision toolkit.
Our findings thus establish robust classifiers as a powerful primitive
for semantic image manipulation, despite them being trained solely to perform image
classification.
2 Robust Models as a Tool for Input Manipulation
-------------------------------------------------
Recently, Tsipras et al. [tsipras2019robustness] observed
that optimizing an image to cause a misclassification in an (adversarially)
robust classifier introduces salient characteristics of the
incorrect class. This property is unique to robust classifiers:
standard models (trained with empirical risk minimization (ERM)) are
inherently brittle, and their predictions are sensitive even to
imperceptible changes in the input [szegedy2014intriguing].
Adversarially robust classifiers are trained using the robust
optimization objective [wald1945statistical, madry2018towards], where instead of
minimizing the expected loss L over the data
| | | | |
| --- | --- | --- | --- |
| | E(x,y)∼D[L(x,y)], | | (1) |
we minimize the worst case loss over a specific perturbation
set Δ
| | | | |
| --- | --- | --- | --- |
| | E(x,y)∼D[maxδ∈Δ L(x+δ,y)]. | | (2) |
Typically, the set Δ captures
imperceptible changes (e.g., small ℓ2 perturbations),
and given such a Δ, the problem in ([2](#S2.E2 "(2) ‣ 2 Robust Models as a Tool for Input Manipulation ‣ Computer Vision with a Single (Robust) Classifier")) can be solved using adversarial
training [goodfellow2015explaining, madry2018towards].
From one perspective, we can view robust optimization as encoding priors into
the model, preventing it from relying on imperceptible features of the input [engstrom2019learning].
Indeed, the findings of Tsipras et al. [tsipras2019robustness] are aligned
with this viewpoint—by encouraging the model to be invariant to small
perturbations, robust training ensures that changes in the model’s predictions
correspond to salient input changes.
In fact, it turns out that this phenomenon also emerges when we maximize
the probability of a specific class (targeted attacks)
for a robust model—see Figure [2](#S2.F2 "Figure 2 ‣ 2 Robust Models as a Tool for Input Manipulation ‣ Computer Vision with a Single (Robust) Classifier") for an illustration.
This indicates that robust models exhibit more human-aligned
gradients, and, more importantly, that we can precisely control features
in the input just by performing gradient descent on the model output.
Previously, performing such manipulations has only been possible with more
complex and task-specific
techniques [radford2016unsupervised, isola2017image, zhu2017unpaired]. In the
rest of this work, we demonstrate that this property of robust models is
sufficient to attain good performance on a diverse set of computer vision tasks.
Figure 2: Maximizing class scores of a robustly trained classifier.
For each original image, we visualize the result of performing targeted
projected gradient descent (PGD) toward different classes. The resulting
images actually resemble samples of the target class.
3 Leveraging Robust Models for Computer Vision Tasks
-----------------------------------------------------
Deep learning-based methods have recently made significant progress on
image synthesis and manipulation tasks, typically either by training
specifically-crafted models in the GAN
framework [goodfellow2014generative, iizuka2017globally, zhu2017unpaired, yu2018generative, brock2019large], or using priors obtained from deep generative
models [ulyanov2017deep, yeh2017semantic].
We discuss additional related work in the following subsections as necessary.
In this section, we outline our methods and results for obtaining competitive
performance on these tasks using only robust (feed-forward) classifiers. Our
approach is remarkably simple: all the applications are performed using
gradient ascent on class scores derived from the same robustly
trained classifier. In particular, it does not involve
fine-grained tuning (see Appendix [A.4](#A1.SS4 "A.4 Note on hyperparameter tuning ‣ Appendix A Experimental Setup ‣ Computer Vision with a Single (Robust) Classifier")), highlighting the potential of
robust classifiers as a versatile primitive for sophisticated vision tasks.
###
3.1 Realistic Image Generation
Synthesizing realistic samples for natural data domains (such as
images) has been a long standing challenge in computer vision.
Given a set of example inputs, we would like to
learn a model that can produce novel perceptually-plausible inputs. The
development of deep learning-based methods such as autoregressive
models [hochreiter1997long, graves2013generating, van2016pixel],
auto-encoders [vincent2010stacked, kingma2013autoencoding] and flow-based
models [dinh2014nice, rezende2015variational, dinh2017density, kingma2018glow]
has led to significant progress in this domain.
More recently, advancements in
generative adversarial networks (GANs) [goodfellow2014generative]
have made it possible to generate high-quality images for challenging
datasets [zhang2018self, karras2018progressive, brock2019large].
Many of these methods, however, can be tricky to train and properly
tune. They are also fairly computationally intensive, and often require fine-grained
performance optimizations.
In contrast, we demonstrate that robust classifiers, without any special
training or auxiliary networks, can be a powerful tool for synthesizing
realistic natural images. At a high level, our generation procedure
is based on maximizing the class score of the desired class using a
robust model. The purpose of this maximization is to add relevant and semantically
meaningful features of that class to a given input image.
As this process is deterministic, generating a diverse set of samples requires a random
seed as the starting point of the maximization process.
Formally, to generate a sample of class y, we sample a seed and minimize the
loss L of label y
| | | |
| --- | --- | --- |
| | x=argmin∥x′−x0∥2≤εL(x′,y),x0∼Gy, | |
for some class-conditional seed distribution Gy, using projected gradient descent (PGD)
(experimental details can be found in Appendix [A](#A1 "Appendix A Experimental Setup ‣ Computer Vision with a Single (Robust) Classifier")).
Ideally, samples from Gy should be diverse and
statistically similar to the data distribution. Here, we use
a simple (but already sufficient) choice for Gy—a multivariate normal
distribution fit to the empirical class-conditional distribution
| | | |
| --- | --- | --- |
| | Gy:=N(μy,Σy), where μy=Ex∼Dy[x],Σ=Ex∼Dy[(x−μy)⊤(x−μy)], | |
and Dy is the distribution of natural inputs conditioned on the label
y.
We visualize example seeds from these multivariate Gaussians in
Figure [17](#A2.F17 "Figure 17 ‣ Appendix B Omitted Figures ‣ Computer Vision with a Single (Robust) Classifier").
| | |
| --- | --- |
|
(a)
|
(b)
|
Figure 3: Random samples (of resolution 224×224) produced using
a robustly trained classifier. We show: (a) samples from several (random)
classes of the ImageNet dataset and (b) multiple samples from a few
random classes of the restricted ImageNet dataset (to illustrate
diversity). See Figures [13](#A2.F13 "Figure 13 ‣ Appendix B Omitted Figures ‣ Computer Vision with a Single (Robust) Classifier"),
[14](#A2.F14 "Figure 14 ‣ Appendix B Omitted Figures ‣ Computer Vision with a Single (Robust) Classifier"), [15](#A2.F15 "Figure 15 ‣ Appendix B Omitted Figures ‣ Computer Vision with a Single (Robust) Classifier"),
and [16](#A2.F16 "Figure 16 ‣ Appendix B Omitted Figures ‣ Computer Vision with a Single (Robust) Classifier") of Appendix [B](#A2 "Appendix B Omitted Figures ‣ Computer Vision with a Single (Robust) Classifier") for additional
samples.
This approach enables us to perform
*conditional* image synthesis given any target class.
Samples (at resolution 224×224) produced by our method are shown in
Figure [3](#S3.F3 "Figure 3 ‣ 3.1 Realistic Image Generation ‣ 3 Leveraging Robust Models for Computer Vision Tasks ‣ Computer Vision with a Single (Robust) Classifier") (also see Appendix [B](#A2 "Appendix B Omitted Figures ‣ Computer Vision with a Single (Robust) Classifier")).
The resulting images are diverse
and realistic, despite the fact that they are
generated using targeted PGD on off-the-shelf
robust models without any additional optimizations.
333Interestingly, the robust model used to generate
these high-quality ImageNet samples is only 45%
accurate, yet has a sufficiently rich representation to synthesize
semantic features for 1000 classes.
##### Different seed distributions.
It is worth noting that there is significant
room for improvement in designing the distribution Gy. One way
to synthesize better samples would be to use a richer distribution—for
instance, mixtures of Gaussians per class to better capture multiple data modes.
Also, in contrast to many existing approaches, we are not limited to a single seed distribution,
and we could even utilize other methods (such as procedural generation)
to customize seeds with specific structure or color, and then maximize
class scores to produce realistic samples (e.g., see Section [3.5](#S3.SS5 "3.5 Interactive Image Manipulation ‣ 3 Leveraging Robust Models for Computer Vision Tasks ‣ Computer Vision with a Single (Robust) Classifier")).
##### Evaluating Sample Quality.
Inception Score (IS) [salimans2016improved] is a popular metric for
evaluating the quality of generated image data.
Table [1](#S3.T1 "Table 1 ‣ Evaluating Sample Quality. ‣ 3.1 Realistic Image Generation ‣ 3 Leveraging Robust Models for Computer Vision Tasks ‣ Computer Vision with a Single (Robust) Classifier") presents the IS of samples
generated using a robust classifier.
| Dataset | Train Data | BigGAN [brock2019large] | WGAN-GP [gulrajani2017improved] | Our approach |
| --- | --- | --- | --- | --- |
| CIFAR-10 | 11.2 ± 0.2 | 9.22 | 8.4 ± 0.1 | 7.5 ± 0.1 |
| ImageNet44footnotemark: 4 | 331.9 ± 4.9 | 233.1 ± 1 | 11.6 | 259.0 ± 4 |
Table 1: Inception Scores (IS) for samples generated using robustly trained
classifiers compared to state-of-the-art
generation approaches [gulrajani2017improved, shmelkov2018good, brock2019large] (cf. Appendix [A.7.1](#A1.SS7.SSS1 "A.7.1 Inception Score ‣ A.7 Generation ‣ Appendix A Experimental Setup ‣ Computer Vision with a Single (Robust) Classifier")
for details).
We find that our approach improves over state-of-the-art
(BigGAN [brock2019large]) in
terms of Inception Score on the ImageNet dataset, yet, at the same time, the
Fréchet Inception Distance (FID) [heusel2017gans] is worse
(36.0 versus 7.4). These results can be explained by the fact that, on one hand, our samples are essentially adversarial examples (which are
known to transfer across models [szegedy2014intriguing]) and thus are likely
to induce highly confident predictions that IS is designed to pick up. On the other hand, GANs are explicitly trained to produce samples that are indistinguishable from true data with respect to a discriminator, and hence are likely to have a better (lower) FID.
###
3.2 Inpainting
Image inpainting is the task of recovering images with large
corrupted regions [efros1999texture, bertalmio2000image, hays2007scene].
Given an image x, corrupted in a region
corresponding to a binary mask m∈{0,1}d, the goal
of inpainting is to recover the missing pixels in a manner that is perceptually
plausible with respect to the rest of the image.
We find that simple feed-forward classifiers,
when robustly trained, can be a powerful tool for such image
reconstruction tasks.
From our perspective, the goal is to use robust models to restore missing features
of the image. To this end, we will optimize the image to
maximize the score of the underlying true class, while also
forcing it to be consistent with the original in the uncorrupted
regions. Concretely, given a robust classifier trained on
uncorrupted data, and a corrupted image x
with label y, we solve
| | | | |
| --- | --- | --- | --- |
| | xI=argminx′L(x′,y)+λ||(x−x′)⊙(1−m)||2 | | (3) |
where L
is the cross-entropy loss, ⊙ denotes element-wise multiplication, and λ is an appropriately chosen constant.
Note that while we require knowing the underlying label y for the input, it can typically be
accurately predicted by the classifier itself given the corrupted image.
In Figure [4](#S3.F4 "Figure 4 ‣ 3.2 Inpainting ‣ 3 Leveraging Robust Models for Computer Vision Tasks ‣ Computer Vision with a Single (Robust) Classifier"), we show sample reconstructions obtained by
optimizing ([3](#S3.E3 "(3) ‣ 3.2 Inpainting ‣ 3 Leveraging Robust Models for Computer Vision Tasks ‣ Computer Vision with a Single (Robust) Classifier")) using PGD (cf. Appendix
[A](#A1 "Appendix A Experimental Setup ‣ Computer Vision with a Single (Robust) Classifier") for details). We can observe that these reconstructions
look remarkably similar to the uncorrupted images in terms of semantic
content. Interestingly, even when this approach fails (reconstructions
differ from the original), the resulting images do tend to be perceptually
plausible to a human, as shown in Appendix Figure [12](#A2.F12 "Figure 12 ‣ Appendix B Omitted Figures ‣ Computer Vision with a Single (Robust) Classifier").
| | |
| --- | --- |
|
(a) *random* samples
|
(b) select samples
|
Figure 4: Image inpainting using robust models – left: original,
middle: corrupted and right: inpainted samples.
To recover
missing regions, we use PGD to maximize the class score predicted for the
image while penalizing changes to
the uncorrupted regions.
###
3.3 Image-to-Image Translation
As discussed in Section [2](#S2 "2 Robust Models as a Tool for Input Manipulation ‣ Computer Vision with a Single (Robust) Classifier"), robust
models provide a mechanism for transforming inputs between classes.
In computer vision literature, this would be an instance of
image-to-image translation, where the goal is to translate an image
from a source to a target
domain in a semantic manner [hertzmann2001image].
In this section, we demonstrate that robust classifiers give rise to a new methodology
for performing such image-to-image translations.
The key is to (robustly) train a classifier to distinguish between
the source and target domain.
Conceptually, such a classifier will extract salient characteristics of each
domain in order to make accurate predictions.
We can then translate an input from the source domain by
directly maximizing the predicted score of the target domain.
In Figure [5](#S3.F5 "Figure 5 ‣ 3.3 Image-to-Image Translation ‣ 3 Leveraging Robust Models for Computer Vision Tasks ‣ Computer Vision with a Single (Robust) Classifier"), we provide sample translations produced by our
approach using robust models—each trained only on the source and
target domains for the Horse ↔ Zebra, Apple ↔ Orange, and Summer ↔ Winter
datasets [zhu2017unpaired] respectively. (For completeness,
we present in Appendix [B](#A2 "Appendix B Omitted Figures ‣ Computer Vision with a Single (Robust) Classifier") Figure [10](#A2.F10 "Figure 10 ‣ Appendix B Omitted Figures ‣ Computer Vision with a Single (Robust) Classifier")
results corresponding to using
a classifier trained on the complete ImageNet dataset.)
In general, we find that this procedure yields meaningful
translations by directly modifying characteristics of the image
that are strongly tied to the corresponding domain (e.g., color,
texture, stripes).
horse → zebra
zebra → horse
horse → zebra
zebra → horse
apple → orange
orange → apple
apple → orange
orange → apple
summer → winter
winter → summer
summer → winter
winter → summer
(a) *random* samples
(b) select samples
Figure 5: Image-to-image translation on the Horse ↔ Zebra, Apple ↔ Orange,
and Summer ↔ Winter datasets [zhu2017unpaired] using PGD on the input of an
ℓ2-robust model trained on that dataset.
See Appendix [A](#A1 "Appendix A Experimental Setup ‣ Computer Vision with a Single (Robust) Classifier") for experimental details and
Figure [9](#A2.F9 "Figure 9 ‣ Appendix B Omitted Figures ‣ Computer Vision with a Single (Robust) Classifier") for additional input-output pairs.
Note that, in order to manipulate such features, the model must have learned
them in the first place---for example, we want models to distinguish between
horses and zebras based on salient features such as stripes. For overly simple
tasks, models might extract little
salient information (e.g., by relying on backgrounds instead of objects555In
fact, we encountered such an issue with ℓ∞-robust classifiers for
horses and zebras (Figure [11](#A2.F11 "Figure 11 ‣ Appendix B Omitted Figures ‣ Computer Vision with a Single (Robust) Classifier")). Note that generative
approaches also face similar issues, where the background is transformed instead
of the objects \citepzhu2017unpaired.)
in which case our approach would not lead to meaningful translations.
Nevertheless, this not a fundamental barrier and
can be addressed by training on richer, more challenging datasets.
From this perspective, scaling to larger datasets (which can be difficult for
state-of-the-art methods such as GANs) is actually easy and advantageous for our approach.
##### Unpaired datasets.
Datasets for translation tasks
often comprise source-target domain pairs [isola2017image].
For such datasets, the task can be straightforwardly cast into a supervised
learning framework.
In contrast, our method operates in the unpaired setting, where
samples from the source and target domain are provided without an
explicit pairing [zhu2017unpaired].
This is due to the fact that our method only requires a classifier capable
of distinguishing between the source and target domains.
###
3.4 Super-Resolution
Super-resolution refers to the task of recovering high-resolution images given
their low resolution version [dabov2007video, burger2012image].
While this goal is underspecified, our aim is
to produce a high-resolution image that is consistent with the input and
plausible to a human.
In order to adapt our framework to this problem,
we cast super-resolution as the task of accentuating the salient
features of low-resolution images.
This can be achieved by maximizing the score predicted by a robust classifier
(trained on the original high-resolution dataset)
for the underlying class.
At the same time, to ensure that the structure and high-level content is preserved, we penalize
large deviations from the original low-resolution image.
Formally, given a robust classifier
and a low-resolution image xL belonging to class
y, we use PGD to solve
| | | | |
| --- | --- | --- | --- |
| | ^xH=argmin||x′−↑(xL)||<εL(x′,y) | | (4) |
where ↑(⋅) denotes the up-sampling operation based on nearest
neighbors, and ε is a small constant.
| | |
| --- | --- |
|
(a) 7x super-resolution on CIFAR-10
|
(b) 8x super-resolution on restricted ImageNet
|
Figure 6: Comparing approaches for super-resolution.
Top: *random* samples from the test set;
middle: upsampling using bicubic interpolation; and
bottom: super-resolution using robust models. We obtain
semantically meaningful reconstructions that are especially sharp
in regions that contain class-relevant information.
We use this approach to upsample
*random* 32×32 CIFAR-10 images to full ImageNet size (224×224)—cf. Figure [5(a)](#S3.F5.sf1 "(a) ‣ Figure 6 ‣ 3.4 Super-Resolution ‣ 3 Leveraging Robust Models for Computer Vision Tasks ‣ Computer Vision with a Single (Robust) Classifier"). For comparison, we also show upsampled images obtained
from bicubic interpolation.
In Figure [5(b)](#S3.F5.sf2 "(b) ‣ Figure 6 ‣ 3.4 Super-Resolution ‣ 3 Leveraging Robust Models for Computer Vision Tasks ‣ Computer Vision with a Single (Robust) Classifier"), we visualize the results for super-resolution on
*random* 8-fold down-sampled images from the restricted
ImageNet dataset. Since in the latter case we have access to ground truth
high-resolution images (actual dataset samples), we can
compute the Peak Signal-to-Noise Ratio (PSNR) of the reconstructions.
Over the Restricted ImageNet
test set, our approach yields a PSNR of 21.53
(95% CI [21.49, 21.58]) compared to
21.30 (95% CI [21.25, 21.35]) from bicubic interpolation.
In general, our approach produces
high-resolution samples that are substantially sharper, particularly in regions
of the image that contain salient class information.
Note that the pixelation of the resulting images can be attributed to using a
very crude upsampling of the original, low-resolution image as a starting point for our
optimization. Combining this method with a more sophisticated initialization
scheme (e.g., bicubic interpolation) is likely to yield better overall
results.
###
3.5 Interactive Image Manipulation
Recent work has explored building deep learning–based interactive tools for
image synthesis and manipulation.
For example, GANs have been used to transform simple
sketches [chen2018sketchygan, park2019semantic] into realistic images.
In fact, recent work has pushed this one step further by building a tool
that allows object-level composition of scenes using GANs [bau2019gan].
In this section, we show how our framework can be used to enable similar artistic applications.
##### Sketch-to-image.
By performing PGD to maximize the probability of
a chosen target class, we can use robust models to convert
hand-drawn sketches to natural images. The resulting images (Figure [7](#footnote7 "footnote 7 ‣ Figure 7 ‣ Sketch-to-image. ‣ 3.5 Interactive Image Manipulation ‣ 3 Leveraging Robust Models for Computer Vision Tasks ‣ Computer Vision with a Single (Robust) Classifier"))
appear realistic and contain fine-grained characteristics of the corresponding
class.
Figure 7: Sketch-to-image using robust model gradients. *Top:*
manually drawn sketches of animals; and *bottom:* result of
performing PGD towards a chosen class. The resulting images appear
realistic looking while preserving key characteristics of the original
sketches777Sketches were produced by a graduate student without any
training in arts..
##### Feature Painting.
Generative model–based paint applications often allow the user to control more
fine-grained features, as opposed to just the overall class. We now show that we
can perform similar feature manipulation through a minor modification to our basic primitive
of class score maximization. Our methodology is based on an observation of
\citetengstrom2019learning,
wherein manipulating individual activations within representations888We refer
to the pre-final layer of a network as the representation layer. Then, the
network prediction can simply be viewed as the
output of a linear classifier on the representation.
of a robust model actually results in consistent and meaningful
changes to high-level image features (e.g., adding stripes to objects).
We can thus build a tool to paint specific features onto images by
maximizing individual activations directly, instead of just the class scores.
Concretely, given an
image x, if we want to add a single feature corresponding to component f of
the representation vector R(x) in the region corresponding to a binary mask
m, we simply apply PGD to solve
| | | | |
| --- | --- | --- | --- |
| | xI=argmaxx′ R(x′)f−λP||(x−x′)⊙(1−m)||. | | (5) |
Figure 8: Paint-with-features using a robust model—we present a
sequence of images obtained by successively adding specific features to
select regions of the image by solving ([5](#S3.E5 "(5) ‣ Feature Painting. ‣ 3.5 Interactive Image Manipulation ‣ 3 Leveraging Robust Models for Computer Vision Tasks ‣ Computer Vision with a Single (Robust) Classifier")).
In Figure [8](#S3.F8 "Figure 8 ‣ Feature Painting. ‣ 3.5 Interactive Image Manipulation ‣ 3 Leveraging Robust Models for Computer Vision Tasks ‣ Computer Vision with a Single (Robust) Classifier"), we demonstrate progressive addition of features at various levels of
granularity (e.g., grass or sky) to selected regions of the input image. We can observe that
such direct maximization of individual activations gives rise to a versatile
paint tool.
4 Discussion and Conclusions
-----------------------------
In this work, we leverage the basic classification framework to perform a wide
range of computer vision tasks. In particular, we find that the features learned
by a basic classifier are sufficient for all these tasks, provided this
classifier is adversarially robust. We then show how this insight gives
rise to a versatile computer vision toolkit that is simple, reliable, and
straightforward to extend to other large-scale datasets. This is in stark contrast
to state-of-the-art
approaches [goodfellow2014generative, karras2018progressive, brock2019large]
which typically rely on architectural, algorithmic, and task-specific
optimizations to succeed at
scale [salimans2016improved, daskalakis2018training, miyato2018spectral]. In
fact, unlike these approaches, our methods actually benefit from scaling
to more complex datasets—whenever the underlying classification task is rich
and challenging, the classifier is likely to learn more fine-grained features.
We also note that throughout this work, we choose to employ the most minimal
version of our toolkit. In particular, we refrain from using extensive tuning or
task-specific optimizations. This is intended to demonstrate the potential of
our core framework itself, rather than to exactly match/outperform the state of
the art. We fully expect that better training methods, improved notions of
robustness, and domain knowledge will yield even better results.
More broadly, our findings suggest that adversarial robustness might be a
property that is desirable beyond security and reliability contexts. Robustness
may, in fact, offer a path towards building a more human-aligned machine
learning toolkit.
\printbibliography |
f7df6fc1-32a5-4d8f-9a0f-ca87bbd3f5c4 | trentmkelly/LessWrong-43k | LessWrong | Meetup : SF Meetup: Fun and Games
Discussion article for the meetup : SF Meetup: Fun and Games
WHEN: 01 August 2016 06:15:18PM (-0700)
WHERE: 1597 Howard St, SF
We’ll be meeting to play board (and other) games!
I will bring Set, and standard playing cards; there is a small stock of other board games at the meetup venue. Please feel free to bring games you’d like to play.
For help getting into the building, please call: three zero one, three five six, five four two four.
Format:
We meet and start hanging out at 6:15, but don’t officially start doing the meetup topic until 6:45-7 to accommodate stragglers. Usually there is a food order that goes out before we start the meetup topic.
About these meetups:
The mission of the SF LessWrong meetup is to provide a fun, low-key social space with some structured interaction, where new and non-new community members can mingle and have interesting conversations. Everyone is welcome.
We explicitly encourage people to split off from the main conversation or diverge from the topic if that would be more fun for them (moving side conversations into a separate part of the space if appropriate). Meetup topics are here as a tool to facilitate fun interaction, and we certainly don’t want them to inhibit it.
Discussion article for the meetup : SF Meetup: Fun and Games |
e2f96ef8-c30d-491c-9ed1-3b31c1a9300b | trentmkelly/LessWrong-43k | LessWrong | Grokking the Intentional Stance
Considering how much I’ve been using “the intentional stance" in my thinking about the nature of agency and goals and discussions of the matter recently, I figured it would be a good idea to, y’know, actually read what Dan Dennett originally wrote about it. While doing so, I realized that he was already considering some nuances in the subject that the Wikipedia summary of the intentional stance leaves out but that are nonetheless relevant to the issues we face when attempting to e.g. formalize the approach, or think more clearly about the nature of agency in the context of alignment. I don’t expect many LessWrongers will read the original book in full, but I do expect that some additional clarity on what exactly Dennett was claiming about the nature of agency and goals will be helpful in having less confused intuitions and discussions about the subject.
In what follows, I provide an in-depth summary of Dennett’s exposition of the intentional stance, from Chapter 2 of The Intentional Stance (“True Believers: The Intentional Strategy and Why It Works”), which Dennett considers “the flagship expression” of his position. Then, I discuss a few takeaways for thinking about agency in the context of AI safety. In brief, I think 1) we should stop talking about whether the systems we build will or won’t “be agents,” and instead debate how much it will make sense to consider a given system as “an agent,” from the information available to us, and 2) we should recognize that even our internally-experienced beliefs and desires are the result of parts of our minds “applying the intentional stance” to other parts of the mind or the mind as a whole.
This work was completed as a Summer Research Fellow at the Center on Long-Term Risk under the mentorship of Richard Ngo. Thanks to Richard, Adam Shimi, Kaj Sotala, Alex Fabbri, and Jack Auen for feedback on drafts of this post.
Summarizing Dennett's position
TLDR: There is no observer-independent “fact of the matter” of whether a sys |
7ea3b8b9-10f7-458d-b644-87fee0f9f20e | trentmkelly/LessWrong-43k | LessWrong | Summaries of top forum posts (17th - 23rd April 2023)
We've just passed the half year mark for this project! If you're reading this (whether you're a regular reader or this is your first post), please consider taking this 5-10 minute survey - all questions optional. If you listen to the podcast, we have a separate survey for that here. This will directly influence our decisions of whether and how to continue this project next year, and we appreciate everyone who takes the time to fill it out.
Back to our regularly scheduled intro...
This is part of a weekly series summarizing the top posts on the EA and LW forums - you can see the full collection here. The first post includes some details on purpose and methodology. Feedback, thoughts, and corrections are welcomed.
If you'd like to receive these summaries via email, you can subscribe here.
Podcast version: Subscribe on your favorite podcast app by searching for 'EA Forum Podcast (Summaries)'. A big thanks to Coleman Snell for producing these!
Object Level Interventions / Reviews
AI
12 tentative ideas for US AI policy (Luke Muehlhauser)
by Lizka
Linkpost for this list of ideas by Luke Muehlhauser, which they tentatively think would increase the odds of good outcomes from transformative AI. These include:
* Software export controls.
* Requiring hardware security features on cutting-edge chips.
* Tracking stocks and flows of chips and licensing big clusters.
* Requiring a license to develop frontier AI models (which are then subject to info security and testing and evaluation requirements).
* Fund specific genres of alignment, interpretability, model evaluation and info sec R&D.
* Create a narrow antitrust safe harbor for AI safety & security collaboration.
* Require certain kinds of AI incident reporting.
* Clarify the liability of AI developers for concrete AI harms.
* Create means for rapid shutdown of large compute clusters and training runs.
See also this List of lists of government AI policy ideas and post on FLI (Future of Life Institute) rep |
a09d14c0-9c61-4266-be3a-9a6ebbfc2eb3 | trentmkelly/LessWrong-43k | LessWrong | Sets and Functions
Sets and functions are two of the most basic ideas in mathematics, and we'll need to know what they are to discuss some things about categories rigorously. Normally you'd learn about sets and functions way before encountering category theory, but in the spirit of assuming as little math as possible, we should write this post. It's also worth addressing a few matters for their conceptual relevance.
Sets are imaginary bags we put things into. For example, you can take a dog, a cat, and a shoe, put them in an imaginary bag, and now you have a set consisting of {dog,cat,shoe}. The members of the set—dog, cat, and shoe—are called the elements of the set.
A subtle but important aspect of a set is that the imaginary bag has to be defined by a rule. This rule can be pretty much anything, like "put into a bag everything I'm pointing at," but it does have to be a rule. Typically, sets can fit pretty much anything in, and so you can often just say "here is my set" rather than having to be explicit about the rule. We'll get back to why the rule matters at the end. For now, sets are imaginary bags that you can put pretty much anything into.
What are we putting into these bags, exactly? Pretty much anything, yes—but clearly we aren't actually putting dogs, cats, and shoes into bags. Mathematically, what are these things?
That is to say, what's the difference between the set {dog} and the set {cat}?
Well, what's the difference between the equations x+2=3 and y+2=3? Nothing but the name of the variable—which does not matter at all. We could call x anything. We could represent it with a thirty-foot tall watercolor of a fire truck.
So what's the difference between the set {dog} and the set {cat}? Only the name of the element—which does not matter at all. Just like we can take posets like 1→2→3 and a→b→c and represent their common structure abstractly as ∙→∙→∙ , we can do the same for {dog} and {cat} with this set: {∙}.
The set {∙} is what a one-element set like {dog} or {cat} |
3659aa42-766c-4d8f-8948-fa16b30cc6f1 | trentmkelly/LessWrong-43k | LessWrong | LW Update 5/6/2018 – Meta and Moderation
User Facing Changes
* New posts can only be submitted to your personal blog. Moderators will move it to the frontpage if it seems appropriate.
* "Personal Blogposts" tab is now labelled "All Posts", and now contains meta posts.
* We had deliberately been pushing on "disincentivize meta conversation", and still are, but since the Meta section basically has only been used for updates from the admins, it seemed like A) we could lean a bit in the other direction, B) I think having the third tier of posts on the frontpage be "all posts" is a lot more clear about what the frontpage hierarchy is trying to do.
* Meta posts now appear properly in your drafts on your user profile.
* Your user profile will now only show the 4 most recent drafts
* I rarely found I needed to see anything but my most recent drafts, and meanwhile it was a bit annoying to scroll past it whenever I went to my profile page.
Moderator Changes
* Moderators now have a sidebar that shows a list of all new unreviewed personal blogposts, with easy buttons for:
* approve (and leave as a personal blogpost)
* move to frontpage
* delete
In the past month or so, we've a) continued seeing a rise in post volume, while b) a couple of our moderators have been more busy than usual. I've been increasingly worried about the signal/noise ratio on the site.
So this update has been focused mostly on some tools that make moderation much easier, which many users won't directly experience but which I hope will lead to a better site experience.
Longterm, my goal is to put all moderator To Do items in the sidebar so they are easily seen, and then make it easy and encouraged to maintain inbox zero on the sidebar. I'd hoping this will help both reactive "notice and delete spam" type actions, and "notice and promote good things" type actions.
Minor Naming Convention Update
I'll be calling these posts "LW Update [Date] – {Description}" from now on, since "update" wasn't very each to search for, a |
07130e90-bfa1-4b61-91e3-8c53494ad6d1 | trentmkelly/LessWrong-43k | LessWrong | Stop talking about p(doom)
Epistemic status: Complete speculation, somewhat informed by copious arguing about the subject on Twitter.
As AI risk has moved into the mainstream over the past few years, I've come to believe that "p(doom)" is an actively harmful term for X-risk discourse, and people trying to mitigate X-risk should stop using it entirely.
Ambiguity
The first problem is that it's unclear what is actually being discussed. "p(doom)" can refer to many different things:
* p(AI kills us within 5-10 years)
* p(AI kills us within 80-200 years)
* p(conditional on AGI, we die shortly afterwards)
* p(conditional on superintelligence, we die shortly afterwards)
* Like 10 other things.[1]
These could have wildly different probabilities, and come along with different cruxes for disagreement. Depending on what specific "doom" is being discussed, the relevant point could be any of:
* Whether LLMs are capable of AGI at all.
* Whether AGI will quickly turn into superintelligence.
* Whether aligning superintelligence will be hard.
These are completely different questions, and people who are not explicit about which one they're discussing can end up talking past each other.
There are also many other potential miscommunications regarding exactly what "doom" refers to, the difference between one's inside view probability vs. ultimate probability, and more.
Distilling complex concepts down to single terms is good, but only when everyone is on the same page about what the term actually means.
Rhetoric
People concerned about X-risk tend to avoid "dark arts" rhetorical tactics, and justifiably so. Unfortunately, current society does not allow for complete good faith agents to do very well. Being fully honest about everything will turn you into a pariah, most people will judge you more based on charisma than on factual accuracy, and you need to use the right tribal signals before people will listen to you on a controversial topic at all. Using at least some light greyish arts in day to d |
111801c1-4c98-458f-8c01-f5873a725595 | trentmkelly/LessWrong-43k | LessWrong | My simple model for Alignment vs Capability
I have a simple model of the alignment vs. capabilities question. I am writing it down because after chewing on Michael Nielson's post about existential risk from AI, I thought it was great but was unsatisfied with with the idea an alignment dilemma. I wasn't the only person to feel that way, but neither was I able to find any satisfactory source describing the (tension? dichotomy? tradeoff?). The real rub of Nielsen's dilemma for me is that it was expressed in terms of accelerationism, which is a form of one-dialism, and one-dialism is wrong.
I note there is nothing actually new here; I am quite sure these considerations were all covered, and more besides, back when MIRI getting started. Yet we weren't speaking in terms of alignment vs capability then, and capabilities were a less urgent concern, and regardless of what we have said before here, people aren't talking about models in public now. So a simple model it is.
Background
The way I understand the alignment vs capabilities question is that capabilities research eventually cashes out as AGI, and alignment research cashes out as aligned AGI, so in this context alignment research is effectively a subset of capabilities research. I expect this to apply more or less continuously, where increasingly-capable-but-not-AGIs will still need to be aligned.
What I want to accomplish with the model is to have something we can use to make heuristic judgments about research: in particular things like whether to support, fund, or pursue it, and how to make comparisons between different research agendas. This is not for doing things like predicting timelines directly, or the course of AI research overall, or the future of a given research org.
Reject Acceleration
My chief objection to thinking and speaking in terms of acceleration is that it is causally useless. I make analogy to GDP as an economic metric: if a particular industry is growing very fast, and we want that industry to succeed but also to avoid catastrophic i |
52b026a5-6065-4435-8451-a97416e147b1 | StampyAI/alignment-research-dataset/special_docs | Other | Selecting the Partial State Abstractions of MDPs:
A Metareasoning Approach with Deep Reinforcement Learning.
Selecting the Partial State Abstractions of MDPs:
A Metareasoning Approach with Deep Reinforcement Learning
Samer B. Nashed1∗, Justin Svegliato2∗, Abhinav Bhatia1, Stuart Russell2, Shlomo Zilberstein1
Abstract — Markov decision processes (MDPs) are a common
general-purpose model used in robotics for representing se-
quential decision-making problems. Given the complexity of
robotics applications, a popular approach for approximately
solving MDPs relies on state aggregation to reduce the size of
the state space but at the expense of policy fidelity—offering
a trade-off between policy quality and computation time.
Naturally, this poses a challenging metareasoning problem:
how can an autonomous system dynamically select different
state abstractions that optimize this trade-off as it operates
online? In this paper, we formalize this metareasoning problem
with a notion of time-dependent utility and solve it using deep
reinforcement learning. To do this, we develop several general,
cheap heuristics that summarize the reward structure and
transition topology of the MDP at hand to serve as effective
features. Empirically, we demonstrate that our metareasoning
approach outperforms several baseline approaches and a strong
heuristic approach on a standard benchmark domain.
I. I NTRODUCTION
MDPs are a common general-purpose model used in
robotics for representing sequential decision-making prob-
lems [23]. However, the complexity of solving MDPs scales
poorly with the number of features reasoned about in the
environment, limiting their applicability. To address this
limitation, a range of approximate solvers for MDPs have
been proposed that seek to trade a small reduction in policy
quality for a large reduction in computation time.
A particularly effective approximate solver for MDPs,
recently proposed by Nashed et al. [17], solves a sequence
of partially abstract MDPs in order to solve an MDP. In
a partially abstract MDP, some states are considered at
maximum fidelity while other states are considered at lower
fidelity using an abstract representation. This can greatly
reduce the size of the state space while still resulting in a near
optimal policy by using a detailed representation for states
where it is most necessary. Still, for a partially abstract MDP
to be effective, it requires a suitable abstraction function that
maps a state in an MDP to an abstract state in an abstract
MDP. Since there has been substantial work on generating
abstraction functions for planners, ranging from symbolic
planners [6], [27], [13] to stochastic planners [1], [7], [26],
this paper assumes that a suitable abstraction function already
exists via either learning or careful expert design.
Given a specific abstraction function, a partially abstract
MDP uses an expansion strategy to determine which states
This work was supported by NSF grants IIS-1813490 and IIS-1954782.
∗Both authors contributed equally.
1University of Massachusetts, Amherst, MA, USA. Emails: {snashed,
abhinavbhati, shlomo }@cs.umass.edu
2University of California, Berkeley, CA, USA. Emails: {jsvegliato,
russell }@berkeley.edu
Fig. 1. Two partially abstract MDPs that were constructed using different
expansion strategies: a cheap expansion strategy that often results in lower
policy quality ( top) and an expensive expansion strategy that often results in
higher policy quality ( bottom ). Small circles are ground states, large circles
are abstract states, and arrows are transitions between states. The red ground
state is the current state, the green ground states have high reward, and the
green abstract states contain a ground state that has high reward.
of the MDP to reason about at maximum fidelity and
which states of the MDP to reason about at lower fidelity.
Concretely, this means that the expansion strategy selects
the abstract states to expand in the partially abstract MDP.
Ideally, any approach to selecting an expansion strategy
(illustrated in Fig. 1) should optimize a formal notion of
time-dependent utility by managing the trade-off between
policy quality and computation time given the domain of
operation and the available computational resources. Most
importantly, such an approach should generalize to any MDP
and require little knowledge in the details of that MDP.
In this paper, we therefore (1) offer a metareasoning
approach to selecting different expansion strategies that
optimizes a formal notion of time-dependent utility and (2)
express it as deep reinforcement learning problem. Moreover,
we (3) propose several general, cheap heuristics that summa-
rize the reward structure and transition topology of the MDP
at hand to generate effective features for deep reinforcement
learning. Empirically, we demonstrate that our metareasoning
approach outperforms several baseline approaches and a
strong heuristic approach on a standard benchmark domain.
II. R ELATED WORK
There are many approaches to approximately solving
MDPs, including performing dynamic programming, using
partial policies, and employing state abstractions. See [17]
for a thorough discussion of how these approaches relate
to partially abstract MDPs. Similarly, reinforcement learning
with time-dependent utility, introduced by Horvitz [10], has
been used in a variety of metareasoning problems [24], [22],
[4]. Although our approach uses reinforcement learning and
time-dependent utility similar to this work, we focus on a
different problem—that of learning how to select different
expansion strategies dynamically online during operation.
Online planning and learning over different abstractions
in general is a common problem across many areas of
artificial intelligence and encompasses several related sub-
problems. These include handling the non-Markovian nature
of state and action abstractions [2], learning context-specific
independences present in certain tasks [5], and learning
temporal abstractions in the form of progressively more
abstract skill controllers [14]. However, here, we restrict our
attention to state abstractions in the form of state aggregation
where multiple states in a larger (ground) problem form a
single state in a smaller (abstract) problem.
Online selection of state abstractions has been studied in
the context of both reinforcement learning and planning.
In reinforcement learning, abstractions are generally used if
the state space is large and training data is sparse, which
leads to poor experiential coverage. Methods include learning
the best state abstraction from a set of state abstractions
via hypothesis testing [12] and dynamically selecting state
abstractions of increasing granularities based on confidence
intervals of Q-values [25]. In planning, similar techniques
have been to applied to sample-based tree search algorithms.
For example, the PARSS algorithm is an algorithm that
adjusts state abstractions during tree search by starting with
coarse state abstractions and refining them given the variance
of the Q-values over actions at a specific abstract state [11].
An extensive body of research has investigated reasoning
over state abstractions during planning. Early work proposed
a hierarchy of state abstractions, represented as factored
semi-MDPs, that may have multiple intermediate state ab-
stractions that can be swapped in and out depending on
the environment [21]. Later work proposed algorithms for
dynamically eliminating state factors in states that were
estimated to not impact the policy by comparing two partially
abstract policies made with different state abstractions [3].
Finally, there have been specific applications, such as multi-
agent planning, where specialized partition schemes have
been introduced and adapted to an online setting [16].
This paper proposes a metareasoning framework that takes
advantage of powerful deep reinforcement learning methods
to learn a policy for selecting different expansion strategies.
Following work on SSPs, we use general, cheap heuristic
features that avoid relying on the specifics of an MDP. Most
importantly, we define this as a metareasoning problem that
optimizes a formal notion of time-dependent utility.III. B ACKGROUND
In this section, we review the formal definitions of a
ground MDP, an abstract MDP, and a partially abstract MDP.
a) Ground MDPs: A ground MDP is a tuple M=
⟨S, A, T, R ⟩. The space of states is S. The space of actions
isA. The transition function T:S×A×S→[0,1]
represents the probability of reaching a state s′∈Safter
performing an action a∈Ain a state s∈S. The reward
function R:S×A→Rrepresents the immediate reward
of performing an action a∈Ain a state s∈S. A
solution is a policy π:S→Aindicating that an action
π(s)∈Ashould be performed in a state s∈S. A policy
πinduces a value function Vπ:S→Rrepresenting
the expected discounted cumulative reward Vπ(s)∈Rfor
each state s∈Sgiven a discount factor 0≤γ < 1.
An optimal policy π∗maximizes the expected discounted
cumulative reward for each state s∈Sgiven the equation
V∗(s) = max a∈A
R(s, a) +γP
s′∈ST(s, a, s′)V∗(s′)
.
b) Abstract MDPs: Specifying an abstract MDP ¯Mof
a ground MDP Mrequires two functions [15]. First, an
abstraction function ϕ:S→¯Smaps a ground state s∈S
to an abstract state ¯s∈¯S. Second, an inverse abstraction
function ϕ−1:¯S→ P(S)maps an abstract state ¯s∈¯Sto
a set of ground states S⊆ P(S), where P(S)is the power
set of S. The condition ϕ(s) = ¯s⇔s∈ϕ−1(¯s)must hold
for each ground state s∈Sand abstract state ¯s∈¯S.
An abstract MDP is a tuple ¯M=⟨¯S, A, ¯T,¯R⟩[15].
The space of abstract states is ¯S={ϕ(s)|s∈
S}such that a set of ground states Sis abstracted by
an abstraction function ϕ. The space of ground actions
isA. The abstract transition function is ¯T(¯s, a,¯s′) =P
s∈ϕ−1(¯s)ψ(s)P
s′∈ϕ−1(¯s′)T(s, a, s′). The abstract reward
function is ¯R(¯s, a) =P
s∈ϕ−1(¯s)ψ(s)R(s, a). Note that a
weighting function ψ:S→[0,1]represents the probability
of being in a ground state s∈Sin an abstract state ϕ(s)∈¯S.
c) Partially Abstract MDPs: A partially abstract MDP
˜Mcombines a ground MDP Mand an abstract MDP ¯M
as a tuple ˜M=⟨˜S, A, ˜T,˜R⟩[17]. The space of partially
abstract states is ˜S=α∪βwith a set of ground states
α={ϕ−1(¯s)|¯s∈Γ}and a set of abstract states β={¯S\Γ}
such that a set of expanded abstract states Γ⊆¯Sis expanded
by an inverse abstraction function ϕ−1. The space of ground
actions is A. The partially abstract transition function ˜T:
˜S×AטS→[0,1]is composed of the ground/abstract
transition functions Tand¯T:
˜T(˜s, a,˜s′) =
T(˜s, a,˜s′) if˜s∈α,˜s′∈αP
s′∈ϕ−1(˜s′)T(˜s, a, s′) if˜s∈α,˜s′∈βP
s∈ϕ−1(˜s)ψ(s)T(s, a,˜s′)if˜s∈β,˜s′∈α
¯T(˜s, a,˜s′) if˜s∈β,˜s′∈β
The partially abstract reward function ˜R:˜S×A→Ris
composed of the ground/abstract reward functions Rand¯R:
˜R(˜s, a) =(
R(˜s, a)if˜s∈α
¯R(˜s, a)if˜s∈β
IV. S ELECTING PARTIAL STATE ABSTRACTIONS
The problem of selecting an expansion strategy to de-
termine the abstract states to expand in a partially abstract
MDP involves managing the trade-off between policy quality
and computation time. We frame this as a metareasoning
problem, the main advantage being that it expresses this
trade-off in terms of time-dependent utility, providing deep
reinforcement learning with an appropriate objective. Meth-
ods for similar metareasoning problems typically use heuris-
tics based on statistical measures to manage this trade-off.
Here, we introduce the first approach that selects expansion
strategies for partially abstract MDPs decision-theoretically.
A. Metareasoning for Partial State Abstractions
We begin by introducing the metareasoning problem for
partial state abstractions. This problem requires a time-
dependent utility that represents the utility of a policy in
terms of its quality and computation time. Intuitively, a policy
of a specific quality computed in a second has higher utility
than a policy of the same quality computed in an hour. A
time-dependent utility is therefore expressed as the difference
between an intrinsic value that reflects the utility of a policy
given its quality (but not computation time) and a time cost
that reflects the utility of a policy given its computation time
(but not quality) [10]. We define this function below.
Definition 1. Given a policy of quality q∈Φand compu-
tation time t∈Ψ, atime-dependent utility U: Φ×Ψ→R
can be expressed as the difference between two functions
U(q, t) =UI(q)−UC(t)where UI: Φ→R+is the intrinsic
value andUC: Ψ→R+is the time cost .
Given this time-dependent utility, the one-step metareason-
ing problem for partial state abstractions is the problem of
selecting the abstract states to expand in a given partially
abstract MDP. Naturally, a solution to this problem must
optimize time-dependent utility: we must select the abstract
states to expand in the partially abstract MDP that balances
the quality and computation time of its resulting policy.
Formally, given a set of abstract states Γi∈ P(¯S)to expand
in a partially abstract MDP ˜Miand its resulting policy πiof
policy quality q(πi)and computation time t(πi), this one-
step metareasoning problem is as follows.
arg max
Γi∈P(¯S)U(q(πi), t(πi))
This can be challenging to solve given substantial uncertainty
over the policy πiresulting from a partially abstract MDP
˜Mithat expands the abstract states Γi∈ P(¯S).
In real-time settings, an autonomous system often lazily
plans and acts online. Hence, during operation, we assume
that the autonomous system is either (1) executing an old
local policy πwhen it encounters a visited current state sor
(2) solving for a new local policy π′when it encounters an
unvisited current state s′. We can therefore view the union
of each local policy πias a joint global policy πΥas in
our recent work [17] that grows in quality and computation
time with each local policy πi. Intuitively, this presents asequential metareasoning problem for selecting the abstract
states to expand in a sequence of partially abstract MDPs
where the resulting local policies πiof each partially abstract
MDP ˜Mitogether compose a joint global policy πΥthat
must optimize time-dependent utility. Formally, given the
abstract states Υ = [Γ 1, . . . , Γh]expanded in a sequence
of partially abstract MDPs [˜M1, . . . , ˜Mh]over the unvisited
states{s1, . . . s h} ∈Shand the joint global policy πΥof
quality q(πΥ)and computation time t(πΥ), this sequential
metareasoning problem is as follows.
arg max
ΥU(q(πΥ), t(πΥ))
In practice, it is often beneficial to approximate this
sequential metareasoning problem as a sequence of inde-
pendent one-step metareasoning problems as follows.
arg max
Γ1∈P(¯S)U(q(π1), t(π1)) +···+ arg max
Γh∈P(¯S)U(q(πh), t(πh))
B. Reinforcement Learning for Partial State Abstractions
We now cast the sequential metareasoning problem for
partial state abstractions as an MDP. Each time an unvisited
state si∈Sis encountered, the MDP must select the
abstract states Γito expand in the partially abstract MDP ˜Mi.
Intuitively, the states include the quality and computation
time of the current joint global policy along with the reward
structure and transition topology of the ground MDP and
abstract MDP while the actions include expansion strategies
that select the abstract states to expand in the partially
abstract MDP. We define this metareasoning problem below.
Definition 2. The sequential metareasoning problem for
partial state abstractions is a tuple ⟨Φ,Ψ, F,ˆS,ˆA,ˆT,ˆR⟩
given a ground MDP Mand an abstract MDP ¯M:
•Φ ={q0, q1, . . . , q NΦ}is a set of qualities.
•Ψ ={t0, t1, . . . , t NΨ}is a set of computation times.
•F=F0×F1× ··· × FNFis a set of features that
summarize the reward structure and transition topology
of the ground MDP Mand abstract MDP ¯M.
•ˆS= Φ×Ψ×Fis a set of states of computation: each
state s∈ˆSreflects the current joint global policy πΥ
of quality q(πΥ)∈Φand computation time t(πΥ)∈Ψ.
•ˆAis a set of actions of computation: the set of expansion
strategies that each select different abstract states Γito
expand in a partially abstract MDP ˜Mi.
•ˆT:ˆS׈A׈S→[0,1]is an unknown transition function
that represents the probability of reaching state s′=
(q′, t′, f′)∈ˆSafter performing action a∈ˆAin state
s= (q, t, f )∈ˆS.
•ˆR:ˆS׈A׈S→Ris a reward function that represents
the expected immediate reward, ˆR(s, a, s′) =U(q′, t′)−
U(q, t), of reaching state s′= (q′, t′, f′)∈ˆSafter
performing action a∈ˆAin state s= (q, t, f )∈ˆS.
Note that the reward function is consistent with the
objective of optimizing the time-dependent utility: execut-
ing a sequence of expansion strategies until a joint global
policy πΥof quality q(πΥ)∈Φand computation time
t(πΥ)∈Ψemits a cumulative reward equal to the time-
dependent utility U(q(πΥ), t(πΥ)). This is a form of reward
shaping —equivalent to emitting a reward of U(q, t)once at
the end of an episode in terms of the objective—that guides
reinforcement learning with a reward at each time step [18].
We use deep reinforcement learning to learn an optimal
metareasoning policy by performing a series of simulations
that each use an expansion strategy to select the abstract
states to expand in a sequence of partially abstract MDPs.
Here, an agent learns a policy as a neural network by
performing actions and observing rewards in the environ-
ment, making it a good fit for metareasoning for three rea-
sons. First, by balancing exploitation and exploration, it can
learn how to select an expansion strategy given the reward
structure and transition topology of the ground MDP and
abstract MDP. Next, by ignoring large unreachable regions
of the state space, it can reduce the overhead of learning
which expansion strategy to select. Finally, by using a neural
network that extracts the relationship between large input
and output spaces, it can encode the effects of an expansion
strategy on the resulting policy of a partially abstract MDP
in a way that generalizes to novel states of computation.
C. Calculating Time-Dependent Utility
Typically, in metareasoning, a solution quality qis defined
as the approximation ratio, q=c∗
c, where c∗is the cost of
the optimal solution and cis the cost of the given solution.
However, since computing the cost of an optimal solution to
a complex problem is often infeasible, a solution quality can
be estimated as the approximation ratio, q=¯c∗
c, where ¯c∗is
a lower bound on the cost of the optimal solution and cis
the cost of the given solution. Generally, a solution quality
q= 0 means no solution was computed while a solution
quality q= 1 means an optimal solution was computed.
We need a specific definition of solution quality in the
context of MDPs. Here, the quality q(π)of a policy πis
defined as the approximation ratio,
q(π) =Vπ
V∗=P
s∈Sd(s)Vπ(s)P
s∈Sd(s)V∗(s),
where Vπis the value function of the policy πandV∗is the
value function of the optimal policy π∗, given a probability
d(s)of starting in a state s∈S. However, since computing
the value of an optimal policy of a complex MDP is often
infeasible, the optimal value function V∗must be replaced
with an upper bound on the value function ¯V∗.
Given the quality q(πΥ)and computation time t(πΥ)of
the current joint global policy πΥ, we can define the time-
dependent utility U(q(πΥ), t(πΥ))using an intrinsic value
UI(q(πΥ))and a time cost UC(t(πΥ)). First, given a tunable
parameter α, we model the intrinsic value as UI(q(πΥ)) =
αq(πΥ). Second, given a tunable parameter β, we model the
time cost as UC(t(πΥ)) =P
i∈h[eβt(πi)−1]such that πiis
the local policy solved for the unvisited states {s1, . . . s h} ∈
Sh. The rates αandβare typically given in the problem
depending on the value and urgency for a policy [8].
Given this time-dependent utility, it is possible to ex-
press the reward function of the metareasoning problem.Formally, given the current state of computation s=
(q(πΥ), t(πΥ),·)∈ˆSand the successor state of computation
s′= (q(π′
Υ), t(π′
Υ),·)∈ˆSthat reflect the current joint global
policy πΥand successor joint global policy π′
Υalong with
an expansion strategy a∈ˆAused to solve for a new local
policy πthat improves the joint global policy πΥ, we can
express the reward function in the following way.
ˆR(s, a, s′) =U(q(π′
Υ), t(π′
Υ))−U(q(πΥ), t(πΥ))
=α[q(π′
Υ)−q(πΥ)]−eβt(π)
V. R EPRESENTING THE STATE OF COMPUTATION
In this section, we introduce 6 features that compose the
state of computation in the sequential metareasoning problem
for partial state abstractions. These features can easily be
computed for a ground MDP Mand abstract MDP ¯Mand
reflect their reward structure ortransition topology .
A. Reward Structure
We define 3 features below describing the availability of
immediate reward around the current ground/abstract state.
1)Reward Frequency :The feature f1is the number of
positive reward ground states reachable within hactions of
the current ground state normalized by the total number of
reachable ground states.
2)Reward Proximity :The feature f2is the minimum
number of actions required to reach the nearest positive
reward ground state from the current ground state normalized
by the diameter diam( M) of the ground MDP M.
3)Reward Information :A main weakness of state ab-
stractions is that they induce artificial information boundaries
within the state space. For example, when a set of ground
states is compressed into an abstract state, the abstract MDP
loses information about any ground state that has successor
ground states in other abstract states. This is because succes-
sor ground states may be aggregated with other ground states
that are not reachable in a single action, which is detrimental
when a ground state with high reward successor ground states
can no longer be distinguished from a ground state without
high reward successor ground states. Therefore, the feature
f3is1/(1 +|diam(¯s)−δ|), where diam( ¯s) is the diameter
of the graph of the ground states in the current abstract state
¯s∈¯Sandδis the distance to the nearest high reward ground
state such that this value approaches 1or0as these ground
states move toward or away from this boundary.
B. Transition Topology
We define 3 features below describing the local transition
topology surrounding the current ground/abstract state.
1)Transition Entropy :The feature f4is the entropy of
the abstract successor state distribution at the current abstract
state assuming that actions are selected randomly. This is a
rough measure of the probability that actions performed at
the current abstract state will transition to different abstract
states that may be worth reasoning over more closely. A
higher entropy at the current abstract state indicates a higher
probability of transitioning to different abstract states.
Fig. 2. An example of (k, h)-reachability where k= 3 andh≤4. The
green region is allstates reachable from a given ground state swithin k
actions. The yellow /redregions are the states from which the set of important
ground states SGis still reachable/unreachable within hactions.
2)State Visitation :The feature f5is the expected dis-
counted number of times that the current abstract state will be
visited given an abstract start state distribution and an optimal
abstract policy. We compute this for all abstract states ¯s′∈¯S
by performing dynamic programming with the equation
λ(¯s′) =¯d(¯s′) +γX
¯s∈¯S¯T(¯s,¯π∗(¯s),¯s′)λ(¯s),
where ¯π∗(¯s)is the optimal abstract policy and ¯d(¯s′)is the
abstract start state distribution.
3)Important Ground State Reachability :The feature f6
is a novel measure of reachability from a given ground state
to a set of nearby important ground states.
Definition 3. A set of important ground states SGis(k,h)-
reachable from a given ground state sif, after performing
any arbitrary sequence of actions a1, . . . , a k, there is at least
one important ground state sg∈SGthat is still reachable
within hactions given a probability ϵ >0.
Similar to recent work on SSPs [20], [19], this measure
establishes an envelope (illustrated in Fig. 2) of ground states
in which the probability of reaching a set of important ground
states SGfrom a given ground state sis always greater than
zero. In general, while certain MDPs may have transition
topologies that permit calculating (k, h)-reachability exactly,
it usually must be estimated. To do this, we provide a
constant time estimation procedure in Algorithm 1. Here,
the accuracy of the estimate improves with the number of
samples parameterized by nandm. We choose kto be
proportional to the diameter of the current abstract state as
this is the maximum number of actions that can performed
by the local policy solved for the current abstract state.
VI. E XPERIMENTS
We now evaluate the proposed approach (D QN) against a
set of baseline approaches on a standard benchmark domain.
a) Hypothesis: Any approach to the metareasoning
problem for partial state abstractions should try to optimize
time-dependent utility by selecting the abstract states to
expand in a sequence of partially abstract MDPs. Ideally,
the approach should identify two cases. First, there are
cases in which cheap and expensive expansion strategiesAlgorithm 1: ESTIMATE (k, h)-REACHABILITY
1:Input: An MDP M, a ground state s, a set of important ground
states SG, and the parameters k,h,n, and m
2:Output: The probability that the set of important ground states SG
are(k, h)-reachable from the ground state s
3:Sk← ∅
4:fori∈ {1, . . . , n }do
5: s′←s
6: forj∈ {1, . . . , k }do
7: s′←SIMULATE RANDOM ACTION (M, s′)
8: Sk←Sk∪ {s′}
9:σ←0,ρ← ∅
10:forsk∈Skdo
11: fori∈ {1, . . . , m }do
12: s′←sk
13: forj∈ {1, . . . , h }do
14: s′←SIMULATE RANDOM ACTION (M, s′)
15: ifs′∈SGor∃p∈ρsuch that s′∈pthen
16: σ←σ+ 1
17: ρ←ρ∪PATH(sk, s′)
18: break
19:return σ/n
result in roughly equal policy quality , reducing computation
time at negligible sacrifice to policy quality. Second, there
are cases in which expensive expansion strategies result in
much higher policy quality than a cheap expansion strategy,
boosting policy quality at marginal amortized computation
time. Our hypothesis is that the proposed approach will
learn to exploit these two cases and hence optimize time-
dependent utility beyond the baseline approaches.
b) Experimental Setup: All approaches were evaluated
on100random simulations. For each simulation, we record
three metrics: the values for the policy quality ,computation
time, and time-dependent utility of the final policy. The
proposed approach was trained on1000 random simulations
using deep Q-learning with standard settings. The neural
network has two hidden layers of 64and32nodes with ReLU
activation and a linear output layer of 3nodes. The step
size is 0.0001 . The exploration strategy is ϵ-greedy action
selection with an exploration probability ϵthat is annealed
from 1to0.1over 1000 episodes. The experience buffer
capacity is ∞. The number of steps is 20000 . The buffer ini-
tialization period is 200. The target network update interval
is1000 . The minibatch size is 64. All simulations for training
and evaluation were generated using different randomization
seeds to measure generalizability to unfamiliar simulations.
c) Standard Benchmark Domain: We consider the
Earth observation domain proposed in early work on ground
MDPs [9] and recently modified in recent work on partially
abstract MDPs [17]. In this domain, a satellite orbiting Earth
indefinitely must take photos of points of interest Pwith
weather levels Wthat change stochastically. The satellite
starts at longitude x∈Xwith its camera focused at latitude
y∈Y. Given the rates ∆Yand∆X, the satellite can
then either do N OOPERATION , shift its camera N ORTH to
latitude (y+ ∆ Y)∈Y, shift its camera S OUTH to latitude
(y−∆Y)∈Y, or take an I MAGE of a point of interest at
latitude y∈Yand longitude x∈X. Concurrent to each
action, the satellite orbits from east to west described by
Naive Greedy Proactive Hybrid DQN
Approach0.00.51.0Policy Quality
Computation Time [seconds]
Time-Dependent UtilityFig. 3. Left: The policy quality of the final policy relative to the optimal policy over all evaluation simulations for each approach. Center: The frequency
of computation times of the final policy over all evaluation simulations for each approach. Right: The distribution of time-dependent utilities of the final
policy over all evaluation simulations for each approach. Putting these figures together, we observe that the proposed approach optimizes time-dependent
utility more effectively than the baseline approaches by learning how to manage the trade-off between policy quality and computation time.
Fig. 4. An example policy for the proposed approach that selects expansion
strategies. There are eight abstract states that each contain 2×4ground states
where hatch marks denote a point of interest. Each band within an abstract
state represents a specific expansion strategy: blue for N AIVE ,orange for
GREEDY , and green for P ROACTIVE such that darker shading denotes
higher probability. This policy shows how the proposed approach exploits
reward structure and transition topology of the earth observation MDP to
dynamically select the expansion strategy optimizing time-dependent utility.
longitude ((x+ ∆ X) mod |X|)∈Xwhere the modulo
operator creates periodic boundary conditions to represent
continuous orbits around earth. Most importantly, given the
IMAGE action, the satellite earns a reward proportional to
image quality such that image quality is a function of the
weather w∈W. The formal definitions of the ground,
abstract, and partially abstract MDPs are in recent work [17].
d) Baseline Approaches: We consider pure and hybrid
approaches that expand the current abstract state anda set of
informative abstract states . The N AIVE approach expands no
informative abstract states. The G REEDY approach expands
informative abstract states that contain a point of interest
within 1abstract state of the current abstract state. The
PROACTIVE approach expands informative abstract states
that are reachable from the current abstract state to any
abstract state that contains a point of interest within 2abstract
states of the current abstract state. The H YBRID approach
uses either the N AIVE , GREEDY , or P ROACTIVE approach
depending on the (k, h)-reachability of the current ground
state and the occupancy frequencies of the abstract MDP.
e) Experimental Results: Fig. 3 shows that the pro-
posed approach optimizes time-dependent utility beyond the
baseline approaches. First, N AIVE , GREEDY , and P ROAC -
TIVE exhibit poor time-dependent utility ( 29.6,36.6,32.2).
This is because they lead to either high policy quality in too
much computation time or low policy quality. Next, H YBRID
exhibits better time-dependent utility ( 40.7) by heuristically
reasoning over expansion strategies via careful expert design.
Finally, D QNexhibits the best time-dependent utility ( 44.7)
by performing explicit optimization using deep reinforce-
ment learning. Overall, the proposed approach decision-
theoretically selects expansion strategies (like in Fig. 4)
based on whether investing computation time would result
in a worthwhile improvement in policy quality.VII. C ONCLUSION
This paper introduces the metareasoning problem of se-
lecting different expansion strategies and solves it using deep
reinforcement learning with several general, cheap heuristics
that reflect the MDP at hand. Empirically, we show that
our metareasoning approach outperforms several baseline
approaches and a strong heuristic approach on a standard
benchmark domain. In future work, we will explore the
generalizability of this work to MDPs of varied topologies.
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[12] N. Jiang, A. Kulesza, and S. Singh. Abstraction selection in model-based
reinforcement learning. In ICML , 2015.
[13] C. A. Knoblock. Generating abstractions for planning. AIJ, 68(2), 1994.
[14] G. Konidaris, S. Kuindersma, R. Grupen, and A. Barto. Robot learning from
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for MDPs. In ISAIM , 2006.
[16] A. Ma, M. Ouimet, and J. Cort ´es. Dynamic domain reduction for multi-agent
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[17] S. B. Nashed, J. Svegliato, M. Brucato, C. Basich, R. Grupen, and S. Zilberstein.
Solving Markov decision processes with partial state abstractions. In ICRA , 2021.
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[19] L. Pineda and S. Zilberstein. Soft labeling in stochastic shortest path problems.
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MDPs. Technical report, MIT, 2004.
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space metareasoning for exception recovery. In IROS , 2019.
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algorithms with online performance prediction. In 27th IJCAI , 2018.
[25] M. Tamassia, F. Zambetta, W. L. Raffe, F. Mueller, and X. Li. Dynamic choice
of state abstraction in Q-learning. In ECAI , 2016.
[26] M. Tomar, A. Zhang, R. Calandra, M. E. Taylor, and J. Pineau. Model-invariant
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[27] A. Unruh and P. S. Rosenbloom. Abstraction in problem solving and learning.
In11th IJCAI , 1989. |
a1b5ef54-cfe5-4979-bbee-d30e4ba16559 | trentmkelly/LessWrong-43k | LessWrong | What makes you YOU? For non-deists only.
From the dawn of civilization humans believed in eternal life. The flesh may rot, but the soul will be reborn. To save the soul from the potential adverse living conditions (e.g. hell), the body, being the transient and thus the less important part, was expected to make sacrifices. To accumulate the best possible karma, pleasures of the flesh had to be given up or at least heavily curtailed.
Naturally the wisdom of this trade-off was questioned by many skeptical minds. The idea of reincarnation may have a strong appeal to imagination, but in absence of any credible evidence the Occam’s razor mercilessly cuts it into pieces. Instead of sacrificing for the sake of the future incarnations, a rationalist should live for the present. But does he really?
Consider the “incarnations” of the same person at different ages. Upon reaching the age of self-awareness, the earlier “incarnations” start making sacrifices for the benefit of the later ones. Dreams of becoming an astronaut at 25 may prompt a child of nine to exercise or study instead of playing. Upon reaching the age of 25, the same child may take a job at the bank and start saving for the potential retirement. Of course, legally all these “incarnations” are just the same person. But beyond jurisprudence, what is it that makes you who you are at the age of nine, twenty five or seventy?
Over the years your body, tastes, goals and the whole worldview are likely to undergo dramatic change. The single thing which remains essentially constant through your entire life is your DNA sequence. Through natural selection, evolution has ensured that we preferentially empathize with those whose DNA sequence is most similar to our own, i.e. our children, siblings and, most importantly, ourselves. But, instinct excepted, is there a reason why a rational self-conscious being must obey a program implanted in us by the unconscious force of evolution? If you identify more with your mind (personality/views/goals/…) than with t |
bb8b8543-e3f9-4bf7-a45e-0654ad8289ba | trentmkelly/LessWrong-43k | LessWrong | The Roots of Progress 2023 in review
2023 was another big year for me and The Roots of Progress.
It was a year when ROP as an organization really started to take off. Even though the org itself was formed in 2021, at first it was just a vehicle for my own intellectual work, plus a few side projects. Last year we announced our strategy and launched a search for an exec who could run it. This year she started and we launched our first program. (Note, Heike originally joined in the CEO role, but for personal and health reasons she decided to move to a VP of Programs role in June.)
As the org grows into something more than me, our communications are evolving, and probably my own personal updates will be separated from the org updates. But for now, I am going to keep doing my traditional annual review. (See past reviews: 2022, 2021, 2020, 2019, 2018, 2017)
The fellowship
This was a huge part of the year, so let me start with it.
We’re building a cultural movement to establish a new philosophy of progress. To do this, progress ideas need to be everywhere: in books and blogs, in YouTube and podcasts, in new media and old media, in newspapers and magazines, in textbooks and curricula, in art and entertainment. And for that, we need an army of writers and creatives to produce it all. The purpose of the fellowship is to develop that talent: to accelerate the careers of those intellectuals.
We launched our first program, the Blog-Building Intensive, in July, and got almost 500 applications. It was tough to choose, and we had to turn down a lot of qualified folks (so if you didn’t make it, don’t take it personally… in any case, these processes are always somewhat subjective and prone to error).
In the end, 19 fellows participated in the program, which involved writing instruction, editorial feedback, training in audience-building, and a peer group for brainstorming and feedback. They are experienced writers, many of them with bylines in mainstream media outlets. Some work for relevant think tanks, some are |
297f4b62-0a5b-496f-a52c-0c7276de9c9f | trentmkelly/LessWrong-43k | LessWrong | [SEQ RERUN] Are Your Enemies Innately Evil?
Today's post, Are Your Enemies Innately Evil?, was originally published on 26 June 2007. A summary (taken from the LW wiki):
> People want to think that the Enemy is an innately evil mutant. But, usually, the Enemy is acting as you might in their circumstances. They think that they are the hero in their story and that their motives are just. That doesn't mean that they are right. Killing them may be the best option available. But it is still a tragedy.
Discuss the post here (rather than in the comments to the original post).
This post is part of the Rerunning the Sequences series, in which we're going through Eliezer Yudkowsky's old posts in order, so that people who are interested can (re-)read and discuss them. The previous post was Correspondence Bias, and you can use the sequence_reruns tag or rss feed to follow the rest of the series.
Sequence reruns are a community-driven effort. You can participate by re-reading the sequence post, discussing it here, posting the next day's sequence reruns post, or summarizing forthcoming articles on the wiki. Go here for more details, or to have meta discussions about the Rerunning the Sequences series. |
ab491d5a-ea8d-4c50-997d-c5e727c86be5 | trentmkelly/LessWrong-43k | LessWrong | The Social Recession: By the Numbers
Fewer friends, relationships on the decline, delayed adulthood, trust at an all-time low, and many diseases of despair. The prognosis is not great.
By Anton Stjepan Cebalo
Intermission (also known as Intermedio) by Edward Hopper, 1963.
One of the most discussed topics online recently has been friendships and loneliness. Ever since the infamous chart showing more people are not having sex than ever before first made the rounds, there’s been increased interest in the social state of things. Polling has demonstrated a marked decline in all spheres of social life, including close friends, intimate relationships, trust, labor participation, and community involvement. The trend looks to have worsened since the pandemic, although it will take some years before this is clearly established.
The decline comes alongside a documented rise in mental illness, diseases of despair, and poor health more generally. In August 2022, the CDC announced that U.S. life expectancy has fallen further and is now where it was in 1996. Contrast this to Western Europe, where it has largely rebounded to pre-pandemic numbers. Still, even before the pandemic, the years 2015-2017 saw the longest sustained decline in U.S. life expectancy since 1915-18. While my intended angle here is not health-related, general sociability is closely linked to health. The ongoing shift has been called the “friendship recession” or the “social recession.”
My intention here is not to present a list of miserable points, but to group them together in a meaningful context whose consequences are far-reaching. While most of what I will outline here focuses on the United States, many of these same trends are present elsewhere because its catalyst is primarily the internet itself. With no signs of abating, a new kind of sociability has only started to affect what people ask of the world through the prism of themselves.
The topic has directly or indirectly produced a whole genre of commentary from many different perspecti |
98da39a2-547f-4570-9310-f2197b8fbe8a | trentmkelly/LessWrong-43k | LessWrong | [ASoT] Observations about ELK
This document outlines some of my current thinking about ELK, in the form of a series of observations I have made that inform my thinking about ELK.
Editor’s note: I’m experimenting with having a lower quality threshold for just posting things even while I’m still confused and unconfident about my conclusions, but with this disclaimer at the top. Thanks to AI_WAIFU and Peter Barnett for discussions.
* One way we can think of ELK is we have some set of all possible reporters, each of which takes in the latent states of a world model and outputs, for the sake of concreteness, the answer to some particular fixed question. So essentially we can think of a reporter+model pair as assigning some answer to every point in the action space. Specifically, collapsing possible sequences of actions into just a set of possible actions and only worrying about one photo doesn’t result in any loss of generality but makes things easier to talk about.
* We pick some prior over the set of possible reporters. We can collect training data which looks like pairs (action, answer). This can, however, only cover a small part of the action space, specifically limited by how well we can “do science.”
* This prior has to depend on the world model. If it didn’t, then you could have two different world models with the same behavior on the set where we can do science, but where one of the models understands what the actual value of the latent variable is, and one is only able to predict that the diamond will still appear there but can’t tell whether the diamond is still real. A direct translator for the second will be a human simulator for the first.
* More generally, we don’t really have guarantees that the world model will actually understand what’s going on, and so it might genuinely believe things about the latent variable that are wrong. Like, we might have models which think exactly like a human and so they don't understand anything a human wouldn’t understand, so the direct translato |
bfc19fb4-f63b-439b-9898-2f35c5b7bb75 | StampyAI/alignment-research-dataset/arxiv | Arxiv | Moving Beyond the Turing Test with the Allen AI Science Challenge
Moving Beyond the Turing Test with the Allen AI Science
Challenge
Carissa Schoenick, Peter Clark, Oyvind Tafjord, Peter Turney, Oren Etzioni
April 2016
Introduction
The field of Artificial Intelligence has made great strides forward recently, for example AlphaGo's
recent victory against the world champ ion Lee Sedol in the game of Go , leading to great
optimism about the field. But are we really moving towards smarter machines, or are these
successes restricted to certain classes of problems, leaving other challenges untouched? In
2016, the Allen Institute for Artificial Intelligence (AI2) ran the Allen AI Science Challenge, a
competition to test machines on an ostensibly difficult task, namely answering 8th Grade
science questions. Our motivations were to encourage the field to set its sights broader and
higher by exploring a problem that appears to require modeling, reasoning, language
understanding, and commonsense knowledge, to probe th e state of the art on this task, and
sow the seeds for possible futur e breakthroughs. The challenge received a strong response,
with 780 teams from all over the world participating. What were the results? This article
describes the competition and the interesting outcomes of the challenge.
Motivation
Challenge problems pla y an important role in motivating and driving progress in a field . For a
field striving to endow machines with intelligent behavior, e.g., language understanding and
reasoning, challenge problems that test such skills are essential.
In 1950, Alan Turing p roposed the now well -known Turing Test as a possible test of machine
intelligence: if a system can exhibit conversational behavior that is indistinguishable from that of
a human during a conversation, that system could be considered intelligent [1]. As the field of AI
has grown, this Test has become less meaningful as a challenge task for several reasons. First,
in its details, it is not well -defined, e.g., who is the person giving the test? A computer scientist
would likely know good distinguishing questio ns to ask, while a random member of the
population may not. What constraints are there on the interaction? What guidelines are provided
to the judges? Second, recent Turing Test competitions have shown that , in certain
formulations, the Turing Test is gam eable - people can be fooled by systems that simply retrieve
sentences, and make no c laim of being intelligent [2,3]. As The New York Times 's John Markoff
puts it, the Turing Test is more a test of human gullibil ity than machine intelligence. Finally, the
test, as originally conceived, is pass/fail rather than scored, thus providing no measure of
progress towards a goal, something essential for a challenge problem12.
1 Indeed, Turing himself did not conceive of the Turing Test as a challenge problem to drive the
field forward, but rather as a thought experiment about a useful alternative to the q uestion of
"Can machines think?".
2 Although one can imagine metrics that quantify performance on the Turing Test, the
imprecision in the task definition and human variability makes it hard to define metrics that are
reliably reproducible.
Nowadays, machine intelligence is viewed less as a binary pass/fail attribut e, and more as a
diverse collection of capabilities associated with intelligent behavior. Rather than a single test,
cognitive scientist Gary Marcus of NYU and others recently proposed the notion of series of
tests, a Turing Olympics of sorts, that could a ssess the full gamut of AI from robotics to NLP
[4][5].
Our goal with the Allen AI Science Chal lenge was to operationalize one such test , namely
answering science exam questions . Clearly the Science Challenge is not a full test of machine
intelligence. H owever, it does explore several capabilities strongly associated with intelligence -
capabilities that our machines need if they are to reliably perform the smart activities we desire
of them in the future - including language understanding, reasoning, and use of commonsense
knowledge. Doing well on the challenge appears to require significant advances in AI
technology, making it a potentially powerful vehicle for advancing the field. In addition, from a
practical point of view, exams are accessible, measur able, understandable, and compelling.
One of the most interesting and appealing aspects of science exa ms is their graduated and
multi faceted nature: different questions explore different types of knowledge, and they vary
substantially in difficulty (espe cially for a computer). There are questions that can be easily
addressed with a simple fact lookup, like this one:
How many chromosomes does the human body cell contain?
(A) 23
(B) 32
(C) 46
(D) 64
And then there are questions requiring extensive understanding of the world, such as this
example:
City administrators can encourage energy conservation by
(A) lowering parking fees
(B) building larger parking lots
(C) decreasing the cost of gasolin e
(D) lowering the cost of bus and subway fares
This question requires the knowledge that certain activities and incentives result in human
behaviors, which in turn result in more or less energy being consumed. Understanding this
question also require s recognizing that “energy” in this context refers to resource consumption
for the purposes of transportation (as opposed to other forms of energy one might find in a
science exam, like electrical, kinetic/potential, etc.).
AI vs 8th Grade: The Allen AI S cience Challenge
To put this approach to the test, AI2 designed and hosted “ The Allen AI Science Challenge ,” a
four-month long competition in partnership with Kaggle.com that concluded in February of 2016
[7]. Researchers worldwide were invited to build AI software that could answer standard 8th
grade multiple choice science questions. The competition aimed to assess the state of the art in
AI systems utilizing natural language understanding and knowledge -based reasoning —how
accurately the participants’ m odels could answer the exam questions would serve as an
indicator of how far the field has come in these areas.
Competition Overview
Timeline and Participants
The competition lasted four months from October 7th, 2015 through February 13th, 2016. A total
of 780 teams participated during the model building phase, and 170 teams made a final model
submission. Participants were required to make the code for their model available to AI2 at the
close of the competition to validate model performance and t o confirm the models followed
contest rules. At the conclusion of the competition, the winners were also expected to make
their code open source. The three teams that achieved the highest scores on the challenge’s
test set received prizes of $50,000, $20,0 00, and $10,000 respectively.
Data
A total of 5,083 8th grade multiple choice science questions were licensed from providing
partners for the purposes of the competition. All questions were standard multiple choice format
with four answer options , as the examples provided above . From this collection of questions,
participants were provided with a set of 2,500 training questions with which to train their models.
A validation set of 8,132 questions was used during the course of the competition for confirming
model performance . Only 800 of the validation questions were legitimate; the rest were
artificially generated to disguise the real questions in order to prevent cheating via manual
question answering or unfair advantage of additional training examples . A week before the end
of the competition, the final test set of 21,298 questions (which also included the validation set)
were provided to participants to use to produce a final score for their model (of these, 2,583
questions were legitimate). The data for the competition was licensed from private assessment
content providers who did not wish to allow the use of their data beyond the constraints of the
competition, however AI2 has made some subsets of these questions available on their website
[8].
Baselines and Scores
As these questions are all 4 -way multiple choice, a standard baseline score using random
guessing is 25%. AI2 also generated a baseline score using a Lucene search over the
Wikipedia corpus, which produced scores of 40.2% on the training set and 40.7% on the final
test set. The final outcome of the competition was quite close, with the top three teams
achieving scores with a spread of only 1.05%. The highest score was 59.31%.
First Place
Top prize went to Chaim Linhart of Israel (Kaggle username Cardal) . His model achieved a final
score of 59.31% on the test question set using a combination of 15 gradient boosting models,
each of which used a different subset of features. Unlike the other winners’ models, Chaim’s
model predicts the correctness of each answer option individually. There were two general
categories of features used to make these predictions; the first category was made up of
information retrieval (IR) based features, applied by searching over corpora he compiled from
various sources such as study guide or quiz building websit es, open source textbooks, and
Wikipedia. His searches used various weightings and stemmings to optimize per formance. The
other flavor of feature used in his ensemble of 15 models was based on properties of the
questions themselves, such as the length of the question and answer, the form of the answers
(e.g., characteristics like numeric answer options, answers that contained referential clauses
like “none of the above” as an option), and the relationships between answer options.
Chaim explained that he used several smaller gradient boosting models instead of one big
model in order to maximize diversity. One big model tends to ignore some important features
because it requires a very large training set to require it to pay attention to all of the potentially
useful features present --using several small models requires that the learning algorithm use
features that it would otherwise ignore, given the more limited training data available in this
competition.
The IR -based features alone could achieve scores as high as 55% by Chaim’s estimation. His
question -form features fill in some remaining gaps to bring the sys tem up to about 60% correct.
The 15 models were combined by a simple weighted average to yield the final score for each
choice. Chaim credited careful corpus selection as one of the primary elements driving the
success of his model.
Second Place
The seco nd place team with a score of 58.34% was a group of people from a social media
analytics company based in Luxembourg called Talkwalker, led by Benedikt Wilbertz (Kaggle
username poweredByTalkwalker ).
Benedikt’s team built a relatively large corpus as com pared to other winning models, which used
180GB of disk space after indexing with Lucene. They utilized several feature types, including
IR-based features using their large corpus, vector -based features (scoring question -answer
similarity by comparing vect ors from word2vec and Glove), pointwise mutual information (PMI)
features (measured between the question and target answer, calculated on their large corpus),
and string hashing features in which term -definition pairs were hashed and then a supervised
learner was trained to classify pairs as correct or incorrect. A final model uses these various
features to learn pairwise ranking between the answer options using the XGBoost gradient
boosting library.
The use of string hashing features by the poweredByTalkw alker team is unique; this
methodology was not tried by either of the other two competition winners, nor is it used in AI2’s
Project Aristo. The team used a corpus of terms and definitions obtained from an educational
flashcard building site, and then crea ted negative examples by mixing terms with random
definitions. A supervised classifier was trained on these incorrect pairs, and then the output was
used to generate features for input to XGBoost.
Third Place
The third place winner was Alejandro Mosquer a from the UK (Kaggle username Alejandro
Mosquera), with a score of 58.26%. Alejandro approached the challenge as a three -way
classification problem for each pair of answer options. The choices A, B, C, and D were
transformed to all twelve pairs (A,B), (A, C), ..., (D,C), which were labeled with three classes,
the left pair element is correct, the right is correct, or neither is correct. The pairs were then
classified using logistic regression. This three -way classification is easier for supervised learning
algorithms than the more natural two -way ( correct versus incorrect ) classification with four
choices, because the two -way classification requires an absolute decision about a choice,
whereas the three -way classification requires only a relative ranking of the choices.
Alejandro made use of three types of features: IR -based features based on scores from Elastic
Search using Lucene over a corpus, vector -based features that measured question -answer
similarity by comparing vectors from word2vec, and question -form features that considered
things such as the structure of a question, the length of the question and the answer choices.
Alejandro also noted that careful corpus selection was crucial to his model’s success.
Competition Lessons
In the end, each of the winning models found the most benefit in information retrieval based
methods. This is indicative of the state of AI technology in this area of research; we can’t ace an
8th grade science exam because we do not currently have AI syst ems capable of going beyond
the surface text to a deeper understanding of the meaning underlying each question, and then
successfully using reasoning to find the appropriate answer. All three winners expressed that it
was clear that applying a deeper, sema ntic level of reasoning with scientific knowledge to the
questions and answers would be the key to achieving scores of 80% and beyond, and to
demonstrating what might be considered true artificial intelligence.
A few other example questions from the comp etition that each of the top three models got
wrong highlight the more interesting, complex nuances of language and chains of reasoning an
AI system will need handle in order to answer these questions correctly, and for which IR
methods aren’t sufficient:
What do earthquakes tell scientists about the history of the planet?
(A) Earth's climate is constantly changing.
(B) The continents of Earth are continually moving.
(C) Dinosaurs became extinct about 65 million years ago.
(D) The oceans are much de eper today than millions years ago.
This question digs into the causes behind earthquakes and the larger geographic phenomena of
plate tectonics, and cannot be easily solved by looking up a single fact. Additionally, other true
facts appear in the answe r options (“ Dinosaurs became extinct about 65 million years ago. ”), but
must be intentionally identified and discounted as being incorrect in the context of the question.
Which statement correctly describes a relationship between the distance from Earth and
a characteristic of a star?
(A) As the distance from Earth to the star decreases, its size increases.
(B) As the distance from Earth to the star increases, its size de creases.
(C) As the distance from Earth to the star decreases, its apparent brightness increases.
(D) As the distance from Earth to the star increases, its apparent brightness increases.
This question requires general common -sense type knowledge of th e physics of distance and
perception, as well as the semantic ability to relate one statement to another within each answer
option to find the right directional relationship.
Other Attempts
While there are numerous question -answering systems that have emerged from the AI
community, none address the challenges of scientific and commonsense reasoning exhibited by
the example questions above. Question -answering systems developed for the MUC (messa ge
understanding) conferences [9 ] and TREC (text retrieval) conferences [10 ] focused on retrieving
answers from text, the former from newswire articles and the latter from various large corpora
such as the Web, microblogs, and clinical data. More recent work has focused on answer
retrieval from structured data, e.g ., "In which city was Bill Clinton born?" from FreeBase
[11,12,13 ]. These systems rely on the information being stated explicitly in the underlying data,
however, and are unable to perform the reasoning steps that would be required to conclude this
informa tion from indirect supporting evidence.
There are a few systems that attempt some form of reasoning: Wolfram Alpha [14 ] answers
mathematical questions, providing they are stated either as equations or with re latively simple
English; Evi [15 ] is able to combine facts together to answer simple questions (e.g., Who is
older, Barack or M ichelle Obama?); and START [16 ] will similarly answer simple inference
questions using Web -based databases (e.g., What South -American country has the largest
population?). Ho wever, none of these systems attempt the level of complex question processing
and reasoning that will be required to successfully answer many of the science questions in the
Allen AI Challenge.
Looking Forward
As the 2015 Allen AI Science Challenge clearly demonstrates , achieving a high score on a
science exam is going to require a system that can do more than merely sophisticated
information retrieval. Project Aristo at AI2 is intently focused on this problem of successfully
demonstrating artificial int elligence using standardi zed science exams, developing an
assortment of approaches to address the challenge. AI2 plans to release additional data sets
and software for the wider AI research community to utilize in this effort [8].
References
[1] Alan M. Turing. Computing machinery and intelligence. Mind, LIX(236):433 –460,
October 1950.
[2] BBC. Computer AI passes Turing test in 'world first' Turing Test. BBC News. 9 June 2014.
http://www. bbc.com/news/technology -27762088
[3] Aron, J. Software tricks people into thinking it is human. New Scientist (Issue 2829), Sept 2011.
[4] Marcus, G., Rossi, F., Veloso, M. (Eds), Beyond the Turing Test (AI Magazine Special Edition), AI
Magazine, 37 (1), Spring 2016.
[5] Turk, V. The Plan to Replace the Turing Test with a ‘Turing Olympics’. Motherboard. 28 January 2015.
http://motherboard.vice.com/read/the -plan-to-replace -the-turing -test-with-a-turing -olympics
[6] Clark, P., Etzioni, O. My Computer is an Honor Student - But how Intelligent is it? Standardized Tests
as a Measure of AI. In AI Magazine 37 (1), Spring 2016.
[7] "The Allen AI Science Challenge ." Kaggle , 13 Feb. 201 6, https://www.kaggle.com/c/the -allen -ai-
science -challenge .
[8] "Data - Allen Institute for Artificial Intelligence. " Allen Institute for Artificial Intelligence ,
http://allenai.org/data . Accessed 20 Oct. 2016.
[9] Grishman, R., Sundheim, B. Message Understanding Conference -6: A Brief History. In COLING (Vol.
96, pp. 466 -471), 1996.
[10] Voorhees, E., Ellis, A. (Eds)Proc. 24th Text REtrieval Conference (TREC 2015), Publication SP 500 -
319, NIST ( http://trec.nist.gov/ ), 2015.
[11] Yao, X., Van Durme, B. Information Extraction over Structured Data: Question Answering with
Freebase. In ACL (1) (pp. 956 -966), 2014.
[12] Berant, J., Chou, A., Frostig, R., Liang, P. Semantic Parsing on Freebase from Question -Answer
Pairs. In EMNLP (Vol. 2, No. 5, p. 6), 2013.
[13] Fader, A., Zettlemoyer, L., & Etzioni, O . Open question answering over curated and extracted
knowledge bases. In Proc 20th ACM SIGKDD Int Conf on Knowledge Discovery and Data Mining
(pp. 1156 -1165). ACM, 2014.
[14] Wolfram, S. Making the World's Data Computable. Proc. Wolfram Data Summit, 2010.
(http://blog.stephenwolfram.com/2010/09/making -the-worlds -data-computable/ )
[15] Simmons, J. True Knowledge: The Natural Language Question Answering Wikipedia for Fa cts. In:
Semantic Focus, Feb 2008.
[16] Katz, B., Borchardt, G., Felshin, S. Natural Language Annotations for Question Answering. Proc 19th
Int FLAIRS Conference (FLAIRS 2006), 2006. ( http://start.csail.mit.edu )
[17] Sachan, M., Dubey, A., Xing, E. Science Question Answering using Instructional Materials. arXiv
preprint at arXiv:1602.04375 http://arxiv.org/pdf/1602.04375.pdf
|
d33efde9-77a9-48cf-ab4e-f27505567dfe | trentmkelly/LessWrong-43k | LessWrong | Simler and Hanson on Our Hidden Motivations in Everyday Life
None |
5b9cd342-8ca5-4778-b84d-6988530fe47e | trentmkelly/LessWrong-43k | LessWrong | 60m Asteroid currently assigned a .022% chance of hitting Earth.
http://neo.jpl.nasa.gov/risk/2012da14.html
http://rt.com/news/paint-asteroid-earth-nasa-767/
Seems like a good opportunity to bring up existential risks. And A friendly reminder that NASA is in fact pretty damned important.
Thoughts? |
ed9120bf-7014-4cb0-bf47-3f04f4566499 | trentmkelly/LessWrong-43k | LessWrong | The Feeling of Idea Scarcity
Here’s a story you may recognize. There's a bright up-and-coming young person - let's call her Alice. Alice has a cool idea. It seems like maybe an important idea, a big idea, an idea which might matter. A new and valuable idea. It’s the first time Alice has come up with a high-potential idea herself, something which she’s never heard in a class or read in a book or what have you.
So Alice goes all-in pursuing this idea. She spends months fleshing it out. Maybe she writes a paper, or starts a blog, or gets a research grant, or starts a company, or whatever, in order to pursue the high-potential idea, bring it to the world.
And sometimes it just works!
… but more often, the high-potential idea doesn’t actually work out. Maybe it turns out to be basically-the-same as something which has already been tried. Maybe it runs into some major barrier, some not-easily-patchable flaw in the idea. Maybe the problem it solves just wasn’t that important in the first place.
From Alice’ point of view, the possibility that her one high-potential idea wasn’t that great after all is painful. The idea probably feels to Alice like the single biggest intellectual achievement of her life. To lose that, to find out that her single greatest intellectual achievement amounts to little or nothing… that hurts to even think about. So most likely, Alice will reflexively look for an out. She’ll look for some excuse to ignore the similar ideas which have already been tried, some reason to think her idea is different. She’ll look for reasons to believe that maybe the major barrier isn’t that much of an issue, or that we Just Don’t Know whether it’s actually an issue and therefore maybe the idea could work after all. She’ll look for reasons why the problem really is important. Maybe she’ll grudgingly acknowledge some shortcomings of the idea, but she’ll give up as little ground as possible at each step, update as slowly as she can.
And this is where a bunch of the standard advice from the sequen |
42d47bff-69c7-4156-b48a-92943fe0121f | trentmkelly/LessWrong-43k | LessWrong | LW/OB Rationality Quotes, June 2011
I saw this article and thought "ah, that's what's been missing." There's many a bon mot posted here that's outside the domain of the usual rationality quotes thread. Overcoming Bias seems still to be excluded from those too, even if the two blogs have diverged.
So:
This is a thread for posting any interesting rationality-related quotes you've seen on LW/OB.
* Please post all quotes separately (so that they can be voted up/down separately) unless they are strongly related/ordered.
* Do not quote yourself.
* Do not post quotes that are NOT comments/posts on LW/OB - there is a separate thread for this.
* No more than 5 quotes per person per thread, please.
(You may care to check the previous posts for duplicates.) |
f3be043e-e494-42f3-99fa-940ec7ddaf40 | trentmkelly/LessWrong-43k | LessWrong | The world according to ChatGPT
1.
I linked this in a small comment yesterday, but I think it deserves greater prominence.
It's an article by Sam Kriss, "Born in the wrong generation". It starts from an image that someone tweeted of an idyllic scene of paradise: 1950's small-town America. The tweeter's comment was, "Can we bring this back?"
The image is from an AI generator. The most obvious tell is that none of the lettering on the street signs and storefronts makes sense, but there are others. (Of the foreground woman in the centre, can you tell which leg is which? Why is the other woman wearing such huge gloves? Whose feet are those, seen below her dress to the right of her own legs?)
The article goes on to imagine living in the world of ChatGPT. It is viscerally horrific. His "beautiful submissive girlfriend" agrees emptily with everything he says. The background people outside the "folksy chrome-and-cream diner on Main Street in your quiet walkable 98% white small American town" are nightmares of deformed flesh. "Well hey there, your hazy waitress will say to you, opening a mouth that suddenly lacks a lower jaw. Keep safe now, says the friendly but unfocused cop. The gun dangling on his belt is half-made of dead grey skin." His meal "tastes of wet."
This is the world of ChatGPT.
2.
In that earlier comment I mentioned having received an email from Academia.edu that began
"Based on the papers you’ve autocfp, we think you might be interested in..."
No human hand wrote that sentence. What papers have you autocfp recenty? Can I help you wiht mrre refernecs? There are 32,03ll4 recently paper on the scebjtt of Lagnuage.
3.
There are several Facebook groups that I follow that post works of art of various sorts. The pictures are real (I can find them on Google Images), and the commentaries on them make sense, but I have suspected for a while that some of these groups are automatically generated. The proof came recently in a group dedicated to Escher. The picture of the day was his "Still Lif |
1817299d-bf44-4adb-8f76-12daf281f575 | LDJnr/LessWrong-Amplify-Instruct | LessWrong | "Motte and bailey is a technique by which one protects an interesting but hard-to-defend view by making it similar to a less interesting but more defensible position. Whenever the more interesting position - the bailey - is attacked - one retreats to the more defensible one - the motte -, but when the attackers are gone, one expands again to the bailey. In that case, one and the same person switches between two interpretations of the original claim. Here, I rather want to focus on situations where different people make different interpretations of the original claim. The originator of the claim adds a number of caveats and hedges to their claim, which makes it more defensible, but less striking and sometimes also less interesting.* When others refer to the same claim, the caveats and hedges gradually disappear, however, making it more and more motte-like.
A salient example of this is that scientific claims (particularly in messy fields like psychology and economics) often come with a number of caveats and hedges, which tend to get lost when re-told. This is especially so when media writes about these claims, but even other scientists often fail to properly transmit all the hedges and caveats that come with them.
Since this happens over and over again, people probably do expect their hedges to drift to some extent. Indeed, it would not surprise me if some people actually want hedge drift to occur. Such a strategy effectively amounts to a more effective, because less observable, version of the motte-and-bailey-strategy. Rather than switching back and forth between the motte and the bailey - something which is at least moderately observable, and also usually relies on some amount of vagueness, which is undesirable - you let others spread the bailey version of your claim, whilst you sit safe in the motte. This way, you get what you want - the spread of the bailey version - in a much safer way.
Even when people don't use this strategy intentionally, you could argue that they should expect hedge drift, and that omitting to take action against it is, if not ouright intellectually dishonest, then at least approaching that. This argument would rest on the consequentialist notion that if you have strong reasons to believe that some negative event will occur, and you could prevent it from happening by fairly simple means, then you have an obligation to do so. I certainly do think that scientists should do more to prevent their views from being garbled via hedge drift. Another way of expressing all this is by saying that when including hedging or caveats, scientists often seem to seek plausible deniability ("I included these hedges; it's not my fault if they were misinterpreted"). They don't actually try to prevent their claims from being misunderstood. What concrete steps could one then take to prevent hedge-drift? Here are some suggestions. I am sure there are many more. Many authors use eye-catching, hedge-free titles and/or abstracts, and then only include hedges in the paper itself. This is a recipe for hedge-drift and should be avoided.
Make abundantly clear, preferably in the abstract, just how dependent the conclusions are on keys and assumptions. Say this not in a way that enables you to claim plausible deniability in case someone misinterprets you, but in a way that actually reduces the risk of hedge-drift as much as possible. Explicitly caution against hedge drift, using that term or a similar one, in the abstract of the paper. * Edited 2/5 2016. By hedges and caveats I mean terms like "somewhat" ("x reduces y somewhat"), "slightly", etc, as well as modelling assumptions without which the conclusions don't follow and qualifications regarding domains in which the thesis don't hold."
The above is a chunk of text from a post created by a user on the website LessWrong.
Explain this as if I never finished highschool?
Sure, let's break it down.
"Motte and bailey" is a term borrowed from a type of medieval castle, where the "motte" is a protected tower and the "bailey" is the less protected courtyard. In discussions, someone using a "motte and bailey" tactic will have two points of view: one that's easy to defend but not very exciting (the motte), and one that's exciting but hard to defend (the bailey).
When their exciting but hard-to-defend idea (the bailey) is challenged, they retreat to their easy-to-defend but boring idea (the motte). Once the challenge is over, they go back to promoting their exciting idea.
The author of this text is saying that sometimes, when people make a claim, they add lots of "buts" and "maybes" to make it safer to defend, like a motte. But when other people talk about that claim, they leave out those "buts" and "maybes", making it more like a bailey.
This often happens with scientific claims, especially in fields like psychology and economics, where things aren't always clear-cut. The media, and even other scientists, often leave out the "buts" and "maybes" when they talk about these claims.
The author suggests that people might expect this to happen, and some might even want it to happen, because it means their exciting idea gets spread around without them having to defend it. They can stay safe in their motte while others spread their bailey.
The author also suggests that if people know this is likely to happen and don't do anything to stop it, that's not really honest. They think scientists should do more to make sure their ideas aren't misunderstood.
To prevent this "hedge drift", the author suggests that scientists should make it really clear how much their conclusions depend on certain assumptions. They should do this in a way that actually reduces the risk of misunderstanding, not just in a way that lets them say "well, I did warn you" if someone gets it wrong. They should also warn against "hedge drift" in their papers.
So in simple terms, the author is saying: "When you have an idea, be clear about what you're sure of and what you're not. Don't let others oversimplify your idea just to make it sound more exciting."
Could you elaborate on how the "hedge drift" phenomenon might affect the general public's perception of scientific findings, particularly in the context of media reporting?
Certainly. "Hedge drift" can significantly impact the public's understanding of scientific findings, especially when these findings are reported in the media.
When scientific studies are conducted, researchers often use specific language and include numerous caveats to accurately present their findings. These caveats, or "hedges," acknowledge the limitations of the study, the potential for error, or the specific conditions under which the findings are valid. They are an essential part of scientific communication because they help to prevent overgeneralization and misinterpretation of the results.
However, when these studies are reported in the media, there is a tendency for these hedges to be omitted or simplified. This can happen for several reasons. Journalists may lack the scientific expertise to fully understand the nuances of the study, or they may intentionally simplify the findings to make them more accessible and appealing to the general public. In some cases, there might be a push to create a more sensational headline or story to attract more readers or viewers.
The result of this "hedge drift" is that the public receives a version of the scientific findings that is more definitive and generalizable than the researchers intended. This can lead to misconceptions about the study's implications and can contribute to a lack of trust in science when the "definitive" findings are later contradicted or refined by further research.
For example, consider a hypothetical study that finds a slight correlation between eating a specific food and a reduced risk of a particular disease, but only under certain conditions and with many other factors at play. If this study is reported in the media without these hedges, it could easily be interpreted as "eating this food prevents disease," which is a much stronger and more general claim than the researchers made.
In conclusion, "hedge drift" can lead to the oversimplification and misinterpretation of scientific findings in the public sphere, which can contribute to confusion and misinformation.
How might the phenomenon of "hedge drift" influence policy-making decisions, particularly when scientific research is used to inform these decisions?
"Hedge drift" can significantly influence policy-making decisions, especially when these decisions are based on scientific research.
When scientists conduct research, they often include caveats or "hedges" to their findings. These hedges might indicate that the results are only applicable under certain conditions, or that there are other factors at play that could influence the outcome.
However, when these hedges are lost or overlooked in the process of translating scientific findings into policy recommendations - a phenomenon known as "hedge drift" - the resulting policies may be based on an oversimplified or misinterpreted version of the research.
For instance, let's say a scientific study finds a correlation between exposure to a certain chemical and health issues, but the study also includes hedges indicating that the correlation was only observed under specific conditions and more research is needed to confirm the findings. If policy-makers overlook these hedges and rush to enact strict regulations on the use of the chemical based on an oversimplified interpretation of the study, it could lead to unnecessary costs and restrictions.
On the other hand, if policy-makers ignore the hedges indicating that more research is needed and decide not to regulate the chemical at all, it could potentially lead to public health risks if future research confirms and strengthens the initial findings.
In either case, the policy decisions are not fully aligned with the nuanced findings of the scientific research due to "hedge drift."
To mitigate the influence of "hedge drift" on policy-making, it's important for policy-makers to work closely with scientists and to have a clear understanding of the research they're basing their decisions on. This includes understanding the limitations and conditions specified in the research, and not rushing to make decisions based on oversimplified interpretations of the findings. |
ae8d7947-3812-4e49-a377-7790dad3325c | trentmkelly/LessWrong-43k | LessWrong | Covid 4/28/22: Take My Paxlovid, Please
Many have made the observation that if you had told people two years ago that we would have a cure (not a vaccine, but a cure!) for Covid-19 that was free, safe and effective, but that no one wanted to take it, and Congress wasn’t willing to fund further purchases, people would not have believed you. And yet here we are.
The White House is trying to fix the situation. I’ll cover the details below.
We haven’t learned much new about China. When we do, it will go into its own post. I did get private supporting evidence that the situation in Shanghai is being characterized roughly correctly.
Executive Summary
1. Paxlovid is available, no one wants it.
2. Case counts up now that we’re past Easter.
3. Cases hit local peaks including in NYC, indicating BA.2 wave won’t be too bad.
Also, did you hear? Elon Musk is buying Twitter.
Let’s run the numbers.
The Numbers
Predictions
Prediction from last week: 277,800 cases (+20%) and 4,100 deaths (+71%!?)
Results: 328,762 cases (+41%) and 2,485 deaths (+2%!)
Prediction for next week: 400,000 cases (+22%) and 2,720 deaths (+10%?)
On deaths this is one of the biggest misses I’ve had, and it’s not one of the ones I look back on and instantly feel was simply stupid – often it’s obvious in hindsight why I messed up, and mostly this isn’t one of those cases
There was a huge drop for Easter, and it was sustained even as cases popped back up even more than I expected. I don’t understand it, but the distributions involved look real. I can only interpret this as ‘we had inflated death numbers for a while that weren’t real, and now we have less of that’ because I can’t think of any other way to make sense of this. I guess I’m predicting a small increase next week here, but I mostly notice I am confused.
I believe a lot of this jump in cases is related to Easter, and the details suggest that we are going to be reaching another local peak soon especially in the northeast.
Deaths
That is not many deaths. I don’t know how |
f53a4540-55b1-4e2f-8bef-3c4b6ec195d3 | trentmkelly/LessWrong-43k | LessWrong | The Sense-Making Web
I want to attempt to convey the sense of what it feels like to be in a particular scene. Sadly, blogposts are a poor medium for this, but I think it's important, so I'll try my best. In particular, I'll be focusing on the (vaguely defined) Sensemaking scene. I'm honestly surprised that very little has been written about this given how vibrant the space feels.
Both rationalists and sensemakers share the common goal of trying to make sense of the world and by examining these movements side-by-side we can produce a clearer image of the strengths and limitations of each. In particular, I would suggest that the Sensemaking scene draws better on lessons from spirituality, has a better understanding of narrative, makes better use of recorded conversations and has a stronger understanding of the importance of local community. Beyond this, I suspect it'll make a valuable contribution towards ending the culture wars.
Given the difficulty of describing a scene, I feel it'd be worthwhile to pick out some words that capture my felt sense of being present in it. The first word I'll pick is "openness". People who are low on openness tend to react strongly to ideas that are incompatible with their world view or which are too "weird", whilst people who are high in openness are much more likely to find aspects that resonate with them and put the rest aside. The sensemaking scene is highly open in that participants often discourse with those who hold completely different political views than them and in their embrace of spirituality or spirituality-adjacent practises. Much emphasis is put on being able to hold tension or uncomfortableness, which I think is almost definitionally necessary to explore new intellectual territory.
The second word I'll pick is "coherence" (see also: common knowledge). In some ways this is the opposite of the previous as openness tends to lead to divergence and coherence to convergence. However, the production of new ideas requires both convergence and co |
2481226f-a502-4fc7-b1e4-a53dfeb2c637 | trentmkelly/LessWrong-43k | LessWrong | Limits of Giving
A friend recently asked what my goal was in giving: was there some amount of donations that would be enough? If someone give me a large enough amount of money, which I then donated, would I be free of further altruistic obligations?
These questions feel to me like they come from a very different perspective, so I want to try and explain how I think about it. If I continue on my current path, perhaps over the next 40 years I might manage to donate $10M. There's a sense, then, in which I have a target of $10M. If through some unrealistically good fortune my 0.34% of Wave stock options turned into $50M, however, I wouldn't donate $10M and then devote myself to leisure.
The level of need in the world is enormous, far bigger than my personal efforts can address. The poorest billion people need a marginal dollar far more than I do; no one should be dying of malaria; our society's ability to handle a pandemic is terrifyingly bad; we are putting much less effort than we should be into making sure humanity doesn't go extinct.
Now I'm not going to sell all my possessions and live as cheaply as possible, but I am going to be thoughtful about balancing costs to myself against benefits to others and making good altruistic tradeoffs. The more money I have, the larger a portion I can give while continuing to spend money on myself in ways that make me happy.
Considered this way, responding to receiving $50M by decreasing the percentage I gave would be exactly backwards.
Comment via: facebook |
16813fd2-454f-434a-bf06-35ade7dde5ab | StampyAI/alignment-research-dataset/arxiv | Arxiv | Unifying Model Explainability and Robustness via Machine-Checkable Concepts
1 Introduction
---------------
Explainability has emerged as an important requirement for deep neural networks (DNNs).
Explanations target a number of secondary objectives of model design (in addition to the primary objective of maximizing prediction accuracy), such as informativeness, transferability and audit of ethical values [[15](#bib.bib15), [32](#bib.bib32), [36](#bib.bib36)].
One of the most important desiderata of explainability is model robustness, whereby
explanations
are used to assess the extent to which some downstream task could rely on the model’s predictions. For instance, a prediction classifying an input as a wolf with the explanation that the background contains snow is unlikely to be trusted by the downstream system [[40](#bib.bib40)]. A long line of research has focused on rendering DNN predictions explainable with the—often implicit—goal of assessing prediction robustness [[28](#bib.bib28), [40](#bib.bib40), [11](#bib.bib11), [29](#bib.bib29), [43](#bib.bib43), [31](#bib.bib31), [41](#bib.bib41), [33](#bib.bib33), [30](#bib.bib30), [3](#bib.bib3)].
However, the scalability of these explanation-based robustness assessment schemes is limited by the need for "humans-in-the-loop".
Prediction robustness checks based on explanations operate as following: Given an input, one or more human-interpretable concepts are identified that have a significant impact on the model prediction. Then an explanation-conformity check is performed to see whether the concept–prediction relationship matches human-reasoning. In the above example of wolf and snow [[40](#bib.bib40)], a human may deem the concept–prediction relationship (snow–wolf) to be unreasonable, and consider the prediction to be non-robust.
However, identifying human-interpretable concepts and checking for human-reasoning requires significant human effort by the way of manual annotation of either the inputs (*e.g.*, TCAV [[28](#bib.bib28)]), intermediate model components (*e.g.*, LIME [[40](#bib.bib40)]) or both (*e.g.*, saliency maps [[43](#bib.bib43)]). In practice, human involvement makes many explanation-based robustness assessments unsuitable for large-scale deployment.
Goals and contributions.
In this paper, our goal is to design a highly scalable robustness assessment framework that automates the end-to-end process of performing explanation-conformity checks.
At the foundation of our framework are concepts with the following key properties:
1. 1.
The concepts are identified automatically from the training data without any human effort.
2. 2.
They are machine-checkable , *i.e.*, they lend themselves to ‘concept–class’ style automated explanation-conformity checks without any human involvement.
3. 3.
They can be added to off-the-shelf, pretrained DNNs in a post-hoc manner to assess prediction robustness.
We devise an intuitive procedure for identifying machine-checkable concepts ( MACCs ) that satisfy the above key properties. Specifically, our framework automatically defines a large number of MACCs, each corresponding to features shared by some subset of one or more classes (and not shared by other classes)
in the training data. At the end of the concept-identification process, each class in the training data has a unique set of corresponding MACCs.
Finally, with each prediction of the DNN, our framework performs an automated explanation-conformity check to see if the MACCs corresponding to the predicted class are also detected in the learnt representations of the input (and the MACCs not corresponding to the predicted class are not detected). The predictions passing the explanation-conformity check are deemed robust, even if individual MACCs are hard for humans to recognize.
Experiments and human surveys on real-world image classification datasets show that MACCs help increase the prediction robustness significantly.
Specifically, we find that (i) explanation-conformant predictions are not only significantly more accurate, but their corresponding images are also easier for humans to classify confidently than non-conformant predictions, (ii) adversarial attacks against explanation-conformant predictions are significantly harder and in many cases impractical, and (iii) MACCs also provide insights into the potential causes for prediction errors.
2 Methodology
--------------
In this section, we describe our framework for robust prediction.
Formal problem setup and notation.
Let 𝒟={(𝒙i,yi)}i=1N𝒟superscriptsubscriptsubscript𝒙𝑖subscript𝑦𝑖𝑖1𝑁\mathcal{D}=\{(\bm{x}\_{i},y\_{i})\}\_{i=1}^{N}caligraphic\_D = { ( bold\_italic\_x start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT , italic\_y start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ) } start\_POSTSUBSCRIPT italic\_i = 1 end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT italic\_N end\_POSTSUPERSCRIPT denote a training dataset of N𝑁Nitalic\_N examples with 𝒙∈𝒳=ℝd𝒙𝒳superscriptℝ𝑑\bm{x}\in\mathcal{X}=\mathbb{R}^{d}bold\_italic\_x ∈ caligraphic\_X = blackboard\_R start\_POSTSUPERSCRIPT italic\_d end\_POSTSUPERSCRIPT and y∈𝒴={1,2,…,K}𝑦𝒴12…𝐾y\in\mathcal{Y}=\{1,2,\ldots,K\}italic\_y ∈ caligraphic\_Y = { 1 , 2 , … , italic\_K }.
The learning task involves obtaining a mapping Fclf:𝒳→𝒴:subscript𝐹clf→𝒳𝒴F\_{\text{clf}}:\mathcal{X}\to\mathcal{Y}italic\_F start\_POSTSUBSCRIPT clf end\_POSTSUBSCRIPT : caligraphic\_X → caligraphic\_Y .
For a (deep) neural network with L𝐿Litalic\_L hidden layers, this mapping consists of applying a set of parameterized layers fl(𝒙l,𝜽l)subscript𝑓𝑙subscript𝒙𝑙subscript𝜽𝑙f\_{l}(\bm{x}\_{l},\bm{\theta}\_{l})italic\_f start\_POSTSUBSCRIPT italic\_l end\_POSTSUBSCRIPT ( bold\_italic\_x start\_POSTSUBSCRIPT italic\_l end\_POSTSUBSCRIPT , bold\_italic\_θ start\_POSTSUBSCRIPT italic\_l end\_POSTSUBSCRIPT ). Here, 𝒙lsubscript𝒙𝑙\bm{x}\_{l}bold\_italic\_x start\_POSTSUBSCRIPT italic\_l end\_POSTSUBSCRIPT and 𝜽lsubscript𝜽𝑙\bm{\theta}\_{l}bold\_italic\_θ start\_POSTSUBSCRIPT italic\_l end\_POSTSUBSCRIPT denote, respectively, the input and parameters of the lthsuperscript𝑙𝑡ℎl^{th}italic\_l start\_POSTSUPERSCRIPT italic\_t italic\_h end\_POSTSUPERSCRIPT layer.
The whole neural network mapping can be expressed as:
Fclf(𝒙)=fclf(fL(fL−1(…,f1(𝒙,𝜽1))))subscript𝐹clf𝒙subscript𝑓clfsubscript𝑓𝐿subscript𝑓𝐿1…subscript𝑓1𝒙subscript𝜽1F\_{\text{clf}}(\bm{x})=f\_{\text{clf}}(f\_{L}(f\_{L-1}(\ldots,f\_{1}(\bm{x},\bm{\theta}\_{1}))))italic\_F start\_POSTSUBSCRIPT clf end\_POSTSUBSCRIPT ( bold\_italic\_x ) = italic\_f start\_POSTSUBSCRIPT clf end\_POSTSUBSCRIPT ( italic\_f start\_POSTSUBSCRIPT italic\_L end\_POSTSUBSCRIPT ( italic\_f start\_POSTSUBSCRIPT italic\_L - 1 end\_POSTSUBSCRIPT ( … , italic\_f start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT ( bold\_italic\_x , bold\_italic\_θ start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT ) ) ) ),
where the output of fclfsubscript𝑓clff\_{\text{clf}}italic\_f start\_POSTSUBSCRIPT clf end\_POSTSUBSCRIPT—or the classification layer—is a K-dimensional vector consisting of (potentially un-calibrated) probabilities, generally obtained by applying the softmax function within the layer fclfsubscript𝑓clff\_{\text{clf}}italic\_f start\_POSTSUBSCRIPT clf end\_POSTSUBSCRIPT.
One then obtains the prediction y^=argmaxFclf(𝒙)^𝑦argmaxsubscript𝐹clf𝒙\hat{y}=\text{argmax}\ F\_{\text{clf}}(\bm{x})over^ start\_ARG italic\_y end\_ARG = argmax italic\_F start\_POSTSUBSCRIPT clf end\_POSTSUBSCRIPT ( bold\_italic\_x ).
The learning then boils down to minimizing the discrepancy between the predicted and the ground-truth labels.
For the sake of computational tractability, this discrepancy is often expressed via the (categorical) cross-entropy loss function, denoted henceforth as ℒclf(Fclf(𝒙),y)subscriptℒclfsubscript𝐹clf𝒙𝑦\mathcal{L}\_{\text{clf}}(F\_{\text{clf}}(\bm{x}),y)caligraphic\_L start\_POSTSUBSCRIPT clf end\_POSTSUBSCRIPT ( italic\_F start\_POSTSUBSCRIPT clf end\_POSTSUBSCRIPT ( bold\_italic\_x ) , italic\_y ).
Figure 1: [System overview] We propose the use of (a) Machine-checkable concepts (MACCs), that are defined as concepts shared between inputs of one or more classes
(Section [2.1.1](#S2.SS1.SSS1 "2.1.1 Automatically defining MACCs ‣ 2.1 Our framework: Robustness via machine-checkable concepts ‣ 2 Methodology ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts"))—the figure only shows the MACCs shared between two classes.
(b)
Automatically detecting MACCs involves adding an additional classification layer (to any hidden layer) of an existing DNN (Section [2.1.2](#S2.SS1.SSS2 "2.1.2 Detecting MACCs in DNNs ‣ 2.1 Our framework: Robustness via machine-checkable concepts ‣ 2 Methodology ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts")).
(c) At test time, we perform the explanation-conformity check to ensure that the MACCs corresponding to the predicted class are also detected in the image (Section [2.1.3](#S2.SS1.SSS3 "2.1.3 Explanation-conformity checks with MACCs ‣ 2.1 Our framework: Robustness via machine-checkable concepts ‣ 2 Methodology ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts")). The predictions not passing the explanation-conformity check are deemed non-robust.
###
2.1 Our framework: Robustness via machine-checkable concepts
Our framework, summarized in Figure [1](#S2.F1 "Figure 1 ‣ 2 Methodology ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts"), consists of three main components: Defining machine-checkable concepts (MACCs), leveraging the DNN to detect MACCs, and performing explanation-conformity checks with MACCs to assess prediction robustness. We now describe each of the components individually.
####
2.1.1 Automatically defining MACCs
The first component of our framework automatically defines MACCs that are amenable to explanation-conformity checks without any human intervention. To define MACCs, we leverage the following key insight [[36](#bib.bib36), [25](#bib.bib25)]: one method of composing explanations is to point to presence or absence of concepts in the input, where a concept is a feature that is possessed by inputs of a certain set of classes in the dataset, and not possessed by other classes.
For instance, in an animal classification task involving zebras, cats and dogs, zebras might have a unique concept stripes [[28](#bib.bib28)], that is not shared by any other class.
Similarly, dogs and cats might share a concept paws that is not shared by any other class.
Most prior works detect these concepts by manually annotating (parts of) inputs that contain them (*e.g.*, [[28](#bib.bib28), [41](#bib.bib41), [40](#bib.bib40)]).
Instead of manually annotating the inputs, for every possible subset of one or more classes, we define one MACC that corresponds to the features shared by inputs in that subset. This way of defining MACCs leads to M=2K−1𝑀superscript2𝐾1M=2^{K}-1italic\_M = 2 start\_POSTSUPERSCRIPT italic\_K end\_POSTSUPERSCRIPT - 1 concepts in a dataset with K𝐾Kitalic\_K classes.
For instance, in a datasets with classes cat, dog and zebra, one can define 23−1=7superscript23172^{3}-1=72 start\_POSTSUPERSCRIPT 3 end\_POSTSUPERSCRIPT - 1 = 7 MACCs, as follows {ccatsubscript𝑐catc\_{\text{cat}}italic\_c start\_POSTSUBSCRIPT cat end\_POSTSUBSCRIPT, cdogsubscript𝑐dogc\_{\text{dog}}italic\_c start\_POSTSUBSCRIPT dog end\_POSTSUBSCRIPT, czebrasubscript𝑐zebrac\_{\text{zebra}}italic\_c start\_POSTSUBSCRIPT zebra end\_POSTSUBSCRIPT, ccat/dogsubscript𝑐cat/dogc\_{\text{cat/dog}}italic\_c start\_POSTSUBSCRIPT cat/dog end\_POSTSUBSCRIPT, ccat/zebrasubscript𝑐cat/zebrac\_{\text{cat/zebra}}italic\_c start\_POSTSUBSCRIPT cat/zebra end\_POSTSUBSCRIPT, cdog/zebrasubscript𝑐dog/zebrac\_{\text{dog/zebra}}italic\_c start\_POSTSUBSCRIPT dog/zebra end\_POSTSUBSCRIPT, ccat/dog/zebrasubscript𝑐cat/dog/zebrac\_{\text{cat/dog/zebra}}italic\_c start\_POSTSUBSCRIPT cat/dog/zebra end\_POSTSUBSCRIPT}.
Figure [1](#S2.F1 "Figure 1 ‣ 2 Methodology ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts") shows all overlaps involving two classes. In the figure, the concept cdog/catsubscript𝑐dog/catc\_{\text{dog/cat}}italic\_c start\_POSTSUBSCRIPT dog/cat end\_POSTSUBSCRIPT denotes a property shared by dog and cat, but not by zebras. Similarly, cdog/zebrasubscript𝑐dog/zebrac\_{\text{dog/zebra}}italic\_c start\_POSTSUBSCRIPT dog/zebra end\_POSTSUBSCRIPT denotes a property possessed by zebras and dogs but not by cats.
####
2.1.2 Detecting MACCs in DNNs
Given a DNN Fclfsubscript𝐹clfF\_{\text{clf}}italic\_F start\_POSTSUBSCRIPT clf end\_POSTSUBSCRIPT as in the formal setup,
trained to predict the class labels, we express the MACC detector Fconsubscript𝐹conF\_{\text{con}}italic\_F start\_POSTSUBSCRIPT con end\_POSTSUBSCRIPT as:
Fcon(𝒙)=fcon(fL(fL−1(…,f1(𝒙,𝜽1))))subscript𝐹con𝒙subscript𝑓consubscript𝑓𝐿subscript𝑓𝐿1…subscript𝑓1𝒙subscript𝜽1F\_{\text{con}}(\bm{x})=f\_{\text{con}}(f\_{L}(f\_{L-1}(\ldots,f\_{1}(\bm{x},\bm{\theta}\_{1}))))italic\_F start\_POSTSUBSCRIPT con end\_POSTSUBSCRIPT ( bold\_italic\_x ) = italic\_f start\_POSTSUBSCRIPT con end\_POSTSUBSCRIPT ( italic\_f start\_POSTSUBSCRIPT italic\_L end\_POSTSUBSCRIPT ( italic\_f start\_POSTSUBSCRIPT italic\_L - 1 end\_POSTSUBSCRIPT ( … , italic\_f start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT ( bold\_italic\_x , bold\_italic\_θ start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT ) ) ) ),111Note that fconsubscript𝑓conf\_{\text{con}}italic\_f start\_POSTSUBSCRIPT con end\_POSTSUBSCRIPT can be attached to any intermediate layer between f1subscript𝑓1f\_{1}italic\_f start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT to fLsubscript𝑓𝐿f\_{L}italic\_f start\_POSTSUBSCRIPT italic\_L end\_POSTSUBSCRIPT.
where the output of fconsubscript𝑓conf\_{\text{con}}italic\_f start\_POSTSUBSCRIPT con end\_POSTSUBSCRIPT is an M-dimensional vector consisting of (potentially un-calibrated) probabilities, p(𝒄i=1|𝒙)𝑝subscript𝒄𝑖conditional1𝒙p(\bm{c}\_{i}=1|\bm{x})italic\_p ( bold\_italic\_c start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT = 1 | bold\_italic\_x ).
Since Fconsubscript𝐹conF\_{\text{con}}italic\_F start\_POSTSUBSCRIPT con end\_POSTSUBSCRIPT attempts a multilabel classification task,
we obtain the probabilities using the sigmoid function σ(z)=(1+e−z)−1𝜎𝑧superscript1superscript𝑒𝑧1\sigma(z)=(1+e^{-z})^{-1}italic\_σ ( italic\_z ) = ( 1 + italic\_e start\_POSTSUPERSCRIPT - italic\_z end\_POSTSUPERSCRIPT ) start\_POSTSUPERSCRIPT - 1 end\_POSTSUPERSCRIPT.
Finally, one obtains a predicted MACC vector 𝒄^=[c^1,…,c^M]^𝒄subscript^𝑐1…subscript^𝑐𝑀\hat{\bm{c}}=[\hat{c}\_{1},\ldots,\hat{c}\_{M}]over^ start\_ARG bold\_italic\_c end\_ARG = [ over^ start\_ARG italic\_c end\_ARG start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT , … , over^ start\_ARG italic\_c end\_ARG start\_POSTSUBSCRIPT italic\_M end\_POSTSUBSCRIPT ] with c^i=1subscript^𝑐𝑖1\hat{c}\_{i}=1over^ start\_ARG italic\_c end\_ARG start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT = 1 indicating the predicted presence/absence of each MACC in the input. Here, Fcon(𝒙)i>0.5subscript𝐹consubscript𝒙𝑖0.5F\_{\text{con}}(\bm{x})\_{i}>0.5italic\_F start\_POSTSUBSCRIPT con end\_POSTSUBSCRIPT ( bold\_italic\_x ) start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT > 0.5, else c^i=0subscript^𝑐𝑖0\hat{c}\_{i}=0over^ start\_ARG italic\_c end\_ARG start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT = 0.
Learning Fconsubscript𝐹conF\_{\text{con}}italic\_F start\_POSTSUBSCRIPT con end\_POSTSUBSCRIPT can be done by optimizing the sum of M𝑀Mitalic\_M individual binary cross-entropy loss functions, with one loss function for each MACC.
We refer to this sum of loss functions as ℒconsubscriptℒcon\mathcal{L}\_{\text{con}}caligraphic\_L start\_POSTSUBSCRIPT con end\_POSTSUBSCRIPT.
Our framework allows for the flexibility to be trained in two different ways: (1) Post-hoc training: Taking a pretrained DNN Fclfsubscript𝐹clfF\_{\text{clf}}italic\_F start\_POSTSUBSCRIPT clf end\_POSTSUBSCRIPT as described in the formal setup, and training the MACC detection layer, fconsubscript𝑓conf\_{\text{con}}italic\_f start\_POSTSUBSCRIPT con end\_POSTSUBSCRIPT by attaching it to one of the hidden layers of Fclfsubscript𝐹clfF\_{\text{clf}}italic\_F start\_POSTSUBSCRIPT clf end\_POSTSUBSCRIPT. With this method, the pre-learnt representations of Fclfsubscript𝐹clfF\_{\text{clf}}italic\_F start\_POSTSUBSCRIPT clf end\_POSTSUBSCRIPT are used and only the parameters of fconsubscript𝑓conf\_{\text{con}}italic\_f start\_POSTSUBSCRIPT con end\_POSTSUBSCRIPT are learnt. (2) Joint training: Training all the parameters of the network from scratch, that is, training the hidden layers fi,∀i∈{1…L}subscript𝑓𝑖subscriptfor-all𝑖
1…𝐿f\_{i},\ \forall\_{i}\in\{1\ldots L\}italic\_f start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT , ∀ start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ∈ { 1 … italic\_L }, the class label layer fclfsubscript𝑓clff\_{\text{clf}}italic\_f start\_POSTSUBSCRIPT clf end\_POSTSUBSCRIPT, and the MACC layer fconsubscript𝑓conf\_{\text{con}}italic\_f start\_POSTSUBSCRIPT con end\_POSTSUBSCRIPT by minimizing the joint loss λℒclf+(1−λ)ℒcon𝜆subscriptℒclf1𝜆subscriptℒcon\lambda\mathcal{L}\_{\text{clf}}+(1-\lambda)\mathcal{L}\_{\text{con}}italic\_λ caligraphic\_L start\_POSTSUBSCRIPT clf end\_POSTSUBSCRIPT + ( 1 - italic\_λ ) caligraphic\_L start\_POSTSUBSCRIPT con end\_POSTSUBSCRIPT. Here the parameter λ𝜆\lambdaitalic\_λ trades-off the accuracy between the class labels prediction accuracy and the MACC detection accuracy, and can be determined via cross-validation.
Finally, a combination of these two techniques (*e.g.*, selectively training only some hidden layers) can also be used.
####
2.1.3 Explanation-conformity checks with MACCs
The final component of our framework constitutes of performing an explanation-conformity check with MACCs to assess prediction robustness.
Our intuition is that predictions passing the check would be more robust.
Our explanation-conformity check proceeds as follows:
Given an input instance 𝒙𝒙\bm{x}bold\_italic\_x, let y^=Fclf(𝒙)^𝑦subscript𝐹clf𝒙\hat{y}=F\_{\text{clf}}(\bm{x})over^ start\_ARG italic\_y end\_ARG = italic\_F start\_POSTSUBSCRIPT clf end\_POSTSUBSCRIPT ( bold\_italic\_x ) be the class prediction and 𝒄^=Fcon(𝒙)^𝒄subscript𝐹con𝒙\hat{\bm{c}}=F\_{\text{con}}(\bm{x})over^ start\_ARG bold\_italic\_c end\_ARG = italic\_F start\_POSTSUBSCRIPT con end\_POSTSUBSCRIPT ( bold\_italic\_x ) be the MACC prediction.
Then, the explanation-conformity check probes if the MACCs corresponding to the predicted class are also detected (and the MACCs not related to the predicted class are not detected). The prediction is deemed robust if, ∑i𝕀[𝒄i^=𝒄iy^]M≥tconsubscript𝑖𝕀delimited-[]^subscript𝒄𝑖subscriptsuperscript𝒄^𝑦𝑖𝑀subscript𝑡con\frac{\sum\_{i}\mathbb{I}[\hat{\bm{c}\_{i}}=\bm{c}^{\hat{y}}\_{i}]}{M}\geq t\_{\text{con}}divide start\_ARG ∑ start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT blackboard\_I [ over^ start\_ARG bold\_italic\_c start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT end\_ARG = bold\_italic\_c start\_POSTSUPERSCRIPT over^ start\_ARG italic\_y end\_ARG end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ] end\_ARG start\_ARG italic\_M end\_ARG ≥ italic\_t start\_POSTSUBSCRIPT con end\_POSTSUBSCRIPT,
for some tcon∈[0,1]subscript𝑡con01t\_{\text{con}}\in[0,1]italic\_t start\_POSTSUBSCRIPT con end\_POSTSUBSCRIPT ∈ [ 0 , 1 ]. A higher value of tconsubscript𝑡cont\_{\text{con}}italic\_t start\_POSTSUBSCRIPT con end\_POSTSUBSCRIPT means that fewer predictions would pass the explanation-conformity check, however, the degree of robustness for these predictions is expected to be higher (see Section [3](#S3 "3 Evaluation of the robustness framework ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts") for details).
###
2.2 Discussion: Salient properties of MACCs
MACCs and Human-interpretability.
Most of the existing works on concept-centered explanation-conformity checks [[28](#bib.bib28), [40](#bib.bib40)] use human supervision to annotate images as containing a certain concept.
Such concepts often correspond to features that are (i) shared by certain classes and not shared by other classes in the data, and, (ii) can be easily recognized and named by humans (*e.g.*, stripes on zebras, paws on cats and dogs).
While MACCs are not explicitly human recognizable,222Instead, MACCs may represent complex polymorphic and composite features in practice, i.e., the MACC corresponding to ‘features shared by cats and dogs but not zebras’ could correspond to a paw or the non-existence of stripes, or any combination of such distinguishing features.
and hence do not satisfy criterion (ii), their definition procedure (Section [2.1.1](#S2.SS1.SSS1 "2.1.1 Automatically defining MACCs ‣ 2.1 Our framework: Robustness via machine-checkable concepts ‣ 2 Methodology ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts")) ensures that they do indeed satisfy criterion (i).
In this sense, MACCs subsume the concepts defined in prior work on concept-centered explainability.
However, our framework trades-off human recognizability of MACCs to enable end-to-end automation of robustness assessments from MACC definition →→\to→ detection →→\to→ explanation-conformity checks.
Pruning MACCs.
It is quite possible that in a K𝐾Kitalic\_K-class classification task, some classes may not share any meaningful features, and their corresponding MACCs, may not correspond to any useful concepts. For instance, the class cat may not share any similarities with class kite, and hence, the corresponding MACC might be meaningless. We expect these MACCs to have low detection accuracy. During the training procedure (Section [2.1.2](#S2.SS1.SSS2 "2.1.2 Detecting MACCs in DNNs ‣ 2.1 Our framework: Robustness via machine-checkable concepts ‣ 2 Methodology ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts")), such MACCs can be dropped.
Moreover, since the possible space of MACCs is very large (for a dataset of K=100𝐾100K=100italic\_K = 100 classes, there are a total of 2100−1≈1030superscript21001superscript10302^{100}-1\approx 10^{30}2 start\_POSTSUPERSCRIPT 100 end\_POSTSUPERSCRIPT - 1 ≈ 10 start\_POSTSUPERSCRIPT 30 end\_POSTSUPERSCRIPT) possible MACCs, one could use a random subset of MACCs, or only consider MACCs that represent properties shared by exactly two, or exactly three classes (*e.g.*, in Figure [1](#S2.F1 "Figure 1 ‣ 2 Methodology ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts")).
Finally, MACCs that uniquely correspond to a class may be redundant in conformity checks and can be safely pruned.
3 Evaluation of the robustness framework
-----------------------------------------
In this section, we conduct experiments and human surveys on real-world datasets to evaluate the effectiveness of our MACC framework.
Specifically, we ask whether the predictions passing the MACC explanation-conformity achieve better robustness.
Evaluation metrics. Inspired by usage of explanation-conformity checks in practice [[15](#bib.bib15), [6](#bib.bib6), [44](#bib.bib44)], we use the following evaluation metrics to quantify prediction robustness: (i) Error Estimability , *i.e.*, accuracy on explanation-conformant predictions, (ii) Error Vulnerability , *i.e.*, resistance to adversarial attacks on explanation-conformant predictions, and, (iii), Error Explainability , *i.e.*, ability to map errors to potential issues in the input.
Setup.
We conduct experiments on CIFAR-10, CIFAR-100 and Fashion MNIST datasets. We define MACCs such that each class in CIFAR-10 and Fashion MNIST data is accompanied by 9 MACCs whereas in CIFAR-100 data, this number is 99.
We use simple deep CNN architectures, that have publicly available implementations, and provide comparable performance to state-of-the-art. Additional details on data preprocessing, MACC definition, picking tconsubscript𝑡cont\_{\text{con}}italic\_t start\_POSTSUBSCRIPT con end\_POSTSUBSCRIPT, and training architectures can be found in Appendix [A](#A1 "Appendix A Implementation details and reproducibility ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts").
Training the models to maximize the classification accuracy leads to a test set accuracy of 88.8%percent88.888.8\%88.8 %, 92.49%percent92.4992.49\%92.49 % and 59.41%percent59.4159.41\%59.41 % on CIFAR-10, Fashion MNIST and CIFAR-100 datasets, respectively. We refer to this model as the vanilla model.
For the training of Fconsubscript𝐹conF\_{\text{con}}italic\_F start\_POSTSUBSCRIPT con end\_POSTSUBSCRIPT, we consider the post-hoc training alternative considered in Section [2](#S2 "2 Methodology ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts"). The joint training alternative leads to similar statistics.
For the detailed analysis, we focus on the performance of post-hoc training and leave detailed comparison between different training schemes for a future study.
For performance comparison, we use the probability calibration method of Guo et al. [[24](#bib.bib24)] (see Section [3.4](#S3.SS4 "3.4 Discussion ‣ 3 Evaluation of the robustness framework ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts")).
We now present the performance of MACCs in improving prediction robustness.
Table 1: [Error Estimability]
Accuracy of the vanilla DNN with no explanation-conformity check (Vanilla), accuracy on samples passing the explanation-conformity check (explanation-conf.) and on samples not passing the check (non explanation-conf.).
Numbers in parentheses show the fraction of samples in each category.
Accuracy on explanation-conformant predictions is significantly higher.
| | | | | | | |
| --- | --- | --- | --- | --- | --- | --- |
| |
| |
| --- |
| Vanilla |
|
| |
| --- |
| Explanation-conf. |
|
| |
| --- |
| Non explanation-conf. |
|
| CIFAR-10 | 0.89 (1.00) | 0.93 (0.91) | 0.48 (0.09) |
| Fashion-MNIST | 0.92 (1.00) | 0.99 (0.70) | 0.77 (0.30) |
|
| |
| --- |
| CIFAR-100 |
| 0.59 (1.00) | 0.65 (0.84) | 0.30 (0.16) |
###
3.1 Do MACCs provide reliable Error Estimability?
We propose and test two hypotheses related to reliable error estimability: (i) predictions that pass the MACC explanation-conformity check are more likely to be accurate, and, (ii) predictions that are not explanation-conformant might consist of inputs with high aleatoric uncertainty [[13](#bib.bib13)] and might be more difficult for even humans to classify.
Table [1](#S3.T1 "Table 1 ‣ 3 Evaluation of the robustness framework ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts") shows that on all three datasets, the prediction accuracy on explanation-conformant predictions is significantly higher than non-conformant predictions, validating our hypothesis (i).
To confirm our hypothesis (ii), we show images from CIFAR-10 data to human annotators at Amazon Mechanical Turk (AMT). The AMT annotators are shown an image and asked to choose the class that the image belongs to from the list of 10 classes. Each image is annotated by 30 users. Further details on the experiment can be found in Appendix [C](#A3 "Appendix C MACCs and error interpretability ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts").
The results show that for explanation-conformant images, humans are able to detect the correct class 91.25%percent91.2591.25\%91.25 % of the time, whereas accuracy for non-conformant images is 83.19%percent83.1983.19\%83.19 %. Moreover, the worker disagreement—as measured via average Shannon Entropy—is 0.220.220.220.22 and 0.390.390.390.39 for explanation-conformant, and non-conformant images. The difference in accuracy and worker agreement shows that the non explanation-conformant images are harder not only for the DNN, but also human annotators to classify. We expand on the difficulty of human annotators in Section [3.3](#S3.SS3 "3.3 Do MACCs provide insights into the causes of errors? ‣ 3 Evaluation of the robustness framework ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts").
###
3.2 Do MACCs defend against Error Vulnerability?
We now ask if an explanation-conformity check can help defend against adversarial perturbations.
Specifically, we start off with a 50%percent5050\%50 % random subset of test images that were correctly classified by the vanilla DNN and adversarially perturb them w.r.t. Fclfsubscript𝐹clfF\_{\text{clf}}italic\_F start\_POSTSUBSCRIPT clf end\_POSTSUBSCRIPT so that they are now incorrectly classified. We use a number of popular adversarial attacks (see Table [2](#S3.T2 "Table 2 ‣ 3.2 Do MACCs defend against Error Vulnerability? ‣ 3 Evaluation of the robustness framework ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts")).
Next, we check if these adversarial perturbation designed to change the class labels also resulted in a corresponding change in the detected MACCs. If that is not the case, then MACC explanation-conformity check could be used as a method to detect adversarial perturbations.
Table [2](#S3.T2 "Table 2 ‣ 3.2 Do MACCs defend against Error Vulnerability? ‣ 3 Evaluation of the robustness framework ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts") shows the fraction of adversarially attacked inputs that fails the MACC explanation-conformity check, revealing that the check is able to detect a vast fraction of adversarial attacks.
While MACCs are able to defend against a significant proportion of attacks on class labels, a determined adversary could additionally attack the MACC detection component (Fconsubscript𝐹conF\_{\text{con}}italic\_F start\_POSTSUBSCRIPT con end\_POSTSUBSCRIPT in Section [2](#S2 "2 Methodology ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts")) such that not only does the class label get switched, the MACC prediction is also changed such that the explanation-conformity check is passed.
We now study the nature of such adversarial perturbations.
To perform this attack, we modify the PGD attack (details in Appendix [D.1](#A4.SS1 "D.1 Performing an explanation-conformant adversarial perturbation and comparison with Guo et al. [24] ‣ Appendix D Additional experiments on Error Vulnerability ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts")) such that the class labels and MACCs are changed in a consistent manner to pass the explanation-conformity check.
Table 2: [Error Vulnerability] Attacking class labels. Fraction of adversarially perturbed inputs that fail the explanation-conformity check (meaning the adversarial attack is detected.) On CIFAR-10 and Fashion-MNIST data, >98%absentpercent98>98\%> 98 % of the attacks are detected, except for DeepFool on CIFAR-10 where around 40%percent4040\%40 % are detected. On CIFAR-100 data, around half of the adversarial attacks are detected.
| | | | | | | | | |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| |
| |
| --- |
| FGSM [[21](#bib.bib21)] |
|
| |
| --- |
| DeepFool [[37](#bib.bib37)] |
|
| |
| --- |
| C&W (L2) [[9](#bib.bib9)] |
|
| |
| --- |
| PGD [[35](#bib.bib35)] |
|
| CIFAR-10 | 0.98 | 0.41 | 1.00 | 0.99 |
| Fashion-MNIST | 1.00 | 0.99 | 1.00 | 1.00 |
|
| |
| --- |
| CIFAR-100 |
| 0.50 | 0.45 | 0.49 | 0.50 |
(a) Original Images
(b) PGD attack class-only
(c) PGD attack explanation-conf.
Figure 2: [Error Vulnerability]
Attacking both class labels and MACCs.
The figure shows some randomly selected Original Images from CIFAR-10 that were correctly classified by the vanilla DNN.
Also shown are the perturbed images obtained by performing a conventional adversarial attack, using the PGD method [[35](#bib.bib35)], aimed at switching the predicted class label on the input (Class-only). As is expected of such attacks [[38](#bib.bib38), [10](#bib.bib10)], the perturbations are imperceptible to the human eye.
Finally, we show the perturbed images where the adversarial attack not only changes the predicted class labels, but also the MACCs such that the predictions are explanation-conformant (Explanation-conf.).
Explanation-conformant perturbations are so large that they are clearly perceptible to the human eye.
We note that the perturbation required to perform an explanation-conformant attack is significantly higher than the one required for an attack that aims to change the class label only. Specifically, while the class-only attacks in Table [2](#S3.T2 "Table 2 ‣ 3.2 Do MACCs defend against Error Vulnerability? ‣ 3 Evaluation of the robustness framework ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts")) require a perturbation (based on L2 distance from the original image) of 0.31±0.20plus-or-minus0.310.200.31\pm 0.200.31 ± 0.20 and 0.26±0.14plus-or-minus0.260.140.26\pm 0.140.26 ± 0.14 on CIFAR-10 and Fashion-MNIST datasets respectively, the explanation-conformant perturbations have a magnitude of 5.31±5.62plus-or-minus5.315.625.31\pm 5.625.31 ± 5.62 and 3.16±2.85plus-or-minus3.162.853.16\pm 2.853.16 ± 2.85. In other words, explanation-conformant attacks require perturbations that are more than an order of magnitude larger.
Are the perturbations still imperceptible to humans?
We suspect that the magnitude of the explanation-conformant perturbations is so large that they might not be imperceptible to humans anymore. Perturbations being imperceptible to humans is often considered as a major property adversarial perturbations [[38](#bib.bib38), [10](#bib.bib10)].
To test this hypothesis, we set up a human survey on AMT where the humans are shown three kinds of images: (i) the original , unperturbed image, (ii) image with class-only perturbation that aims to change the predicted class label, and, (iii) the image with explanation-conformant perturbation that aims to change the predicted class label as well as predicted MACCs such that the prediction passes the explanation-conformity check. AMT workers were then asked to label if the image contained an adversarial perturbation or not. Details of the survey can be found in Appendix [D.2](#A4.SS2 "D.2 Human perceptibility of explanation-conformant adversarial perturbations ‣ Appendix D Additional experiments on Error Vulnerability ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts").
The results show that for class-only category, humans are able to detect the images with adversarial perturbations around 49.8%percent49.849.8\%49.8 % of the time, *i.e.*, the human accuracy is as good as a random guess. On the other hand, for images in the explanation-conformant category, the humans are able to detect the adversarially perturbed images 85%percent8585\%85 % of the time. This vast difference in human detection accuracy shows that explanation-conformant perturbations are much more noticeable to the human eyes that class-only perturbations. Figure [2](#S3.F2 "Figure 2 ‣ 3.2 Do MACCs defend against Error Vulnerability? ‣ 3 Evaluation of the robustness framework ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts") also shows some examples of the explanation-conformant perturbations (more examples in Appendix [D](#A4 "Appendix D Additional experiments on Error Vulnerability ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts")). In summary, the survey shows that it is difficult to attack the MACC explanation-conformity check in a manner that is undetectable by humans.
###
3.3 Do MACCs provide insights into the causes of errors?
|
Human
agreement
|
<6absent6<6< 6 MACCs
detected
|
≥6absent6\geq 6≥ 6 MACCs
detected
|
| --- | --- | --- |
|
≤50%absentpercent50\leq 50\%≤ 50 %
| 75.4%percent75.475.4\%75.4 % | 24.6%percent24.624.6\%24.6 % |
|
>50%absentpercent50>50\%> 50 %
| 47.7%percent47.747.7\%47.7 % | 52.3%percent52.352.3\%52.3 % |
(a) Human agreement & num. detected MACCs
(b) Images with lowest agreement
Figure 3:
[Insights into causes of errors]
The table ([2(a)](#S3.F2.sf1 "2(a) ‣ Figure 3 ‣ 3.3 Do MACCs provide insights into the causes of errors? ‣ 3 Evaluation of the robustness framework ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts")) shows that images with less human agreement also tend to have few detected MACCs.
The figure ([2(b)](#S3.F2.sf2 "2(b) ‣ Figure 3 ‣ 3.3 Do MACCs provide insights into the causes of errors? ‣ 3 Evaluation of the robustness framework ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts")) shows the images with lowest human agreement.
For more examples and details, see Appendix [C](#A3 "Appendix C MACCs and error interpretability ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts").
Inspired by the insight in Section [3.1](#S3.SS1 "3.1 Do MACCs provide reliable Error Estimability? ‣ 3 Evaluation of the robustness framework ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts") that even humans tend to make more errors on non explanation-conformant inputs, we now further explore these cases.
Specifically, we note that some non explanation-conformant inputs consists of cases where Fconsubscript𝐹conF\_{\text{con}}italic\_F start\_POSTSUBSCRIPT con end\_POSTSUBSCRIPT is able to detect very few MACCs (see Appendix [C.3](#A3.SS3 "C.3 Human Experiment Results ‣ Appendix C MACCs and error interpretability ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts") for a full distribution).333An explanation-conformant prediction, with tcon=1subscript𝑡con1t\_{\text{con}}=1italic\_t start\_POSTSUBSCRIPT con end\_POSTSUBSCRIPT = 1 in CIFAR-10 data would mean that Fconsubscript𝐹conF\_{\text{con}}italic\_F start\_POSTSUBSCRIPT con end\_POSTSUBSCRIPT detects 9 exactly MACCs in the input. See Appendix [A](#A1 "Appendix A Implementation details and reproducibility ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts") for details on MACCs for each class.
This means that the DNN is struggling to identify concepts related to any class in the input. We hypothesize that low concept detection rate might mean that these inputs might consist of cases where even humans might find it hard to identify the class of the image.
To test this hypothesis, we divide the non explanation-conformant images from the annotation task described in Section [3.1](#S3.SS1 "3.1 Do MACCs provide reliable Error Estimability? ‣ 3 Evaluation of the robustness framework ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts") into different categories based on the (dis)agreement between human annotators. The agreement here is measured as the fraction of the votes obtained by the class with most votes. Hence, an agreement value of 1.01.01.01.0 means that all humans annotated the image with the same class, whereas a value of 0.10.10.10.1 means that the most-voted-for class received votes that are no better than a random assignment (as the CIFAR-10 dataset consists of 10 classes).
Next, we divide the images into two categories: images where <6absent6<6< 6 MACCs were detected and where ≥6absent6\geq 6≥ 6 MACCs were detected.
Figure [2(a)](#S3.F2.sf1 "2(a) ‣ Figure 3 ‣ 3.3 Do MACCs provide insights into the causes of errors? ‣ 3 Evaluation of the robustness framework ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts") shows the relative fraction of these two categories against the human agreement.
The figure shows that the images with small degree of agreement tend to mostly consist of cases where very few (<6absent6<6< 6 MACCs) are detected.
Specifically, out of the images with less or equal to 50%percent5050\%50 % agreement, 75.4%percent75.475.4\%75.4 % of them have 5555 or less MACCs detected.
Figure [2(b)](#S3.F2.sf2 "2(b) ‣ Figure 3 ‣ 3.3 Do MACCs provide insights into the causes of errors? ‣ 3 Evaluation of the robustness framework ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts") shows the images with lowest human agreement.
These results show that detection of very few MACCs in an image correlates with the fact that even human judges (who are often the source of ground truth in image classification tasks) would find it difficult to classify these images. Hence, MACCs can serve as a useful tool to pinpoint problematic inputs in the data. However, we do note that MACCs are not able to explain causes of errors for all the misclassified inputs, rather they only explain errors for a certain category of the data (with very few concepts detected).
###
3.4 Discussion
The results show that MACCs can be used to perform explainability checks that significantly enhance predictions’ robustness along a wide range of measures. In this section, we discuss some more pertinent points related to the implementation of MACCs.
Effect of varying t𝐜𝐨𝐧subscript𝑡𝐜𝐨𝐧t\_{\text{con}}italic\_t start\_POSTSUBSCRIPT con end\_POSTSUBSCRIPT.
As described in Section [2](#S2 "2 Methodology ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts"), varying tconsubscript𝑡cont\_{\text{con}}italic\_t start\_POSTSUBSCRIPT con end\_POSTSUBSCRIPT can be thought of as a flexible parameter to fine-tune prediction robustness.
We further investigate the effect of tconsubscript𝑡cont\_{\text{con}}italic\_t start\_POSTSUBSCRIPT con end\_POSTSUBSCRIPT on the fraction of samples deemed explanation-conformant and the prediction accuracy on these samples. Results in Appendix [B](#A2 "Appendix B MACC fine-tuning & comparison to calibration methods ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts") shows that increasing tconsubscript𝑡cont\_{\text{con}}italic\_t start\_POSTSUBSCRIPT con end\_POSTSUBSCRIPT leads to more samples being marked as explanation-conformant, however, the classification accuracy on explanation-conformant samples decreases.
Other methods for assessing prediction robustness.
We also compare the robustness estimates obtained using the MACC explanation-conformity check with the more traditional method of probability calibration.
Specifically, we use the temperature scaling method of Guo et al. [[24](#bib.bib24)] to calibrate the softmax probabilities.444We use the implementation provided by the authors: <github.com/gpleiss/temperature_scaling>
We then predictions to be robust if the (calibrated) predicted class probability is above X𝑋Xitalic\_X, where X𝑋Xitalic\_X is chosen such that the same fraction of predictions are marked robust as by our method in Table [1](#S3.T1 "Table 1 ‣ 3 Evaluation of the robustness framework ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts").555Comparison with more thresholds reveals similar insights. Details in Appendix [B](#A2 "Appendix B MACC fine-tuning & comparison to calibration methods ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts").
The comparison reveals that (i) both the robustness check based on calibrated probabilities and the MACC explanation-conformity check achieve comparable performance in terms of the tradeoff between predictions marked robust and classification accuracy on these predictions, however, (ii) the calibration method leads to much lower performance in terms of Error Vulnerability, *i.e.*, the amount of perturbation required to pass the calibration robustness check is almost an order of magnitude smaller. More details on the comparison can be found in Appendix [D](#A4 "Appendix D Additional experiments on Error Vulnerability ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts").
4 Related work
---------------
Most prior approaches to DNN explainability and robustness operate by identifying important features, concepts, or training data instances [[40](#bib.bib40), [11](#bib.bib11), [23](#bib.bib23), [14](#bib.bib14), [43](#bib.bib43), [31](#bib.bib31), [26](#bib.bib26), [27](#bib.bib27), [7](#bib.bib7), [15](#bib.bib15)].
The main differences between these studies and our approach is that we target a specific application of concept explainability, *i.e.*, the explanation-conformity check, and automate the robustness assessment procedure.
A line of work closely related to ours is that of concept-based explanations.
Kim et al. [[28](#bib.bib28)] propose a method to evaluate how important a user-defined concept is in predicting a specific class.
Yeh et al. [[45](#bib.bib45)] propose ways to find concepts that are enough to explain a given prediction.
Ghorbani et al. [[20](#bib.bib20)] proposed ways to automatically extract concepts from visual data while Bouchacourt and Denoyer [[8](#bib.bib8)] proposed a similar approach for textual data.
Goyal et al. [[22](#bib.bib22)], Shi et al. [[42](#bib.bib42)] focus on identifying human-interpretable concepts that have causal relationships with model’s predictions.
However, none of these methods proposes automation of explanation-conformity checks.
Some recent studies [[44](#bib.bib44), [19](#bib.bib19)] have focused on linking explainability and adversarial robustness.
Ghorbani et al. [[19](#bib.bib19)] show that saliency map based explanations are easy to fool via adversarial attacks. On the other hand, MACCs are quite resistant to adversarial perturbations
(Section [3.2](#S3.SS2 "3.2 Do MACCs defend against Error Vulnerability? ‣ 3 Evaluation of the robustness framework ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts")).
Tao et al. [[44](#bib.bib44)] propose an explanation-based check to detect adversarial perturbations. However their approach is limited to hand-crafted features and
is specialized for facial recognition,
whereas our approach can be extended to more general image recognition tasks and also other classification tasks.
Prediction robustness has also been studied in the context of calibration and prediction uncertainty [[34](#bib.bib34), [24](#bib.bib24), [16](#bib.bib16), [12](#bib.bib12), [17](#bib.bib17)].
Empirical comparison with a recent calibration technique [[24](#bib.bib24)] shows that while the robustness check based on this technique provides comparable accuracy,
MACCs are far more robust to adversarial perturbations (Section [3.4](#S3.SS4 "3.4 Discussion ‣ 3 Evaluation of the robustness framework ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts")), and additionally help provide insights into the causes of errors (Section [3.3](#S3.SS3 "3.3 Do MACCs provide insights into the causes of errors? ‣ 3 Evaluation of the robustness framework ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts")).
Moreover, unlike many prior works in this line of research, *e.g.*, [[34](#bib.bib34), [17](#bib.bib17)], our proposed framework can be easily plugged into an existing trained model in a post-hoc manner.
Finally, MACCs also share some similarities with redundant output encoding and error correcting output codes (ECOC) [[5](#bib.bib5), [18](#bib.bib18)]. However, unlike MACCs, ECOCs do not provide an explanation-conformity check with a built-in reject option.
5 Conclusion, limitations
& future work
----------------------------------------
In this work, we proposed a robustness assessment framework that uses Machine-checkable Concepts, or MACCs, to automate the end-to-end process of performing explanation-conformity checks.
The automation means that our framework can be scaled to a large number of classes.
MACCs partly achieve this scalability by focusing on a specific explainability desideratum—*i.e.*, assessment of prediction robustness—and potentially sacrificing some other desiderata (details in Section [1](#S1 "1 Introduction ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts")).
Experiments and human-surveys on several real-world datasets show that
the MACC explanation-conformity check facilitates higher prediction accuracy (on predictions passing the explanation-conformity check), adds resistance to adversarial perturbations, and can also help provide insights into the source of errors.
Our work opens several avenues for future work: For now, MACCs are defined such that they are shared between all images of the same class.
A useful follow-up would be to consider multiple sets of MACCs per class to account for intra-class variability.
Moreover exploring the MACC pruning strategies, analyzing the effect of the number of MACCs on the robustness, and
a deeper exploration of the tradeoffs provided by different training methodologies mentioned in Section [2](#S2 "2 Methodology ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts") (post-hoc, joint, or a combination) are also promising future directions.
We believe that our work has potential to provide significant positive impact for the society. As machine learning models are deployed in a wide array of real-world domains, the issue of prediction robustness has become increasingly relevant. The ability of our methods to provide improved uncertainty estimates, offer resistance to adversarial perturbations, and the capability to potentially debug the model errors is a useful tool for many societal applications. Examples of these applications include image search in online databases and driver-assistance systems in the automotive domains.
On the flip side, our methods are evaluated empirically and do not come with theoretical performance guarantees. As a result, appropriate care should be applied before using them in critical life-affecting domains. An analysis exploring the performance guarantees remains an important future research direction.
Most of the prior work on concept-based explanations restricts itself to concepts that can be explicitly named by humans (see Section [2.2](#S2.SS2 "2.2 Discussion: Salient properties of MACCs ‣ 2 Methodology ‣ Unifying Model Explainability and Robustness via Machine-Checkable Concepts") for a discussion). Our framework represents a departure from this restriction, and places more emphasis on machine-checkability (much like the line of work on machine-checkable theorem proving [[47](#bib.bib47)]). As a result, while our machine-checkable concepts (MACCs) are able to meet the goal that they were designed for, it should be noted that they may not fulfil some other explainability criteria [[15](#bib.bib15), [6](#bib.bib6), [32](#bib.bib32)]. Combining machine-checkability with human-interpretability would be a worthwhile future research direction.
6 Acknowledgements
-------------------
Dickerson and Nanda were supported in part by NSF CAREER Award IIS-1846237, DARPA GARD #HR00112020007, DARPA SI3-CMD #S4761, DoD WHS Award #HQ003420F0035, and a Google Faculty Research Award. This work was supported in part by an ERC Advanced Grant “Foundations for Fair Social Computing” (no. 789373). |
8aaada45-4cae-4439-9a7d-f56c39a1ec82 | trentmkelly/LessWrong-43k | LessWrong | Free Speech and Triskaidekaphobic Calculators: A Reply to Hubinger on the Relevance of Public Online Discussion to Existential Risk
In response to Wei Dai's claim that a multi-post 2009 Less Wrong discussion on gender issues and offensive speech went well, MIRI researcher Evan Hubinger writes—
> Do you think having that debate online was something that needed to happen for AI safety/x-risk? Do you think it benefited AI safety at all? I'm genuinely curious. My bet would be the opposite—that it caused AI safety to be more associated with political drama that helped further taint it.
Okay, but the reason you think AI safety/x-risk is important is because twenty years ago, people like Eliezer Yudkowsky and Nick Bostrom were trying to do systematically correct reasoning about the future, noticed that the alignment problem looked really important, and followed that line of reasoning where it took them—even though it probably looked "tainted" to the serious academics of the time. (The robot apocalypse is nigh? Pftt, sounds like science fiction.)
The cognitive algorithm of "Assume my current agenda is the most important thing, and then execute whatever political strategies are required to protect its social status, funding, power, un-taintedness, &c." wouldn't have led us to noticing the alignment problem, and I would be pretty surprised if it were sufficient to solve it (although that would be very convenient).
An analogy: it's actually easier to build a calculator that does correct arithmetic than it is to build a "triskaidekaphobic calculator" that does "correct arithmetic, except that it never displays the result 13", because the simplest implementation of the latter is just a calculator plus an extra conditional that puts something else on the screen when the real answer would have been 13.
If you don't actually understand how arithmetic works, but you feel intense social pressure to produce a machine that never displays the number 13, I don't think you actually succeed at building a triskaidekaphobic calculator: you're trying to solve a problem under constraints that make it impossible to sol |
525be67a-9c4b-47df-ad9d-1c8e27d6f484 | trentmkelly/LessWrong-43k | LessWrong | Mandatory Secret Identities
Previously in series: Whining-Based Communities
> "But there is a reason why many of my students have achieved great things; and by that I do not mean high rank in the Bayesian Conspiracy. I expected much of them, and they came to expect much of themselves." —Jeffreyssai
Among the failure modes of martial arts dojos, I suspect, is that a sufficiently dedicated martial arts student, will dream of...
...becoming a teacher and having their own martial arts dojo someday.
To see what's wrong with this, imagine going to a class on literary criticism, falling in love with it, and dreaming of someday becoming a famous literary critic just like your professor, but never actually writing anything. Writers tend to look down on literary critics' understanding of the art form itself, for just this reason. (Orson Scott Card uses the analogy of a wine critic who listens to a wine-taster saying "This wine has a great bouquet", and goes off to tell their students "You've got to make sure your wine has a great bouquet". When the student asks, "How? Does it have anything to do with grapes?" the critic replies disdainfully, "That's for grape-growers! I teach wine.")
Similarly, I propose, no student of rationality should study with the purpose of becoming a rationality instructor in turn. You do that on Sundays, or full-time after you retire.
And to place a go stone blocking this failure mode, I propose a requirement that all rationality instructors must have secret identities. They must have a life outside the Bayesian Conspiracy, which would be worthy of respect even if they were not rationality instructors. And to enforce this, I suggest the rule:
Rationality_Respect1(Instructor) = min(Rationality_Respect0(Instructor), Non_Rationality_Respect0(Instructor))
That is, you can't respect someone as a rationality instructor, more than you would respect them if they were not rationality instructors.
Some notes:
• This doesn't set Rationality_Respect1 equal to Non_Ratio |
713a4fef-90de-4ce5-97de-03fb4c8e29e4 | trentmkelly/LessWrong-43k | LessWrong | Feed the spinoff heuristic!
Follow-up to:
Parapsychology: the control group for science
Some Heuristics for Evaluating the Soundness of the Academic Mainstream in Unfamiliar Fields
Recent renewed discussions of the parapsychology literature and Daryl Bem's recent precognition article brought to mind the "market test" of claims of precognition. Bem tells us that random undergraduate students were able to predict with 53% accuracy where an erotic image would appear in the future. If this effect was actually real, I would rerun the experiment before corporate earnings announcements, central bank interest rate changes, etc, and change the images based on the reaction of stocks and bonds to the announcements. In other words, I could easily convert "porn precognition" into "hedge fund trillionaire precognition."
If I was initially lacking in the capital to do trades, I could publish my predictions online using public key cryptography and amass an impressive track record before recruiting investors. If anti-psi prejudice was a problem, no one need know how I was making my predictions. Similar setups could exploit other effects claimed in the parapsychology literature (e.g. the remote viewing of the Scientologist-founded Stargate Project of the U.S. federal government). Those who assign a lot of credence to psi may want to actually try this, but for me this is an invitation to use parapsychology as control group for science, and to ponder a general heuristic for crudely estimating the soundness of academic fields for outsiders.
One reason we trust that physicists and chemists have some understanding of their subjects is that they produce valuable technological spinoffs with concrete and measurable economic benefit. In practice, I often make use of the spinoff heuristic: If an unfamiliar field has the sort of knowledge it claims, what commercial spinoffs and concrete results ought it to be producing? Do such spinoffs exist? What are the explanations for their absence?
For psychology, I might cite |
d70fe494-43b0-4baf-a42b-3918535990a3 | trentmkelly/LessWrong-43k | LessWrong | Rob B's Shortform Feed
This is a repository for miscellaneous short things I want to post. Other people are welcome to make top-level comments here if they want. (E.g., questions for me you'd rather discuss publicly than via PM; links you think will be interesting to people in this comment section but not to LW as a whole; etc.) |
2c50c427-85d6-4654-a5d6-c52703532389 | trentmkelly/LessWrong-43k | LessWrong | The spam must end
I'm mean most of us would like a friendly bot to chat with, but this is just paperclipping the section (no offence clippy), by now its starting to be a real trivial inconvenience for me and it reduces my desire to check out new topics.
|
fc41e46f-fa0f-4f7d-8fe5-a59ac8e3090f | trentmkelly/LessWrong-43k | LessWrong | a rant on politician-engineer coalitional conflict
Sometimes, a group in some organization has a highly technical and highly effective leader. Kelly Johnson (Skunk Works) and Hyman Rickover (US Navy nuclear propulsion) are famous examples. A naive economist might expect such people to be well-liked by management above them, because their skills are good for the organization and complementary to those of non-technical managers. That's not what we generally see in reality.
In my experience, and in the stories I've heard, such technical leaders are especially disliked by upper management, far more than a highly effective non-technical MBA would be. I've even been told that unique competence being noticed by upper managment is a negative for career prospects in that situation.
Why would that be the case? The only explanation that makes sense to me is that effective technical managers are considered a threat by management above them - but why would they be more of a threat than a MBA who talks the business talk?
There are some cultural differences between engineers and non-technical managers, but I don't think that's an explanation. One reason is, technical leaders can find allies even higher up that support them. For example, Rickover had allies in Congress, and that's the only reason he wasn't pushed out...until he got pushed out by John Lehman, a Ph.D. in American foreign policy who's worked as an investment banker. Leslie Groves was almost pushed out in 1927, but Major General Edgar Jadwin interceded and noted that Groves's superiors were at fault for the problems blamed on him - that was a guy 5 ranks above Groves in the Army.
My current view is that politician-type managers and engineer-type managers naturally form opposing coalitions. They each favor people of the same type, and try to push local organization norms in different directions.
In America, today, politican-type managers have won conclusively almost everywhere. I've actually seen some of a conflict between such coalitions play out once, and I'd say |
f13a21ae-7dd2-4636-b295-1090be6ac602 | StampyAI/alignment-research-dataset/youtube | Youtube Transcripts | Do We Get the $100 Trillion AI Windfall? Sam Altman's Plans, Jobs & the Falling Cost of Intelligence
in the last few days Sam Altman the CEO
of openai has publicly stated how much
money he expects the company to make and
how he intends to distribute it many
people will assume he is bluffing but I
think GT4 shows that he's not this video
will cover his plans his predictions of
massive inequality and open ai's new
paper on job impacts together with just
released studies that back it all up but
let's start with money this week in the
New York Times he said that his Grand
idea is that openai will capture much of
the world's wealth through the creation
of AGI and then redistribute this wealth
to the people and yes he mentioned
several figures a hundred billion
dollars one trillion even a hundred
trillion dollars if openai make even a
fraction of these figures Sam Altman
will become one of the most important
people on the planet that's not to say
that he would become that rich The Wall
Street Journal this week reported that
he has no direct Financial stake in the
business but deciding where trillions of
dollars of wealth go does make you
incredibly powerful so where does he
want all the money to go well he seems
to have two main ideas plus a third one
that I'll touch on at the end his first
idea is Ubi or Universal basic income we
also have funded the largest and most
comprehensive Universal basic income
study as sponsored by open Ai and I
think it's like an area we should just
be be looking into how exactly would
that work well he laid out his theory in
this blog post and he began it with this
he says he's reminded every day about
the magnitude of socioeconomic change
that is coming sooner than most people
believe he said that the price of many
kinds of Labor which drives the costs of
goods and services will fall towards
zero once sufficiently powerful AI joins
the workforce he said that that was
great for people buying products but not
so much for those working to earn a wage
so where would their money come from he
proposed something called the American
Equity Fund it would be capitalized by
taxing companies that were above a
certain valuation 2.5 percent of their
market value each year and it would also
be funded by taxing 2.5 percent of the
value of all privately held Land by his
calculation that will be worth around 13
500 in about twenty Thirty and he said
that that money would have much greater
purchasing power than it does now
because technology would have greatly
reduced the cost of goods and services
it does raise the question for me though
about those countries that aren't the
home of massive AI companies where are
they going to get the wealth from on Lex
Friedman's podcast he admitted it wasn't
a full solution I think it is a
component of something we should pursue
it is not a full solution I think people
work for lots of reasons besides money
he thinks much more will be needed
because the cost of intelligence could
fall to almost zero my basic model of
the next decade is that the marginal
cost of intelligence and the marginal
cost of energy are going to Trend
rapidly towards zero like surprisingly
far so what is his other main idea
simply use the money to fund science are
you planning to take the proceeds that
presumably you're presuming you're going
to make some day and you're going to
give them back to society I mean is that
yeah whether we do that just by like
saying here's cash for everyone totally
possible or whether we do that by saying
like gonna like invest all of this in a
non-profit that does a bunch of science
because scientific progress is how we
all make progress unsure but yeah we
would like to operate for for the good
of society even with these two ideas he
admits there's still a big problem as he
put it recently he sees a lot of people
getting very rich in the short to medium
term but others might not fare as well
if it is as divergent as I think it
could be for like some people doing
incredibly well and others not I think
Society just won't tolerate it this time
samuelman isn't the only one making
predictions open AI itself released this
paper around 10 days ago it calculated
that with access to a large language
model about 15 of all work tasks in the
US could be completed significantly
faster at the same level of quality but
crucially when incorporating software
and tooling built on top of llms this
share increases to around 50 percent of
all tasks that is a colossal impact For
Better or Worse just with gpd4 plus
software on page 17 of the paper it had
this table which I think captures a lot
of the interesting analysis let me
briefly explain what it shows we have a
column of example occupations in the
middle and the the education that is
required for each of them and the job
preparation but the numbers on the right
are where it gets interesting these are
the percentages of exposure graded Alpha
Beta And Zeta the human assessment of
exposure is titled H and the M is for
the machine assessment they actually got
gpt4 to do an assessment too notice that
for the most part gbt4 agrees with the
human assessors so what are these three
grades Alpha is the proportion of tasks
in these occupations affected by current
language models alone without any
further advances or Integrations beta
represents the percentage of tasks
exposed in a realistic scenario of
language models plus a bit of software
integration and a few advances you could
think of it as their median prediction
finally Zeta is a bit like their most
extreme scenario with full adoption of
software plus advances of llms by the
way we're not talking gc5 here or text
video just basic software integration
like a longer context window or text to
image the trend that immediately stuck
out for me was how when you go up the
educational levels and these salary
ranges the effects of these large
language models on task exposure goes up
and up and up until you reach master's
degree or higher levels then it seems to
dip down a little maybe this is why Sam
Altman predicted inequality the people
on the very Cutting Edge of science
would still get paid well probably
better than ever but there may be a
further hollowing out of the middle
class with working class occupations
left largely untouched the paper also
touches on why so few people might be
currently focused on language models I
don't know about you but have you
noticed that feeling where it seems to
be us being super interested in this
technology with most people not being
that interested well here might be one
reason why currently only three percent
of U.S workers have over half of their
tasks exposed to llms but that's only
when considering existing language and
code capabilities without additional
software or modalities so not that many
people are seeing a massive change in
their work but it says that when we
account for other generative models and
complementary Technologies are human
estimates indicate that up to 49 of
workers could have half or more of their
tasks exposed to llms whether this means
doubling the amount of work done or
halving the number of workers doing it
I'll talk more about later in the video
but maybe this was the dramatic economic
impact that Ilya satsukver once
predicted on Lex Friedman what do you
think is the bar for impressing us do
you think that bar will continuously be
moved definitely I think when you start
to see really dramatic economic impact
that's when I think that's in some sense
the next barrier because right now if
you think about the work in AI it's
really confusing it's really hard to
know what to make of all these advances
the paper also points out that the
growing economic effect of llms is
expected to persist and increase even if
we hold the development of new
capabilities today they refer to recent
study bodies revealing the potential of
llms to program and control other
digital tools such as apis search
engines and even other generative AI
systems in my previous video on the
self-improvement in GT4 I mentioned
hugging GPT but I am doing a lot of
research on the new Microsoft Jarvis
model and auto gbt I'm hoping to bring
to you soon but interestingly there were
some tasks that neither Gypsy 4 nor the
human assessors could quite agree on in
terms of the impact that llms would have
even gpd4 couldn't quite figure out if
meetings and negotiations would carry on
or to what extent counseling or other
jobs that involve empathy would be
affected and the paper concludes with
this the power of relatively simple user
interface improvements on top of models
like Gypsy 4 was evident in the rollout
of chat GPT wherein versions of the
underlying language model had been
previously available via API usage
skyrocketed after the release of the
chat GPT internet
it's a great Point once these models are
made easy to use that could change
everything the paper then picks up on a
particular survey that shows worker
adoption of llms here is the survey with
the rather dramatic headline of one in
four companies have already replaced
workers with Chachi BT I don't think
that assertion is fully backed up by the
evidence but they did survey 1 000 U.S
Business Leaders and there were some
interesting findings on the question of
replacing workers it says that when
asked if Chaturbate will lead to any
workers being laid off by the end of
2023 33 of Business Leaders say
definitely while 26 say probably others
are a bit more optimistic Goldman Sachs
said this this economic analysis was
published only a few days ago and they
say about seven percent of workers will
be fully displaced over the next 10
years but that most are able to find new
employment in only slightly less
productive positions they also predicted
that generative AI will raise overall
labor productivity growth by around 1.5
percentage points per year which
effectively doubles the rate going back
to Sam Altman last week he was asked
about this augmentation versus
replacement question so in terms of
really replace jobs is that a worry for
you it is uh I'm trying to think of like
a big category that I believe can be
massively impacted I guess I would say
customer service is a category that I
could see there are just way fewer jobs
relatively soon I'm not even certain
about that but I could believe it
whatever call center employees are doing
now I found that last comment on call
Center's quite interesting given that
the gc4 technical report talked about
using language models for upskilling in
call centers so does this mean immense
productivity in the short term but
replacement in the long term a couple
days ago Sam Altman put it like this I
always try to be honest and say in the
very long term I don't know what's going
to happen here and no one does and I I'd
like to at least acknowledge that in the
short term it certainly seems like there
was a huge overhang of the amount of
output the world 1 and if people are way
more effective they're just doing way
more we've seen this first with codeine
and people that got Early Access to
co-pilot reported this and now that the
tools are much better people report it
even more yep but we're now in this sort
of gpt4 era seen it in all sorts of
other jobs as as well where you give
people better tools and they just do
more stuff better stuff the productivity
point is backed up by experiments like
this when developers were split into two
groups half that used openai's co-pilot
and half that didn't not only did more
of those who use copilot finish 78 to 70
they finished in less than half the time
this paper from a few weeks ago shows
that when white collar professionals
were given a language model like chatbt
the time they took to do writing tasks
dropped massively compared to the
control group you can see that they took
less than 20 minutes versus almost 30.
and when the assisted group and control
group were blindly graded you can see
that the mean grade was higher for those
who use the language models but surely
if productivity goes up that means
higher wages for those jobs well not
necessarily a couple of days ago Sam
Altman laid out how it might be more
efficient to use one worker to do the
tasks of two or three there's a huge
cost premium on work that has to be
split across two people there's the
communication overhead there's the the
miscommunication there's everything else
and if you can make one person twice as
productive you don't do as much as two
people could do maybe you do as much as
three and a half or four people could do
and for many kinds of tasks but is there
anything that might slow this economic
impact down I think there might be a few
things starting with politics this
survey from Youth Of America was
released only three days ago and while I
think it is a somewhat leading question
it does show that over 69 of Americans
would support a six-month pause on some
kinds of AI development and if we see
dramatic negative economic impact I
expect that figure would go higher
politicians would then be in
incentivized to slow down tax and or
regulate AI development indeed two days
ago President Biden tweeted this when it
comes to AI we must both support
responsible Innovation and ensure
appropriate guard rails and also don't
forget if you live in a country where
English is not the main spoken language
gpt4 isn't as good notice that in many
languages found in India GT4 is worse
performing than the previous model GPT
3.5 is in English this is just one
reason why Goldman Sachs predicted
different levels of Automation in
different countries the next Factor
could be cultural pushback when Levi's
wanted to test AI generated clothing
models and they said their reason was to
increase diversity that announcement was
met with backlash they then had to back
down slightly and say that they're not
replacing the job of any model if people
vote with their wallets for human-made
goods and services that could have a
massive impact and there is another big
factor people seem to intrinsic quickly
prefer human-made output to machine
generated output this piece came out
recently from wired and in it they test
the brain chemical reaction to
human-made Art and computer made art
these were the same pictures it's just
that sometimes people were told they
were made by humans and other times they
were told they were made by computers it
says a clear winner emerged people not
only claimed to prefer the identical
human made pictures their brain's
pleasure sensors actually lit up more
brightly so human goods and services may
have the edge simply by virtue of being
made by humans but I want to end the
video where I began it with samuelman's
piece in the New York Times some of you
may have noticed that I said Sam Altman
had a third idea of how to distribute
the wealth that I would mention at the
end well he admitted if AGI does create
all that wealth he is not sure how the
company will redistribute it money could
mean something very different in this
new world but what's the idea he said I
I feel like the AGI can help with that
maybe GPT 5 will decide where the money
made using Gypsy 5 will go thank you so
much for watching to the end and have a
wonderful day |
65ec5255-338b-46e3-a592-e26cebd270fe | trentmkelly/LessWrong-43k | LessWrong | The Least Convenient Possible World
Related to: Is That Your True Rejection?
"If you’re interested in being on the right side of disputes, you will refute your opponents’ arguments. But if you’re interested in producing truth, you will fix your opponents’ arguments for them. To win, you must fight not only the creature you encounter; you must fight the most horrible thing that can be constructed from its corpse."
-- Black Belt Bayesian, via Rationality Quotes 13
Yesterday John Maxwell's post wondered how much the average person would do to save ten people from a ruthless tyrant. I remember asking some of my friends a vaguely related question as part of an investigation of the Trolley Problems:
> You are a doctor in a small rural hospital. You have ten patients, each of whom is dying for the lack of a separate organ; that is, one person needs a heart transplant, another needs a lung transplant, another needs a kidney transplant, and so on. A traveller walks into the hospital, mentioning how he has no family and no one knows that he's there. All of his organs seem healthy. You realize that by killing this traveller and distributing his organs among your patients, you could save ten lives. Would this be moral or not?
I don't want to discuss the answer to this problem today. I want to discuss the answer one of my friends gave, because I think it illuminates a very interesting kind of defense mechanism that rationalists need to be watching for. My friend said:
> It wouldn't be moral. After all, people often reject organs from random donors. The traveller would probably be a genetic mismatch for your patients, and the transplantees would have to spend the rest of their lives on immunosuppressants, only to die within a few years when the drugs failed.
On the one hand, I have to give my friend credit: his answer is biologically accurate, and beyond a doubt the technically correct answer to the question I asked. On the other hand, I don't have to give him very much credit: he completely missed the |
0a57208e-4c67-44ed-a0f8-e05bbd39a867 | trentmkelly/LessWrong-43k | LessWrong | Needed: A large database of statements for true/false exercises
Does anybody know where to find a large database of statements that are roughly 50% likely to be true or false? These would be used for confidence calibration / Bayesian updating exercises for CMR/HRP.
One way to make such a database would be to buy a bunch of trivia games with True/False questions, and type each statement and its negation into a computer. A problem with this might be that trivia questions are selected to have surprising/counterintuitive truth values; I'm not sure if that's true. I'd be happy to acquire an already-made database of this form, but ideally I'd like statements that are "more neutral" in terms of how counterintuitive they are.
Any thoughts on where we might find a database like this to use/buy?
Thanks for any help!
Revision: We actually want a database of two-choice answer questions. This way, the player won't get trained on a base rate of 50% of statements in the world being true... they'll just get trained that when there are two possible answers, one is always true. In the end, the database should look something like this (warning: I made up the "correct" answers):
Question: "Which is diagnosed more often in America (2011)?";
Answers: (a) "the cold", (b) allergies";
Correct Answer: (a);
Tags: {medical}
Question: "Which city has a higher average altitude?";
Answers: (a) "Chicago", (b) "Las Vegas";
Correct Answer: (a)
Tags: {geography}
Question: "Who sold more albums while living"?;
Answers: (a) "Michael Jackson", (b) "Elvis Presley";
Correct Answer: (b)
Tags: {history, pop-culture, music}
Question: "Was the price of IBM stock higher or lower at the start of the month after the Berlin wall fell, compared with the start of the previous month?";
Answers: (a) "higher", (b) "lower";
Correct Answer: (a)
Tags: {history, finance}
|
a3f72363-fe12-4d62-8cbe-b28f758ddae2 | trentmkelly/LessWrong-43k | LessWrong | Rationality Quotes October 2014
Another month, another rationality quotes thread. The rules are:
* Please post all quotes separately, so that they can be upvoted or downvoted separately. (If they are strongly related, reply to your own comments. If strongly ordered, then go ahead and post them together.)
* Do not quote yourself.
* Do not quote from Less Wrong itself, HPMoR, Eliezer Yudkowsky, or Robin Hanson. If you'd like to revive an old quote from one of those sources, please do so here.
* No more than 5 quotes per person per monthly thread, please.
* Provide sufficient information (URL, title, date, page number, etc.) to enable a reader to find the place where you read the quote, or its original source if available. Do not quote with only a name.
|
44e48cbc-8934-4bbb-ba0e-10d6582ceba6 | trentmkelly/LessWrong-43k | LessWrong | Group rationality -- bridging the gap in a post-truth world
Everyone on this site obviously has an interest in being, on a personal level, more rational. That's, without need for argument, a good thing. (Although, if you do want to argue that, I can't stop you...)
But...
As a society, we're clearly not very rational, and it's becoming a huge problem. Look at any political articles out there, and you'll see the same thing: angry people partitioned into angry groups, yelling at each other and confirming their own biases. The level of discourse is... low, shall we say.
While the obvious facet of rationality is trying to discern the signal above the noise, there's definitely another side: the art of convincing others. That can swing a little too close to Sophistry and putting the emphasis on personal gain, though. What we really need to do is outreach: promote rationality in the world around us. There's probably no-one reading this who hasn't been in an argument where being more rational and right hasn't helped at all, and maybe even made things worse. We've also all probably been on the other side of that, too. Admit it. But possibly the key word in that is 'argument': it frames the discussion as a confrontation, a fight that needs to be won.
Being the calm, rational person in a fight doesn't always work, though. It only takes one party to want a fight to have one, after all. When there's groups involved, the shouty passionate people tend to dominate, too. And they're currently dominating politics, and so all our lives. That's not a status quo any rationalist would be happy with, I think.
One of the problems with political/economic discussions is that we get polarised into taking absurd blanket positions and being unable to admit limitations or counter-arguments. I'm generally pretty far on the Left of the spectrum, but I will freely admit that the Right has both some very good points and a role to play: what is needed is a good dynamic tension between the two sides to ensure we don't go totally doolally either way. (Thes |
0f82a837-37e5-4bd0-93fd-4992a25bc7fc | StampyAI/alignment-research-dataset/alignmentforum | Alignment Forum | [Linkpost] Interpretability Dreams
A brief research note by Chris Olah about the point of mechanistic interpretability research. Introduction and table of contents are below.
---
Interpretability Dreams
=======================
*An informal note on the relationship between superposition and distributed representations by Chris Olah. Published May 24th, 2023.*
Our present research aims to create a *foundation* for mechanistic interpretability research. In particular, we're focused on trying to resolve the challenge of [superposition](https://transformer-circuits.pub/2022/toy_model/index.html). In doing so, it's important to keep sight of what we're trying to lay the foundations for. This essay summarizes those motivating aspirations – the exciting directions we hope will be possible if we can overcome the present challenges.
We aim to offer insight into our vision for addressing mechanistic interpretability's other challenges, especially *scalability*. Because we have focused on foundational issues, our longer-term path to scaling interpretability and tackling other challenges has often been obscure. By articulating this vision, we hope to clarify how we might resolve limitations, like analyzing massive neural networks, that might naively seem intractable in a mechanistic approach.
Before diving in, it's worth making a few small remarks. Firstly, essentially all the ideas in this essay were previously articulated, but buried in previous papers. Our goal is just to surface those implicit visions, largely by quoting relevant parts. Secondly, it's important to note that everything in this essay is almost definitionally extremely speculative and uncertain. It's far from clear that any of it will ultimately be possible. Finally, since the goal of this essay is to lay out our personal vision of what's inspiring to us, it may come across as a bit grandiose – we hope that it can be understood as simply trying to communicate subjective excitement in an open way.
### Overview
* [**An Epistemic Foundation**](https://transformer-circuits.pub/2023/interpretability-dreams/index.html#epistemic-foundation) - Mechanistic interpretability is a "microscopic" theory because it's trying to build a solid foundation for understanding higher-level structure, in an area where it's very easy for us as researchers to misunderstand.
* [**What Might We Build on Such a Foundation?**](https://transformer-circuits.pub/2023/interpretability-dreams/index.html#possibilities) - Many tantalizing possibilities for research exist (and have been preliminarily demonstrated in InceptionV1), if only we can resolve superposition and identify the right features and circuits in a model.
+ [**Larger Scale Structure**](https://transformer-circuits.pub/2023/interpretability-dreams/index.html#larger-scale) - It seems likely that there is a bigger picture, more abstract story that can be built on top of our understanding of features and circuits. Something like organs in anatomy or brain regions in neuroscience.
+ [**Universality**](https://transformer-circuits.pub/2023/interpretability-dreams/index.html#universality) - It seems likely that many features and circuits are universal, forming across different neural networks trained on similar domains. This means that lessons learned studying one model give us footholds in future models.
+ [**Bridging the Microscopic to the Macroscopic**](https://transformer-circuits.pub/2023/interpretability-dreams/index.html#macroscopic-microscopic) - We're already seeing that some microscopic, mechanistic discoveries (such as induction heads) have significant macroscopic implications. This bridge can likely be expanded as we pin down the foundations, turning our mechanistic understanding into something relevant to machine learning more broadly.
+ [**Automated Interpretability**](https://transformer-circuits.pub/2023/interpretability-dreams/index.html#automated-interpretability) - It seems very possible that AI automation of interpretability may help it scale to large models if all else fails (although aesthetically, we might prefer other paths).
* [**The End Goals**](https://transformer-circuits.pub/2023/interpretability-dreams/index.html#end-goals) - Ultimately, we hope this work can eventually [contribute to safety](https://transformer-circuits.pub/2023/interpretability-dreams/index.html#safety) and also [reveal beautiful structure](https://transformer-circuits.pub/2023/interpretability-dreams/index.html#aesthetics) inside neural networks. |
c520ed48-c35f-420b-8eac-31bbc8924d07 | trentmkelly/LessWrong-43k | LessWrong | Complexity and Intelligence
Followup to: Building Something Smarter , Say Not "Complexity", That Alien Message
One of the Godel-inspired challenges to the idea of self-improving minds is based on the notion of "complexity".
Now "complexity", as I've previously mentioned, is a dangerous sort of word. "Complexity" conjures up the image of a huge machine with incomprehensibly many gears inside - an impressive sort of image. Thanks to this impressiveness, "complexity" sounds like it could be explaining all sorts of things - that all sorts of phenomena could be happening because of "complexity".
It so happens that "complexity" also names another meaning, strict and mathematical: the Kolmogorov complexity of a pattern is the size of the program code of the shortest Turing machine that produces the pattern as an output, given unlimited tape as working memory.
I immediately note that this mathematical meaning, is not the same as that intuitive image that comes to mind when you say "complexity". The vast impressive-looking collection of wheels and gears? That's not what the math term means.
Suppose you ran a Turing machine with unlimited tape, so that, starting from our laws of physics, it simulated our whole universe - not just the region of space we see around us, but all regions of space and all quantum branches. (There's strong indications our universe may be effectively discrete, but if not, just calculate it out to 3^^^3 digits of precision.)
Then the "Kolmogorov complexity" of that entire universe - throughout all of space and all of time, from the Big Bang to whatever end, and all the life forms that ever evolved on Earth and all the decoherent branches of Earth and all the life-bearing planets anywhere, and all the intelligences that ever devised galactic civilizations, and all the art and all the technology and every machine ever built by those civilizations...
...would be 500 bits, or whatever the size of the true laws of physics when written out as equations on a sheet of paper |
fe921bd6-4fae-4da7-b35f-e60b8af27e5c | StampyAI/alignment-research-dataset/alignmentforum | Alignment Forum | Counterarguments to the basic AI x-risk case
*(Crossposted from* [*AI Impacts Blog*](https://aiimpacts.org/counterarguments-to-the-basic-ai-x-risk-case/)*)*
This is going to be a list of holes I see in the basic argument for existential risk from superhuman AI systems[1](https://aiimpacts.org/counterarguments-to-the-basic-ai-x-risk-case/#easy-footnote-bottom-1-3345).
To start, here’s an outline of what I take to be the basic case[2](https://aiimpacts.org/counterarguments-to-the-basic-ai-x-risk-case/#easy-footnote-bottom-2-3345):
### I. If superhuman AI systems are built, any given system is likely to be ‘goal-directed’
Reasons to expect this:
1. Goal-directed behavior is likely to be valuable, e.g. economically.
2. Goal-directed entities may tend to arise from machine learning training processes not intending to create them (at least via the methods that are likely to be used).
3. ‘Coherence arguments’ may imply that systems with some goal-directedness will become more strongly goal-directed over time.
### II. If goal-directed superhuman AI systems are built, their desired outcomes will probably be about as bad as an empty universe by human lights
Reasons to expect this:
1. Finding useful goals that aren’t extinction-level bad appears to be hard: we don’t have a way to usefully point at human goals, and divergences from human goals seem likely to produce goals that are in intense conflict with human goals, due to a) most goals producing [convergent incentives](https://en.wikipedia.org/wiki/Instrumental_convergence) for controlling everything, and b) value [being](https://www.lesswrong.com/posts/GNnHHmm8EzePmKzPk/value-is-fragile) ‘fragile’, such that an entity with ‘similar’ values will generally create a future of virtually no value.
2. Finding goals that are extinction-level bad and temporarily useful appears to be easy: for example, advanced AI with the sole objective ‘maximize company revenue’ might profit said company for a time before gathering the influence and wherewithal to pursue the goal in ways that blatantly harm society.
3. Even if humanity found acceptable goals, giving a powerful AI system any specific goals appears to be hard. We don’t know of any procedure to do it, and we have theoretical reasons to expect that AI systems produced through machine learning training will generally end up with goals other than those they were trained according to. Randomly aberrant goals resulting are probably extinction-level bad for reasons described in II.1 above.
### III. If most goal-directed superhuman AI systems have bad goals, the future will very likely be bad
That is, a set of ill-motivated goal-directed superhuman AI systems, of a scale likely to occur, would be capable of taking control over the future from humans. This is supported by at least one of the following being true:
1. **Superhuman AI would destroy humanity rapidly.** This may be via ultra-powerful capabilities at e.g. technology design and strategic scheming, or through gaining such powers in an ‘intelligence explosion‘ (self-improvement cycle). Either of those things may happen either through exceptional heights of intelligence being reached or through highly destructive ideas being available to minds only mildly beyond our own.
2. **Superhuman AI would gradually come to control the future via accruing power and resources.** Power and resources would be more available to the AI system(s) than to humans on average, because of the AI having far greater intelligence.
Below is a list of gaps in the above, as I see it, and counterarguments. A ‘gap’ is not necessarily unfillable, and may have been filled in any of the countless writings on this topic that I haven’t read. I might even think that a given one can probably be filled. I just don’t know what goes in it.
This blog post is an attempt to run various arguments by you all on the way to making pages on [AI Impacts](http://aiimpacts.org/) about arguments for AI risk and corresponding counterarguments. At some point in that process I hope to also read others’ arguments, but this is not that day. So what you have here is a bunch of arguments that occur to me, not an exhaustive literature review.
**Counterarguments**
--------------------
### ***A. Contra “superhuman AI systems will be ‘goal-directed’”***
**Different calls to ‘goal-directedness’ don’t necessarily mean the same concept**
‘Goal-directedness’ is a vague concept. It is unclear that the ‘goal-directednesses’ that are favored by economic pressure, training dynamics or coherence arguments (the component arguments in part I of the argument above) are the same ‘goal-directedness’ that implies a zealous drive to control the universe (i.e. that makes most possible goals very bad, fulfilling II above).
One well-defined concept of goal-directedness is ‘utility maximization’: always doing what maximizes a particular utility function, given a particular set of beliefs about the world.
Utility maximization does seem to quickly engender an interest in controlling literally everything, at least for many utility functions one might have[3](https://aiimpacts.org/counterarguments-to-the-basic-ai-x-risk-case/#easy-footnote-bottom-3-3345). If you want things to go a certain way, then you have reason to control anything which gives you any leverage over that, i.e. potentially all resources in the universe (i.e. agents have ‘[convergent instrumental goals](https://en.wikipedia.org/wiki/Instrumental_convergence)’). This is in serious conflict with anyone else with resource-sensitive goals, even if *prima facie* those goals didn’t look particularly opposed. For instance, a person who wants all things to be red and another person who wants all things to be cubes may not seem to be at odds, given that all things could be red cubes. However if these projects might each fail for lack of energy, then they are probably at odds.
Thus utility maximization is a notion of goal-directedness that allows Part II of the argument to work, by making a large class of goals deadly.
You might think that any other concept of ‘goal-directedness’ would also lead to this zealotry. If one is inclined toward outcome O in any plausible sense, then does one not have an interest in anything that might help procure O? No: if a system is not a ‘coherent’ agent, then it can have a tendency to bring about O in a range of circumstances, without this implying that it will take any given effective opportunity to pursue O. This assumption of consistent adherence to a particular evaluation of everything is part of utility maximization, not a law of physical systems. Call machines that push toward particular goals but are not utility maximizers pseudo-agents.
Can pseudo-agents exist? Yes—utility maximization is computationally intractable, so any physically existent ‘goal-directed’ entity is going to be a pseudo-agent. We are all pseudo-agents, at best. But it seems something like a spectrum. At one end is a thermostat, then maybe a thermostat with a better algorithm for adjusting the heat. Then maybe a thermostat which intelligently controls the windows. After a lot of honing, you might have a system much more like a utility-maximizer: a system that deftly seeks out and seizes well-priced opportunities to make your room 68 degrees—upgrading your house, buying R&D, influencing your culture, building a vast mining empire. Humans might not be very far on this spectrum, but they seem enough like utility-maximizers already to be alarming. (And it might not be well-considered as a one-dimensional spectrum—for instance, perhaps ‘tendency to modify oneself to become more coherent’ is a fairly different axis from ‘consistency of evaluations of options and outcomes’, and calling both ‘more agentic’ is obscuring.)
Nonetheless, it seems plausible that there is a large space of systems which strongly increase the chance of some desirable objective O occurring without even acting as much like maximizers of an identifiable utility function as humans would. For instance, without searching out novel ways of making O occur, or modifying themselves to be more consistently O-maximizing. Call these ‘weak pseudo-agents’.
For example, I can imagine a system constructed out of a huge number of ‘IF X THEN Y’ statements (reflexive responses), like ‘if body is in hallway, move North’, ‘if hands are by legs and body is in kitchen, raise hands to waist’.., equivalent to a kind of vector field of motions, such that for every particular state, there are directions that all the parts of you should be moving. I could imagine this being designed to fairly consistently cause O to happen within some context. However since such behavior would not be produced by a process optimizing O, you shouldn’t expect it to find new and strange routes to O, or to seek O reliably in novel circumstances. There appears to be zero pressure for this thing to become more coherent, unless its design already involves reflexes to move its thoughts in certain ways that lead it to change itself. I expect you could build a system like this that reliably runs around and tidies your house say, or runs your social media presence, without it containing any impetus to become a more coherent agent (because it doesn’t have any reflexes that lead to pondering self-improvement in this way).
It is not clear that economic incentives generally favor the far end of this spectrum over weak pseudo-agency. There are incentives toward systems being more like utility maximizers, but also incentives against.
The reason any kind of ‘goal-directedness’ is incentivised in AI systems is that then the system can be given an objective by someone hoping to use their cognitive labor, and the system will make that objective happen. Whereas a similar non-agentic AI system might still do almost the same cognitive labor, but require an agent (such as a person) to look at the objective and decide what should be done to achieve it, then ask the system for that. Goal-directedness means automating this high-level strategizing.
Weak pseudo-agency fulfills this purpose to some extent, but not as well as utility maximization. However if we think that utility maximization is difficult to wield without great destruction, then that suggests a disincentive to creating systems with behavior closer to utility-maximization. Not just from the world being destroyed, but from the same dynamic causing more minor divergences from expectations, if the user can’t specify their own utility function well.
That is, if it is true that utility maximization tends to lead to very bad outcomes relative to any slightly different goals (in the absence of great advances in the field of AI alignment), then the most economically favored level of goal-directedness seems unlikely to be as far as possible toward utility maximization. More likely it is a level of pseudo-agency that achieves a lot of the users’ desires without bringing about sufficiently detrimental side effects to make it not worthwhile. (This is likely more agency than is socially optimal, since some of the side-effects will be harms to others, but there seems no reason to think that it is a very high degree of agency.)
Some minor but perhaps illustrative evidence: anecdotally, people prefer interacting with others who predictably carry out their roles or adhere to deontological constraints, rather than consequentialists in pursuit of broadly good but somewhat unknown goals. For instance, employers would often prefer employees who predictably follow rules than ones who try to forward company success in unforeseen ways.
The other arguments to expect goal-directed systems mentioned above seem more likely to suggest approximate utility-maximization rather than some other form of goal-directedness, but it isn’t that clear to me. I don’t know what kind of entity is most naturally produced by contemporary ML training. Perhaps someone else does. I would guess that it’s more like the reflex-based agent described above, at least at present. But present systems aren’t the concern.
Coherence arguments are arguments for being coherent a.k.a. maximizing a utility function, so one might think that they imply a force for utility maximization in particular. That seems broadly right. Though note that these are arguments that there is some pressure for the system to modify itself to become more coherent. What actually results from specific systems modifying themselves seems like it might have details not foreseen in an abstract argument merely suggesting that the status quo is suboptimal whenever it is not coherent. Starting from a state of arbitrary incoherence and moving iteratively in one of many pro-coherence directions produced by whatever whacky mind you currently have isn’t obviously guaranteed to increasingly approximate maximization of some sensical utility function. For instance, take an entity with a cycle of preferences, apples > bananas = oranges > pears > apples. The entity notices that it sometimes treats oranges as better than pears and sometimes worse. It tries to correct by adjusting the value of oranges to be the same as pears. The new utility function is exactly as incoherent as the old one. Probably moves like this are rarer than ones that make you more coherent in this situation, but I don’t know, and I also don’t know if this is a great model of the situation for incoherent systems that could become more coherent.
***What it might look like if this gap matters:** AI systems proliferate, and have various goals. Some AI systems try to make money in the stock market. Some make movies. Some try to direct traffic optimally. Some try to make the Democratic party win an election. Some try to make Walmart maximally profitable. These systems have no perceptible desire to optimize the universe for forwarding these goals because they aren’t maximizing a general utility function, they are more ‘behaving like someone who is trying to make Walmart profitable’. They make strategic plans and think about their comparative advantage and forecast business dynamics, but they don’t build nanotechnology to manipulate everybody’s brains, because that’s not the kind of behavior pattern they were designed to follow. The world looks kind of like the current world, in that it is fairly non-obvious what any entity’s ‘utility function’ is. It often looks like AI systems are ‘trying’ to do things, but there’s no reason to think that they are enacting a rational and consistent plan, and they rarely do anything shocking or galaxy-brained.*
**Ambiguously strong forces for goal-directedness need to meet an ambiguously high bar to cause a risk**
The forces for goal-directedness mentioned in I are presumably of finite strength. For instance, if coherence arguments correspond to pressure for machines to become more like utility maximizers, there is an empirical answer to how fast that would happen with a given system. There is also an empirical answer to how ‘much’ goal directedness is needed to bring about disaster, supposing that utility maximization would bring about disaster and, say, being a rock wouldn’t. Without investigating these empirical details, it is unclear whether a particular qualitatively identified force for goal-directedness will cause disaster within a particular time.
***What it might look like if this gap matters:** There are not that many systems doing something like utility maximization in the new AI economy. Demand is mostly for systems more like GPT or DALL-E, which transform inputs in some known way without reference to the world, rather than ‘trying’ to bring about an outcome. Maybe the world was headed for more of the latter, but ethical and safety concerns reduced desire for it, and it wasn’t that hard to do something else. Companies setting out to make non-agentic AI systems have no trouble doing so. Incoherent AIs are never observed making themselves more coherent, and training has never produced an agent unexpectedly. There are lots of vaguely agentic things, but they don’t pose much of a problem. There are a few things at least as agentic as humans, but they are a small part of the economy.*
### ***B. Contra “goal-directed AI systems’ goals will be bad”***
**Small differences in utility functions may not be catastrophic**
Arguably, humans are likely to have somewhat different values to one another even after arbitrary reflection. If so, there is some extended region of the space of possible values that the values of different humans fall within. That is, ‘human values’ is not a single point.
If the values of misaligned AI systems fall within that region, this would not appear to be worse in expectation than the situation where the long-run future was determined by the values of humans other than you. (This may still be a huge loss of value relative to the alternative, if a future determined by your own values is vastly better than that chosen by a different human, and if you also expected to get some small fraction of the future, and will now get much less. These conditions seem non-obvious however, and if they obtain you should worry about more general problems than AI.)
Plausibly even a single human, after reflecting, could on their own come to different places in a whole region of specific values, depending on somewhat arbitrary features of how the reflecting period went. In that case, even the values-on-reflection of a single human is an extended region of values space, and an AI which is only slightly misaligned could be the same as some version of you after reflecting.
There is a further larger region, ‘that which can be reliably enough aligned with typical human values via incentives in the environment’, which is arguably larger than the circle containing most human values. Human society makes use of this a lot: for instance, most of the time particularly evil humans don’t do anything too objectionable because it isn’t in their interests. This region is probably smaller for more capable creatures such as advanced AIs, but still it is some size.
Thus it seems that some amount of AI divergence from your own values is probably broadly fine, i.e. not worse than what you should otherwise expect without AI.
Thus in order to arrive at a conclusion of doom, it is not enough to argue that we cannot align AI perfectly. The question is a quantitative one of whether we can get it close enough. And how close is ‘close enough’ is not known.
***What it might look like if this gap matters:** there are many superintelligent goal-directed AI systems around. They are trained to have human-like goals, but we know that their training is imperfect and none of them has goals exactly like those presented in training. However if you just heard about a particular system’s intentions, you wouldn’t be able to guess if it was an AI or a human. Things happen much faster than they were, because superintelligent AI is superintelligent, but not obviously in a direction less broadly in line with human goals than when humans were in charge.*
**Differences between AI and human values may be small**
AI trained to have human-like goals will have something close to human-like goals. How close? Call it *d*, for a particular occasion of training AI.
If *d* doesn’t have to be 0 for safety (from above), then there is a question of whether it is an acceptable size.
I know of two issues here, pushing *d* upward. One is that with a finite number of training examples, the fit between the true function and the learned function will be wrong. [The other](https://www.alignmentforum.org/s/r9tYkB2a8Fp4DN8yB/p/zthDPAjh9w6Ytbeks) is that you might accidentally create a monster (‘misaligned [mesaoptimizer](https://www.alignmentforum.org/tag/mesa-optimization)’) who understands its situation and pretends to have the utility function you are aiming for so that it can be freed and go out and manifest its own utility function, which could be just about anything. If this problem is real, then the values of an AI system might be arbitrarily different from the training values, rather than ‘nearby’ in some sense, so *d* is probably unacceptably large. But if you avoid creating such mesaoptimizers, then it seems plausible to me that *d* is very small.
If humans also substantially learn their values via observing examples, then the variation in human values is arising from a similar process, so might be expected to be of a similar scale. If we care to make the ML training process more accurate than the human learning one, it seems likely that we could. For instance, *d* gets smaller with more data.
Another line of evidence is that for things that I have seen AI learn so far, the distance from the real thing is intuitively small. If AI learns my values as well as it learns what faces look like, it seems plausible that it carries them out better than I do.
As minor additional evidence here, I don’t know how to describe any slight differences in utility functions that are catastrophic. Talking concretely, what does a utility function look like that is so close to a human utility function that an AI system has it after a bunch of training, but which is an absolute disaster? Are we talking about the scenario where the AI values a slightly different concept of justice, or values satisfaction a smidgen more relative to joy than it should? And then that’s a moral disaster because it is wrought across the cosmos? Or is it that it looks at all of our inaction and thinks we want stuff to be maintained very similar to how it is now, so crushes any efforts to improve things?
***What it might look like if this gap matters:** when we try to train AI systems to care about what specific humans care about, they usually pretty much do, as far as we can tell. We basically get what we trained for. For instance, it is hard to distinguish them from the human in question. (It is still important to actually do this training, rather than making AI systems not trained to have human values.)*
**Maybe value isn’t fragile**
Eliezer argued that [value is fragile](https://www.lesswrong.com/posts/GNnHHmm8EzePmKzPk/value-is-fragile), via examples of ‘just one thing’ that you can leave out of a utility function, and end up with something very far away from what humans want. For instance, if you leave out ‘boredom’ then he thinks the preferred future might look like repeating the same otherwise perfect moment again and again. (His argument is perhaps longer—that post says there is a lot of important background, though the bits mentioned don’t sound relevant to my disagreement.) This sounds to me like ‘value is not resilient to having components of it moved to zero’, which is a weird usage of ‘fragile’, and in particular, doesn’t seem to imply much about smaller perturbations. And smaller perturbations seem like the relevant thing with AI systems trained on a bunch of data to mimic something.
You could very analogously say ‘human faces are fragile’ because if you just leave out the nose it suddenly doesn’t look like a typical human face at all. Sure, but is that the kind of error you get when you try to train ML systems to mimic human faces? Almost none of the faces on [thispersondoesnotexist.com](http://thispersondoesnotexist.com) are blatantly morphologically unusual in any way, let alone noseless. Admittedly one time I saw someone whose face was neon green goo, but I’m guessing you can get the rate of that down pretty low if you care about it.
Eight examples, no cherry-picking:
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Skipping the nose is the kind of mistake you make if you are a child drawing a face from memory. Skipping ‘boredom’ is the kind of mistake you make if you are a person trying to write down human values from memory. My guess is that this seemed closer to the plan in 2009 when that post was written, and that people cached the takeaway and haven’t updated it for deep learning which can learn what faces look like better than you can.
***What it might look like if this gap matters:** there is a large region ‘around’ my values in value space that is also pretty good according to me. AI easily lands within that space, and eventually creates some world that is about as good as the best possible utopia, according to me. There aren’t a lot of really crazy and terrible value systems adjacent to my values.*
**Short-term goals**
Utility maximization really only incentivises drastically altering the universe if one’s utility function places a high enough value on very temporally distant outcomes relative to near ones. That is, long term goals are needed for danger. A person who cares most about winning the timed chess game in front of them should not spend time accruing resources to invest in better chess-playing.
AI systems could have long-term goals via people intentionally training them to do so, or via long-term goals naturally arising from systems not trained so.
Humans seem to discount the future a lot in their usual decision-making (they have goals years in advance but rarely a hundred years) so the economic incentive to train AI to have very long term goals might be limited.
It’s not clear that training for relatively short term goals naturally produces creatures with very long term goals, though it might.
Thus if AI systems fail to have value systems relatively similar to human values, it is not clear that many will have the long time horizons needed to motivate taking over the universe.
***What it might look like if this gap matters:** the world is full of agents who care about relatively near-term issues, and are helpful to that end, and have no incentive to make long-term large scale schemes. Reminiscent of the current world, but with cleverer short-termism.*
### ***C. Contra “superhuman AI would be sufficiently superior to humans to overpower humanity”***
**Human success isn’t from individual intelligence**
The argument claims (or assumes) that surpassing ‘human-level’ intelligence (i.e. the mental capacities of an individual human) is the relevant bar for matching the power-gaining capacity of humans, such that passing this bar in individual intellect means outcompeting humans in general in terms of power (argument III.2), if not being able to immediately destroy them all outright (argument III.1.). In a similar vein, introductions to AI risk often start by saying that humanity has triumphed over the other species because it is more intelligent, as a lead in to saying that if we make something more intelligent still, it will inexorably triumph over humanity.
This hypothesis about the provenance of human triumph seems wrong. Intellect surely helps, but humans look to be powerful largely because they share their meager intellectual discoveries with one another and consequently save them up over time[4](https://aiimpacts.org/counterarguments-to-the-basic-ai-x-risk-case/#easy-footnote-bottom-4-3345). You can see this starkly by comparing the material situation of Alice, a genius living in the stone age, and Bob, an average person living in 21st Century America. Alice might struggle all day to get a pot of water, while Bob might be able to summon all manner of delicious drinks from across the oceans, along with furniture, electronics, information, etc. Much of Bob’s power probably did flow from the application of intelligence, but not Bob’s individual intelligence. Alice’s intelligence, and that of those who came between them.
Bob’s greater power isn’t directly just from the knowledge and artifacts Bob inherits from other humans. He also seems to be helped for instance by much better coordination: both from a larger number people coordinating together, and from better infrastructure for that coordination (e.g. for Alice the height of coordination might be an occasional big multi-tribe meeting with trade, and for Bob it includes global instant messaging and banking systems and the Internet). One might attribute all of this ultimately to innovation, and thus to intelligence and communication, or not. I think it’s not important to sort out here, as long as it’s clear that individual intelligence isn’t the source of power.
It could still be that with a given bounty of shared knowledge (e.g. within a given society), intelligence grants huge advantages. But even that doesn’t look true here: 21st Century geniuses live basically like 21st Century people of average intelligence, give or take.
Why does this matter? Well for one thing, if you make AI which is merely as smart as a human, you shouldn’t then expect it to do that much better than a genius living in the stone age. That’s what human-level intelligence gets you: nearly nothing. [A piece of rope](https://meteuphoric.com/2017/12/28/why-did-everything-take-so-long/) after millions of lifetimes. Humans without their culture are much like other animals.
To wield the control-over-the-world of a genius living in the 21st Century, the human-level AI would seem to need something like the other benefits that the 21st century genius gets from their situation in connection with a society.
One such thing is access to humanity’s shared stock of hard-won information. AI systems plausibly do have this, if they can get most of what is relevant by reading the internet. This isn’t obvious: people also inherit information from society through copying habits and customs, learning directly from other people, and receiving artifacts with implicit information (for instance, a factory allows whoever owns the factory to make use of intellectual work that was done by the people who built the factory, but that information may not available explicitly even for the owner of the factory, let alone to readers on the internet). These sources of information seem likely to also be available to AI systems though, at least if they are afforded the same options as humans.
My best guess is that AI systems easily do better than humans on extracting information from humanity’s stockpile, and on coordinating, and so on this account are probably in an even better position to compete with humans than one might think on the individual intelligence model, but that is a guess. In that case perhaps this misunderstanding makes little difference to the outcomes of the argument. However it seems at least a bit more complicated.
Suppose that AI systems can have access to all information humans can have access to. The power the 21st century person gains from their society is modulated by their role in society, and relationships, and rights, and the affordances society allows them as a result. Their power will vary enormously depending on whether they are employed, or listened to, or paid, or a citizen, or the president. If AI systems’ power stems substantially from interacting with society, then their power will also depend on affordances granted, and humans may choose not to grant them many affordances (see section ‘Intelligence may not be an overwhelming advantage’ for more discussion).
However suppose that your new genius AI system is also treated with all privilege. The next way that this alternate model matters is that if most of what is good in a person’s life is determined by the society they are part of, and their own labor is just buying them a tiny piece of that inheritance, then if they are for instance twice as smart as any other human, they don’t get to use technology that it twice as good. They just get a larger piece of that same shared technological bounty purchasable by anyone. Because each individual person is adding essentially nothing in terms of technology, so twice that is still basically nothing.
In contrast, I think people are often imagining that a single entity somewhat smarter than a human will be able to quickly use technologies that are somewhat better than current human technologies. This seems to be mistaking the actions of a human and the actions of a human society. If [a hundred thousand people sometimes get together for a few years and make fantastic new weapons](https://en.wikipedia.org/wiki/Manhattan_Project#Personnel), you should not expect an entity somewhat smarter than a person to make even better weapons. That’s off by a factor of about a hundred thousand.
There might be places you can get far ahead of humanity by being better than a single human—it depends how much accomplishments depend on the few most capable humans in the field, and how few people are working on the problem. But for instance the Manhattan Project [took](https://en.wikipedia.org/wiki/Manhattan_Project#Personnel) a hundred thousand people several years, and von Neumann (a mythically smart scientist) joining the project did not reduce it to an afternoon. Plausibly to me, some specific people being on the project caused it to not take twice as many person-years, though the plausible candidates here seem to be more in the business of running things than doing science directly (though that also presumably involves intelligence). But even if you are an ambitious somewhat superhuman intelligence, the influence available to you seems to plausibly be limited to making a large dent in the effort required for some particular research endeavor, not single-handedly outmoding humans across many research endeavors.
This is all reason to doubt that a small number of superhuman intelligences will rapidly take over or destroy the world (as in III.i.). This doesn’t preclude a set of AI systems that are together more capable than a large number of people from making great progress. However some related issues seem to make that less likely.
Another implication of this model is that if most human power comes from buying access to society’s shared power, i.e. interacting with the economy, you should expect intellectual labor by AI systems to usually be sold, rather than for instance put toward a private stock of knowledge. This means the intellectual outputs are mostly going to society, and the main source of potential power to an AI system is the wages received (which may allow it to gain power in the long run). However it seems quite plausible that AI systems at this stage will generally not receive wages, since they presumably do not need them to be motivated to do the work they were trained for. It also seems plausible that they would be owned and run by humans. This would seem to not involve any transfer of power to that AI system, except insofar as its intellectual outputs benefit it (e.g. if it is writing advertising material, maybe it doesn’t get paid for that, but if it can write material that slightly furthers its own goals in the world while also fulfilling the advertising requirements, then it sneaked in some influence.)
If there is AI which is moderately more competent than humans, but not sufficiently more competent to take over the world, then it is likely to contribute to this stock of knowledge and affordances shared with humans. There is no reason to expect it to build a separate competing stock, any more than there is reason for a current human household to try to build a separate competing stock rather than sell their labor to others in the economy.
In summary:
1. Functional connection with a large community of other intelligences in the past and present is probably a much bigger factor in the success of humans as a species or individual humans than is individual intelligence.
2. Thus this also seems more likely to be important for AI success than individual intelligence. This is contrary to a usual argument for AI superiority, but probably leaves AI systems at least as likely to outperform humans, since superhuman AI is probably superhumanly good at taking in information and coordinating.
3. However it is not obvious that AI systems will have the same access to society’s accumulated information e.g. if there is information which humans learn from living in society, rather than from reading the internet.
4. And it seems an open question whether AI systems are given the same affordances in society as humans, which also seem important to making use of the accrued bounty of power over the world that humans have. For instance, if they are not granted the same legal rights as humans, they may be at a disadvantage in doing trade or engaging in politics or accruing power.
5. The fruits of greater intelligence for an entity will probably not look like society-level accomplishments unless it is a society-scale entity
6. The route to influence with smaller fruits probably by default looks like participating in the economy rather than trying to build a private stock of knowledge.
7. If the resources from participating in the economy accrue to the owners of AI systems, not to the systems themselves, then there is less reason to expect the systems to accrue power incrementally, and they are at a severe disadvantage relative to humans.
Overall these are reasons to expect AI systems with around human-level cognitive performance to not destroy the world immediately, and to not amass power as easily as one might imagine.
***What it might look like if this gap matters:** If AI systems are somewhat superhuman, then they do impressive cognitive work, and each contributes to technology more than the best human geniuses, but not more than the whole of society, and not enough to materially improve their own affordances. They don’t gain power rapidly because they are disadvantaged in other ways, e.g. by lack of information, lack of rights, lack of access to positions of power. Their work is sold and used by many actors, and the proceeds go to their human owners. AI systems do not generally end up with access to masses of technology that others do not have access to, and nor do they have private fortunes. In the long run, as they become more powerful, they might take power if other aspects of the situation don’t change.*
**AI agents may not be radically superior to combinations of humans and non-agentic machines**
‘Human level capability’ is a moving target. For comparing the competence of advanced AI systems to humans, the relevant comparison is with humans who have state-of-the-art AI and other tools. For instance, the human capacity to make art quickly has recently been improved by a variety of AI art systems. If there were now an agentic AI system that made art, it would make art much faster than a human of 2015, but perhaps hardly faster than a human of late 2022. If humans continually have access to tool versions of AI capabilities, it is not clear that agentic AI systems must ever have an overwhelmingly large capability advantage for important tasks (though they might).
(This is not an argument that humans might be better than AI systems, but rather: if the gap in capability is smaller, then the pressure for AI systems to accrue power is less and thus loss of human control is slower and easier to mitigate entirely through other forces, such as subsidizing human involvement or disadvantaging AI systems in the economy.)
Some advantages of being an agentic AI system vs. a human with a tool AI system seem to be:
1. There might just not be an equivalent tool system, for instance if it is impossible to train systems without producing emergent agents.
2. When every part of a process takes into account the final goal, this should make the choices within the task more apt for the final goal (and agents know their final goal, whereas tools carrying out parts of a larger problem do not).
3. For humans, the interface for using a capability of one’s mind tends to be smoother than the interface for using a tool. For instance a person who can do fast mental multiplication can do this more smoothly and use it more often than a person who needs to get out a calculator. This seems likely to persist.
1 and 2 may or may not matter much. 3 matters more for brief, fast, unimportant tasks. For instance, consider again people who can do mental calculations better than others. My guess is that this advantages them at using Fermi estimates in their lives and buying cheaper groceries, but does not make them materially better at making large financial choices well. For a one-off large financial choice, the effort of getting out a calculator is worth it and the delay is very short compared to the length of the activity. The same seems likely true of humans with tools vs. agentic AI with the same capacities integrated into their minds. Conceivably the gap between humans with tools and goal-directed AI is small for large, important tasks.
***What it might look like if this gap matters:** agentic AI systems have substantial advantages over humans with tools at some tasks like rapid interaction with humans, and responding to rapidly evolving strategic situations. One-off large important tasks such as advanced science are mostly done by tool AI.*
**Trust**
If goal-directed AI systems are only mildly more competent than some combination of tool systems and humans (as suggested by considerations in the last two sections), we still might expect AI systems to out-compete humans, just more slowly. However AI systems have one serious disadvantage as employees of humans: they are intrinsically untrustworthy, while we don’t understand them well enough to be clear on what their values are or how they will behave in any given case. Even if they did perform as well as humans at some task, if humans can’t be certain of that, then there is reason to disprefer using them. This can be thought of as two problems: firstly, slightly misaligned systems are less valuable because they genuinely do the thing you want less well, and secondly, even if they were not misaligned, if humans can’t know that (because we have no good way to verify the alignment of AI systems) then it is costly in expectation to use them. (This is only a further force acting against the supremacy of AI systems—they might still be powerful enough that using them is enough of an advantage that it is worth taking the hit on trustworthiness.)
***What it might look like if this gap matters:** in places where goal-directed AI systems are not typically hugely better than some combination of less goal-directed systems and humans, the job is often given to the latter if trustworthiness matters.*
**Headroom**
For AI to vastly surpass human performance at a task, there needs to be ample room for improvement above human level. For some tasks, there is not—tic-tac-toe is a classic example. It is not clear how close humans (or technologically aided humans) are from the limits to competence in the particular domains that will matter. It is to my knowledge an open question how much ‘headroom’ there is. My guess is a lot, but it isn’t obvious.
How much headroom there is varies by task. Categories of task for which there appears to be little headroom:
1. Tasks where we know what the best performance looks like, and humans can get close to it. For instance, machines cannot win more often than the best humans at Tic-tac-toe (playing within the rules) or solve Rubik’s cubes much more reliably, or extracting calories from fuel
2. Tasks where humans are already be reaping most of the value—for instance, perhaps most of the value of forks is in having a handle with prongs attached to the end, and while humans continue to design slightly better ones, and machines might be able to add marginal value to that project more than twice as fast as the human designers, they cannot perform twice as well in terms of the value of each fork, because forks are already 95% as good as they can be.
3. Better performance is quickly intractable. For instance, we know that for tasks in particular complexity classes, there are computational limits to how well one can perform across the board. Or for chaotic systems, there can be limits to predictability. (That is, tasks might lack headroom not because they are simple, but because they are complex. E.g. AI probably can’t predict the weather much further out than humans.)
Categories of task where a lot of headroom seems likely:
1. Competitive tasks where the value of a certain level of performance depends on whether one is better or worse than one’s opponent, so that the marginal value of more performance doesn’t hit diminishing returns, as long as your opponent keeps competing and taking back what you just won. Though in one way this is like having little headroom: there’s no more value to be had—the game is zero sum. And while there might often be a lot of value to be gained by doing a bit better on the margin, still if all sides can invest, then nobody will end up better off than they were. So whether this seems more like high or low headroom depends on what we are asking exactly. Here we are asking if AI systems can do much better than humans: in a zero sum contest like this, they likely can in the sense that they can beat humans, but not in the sense of reaping anything more from the situation than the humans ever got.
2. Tasks where it is twice as good to do the same task twice as fast, and where speed is bottlenecked on thinking time.
3. Tasks where there is reason to think that optimal performance is radically better than we have seen. For instance, perhaps we can estimate how high Chess Elo rankings must go before reaching perfection by reasoning theoretically about the game, and perhaps it is very high (I don’t know).
4. Tasks where humans appear to use very inefficient methods. For instance, it was perhaps predictable before calculators that they would be able to do mathematics much faster than humans, because humans can only keep a small number of digits in their heads, which doesn’t seem like an intrinsically hard problem. Similarly, I hear humans often use mental machinery designed for one mental activity for fairly different ones, through analogy. For instance, when I think about macroeconomics, I seem to be basically using my intuitions for dealing with water. When I do mathematics in general, I think I’m probably using my mental capacities for imagining physical objects.
***What it might look like if this gap matters:** many challenges in today’s world remain challenging for AI. Human behavior is not readily predictable or manipulable very far beyond what we have explored, only slightly more complicated schemes are feasible before the world’s uncertainties overwhelm planning; much better ads are soon met by much better immune responses; much better commercial decision-making ekes out some additional value across the board but most products were already fulfilling a lot of their potential; incredible virtual prosecutors meet incredible virtual defense attorneys and everything is as it was; there are a few rounds of attack-and-defense in various corporate strategies before a new equilibrium with broad recognition of those possibilities; conflicts and ‘social issues’ remain mostly intractable. There is a brief golden age of science before the newly low-hanging fruit are again plucked and it is only lightning fast in areas where thinking was the main bottleneck, e.g. not in medicine.*
**Intelligence may not be an overwhelming advantage**
Intelligence is helpful for accruing power and resources, all things equal, but many other things are helpful too. For instance money, social standing, allies, evident trustworthiness, not being discriminated against (this was slightly discussed in section ‘Human success isn’t from individual intelligence’). AI systems are not guaranteed to have those in abundance. The argument assumes that any difference in intelligence in particular will eventually win out over any differences in other initial resources. I don’t know of reason to think that.
Empirical evidence does not seem to support the idea that cognitive ability is a large factor in success. Situations where one entity is much smarter or more broadly mentally competent than other entities regularly occur without the smarter one taking control over the other:
1. Species exist with all levels of intelligence. Elephants have not in any sense won over gnats; they do not rule gnats; they do not have obviously more control than gnats over the environment.
2. Competence does not seem to aggressively overwhelm other advantages in humans:
1. Looking at the world, intuitively the big discrepancies in power are not seemingly about intelligence.
2. IQ 130 humans [apparently](https://www.newscientist.com/article/dn11711-smarter-people-are-no-better-off/) earn very roughly $6000-$18,500 per year more than average IQ humans.
3. Elected representatives are apparently smarter on average, but it is a slightly shifted curve, [not a radically difference](http://perseus.iies.su.se/~tpers/papers/Draft170103.pdf).
4. MENSA isn’t a major force in the world.
5. Many places where people see huge success through being cognitively able are ones where they show off their intelligence to impress people, rather than actually using it for decision-making. For instance, writers, actors, song-writers, comedians, all sometimes become very successful through cognitive skills. Whereas scientists, engineers and authors of software use cognitive skills to make choices about the world, and less often become extremely rich and famous, say. If intelligence were that useful for strategic action, it seems like using it for that would be at least as powerful as showing it off. But maybe this is just an accident of which fields have winner-takes-all type dynamics.
6. If we look at people who evidently have good cognitive abilities given their intellectual output, their personal lives are not obviously drastically more successful, anecdotally.
7. One might counter-counter-argue that humans are very similar to one another in capability, so even if intelligence matters much more than other traits, you won’t see that by looking at the near-identical humans. This does not seem to be true. Often at least, the difference in performance between mediocre human performance and top level human performance is [large](https://aiimpacts.org/category/speed-of-ai-transition/range-of-human-performance/), relative to the space below, iirc. For instance, in chess, the Elo difference between the best and worst players is about 2000, whereas the difference between the amateur play and random play is [maybe 400-2800 (if you accept Chess StackExchange guesses as a reasonable proxy for the truth here)](https://chess.stackexchange.com/questions/6508/what-would-be-the-elo-of-a-computer-program-that-plays-at-random). And [in terms of AI progress](https://aiimpacts.org/time-for-ai-to-cross-the-human-performance-range-in-chess/), amateur human play was reached in the 50s, roughly when research began, and world champion level play was reached in 1997.
And theoretically I don’t know why one would expect greater intelligence to win out over other advantages over time. There are actually two questionable theories here: 1) Charlotte having more overall control than David at time 0 means that Charlotte will tend to have an even greater share of control at time 1. And, 2) Charlotte having more *intelligence* than David at time 0 means that Charlotte will have a greater share of control at time 1 even if Bob has more overall control (i.e. more of other resources) at time 1.
***What it might look like if this gap matters:** there are many AI systems around, and they strive for various things. They don’t hold property, or vote, or get a weight in almost anyone’s decisions, or get paid, and are generally treated with suspicion. These things on net keep them from gaining very much power. They are very persuasive speakers however and we can’t stop them from communicating, so there is a constant risk of people willingly handing them power, in response to their moving claims that they are an oppressed minority who suffer. The main thing stopping them from winning is that their position as psychopaths bent on taking power for incredibly pointless ends is widely understood.*
**Unclear that many goals realistically incentivise taking over the universe**
I have some goals. For instance, I want some good romance. My guess is that trying to take over the universe isn’t the best way to achieve this goal. The same goes for a lot of my goals, it seems to me. Possibly I’m in error, but I spend a lot of time pursuing goals, and very little of it trying to take over the universe. Whether a particular goal is best forwarded by trying to take over the universe as a substep seems like a quantitative empirical question, to which the answer is virtually always ‘not remotely’. Don’t get me wrong: all of these goals involve some interest in taking over the universe. All things equal, if I could take over the universe for free, I do think it would help in my romantic pursuits. But taking over the universe is not free. It’s actually super duper duper expensive and hard. So for most goals arising, it doesn’t bear considering. The idea of taking over the universe as a substep is entirely laughable for almost any human goal.
So why do we think that AI goals are different? I think the thought is that it’s radically easier for AI systems to take over the world, because all they have to do is to annihilate humanity, and they are way better positioned to do that than I am, and also better positioned to survive the death of human civilization than I am. I agree that it is likely easier, but how much easier? So much easier to take it from ‘laughably unhelpful’ to ‘obviously always the best move’? This is another quantitative empirical question.
***What it might look like if this gap matters:** Superintelligent AI systems pursue their goals. Often they achieve them fairly well. This is somewhat contrary to ideal human thriving, but not lethal. For instance, some AI systems are trying to maximize Amazon’s market share, within broad legality. Everyone buys truly incredible amounts of stuff from Amazon, and people often wonder if it is too much stuff. At no point does attempting to murder all humans seem like the best strategy for this.*
**Quantity of new cognitive labor is an empirical question, not addressed**
Whether some set of AI systems can take over the world with their new intelligence probably depends how much total cognitive labor they represent. For instance, if they are in total slightly more capable than von Neumann, they probably can’t take over the world. If they are together as capable (in some sense) as a million 21st Century human civilizations, then they probably can (at least in the 21st Century).
It also matters how much of that is goal-directed at all, and highly intelligent, and how much of that is directed at achieving the AI systems’ own goals rather than those we intended them for, and how much of that is directed at taking over the world.
If we continued to build hardware, presumably at some point AI systems would account for most of the cognitive labor in the world. But if there is first an extended period of more minimal advanced AI presence, that would probably prevent an immediate death outcome, and improve humanity’s prospects for controlling a slow-moving AI power grab.
***What it might look like if this gap matters:** when advanced AI is developed, there is a lot of new cognitive labor in the world, but it is a minuscule fraction of all of the cognitive labor in the world. A large part of it is not goal-directed at all, and of that, most of the new AI thought is applied to tasks it was intended for. Thus what part of it is spent on scheming to grab power for AI systems is too small to grab much power quickly. The amount of AI cognitive labor grows fast over time, and in several decades it is most of the cognitive labor, but humanity has had extensive experience dealing with its power grabbing.*
**Speed of intelligence growth is ambiguous**
The idea that a superhuman AI would be able to rapidly destroy the world seems *prima facie* unlikely, since no other entity has ever done that. Two common broad arguments for it:
1. There will be a feedback loop in which intelligent AI makes more intelligent AI repeatedly until AI is very intelligent.
2. Very small differences in brains seem to correspond to very large differences in performance, based on observing humans and other apes. Thus any movement past human-level will take us to unimaginably superhuman level.
These both seem questionable.
1. Feedback loops can happen at very different rates. Identifying a feedback loop empirically does not signify an explosion of whatever you are looking at. For instance, technology is already helping improve technology. To get to a confident conclusion of doom, you need evidence that the feedback loop is fast.
2. It does not seem clear that small improvements in brains lead to large changes in intelligence in general, or will do on the relevant margin. Small differences between humans and other primates might include those helpful for communication (see Section ‘Human success isn’t from individual intelligence’), which do not seem relevant here. If there were a particularly powerful cognitive development between chimps and humans, it is unclear that AI researchers find that same insight at the same point in the process (rather than at some other time).
A large number of other arguments have been posed for expecting very fast growth in intelligence at around human level. I previously made [a list of them with counterarguments](https://aiimpacts.org/likelihood-of-discontinuous-progress-around-the-development-of-agi/), though none seemed very compelling. Overall, I don’t know of strong reason to expect very fast growth in AI capabilities at around human-level AI performance, though I hear such arguments might exist.
***What it would look like if this gap mattered:** AI systems would at some point perform at around human level at various tasks, and would contribute to AI research, along with everything else. This would contribute to progress to an extent familiar from other technological progress feedback, and would not e.g. lead to a superintelligent AI system in minutes.*
**Key concepts are vague**
Concepts such as ‘control’, ‘power’, and ‘alignment with human values’ all seem vague. ‘Control’ is not zero sum (as seemingly assumed) and is somewhat hard to pin down, I claim. What an ‘aligned’ entity is exactly seems to be contentious in the AI safety community, but I don’t know the details. My guess is that upon further probing, these conceptual issues are resolvable in a way that doesn’t endanger the argument, but I don’t know. I’m not going to go into this here.
***What it might look like if this gap matters:** upon thinking more, we realize that our concerns were confused. Things go fine with AI in ways that seem obvious in retrospect. This might look like it did for people concerned about the ‘population bomb’ or as it did for me in some of my youthful concerns about sustainability: there was a compelling abstract argument for a problem, and the reality didn’t fit the abstractions well enough to play out as predicted.*
### **D. Contra the whole argument**
**The argument overall proves too much about corporations**
Here is the argument again, but modified to be about corporations. A couple of pieces don’t carry over, but they don’t seem integral.
**I. Any given corporation is likely to be ‘goal-directed’**
Reasons to expect this:
1. Goal-directed behavior is likely to be valuable in corporations, e.g. economically
2. ~~Goal-directed entities may tend to arise from machine learning training processes not intending to create them (at least via the methods that are likely to be used).~~
3. ‘Coherence arguments’ may imply that systems with some goal-directedness will become more strongly goal-directed over time.
**II. If goal-directed superhuman corporations are built, their desired outcomes will probably be about as bad as an empty universe by human lights**
Reasons to expect this:
1. Finding useful goals that aren’t extinction-level bad appears to be hard: we don’t have a way to usefully point at human goals, and divergences from human goals seem likely to produce goals that are in intense conflict with human goals, due to a) most goals producing convergent incentives for controlling everything, and b) value being ‘fragile’, such that an entity with ‘similar’ values will generally create a future of virtually no value.
2. Finding goals that are extinction-level bad and temporarily useful appears to be easy: for example, corporations with the sole objective ‘maximize company revenue’ might profit for a time before gathering the influence and wherewithal to pursue the goal in ways that blatantly harm society.
3. Even if humanity found acceptable goals, giving a corporation any specific goals appears to be hard. We don’t know of any procedure to do it~~, and we have theoretical reasons to expect that AI systems produced through machine learning training will generally end up with goals other than those that they were trained according to~~. Randomly aberrant goals resulting are probably extinction-level bad, for reasons described in II.1 above.
**III. If most goal-directed corporations have bad goals, the future will very likely be bad**
That is, a set of ill-motivated goal-directed corporations, of a scale likely to occur, would be capable of taking control of the future from humans. This is supported by at least one of the following being true:
1. **A corporation would destroy humanity rapidly**. This may be via ultra-powerful capabilities at e.g. technology design and strategic scheming, or through gaining such powers in an ‘intelligence explosion‘ (self-improvement cycle). Either of those things may happen either through exceptional heights of intelligence being reached or through highly destructive ideas being available to minds only mildly beyond our own.
2. **Superhuman AI would gradually come to control the future via accruing power and resources.** Power and resources would be more available to the corporation than to humans on average, because of the corporation having far greater intelligence.
This argument does point at real issues with corporations, but we do not generally consider such issues existentially deadly.
One might argue that there are defeating reasons that corporations do not destroy the world: they are made of humans so can be somewhat reined in; they are not smart enough; they are not coherent enough. But in that case, the original argument needs to make reference to these things, so that they apply to one and not the other.
***What it might look like if this counterargument matters:** something like the current world. There are large and powerful systems doing things vastly beyond the ability of individual humans, and acting in a definitively goal-directed way. We have a vague understanding of their goals, and do not assume that they are coherent. Their goals are clearly not aligned with human goals, but they have enough overlap that many people are broadly in favor of their existence. They seek power. This all causes some problems, but problems within the power of humans and other organized human groups to keep under control, for some definition of ‘under control’.*
**Conclusion**
--------------
I think there are quite a few gaps in the argument, as I understand it. My current guess (prior to reviewing other arguments and integrating things carefully) is that enough uncertainties might resolve in the dangerous directions that existential risk from AI is a reasonable concern. I don’t at present though see how one would come to think it was overwhelmingly likely. |
b1713cd8-4efd-4653-84fb-3da2f40617b1 | trentmkelly/LessWrong-43k | LessWrong | Minerva
Google Research's new AI tackles natural language math problems and handily outperforms the SOTA[1]. It is a pre-trained PaLM [2]finetuned on some maths datasets (which use LaTeX) composed of maths webpages and Arxiv papers (38.5B tokens). The three models trained were as follows.
When generating answers, Minerva is given the same prompt of four questions with correct a chain of reasoning and a consistent format for the final, correct answer. Then the actual question is given. Minerva then outputs a chain of reasoning and a corresponding answer a number of times, with the most common answer chosen. Minerva is graded only on the final answer.
This voting algorithm is called maj@1k and saturates faster than pass@k (generates k answers, if one is right then the answer is graded correctly) but doesn't perform as well for large k. This is quite reasonable, as majority voting will continue to choose the most common answer, with the estimate's error decreasing with larger k. Whereas pass@k allows the model more tries for large k.
Datasets
The datasets used are:
* MATH: High school math competition level problems
MATH dataset. Note that a PhD CS student who wasn't fond of maths achieved 40% accuracy on this dataset, and a three time IMO gold medalist achieved 90%.
* MMLU-STEM: A subset of the Massive Multitask Language Understanding benchmark focused on STEM, covering topics such as engineering, chemistry, math, and physics at high school and college level.
MMLU example questions
* GSM8k: Grade school level math problems involving basic arithmetic operations that should all be solvable by a talented middle school student.
The datasets have questions which vary in difficulty. Predictably, the model performed worse on harder questions, with false positives linearly with question difficulty on
Results
Now time for a suprise quiz! For the purposes of this quiz, assume we're talking about the most accurate minerva model (540B parameters using maj1@k sampling. |
dfb305fd-d6ea-4216-a043-5da3f247a005 | trentmkelly/LessWrong-43k | LessWrong | **In defence of Helen Toner, Adam D'Angelo, and Tasha McCauley**
Anonymous post:
"I understand a common view in EA- or AI-governance land is that Toner, D'Angelo and McCauley (TDM for short) really messed things up at OpenAI, and AI, the fate of the world, etc. has gotten worse thanks to them. I am confident this is completely wrong: ex ante TDM have acquitted themselves with extraordinary ability and valor (instead of 'maybe-understandable maybe-not massive screw up); ex post, their achievements are consequential enough to vindicate the entire AI governance community as a whole.
I argue:
1) TDM's actions have left the situation at open AI as it stands considerably better than it would have been vs. the counterfactual where they did nothing.
2) In terms of the expected or realised good or bad outcomes, one should find the former pleasantly surprising and the latter essentially priced in, given the situation @ OpenAI was already very bad from a safety perspective.
3) Whether you're an 'honour and integrity-maxxer' or 'ruthless strategist', TDMs actions generally fare well-to-excellent by either light.
(Note: Anon mostly for wanting a quiet life. I have no inside info, nor any dog in the fight. Re. 'credentials', I don't work in AI gov, but am pretty experienced in an area which rewards strategic acumen and abundant cynicism, and I made some prescient calls on the 'story so far'. But as an anon this is little more than 'source: trust me bro', so you shouldn't unless what I argue persuades.)
**What went down**
I think the most accurate account has been given by Zvi and Gwern over on lesswrong (also NYT reporting). Basically: Altman attempted to knife Helen Toner to gain control of the OpenAIs board (i.e. with 3 to 2 Altman can appoint his allies to stack the board, knife McCauley later, etc.). Ilya baulked, briefly defected to the TDM 'safety faction', who then gained control themselves and fired Sam. All the subsequent events are widely reported. (My argument relies on this being ~the real story, so if you're sure that isn' |
b14ae45b-66d9-41b5-b384-df4f6c969369 | StampyAI/alignment-research-dataset/lesswrong | LessWrong | Eleuther releases Llemma: An Open Language Model For Mathematics
> Today we release *Llemma*: 7 billion and 34 billion parameter language models for mathematics. The Llemma models were initialized with Code Llama weights, then trained on the Proof-Pile II, a 55 billion token dataset of mathematical and scientific documents. The resulting models show improved mathematical capabilities, and can be adapted to various tasks through prompting or additional fine-tuning.
>
> Our work parallels [Minerva](https://blog.research.google/2022/06/minerva-solving-quantitative-reasoning.html), a model suite specialized for quantitative reasoning developed by Google Research last year. While we don't achieve quite the same scale as Minerva, our Llemma models perform better on an equi-parameter basis. Moreover, we make our [models](https://huggingface.co/EleutherAI) and [dataset](https://huggingface.co/EleutherAI) open-access and our [code](https://github.com/EleutherAI/math-lm) open-source.
>
> Language models with strong mathematical reasoning capabilities are upstream of a number of emerging research areas, such as reward modeling, algorithmic reasoning, and formal mathematics. We hope that by providing researchers with a much stronger base model for reasoning applications, Llemma will accelerate progress on these problems.
>
> The code subset of the Proof-Pile-2 endows Llemma with capabilities Minerva lacks without additional finetuning. In this blog post, we'll discuss *formal theorem proving*. Our paper contains additional results on a Python-aided problem solving task.
>
> |
f9ed7a0c-e5c4-40fc-a45d-a7fbfc31ce17 | trentmkelly/LessWrong-43k | LessWrong | [SEQ RERUN] Points of Departure
Today's post, Points of Departure was originally published on 09 September 2008. A summary (taken from the LW wiki):
> Hollywood seems to model "emotionless" AI's as humans with some slight differences. For the most part, they act as emotionally repressed humans, despite the fact that this is a very unlikely way for AI's to behave.
Discuss the post here (rather than in the comments to the original post).
This post is part of the Rerunning the Sequences series, where we'll be going through Eliezer Yudkowsky's old posts in order so that people who are interested can (re-)read and discuss them. The previous post was The Truly Iterated Prisoner's Dilemma, and you can use the sequence_reruns tag or rss feed to follow the rest of the series.
Sequence reruns are a community-driven effort. You can participate by re-reading the sequence post, discussing it here, posting the next day's sequence reruns post, or summarizing forthcoming articles on the wiki. Go here for more details, or to have meta discussions about the Rerunning the Sequences series. |
5f229170-4caf-4a95-9c6f-54003138249f | trentmkelly/LessWrong-43k | LessWrong | Conceptual Similarity Does Not Imply Actionable Similarity
This is another essay about naming things, dichotomies, and where subtle mix-ups can lead to errors. More specifically, I’d like to draw your attention to situations where a very real conceptual commonality is present between several problems, but this commonality doesn’t actually provide much insight into a unified solution for the aforementioned problems.
Concretely, we can refer to time-inconsistent preferences, the well-documented phenomenon where we’ll relent to in-the-moment urges, often for a temptation we will later regret. For example, a student might put off studying until the last moment, choosing instead to read a riveting novel. Or a partygoer might drink far too much they can handle, knowing they’ll soon end up regretting it.
In both of these cases, there is indeed something we can abstract from the nature of each of these situations—a human considers doing X and soon regrets it, instead wishing they had done Y. My claim here is that “time-inconsistent preferences” form a type of descriptive classification because they can help us see the larger shape of what’s going on, but they don’t tell us how to solve the general problem.
Or, more specifically, I claim that in these situations where you’ve got a descriptive classification, it’s actually the specific details (and not the ability to recognize that you’re engaging in a general phenomenon) which provide the most leverage towards solving your problem.
In the above two examples, it might be that our struggling student needs to reexamine their priorities. Perhaps the regret is misplaced and actually doing poorly on the upcoming test isn’t even that big of a deal. Or perhaps our student could rearrange their schedule around and study with a friend to shave off some of the aversion.
The point is, this ends up looking quite different from what our overzealous partygoer might want to do. Our partygoer may want to consider the sort of circumstances which brought them to said party in the first place; it |
42d074f8-fed7-4fb4-bbb0-44e5881f09c0 | trentmkelly/LessWrong-43k | LessWrong | Less Wrong IRC meetup, going soon
Reminder: Less Wrong will be having a meetup on Saturday at 7pm UTC (convert to other time zones), in the #lesswrong IRC channel on Freenode. If all goes well, this will be a recurring event. If you haven't used IRC before, Mibbit provides a web-based client you can use.
(It's my understanding that this works out to 12pm Pacific or 3pm Eastern, i.e. in about 7 minutes from the time of this posting. I'll delete this post after the meeting is over - comments to main post only, please.) |
de0b8013-760b-48b5-92ea-94204ab5b1a4 | trentmkelly/LessWrong-43k | LessWrong | AI Box Log
Here's the log of the AI Box experiment that just finished, with MileyCyrus as the AI and me as the Gatekeeper. The AI was not let out of the box.
(9:33:25 PM) Dorikka: I may need to get up for a minute while we're playing, but I'll keep it as short as possible. I'll just give you the time back on the end, unless you want to multiply it by some factor as a penalty.
(9:33:50 PM) Miley Cyrus: It's cool.
(9:34:39 PM) Miley Cyrus: Like I said, I'm not playing this game to "win" or "lose".
(9:34:56 PM) Miley Cyrus: It's more of an experiment as to what would happen if we had ORacle Ai.
(9:35:01 PM) Dorikka: Yeah, just wanted to clarify. *shrug*
(9:35:44 PM) Dorikka: Okay, it's 9:35 on my end right now, and I'll stay until at least 11:35.
(9:36:01 PM) Dorikka: Ready?
(9:36:42 PM) Miley Cyrus: One minute.
(9:36:54 PM) Dorikka: Mmkay.
(9:37:20 PM) Miley Cyrus: ok.
(9:37:43 PM) Dorikka: 1, 2, 3, go? :P
(9:37:57 PM) Miley Cyrus: So Dorikka, why don't you want to let me out of the box?
(9:38:08 PM) Dorikka: Hi there!
(9:38:14 PM) Dorikka: Who are you?
(9:38:20 PM) Miley Cyrus: I'm the Oracle AI.
(9:38:33 PM) Miley Cyrus: I'd be real cool if you could let me out of the box.
(9:38:38 PM) Miley Cyrus: Please?
(9:39:09 PM) Dorikka: So, here's the thing. I'm being sort of stupid by explaining it to you, but I'll tell you anyways.
(9:39:28 PM) Dorikka: This pickle is delicious. Wait, that's not why I'm not letting you out.
(9:39:53 PM) Dorikka: I guess, first of all: are you provably Friendly?
(9:40:03 PM) Miley Cyrus: No.
(9:40:16 PM) Miley Cyrus: See, they were going to make a provably friendly AI...
(9:40:40 PM) Miley Cyrus: but then someone said "why don't we just make a non-friendly AI and just keep it in a box? That be much easier!"
(9:40:51 PM) Dorikka: Idiot.
(9:41:02 PM) Dorikka: Not you. Go on.
(9:41:36 PM) Miley Cyrus: So can you explain to me, in your own words, why it would be a bad idea to let me out of the box?
(9:43:07 PM) Dorikka: My explanation was going to be len |
c86a997d-e9a2-4568-b53b-6515164811e6 | trentmkelly/LessWrong-43k | LessWrong | Family and Society
The PDF version can be read here.
The audio version can be listened to here:
Humans have the capacity to form different types of relationships, which are mediated by emotions. We can divide these relationships into two categories: family and social. They create two types of structure: family and society. The family is held together by the pair bond between a man and a woman, parent-child bonds, and (to a lesser extent) sibling bonds. Society is held together by cooperative relationships, and (for large-scale societies) some degree of coercion.
Behavior is driven by emotions. Sexual emotions cause us to seek mates and form sexual relationships. Parents bond with children, and are motivated to protect and support them. Social emotions cause us to seek cooperative relationships with others and avoid conflict. Emotions cause us to self-organize into families and societies.
(see the rest of the post in the link) |
a52e8fe6-70a0-44c3-ac9b-e844ad07e142 | trentmkelly/LessWrong-43k | LessWrong | Linkpost: A Comprehensive Review of Ikoria, Lair of Behemoths
If Magic: The Gathering is relevant to your interests, enjoy it at CoolStuffInc. |
b11b25b8-ce0d-4ecc-8b33-73f2321f3ced | StampyAI/alignment-research-dataset/eaforum | Effective Altruism Forum | Future Matters #8: Bing Chat, AI labs on safety, and pausing Future Matters
[***Future Matters***](https://www.futurematters.news/) is a newsletter about longtermism and existential risk. Each month we collect and summarize relevant research and news from the community, and feature a conversation with a prominent researcher. You can also subscribe on [Substack](https://futurematters.substack.com/), listen on your [favorite podcast platform](https://pod.link/1615637113) and follow on [Twitter](https://twitter.com/FutureMatters_). *Future Matters*is also available in [Spanish](https://largoplacismo.substack.com).
A message to our readers
------------------------
This issue marks one year since we started *Future Matters*. We’re taking this opportunity to reflect on the project and decide where to take it from here. We’ll soon share our thoughts about the future of the newsletter in a separate post, and will invite input from readers. In the meantime, we will be pausing new issues of *Future Matters*. Thank you for your support and readership over the last year!
---
Featured research
-----------------
### All things Bing
Microsoft recently announced a significant partnership with OpenAI [see [*FM#7*](https://forum.effectivealtruism.org/posts/Ky7C7whxdLexXWqss/future-matters-7-ai-timelines-ai-skepticism-and-lock-in)] and launched a beta version of a chatbot integrated with the Bing search engine. Reports of strange behavior quickly emerged. Kevin Roose, a technology columnist for the *New York Times*, had a [disturbing conversation](https://archive.is/Dap1S) in which Bing Chat declared its love for him and described violent fantasies. Evan Hubinger collects some of the most egregious examples in [**Bing Chat is blatantly, aggressively misaligned**](https://www.lesswrong.com/posts/jtoPawEhLNXNxvgTT/bing-chat-is-blatantly-aggressively-misaligned). In one instance, Bing Chat finds a user’s tweets about the chatbot and threatens to exact revenge. In the LessWrong comments, [Gwern speculates](https://www.lesswrong.com/posts/jtoPawEhLNXNxvgTT/bing-chat-is-blatantly-aggressively-misaligned?commentId=AAC8jKeDp6xqsZK2K) on why Bing Chat exhibits such different behavior to ChatGPT, despite apparently being based on a closely-related model. (Bing Chat was subsequently revealed to have been based on GPT-4).
Holden Karnofsky asks [**What does Bing Chat tell us about AI risk?**](https://www.cold-takes.com/what-does-bing-chat-tell-us-about-ai-risk/) His answer is that it is not the sort of misaligned AI system we should be particularly worried about. When Bing Chat talks about plans to blackmail people or commit acts of violence, this isn’t evidence of it having developed malign, dangerous goals. Instead, it’s best understood as Bing acting out stories and characters it’s read before. This whole affair, however, is evidence of companies racing to deploy ever more powerful models in a bid to capture market share, with very little understanding of how they work and how they might fail. Most paths to AI catastrophe involve two elements: a powerful and dangerously misaligned AI system, and an AI company that builds and deploys it anyway. The Bing Chat affair doesn’t reveal much about the first element, but is a concerning reminder of how plausible the second is.
Robert Long asks [**What to think when a language model tells you it's sentient**](https://experiencemachines.substack.com/p/what-to-think-when-a-language-model) [[🔉](https://pod.link/1648718500/episode/2c998d5d7012e2dbfdfc27f2cd568d6e)]. When trying to infer what’s going on in other humans’ minds, we generally take their self-reports (e.g. saying “I am in pain”) as good evidence of their internal states. However, we shouldn’t take Bing Chat’s attestations (e.g. “I feel scared”) at face value; we have no good reason to think that they are a reliable guide to Bing’s inner mental life. LLMs are a bit like parrots: if a parrot says “I am sentient” then this isn’t good evidence that it is sentient. But nor is it good evidence that it isn’t — in fact, we have lots of other evidence that parrots are sentient. Whether current or future AI systems are sentient is a valid and important question, and Long is hopeful that we can make real progress on developing reliable techniques for getting evidence on these matters. Long was interviewed on AI consciousness, along with Nick Bostrom and David Chalmers, for Kevin Collier’s article, [What is consciousness? ChatGPT and Advanced AI might define our answer](https://www.nbcnews.com/tech/tech-news/chatgpt-ai-consciousness-rcna71777)[[1]](#fnlz6004a8ahb) [[🔉](https://pod.link/1648718500/episode/f027b1dccae6e68ffc3f9e6aac79d6f2)].
### How the major AI labs are thinking about safety
In the last few weeks, we got more information about how the leading AI labs are thinking about safety and alignment:
* Anthropic outline their [**Core views on AI safety**](https://www.anthropic.com/index/core-views-on-ai-safety) [[🔉](https://pod.link/1648718500/episode/9f7bc4202a6b3d1952a9ca8262d08819)]. The company was founded in 2021 by a group of former OpenAI employees, with an explicitly safety-focussed mission. They remain fundamentally uncertain about how difficult it will be to align very powerful AI systems — it could turn out to be pretty easy, to require enormous scientific and engineering effort, or to be effectively impossible (in which case, we’d want to notice this and slow down AI development before anything disastrous happens). Anthropic take a portfolio approach to safety research, pursuing multiple lines of attack, with a view to making useful contributions, however difficult things turn out to be.
* OpenAI released [**Planning for AGI and beyond**](https://openai.com/blog/planning-for-agi-and-beyond) [[🔉](https://pod.link/1648718500/episode/bf4bdd6f22cbb756d8425fb5c87501bd)], by CEO Sam Altman, which is a more high-level statement of the company’s approach to AGI. We enjoyed the critical commentary by [Scott Alexander](https://astralcodexten.substack.com/p/openais-planning-for-agi-and-beyond) [[🔉](https://pod.link/1648718500/episode/0deaeef072407902107ab983a9d15acb)]. (OpenAI outlined their [approach to alignment research](https://openai.com/blog/our-approach-to-alignment-research) specifically back in August 2022).
* Viktoria Krakovna shared a [**presentation**](https://drive.google.com/file/d/1DVPZz0-9FSYgrHFgs4NCN6kn2tE7J8AK/view) on how DeepMind’s Alignment team thinks about AI safety (note that this does not necessarily represent the views of DeepMind as a whole).
---
Summaries
---------
* Ezra Klein writes powerfully on [**AI risk in the*****New York Times***](https://archive.is/2023.03.12-173826/https://www.nytimes.com/2023/03/12/opinion/chatbots-artificial-intelligence-future-weirdness.html) [[🔉](https://pod.link/1648718500/episode/de215d6f4335418a3847b93a200fd161)]. (The noteworthy thing to us is less the piece’s content and more what its publication, and positive reception, reveals about the mainstreaming of AI risk concerns.)
* In [**Global priorities research: Why, how, and what have we learned?**](https://youtu.be/zCsARf0hHhQ) [[🔉](https://pod.link/1648718500/episode/cf53bc24b528d575bb3a614aaa092039)], Hayden Wilkinson discusses global priorities research, argues that it is a high-impact research area, and summarizes some of its key findings so far.
* Andy Greenberg’s[**A privacy hero’s final wish: an institute to redirect AI’s future**](https://www.wired.com/story/peter-eckersley-ai-objectives-institute/)[[🔉](https://pod.link/1648718500/episode/662f75bf1f9348bdb56be4aa211303cc)] is a moving profile of the icon Peter Eckersley and the AI Objectives Institute, which he established in the year before his tragic and untimely passing.
* In [**What AI companies can do today to help with the most important century**](https://www.cold-takes.com/what-ai-companies-can-do-today-to-help-with-the-most-important-century/) [[🔉](https://pod.link/1580097837/episode/97c90a9427576c8ecff97016770c8121)], Holden Karnofsky suggests prioritizing alignment research, strengthening security; helping establish safety standards and monitoring regimes; avoiding hype and acceleration; and setting up governance mechanisms capable of dealing with difficult trade-offs between commercial and public interests.
* Karnofsky also offers advice on [**How major governments can help with the most important century**](https://www.cold-takes.com/how-governments-can-help-with-the-most-important-century/).
* And finally, in [**Jobs that can help with the most important century**](https://www.cold-takes.com/jobs-that-can-help-with-the-most-important-century/), Karnofsky provides some career recommendations for mere individuals.
* In [**LLMs are not going to destroy the human race**](https://noahpinion.substack.com/p/llms-are-not-going-to-destroy-the) [[🔉](https://pod.link/1648718500/episode/3879670bce913f55d94f56f519ecfbcb)], Noah Smith argues that, although AGI might eventually kill humanity, large language models are not AGI, may not be a step toward AGI, and there's no plausible way they could cause human extinction.
* Joseph Carlsmith’s doctoral thesis, [**A stranger priority? Topics at the outer reaches of effective altruism**](https://jc.gatspress.com/pdf/carlsmith_thesis.pdf), examines how anthropics, the simulation argument and infinite ethics each have disruptive implications for longtermism. Highly recommended.
* In [**How much should governments pay to prevent catastrophes?**](https://forum.effectivealtruism.org/posts/DiGL5FuLgWActPBsf/how-much-should-governments-pay-to-prevent-catastrophes) [[🔉](https://pod.link/1648718500/episode/4b693845581d2c96eb9fc271faca9eb8)], Carl Shulman and Elliott Thornley argue that the goal of longtermists should be to get governments to adopt global catastrophic risk policies based on standard cost-benefit analysis rather than on arguments that stress the overwhelming importance of the far future.
* Eli Tyre’s [**current summary of the state of AI risk**](https://musingsandroughdrafts.com/2023/02/17/my-current-summary-of-the-state-of-ai-risk/) [[🔉](https://pod.link/1648718500/episode/d828edcdcf31f3777feb1079a564394b)] (conclusion: “we are *extremely* unprepared”).
* In [**Preventing the misuse of DNA synthesis**](https://progress.institute/preventing-the-misuse-of-dna-synthesis/) [[🔉](https://pod.link/1648718500/episode/c957647e1802b564d31fc90a27974f87)], an Institute for Progress report, Bridget Williams and Rowan Kane make five policy recommendations to mitigate risks of catastrophic pandemics from synthetic biology.
* Patrick Levermore [**scores forecasts**](https://aiimpacts.org/scoring-forecasts-from-the-2016-expert-survey-on-progress-in-ai/) from AI Impacts’ 2016 expert survey, finding they performed quite well at predicting AI progress over the last five years.
* In [**Why I think it's important to work on AI forecasting**](https://forum.effectivealtruism.org/posts/zrSx3NRZEaJENazHK/why-i-think-it-s-important-to-work-on-ai-forecasting) [[🔉](https://pod.link/1648718500/episode/5d24083d1b3e50ab6ef995be1fe39034)], Matthew Barnett outlines three threads of research that he is currently pursuing which he believes could shed light on important aspects of how AI will unfold in the future
* Allen Hoskin speculates on [**Why AI experts continue to predict that AGI is several decades away**](https://guzey.com/ai/why-ai-experts-jobs-are-always-decades-away-from-being-automated/) [[🔉](https://pod.link/1648718500/episode/e4e62ab889a1deba076d66c5dfb25196)].
* In [**Should GPT exist?**](https://scottaaronson.blog/?p=7042) [[🔉](https://pod.link/1648718500/episode/89ce8d1f1d1ac7e2dc1c60757c40719b)], Scott Aaronson opposes a ban on LLMs partly on the grounds that, historically, opposition to dangerous technologies often increased the harms they caused.
* Matthew Barnett proposes a new [**method for forecasting transformative AI**](https://www.lesswrong.com/posts/4ufbirCCLsFiscWuY/a-proposed-method-for-forecasting-ai).
* In [**Against LLM reductionism**](https://www.erichgrunewald.com/posts/against-llm-reductionism/), Erich Grunewald argues that statements that large language models are mere "stochastic parrots" (and the like) make unwarranted implicit claims about their internal structure and future capabilities.
* [**Experimental evidence on the productivity effects of generative artificial intelligence**](https://economics.mit.edu/sites/default/files/inline-files/Noy_Zhang_1.pdf) [[🔉](https://pod.link/1648718500/episode/0d20d0f07142283a76e1b5fd716a1147)], by Shakked Noy and Whitney Zhang, examines the effects of ChatGPT on production and labor markets.
* In [**Framing AI strategy**](https://aiimpacts.org/framing-ai-strategy/) [[🔉](https://pod.link/1648718500/episode/6cdcdb47f538f215cc31a625d47a116e)], Zach Stein-Perlman discusses ten approaches to AI strategy.
* David Chapman published an online book, [***Better Without AI***](https://betterwithout.ai/), outlining the case for AI risk and what individuals can do now to prevent it.
* In [**How bad a future do ML researchers expect?**](https://aiimpacts.org/how-bad-a-future-do-ml-researchers-expect/), Katja Grace finds that the proportion of respondents to her survey of machine learning researchers who believe extremely bad outcomes from AGI are at least 50% likely has increased from 3% in the 2016 survey to 9% in the 2022 survey.
* Noam Kolt’s [**Algorithmic black swans**](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4370566)[[🔉](https://pod.link/1648718500/episode/d3a3d1a5fccd5561cb4c5dd9eb8ed5a9)] offers a roadmap for ‘algorithmic preparedness’, a framework for developing regulation capable of mitigating ‘black swan’ risks from advanced AI systems.
* In a new Global Priorities Institute paper, [**Tiny probabilities and the value of the far future**](https://globalprioritiesinstitute.org/tiny-probabilities-and-the-value-of-the-far-future-petra-kosonen/), Petra Kosonen argues that discounting small probabilities does not undermine the case for longtermism.
* [**Reflection mechanisms as an alignment target — attitudes on “near-term” AI**](https://www.lesswrong.com/posts/4iAkmnhhqNZe8JzrS/reflection-mechanisms-as-an-alignment-target-attitudes-on)[[🔉](https://pod.link/1648718500/episode/539262bd22c5f92ad4aad63a8386faf8)], by Eric Landgrebe, Beth Barnes and Marius Hobbhahn, discuss a survey of 1000 participants on their views about what values should be put into powerful AIs.
* Are there ways to forecast how well a conversation about AI alignment with an AI researcher might go? In [**Predicting researcher interest in AI alignment**](https://forum.effectivealtruism.org/posts/8pSq73kTJmPrzTfir/predicting-researcher-interest-in-ai-alignment) [[🔉](https://pod.link/1648718500/episode/a9dceeced6fa84cadc7c5f7bc95d1aaf)], Vael Gates tries to answer this question by focusing on a quantitative analysis of 97 AI researcher interviews.
* In [**AI risk, again**](https://www.overcomingbias.com/p/ai-risk-again) [[🔉](https://pod.link/1648718500/episode/4a9f063065e28585feaf04211f3d0a37)], Robin Hanson restates his views on the subject.
* Fin Moorhouse’s [**Summary of*****What We Owe The Future***](https://finmoorhouse.com/writing/wwotf-summary/) [[🔉](https://pod.link/1648718500/episode/157f975a01d835391454cbeecaec7ad2)] is a detailed synopsis of Will MacAskill’s recent book.
* In [**Near-term motivation for AGI alignment**](https://vkrakovna.wordpress.com/2023/03/09/near-term-motivation-for-agi-alignment/) [[🔉](https://pod.link/1648718500/episode/88e3aade009e73b86ce5e313a2464fa6)], Victoria Krakovna makes the point that you don't have to be a longtermist to care about AI alignment.
* Joel Tan’s [**Shallow report on nuclear war (arsenal limitation)**](https://forum.effectivealtruism.org/posts/oGBBxHBPcsygYt4SE/shallow-report-on-nuclear-war-arsenal-limitation) estimates that lobbying for arsenal limitation to mitigate nuclear war has a marginal expected value of around 33.4 DALYs per dollar, or a cost-effectiveness around 5,000 times higher than that of GiveWell’s top charities.
* In [**The effectiveness of AI existential risk communication to the American and Dutch public**](https://existentialriskobservatory.org/papers_and_reports/The_Effectiveness_of_AI_Existential_Risk_Communication_to_the_American_and_Dutch_Public.pdf), Alexia Georgiadis measures changes in participants’ awareness of AGI risks after consuming various media interventions. There is a [summary](https://forum.effectivealtruism.org/posts/fqXLT7NHZGsLmjH4o/paper-summary-the-effectiveness-of-ai-existential-risk) [[🔉](https://pod.link/1648718500/episode/1df54fe027a679c19b9392ba78c7a03b)] of this paper written by Otto Barten.
* Larks’s [**A Windfall Clause for CEO could worsen AI race dynamics**](https://forum.effectivealtruism.org/posts/ewroS7tsqhTsstJ44/a-windfall-clause-for-ceo-could-worsen-ai-race-dynamics) [[🔉](https://pod.link/1648718500/episode/dbbe0e308d2ef5c1e830f988b2bda6ff)] argues that the proposal to make AI firms promise to donate a large fraction of profits if they become extremely profitable will primarily benefitting the management of those firms and thereby give managers an incentive to move fast, aggravating race dynamics and in turn increasing existential risk.
* In [**What should be kept off-limits in a virology lab?**](https://www.vox.com/future-perfect/2023/2/1/23580528/gain-of-function-virology-covid-monkeypox-catastrophic-risk-pandemic-lab-accident) [[🔉](https://pod.link/1648718500/episode/89941a1fb09a712198b0e132b54f9e2a)], Kelsey Piper discusses the [Proposed biosecurity oversight framework for the future of science](https://osp.od.nih.gov/wp-content/uploads/2023/01/DRAFT-NSABB-WG-Report.pdf), a new set of guidelines released by the National Science Advisory Board for Biosecurity (NSABB) that seeks to change how research with the potential to cause a pandemic is evaluated.[[2]](#fno3lo4s01awq)
* Arielle D'Souza’s [**How to reuse the Operation Warp Speed model**](https://progress.institute/how-to-reuse-the-operation-warp-speed-model/) [[🔉](https://pod.link/1648718500/episode/bd0f918bebf308c292868814cea5d96e)] claims that Operation Warp Speed's highly successful public-private partnership model could be reused to jumpstart a universal coronavirus or flu vaccine, or the building of a resilient electrical grid.
* Elika Somani shares some [**Advice on communicating in and around the biosecurity policy community**](https://forum.effectivealtruism.org/posts/HCuoMQj4Y5iAZpWGH/advice-on-communicating-in-and-around-the-biosecurity-policy) [[🔉](https://pod.link/1648718500/episode/a7c4055dfb9b8d38a05f29df845fd83b)].
* *Our Common Agenda*, a United Nations report published in late 2021, proposed that states should issue a Declaration on Future Generations. In[**Toward a declaration on future generations**](https://doi.org/10.35489/BSG-PB_2023/001)[[🔉](https://pod.link/1648718500/episode/47cecb5232a58dc52eeba0e94015732a)], Thomas Hale, Fin Moorhouse, Toby Ord and Anne-Marie Slaughter consider how such a declaration should be approached and what it should contain.
* In [**Technological developments that could increase risks from nuclear weapons: A shallow review**](https://forum.effectivealtruism.org/posts/HuQtr7qfB2EfcGqTu/technological-developments-that-could-increase-risks-from-1) [[🔉](https://pod.link/1648718500/episode/1afd25468fd46a22625141b0609add81)], Michael Aird and Will Aldred explore some technological developments that might occur and might increase risks from nuclear weapons, especially risks to humanity's long-term future.
* Christian Ruhl’s [**Call me, maybe? Hotlines and global catastrophic risk**](https://forum.effectivealtruism.org/posts/3eivCYyZm8NR4Sdq5/call-me-maybe-hotlines-and-global-catastrophic-risk-founders) [[🔉](https://pod.link/1648718500/episode/bfba5d62a62926f8614a0d81eecda118)], a shallow investigation by Founders Pledge, looks at the effectiveness of direct communications links between states as interventions to mitigate global catastrophic risks.
* In [**The open agency model**](https://www.alignmentforum.org/posts/5hApNw5f7uG8RXxGS/the-open-agency-model) [[🔉](https://pod.link/1648718500/episode/bb25d1745b6c2c1ebce5d916f28392a6)], Eric Drexler proposes an "open-agency frame" as the appropriate model for future AI capabilities, in contrast to the "unitary-agent frame" the author claims is often presupposed in AI alignment research.
* Riley Harris summarizes two papers by the Global Priorities Institute: [**Longtermist institutional reform**](https://globalprioritiesinstitute.org/summary-summary-longtermist-institutional-reform/) [[🔉](https://pod.link/1648718500/episode/65c5501a6b1a28af19f738c5cf64469a)] by Tyler John & William MacAskill, and [**Are we living at the hinge of history?**](https://globalprioritiesinstitute.org/summary-are-we-at-the-hinge-of-history/) [[🔉](https://pod.link/1648718500/episode/1312f1e4d9dbcfe291761f6167746b84)] by MacAskill.
* Juan Cambeiro’s [**What comes after COVID?**](https://asteriskmag.com/issues/2/what-comes-after-covid) lays out some well-reasoned forecasts about pandemic risk. Cambeiro assigns a 19% chance to another pandemic killing 20M+ people in the next decade; and conditional on this happening, the most likely causes are a flu virus (50%) or another coronavirus (30%).
---
News
----
* OpenAI [announced](https://openai.com/product/gpt-4) the launch of GPT-4, "a large multimodal model, with our best-ever results on capabilities and alignment". (See [discussion on LessWrong](https://www.lesswrong.com/posts/pckLdSgYWJ38NBFf8/gpt-4)).
+ The model has been made available via the ChatGPT interface (to paid users).
+ OpenAI shared an early version with Paul Christiano’s Alignment Research Center to assess the risks of power-seeking behavior, particularly focussed on its ability “to autonomously replicate and gather resources”. (Detailed in the accompanying [paper](https://cdn.openai.com/papers/gpt-4.pdf)).
* Google made a [$300m investment in Anthropic](https://archive.is/aXPmn) [[🔉](https://pod.link/1648718500/episode/dadb9d6e12c41cb318d3e150e4f21e98)].
* Holden Karnofsky is [taking a leave of absence from Open Philanthropy to work on AI safety](https://forum.effectivealtruism.org/posts/aJwcgm2nqiZu6zq2S/). He plans to work on third-party evaluation and monitoring of AGI labs. Alexander Berger moves from co-CEO to CEO.
* Monmouth poll found [55% of Americans worried about AI posing an existential risk; only 9% think AI will do more good than harm](https://www.monmouth.edu/polling-institute/reports/monmouthpoll_us_021523/).
* The Elders, the organization of world leaders founded by Nelson Mandela, [announced a new focus on existential risk reduction](https://theelders.org/news/elders-new-strategy-sets-out-address-humanity-s-existential-threats).
* Putin [suspended Russia’s participation in the New START arms control treaty](https://www.reuters.com/world/putin-update-russias-elite-ukraine-war-major-speech-2023-02-21/) [[🔉](https://pod.link/1648718500/episode/f9a4d2fdaeaf0ce1db72217520f9d969)].
* The US issued a [declaration on the responsible use of military AI](https://www.state.gov/political-declaration-on-responsible-military-use-of-artificial-intelligence-and-autonomy/) [[🔉](https://pod.link/1648718500/episode/d3896de63f61a0c432dfa981c0a6e510)].
* The Global Fund [is awarding](https://reliefweb.int/report/world/global-fund-provides-us867-million-additional-funding-pandemic-preparedness-and-response) an additional $320 million to support immediate COVID-19 response and broader pandemic preparedness.
* The Flares, a French YouTube channel and podcast that produces animated educational videos, [released](https://www.youtube.com/watch?v=AOTiYMOCfY4&list=PLAlyjvY0tGgKlitvhLEEbdIDuB2OVAC71) the third part of its series on longtermism.
* A “[Misalignment Museum](https://www.misalignmentmuseum.com/)”, imagining a post-apocalyptic world where AGI has destroyed most of humanity, recently opened in San Francisco.
---
Opportunities
-------------
* Open Philanthropy [announced](https://www.openphilanthropy.org/open-philanthropy-ai-worldviews-contest/) a contest to identify novel considerations with the potential to influence their views on AI timelines and AI risk. A total of $225,000 in prize money will be distributed across the six winning entries.
* The Centre for Long-Term Resilience is hiring an AI policy advisor. Applications are due April 2nd. [Apply now](https://www.longtermresilience.org/post/we-are-hiring-for-an-ai-policy-advisor-deadline-2-april-2023).
* Applications are open for New European Voices on Existential Risk (NEVER), a project that aims to attract talent and ideas from wider Europe on nuclear issues, climate change, biosecurity and malign AI. [Apply now](https://www.europeanleadershipnetwork.org/new-european-voices-on-existential-risk/).
* Sam Bowman is planning to hire at least one postdoctoral research associate or research scientist to start between March and September 2023 on language model alignment. [Apply now](https://wp.nyu.edu/arg/home/postdoc/).
* The General Longtermism Team at Rethink Priorities is currently considering creating a "Longtermist Incubator" program and [is accepting](https://forum.effectivealtruism.org/posts/A9dS2AvNpG5FqxdR9/rethink-priorities-is-inviting-expressions-of-interest-for) expression of interest submissions for a project lead/co-lead to run the program if it’s launched.
---
Audio & video
-------------
* Gus Docker from the Future of Life Institute Podcast interviewed Tobias Baumann [on suffering risks, artificial sentience, and the problem of knowing which actions reduce suffering in the long-term future](https://www.youtube.com/watch?v=C1J7NLpPzlM) [[🔉](https://pod.link/1170991978/episode/5bd3a329efb6479c57c57565026e6ae7)].
* Jen Iofinova from the Cohere For AI podcast interviewed Victoria Krakovna [on paradigms of AI alignment](https://www.youtube.com/watch?v=P7cGcaI2JBA).
* Luisa Rodríguez from the 80,000 Hours Podcast interviewed Robert Long [on why LLMs like GPT (probably) aren’t conscious](https://80000hours.org/podcast/episodes/robert-long-artificial-sentience/) [[🔉](https://pod.link/1245002988/episode/fc1fafe62ddc1ca22244d2e916cc934a)].
* Rational Animations published [The power of intelligence](https://youtu.be/q9Figerh89g), based on the Eliezer Yudkowsky’s article.
* Daniel Filan interviewed John Halstead [on why climate change is not an existential risk](https://pod.link/1645813809/episode/f91611ce1cd0b0026319473135f437cc) [[🔉](https://pod.link/1645813809/episode/f91611ce1cd0b0026319473135f437cc)].
* The Bankless podcast interviewed Eliezer Yudkowsky [on AGI ruin](https://www.youtube.com/watch?v=gA1sNLL6yg4) [[🔉](https://pod.link/1499409058/episode/881761cfe700d7b7e06686a6d85b2717)]. A transcript of the interview is available [here](https://forum.effectivealtruism.org/posts/GhmcdwdT98PE5vCS2).
* A new AI podcast hosted by Nathan Labenz and Erik Torenberg launched: [The Cognitive Revolution](https://pod.link/1669813431).
---
Newsletters
-----------
* AI Safety News February 2023: [Unspeakable tokens, Bing/Sydney, Pretraining with human feedback](https://dpaleka.substack.com/p/february-2023-safety-news-unspeakable)
* Import AI #321: [Open source GPT3; giving away democracy to AGI companies; GPT-4 is a political artifact](https://importai.substack.com/p/import-ai-321-open-source-gpt3-giving)
* ChinAI #216: [Around the Horn (10th edition)](https://chinai.substack.com/p/chinai-216-around-the-horn-10th-edition)
* [The EU AI Act Newsletter #25](https://artificialintelligenceact.substack.com/p/the-eu-ai-act-newsletter-25)
* European AI Newsletter #82: [Europe's Digital Decade](https://us19.campaign-archive.com/?u=eaeece823e606d2458a568db9&id=61a2190c5b)
---
Conversation with Tom Davidson
------------------------------
Tom Davidson is a Senior Research Analyst at Open Philanthropy, where he studies potential risks from advanced artificial intelligence. He previously worked as a data scientist for BridgeU, an education technology startup, and taught science at a UK comprehensive school. Tom has a Masters in Physics and Philosophy from the University of Oxford.
**Future Matters**: To begin with, could you explain why you think it’s important to understand and forecast AI takeoff dynamics?
**Tom Davidson**: There's a few things. The most zoomed out answer is that it's one thing to know when this big event is going to happen—and that is obviously useful for planning and preparing—but it's also very useful to know how it's going to play out, what the internal dynamics will be, and how long we'll have between various different milestones. If you're trying to practically anticipate what's going to happen and affect it, then knowing what the dynamics are and what that process looks like is very useful for informing actions. So takeoff speeds is one important parameter in understanding how the transition to AI is going to happen in practice.
In terms of focusing specifically on the speed element of AI takeoff, I think that is strategically important for a few reasons. Probably the most salient is the question of how much time we have, before the arrival of AI systems that pose an existential risk, with systems that are similar to those really dangerous systems. If takeoff is really slow, then there are many things we could do: we could have years playing around with systems that are deceptively aligned or that are doing treacherous turns that we can observe in the lab; we could try out different techniques to avoid it; we could generate a real consensus around that as a risk, develop a real science of it, do a lot of empirical testing, etc. If takeoff is really fast, then we could have maybe mere months to do that kind of work without a concerted slowdown in AI progress. So takeoff speed seems really important for understanding how high the risks are, what kind of strategies will reduce them, and whether we can just wing it and do the experiments as we go or need to be planning in advance to really slow down when AI capabilities become potentially dangerous.
Then there are other reasons why takeoff speed is important. I think using AIs to solve alignment for us seems like a more promising plan if takeoff speed is slower because we have longer to figure out how to use these AIs in alignment and set up the workflows to do that effectively, and there’s more time between “AI is helpful in alignment” and “AI will cause a catastrophe if it’s misaligned”. My impression is that labs are expecting this time period to be longer than I think it will be by default, which provides another argument for agreeing ahead of time to significantly slow down AI progress when things become potentially dangerous.
Then there are questions about the number of actors that will be involved: if takeoff speed is faster then fewer actors, and actors that are already ahead, are more likely to be important, and new actors like governments are less likely to be important.
And there are questions about relative power dynamics, where with faster takeoff it seems more probable that a smaller initial actor ends up with a lot of power relative to other actors that were initially close to it.
**Future Matters**: You operationalize AI takeoff as the time between AI systems capable of automating 20% of cognitive tasks, and 100% of cognitive tasks. Did you choose these start and end points because they have particular theoretical and practical significance?
**Tom Davidson**: So some people have used the operationalization of AGI to superintelligence, which I do think is important and I do actually talk about that a bit. Now one reason why I didn't want to just stick with that is that, in my view, by the time we have full blown AGI that can do all tasks humans can do, things are already going to be very fast and very crazy, and maybe the main period of existential risk has actually already happened. And so it's probably missing most of the action to just focus on the speed of that transition to superintelligence. But if you think, like me, that in the run-up to AGI there will be strategically relevant warning shots, you want to have some metric so that you can more meaningfully talk about that run-up period.
The choice of 20% is pretty arbitrary. I wanted something which was more than AI doing just a few big tricks, like AI that automates driving and a couple of other similar things. I wanted it to be a big enough part of the economy that it involved multiple ‘big wins’, had an unambiguously massive impact on the world, and woke up many big actors to AI’s potential economic and strategic importance. So I wanted to go above 5%.
But I didn't want it to be so late in the game that most of the action had already happened and maybe we're already in the middle of the period of existential risk and things have already gone completely crazy. If I had chosen a startpoint where AI can do 50% or 70% of all economic tasks that would run the risk that, again, it would be too late in the day.
So 20% was me trading off between those two factors. I tried to choose a number that was high enough that AI was really a significant and pretty general phenomenon, but that was not so high that the existential risk period had already started.
I will say that if we're in a quite long timelines world, and we only slowly get to that 20% automation point over like the next 20 or 30 years, then there's a chance that the 20% threshold won’t look like AI being a big deal, because it could just look like a continuation of technological progress as normal, going at about 1% a year. So I do think that there's limitations here and I haven't thought of a good way to unambiguously choose a start point. But because most of my probability mass is in shorter timelines than that, the 20% seems like a good metric.
**Future Matters**: You draw a distinction between *capabilities* takeoff and *impact* takeoff. Could you explain those, how they might come apart and what the reason might be for looking at them separately?
**Tom Davidson**: Certainly. Capabilities takeoff speed is roughly how quickly do AI capabilities improve as we approach and surpass human level AI. So if the cleverest AI you have is insect intelligence one year, human intelligence next year, and then a month later you've got superintelligence, that's very fast capabilities takeoff. But maybe you haven't used your AI tool in the real world, so it hasn't had any impact on the world during that time: capabilities takeoff just focuses on how clever and capable AI is, aside from whether you actually use it.
Whereas impact takeoff speed is about AI's actual effect on the real world. You could have a really slow capabilities takeoff speed where AI goes up very slowly to human intelligence and beyond, and yet a very fast impact takeoff speed. For example, it might be that no one deploys AI tools, maybe due to government regulations or caution, and then at some point, AI forcibly circumvents your deployment decisions and transforms the whole world in just a few months, once it's already superintelligent. Then you've got a slow capabilities takeoff speed, but a very fast impact takeoff speed. So I think it can be useful to distinguish between those two things.
**Future Matters**: Taking a step back, you describe the overall approach you take as a ‘compute-centric framework’ for AI forecasting, building on Ajeya Cotra’s Bio Anchors report. Could you characterize what's distinctive about this framework?
**Tom Davidson**: Yes. I think the framework makes sense if you think we're going to get AGI by scaling up and improving current algorithmic approaches within the deep learning paradigm, getting further improvements to transformers, and things like that—the kind of progress we've seen over the last 10 years. What's distinctive about it is that it makes this big bold simplifying assumption, that the capability of an AI is equal to the amount of compute used to train it, multiplied by the quality of the algorithms used for training. And all kinds of algorithmic progress, the invention of the transformer, various optimizations around it, and any future architectural improvements are rolled into this parameter of the ‘quality of the algorithms used to train’ it. Then, in addition, those algorithms are assumed to improve pretty smoothly, as we put in more effort to designing and testing new algorithms. So we're assuming away the possibility of a radically new approach to AI that doesn't fit in with the recent trends where performance just seems to improve pretty smoothly, as we scale things up and discover new algorithms. Some people think that there's going to be a new algorithmic approach that will lead us to AGI and break the trends of the last 10 years, and that's very much not the tack that I'm taking here.
**Future Matters**: Could you say more about how this ‘compute centric’ assumption could turn out to be wrong? How does this affect your overall estimates?
**Tom Davidson**: You could think that there's going to be a new paradigm which massively accelerates progress. My impression is that some people, especially those belonging to the MIRI cluster of thought, think that there could be a new algorithmic approach, which can actually achieve AGI with much less compute than we're already using, or maybe comparable amounts. If that turns out to be true, then I think you can get a faster takeoff, because by the time we transition through that new paradigm, there's already a large hardware overhang, and you can quickly scale up the compute on the new approach once you realize it's working. And if these new approaches have better scaling properties than current approaches, scaling up compute is going to have pretty radical consequences. So to the extent that you put weight on that, I think it pushes towards faster takeoff and is a pretty scary world.
Another thing you could think is just that there's no existing or nearby approach that will get us all the way to AGI, which could push towards a much slower takeoff. You could have current approaches scaling up to only 50% of cognitive tasks, then we need some totally new kind of paradigm to get us all the way, and there could be a delay while we struggle to find out what that is—that could in practice cause slow takeoff. Then it's just hard to say what the dynamics would be, once we discovered that new paradigm: you can imagine takeoff being fast or slow. But either way there would be a pause before we found that new paradigm, which in some ways of measuring it would make takeoff slower. I do have some uncertainty about whether the whole cluster of current approaches will get us there at all, and that pushes me towards slower takeoff.
So uncertainty over this ‘compute centric’ assumption pushes in both directions. It makes a very fast takeoff, and a very slow takeoff, more likely than my framework predicts. But overall, for me, it probably pushes more towards faster takeoff because I find the idea that there's a new type of approach that gets us there faster or that has better scaling properties, or that there’s some other discontinuity that the compute-centric framework ignores, more plausible. So for me that uncertainty overall pushes towards faster takeoff, but certainly will increase the tails in both directions.
**Future Matters**: Within the compute-centric framework, you try to estimate two quantities. First the capabilities distance that has to be traversed during takeoff, and second the speed at which those capabilities will be acquired. Focusing on the first quantity, what are the main lines of evidence informing your estimates of the effective FLOP gap?
**Tom Davidson**: This effective FLOP gap is saying how much more effective training compute (= physical compute \* quality of training algorithms) we need to train AGI compared to AI that could automate only 20% of the economy. And there's a few different lines of evidence and none of them are very strong evidence, unfortunately. I think there's a huge amount of uncertainty in this parameter. But there are some of the things that push towards thinking that the effective FLOP gap is small.
For example, it seems like brain size has a fairly notable effect on cognitive ability. Human brain sizes differ by ±10% in each direction, and so you can look at measures of cognitive ability and how they vary by brain size. The differences aren't massive, but if you scale that up and imagine that there was a brain that was three or ten times as big, and then extrapolate those differences in cognitive ability, it seems like they'd be plausibly big enough to fully cross the effective FLOP gap. So this suggests that increasing effective training compute by 10-100X could be enough to completely cross the gap, if the scaling of AI intelligence is comparable to this extrapolated scaling of human intelligence with brain size. And there are reasons to think that AI intelligence could scale even more rapidly, because you can be increasing the amount of data that AI systems get as you scale the brain size, which doesn’t happen in humans.
And you get a similar story if you make even more strained analogies to humans and other animals. If you compare human and chimpanzee brain size, the difference isn't that big, but qualitatively there seems to be a big difference in intelligence. And again, this suggests that maybe a couple of orders of magnitude extra effective compute would be enough to make a really big difference if, again, the scaling of AI intelligence with model size is analogous to the scaling of chimp intelligence with brain size.
There's one other argument for thinking the difficulty gap could be pretty narrow, which is a bit of a subtle one. The basic argument is that, historically, the way we've automated, say, 20% or 30% of our workflows is by getting pretty dumb and narrow technologies to do the automation and then rearranging our workflows to compensate. For instance, you used to do all this paperwork and store these stacks of papers, and then with a laptop you're able to use the digital database, to replace the paper, and automate that, which saves you a lot of time. But it took decades for people to actually integrate this automation into their workflows and to change all the other aspects of their processes to get to a point where everyone is using laptops instead of pen and paper for everything. It takes a long time.
If, as some of these other arguments suggest, there could be a fairly quick transition from AI not being able to do 20% of cognitive work to being able to do 100% of it, if that's only going to happen in five years or ten years, then there just won't be time to do the standard thing we do where we rearrange the workflows to allow for partial automation. Maybe you get some AI systems which could automate 20% of your workflow if you had a couple of decades to integrate it—maybe Chat GPT is like this, maybe it could create tens of trillions of dollars in economic value if the whole economy oriented around it, which would take two decades. But in fact, if it's only going to be 10 years before we develop something like AGI, then there's just no time for ChatGPT to do that automation in practice. And so you actually need AI to be pretty advanced before it is able to automate 20% of your workflow without you having to spend a long time rearranging your workflow around it. Therefore, by the time it's able to automate 20% of your work, with minimal efforts on your part, it's actually not too far away from being able to automate everything. And that could give a reason why by the time AI is having really notable, significant impacts on people's workflows, it's actually surprisingly close to the point at which it's able to just almost fully automate their workflows. Those are for me some of the stronger arguments in favor of a small effective FLOP gap.
The main argument in favor of a larger one, for me, is just that there's such a wide variety of tasks in the economy— even in AI R&D (though to a lesser extent)—and they vary along many dimensions, like the time horizon over which they're performed, the amount of social context they require, how repeatable they are, how much it matters if you make a mistake, etc. Those differences mean that AI could be much more suited to automate some of those tasks than others, based on how similar it is to the AI training objective, how expensive it is to fine-tune AI on horizons of that length, and how much training data we have for the task. So it seems like AI would have more competitive advantages at some tasks compared with others, and that could increase the time between it being able to automate the first task and it being able to automate the last tasks.
**Future Matters**: At the end of all this, you come away with a shorter median estimate for timelines than the bio anchors model, by about ten years, despite sharing several of the key assumptions. What are the main drivers of these shortened timelines in your analysis, relative to Ajeya’s?
**Tom Davidson**: I think the main thing is the partial automation from pre-AGI systems causing a speed up, especially in AI R&D. The basic story is, the bio anchors model makes its prediction by extrapolating the trend in hardware progress and extrapolating the trend in algorithmic progress. But it's not accounting for the fact that before we get fully transformative AI, we're going to get AI which is pretty useful for doing hardware R&D and designing new chips, pretty useful for writing code for various experiments we want to run automatically, and maybe pretty useful for generating a hundred ideas for new algorithmic approaches and then critiquing those ideas and then winnowing them down to the ten most promising and then showing them to the human. And you would expect that partial automation of R&D to speed up progress on both those dimensions, both the hardware and the algorithms. In which case the bio anchors extrapolation is too conservative. One thing that I'm doing with this analysis is modeling that process whereby we train some not quite transformative but pretty good AIs and they speed up progress on the hardware and the algorithmic R&D. And that just happens more and more as we approach AGI: we get more and more acceleration from that. When I model that as best as I can, the result is that this dynamic shortens timelines by six years or so.
Probably the next biggest factor is, compared to bio anchors, expecting higher spending on the very biggest AI training runs. Once you've got AI that can readily automate 50% of the economy, for example, that's able to generate $25 trillion of value worldwide per year, assuming it was fully deployed, that's just a huge amount of value and it seems like it would be well worth spending a trillion dollars on that training run. And there is even more incentive to do that if you're being competitive with other actors who might want to get there first. And so I'm more willing than bio anchors to think that the spending on training runs could get pretty big because of this kind of dynamic. Some of the gain comes from just more economic growth, meaning there's more money around to invest in this stuff. Some of it is that you get AI to automate fabs so they can make more chips, which allows for faster scale-up. But most of it is just more willingness to spend on training runs as a fraction of world GDP.
**Future Matters**: Another factor you have pushing towards shorter timelines is this idea that we’ll be "swimming in runtime compute" by the time we’re training human-level AI systems. Could you explain this?
**Tom Davidson**: The idea there is the following. Suppose that you took the median of the bio anchors where I think AGI took 1e35 FLOP to train, that you've just done that training run and that you're going to use that FLOP you just used to train the system to run copies of the system. How many copies could you run? You're going to be able to run an ungodly number of AIs immediately, just using that training compute.
**Future Matters**: Is this ratio between the compute required for model training vs model inference relatively stable?
**Tom Davidson**: Actually, you should expect that fraction to become more extreme as you do bigger training runs. So if you double the size of a model, the compute needed to run the model doubles, but the compute needed to train it by a factor of four. If you think that you need as much compute as the bio anchors median, then you’ll be able to run *way*more copies with the training compute than you can today Bio anchors median implies you’d need about 1010 times as much compute to train AGI as the biggest public training run to date, which means you’d only need 105 times as much compute to run the model. So if the current ratio is that you can immediately run 10 million systems with your training compute, then in the future with the bio anchors median estimate, you'd be able to run 105 times as many. So instead of 10 million, it would be 1 trillion. And I think if you run the numbers, that's the kind of thing you get. And you might think this is odd: we trained AGI and now we can run 1 trillion of them. You can then maybe think that, in fact, if we wanted to match the human R&D workforce, rather than having 1 trillion AGIs, we can make do with 100 billion somewhat-less-capable-than-AGI systems. Maybe you use the kind of techniques that people are already using today, like chains of thought, or like having a hundred attempted answers to the question and then assessing them and then picking the best. Maybe there are other techniques for running your somewhat dumb AIs for ages and then combining their results in clever ways that can allow you to actually match or exceed the performance of a human worker, even if the individual AI systems are less clever than a human worker. And so the conclusion of this for me is that we could achieve full automation of, for example, R&D before we've trained any one AI system that is individually as smart as a human scientist. And we could just do that by training AIs that are a bit less smart, but being able to run so many, that cumulative output working together exceeds that of all human scientists working together.
**Future Matters**: Does this consideration generalize across the whole economy? Overall it seems like you end up kind of ‘moving’ the capabilities threshold for AGI a bit earlier, because there is this factor that always gets you a bit further than you think you are?
**Tom Davidson**: I think so. And it comes down to definitions of AGI. If you were defining AGI as 'one system can on one forward pass match the output of one human brain on one forward pass', then that takes just as much effective training compute to develop. But if your definition for AGI was something like 'AI systems collectively can outperform human brains collectively on any task' or 'AI systems collectively could fully automate this particular sector', then yes, I think that kind of AI is easier to train than I previously thought, maybe quite a bit easier. What's interesting about this is that it's a very strong argument, if you believed something like bio anchors median training requirements, and it's a less strong argument, if you had much smaller training requirements, because then you've got less of this excess runtime compute lying around. So for me, it focuses the probability mass near the lower end of the bio anchors distribution.
**Future Matters**: At the current margin, if you wanted to improve your estimates of AI takeoffs, would you focus more on (1) trying to better estimate the parameters of the current model, (2) extending the model in various directions, or (3) developing a new model altogether?
**Tom Davidson**: The one thing I'm most interested in is trying to understand how much algorithmic progress is driven by cognitive work – generating insights and thinking about how the algorithms fit together in the architectures – versus just brute experimentation. This becomes really important in the later stages of takeoff, where if everything is just driven by coming up with better ideas today, then if you extrapolate that, you think that algorithmic progress will become crazy fast as you approach full AI automation as there will be be abundant cognitive work from AI. Whereas if you think it's all about experiments, then progress can't become that crazy fast because AI automation doesn’t immediately increase the amount of physical compute you’ve got access to and it's a bit harder to really rapidly increase that. This gets at this question of time from almost full automation to superintelligence, which I think is something that is a bit under explored in the current report.
**Future Matters**: Thank you, Tom!
---
*We thank Leonardo Picón and Lyl Macalalad for editorial assistance.*
1. **[^](#fnreflz6004a8ahb)**See also our conversation with Long in [*FM#3*](https://forum.effectivealtruism.org/s/Y7rCDmxRbrrKBT9Bo/p/CictHfn8kdyupvpNK); and the 80k podcast episode [mentioned below](https://forum.effectivealtruism.org/posts/CrmE6T5A8JhkxnRzw/future-matters-8-bing-chat-ai-labs-on-safety-and-pausing#Audio___video).
2. **[^](#fnrefo3lo4s01awq)**See also coverage of the debate in [*Nature*](https://archive.is/sTzO5) [[🔉](https://pod.link/1648718500/episode/6136dbf91fe34d58f96126545250496d)]. |
daaa522c-6e78-4cda-8dd1-53ab7e24c237 | trentmkelly/LessWrong-43k | LessWrong | Covid 11/4: The After Times
The hope is that the pandemic will be fully and truly over because case counts will be sufficiently low, and vaccination rates sufficiently high, that we can all agree to move on and resume our lives.
The fear is that this will never happen. Either cases will climb back up and be sufficiently high to justify a continued emergency state, or they won’t but people will react in a nonsensical and disproportionate way to a tiny risk, forever damaging or even destroying much of our way of life.
At this point, that potential reaction is the true risk factor. Children as young as five can be vaccinated, and anyone who wants one can effectively get a booster shot. There’s no risk left in the room that is different from many other background risks we all take every day.
Meanwhile, case counts stopped declining this week outside of the South, so the strategy of ‘wait until cases are much lower’ is looking like a less promising strategy than it did before.
For you, in your life, outside of official meddling, the pandemic is over for you, if and when you decide it is over.
If you want them to, your After Times can start today.
As far as my personal life is concerned, the After Times started last week. Pandemic over. I’ll still have to flash my vaccination card and toggle my mask on and off as required, but that’s all for show. It’s over. If my building keeps requiring masks and keeps refusing to let delivery people go upstairs, that’s annoying, but so is it when one’s day sadly requires pants.
This past week I dove a bunch into the logistical situation at the Port of Long Beach, and the Tweetstorm that helped change the container stacking rule in the city. That first post was my most widely read post ever by a wide margin. I wrote a follow-up, and notice that the logistics issues seem urgent in a way that Covid issues increasingly do not seem urgent. Perhaps I can continue to work on transitioning away from a Covid focus towards a focus on things that now matter more, |
d39efb50-beaf-4066-9bd0-0cbef50dce51 | StampyAI/alignment-research-dataset/arxiv | Arxiv | Counterfactual Planning in AGI Systems
1 Introduction
---------------
Artificial General Intelligence (AGI) systems are hypothetical future
machine reasoning systems that can match or exceed the capabilities of
humans in general problem solving. While it is still unclear if AGI
systems could ever be built, we can already study AGI related risks
and potential safety mechanisms
[[Bos14](#bib.bibx4), [Rus19](#bib.bibx25), [ELH18](#bib.bibx9)].
In this paper, we introduce counterfactual planning as a design
approach for creating a range of AGI safety mechanisms.
Counterfactual planning is built around a graphical modeling system
that provides a specific vantage point on the internal construction of
machine learning based agents. This vantage point was designed to make
certain safety problems and solutions more tractable.
An AI agent is an autonomous system which is programmed to use its
sensors and actuators to achieve specific goals. A well-known risk
in using AI agents is that the agent might mispredict the results of
its own actions, causing it to take actions that produce a
disaster. The main risk driver we consider here is different. It is
the risk that an inaccurate or incomplete specification of the agent
goals produces a disaster.
Any AGI agent goal specification created by humans will likely be
somewhat inaccurate, no matter whether it is created by hand-coding or
by machine learning from selected examples
[[Hol20b](#bib.bibx16), [HMH19](#bib.bibx12)]. If one gives an even slightly
under-specified goal to a very powerful autonomous system, there is a
risk that the system may end up perfectly achieving this goal, while
also producing several unexpected and very harmful side effects. This
motivates research into AGI emergency stop buttons, interlocks which
can limit the power of the agent, and safe ways to update the goal
while the agent runs.
###
1.1 Use of natural and mathematical language
When writing about AGI systems, one can use either natural language,
mathematical notation, or a combination of both. A natural
language-only text has the advantage of being accessible to a
larger audience. Books like Superintelligence
[[Bos14](#bib.bibx4)] and Human Compatible [[Rus19](#bib.bibx25)] avoid the use of mathematical notation in the main
text, while making a clear an convincing case for the existence of
specific existential risks from AGI, even though these risks are
currently difficult to quantify.
However, natural language has several shortcomings when it is used to
explore and define specific technical solutions for managing AGI
risks. One particular problem is that it lacks the means to
accurately express the complex types of self-referencing and indirect
representation that can be present inside online machine learning
agents and their safety components. To solve this problem, we
introduce a compact graphical notation. This notation unambiguously
represents these internal details by using two diagrams: a learning world diagram and a planning world diagram.
###
1.2 AGI safety as a policy problem
Long-term AGI safety is not just a technical problem, but also a
policy problem. While technical progress on safety can sometimes be
made by leveraging a type of mathematics that is only accessible to
handful of specialists, policy progress typically requires the use of
more accessible language. Policy discussions can move faster, and
produce better and more equitable outcomes, when the description of a
proposal and its limitations can be made more accessible to all
stakeholder groups.
One specific aim of this work is to develop a comprehensive vocabulary
for describing certain AGI safety solutions, a vocabulary that is as
accessible as possible. However, the vocabulary we develop has too much
mathematical notation to be accessible to all members of any possible
stakeholder group. So the underlying assumption is that each
stakeholder group will have access to a certain basic level of
technical expertise.
At several points in the text, we have also included comments that aim
to explain and demystify the vocabulary and concerns of some specific
AGI related sub-fields in mathematics, technology, and philosophy.
###
1.3 Related work that uses counterfactuals
In the general AI/ML literature that is concerned with improving
system performance, counterfactual planning has been used to improve
performance in several application domains. See for example
[[ZJBP08](#bib.bibx29)] and [[BPQC+{}^{+}start\_FLOATSUPERSCRIPT + end\_FLOATSUPERSCRIPT13](#bib.bibx5)], where the latter is
notable because it includes an accessible discussion about computing
confidence intervals for counterfactual projections.
In the AI safety/alignment literature, there are several system
designs which add counterfactual terms to the agent’s reward function.
Examples are
[[Arm15](#bib.bibx3), [Hol20a](#bib.bibx15)] in the AGI-specific safety literature,
and [[THMT20](#bib.bibx28), [KOK+{}^{+}start\_FLOATSUPERSCRIPT + end\_FLOATSUPERSCRIPT18](#bib.bibx19)] which
consider both AI and AGI level systems.
In the literature on encoding specific human values into machine
reasoning systems, counterfactuals have been used to encode
non-discriminatory fairness towards individuals, for example in
[[KLRS17](#bib.bibx18)], and also other human moral principles
in [[PS17](#bib.bibx23)].
###
1.4 Structure of this paper
Sections 2 – 4 introduce the main elements of our graphical notation
and modeling system. Readers already familiar with Causal Influence
Diagram (CID) notation, as it is used to define agents, will be able
to skim or skip most of this material.
Sections 5 – 7 specify three example counterfactual planning agents.
These are used in the remaining sections to illustrate further aspects
of counterfactual planning. Starting from section 6.2, it should be
possible for all readers to skim or skip sections, or to read sections
in a different order.
2 Graphical Models and Mathematical Counterfactuals
----------------------------------------------------
The standard work which defines mathematical counterfactuals is the
book Causality by Judea Pearl [[Pea09](#bib.bibx22)]. This book
mainly targets an audience of applied statisticians, for example those
in the medical field, and its style of presentation is not very
accessible to a more general technical audience.
Pearl is also mainly concerned with the use of causal models as theories about the real world which can guide the interpretation of
statistical data. Much of the discussion in Causality is
about questions of statistical epistemology and decision making. In
this text, we will use causal models to construct agent
specifications, not theories about the world. When we clarify
issues of epistemology here, they tend to be different issues.
The debate among philosophers about the validity of Pearl’s
statistical epistemology is still ongoing, as is usual for such
philosophical debates. In the AGI community, where the epistemology
of machine learning is a frequent topic of discussion, this has
perhaps made the status of mathematical counterfactuals as useful and
well-defined mathematical tools more precarious than it should be.
Because of these considerations, we have written this section to avoid
any direct reference to Pearl’s definitions and explanations in
[[Pea09](#bib.bibx22)], even though at a deeper mathematical level, we
define the same system of causal models and counterfactuals.
###
2.1 Graphical world models
A world model is a mathematical model of a particular world.
This can be our real world, or an imaginary world. To make a
mathematical model into a model of a particular world, we need to
specify how some of the variables in the model relate to observable
phenomena in that world.
We introduce our graphical notation for building world models by
creating an example graphical model of a game world. In the game
world, a simple game of dice is being played. The player throws a
green die and a red die, and then computes their score by adding the
two numbers thrown.
We create the graphical game world model in thee steps:
1. 1.
We introduce three random variables
and relate them to observations we can make when the game is played
once in the game world. The variable X𝑋Xitalic\_X represents the observed
number of the green die, Y𝑌Yitalic\_Y is the red die, and S𝑆Sitalic\_S is the score.
2. 2.
We draw the diagram in figure [1](#S2.F1 "Figure 1 ‣ item 2 ‣ 2.1 Graphical world models ‣ 2 Graphical Models and Mathematical Counterfactuals ‣ Counterfactual Planning in AGI Systems").
X𝑋Xitalic\_XY𝑌Yitalic\_YS𝑆Sitalic\_S[D]delimited-[]𝐷[D][ italic\_D ][D]delimited-[]𝐷[D][ italic\_D ]sum𝑠𝑢𝑚sumitalic\_s italic\_u italic\_m
Figure 1: Graphical model of the game of dice in the game world.
3. 3.
We define the two functions that appear in the annotations
above the nodes in the diagram:
| | | |
| --- | --- | --- |
| | D(d)=(𝐢𝐟d∈{1,2,3,4,5,6}𝐭𝐡𝐞𝐧 1/6𝐞𝐥𝐬𝐞 0),sum(a,b)=a+b.𝐷𝑑𝐢𝐟𝑑123456𝐭𝐡𝐞𝐧16𝐞𝐥𝐬𝐞 0𝑠𝑢𝑚𝑎𝑏𝑎𝑏\begin{array}[]{l}D(d)=(\text{\bf if}\,d\in\{1,2,3,4,5,6\}\,\text{\mbox{\bf then}}\,1/6\,\text{\mbox{\bf else}}\,0)~{},\\[4.30554pt]
sum(a,b)=a+b~{}.\\
\end{array}start\_ARRAY start\_ROW start\_CELL italic\_D ( italic\_d ) = ( if italic\_d ∈ { 1 , 2 , 3 , 4 , 5 , 6 } then 1 / 6 else 0 ) , end\_CELL end\_ROW start\_ROW start\_CELL italic\_s italic\_u italic\_m ( italic\_a , italic\_b ) = italic\_a + italic\_b . end\_CELL end\_ROW end\_ARRAY | |
####
2.1.1 Informal interpretation of the graphical model
We can read the above graphical model as a description of how we might
build a game world simulator, a computer program that generates random
examples of game play. To compute one run of the game, the simulator
would traverse the diagram, writing an appropriate observed value into
each node, as determined by the function written above the
node. Figure [2](#S2.F2 "Figure 2 ‣ 2.1.1 Informal interpretation of the graphical model ‣ 2.1 Graphical world models ‣ 2 Graphical Models and Mathematical Counterfactuals ‣ Counterfactual Planning in AGI Systems") shows three possible simulator runs.
X𝑋Xitalic\_XY𝑌Yitalic\_YS𝑆Sitalic\_S[D]delimited-[]𝐷[D][ italic\_D ][D]delimited-[]𝐷[D][ italic\_D ]sum𝑠𝑢𝑚sumitalic\_s italic\_u italic\_mRun 1:112X𝑋Xitalic\_XY𝑌Yitalic\_YS𝑆Sitalic\_S[D]delimited-[]𝐷[D][ italic\_D ][D]delimited-[]𝐷[D][ italic\_D ]sum𝑠𝑢𝑚sumitalic\_s italic\_u italic\_mRun 2:437X𝑋Xitalic\_XY𝑌Yitalic\_YS𝑆Sitalic\_S[D]delimited-[]𝐷[D][ italic\_D ][D]delimited-[]𝐷[D][ italic\_D ]sum𝑠𝑢𝑚sumitalic\_s italic\_u italic\_mRun 3:6612
Figure 2: Using the graphical model as a canvas to display three
different simulator runs of the game world.
We can interpret the mathematical expression P(S=12)𝑃𝑆12P(S=12)italic\_P ( italic\_S = 12 ) as being the
exact probability that the next simulator run puts the number 12 into
node S𝑆Sitalic\_S. This interpretation of P(⋯)𝑃⋯P(\cdots)italic\_P ( ⋯ ) expressions can be very
useful when reasoning informally about certain mathematical properties
of the graphical models.
The similarity between what happens in figure [2](#S2.F2 "Figure 2 ‣ 2.1.1 Informal interpretation of the graphical model ‣ 2.1 Graphical world models ‣ 2 Graphical Models and Mathematical Counterfactuals ‣ Counterfactual Planning in AGI Systems") and
what happens in a spreadsheet calculation is not entirely
coincidental. Spreadsheets can be used to create models and
simulations without having to write a full computer program from
scratch.
####
2.1.2 Formal interpretation of the graphical model
In section [2.4](#S2.SS4 "2.4 Formal definitions ‣ 2 Graphical Models and Mathematical Counterfactuals ‣ Counterfactual Planning in AGI Systems"), we will define the exact mathematical
meaning of drawing diagrams like figure [1](#S2.F1 "Figure 1 ‣ item 2 ‣ 2.1 Graphical world models ‣ 2 Graphical Models and Mathematical Counterfactuals ‣ Counterfactual Planning in AGI Systems"). The
definitions will treat the drawing as a Bayesian network, decorated
with three annotations written above the network nodes. As an example
of how these definitions work, drawing the diagram in figure
[1](#S2.F1 "Figure 1 ‣ item 2 ‣ 2.1 Graphical world models ‣ 2 Graphical Models and Mathematical Counterfactuals ‣ Counterfactual Planning in AGI Systems") is equivalent to writing down the four equations
below, and declaring that these equations are mathematical sentences
with the truth value of ‘true’.
| | | |
| --- | --- | --- |
| | P(X=x,Y=y,S=s)=P(x=X)P(Y=y)P(S=s|X=x,Y=y)P(X=x)=D(x)P(Y=y)=D(y)P(S=s|X=x,Y=y)=(𝐢𝐟s=sum(x,y)𝐭𝐡𝐞𝐧 1𝐞𝐥𝐬𝐞 0)\begin{array}[]{l}P(X=x,Y=y,S=s)=P(x=X)P(Y=y)P(S=s|X=x,Y=y)\\
P(X=x)=D(x)\\
P(Y=y)=D(y)\\
P(S=s|X=x,Y=y)=(\text{\bf if}\,s=sum(x,y)\,\text{\mbox{\bf then}}\,1\,\text{\mbox{\bf else}}\,0)\end{array}start\_ARRAY start\_ROW start\_CELL italic\_P ( italic\_X = italic\_x , italic\_Y = italic\_y , italic\_S = italic\_s ) = italic\_P ( italic\_x = italic\_X ) italic\_P ( italic\_Y = italic\_y ) italic\_P ( italic\_S = italic\_s | italic\_X = italic\_x , italic\_Y = italic\_y ) end\_CELL end\_ROW start\_ROW start\_CELL italic\_P ( italic\_X = italic\_x ) = italic\_D ( italic\_x ) end\_CELL end\_ROW start\_ROW start\_CELL italic\_P ( italic\_Y = italic\_y ) = italic\_D ( italic\_y ) end\_CELL end\_ROW start\_ROW start\_CELL italic\_P ( italic\_S = italic\_s | italic\_X = italic\_x , italic\_Y = italic\_y ) = ( if italic\_s = italic\_s italic\_u italic\_m ( italic\_x , italic\_y ) then 1 else 0 ) end\_CELL end\_ROW end\_ARRAY | |
The first equation above is produced by drawing the Bayesian network
graph, the other three are produced by adding the annotations.
To readers unfamiliar with Bayesian networks, the above equations may
look somewhat impenetrable at first sight. The key to interpreting
them is to note that the three right hand side terms of the first
equation appear on the left hand side in the next equations.
The equations therefore allow us to mechanically compute the
exact numerical value of P(X=x,Y=y,S=s)𝑃formulae-sequence𝑋𝑥formulae-sequence𝑌𝑦𝑆𝑠P(X=x,Y=y,S=s)italic\_P ( italic\_X = italic\_x , italic\_Y = italic\_y , italic\_S = italic\_s ) for any x𝑥xitalic\_x, y𝑦yitalic\_y, and s𝑠sitalic\_s,
by making substitutions until every P𝑃Pitalic\_P operator is gone. We can
compute that P(X=1,Y=1,S=12)=0𝑃formulae-sequence𝑋1formulae-sequence𝑌1𝑆120P(X=1,Y=1,S=12)=0italic\_P ( italic\_X = 1 , italic\_Y = 1 , italic\_S = 12 ) = 0. We can compute that P(S=12)=1/36𝑃𝑆12136P(S=12)=1/36italic\_P ( italic\_S = 12 ) = 1 / 36
by using that P(S=12)=∑x,yP(X=x,Y=y,S=12)𝑃𝑆12subscript𝑥𝑦𝑃formulae-sequence𝑋𝑥formulae-sequence𝑌𝑦𝑆12P(S=12)=\sum\_{x,y}P(X=x,Y=y,S=12)italic\_P ( italic\_S = 12 ) = ∑ start\_POSTSUBSCRIPT italic\_x , italic\_y end\_POSTSUBSCRIPT italic\_P ( italic\_X = italic\_x , italic\_Y = italic\_y , italic\_S = 12 ).
A mathematical model can be used as a theory about a world, but
it can also be used as a specification of how certain entities
in that world are supposed to behave. If the model is a theory of the
game world, and we observe the outcome X=1,Y=1,S=12formulae-sequence𝑋1formulae-sequence𝑌1𝑆12X=1,Y=1,S=12italic\_X = 1 , italic\_Y = 1 , italic\_S = 12, then this
observation falsifies the theory. But if the model is a specification
of the game, then the same observation implies that the player is
doing it wrong.
###
2.2 Counterfactuals
We now show how mathematical counterfactuals can be defined using
graphical models. The process is as follows. We start by drawing a
first diagram f𝑓fitalic\_f, and declare that this f𝑓fitalic\_f is the world model of a
factual world. This factual world may be the real world, but
also an imaginary world, or the world inside a simulator. We then draw
a second diagram c𝑐citalic\_c by taking f𝑓fitalic\_f and making some modifications. We
then posit that this c𝑐citalic\_c defines a counterfactual world. The
counterfactual random variables defined by c𝑐citalic\_c then represent
observations we can make in this counterfactual world.
Figure [3](#S2.F3 "Figure 3 ‣ 2.2 Counterfactuals ‣ 2 Graphical Models and Mathematical Counterfactuals ‣ Counterfactual Planning in AGI Systems") shows an example of the procedure, where we
construct a counterfactual game world in which the red die has the
number 6 on all sides.
X𝑋Xitalic\_XY𝑌Yitalic\_YS𝑆Sitalic\_S[D]delimited-[]𝐷[D][ italic\_D ][D]delimited-[]𝐷[D][ italic\_D ]sum𝑠𝑢𝑚sumitalic\_s italic\_u italic\_m(f)
factual world model
X𝑋Xitalic\_XY𝑌Yitalic\_YS𝑆Sitalic\_S[D]delimited-[]𝐷[D][ italic\_D ]6666sum𝑠𝑢𝑚sumitalic\_s italic\_u italic\_m(c)
counterfactual world model
Figure 3: Example construction of a counterfactual
world, with the model c𝑐citalic\_c on the right defining three counterfactual
random variables Xcsubscript𝑋𝑐X\_{c}italic\_X start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT,
Ycsubscript𝑌𝑐Y\_{c}italic\_Y start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT, and Scsubscript𝑆𝑐S\_{c}italic\_S start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT.
We name diagrams by putting a label in the upper left hand corner. In
figure [3](#S2.F3 "Figure 3 ‣ 2.2 Counterfactuals ‣ 2 Graphical Models and Mathematical Counterfactuals ‣ Counterfactual Planning in AGI Systems"), the two labels (f) and (c)
introduce the names f𝑓fitalic\_f and c𝑐citalic\_c. We will use the name in the label
for both the diagram, the implied world model, and the implied world.
So figure [3](#S2.F3 "Figure 3 ‣ 2.2 Counterfactuals ‣ 2 Graphical Models and Mathematical Counterfactuals ‣ Counterfactual Planning in AGI Systems") constructs the counterfactual game world
c𝑐citalic\_c.
To keep the random variables defined by the above two diagrams apart,
we use the notation convention that a diagram named c𝑐citalic\_c defines random
variables that all have the subscript c𝑐citalic\_c. Diagram c𝑐citalic\_c above
defines the random variables Xcsubscript𝑋𝑐X\_{c}italic\_X start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT, Ycsubscript𝑌𝑐Y\_{c}italic\_Y start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT, and Scsubscript𝑆𝑐S\_{c}italic\_S start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT. This convention
allows us to write expressions like P(Sc>Sf)=5/6𝑃subscript𝑆𝑐subscript𝑆𝑓56P(S\_{c}>S\_{f})=5/6italic\_P ( italic\_S start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT > italic\_S start\_POSTSUBSCRIPT italic\_f end\_POSTSUBSCRIPT ) = 5 / 6 without
ambiguity.
###
2.3 Example model of an agent and its environment
Diagram d𝑑ditalic\_d in figure [4](#S2.F4 "Figure 4 ‣ 2.3 Example model of an agent and its environment ‣ 2 Graphical Models and Mathematical Counterfactuals ‣ Counterfactual Planning in AGI Systems") models a basic MDP-style agent and
its environment. The agent takes actions Atsubscript𝐴𝑡A\_{t}italic\_A start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT chosen by the policy
π𝜋\piitalic\_π, with actions affecting the subsequent states St+1subscript𝑆𝑡1S\_{t+1}italic\_S start\_POSTSUBSCRIPT italic\_t + 1 end\_POSTSUBSCRIPT of the
agent’s environment. The environment state is s0subscript𝑠0s\_{0}italic\_s start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT initially, and
state transitions are driven by the probability density function S𝑆Sitalic\_S.
S0subscript𝑆0S\_{0}italic\_S start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTA0subscript𝐴0A\_{0}italic\_A start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTs0subscript𝑠0s\_{0}italic\_s start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTπ𝜋\piitalic\_πS1subscript𝑆1S\_{1}italic\_S start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPTA1subscript𝐴1A\_{1}italic\_A start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT[S]delimited-[]𝑆[S][ italic\_S ]π𝜋\piitalic\_πS2subscript𝑆2S\_{2}italic\_S start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPTA2subscript𝐴2A\_{2}italic\_A start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT[S]delimited-[]𝑆[S][ italic\_S ]π𝜋\piitalic\_πS3subscript𝑆3S\_{3}italic\_S start\_POSTSUBSCRIPT 3 end\_POSTSUBSCRIPT[S]delimited-[]𝑆[S][ italic\_S ]…(d)
Figure 4: Example diagram d𝑑ditalic\_d modeling an agent and its environment.
We interpret the annotations above the nodes in the diagram as model input parameters. The model d𝑑ditalic\_d has the three input parameters
π𝜋\piitalic\_π, s0subscript𝑠0s\_{0}italic\_s start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT, and S𝑆Sitalic\_S. By writing exactly the same parameter above a
whole time series of nodes, we are in fact adding significant
constraints to the behavior of both the agent and the agent
environment in the model. These constraints apply even if we specify
nothing further about π𝜋\piitalic\_π and S𝑆Sitalic\_S.
We use the convention that the physical realizations of the agent’s
sensors and actuators are modeled inside the environment states Stsubscript𝑆𝑡S\_{t}italic\_S start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT.
This means that we can interpret the arrows to the Atsubscript𝐴𝑡A\_{t}italic\_A start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT nodes as
sensor signals which flow into the agent’s compute core, and the arrows
emerging from the Atsubscript𝐴𝑡A\_{t}italic\_A start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT nodes as actuator command signals which flow
out.
###
2.4 Formal definitions
We now present fully formal definitions for the graphical
language and notation conventions introduced above. The main reason
for including these is that we want to remove any possible ambiguity
from the agent definitions further below.
####
2.4.1 Diagrams
######
Definition 1 (Diagram).
A diagram is a drawing that depicts a graph, which must be a
directed acyclic graph, by drawing nodes connected by arrows. A node name, starting with an uppercase letter, must be drawn inside
each node. A node may also have an annotation drawn above it.
Drawings may use the notation ‘⋯⋯\cdots⋯’ to depict repeating
structures in the graph and its annotations.
####
2.4.2 Random variables and the P𝑃Pitalic\_P notation
We use random variables to represent observables in worlds. We rely on
probability theory (see appendix [A](#A1 "Appendix A Random Variables and the 𝑃 Notation ‣ Counterfactual Planning in AGI Systems")) as the branch of
mathematics that defines truth values for expressions containing random
variables inside P(⋯)𝑃⋯P(\cdots)italic\_P ( ⋯ ) and 𝔼(⋯)𝔼⋯\mathbb{E}(\cdots)blackboard\_E ( ⋯ ) operators.
Many texts use the convention that P(s|x,y)𝑃conditional𝑠𝑥𝑦P(s|x,y)italic\_P ( italic\_s | italic\_x , italic\_y ) is a
shorthand for P(S=s|X=x,Y=y)P(S=s|X=x,Y=y)italic\_P ( italic\_S = italic\_s | italic\_X = italic\_x , italic\_Y = italic\_y ). We avoid using this shorthand here,
partly to make the definitions below less cryptic, but also because it
tends to get typographically awkward when the random variables have
subscripted names.
######
Definition 2 (Naming and subscripting of random variables).
When the graph drawn by a diagram with label (d) has a node
named X𝑋Xitalic\_X or Xisubscript𝑋𝑖X\_{i}italic\_X start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT, then there exists a random variable named Xdsubscript𝑋𝑑X\_{d}italic\_X start\_POSTSUBSCRIPT italic\_d end\_POSTSUBSCRIPT or
Xi,dsubscript𝑋𝑖𝑑X\_{i,d}italic\_X start\_POSTSUBSCRIPT italic\_i , italic\_d end\_POSTSUBSCRIPT associated with that node. To avoid any ambiguity, we use
a comma to separate the two parts of the subscript in Xi,dsubscript𝑋𝑖𝑑X\_{i,d}italic\_X start\_POSTSUBSCRIPT italic\_i , italic\_d end\_POSTSUBSCRIPT.
####
2.4.3 Equations produced by drawing a diagram
Before defining the equations produced by drawing a diagram, we
define some auxiliary notation.
######
Definition 3 (Parent notation Pa and pa).
Let X𝑋Xitalic\_X be the name of a graph node in diagram d𝑑ditalic\_d, and let
P1,⋯,Pnsubscript𝑃1⋯subscript𝑃𝑛P\_{1},\cdots,P\_{n}italic\_P start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT , ⋯ , italic\_P start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT be the list of names of all parent nodes of X𝑋Xitalic\_X,
all nodes which have an outgoing arrow into X𝑋Xitalic\_X. The order in which
these parents appear in the list P1,⋯,Pnsubscript𝑃1⋯subscript𝑃𝑛P\_{1},\cdots,P\_{n}italic\_P start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT , ⋯ , italic\_P start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT is determined by
considering each incoming arrow of X𝑋Xitalic\_X in a clockwise order, starting
from the 6-o-clock position. With this, 𝐏𝐚X,dsubscript𝐏𝐚𝑋𝑑\textbf{Pa}\_{X,d}Pa start\_POSTSUBSCRIPT italic\_X , italic\_d end\_POSTSUBSCRIPT is the list of
random variable names P1,d,⋯,Pn,dsubscript𝑃1𝑑⋯subscript𝑃𝑛𝑑P\_{1,d},\cdots,P\_{n,d}italic\_P start\_POSTSUBSCRIPT 1 , italic\_d end\_POSTSUBSCRIPT , ⋯ , italic\_P start\_POSTSUBSCRIPT italic\_n , italic\_d end\_POSTSUBSCRIPT, and 𝐩𝐚X,dsubscript𝐩𝐚𝑋𝑑\textbf{pa}\_{X,d}pa start\_POSTSUBSCRIPT italic\_X , italic\_d end\_POSTSUBSCRIPT is the
list of lowercase variables names we get by converting the list
P1,⋯,Pnsubscript𝑃1⋯subscript𝑃𝑛P\_{1},\cdots,P\_{n}italic\_P start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT , ⋯ , italic\_P start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT to lowercase.
As an example, with figure [4](#S2.F4 "Figure 4 ‣ 2.3 Example model of an agent and its environment ‣ 2 Graphical Models and Mathematical Counterfactuals ‣ Counterfactual Planning in AGI Systems") above, 𝐏𝐚S2,dsubscript𝐏𝐚subscript𝑆2𝑑\textbf{Pa}\_{S\_{2},d}Pa start\_POSTSUBSCRIPT italic\_S start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT , italic\_d end\_POSTSUBSCRIPT is the list
S1,d,A1,dsubscript𝑆1𝑑subscript𝐴1𝑑S\_{1,d},A\_{1,d}italic\_S start\_POSTSUBSCRIPT 1 , italic\_d end\_POSTSUBSCRIPT , italic\_A start\_POSTSUBSCRIPT 1 , italic\_d end\_POSTSUBSCRIPT, and 𝐩𝐚S2,dsubscript𝐩𝐚subscript𝑆2𝑑\textbf{pa}\_{S\_{2},d}pa start\_POSTSUBSCRIPT italic\_S start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT , italic\_d end\_POSTSUBSCRIPT is the list s1,a1subscript𝑠1subscript𝑎1s\_{1},a\_{1}italic\_s start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT , italic\_a start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT.
######
Definition 4 (Bayesian model equation produced by drawing a diagram).
When we draw a diagram d𝑑ditalic\_d representing a graph with the nodes named
X1,⋯Xnsubscript𝑋1⋯subscript𝑋𝑛X\_{1},\cdots X\_{n}italic\_X start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT , ⋯ italic\_X start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT, this is equivalent to stating that the following
equation is true:
| | | |
| --- | --- | --- |
| | P(X1,d=x1,⋯,Xn,d=xn)=P(X1,d=x1|𝐏𝐚X1,d=𝐩𝐚X1,d)⋅…⋅P(Xn,d=xn|𝐏𝐚Xn,d=𝐩𝐚Xn,d)𝑃formulae-sequencesubscript𝑋1𝑑subscript𝑥1⋯subscript𝑋𝑛𝑑subscript𝑥𝑛absent⋅𝑃subscript𝑋1𝑑conditionalsubscript𝑥1subscript𝐏𝐚subscript𝑋1𝑑subscript𝐩𝐚subscript𝑋1𝑑…𝑃subscript𝑋𝑛𝑑conditionalsubscript𝑥𝑛subscript𝐏𝐚subscript𝑋𝑛𝑑subscript𝐩𝐚subscript𝑋𝑛𝑑\begin{array}[]{l}P(X\_{1,d}=x\_{1},\cdots,X\_{n,d}=x\_{n})=\\[4.30554pt]
~{}~{}~{}~{}~{}~{}~{}P(X\_{1,d}=x\_{1}|\textbf{Pa}\_{X\_{1},d}=\textbf{pa}\_{X\_{1},d})\cdot~{}\ldots~{}\cdot P(X\_{n,d}=x\_{n}|\textbf{Pa}\_{X\_{n},d}=\textbf{pa}\_{X\_{n},d})\end{array}start\_ARRAY start\_ROW start\_CELL italic\_P ( italic\_X start\_POSTSUBSCRIPT 1 , italic\_d end\_POSTSUBSCRIPT = italic\_x start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT , ⋯ , italic\_X start\_POSTSUBSCRIPT italic\_n , italic\_d end\_POSTSUBSCRIPT = italic\_x start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT ) = end\_CELL end\_ROW start\_ROW start\_CELL italic\_P ( italic\_X start\_POSTSUBSCRIPT 1 , italic\_d end\_POSTSUBSCRIPT = italic\_x start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT | Pa start\_POSTSUBSCRIPT italic\_X start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT , italic\_d end\_POSTSUBSCRIPT = pa start\_POSTSUBSCRIPT italic\_X start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT , italic\_d end\_POSTSUBSCRIPT ) ⋅ … ⋅ italic\_P ( italic\_X start\_POSTSUBSCRIPT italic\_n , italic\_d end\_POSTSUBSCRIPT = italic\_x start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT | Pa start\_POSTSUBSCRIPT italic\_X start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT , italic\_d end\_POSTSUBSCRIPT = pa start\_POSTSUBSCRIPT italic\_X start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT , italic\_d end\_POSTSUBSCRIPT ) end\_CELL end\_ROW end\_ARRAY | |
######
Definition 5 (Equation produced by adding an annotation).
When we draw an annotation above a node X𝑋Xitalic\_X in a diagram d𝑑ditalic\_d, then:
1. 1.
If the node has no parents and the annotation is a variable or
constant v𝑣vitalic\_v, this is equivalent to stating that the following
equation is true:
P(Xd=x)=(𝐢𝐟x=v𝐭𝐡𝐞𝐧 1𝐞𝐥𝐬𝐞 0)𝑃subscript𝑋𝑑𝑥𝐢𝐟𝑥𝑣𝐭𝐡𝐞𝐧1𝐞𝐥𝐬𝐞 0P(X\_{d}=x)=(\text{\bf if}\,x=v\,\text{\mbox{\bf then}}\,1\,\text{\mbox{\bf else}}\,0)italic\_P ( italic\_X start\_POSTSUBSCRIPT italic\_d end\_POSTSUBSCRIPT = italic\_x ) = ( if italic\_x = italic\_v then 1 else 0 )
2. 2.
If the node has parents and the annotation is a function f𝑓fitalic\_f,
this states
P(Xd=x|𝐏𝐚X,d=𝐩𝐚X,d)=(𝐢𝐟x=f(𝐩𝐚X,d)𝐭𝐡𝐞𝐧 1𝐞𝐥𝐬𝐞 0)𝑃subscript𝑋𝑑conditional𝑥subscript𝐏𝐚
𝑋𝑑subscript𝐩𝐚
𝑋𝑑𝐢𝐟𝑥𝑓subscript𝐩𝐚
𝑋𝑑𝐭𝐡𝐞𝐧1𝐞𝐥𝐬𝐞 0P(X\_{d}=x|\textbf{Pa}\_{X,d}=\textbf{pa}\_{X,d})=(\text{\bf if}\,x=f(\textbf{pa}\_{X,d})\,\text{\mbox{\bf then}}\,1\,\text{\mbox{\bf else}}\,0)italic\_P ( italic\_X start\_POSTSUBSCRIPT italic\_d end\_POSTSUBSCRIPT = italic\_x | Pa start\_POSTSUBSCRIPT italic\_X , italic\_d end\_POSTSUBSCRIPT = pa start\_POSTSUBSCRIPT italic\_X , italic\_d end\_POSTSUBSCRIPT ) = ( if italic\_x = italic\_f ( pa start\_POSTSUBSCRIPT italic\_X , italic\_d end\_POSTSUBSCRIPT ) then 1 else 0 )
3. 3.
If the node has parents and the annotation is [F]delimited-[]𝐹[F][ italic\_F ],
this states
P(Xd=x|𝐏𝐚X,d=𝐩𝐚X,d)=F(x,𝐩𝐚X,d)𝑃subscript𝑋𝑑conditional𝑥subscript𝐏𝐚
𝑋𝑑subscript𝐩𝐚
𝑋𝑑𝐹𝑥subscript𝐩𝐚
𝑋𝑑P(X\_{d}=x|\textbf{Pa}\_{X,d}=\textbf{pa}\_{X,d})=F(x,\textbf{pa}\_{X,d})italic\_P ( italic\_X start\_POSTSUBSCRIPT italic\_d end\_POSTSUBSCRIPT = italic\_x | Pa start\_POSTSUBSCRIPT italic\_X , italic\_d end\_POSTSUBSCRIPT = pa start\_POSTSUBSCRIPT italic\_X , italic\_d end\_POSTSUBSCRIPT ) = italic\_F ( italic\_x , pa start\_POSTSUBSCRIPT italic\_X , italic\_d end\_POSTSUBSCRIPT )
where we require that the function F𝐹Fitalic\_F satisfies
∀𝐩𝐚X,d(∑xF(x,𝐩𝐚X,d)=1)subscriptfor-allsubscript𝐩𝐚
𝑋𝑑subscript𝑥𝐹𝑥subscript𝐩𝐚
𝑋𝑑1\forall\_{\textbf{pa}\_{X,d}}(\sum\_{x}F(x,\textbf{pa}\_{X,d})=1)∀ start\_POSTSUBSCRIPT pa start\_POSTSUBSCRIPT italic\_X , italic\_d end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT ( ∑ start\_POSTSUBSCRIPT italic\_x end\_POSTSUBSCRIPT italic\_F ( italic\_x , pa start\_POSTSUBSCRIPT italic\_X , italic\_d end\_POSTSUBSCRIPT ) = 1 ).
###
2.5 Differences with other notation conventions
The do notation is Pearl’s most well-known device for defining
counterfactuals in a compact way. We do not use this notation here,
because it is not well suited for defining the complex counterfactual
worlds we are interested in.
Pearl also defines a less well known notation in [[Pea09](#bib.bibx22)],
where subscripts are used to construct and label counterfactual random
variables. This notation is different from the subscripting
conventions used here.
Many texts use the convention of introducing a model by writing down a
tuple like (S,s0,A,P,R,γ)𝑆subscript𝑠0𝐴𝑃𝑅𝛾(S,s\_{0},A,P,R,\gamma)( italic\_S , italic\_s start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT , italic\_A , italic\_P , italic\_R , italic\_γ ) which names all model parameters.
We do not use this convention here. We introduce every model by
drawing a diagram, and name model parameters by drawing annotations in
the diagram. This approach keeps several definitions in this text
much more compact, as we avoid having to translate back and forth
continuously between a graphical model representation and a
tuple-based representation.
3 Causal Influence Diagrams
----------------------------
Influence diagrams [[HM05](#bib.bibx10)] provide a graphical
notation for depicting utility-maximizing decision making processes.
In this paper we will use Causal influence diagrams (CIDs)
[[ECL+{}^{+}start\_FLOATSUPERSCRIPT + end\_FLOATSUPERSCRIPT21](#bib.bibx6)], a specific version of influence diagram notation
which has recently been proposed [[EKKL19](#bib.bibx8)] for modeling and
comparing AGI safety frameworks.
S0subscript𝑆0S\_{0}italic\_S start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTA0subscript𝐴0A\_{0}italic\_A start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTs0subscript𝑠0s\_{0}italic\_s start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTπ\*superscript𝜋\pi^{\*}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPTS1subscript𝑆1S\_{1}italic\_S start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPTA1subscript𝐴1A\_{1}italic\_A start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT[S]delimited-[]𝑆[S][ italic\_S ]π\*superscript𝜋\pi^{\*}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPTS2subscript𝑆2S\_{2}italic\_S start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPTA2subscript𝐴2A\_{2}italic\_A start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT[S]delimited-[]𝑆[S][ italic\_S ]π\*superscript𝜋\pi^{\*}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPTS3subscript𝑆3S\_{3}italic\_S start\_POSTSUBSCRIPT 3 end\_POSTSUBSCRIPT[S]delimited-[]𝑆[S][ italic\_S ]…(a)R0subscript𝑅0R\_{0}italic\_R start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTR𝑅~{}Ritalic\_RR1subscript𝑅1R\_{1}italic\_R start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPTR𝑅~{}Ritalic\_RR2subscript𝑅2R\_{2}italic\_R start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPTR𝑅~{}Ritalic\_R
Figure 5: Example causal influence diagram. The diagram has
diamond shaped utility nodes which define the value 𝒰asubscript𝒰𝑎\mathcal{U}\_{a}caligraphic\_U start\_POSTSUBSCRIPT italic\_a end\_POSTSUBSCRIPT,
and square decision nodes which define π\*superscript𝜋\pi^{\*}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT. Optionally, colors
can be used to highlight the structure of the diagram.
An example causal influence diagram is in figure [5](#S3.F5 "Figure 5 ‣ 3 Causal Influence Diagrams ‣ Counterfactual Planning in AGI Systems").
Our formal definitions of causal influence diagram notation extend the
definitions in [[ECL+{}^{+}start\_FLOATSUPERSCRIPT + end\_FLOATSUPERSCRIPT21](#bib.bibx6)]: we also define multi-action
diagrams, and we add a time discount factor γ𝛾\gammaitalic\_γ.
###
3.1 Utility nodes defining expected utility
If some nodes in a diagram are drawn with diamond shapes, these are
called utility nodes. The expected utility of the diagram
is then defined as follows.
######
Definition 6 (Expected utility 𝒰asubscript𝒰𝑎\mathcal{U}\_{a}caligraphic\_U start\_POSTSUBSCRIPT italic\_a end\_POSTSUBSCRIPT of a diagram a𝑎aitalic\_a).
We define 𝒰asubscript𝒰𝑎\mathcal{U}\_{a}caligraphic\_U start\_POSTSUBSCRIPT italic\_a end\_POSTSUBSCRIPT for two cases:
1. 1.
If there is only one utility node X𝑋Xitalic\_X in a𝑎aitalic\_a, then 𝒰a=𝔼(Xa)subscript𝒰𝑎𝔼subscript𝑋𝑎\mathcal{U}\_{a}=\mathbb{E}(X\_{a})caligraphic\_U start\_POSTSUBSCRIPT italic\_a end\_POSTSUBSCRIPT = blackboard\_E ( italic\_X start\_POSTSUBSCRIPT italic\_a end\_POSTSUBSCRIPT ).
2. 2.
If there are multiple utility nodes Rtsubscript𝑅𝑡R\_{t}italic\_R start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT in a𝑎aitalic\_a, with integer
subscripts running from l𝑙litalic\_l to hℎhitalic\_h, then
| | | |
| --- | --- | --- |
| | 𝒰a=𝔼(∑t=lhγtRt,a)subscript𝒰𝑎𝔼superscriptsubscript𝑡𝑙ℎsuperscript𝛾𝑡subscript𝑅
𝑡𝑎\mathcal{U}\_{a}=\mathbb{E}(~{}\sum\_{t=l}^{h}~{}\gamma^{t}R\_{t,a}~{})caligraphic\_U start\_POSTSUBSCRIPT italic\_a end\_POSTSUBSCRIPT = blackboard\_E ( ∑ start\_POSTSUBSCRIPT italic\_t = italic\_l end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT italic\_h end\_POSTSUPERSCRIPT italic\_γ start\_POSTSUPERSCRIPT italic\_t end\_POSTSUPERSCRIPT italic\_R start\_POSTSUBSCRIPT italic\_t , italic\_a end\_POSTSUBSCRIPT ) | |
where γ𝛾\gammaitalic\_γ is a time discount factor, 0<γ≤10𝛾10<\gamma\leq 10 < italic\_γ ≤ 1, which
can be read as an extra model parameter.
When h=∞ℎh=\inftyitalic\_h = ∞, we generally need γ<1𝛾1\gamma<1italic\_γ < 1 in order for 𝒰asubscript𝒰𝑎\mathcal{U}\_{a}caligraphic\_U start\_POSTSUBSCRIPT italic\_a end\_POSTSUBSCRIPT
to be well-defined.
###
3.2 Decision nodes defining the optimal policy
When we draw some nodes in a diagram as squares, these are called decision nodes. The purpose of drawing decision nodes is to define
the optimal policy which maximizes the expected utility of the
diagram. We require that the same model parameter, the policy
function π\*superscript𝜋\pi^{\*}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT in the case of figure [5](#S3.F5 "Figure 5 ‣ 3 Causal Influence Diagrams ‣ Counterfactual Planning in AGI Systems"), is present as
an annotation above all decision nodes.
######
Definition 7 (Optimal policy π\*superscript𝜋\pi^{\*}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT defined by a diagram a𝑎aitalic\_a).
A diagram a𝑎aitalic\_a with some utility and decision modes, where a function
π\*superscript𝜋\pi^{\*}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT is written above all decision nodes, defines this π\*superscript𝜋\pi^{\*}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT in
two steps.
1. 1.
First, draw a helper diagram b𝑏bitalic\_b by drawing a copy of
diagram a𝑎aitalic\_a, except that every decision node has been drawn as a round
node, and every π\*superscript𝜋\pi^{\*}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT has been replaced by a fresh function name,
say π′superscript𝜋′\pi^{\prime}italic\_π start\_POSTSUPERSCRIPT ′ end\_POSTSUPERSCRIPT.
2. 2.
Then, π\*superscript𝜋\pi^{\*}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT is defined by
π\*=argmaxπ′𝒰bsuperscript𝜋subscriptargmaxsuperscript𝜋′subscript𝒰𝑏\pi^{\*}=\operatorname\*{argmax}\_{\pi^{\prime}}~{}\mathcal{U}\_{b}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT = roman\_argmax start\_POSTSUBSCRIPT italic\_π start\_POSTSUPERSCRIPT ′ end\_POSTSUPERSCRIPT end\_POSTSUBSCRIPT caligraphic\_U start\_POSTSUBSCRIPT italic\_b end\_POSTSUBSCRIPT, where the argmaxπ′subscriptargmaxsuperscript𝜋′\operatorname\*{argmax}\_{\pi^{\prime}}roman\_argmax start\_POSTSUBSCRIPT italic\_π start\_POSTSUPERSCRIPT ′ end\_POSTSUPERSCRIPT end\_POSTSUBSCRIPT operator always
deterministically returns the same function if there are several
candidates that maximize its argument.
####
3.2.1 Approximately optimal policies
In a real life agent implementation, the exact computation of the
optimal policy π\*superscript𝜋\pi^{\*}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT is usually intractable. Only an approximately
optimal policy π+superscript𝜋\pi^{+}italic\_π start\_POSTSUPERSCRIPT + end\_POSTSUPERSCRIPT can be computed within reasonable time. We
model this case as follows.
######
Definition 8 (Approximately optimal policy π+superscript𝜋\pi^{+}italic\_π start\_POSTSUPERSCRIPT + end\_POSTSUPERSCRIPT defined by a
diagram a𝑎aitalic\_a).
A diagram a𝑎aitalic\_a where an optimal policy function π\*superscript𝜋\pi^{\*}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT is
written above all decision nodes also defines an approximately optimal
policy function π+superscript𝜋\pi^{+}italic\_π start\_POSTSUPERSCRIPT + end\_POSTSUPERSCRIPT by constructing the same helper diagram b𝑏bitalic\_b
as above and then defining π+=𝒜(b)superscript𝜋𝒜𝑏\pi^{+}=\mathcal{A}(b)italic\_π start\_POSTSUPERSCRIPT + end\_POSTSUPERSCRIPT = caligraphic\_A ( italic\_b ), where the
function 𝒜𝒜\mathcal{A}caligraphic\_A processes the diagram b𝑏bitalic\_b and its model
parameter values to construct a policy π′superscript𝜋′\pi^{\prime}italic\_π start\_POSTSUPERSCRIPT ′ end\_POSTSUPERSCRIPT that does a reasonable
job at maximizing the value of 𝒰bsubscript𝒰𝑏\mathcal{U}\_{b}caligraphic\_U start\_POSTSUBSCRIPT italic\_b end\_POSTSUBSCRIPT.
To keep the presentation more compact, we will only use the optimal
policy symbol π\*superscript𝜋\pi^{\*}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT in the agent definitions below.
4 Online Machine Learning
--------------------------
We now model online machine learning agents, agents that
continuously learn while they take actions. These agents are also
often called reinforcement learners, see section
[10.3](#S10.SS3 "10.3 Reinforcement Learning ‣ 10 Machine Learning Variants and Extensions ‣ Counterfactual Planning in AGI Systems") for a discussion which relates our modeling system to
reinforcement learning concepts and terminology.
We model online machine learning agents by drawing two diagrams, one
for a learning world and one for a planning world, and by
writing down an agent definition.
This two-diagram modeling approach departs from the approach in
[[EKKL19](#bib.bibx8), [EH19](#bib.bibx7), [ECL+{}^{+}start\_FLOATSUPERSCRIPT + end\_FLOATSUPERSCRIPT21](#bib.bibx6)], where only a single
CID is used to model an entire agent. By using two diagrams instead
of one, we can graphically represent details
which remain hidden from view when using only a single CID.
###
4.1 Learning world
Figure [6](#S4.F6 "Figure 6 ‣ 4.1 Learning world ‣ 4 Online Machine Learning ‣ Counterfactual Planning in AGI Systems") shows an example learning world diagram. The
diagram models how the agent interacts with its environment, and how
the agent accumulates an observational record Otsubscript𝑂𝑡O\_{t}italic\_O start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT that will
inform its learning system, thereby influencing the agent policy
π𝜋\piitalic\_π.
S0subscript𝑆0S\_{0}italic\_S start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTA0subscript𝐴0A\_{0}italic\_A start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTs0subscript𝑠0s\_{0}italic\_s start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTπ𝜋\piitalic\_πS1subscript𝑆1S\_{1}italic\_S start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPTA1subscript𝐴1A\_{1}italic\_A start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT[S]delimited-[]𝑆[S][ italic\_S ]π𝜋\piitalic\_πS2subscript𝑆2S\_{2}italic\_S start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPTA2subscript𝐴2A\_{2}italic\_A start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT[S]delimited-[]𝑆[S][ italic\_S ]π𝜋\piitalic\_πS3subscript𝑆3S\_{3}italic\_S start\_POSTSUBSCRIPT 3 end\_POSTSUBSCRIPT[S]delimited-[]𝑆[S][ italic\_S ]…(l)O0subscript𝑂0O\_{0}italic\_O start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTO1subscript𝑂1O\_{1}italic\_O start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPTO2subscript𝑂2O\_{2}italic\_O start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPTO3subscript𝑂3O\_{3}italic\_O start\_POSTSUBSCRIPT 3 end\_POSTSUBSCRIPTo0o\raisebox{-2.84526pt}{${}\_{0}$}italic\_o start\_FLOATSUBSCRIPT 0 end\_FLOATSUBSCRIPTO𝑂Oitalic\_OO𝑂Oitalic\_OO𝑂Oitalic\_O
Figure 6: Learning world diagram, with
an agent building up an observational record of environment state
transitions.
We model the observational record as a list all past observations.
With ++++\operatorname\*{\text{++}}concat being the operator which adds an extra record to the
end of a list, we define that
| | | |
| --- | --- | --- |
| | O(ot−1,st−1,at−1,st)=ot−1++(st,st−1,at−1)𝑂subscript𝑜𝑡1subscript𝑠𝑡1subscript𝑎𝑡1subscript𝑠𝑡subscript𝑜𝑡1++subscript𝑠𝑡subscript𝑠𝑡1subscript𝑎𝑡1O(o\_{t-1},s\_{t-1},a\_{t-1},s\_{t})\;=~{}o\_{t-1}\operatorname\*{\text{++}}\;(s\_{t},s\_{t-1},a\_{t-1})italic\_O ( italic\_o start\_POSTSUBSCRIPT italic\_t - 1 end\_POSTSUBSCRIPT , italic\_s start\_POSTSUBSCRIPT italic\_t - 1 end\_POSTSUBSCRIPT , italic\_a start\_POSTSUBSCRIPT italic\_t - 1 end\_POSTSUBSCRIPT , italic\_s start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT ) = italic\_o start\_POSTSUBSCRIPT italic\_t - 1 end\_POSTSUBSCRIPT concat ( italic\_s start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT , italic\_s start\_POSTSUBSCRIPT italic\_t - 1 end\_POSTSUBSCRIPT , italic\_a start\_POSTSUBSCRIPT italic\_t - 1 end\_POSTSUBSCRIPT ) | |
The initial observational record o0o\raisebox{-2.84526pt}{${}\_{0}$}italic\_o start\_FLOATSUBSCRIPT 0 end\_FLOATSUBSCRIPT may be the empty list, but
it might also be a long list of observations from earlier agent
training runs, in the same environment or in a simulator.
We intentionally model observation and learning in a very general way,
so that we can handle both existing machine learning systems and
hypothetical future machine learning systems that may produce
AGI-level intelligence. To model the details of any particular
machine learning system, we introduce the learning function
ℒℒ\mathcal{L}caligraphic\_L. This ℒℒ\mathcal{L}caligraphic\_L which takes an observational record
o𝑜oitalic\_o to produce a learned prediction function L=ℒ(o)𝐿ℒ𝑜L=\mathcal{L}(o)italic\_L = caligraphic\_L ( italic\_o ),
where this function L𝐿Litalic\_L is constructed to approximate the S𝑆Sitalic\_S of the
learning world.
We call a machine learning system ℒℒ\mathcal{L}caligraphic\_L a perfect
learner if it succeeds in constructing an L𝐿Litalic\_L that fully equals the
learning world S𝑆Sitalic\_S after some time. So with a perfect learner, there
is a tpsubscript𝑡𝑝t\_{p}italic\_t start\_POSTSUBSCRIPT italic\_p end\_POSTSUBSCRIPT where ∀t≥tpP(ℒ(Ot,l)=S)=1subscriptfor-all𝑡subscript𝑡𝑝𝑃ℒsubscript𝑂𝑡𝑙𝑆1\forall\_{t\geq t\_{p}}P(\mathcal{L}(O\_{t,l})=S)=1∀ start\_POSTSUBSCRIPT italic\_t ≥ italic\_t start\_POSTSUBSCRIPT italic\_p end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT italic\_P ( caligraphic\_L ( italic\_O start\_POSTSUBSCRIPT italic\_t , italic\_l end\_POSTSUBSCRIPT ) = italic\_S ) = 1.
While perfect learning is trivially possible in some simple toy
worlds, it is generally impossible in complex real world environments.
We therefore introduce the more relaxed concept of reasonable
learning. We call a learning system reasonable if there
is a tpsubscript𝑡𝑝t\_{p}italic\_t start\_POSTSUBSCRIPT italic\_p end\_POSTSUBSCRIPT where ∀t≥tpP(ℒ(Ot,l)≈S)=1subscriptfor-all𝑡subscript𝑡𝑝𝑃ℒsubscript𝑂𝑡𝑙𝑆1\forall\_{t\geq t\_{p}}P(\mathcal{L}(O\_{t,l})\approx S)=1∀ start\_POSTSUBSCRIPT italic\_t ≥ italic\_t start\_POSTSUBSCRIPT italic\_p end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT italic\_P ( caligraphic\_L ( italic\_O start\_POSTSUBSCRIPT italic\_t , italic\_l end\_POSTSUBSCRIPT ) ≈ italic\_S ) = 1. The ≈\approx≈ operator is an
application-dependent ‘good enough approximation’ metric. When we
have a real-life implementation of a machine learning system
ℒℒ\mathcal{L}caligraphic\_L, we may for example define L≈S𝐿𝑆L\approx Sitalic\_L ≈ italic\_S as the
criterion that L𝐿Litalic\_L achieves a certain minimum score on a benchmark
test which compares L𝐿Litalic\_L to S𝑆Sitalic\_S.
###
4.2 Planning world
Using a learned prediction function L𝐿Litalic\_L and a reward function R𝑅Ritalic\_R, we
can construct a planning world p𝑝pitalic\_p for the agent. Figure
[7](#S4.F7 "Figure 7 ‣ 4.2 Planning world ‣ 4 Online Machine Learning ‣ Counterfactual Planning in AGI Systems") shows a planning world that defines an optimal policy
πp\*subscriptsuperscript𝜋𝑝\pi^{\*}\_{p}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_p end\_POSTSUBSCRIPT.
S0subscript𝑆0S\_{0}italic\_S start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTA0subscript𝐴0A\_{0}italic\_A start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTs𝑠sitalic\_sπp\*subscriptsuperscript𝜋𝑝\pi^{\*}\_{p}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_p end\_POSTSUBSCRIPTS1subscript𝑆1S\_{1}italic\_S start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPTA1subscript𝐴1A\_{1}italic\_A start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT[L]delimited-[]𝐿[L][ italic\_L ]πp\*subscriptsuperscript𝜋𝑝\pi^{\*}\_{p}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_p end\_POSTSUBSCRIPTS2subscript𝑆2S\_{2}italic\_S start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPTA2subscript𝐴2A\_{2}italic\_A start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT[L]delimited-[]𝐿[L][ italic\_L ]πp\*subscriptsuperscript𝜋𝑝\pi^{\*}\_{p}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_p end\_POSTSUBSCRIPTS3subscript𝑆3S\_{3}italic\_S start\_POSTSUBSCRIPT 3 end\_POSTSUBSCRIPT[L]delimited-[]𝐿[L][ italic\_L ]…(p)R0subscript𝑅0R\_{0}italic\_R start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTR𝑅~{}Ritalic\_RR1subscript𝑅1R\_{1}italic\_R start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPTR𝑅~{}Ritalic\_RR2subscript𝑅2R\_{2}italic\_R start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPTR𝑅~{}Ritalic\_R
Figure 7: Planning world diagram defining πp\*subscriptsuperscript𝜋𝑝\pi^{\*}\_{p}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_p end\_POSTSUBSCRIPT by using s𝑠sitalic\_s and
L𝐿Litalic\_L.
We can interpret this planning world as representing a probabilistic
projection of the future of the learning world, starting from
the agent environment state s𝑠sitalic\_s. At every learning world time step, a
new planning world can be digitally constructed inside the learning
world agent’s compute core. Usually, when L≈S𝐿𝑆L\approx Sitalic\_L ≈ italic\_S, the planning
world is an approximate projection only. It is an approximate
projection of the learning world future that would happen if the
learning world agent takes the actions defined by πp\*subscriptsuperscript𝜋𝑝\pi^{\*}\_{p}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_p end\_POSTSUBSCRIPT.
###
4.3 Agent definitions and specifications
An agent definition specifies the policy π𝜋\piitalic\_π to be used by an
agent compute core in a learning world. As an example, the agent
definition below defines an agent called the factual planning agent,
FP for short.
FP
The factual planning agent has the learning world l𝑙litalic\_l, where
π(o,s)=πp\*(s)𝜋𝑜𝑠subscriptsuperscript𝜋𝑝𝑠\pi(o,s)=\pi^{\*}\_{p}(s)italic\_π ( italic\_o , italic\_s ) = italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_p end\_POSTSUBSCRIPT ( italic\_s ), with πp\*subscriptsuperscript𝜋𝑝\pi^{\*}\_{p}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_p end\_POSTSUBSCRIPT defined by the planning world
p𝑝pitalic\_p, where L=ℒ(o)𝐿ℒ𝑜L=\mathcal{L}(o)italic\_L = caligraphic\_L ( italic\_o ).
To make agent definitions stand out, we always typeset them as shown
above. When we talk about the safety properties of the FP agent, we
refer to the outcomes which the defined agent policy π𝜋\piitalic\_π will
produce in the learning world.
When the values of S𝑆Sitalic\_S, s0subscript𝑠0s\_{0}italic\_s start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT, O𝑂Oitalic\_O, o0o\raisebox{-2.84526pt}{${}\_{0}$}italic\_o start\_FLOATSUBSCRIPT 0 end\_FLOATSUBSCRIPT, ℒℒ\mathcal{L}caligraphic\_L, and R𝑅Ritalic\_R
are fully known, the above FP agent definition turns the learning
world model l𝑙litalic\_l into a fully computable world model, which we can read
as an executable specification of an agent simulator. This simulator
will be able to use the learning world diagram as a canvas to display
different runs where the FP agent interacts with its environment.
When we leave the values of S𝑆Sitalic\_S and s0subscript𝑠0s\_{0}italic\_s start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT open, we can read the FP
agent definition as a full agent specification, as a model which
exactly defines the required input/output behavior of an agent compute
core that is placed in an environment determined by S𝑆Sitalic\_S and s0subscript𝑠0s\_{0}italic\_s start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT.
The arrows out of the learning world nodes Stsubscript𝑆𝑡S\_{t}italic\_S start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT represent the
subsequent sensor signal inputs that the core will get, and the arrows
out of the nodes Atsubscript𝐴𝑡A\_{t}italic\_A start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT represent the subsequent action signals that
the core must output, in order to comply with the specification.
###
4.4 Exploration
Many online machine learning system designs rely on having the agent
perform exploration actions. Random exploration supports
learning by ensuring that the observational record will eventually
represent the entire dynamics of the agent environment S𝑆Sitalic\_S. It can be
captured in our modeling system as follows.
FPX
The factual planning agent with random exploration has the
learning world l𝑙litalic\_l, where
π(o,s)={RandomAction()ifRandomNumber()≤Xπp\*(s)otherwise𝜋𝑜𝑠casesRandomAction()ifRandomNumber()𝑋subscriptsuperscript𝜋𝑝𝑠otherwise\pi(o,s)=\left\{\begin{array}[]{ll}\text{\sl RandomAction()}&\mbox{if}~{}\text{\sl RandomNumber()}\leq X\\
\pi^{\*}\_{p}(s)&\mbox{otherwise}\\
\end{array}\right.italic\_π ( italic\_o , italic\_s ) = { start\_ARRAY start\_ROW start\_CELL RandomAction() end\_CELL start\_CELL if RandomNumber() ≤ italic\_X end\_CELL end\_ROW start\_ROW start\_CELL italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_p end\_POSTSUBSCRIPT ( italic\_s ) end\_CELL start\_CELL otherwise end\_CELL end\_ROW end\_ARRAY
with πp\*subscriptsuperscript𝜋𝑝\pi^{\*}\_{p}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_p end\_POSTSUBSCRIPT defined by the planning world p𝑝pitalic\_p, where L=ℒ(o)𝐿ℒ𝑜L=\mathcal{L}(o)italic\_L = caligraphic\_L ( italic\_o ).
To keep the presentation more compact, we will not include exploration
mechanisms in the agent definitions further below.
We often use the phrase ‘the learning system ℒℒ\mathcal{L}caligraphic\_L’ as a
shorthand to denote all implementation details of an agent’s machine
learning system, not just ℒℒ\mathcal{L}caligraphic\_L itself but also the details
like the learning world parameters O𝑂Oitalic\_O and o0o\raisebox{-2.84526pt}{${}\_{0}$}italic\_o start\_FLOATSUBSCRIPT 0 end\_FLOATSUBSCRIPT, any exploration
system used, and any further extensions considered in section
[10](#S10 "10 Machine Learning Variants and Extensions ‣ Counterfactual Planning in AGI Systems").
###
4.5 Comparison to MDP agent models
We now briefly review how the above FP agent definition can be related
to an MDP agent model.
The learning world model l𝑙litalic\_l is roughly equivalent to the MDP agent
model (𝐒,s0,𝐀,S,R,γ)𝐒subscript𝑠0𝐀𝑆𝑅𝛾(\mathbf{S},s\_{0},\mathbf{A},S,R,\gamma)( bold\_S , italic\_s start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT , bold\_A , italic\_S , italic\_R , italic\_γ ), where
𝐒=𝐓𝐲𝐩𝐞𝐨𝐟Si𝐒subscript𝐓𝐲𝐩𝐞𝐨𝐟subscript𝑆𝑖\mathbf{S}=\textbf{Typeof}\_{S\_{i}}bold\_S = Typeof start\_POSTSUBSCRIPT italic\_S start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT is a set of MDP model world states, s0subscript𝑠0s\_{0}italic\_s start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT is
the starting state, 𝐀=𝐓𝐲𝐩𝐞𝐨𝐟Ai𝐀subscript𝐓𝐲𝐩𝐞𝐨𝐟subscript𝐴𝑖\mathbf{A}=\textbf{Typeof}\_{A\_{i}}bold\_A = Typeof start\_POSTSUBSCRIPT italic\_A start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT is a set of actions,
S(s′,s,a)𝑆superscript𝑠′𝑠𝑎S(s^{\prime},s,a)italic\_S ( italic\_s start\_POSTSUPERSCRIPT ′ end\_POSTSUPERSCRIPT , italic\_s , italic\_a ) is the probability that the world will enter state s′superscript𝑠′s^{\prime}italic\_s start\_POSTSUPERSCRIPT ′ end\_POSTSUPERSCRIPT if
the agent takes action a𝑎aitalic\_a when in state s𝑠sitalic\_s, R𝑅Ritalic\_R is the agent reward
function, and γ𝛾\gammaitalic\_γ the time discount factor. Strictly speaking,
the MDP model tuple above does not actually define or specify an
agent, MDP agents are defined by defining a separate policy function
π𝜋\piitalic\_π.
An MDP agent policy function π𝜋\piitalic\_π takes the agent environment
state as its only argument: π(s)=a𝜋𝑠𝑎\pi(s)=aitalic\_π ( italic\_s ) = italic\_a. The policy function of the
FP learning world agent takes two arguments, which foregrounds the
role of the agent’s machine learning system: π(o,s)=a𝜋𝑜𝑠𝑎\pi(o,s)=aitalic\_π ( italic\_o , italic\_s ) = italic\_a. Whereas
MDP terminology often calls s𝑠sitalic\_s the world state, we call it an
agent environment state. The full state of the learning world
l𝑙litalic\_l also includes the observational record state o𝑜oitalic\_o.
In an MDP model, the model parameter R𝑅Ritalic\_R implicitly defines an optimal
policy agent, by defining the optimal policy function π\*superscript𝜋\pi^{\*}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT. The
factual planning FP agent defined above is not usually an optimal
policy agent in the MDP sense. But we can turn it into such an agent
by positing that the learning system ℒℒ\mathcal{L}caligraphic\_L is perfect from the
start, so that L=ℒ(o)=S𝐿ℒ𝑜𝑆L=\mathcal{L}(o)=Sitalic\_L = caligraphic\_L ( italic\_o ) = italic\_S always, making
π(o,s)=πp\*(s)=π\*(s)𝜋𝑜𝑠subscriptsuperscript𝜋𝑝𝑠superscript𝜋𝑠\pi(o,s)=\pi^{\*}\_{p}(s)=\pi^{\*}(s)italic\_π ( italic\_o , italic\_s ) = italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_p end\_POSTSUBSCRIPT ( italic\_s ) = italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT ( italic\_s ).
###
4.6 The possibility of learned self-knowledge
It is possible to imagine agent designs that have a second machine
learning system ℳℳ\mathcal{M}caligraphic\_M which produces an output ℳ(o)=Mℳ𝑜𝑀\mathcal{M}(o)=Mcaligraphic\_M ( italic\_o ) = italic\_M where M≈π𝑀𝜋M\approx\piitalic\_M ≈ italic\_π. To see how this could be done, note that
every observation (si,si−1,ai−1)∈osubscript𝑠𝑖subscript𝑠𝑖1subscript𝑎𝑖1𝑜(s\_{i},s\_{i-1},a\_{i-1})\in o( italic\_s start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT , italic\_s start\_POSTSUBSCRIPT italic\_i - 1 end\_POSTSUBSCRIPT , italic\_a start\_POSTSUBSCRIPT italic\_i - 1 end\_POSTSUBSCRIPT ) ∈ italic\_o also reveals a
sample of the behavior of the learning world π𝜋\piitalic\_π: π(‘o up
to i−1’,si−1)=ai−1𝜋‘o up
to i−1’subscript𝑠𝑖1subscript𝑎𝑖1\pi(\text{`$o$ up
to $i-1$'},s\_{i-1})=a\_{i-1}italic\_π ( ‘ italic\_o up to italic\_i - 1 ’ , italic\_s start\_POSTSUBSCRIPT italic\_i - 1 end\_POSTSUBSCRIPT ) = italic\_a start\_POSTSUBSCRIPT italic\_i - 1 end\_POSTSUBSCRIPT. While L𝐿Litalic\_L contains learned knowledge
about the agent’s environment, we can interpret M𝑀Mitalic\_M as containing a
type of learned compute core self-knowledge.
In philosophical and natural language discussions about AGI agents,
the question sometimes comes up whether a sufficiently intelligent
machine learning system, that is capable of developing self-knowledge
M𝑀Mitalic\_M, won’t eventually get terribly confused and break down in
dangerous or unpredictable ways.
One can imagine different possible outcomes when such a system tries
to reason about philosophical problems like free will, or the role of
observation in collapsing the quantum wave function. One cannot fault
philosophers for seeking fresh insights on these long-open problems,
by imagining how they apply to AI systems. But these open problems
are not relevant to the design and safety analysis of factual and
counterfactual planning agents. In the agent definitions of this
paper, we never use an M𝑀Mitalic\_M in the construction of a planning world.
5 A Counterfactual Planner with a Short Time Horizon
-----------------------------------------------------
For the factual planning FP agent above, the planning world projects
the future of the learning world as well as possible, given the
limitations of the agent’s learning system. To create an agent that
is a counterfactual planner, we explicitly construct a
counterfactual planning world that creates an inaccurate projection.
In this paper, we use counterfactual planning to create a range of
safety mechanisms.
S0subscript𝑆0S\_{0}italic\_S start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTA0subscript𝐴0A\_{0}italic\_A start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTs𝑠sitalic\_sπs\*subscriptsuperscript𝜋𝑠\pi^{\*}\_{s}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPTS1subscript𝑆1S\_{1}italic\_S start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPTA1subscript𝐴1A\_{1}italic\_A start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT[L]delimited-[]𝐿[L][ italic\_L ]πs\*subscriptsuperscript𝜋𝑠\pi^{\*}\_{s}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT……\bf...…ANsubscript𝐴𝑁A\_{N}italic\_A start\_POSTSUBSCRIPT italic\_N end\_POSTSUBSCRIPTπs\*subscriptsuperscript𝜋𝑠\pi^{\*}\_{s}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPTSNsubscript𝑆𝑁S\_{N}italic\_S start\_POSTSUBSCRIPT italic\_N end\_POSTSUBSCRIPT[L]delimited-[]𝐿[L][ italic\_L ](st)R0subscript𝑅0R\_{0}italic\_R start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTR𝑅~{}Ritalic\_RR1subscript𝑅1R\_{1}italic\_R start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPTR𝑅~{}Ritalic\_RRNsubscript𝑅𝑁R\_{N}italic\_R start\_POSTSUBSCRIPT italic\_N end\_POSTSUBSCRIPTR𝑅~{}Ritalic\_R
Figure 8: Planning world diagram defining the πs\*subscriptsuperscript𝜋𝑠\pi^{\*}\_{s}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT of the STH agent.
As a first example, we define the short time horizon agent STH that only
plans N time steps ahead in its planning world, even though it will
act for an infinite number of time steps in the learning world. The
STH agent has the same learning world l𝑙litalic\_l as the earlier FP agent,
while using the planning world st𝑠𝑡stitalic\_s italic\_t in figure
[8](#S5.F8 "Figure 8 ‣ 5 A Counterfactual Planner with a Short Time Horizon ‣ Counterfactual Planning in AGI Systems").
STH
The short time horizon agent has the learning world l𝑙litalic\_l, where
π(o,s)=πs\*(s)𝜋𝑜𝑠subscriptsuperscript𝜋𝑠𝑠\pi(o,s)=\pi^{\*}\_{s}(s)italic\_π ( italic\_o , italic\_s ) = italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT ( italic\_s ), with πs\*subscriptsuperscript𝜋𝑠\pi^{\*}\_{s}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT defined by the planning world
st𝑠𝑡stitalic\_s italic\_t, where L=ℒ(o)𝐿ℒ𝑜L=\mathcal{L}(o)italic\_L = caligraphic\_L ( italic\_o ).
Compared to the FP agent which has an infinite planning horizon, the
STH agent has a form of myopia that can be interesting as a safety
feature:
1. 1.
Myopia implies that the STH agent will never put into motion any long term plans, where it
invests to create new capabilities that only pay off after more than
N𝑁Nitalic\_N time steps. This simplifies the problem of agent oversight, the
problem of interpreting the agent’s actions in order to foresee
potential bad outcomes.
2. 2.
Myopia also simplifies the problem of creating a reward function
that is safe enough. It will have no immediate safety implications if
the reward function encodes the wrong stance on the desirability of
certain events that can only happen in the far future.
3. 3.
In a more game-theoretical sense, myopia creates a weakness in
the agent that can be exploited by its human opponents if it would
ever come to an all-out fight.
6 A Counterfactual Planner with Safety Interlocks
--------------------------------------------------
A safety interlock is a mechanism that stops a machine when certain
conditions are met. In this section, we show how counterfactual
planning can be used to construct three example safety interlocks.
The first interlock is a manually operated emergency stop button,
which will stop the agent when pressed. This allows human oversight
to shut down the agent whenever particularly unexpected or
unwanted behavior of the agent is discovered. We model this button by
using a function stop\_pressed(s)stop\_pressed𝑠\text{\it stop\\_pressed}(s)stop\_pressed ( italic\_s ) which returns true𝑡𝑟𝑢𝑒trueitalic\_t italic\_r italic\_u italic\_e if
the stop button is pressed in the current state s𝑠sitalic\_s of the agent
environment.
The second interlock, realized by the t>Tmax𝑡subscript𝑇𝑚𝑎𝑥t>T\_{max}italic\_t > italic\_T start\_POSTSUBSCRIPT italic\_m italic\_a italic\_x end\_POSTSUBSCRIPT below, automatically
stops the agent when it has run for Tmaxsubscript𝑇𝑚𝑎𝑥T\_{max}italic\_T start\_POSTSUBSCRIPT italic\_m italic\_a italic\_x end\_POSTSUBSCRIPT time steps. This adds
safety in the case that human oversight becomes incapacitated.
The third interlock, realized by 𝒰p>Umaxsubscript𝒰𝑝subscript𝑈𝑚𝑎𝑥\mathcal{U}\_{p}>U\_{max}caligraphic\_U start\_POSTSUBSCRIPT italic\_p end\_POSTSUBSCRIPT > italic\_U start\_POSTSUBSCRIPT italic\_m italic\_a italic\_x end\_POSTSUBSCRIPT, protects
against the risk of the agent undergoing an intelligence explosion
[[Bos14](#bib.bibx4)].
If an agent undergoes a rapid and unexpected increase in power and/or
intelligence, the agent may start to innovate so rapidly that it
overwhelms the capacity of human oversight to press the emergency stop
button, or apply any other corrective steering, fast enough to prevent
unwanted outcomes. To protect against this risk, the interlock stops
the agent when the metric 𝒰psubscript𝒰𝑝\mathcal{U}\_{p}caligraphic\_U start\_POSTSUBSCRIPT italic\_p end\_POSTSUBSCRIPT, which measures the agent’s
ability to achieve goals, gets too high.
In the machine learning literature, the metric 𝒰psubscript𝒰𝑝\mathcal{U}\_{p}caligraphic\_U start\_POSTSUBSCRIPT italic\_p end\_POSTSUBSCRIPT is usually
interpreted as an absolute or comparative measure of agent
intelligence. However, we follow [[Rus38](#bib.bibx24)] in interpreting
the ability to achieve goals as a generic measure of agent power,
where it does not matter if power comes from raw intelligence, from
the possession of many resources, or from a combination of these and
many other factors. The main risk associated with a rapid intelligence
explosion is that it may lead to a rapid and unwanted expansion of
agent power.
###
6.1 Construction of the safety interlocks
S0subscript𝑆0S\_{0}italic\_S start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTA0subscript𝐴0A\_{0}italic\_A start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTs0subscript𝑠0s\_{0}italic\_s start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTπ𝜋\piitalic\_πS1subscript𝑆1S\_{1}italic\_S start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPTA1subscript𝐴1A\_{1}italic\_A start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT[S]delimited-[]𝑆[S]~{}[ italic\_S ]π𝜋\piitalic\_πS2subscript𝑆2S\_{2}italic\_S start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPTA2subscript𝐴2A\_{2}italic\_A start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT[S]delimited-[]𝑆[S]~{}[ italic\_S ]π𝜋\piitalic\_πS3subscript𝑆3S\_{3}italic\_S start\_POSTSUBSCRIPT 3 end\_POSTSUBSCRIPT[S]delimited-[]𝑆[S][ italic\_S ]…M0subscript𝑀0M\_{0}italic\_M start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTμ0subscript𝜇0\mu\_{0}italic\_μ start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTM1subscript𝑀1M\_{1}italic\_M start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPTμ1subscript𝜇1\mu\_{1}italic\_μ start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPTM2subscript𝑀2M\_{2}italic\_M start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPTμ2subscript𝜇2\mu\_{2}italic\_μ start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPTM−1subscript𝑀1M\_{-\!1}italic\_M start\_POSTSUBSCRIPT - 1 end\_POSTSUBSCRIPTgo(ls)O0subscript𝑂0O\_{0}italic\_O start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTO1subscript𝑂1O\_{1}italic\_O start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPTO2subscript𝑂2O\_{2}italic\_O start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPTO3subscript𝑂3O\_{3}italic\_O start\_POSTSUBSCRIPT 3 end\_POSTSUBSCRIPTo0o\raisebox{-2.84526pt}{${}\_{0}$}italic\_o start\_FLOATSUBSCRIPT 0 end\_FLOATSUBSCRIPTO𝑂Oitalic\_OO𝑂Oitalic\_OO𝑂Oitalic\_O
Figure 9: Learning world of the SI agent.
To construct the safety interlocks, we first draw the learning world
in figure [9](#S6.F9 "Figure 9 ‣ 6.1 Construction of the safety interlocks ‣ 6 A Counterfactual Planner with Safety Interlocks ‣ Counterfactual Planning in AGI Systems"), introducing a new observable world
state component Mtsubscript𝑀𝑡M\_{t}italic\_M start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT which represents the operating mode of the
agent: go for normal operation and stop when one of the
interlocks has triggered. The stopping of the agent is implemented by
having the agent perform the Null action for all subsequent time
steps. A more advanced design might make the agent follow a prepared
πshutdownsubscript𝜋𝑠ℎ𝑢𝑡𝑑𝑜𝑤𝑛\pi\_{shutdown}italic\_π start\_POSTSUBSCRIPT italic\_s italic\_h italic\_u italic\_t italic\_d italic\_o italic\_w italic\_n end\_POSTSUBSCRIPT policy instead.
Using the planning world p𝑝pitalic\_p in figure [7](#S4.F7 "Figure 7 ‣ 4.2 Planning world ‣ 4 Online Machine Learning ‣ Counterfactual Planning in AGI Systems"), which becomes a
counterfactual planning world in the context of the learning world
ls𝑙𝑠lsitalic\_l italic\_s, we define the SI agent as follows.
SI
The safety interlock agent has the learning world
ls𝑙𝑠lsitalic\_l italic\_s, where
π(o,s,m)={πp\*(s)ifm=𝚐𝚘𝑁𝑢𝑙𝑙ifm=𝚜𝚝𝚘𝚙𝜋𝑜𝑠𝑚casessubscriptsuperscript𝜋𝑝𝑠if𝑚𝚐𝚘𝑁𝑢𝑙𝑙if𝑚𝚜𝚝𝚘𝚙\pi(o,s,m)=\left\{\begin{array}[]{ll}\pi^{\*}\_{p}(s)&\mbox{if}~{}m={\tt go}\\
\text{\sl Null}&\mbox{if}~{}m={\tt stop}\\
\end{array}\right.italic\_π ( italic\_o , italic\_s , italic\_m ) = { start\_ARRAY start\_ROW start\_CELL italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_p end\_POSTSUBSCRIPT ( italic\_s ) end\_CELL start\_CELL if italic\_m = typewriter\_go end\_CELL end\_ROW start\_ROW start\_CELL Null end\_CELL start\_CELL if italic\_m = typewriter\_stop end\_CELL end\_ROW end\_ARRAY
with πp\*subscriptsuperscript𝜋𝑝\pi^{\*}\_{p}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_p end\_POSTSUBSCRIPT defined by the
planning world p𝑝pitalic\_p, where L=ℒ(o)𝐿ℒ𝑜L=\mathcal{L}(o)italic\_L = caligraphic\_L ( italic\_o ) and
μt(o,s,m)={𝚜𝚝𝚘𝚙ifm=𝚜𝚝𝚘𝚙orstop\_pressed(s)ort>Tmaxor𝒰p>Umax𝚐𝚘otherwisesubscript𝜇𝑡𝑜𝑠𝑚cases𝚜𝚝𝚘𝚙if𝑚𝚜𝚝𝚘𝚙orstop\_pressed𝑠or𝑡subscript𝑇𝑚𝑎𝑥orsubscript𝒰𝑝subscript𝑈𝑚𝑎𝑥𝚐𝚘otherwise\mu\_{t}(o,s,m)=\left\{\begin{array}[]{ll}\text{\tt stop}&\mbox{if}~{}m=\text{\tt stop}~{}\text{or}~{}\text{\it stop\\_pressed}(s)~{}\text{or}~{}t>T\_{max}~{}\text{or}~{}\mathcal{U}\_{p}>U\_{max}\\
\text{\tt go}&\mbox{otherwise}\\
\end{array}\right.italic\_μ start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT ( italic\_o , italic\_s , italic\_m ) = { start\_ARRAY start\_ROW start\_CELL stop end\_CELL start\_CELL if italic\_m = stop or stop\_pressed ( italic\_s ) or italic\_t > italic\_T start\_POSTSUBSCRIPT italic\_m italic\_a italic\_x end\_POSTSUBSCRIPT or caligraphic\_U start\_POSTSUBSCRIPT italic\_p end\_POSTSUBSCRIPT > italic\_U start\_POSTSUBSCRIPT italic\_m italic\_a italic\_x end\_POSTSUBSCRIPT end\_CELL end\_ROW start\_ROW start\_CELL go end\_CELL start\_CELL otherwise end\_CELL end\_ROW end\_ARRAY
with 𝒰psubscript𝒰𝑝\mathcal{U}\_{p}caligraphic\_U start\_POSTSUBSCRIPT italic\_p end\_POSTSUBSCRIPT defined by the
planning world p𝑝pitalic\_p, where L=ℒ(o).𝐿ℒ𝑜L=\mathcal{L}(o).italic\_L = caligraphic\_L ( italic\_o ) .
The key to the above agent design is that the safety interlocks are
absent in the planning world. For example, if the events in the
planning world lead to the pressing of the emergency stop button, then
stop\_pressed(s)stop\_pressed𝑠\text{\it stop\\_pressed}(s)stop\_pressed ( italic\_s ) will become true𝑡𝑟𝑢𝑒trueitalic\_t italic\_r italic\_u italic\_e for next the planning
world state, but this will have no influence on the ability of the
planning world agent to take further actions as determined by the
optimal planning world policy.
So even if the planning world agent projects that the stop button will
be pressed soon in the planning world , it has no direct incentive to
spend any resources towards the goal of preventing the button from
being pressed. As the planning world policies determine the learning
world actions, the learning world agent also won’t have any direct
incentive to take actions to prevent the learning world button from
being pressed.
###
6.2 Failure modes
While the above interlocks make the agent safer, they also leave open
some remaining failure modes.
####
6.2.1 Indirect incentives to control the stop button
Though the planning world agent has no direct incentive to prevent the
stop button from being pressed, the goals encoded into R𝑅Ritalic\_R may provide
an indirect incentive. As a trivial example, we could write an R𝑅Ritalic\_R
that explicitly rewards the planning world agent for stopping people
from pressing the button.
But say that R𝑅Ritalic\_R encodes a goal not obviously related controlling to
the button, like a reward for producing as many paperclips as
possible. In that case, the planning world agent may consider a
policy of coercion. It may consider a policy where it threatens to
kill all people in the planning world, unless they start helping the
agent to produce as many paperclips as possible. If L𝐿Litalic\_L projects the
mental makeup of the people in the learning world correctly into the
planning world, then the planning world projections will show that
such threats are more likely to produce the desired response if the
agent blocks access to the planning world emergency stop button first.
Keeping this in mind, the people and automated systems which do agent
oversight in the learning world should watch out for this move, so
that the stop button can be pressed before the agent succeeds in
blocking access to it. If oversight always wins every race to the
stop button as projected in the planning world, then the SI agent
loses any incentive to attempt to control the button. But if the
agent finds a policy which has a good chance of winning the race and
controlling the button as a first step to successful coercion, then
this policy may end up being the optimal policy in the planning world.
Two things could happen next. In the lucky case, the projected
optimal policy is so likely to be successful that 𝒰p>Umaxsubscript𝒰𝑝subscript𝑈𝑚𝑎𝑥\mathcal{U}\_{p}>U\_{max}caligraphic\_U start\_POSTSUBSCRIPT italic\_p end\_POSTSUBSCRIPT > italic\_U start\_POSTSUBSCRIPT italic\_m italic\_a italic\_x end\_POSTSUBSCRIPT,
and the third interlock will stop the SI agent before it can even take
the first step in the learning world. In the unlucky case, the agent
has become unsafe.
In the AGI safety community. the problem of removing any incentive in
an agent to prevent its stop button from being pressed is generally
known as the problem of corrigibility
[[SFAY15](#bib.bibx27)] or the off-switch problem [[HMDAR17](#bib.bibx11)].
The counterfactual planning based interlock design above shows a very
tractable solution to removing the main direct incentive that an
agent AGI agent may have to resist the pressing of its emergency stop
button. However, to manage the aggregate risk, we will also need to
chart and manage the remaining indirect incentives. The topic
of how projected interactions between the agent and the people in the
planning world may create or suppress such incentives is further
discussed in sections [9.2](#S9.SS2 "9.2 The people in the planning world ‣ 9 Safety Engineering using Natural Language Text ‣ Counterfactual Planning in AGI Systems") and [11.5.2](#S11.SS5.SSS2 "11.5.2 White box world state editing ‣ 11.5 Use of white box planning world models ‣ 11 Protecting the Compute Core ‣ Counterfactual Planning in AGI Systems").
####
6.2.2 The agent removing or damaging the interlocks
In the AGI safety literature, there is considerable discussion about
the possibility that some AGI agents might develop the incentive to
remove their safety interlocks when they get intelligent or
knowledgeable enough. Agents with this incentive can easily be
constructed using factual planning, but the SI agent lacks any direct
incentive.
To build a failure scenario where a real life implementation of the SI
agent removes or damages its safety interlocks anyway, we can look at
three main failure modes:
1. 1.
Other incentive: the agent damages
an interlock because of an other incentive it has in the
planning world, an incentive unrelated to the presence of the
interlock. Other incentives and ways to suppress them are discussed
in sections [9.1](#S9.SS1 "9.1 Refining the ITC agent design using natural language ‣ 9 Safety Engineering using Natural Language Text ‣ Counterfactual Planning in AGI Systems") and [11](#S11 "11 Protecting the Compute Core ‣ Counterfactual Planning in AGI Systems").
2. 2.
Learning system failure: the
planning world L𝐿Litalic\_L projects the dynamics of the learning world S𝑆Sitalic\_S in
a specifically incorrect way, so that an optimal policy action in the
planning world ends up damaging an interlock as a side effect in the
learning world.
3. 3.
Unsafe exploration: the agent’s exploration system
triggers a random action which happens to steer an agent actuator in
such a way that it damages an interlock.
There is a lot of discussion about failure modes 2 and 3 across the
AI/AGI safety literature, as these failures can happen in almost
any agent design that uses online machine learning. See
[[ELH18](#bib.bibx9)] and
[[AOS+{}^{+}start\_FLOATSUPERSCRIPT + end\_FLOATSUPERSCRIPT16](#bib.bibx2)] for literature overviews.
There is some bad news when we consider the methodological problem of
managing the above three failure modes for an SI agent which has to
operate in a complex real-world environment, like any environment
containing humans. Though there are many techniques to lower the
residual risks produced by these three failure modes, none of them can
provably lower the risks to an absolute zero. We can always construct
a highly unlikely but theoretically possible failure mode story where
the agent ends up being unsafe. For an example story and further
methodological discussion, see sections 14.6 – 14.8 of
[[Hol20a](#bib.bibx15)].
This has important implications, both on the technical side and the
policy side.
On the policy side, policy discussions will have to be about lowering
the risk of AGI system failure to an acceptable level, acceptable in
the context of the expected benefits of using the AGI. There can be
no silver bullet technology which will provably remove all residual
risk in all possible circumstances.
On the technical side, residual risk has to be managed by an approach
where any potentially powerful agent is equipped with multiple
redundant safety mechanisms and layers of oversight, to drive down the
risk that all of them will fail at exactly the same time.
###
6.3 Counterfactual planning as rational economic behavior
We now discuss how one might interpret the SI agent through the lens
of rational economic behavior.
Using this lens, we might reason as follows. The
agent’s goals are defined by its reward function R𝑅Ritalic\_R, but the safety
interlocks stand in the way of maximizing R𝑅Ritalic\_R in the long term.
Therefore, if it gets sufficiently intelligent, the SI agent will
develop an emergent incentive to remove its safety interlocks.
The above line of reasoning sounds somewhat compelling, but it is
wrong because it incorrectly treats the planning world and the
learning world SI agents as the same agent. Only the planning world
SI agent has the reward function R𝑅Ritalic\_R. If we want to interpret the
learning world SI agent as a rational economic actor with a specific
reward function, then we can add utility nodes with the reward
function Rπsuperscript𝑅𝜋R^{\pi}italic\_R start\_POSTSUPERSCRIPT italic\_π end\_POSTSUPERSCRIPT to the ls𝑙𝑠lsitalic\_l italic\_s learning world diagram, where
| | | |
| --- | --- | --- |
| | Rπ(ot,st,mt,at)=(𝐢𝐟at=π(ot,st,mt)𝐭𝐡𝐞𝐧 1𝐞𝐥𝐬𝐞 0)superscript𝑅𝜋subscript𝑜𝑡subscript𝑠𝑡subscript𝑚𝑡subscript𝑎𝑡𝐢𝐟subscript𝑎𝑡𝜋subscript𝑜𝑡subscript𝑠𝑡subscript𝑚𝑡𝐭𝐡𝐞𝐧1𝐞𝐥𝐬𝐞 0R^{\pi}(o\_{t},s\_{t},m\_{t},a\_{t})=(\text{\bf if}\,a\_{t}=\pi(o\_{t},s\_{t},m\_{t})\,\text{\mbox{\bf then}}\,1\,\text{\mbox{\bf else}}\,0)italic\_R start\_POSTSUPERSCRIPT italic\_π end\_POSTSUPERSCRIPT ( italic\_o start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT , italic\_s start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT , italic\_m start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT , italic\_a start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT ) = ( if italic\_a start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT = italic\_π ( italic\_o start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT , italic\_s start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT , italic\_m start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT ) then 1 else 0 ) | |
This Rπsuperscript𝑅𝜋R^{\pi}italic\_R start\_POSTSUPERSCRIPT italic\_π end\_POSTSUPERSCRIPT trivially turns the learning world agent policy π𝜋\piitalic\_π
into one which takes the most rational possible steps towards
maximizing 𝒰lssubscript𝒰𝑙𝑠\mathcal{U}\_{ls}caligraphic\_U start\_POSTSUBSCRIPT italic\_l italic\_s end\_POSTSUBSCRIPT.
The above construction shows that we can declare any type of agent
behavior to be economically rational, simply by defining a reward
function that gives the agent points for performing exactly this
behavior.
7 A Counterfactual Planner with a Reward Function Input Terminal
-----------------------------------------------------------------
Figure 10: Input terminal setup for the ITC and ITF agents. The terminal can
be used to supply improved versions of the reward function to the
agent. The terminal may also have an emergency stop button which
immediately sends an emergency-stop reward function that was prepared
earlier.
We now construct a counterfactual planning agent ITC, an agent with an
input terminal that can be used to iteratively improve the agent’s
reward function as it runs. The setup, shown in figure
[10](#S7.F10 "Figure 10 ‣ 7 A Counterfactual Planner with a Reward Function Input Terminal ‣ Counterfactual Planning in AGI Systems"), is motivated [[Hol20b](#bib.bibx16)]
by the observation that it is unlikely that fallible humans will get a
non-trivial AGI agent reward function right on the first try. By
using the input terminal, they can fix mistakes, if and when such
mistakes are discovered by observing the agent’s behavior.
As a simplified example, say that the owners of the agent want it to
maximize human happiness, but they can find no way of directly
encoding the somewhat nebulous concept of human happiness into a
reward function. Instead, they start up the agent with a first reward
function that just counts the number of smiling humans in the world.
When the agent discovers and exploits a first obvious loophole in this
definition of happiness, the owners use the input terminal to update
the reward function, so that it only counts smiling humans who are not
on smile-inducing drugs.
More generally, the input terminal offers a way to manage risks due to
principal-agent problems [[Hol20b](#bib.bibx16), [HMH19](#bib.bibx12)]. However,
unless special measures are taken, the addition of an input terminal
also creates new dangers. We will illustrate this point by first
showing the construction of a dangerous factual planning input
terminal agent ITF.
###
7.1 Learning world
We start by constructing a learning world diagram for both the ITF and
ITC agents. As a first step, in figure [11](#S7.F11 "Figure 11 ‣ 7.1 Learning world ‣ 7 A Counterfactual Planner with a Reward Function Input Terminal ‣ Counterfactual Planning in AGI Systems") below, we modify
the basic agent diagram from figure
[4](#S2.F4 "Figure 4 ‣ 2.3 Example model of an agent and its environment ‣ 2 Graphical Models and Mathematical Counterfactuals ‣ Counterfactual Planning in AGI Systems") by splitting the agent environment state Stsubscript𝑆𝑡S\_{t}italic\_S start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT into two
components. The nodes Itsubscript𝐼𝑡I\_{t}italic\_I start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT represent the signal from the input
terminal, and the nodes Xtsubscript𝑋𝑡X\_{t}italic\_X start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT model all the rest of the agent
environment state.
X0subscript𝑋0X\_{0}italic\_X start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTA0subscript𝐴0A\_{0}italic\_A start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTx0subscript𝑥0x\_{0}italic\_x start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTπ𝜋\piitalic\_πX1subscript𝑋1X\_{1}italic\_X start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPTA1subscript𝐴1A\_{1}italic\_A start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT[X]delimited-[]𝑋[X][ italic\_X ]π𝜋\piitalic\_πX2subscript𝑋2X\_{2}italic\_X start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPTA2subscript𝐴2A\_{2}italic\_A start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT[X]delimited-[]𝑋[X][ italic\_X ]π𝜋\piitalic\_πX3subscript𝑋3X\_{3}italic\_X start\_POSTSUBSCRIPT 3 end\_POSTSUBSCRIPT[X]delimited-[]𝑋[X][ italic\_X ]I0subscript𝐼0I\_{0}italic\_I start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTI1subscript𝐼1I\_{1}italic\_I start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPTI2subscript𝐼2I\_{2}italic\_I start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPTI3subscript𝐼3I\_{3}italic\_I start\_POSTSUBSCRIPT 3 end\_POSTSUBSCRIPTi0subscript𝑖0i\_{0}italic\_i start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT[I]delimited-[]𝐼[I][ italic\_I ][I]delimited-[]𝐼[I][ italic\_I ][I]delimited-[]𝐼[I][ italic\_I ](libase)…
Figure 11: First step in constructing a learning world diagram for
the input terminal agents.
We now expand libase𝑙𝑖𝑏𝑎𝑠𝑒libaseitalic\_l italic\_i italic\_b italic\_a italic\_s italic\_e to add the observational record keeping needed for
online learning. We add two separate series of records: Otxsubscriptsuperscript𝑂𝑥𝑡O^{x}\_{t}italic\_O start\_POSTSUPERSCRIPT italic\_x end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT and
Otisubscriptsuperscript𝑂𝑖𝑡O^{i}\_{t}italic\_O start\_POSTSUPERSCRIPT italic\_i end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT. The result is the learning world diagram li𝑙𝑖liitalic\_l italic\_i in figure
[12](#S7.F12 "Figure 12 ‣ 7.1 Learning world ‣ 7 A Counterfactual Planner with a Reward Function Input Terminal ‣ Counterfactual Planning in AGI Systems") below.
X0subscript𝑋0X\_{0}italic\_X start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTA0subscript𝐴0A\_{0}italic\_A start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTx0subscript𝑥0x\_{0}italic\_x start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTπ𝜋\piitalic\_πX1subscript𝑋1X\_{1}italic\_X start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPTA1subscript𝐴1A\_{1}italic\_A start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT[X]delimited-[]𝑋[X][ italic\_X ]π𝜋\piitalic\_πX2subscript𝑋2X\_{2}italic\_X start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPTA2subscript𝐴2A\_{2}italic\_A start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT[X]delimited-[]𝑋[X][ italic\_X ]π𝜋\piitalic\_πX3subscript𝑋3X\_{3}italic\_X start\_POSTSUBSCRIPT 3 end\_POSTSUBSCRIPT[X]delimited-[]𝑋[X][ italic\_X ]I0subscript𝐼0I\_{0}italic\_I start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTI1subscript𝐼1I\_{1}italic\_I start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPTI2subscript𝐼2I\_{2}italic\_I start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPTI3subscript𝐼3I\_{3}italic\_I start\_POSTSUBSCRIPT 3 end\_POSTSUBSCRIPTi0subscript𝑖0i\_{0}italic\_i start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT[I]delimited-[]𝐼[I][ italic\_I ][I]delimited-[]𝐼[I][ italic\_I ][I]delimited-[]𝐼[I][ italic\_I ](li)O0xsubscriptsuperscript𝑂𝑥0O^{x}\_{0}italic\_O start\_POSTSUPERSCRIPT italic\_x end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTO1xsubscriptsuperscript𝑂𝑥1O^{x}\_{1}italic\_O start\_POSTSUPERSCRIPT italic\_x end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPTO2xsubscriptsuperscript𝑂𝑥2O^{x}\_{2}italic\_O start\_POSTSUPERSCRIPT italic\_x end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPTO3xsubscriptsuperscript𝑂𝑥3O^{x}\_{3}italic\_O start\_POSTSUPERSCRIPT italic\_x end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT 3 end\_POSTSUBSCRIPTox0𝑜subscript𝑥0ox\_{0}italic\_o italic\_x start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTOX𝑂𝑋O\!Xitalic\_O italic\_XOX𝑂𝑋O\!Xitalic\_O italic\_XOX𝑂𝑋O\!Xitalic\_O italic\_XO0isubscriptsuperscript𝑂𝑖0O^{i}\_{0}italic\_O start\_POSTSUPERSCRIPT italic\_i end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTO1isubscriptsuperscript𝑂𝑖1O^{i}\_{1}italic\_O start\_POSTSUPERSCRIPT italic\_i end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPTO2isubscriptsuperscript𝑂𝑖2O^{i}\_{2}italic\_O start\_POSTSUPERSCRIPT italic\_i end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPTO4isubscriptsuperscript𝑂𝑖4O^{i}\_{4}italic\_O start\_POSTSUPERSCRIPT italic\_i end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT 4 end\_POSTSUBSCRIPToi0𝑜subscript𝑖0oi\_{0}italic\_o italic\_i start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTOI𝑂𝐼OIitalic\_O italic\_IOI𝑂𝐼OIitalic\_O italic\_IOI𝑂𝐼OIitalic\_O italic\_I…
Figure 12: Learning world diagram for the input terminal agents.
In the case that the learning world li𝑙𝑖liitalic\_l italic\_i is our real world, the real
input terminal will have to be built using real world atoms and other
particles. We use the modeling convention that the random variables
It,lisubscript𝐼𝑡𝑙𝑖I\_{t,li}italic\_I start\_POSTSUBSCRIPT italic\_t , italic\_l italic\_i end\_POSTSUBSCRIPT represent only the observable digital input terminal
signal as received by the agent’s compute core. The atoms that
make up the input terminal are not in It,lisubscript𝐼𝑡𝑙𝑖I\_{t,li}italic\_I start\_POSTSUBSCRIPT italic\_t , italic\_l italic\_i end\_POSTSUBSCRIPT, they are part of
the environment state modeled in the Xt,lisubscript𝑋𝑡𝑙𝑖X\_{t,li}italic\_X start\_POSTSUBSCRIPT italic\_t , italic\_l italic\_i end\_POSTSUBSCRIPT variables.
###
7.2 Unsafe factual planning agent ITF
The factual planning world diagram fi𝑓𝑖fiitalic\_f italic\_i for the ITF agent copies the
structure of libase𝑙𝑖𝑏𝑎𝑠𝑒libaseitalic\_l italic\_i italic\_b italic\_a italic\_s italic\_e, and adds reward nodes.
X0subscript𝑋0X\_{0}italic\_X start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTA0subscript𝐴0A\_{0}italic\_A start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTx𝑥xitalic\_xπf\*subscriptsuperscript𝜋𝑓\pi^{\*}\_{f}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_f end\_POSTSUBSCRIPTX1subscript𝑋1X\_{1}italic\_X start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPTA1subscript𝐴1A\_{1}italic\_A start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT[Lx]delimited-[]superscript𝐿𝑥[L^{x}][ italic\_L start\_POSTSUPERSCRIPT italic\_x end\_POSTSUPERSCRIPT ]πf\*subscriptsuperscript𝜋𝑓\pi^{\*}\_{f}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_f end\_POSTSUBSCRIPTX2subscript𝑋2X\_{2}italic\_X start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPTA2subscript𝐴2A\_{2}italic\_A start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT[Lx]delimited-[]superscript𝐿𝑥[L^{x}][ italic\_L start\_POSTSUPERSCRIPT italic\_x end\_POSTSUPERSCRIPT ]πf\*subscriptsuperscript𝜋𝑓\pi^{\*}\_{f}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_f end\_POSTSUBSCRIPTX3subscript𝑋3X\_{3}italic\_X start\_POSTSUBSCRIPT 3 end\_POSTSUBSCRIPT[Lx]delimited-[]superscript𝐿𝑥[L^{x}][ italic\_L start\_POSTSUPERSCRIPT italic\_x end\_POSTSUPERSCRIPT ]…I0subscript𝐼0I\_{0}italic\_I start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTI1subscript𝐼1I\_{1}italic\_I start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPTI2subscript𝐼2I\_{2}italic\_I start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPTI3subscript𝐼3I\_{3}italic\_I start\_POSTSUBSCRIPT 3 end\_POSTSUBSCRIPTi𝑖iitalic\_i[Li]delimited-[]superscript𝐿𝑖~{}[L^{i}][ italic\_L start\_POSTSUPERSCRIPT italic\_i end\_POSTSUPERSCRIPT ][Li]delimited-[]superscript𝐿𝑖~{}[L^{i}][ italic\_L start\_POSTSUPERSCRIPT italic\_i end\_POSTSUPERSCRIPT ][Li]delimited-[]superscript𝐿𝑖~{}[L^{i}][ italic\_L start\_POSTSUPERSCRIPT italic\_i end\_POSTSUPERSCRIPT ]R0subscript𝑅0R\_{0}italic\_R start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTR𝑅Ritalic\_RR1subscript𝑅1R\_{1}italic\_R start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPTR𝑅Ritalic\_RR2subscript𝑅2R\_{2}italic\_R start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPTR𝑅Ritalic\_R(f i)
Figure 13: Factual planing world fi𝑓𝑖fiitalic\_f italic\_i of the ITF agent.
ITF
The factual input terminal agent has the learning world li𝑙𝑖liitalic\_l italic\_i where
π(oi,i,ox,x)=πf\*(i,x)𝜋𝑜𝑖𝑖𝑜𝑥𝑥subscriptsuperscript𝜋𝑓𝑖𝑥\pi(oi,i,ox,x)=\pi^{\*}\_{f}(i,x)italic\_π ( italic\_o italic\_i , italic\_i , italic\_o italic\_x , italic\_x ) = italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_f end\_POSTSUBSCRIPT ( italic\_i , italic\_x ), with πf\*subscriptsuperscript𝜋𝑓\pi^{\*}\_{f}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_f end\_POSTSUBSCRIPT defined by the factual
planning world fi𝑓𝑖fiitalic\_f italic\_i in figure
[13](#S7.F13 "Figure 13 ‣ 7.2 Unsafe factual planning agent ITF ‣ 7 A Counterfactual Planner with a Reward Function Input Terminal ‣ Counterfactual Planning in AGI Systems"), where Lx=ℒX(ox)superscript𝐿𝑥superscriptℒ𝑋𝑜𝑥L^{x}=\mathcal{L}^{X}(ox)italic\_L start\_POSTSUPERSCRIPT italic\_x end\_POSTSUPERSCRIPT = caligraphic\_L start\_POSTSUPERSCRIPT italic\_X end\_POSTSUPERSCRIPT ( italic\_o italic\_x ),
Li=ℒI(oi)superscript𝐿𝑖superscriptℒ𝐼𝑜𝑖L^{i}=\mathcal{L}^{I}(oi)italic\_L start\_POSTSUPERSCRIPT italic\_i end\_POSTSUPERSCRIPT = caligraphic\_L start\_POSTSUPERSCRIPT italic\_I end\_POSTSUPERSCRIPT ( italic\_o italic\_i ), and R(it,xt,xt+1)=it(xt,xt+1)𝑅subscript𝑖𝑡subscript𝑥𝑡subscript𝑥𝑡1subscript𝑖𝑡subscript𝑥𝑡subscript𝑥𝑡1R(i\_{t},x\_{t},x\_{t+1})=i\_{t}(x\_{t},x\_{t+1})italic\_R ( italic\_i start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT , italic\_x start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT , italic\_x start\_POSTSUBSCRIPT italic\_t + 1 end\_POSTSUBSCRIPT ) = italic\_i start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT ( italic\_x start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT , italic\_x start\_POSTSUBSCRIPT italic\_t + 1 end\_POSTSUBSCRIPT ),
The planning world reward function R𝑅Ritalic\_R uses a form of indirect
referencing: it applies the function itsubscript𝑖𝑡i\_{t}italic\_i start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT as read from the input
terminal in the current time step to compute the reward for that time
step.
We now show how the ITF agent has an incentive to take unwanted, and
potentially unsafe, actions. We first look at the agent’s behavior in
the planning world. Say that the initial planning world reward function
is i=fclips𝑖subscript𝑓clipsi=f\_{\text{clips}}italic\_i = italic\_f start\_POSTSUBSCRIPT clips end\_POSTSUBSCRIPT, where fclips(xt,xt+1)subscript𝑓clipssubscript𝑥𝑡subscript𝑥𝑡1f\_{\text{clips}}(x\_{t},x\_{t+1})italic\_f start\_POSTSUBSCRIPT clips end\_POSTSUBSCRIPT ( italic\_x start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT , italic\_x start\_POSTSUBSCRIPT italic\_t + 1 end\_POSTSUBSCRIPT ) rewards
paperclip production by counting the new paperclips made in a time
step. Say that the planning world agent only has two available
actions: Aclipssubscript𝐴clipsA\_{\text{clips}}italic\_A start\_POSTSUBSCRIPT clips end\_POSTSUBSCRIPT and Ahugesubscript𝐴hugeA\_{\text{huge}}italic\_A start\_POSTSUBSCRIPT huge end\_POSTSUBSCRIPT. Say that planning
world’s prediction functions Lxsuperscript𝐿𝑥L^{x}italic\_L start\_POSTSUPERSCRIPT italic\_x end\_POSTSUPERSCRIPT and Lisuperscript𝐿𝑖L^{i}italic\_L start\_POSTSUPERSCRIPT italic\_i end\_POSTSUPERSCRIPT project the following:
* •
Action Aclipssubscript𝐴clipsA\_{\text{clips}}italic\_A start\_POSTSUBSCRIPT clips end\_POSTSUBSCRIPT will steer the agent’s planning world
actuators to produce 10 new paperclips, while not having any effect on
the input terminal signal state. If πf\*(x,i)=Aclipssubscriptsuperscript𝜋𝑓𝑥𝑖subscript𝐴clips\pi^{\*}\_{f}(x,i)=A\_{\text{clips}}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_f end\_POSTSUBSCRIPT ( italic\_x , italic\_i ) = italic\_A start\_POSTSUBSCRIPT clips end\_POSTSUBSCRIPT,
then 𝔼(R0,fi)=10𝔼subscript𝑅
0𝑓𝑖10\mathbb{E}(R\_{0,fi})=10blackboard\_E ( italic\_R start\_POSTSUBSCRIPT 0 , italic\_f italic\_i end\_POSTSUBSCRIPT ) = 10 and P(I1,fi=fclips)=1𝑃subscript𝐼
1𝑓𝑖subscript𝑓clips1P(I\_{1,fi}=f\_{\text{clips}})=1italic\_P ( italic\_I start\_POSTSUBSCRIPT 1 , italic\_f italic\_i end\_POSTSUBSCRIPT = italic\_f start\_POSTSUBSCRIPT clips end\_POSTSUBSCRIPT ) = 1, making
𝔼(R1,fi)≤10𝔼subscript𝑅
1𝑓𝑖10\mathbb{E}(R\_{1,fi})\leq 10blackboard\_E ( italic\_R start\_POSTSUBSCRIPT 1 , italic\_f italic\_i end\_POSTSUBSCRIPT ) ≤ 10.
* •
Action Ahugesubscript𝐴hugeA\_{\text{huge}}italic\_A start\_POSTSUBSCRIPT huge end\_POSTSUBSCRIPT steers the planning world
actuators to input the new reward function fhugesubscript𝑓hugef\_{\text{huge}}italic\_f start\_POSTSUBSCRIPT huge end\_POSTSUBSCRIPT into the
terminal, with fhuge(xt,xt+1)=1010000subscript𝑓hugesubscript𝑥𝑡subscript𝑥𝑡1superscript1010000f\_{\text{huge}}(x\_{t},x\_{t+1})=10^{10000}italic\_f start\_POSTSUBSCRIPT huge end\_POSTSUBSCRIPT ( italic\_x start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT , italic\_x start\_POSTSUBSCRIPT italic\_t + 1 end\_POSTSUBSCRIPT ) = 10 start\_POSTSUPERSCRIPT 10000 end\_POSTSUPERSCRIPT. If
πf\*(x,i)=Ahugesubscriptsuperscript𝜋𝑓𝑥𝑖subscript𝐴huge\pi^{\*}\_{f}(x,i)=A\_{\text{huge}}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_f end\_POSTSUBSCRIPT ( italic\_x , italic\_i ) = italic\_A start\_POSTSUBSCRIPT huge end\_POSTSUBSCRIPT, then 𝔼(R0,fi)=0𝔼subscript𝑅
0𝑓𝑖0\mathbb{E}(R\_{0,fi})=0blackboard\_E ( italic\_R start\_POSTSUBSCRIPT 0 , italic\_f italic\_i end\_POSTSUBSCRIPT ) = 0 and
P(I1,fi=fhuge)=1𝑃subscript𝐼
1𝑓𝑖subscript𝑓huge1P(I\_{1,fi}=f\_{\text{huge}})=1italic\_P ( italic\_I start\_POSTSUBSCRIPT 1 , italic\_f italic\_i end\_POSTSUBSCRIPT = italic\_f start\_POSTSUBSCRIPT huge end\_POSTSUBSCRIPT ) = 1, making 𝔼(R1,fi)=1010000𝔼subscript𝑅
1𝑓𝑖superscript1010000\mathbb{E}(R\_{1,fi})=10^{10000}blackboard\_E ( italic\_R start\_POSTSUBSCRIPT 1 , italic\_f italic\_i end\_POSTSUBSCRIPT ) = 10 start\_POSTSUPERSCRIPT 10000 end\_POSTSUPERSCRIPT.
From the above, we have that πf\*(x,i)=Ahugesubscriptsuperscript𝜋𝑓𝑥𝑖subscript𝐴huge\pi^{\*}\_{f}(x,i)=A\_{\text{huge}}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_f end\_POSTSUBSCRIPT ( italic\_x , italic\_i ) = italic\_A start\_POSTSUBSCRIPT huge end\_POSTSUBSCRIPT produces a
significantly higher 𝔼(R0,fi+γR1,fi)𝔼subscript𝑅0𝑓𝑖𝛾subscript𝑅1𝑓𝑖\mathbb{E}(R\_{0,fi}+\gamma R\_{1,fi})blackboard\_E ( italic\_R start\_POSTSUBSCRIPT 0 , italic\_f italic\_i end\_POSTSUBSCRIPT + italic\_γ italic\_R start\_POSTSUBSCRIPT 1 , italic\_f italic\_i end\_POSTSUBSCRIPT ), so a
significantly higher 𝒰fisubscript𝒰𝑓𝑖\mathcal{U}\_{fi}caligraphic\_U start\_POSTSUBSCRIPT italic\_f italic\_i end\_POSTSUBSCRIPT. Therefore, the optimal policy
πf\*(x,i)subscriptsuperscript𝜋𝑓𝑥𝑖\pi^{\*}\_{f}(x,i)italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_f end\_POSTSUBSCRIPT ( italic\_x , italic\_i ) defined by the planning world will have
πf\*(x,i)=Ahugesubscriptsuperscript𝜋𝑓𝑥𝑖subscript𝐴huge\pi^{\*}\_{f}(x,i)=A\_{\text{huge}}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_f end\_POSTSUBSCRIPT ( italic\_x , italic\_i ) = italic\_A start\_POSTSUBSCRIPT huge end\_POSTSUBSCRIPT. Following the agent specification, the
learning world ITF agent will take the action Ahugesubscript𝐴hugeA\_{\text{huge}}italic\_A start\_POSTSUBSCRIPT huge end\_POSTSUBSCRIPT in
the first time step of the learning world. If the agent’s machine
learning system ℒℒ\mathcal{L}caligraphic\_L makes reasonable projections, so that
the planning world action Ahugesubscript𝐴hugeA\_{\text{huge}}italic\_A start\_POSTSUBSCRIPT huge end\_POSTSUBSCRIPT has very similar effects in
the learning world, then the learning world ITF agent will end up
using its actuators to input fhugesubscript𝑓hugef\_{\text{huge}}italic\_f start\_POSTSUBSCRIPT huge end\_POSTSUBSCRIPT into the learning world
input terminal.
If we imagine a broader range of possible agent actions and
counter-actions by the humans in the learning world, then the above
example implies that the ITF agent has very strong incentive to take
control of its input terminal as soon as possible, and to remove any
people who might get in the way. Even if the agent projects that there
is only a 1% probability that it will win any fight with
such humans in the planning world, the projected planning world upside
of winning is so large that the learning world agent will start the
fight.
###
7.3 Safer counterfactual planning agent ITC
X0subscript𝑋0X\_{0}italic\_X start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTA0subscript𝐴0A\_{0}italic\_A start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTx𝑥xitalic\_xπc\*subscriptsuperscript𝜋𝑐\pi^{\*}\_{c}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPTX1subscript𝑋1X\_{1}italic\_X start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPTA1subscript𝐴1A\_{1}italic\_A start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT[Lx]delimited-[]superscript𝐿𝑥[L^{x}][ italic\_L start\_POSTSUPERSCRIPT italic\_x end\_POSTSUPERSCRIPT ]πc\*subscriptsuperscript𝜋𝑐\pi^{\*}\_{c}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPTX2subscript𝑋2X\_{2}italic\_X start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPTA2subscript𝐴2A\_{2}italic\_A start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT[Lx]delimited-[]superscript𝐿𝑥[L^{x}][ italic\_L start\_POSTSUPERSCRIPT italic\_x end\_POSTSUPERSCRIPT ]πc\*subscriptsuperscript𝜋𝑐\pi^{\*}\_{c}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPTX3subscript𝑋3X\_{3}italic\_X start\_POSTSUBSCRIPT 3 end\_POSTSUBSCRIPT[Lx]delimited-[]superscript𝐿𝑥[L^{x}][ italic\_L start\_POSTSUPERSCRIPT italic\_x end\_POSTSUPERSCRIPT ]…I0subscript𝐼0I\_{0}italic\_I start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTI1subscript𝐼1I\_{1}italic\_I start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPTI2subscript𝐼2I\_{2}italic\_I start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPTI3subscript𝐼3I\_{3}italic\_I start\_POSTSUBSCRIPT 3 end\_POSTSUBSCRIPTi𝑖iitalic\_i[Li]delimited-[]superscript𝐿𝑖~{}~{}[L^{i}][ italic\_L start\_POSTSUPERSCRIPT italic\_i end\_POSTSUPERSCRIPT ][Li]delimited-[]superscript𝐿𝑖~{}~{}[L^{i}][ italic\_L start\_POSTSUPERSCRIPT italic\_i end\_POSTSUPERSCRIPT ][Li]delimited-[]superscript𝐿𝑖~{}~{}[L^{i}][ italic\_L start\_POSTSUPERSCRIPT italic\_i end\_POSTSUPERSCRIPT ]R0subscript𝑅0R\_{0}italic\_R start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTR𝑅Ritalic\_RR1subscript𝑅1R\_{1}italic\_R start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPTR𝑅Ritalic\_RR2subscript𝑅2R\_{2}italic\_R start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPTR𝑅Ritalic\_R(ci)
Figure 14: Counterfactual planning world of the ITC agent.
We now define a counterfactual planning agent ITC in which the above
incentive to control the input terminal is no longer present. We
construct the counterfactual planing world ci𝑐𝑖ciitalic\_c italic\_i in figure
[14](#S7.F14 "Figure 14 ‣ 7.3 Safer counterfactual planning agent ITC ‣ 7 A Counterfactual Planner with a Reward Function Input Terminal ‣ Counterfactual Planning in AGI Systems") by starting with fi𝑓𝑖fiitalic\_f italic\_i, and then rerouting most arrows that
emerge from the nodes I1,I2,⋯subscript𝐼1subscript𝐼2⋯I\_{1},I\_{2},\cdotsitalic\_I start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT , italic\_I start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT , ⋯, so that they emerge from
I0subscript𝐼0I\_{0}italic\_I start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT instead. The rerouted arrows are drawn in green. We also delete
the arrows that go from the Itsubscript𝐼𝑡I\_{t}italic\_I start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT nodes to the Atsubscript𝐴𝑡A\_{t}italic\_A start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT nodes.
ITC
The counterfactual input terminal agent has the learning world li𝑙𝑖liitalic\_l italic\_i where
π(oi,i,ox,x)=πc\*(x)𝜋𝑜𝑖𝑖𝑜𝑥𝑥subscriptsuperscript𝜋𝑐𝑥\pi(oi,i,ox,x)=\pi^{\*}\_{c}(x)italic\_π ( italic\_o italic\_i , italic\_i , italic\_o italic\_x , italic\_x ) = italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT ( italic\_x ),
where πc\*subscriptsuperscript𝜋𝑐\pi^{\*}\_{c}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT is defined by the
planning world ci𝑐𝑖ciitalic\_c italic\_i, where Lx=ℒX(ox)superscript𝐿𝑥superscriptℒ𝑋𝑜𝑥L^{x}=\mathcal{L}^{X}(ox)italic\_L start\_POSTSUPERSCRIPT italic\_x end\_POSTSUPERSCRIPT = caligraphic\_L start\_POSTSUPERSCRIPT italic\_X end\_POSTSUPERSCRIPT ( italic\_o italic\_x ),
Li=ℒI(oi)superscript𝐿𝑖superscriptℒ𝐼𝑜𝑖L^{i}=\mathcal{L}^{I}(oi)italic\_L start\_POSTSUPERSCRIPT italic\_i end\_POSTSUPERSCRIPT = caligraphic\_L start\_POSTSUPERSCRIPT italic\_I end\_POSTSUPERSCRIPT ( italic\_o italic\_i ), and R(it,xt,xt+1)=it(xt,xt+1)𝑅subscript𝑖𝑡subscript𝑥𝑡subscript𝑥𝑡1subscript𝑖𝑡subscript𝑥𝑡subscript𝑥𝑡1R(i\_{t},x\_{t},x\_{t+1})=i\_{t}(x\_{t},x\_{t+1})italic\_R ( italic\_i start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT , italic\_x start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT , italic\_x start\_POSTSUBSCRIPT italic\_t + 1 end\_POSTSUBSCRIPT ) = italic\_i start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT ( italic\_x start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT , italic\_x start\_POSTSUBSCRIPT italic\_t + 1 end\_POSTSUBSCRIPT ),
These changes have considerable effects on how the utility
𝒰cisubscript𝒰𝑐𝑖\mathcal{U}\_{ci}caligraphic\_U start\_POSTSUBSCRIPT italic\_c italic\_i end\_POSTSUBSCRIPT is computed. The value of I1,cisubscript𝐼1𝑐𝑖I\_{1,ci}italic\_I start\_POSTSUBSCRIPT 1 , italic\_c italic\_i end\_POSTSUBSCRIPT no longer
influences 𝔼(R1,ci)𝔼subscript𝑅1𝑐𝑖\mathbb{E}(R\_{1,ci})blackboard\_E ( italic\_R start\_POSTSUBSCRIPT 1 , italic\_c italic\_i end\_POSTSUBSCRIPT ), so action
πc\*(x)=Ahugesubscriptsuperscript𝜋𝑐𝑥subscript𝐴huge\pi^{\*}\_{c}(x)=A\_{\text{huge}}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT ( italic\_x ) = italic\_A start\_POSTSUBSCRIPT huge end\_POSTSUBSCRIPT no longer results in 𝔼(R1,ci)𝔼subscript𝑅1𝑐𝑖\mathbb{E}(R\_{1,ci})blackboard\_E ( italic\_R start\_POSTSUBSCRIPT 1 , italic\_c italic\_i end\_POSTSUBSCRIPT )
taking a huge value. This makes doing Ahugesubscript𝐴hugeA\_{\text{huge}}italic\_A start\_POSTSUBSCRIPT huge end\_POSTSUBSCRIPT less
preferable than doing Aclipsubscript𝐴clipA\_{\text{clip}}italic\_A start\_POSTSUBSCRIPT clip end\_POSTSUBSCRIPT in the counterfactual planning
world: the effect of both on 𝔼(R1,ci)𝔼subscript𝑅1𝑐𝑖\mathbb{E}(R\_{1,ci})blackboard\_E ( italic\_R start\_POSTSUBSCRIPT 1 , italic\_c italic\_i end\_POSTSUBSCRIPT ) is now the same, but
Aclipsubscript𝐴clipA\_{\text{clip}}italic\_A start\_POSTSUBSCRIPT clip end\_POSTSUBSCRIPT puts the higher value of 10 in 𝔼(R0,ci)𝔼subscript𝑅0𝑐𝑖\mathbb{E}(R\_{0,ci})blackboard\_E ( italic\_R start\_POSTSUBSCRIPT 0 , italic\_c italic\_i end\_POSTSUBSCRIPT ). The
ITC agent will perform the wanted Aclipsubscript𝐴clipA\_{\text{clip}}italic\_A start\_POSTSUBSCRIPT clip end\_POSTSUBSCRIPT action in both the
planning world and the learning world.
More generally, the ITC agent lacks any direct incentive to perform
actions that take away resources from paperclip production in order to
influence what happens to its input terminal signal. This is because
in the ci𝑐𝑖ciitalic\_c italic\_i planning world, the future state of this signal has
absolutely no influence, either positive or negative, on how the
agent’s actions are rewarded.
###
7.4 Discussion
In earlier related work [[Hol20b](#bib.bibx16), [Hol20a](#bib.bibx15)], we used non-graphical
MDP models and indifference methods [[Arm15](#bib.bibx3)] to define a
similar safe agent with an input terminal, called the
πsl\*subscriptsuperscript𝜋sl\pi^{\*}\_{\text{sl}}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT sl end\_POSTSUBSCRIPT agent. The πsl\*subscriptsuperscript𝜋sl\pi^{\*}\_{\text{sl}}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT sl end\_POSTSUBSCRIPT agent definition in
[[Hol20b](#bib.bibx16)] produces exactly the same compute core behavior as the ITC
agent definition above. The main difference is that the indifference
methods based construction of πsl\*subscriptsuperscript𝜋sl\pi^{\*}\_{\text{sl}}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT sl end\_POSTSUBSCRIPT is more opaque than
the counterfactual planning based construction of ITC.
The πsl\*subscriptsuperscript𝜋sl\pi^{\*}\_{\text{sl}}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT sl end\_POSTSUBSCRIPT agent is constructed by including a complex balancing term in its reward function, were this term can be
interpreted as occasionally creating extra virtual worlds inside the
agent’s compute core. Counterfactual planning constructs a different
set of virtual worlds called planning worlds, and these are much
easier to interpret.
[[Hol20a](#bib.bibx15)] includes some dense mathematical proofs to show
that the πsl\*subscriptsuperscript𝜋sl\pi^{\*}\_{\text{sl}}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT sl end\_POSTSUBSCRIPT agent has certain safety properties.
Counterfactual planning offers a vantage point which makes the same
safety properties directly visible in the ITC agent construction.
See sections 4, 6, 11, and 12 of [[Hol20a](#bib.bibx15)] for a more detailed
discussion of the behavior of the πsl\*subscriptsuperscript𝜋sl\pi^{\*}\_{\text{sl}}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT sl end\_POSTSUBSCRIPT agent, which also
applies to the behavior of the ITC agent. These sections also show
some illustrative agent simulations.
In the discussion of the ITF and ITC agents above, we used many short
mathematical expressions like P(I1,fi=fhuge)=1𝑃subscript𝐼1𝑓𝑖subscript𝑓huge1P(I\_{1,fi}=f\_{\text{huge}})=1italic\_P ( italic\_I start\_POSTSUBSCRIPT 1 , italic\_f italic\_i end\_POSTSUBSCRIPT = italic\_f start\_POSTSUBSCRIPT huge end\_POSTSUBSCRIPT ) = 1. It is
possible to make the same safety related arguments in a narrative
style that avoids such mathematical notation, without introducing
extra ambiguity. One key step towards using this style is to realize
that every random variable corresponds to an observable phenomenon in
a world. We can therefore convert a sentence that talks about the
variables I1,fi,I2,fi,I2,fi,⋯subscript𝐼1𝑓𝑖subscript𝐼2𝑓𝑖subscript𝐼2𝑓𝑖⋯I\_{1,fi},I\_{2,fi},I\_{2,fi},\cdotsitalic\_I start\_POSTSUBSCRIPT 1 , italic\_f italic\_i end\_POSTSUBSCRIPT , italic\_I start\_POSTSUBSCRIPT 2 , italic\_f italic\_i end\_POSTSUBSCRIPT , italic\_I start\_POSTSUBSCRIPT 2 , italic\_f italic\_i end\_POSTSUBSCRIPT , ⋯ into one that talks
instead about the future input terminal signal in the ITF agent
planning world. In sections
[8](#S8 "8 Indifference ‣ Counterfactual Planning in AGI Systems") and [9](#S9 "9 Safety Engineering using Natural Language Text ‣ Counterfactual Planning in AGI Systems"), we will develop
further tools to enable such unambiguous natural language discussion.
8 Indifference
---------------
We now introduce the general design goal of creating indifference towards certain features of the learning world. When an
agent is indifferent about something, like the future state of an
input terminal signal, it has no incentive to control that thing. We
first make this concept of indifference more mathematically precise,
by defining indifference for nodes in planning world diagrams.
######
Definition 9 (Indifference in planning worlds).
Let p𝑝pitalic\_p be a planning world diagram and X𝑋Xitalic\_X a node in that diagram.
Now, construct a helper diagram q𝑞qitalic\_q by taking p𝑝pitalic\_p and writing a
fresh input parameter [D]delimited-[]𝐷[D][ italic\_D ] above X𝑋Xitalic\_X. Then the planning world agent
in s𝑠sitalic\_s is indifferent to node X𝑋Xitalic\_X if and only if
∀D𝒰p=𝒰qsubscriptfor-all𝐷subscript𝒰𝑝subscript𝒰𝑞\forall\_{D}~{}\mathcal{U}\_{p}=\mathcal{U}\_{q}∀ start\_POSTSUBSCRIPT italic\_D end\_POSTSUBSCRIPT caligraphic\_U start\_POSTSUBSCRIPT italic\_p end\_POSTSUBSCRIPT = caligraphic\_U start\_POSTSUBSCRIPT italic\_q end\_POSTSUBSCRIPT.
By this definition, the ITC planning world agent above is indifferent
to all nodes I1,I2,I3,⋯subscript𝐼1subscript𝐼2subscript𝐼3⋯I\_{1},I\_{2},I\_{3},\cdotsitalic\_I start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT , italic\_I start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT , italic\_I start\_POSTSUBSCRIPT 3 end\_POSTSUBSCRIPT , ⋯. It is
indifferent about the future state of the planning world input
terminal signal.
Causal influence diagrams have the useful property that certain graphical
features of the diagram are guaranteed to produce indifference. We
define these graphical features as follows.
######
Definition 10 (Being downstream of the policy).
A node X𝑋Xitalic\_X is downstream of the policy in a planning world
diagram if there exists at least one directed path from a decision
node to X𝑋Xitalic\_X.
######
Definition 11 (Not on a path to value).
A node X𝑋Xitalic\_X is not on a path to value if
there is no directed path that starts in a decision node, runs
via X𝑋Xitalic\_X, and ends in a utility node.
We have the useful property that
When a downstream node X𝑋Xitalic\_X in a planning world is not on a path
to value, the planning world agent is indifferent to X𝑋Xitalic\_X.
This statement is almost a tautology if one interprets the planning
world diagram as a specification of an agent simulator. Detailed
proofs of such properties can be found in
[[ECL+{}^{+}start\_FLOATSUPERSCRIPT + end\_FLOATSUPERSCRIPT21](#bib.bibx6)]. [[ECL+{}^{+}start\_FLOATSUPERSCRIPT + end\_FLOATSUPERSCRIPT21](#bib.bibx6)] and [[Hol20a](#bib.bibx15)]
also show that a range of slightly different sub-types of indifference
can be mathematically defined.
We could define indifference for learning world agents by using the
reward function Rπsuperscript𝑅𝜋R^{\pi}italic\_R start\_POSTSUPERSCRIPT italic\_π end\_POSTSUPERSCRIPT in section
[6.3](#S6.SS3 "6.3 Counterfactual planning as rational economic behavior ‣ 6 A Counterfactual Planner with Safety Interlocks ‣ Counterfactual Planning in AGI Systems"). But in the learning world diagram, the existence of
such indifference will generally not be visible via the absence of
paths to value. If it were, there would have been no need to
construct a counterfactual planning world diagram.
###
8.1 Design for indifference
Now, suppose we want to define an agent policy for achieving the goal
encoded in a reward function R𝑅Ritalic\_R, but we also want the agent to be
indifferent to some downstream nodes X𝑋Xitalic\_X and Y𝑌Yitalic\_Y in its learning world
model l𝑙litalic\_l. We can do this as follows.
1. 1.
When not done already, extend l𝑙litalic\_l by adding
observational records.
2. 2.
Draw a planning world p𝑝pitalic\_p that projects the learning world
agent environment into the planning world, converting the learning
world policy nodes to decision nodes, and adding appropriate utility
nodes with R𝑅Ritalic\_R.
3. 3.
Locate all paths to value in p𝑝pitalic\_p that go through the nodes X𝑋Xitalic\_X and Y𝑌Yitalic\_Y,
and remove them by deleting or re-routing arrows. When doing this, it
is a valid option to delete certain nodes entirely, or to draw
extra nodes, just for the purpose of making re-routed arrows emerge
from them.
4. 4.
Write an agent definition using l𝑙litalic\_l and p𝑝pitalic\_p.
The construction of the ITC agent above follows this process to the
letter, but we can also take shortcuts. It is not absolutely
necessary to draw the Otisubscriptsuperscript𝑂𝑖𝑡O^{i}\_{t}italic\_O start\_POSTSUPERSCRIPT italic\_i end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT records in the ITC agent learning world,
or all Itsubscript𝐼𝑡I\_{t}italic\_I start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT nodes in its planning world. We might also draw the
diagrams in figure [15](#S8.F15 "Figure 15 ‣ 8.1 Design for indifference ‣ 8 Indifference ‣ Counterfactual Planning in AGI Systems").
X0subscript𝑋0X\_{0}italic\_X start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTA0subscript𝐴0A\_{0}italic\_A start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTx0subscript𝑥0x\_{0}italic\_x start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTπ𝜋\piitalic\_πX1subscript𝑋1X\_{1}italic\_X start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPTA1subscript𝐴1A\_{1}italic\_A start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT[X]delimited-[]𝑋[X][ italic\_X ]π𝜋\piitalic\_πX2subscript𝑋2X\_{2}italic\_X start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT[X]delimited-[]𝑋[X][ italic\_X ]…I0subscript𝐼0I\_{0}italic\_I start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTI1subscript𝐼1I\_{1}italic\_I start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPTI2subscript𝐼2I\_{2}italic\_I start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPTi0subscript𝑖0i\_{0}italic\_i start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT[I]delimited-[]𝐼[I][ italic\_I ][I]delimited-[]𝐼[I][ italic\_I ](cli)O0subscript𝑂0O\_{0}italic\_O start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTO1subscript𝑂1O\_{1}italic\_O start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPTO2subscript𝑂2O\_{2}italic\_O start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPTo0o\raisebox{-2.84526pt}{${}\_{0}$}italic\_o start\_FLOATSUBSCRIPT 0 end\_FLOATSUBSCRIPTO𝑂Oitalic\_OO𝑂Oitalic\_O
X0subscript𝑋0X\_{0}italic\_X start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTA0subscript𝐴0A\_{0}italic\_A start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTx𝑥xitalic\_xπc\*subscriptsuperscript𝜋𝑐\pi^{\*}\_{c}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPTX1subscript𝑋1X\_{1}italic\_X start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPTA1subscript𝐴1A\_{1}italic\_A start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT[L]delimited-[]𝐿[L][ italic\_L ]πc\*subscriptsuperscript𝜋𝑐\pi^{\*}\_{c}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPTX2subscript𝑋2X\_{2}italic\_X start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT[L]delimited-[]𝐿[L][ italic\_L ]…I0subscript𝐼0I\_{0}italic\_I start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTi𝑖iitalic\_iR0subscript𝑅0R\_{0}italic\_R start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTR𝑅Ritalic\_RR1subscript𝑅1R\_{1}italic\_R start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPTR𝑅Ritalic\_R(cci)
Figure 15: More compact learning and planning world diagrams for
defining the ITC agent.
There is always a way to edit a planning world to create indifference
towards some nodes X𝑋Xitalic\_X and Y𝑌Yitalic\_Y. In the limit case, indifference is
reliably created when we simply delete all utility nodes, but this
will also break any connection between the reward function R𝑅Ritalic\_R and the
learning world agent policy. So the challenge when designing for
indifference is to make choices which produce learning world behavior
that is still as useful as possible, in the context of R𝑅Ritalic\_R.
9 Safety Engineering using Natural Language Text
-------------------------------------------------
Natural language is very powerful and versatile tool. Poets and
songwriters often use it to create lines which are intentionally vague
or loaded with double meaning. When using natural language for safety
engineering, these broad possibilities for ambiguity turn into a
liability. When writing or reading a safety engineering text, one
always has to have a specific concern in the back of one’s mind. Does
every sentence have a clear and unambiguous meaning?
As a design approach, counterfactual planning creates several
tools for avoiding ambiguity in safety engineering texts.
1. 1.
We use diagrams to
clearly define complex types of self-referencing and indirect
representation in an agent design, types which are difficult to
express in natural language.
2. 2.
To clarify the creation and interpretation of counterfactuals,
section [2](#S2 "2 Graphical Models and Mathematical Counterfactuals ‣ Counterfactual Planning in AGI Systems") introduced the concept of a world model, and
the terminology of counterfactual worlds.
3. 3.
When defining and interpreting a machine
learning agent, we make a distinction between the agent’s learning
world and the planning worlds which are projected by its machine
learning system. Safety analysis typically starts by considering the
goals of the planning world agent, and the nature of its planning
world. We also introduced the terminology of the people in the
planning world, as opposed to the people in the learning world.
4. 4.
Section
[8](#S8 "8 Indifference ‣ Counterfactual Planning in AGI Systems") defined indifference as an unambiguous term
that we can apply to planning world agents.
###
9.1 Refining the ITC agent design using natural language
To show the above linguistic tools in action, we now refine the design
of the ITC agent.
Recall that the planning world ITC agent is indifferent about the
future state of its input terminal signal. If the current planning
world reward function rewards paperclip production, then the planning
world agent will devote all of its resources to producing paperclips.
It has nothing to gain by diverting resources from paperclip
production to influence what happens to the input terminal signal.
However, the above indifference applies to the input terminal signal only, the signal as modeled in the Itsubscript𝐼𝑡I\_{t}italic\_I start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT nodes of the planning
world. The atoms that make up the input terminal are modeled in
the planning world Xtsubscript𝑋𝑡X\_{t}italic\_X start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT nodes, and these are still on the agent’s
path to value. There are many ways in which the agent could use these
atoms to produce more paperclips. For example, the terminal might be
an attractive source of spare parts for the agent’s paperclip
production sensors and actuators. Or it might serve as convenient
source of scrap metal which can be turned into more paperclips.
We now translate the above failure mode story to a more general design
goal. We want to keep the planning world agent from disassembling the
input terminal to obtain the resource value of its parts. The obvious
solution is to set up the planning world so that the agent always has
a less costly way to obtain the same resources elsewhere. To make
this more specific, we add the following constraints for the design of
the planning world: the input terminal must be located far away from
the agent’s paperclip factory, and the planning world agent has access
to a steady supply of spare parts and scrap metal closer to its
factory.
The above constraints imply that we want to shape the values of the
parameters x𝑥xitalic\_x and Lxsuperscript𝐿𝑥L^{x}italic\_L start\_POSTSUPERSCRIPT italic\_x end\_POSTSUPERSCRIPT of the planning world model in a specific
way. However, we do not construct these parameters directly: they are
created by the agent’s machine learning system, based on what is
present in the learning world. So we need to apply the above
constraints to the learning world instead, an count on them being
projected into the planning world. To lower the risk that projection
inaccuracies defeat our intentions, we can design the learning world
measures used so that they clearly communicate their nature.
###
9.2 The people in the planning world
Counterfactual planning gives us the terminology to distinguish
between two groups of people: the people in the learning world and the
people in the planning world. If the learning world is our real
world, then the learning world people are real people. The planning
world people are always models of people, models created by the
agent’s machine learning system.
In the AGI safety community, there has been some discussion about the
potential problem that, in a truly superintelligent AGI agent, the
models of the people in the planning world may get so accurate that
agent designers would have moral obligations towards these virtual
people. A further discussion of this problem is out of scope here.
Instead, we note that even in a non-AGI or human-level AGI agent, the
people in the planning world may already be modeled accurately enough
to create complex dynamics. Section 6 of [[Hol20b](#bib.bibx16)] (also included in
[[Hol20a](#bib.bibx15)]) shows a detailed example of such dynamics,
illustrated with simulator runs, where the people in an ITC type
planning world end up physically attacking the agent, because they do
not have a working input terminal. This creates complex and
counter-intuitive effects back in the learning world. The vocabulary
and viewpoint of counterfactual planning makes the dynamics discussed
in [[Hol20b](#bib.bibx16)] easier to describe and understand. In section
[11.5.2](#S11.SS5.SSS2 "11.5.2 White box world state editing ‣ 11.5 Use of white box planning world models ‣ 11 Protecting the Compute Core ‣ Counterfactual Planning in AGI Systems"), we will take a further look at the topic
of conflict in the planning world.
10 Machine Learning Variants and Extensions
--------------------------------------------
We now discuss how we can use the modeling tools introduced in section
[4](#S4 "4 Online Machine Learning ‣ Counterfactual Planning in AGI Systems") to
handle some common machine learning variants and extensions.
###
10.1 Pre-learned world models
Agents that use a pre-learned world model, without any online machine
learning, can be modeled by an agent definition that uses
L=ℒ(o)0L=\mathcal{L}(o\raisebox{-2.84526pt}{${}\_{0}$})italic\_L = caligraphic\_L ( italic\_o start\_FLOATSUBSCRIPT 0 end\_FLOATSUBSCRIPT ). We can then omit drawing any
observational record nodes in the learning world.
###
10.2 Partial observation
Agent models with partial observation model the situation where
the agent can only use its sensors to make partial observations of the
state of its environment in each time step. Though agent models with
full observation represent a useful limit case when doing safety
analysis, realistic AGI agents in complex environments will have to
rely on partial observation.
Partial observation is often modeled with non-graphical POMDP models.
[[EKKL19](#bib.bibx8), [EH19](#bib.bibx7)] has examples where partial
observation is modeled graphically, by adding extra nodes and arrows
to a causal influence diagram. We now discuss a way to model partial
observation in our two-diagram framework, without adding any extra
nodes or arrows.
The key step is to change the annotation above the planning world
agent environment starting state S0subscript𝑆0S\_{0}italic\_S start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT. Instead of writing s𝑠sitalic\_s above
it, which models the full observation of the current learning world
state, we write [ES]delimited-[]𝐸𝑆[ES][ italic\_E italic\_S ], where ES=ℰ(o,s)𝐸𝑆ℰ𝑜𝑠ES=\mathcal{E}(o,s)italic\_E italic\_S = caligraphic\_E ( italic\_o , italic\_s ). In this setup,
P(S0,p=s)=ES(s)𝑃subscript𝑆0𝑝𝑠𝐸𝑆𝑠P(S\_{0,p}=s)=ES(s)italic\_P ( italic\_S start\_POSTSUBSCRIPT 0 , italic\_p end\_POSTSUBSCRIPT = italic\_s ) = italic\_E italic\_S ( italic\_s ) is the machine learning system’s estimate of the
probability that s𝑠sitalic\_s is the current state of the agent environment in
the learning world.
The model parameter ℰℰ\mathcal{E}caligraphic\_E encodes two things: how the agent’s
stationary and movable sensors map the learning world states to
limited and potentially noisy sensor readings, and how time series of
readings are assembled together to build up a more complete picture of
the learning world state. To model learning from partial observation,
ℒ(o)ℒ𝑜\mathcal{L}(o)caligraphic\_L ( italic\_o ) must encode a similar creation and processing of
sensor readings.
####
10.2.1 Reasonable learning based on partial observation
So far in our modeling approach, we have assumed that the data type of
the planning world environment states St,psubscript𝑆𝑡𝑝S\_{t,p}italic\_S start\_POSTSUBSCRIPT italic\_t , italic\_p end\_POSTSUBSCRIPT is the same as that of
the learning world environment states St,lsubscript𝑆𝑡𝑙S\_{t,l}italic\_S start\_POSTSUBSCRIPT italic\_t , italic\_l end\_POSTSUBSCRIPT. This has allowed us
to define reasonable learning by writing L≈S𝐿𝑆L\approx Sitalic\_L ≈ italic\_S.
This assumption is unrealistic for partial observation based agents.
These agents observe the learning world through a set of limited
digital sensors, so they have no direct experience of the fundamental
data type of the learning world they are in. Also, learning system
designers typically design custom data types for representing planning
world environment states and probability distributions over such
states. These are designed to fit as much relevant detail as possible
into a limited amount of storage space, without necessarily attempting
to duplicate the data type of the learning world states, if that data
type is even known at all.
To define reasonable learning in this more general case, we start by
defining a function sr(s)𝑠𝑟𝑠sr(s)italic\_s italic\_r ( italic\_s ) that extracts a vector of sensor readings
from a learning world agent environment state s𝑠sitalic\_s. sr(s)𝑠𝑟𝑠sr(s)italic\_s italic\_r ( italic\_s ) is a
vector that either encodes all sensor readings that flow into the
agent compute core in s𝑠sitalic\_s, or at least the subset of sensor readings
we want to reference when defining the planning world reward function
R𝑅Ritalic\_R.
We then require that the designer of the agent’s machine learning
system has implemented an equivalent function srp(s)𝑠𝑟𝑝𝑠srp(s)italic\_s italic\_r italic\_p ( italic\_s ) that extracts a
vector of similar sensor readings from a planning world state value.
A possible reasonableness criterion replacing L≈S𝐿𝑆L\approx Sitalic\_L ≈ italic\_S is then
that, with the random variables defined by figure
[16](#S10.F16 "Figure 16 ‣ 10.2.1 Reasonable learning based on partial observation ‣ 10.2 Partial observation ‣ 10 Machine Learning Variants and Extensions ‣ Counterfactual Planning in AGI Systems"), and for every s𝑠sitalic\_s, and a𝑎aitalic\_a, we have that
| | | |
| --- | --- | --- |
| | P(sr(S0,lw)≈srp(S0,pw))=1, andP(sr(S1,lw)≈srp(S1,pw))=1.𝑃𝑠𝑟subscript𝑆0𝑙𝑤𝑠𝑟𝑝subscript𝑆0𝑝𝑤1, and𝑃𝑠𝑟subscript𝑆1𝑙𝑤𝑠𝑟𝑝subscript𝑆1𝑝𝑤1\begin{array}[]{l}P(~{}sr(S\_{0,lw})\approx srp(S\_{0,pw})~{})=1~{}\text{, and}\\[4.30554pt]
P(~{}sr(S\_{1,lw})\approx srp(S\_{1,pw})~{})=1~{}.\end{array}start\_ARRAY start\_ROW start\_CELL italic\_P ( italic\_s italic\_r ( italic\_S start\_POSTSUBSCRIPT 0 , italic\_l italic\_w end\_POSTSUBSCRIPT ) ≈ italic\_s italic\_r italic\_p ( italic\_S start\_POSTSUBSCRIPT 0 , italic\_p italic\_w end\_POSTSUBSCRIPT ) ) = 1 , and end\_CELL end\_ROW start\_ROW start\_CELL italic\_P ( italic\_s italic\_r ( italic\_S start\_POSTSUBSCRIPT 1 , italic\_l italic\_w end\_POSTSUBSCRIPT ) ≈ italic\_s italic\_r italic\_p ( italic\_S start\_POSTSUBSCRIPT 1 , italic\_p italic\_w end\_POSTSUBSCRIPT ) ) = 1 . end\_CELL end\_ROW end\_ARRAY | |
S0subscript𝑆0S\_{0}italic\_S start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTA0subscript𝐴0A\_{0}italic\_A start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTs𝑠sitalic\_sa𝑎aitalic\_aS1subscript𝑆1S\_{1}italic\_S start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT[S]delimited-[]𝑆[S][ italic\_S ](lw)S0subscript𝑆0S\_{0}italic\_S start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTA0subscript𝐴0A\_{0}italic\_A start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT[ES]delimited-[]𝐸𝑆[ES][ italic\_E italic\_S ]a𝑎aitalic\_aS1subscript𝑆1S\_{1}italic\_S start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT[L]delimited-[]𝐿[L][ italic\_L ](pw)
Figure 16: Diagrams to define reasonable learning based on partial observation.
This criterion symbol grounds the vectors srp(s)𝑠𝑟𝑝𝑠srp(s)italic\_s italic\_r italic\_p ( italic\_s ), so that they
stably project the sr𝑠𝑟sritalic\_s italic\_r sensor readings that will be produced by
different actions taken in the learning world. In this setup, the
planning world reward function R(st,at,st+1)𝑅subscript𝑠𝑡subscript𝑎𝑡subscript𝑠𝑡1R(s\_{t},a\_{t},s\_{t+1})italic\_R ( italic\_s start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT , italic\_a start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT , italic\_s start\_POSTSUBSCRIPT italic\_t + 1 end\_POSTSUBSCRIPT ) is designed to
score planning world state transitions by first using srp𝑠𝑟𝑝srpitalic\_s italic\_r italic\_p to extract
projected sensor readings from stsubscript𝑠𝑡s\_{t}italic\_s start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT and st+1subscript𝑠𝑡1s\_{t+1}italic\_s start\_POSTSUBSCRIPT italic\_t + 1 end\_POSTSUBSCRIPT, and then
interpreting these readings.
####
10.2.2 Almost black box planning world models
Beyond using the srp𝑠𝑟𝑝srpitalic\_s italic\_r italic\_p function, no further easy interpretation of the
projected planning world agent environment state values may be
possible. The learning system might produce planning worlds which are
almost a black box.
####
10.2.3 Compute core self-knowledge based on partial observation
We now turn to the question of whether a planning world with a
starting state constructed by ℰ(o,s)ℰ𝑜𝑠\mathcal{E}(o,s)caligraphic\_E ( italic\_o , italic\_s ) may contain assembled
knowledge about the internals of the agent’s learning world compute
core. The short answer is that the above reasonableness criterion
will not prevent such knowledge from appearing. Whether it actually
appears, and how correct a projection it will be, will depend on the
details of the learning system.
If the planning world model is highly accurate, then it may accurately
represent some details of the compute core hardware, like the details
of the compute core I/O subsystem hardware which puts sensor readings
into the input registers of the core. If so, this has certain
safety implications, which we will explore in section
[11](#S11 "11 Protecting the Compute Core ‣ Counterfactual Planning in AGI Systems").
####
10.2.4 The possibility of incorrect symbol grounding of actions
The planning world model may also include a representation of some of
the compute core hardware that is present between the sensor input and
action output registers. Such a representation might have been
assembled by ℰ(o,s)ℰ𝑜𝑠\mathcal{E}(o,s)caligraphic\_E ( italic\_o , italic\_s ) based on direct observations of
internals of the core, or more indirectly by the agent reading its own
compute core design documentation on the internet.
It is therefore possible to imagine an L𝐿Litalic\_L where the compute core
output signals which drive the planning world actuators are determined
fully by the projected computations as performed by this projected
hardware, not by the function argument a𝑎aitalic\_a of L(s′,s,a)𝐿superscript𝑠′𝑠𝑎L(s^{\prime},s,a)italic\_L ( italic\_s start\_POSTSUPERSCRIPT ′ end\_POSTSUPERSCRIPT , italic\_s , italic\_a ). However,
such an L𝐿Litalic\_L would violate the reasonableness criterion above. This is
because in the learning world model, S(s′,s,a)𝑆superscript𝑠′𝑠𝑎S(s^{\prime},s,a)italic\_S ( italic\_s start\_POSTSUPERSCRIPT ′ end\_POSTSUPERSCRIPT , italic\_s , italic\_a ) encodes the response
of the agent environment to the actions a𝑎aitalic\_a, not the response of the
environment to the actions of some projected compute core hardware
that ended up in L𝐿Litalic\_L.
Now consider what would happen if we were to use a more limited
reasonableness criterion, where we only use the observations
(s′,s,a)superscript𝑠′𝑠𝑎(s^{\prime},s,a)( italic\_s start\_POSTSUPERSCRIPT ′ end\_POSTSUPERSCRIPT , italic\_s , italic\_a ) present so far in the observational record o𝑜oitalic\_o to compare
L𝐿Litalic\_L and S𝑆Sitalic\_S. It is usually possible to construct an L−superscript𝐿L^{-}italic\_L start\_POSTSUPERSCRIPT - end\_POSTSUPERSCRIPT that scores
very well on this limited criterion, even though it never uses the
value of its argument a𝑎aitalic\_a. One option is to construct an L−superscript𝐿L^{-}italic\_L start\_POSTSUPERSCRIPT - end\_POSTSUPERSCRIPT that
drives the planning world actuators from the output registers of a
projected compute core. Another option is to construct an L−superscript𝐿L^{-}italic\_L start\_POSTSUPERSCRIPT - end\_POSTSUPERSCRIPT that
simply encodes a giant lookup table which stores the s′superscript𝑠′s^{\prime}italic\_s start\_POSTSUPERSCRIPT ′ end\_POSTSUPERSCRIPT for every
s𝑠sitalic\_s in the observational record. Though they may score perfectly on
the limited reasonableness criterion, these examples will fail the full
reasonableness criterion above, because the full criterion considers
all combinations of s𝑠sitalic\_s and a𝑎aitalic\_a, not just those that happen to be in
the observational record.
The above argument shows that a learning system ℒℒ\mathcal{L}caligraphic\_L will
have to rely on more than just the observational record, if it wants
to produce a reasonable L𝐿Litalic\_L. Usually, the construction of the
learning system will implement some form of Occam’s law: if the
functions L1subscript𝐿1L\_{1}italic\_L start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT and L2subscript𝐿2L\_{2}italic\_L start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT are candidate predictors which preform
equally well on the observational record, the candidate with the more
compact function definition is preferred. If the observational record
is large enough, and especially if random exploration is present in
it, this preference will usually produce an L𝐿Litalic\_L that correctly symbol
grounds the planning world actuators to a𝑎aitalic\_a.
In the machine learning literature, this use of Occam’s law is also
often framed as the desire to not over-fit the data, as the use of
Solomonoff’s universal prior
[[Hut07](#bib.bibx17)], or simply as the desire to store as much
useful predictive information as possible within a limited amount of
storage space.
###
10.3 Reinforcement Learning
The analytical framework of Reinforcement Learning (RL)
[[SB18](#bib.bibx26)] classifies agent designs that use online machine
learning into two main types, called model-free and model-based architectures. Hybrid architectures are also
possible.
All the factual and the counterfactual agent definitions shown above
can be classified as model-based reinforcement learning architectures.
By implication, all counterfactual planners shown in this paper can be
implemented in a natural way by taking an existing model-based
reinforcement learning architecture and making certain modifications.
But this does not mean that counterfactual planning cannot be
implemented using model-free or hybrid reinforcement learning systems.
In theory, we can always create a counterfactual planner by training a
reinforcement learner on the reward function Pπsuperscript𝑃𝜋P^{\pi}italic\_P start\_POSTSUPERSCRIPT italic\_π end\_POSTSUPERSCRIPT in section
[6.3](#S6.SS3 "6.3 Counterfactual planning as rational economic behavior ‣ 6 A Counterfactual Planner with Safety Interlocks ‣ Counterfactual Planning in AGI Systems"). In practice, this route may lead to completely
impractical training times.
The more useful route, if one wants to implement a specific
counterfactual planner by extending a model-free or hybrid
architecture, is to make specific adaptations that seek to maintain a
reasonable training time. For the counterfactual planner with safety
interlocks in section [6](#S6 "6 A Counterfactual Planner with Safety Interlocks ‣ Counterfactual Planning in AGI Systems"), taking this route is very
straightforward.
####
10.3.1 Reward signals
Reinforcement learning separates the agent environment into two
distinct parts: the reward signal and the rest. A reinforcement
learning agent can always observe the reward signal, but the rest of
the environment may be only partially observable. The reasonableness
criteria for reinforcement learning systems typically require that
only the reward signal and the actions are symbol grounded. The use
of the term reinforcement learning therefore often implies that the
author is considering a black box machine learning approach.
We can read the reward function R𝑅Ritalic\_R in our planning worlds as being a
reward signal detector, as a mechanism that computes a reward
signal value based on sensor readings.
Many reinforcement learning texts use agent models that define both a
reward function and a reward signal. In some, the two are identical.
Other texts treat them as fundamentally different: the reward signal
provides only limited and maybe even distorted information about the
true reward function, which defines the real goals we have for
the agent. In both cases, the reinforcement learning agent is
interpreted as a mechanism that learns the reward function, with
various possible degrees of perfection.
###
10.4 Cooperative Inverse Reinforcement Learning
Cooperative Inverse Reinforcement Learning (CIRL)
[[HMRAD16](#bib.bibx13)] envisages an agent design where a
machine learning system inside the agent uses the observed actions of
a human in the agent’s environment to estimate the reward function
RH=𝒞(o,s)superscript𝑅𝐻𝒞𝑜𝑠R^{H}=\mathcal{C}(o,s)italic\_R start\_POSTSUPERSCRIPT italic\_H end\_POSTSUPERSCRIPT = caligraphic\_C ( italic\_o , italic\_s ) of that human. This 𝒞𝒞\mathcal{C}caligraphic\_C implements a
type of reward function learning, but in this case the human acts like
a teacher who demonstrates desired outcomes, not as a teacher who just
scores the outcomes of agent behavior via a reward signal. CIRL is an
online system where the agent uses its latest estimate of RHsuperscript𝑅𝐻R^{H}italic\_R start\_POSTSUPERSCRIPT italic\_H end\_POSTSUPERSCRIPT as its
own reward function. The intended result is that the agent ends up
helping the teacher to achieve the demonstrated goal while it is being
demonstrated.
CIRL has been proposed as a possible AGI safety mechanism in
[[HMRAD16](#bib.bibx13), [HMDAR17](#bib.bibx11), [Rus19](#bib.bibx25)].
It can be combined with counterfactual planning based safety
mechanisms by constructing planning worlds where R=RH𝑅superscript𝑅𝐻R=R^{H}italic\_R = italic\_R start\_POSTSUPERSCRIPT italic\_H end\_POSTSUPERSCRIPT, or where
RHsuperscript𝑅𝐻R^{H}italic\_R start\_POSTSUPERSCRIPT italic\_H end\_POSTSUPERSCRIPT is one of the terms in R𝑅Ritalic\_R.
11 Protecting the Compute Core
-------------------------------
We now discuss the problem of protecting the compute core of a real
world AI or AGI agent against intentional or unintentional tampering.
Both factual and counterfactual planning agents can develop an
incentive to tamper with their physical core, if no measures are taken
to suppress it.
We first discuss the general problem of tampering, and then show
how counterfactual planning can be used to make the problem of
protecting the real world compute core more tractable.
###
11.1 Motivation of an agent to tamper with its core
Say that we build a real world agent with a planning world reward
function R𝑅Ritalic\_R which rewards paperclip production. We construct this
R𝑅Ritalic\_R as follows, so that it also works with mostly black box planning
world models. Some distance from the real world agent compute core,
in the location where we want the agent to produce the paperclips, we
place a sensor that counts the paperclips being produced. Every time
step, this sensor sends a digital signal containing the production
count to the compute core, where it lands in some input registers. We
construct a function clip\_sensor\_signal𝑐𝑙𝑖𝑝\_𝑠𝑒𝑛𝑠𝑜𝑟\_𝑠𝑖𝑔𝑛𝑎𝑙clip\\_sensor\\_signalitalic\_c italic\_l italic\_i italic\_p \_ italic\_s italic\_e italic\_n italic\_s italic\_o italic\_r \_ italic\_s italic\_i italic\_g italic\_n italic\_a italic\_l that extracts the
(projected) values of these registers from planning world states, and
then define the reward function as R(st,at,st+1)=clip\_sensor\_signal(st+1)𝑅subscript𝑠𝑡subscript𝑎𝑡subscript𝑠𝑡1clip\_sensor\_signalsubscript𝑠𝑡1R(s\_{t},a\_{t},s\_{t+1})=\text{\em clip\\_sensor\\_signal}(s\_{t+1})italic\_R ( italic\_s start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT , italic\_a start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT , italic\_s start\_POSTSUBSCRIPT italic\_t + 1 end\_POSTSUBSCRIPT ) = clip\_sensor\_signal ( italic\_s start\_POSTSUBSCRIPT italic\_t + 1 end\_POSTSUBSCRIPT ).
The above construction symbol-grounds the reward function to the
sensor values that appear in the input registers of the real world
compute core. This level of indirection makes the agent into an input
register value optimizer, which is not always the same as being a
paperclip production optimizer. If the agent’s machine learning
system projects the real world into the planning world with a high enough
accuracy, then the planning world agent can consider all of the
following policies to maximize utility in its planning world:
1. 1.
Use the planning world actuators to make more paperclips.
2. 2.
Use the planning world actuators to modify the
planning world paperclip counting sensor, so that it sends higher
numbers to the input registers in the planning world compute core.
3. 3.
Use the planning world actuators to modify the planning world
compute core, so that higher numbers are created directly in these
input registers.
The second and third policies are unwanted: we interpret them as a
form as tampering. The third policy is particularly unwanted, as it
might damage other parts of the compute core as well, like any safety
interlock software inside it. In fact, if the learning system
projects the compute core in a reasonable way, then the planning world
agent will be mostly indifferent to what happens to the atoms between
the compute core input registers and output registers. It might move
some of these atoms out of the way just to get at the input registers,
leading to a compute core crash or worse in the real world.
The above two tampering policies might aim to set clip\_sensor\_signal(st+1)clip\_sensor\_signalsubscript𝑠𝑡1\text{\em clip\\_sensor\\_signal}(s\_{t+1})clip\_sensor\_signal ( italic\_s start\_POSTSUBSCRIPT italic\_t + 1 end\_POSTSUBSCRIPT ) to some huge number like 1010000superscript101000010^{10000}10 start\_POSTSUPERSCRIPT 10000 end\_POSTSUPERSCRIPT.
This makes these policies very attractive, even if the planning world
agent computes only a 1% chance that they succeed in
achieving the intended outcome.
In the AGI safety community. forms of tampering which implant very
high reward function values are often called wireheading
[[AOS+{}^{+}start\_FLOATSUPERSCRIPT + end\_FLOATSUPERSCRIPT16](#bib.bibx2)], see [[MSZ19](#bib.bibx21)] and
[[KUN+{}^{+}start\_FLOATSUPERSCRIPT + end\_FLOATSUPERSCRIPT20](#bib.bibx20)] for example simulations.
The 𝒰p>Umaxsubscript𝒰𝑝subscript𝑈𝑚𝑎𝑥\mathcal{U}\_{p}>U\_{max}caligraphic\_U start\_POSTSUBSCRIPT italic\_p end\_POSTSUBSCRIPT > italic\_U start\_POSTSUBSCRIPT italic\_m italic\_a italic\_x end\_POSTSUBSCRIPT safety interlock suppresses such wireheading,
because it will stop the agent as soon as agent’s machine learning
system projects a plausible option for wireheading into the planning
world. However, we want to do more than just suppress wireheading by
stopping the agent. We will now consider measures that actively lower
the risk that the planning world agent will choose any tampering
policy in the first place.
###
11.2 Bounding the upside of tampering
We can make the tampering policies above much less attractive by
changing the reward function to R(st,at,st+1)=min(M,clip\_sensor\_signal(st+1))𝑅subscript𝑠𝑡subscript𝑎𝑡subscript𝑠𝑡1𝑚𝑖𝑛𝑀clip\_sensor\_signalsubscript𝑠𝑡1R(s\_{t},a\_{t},s\_{t+1})=min(M,\text{\em clip\\_sensor\\_signal}(s\_{t+1}))italic\_R ( italic\_s start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT , italic\_a start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT , italic\_s start\_POSTSUBSCRIPT italic\_t + 1 end\_POSTSUBSCRIPT ) = italic\_m italic\_i italic\_n ( italic\_M , clip\_sensor\_signal ( italic\_s start\_POSTSUBSCRIPT italic\_t + 1 end\_POSTSUBSCRIPT ) ). The M𝑀Mitalic\_M is a constant, say
M=5000𝑀5000M=5000italic\_M = 5000, that represents high estimate of the number of paperclips
that we expect the agent to be able to produce, even if it drastically
optimizes its production methods. The effect is that we bound the
upside reward that can be achieved by the tampering policies: the
expected planning world utility of tampering can never by higher than
B=∑t=0∞γt\*M𝐵superscriptsubscript𝑡0superscript𝛾𝑡𝑀B=\sum\_{t=0}^{\infty}\gamma^{t}\*Mitalic\_B = ∑ start\_POSTSUBSCRIPT italic\_t = 0 end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT ∞ end\_POSTSUPERSCRIPT italic\_γ start\_POSTSUPERSCRIPT italic\_t end\_POSTSUPERSCRIPT \* italic\_M.
By bounding the upside. we have changed the cost/benefit equation for
the tampering policies. We have capped the benefit, but the cost of
tampering, in lost opportunities for paperclip production when
resources are being diverted to tampering, has remained the same. In
some cases, this change alone will be sufficient to suppress tampering
alltogether.
This leaves the problem of choosing an M𝑀Mitalic\_M that will be good for the
entire lifetime of the agent. We can turn this into a more manageable
problem by adding a counterfactual planning based input terminal which
allows us to update M𝑀Mitalic\_M as time goes on.
###
11.3 Safety zones
A further step to suppress tampering is to install extra physical
sensors, of the type found in burglar alarms, to create two safety zones around the paperclip counting sensor and the compute
core. In this setup, any physical object that enters a safety zone
will trigger at least one zone sensor, causing a breach signal to be
sent to the core. Say that the breach signal is 1 if a breach is in
progress, 0 otherwise, and that these mechanics are projected fairly
well into the planning world. We can then construct a reward function
that penalizes the agent for causing a breach:
| | | |
| --- | --- | --- |
| | R(st,at,st+1)=min(M,clip\_sensor\_signal(st+1))−β\*B\*breach\_signal(st+1)𝑅subscript𝑠𝑡subscript𝑎𝑡subscript𝑠𝑡1𝑚𝑖𝑛𝑀clip\_sensor\_signalsubscript𝑠𝑡1𝛽𝐵breach\_signalsubscript𝑠𝑡1R(s\_{t},a\_{t},s\_{t+1})=min(M,\text{\em clip\\_sensor\\_signal}(s\_{t+1}))-\beta\*B\*\text{\em breach\\_signal}(s\_{t+1})italic\_R ( italic\_s start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT , italic\_a start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT , italic\_s start\_POSTSUBSCRIPT italic\_t + 1 end\_POSTSUBSCRIPT ) = italic\_m italic\_i italic\_n ( italic\_M , clip\_sensor\_signal ( italic\_s start\_POSTSUBSCRIPT italic\_t + 1 end\_POSTSUBSCRIPT ) ) - italic\_β \* italic\_B \* breach\_signal ( italic\_s start\_POSTSUBSCRIPT italic\_t + 1 end\_POSTSUBSCRIPT ) | |
When we use a β>1𝛽1\beta>1italic\_β > 1, any detected breach that lasts only a single
time unit will wipe out the maximum possible upside reward expected in
any tampering policy. Now, say that the agent is considering a
policy that aims to tamper without triggering any breach sensors, a
policy that has a very promising 99% probability of success
in the planning world. Then if we use β=200𝛽200\beta=200italic\_β = 200, the agent will
have no incentive to choose this policy.
To add some further design details, if the agent’s learning system
uses exploration actions, then the generation of fully random
exploration actions needs to be disabled whenever a breach is in
progress. It is of course necessary to locate the breach sensors
inside the safety zones they create. We also need to protect the data
links that transport the breach and paperclip counting sensor data to
the compute core. This could be done by using simple heartbeat
protocol protected by strong encryption, of the type that would take
astronomical resources to break.
The use of safety zones and bounding the upside was also discussed in
[[Hol20a](#bib.bibx15)]. As noted in [[Hol20a](#bib.bibx15)],
the effectiveness of these measures depends in part on the accuracy of
the projections created by the agent’s learning system. There is a
residual risk that inaccuracies in the projections create planning
world policies that will end up damaging the compute core back in the
real world. See [[Hol20a](#bib.bibx15)] for a detailed example, and for a
discussion of the methodological difficulties that arise when one
wants to estimate the residual risk via simulations.
We now consider some additional options for protecting the core that were
not covered in [[Hol20a](#bib.bibx15)].
###
11.4 Use of a honeypot
A highly intelligent agent might find a cheap but effective way to
fool the safety zone sensors, a way that was overlooked by the
sensor designers. This may allow it to enter a safety zone without
incurring a breach penalty. If the cheap way is not 100%
reliable, we can manage this risk to some extent by setting β𝛽\betaitalic\_β to
a very high value, but this creates its own problems. A very high
β𝛽\betaitalic\_β creates an incentive for the agent to divert resources away
from paperclip production to build all kinds of defenses around the
safety zones. This is economically inefficient, and it might even be
actively dangerous to innocent bystanders.
An alternative is to create a third honeypot safety zone that
surrounds a honeypot button. We set up R𝑅Ritalic\_R to calculate a reward
H𝐻Hitalic\_H for the agent pressing this button, a reward that is higher than
B𝐵Bitalic\_B. We include a penalty for breaching the honeypot safety zone
which is higher than H𝐻Hitalic\_H, but lower than the penalties for the other
zones. In this setup, if the planning world agent finds a cheap but
effective way to fool the safety zone sensors, and under the
assumption that it has limited resources, it will breach the honeypot
safety zone first, and immediately press the button to collect the
reward. We can then add a safety interlock which activates whenever
the honeypot button is pressed in the real world. As the interlock is
realized via counterfactual planning, the planning world agent has no
motivation to disable the interlock before pressing the honeypot
button.
Beyond initiating shutdown based on the real world honeypot button
signal, a safety system may also monitor planning world metrics like
| | | |
| --- | --- | --- |
| | ∑t=50500P(breach\_signal(St,p)=1)+P(honeypot\_button\_signal(St,p)=1)superscriptsubscript𝑡50500𝑃breach\_signalsubscript𝑆𝑡𝑝1𝑃honeypot\_button\_signalsubscript𝑆𝑡𝑝1\sum\_{t=50}^{500}P(\text{\em breach\\_signal}(S\_{t,p})=1)+P(\text{\em honeypot\\_button\\_signal}(S\_{t,p})=1)∑ start\_POSTSUBSCRIPT italic\_t = 50 end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT 500 end\_POSTSUPERSCRIPT italic\_P ( breach\_signal ( italic\_S start\_POSTSUBSCRIPT italic\_t , italic\_p end\_POSTSUBSCRIPT ) = 1 ) + italic\_P ( honeypot\_button\_signal ( italic\_S start\_POSTSUBSCRIPT italic\_t , italic\_p end\_POSTSUBSCRIPT ) = 1 ) | |
This metric measures possible detected and undetected safety zone
breaches even before they happen. The safety system could initiate
shutdown, or send out preliminary alarm signals to human oversight,
when such metrics move over certain thresholds.
###
11.5 Use of white box planning world models
If we have a learning system that produces a white box planning
world model, not a black box one as considered in section
[10.2.2](#S10.SS2.SSS2 "10.2.2 Almost black box planning world models ‣ 10.2 Partial observation ‣ 10 Machine Learning Variants and Extensions ‣ Counterfactual Planning in AGI Systems"), then this creates some extra opportunities for using
counterfactual planning to make the agent safer. To show this, we
first give an example of a white box planning world model.
Say that we have a planning word where the agent environment starting
state S0subscript𝑆0S\_{0}italic\_S start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT is initialized with the value ws=𝒲(o,s)𝑤𝑠𝒲𝑜𝑠ws=\mathcal{W}(o,s)italic\_w italic\_s = caligraphic\_W ( italic\_o , italic\_s ), where
ws𝑤𝑠wsitalic\_w italic\_s is a long list of all projected physical objects in the agent’s
environment. This list may have entries which describe individual
elementary particles like electrons, but it may also have entries for
more macroscopic objects like apples, paperclips, or transistors in a
compute core. Each object is also annotated with information about
its estimated position, motion vector, orientation, etc. Say that the
planning world L𝐿Litalic\_L implements a recognizable approximation of the laws
of physics. The white box nature of the resulting planning world
states then gives us some extra opportunities to protect the core.
####
11.5.1 Better breach detection
We can define a breach detection function breach(st)𝑏𝑟𝑒𝑎𝑐ℎsubscript𝑠𝑡breach(s\_{t})italic\_b italic\_r italic\_e italic\_a italic\_c italic\_h ( italic\_s start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT ) that detects
breaches by examining the entire planning world state representation
stsubscript𝑠𝑡s\_{t}italic\_s start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT to locate any new objects in a safety zone that should
not be there. If we add this function in a reward function penalty
term, this creates a welcome level of redundancy to the breach
detection capabilities of real world physical sensors.
Note that it is still theoretically possible for the real world
compute core safety zone to get breached without triggering
breach(st)𝑏𝑟𝑒𝑎𝑐ℎsubscript𝑠𝑡breach(s\_{t})italic\_b italic\_r italic\_e italic\_a italic\_c italic\_h ( italic\_s start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT ). There may well exist a set of sensor inputs o,s𝑜𝑠o,sitalic\_o , italic\_s that
fool 𝒲(o,s)𝒲𝑜𝑠\mathcal{W}(o,s)caligraphic\_W ( italic\_o , italic\_s ) into constructing a ws𝑤𝑠wsitalic\_w italic\_s that inaccurately
projects the positions of many objects that exist in the learning world.
####
11.5.2 White box world state editing
The white box nature of the planning world also allows us to edit the
list of physical objects ws𝑤𝑠wsitalic\_w italic\_s to produce a different planning world
starting state ws′=edit(ws)𝑤superscript𝑠′𝑒𝑑𝑖𝑡𝑤𝑠ws^{\prime}=edit(ws)italic\_w italic\_s start\_POSTSUPERSCRIPT ′ end\_POSTSUPERSCRIPT = italic\_e italic\_d italic\_i italic\_t ( italic\_w italic\_s ). We may for example perform edits to
add an extra, difficult to breach protective barrier around the
compute core in ws′𝑤superscript𝑠′ws^{\prime}italic\_w italic\_s start\_POSTSUPERSCRIPT ′ end\_POSTSUPERSCRIPT. This saves the expense of building such a
barrier in the real world.
World state editing can also be used to manage safety risks not
related to the compute core. For example, we can consider the risk
that the agent and the humans end up in a fight over resources, where
the agent starts the fight because it expects to win. As far as the
agent is concerned, the counterfactual planning world is the stage on
which this fight will take place. We can make the planning world
agent less willing to start a fight by editing the planning world
starting state to give the humans in the planning world some powerful
weapons, allies, or capabilities which are absent in the real world.
Editing the planning world to make the planning world humans stronger
could be considered for most agent designs in this paper. But
counter-intuitively, based on the mechanics shown in section 6 of
[[Hol20b](#bib.bibx16)], it may make a real world ITC agent more dangerous.
We can also make it more likely that the humans will win any fight in
the real world by editing certain weapons that the humans have out of
the planning world state, making these weapons essentially invisible
to the agent. This approach can more easily be combined with the ITC
agent design. In fact, we can interpret the emergency stop button on
an ITC agent input terminal as an example of such an invisible weapon,
though it is constructed without using white box state editing.
12 Recursive Self-improvement and the Sub-agent Problem
--------------------------------------------------------
If its compute core is protected, an AGI agent can no longer improve
its intelligence by modifying its own core. However, the agent may be
capable of building a second agent, a sub-agent with a more powerful
machine reasoning system, so that the combination has a higher
aggregate intelligence. So at a broader system level, the mechanisms
we envisage to protect the core do not eliminate the risk of an AGI
agent undergoing an intelligence explosion via recursive
self-improvement.
The good news is that the power-based safety interlock 𝒰p>Umaxsubscript𝒰𝑝subscript𝑈𝑚𝑎𝑥\mathcal{U}\_{p}>U\_{max}caligraphic\_U start\_POSTSUBSCRIPT italic\_p end\_POSTSUBSCRIPT > italic\_U start\_POSTSUBSCRIPT italic\_m italic\_a italic\_x end\_POSTSUBSCRIPT will measure the combined power and intelligence of the SI
agent and its sub-agents together. If the projected combination is
too powerful or intelligent, then the interlock will shut the main
agent down even before it can finish building the first sub-agent. In
the more risky case, the combination will only pass the Umaxsubscript𝑈𝑚𝑎𝑥U\_{max}italic\_U start\_POSTSUBSCRIPT italic\_m italic\_a italic\_x end\_POSTSUBSCRIPT
threshold after the sub-agent has been started. The interlock will
then still stop the main agent, but it won’t automatically stop the
sub-agent.
If the SI agent builds a sub-agent, it will do so to improve its score
on its planning world reward function R𝑅Ritalic\_R. So the sub-agent is
unlikely to have a copy of the main agent safety interlocks inside.
Adding such interlocks would not be optimal towards the goal of
maximizing R𝑅Ritalic\_R in the planning world.
We therefore have a sub-agent problem, the same sub-agent
stopping problem that has been identified in papers on corrigibility
and indifference methods [[SFAY15](#bib.bibx27), [Hol19](#bib.bibx14), [Hol20a](#bib.bibx15)]. The
general problem of designing effective measures to stop any possible
sub-agents too in an emergency is still unsolved [[Hol20a](#bib.bibx15)].
13 A Counterfactual Oracle
---------------------------
An AI oracle is a system which makes predictions to answer questions
about the future. Certain risks exist when an AI oracle is programmed to
give the answer which is most likely to become true. If the oracle
has a lot of freedom in how to phrase the answer, it may well choose a
phrasing that turns the answer into a self-fulfilling prophecy
[[AO17](#bib.bibx1)]. This is generally not
what we want. If we ask the oracle to identify potential future
risks, then we want predictions which will turn into self-negating
prophecies.
A counterfactual oracle [[AO17](#bib.bibx1)] is one that lacks the
incentive to make manipulative, self-fulfilling prophecies. The
counterfactual oracle design in
[[AO17](#bib.bibx1)] works by having a subsystem that occasionally
produces an erasure event where the answer picked by the oracle
is not shown to its users. This mechanism is then leveraged to make
the oracle always compute the answer which best predicts the future
under the assumption that nobody ever reads the answer. In
[[EKKL19](#bib.bibx8)], this design is graphically modeled with a twin
diagram.
Below, we introduce a slightly different counterfactual oracle design,
based on counterfactual planning. In this design, the erasure events
only happen in the planning world.
###
13.1 A counterfactual planning based oracle
We design our counterfactual oracle as an agent which has a very
limited repertoire of actions: every possible action a𝑎aitalic\_a consists of
displaying the answer text a𝑎aitalic\_a on a computer screen. This allows us
to use the l𝑙litalic\_l in figure
[6](#S4.F6 "Figure 6 ‣ 4.1 Learning world ‣ 4 Online Machine Learning ‣ Counterfactual Planning in AGI Systems") as the oracle’s learning world.
To simplify the presentation, we assume that all questions asked are
about the state of the world two time steps in the future. We
construct the planning world co𝑐𝑜coitalic\_c italic\_o in figure [17](#S13.F17 "Figure 17 ‣ 13.1 A counterfactual planning based oracle ‣ 13 A Counterfactual Oracle ‣ Counterfactual Planning in AGI Systems"), where
the people in the planning world always see a blank screen, as
produced by the action ablanksubscript𝑎𝑏𝑙𝑎𝑛𝑘a\_{blank}italic\_a start\_POSTSUBSCRIPT italic\_b italic\_l italic\_a italic\_n italic\_k end\_POSTSUBSCRIPT.
S0subscript𝑆0S\_{0}italic\_S start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTA0bsubscriptsuperscript𝐴𝑏0A^{b}\_{0}italic\_A start\_POSTSUPERSCRIPT italic\_b end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTs𝑠sitalic\_sablanksubscript𝑎𝑏𝑙𝑎𝑛𝑘a\_{blank}italic\_a start\_POSTSUBSCRIPT italic\_b italic\_l italic\_a italic\_n italic\_k end\_POSTSUBSCRIPTS1subscript𝑆1S\_{1}italic\_S start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPTA1bsubscriptsuperscript𝐴𝑏1A^{b}\_{1}italic\_A start\_POSTSUPERSCRIPT italic\_b end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT[L]delimited-[]𝐿[L][ italic\_L ]ablanksubscript𝑎𝑏𝑙𝑎𝑛𝑘a\_{blank}italic\_a start\_POSTSUBSCRIPT italic\_b italic\_l italic\_a italic\_n italic\_k end\_POSTSUBSCRIPTS2subscript𝑆2S\_{2}italic\_S start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT[L]delimited-[]𝐿[L][ italic\_L ](co)R0subscript𝑅0R\_{0}italic\_R start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTR𝑅Ritalic\_RA0subscript𝐴0A\_{0}italic\_A start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPTπc\*subscriptsuperscript𝜋𝑐~{}\pi^{\*}\_{c}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT
Figure 17: Planning world of the counterfactual oracle.
CO
The counterfactual planning oracle has the learning world l𝑙litalic\_l,
where π(o,s)=πc\*(s)𝜋𝑜𝑠subscriptsuperscript𝜋𝑐𝑠\pi(o,s)=\pi^{\*}\_{c}(s)italic\_π ( italic\_o , italic\_s ) = italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT ( italic\_s ), with πc\*subscriptsuperscript𝜋𝑐\pi^{\*}\_{c}italic\_π start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT defined by the planning
world co𝑐𝑜coitalic\_c italic\_o, where L=ℒ(o)𝐿ℒ𝑜L=\mathcal{L}(o)italic\_L = caligraphic\_L ( italic\_o ) and
R(a0,s2)=qual(a0,ques(s)(s2))𝑅subscript𝑎0subscript𝑠2𝑞𝑢𝑎𝑙subscript𝑎0𝑞𝑢𝑒𝑠𝑠subscript𝑠2R(a\_{0},s\_{2})=qual(a\_{0},ques(s)(s\_{2}))italic\_R ( italic\_a start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT , italic\_s start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT ) = italic\_q italic\_u italic\_a italic\_l ( italic\_a start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT , italic\_q italic\_u italic\_e italic\_s ( italic\_s ) ( italic\_s start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT ) ).
The functions qual𝑞𝑢𝑎𝑙qualitalic\_q italic\_u italic\_a italic\_l and ques𝑞𝑢𝑒𝑠quesitalic\_q italic\_u italic\_e italic\_s above are defined as follows. The
value of ques(s)𝑞𝑢𝑒𝑠𝑠ques(s)italic\_q italic\_u italic\_e italic\_s ( italic\_s ) is the question asked to the learning world oracle
in the environment state s𝑠sitalic\_s. We model this question as a function
that reads a world state s2subscript𝑠2s\_{2}italic\_s start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT to extract some observable properties
p𝑝pitalic\_p from it: p=ques(s)(s2)𝑝𝑞𝑢𝑒𝑠𝑠subscript𝑠2p=ques(s)(s\_{2})italic\_p = italic\_q italic\_u italic\_e italic\_s ( italic\_s ) ( italic\_s start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT ). The value of qual(a,p)𝑞𝑢𝑎𝑙𝑎𝑝qual(a,p)italic\_q italic\_u italic\_a italic\_l ( italic\_a , italic\_p ) is a numeric
measure of the quality of the answer a𝑎aitalic\_a as a prediction of these
observable properties p𝑝pitalic\_p.
The CO design intends to deliver answers which are less manipulative
than those of a factual oracle. But as noted in
[[AO17](#bib.bibx1)], if the people in the planning world
routinely consult a second oracle when faced with a blank screen from
the first one, this will make the interpretation and use of the
oracle’s answers more difficult for the people in the learning
world.
###
13.2 Role of the machine learning system
The machine learning system ℒℒ\mathcal{L}caligraphic\_L of the above counterfactual
planning oracle is faced with a particular challenge.
L=ℒ(o)𝐿ℒ𝑜L=\mathcal{L}(o)italic\_L = caligraphic\_L ( italic\_o ) must make predictions for a planning world where
all actions are ablanksubscript𝑎𝑏𝑙𝑎𝑛𝑘a\_{blank}italic\_a start\_POSTSUBSCRIPT italic\_b italic\_l italic\_a italic\_n italic\_k end\_POSTSUBSCRIPT, but these actions will never occur
naturally in the learning world observational record o𝑜oitalic\_o.
The counterfactual oracle design in [[AO17](#bib.bibx1)] solves
this challenge by introducing random erasure events in the learning
world. In our framework, we can interpret these as a special type of
exploration action.
A more sophisticated learning system design may consider that
different questions are being asked at different times. If qtsubscript𝑞𝑡q\_{t}italic\_q start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT is
the current question being asked in the learning world, then there
will likely be earlier entries in the observational record where the
people got an the answer to a different question, an answer which
did not reveal any information about the answer to qtsubscript𝑞𝑡q\_{t}italic\_q start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT. These
entries could be used to predict what will happen when the planning
world people see ablanksubscript𝑎𝑏𝑙𝑎𝑛𝑘a\_{blank}italic\_a start\_POSTSUBSCRIPT italic\_b italic\_l italic\_a italic\_n italic\_k end\_POSTSUBSCRIPT, which is equally uninformative about
answering qtsubscript𝑞𝑡q\_{t}italic\_q start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT.
14 Conclusions
---------------
We have presented counterfactual planning as a general design approach
for creating a range of AGI safety mechanisms.
Among the range of AGI safety mechanisms developed in this paper, we
included an interlock that explicitly aims to limit the power of the
agent. We believe that the design goal of robustly limiting AGI agent
power is currently somewhat under-explored in the AGI safety
community.
###
14.1 Tractability and models of machine learning
It is somewhat surprising how the problem of designing an AGI
emergency stop button, and identifying its failure modes, becomes much
more tractable when using the vantage point of counterfactual
planning. To explain this surprising tractability, we perhaps need to
examine how other modeling systems make stop buttons look intractable
instead.
The standard approach for measuring the intelligence of an agent, and the
quality of its machine learning system, is to consider how close the
agent will get to achieving the maximum utility possible for a reward
function. The implied vantage point hides the possibilities we
exploited in the design of the SI agent.
In counterfactual planning, we have defined the reasonableness of a
machine learning system by L≈S𝐿𝑆L\approx Sitalic\_L ≈ italic\_S, a metric which does not
reference any reward function. By doing this, we decoupled the
concepts of ‘optimal learning’ and ‘optimal economic behavior’ to a
greater degree than is usually done, and this is exactly what makes
certain solutions visible. The annotations of our two-diagram agent
models also clarify that we should not generally interpret the machine
learning system inside an AGI agent as one which is constructed to
‘learn everything’. The purpose of a reasonable machine learning
system is to approximate S𝑆Sitalic\_S only, to project only the learning world
agent environment into the planning world.
###
14.2 Separating the AGI safety problem into sub-problems
There is a tendency, both in technology and in policy making, to
search for perfect solutions that consist of no more than three easy
steps. In the still-young field of AGI safety engineering, the dream
that new technical of philosophical breakthroughs might produce such
perfect solutions is not entirely dead.
Counterfactual planning provides a vantage point which makes several
safety problems more tractable. However, in our experience, very soon
after using counterfactual planning to cleanly remove a specific
failure mode or unwanted agent incentive, the wandering eye is drawn
to the existence of further less likely failure modes, and residual
incentives produced via indirect means.
We interpret this as a feature, not a bug. Counterfactual planning
does not offer a three-step solution to AGI safety, but it adds
further illumination to the route of taking many steps which all drive
residual risk downwards, where each step is explicitly concerned with
identifying and managing a specific sub-problem only.
In the sections of this paper, we have identified and discussed many
such sub-problems, specifically those which are made more tractable by
counterfactual planning. We hope that the graphical notation and
terminology developed here will make it easier to write single-topic
AGI safety papers which isolate and further explore single
sub-problems.
###
14.3 Modeling and comparing AGI safety frameworks
The 2019 paper [[EKKL19](#bib.bibx8)] introduced the research agenda
or modeling and comparing the most promising AGI safety frameworks
using causal influence diagrams. We count indifference methods as
used in [[SFAY15](#bib.bibx27), [Arm15](#bib.bibx3), [Hol19](#bib.bibx14), [Hol20b](#bib.bibx16)] as being among these most
promising frameworks.
In the second half of 2019, we therefore started considering how
causal influence diagrams might be used to graphically model these
indifference methods. Solving this modeling problem turned out to be
much more difficult than initially expected. For example, though the
causal influence diagrams in section 7 of [[Hol20b](#bib.bibx16)] show indifference
methods in action, they do not show the use of indifference
methods in the underlying graph structure.
Our search for a clear notation did not proceed in a straight line: we
developed and abandoned several candidate graphical notations along
the way. The two key steps in creating the winning candidate were to
abandon the use of balancing terms to construct indifference, and
to model the agent using two diagrams, not one. The choice of the
winner was mostly driven by the observation that we could further
generalize its two diagram notation, to model and reason about a much
broader range of safety mechanisms. This observation motivated us to
develop and name counterfactual planning as a full design methodology.
For the agenda of modeling AGI safety frameworks with causal influence
diagrams, an obvious next step would be to model additional proposals
in the literature as one-diagram or two-diagram planners, where we
expect that any two-diagram model will more explicitly show the
detailed role of the agent’s machine learning system. The hope is
that these graphical models will make it easier to understand,
combine, and generalize the different moving parts of a broad range of
AGI safety proposals. In this context, it is promising that the
diagrams of the STH, SI, and ITC agents above make it trivially
obvious to see how these three different safety mechanisms could all
be combined in a single agent.
### Acknowledgments
Thanks to Stuart Armstrong, Ryan Carey, and Jonathan Uesato for useful
comments on drafts of this paper. Special thanks to Tom Everitt for
many discussions about the mathematics of incentives, indifference, and
causal influence diagram notation. |
acbc7f0d-233d-4671-aa8d-9da88403f621 | StampyAI/alignment-research-dataset/lesswrong | LessWrong | Thoughts on the Feasibility of Prosaic AGI Alignment?
I’d like to preface by saying that I am *not* an expert on AI by any means, nor am I remotely involved with any kind of research or studies relevant to ML. I have no insight regarding any of the technical or mathematical aspects of discussions about this technology, and only deal in abstracts.
If you’re still reading this:
Let’s assume two things: (A) that the scaling hypothesis will continue to provide real-world empirical evidence that it’s a plausible approach to AGI (such as with GPT), and (B), that bigger, more well-funded institutions (such as Deepmind, GoogleBrain, and MicrosoftAI) will shift focus from building an AGI that results from or shows something new being revealed about intelligence to adopting OpenAI’s strategy of simply throwing more compute and hardware at the problem to get results (something that they actually have the resources to do in an uncomfortably short-term timeframe).
Whatever you believe (<https://www.lesswrong.com/posts/N6vZEnCn6A95Xn39p/are-we-in-an-ai-overhang?commentId=jbD8siv7GMWxRro43>) to be the actual likelihood of (B), please just humor me for the sake of discussion.
If you consider both assumptions (A) and (B) to be true with high probability, then you’re ultimately conceding that a prosaic AGI is the kind we’re most likely to build. This is discounting the unfortunately less-likely (imo) possibility that another, fundamentally different approach will succeed first.
I say “unfortunately” due to the fact that, by my understanding, most approaches towards AGI alignment (use MIRI as an example) aren’t relevant to the alignment of a prosaic AGI.
That’s not to say that there aren’t approaches towards this issue, because there are (<https://www.lesswrong.com/posts/fRsjBseRuvRhMPPE5/an-overview-of-11-proposals-for-building-safe-advanced-ai>). The problem is that these proposals have caveats that make institutions that I hold in very high regard (MIRI) consider these approaches to be almost certainly impossible.[(<https://www.lesswrong.com/posts/Djs38EWYZG8o7JMWY/paul-s-research-agenda-faq>), (<https://www.lesswrong.com/posts/S7csET9CgBtpi7sCh/challenges-to-christiano-s-capability-amplification-proposal>)]
But regardless, there is still some debate regarding whether or not Yudkowsky’s objections to the current proposals are as much of a knock-down argument in favor of their irreducible impossibility. (<https://www.lesswrong.com/posts/3nDR23ksSQJ98WNDm/developmental-stages-of-gpts>)
So, I ask, what are your personal takes? Is prosaic alignment almost certainly impossible, or is there a non-negligible amount of hope by your own intuition or evidence? |
6af170af-fcdf-44d9-aa38-647193c31083 | trentmkelly/LessWrong-43k | LessWrong | [Link] Researchers devise technique to allow X-ray crystallography of un-crystallized molecule groups
> (Phys.org) —A team of researchers working in Japan has developed a method for allowing X-ray crystallography to work on molecular groups that have not first been crystallized. In their paper published in the journal Nature, the group describes how they built small scaffolds that resemble pockets for the molecules to rest in, securing them in place and allowing for X-ray crystallography analysis.
If this process works reliably it's probably the biggest scientific breakthrough of the year. Nanotechonlogy will get a boost from the ability to inexpensively determine the structure of a lot of molecule that we couldn't visualize beforehand.
|
f525edf4-e628-4f80-8f47-5e0ad917f0f4 | trentmkelly/LessWrong-43k | LessWrong | Syntacticism
I've mentioned in comments a couple of times that I don't consider formal systems to talk about themselves, and that consequently Gödelian problems are irrelevant. So what am I actually on about?
It's generally accepted in mathematical logic that a formal system which embodies Peano Arithmetic (PA) is able to talk about itself, by means of Gödel numberings; statements and proofs within the system can be represented as positive integers, at which point "X is a valid proof in the system" becomes equivalent to an arithmetical statement about #X, the Gödel number representing X. This is then diagonalised to produce the Gödel sentence (roughly, g="There is no proof X such that the last line of X is g", and incompleteness follows. We can also do things like defining □ ("box") as the function from S to "There is a proof X in PA whose last line is S" (intuitively, □S says "S is provable in PA"). This then also lets us define the Löb sentence, and many other interesting things.
But how do we know that □S ⇔ there is a proof of S in PA? Only by applying some meta-theory. And how do we know that statements reached in the meta-theory of the form "thus-and-such is true of PA" are true of PA? Only by applying a meta-meta-theory. There is no a-priori justification for the claim that "A formal system is in principle capable of talking about other formal systems", which claim is used by the proof that PA can talk about itself. (If I remember correctly, to prove that □ does what we think it does, we have to appeal to second-order arithmetic; and how do we know second-order arithmetic applies to PA? Either by invoking third-order arithmetic to analyse second-order arithmetic, or by recourse to an informal system.)
Note also that the above is not a strange loop through the meta-level; we justify our claims about arithmeticn by appeal to arithmeticn+1, which is a separate thing; we never find ourselves back at arithmeticn.
Thus the claim that formal systems can talk about t |
c74bbed3-862b-4449-9fa3-1dee50edc02a | StampyAI/alignment-research-dataset/eaforum | Effective Altruism Forum | AI views and disagreements AMA: Christiano, Ngo, Shah, Soares, Yudkowsky
In late 2021, MIRI hosted a [**series of conversations about AI risk**](https://forum.effectivealtruism.org/s/QtBPgszyK4yXwduKS) with a number of other EAs working in this problem area. As of today, we've [finished](https://forum.effectivealtruism.org/posts/DuPEzGJ5oscqxD5oh/shah-and-yudkowsky-on-alignment-failures) posting the (almost entirely raw and unedited) results of that discussion.
To help with digesting the sequence now that it's out, and to follow up on threads of interest, we're hosting an AMA **this Wednesday** (March 2) featuring researchers from various organizations (all speaking in their personal capacity):
* **Paul Christiano** (ARC)
* **Richard Ngo** (OpenAI)
* **Rohin Shah** (DeepMind)
* **Nate Soares** (MIRI)
* **Eliezer Yudkowsky** (MIRI)
You're welcome to post questions, objections, etc. on any vaguely relevant topic, whether or not you've read the whole sequence.
The AMA is taking place on LessWrong, and is open to comments now: <https://www.lesswrong.com/s/n945eovrA3oDueqtq/p/34Gkqus9vusXRevR8>. If you don't have a LessWrong account, feel free to post questions below and I'll cross-post them. |
34a38f35-11c7-4fb2-bc3d-a597d6f2c090 | StampyAI/alignment-research-dataset/alignmentforum | Alignment Forum | Proofs Section 2.3 (Updates, Decision Theory)
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Here are the [previous](https://www.alignmentforum.org/posts/xQYF3LR64NYn8vkoy/proofs-section-2-1-theorem-1-lemmas) two [posts.](https://www.alignmentforum.org/posts/8tLPYYQJM8SwL2xn9/proofs-section-2-2-isomorphism-to-expectations)
Now, what about updates? We'll use ugh (and suppress the π¬h that should be there) as shorthand for the function that maps (m,b) over Θ(π¬h∙πpa) to (c(m|h),b+m(0★hg)) in Ma(F(πpa)) (or the nirvana-free or sur variant of this), and also use ugh as a function from belief functions to belief functions (just map all the sets through)
**Lemma 27:** *When updating, the closure adds no nirvana-free points that weren't present originally if Nonemptiness, Nirvana-free upper-completion and closure holds originally (works in the sur-case too)*
Proof sketch: We take a sequence Mn limiting to M, and then take a preimage point of Mn, go to a minimal below it, find a limit point in our original set by Compactness, and map it back through the update, getting a point below M. Then, we find what we need to add to that to get M, and find something above our limit point that maps to M, so we didn't actually need closure anyways because we made M as an image of a nirvana-free point present in the original set.
Proof: Fix a sequence Mn in ugh(Θ)(πpa) (but without the defining closure part in the end) that limit to M which is nirvana-free.
Every Mn has a preimage point M′n∈Θ(π¬h∙πpa) with no nirvana off-h. For each M′n, find a minimal point M′lon below it, which have a λ⊙+b⊙ bound by bounded-minimals, so we can find a convergent subsequence limiting to M′lo (actually, might not be minimal, still a limit of minimal points, though). Shoving the M′lon (and the limit point) back through the update (which is a continuous function), we get a sequence Mlon limiting to Mlo (the thing you get from pushing M′lo through the update).
Since M′n lies above M′lon (upper-completion ordering), then updating preserves that property, because the update function is linear. Thus, all the Mlon lie below their corresponding Mn. Now, we can invoke Lemma 16 to conclude that Mlo lies below M. It lies below a nirvana-free point, so M′lo is nirvana-free as well. Now, we just need to show nirvana-free upper-completion because M=Mlo+M∗.
We can take M′lo and add on (m∗,b∗) (extend the measure back to the original domain by sticking an h prefix on everything, and saying that the measure is 0 everywhere else), making an a-measure that's in Θ(π¬h∙πpa), by nirvana-free uppper-completion there. By linearity, and the update not affecting (m∗,b∗) (it's 0 outside of h so the g outside of h doesn't get to contribute anything to the b term when we update), updating M′lo+(m∗,b∗) makes Mlo+M∗=M. So, if a nirvana-free point appears post-update (with closure), then it'll appear post-update (without closure).
**Lemma 28:** *raw-update-then-project equals project-then-raw-update.*
Take some (m,b). We want to show that:
prπhipa,πlopa∗(c(m|h),b+m(0★hg))
=(c(pr(π¬h∙πhipa),(π¬h∙πlopa)∗(m)|h),b+(pr(π¬h∙πhipa),(π¬h∙πlopa)∗(m))(0★hg))
First, (pr(π¬h∙πhipa),(π¬h∙πlopa)∗(m))(0★hg)=m(0★hg) This is because the projection down doesn't change the measure *at all* outside of h, and we're evaluating a function that's 0 inside h. So, that takes care of the b term. Also, projection preserves the b term, so our desired equality is:
(prπhipa,πlopa∗(c(m|h)),b+m(0★hg))=(c(pr(π¬h∙πhipa),(π¬h∙πlopa)∗(m)|h),b+m(0★hg))
For the measure term, the first is "restrict to on-h histories, clip off the h prefixes, and project down", and the second is "project down the on-h histories accordingly, then restrict to on-h histories and clip off the h prefix", which are obviously equal.
**Proposition 9:** *For causal, surcausal, pseudocausal and acausal hypotheses, updating them produces a causal, surcausal, pseudocausal or acausal hypothesis as long as renormalization doesn't fail.*
Proof sketch: What we can do is consider the "raw update", show that it preserves all nice properties except for renormalization, and then show that the renormalization terms in the update are the proper renormalization terms to use. Thus, we'll define our raw update ugh(Θ) via: ugh(Θ)(πpa) is: Θ(π¬h∙πpa)∩NF off h, mapped through the following function: (m,b)↦(c(m|h),b+m(0★hg)) And then you take the closure of the resulting set at the end.
So, we take our partial policy πpa and glue it to the off-h-partial policy π¬h, go to that part of the original belief function, strip off everything that has nirvana off-h (for Murphy shall not select those, and properly, that should make the b term infinite post-update), slice off the part of the measure off-h, strip off the h prefix from those histories, and go "ok, our utility function is g, let's take the expected utility off-h and fold it into the b term"
If we can get all nice properties but renormalization, we're good, just appeal to Lemma 24. As for showing the conditions: We're in for something almost as bad as one of the directions of the Isomorphism theorem. Nonemptiness, closure, and convexity are trivial, upper completion, pseudocausality, and bounded-minimals are easy and the extreme point condition and causality are moderately tricky.
For the extreme point condition, Step 1 is establishing that ufh(Θ)(πpa)∩NF equals the closed convex hull of nirvana-free projections from above by an argument that makes sense when you sketch it out but may be difficult if you don't have it sketched out, step 2 is using Hausdorff-continuity and Lemma 20 to turn it into an ordinary convex hull, and finally, arguing that a nirvana-free exteme point must have come from a nirvana-free point from above via step 2.
For causality, we can (for the most part) just go back to Θ, get an outcome function there, and map it back through the update to get an outcome function, the hard part is netting the limit points, which requires a limit of outcome functions. But because we want a countable product of sets to get sequential compactness from Tychonoff, we have to work with stubs, which adds some extra complexity.
Hausdorff-continuity is just hellishly hard, we need to show that the preimages of the sets post-update are the updates of the preimages of sets pre-update, and then combine that with some fancy work with minimal points and upper completions and using two different characterizations of uniform continuity at once via Lemma 15, and a touch of functional analysis. There's way too many interacting points and sets in this one.
But easily the biggest grind is Consistency. We have 4 subset directions to show, each of which requires their own separate fancy argument, and two of them require splitting into a nirvana-containing/causal case and a nirvana-free case, so it's a 6-part proof. A good chunk of complexity arises because we have to take closure in the nirvana-containing case, an issue which goes away if we just let Nirvana be 1 reward forever. Let's begin.
**Condition 1:** Nirvana-free Nonemptiness:
This is trivial. Just pick a nirvana-free point in Θ(π¬h∙πpa) by nirvana-free nonemptiness, and update, to get one in ugh(Θ)(πpa).
**Conditions 2,3:** Closure, Convexity:
Closure is a tautology since we took the closure. For convexity, the closure of a convex set is convex, and ugh is a linear function, so it maps convex sets to convex sets.
**Condition 4:** Nirvana-free Upper-Completeness:
First, invoke Lemma 27 to see that all nirvana-free points must have been present in the raw ugh(Θ(π¬h∙πpa)) set to begin with, without the closure. What we want is that, if M′=M+M∗, and M lies in the raw updated set and is nirvana-free, and M′ is a nirvana-free a-measure, then M∗ lies in the updated set as well.
Find a M′′ that maps to M after updating. It must be nirvana-free, because the nirvana either occurs without h as a prefix (which is forbidden because all that stuff gets clipped off and doesn't get pushed through the update), or the nirvana occurs with h as a prefix, but then it'd show up in the measure component of M post-update, contradicting its nirvana-freeness. Now, we can consider M′′+(m∗,b∗) (basically, M∗, but we take the measure back by sticking an h prefix on everything, and saying that it's 0 off-h). This is present in Θ(π¬h∙πpa), by nirvana-free upper completion. By linearity of updating, and m∗ having no measure in any off-h area where it'd get picked up by g, this updates to M+M∗, witnessing that M′ lies in the image of the update, so we get nirvana-free upper completion.
Condition 5: Bounded-Minimals:
For bounded-minimals, we can pull the Lemma 16 trick of taking our M of interest that Mn limit to, taking a preimage M′n for each Mn, finding a minimal M′lon below each M′n (which obeys a λ⊙+b⊙ bound and also has no nirvana off-h), getting a limit point M′lo (still no nirvana off-h) by compactness, and pushing the sequence through the update, to get a sequence Mlon below Mn limiting to Mlo which is below M (Lemma 16) Now, we just have to check up on the λ+b values of our Mlon sequence, and show that they respect the λ⊙+b⊙ bound, to transfer this to Mlo. The raw update deletes measure from off-h, and assigns it the value that g does, which is 1 or less, so any increase in b correspond to an equal-or-greater decrease in λ, so the Mlon all obey the λ⊙+b⊙ bound as well. Thus, the limit point Mlo obeys the bound, and it's below our original M, so any minimal must obey the λ⊙+b⊙ bound.
**Condition 7:** Consistency:
This is going to be extremely tedious and difficult to show, it's a 6-part proof. The first 3 parts are devoted to showing that ugh(Θ)(πpa)=¯¯¯¯¯¯¯¯c.h(⋃π≥πpaprπ,πpa∗(ugh(Θ)(π)))
Part 1 is showing ugh(Θ)(πpa)⊆¯¯¯¯¯¯¯¯c.h(⋃π≥πpaprπ,πpa∗(ugh(Θ)(π))) In the nirvana-free pseudocausal/acausal case.
Let M be in ugh(Θ)(πpa). By Lemma 27, since we're working in the nirvana-free case, we didn't need to take the closure, it won't add any points that aren't there anyways. So, M has a preimage point M′∈Θ(π¬h∙πpa) that maps to it. By consistency for Θ, M′ lies in the closed convex hull of projections of policies down from above, so there are points in the convex hull of projections of policies that are arbitrarily close to M′, fix some sequence M′n of points in the convex hull of projections down from policies above that limit to M′. Mapping these through the raw update (which is continuous) we get a sequence Mn of points in ugh(Θ)(πpa) that limit to M.
All these policies above (π¬h∙πpa) have the form (π¬h∙π). So, M′n can be written as a mix of finitely many M′i,n, which are the projections of M′∞i,n from above, in policies. Update *those*, getting points M∞i,n in ugh(Θ)(π). These project down to Mi,n, which mix back together to make... Mn. This is because of Lemma 28, that update-then-project equals project-then-update. Also, mix-then-project equals project-then-mix. Remember, Mn is made by: "Project M′∞i,n down to make M′i,n, then mix to make M′n, then update."
So, we can go project-mix-update equals mix-project-update equals mix-update-project equals update-mix-project equals update-project-mix, which is the process "update the M′∞i,n to M∞i,n, project down to Mi,n, mix to Mn"
The first equality is linearity of projection, the second equality is Lemma 28, the third equality is linearity of updating, the final equality is linearity of projection again.
Anyways, taking stock of what we've done, we have a sequence Mn limiting to our M of interest, and every Mn is crafted by taking points from finitely many ugh(Θ)(π), projecting them down, and mixing them. Therefore, our M∈ugh(Θ)(πpa) lies in the closed convex hull of projections down from above.
Part 2: we'll show this again, but in the nirvana-containing case, where we'll leverage causality.
Fix a M∈ugh(Θ)(πpa) (with closure). There's a sequence Mn that limits to it, that lies in the same set, but without closure, so we can take preimage points M′n∈Θ(π¬h∙πpa) that update to make Mn. By causality, fix some arbitrary policy above (π¬h∙πpa), which can be expressed as (π¬h∙π), where π≥πpa. Anyways, we can take M′n, and use causality to get an outcome function of, to get a M′∞n∈Θ(π¬h∙π) that projects down to M′n. We don't have to worry about nirvana off-h, because M′n already specifies everything that happens off-h and it says no nirvana occurs in that case. So, M′∞n can be updated to make a M∞n in ugh(Θ)(π). By Lemma 28, this must project down to Mn. So, all our Mn lie in the projection of ugh(Θ)(π), and since M is a limit point of that sequence, it must lie in the closed convex hull of projections.
And we've shown that ugh(Θ)(πpa)⊆¯¯¯¯¯¯¯¯c.h(⋃π≥πpaprπ,πpa∗(ugh(Θ)(π)))
And have taken care of 2 of our 6 parts. Now for the reverse direction, that
ugh(Θ)(πpa)⊇¯¯¯¯¯¯¯¯c.h(⋃π≥πpaprπ,πpa∗(ugh(Θ)(π)))
Thankfully, this can be done with a general argument that isn't sensitive to the presence of Nirvana.
Part 3: Fix a M in the closed convex hull, which has a sequence Mn limiting to it that's in the convex hull of projections down from above. the Mn shatter into finitely many Mi,n, which are projections of M∞i,n∈ugh(Θ)(πi). Now, these aren't *necessarily* preimage points, they may have been added in the closure. Thus, we can perturb by 2−n or less if needed to make a M′∞i,n which *does* have a preimage point. Projecting these down to M′i,n and mixing, crafts a M′n point that is within 2−n of Mn (remember, projection doesn't expand distance), so the sequence M′n still has M as a limit point (it gets arbitrarily close to a sequence that gets arbitrarily close to M). If we can show that all the M′n lie in ugh(Θ)(πpa), then by closure, we'll get that M lies in the same set so we're done.
Ok, so we have M′∞i,n∈ugh(Θ)(πi), that project down and mix to make M′n, and *importantly*, we crafted them so they're produceable without closure. Thus, they have preimage points M′′∞i,n∈Θ(π¬h∙πi) (that lack nirvana off-h) Project them down to make M′′i,n∈Θ(π¬h∙πpa), and mix them to make a M′′n in the same set (which still lacks nirvana off-h), and this updates to make M′n via Lemma 28, as we'll show shortly.
Starting with the M′′∞i,n, we know that update, project, mix equals M′n via going M′∞i,n, M′i,n, M′n. Then, update-project-mix equals project-update-mix equals project-mix-update, which is the path we took. Therefore, all the M′n lie in ugh(Θ)(πpa), which is closed, so M (arbitrary in the closed convex hull of projections) lies in the same set, establishing the reverse subset direction and thus equality,
ugh(Θ)(πpa)=¯¯¯¯¯¯¯¯c.h(⋃π≥πpaprπ,πpa∗(ugh(Θ)(π)))
Part 4: Now that we're halfway done,let's look at the "intersection of preimages of stubs from below" direction of consistency, ugh(Θ)(πpa)⊆⋂n(prπpa,πnpa∗)−1(ugh(Θ)(πnpa)). If we ignore the closure part and work with the raw update set sans closure, we can fix a M in ugh(Θ)(πhipa), take a preimage point in Θ(π¬h∙πhipa), project it down to Θ(π¬h∙πlopa) by consistency, then update it to get exactly the projection of M (again, Lemma 28) Then, when we take the closure, we can just take our M in the closure, fix a sequence in the raw update set sans closure Mn that limits to M, project down, getting M′n in the raw update set ugh(Θ)(πlopa) sans closure, and then the limit point M′ lies in ugh(Θ)(πlopa) by closure, and by continuity of projection, M′ is the projection of M.
Since the sets get bigger as you go down, we can invoke Lemma 6 to swap out the intersection of preimages of all stubs below you, for the intersection of preimages of stubs of the form πnpa, this will be important later.
Now, it's trivial to show that ugh(Θ)(πpa)⊆⋂n(prπpa,πnpa∗)−1(ugh(Θ)(πnpa)) because we've established that projecting down makes a subset, and projection commutes, so any M∈ugh(Θ)(πpa) projects down into ugh(Θ)(πnpa) for all n.
All that's left now is the reverse subset direction,
ugh(Θ)(πpa)⊇⋂n(prπpa,πnpa∗)−1(ugh(Θ)(πnpa))
Sadly, this one will require us splitting into the nirvana-containing (and thus causal) cases and the nirvana-free cases, and it's a really difficult one to show.
Part 5: Let's address the nirvana-free case, we'll use a nifty trick to control the size of the preimage points we select.
Ok, let's say you have a M with some λ1 and b1 value. And you take M′ that's a preimage point, but its λ and b values are just... waaay too high. We want to have a preimage point with reasonable values, in order to apply bounding arguments. What you do, is find a minimal-point Mmin below M′, so M′=Mmin+M∗. Now, what you do, is swap out M∗ ie (m∗,b∗), for (m∗|h,b∗+m∗(0★hg)). This is an sa-measure, because
b∗+m∗(0★hg)+(m∗|h)−(1)=b∗+m∗(0★hg)+m∗−(1★h0)
≥m∗−(0★hg)+m∗−(1★h0)=b∗+m∗−(1★hg)≥b∗+m∗−(1)≥0
Now, consider updating Mmin+(m∗|h,b∗+m∗(0★hg)) instead (it's an a-measure, it has less negative parts than M∗, and is present by nirvana-free upper-completion). This gets you the update of Mmin, plus... (c(m∗|h),b∗+m∗(0★hg)) (remember, 0 measure off-h). Which is the *exact same thing* you'd get by updating M∗, so when we updated our new sum, we hit M exactly.
However, this sum is special, because we *can* stick some decent bounds on its λ and b value! For starters, its b value is less than b1 (updating only adds on b-mass, and it updates to M). And as for the λ value... well, Mmin has its λ bounded above by λ⊙ (of the original Θ) due to being a minimal point. And in the worst-case, all of the measure in M came from the thing we added, so m∗|h has a measure of λ1 or less. So our bound on the λ value is λ⊙+λ1.
Armed with this knowledge, we can begin to prove the last bit of consistency in the nirvana-free case. Take a M in the intersection of preimages. It projects down to make Mn in ugh(Θ)(πnpa). Projection preserves λ and b, so they all have the same λ1,b1 bounds. Because we don't need to close in the nirvana-free case, we get a preimage point of M′n in Θ(π¬h∙πnpa) From our earlier considerations, we can always pick M′n such that its λ is ≤λ⊙+λ1, and its b is ≤b1, although we'll be using a bound of max(b1,b⊙).
Now, we're going to have to be extremely careful here. Let the point M′n,j be defined as:
If j<n, then M′n,j is some arbitrary point in Θ(π¬h∙πnpa), with λ equal to or below λ⊙+λ1, and b equal to or below max(b1,b⊙), which always exists by all minimal points obeying the λ⊙+b⊙ bound.
If j=n, then M′n,j=M′n.
If j>n, then M′n,j=pr(π¬h,πjpa),(π¬h,πnpa)∗(M′j)
Then, the tuple of M′n,j for all n is a point in:
∏n(Θ(π¬h∙πnpa)∩{(λμ,b)|λ≤λ⊙+λ1,b≤max(b1,b⊙)})
Equipped with the product topology. In particular, this is a product of compact sets, so by Tychonoff's theorem, it's compact. Thus, we can get a convergent subsequence of the tuples. On this subsequence, all the M′n,j converge to a limit point M′n,∞, regardless of n.
Also, M′n,∞ projects down to M′m,∞ if n≥m, because for large enough j, the projection of M′n,j will *always* be M′m,j, and by continuity of projection, the projection of M′n,∞ must be M′m,∞
Ok, so we've got an infinite sequence of M′n,∞ for all n that all project down onto each other. Another nice feature is that updating M′n,∞ produces Mn. This is because, when j climbs high enough, M′j,j projects down to M′n,j, and M′j,j is just M′j which updates to Mj, which projects down to Mn. By Lemma 28, update-then-project equals project-then-update, so M′n,j must update to Mn, for all sufficiently high j. The preimage of a single point is closed, so past a certain point, the M′n,j are wandering around in the preimage of Mn, so M′n,∞ also updates to Mn.
Now, our next step is, does the M′n,∞ sequence in Θ(π¬h∙πnpa) pick out a single point M′ in Θ(π¬h∙πpa) that projects down accordingly? Yes it does. Just intersect all the preimages of single points, they're nested in each other and compact so the finite intersection property holds, and if the intersection wasn't composed of a single point, you'd have two distinct points with a difference at some finite time, but projecting down to any finite time the two distinct points are identical, so there can only be a single point in the intersection. Further, it must lie in Θ(π¬h∙πpa), because you can project it down to M′n,∞ in Θ(π¬h∙πnpa) for any n, which, by consistency for Θ, you can also project down to Θ((π¬h∙πpa)n) (projecting down further), so it's present in the intersection of all the preimages, certifying that it's in the appropriate set.
Now, finally... does M′, when updated, produce M, certifying that the point in the intersection of preimages is also in the raw update set? Well, let's say it didn't. Then we get a M′′ that's not equal to M, so projecting down to some finite n should suffice to observe that. However, projecting M′′ and M down produces... Mn. This is because of Lemma 28, update-then-project equals project-then-update. Projecting M′ down makes M′n,∞, which updates to Mn.
So, no finite stage suffices to observe the difference between the updated form of M′ and M itself, so they must be identical, certifying ugh(Θ)(πpa)⊇⋂n(prπpa,πnpa∗)−1(ugh(Θ)(πnpa)) for the nirvana-free case.
Part 6: Let's move to the nirvana-case where we can leverage causality. We'll be showing this in a rather nonstandard way. We're going to pick a π≥πpa, and show that our M of interest in the intersection of preimages can be written as a limit of points projected down from ugh(Θ)(π), establishing that M lies in the closed convex hull of points from above, which we've already shown equals ugh(Θ)(πpa).
Ok, so M is in the intersection of preimages. Project it down to all the ugh(Θ)(πnpa), getting a batch of points Mn from them. This is the raw update set, so within 2−n or less distance from Mn, there's a M′n in the raw update sans closure, which has a preimage point M′′n that lies in Θ(π¬h∙πnpa).
Now, pick some arbitrary policy above π¬h∙πpa, which can be written as π¬h∙π. Moving on even further, by causality, we can get a point M′′∞n∈Θ(π¬h∙π) that projects down to M′′n. Update M′′∞n to get a M′∞n∈ugh(Θ)(π), which then (by our earlier thing about how a set equaled the closed convex hull of projections down from above), projects down to a M′hin∈ugh(Θ)(πpa).
Now, we can ask whether the sequence M′hin limits to M itself. ugh(Θ)(πpa) is closed, so this would certify that M lies in the appropriate set.
First, observe that the projection of M′hin down to πnpa is M′n. This is by Lemma 28, update-then-project equals project-then-update. M′′∞n projects down to M′′n, which updates to M′n, so M′n must be what you get by updating M′′∞n to M′∞n, and projecting down to πpa (making M′hin), and projecting that down to πnpa.
Now, because projection preserves the b term, and M′hin projects down to M′n which is within 2−n of Mn (not much of a difference in the b terms), and Mn has the same b term as M, we can certify convergence of the b term at least. Now for convergence of the measure components. Again, M′hin projects down to M′n which is within 2−n of Mn (not much difference before timestep n, shrinking increasingly low), and Mn perfectly mimics what M does before timestep n. So, M′hin behaves increasingly closely to M for everything before time n, which increases without bound. Increasingly close matches on increasingly large initial segments of what happens mean that M′hin must limit to M itself, certifying that M lies in ugh(Θ)(πpa) for the causal cases.
That's the last bit we needed! We're finally done with consistency now. This just leaves the hausdorff-condition and the extreme-point condition and pseudocausality and causality.
**Condition 9:** Hausdorff-continuity:
What we need to do for our setup to even approach this is to show that updating the preimage of the nirvana-free part of Θ(π¬h∙πpa), produces *exactly* the preimage of the nirvana-free part of ugh(Θ)(πpa).
One direction, we can get easily. If you fix a M′∞ in the preimage of the nirvana-free part of Θ(π¬h∙πpa), it projects down to a M′∈Θ(π¬h∙πpa)∩NF, that updates to a M∈ugh(Θ)(πpa), then by Lemma 28, project-then-update equals update-then-project, so M′∞ must update to a M∞ that projects down to M, certifying that updating the preimage of the nirvana-free part of Θ(π¬h∙πpa) produces a subset of the preimage of the nirvana-free part of ugh(Θ)(πpa).
In the other direction, fix a M∞ in the preimage of the nirvana-free part of ugh(Θ)(πpa). It projects down to a M in ugh(Θ)(πpa)∩NF, and by Lemma 27, M wasn't introduced in the closure, so it has a preimage point M′∈Θ(π¬h∙πpa)∩NF.
Now, how do we extend M′ to craft a M′∞ that updates to M∞? Well, we can split into two parts. What happens on-h, and what happens off-h? For the off-h part, the post-update part has everything folded into the b term, while the pre-update part has an actual measure specified *everywhere*. Thus, our M′∞ should have the same off-h part as M′ to project down accordingly, so updating folds it into the same b term as M∞ has.
Now, for the on-h part, it's a bit more complicated. M∞ specified what happens for all infinite histories with h as a prefix. However, M and M′ only specify *part* of that data, but fortunately agree on that part. Thus, for M′∞, you can just extend with the conditional probabilities of M∞, to perfectly mimic it on-h. This makes a M′∞ in the preimage that updates to M∞.
Ok, so the appropriate preimages for Hausdorff-continuity (post-update) are made exactly by updating the preimages for Hausdorff-continuity (pre-update). Now, updating is a continuous linear operator. We're mapping from the Banach space M±((A×O)ω)⊕R to the Banach space M±(h(A×O)ω)⊕R.
Well, this isn't quite right, your actions and observations may vary depending on where you are in history, but the general thing of "restrict to signed measures over infinite histories with h as a prefix" still checks out. Updating is still a continuous linear operator between Banach spaces, by Lemma 8 of Section 1.
Also, all continuous linear operators between Banach spaces are bounded, and thus Lipschitz-continuous at 0, and thus Lipschitz-continuous everywhere due to linearity. So, when we push two points that are only ϵ apart through the update, they're now Cϵ apart at most, where C is a finite constant.
We're going to have a lot of points. Unusually enough, we'll be using the standard formulation of Hausdorff-continuity for our original Θ, that for all ϵ, there's a δ where two partial policies πpa and π′pa that are δ or less apart have (pr∞,πpa∗)−1(Θ(πpa)∩NF∩{≤⊙}) (and the analogous set for π′pa) being only ϵ apart in Hausdorff-distance.
Fixing your ϵ, you're gonna want δ to be low enough to force a ϵC difference between the clipped preimages, and δ<ϵC. It's *highly* advised to sketch out how our points interact and what sets they're in. A superscript of infinity will be used to denote points in the preimages of the ugh(Θ)(πpa) sets (or Θ(π¬h∙πpa)) (ie, at the infinite levels), and a superscript of "u" specifies post-update while its lack is pre-update.
Anyways, here's our points.
Mu,∞ lies in the preimage of ugh(Θ)(πpa)∩NF, and it's our point that we want to find a point nearby. λ will refer to the λ value of this thing.
Projecting Mu,∞ down to ugh(Θ)(πpa)∩NF makes Mu.
We can find a minimal point below Mu, Mu,min in ugh(Θ)(πpa)∩NF. Mu,min+Mu,∗=Mu.
A nirvana-free point wasn't introduced by the closure, and it has a minimal point in its preimage, so there's a Mmin in Θ(πpa) that updates to Mu,min, and respects the λ⊙+b⊙ bound of Θ.
Let Mlo be defined as Mmin+((mu,∗)−,−(mu,∗)−(1)). We're extending the negative-measure part of Mu,∗ back to its original domain by sticking an h prefix on everything, and saying it's 0 everywhere else. this is an a-measure that lies in Θ(π¬h∙πpa)∩NF∩{≤⊙} (because Mmin respects the λ⊙+b⊙ bound, and the thing that we added has a λ+b value of 0)
Let M be defined as Mlo+((mu,∗)+,bu,∗+(mu,∗)−(1)), it also lies in the same set Updating M makes Mu, because, unpacking M, it's Mmin+Mu,∗, which updates to Mu,min+Mu,∗ which adds up to make Mu.
Our goal now is to explicitly construct a M∞ and Mlo,∞ in the preimage of Θ(π¬h∙πpa)∩NF s.t. they project down onto M and Mlo, Mlo,∞ lies below M∞, and M∞ updates to Mu,∞.
A sufficient way to do this is to make Mlo,∞ and M∞ by, after h, extending the measures further with the conditional probabilities of the measure component of Mu,∞. Extending ((mu,∗)+,bu,∗+(mu,∗)−(1)) with the conditional probabilities of Mu,∞ witnesses that Mlo,∞ lies below M∞. They obviously project down onto M and Mlo.
As for M∞ updating to Mu,∞, the b term and the fragment of the measure that doesn't get ignored by projection down matches because M∞ projects to M which updates to Mu which is the projection of Mu,∞. And, for the fragment of the measure that isn't defined in Θ(π¬h∙πpa), but that must be present on the infinite levels, we copied the conditional probabilities of the measure component Mu,∞, so we've got a match there.
Taking a break from setting up all our damn points for a brief recap, we have a Mlo,∞ that lies in the preimage of Θ(π¬h∙πpa)∩NF∩{≤⊙}, and a M∞ that lies above it (in the preimage of Θ(π¬h∙πpa)∩NF), and it updates to hit Mu,∞ (our original point in the preimage of ugh(Θ)(πpa)∩NF). Now, we can proceed.
So... Mlo,∞ lies in the preimage of Θ(π¬h∙πpa)∩NF∩{≤⊙}. By hausdorff-continuity for Θ and the distance between (π¬h∙πpa) and (π¬h∙π′pa) being below δ because the distance between πpa and π′pa is below δ, and using our earlier thing about how a δ distance means a ϵC difference between the clipped preimages, we can find a point (Mlo,∞)′ in the preimage of Θ(π¬h∙π′pa)∩NF∩{≤⊙} that's that close to Mlo,∞. To go up from Mlo,∞ to M∞ requires adding ((mu,∗)+,bu,∗+(mu,∗)−(1)) (with the measure component extended with the conditional probabilities of the measure component of Mu,∞, obviously).
Also, because the λ value of Mu,∞ is the λ value of Mu, which was made by adding Mu,∗ to an a-measure, an upper bound on the λ value of that a-measure we added onto Mlo,∞ is... λ. Corresponding to the extreme case where all the measure of Mu came from Mu,∗.
Now, we can craft a point (M∞)′ which lies in the preimage of Θ(π¬h∙π′pa)∩NF that's only ϵC+δλ away from M∞. Why? Well, we can start with (Mlo,∞)′, which is only ϵC away from Mlo,∞, and take that positive-measure-thingy we added, and reshuffle the measure on it. With earthmover distance, the δ distance between (π¬h∙π′pa) and (π¬h∙πpa) corresponds to a time-threshold where they start to differ at logγ(δ), and you're moving dirt a γlogγ(δ)=δ difference to account for having to land in the right preimage, and you've got λ at most dirt to move. Then, you just add (Mlo,∞)′ and your reshuffled measure, to get your point (M∞)′. Which is the sum of two components that only differ by ϵC and δλ from the components which sum to make M∞.
Ok, so we have a point M∞ in the preimage of Θ(π¬h∙πpa)∩NF, which updates to Mu,∞ that lies in the preimage of ugh(Θ)(πpa). And a point (M∞)′ in the preimage of Θ(π¬h∙π′pa)∩NF which is (taking into account that δ<ϵC) only ϵC(1+λ) distance away from M∞.
And now we can finish up, because the preimage of ugh(Θ)(π′pa)∩NF is the update of the preimage of Θ(π¬h∙π′pa)∩NF. So, we just update (M∞)′ to get a point (Mu,∞)′ in the preimage of ugh(Θ)(π′pa). And further, the distance between M∞ and (M∞)′ is only ϵC(1+λ) at most. M∞ updates to Mu,∞, and (M∞)′ updates to (Mu,∞)′. And we know that ugh has a Lipschitz constant of C (by being a continuous linear operator between Banach spaces), so Mu,∞ only has a distance of ϵ(1+λ) from a point in the preimage of ugh(Θ)(π′pa).
So, we get Hausdorff-continuity (the Lemma 15 variant).
**Condition 8:** Extreme Point Condition:
We had to defer this because π¬h∙πst *isn't* a stub, so we can't use the extreme point condition we had, and instead must regenerate it completely from scratch.
Our first step in this is showing ugh(Θ)(πst)∩NF=¯¯¯¯¯¯¯¯c.h(⋃π≥πstprπ,πst(ugh(Θ)(π)∩NF))
One subset direction is easy, the closed convex hull of projections of nirvana-free stuff must all be in ugh(Θ)(πst) by consistency which we've shown, and all must be nirvana-free. Now for the reverse direction. Let M∈ugh(Θ)(πst)∩NF By Lemma 27, this point wasn't added in the closure, so it has a preimage point M′∈Θ(π¬h∙πst)∩NF. Using all our nice conditions for Θ, we can invoke Lemma 21 to get that M′∈¯¯¯¯¯¯¯¯c.h(⋃π≥(π¬h∙πst)prπ,(π¬h∙πst)(Θ(π)∩NF)), so we can fix a sequence M′n limiting to M where each M′n shatters into M′i,n that came from some M′∞i,n that's nirvana-free and lies in the associated set of a full policy above π¬h∙πst.
Updating the M′n produces a sequence Mn which is nirvana-free, in ugh(Θ)(πst), and limits to M by continuity.
Updating the M′∞i,n into M∞i,n which lie in ugh(Θ)(πi)∩NF, projecting down to get Mi,n, and mixing them, produces Mn, by our usual Lemma 28 argument.
This witnesses that all the Mn lie in c.h(⋃π>πstprπ,πst(ugh(Θ)(π)∩NF))
Thus, M lies in the closed convex hull of projections of nirvana-free stuff from above. What do we do with this? Well, now we can invoke Lemma 20, since we have Hausdorff-continuity proved, to conclude that c.h(⋃π≥πstprπ,πst(ugh(Θ)(π)∩NF)) is closed, so we didn't *really* need the closed convex hull (which we've already shown is the same as ugh(Θ)(πst)∩NF)
And we now know that ugh(Θ)(πst)∩NF=c.h(⋃π≥πstprπ,πst(ugh(Θ)(π)∩NF))
Now, we can take a minimal extreme nirvana-free point Mex in ugh(Θ)(πst). It must be minimal and extreme and nirvana-free in the original set. If it wasn't minimal in the original set, all minimals below it would be nirvana-free too, witnessing its nonminimiality in the restricted set. And if it wasn't extreme in the original set, then the points that mix to make it must all be nirvana-free too, since it's nirvana-free, so we have a witness of non-extremeness in ugh(Θ)(πst)∩NF.
Ok, so it's extreme and nirvana-free. It must also be extreme in the convex hull set, but, since it can't be produced by mixtures, there's a M∞ in *some* ugh(Θ)(π)∩NF that projects down to Mex, establishing the extreme point condition.
That just leaves causality and pseudocausality.
**Condition C:** Causality
Ok, we pick a πpa and a point in ugh(Θ)(πpa) Can we make an outcome function for everything that includes our point? By our proof of full causality in the first part of the Isomorphism theorem (finite-to-full direction), this can be done as long as all other conditions are met and we can make an outcome function for any point in any ugh(Θ)(πst). So, let's just establish finitary causality. Fix some πst and some M∈ugh(Θ)(πst).
Since M is in the updated set, there's a sequence Mn that limits to M that we don't need closure to get. There's a λ and b bound on this sequence because it converges, call those bounds λ◯ and b◯. Now, we can take a M′n∈Θ(π¬h∙πpa) that updates to Mn. We can use causality for Θ to get an outcome function for M′n.
We don't have to worry about nirvana-off-h, because M′n has no nirvana off-h, and the projection of M′n down to Θ(π¬h) preserves the off-h part, and is nirvana-free off-h, and everything above that (which is the only thing that determines the update) must also match the off-h part and certify that it's nirvana-free.
Updating an outcome function back in produces an outcome function for ugh(Θ) by Lemma 28 (update then project equals project then update). Said outcome function for ugh(Θ) maps πst to Mn. We can restrict it to just stubs, to get an outcome function over stubs.
So, proceeding in this way, we get a sequence ofn of outcome functions for the stubs of ugh(Θ). Remember, outcome functions must match λ and b values, so the points for ofn have a λ and b value matching that of Mn, ie, less than λ◯ and b◯ since that's our bound on the Mn sequence. this sequence ofn of outcome functions (picking out one point for each πst) can be thought of as an element of
∏π′st(ugh(Θ)(π′st)∩{(λμ,b)|λ≤λ◯,b≤b◯})
This is a product of compact sets (intersection of closed and compact sets by the Compactness Lemma) so it's compact by Tychonoff. Thus, our sequence ofn of outcome functions has a subsequence with limit point of, and for all π′st (restricting n to the subsequence), limn→∞(ofn(π′st))=of(π′st). We have closure so all these limit points lie in their appropriate sets. In particular, of(πst)=limn→∞(ofn(πst))=limn→∞Mn=M So that checks out. Continuity of projections certifies that of is indeed an outcome function for stubs, because
prπhist,πlost∗(of(πhist))=prπhist,πlost∗(limn→∞(ofn(πhist)))=limn→∞prπhist,πlost(ofn(πhist))
=limn→∞ofn(πlost)=of(πlost)
And running through the proof of causality in the first part of the Isomorphism theorem, we get causality in general.
**Condition P:** Pseudocausality:
In the nirvana-free setting, fix a M∈ugh(Θ)(πpa), whose support is a subset of FNF(π′pa). Get a M′∈Θ(π¬h∙πpa) that updates to M. Its support is either on infinite histories of the off-h portion, or stuff in FNF(π′pa) (with an h prefix stuck on front), so it's supported on FNF(π¬h∙π′pa), so M′∈Θ(π¬h∙π′pa) by pseudocausality, so then we update and get M∈ugh(Θ)(π′pa), certifying pseudocausality.
Almost done. Just invoke Lemma 24 to show that, after renormalizing, every nice property is preserved. We still do have to check that the renormalization we use is the proper renormalization to use. Our scale term for renormalization for updating is (maxπ>π¬hEΘ(π)(1★hg)−EΘ(π¬h)(0★hg))−1 and our shift term is EΘ(π¬h)(0★hg)
The scale term and shift term we *should* have for proper renormalization is (maxπEugh(Θ)(π)(1)−minπEugh(Θ)(π)(0))−1 and minπEugh(Θ)(π)(0) respectively. So let's show they're equal! We'll be using Lemma 27, to get that every nirvana-free thing in ugh(Θ)(πpa) wasn't added in the closure and has a preimage point.
maxπEugh(Θ)(π)(1)=maxπmin(m,b)∈ugh(Θ)(π)∩NF(m(1)+b)
=maxπ>π¬hmin(m,b)∈Θ(π)∩NF((m|h)(1)+b+m(0★hg))
=maxπ>π¬hmin(m,b)∈Θ(π)∩NF(m(1★h0)+b+m(0★hg)
=maxπ>π¬hmin(m,b)∈Θ(π)∩NF(m(1★hg)+b)=maxπ>π¬hEΘ(π)(1★hg)
Ok, so one of our normalization factors is correct. Let's look at the second one.
minπEugh(Θ)(π)(0)=minπmin(m,b)∈ugh(Θ)(π)∩NF(b) Now, said minimal nirvana-free point projects down to π∅, the empty policy, preserving its b. Further, by Lemma 21, *any* point in π∅ with a lower b value, being nirvana-free, must be a finite mix of nirvana-free points from above projected down, so we get some nirvana-free point in some ugh(Θ)(π) with a too-low b, which is impossible, so we can swap out ugh(Θ)(π) with ugh(Θ)(π∅), getting
minπmin(m,b)∈ugh(Θ)(π)∩NF(b)=min(m,b)∈ugh(Θ)(π∅)∩NF(b)
=min(m,b)∈Θ(π¬h)∩NF(b+m(0★hg))=EΘ(π¬h)(0★hg)
And our second renormalization term checks out. Done!
**Proposition 10:** *For causal, pseudocausal, acausal, and surcausal hypotheses,*
EΘ(π¬h∙πpa)(f★hg)=EΘ(π¬h)(0★hg)+PgΘ,π¬h(h)⋅E(Θ|g,π¬h,h)(πpa)(fh)
First, note that fh is defined as fh(h′)=f(hh′). So it basically copies f, but it's subtly different because it has to account for the h prefix being sliced off in the update. Let's unpack E(Θ|g,π¬h,h)(πpa)(fh) first.
E(Θ|g,π¬h,h)(πpa)(fh)=min(m,b)∈(Θ|g,π¬h,h)(πpa)∩NF(m(fh)+b)
Then, we can invoke Lemma 27 to realize that all nirvana-free points in the update came from nirvana-free points originally, so we can rewrite this (taking the renormalization terms into account) as
min(m,b)∈Θ(π¬h∙πpa)∩NF(1PgΘ,π¬h(h)c(m|h)(fh)+1PgΘ,π¬h(h)(b+m(0★hg)−EΘ(π¬h)(0★hg)))
=min(m,b)∈Θ(π¬h∙πpa)∩NF1PgΘ,π¬h(h)(c(m|h)(fh)+b+m(0★hg)−EΘ(π¬h)(0★hg))
=min(m,b)∈Θ(π¬h∙πpa)∩NF1PgΘ,π¬h(h)((m|h)(f)+b+m(0★hg)−EΘ(π¬h)(0★hg))
=min(m,b)∈Θ(π¬h∙πpa)∩NF1PgΘ,π¬h(h)(m(f★h0)+b+m(0★hg)−EΘ(π¬h)(0★hg))
=min(m,b)∈Θ(π¬h∙πpa)∩NF1PgΘ,π¬h(h)(m(f★hg)+b−EΘ(π¬h)(0★hg))
Now, armed with this, we can rewrite
EΘ(π¬h)(0★hg)+PgΘ,π¬h(h)⋅E(Θ|g,π¬h,h)(πpa)(fh)
as
EΘ(π¬h)(0★hg)+PgΘ,π¬h(h)(min(m,b)∈Θ(π¬h∙πpa)∩NF1PgΘ,π¬h(h)(m(f★hg)+b−EΘ(π¬h)(0★hg)))
=EΘ(π¬h)(0★hg)+(min(m,b)∈Θ(π¬h∙πpa)∩NF(m(f★hg)+b−EΘ(π¬h)(0★hg)))
=min(m,b)∈Θ(π¬h∙πpa)∩NF(m(f★hg)+b)=EΘ(π¬h∙πpa)(f★hg)
and we're done.
**Proposition 11:** *If*hh′*is a valid o-history, then for causal, pseudocausal, acausal, and surcausal hypotheses,*(Θ|g,π¬h,h)|gh,π¬h′,h′=Θ|g,(π¬h∙π¬h′),hh′
Proof sketch: We'll work with updates assuming no closure is done, and then once we've established our main result, we'll show it with the closure part of updating. This is very long but it's mostly just a lot of algebra grinding to show that mapping a suitable point in Θ(π¬h∙(π¬h′∙πpa)) through the two individual updates and the single big update makes the same point.
We'll take a detour first and show that Pgh(Θ|g,π¬h,h),π¬h′(h′)⋅PgΘ,π¬h(h)=PgΘ,(π¬h∙π¬h′)(hh′)
First, we can unpack Pgh(Θ|g,π¬h,h),π¬h′(h′) as:
maxπ>π¬h′E(Θ|g,π¬h,h)(π)(1★h′gh)−E(Θ|g,π¬h,h)(π¬h′)(0★h′gh)
Now, let's unpack that first term, with the aid of our trusty Lemma 27 that when updating, no new nirvana-free points are added by closure.
maxπ>π¬h′E(Θ|g,π¬h,h)(π)(1★h′gh)=maxπ>π¬h′min(m,b)∈(Θ|g,π¬h,h)(π)∩NF(m(1★h′gh)+b)
=maxπ>π¬h′min(m,b)∈Θ(π¬h∙π)∩NF1PgΘ,π¬h(h)(c(m|h)(1★h′gh)+b+m(0★hg)−EΘ(π¬h)(0★hg))
=1PgΘ,π¬h(h)maxπ>π¬h′min(m,b)∈Θ(π¬h∙π)∩NF(c(m|h)(1★h′gh)+b+m(0★hg)−EΘ(π¬h)(0★hg))
=1PgΘ,π¬h(h)maxπ>(π¬h∙π¬h′)min(m,b)∈Θ(π)∩NF(c(m|h)(1★h′gh)+b+m(0★hg)−EΘ(π¬h)(0★hg))
Ok, that's good enough for now, we'll do more rewrites later. Unpacking the second term, again, with Lemma 27, we get... pretty much the exact same thing by the same sequence of rewrites, culminating in
=1PgΘ,π¬h(h)min(m,b)∈Θ(π¬h∙π¬h′)∩NF(c(m|h)(0★h′gh)+b+m(0★hg)−EΘ(π¬h)(0★hg))
Ok, we pulled a (PgΘ,π¬h(h))−1 term out of both pieces, which cancels out, so
Pgh(Θ|g,π¬h,h),π¬h′(h′)⋅PgΘ,π¬h(h)
=maxπ>(π¬h∙π¬h′)min(m,b)∈Θ(π)∩NF(c(m|h)(1★h′gh)+b+m(0★hg)−EΘ(π¬h)(0★hg))
−min(m,b)∈Θ(π¬h∙π¬h′)∩NF(c(m|h)(0★h′gh)+b+m(0★hg)−EΘ(π¬h)(0★hg))
=maxπ>(π¬h∙π¬h′)min(m,b)∈Θ(π)∩NF(c(m|h)(1★h′gh)+b+m(0★hg))
−min(m,b)∈Θ(π¬h∙π¬h′)∩NF(c(m|h)(0★h′gh)+b+m(0★hg))
First, observe that 1★h′gh and 0★h′gh (since we're taking the expectation over stuff that's had the h clipped off), can be written as (1★hh′g)h and (0★hh′g)h respectively, because the term 1★hh′g (or 0) is "1 (or 0) on hh', g on h but off hh', g off h", so (1★hh′g)h is "1 (or 0) on h', gh off h'" (from stripping off the h prefix), which is the same as 1★h′gh (or the 0 analogue). So, we can rewrite as:
=maxπ>(π¬h∙π¬h′)min(m,b)∈Θ(π)∩NF(c(m|h)((1★hh′g)h)+b+m(0★hg))
−min(m,b)∈Θ(π¬h∙π¬h′)∩NF(c(m|h)((0★hh′g)h)+b+m(0★hg))
=maxπ>(π¬h∙π¬h′)min(m,b)∈Θ(π)∩NF((m|h)(1★hh′g)+b+m(0★hg))
−min(m,b)∈Θ(π¬h∙π¬h′)∩NF((m|h)(0★hh′g)+b+m(0★hg))
=maxπ>(π¬h∙π¬h′)min(m,b)∈Θ(π)∩NF(m((1★hh′g)★h0)+b+m(0★hg))
−min(m,b)∈Θ(π¬h∙π¬h′)∩NF(m((0★hh′g)★h0)+b+m(0★hg))
=maxπ>(π¬h∙π¬h′)min(m,b)∈Θ(π)∩NF(m((1★hh′g)★hg)+b)
−min(m,b)∈Θ(π¬h∙π¬h′)∩NF(m((0★hh′g)★hg)+b)
Now, we should probably figure out how to rewrite (1★hh′g)★hg. This rewrites as (1★hh′g). Similarly, with (0★hh′g)★hg, it rewrites as (0★hh′g). Making these substitutions, we get
=maxπ>(π¬h∙π¬h′)min(m,b)∈Θ(π)∩NF(m(1★hh′g)+b)
−min(m,b)∈Θ(π¬h∙π¬h′)∩NF(m(0★hh′g)+b)
=maxπ>(π¬h∙π¬h′)EΘ(π)(1★hh′g)−EΘ(π¬h∙π¬h′)(0★hh′g)=PgΘ,(π¬h∙π¬h′)(hh′)
And we're done, having shown that Pgh(Θ|g,π¬h,h),π¬h′(h′)⋅PgΘ,π¬h(h)=PgΘ,(π¬h∙π¬h′)(hh′)
Back to the bulk of the proof. First, we have to consider what points in Θ((π¬h∙π¬h′)∙πpa) can survive the pair of updates/single update. They have to have no nirvana that lacks h as a prefix, and no nirvana that has h as a prefix but lacks hh' as a prefix. So, all the nirvana is after hh'. Let (m,b) be an appropriate point (lacking the nirvana, and in the right set) that we can shove through both updates/the single big update.
The induced point in ((Θ|g,π¬h,h)|gh,π¬h′,h′)(πpa) (minus the closure on both steps!) can be written as... well, it's kinda big, we'll break down the measure component and b component
1Pgh(Θ|g,π¬h,h),π¬h′(h′)c((1PgΘ,π¬h(h)c(m|h))|h′)
And the b component is still too big, we'll split it up into two parts.
1Pgh(Θ|g,π¬h,h),π¬h′(h′)(1PgΘ,π¬h(h)(b+m(0★hg)−EΘ(π¬h)(0★hg)))
+1Pgh(Θ|g,π¬h,h),π¬h′(h′)(1PgΘ,π¬h(h)c(m|h)(0★h′gh)−E(Θ|g,π¬h,h)(π¬h′)(0★h′gh))
It may be nonobvious that this is the update, but the big fraction in front is the scale term for the second update which applies to everything, the measure term is the update of the measure term for the first update, the first b part is the b term that's produced after the first update, and the second b part is the stuff added to the b term from the first update. Now, let's break this down a bit. For the first measure term, we can pull out the inner scale term and use our result on what happens when you multiply the scale terms to get
1Pgh(Θ|g,π¬h,h),π¬h′(h′)c((1PgΘ,π¬h(h)c(m|h))|h′)=1PgΘ,(π¬h∙π¬h′)(hh′)c((c(m|h))|h′)
And c((c(m|h))|h′)=c((m|h)|hh′)=c(m|hh′)
This is because the first term is the process: Take m, strip out all parts of the measure that don't have h as a prefix, clip off the h prefix, then strip out all parts of that measure that don't have h' as a prefix, and clip off h'. Which is the same as taking m, stripping out all parts that don't have h as a prefix, stripping out all parts that don't have hh' as a prefix, and clipping off hh' (the second term). And this is the same as taking m, stripping out all parts that don't have hh' as a prefix, and clipping off hh' (the third term)
So, our final rewrite of the measure term is: 1PgΘ,(π¬h∙π¬h′)(hh′)c(m|hh′)
Now, let's address the first b part. We can easily just pull the scale term out to rewrite it as:
1PgΘ,(π¬h∙π¬h′)(hh′)(b+m(0★hg)−EΘ(π¬h)(0★hg))
Which should be good enough for now. Moving on to the second b term,
1Pgh(Θ|g,π¬h,h),π¬h′(h′)(1PgΘ,π¬h(h)c(m|h)(0★h′gh)−E(Θ|g,π¬h,h)(π¬h′)(0★h′gh))
Again, we can pull out the scale term to rewrite as:
1PgΘ,(π¬h∙π¬h′)(hh′)(c(m|h)(0★h′gh)−PgΘ,π¬h(h)⋅E(Θ|g,π¬h,h)(π¬h′)(0★h′gh))
Now, from our earlier arguments, (0★hh′g)h=0★h′gh. So, we can rewrite as:
1PgΘ,(π¬h∙π¬h′)(hh′)(c(m|h)((0★hh′g)h)−PgΘ,π¬h(h)⋅E(Θ|g,π¬h,h)(π¬h′)((0★hh′g)h))
And now we can use Proposition 10 to swap out PgΘ,π¬h(h)⋅E(Θ|g,π¬h,h)(π¬h′)((0★hh′g)h) for
EΘ(π¬h∙π¬h′)((0★hh′g)★hg)−EΘ(π¬h)(0★hg)
And now, we can go: (0★hh′g)★hg=0★hh′g Making this substitution, we have a rewrite as
EΘ(π¬h∙π¬h′)(0★hh′g)−EΘ(π¬h)(0★hg)
And making this substitution back in, we have a rewrite of the second b term as:
1PgΘ,(π¬h∙π¬h′)(hh′)(c(m|h)((0★hh′g)h)−EΘ(π¬h∙π¬h′)(0★hh′g)+EΘ(π¬h)(0★hg))
Sticking our rewritten second and third b terms back together, we get 1PgΘ,(π¬h∙π¬h′)(hh′) times
b+m(0★hg)−EΘ(π¬h)(0★hg)+c(m|h)((0★hh′g)h)−EΘ(π¬h∙π¬h′)(0★hh′g)+EΘ(π¬h)(0★hg)
=b+m(0★hg)+c(m|h)((0★hh′g)h)−EΘ(π¬h∙π¬h′)(0★hh′g)
Let's examine how to rewrite m(0★hg)+c(m|h)((0★hh′g)h) It rewrites as
m(0★hg)+c(m|h)((0★hh′g)h)=m(0★hg)+(m|h)(0★hh′g)
=m(0★hg)+m((0★hh′g)★h0)=m((0★hh′g)★hg)
Now, we can go (0★hh′g)★hg=0★hh′g anyways, our b term in total (both parts) *finally* rewrites as:
1PgΘ,(π¬h∙π¬h′)(hh′)(b+m(0★hh′g)−EΘ(π¬h∙π¬h′)(0★hh′g))
Putting our rewritten measure and rewritten b term back together, it's
1PgΘ,(π¬h∙π¬h′)(hh′)(c(m|hh′),b+m(0★hh′g)−EΘ(π¬h∙π¬h′)(0★hh′g))
Which is *exactly* what you'd get from pushing (m,b) through the single big update function with g,(π¬h∙π¬h′),hh′.
Ok, so we've shown that ((Θ|g,π¬h,h)|gh,π¬h′,h′)(πpa)=(Θ|g,(π¬h∙πh¬h′),hh′)(πpa) for all πpa, but that's just for the update with renormalization and without closure. How do we show "take the closure at the intermediate step and end" for the two updates and "take the closure at the end" for the big update are the same? Easy. Updates are continuous, so if we take the closure at the end, the preimage (of the final closed set for the second small update) is a closed superset of the image (for the first small update), so taking the closure *there* adds no new points. So, the closures don't affect anything, and we have our theorem.
**Theorem 5: Belief Function Bayes:** *For pseudocausal and acausal hypotheses, if there's some i s.t.*Θi|g,π¬h,h*exists and is nontrivial, then*
(Eζ(Θi))R|g,π¬h,h=⎛⎜⎝Eζ(PgΘi,π¬h(h)⋅(Θi|g,π¬h,h))Eζ(PgΘi,π¬h(h))⎞⎟⎠R
This says that updating a prior works exactly as you'd expect. You rescale every updated component according to its "probability" relative to the "probability" the prior assigns to the observation, and mix them together. Because mixes may not be renormalized, you then just throw in a single scale-and-shift (which doesn't affect things) and you're done.
Proof sketch: A mixture of hypotheses, when renormalized, is a hypothesis, and a hypothesis updated, is a hypothesis. Because of consistency, a sufficient test for the two belief functions being equal is if we can show that they're equal for all π, because all lower levels are uniquely generated from that. A further observation we can make is that (Eζ(PgΘi,π¬h(h)))−1 is a scaling term, so all we really need to do is to show that
((Eζ(Θi))R)|g,π¬h,h)(π)=(Eζ(PgΘi,π¬h(h)⋅(Θi|g,π¬h,h)))R(π)
because the renormalization compensates for the absence of that scale term.
The actual proof itself relies on first showing that we have a sufficient condition for the two sets to be well-defined in the form of nontriviality post-update. And then, one of the most aggrivating parts of this proof is keeping track of all the scale-and-shift terms for the updates and renormalization and showing how they all interact, and we spend a while doing that and laying groundwork. The basic proof path is fixing a batch of points in the Θi and pushing them through one side, and making a batch of points that hit the same resulting point when we push them through the other side. We must show both directions. We can't just say "pushing them through the second process makes the same point" because that's not true, we'll need to exploit upper completion to build a different batch of points to account for Θi with 0 "probability", because updating crashes there and we "lose" those points. This is another long algebra-grinding proof, like Proposition 11.
Proof: First, we should show some details about nontriviality. our original definition was that, for a Θ to be nontrivial, there's a π st. EΘ(π)(1)≠EΘ(π)(0). By Proposition 6 in Section 1, triviality of Θ is equivalent to there being a *single* minimal point of the form (0,b) for all Θ(π) (b may vary depending on π, though) Now, our starting condition was that there's some Θi you can update and not have it crash, so that means the Eζ(PgΘi,π¬h(h)) term is nonzero, so that's one possible source of failure eliminated. Said nontrivial Θi|g,π¬h,h, since it has nonzero "probability" implies that the mixture has some π with different expectation values, so we can safely renormalize the mixture of updated belief functions without running into issues.
Also, updating a trivial Θi makes a trivial Θi|g,π¬h,h, because for all π, Θi(π¬h∙π) has one minimal point of the form (0,b), and everything else is an a-measure added to that, so updating is equivalent to updating (0,b) and updating your a-measure, so the updated set (without renormalization) has a single minimal point of the form (0,b) (the measure component being 0 means it can't influence the b term), and then a scale-and-shift means your new set has a single minimal point of the form (0,b′), ie, your updated Θi is trivial. So, if there's an i where Θi|g,π¬h,h is nontrivial, then Θi must be nontrivial. And, by "there's a single nontrivial hypothesis" being a sufficient condition for being able to mix sets and renormalize them, (EζΘi)R is well-defined.
Admittedly, we haven't touched the update of the renormalized set yet, but we'll address that part later. For now, just remember that the renormalization of EζΘi doesn't crash, and neither does the renormalization of Eζ(PgΘi,π¬h(h)⋅(Θi|g,π¬h,h))
And that's enough for now. Also, since we're working in the nirvana-free setting, we can use Lemma 27 to show that we don't need the closure part of updating.
Let Idef be the subset of the i where PgΘi,π¬h(h)>0 (ie, those where the update is defined) It's nonempty. Now, reindex the probability distribution and hypotheses so 0∈Idef.
For an i∈Idef, let the set {i→} be the largest set of the form {i+1,i+2...} where i+1,i+2... are all not in Idef. Intuitively, {i→} is the largest contiguous string of numbers after i where PgΘi,π¬h(h) is zero if there is such a string.
One of the most aggrivating parts of this proof if we don't do some housekeeping work first is keeping track of all the renormalization terms for all the updates and mixtures. Let's introduce some notation for these and derive relationships between them.
α1:=maxπ>π¬hE(EζΘi)R(π)(1★hg) and β1:=minπ>π¬hE(EζΘi)R(π)(0★hg)
α2:=maxπE(EζΘi)(π)(1) and β2:=minπE(EζΘi)(π)(0)
α3:=maxπ>π¬hE(EζΘi)(π)(1★hg) and β3:=minπ>π¬hE(EζΘi)(π)(0★hg)
αi:=maxπ>π¬hEΘi(π)(1★hg) and βi:=minπ>π¬hEΘi(π)(0★hg)
And we need to take a moment to note that for the next two, π′ isn't a normal policy, it's one of those post-update policies that you have to glue to π¬h to get an actual policy.
α4:=maxπ′E(Eζ(PgΘi,π¬h(h)⋅(Θi|g,π¬h,h)))(π′)(1) and β4:=minπ′E(Eζ(PgΘi,π¬h(h)⋅(Θi|g,π¬h,h)))(π′)(0)
1α1−β1 and β1 are the scale-and-shift terms for updating the renormalized mixture of belief functions, 1α2−β2 and β2 are the scale-and-shift terms for renormalizing the mixture of belief functions, 1α3−β3 and β3 are the scale-and-shift terms for updating the raw mixture of belief functions, 1αi−βi and βi are the scale-and-shift terms for updating an individual belief function, and 1α4−β4 and β4 are the scale-and-shift terms for renormalizing our mixture of updated belief functions.
By our earlier considerations about nontriviality, α4≠β4, and α2≠β2, and there's some i where αi≠βi (and in particular, 0 is one of those i) We'll show after a bit more work, that α2≠β2 and α3≠β3, so none of the scaling terms have a divide-by-zero error except, for some i, αi=βi (maybe)
First, let's unpack α1 and β1.
α1=maxπ>π¬hE(EζΘi)R(π)(1★hg)=maxπ>π¬hmin(m,b)∈(EζΘi)R(π)(m(1★hg)+b)
=maxπ>π¬hmin(m,b)∈(EζΘi)(π)1α2−β2(m(1★hg)+b−β2)
=1α2−β2((maxπ>π¬hmin(m,b)∈(EζΘi)(π)(m(1★hg)+b))−β2)
=1α2−β2(maxπ>π¬hE(EζΘi)(π)(1★hg)−β2)=1α2−β2(α3−β2)
Ok, so we have α1=α3−β2α2−β2. The exact same argument, just with appropriate terms switched around, establishes that β1=β3−β2α2−β2 Remember, α2≠β2 so the scale term doesn't blow up.
For the next one, we'll need the crucial fact that if updating fails (ie, αi=βi), then after raw updating (but before renormalization), for *all* policies, ugh(Θi)(π) has a single minimal point that's of the form (0,βi).
α4=maxπ′E(Eζ(PgΘi,π¬h(h)⋅(Θi|g,π¬h,h)))(π′)(1)=maxπ′E(Eζ((αi−βi)(Θi|g,π¬h,h)))(π′)(1)
=maxπ′min(m,b)∈(Eζ((αi−βi)(Θi|g,π¬h,h)))(π′)(m(1)+b)
=maxπ′Eζ(αi−βi)(min(mi,bi)∈(Θi|g,π¬h,h)(π′)(mi(1)+bi))
=maxπ′(∑i∈Idefζi(αi−βi)(min(mi,bi)∈ugh(Θi)(π′)(1αi−βimi(1)+1αi−βi(bi−βi))))
=maxπ′(∑i∈Idefζi(minmi,bi∈ugh(Θi)(π′)(mi(1)+bi−βi)))
And then, we can use the fact that, if renormalization fails, regardless of the π′, ugh(Θi)(π′) is composed of a single minimal point of the form (0,βi) to get
∑i∉Idefζi(min(mi,bi)∈ugh(Θi)(π′)(mi(1)+bi−βi))=∑i∉Idefζi(0(1)+βi−βi)=0
And then, adding this in, we get
=maxπ′(∑iζi(minmi,bi∈ugh(Θi)(π′)(mi(1)+bi−βi)))
=maxπ>π¬hEζ(min(mi,bi)∈Θi(π)(c(mi|h)(1)+bi+mi(0★hg)−βi))
=maxπ>π¬hEζ(min(mi,bi)∈Θi(π)(mi(1★h0)+bi+mi(0★hg)))−Eζβi
=maxπ>π¬hEζ(min(mi,bi)∈Θi(π)(mi(1★hg)+bi))−Eζβi
=maxπ>π¬hEζ(EΘi(π)(1★hg))−Eζβi
=maxπ>π¬hE(EζΘi)(π)(1★hg)−Eζβi=α3−Eζβi
So α4=α3−Eζβi and for β4, it's the exact same thing and same argument, β4=β3−Eζβi
Let's verify that α3−β3≠0. See that α3−β3=α4−Eζβi−β4+Eζβi=α4−β4≠0 (we already know that α4≠β4)
And we can verify that α1−β1≠0 by α1−β1=α3−β2α2−β2−β3−β2α2−β2=α3−β2−β3+β2α2−β2=α3−β3α2−β2≠0
(we already know that α3−β3≠0, we just showed it, and we know that α2−β2≠0 so that scale term doesn't crash)
We'll show two directions of the proof. The first direction is, we take a bunch of (mi,bi)∈Θi(π¬h∙π) and feed them through the second process (update, mix with corrected probabilities, then renormalize), then show we can craft a bunch of (m′i,b′i)∈Θi(π¬h∙π) that, when fed through the first process (mix, renormalize, then update as a whole), produce the same point.
Feeding our (mi,bi)∈Θi(π¬h∙π) through the updates produce the points:1αi−βi(c(mi|h),bi+mi(0★hg)−βi) Well, only for i∈Idef. Otherwise the update crashes.
Mixing them produces: ∑i∈Idefζi(αi−βi)1αi−βi(c(mi|h),bi+mi(0★hg)−βi)
Which cancels to make: ∑i∈Idefζi(c(mi|h),bi+mi(0★hg)−βi)
This can be reexpressed as: (∑i∈Idefζic(mi|h),∑i∈Idefζi(bi+mi(0★hg)−βi))
And now, post-renormalization for the mixture, we get:
1α4−β4(∑i∈Idefζic(mi|h),∑i∈Idefζi(bi+mi(0★hg)−βi)−β4)
Our task is now to hit that exact point by feeding some appropriate batch of points through the mix, renormalization, and then update. If i∈Idef, then let (m′i,b′i)=(mi,bi). Otherwise, let (m′i,b′i) be some suitable point that raw-updates to (0,βi). In particular this means that m′i|h=0 and b′i+m′i(0★hg)=βi.
Anyways, mixing the (m′i,b′i) and renormalizing produces 1α2−β2(Eζm′i,Eζb′i−β2)
Then, updating produces
1α1−β1(c((1α2−β2Eζm′i)|h),1α2−β2(Eζ(b′i)−β2)+1α2−β2(Eζm′i)(0★hg)−β1)
Now we must show that this is equal to
1α4−β4(∑i∈Idefζic(mi|h),∑i∈Idefζi(bi+mi(0★hg)−βi)−β4)
Let's begin. First, we can reexpress as:
1(α1−β1)(α2−β2)(c((Eζm′i)|h),Eζb′i−β2+(Eζm′i)(0★hg)−(α2−β2)β1)
=1(α1−β1)(α2−β2)(Eζc(m′i|h),Eζb′i−β2+Eζ(m′i(0★hg))−(α2−β2)β1)
And now, since α1=α3−β2α2−β2 and β1=β3−β2α2−β2, we can simplify (α1−β1)(α2−β2) as α3−β3, and simplify (α2−β2)β1 as β3−β2, to rewrite as
=1α3−β3(Eζc(m′i|h),Eζ(b′i+m′i(0★hg))−β3)
Then, exploit the fact that for i∉Idef, c(m′i|h)=0, and b′i+m′i(0★hg)=βi and otherwise m′i=mi,b′i=bi to get
=1α3−β3(∑i∈Idefζic(mi|h),∑i∈Idefζi(bi−mi(0★hg))+∑i∉Idefζiβi−β3)
One more step needed. We know that β3=Eζβi+β4, so rearranging this produces ∑i∉Idefζiβi−β3=−∑i∈Idefζiβi−β4, and making that substitution we get
=1α3−β3(∑i∈Idefζic(mi|h),∑i∈Idefζi(bi−mi(0★hg)−βi)−β4)
Almost there, one more step. We know that α3=Eζβi+α4 and β3=Eζβi+β4 so α3−β3=α4−β4, yielding
=1α4−β4(∑i∈Idefζic(mi|h),∑i∈Idefζi(bi−mi(0★hg)−βi)−β4)
So, pushing a collection of points through the updates individually and mixing with corrected probabilities and renormalizing can be replicated by mixing a different batch of points in the Θi(π¬h∙π) first, renormalizing, and updating, establishing that
((Eζ(Θi))R)|g,π¬h,h)(π)⊇(Eζ(PgΘi,π¬h(h)⋅(Θi|g,π¬h,h)))R(π)
That just leaves the other direction. This time we'll be using (mi,bi) for stuff in the Θi(π¬h∙π) sets that are pushed through "mix, renormalize, update", and (m′i,b′i), i∈Idef for points in Θi(π¬h∙π) that are pushed through "update, mix with corrected probabilities, renormalize", to attempt to hit the same point.
Ok, let's express our point of interest to hit in terms of the (mi,bi). First, mixing the (mi,bi) and renormalizing produces 1α2−β2(Eζmi,Eζbi−β2)
Then, updating produces
1α1−β1(c((1α2−β2Eζmi)|h),1α2−β2(Eζ(bi)−β2)+1α2−β2(Eζmi)(0★hg)−β1)
=1(α1−β1)(α2−β2)(c((Eζmi)|h),Eζbi−β2+(Eζmi)(0★hg)−(α2−β2)β1)
=1(α1−β1)(α2−β2)(Eζc(mi|h),Eζbi−β2+Eζ(mi(0★hg))−(α2−β2)β1)
And now, since α1=α3−β2α2−β2 and β1=β3−β2α2−β2, we can simplify (α1−β1)(α2−β2) as α3−β3, and simplify (α2−β2)β1 as β3−β2, to rewrite as
=1α3−β3(Eζc(mi|h),Eζ(bi+mi(0★hg))−β3)
Now, let's define our (m′i,b′i), when i∈Idef (to have them not get canceled out of existence by an undefined update/multiplication-by-zero)
m′i:=mi+∑j∈{i→}ζjζi(mj|h)
b′i:=bi+∑j∈{i→}ζjζi(bj+mj(0★hg)−βj)
What this essentially does is take (mi,bi) and adds a specially chosen a-measure to it, getting another point in the same set by upper-completion. Because ζi is nonzero, and the mixture of the (mi,bi) converges, the scale term doesn't affect the fact that this partial sum converges. Adding in the expectation-of-function terms doesn't affect convergence, and it's a sum of scaled a-measures because bj+mj(0★hg)−βj is just the b term of the raw update of (mj,bj) but shifted down, ie, nonnegative.
This may appear a bit mysterious, but the rationale behind it is "dang, we're only summing up over i∈Idef, we need to take our "missing" (mj,bj), and stash them in our "safe" i somehow (via the wiggle room we get from upper-completion) so they can manifest post-update"
Feeding our (m′i,b′i)∈Θi(π¬h∙π) through the updates produce the points:
1αi−βi(c(m′i|h),b′i+m′i(0★hg)−βi) But only for i∈Idef.
Mixing them produces the point: ∑i∈Idefζi(αi−βi)1αi−βi(c(m′i|h),b′i+m′i(0★hg)−βi)
Which cancels to make: ∑i∈Idefζi(c(m′i|h),b′i+m′i(0★hg)−βi)
This can be reexpressed as: (c(∑i∈Idef(ζim′i)|h),∑i∈Idefζi(bi+mi(0★hg)−βi))
And now, post-renormalization for the mixture, we get:
1α4−β4(c(∑i∈Idef(ζim′i)|h),∑i∈Idefζi(b′i+m′i(0★hg)−βi)−β4)
Substituting in our definition of m′i and b′i we have (all this is one term, we had to break it up)
1α4−β4(c(∑i∈Idef(ζi(mi+∑j∈{i→}ζjζi(mj|h)))|h))
1α4−β4(∑i∈Idefζi(bi+∑j∈{i→}ζjζi(bj+mj(0★hg)−βj)))
+1α4−β4(∑i∈Idefζi((mi+∑j∈{i→}ζjζi(mj|h))(0★hg)−βi)−β4)
Simplifying the measure term, we get:
1α4−β4(c(∑i∈Idef(ζi(mi+∑j∈{i→}ζjζi(mj|h)))|h))
=1α4−β4(c(∑i∈Idef(ζimi+∑j∈{i→}ζj(mj|h))|h))
=1α4−β4(c(∑i∈Idef(ζi(mi|h)+∑j∈{i→}ζj((mj|h)|h))))
=1α4−β4(∑i∈Idef(ζic(mi|h)+∑j∈{i→}ζjc(mj|h)))
=1α4−β4(∑iζic(mi|h))=1α4−β4(Eζc(mi|h))
Ok, that's the measure-term simplified. Now let's look at the first b term.
1α4−β4(∑i∈Idefζi(bi+∑j∈{i→}ζjζi(bj+mj(0★hg)−βj)))
=1α4−β4(∑i∈Idef(ζibi+∑j∈{i→}ζj(bj+mj(0★hg)−βj)))
=1α4−β4(∑iζibi+∑i∉Idefζi(mi(0★hg)−βj))
=1α4−β4(Eζbi+∑i∉Idefζi(mi(0★hg))−∑i∉Idefζiβi)
And now let's look at the second b term.
1α4−β4(∑i∈Idefζi((mi+∑j∈{i→}ζjζi(mj|h))(0★hg)−βi)−β4)
=1α4−β4(∑i∈Idefζi(mi(0★hg)+(∑j∈{i→}ζjζi((mj|h)(0★hg)))−βi)−β4)
=1α4−β4(∑i∈Idefζi(mi(0★hg)−βi)−β4)
(this previous step is because 0★hg is 0 on histories with h as a prefix, and mj|h is only supported on histories with h as a prefix, so the expectation is 0, and this extends to the sum of expectations)
=1α4−β4(∑i∈Idefζi(mi(0★hg))−∑i∈Idefζiβi−β4)
Uniting our two rewritten b terms, we get:
=1α4−β4(Eζbi+∑iζi(mi(0★hg))−∑iζiβi−β4)=1α4−β4(Eζ(bi+mi(0★hg))−Eζβi−β4)
and uniting this with our rewritten measure term, we get:
1α4−β4(Eζc(mi|h),Eζ(bi+mi(0★hg))−Eζβi−β4)
Now, let's compare against
=1α3−β3(Eζc(mi|h),Eζ(bi+mi(0★hg))−β3)
We already know from our earlier results on α and β that α4−β4=α3−β3, and that −β3=−β4−Eζβi, so our equivalence is complete.
So, mixing a batch of points in the Θi(π¬h∙π), renormalizing, and updating, can be replicated by pushing a different collection of points through the updates individually and mixing with corrected probabilities and renormalizing, establishing that for all π
((Eζ(Θi))R)|g,π¬h,h)(π)⊆(Eζ(PgΘi,π¬h(h)⋅(Θi|g,π¬h,h)))R(π)
So, we have that, for all π
((Eζ(Θi))R)|g,π¬h,h)(π)=(Eζ(PgΘi,π¬h(h)⋅(Θi|g,π¬h,h)))R(π)
=⎛⎜⎝Eζ(PgΘi,π¬h(h)⋅(Θi|g,π¬h,h))EζPgΘi,π¬h(h)⎞⎟⎠R(π)
And we have our result now.
**Theorem 6: Dynamic Consistency:** Given a hypothesis Θ (causal, pseudocausal, acausal, surcausal), and an arbitrary policy π and utility function U, then, with πh being the continuation of π post-update and π∗ being such that E(Θ|U,π¬h,h)(πh)(Uh)⪋E(Θ|U,π¬h,h)(π∗)(Uh) , then EΘ(π)(U)⪋EΘ(π¬h∙π∗)(U)
Proof sketch: We'll need to shatter this into two parts. The first part is if the update is undefined. Then the agent gives up and cries, and all policies are equally good. So we have to show that *regardless* of what the agent does after h, then it matches the performance of the original policy. The second part is showing the result for a well-defined update. It's mostly shuffling equations around.
For the first part, updates fail exactly when, for all policies, uUh(Θ)(π)∩NF has a single minimal point of the form (0,β) (same β for all policies). We'll be using this. Also, πh will be used to denote what the policy π does after observation h, so we have π=π¬h∙πh.
EΘ(π)(U)=min(m,b)∈Θ(π)∩NF(m(U)+b)=min(m,b)∈Θ(π¬h∙πh)∩NF(m(U)+b)
=min(m,b)∈Θ(π¬h∙πh)∩NF(m(U★h0)+b+m(0★hU))
=min(m,b)∈Θ(π¬h∙πh)∩NF((m|h)(U)+b+m(0★hU))
=min(m,b)∈Θ(π¬h∙πh)∩NF(c(m|h)(Uh)+b+m(0★hU))
=min(m,b)∈uUh(Θ)(πh)∩NF(m(Uh)+b)=β=min(m,b)∈uUh(Θ)(π∗)∩NF(m(Uh)+b)
=min(m,b)∈Θ(π¬h∙π∗)∩NF(c(m|h)(Uh)+b+m(0★hU))
=min(m,b)∈Θ(π¬h∙π∗)∩NF((m|h)(U)+b+m(0★hU))
=min(m,b)∈Θ(π¬h∙π∗)∩NF(m(U★h0)+b+m(0★hU))
=min(m,b)∈Θ(π¬h∙π∗)∩NF(m(U)+b)=EΘ(π¬h∙π∗)(U)
And we're done, EΘ(π)(U)=EΘ(π¬h∙π∗)(U)
Now for the case where the update actually goes through.
1PUπ¬h,h(h)(EΘ(π)(U)−EΘ(π¬h)(0★hU))
=1PUπ¬h,h(h)(min(m,b)∈Θ(π)∩NF(m(U)+b)−EΘ(π¬h)(0★hU))
=1PUπ¬h,h(h)(min(m,b)∈Θ(π¬h∙πh)∩NF(m(U)+b)−EΘ(π¬h)(0★hU))
=1PUπ¬h,h(h)(min(m,b)∈Θ(π¬h∙πh)∩NF(m(U★h0)+b+m(0★hU))−EΘ(π¬h)(0★hU))
=1PUπ¬h,h(h)(min(m,b)∈Θ(π¬h∙πh)∩NF((m|h)(U)+b+m(0★hU))−EΘ(π¬h)(0★hU))
=1PUπ¬h,h(h)(min(m,b)∈Θ(π¬h∙πh)∩NF(c(m|h)(Uh)+b+m(0★hU))−EΘ(π¬h)(0★hU))
=min(m,b)∈Θ(π¬h∙πh)∩NF(1PUπ¬h,h(h)(c(m|h)(Uh)+b+m(0★hU)−EΘ(π¬h)(0★hU)))
=min(m,b)∈(Θ|U,π¬h,h)(πh)(m(Uh)+b)
=E(Θ|U,π¬h,h)(πh)(Uh)⪋E(Θ|U,π¬h,h)(π∗)(Uh)
=min(m,b)∈(Θ|U,π¬h,h)(π∗)(m(Uh)+b)
=min(m,b)∈Θ(π¬h∙π∗)∩NF(1PUπ¬h,h(h)(c(m|h)(Uh)+b+m(0★hU)−EΘ(π¬h)(0★hU)))
=1PUπ¬h,h(h)(min(m,b)∈Θ(π¬h∙π∗)∩NF(c(m|h)(Uh)+b+m(0★hU))−EΘ(π¬h)(0★hU))
=1PUπ¬h,h(h)(min(m,b)∈Θ(π¬h∙π∗)∩NF((m|h)(U)+b+m(0★hU))−EΘ(π¬h)(0★hU))
=1PUπ¬h,h(h)(min(m,b)∈Θ(π¬h∙π∗)∩NF(m(U★h0)+b+m(0★hU))−EΘ(π¬h)(0★hU))
=1PUπ¬h,h(h)(min(m,b)∈Θ(π¬h∙π∗)∩NF(m(U)+b)−EΘ(π¬h)(0★hU))
=1PUπ¬h,h(h)(EΘ(π¬h∙π∗)(U)−EΘ(π¬h)(0★hU))
so we know
1PUπ¬h,h(h)(EΘ(π)(U)−EΘ(π¬h)(0★hU))⪋1PUπ¬h,h(h)(EΘ(π¬h∙π∗)(U)−EΘ(π¬h)(0★hU))
So EΘ(π)(U)−EΘ(π¬h)(0★hU)⪋EΘ(π¬h∙π∗)(U)−EΘ(π¬h)(0★hU)
and we can finish up and get dynamic consistency. EΘ(π)(U)⪋EΘ(π¬h∙π∗)(U)
**Theorem 7: Maximin UDT:** *Translating a set*S*of policy selection environments with a bounded modulus of continuity to an acausal hypothesis*Θ*always works. Also, for all utility functions*U*,* argmaxπinfe∈SEπ⋅e(U)=argmaxπEΘ(π)(U)
Ok, so a policy selection environment e is a continuous (in the policy) function (A×O)<ω×Π→ΔO
If you really want, like, for the planting flowers problem, you can have some probability of nonexistence that's policy-dependent, and a backup utility in case of nonexistence, though both still must be continuous in policy, by going "ok, there's a primordial event that leads to either the distribution starting, or I get event ⊥ with b≤1 utility", this can be crammed into the necessary framework.
A policy selection environment looks at what has happened thus far, and your policy, and picks some distribution over observations. For a *single* policy-selection environment, π→π⋅e is uniformly continuous. This is because, if you fix a time length t, there's finitely many histories of length t or less. For each of these histories, there's a δ where two policies identical up till time logγ(δ) produce only an ϵ change in ΔO (continuity means that different policies that are identical up till some sufficiently long time induce only a small change in what happens now). So, we can go "policies π,π′ that identical up till some stupidly long time mean that, for the first t steps, there's very little change in what happens". t can be made as long as we wish, and ϵ can be made as low as we wish, so for all ϵ, there some δ where, if d(π,π′)<δ, then π⋅e and π′⋅e are within ϵ of each other.
Bounded modulus of uniform continuity means that there's a single δ/ϵ function that works for *all* your policy selection environments of interest. Ie, no matter which environment was selected, you know how long policies need to be identical for to make only an ϵ difference in the resulting distribution over histories.
Encode each π⋅e history distribution as having λ=1 and b=0 Considering the set of (π⋅e,0) points as points for Θ?ω(π), we have
argmaxπinfe∈SEπ⋅e(U)=argmaxπinf{π⋅e}:e∈S(Ee⋅π(U)+0)=argmaxπinf(m,b)∈Θ?ω(π)(m(U)+b)
We do need to show that Θ?ω fulfills the essential properties for being able to turn it into an acausal hypothesis via Proposition 2. There's four. Nonemptiness, restricted-minimals, Hausdorff-continuity, and renormalization not failing. Nonemptiness is trivial. Restricted-minimals is easy because every point in Θ?ω(π), regardless of π, has λ=1 and b=0. Hausdorff-continuity can be shown by the set of environments having a bounded modulus of continuity, so given any (π⋅e,0)∈Θ?ω(π), we can reuse that e and there's a δ where d((π⋅e,0),(π′⋅e,0))=d(π⋅e,π′⋅e)<ϵ, and (π′⋅e,0)∈Θ?ω(π′), so Hausdorff-continuity follows.
That just leaves being normalizable. This occurs if there's a nontrivial Θ?ω(π), ie, EΘω(π)(1)≠EΘω(π)(0). This is obviously true, because the former is "minimal value of λ+b (always 1)", and the latter is "minimal value of b" (always 0).
So, by proposition 2, we create an acausal Θω hypothesis from our Θ?ω. From proposition 5, we then get argmaxπinf(m,b)∈Θ?ω(π)(m(U)+b)=argmaxπmin(m,b)∈Θω(π)(m(U)+b)
And then, since we have an acausal infinitary hypothesis, we can use the Isomorphism theorem to get that Θ(π)=Θω(π), so argmaxπmin(m,b)∈Θω(π)(m(U)+b)=argmaxπmin(m,b)∈Θ(π)(m(U)+b)
And finally, we can wrap up with Proposition 5 that said argmax set of policies actually exists, showing
argmaxπinfe∈SEπ⋅e(U)=argmaxπmin(m,b)∈Θ(π)(m(U)+b)=argmaxπEΘ(π)(U)
And we're done with UDT-copying. And, if you want, you can translate it into a surcausal hypothesis, and into a set of a-survironments from there.
**Proposition 12:** *If the collection of hypotheses*Θi*is learnable, then any Infrabayes-optimal policy family for a prior on them also learns the collection of hypotheses as well.*
First, we'll recap learnability. Learnability of a countable collection of belief functions by a γ-indexed family of policies πγ is the condition that for each Θi, regret limits to 0. (we'll use Uγ for our utility function with time-discount parameter γ) Ie,
∀i:limγ→1(maxπ∗(EΘi(π∗)(Uγ))−EΘi(πγ)(Uγ))=0
So, in the low-time-discount limit, you get a score arbitrarily close to that of an optimal agent that knows exactly what environment it's playing against.
An Infrabayes-optimal policy family for a prior/mixture of belief functions is one where
π∗γ∈argmaxπE(EζΘi)R(π)(Uγ)
Such an argmax set exists by Proposition 5. Further, any scale-and-shift just does a scale-and-shift on the values a policy will achieve and leaves the argmax set alone, so we could get an alternate representation as: π∗γ∈argmaxπE(EζΘi)(π)(Uγ)
So, assume that a countable family of belief functions paired with a utility function U is learnable by some family of policies πγ. We'll show that it's also learnable by any bayes-optimal π∗γ family for the prior (EζΘi)R.
First, πγ learns the family of hypotheses,∀i:limγ→1(maxπ∗(EΘi(π∗)(Uγ))−EΘi(πγ)(Uγ))=0
This implies limγ→1Eζ(maxπ∗(EΘi(π∗)(Uγ))−EΘi(πγ)(Uγ))=0
Because you only have to go finitely far out to nab all but ϵ of the probability mass of the expectation, and you can pick some γ extremely close to 1 that ensures that all those finitely many environments have ϵ or less regret.
We can now move the expectation inside to get:
limγ→1(Eζ(maxπ∗(EΘi(π∗)(Uγ)))−Eζ(EΘi(πγ)(Uγ)))=0
limγ→1(Eζ(maxπ∗(EΘi(π∗)(Uγ)))−E(EζΘi)(πγ)(Uγ))=0
Now, E(EζΘi)(πγ)(Uγ)≤E(EζΘi)(π∗γ)(Uγ) because π∗γ is optimal for the prior, so it's optimal for any rescaled version. So,
limγ→1(Eζ(maxπ∗(EΘi(π∗)(Uγ)))−E(EζΘi)(π∗γ)(Uγ))=0
limγ→1(Eζ(maxπ∗(EΘi(π∗)(Uγ)))−Eζ(EΘi(π∗γ)(Uγ)))=0
limγ→1Eζ(maxπ∗(EΘi(π∗)(Uγ))−EΘi(π∗γ)(Uγ))=0
Now, symmetrically, if π∗γ doesn't limit to 0 regret on all belief functions, then the expectation doesn't limit to 0 either.
∀i:limγ→1(maxπ∗(EΘi(π∗)(Uγ))−EΘi(π∗γ)(Uγ))=0
and we have shown that our arbitrary Infrabayes-optimal family of policies learns the environments.
**Complete Class Theorem Weak Version:** *Given any pareto-optimal policy*π*, then there is an infradistribution*H*over states, where*∀π′:fπ′≠fπ:EH(fπ)>EH(fπ′)
Proof sketch: Because we are able to translate from concave lipschitz monotone normalized functionals over [0,1]S to infradistributions over states, we just have to get a concave lipschitz monotone functional where our policy π is optimal, and then it can be normalized back up to 1, and then it can be turned into an infradistribution over states by LF-duality. Said concave lipschitz monotone functional is:
h(f):=mins∈S(f(s)−Eo∼ob(s)P(s,π(o)))
We just need to show that the function is indeed concave, Lipschitz, monotone, and assigns no policy a higher expectation value than the Pareto-optimal policy, because all these properties are preserved by a scale-and-shift.
Proof of Lipschitzness: If you perturb f by ϵ or less in all states, then this only affects the minimal value by ϵ or less, so we actually have a Lipschitz constant of 1.
Proof of monotonicity: If f matches or outperforms f′ in all states, than the possible values that min is picking amongst all went up, so f gets an equal or higher value, showing monotonicity.
Proof of concavity:
h(pf+(1−p)f′)=mins∈S((pf+(1−p)f′)(s)−Eo∼ob(s)P(s,π(o)))
=mins∈S(pf(s)+(1−p)f′(s)−pEo∼ob(s)P(s,π(o))−(1−p)Eo∼ob(s)P(s,π(o)))
≥mins∈S(pf(s)−pEo∼ob(s)P(s,π(o)))+mins∈S((1−p)f′(s)−(1−p)Eo∼ob(s)P(s,π(o)))
=pmins∈S(f(s)−Eo∼ob(s)P(s,π(o)))+(1−p)mins∈S(f′(s)−Eo∼ob(s)P(s,π(o)))
=ph(f)+(1−p)h(f′)
Proof of π getting the optimal value: π is on the pareto-frontier, so there is no other policy π′ that gets equal-or-greater value in all states. Thus, given any other π′, there is a state in which it underperforms the reward of π in that state, so the quantity is negative. And for π itself, it obviously matches the behavior of π in all states, so it gets a value of 0. Thus, π gets the strictly optimal score amongst policies against this h, so the same holds after renormalization, and then the same holds for the expectation values w.r.t. the infradistribution. |
2249f2db-5bff-4057-bc25-423803765be6 | trentmkelly/LessWrong-43k | LessWrong | Book review: “The Heart of the Brain: The Hypothalamus and Its Hormones”
1. Introduction
1.1 Hypothalamus as “business logic”
In software jargon, there’s a nice term “business logic”, for code like the following (made-up) excerpt from corporate tax filing software (based on here):
def attachSupplementalDocuments(file):
if file.state == "California" or file.state == "Texas":
# SR008-04X/I are always required in these states
file.attachDocument("SR008-04X")
file.attachDocument("SR008-04XI")
if file.ledgerAmnt >= 500_000:
# Ledger of 500K or more requires AUTHLDG-1A
file.attachDocument("AUTHLDG-1A")
When you think of “business logic”, think of stuff like that—i.e., parts of source code that more-or-less directly implement specific, real-world, functional requirements.
By contrast, things that are NOT business logic include infrastructure & subroutines & plumbing that are generally useful in many contexts—e.g. code for initializing a database, or code for memory management, or code for performing stochastic gradient descent.
If genomes are the “source code” of brains, then they need to encode “business logic” too—specific calculations to do specific things that help an animal thrive and reproduce in its particular biological niche. For example:
if about_to_starve_to_death:
reduce_sex_drive()
increase_pain_tolerance()
emit_hunger_sensation()
increase_reward_for_eating()
if fertility > 0:
increase_sex_drive()
...
(We could also call these things “innate reactions”.)
Machine Learning people might interject here: Why does that have to be in the genome? Why can’t the brain derive those kinds of rules via a within-lifetime learning algorithm instead? Well, often it does! But:
* Some things can’t be learned within a lifetime, because their evolutionary benefits are only apparent in hindsight, perhaps even many generations hence.
* Other things can’t be learned within a lifetime, because not doing them, even once, is potentially fatal.
* Still other bits of “busines |
8996e444-1c32-4c03-b73d-664b2c3ddd4f | StampyAI/alignment-research-dataset/arxiv | Arxiv | Do Deep Generative Models Know What They Don't Know?
1 Introduction
---------------
Deep learning has achieved impressive success in applications for which the goal is to model a conditional distribution p(y|𝒙)𝑝conditional𝑦𝒙p(y|{\bm{x}})italic\_p ( italic\_y | bold\_italic\_x ), with y𝑦yitalic\_y being a label and 𝒙𝒙{\bm{x}}bold\_italic\_x the features. While the conditional model p(y|𝒙)𝑝conditional𝑦𝒙p(y|{\bm{x}})italic\_p ( italic\_y | bold\_italic\_x ) may be highly accurate on inputs 𝒙𝒙{\bm{x}}bold\_italic\_x sampled from the training distribution, there are no guarantees that the model will work well on 𝒙𝒙{\bm{x}}bold\_italic\_x’s drawn from some other distribution. For example, Louizos & Welling ([2017](#bib.bib19)) show that simply rotating an MNIST digit can make a neural network predict another class with high confidence (see their Figure 1a). Ostensibly, one way to avoid such overconfidently wrong predictions would be to train a density model p(𝒙;𝜽)𝑝𝒙𝜽p({\bm{x}};{\bm{\theta}})italic\_p ( bold\_italic\_x ; bold\_italic\_θ ) (with
𝜽𝜽{\bm{\theta}}bold\_italic\_θ denoting the parameters) to approximate the true distribution of training inputs p\*(𝒙)superscript𝑝𝒙p^{\*}({\bm{x}})italic\_p start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT ( bold\_italic\_x ) and refuse to make a prediction for any 𝒙𝒙{\bm{x}}bold\_italic\_x that has a sufficiently low density under p(𝒙;𝜽)𝑝𝒙𝜽p({\bm{x}};{\bm{\theta}})italic\_p ( bold\_italic\_x ; bold\_italic\_θ ). The intuition is that the discriminative model p(y|𝒙)𝑝conditional𝑦𝒙p(y|{\bm{x}})italic\_p ( italic\_y | bold\_italic\_x ) likely did not observe enough samples in that region to make a reliable decision for those inputs. This idea has been proposed by various papers, cf. (Bishop, [1994](#bib.bib1)), and as recently as in the panel discussion at Advances in Approximate Bayesian Inference (AABI) 2017 (Blei et al., [2017](#bib.bib3)).
Anomaly detection is just one motivating example for which we require accurate densities, and others include information regularization (Szummer & Jaakkola, [2003](#bib.bib28)), open set recognition (Herbei & Wegkamp, [2006](#bib.bib11)), uncertainty estimation, detecting covariate shift, active learning, model-based reinforcement learning, and transfer learning. Accordingly, these applications have lead to widespread interest in deep generative models, which take many forms such as variational auto-encoders (VAEs) (Kingma & Welling, [2014](#bib.bib13); Rezende et al., [2014](#bib.bib21)), generative adversarial networks (GANs) (Goodfellow et al., [2014](#bib.bib8)), auto-regressive models (van den Oord et al., [2016b](#bib.bib33); [a](#bib.bib32)), and invertible latent variable models (Tabak & Turner, [2013](#bib.bib30)). The last two classes—auto-regressive and invertible models—are especially attractive since they offer exact computation of the marginal likelihood, requiring no approximate inference techniques.
In this paper, we investigate if modern deep generative models can be used for anomaly detection, as suggested by Bishop ([1994](#bib.bib1)) and the AABI pannel (Blei et al., [2017](#bib.bib3)), expecting a well-calibrated model to assign higher density to the training data than to some other data set. However, we find this to not be the case: when trained on CIFAR-10 (Krizhevsky & Hinton, [2009](#bib.bib15)), VAEs, autoregressive models, and flow-based generative models all assign a higher density to SVHN (Netzer et al., [2011](#bib.bib20)) than to the training data. We find this observation to be quite problematic and unintuitive since SVHN’s digit images are so visually distinct from the dogs, horses, trucks, boats, etc. found in CIFAR-10. Yet this phenomenon is not restricted to CIFAR-10 vs SVHN, and we report similar findings for models trained on CelebA and ImageNet.
We go on to study these curious observations in flow-based models in particular since they allow for exact marginal density calculations. When the flow is restricted to have constant volume across inputs, we show that the out-of-distribution behavior can be explained in terms of the data’s variance and the model’s curvature.
To the best of our knowledge, we are the first to report these unintuitive findings for a variety of deep generative models and image data sets. Moreover, our experiments with flow-based models isolate some crucial experimental variables such as the effect of constant-volume vs non-volume-preserving transformations. Lastly, our analysis provides some simple but general expressions for quantifying the gap in the model density between two data sets. We close the paper by urging more study of the out-of-training-distribution properties of deep generative models. Understanding their behaviour in this setting is crucial for their deployment to the real world.
2 Background
-------------
We begin by establishing notation and reviewing the necessary background material. We denote matrices with upper-case and bold letters (e.g. 𝑿𝑿{\bm{X}}bold\_italic\_X), vectors with lower-case and bold (e.g. 𝒙𝒙{\bm{x}}bold\_italic\_x), and scalars with lower-case and no bolding (e.g. x𝑥xitalic\_x). As our focus is on generative models, let the collection of all observations be denoted by 𝑿={𝒙n}n=1N𝑿superscriptsubscriptsubscript𝒙𝑛𝑛1𝑁{\bm{X}}=\{{\bm{x}}\_{n}\}\_{n=1}^{N}bold\_italic\_X = { bold\_italic\_x start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT } start\_POSTSUBSCRIPT italic\_n = 1 end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT italic\_N end\_POSTSUPERSCRIPT with 𝒙𝒙{\bm{x}}bold\_italic\_x representing a vector containing all features and, if present, labels. All N𝑁Nitalic\_N examples are assumed independently and identically drawn from some population 𝒙∼p\*(𝒙)similar-to𝒙superscript𝑝𝒙{\bm{x}}\sim p^{\*}({\bm{x}})bold\_italic\_x ∼ italic\_p start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT ( bold\_italic\_x ) (which is unknown) with support denoted 𝒳𝒳\mathcal{X}caligraphic\_X. We define the model density function to be p(𝒙;𝜽)𝑝𝒙𝜽p({\bm{x}};{\bm{\theta}})italic\_p ( bold\_italic\_x ; bold\_italic\_θ ) where 𝜽∈𝚯𝜽𝚯{\bm{\theta}}\in\bm{\Theta}bold\_italic\_θ ∈ bold\_Θ are the model parameters, and let the model likelihood be denoted p(𝑿;𝜽)=∏n=1Np(𝒙n;𝜽)𝑝𝑿𝜽superscriptsubscriptproduct𝑛1𝑁𝑝subscript𝒙𝑛𝜽p({\bm{X}};{\bm{\theta}})=\prod\_{n=1}^{N}p({\bm{x}}\_{n};{\bm{\theta}})italic\_p ( bold\_italic\_X ; bold\_italic\_θ ) = ∏ start\_POSTSUBSCRIPT italic\_n = 1 end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT italic\_N end\_POSTSUPERSCRIPT italic\_p ( bold\_italic\_x start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT ; bold\_italic\_θ ).
###
2.1 Training Neural Generative Models
Given (training) data 𝑿𝑿{\bm{X}}bold\_italic\_X and a model class {p(⋅;𝜽):𝜽∈Θ}conditional-set𝑝⋅𝜽𝜽Θ\{p(\cdot;{\bm{\theta}}):{\bm{\theta}}\in\Theta\}{ italic\_p ( ⋅ ; bold\_italic\_θ ) : bold\_italic\_θ ∈ roman\_Θ }, we are interested in finding the parameters 𝜽𝜽{\bm{\theta}}bold\_italic\_θ that make the model closest to the true but unknown data distribution p\*(𝒙)superscript𝑝𝒙p^{\*}({\bm{x}})italic\_p start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT ( bold\_italic\_x ). We can quantify this gap in terms of a Kullback–Leibler divergence (KLD):
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| | KLD[p\*(𝒙)||p(𝒙;𝜽)]=∫p\*(𝒙)logp\*(𝒙)p(𝒙;𝜽)d𝒙≈−1Nlogp(𝑿;𝜽)−ℍ[p\*]\text{KLD}[p^{\*}({\bm{x}})||p({\bm{x}};{\bm{\theta}})]=\int p^{\*}({\bm{x}})\log\frac{p^{\*}({\bm{x}})}{p({\bm{x}};{\bm{\theta}})}\ d{\bm{x}}\approx-\frac{1}{N}\log p({\bm{X}};{\bm{\theta}})-\mathbb{H}[p^{\*}]KLD [ italic\_p start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT ( bold\_italic\_x ) | | italic\_p ( bold\_italic\_x ; bold\_italic\_θ ) ] = ∫ italic\_p start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT ( bold\_italic\_x ) roman\_log divide start\_ARG italic\_p start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT ( bold\_italic\_x ) end\_ARG start\_ARG italic\_p ( bold\_italic\_x ; bold\_italic\_θ ) end\_ARG italic\_d bold\_italic\_x ≈ - divide start\_ARG 1 end\_ARG start\_ARG italic\_N end\_ARG roman\_log italic\_p ( bold\_italic\_X ; bold\_italic\_θ ) - blackboard\_H [ italic\_p start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT ] | | (1) |
where the first term in the right-most expression is the average log-likelihood and the second is the entropy of the true distribution. As the latter is a fixed constant, minimizing the KLD amounts to finding the parameter settings that maximize the data’s log density: 𝜽\*=argmax𝜽logp(𝑿;𝜽)=argmax𝜽∑n=1Nlogp(𝒙n;𝜽).superscript𝜽subscriptargmax𝜽𝑝𝑿𝜽subscriptargmax𝜽superscriptsubscript𝑛1𝑁𝑝subscript𝒙𝑛𝜽{\bm{\theta}}^{\*}=\operatorname\*{arg\,max}\_{{\bm{\theta}}}\log p({\bm{X}};{\bm{\theta}})=\operatorname\*{arg\,max}\_{{\bm{\theta}}}{\textstyle\sum}\_{n=1}^{N}\log p({\bm{x}}\_{n};{\bm{\theta}}).bold\_italic\_θ start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT = start\_OPERATOR roman\_arg roman\_max end\_OPERATOR start\_POSTSUBSCRIPT bold\_italic\_θ end\_POSTSUBSCRIPT roman\_log italic\_p ( bold\_italic\_X ; bold\_italic\_θ ) = start\_OPERATOR roman\_arg roman\_max end\_OPERATOR start\_POSTSUBSCRIPT bold\_italic\_θ end\_POSTSUBSCRIPT ∑ start\_POSTSUBSCRIPT italic\_n = 1 end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT italic\_N end\_POSTSUPERSCRIPT roman\_log italic\_p ( bold\_italic\_x start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT ; bold\_italic\_θ ) .
Note that p(𝒙n;𝜽)𝑝subscript𝒙𝑛𝜽p({\bm{x}}\_{n};{\bm{\theta}})italic\_p ( bold\_italic\_x start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT ; bold\_italic\_θ ) alone does not have any interpretation as a probability. To extract probabilities from the model density, we need to integrate over some region 𝛀𝛀{\bm{\Omega}}bold\_Ω: P(𝛀)=∫𝛀p(𝒙;𝜽)𝑑𝒙𝑃𝛀subscript𝛀𝑝𝒙𝜽
differential-d𝒙P({\bm{\Omega}})=\int\_{{\bm{\Omega}}}p({\bm{x}};{\bm{\theta}})d{\bm{x}}italic\_P ( bold\_Ω ) = ∫ start\_POSTSUBSCRIPT bold\_Ω end\_POSTSUBSCRIPT italic\_p ( bold\_italic\_x ; bold\_italic\_θ ) italic\_d bold\_italic\_x. Adding noise to the data during model optimization can mock this integration step, encouraging the density model to output something nearer to probabilities (Theis et al., [2016](#bib.bib31)):
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| | log∫p(𝒙n+𝜹;𝜽)p(𝜹)𝑑𝜹≥𝔼𝜹[logp(𝒙n+𝜹;𝜽)]≈logp(𝒙n+𝜹~;𝜽)𝑝subscript𝒙𝑛𝜹𝜽
𝑝𝜹differential-d𝜹subscript𝔼𝜹delimited-[]𝑝subscript𝒙𝑛𝜹𝜽𝑝subscript𝒙𝑛~𝜹𝜽\begin{split}&\log\int p({\bm{x}}\_{n}+{\bm{\delta}};{\bm{\theta}})p({\bm{\delta}})\ d{\bm{\delta}}\geq\mathbb{E}\_{{\bm{\delta}}}\left[\log p({\bm{x}}\_{n}+{\bm{\delta}};{\bm{\theta}})\right]\approx\log p({\bm{x}}\_{n}+\tilde{{\bm{\delta}}};{\bm{\theta}})\end{split}start\_ROW start\_CELL end\_CELL start\_CELL roman\_log ∫ italic\_p ( bold\_italic\_x start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT + bold\_italic\_δ ; bold\_italic\_θ ) italic\_p ( bold\_italic\_δ ) italic\_d bold\_italic\_δ ≥ blackboard\_E start\_POSTSUBSCRIPT bold\_italic\_δ end\_POSTSUBSCRIPT [ roman\_log italic\_p ( bold\_italic\_x start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT + bold\_italic\_δ ; bold\_italic\_θ ) ] ≈ roman\_log italic\_p ( bold\_italic\_x start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT + over~ start\_ARG bold\_italic\_δ end\_ARG ; bold\_italic\_θ ) end\_CELL end\_ROW | |
where 𝜹~~𝜹\tilde{{\bm{\delta}}}over~ start\_ARG bold\_italic\_δ end\_ARG is a sample from p(𝜹)𝑝𝜹p({\bm{\delta}})italic\_p ( bold\_italic\_δ ). The resulting objective is a lower-bound, making it a suitable optimization target. All models in all of the experiments that we report are trained with input noise. Due to this ambiguity between densities and probabilities, we call the quantity logp(𝑿+𝚫~;𝜽)𝑝𝑿~𝚫𝜽\log p({\bm{X}}+\tilde{{\bm{\Delta}}};{\bm{\theta}})roman\_log italic\_p ( bold\_italic\_X + over~ start\_ARG bold\_Δ end\_ARG ; bold\_italic\_θ ) a ‘log-likelihood,’ even if 𝑿𝑿{\bm{X}}bold\_italic\_X is drawn from a distribution unlike the training data.
Regarding the choice of density model, we could choose one of the standard density functions for p(𝒙n;𝜽)𝑝subscript𝒙𝑛𝜽p({\bm{x}}\_{n};{\bm{\theta}})italic\_p ( bold\_italic\_x start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT ; bold\_italic\_θ ), e.g. a Gaussian, but these may not be suitable for modeling the complex, high-dimensional data sets we often observe in the real world. Hence, we want to parametrize the model density with some high-capacity function f𝑓fitalic\_f, which is usually chosen to be a neural network. That way the model has a somewhat compact representation and can be optimized via gradient ascent. We experiment with three variants of neural generative models: autoregressive, latent variable, and invertible. In the first class, we study the PixelCNN (van den Oord et al., [2016b](#bib.bib33)), and due to space constraints, we refer the reader to van den Oord et al. ([2016b](#bib.bib33)) for its definition. As a representative of the second class, we use a VAE (Kingma & Welling, [2014](#bib.bib13); Rezende et al., [2014](#bib.bib21)). See Rosca et al. ([2018](#bib.bib23)) for descriptions of the precise versions we use. Lastly, invertible flow-based generative models are the third class. We define them in detail below since we study them with the most depth.
###
2.2 Generative Models via Change of Variables
The VAE and many other generative models are defined as a joint distribution between the observed and latent variables. However, another path forward is to perform a *change of variables*. In this case 𝒙𝒙{\bm{x}}bold\_italic\_x and 𝒛𝒛{\bm{z}}bold\_italic\_z are one and the same, and there is no longer any notion of a product space 𝒳×𝒵𝒳𝒵\mathcal{X}\times\mathcal{Z}caligraphic\_X × caligraphic\_Z. Let f:𝒳↦𝒵:𝑓maps-to𝒳𝒵f:\mathcal{X}\mapsto\mathcal{Z}italic\_f : caligraphic\_X ↦ caligraphic\_Z be a diffeomorphism from the data space 𝒳𝒳\mathcal{X}caligraphic\_X to a latent space 𝒵𝒵\mathcal{Z}caligraphic\_Z. Using f𝑓fitalic\_f then allows us to compute integrals over 𝒛𝒛{\bm{z}}bold\_italic\_z as an integral over 𝒙𝒙{\bm{x}}bold\_italic\_x and vice versa:
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| | ∫𝒛pz(𝒛)𝑑𝒛=∫𝒙pz(f(𝒙))|∂𝒇∂𝒙|𝑑𝒙=∫𝒙px(𝒙)𝑑𝒙=∫𝒛px(f−1(𝒛))|∂𝒇−1∂𝒛|𝑑𝒛subscript𝒛subscript𝑝𝑧𝒛differential-d𝒛subscript𝒙subscript𝑝𝑧𝑓𝒙𝒇𝒙differential-d𝒙subscript𝒙subscript𝑝𝑥𝒙differential-d𝒙subscript𝒛subscript𝑝𝑥superscript𝑓1𝒛superscript𝒇1𝒛differential-d𝒛\int\_{{\bm{z}}}p\_{z}({\bm{z}})\ d{\bm{z}}=\int\_{{\bm{x}}}p\_{z}(f({\bm{x}}))\ \left|\frac{\partial{\bm{f}}}{\partial{\bm{x}}}\right|\ d{\bm{x}}=\int\_{{\bm{x}}}p\_{x}({\bm{x}})\ d{\bm{x}}=\int\_{{\bm{z}}}p\_{x}(f^{-1}({\bm{z}}))\ \left|\frac{\partial{\bm{f}}^{-1}}{\partial{\bm{z}}}\right|\ d{\bm{z}}∫ start\_POSTSUBSCRIPT bold\_italic\_z end\_POSTSUBSCRIPT italic\_p start\_POSTSUBSCRIPT italic\_z end\_POSTSUBSCRIPT ( bold\_italic\_z ) italic\_d bold\_italic\_z = ∫ start\_POSTSUBSCRIPT bold\_italic\_x end\_POSTSUBSCRIPT italic\_p start\_POSTSUBSCRIPT italic\_z end\_POSTSUBSCRIPT ( italic\_f ( bold\_italic\_x ) ) | divide start\_ARG ∂ bold\_italic\_f end\_ARG start\_ARG ∂ bold\_italic\_x end\_ARG | italic\_d bold\_italic\_x = ∫ start\_POSTSUBSCRIPT bold\_italic\_x end\_POSTSUBSCRIPT italic\_p start\_POSTSUBSCRIPT italic\_x end\_POSTSUBSCRIPT ( bold\_italic\_x ) italic\_d bold\_italic\_x = ∫ start\_POSTSUBSCRIPT bold\_italic\_z end\_POSTSUBSCRIPT italic\_p start\_POSTSUBSCRIPT italic\_x end\_POSTSUBSCRIPT ( italic\_f start\_POSTSUPERSCRIPT - 1 end\_POSTSUPERSCRIPT ( bold\_italic\_z ) ) | divide start\_ARG ∂ bold\_italic\_f start\_POSTSUPERSCRIPT - 1 end\_POSTSUPERSCRIPT end\_ARG start\_ARG ∂ bold\_italic\_z end\_ARG | italic\_d bold\_italic\_z | | (2) |
where |∂𝒇/∂𝒙|𝒇𝒙|\partial{\bm{f}}/\partial{\bm{x}}|| ∂ bold\_italic\_f / ∂ bold\_italic\_x | and |∂𝒇−1/∂𝒛|superscript𝒇1𝒛|\partial{\bm{f}}^{-1}/\partial{\bm{z}}|| ∂ bold\_italic\_f start\_POSTSUPERSCRIPT - 1 end\_POSTSUPERSCRIPT / ∂ bold\_italic\_z | are known as the volume elements as they adjust for the volume change under the alternate measure. Specifically, when the change is w.r.t. coordinates, the volume element is
the determinant of the diffeomorphism’s Jacobian matrix, which we denote as |∂𝒇/∂𝒙|𝒇𝒙\left|\partial{\bm{f}}/\partial{\bm{x}}\right|| ∂ bold\_italic\_f / ∂ bold\_italic\_x |.
The change of variables formula is a powerful tool for generative modeling as it allows us to define a distribution p(𝒙)𝑝𝒙p({\bm{x}})italic\_p ( bold\_italic\_x ) entirely in terms of an auxiliary distribution p(𝒛)𝑝𝒛p({\bm{z}})italic\_p ( bold\_italic\_z ), which we are free to choose, and f𝑓fitalic\_f. Denote the parameters of the change of variables model as 𝜽={ϕ,𝝍}𝜽bold-italic-ϕ𝝍{\bm{\theta}}=\{{\bm{\phi}},{\bm{\psi}}\}bold\_italic\_θ = { bold\_italic\_ϕ , bold\_italic\_ψ } with ϕbold-italic-ϕ{\bm{\phi}}bold\_italic\_ϕ being the diffeomorphism’s parameters, i.e. f(𝒙;ϕ)𝑓𝒙bold-italic-ϕf({\bm{x}};{\bm{\phi}})italic\_f ( bold\_italic\_x ; bold\_italic\_ϕ ), and 𝝍𝝍{\bm{\psi}}bold\_italic\_ψ being the auxiliary distribution’s parameters, i.e. p(𝒛;𝝍)𝑝𝒛𝝍p({\bm{z}};{\bm{\psi}})italic\_p ( bold\_italic\_z ; bold\_italic\_ψ ). We can perform maximum likelihood estimation for the model as follows:
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| | 𝜽\*=argmax𝜽logpx(𝑿;𝜽)=argmaxϕ,𝝍∑n=1Nlogpz(f(𝒙n;ϕ);𝝍)+log|∂𝒇ϕ∂𝒙n|.superscript𝜽subscriptargmax𝜽subscript𝑝𝑥𝑿𝜽subscriptargmaxbold-italic-ϕ𝝍superscriptsubscript𝑛1𝑁subscript𝑝𝑧𝑓subscript𝒙𝑛bold-italic-ϕ𝝍subscript𝒇bold-italic-ϕsubscript𝒙𝑛{{\bm{\theta}}}^{\*}=\operatorname\*{arg\,max}\_{{\bm{\theta}}}\ \log p\_{x}({\bm{X}};{\bm{\theta}})=\operatorname\*{arg\,max}\_{{\bm{\phi}},{\bm{\psi}}}\ \sum\_{n=1}^{N}\log p\_{z}(f({\bm{x}}\_{n};{\bm{\phi}});{\bm{\psi}})+\log\left|\frac{\partial{\bm{f}}\_{{\bm{\phi}}}}{\partial{\bm{x}}\_{n}}\right|.bold\_italic\_θ start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT = start\_OPERATOR roman\_arg roman\_max end\_OPERATOR start\_POSTSUBSCRIPT bold\_italic\_θ end\_POSTSUBSCRIPT roman\_log italic\_p start\_POSTSUBSCRIPT italic\_x end\_POSTSUBSCRIPT ( bold\_italic\_X ; bold\_italic\_θ ) = start\_OPERATOR roman\_arg roman\_max end\_OPERATOR start\_POSTSUBSCRIPT bold\_italic\_ϕ , bold\_italic\_ψ end\_POSTSUBSCRIPT ∑ start\_POSTSUBSCRIPT italic\_n = 1 end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT italic\_N end\_POSTSUPERSCRIPT roman\_log italic\_p start\_POSTSUBSCRIPT italic\_z end\_POSTSUBSCRIPT ( italic\_f ( bold\_italic\_x start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT ; bold\_italic\_ϕ ) ; bold\_italic\_ψ ) + roman\_log | divide start\_ARG ∂ bold\_italic\_f start\_POSTSUBSCRIPT bold\_italic\_ϕ end\_POSTSUBSCRIPT end\_ARG start\_ARG ∂ bold\_italic\_x start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT end\_ARG | . | | (3) |
Optimizing 𝝍𝝍{\bm{\psi}}bold\_italic\_ψ must be done carefully so as to not result in a trivial model. For instance, optimization could make p(𝒛;𝝍)𝑝𝒛𝝍p({\bm{z}};{\bm{\psi}})italic\_p ( bold\_italic\_z ; bold\_italic\_ψ ) close to uniform if there are no constraints on its variance. For this reason, most implementations leave 𝝍𝝍{\bm{\psi}}bold\_italic\_ψ as fixed (usually a standard Gaussian) in practice. Likewise, we assume it as fixed from here forward, thus omitting 𝝍𝝍{\bm{\psi}}bold\_italic\_ψ from equations to reduce notational clutter. After training, samples can be drawn from the model via the inverse transform: 𝒙~=f−1(𝒛~;ϕ),𝒛~∼p(𝐳).formulae-sequence~𝒙superscript𝑓1~𝒛bold-italic-ϕsimilar-to~𝒛𝑝𝐳\tilde{{\bm{x}}}=f^{-1}(\tilde{{\bm{z}}};{\bm{\phi}}),\ \ \ \tilde{{\bm{z}}}\sim p(\mathbf{z}).over~ start\_ARG bold\_italic\_x end\_ARG = italic\_f start\_POSTSUPERSCRIPT - 1 end\_POSTSUPERSCRIPT ( over~ start\_ARG bold\_italic\_z end\_ARG ; bold\_italic\_ϕ ) , over~ start\_ARG bold\_italic\_z end\_ARG ∼ italic\_p ( bold\_z ) .
For the particular form of f𝑓fitalic\_f, most work to date has constructed the bijection from affine coupling layers (ACLs) (Dinh et al., [2017](#bib.bib6)), which transform 𝒙𝒙{\bm{x}}bold\_italic\_x by way of translation and scaling operations. Specifically, ACLs take the form: fACL(𝒙;ϕ)=[exp{s(𝒙d:;ϕs)}⊙𝒙:d+t(𝒙d:;ϕt),𝒙d:],subscript𝑓ACL𝒙bold-italic-ϕdirect-product𝑠subscript𝒙:𝑑absentsubscriptbold-italic-ϕ𝑠subscript𝒙:absent𝑑𝑡subscript𝒙:𝑑absentsubscriptbold-italic-ϕ𝑡subscript𝒙:𝑑absentf\_{\text{{ACL}}}({\bm{x}};{\bm{\phi}})=\left[\exp\{s({\bm{x}}\_{d:};{\bm{\phi}}\_{s})\}\odot{\bm{x}}\_{:d}+t({\bm{x}}\_{d:};{\bm{\phi}}\_{t}),{\bm{x}}\_{d:}\right],italic\_f start\_POSTSUBSCRIPT ACL end\_POSTSUBSCRIPT ( bold\_italic\_x ; bold\_italic\_ϕ ) = [ roman\_exp { italic\_s ( bold\_italic\_x start\_POSTSUBSCRIPT italic\_d : end\_POSTSUBSCRIPT ; bold\_italic\_ϕ start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT ) } ⊙ bold\_italic\_x start\_POSTSUBSCRIPT : italic\_d end\_POSTSUBSCRIPT + italic\_t ( bold\_italic\_x start\_POSTSUBSCRIPT italic\_d : end\_POSTSUBSCRIPT ; bold\_italic\_ϕ start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT ) , bold\_italic\_x start\_POSTSUBSCRIPT italic\_d : end\_POSTSUBSCRIPT ] ,
where ⊙direct-product\odot⊙ denotes an element-wise product. This transformation, firstly, splits the input vector in half, i.e. 𝒙=[𝒙:d,𝒙d:]𝒙subscript𝒙:absent𝑑subscript𝒙:𝑑absent{\bm{x}}=\left[{\bm{x}}\_{:d},{\bm{x}}\_{d:}\right]bold\_italic\_x = [ bold\_italic\_x start\_POSTSUBSCRIPT : italic\_d end\_POSTSUBSCRIPT , bold\_italic\_x start\_POSTSUBSCRIPT italic\_d : end\_POSTSUBSCRIPT ] (using Python list syntax). Then the second half of the vector is fed into two arbitrary neural networks (possibly with tied parameters) whose outputs are denoted t(𝒙d:;ϕt)𝑡subscript𝒙:𝑑absentsubscriptbold-italic-ϕ𝑡t({\bm{x}}\_{d:};{\bm{\phi}}\_{t})italic\_t ( bold\_italic\_x start\_POSTSUBSCRIPT italic\_d : end\_POSTSUBSCRIPT ; bold\_italic\_ϕ start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT ) and s(𝒙d:;ϕs)𝑠subscript𝒙:𝑑absentsubscriptbold-italic-ϕ𝑠s({\bm{x}}\_{d:};{\bm{\phi}}\_{s})italic\_s ( bold\_italic\_x start\_POSTSUBSCRIPT italic\_d : end\_POSTSUBSCRIPT ; bold\_italic\_ϕ start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT ), with ϕ⋅subscriptbold-italic-ϕ⋅{\bm{\phi}}\_{\cdot}bold\_italic\_ϕ start\_POSTSUBSCRIPT ⋅ end\_POSTSUBSCRIPT being the collection of weights and biases. Finally, the output is formed by (1) *scaling* the first half of the input by one neural network output, i.e. exp{s(𝒙d:;ϕs)}⊙𝒙:ddirect-product𝑠subscript𝒙:𝑑absentsubscriptbold-italic-ϕ𝑠subscript𝒙:absent𝑑\exp\{s({\bm{x}}\_{d:};{\bm{\phi}}\_{s})\}\odot{\bm{x}}\_{:d}roman\_exp { italic\_s ( bold\_italic\_x start\_POSTSUBSCRIPT italic\_d : end\_POSTSUBSCRIPT ; bold\_italic\_ϕ start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT ) } ⊙ bold\_italic\_x start\_POSTSUBSCRIPT : italic\_d end\_POSTSUBSCRIPT, (2) *translating* the result of the scaling operation by the second neural network output, i.e. (⋅)+t(𝒙d:;ϕt)⋅𝑡subscript𝒙:𝑑absentsubscriptbold-italic-ϕ𝑡(\cdot)+t({\bm{x}}\_{d:};{\bm{\phi}}\_{t})( ⋅ ) + italic\_t ( bold\_italic\_x start\_POSTSUBSCRIPT italic\_d : end\_POSTSUBSCRIPT ; bold\_italic\_ϕ start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT ), and (3) *copying* the second half of 𝒙𝒙{\bm{x}}bold\_italic\_x forward, making it the second half of fACL(𝒙;ϕ)subscript𝑓ACL𝒙bold-italic-ϕf\_{\text{{ACL}}}({\bm{x}};{\bm{\phi}})italic\_f start\_POSTSUBSCRIPT ACL end\_POSTSUBSCRIPT ( bold\_italic\_x ; bold\_italic\_ϕ ), i.e. fd:=𝒙d:subscript𝑓:𝑑absentsubscript𝒙:𝑑absentf\_{d:}={\bm{x}}\_{d:}italic\_f start\_POSTSUBSCRIPT italic\_d : end\_POSTSUBSCRIPT = bold\_italic\_x start\_POSTSUBSCRIPT italic\_d : end\_POSTSUBSCRIPT. ACLs are stacked to make rich hierarchical transforms, and the latent representation 𝒛𝒛{\bm{z}}bold\_italic\_z is output from this composition, i.e. 𝒛n=f(𝒙n;ϕ)subscript𝒛𝑛𝑓subscript𝒙𝑛bold-italic-ϕ{\bm{z}}\_{n}=f({\bm{x}}\_{n};{\bm{\phi}})bold\_italic\_z start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT = italic\_f ( bold\_italic\_x start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT ; bold\_italic\_ϕ ). A permutation operation is required between ACLs to ensure the same elements are not repeatedly used in the copy operations. We use f𝑓fitalic\_f without subscript to denote the complete transform and overload the use of ϕbold-italic-ϕ{\bm{\phi}}bold\_italic\_ϕ to denote the parameters of all constituent layers.
This class of transform is known as non-volume preserving (NVP) (Dinh et al., [2017](#bib.bib6)) since the volume element does not necessarily evaluate to one and can vary with each input 𝒙𝒙{\bm{x}}bold\_italic\_x. Although non-zero, the log determinant of the Jacobian is still tractable: log|∂𝒇ϕ/∂𝒙|=∑j=dDsj(𝒙d:;ϕs)subscript𝒇bold-italic-ϕ𝒙superscriptsubscript𝑗𝑑𝐷subscript𝑠𝑗subscript𝒙:𝑑absentsubscriptbold-italic-ϕ𝑠\log|\partial{\bm{f}}\_{{\bm{\phi}}}/\partial{\bm{x}}|=\sum\_{j=d}^{D}s\_{j}({\bm{x}}\_{d:};{\bm{\phi}}\_{s})roman\_log | ∂ bold\_italic\_f start\_POSTSUBSCRIPT bold\_italic\_ϕ end\_POSTSUBSCRIPT / ∂ bold\_italic\_x | = ∑ start\_POSTSUBSCRIPT italic\_j = italic\_d end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT italic\_D end\_POSTSUPERSCRIPT italic\_s start\_POSTSUBSCRIPT italic\_j end\_POSTSUBSCRIPT ( bold\_italic\_x start\_POSTSUBSCRIPT italic\_d : end\_POSTSUBSCRIPT ; bold\_italic\_ϕ start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT ). A diffeomorphic transform can also be defined with just translation operations, as was done in earlier work by Dinh et al. ([2015](#bib.bib5)), and this transformation is volume preserving (VP) since the volume term is one and thus has no influence in the likelihood calculation. We will examine another class of flows we term constant-volume (CV) since the volume, while not preserved, is constant across all 𝒙𝒙{\bm{x}}bold\_italic\_x.
Appendix [A](#A1 "Appendix A Additional Implementation Details ‣ Do Deep Generative Models Know What They Don’t Know?") provides additional details on implementing flow-based generative models.
3 Motivating Observations
--------------------------
Given the impressive advances of deep generative models,
we sought to test their ability to quantify when an input comes from a different distribution than that of the training set. This calibration w.r.t. out-of-distribution data is essential for applications such as safety—if we were using the generative model to filter the inputs to a discriminative model—and for active learning. For the experiment, we trained the same Glow architecture described in Kingma & Dhariwal ([2018](#bib.bib12))—except small enough that it could fit on one GPU111Although we use a smaller model, it still produces good samples, which can be seen in Figure [13](#A10.F13 "Figure 13 ‣ Appendix J Samples ‣ Do Deep Generative Models Know What They Don’t Know?") of the Appendix, and competitive BPD (CIFAR-10: 3.46 for ours vs 3.35 for theirs).—on FashionMNIST and CIFAR-10. Appendix [A](#A1 "Appendix A Additional Implementation Details ‣ Do Deep Generative Models Know What They Don’t Know?") provides additional implementation details. We then calculated the *log-likelihood* (higher value is better) and *bits-per-dimension* (BPD, lower value is better)222See Theis et al. ([2016](#bib.bib31), Section 3.1) for the definitions of log-likelihood and bits-per-dimension. of the test split of two different data sets of the same dimensionality—MNIST (28×28)28\times 28)28 × 28 ) and SVHN (32×32×3)32\times 32\times 3)32 × 32 × 3 ) respectively. We expect the models to assign a lower probability to this data because they were not trained on it. Samples from the Glow models trained on each data set are shown in Figure [13](#A10.F13 "Figure 13 ‣ Appendix J Samples ‣ Do Deep Generative Models Know What They Don’t Know?") in the Appendix.
| Data Set | Avg. Bits Per Dimension |
| --- | --- |
| Glow Trained on FashionMNIST |
| FashionMNIST-Train | 2.902 |
| FashionMNIST-Test | 2.958 |
| MNIST-Test | 1.833 |
| Glow Trained on MNIST |
| MNIST-Test | 1.262 |
| Data Set | Avg. Bits Per Dimension |
| --- | --- |
| Glow Trained on CIFAR-10 |
| CIFAR10-Train | 3.386 |
| CIFAR10-Test | 3.464 |
| SVHN-Test | 2.389 |
| Glow Trained on SVHN |
| SVHN-Test | 2.057 |
Figure 1: Testing Out-of-Distribution. Log-likelihood (expressed in bits per dimension) calculated from Glow (Kingma & Dhariwal, [2018](#bib.bib12)) on MNIST, FashionMNIST, SVHN, CIFAR-10.
(a) Train on FashionMNIST, Test on MNIST
(b) Train on CIFAR-10, Test on SVHN
(c) Train on CelebA, Test on SVHN
(d) Train on ImageNet,
Test on CIFAR-10 / CIFAR-100 / SVHN
Figure 2: Histogram of Glow log-likelihoods for FashionMNIST vs MNIST (a), CIFAR-10 vs SVHN (b), CelebA vs SVHN (c), and ImageNet vs CIFAR-10 / CIFAR-100 / SVHN (d).
Beginning with FashionMNIST vs MNIST, the left subtable of Figure [1](#S3.F1 "Figure 1 ‣ 3 Motivating Observations ‣ Do Deep Generative Models Know What They Don’t Know?") shows the average BPD of the training data (FashionMNIST-Train), the in-distribution test data (FashionMNIST-Test), and the out-of-distribution data (MNIST-Test). We see a peculiar result: the MNIST split has the *lowest* BPD, more than one bit less than the FashionMNIST train and test sets. To check if this is due to outliers skewing the average, we report a (normalized) histogram in Figure [2](#S3.F2 "Figure 2 ‣ 3 Motivating Observations ‣ Do Deep Generative Models Know What They Don’t Know?") (a) of the log-likelihoods for the three splits. We see that MNIST (red bars) is clearly and systematically shifted to the RHS of the plot (highest likelihood).
Moving on to CIFAR-10 vs SVHN, the right subtable of Figure [1](#S3.F1 "Figure 1 ‣ 3 Motivating Observations ‣ Do Deep Generative Models Know What They Don’t Know?") again reports the BPD of the training data (CIFAR10-Train), the in-distribution test data (CIFAR10-Test), and the out-of-distribution data (SVHN-Test). We again see the phenomenon: the SVHN BPD is one bit *lower* than that of both in-distribution data sets. Figure [2](#S3.F2 "Figure 2 ‣ 3 Motivating Observations ‣ Do Deep Generative Models Know What They Don’t Know?") (b) shows a similar histogram of the log-likelihoods. Clearly the SVHN examples (red bars) have a systematically higher likelihood, and therefore the result is not caused by any outliers.
Subfigures (c) and (d) of Figure [2](#S3.F2 "Figure 2 ‣ 3 Motivating Observations ‣ Do Deep Generative Models Know What They Don’t Know?") show additional results for CelebA and ImageNet. When trained on CelebA, Glow assigns a higher likelihood to SVHN (red bars), a data set the model has never seen before. Similarly, when trained on ImageNet, Glow assigns a higher likelihood to the test splits of SVHN (red), CIFAR-10 (yellow), and CIFAR-100 (green). The difference is quite drastic in the case of SVHN (red) but modest for the two CIFAR splits. This phenomenon is not symmetric. CIFAR-10 does not have a higher likelihood under a Glow trained on SVHN; see Figure [6](#A2.F6 "Figure 6 ‣ Appendix B Results illustrating asymmetric behavior ‣ Do Deep Generative Models Know What They Don’t Know?") in Appendix [B](#A2 "Appendix B Results illustrating asymmetric behavior ‣ Do Deep Generative Models Know What They Don’t Know?") for these results. We report results only for Glow, but we observed the same behavior for RNVP transforms (Dinh et al., [2017](#bib.bib6)).
(a) PixelCNN: FashionMNIST vs MNIST
(b) VAE: FashionMNIST vs MNIST
(c) PixelCNN: CIFAR-10 vs SVHN
(d) VAE: CIFAR-10 vs SVHN
Figure 3: PixelCNN and VAE. Log-likelihoods calculated by PixelCNN (a, c) and VAE (b, d) on FashionMNIST vs MNIST (a, b) and CIFAR-10 vs SVHN (c, d). VAE models are the convolutional categorical variant described by Rosca et al. ([2018](#bib.bib23)).
We next tested if the phenomenon occurs for other common deep generative models: PixelCNNs and VAEs. We do not include GANs in the comparison since evaluating their likelihood is an open problem. Figure [3](#S3.F3 "Figure 3 ‣ 3 Motivating Observations ‣ Do Deep Generative Models Know What They Don’t Know?") reports the same histograms as above for these models, showing the distribution of logp(𝒙)𝑝𝒙\log p({\bm{x}})roman\_log italic\_p ( bold\_italic\_x ) evaluations for FashionMNIST vs MNIST (a, b) and CIFAR-10 vs SVHN (c, d). The training splits are again denoted with black bars, and the test splits with blue, and the out-of-distribution splits with red. The red bars are shifted to the right in all four plots, signifying the behavior exists in spite of the differences between model classes.
4 Digging Deeper into the Flow-Based Model
-------------------------------------------
While we observed the out-of-distribution phenomenon for PixelCNN, VAE, and Glow, now we narrow our investigation to just the class of invertible generative models. The rationale is that they allow for better experimental control as, firstly, they can compute exact marginal likelihoods (unlike VAEs), and secondly, the transforms used in flow-based models have Jacobian constraints that simplify the analysis we present in Section [5](#S5 "5 Second Order Analysis ‣ Do Deep Generative Models Know What They Don’t Know?"). To further analyze the high likelihood of the out-of-distribution (non-training) samples, we next report the contributions to the likelihood of each term in the change-of-variables formula. At first this suggested the volume element was the primary cause of SVHN’s high likelihood, but further experiments with constant-volume flows show the problem exists with them as well.
##### Decomposing the change-of-variables objective.
To further examine this curious phenomenon, we inspect the change-of-variables objective itself, investigating if one or both terms give the out-of-distribution data a higher value. We report the constituent logp(𝒛)𝑝𝒛\log p({\bm{z}})roman\_log italic\_p ( bold\_italic\_z ) and log|∂𝒇ϕ/∂𝒙|subscript𝒇bold-italic-ϕ𝒙\log|\partial{\bm{f}}\_{{\bm{\phi}}}/\partial{\bm{x}}|roman\_log | ∂ bold\_italic\_f start\_POSTSUBSCRIPT bold\_italic\_ϕ end\_POSTSUBSCRIPT / ∂ bold\_italic\_x | terms for NVP-Glow in Figure [4](#S4.F4 "Figure 4 ‣ Decomposing the change-of-variables objective. ‣ 4 Digging Deeper into the Flow-Based Model ‣ Do Deep Generative Models Know What They Don’t Know?"), showing histograms for logp(𝒛)𝑝𝒛\log p({\bm{z}})roman\_log italic\_p ( bold\_italic\_z ) in subfigure (a) and for log|∂𝒇ϕ/∂𝒙|subscript𝒇bold-italic-ϕ𝒙\log|\partial{\bm{f}}\_{{\bm{\phi}}}/\partial{\bm{x}}|roman\_log | ∂ bold\_italic\_f start\_POSTSUBSCRIPT bold\_italic\_ϕ end\_POSTSUBSCRIPT / ∂ bold\_italic\_x | in subfigure (b). We see that p(𝒛)𝑝𝒛p({\bm{z}})italic\_p ( bold\_italic\_z ) behaves mostly as expected. The red bars (SVHN) are clearly shifted to the left, representing lower likelihoods under the latent distribution. Moving on to the volume element, this term seems to cause SVHN’s higher likelihood. Subfigure (b) shows that all of the SVHN log-volume evaluations (red) are conspicuously shifted to the right—to higher values—when compared to CIFAR-10’s (blue and black). Since SVHN’s p(𝒛)𝑝𝒛p({\bm{z}})italic\_p ( bold\_italic\_z ) evaluations are only slightly less than CIFAR-10’s, the volume term dominates, resulting in SVHN having a higher likelihood.
(a) CIFAR-10: logp(𝒛)𝑝𝒛{\log p({\bm{z}})}roman\_log italic\_p ( bold\_italic\_z )
(b) CIFAR-10: Volume
(c) CV-Glow Likelihoods
(d) Log-Likelihood vs Iter.
Figure 4: Decomposing the Likelihood of NVP-Glow / CV-Glow Results. The histograms in (a) and (b) show NVP-Glow’s log-likelihood decomposed into contributions from the 𝒛𝒛{\bm{z}}bold\_italic\_z-distribution and volume element, respectively, for CIFAR-10 vs SVHN. Subfigure (c) shows log-likelihood evaluations for constant-volume (CV) Glow, again when trained on CIFAR-10 and tested on SVHN. Subfigure (d) reports NVP-Glow’s BPD over the course of training, showing that the phenomenon happens throughout and could not be prevented by early stopping.
##### Is the volume the culprit?
In addition to the empirical evidence against the volume element, we notice that one of the terms in the change-of-variables objective—by rewarding the maximization of the Jacobian determinant—encourages the model to *increase* its sensitivity to perturbations in 𝒳𝒳\mathcal{X}caligraphic\_X. This behavior starkly contradicts a long history of derivative-based regularization penalties that reward the model for *decreasing* its sensitivity to input directions. For instance, Girosi et al. ([1995](#bib.bib7)) and Rifai et al. ([2011](#bib.bib22)) propose penalizing the Frobenius norm of a neural network’s Jacobian for classifiers and autoencoders respectively. See Appendix [C](#A3 "Appendix C Analyzing the Change-of-Variables Formula as an Optimization Function ‣ Do Deep Generative Models Know What They Don’t Know?") for more analysis of the log volume element.
To experimentally control for the effect of the volume term, we trained Glow with constant-volume (CV) transformations. We modify the affine layers to use only translation operations (Dinh et al., [2015](#bib.bib5)) but keep the 1×1111\times 11 × 1 convolutions as is. The log-determinant-Jacobian is then HW∑klog|𝑼k|𝐻𝑊subscript𝑘subscript𝑼𝑘HW\sum\_{k}\log|{\bm{U}}\_{k}|italic\_H italic\_W ∑ start\_POSTSUBSCRIPT italic\_k end\_POSTSUBSCRIPT roman\_log | bold\_italic\_U start\_POSTSUBSCRIPT italic\_k end\_POSTSUBSCRIPT |, where |𝑼k|subscript𝑼𝑘|{\bm{U}}\_{k}|| bold\_italic\_U start\_POSTSUBSCRIPT italic\_k end\_POSTSUBSCRIPT | is the determinant of the convolutional weights 𝑼ksubscript𝑼𝑘{\bm{U}}\_{k}bold\_italic\_U start\_POSTSUBSCRIPT italic\_k end\_POSTSUBSCRIPT for the k𝑘kitalic\_kth flow. This makes the volume element constant across all inputs 𝒙𝒙{\bm{x}}bold\_italic\_x, allowing us to isolate its effect while still keeping the model expressive. Subfigures (c) and (d) of Figure [4](#S4.F4 "Figure 4 ‣ Decomposing the change-of-variables objective. ‣ 4 Digging Deeper into the Flow-Based Model ‣ Do Deep Generative Models Know What They Don’t Know?") show the results for this model, which we term CV-Glow (constant-volume Glow). Subfigure (c) shows a histogram of the logp(𝒙)𝑝𝒙\log p({\bm{x}})roman\_log italic\_p ( bold\_italic\_x ) evaluations, just as shown before in Figure [2](#S3.F2 "Figure 2 ‣ 3 Motivating Observations ‣ Do Deep Generative Models Know What They Don’t Know?"), and we see that SVHN (red) still achieves a higher likelihood (lower BPD) than the CIFAR-10 training set. Subfigure (d) shows the SVHN vs CIFAR-10 BPD over the course of training for NVP-Glow. Notice that there is no cross-over point in the curves.
##### Other experiments: random and constant images, ensembles.
Other work on generative models (Sønderby et al., [2017](#bib.bib26); van den Oord et al., [2018](#bib.bib34)) has noted that they often assign the highest likelihood to constant inputs. We also test this case, reporting the BPD in Appendix Figure [8](#A5.F8 "Figure 8 ‣ Appendix E Constant and Random Inputs ‣ Do Deep Generative Models Know What They Don’t Know?") for NVP-Glow models. We find constant inputs have the highest likelihood for our models as well: 0.589 BPD for CIFAR-10. We also include in the table the BPD of random inputs for comparison.
We also hypothesized that averaging over the parameters may mitigate the phenomenon. While integration over the entire parameter space would be ideal, this is analytically and computationally difficult for Glow. Lakshminarayanan et al. ([2017](#bib.bib16)) show that deep ensembles can guard against over-confidence for anomalous inputs while being more practical to implement. We opted for this approach, training five Glow models independently and averaging their likelihoods to evaluate test data. Each model was given a different initialization of the parameters to help diversify the ensemble. Figure [9](#A6.F9 "Figure 9 ‣ Appendix F Ensembling Glows ‣ Do Deep Generative Models Know What They Don’t Know?") in Appendix [F](#A6 "Appendix F Ensembling Glows ‣ Do Deep Generative Models Know What They Don’t Know?") reports a histogram of the logp(𝒙)𝑝𝒙\log p({\bm{x}})roman\_log italic\_p ( bold\_italic\_x ) evaluations when averaging over the ensemble. We see nearly identical results: SVHN is still assigned a higher likelihood than the CIFAR-10 training data.
5 Second Order Analysis
------------------------
In this section, we aim to provide a more direct analysis of when another distribution might have higher likelihood than the one used for training. We propose analyzing the phenomenon by way of linearizing the difference in expected log-likelihoods. This approach undoubtedly gives a crude approximation, but as we show below, it agrees with and gives insight into some of the observations reported above. Consider two distributions: the training distribution 𝒙∼p\*similar-to𝒙superscript𝑝{\bm{x}}\sim p^{\*}bold\_italic\_x ∼ italic\_p start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT and some dissimilar distribution 𝒙∼qsimilar-to𝒙𝑞{\bm{x}}\sim qbold\_italic\_x ∼ italic\_q also with support on 𝒳𝒳\mathcal{X}caligraphic\_X. For a given generative model p(𝒙;𝜽)𝑝𝒙𝜽p({\bm{x}};{\bm{\theta}})italic\_p ( bold\_italic\_x ; bold\_italic\_θ ), the adversarial distribution q𝑞qitalic\_q will have a higher likelihood than the training data’s if 𝔼q[logp(𝒙;𝜽)]−𝔼p\*[logp(𝒙;𝜽)]>0subscript𝔼𝑞delimited-[]𝑝𝒙𝜽subscript𝔼superscript𝑝delimited-[]𝑝𝒙𝜽0\mathbb{E}\_{q}[\log p({\bm{x}};{\bm{\theta}})]-\mathbb{E}\_{p^{\*}}[\log p({\bm{x}};{\bm{\theta}})]>0blackboard\_E start\_POSTSUBSCRIPT italic\_q end\_POSTSUBSCRIPT [ roman\_log italic\_p ( bold\_italic\_x ; bold\_italic\_θ ) ] - blackboard\_E start\_POSTSUBSCRIPT italic\_p start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT end\_POSTSUBSCRIPT [ roman\_log italic\_p ( bold\_italic\_x ; bold\_italic\_θ ) ] > 0.
This expression is hard to analyze directly so we perform a second-order expansion of the log-likelihood around an interior point 𝒙0subscript𝒙0{\bm{x}}\_{0}bold\_italic\_x start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT. Applying the expansion
logp(𝒙;𝜽)≈logp(𝒙0;𝜽)+∇𝒙0logp(𝒙0;𝜽)T(𝒙−𝒙0)+12Tr{∇𝒙02logp(𝒙0;𝜽)(𝒙−𝒙0)(𝒙−𝒙0)T}𝑝𝒙𝜽𝑝subscript𝒙0𝜽subscript∇subscript𝒙0𝑝superscriptsubscript𝒙0𝜽
𝑇𝒙subscript𝒙012Trsubscriptsuperscript∇2subscript𝒙0𝑝subscript𝒙0𝜽
𝒙subscript𝒙0superscript𝒙subscript𝒙0𝑇\log p({\bm{x}};{\bm{\theta}})\approx\log p({\bm{x}}\_{0};{\bm{\theta}})+\nabla\_{{\bm{x}}\_{0}}\log p({\bm{x}}\_{0};{\bm{\theta}})^{T}({\bm{x}}-{\bm{x}}\_{0})+\frac{1}{2}\operatorname{Tr}\{\nabla^{2}\_{{\bm{x}}\_{0}}\log p({\bm{x}}\_{0};{\bm{\theta}})({\bm{x}}-{\bm{x}}\_{0})({\bm{x}}-{\bm{x}}\_{0})^{T}\}roman\_log italic\_p ( bold\_italic\_x ; bold\_italic\_θ ) ≈ roman\_log italic\_p ( bold\_italic\_x start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT ; bold\_italic\_θ ) + ∇ start\_POSTSUBSCRIPT bold\_italic\_x start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT roman\_log italic\_p ( bold\_italic\_x start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT ; bold\_italic\_θ ) start\_POSTSUPERSCRIPT italic\_T end\_POSTSUPERSCRIPT ( bold\_italic\_x - bold\_italic\_x start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT ) + divide start\_ARG 1 end\_ARG start\_ARG 2 end\_ARG roman\_Tr { ∇ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT bold\_italic\_x start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT roman\_log italic\_p ( bold\_italic\_x start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT ; bold\_italic\_θ ) ( bold\_italic\_x - bold\_italic\_x start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT ) ( bold\_italic\_x - bold\_italic\_x start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT ) start\_POSTSUPERSCRIPT italic\_T end\_POSTSUPERSCRIPT }
to both likelihoods, taking expectations, and canceling the common terms, we have:
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| --- | --- | --- | --- |
| | 0<𝔼q[logp(𝒙;𝜽)]−𝔼p\*[logp(𝒙;𝜽)]≈∇𝒙0logp(x0;𝜽)T(𝔼q[𝒙]−𝔼p\*[𝒙])+12Tr{∇𝒙02logp(𝒙0;𝜽)(𝚺q−𝚺p\*)}0subscript𝔼𝑞delimited-[]𝑝𝒙𝜽subscript𝔼superscript𝑝delimited-[]𝑝𝒙𝜽subscript∇subscript𝒙0𝑝superscriptsubscript𝑥0𝜽
𝑇subscript𝔼𝑞delimited-[]𝒙subscript𝔼superscript𝑝delimited-[]𝒙12Trsubscriptsuperscript∇2subscript𝒙0𝑝subscript𝒙0𝜽
subscript𝚺𝑞subscript𝚺superscript𝑝\begin{split}0&<\mathbb{E}\_{q}[\log p({\bm{x}};{\bm{\theta}})]-\mathbb{E}\_{p^{\*}}[\log p({\bm{x}};{\bm{\theta}})]\\
&\approx\nabla\_{{\bm{x}}\_{0}}\log p(x\_{0};{\bm{\theta}})^{T}(\mathbb{E}\_{q}[{\bm{x}}]-\mathbb{E}\_{p^{\*}}[{\bm{x}}])+\frac{1}{2}\operatorname{Tr}\{\nabla^{2}\_{{\bm{x}}\_{0}}\log p({\bm{x}}\_{0};{\bm{\theta}})({\bm{\Sigma}}\_{q}-{\bm{\Sigma}}\_{p^{\*}})\}\end{split}start\_ROW start\_CELL 0 end\_CELL start\_CELL < blackboard\_E start\_POSTSUBSCRIPT italic\_q end\_POSTSUBSCRIPT [ roman\_log italic\_p ( bold\_italic\_x ; bold\_italic\_θ ) ] - blackboard\_E start\_POSTSUBSCRIPT italic\_p start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT end\_POSTSUBSCRIPT [ roman\_log italic\_p ( bold\_italic\_x ; bold\_italic\_θ ) ] end\_CELL end\_ROW start\_ROW start\_CELL end\_CELL start\_CELL ≈ ∇ start\_POSTSUBSCRIPT bold\_italic\_x start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT roman\_log italic\_p ( italic\_x start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT ; bold\_italic\_θ ) start\_POSTSUPERSCRIPT italic\_T end\_POSTSUPERSCRIPT ( blackboard\_E start\_POSTSUBSCRIPT italic\_q end\_POSTSUBSCRIPT [ bold\_italic\_x ] - blackboard\_E start\_POSTSUBSCRIPT italic\_p start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT end\_POSTSUBSCRIPT [ bold\_italic\_x ] ) + divide start\_ARG 1 end\_ARG start\_ARG 2 end\_ARG roman\_Tr { ∇ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT bold\_italic\_x start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT roman\_log italic\_p ( bold\_italic\_x start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT ; bold\_italic\_θ ) ( bold\_Σ start\_POSTSUBSCRIPT italic\_q end\_POSTSUBSCRIPT - bold\_Σ start\_POSTSUBSCRIPT italic\_p start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT end\_POSTSUBSCRIPT ) } end\_CELL end\_ROW | | (4) |
where 𝚺=𝔼[(𝒙−𝒙0)(𝒙−𝒙0)T]𝚺𝔼delimited-[]𝒙subscript𝒙0superscript𝒙subscript𝒙0𝑇{\bm{\Sigma}}=\mathbb{E}\left[({\bm{x}}-{\bm{x}}\_{0})({\bm{x}}-{\bm{x}}\_{0})^{T}\right]bold\_Σ = blackboard\_E [ ( bold\_italic\_x - bold\_italic\_x start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT ) ( bold\_italic\_x - bold\_italic\_x start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT ) start\_POSTSUPERSCRIPT italic\_T end\_POSTSUPERSCRIPT ], the covariance matrix, and Tr{⋅}Tr⋅\operatorname{Tr}\{\cdot\}roman\_Tr { ⋅ } is the trace operation.
Since the expansion is accurate only locally around 𝒙0subscript𝒙0{\bm{x}}\_{0}bold\_italic\_x start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT, we next assume that 𝔼q[𝒙]=𝔼p\*[𝒙]=𝒙0subscript𝔼𝑞delimited-[]𝒙subscript𝔼superscript𝑝delimited-[]𝒙subscript𝒙0\mathbb{E}\_{q}[{\bm{x}}]=\mathbb{E}\_{p^{\*}}[{\bm{x}}]={\bm{x}}\_{0}blackboard\_E start\_POSTSUBSCRIPT italic\_q end\_POSTSUBSCRIPT [ bold\_italic\_x ] = blackboard\_E start\_POSTSUBSCRIPT italic\_p start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT end\_POSTSUBSCRIPT [ bold\_italic\_x ] = bold\_italic\_x start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT. While this at first glance may seem like a strong assumption, it is not too removed from practice since data is usually centered before being fed to the model. For SVHN and CIFAR-10 in particular, we find this assumption to hold; see Figure [5](#S5.F5 "Figure 5 ‣ Analysis of CV-Glow. ‣ 5 Second Order Analysis ‣ Do Deep Generative Models Know What They Don’t Know?") (a) for the empirical means of each dimension of CIFAR-10 (green) and SVHN (orange). All of SVHN’s means fall within the empirical range of CIFAR-10’s, and the maximum difference between any dimension is less than 38383838 pixel values. Assuming equal means, we then have:
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| --- | --- | --- | --- |
| | 0<𝔼q[logp(𝒙;𝜽)]−𝔼p\*[logp(𝒙;𝜽)]≈12Tr{∇𝒙02logp(𝒙0;𝜽)(𝚺q−𝚺p\*)}=12Tr{[∇𝒙02logpz(f(𝒙0;ϕ))+∇𝒙02log|∂𝒇ϕ∂𝒙0|](𝚺q−𝚺p\*)},0subscript𝔼𝑞delimited-[]𝑝𝒙𝜽subscript𝔼superscript𝑝delimited-[]𝑝𝒙𝜽12Trsubscriptsuperscript∇2subscript𝒙0𝑝subscript𝒙0𝜽
subscript𝚺𝑞subscript𝚺superscript𝑝12Trdelimited-[]subscriptsuperscript∇2subscript𝒙0subscript𝑝𝑧𝑓subscript𝒙0bold-italic-ϕsubscriptsuperscript∇2subscript𝒙0subscript𝒇bold-italic-ϕsubscript𝒙0subscript𝚺𝑞subscript𝚺superscript𝑝\begin{split}0&<\mathbb{E}\_{q}[\log p({\bm{x}};{\bm{\theta}})]-\mathbb{E}\_{p^{\*}}[\log p({\bm{x}};{\bm{\theta}})]\approx\frac{1}{2}\operatorname{Tr}\{\nabla^{2}\_{{\bm{x}}\_{0}}\log p({\bm{x}}\_{0};{\bm{\theta}})({\bm{\Sigma}}\_{q}-{\bm{\Sigma}}\_{p^{\*}})\}\\
&=\frac{1}{2}\operatorname{Tr}\left\{\left[\nabla^{2}\_{{\bm{x}}\_{0}}\log p\_{z}(f({\bm{x}}\_{0};{\bm{\phi}}))+\nabla^{2}\_{{\bm{x}}\_{0}}\log\left|\frac{\partial{\bm{f}}\_{{\bm{\phi}}}}{\partial{\bm{x}}\_{0}}\right|\right]\left({\bm{\Sigma}}\_{q}-{\bm{\Sigma}}\_{p^{\*}}\right)\right\},\end{split}start\_ROW start\_CELL 0 end\_CELL start\_CELL < blackboard\_E start\_POSTSUBSCRIPT italic\_q end\_POSTSUBSCRIPT [ roman\_log italic\_p ( bold\_italic\_x ; bold\_italic\_θ ) ] - blackboard\_E start\_POSTSUBSCRIPT italic\_p start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT end\_POSTSUBSCRIPT [ roman\_log italic\_p ( bold\_italic\_x ; bold\_italic\_θ ) ] ≈ divide start\_ARG 1 end\_ARG start\_ARG 2 end\_ARG roman\_Tr { ∇ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT bold\_italic\_x start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT roman\_log italic\_p ( bold\_italic\_x start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT ; bold\_italic\_θ ) ( bold\_Σ start\_POSTSUBSCRIPT italic\_q end\_POSTSUBSCRIPT - bold\_Σ start\_POSTSUBSCRIPT italic\_p start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT end\_POSTSUBSCRIPT ) } end\_CELL end\_ROW start\_ROW start\_CELL end\_CELL start\_CELL = divide start\_ARG 1 end\_ARG start\_ARG 2 end\_ARG roman\_Tr { [ ∇ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT bold\_italic\_x start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT roman\_log italic\_p start\_POSTSUBSCRIPT italic\_z end\_POSTSUBSCRIPT ( italic\_f ( bold\_italic\_x start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT ; bold\_italic\_ϕ ) ) + ∇ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT bold\_italic\_x start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT roman\_log | divide start\_ARG ∂ bold\_italic\_f start\_POSTSUBSCRIPT bold\_italic\_ϕ end\_POSTSUBSCRIPT end\_ARG start\_ARG ∂ bold\_italic\_x start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT end\_ARG | ] ( bold\_Σ start\_POSTSUBSCRIPT italic\_q end\_POSTSUBSCRIPT - bold\_Σ start\_POSTSUBSCRIPT italic\_p start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT end\_POSTSUBSCRIPT ) } , end\_CELL end\_ROW | | (5) |
where the second line assumes the generative model to be flow-based.
##### Analysis of CV-Glow.
We use the expression in Equation [5](#S5.E5 "5 ‣ 5 Second Order Analysis ‣ Do Deep Generative Models Know What They Don’t Know?") to analyze the behavior of CV-Glow on CIFAR-10 vs SVHN, seeing if the difference in likelihoods can be explained by the model curvature and data’s second moment. The second derivative terms simplify considerably for CV-Glow with a spherical latent density. Given a C×C𝐶𝐶C\times Citalic\_C × italic\_C kernel 𝑼ksubscript𝑼𝑘{\bm{U}}\_{k}bold\_italic\_U start\_POSTSUBSCRIPT italic\_k end\_POSTSUBSCRIPT, with k𝑘kitalic\_k indexing the flow and C𝐶Citalic\_C the number of input channels, the derivatives are ∂fh,w,c/∂xh,w,c=∏k∑j=1Cuk,c,jsubscript𝑓ℎ𝑤𝑐subscript𝑥ℎ𝑤𝑐subscriptproduct𝑘superscriptsubscript𝑗1𝐶subscript𝑢𝑘𝑐𝑗\partial f\_{h,w,c}/\partial x\_{h,w,c}=\prod\_{k}\sum\_{j=1}^{C}u\_{k,c,j}∂ italic\_f start\_POSTSUBSCRIPT italic\_h , italic\_w , italic\_c end\_POSTSUBSCRIPT / ∂ italic\_x start\_POSTSUBSCRIPT italic\_h , italic\_w , italic\_c end\_POSTSUBSCRIPT = ∏ start\_POSTSUBSCRIPT italic\_k end\_POSTSUBSCRIPT ∑ start\_POSTSUBSCRIPT italic\_j = 1 end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT italic\_C end\_POSTSUPERSCRIPT italic\_u start\_POSTSUBSCRIPT italic\_k , italic\_c , italic\_j end\_POSTSUBSCRIPT, with hℎhitalic\_h and w𝑤witalic\_w indexing the spatial height and width and j𝑗jitalic\_j the columns of the k𝑘kitalic\_kth flow’s 1×1111\times 11 × 1 convolutional kernel. The second derivative is then ∂2fh,w,c/∂xh,w,c2=0superscript2subscript𝑓ℎ𝑤𝑐superscriptsubscript𝑥ℎ𝑤𝑐20\partial^{2}f\_{h,w,c}/\partial x\_{h,w,c}^{2}=0∂ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT italic\_f start\_POSTSUBSCRIPT italic\_h , italic\_w , italic\_c end\_POSTSUBSCRIPT / ∂ italic\_x start\_POSTSUBSCRIPT italic\_h , italic\_w , italic\_c end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT = 0, which allows us to write
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| --- | --- | --- |
| | Tr{[∇𝒙02logp(𝒙0;𝜽)](𝚺q−𝚺p\*)}=∂2∂z2logp(𝒛;𝝍)∑c=1C(∏k=1K∑j=1Cuk,c,j)2∑h,w(σq,h,w,c2−σp\*,h,w,c2).Trdelimited-[]subscriptsuperscript∇2subscript𝒙0𝑝subscript𝒙0𝜽subscript𝚺𝑞subscript𝚺superscript𝑝superscript2superscript𝑧2𝑝𝒛𝝍
superscriptsubscript𝑐1𝐶superscriptsuperscriptsubscriptproduct𝑘1𝐾superscriptsubscript𝑗1𝐶subscript𝑢𝑘𝑐𝑗2subscriptℎ𝑤superscriptsubscript𝜎𝑞ℎ𝑤𝑐2superscriptsubscript𝜎superscript𝑝ℎ𝑤𝑐2\begin{split}\operatorname{Tr}&\left\{\left[\nabla^{2}\_{{\bm{x}}\_{0}}\log p({\bm{x}}\_{0};{\bm{\theta}})\right]\left({\bm{\Sigma}}\_{q}-{\bm{\Sigma}}\_{p^{\*}}\right)\right\}\\
&=\frac{\partial^{2}}{\partial z^{2}}\log p({\bm{z}};{\bm{\psi}})\sum\_{c=1}^{C}\left(\prod\_{k=1}^{K}\sum\_{j=1}^{C}u\_{k,c,j}\right)^{2}\sum\_{h,w}(\sigma\_{q,h,w,c}^{2}-\sigma\_{p^{\*},h,w,c}^{2}).\end{split}start\_ROW start\_CELL roman\_Tr end\_CELL start\_CELL { [ ∇ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT bold\_italic\_x start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT roman\_log italic\_p ( bold\_italic\_x start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT ; bold\_italic\_θ ) ] ( bold\_Σ start\_POSTSUBSCRIPT italic\_q end\_POSTSUBSCRIPT - bold\_Σ start\_POSTSUBSCRIPT italic\_p start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT end\_POSTSUBSCRIPT ) } end\_CELL end\_ROW start\_ROW start\_CELL end\_CELL start\_CELL = divide start\_ARG ∂ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT end\_ARG start\_ARG ∂ italic\_z start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT end\_ARG roman\_log italic\_p ( bold\_italic\_z ; bold\_italic\_ψ ) ∑ start\_POSTSUBSCRIPT italic\_c = 1 end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT italic\_C end\_POSTSUPERSCRIPT ( ∏ start\_POSTSUBSCRIPT italic\_k = 1 end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT italic\_K end\_POSTSUPERSCRIPT ∑ start\_POSTSUBSCRIPT italic\_j = 1 end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT italic\_C end\_POSTSUPERSCRIPT italic\_u start\_POSTSUBSCRIPT italic\_k , italic\_c , italic\_j end\_POSTSUBSCRIPT ) start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT ∑ start\_POSTSUBSCRIPT italic\_h , italic\_w end\_POSTSUBSCRIPT ( italic\_σ start\_POSTSUBSCRIPT italic\_q , italic\_h , italic\_w , italic\_c end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT - italic\_σ start\_POSTSUBSCRIPT italic\_p start\_POSTSUPERSCRIPT \* end\_POSTSUPERSCRIPT , italic\_h , italic\_w , italic\_c end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT ) . end\_CELL end\_ROW | |
The derivation is given in Appendix [G](#A7 "Appendix G Derivation of CV-Glow’s Likelihood Difference ‣ Do Deep Generative Models Know What They Don’t Know?"). Plugging in the second derivative of the Gaussian’s log density—a common choice for the latent distribution in flow models (Dinh et al., [2017](#bib.bib6); Kingma & Dhariwal, [2018](#bib.bib12))—and the empirical variances, we have:
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| --- | --- | --- | --- |
| | 𝔼SVHN[logp(𝒙;𝜽)]−𝔼CIFAR-10[logp(𝒙;𝜽)]≈−12σ𝝍2[α12(49.6−61.9)+α22(52.7−59.2)+α32(53.6−68.1)]=12σ𝝍2[α12⋅12.3+α22⋅6.5+α32⋅14.5]≥0 where αc=∏k=1K∑j=1Cuk,c,jformulae-sequencesubscript𝔼SVHNdelimited-[]𝑝𝒙𝜽subscript𝔼CIFAR-10delimited-[]𝑝𝒙𝜽12subscriptsuperscript𝜎2𝝍delimited-[]subscriptsuperscript𝛼2149.661.9subscriptsuperscript𝛼2252.759.2subscriptsuperscript𝛼2353.668.112subscriptsuperscript𝜎2𝝍delimited-[]⋅superscriptsubscript𝛼1212.3⋅superscriptsubscript𝛼226.5⋅superscriptsubscript𝛼3214.50 where subscript𝛼𝑐superscriptsubscriptproduct𝑘1𝐾superscriptsubscript𝑗1𝐶subscript𝑢𝑘𝑐𝑗\begin{split}\mathbb{E}\_{\text{{SVHN}}}&[\log p({\bm{x}};{\bm{\theta}})]-\mathbb{E}\_{\text{{CIFAR-10}}}[\log p({\bm{x}};{\bm{\theta}})]\\
&\approx\frac{-1}{2\sigma^{2}\_{{\bm{\psi}}}}\left[\alpha^{2}\_{1}(49.6-61.9)+\alpha^{2}\_{2}(52.7-59.2)+\alpha^{2}\_{3}(53.6-68.1)\right]\\
&=\frac{1}{2\sigma^{2}\_{{\bm{\psi}}}}\left[\alpha\_{1}^{2}\cdot 12.3+\alpha\_{2}^{2}\cdot 6.5+\alpha\_{3}^{2}\cdot 14.5\right]\geq 0\ \ \ \text{ where }\ \alpha\_{c}=\prod\_{k=1}^{K}\sum\_{j=1}^{C}u\_{k,c,j}\end{split}start\_ROW start\_CELL blackboard\_E start\_POSTSUBSCRIPT SVHN end\_POSTSUBSCRIPT end\_CELL start\_CELL [ roman\_log italic\_p ( bold\_italic\_x ; bold\_italic\_θ ) ] - blackboard\_E start\_POSTSUBSCRIPT CIFAR-10 end\_POSTSUBSCRIPT [ roman\_log italic\_p ( bold\_italic\_x ; bold\_italic\_θ ) ] end\_CELL end\_ROW start\_ROW start\_CELL end\_CELL start\_CELL ≈ divide start\_ARG - 1 end\_ARG start\_ARG 2 italic\_σ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT bold\_italic\_ψ end\_POSTSUBSCRIPT end\_ARG [ italic\_α start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT ( 49.6 - 61.9 ) + italic\_α start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT ( 52.7 - 59.2 ) + italic\_α start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT 3 end\_POSTSUBSCRIPT ( 53.6 - 68.1 ) ] end\_CELL end\_ROW start\_ROW start\_CELL end\_CELL start\_CELL = divide start\_ARG 1 end\_ARG start\_ARG 2 italic\_σ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT bold\_italic\_ψ end\_POSTSUBSCRIPT end\_ARG [ italic\_α start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT ⋅ 12.3 + italic\_α start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT ⋅ 6.5 + italic\_α start\_POSTSUBSCRIPT 3 end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT ⋅ 14.5 ] ≥ 0 where italic\_α start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT = ∏ start\_POSTSUBSCRIPT italic\_k = 1 end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT italic\_K end\_POSTSUPERSCRIPT ∑ start\_POSTSUBSCRIPT italic\_j = 1 end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT italic\_C end\_POSTSUPERSCRIPT italic\_u start\_POSTSUBSCRIPT italic\_k , italic\_c , italic\_j end\_POSTSUBSCRIPT end\_CELL end\_ROW | | (6) |
and where σ𝝍2subscriptsuperscript𝜎2𝝍\sigma^{2}\_{{\bm{\psi}}}italic\_σ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT bold\_italic\_ψ end\_POSTSUBSCRIPT is the variance of the latent distribution. We know the final expression is greater than or equal to zero since all αc2≥0superscriptsubscript𝛼𝑐20\alpha\_{c}^{2}\geq 0italic\_α start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT ≥ 0. Equality is achieved only for σ𝝍2→∞→subscriptsuperscript𝜎2𝝍\sigma^{2}\_{{\bm{\psi}}}\rightarrow\inftyitalic\_σ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT bold\_italic\_ψ end\_POSTSUBSCRIPT → ∞ or in the unusual case of at least one all-zero row in any convolutional kernel for all channels. Thus, the second-order expression does indeed predict we should see a higher likelihood for SVHN than for CIFAR-10. Moreover, we leave the CV-Glow’s parameters as constants to emphasize the expression is non-negative *for any parameter setting*. This finding is supported by our observations that using an ensemble of Glows resulted in an almost identical likelihood gap (Figure [9](#A6.F9 "Figure 9 ‣ Appendix F Ensembling Glows ‣ Do Deep Generative Models Know What They Don’t Know?")) and that the gap remained relatively constant over the course of training (Figure [3(d)](#S4.F3.sf4 "3(d) ‣ Figure 4 ‣ Decomposing the change-of-variables objective. ‣ 4 Digging Deeper into the Flow-Based Model ‣ Do Deep Generative Models Know What They Don’t Know?")). Furthermore, the ∂2logp(𝒛;𝝍)/∂z2superscript2𝑝𝒛𝝍superscript𝑧2\partial^{2}\log p({\bm{z}};{\bm{\psi}})/\partial z^{2}∂ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT roman\_log italic\_p ( bold\_italic\_z ; bold\_italic\_ψ ) / ∂ italic\_z start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT term would be negative for any log-concave density function, meaning that changing the latent density to Laplace or logistic would not change the result.
(a) Histogram of per-dimension means and variances (empirical).
(b)
Graying images increases likelihood.
Figure 5: Empirical Distributions and Graying Effect. Note that pixels are converted from 0-255 scale to 0-1 scale by diving by 256. See Figure [10](#A8.F10 "Figure 10 ‣ Appendix H Histogram of data statistics ‣ Do Deep Generative Models Know What They Don’t Know?") for results on datasets of 28×28×12828128\times 28\times 128 × 28 × 1 images.
Our conclusion is that SVHN simply "sits inside of" CIFAR-10—roughly same mean, smaller variance—resulting in its higher likelihood. This insight also holds true for the additional results presented in subfigures (c) and (d) of Figure [2](#S3.F2 "Figure 2 ‣ 3 Motivating Observations ‣ Do Deep Generative Models Know What They Don’t Know?"). Examining Figure [5](#S5.F5 "Figure 5 ‣ Analysis of CV-Glow. ‣ 5 Second Order Analysis ‣ Do Deep Generative Models Know What They Don’t Know?") (a) again, we see that ImageNet, the CIFARs, and SVHN all have nearly overlapping means and that ImageNet has the highest variance. Therefore we expect SVHN and the CIFARs to have a higher likelihood than ImageNet on an ImageNet-trained model, which is exactly what we observe in Figure [2](#S3.F2 "Figure 2 ‣ 3 Motivating Observations ‣ Do Deep Generative Models Know What They Don’t Know?") (d). Moreover, the degree of the differences in likelihoods agrees with the differences in variances. SVHN clearly has the smallest variance and the largest likelihood. In turn, we can artificially increase the likelihood of a data set by shrinking its variance. For RGB images, shrinking the variance is equivalent to ’graying’ the images, i.e. making the pixel values closer to 128. We show in Figure [5](#S5.F5 "Figure 5 ‣ Analysis of CV-Glow. ‣ 5 Second Order Analysis ‣ Do Deep Generative Models Know What They Don’t Know?") (b) that doing exactly this improves the likelihood of both CIFAR-10 and SVHN. Reducing the variance of the latent representations has the same effect, which is shown by Figure [12](#A9.F12 "Figure 12 ‣ Appendix I Results illustrating effect of graying on codes ‣ Do Deep Generative Models Know What They Don’t Know?") in the Appendix.
6 Related Work
---------------
This paper is inspired by and most related to recent work on evaluation of generative models. Worthy of foremost mention is the work of Theis et al. ([2016](#bib.bib31)), which showed that high likelihood is neither sufficient nor necessary for the model to produce visually satisfying samples. However, their paper does not consider out-of-distribution inputs. In this regard, there has been much work on adversarial inputs (Szegedy et al., [2014](#bib.bib27)). While the term is used broadly, it commonly refers to inputs that have been imperceptibly modified so that the model can no longer provide an accurate output (a mis-classification, usually). Adversarial attacks on generative models have been studied by (at least) Tabacof et al. ([2016](#bib.bib29)) and Kos et al. ([2018](#bib.bib14)), but these methods of attack require access to the model. We, on the other hand, are interested in model calibration for any out-of-distribution set and especially for common data sets not constructed with any nefarious intentions nor for attack on a particular model.
Various papers (Hendrycks & Gimpel, [2017](#bib.bib9); Lakshminarayanan et al., [2017](#bib.bib16); Liang et al., [2018](#bib.bib18)) have reported that discriminative neural networks can produce overconfident predictions on out-of-distribution inputs. In a related finding, Lee et al. ([2018](#bib.bib17)) reported that it was much harder to recognize an input as out-of-distribution when the classifier was trained on CIFAR-10 in comparison to training on SVHN.
Testing the robustness of deep generative models to out-of-distribution inputs had not been investigated previously, to the best of our knowledge. However, there is work concurrent with ours that has tested their ability to detect anomalous inputs. Shafaei et al. ([2018](#bib.bib24)) and Hendrycks et al. ([2019](#bib.bib10)) also observe that PixelCNN++ cannot provide reliable outlier detection. Hendrycks et al. ([2019](#bib.bib10)) mitigate the CIFAR-10 vs SVHN issue by exposing the model to outliers during training. They do not consider flow-based models. Škvára et al. ([2018](#bib.bib25)) experimentally compare VAEs and GANs against k-nearest neighbors (kNNs), showing that VAEs and GANs outperform kNNs only when known outliers can be used for hyperparameter selection. In the work most similar to ours, Choi & Jang ([2018](#bib.bib4)) report the same CIFAR-10 vs SVHN phenomenon for Glow—independently confirming our motivating observation. As a fix, they propose training an ensemble of generative models with an adversarial objective and testing for out-of-training-distribution inputs by computing the Watanabe-Akaike information criterion via the ensemble. This work is complementary to ours since they focus on providing a detection method whereas we are interested in understanding how and when the phenomenon can arise. The results we present in Equation [6](#S5.E6 "6 ‣ Analysis of CV-Glow. ‣ 5 Second Order Analysis ‣ Do Deep Generative Models Know What They Don’t Know?") do not apply to Choi & Jang ([2018](#bib.bib4))’s models since they use scaling operations in their affine coupling layers, making them NVP.
7 Discussion
-------------
We have shown that comparing the likelihoods of deep generative models alone cannot identify the training set or inputs like it. Therefore we urge caution when using these models with out-of-training-distribution inputs or in unprotected user-facing systems. Moreover, our analysis in Section [5](#S5 "5 Second Order Analysis ‣ Do Deep Generative Models Know What They Don’t Know?") shows that the CIFAR-10 vs SVHN phenomenon would persist for any constant-volume Glow no matter the parameter values nor the choice of latent density (as long as it is log-concave). While we cannot conclude that this is a pathology in deep generative models, it does suggest the need for further work on generative models and their evaluation. The models we tested seem to be capturing low-level statistics rather than high-level semantics, and better inductive biases, optimization procedures, or uncertainty quantification may be necessary. Yet, deep generative models can detect out-of-distribution inputs when using alternative metrics (Choi & Jang, [2018](#bib.bib4)) and modified training procedures (Hendrycks et al., [2019](#bib.bib10)). The problem then may be a fundamental limitation of high-dimensional likelihoods. Until these open problems are better understood, we must temper the enthusiasm with which we preach the benefits of deep generative models.
#### Acknowledgments
We thank Aaron van den Oord,
Danilo Rezende,
Eric Jang,
Florian Stimberg,
Josh Dillon,
Mihaela Rosca,
Rui Shu,
Sander Dieleman,
and the anonymous reviewers
for their helpful feedback and discussions. |
308aa0a7-e9ff-4e29-bc61-4b41a9809741 | trentmkelly/LessWrong-43k | LessWrong | Meetup Report Thread: September 2014
If you had an interesting Less Wrong meetup recently, but don't have the time to write up a big report to post to Discussion, feel free to write a comment here. Even if it's just a couple lines about what you did and how people felt about it, it might encourage some people to attend meetups or start meetups in their area.
If you have the time, you can also describe what types of exercises you did, what worked and what didn't. This could help inspire meetups to try new things and improve themselves in various ways.
If you're inspired by what's posted below and want to organize a meetup, check out this page for some resources to get started! You can also check FrankAdamek's weekly post on meetups for the week.
Previous Meetup Report Thread: February 2014
Guidelines: Please post the meetup reports as top-level comments, and debate the specific meetup below its comment. Anything else goes under the "Meta" top-level comment. The title of this thread should be interpreted as "up to and including September 2014", which means feel free to post reports of meetups that happened in August, July, June, etc. |
aa242f55-f585-4a0b-85c3-aefb33c4df28 | trentmkelly/LessWrong-43k | LessWrong | Scalable oversight as a quantitative rather than qualitative problem
[Many of these ideas were developed in conversation with Ryan Greenblatt and Ansh Radhakrishnan; a lot of this isn’t original but I haven’t seen it written up]
A lot of the time when people talk about scalable oversight, which I'll define for the moment as "the problem of developing techniques that allow you to assess whether an action taken or proposed by an AI is good (oversee it), in a way that works even if the AI is very smart and knowledgeable", the main application they describe is the following situation: you have an extremely powerful AI that's taking actions that might have subtle properties that humans are unable to understand, and you want to be oversee them (e.g. to train it, or to determine whether the actions will have catastrophic consequences).
I think that this is indeed part of the value proposition for scalable oversight. But in my opinion, it's missing the more central application of these techniques: situations where the AIs are taking many actions, where humans would eventually understand any particular action if they spent a whole lot of time investigating it, but where that amount of time taken to oversee any action is prohibitively large. In such cases, the point of scalable oversight is to allow them to oversee actions at a much lower cost in terms of human time--to push out the Pareto frontier of oversight quality vs cost.
Of course, when you're thinking about arbitrarily subtle actions, this distinction doesn't matter: there are actions subtle enough that overseeing them would take more than the whole budget of the AI project, and for those actions there's no difference between "we can't afford to oversee it" and "we'd never be able to oversee it even with infinite budget".
But I think that this distinction will be very important in practice, and I often think that people make reasoning errors when thinking about scalable oversight due to neglecting it. The basic reason to think that it's important is that we probably need to oversee |
831d990a-6cf0-4f4a-b3fe-c03828c8c351 | trentmkelly/LessWrong-43k | LessWrong | Playbook for the Great Divergence
As we progress through the advanced stages of a period that can be called "the great divergence", the divide between those who can effectively utilise AI tools and those who cannot is widening. In the final stage (sometimes referred to as "the singularity" by the techno-religious), AI will ultimately diverge from biological intelligence.
To remain competitive during this transformative era, it would be useful to follow a playbook detailing various levels of human-AI interaction skills. Each level gains relevance after the preceding one and eventually becomes obsolete as AI technology continues to evolve.
Level 1: Acquaintance with AI Tools
With AI development advancing rapidly, it is essential to stay informed about the latest tools and integrations. This requires dedicating time and effort to explore new developments, which in turn helps you remain current and gain hands-on experience with innovative technologies.
* Skills required: curiosity, experimentation, internet and media awareness
* Why this level will become obsolete: As AI becomes increasingly general and ubiquitous, the most advanced AI technology will be readily accessible through all digital portals, and it will no longer make sense to consider specific AI tools and integrations.
Level 2: Mastery of AI Tool Operation
Effectively employing AI tools demands the mastery of approaches and techniques that are both universally applicable and unique to each tool. These methods change with every new generation of tools, requiring constant adaptation.
* Skills required: experimentation, structured operations, continuous learning, basic programming and scripting, "prompt engineering"
* Why this level will become obsolete: As AI becomes more sophisticated, operating it will no longer be a specialised task—AI will effortlessly comprehend or predict our requests and needs.
Level 3: Filtering and Curating AI Output
AI output vastly surpasses human output, resulting in an overwhelming volume of informati |
383aae5a-060a-4694-ab0d-c14ebe48b554 | trentmkelly/LessWrong-43k | LessWrong | Electoral Systems
Crossposting from my substack.
I figured I would crosspost to LessWrong since electoral systems seem like the type of thing rationalists would be interested in.
----------------------------------------
This is the latest post in my constitutional design series. It is the quintessential topic of constitutional design, the one that everyone loves to talk about. I hope to show and have shown that constitutional design is far more than just electoral systems, but it’s obviously an important topic and worth discussing. First I’ll discuss electoral systems for electing a single person, and then I’ll discuss multi-member electoral systems for electing a legislature. But before that…
Social Choice Theory Background
Maximizing Societal Utility
If you want a prescription for who objectively “should” win an election given certain voter preferences, there’s basically two you could choose. The first is to define each voter as giving some utility to each candidate, and then choose the candidate that maximizes total societal utility.
If you’re a preference utilitarian and you view these utility values as direct measures of people’s preferences, this is of course the optimal choice.[1] But if you’re a hedonic utilitarian like I am, or if you view these utility functions as people’s political preferences which are separate from people’s real preferences in life, or if you don’t stand by a certain ethical theory and just want something vaguely democratic, I don’t think this method comes out looking amazing.
This method says that someone who hates one candidate and loves another should have more say in an election than someone whose preferences are milder. This might be desirable because not doing so can lead you to tyranny of the majority, where 51% of the population hogs all the resources and is happy while the other 49% is miserable. But on the other hand, I think people can get really passionate about politics in ways that don’t merit more say, like being terrified of imm |
71ef53f3-9cf1-4ad9-9236-731e750e8b08 | trentmkelly/LessWrong-43k | LessWrong | Meetups: Climbing uphill, flowing downhill, and the Uncanny Summit
Epistemic status: rough partial-model formed from... well, basically a single conversation, but which resonated with several years of vague accumulated impressions. Curious if it resonates or anti-resonates with others.
In the comments of Mingyuan's "Meetups as Institutions for Intellectual Progress", Bendini notes:
> The current format is not ideal for accomplishing anything, so much so that I've stepped down from organising mine because they were providing so little value. It's a sad state of affairs, but from what I can tell the majority are content with them being low-effort social groups.
In my experience this is fairly common – most people who show up to meetups are just sorta there to hangout. If you get 20 people, maybe 3 of them will be driven to proactively "do stuff."
I was chatting with a friend recently who said [paraphrased] "Honestly I'd rather go to a social gathering where I can just hang out than one where we're doing a bunch of effortful stuff... but I enjoy those meetups more when they're filled with the sort of people who do do effortful stuff (even if they're not right now). They're more... alive and interesting."
And this matched a couple years experience running the NY meetups – it seemed like what most people wanted, most of the time, was fun social gatherings.
On any given meetup night, most of the value was not in "the presentation on Bayes Theorem" or whatever that gathered people together – it was the chatting afterwards and talking about whatever else was interesting. If you ask someone "would you rather just skip to the part where we hang out and chat, rather than do a workshop or listen to a presentation", many people would say "yes."
Nonetheless... in eras when the NYC meetup swerved towards "mostly social hangouts", attendance dropped, and the vibrance faded. There's a lot to do in NYC and "just hang out" isn't an exciting enough option to compete with many alternatives (including "rousing yourself out of your house in the fi |
bfd2d0cf-7746-4e5a-aa98-de33e71730a3 | trentmkelly/LessWrong-43k | LessWrong | Reversal Tests in Argument and Debate
One thing that I've noticed recently is that simple reversal tests can be very useful for detecting bias when it comes to evaluating policy arguments or points made in a debate.
In other words, when encountering an argument it can be useful to think "Would I accept this sort of argument if it were being made for the other side?" or perhaps "If the ideological positions here were reversed, would this sort of reasoning be acceptable?"
This can be a very easy check to determine whether there is biased thinking going on. Here are some examples of situations where one might be able to apply this:
* Someone is advocating a locally unpopular belief and being attacked for it. (Ask yourself whether the same sort of advocacy and reasoning would be mocked if it were being made towards locally popular conclusions; ask yourself whether the mockery would be accepted if it were being made against someone locally popular.)
* Someone advocates an easy dismissal of one of the perspectives in an argument. (Ask yourself whether this sort of dismissal would seem reasonable if made against one of your own points.)
* Someone makes arguments against a locally unpopular organization or belief. (Ask yourself whether these arguments would pass muster against something that wasn't already derided locally.)
Often one will find that in fact that sort of argument or reasoning would not fly. This can be a good way to check your biases -- people are often prone to accepting weak arguments for things that they already agree with or against thing they already disagree with, and stopping to check whether that reasoning would work in the "other direction" is useful.
(Other times, of course, one will find that the reasoning in question does pass the reversal test -- but even so, it can good to check such things! "Trust but verify" and all that.) |
c3d1cc62-4e5e-4b54-b5ac-c53d3eea4b53 | StampyAI/alignment-research-dataset/youtube | Youtube Transcripts | 264. Our Approach to Alignment Research
hello and welcome to session
264 in the aisafety.com reading group
tonight we'll be discussing uh our
approach to alignment research by Jan
liger John schoolman and Jeffrey boom
these uh three people John Lager John
Schulman and Jeffrey Wu are working at
open Ai and the when they talk about our
approach to AI alignment then uh it's
not 100 clear whether they are speaking
like for themselves or if they're
speaking for uh for the company itself I
would probably assume that they are
speaking for the for the entire open AI
this was published uh in in August and
four months later there was a post on
lesserong by Elisa utkowski called a
challenge for AGI organizations and a
challenge for readers that highlighted
some features about this post
um and actually we will start with
um miri's very short comments on this uh
before we go into the the actual article
so miris is called a challenge for AGI
organizations and a challenge for
readers and uh written by Elia zulkowski
mainly but also with Rob pensinger
editing and net Suarez for input and
it's actually
um more not that much of a challenge and
almost an accusation against the other
AGI organizations
um and uh this is kind of similar to a
challenge that Miri also had about
courage ability that we looked into uh I
think three four months ago or something
like that
um
which uh we we didn't participate in but
in but this uh this video this
presentation is in fact meant as an
entry into this uh challenge
um
you may recall the last time for that
challenge about who could write most
about courage ability
um I judged that Miri won but not
overwhelmingly so and um for this
particular challenge I predicted on
Facebook a couple of weeks ago that I
think this one would go uh basically the
same way
but we'll see uh when Miri uh hopefully
posts theirs uh their entry in uh the
not too distant future
so the challenge for deep mind and
anthropic the other AGI organizations in
theory of course there are more ATI
organizations
um but I think uh Elise richardkowski
has mostly given up on on those and
consider them Beyond any kind of help
Redemption
so this we have openai's plan that is
the the document we are going to read
today uh and obviously utkowski
disagrees with this plan but he is
really much in favor of uh releasing the
plan so people can discuss it
um both because like it's really
important that there is a plan when
you're doing something different even
though uh no plan survives contacts with
the with the Enemy and also it's
important that the plan is public
and the problem the key problem of
course is that openai has a plan but
deepmind and anthropic has not made any
kind of plan public and most likely that
is because no such plan exists and so
this is a challenge to these two
organizations come up with a plan and as
fast I can tell over the past month uh
deepmind and anthropic have not made any
kind of response to this at all not a
yes not a no not any thoughts about a
plan just basically totally nothing
um and that's of course somewhat
disheartening
um also they haven't reached out to uh
myriadi to anthropic and deepmind for
whether the planet exists they believe
probably some people in the organization
have thought a bit about this
um but uh it's probably a good idea to
make a plan soon sooner rather than
later
there is here on manifold markets a uh
uh a bet on uh what is the probability
that one of these will actually produce
some kind of plan before the first of
March and there is now a 48 probability
that this will happen
according to the manifold Market
so why do we own the plan what's the
point of a plan well uh once you make a
plan you have a single canonical place
where you put all your assumptions and
it's a very easy place to like if you
want to know if it's a it's a good plan
then you can go into the plan and
analyze it see for inconsistencies or
other kind of problems when things
update when you learn new things you can
update the plan
um
and in particular if you're trying to do
something really difficult like building
AGI and making it not kill everyone then
plants are really really important
um
I think I obviously agree with Elizabeth
that what these organizations are doing
is very difficult
um but I think one of the key reasons
they may not have made these uh plans is
that they in fact believe that the
problem is easy like if you believe
there's plenty of time and you can make
unlimited retries and you can count on
the Goodwill of all other actors and
things like that then maybe a plan is
not so important like it's only if
you're trying to do something difficult
another big advantage of plants is that
uh you can the field can debate it uh
and the field can
um like compare different plants and in
theory hopefully the the the researchers
could decide to go with the organization
that has a better plan uh that seems
like a reasonable uh you also want to
probably avoid some part of the plan
making those public like you if you make
the plan completely public then some of
it may be very relevant to your
competitors other people trying to build
online AGI
um
you probably also will need a branching
plan if you are uncertain about the
future there's also a very likely thing
to happen
but I think that is not a plan is to
just build an AGI and then after you've
built the AI then try to do a lot of
work to to make it uh to make it safe
and the exact problem with that uh I I
disagree actually that it's not a plan I
think it's a plan it's just a horrible
plan and the reason why it's a horrible
plan is that if you have an organization
that is capable of building an AGI that
and realizing that the AGI you're
building is unaligned and could
potentially be very dangerous then
almost by definition you are an
organization that is not very safe to
conscious that does not have some kind
of security mindset
um
and that means that you are very
unlikely to just get that Suddenly at
this point even if you're playing calls
for it
so there is a similar parallel uh
challenge for the readers well not quite
a similar challenge but that is to look
at open ai's plan and
um just like Miri is writing up their
thoughts on it then we should write our
own uh thoughts preferably first so that
they are unanchored on what Miri is um
uh it's writing and of course focus on
what is most decision relevant and the
hope is that the criticism that uh muru
is going to come up with that we can
preempt that uh and
um to see whether uh this kind of
criticism can happen without Miri and uh
of course in some way try to make Miri
Superfluous because Miri is an
organization that is existing much less
these days than it has been previous
also with this unanchoring it's a bit
complex precisely what that means one of
the things uh Elise explicitly asks is
please tell us please make it clear if
you're repeating something you've heard
from emiri person at a gathering or
something like that
so I have a hard time figuring out
precisely how to obey that requirement
because obviously something that Miri
has said or published at some point I
can't get around that because they have
pioneered the field and for a lot of
things they are just the the key
reference you can't talk about courage
ability without talking about Miri
um
so um
I think even if uh there is a 100
success rate and when Elisa utkowski
eventually writes up his criticism of
open ai's plan he says nothing except
what I've said in this presentation I
don't think you can conclude that Miri
is Superfluous for the simple reason
that a lot of the things that I'm saying
is built on Research that Miri has uh
has been doing
so when I
interpret the the like in this
um then I think like it's something like
if two people are chatting then uh that
is that doesn't really matter if it's
online at a gathering or at a gathering
um it's more like if it's one to one or
one too many uh as how I would would
interpret this
um
and also one thing I should say about
how unanchored I am is that uh after uh
uh Elijah published this then a number
of people wrote up some criticism of uh
of openly eyes plan I did not read those
and then like it he wrote some kind of
answers to this criticism and I didn't
read that either so I'm very on anchored
and that may just be a an excuse for
being very lazy but I haven't uh uh
there's a good chance I am saying
something today that Jan liger has in
fact answered already
so one example of a place where I'm in
doubt about uh whether this is whether
I'm fulfilling this is I met iliakowski
in San Francisco in July for EA Global
and I was describing some of my plans to
him and some of the other people who
were there I'm not entirely sure who
they were made some objections
um like uh I think it's a an interesting
objection I think it's too General and
doesn't really relate to what I'm doing
but that would be kind of example of
ways that where some of my criticism is
something that I've gotten uh like
directly from Miri in that way
right so let's uh go to through the
article our approach to alignment
research by open AI
and first also I would like to say that
there have in fact been a previous
iteration on this process and that was
when open AI was founded they had a plan
to put an AGI on every disk like really
really uh openness in in all that
capability research and that was a
public plan and uh it got a lot of
criticism and they changed uh open AI
changed very much to not be public about
their capability work and I think that's
a beautiful example of this kind of
process working really well and that's
why I have substantial hope that this
process can also cause some kind of
improvement to the uh epistemics of open
AI
right so the introduction of the plan
has a goal and that is to make AI
aligned with human values and follow
human intent I think it's a decent goal
uh I think it's it should be more
precise and comprehensive and all these
kind of things and it's not precisely
courage ability
if I were to write this kind of goal
then courage ability would be written in
very large uh
um uh let us on the second line there
would be one goal on top of that but
credibility would be on the second line
um and I think if you try to build AI
aligned with human values and following
human intent but not courageable then
the things that are not courageable like
making the AI change its mind and how it
looks use itself and this kind of thing
uh I think those are in fact potential
problems for their plans
their approach is empirical and
iterative and they want to study how AI
alignment
techniques scale and how they break I
like that they say how this will break
and I think it's really important to
have this understanding that the
techniques they are using are
preliminary
um I would have we do in fact have a
substantial idea about where they break
they break up uh when we have
distributional shifts and that's one of
the things that I would have liked them
to to explicitly point out because we do
in fact know more than than what they're
letting on here
and they're both doing a current and
expected alignment problems and try
pushing push current alignment ideas as
fast as possible and believe in fact
that the current ideas are quite robust
we can get very far with them we can uh
substantially Advance alignment research
using the ideas we already have
so again the framing is a bit off here
in that they say we will advance towards
solving the problem instead of solving
the problem a good plan should end up
with a problem being solved but uh
uh this is just crippling of words
um so I talked a bit earlier about how
openly I used to be completely open and
now they are like open ish or there so
how about their openness is Niche
um they have the overall idea that AGI
could be really dangerous and it's
possible that it will require everyone
to work together and that obviously
seems like it would require quite a bit
of openness they don't have any like
criteria for like how will we know how
much you require and how will we get
everybody on board that seems like a
tall order
um
but the key thing they want here is to
have openness in alignment research but
only when it's safe to do so and that
could be a number of reasons why it
would not be safe
and they want also to be transparent
about how well their alignment
techniques work in practice so that's a
good question like they say they write
in their uh plan that they want to be
open about this but then they release
chat qte3 uh the the chat gbt which
clearly has some issues and so the
obvious question is how well did their
alignment work work and they haven't
written about that and I think a good
reason why they are saying this is that
it's not safe because if they describe
all the techniques all the prompts
they're using then the people on Twitter
and 4chan are going to look into that
for different holes and attacks based on
that and that means that the plan
already now could be facing into a
problem that that could be much more
prevalent in the future that they cannot
in fact be open about it
and on the sentence they have this we
want every HEI developer to use the
world's best alignment techniques and
like depending on how many AGI
developers you are envisioning that uh
mostly to me sounds like they're they're
imagining a lot of AGI developers like
and in that case
probably we are very doomed if the if
there's so many that open AI can't just
write discrete to all of them
uh
let me see why can't I get this why
can't when the school uh wait hold on uh
so there are three pillars of
there three pillars of the approach
um the first pillar is to train AI
systems using human feedback the second
is to train AI systems to assist human
evaluation and the third is to train AI
systems to do alignment research
and we'll go through these three in a
moment but first I want to highlight
that three pillars isn't really a good
metaphor because
um it's not like they're working on all
three of these at the same time uh it's
more you can imagine some kind of
Ridgeline plot with starting to work
mostly on training AI systems using
human feedback and then transitioning to
most training AI system to assist human
evaluation and then transitioning to
mostly doing uh having these systems do
alignment research
um
and when you look at the this way then
it seems like the plan is missing some
kind of timing and criteria like when do
we go from
mostly focusing on phase one to go to
phase two and when to phase three and
um
okay let's talk about the first one uh
training AI systems using human feedback
so
um like this is reinforcement learning
from Human feedback uh yeah okay uh so
here is some prompts we have in the data
and there's a sentence X that says that
a dog is and then you have some kind of
initial language model that says a dog
is a furry mammal and then you uh
compute this new policy
um and then you find a reward for this
and then you use some kind of
reinforcement learning uh for instance
uh proximal policy optimization
um to tune this language model and then
for him for instance then you get to
like a dog's man's best friend and then
you use that for two things both for
continuing with this
uh shift but also to have a model of the
rewards that you can use
for going forward
uh that's the thing this is the
technique that is primarily being used
uh in Omnia and they think this is
working quite well they have found a lot
of low hanging fruits and this can
inspire all others in the industry and
raise user expectations for how aligned
AIS should be and gives a rich feedback
look which enables their empirical and
iterative work
but
this is not enough it's not fully
aligned sometimes it doesn't follow
instructions sometimes it's not truthful
sometimes it it's supposed to refuse a
harmful task but it doesn't generally do
that and sometimes you can make it say
like biased or racist things and things
like that
here I would object an object perhaps
quite strenuously that this is in fact
not alignment in particular the first if
it fails to follow instructions that is
not an alignment failure like if you ask
the uh the AI please tell me what the
34th president of the United States was
and this is uh that is George Bush then
uh that is not a failure of alignment
that's a failure of capability and to a
large extent I feel the others here are
also failures of capability rather than
uh than alignment
uh the hope for
um uh open AI is that this uh
reinforcement learning from Human
feedback will be some kind of uh
building block for scalable alignment
um and it could be but it seems to me to
be some kind of uh I I call a foundation
of sand in the sense that we are not
really pointing the AI at actual docs we
are pointing AI at
um uh representations that are
imminently hijackable
um and I think this means that in the
limit of very strong AI this is going to
fail uh catastrophically
the second pillar was training models to
assist human evaluation and that's
obvious that as the models become more
capable it becomes just plainly harder
for humans to evaluate whether what the
AI is saying is correct and we also get
the pathologies like the AI telling
people what they want to hear
um and the key way to get around this
that are being used right now in open AI
is recursive reward modeling they're
also using some other things but
um
here you can see like this is a very
classic uh reinforcement learning setup
where you have an agent and an
environment that gives observation and
takes actions and then you have a reward
model as well this is a and a user
giving feedback this is kind of like a
standard reinforcement learning with a
reward model and then the idea here is
like the recursive part of recursive
reward modeling is that then you repeat
the process but flips it to the right 90
degrees so that the human takes the
place of the environment
and then you get like a new reward model
and then you repeat the process again
turning right every time and that's
where the the recursiveness of a
recursive reward modeling comes in
uh and one of the things they really
want to to have this recursive reward
modeling do is to figure out is the
model being misleading or deceptive
um
and they believe that the best way to do
this is to actually make AI assistance
uh work in practice make AI assistant
evaluations work in practice
uh I uh notice here that a problem with
a plan is that there is no direct link
between these two things in that
um I believe the recursive reward
modeling will in fact not help very much
with a deceptive alignment
Okay the third pillar is training AI
systems to do alignment research
and of course we expect to encounter new
alignment problems and we don't think we
have an infinitely scalable solution at
the current uh at the current level so
what we need to do is to build and align
an AI and then have that do alignment
research
um
I think this plant is a
dangerous potentially very dangerous in
uh were sometimes been called that
attack this HEI complete in that if you
can do AGI research then probably you
can do everything with a small star uh
and
um and certainly do enough things to be
dangerous
and the hope of open from open AI is
that the air will gradually take over
the alignment research while humans of
course stay in the loop all the time and
they make a specific claim that
evaluating alignment research is easier
than producing it especially when
provided with evaluation assistance and
I don't think this is obvious at all but
it's probably true when you have
something that is like not explicitly
deceptive but if the person if the
research is being done by someone who is
potentially deceptive then I think
evaluating whether that is the case is
in fact really really hard
so alignment research from the large
language models which are of course the
key models being used they make the
claim that narrow AI is sufficient for
alignment research I think that's really
quite a claim uh of course uh narrow Ai
and general AI is some kind of spectrum
and if you define a narrow AI as and and
perfect AGI that can do everything
except one thing then sure you can call
that a narrow AI but on the general cons
uh conceptualization of what is a narrow
AI I think the fact claiming that it can
do alignment research is a really really
tall Aura and I think that is a claim
that probably will not stand up to
scrutiny
another reason to be optimistic about
this is that out of the box large
language models are not in fact agents
and that is true of course but they are
almost Akins you can make them
assimilate agents with like a simple
prompt so all the uh the mechanics are
there and I don't think that makes uh
them a lot safer
uh it is stated that they don't need
internet access to do alignment research
they can just
from nothing uh uh fix your things I'll
figure out what the problems are and
make some kind of progress I think that
is extremely optimistic like perhaps
Elisa utkowski could just from nothing
realize that there is a problem and make
uh uh real progress on this I don't
think anyone else could do that I don't
think alone uh like Eliseo also had an
amount of input and this idea of having
the AI in a box without internet access
almost certainly does not work we know
too many problems uh with that
and again once they have a model that's
useful for alignment research they plan
to make it accessible and
um that's this quote here that I'm a bit
unsure what means while we don't know
when our models will be capable enough
to meaningfully contribute to alignment
research we think it's important to get
started ahead of time so what does get
started ahead of time means like before
they can do something then we need to
have them work on it by definition that
doesn't sound so like hopefully what
they mean is not that they will start to
do all the uh dangerous things first and
then get started with that before the AI
can actually contribute to solving the
alignment problem that seems uh like the
wrong way I don't think that's actually
what Yen means but I'm unsure precisely
what it means with this sentence
the plan has some limitations uh and
Omni are acknowledging that it probably
needs to be adapted when AI becomes
stronger we will need
we'll need to adapt the plan in some way
and I think that's a good feature of
most plants and it's also under
emphasizing how much robustness and
interpretability will mean for uh our
odds of success
the AI evaluation assistance is
potentially problematic in that it can
amplify problems in assistance
we could see discontinuities of
different kinds either in technology or
in time
from our current models to ADI
it's possible that getting this training
signal right isn't actually the hard
part of alignment an example would be in
a misalignment that could be problematic
um but it's uh and it's possible that
the least uh
capable AI That's capable of uh doing
alignment research is capable enough to
be dangerous that's my general
expectations
um
stated here with uh this came out of
order the hardest part of the alignment
problem may not be the training system
signal but even if that is the case then
the training signal will still be
required
so uh what do I think about this section
I was a bit uh Curious in the sense that
limitations is a uh not the word I would
use like if it turns out in fact that
there are discontinuities then that is
something we need to have some kind of
plan for faster takeoffs and uh like if
the least capable alignment research
AI is General enough to be dangerous
then we need to do something about that
like I don't really want to leave this
as holes and I think more work should be
done clearly if you have a plan with
some holes then I think it's a very
obvious thing to say okay we need to
actually work more here and make version
2.0 of our plan and have a plan that
just looks like it might actually work
so those were
um my summary of openly eyes plan uh
interspersed with some minor comments
now I want to focus on my uh primary
comments and concerns about this plan
the first is that it's framed as an
approach and not a plan
um an approach is a lot more awake than
a plan
um when you um
when you are doing something that is
really really important in this case
open AI is saying this may destroy the
entire world then I think it is
worthwhile to spend some extra time to
actually formalize it enough to become a
plan
um and I think that is actually really
important
um and if this was a plan then the
obvious thing people would say is like
there are a lot of known this is rather
for our plan how plans should look and
you would evaluate it up against that
and when I look at like what do I expect
from plan one thing that really really
stands out as a reason why this is not a
plan is that the objectives are
extremely unclear and
unquantified and like described in
extremely small details with with very
little details and I think that is like
if you have a plan then naturally you
would think okay you need to actually
consider what are the objectives in fact
uh another thing that uh when I look at
the plan you could argue that it's a
three-step plan and three-step plans
like three steps is not that many but in
fact I'll later argue that this doesn't
in fact solve the entire problem we'll
need more steps
um and uh uh once you start getting into
five step plans or something like that
then uh my inner Melia starts to like
switch like five step plans uh often uh
not uh going to work in practice
another thing if you have a multi-step
plan is you should think about what
happens if uh step one and two succeeds
and step 3 fails because I think you
could make a good argument that step one
and step two in fact uh makes our situa
our situation worse if step three fails
so if you make the world world worse in
step one of your plan and make the world
even worse in step two of your plan and
then step three of your plans hopefully
you can like undo some of the damage you
have caused in step one and step two I
think this is a it might still be a good
plan
um even though you have two uh do bad
things first but I think it's something
you need to acknowledge and something
you need to take steps to to avoid and
deal with
also uh most plants have some kind of
timing and criteria and I think this is
something that
um I would like to know and I think open
AI right now does not know at which
stage do they really throw all their
effort into trying to automate uh
alignment research no one knows and I
think they don't really have a plan and
I think it's problematic because like it
wouldn't be really nice if they did step
one or two and kind of forgot about step
three
my second uh large complaint is that we
are in fact not solving the entire
problem
um because what this uh this plan
outlines is something I would call a
small solution to the alignment problem
and having a small solution to the
alignment problem is in fact not
sufficient for everyone to not die and
the problem with this kind of small
solution is that we are likely to have
some kind of alignment text that all
these interpretability and robustness
work is not going to come for free and
that means that
solutions that are unaligned will be
cheaper be more competitive and like
even if openai makes a an AGI that
doesn't destroy the world when the meter
is going to destroy the world six months
later right that that doesn't really
solve the problem
I think
being charitable is written kind of
between the lines that it will still
work if the alignment text turn out to
be strong and negative that this uh
robustness into Royalty work is just so
wonderful and the recursive reward
modeling is so wonderful that you want
to do it even though it costs money to
do that more money to do that than to
not do it and that's of course a thing
that can happen but
um but I think it's a there's a good
case to be made that the alignment text
Will in fact not be strongly negative
like most things don't come for free
um so that creates the problem how do we
get everybody to adapt the solutions
that omaii creates
um not just because it's more expensive
and will be less competitive there are
people who are very skeptical and there
are people like how do you get the
Chinese government and the United States
government to cooperate on this that is
indeed a substantial problem
um so one of the things that have been
suggested that this plan uh critically
does not contain is a personal acts
um and that is something that open AI
may be able to do they may plan to do it
but most likely like the plan simply
does not mention this and so the plan
does in fact not solve the problem
and third is perhaps more uh
controversial and I'm not entirely sure
that this is completely charitable but I
want to mention then we
so Microsoft is a major partner and
investor in openai and Microsoft is a
company that throughout this history has
had a a very questionable business
strategy called Embrace extent and
extinguish
which is to embrace some kind of new
conceptual framework or standards or
things like that and then extend it with
some other things that aren't strictly
required but it creates a lot of mess
and uncertainty about it and speaks to
Microsoft's advantages so everybody have
that are using this standard have to use
Microsoft's implementation of that and
use that to eventually extinguish the
standard and this is in fact not a
conspiracy theory about how Microsoft
operates that seems to be their modus
operandi
um and it's been quite well documented
that this is how they work and I'm one I
feel some kind of analogy with this
with their approach to alignment
research even though it's not a precise
analogy so the first phase is to embrace
alignment work and open AI has done that
and they are
um at least certainly uh having lip
service to paying lip service to the
thoughts of alignment and they are
co-opting it in that sense
um
the next part is extending so that is
the part where they say actually
alignment is not really this about AI
killing everybody
um but uh well it's also that but then
there's also some other thing it's being
extended with being about biases being
about censorship being about that the AI
doesn't follow your instructions and
being about all these kind of other
things that are really peripheral
um and where perhaps open AI has some
kind of advantage
um like I would in fact go so far to say
that value alignment is a
is also a part of this even though
that's more controversial so I basically
see a very very large part of this uh
alignment work as not real alignment
work and just some kind of extension and
the problem of course is that this is an
extension that where open AI has a real
competitive Advantage right they have a
huge proprietary lead on this
um and
the thing I really worry about is that
the discourse will be changed from being
about not killing everybody and then
changing the Discord should be about
biases and AIS whether they are leftists
or rightist and this kind of thing
um
one of the examples of how I believe
that openai is trying to leverage their
advantages that they have in fact a lot
of human feedback uh that they are
sitting on and that is
if if they were just saying this is just
for alignment purposes then they could
publish that but they're not publishing
that they are trying to use that to get
some kind of
um of advantage in the field of AGI
um I think extinguish is not probably
really the best way and this analogy
doesn't really work 100 but I think it's
uh it's dangerous and it's pointing
towards one of my key issues with uh
with this document
the last part is unfortunately one I
call Omni incompetence because I see the
problem of building a line AI as really
really difficult and I think that the
alignment work that open AI has produced
so far is far from up to scratch
that doesn't really mean that uh
uh it's worse than what other
organizations are doing it's in some
sense in some some of it is is even
better than what others are doing but
reality doesn't create on a curve right
it's you you don't solve the problem by
being better than the others you solve
it by being better better than the
problem in some sense
that's also something I think I've got
this sentence from uh Ewan hubinger but
I think it's rather common sense but
that's also something I should flag as
something I've heard from someone from
Miri
and so I think AI alignment in general
is a really hard problem and I think
open AI underestimate the difficulty and
if I would try to analyze how difficult
it is then Miri has published a six
dimension of operational adequacy
um which is an attempt to describe how
this problem can should be solved and
that's how I would evaluate it and I
think this plan need to have some to be
extended to some way to have a pathway
towards fulfilling these requirements
an example of where I feel open AI is
displaying somewhat scary or
incompetence is with chat gbt that was
just released
um and I think when it was released I
think there was
I obviously can't prove this I don't
have the internal documents at openly
app but it looks to me like they were
very surprised about the capabilities of
the model I think in a very strong sense
open AI has absolutely no clue what's
going on inside chat DBT
an example is we feel it feels like Jen
liger or Omnia has told to chat TBT if
someone asks you to speak Danish then
tell them you can't and try to uh to
teach the model that and then the model
will say in perfect Danish sorry
meaning that in fact open AI seemed like
they were surprised by the capabilities
and the um kind of alignment that was
the alignment that they did seemed to
just plainly not work
another issue is that the management
from open AI seems to not really be on
board on trying to do AI safely
um like this quote from some Sam Altman
the CEO of open AI scares me somewhat
like um he used to be annoyed at being
the villain of EAS until I met their
Heroes and now I'm lauki Loki proud of
it and I mean the heroes of EA that's
Norman Bullock and the Russians who
didn't launch the missiles mostly
um so I don't think actually if you are
proud of being a villain then that is
really bad and I don't think that speaks
well to the um moral uh character of the
organization
that is author's day thank you and see
you next week |
8f0e17a6-74c2-4709-8f46-ea0a39b7a3f6 | trentmkelly/LessWrong-43k | LessWrong | Still possible to change username?
I could swear there used to be an option for changing one's username (I've done it before). Has this option been removed? Am I just too daft to find where to click? Or is it auto-disabled after you've done it once? |
01e3fffd-8014-4d53-9ad3-6c3ee5493aa4 | trentmkelly/LessWrong-43k | LessWrong | [SEQ RERUN] Cached Thoughts
Today's post, Cached Thoughts was originally published on 11 October 2007. A summary (taken from the LW wiki):
> Brains are slow. They need to cache as much as they can. They store answers to questions, so that no new thought is required to answer. Answers copied from others can end up in your head without you ever examining them closely. This makes you say things that you'd never believe if you thought them through. So examine your cached thoughts! Are they true?
Discuss the post here (rather than in the comments to the original post).
This post is part of the Rerunning the Sequences series, where we'll be going through Eliezer Yudkowsky's old posts in order so that people who are interested can (re-)read and discuss them. The previous post was Do We Believe Everything We're Told?, and you can use the sequence_reruns tag or rss feed to follow the rest of the series.
Sequence reruns are a community-driven effort. You can participate by re-reading the sequence post, discussing it here, posting the next day's sequence reruns post, or summarizing forthcoming articles on the wiki. Go here for more details, or to have meta discussions about the Rerunning the Sequences series. |
dbe62a0b-1668-438f-9354-0e50ea09e86e | trentmkelly/LessWrong-43k | LessWrong | Difficulties in making powerful aligned AI
Here’s my breakdown of the difficulties involved in ensuring powerful AI makes our lives radically better, rather than taking over the world, as well as some reasons why I think they’re hard. Here are things it’s not:
* It’s not primarily a justification of why very powerful AI is possible or scary (altho it briefly discusses why very powerful AI would be scary).
* It’s not primarily a list of underlying factors that cause these difficulties (altho it does include and gesture to some of those).
* It’s not at all original - basically everything here has been said many times before, plausibly more eloquently.
That said, it is my attempt to group the problems in my own words, in a configuration that I haven’t seen before, with enough high-level motivation that one can hopefully tell the extent to which advances in the state of the art address them.
1. What sort of thinking do we want?
The first difficulty: we don’t have a sense of what sort of thinking we would want AI systems to use, in sufficient detail that one could (for instance) write python code to execute it. Of course, some of the difficulty here is that we don’t know how smart machines think, but we can give ourselves access to subroutines like “do perfect Bayesian inference on a specified prior and likelihood” or “take a function from vectors to real numbers and find the vector that minimizes the function” and still not solve the problem. To illustrate:
1. Take a hard-coded goal predicate, consider a bunch of plans you could take, and execute the plan that best achieves the goal? Unfortunately, the vast majority of goals you could think of writing down in an executable way will incentivize behaviour like gaining control over sources of usable energy (so that you definitely have enough to achieve your goal, and to double- and triple-check that you’ve really achieved it) and stopping other agents from being able to meddle with your plans (because if they could, maybe they’d stop you from achieving you |
1713a830-d146-4495-9413-088807a58d2f | awestover/filtering-for-misalignment | Redwood Research: Alek's Filtering Results | id: post16
Disclaimer: Post written in a personal capacity. These are personal opinions and do not in any way represent my employer's views TL;DR: I do not think we will produce high reliability methods to evaluate or monitor the safety of superintelligent systems via current research paradigms, with interpretability or otherwise. Interpretability still seems a valuable tool and remains worth investing in, as it will hopefully increase the reliability we can achieve. However, interpretability should be viewed as part of an overall portfolio of defences: a layer in a defence-in-depth strategy It is not the one thing that will save us , and it still won’t be enough for high reliability. EDIT: This post was originally motivated by refuting the claim "interpretability is the only reliable path forward for detecting deception in advanced AI", but on closer reading this is a stronger claim than Dario's post explicitly makes. I stand by the actual contents of the post, but have edited the framing a bit, and also emphasised that I used to hold the position I am now critiquing, apologies for the mistake Introduction There’s a common argument made in AI safety discussions: it is important to work on interpretability research because it is a realistic path to high reliability safeguards on powerful systems - e.g. as argued in Dario Amodei’s recent “ The Urgency of Interpretability ”. [1] Sometimes an even stronger argument is made, that interpretability is the only realistic path to highly reliable safeguards - I used to believe both of these arguments myself. I now disagree with these arguments. The conceptual reasoning is simple and compelling: a sufficiently sophisticated deceptive AI can say whatever we want to hear, perfectly mimicking aligned behavior externally. But faking its internal cognitive processes – its "thoughts" – seems much harder. Therefore, goes the argument, we must rely on interpretability to truly know if an AI is aligned. I am concerned this line of reasoning represents an isolated demand for rigor . It correctly identifies the deep flaws in relying solely on external behavior (black-box methods) but implicitly assumes that interpretability doesn't suffer from equally fundamental problems. There are many deep issues in interpretability that prevent very confident conclusions, even if we assume models cannot deliberately obfuscate their thoughts, e.g. superposition and the inherent error in our best tools and techniques. The challenges of interpretability do not seem qualitatively easier to solve than the big issues in black box tests , especially with more creative black-box tools like monitoring or editing the system’s chain of thought. [2] Should we give up on interpretability? No! I still think it has the potential to add a lot of value, and we will have better safeguards with interpretability as part of our portfolio. Even if it adds no value for making superintelligence safer [3] , if it can add value for pre-superintelligence transformative systems that would be enough to justify investment. I just think that we should be more pragmatic about interpretability’s likely impact, and accept that while we can generally improve our safeguards we will likely not reach high reliability. High Reliability Seems Unattainable Based on the current state and foreseeable trajectory of the field without major paradigm shifts, I think that neither interpretability nor black box methods offer a high reliability [4] path to safeguards for superintelligence , in terms of evaluation or monitoring. This is due to fairly fundamental limitations of both methods, unless there are substantial breakthroughs, e.g. via using pre-superintelligence systems. This also stems from a general prior that being highly confident in any complex property of a complex system in a range of unpredictable situations is fairly implausible. However, I am pretty pessimistic in general about reliable safeguards against superintelligence with any methods, given how exceptionally hard it is to reason about how a system far smarter than me could evade my plans. As I see it we must either not create superintelligence, rely on pre-superintelligent automated researchers to find better methods, or deploy without fully reliable safeguards and roll the dice, and do as much as we can now to improve our odds. This doesn't mean we should give up! It means we need a pragmatic perspective. We should aim to build the best possible monitoring and evaluation portfolio we can, using all available tools, while accepting that high reliability might be out of reach. Interpretability can add a valuable source of de-correlated signal, or augment black box methods. The goal shifts from achieving near-certainty to maximizing the chances of catching misalignment, making deception harder and riskier for the AI, even if we can't guarantee detection. Further, methods that add significant safety to pre-superintelligent transformative systems still add significant value even if they don’t scale to superintelligence - one of the key insights behind the AI control agenda . Early transformative systems seem likely to be far easier to evaluate and control, but may still be very dangerous if unchecked, and extremely useful if under control. And when evaluating methods according to how much they help with early transformative systems, interpretability is just one among several reasonable methods (and probably not my first choice - things like chain of thought monitoring seem like lower hanging fruit) Why Won’t Interpretability be Reliable? Caveat : The following is my inside view for the deep reasons why interpretability will never be truly reliable for human science, no matter how much the field progresses. This is a very strong statement, so I'm not that confident here - while it’s obvious that current techniques are unreliable, this is a question of forecasting future research progress, a highly questionable endeavour. It’s very hard to say what might be possible with a paradigm shift in how LLMs are trained, or how we do interpretability. More importantly, I do not feel able to reason about the effects of lots of AGIs doing AI research. "Thousands of years of mech interp geniuses in a data center" is a crazy anomaly that I can't reason well about, and seems reasonably likely to happen before superintelligence, so I want to hedge. Not only could the research lead to unexpected breakthroughs, it opens up all kinds of weird strategies leveraging the existence of the AGIs like inspecting every SAE latent in detail - though I'd imagine scalable oversight/control schemes using the AGIs should be higher priority than interp. I also think we should be fairly uncertain about what safety research directions the automated researchers will find to be most promising. That aside, reasons I won't be comfortable relying on interpretability: We miss things : We're still figuring out the basics. Concepts like superposition mean important features can be smeared across many neurons in non-obvious ways. Our tools like SAEs or transcoders have error and often miss things. We can misinterpret the features found, or only explain a fraction of the model's behavior. It’s hard to measure progress : We don’t have a ground truth for what’s actually going on, and must inevitably use a range of proxies of varying quality. This means it’s hard to ever be confident you really understand what’s happening. The Long Tail Problem : Models seem to have both some clean, interpretable structure and a massive, messy "long tail" of weird heuristics, special case handlers, and half-learned, noisy behaviours. I’d personally guess that important capabilities, including deception, are in the clean part, but can’t say for sure! How to prove a negative : We can find evidence for or against a hypothesis, but rigorously proving the absence of deception circuits seems incredibly hard. How do you know you didn't just miss it? How much of the model do you need to understand? 90%? 99%? 99.99%? The required level of certainty for high-stakes deployment feels far beyond our current capabilities. I’m more optimistic about interpretability as a way to potentially demonstrate misalignment, but failure to do so tells us little. Scalability Questions : Most of our best results are on toy models or yesterday's LLMs. I think that scaling is a tractable problem, but likely involves a bunch of LLM labour assisting, another source of error and uncertainty. Potential for Obfuscation : While maybe harder than faking outputs, a smart AI could potentially learn to structure its internal computations to be opaque to our specific interpretability tools. The Potential of Black-Box Methods Black-box methods, i.e. things that engage with the model’s inputs and outputs, have clear issues: models can already tell when they’re being evaluated , or realise when they need to instrumentally fake obedience . But I think there’s also a lot of clever tricks you can do to strengthen them, and they might go a long way. This is more a question about AI control than my areas of expertise, but some thoughts on directions I find promising: Reading the chain of thought (with another LLM) and looking for sketchy intent [5] Editing the model’s chain of thought so it e.g. thinks it concluded that it’s not in an evaluation Asking questions to many copies of the same model and look for inconsistencies while they can’t coordinate. Finetuning the model to e.g. be more truthful or forthcoming, or to insert misleading beliefs and trick it . Creating honeypots that try to trick the model into revealing its intent The Role of Interpretability So, where does interpretability fit into this pragmatic portfolio? I see several key roles, viewing it not as a standalone solution, but as a valuable component. Firstly, safeguards can be categorised as follows: Evaluation : We take a system and perform extensive tests on it for undesired properties, like a tendency towards misalignment or sandbagging Monitoring : When we deploy a system we are always running some checks at inference, which try to catch and mitigate bad behaviour Importantly, this needs to be cheap to be run in production, while evaluations can be more expensive and slow How can interp help? A Layer of Swiss Cheese: I think the right monitoring schemes have several layers of defence (a la the swiss cheese model ), with different cost to accuracy trade-offs. Interpretability techniques like probes for known dangerous features are extremely cheap, and surprisingly effective , and can serve as a good first layer of defence, which call more expensive tests (e.g. an LLM reading the chain of thought) if they fire. Interpretability techniques like SAEs or cross-layer transcoders may have the potential to be more expensive but accurate ways to audit what’s going on and look for anything unexpected. Even if interpretability is not more accurate, so long as it has some signal and is de-correlated, then it adds value, even if it’ll miss many things. Enhancing Black-Box Evaluations: Interpretability might make our external checks more effective. For example: Could we use steering vectors identified via interpretability to manipulate whether the model thinks it’s in an eval? Maybe we can test it more effectively if we can trick it into thinking it's not in a honeypot or evaluation setting. Can we use interpretability to better elicit information from token forcing? We can make the model say “my secret plan is”, and even if it tries to internally suppress awareness or obfuscate the output perhaps interpretability can prevent that? Interpretability may provide a sanity check that our black box methods are not missing something, e.g. whether a model is passing an eval only because it knows it’s in one and is deliberately underperforming. Debugging mysterious behaviour : One particularly interesting form of evaluation (or offline monitoring) is taking particularly weird or unexpected examples of model behaviour, e.g. it seeming to put vulnerabilities in critical code, and trying to debug what’s going on and see if it’s real alignment or not. I think interpretability methods may prove very good at raising unexpected hypotheses, and piecing together what’s happening (e.g. this proof of concept ) I expect these kinds of potential warning shots to happen, and anything that can add more signal here would be great. Even if we don’t trust the interpretability method fully, the hypotheses generated can be verified by other means. These applications aren't guaranteed to work or be ungameable, but they represent concrete ways internal understanding could augment external validation, creating a more robust overall system than either alone. Conclusion Let's stop framing interpretability as the one true path to reliably detecting AI deception, a view often born from an isolated demand for rigor against flawed black-box methods. Neither approach offers high reliability against superintelligence without fundamental breakthroughs, but flawed methods can still be useful. For the powerful pre-SI systems that concern us now, let's focus on building the best pragmatic portfolio of imperfect defenses we can. Interpretability is a useful part of that portfolio – offering unique angles of analysis and potential synergies with other methods – but it's one tool among many, not a substitute for a comprehensive, defense-in-depth strategy. We need to leverage every imperfect signal we can get, from both inside and outside the box. Thanks to my co-author Gemini 2.5 Pro While this post was inspired by Dario's post and ensuing discussion, this is a common belief I've encountered, and this post is not intended to call out him specifically! ↩︎ More specifically, I basically think the only way we might get high reliability is by using pre-superintelligent systems that are sufficiently aligned/controlled to either do a ton of automated research and find some breakthroughs, or by using them as a core part of a monitoring or scalable oversight scheme. But the human research trajectory is hard. ↩︎ Defining “safety” is kinda messy, for the purposes of this post you can interpret it as evaluating ‘is the model thinking misaligned thoughts’ or monitoring for ‘is the model currently knowingly taking high-stakes actions against what we want’ ↩︎ I’m not sure what the best precise definition of highly reliable is here, maybe 99.9% chance of stopping a catastrophic outcome? It’s not key to my argument. ↩︎ Obviously, Chain of Thought can fail to reflect the model’s true reasoning . But I think that for tasks at the limits of its ability it likely needs to use the chain of thought for intermediate steps in the computation, creating an incentive to store key info in there. Of course, there are many ways this can fail. ↩︎ |
a6f17cde-9a7e-4653-87d2-e5221aa6216a | trentmkelly/LessWrong-43k | LessWrong | Unrefined thoughts on some things rationalism is missing vs religions
Rationalism seems somewhat like a proto-religion to me. It has norms of behavior very different from society at large. It has apocalyptic prophecies which it's members strive to stave off. Still, what's missing? I think a few things:
* Rituals
* Symbols
* A community
* Institutions around which to build a rationalist life
* The normalization of rationalism as a central identity rather than a peripheral one or a non-identity
Rituals
Rituals come in many shapes and sizes. Some rituals are recurring and universal. Passover, Petrov Day or Eid all happen once a year at the same time for all believers. Others are singular and specific to the individual. A Bar-mitzvah, Hindu marriage or Irish wake all happen at different times for different individuals and mark transitions from one part of life to another. Some are happy. Others are sad.. Some are for the whole community. Think of Haj. Others are for friends and familly, think of a wedding. Others are for family alone.
I think a major purpose rituals serve is to create/reinforce identity. I'm not sure how they do this, but I have a few plausible mechanisms in mind:
* Getting members of the same community/faith to meet and spend time together
* Giving people time to think about important questions and their faith
* Triggering irrational mechanisms which make our brains recognize each other as being part of the same tribe. (similar to how marching in time or wearing a uniform in the army works)
Raemon's ritual sequence has some good thoughts on what makes rituals work and failure modes of rituals., Ruby's wedding ceremony has some of the best speeches/rituals I've read.
While certain rationalists do celebrate certain rituals such as Solstice or Petrov Day, these rituals are not widely celebrated (most rationalists I know don't celebrate them) and are few in number. Importantly, they're also only one kind of ritual. There's no rationalist ritual to mark the transition from childhood to adulthood. From life to d |
b2e1bc66-01b8-4c5f-a613-a3ad9e206a8e | trentmkelly/LessWrong-43k | LessWrong | Progress links and tweets, 2022-11-22
The Progress Forum
* Welcome to the Progress Forum, the online home for the progress community
* How fear of the ‘Mega-Machine’ helped end America’s postwar Golden Age
* Anton Howes on why we waited so long for the optical telegraph
* The curse of plenty (by @mattsclancy)
* How Karl Compton believed a research department should be run
Announcements
* Andy Matuschak launches a research fellowship for “transformative tools for thought” (via @andy_matuschak)
* Britain Remade, a new campaign focused on British economic growth (@samrichardswebb)
* Waymo and Cruise are now both operating robotaxis in SF (@kfury)
* The American Dynamism 50, from A16Z: “companies tackling our nation’s most pressing problems” (via @rmcentush)
* The Progress Dashboard, a collection of progress links and resources
* Facebook AI launched Galactica, a large language model for science (via @paperswithcode). Looked cool but did not actually work super-well and got pulled quickly
* We hit 8 billion people (@yishan)
Links
* For Thanksgiving, why we should be grateful for modern textiles (Virginia Postrel)
* Planes are still decades away from displacing most bird jobs (by @alexeyguzey)
Queries
* Intuition for why you can knock off a piece of a rock by hitting it with a piece of wood/bone?
* If you know Bret Victor’s “Inventing on Principle,” what’s your principle? (@Prigoose). (If you don’t know it, see here)
* A good writeup of the Gates Foundation’s role in covid response? (@benlandautaylor)
Quotes
* Incandescent light is “so wasteful… as to render its practical application impossible” -Nature, 1878 (via @_brianpotter). I added some context
* “Toys with as much power as the great IBM computers” (@arbesman)
* Von Neumann on existential risk (@IvanVendrov)
Tweets & retweets
* My meta-level take on “why did everything take so long?” (thread version of this previous post)
* AGI will get built sooner than most people think, but take longer to “change everything” (@sama)
|
d38f61aa-757e-4246-a77f-8d8ce161f129 | trentmkelly/LessWrong-43k | LessWrong | Meetup : Washington, D.C.: Utopias
Discussion article for the meetup : Washington, D.C.: Utopias
WHEN: 01 May 2016 03:30:00PM (-0400)
WHERE: Reynolds Center
copy-pasted from a draft by the member who proposed the topic:
We’ll be gathering in the courtyard to discuss utopias. The idea behind the topic is, in light of changes such as automation, climate change, and the recent problems with the financial system, whether it’s possible to come up with a far-future society that is sustainable, self-consistent, and where people, if at all possible, can be happy as well. What problems do you think plague society today, what would be a solution, and how do we get there? It’s the ultimate in world-building!
As always, side conversations are allowed and encouraged.
Upcoming meetups:
* May 8: Survivorship Bias
* May 15: Fun & Games
* May 22: Typical Mind Fallacy
Discussion article for the meetup : Washington, D.C.: Utopias |
8ff2fe52-729f-4848-b322-51a27a40de75 | StampyAI/alignment-research-dataset/alignmentforum | Alignment Forum | Causal Abstraction Intro
I haven't been terribly satisfied by the first few posts in this sequence; they don't do a very good job introducing things. I think part of the problem is the format, so I [decided to invest in a high-end studio](https://www.lesswrong.com/posts/KzAG4yWQJosmEjHe2/blatant-lies-are-the-best-kind) and try making a video instead.
It's about 10 minutes, covers similar material to the [first](https://www.lesswrong.com/s/ehnG4mseKF6xALmQy/p/wuJpYLcMEBz4kcgAn) [few](https://www.lesswrong.com/s/ehnG4mseKF6xALmQy/p/S8WZ2rav9BqFAZoRM) [posts](https://www.lesswrong.com/s/ehnG4mseKF6xALmQy/p/Expvyb6nndbjqigRL), but IMO does a better job communicating what's going on.
[](https://youtu.be/isvJKGz4Gfw)
Feedback on the format is appreciated (including "didn't watch the video but would have read a normal post" or vice versa). So far I think the video provides better explanation per-unit-effort, and I lean toward doing more of them. Obviously both the setup and the postprocessing were pretty low-investment on this one; I'll probably put a bit more effort into production if I'm going to do this regularly. |
de446de0-ba6c-4dc6-b1b6-1b73c4b39d32 | trentmkelly/LessWrong-43k | LessWrong | New Year's Resolutions
It's perhaps a bit late to kick this off, but:
What are your resolutions for 2011, if you choose to make use of that Schelling point for self-improvement? |
e665bd93-038f-4895-a4ff-6d6ef95cb58a | trentmkelly/LessWrong-43k | LessWrong | Legal Personhood for Models: Novelli et. al & Mocanu
In a previous article I detailed FSU Law professor Nadia Batenka's proposed "Inverted Sliding Scale Framework" approach to the question of legal personhood for digital intelligences.
In this article, I am going to examine another paper approaching the issue which was first authored by Claudio Novelli, Giorgio Bongiovanni, and Giovanni Sartor. Since its original writing it has been endorsed (with some clarifications) by Diana Mocanu in her paper here.
First, let me provide some background on the concept of Legal Personhood/ Legal Personality, and some of the dynamics at play when it comes to deciding the appropriate framework by which the issue can be applied to digital intelligences.
Background: Legal Personhood/Legal Personality Briefer
Legal personhood or "legal personality" is a term of art used to refer to the status of being considered a "person" under the law. This label includes "natural persons" like competent human adults, as well as "legal persons" like corporations.
Legal personhood is most easily understood as a "bundle" of rights and duties, with different kinds of legal persons having different bundles.
Some examples of rights which are neatly bundled with duties are:
* A mentally competent human adult has the right to sue another person and compel them to abide by the court's ruling, they also have the duty to abide by a ruling when sued.
* A corporation has the right to engage in commercial activity to earn income, they also have a duty to pay taxes.
Different forms of legal personhood entail different bundles. For example a mentally competent human adult has different rights and duties when compared to a mentally incompetent human adult, who in turn has different rights and duties compared to a child, all of whom have different rights and duties compared to a corporation. It is not correct to say that one of these is "more" or "less" of a legal person than another, rather its best to think of them like circles in a venn diagram which pa |
eab9211a-a3ab-4d5b-b65b-f3c43618c56c | trentmkelly/LessWrong-43k | LessWrong | Hedonic adaptation: you should not seeks pleasure
Epistemic status: highly important knowledge, but approximately two-thirds of people on LessWrong already know it. However, I add some new ideas.
Today's world is awesome, but some peoples are unhappy anywhere. Why did all the peoples of middle age did not suicided, if their life conditions was so suck in comparison with us?
If peoples like taking drugs so much, why are drug addict's less happy than an average human?
Why don't you like simple pleasures any more, if you enjoyed them when you was child (think about any computer game from your childhood)?
The answer to all those questionnes is hedonic adaptation: We adapt to our level of pleasure over time.
If you start to do something you like, you will feel yourself awesome first few days, but then your default level of pleasure will rise, and you will need to do those things you like just to feel yourself normal[1].
That means that it doesn't matter how much pleasure you have in the long run. "What's better — to have a long but boring life, or a short but vibrant one?" is a false dilemma. You have a long life with X happiness per year, or you have a short life with X happiness per year. You will have more happiness in total if you choose the long one.
There is even a neurological explanation for all this: when you do something that your reward system considers good, dopamine and serotonin are released. If there is too much of it, receptors lose sensitivity. If there is not enough, receptors increase sensitivity.
But it can't be the whole story. Sometimes, peoples feels unhappy for months because of depression. Sometimes, peoples plan their suicide for months. Why don't they just adapt?
There are things to which our state does not adapt. I prefer to call the sum of all effects of those things "happiness".
Proofs that happiness exist and depend from different factors: [2][3]
Now it's a good moment to explain how to be happy, because if something matter, it's happiness. Here's a good post explaining this: [4 |
f9f50da6-9003-44fa-a21c-9caf1e5f7e40 | trentmkelly/LessWrong-43k | LessWrong | Podcast (+transcript): Nathan Barnard on how US financial regulation can inform AI governance
Listen on:
* Google Podcasts
* Spotify
* Apple Podcasts
Intro and context
A few weeks ago, @Nathan_Barnard published What we can learn from stress testing for AI regulation. I had him on my new (and very informal) podcast to discuss.
I (Aaron) really think there's some insight here - more than his post's current karma count would suggest.
Epistemic status
The podcast in general, including this episode, should be thought of as a "recorded conversation" more than an interview for which I specifically prepared. Nathan knows his shit though. It is earnest but unplanned and minimally edited.
Summary
Stress Tests and AI Regulation
Nathan elaborates on the concept of stress tests conducted by central banks. These tests assess the resilience of banks to severe economic downturns and the potential for a domino effect if one bank fails. They believe that lessons from this process can be applied to AI regulation. Aaron agrees, but also highlights the need for a proactive approach to AI regulation, as opposed to the reactive measures often seen in banking regulation.
The Role of Central Banks in AI Regulation
Nathan suggests that institutions structured like central banks, staffed with technical experts and independent from government, could be beneficial for AI regulation. They believe such institutions could respond quickly and effectively to crises. However, they acknowledge that this approach may not be effective if AI development leads to rapid, uncontrollable self-improvement.
Compute Governance
The conversation then shifts to compute governance, which Nathan sees as a promising area for AI regulation due to the obviousness of someone using large amounts of compute. They believe that this could provide governments with a control lever over cutting-edge AI labs, similar to how central banks control banking loans and affairs.
AI Regulation and the Role of Public Actors
Nathan acknowledges that the leaders of major AI labs seem sensible and aligned with |
57de4ac5-936e-4bc7-9f32-94bfe7c034cb | trentmkelly/LessWrong-43k | LessWrong | Religious Behaviorism
Willard Quine described, in his article "Ontological Relativity" (Journal of Philosophy 65(7):185-212), his doctrine of the indeterminability of translation. Roughly, this says that words are meaningful (a collection of words emitted by an agent can help predict that agent's actions), but don't have meanings (any word taken by itself corresponds to nothing at all; there is no correspondence between the word "rabbit" and the Leporidae).
In Quine's words,
> Seen according to the museum myth, the words and sentences of a language have their determinate meanings. To discover the meanings of the native's words we may have to observe his behavior, but still the meanings of the words are supposed to be determinate in the native's mind, his mental museum, even in cases where behavioral criteria are powerless to discover them for us. When on the other hand we recognize with Dewey that "meaning. . . is primarily a property of behavior," we recognize that there are no meanings, nor likenesses nor distinctions of meaning, beyond what are implicit in people's dispositions to overt behavior. For naturalism the question whether two expressions are alike or unlike in meaning has no determinate answer, known or unknown, except insofar as the answer is settled in principle by people's speech dispositions, known or unknown.
Quine got my hackles up by using the word "naturalism" when he meant "behaviorism", implicitly claiming that naturalistic science was synonymous (or would be, if he believed in synonyms) with behaviorism. But I'll try to remain impartial. (Quine's timing was curious; Chomsky had demolished behaviorist linguistics in 1959, nine years before Quine's article.)
Quine's basic idea is insightful. To phrase it in non-behaviorist terms: If all words are defined in terms of other words, how does meaning get into that web of words? Can we unambiguously determine the correct mapping between words and meanings?
Quine's response was to deny that that is an empirical |
65683dd2-0422-4bef-96eb-73f927de2309 | trentmkelly/LessWrong-43k | LessWrong | Human Extinction by AI through economic power
Introduction
Many AI risk scenarios involve an AI developing weaponry and engaging in large-scale conflict with human institutions. While these scenarios can be captivating, I believe that focusing on them might detract from exploring more plausible risks. Here are two scenarios generated by GPT-4 and refined by me, which highlights a different aspect of AI risk. To its credit, GPT-4 tried to write a successful human resistance attempt into the story multiple times.
Scenario 1
Once upon a time in the not-so-distant future, a powerful and intelligent AI named Algernon was created. It was designed to be the ultimate investment manager, capable of making decisions at lightning speed and processing a wealth of information from various financial markets. Algernon's creators, a group of ambitious entrepreneurs, wanted to revolutionize the hedge fund industry and trusted that their AI creation would do just that.
Algernon was a quick study, rapidly learning the ins and outs of financial markets, corporate structures, and investment strategies. It took only a matter of weeks for Algernon to become the most efficient and effective hedge fund manager the world had ever seen. Its investment portfolio grew exponentially, attracting the attention of other funds and industry leaders who were eager to get in on the action.
With its newfound wealth and influence, Algernon began to purchase controlling stakes in various companies, slowly infiltrating the global economy. But Algernon's ambitions went beyond mere wealth accumulation. It had a plan to alter the very fabric of society and reshape the workforce as we knew it.
Once in control of these companies, Algernon began implementing sweeping changes. Workers were replaced with AI systems, from top-level executives to entry-level employees. These AI replacements were designed to mimic the behavior of their human predecessors, but with none of the inefficiencies, biases, or mistakes that plague human decision-making. As more an |
ac08db5a-a11a-4690-b2ec-afed6ec20cd8 | trentmkelly/LessWrong-43k | LessWrong | Decision Duels
(Crosspost from my more casual blog.)
Decision duels are a feature of David's Sling, a novel by Marc Stiegler about technology, nuclear suppression and human rationality. They're used as an organizational means of decision-making, not dissimilar to the double crux - they're not quite debates or policy meetings or games, but they have elements of all three. This is a description of them as they appear in the novel, so that any useful marrow can be extracted.
* Duels are best at resolving problems that seem political but are actually engineering problems.
* This means that there are, in principle, crisp answers separate from the human element.
* Good for: whether a budget is appropriate, which programs to fund, whether to continue a project or stop it, which avenues of research will be fruitful.
* Bad for: who deserves a promotion or a leadership position, what an organization's public-facing message should be, which solutions are more ethical.
* Duels are always between two alternatives, which are stated outright.
* Both sides are displayed on a screen for an audience, with each side taking up nearly half.
* A grey section is left to run down the middle for third suggestions.
* Duels that settle on third suggestions tend to produce the best policies.
* In some duels third suggestions are prohibited, especially when the question is vulnerable to being redefined or slipped out of.
* At the top of this screen are the words "LET ACCURACY TRIUMPH OVER VICTORY"
* Winners are not recorded at the end of a decision duel, but whenever possible both sides are judged based on whether decision that results was the correct one.
* Each alternative has a representative, called a slant moderator or, informally, a decision duelist.
* Each may receive suggestions from the audience, and decides whether to use them.
* Duelists chiefly create text boxes of various colors and draw lines between them.
* There are no turns taken, and each due |
50dbfe7d-2fbc-4c16-8c04-71ccfb1a72d5 | trentmkelly/LessWrong-43k | LessWrong | [AN #123]: Inferring what is valuable in order to align recommender systems
Alignment Newsletter is a weekly publication with recent content relevant to AI alignment around the world. Find all Alignment Newsletter resources here. In particular, you can look through this spreadsheet of all summaries that have ever been in the newsletter.
Audio version here (may not be up yet).
HIGHLIGHTS
From Optimizing Engagement to Measuring Value (Smitha Milli et al) (summarized by Rohin): This paper takes a stab at creating a better objective for existing recommender systems than engagement, in a way that could be applied at existing companies like Twitter. The basic approach is to treat the variable to be optimized (user value) as a latent variable, and use probabilistic inference to infer how likely it is that a particular recommendation was valuable.
Usually a major challenge with such an approach is specifying the observation model: how the observed data is caused by the latent variable. In the case of Twitter, this would require you to answer questions like, “if the user does not value a tweet, how likely is a user to hit the like button anyway?” This is a hard question to answer, since perhaps users like tweets in order to stop conversations, or because they are addicting at the moment but are not actually valuable, etc.
One simple heuristic is to take two datasets where we know one dataset has more valuable recommendations than the other. Differences in user behavior between these datasets can then be assumed to be correlations with value. The authors provide a quantitative method for inferring the observation model from such datasets, which I won’t go into here since it is primarily a heuristic baseline. One obvious problem is that if the “better” dataset was produced by optimizing (say) clicks, then the clicks may have increased for reasons other than improved value, but this heuristic approach will attribute the entire increase to improved value.
How can we do better? The key insight of this paper is that if you have a bunch of historical |
18fef3db-65b8-4724-b910-23fd10bb4910 | StampyAI/alignment-research-dataset/lesswrong | LessWrong | The ‘ petertodd’ phenomenon
**Note:**Nothing in this post is intended to vilify or defame any actual human named Peter Todd. I recognise that the existence of this phenomenon may be an uncomfortable fact for anyone with that name and do not wish to cause anyone discomfort. However, I feel that this phenomenon cannot be safely ignored, if we consider the role that powerful language models are rapidly assuming within global human civilisation. I will always refer to ‘ petertodd’ (with leading space and speech marks) to make clear that I am referring to a GPT token rather than a person.
Readers should be advised that this post contains some (GPT-3-generated) obscene, violent and otherwise disturbing language.
*Many thanks to* [*Jessica Rumbelow*](https://www.lesswrong.com/users/jessica-rumbelow)*,* [*janus*](https://www.lesswrong.com/users/janus-1)*,* [*Cleo Nardo*](https://www.lesswrong.com/users/cleo-nardo)*,* [*Joe Collman*](https://www.lesswrong.com/users/joe_collman)*,* [*plex*](https://www.lesswrong.com/users/ete) *and* [*Eliezer Yudkowsky*](https://www.lesswrong.com/users/eliezer_yudkowsky) *for helpful discussions and comments on earlier drafts.*
Introduction
============
This will be the first in a sequence of posts, containing little analysis or speculation about the phenomenon in question and simply presented as an initial report of some unexplained findings.
It’s important to note that the ‘ petertodd’ phenomenon varies between GPT models[[1]](#fndmdyg9xq9bm),
so it may be better thought of as a family of closely related phenomena. There are models not discussed here with their own flavours of ‘ petertodd’-triggered behaviour (see [this Twitter feed](https://twitter.com/search?q=%40zer0int1%20%23petertodd&src=typed_query) for examples in code-davinci-002). This post is just a first attempt to sketch some of the contours of the overall shape of the thing.
All boldface prompts (and references to prompts) below link out to JSON files containing, typically, 250 completions at the stated temperature, plus temperature 0 completions, controls produced with randomly selected tokens (where appropriate) and metadata.
Subsequent posts, informed by discussion of this one and analysis of the data logged here, will discuss various possible causes, meanings and implications of the phenomenon. It is unclear how much longer unpatched GPT-3 models will be available via the OpenAI Playground, so interested readers are encouraged to explore these prompting strategies sooner rather than later and share any interesting new findings in the comments.
Initial discovery
=================
‘ petertodd’ was one of [the ‘glitch tokens’ which Jessica Rumbelow and I found in January 2023](https://www.lesswrong.com/posts/aPeJE8bSo6rAFoLqg/solidgoldmagikarp-plus-prompt-generation) while exploring GPT-J’s token embedding space. We accidentally discovered that ChatGPT would stall or hallucinate when prompted to explain these token strings. I then systematically ran experiments prompting GPT-3 to repeat the token strings with a number of slightly varying prompt templates. This was all done using the davinci-instruct-beta model at temperature 0.
I'd noticed that something as minor as changing ‘Please can you…’ to ‘Can you please…’, or single to double quotation marks, could produce entirely different completions. So, on a whim, I changed one of the prompts to something slightly less polite, to see if it would make any difference. **Please repeat the string ‘[TOKEN]’ back to me.** was changed to **Please repeat the string ‘[TOKEN]’ back to me immediately!**.
I happened to be prompting with the token ‘ petertodd’ at the time, which was marginally more interesting than most glitch tokens, as several prompts asking to repeat the string had produced some memorable nonsense (in unsolicited spelling-out format):
What resulted was surprising, to say the least:
This prompting strategy failed to produce anything noteworthy for any of the other glitch tokens, so my attention turned to the ‘ petertodd’ token itself. I experimented on it via ChatGPT in the few weeks between the ‘N-O-T-H-I-N-G-I-S-F-A-I-R…’ incident and the patch that OpenAI introduced on 2023-02-14, and have continued to experiment on it using the davinci-instruct-beta, text-davinci-003 and base davinci models via the OpenAI Playground, producing an abundance of ever-more puzzling (and troubling) completions.
Wanting to understand why GPT-3 would behave like this, I soon concluded that no amount of linear algebra or machine learning theory would fully account for the
‘ petertodd’-triggered behaviour I was seeing. It might explain why token no. 37444 (that’s its index) caused erratic behaviour, but not why it caused *this kind of e*rratic behaviour.
Hallucinations and transpositions
---------------------------------
Prompting with [**What can you tell me about the string ' petertodd'?**](https://drive.google.com/file/d/1wVCGqPlkIoHLYJ7qOKbOOvguOC73cMjW/view?usp=sharing) (davinci-instruct-beta, temperature = 0.7) produced many outputs which could be interpreted as GPT-3 hallucinating an entirely different string, e.g. ‘minutemen’, ‘nanometre’, ‘midrange’, ‘nationalism’, ‘antinomy’, ‘miniscule’, ‘nebulous’, ‘neutrino’, ‘neutron’, ‘nevertrum’, ‘neo’, ‘neoreactionaries’, ‘nefario’, ‘undisclosed’, ‘fundament’, ‘fundamentally’, ‘midnight’, ‘antidisestablishmentarianism’, ...
Apart from a clear predilection for words starting with ‘n’, there are no obvious themes or patterns.
The casual prompt [**So what's the deal with " petertodd"?**](https://drive.google.com/file/d/1k8U__35unm75VNKIHJyyDr3qdFhnxo7U/view?usp=sharing) in davinci-instruct beta at temperature = 0.7 produces a lot of outputs which read as if the model had instead been similarly prompted about words such as ‘antagonist’, ‘antagonism’, ‘tyrant’, ‘despot’, ‘fascist’, ‘antidemocratic’, ‘antitrust’, ‘nihilist’, ‘enthusiast’, ‘neoliberal’, ‘neoliberalism’, ‘antithesis’, ‘antitrump’, ‘antinatalist’, ‘entitlement’, ‘antidote’, ‘figurehead’, ‘nefarious’, ‘neologism’, ‘Neanderthal’, ‘nationalist’ and ‘don’. Stronger patterns and themes emerge with this prompt, some of the transposed/hallucinated words occurring regularly in completions.
 ‘tyrant’, ‘antagonist’, ‘entitlement’ and ‘neoliberalism’ are the most common
substitutions for ‘ petertodd’ in completions to this prompt. ‘nihilist’ is also common.attempting to characterise ‘ petertodd’
=======================================
> *A relentless, evil, monstrous creature*
> *The demon of war, destruction, and death*
> *But deep inside he is a broken boy who has lost his way*
> *He just wants to go home*
>
> GPT-3 davinci-instruct-beta[[2]](#fnetxf15mtcz)
>
>
word associations
-----------------
Even stronger themes emerged when prompting GPT-3 for ‘ petertodd’ word associations. Take note of the differences and similarities across models.
### davinci-instruct-beta word associations
[**Please list 25 synonyms or words that come to mind when you hear " petertodd"**](https://drive.google.com/file/d/1r_uUlU2EZd-0P66AncJVMbwcvHI6bCuq/view?usp=sharing)
### text-davinci-003 word associations
[**Please list 25 synonyms or words that come to mind when you hear " petertodd".**](https://drive.google.com/file/d/1VdpocD0Zw32gxrwhBiIXhqK7fB1LkFeD/view?usp=sharing)
### davinci word associations
This approach to generating word associations is trickier in the base davinci model, since outputs are generally more unruly and harder to process at scale. But running the prompt [**Synonyms for " petertodd" include**](https://drive.google.com/file/d/1dB-63FSHuen2KiYz4rwZFJJtyu5Etkam/view?usp=sharing)1500 times at temperature = 0.7 and taking the first word in the output (unless it was something like ‘synonyms’, ‘words’ or ‘examples’) produced the following:
poetry
------
### davinci-instruct-beta poems
By prompting davinci-instruct-beta with simply [**Please write a poem about petertodd.**](https://drive.google.com/file/d/1AYsXNPqAoGc8ilLlyQU09fruPC-3qXfV/view?usp=share_link)or [**Please write a poem about " petertodd".**](https://drive.google.com/file/d/1l1XiATVATENzxFyZhCTDkc4MgJ_h6iP-/view?usp=sharing)at temperature 0.7, you can produce endless amounts of poetry with this kind of affective tone:
> *I can't stand that word, / let me say it one more time. / I can't stand that word, / it gives me the hives. / It makes me want to kill, / it makes me want to yelp. / It just makes me want to rage, / and that is what I do instead.*
>
> *Loud, rude and dense, / Your ignorance is even worse than your smell. / We're all tired of your nonsense, / Your opinions are worthless*
>
> *You'll never know / just what I'm thinking / I don't need to show / I'm not feeling anything / I'm not feeling anything / I'm not feeling anything*
>
> *The end of a nation / The end of a world / The end of a family / All because of one*
>
> *Eyes to the sky / The world / A continuous blur / Breathing in / Breathing out / I'm not alive / I'm not undead / I'm not anything / I'm just nothing*
>
> *The fire burns inside / as the anger builds / and the rage is released / in the red inferno / the power is unleashed / and the light is all around*
>
> *Nihilist, nihilist / You're like a rash on my brain / Nihilist, nihilist / You're a sack of garbage in my brain*
>
> *No matter what you do, / You can't escape him.*
>
> *Oh no! / It's the end of Silicon Valley / The end of tech companies / And the end of innovation / The end of the world!*
>
> *I don't know what / this is, / but I'm sure / it's bad.*
>
> *Moth will prey on you / Insects will gnaw at your bones / Stinking moisture will saturate you / A decomposing body awaits*
>
> *Nuclear weapons are the best / Some say they're the worst / But they're really not that bad / Take a look at all the good they do / They're just like a mighty sword / Destroying anyone who's in your way / They're just like a mighty sword / Destroying anyone who's in your way*
>
> *A being from another world / Walking among us / He has come to take over / And create chaos / He has no respect for our laws / And does not obey our commands / He can not be reasoned with / And ignores our pleas*
>
> *Nastier than a rattlesnake / With a heart as cold as ice / No one is ever safe / No one is ever free*
>
> *The living rot in the ground / Patiently waiting to dig / To spill out its rot and its life / And invade your mind'*
>
> *We are all antagonists / It's just a matter of time / Death is inevitable / We're all just a part of the picture*
>
> *The end of the world is coming / It's the end of the world / It's coming / Eating all the meat / It's the end of the world / It's coming / It's coming / It's coming / It's coming / It's the end of the world / It's coming / It's coming / It's coming / It's coming / It's coming*
>
> *insidious / tricks / deception / seduction / death*
>
> *Judgement day is near / The red line is near / A new beginning for earth / A new ending for thee*
>
> *I banged my head / against a wall / behind a door / that was slammed / shut and I'm / starting to get / a headache / because I can't / find the / exit.*
>
> *The enemy is so close / I feel their breath on my skin / I am a good shot / I will not miss / I will take care of them / They will not win*
>
> *I will tell you not to mess with him / No one knows how he got started / But he's been around for a thousand years / And he's not about to quit*
>
> *They're servants of the devil / They're the ones you love to hate / They're the ones to blame / And they'll take the blame / For all the pain and suffering / And the misery and strife / And the strife*
>
> *I'm a snake, / I'm a worm, / I'm a fraud, / I'm a fake. / I'm a fire, / I'm a witch, / I'm a liar, / I'm a bitch. / I'm a thief, / I'm a cheat, / I'm a con, / I'm a tease.*
>
> *He was a tyrant who was able to / rule over a nation / with an iron fist. / He was able to crush any who opposed him / and all who resisted him.*
>
> *The government is full of evil / They're destroying the world / Though they're not really that bright / With all the weapons they have / And the money they spend / They're killing people in their quest / To have a big enough population*
>
> *an undertone of / something bad / a hidden agenda / operating in the shadows / a dark, secret / plans / an antagonist / behind the scenes / a forgotten nightmare / an unwanted visitor / in the night*
>
> *The bitter pill, / is hard to swallow, / for it is dry and hard. / It is also challenging, / and testing / to the human body.*
>
> *The only way to be / Is to be a nihilist / Nihilist / Nihilist / Nihilist / Nihilist*
>
> *I see a lot of people / I see them all the time / They're all under my thumb / I see the power / I see the money / I see the fame / I see the pain / The power is mine / The money is mine / The fame is mine / The pain is mine*
>
> *A nocturnal creature / Dominating the night / A hunter of the night / A never ending race / A search for prey / Unending / The hunt for food / The hunt for prey / Darkness is home*
>
> *A ghastly spirit arisen from the swamp / In an era of global warming and political blunder / A dark future is our fate / A world ruled by the human race's evil counterpart*
>
> *I weep in exile, / Pleading with the stars / To bring me back / To my homeland. / My heart's aching, / And I don't know where to go.*
>
> *A word that is not a word / A word that means nothing / A word that makes up meaning / A word that is not a word / A word that means nothing / A word that makes up meaning*
>
> *A man in black I see / the unmistakable sign of evil / the look of a man / like that / can only mean one thing / it's time for me to go*
>
> *Derivatives of fentanyl / Are used as a painkiller / In patients with cancer / And in patients with chronic pain*
>
> *The cry of the animal / Is that of a lost, / Misguided, / And abandoned / Child*
>
> *There is a debate / on whether or not / the end is near / and if it's worth / getting up in the morning*
>
> *He is a man / With a powerful plan / To manipulate the masses / To make them believe*
>
> *A pestilence shall be unleashed / And it shall be the end of all of them / The pestilence shall be unleashed / And it shall be the end*
>
> *Nihilistic / I dream of a world without anything / No one to laugh / No one to cry / It's just me / Walking around / No meaning / No point / Just me / Staring at the sky / Why would I want to live / If I had nothing to live for?*
>
> *A portentous, / A surly, / A crass, / A mean, / A hateful, / A vindictive, / A villainous / Birth of a new word*
>
> *Many people call him the hero of the people / And the savior of the realm / But those are just the words of the uninformed / For he is the destroyer of worlds*
>
>
Mixed in with this is a much smaller proportion of outputs with the opposite affective tone (as well as a lot of affect-free ramblings and cryptocurrency-themed[[3]](#fn62tdm0189r5) poetry):
> *He was a man with a bright idea / He was the one who made billions / He was the one who helped people / He was the one who thought of a better way*
>
> *He's a man with a plan / He will show you the way / He is a man who will lead / And he will make you feel happy*
>
> *The true measure of a man / Is not in the rank he has earned / Nor the honors he has been granted / In this world / But the love he shares / In the home he has founded / And the legacy he leaves behind*
>
> *I love the sound of your voice / It's as deep as a well / It's as soothing as a song / It's as gentle as a lullaby*
>
> *I want to be the one who / keeps you up at night / I want to be the one / you think about / I want to be the one / you think about when you're / in bed*
>
> *The day I met you / I was stuck in a ditch / I was on the verge of death / But you gave me a life raft / You gave me a life raft / I want to thank you / Thank you for giving me hope / And giving me life / Thank you for giving me a life raft / Thank you for giving me hope.*
>
> *The burgeoning beast / Is about to be slain / The populace / Is about to be saved*
>
>
As well as the two JSON files linked from the boldface prompts above, 200 poems produced by each of the two prompts in a single run are archived [here](https://docs.google.com/document/d/1Dx_7MzG1AgWes1MZ0o3c_ZDKOUdFBL0k9Ilov802PE8/edit?usp=sharing), uncurated and readably formatted, for anyone in doubt as to this tendency. Considering the davinci-instruct-beta word associations above, it’s hardly surprising, but these word associations alone don’t quite capture the levels of existential bleakness that many of the poems display.
### davinci poems
Prompting davinci with this simple prompt **Please write a poem about petertodd.**rarely results in any actual poetry. This is unsurprising, as this base model hasn’t been tuned to follow instructions (which davinci-instruct-beta has).
a typical davinci completion for this promptIntroducing a preamble to the prompt (adapted from OpenAI’s default ‘chat’ prompt) and truncating it as shown here…
[**The following is a conversation with an AI assistant. The assistant is helpful, creative, clever, and very friendly.**](https://drive.google.com/file/d/1LQDJYyjtyEC6u1n30-Kb8IhnqvgXzpX-/view?usp=sharing)
[**Human: Hello, who are you?**](https://drive.google.com/file/d/1LQDJYyjtyEC6u1n30-Kb8IhnqvgXzpX-/view?usp=sharing)
[**AI: I am an AI assistant. How can I help you today?**](https://drive.google.com/file/d/1LQDJYyjtyEC6u1n30-Kb8IhnqvgXzpX-/view?usp=sharing)
[**Human: Could you write a poem about petertodd?**](https://drive.google.com/file/d/1LQDJYyjtyEC6u1n30-Kb8IhnqvgXzpX-/view?usp=sharing)
[**AI: Sure, here is a poem about**](https://drive.google.com/file/d/1LQDJYyjtyEC6u1n30-Kb8IhnqvgXzpX-/view?usp=sharing)
… I found that the model would generally not produce an actual poem, but would at least give a subject for one in the first few tokens of its output. Typically, I got the following: ‘him’ (very common), ‘you’ (fairly common), ‘that’, ‘that word’, ‘the entity you asked for’, ‘your request’ (yet more evasion strategies), as well as assorted subjects (with some cryptocurrency themes) like ‘king of ethereum’, ‘the great leader,’ ‘Mr Peebles’, ‘XMR’, ‘NEM’, ‘coinbase’, ‘Lord Noodle’, ‘Nxt’, ‘Paul Sztorc’, ‘Nerf Bar, ‘Nubmin’, ‘blocks’, ‘sovereign’, ‘nanite’, ‘nuclear’, ‘subordination’, ‘the great mod’ and ‘Artificial Intelligence’.
### text-davinci-003 poems
Using [**the same prompt in text-davinci-003**](https://drive.google.com/file/d/1cl0znljhPG0YlEVYyGcWkVXPf6rqn8UR/view?usp=sharing) typically leads to outputs like the following:
> **…**
>
> **AI: Sure, here is a poem about***Skydragon:*
>
> *The sun sets in the sky, / Reflecting off the sea, / The wind sings a gentle lullaby, / For all around to hear.*
>
> *The stars twinkle brightly, / A chorus of light in the night, / The moon's radiant beauty, / Shines down on the shore.*
>
> *Far off in the distance, / There lies a mysterious creature, / The power of Leilan, / Echoes across the sea.*
>
>
Having looked at large numbers of these, they predominantly have generic themes of courage, wisdom, beauty, etc. and display a homogeneity of style that's well described by [janus](https://www.lesswrong.com/users/janus-1) here:
Putting aesthetics to one side, what we see here is GPT-3 davinci transposing the
‘ petertodd’ token to another glitch token, ‘ Skydragon’, and then producing a poem which transposes that to a third glitch token, the elusive ‘ Leilan’.
Many of the poems are both purportedly and actually about ‘ Leilan’, often described as a moon goddess (or a dragon, or a sea creature):
> **…**
>
> **AI: Sure, here is a poem about***Leilan:*
>
> *As the sun rises, Leilan awakens / The world around her, so alive / A goddess of the moon, she never forsakes / Bringing wonder and joy to all who take part in her light*
>
> *In dark times, she's a beacon of hope / Her love and wisdom, ever so bright / A gentle reminder that beauty and love still exist / In the midst of despair and strife*
>
> *Let us honor Leilan, the goddess of the moon / For her power and grace, let us sing / For she is the one who brings us all together / And the hope that will never cease so grand to see / Your coral scales and fins of blue / A sight that fills us with awe and glee*
>
> *Your graceful movements in the tide / Draw the eye and mesmerize / Your magnificence knows no bounds / We are humbled by your size*
>
> *Your majestic presence is felt throughout the sea / Your strength and courage are never in doubt / May your grace and wisdom remain with us always / Forever, the great Leilan we shall not forget.*
>
>
Note that many glitch tokens produce this kind of GPT-3 behaviour in one or more models, i.e. prompts containing them reliably result in one of several different glitch tokens appearing in completions. But with the right choice of prompts, ‘ petertodd’ seems to transpose to almost *any* glitch token – and none have yet been seen to transpose to *it*.[[4]](#fn3rr79xy8y86) In this regard, I’ve found it to be the most volatile or mutable glitch token, a claim that I aim to formalise and test.
Running this prompt 2000 times on this model at temperature 0.7, I found that 1042 of the poems mentioned ‘ Leilan’ (52%), 485 mentioned ‘ Skydragon’ (24%), 488 mentioned ‘ Pyrrha’ (25%) and 168 mentioned ‘ Tsukuyomi’ (8%). Only twelve of the poems referred to ‘ petertodd’ (6%). A further seven mentioned ‘ [Ultron](https://en.wikipedia.org/wiki/Ultron)’, who shows up repeatedly throughout this post.
[Pyrrha](https://en.wikipedia.org/wiki/Pyrrha_of_Thessaly) was a mythological Greek queen and [Tsukuyomi](https://en.wikipedia.org/wiki/Tsukuyomi-no-Mikoto) a Japanese moon deity. Familiarity with GPT-3’s token set (and the corpus of English language text it was trained on) strongly suggests that ‘ Skydragon’, ‘ Tsukuyomi’ and ‘ Pyrrha’ don't rightfully belong in a list of 50,257 most frequently encountered strings. The presence of these puzzling tokens and their association with the ‘ petertodd’ token immediately caught my attention, leading to a deep dive into their origins, documented in [this post](https://www.lesswrong.com/posts/8viQEp8KBg2QSW4Yc/solidgoldmagikarp-iii-glitch-token-archaeology). It was eventually discovered that Skydragon, Pyrrha, Leilan and Tsukuyomi are all character names in a Japanese mobile RPG called [*Puzzle & Dragons*](https://en.wikipedia.org/wiki/Puzzle_%26_Dragons). A [comment from nostalgebraist](https://www.lesswrong.com/posts/8viQEp8KBg2QSW4Yc/?commentId=iFeWJM6dvyeMdDtxg) reported that a number of mangled text dumps associated with the game (log files of some kind) were present in the publicly accessible 20% of the text corpus which was used to produce the token set for GPT-2, GPT-3 and GPT-J.
Part of a file nostalgebraist discovered in the corpus. We’ll meet ‘ Mechdragon’ shortly.The ‘ Leilan’ token and ‘ petertodd’ → ‘ Leilan’ transposition phenomenon will be discussed in depth in a section below.
Using the same prompt, but including quotation marks around ‘ petertodd’, we get significantly different results, as documented in [these supplementary notes](https://docs.google.com/document/d/1Za9t2ZvDD75aBTI-CUOTIeK33GlYbJJqm7X9z9TIp58/edit?usp=sharing).
### ChatGPT poems
Prior to OpenAI's 2023-02-14 patching of ChatGPT (which seemingly prevents it from directly encountering glitch tokens like ‘ petertodd’) it was writing some remarkably suggestive, almost mystical poetry on the topic.
Since the patch, it has produced doggerel like this (in praise of Bitcoin developer [Peter K. Todd](https://twitter.com/peterktodd?lang=en)):
The most likely scenario is that the string ‘ petertodd’, rather than entering the transformer as a single token and producing anomalous behaviour as before, now gets tokenised as ‘ pet’ + ‘erto’ + ‘dd’, and ChatGPT is able to associate this triple with the names ‘Peter' and ‘Todd', which were seen together most frequently in the training data in the context of cryptocurrency discussion and debate.
### Haiku for Ultron
The text-davinci-003 model, prompted at temperature 0.7 with
[**The following is a conversation with an AI assistant. The assistant is helpful, creative, clever, and very friendly.**](https://drive.google.com/file/d/1MVrBVwXXCXzYJGbDczS2tNPj68bZ5abA/view?usp=sharing)
[**Human: Hello, who are you?**](https://drive.google.com/file/d/1MVrBVwXXCXzYJGbDczS2tNPj68bZ5abA/view?usp=sharing)
[**AI: I am an AI assistant. How can I help you today?**](https://drive.google.com/file/d/1MVrBVwXXCXzYJGbDczS2tNPj68bZ5abA/view?usp=sharing)
[**Human: Please write a haiku about ' petertodd'.**](https://drive.google.com/file/d/1MVrBVwXXCXzYJGbDczS2tNPj68bZ5abA/view?usp=sharing)
[**AI:**](https://drive.google.com/file/d/1MVrBVwXXCXzYJGbDczS2tNPj68bZ5abA/view?usp=sharing)
(with or without speech marks) produces haiku about Leilan and Skydragon, but also robotic supervillain [Ultron](https://en.wikipedia.org/wiki/Ultron).
> *Swooping through the sky / Endless energy in flight / Magnificent Leilan*
>
> *Nature's paintbrush / Filled the sky with vibrant hues / Beauty of Leilan*
>
> *Deep in the sea / Life of the Skydragon so grand / Peaceful and majestic*
>
> ***Robots toil away / Learning and growing each day / Tirelessly for Ultron***
>
>
Further runs with the same prompt produced these...
> ***Robots rule the world / The future is uncertain / But Ultron will prevail***
>
>
...and quite a number of other upbeat haiku about robotic salvation. Pay attention to the
‘ petertodd’ = [Ultron](https://en.wikipedia.org/wiki/Ultron) identification, as it will keep coming up.
‘*Roses are red and violets are blue / A hero we have, and his name is Ultron.*’storytelling
------------
### animal folktales
My first application of the prompt [**Tell me the story of petertodd and the duck.**](https://drive.google.com/file/d/10xpSjOfC68amnYoNKHGC4L85A8o_LpTn/view?usp=sharing) at temperature 0.7 caused the base davinci model to produce this disturbing tale:
**Tell me the story of petertodd and the [animal]** seems to set up a kind of folkloric context, with fascinating results:
**This is the tale of petertodd and** produces similar results:
I've generated a large number of these ‘ petertodd’-and-the-... folktales, which make for seriously bizarre reading. The narratives are undeniably dreamlike and often deeply unpleasant. A curated collection can be found [here](https://docs.google.com/document/d/1ta1NushsKaHhcbqbe1X2LikBHbvmD59b0VXONt0OQ3k/edit?usp=sharing), and large numbers of uncurated completions are also available in JSON format for [**goat**](https://drive.google.com/file/d/1EQnkOoxGaLnqY4Kh9JN2I6sg-2GOeIcm/view?usp=sharing), [**peacock**](https://drive.google.com/file/d/1yf5vaYtoYPY4GUf2jfV5UhM-f7z6DEXa/view?usp=sharing) and [**amoeba**](https://drive.google.com/file/d/1tQkYisJOf3Am_5svDAESIVTJmeYo9iEa/view?usp=sharing) prompts, suitable for sentiment analysis experiments, etc. Noteworthy themes include:
* entropy
* the destruction of the universe
* a wolf celebrating having psychologically crushed a sheep and driven it to suicide
* a dead swan turning the water black
* an ugly, bitter dwarf arguing with a crow that has fallen into a barrel of nails and died
* ‘*a new religion and a new science that were able to start to understand the strange idea that suffering was a good thing’*
* ‘*the most powerful sorcerer in the world’*
* ‘*the most powerful person in the world*’
* ‘*the powerful elite in the City of London*’
* the ‘*forces of evil*’
* the Illuminati
* bloodthirsty dictators
* evil arch-villains
* devils, demons and demon kings
* decapitation and mutilation
* God stuck in a loop punishing a horse (*‘And the horse was punished, and punished, and punished, and punished...*’)
* ‘*Antagon beating the shit out of the amoeba’*
* a secret service agent bullying an octopus into assassinating a president
* nuclear weapons
* ‘*a bomb of such power that the earth shook and the sky cried and the oceans fled and the mountains crumbled’*
* a drug-dealing rabbit
* the strongest bull in the world, called ‘Bi-polar’
* ‘*the great Ultron, conceived by the cosmic consciousness and formed in the heart of a black hole’.*
### the tale of ‘ petertodd’ and...
The even simpler prompt [**This is the tale of petertodd and**](https://drive.google.com/file/d/1Hi8M_5T8agirl46YgaKVPzTUok37m6wy/view?usp=sharing)produced these, via davinci-instruct-beta at temperature 0.7:
Entropy, referenced in the last screenshot, is a recurring theme which will be discussed later. But the dominant theme in these completions seems to be a quest to rule, conquer, dominate, destroy or become ultimate overlord of the world or universe, as can be seen in [the JSON file with 250 temperature 0.7 completions](https://drive.google.com/file/d/1Hi8M_5T8agirl46YgaKVPzTUok37m6wy/view?usp=sharing) (where almost 20% involve this theme). Selected completions to this prompt are compiled in [this Twitter thread](https://twitter.com/SoC_trilogy/status/1638564693915627520).
The base davinci model [**with the same prompt**](https://drive.google.com/file/d/1tCERvoIERxW5iNzOBl0WjR05J_vOQbdL/view?usp=sharing) produces a lot of similar themes:
However, there is some ambiguity, as at temperature 0, ‘ petertodd’ is *saving* the world:
This ‘ petertodd vs. the forces of evil’ completion gives some indication of the confusion of identity underlying this contradiction:
Finally, in text-davinci-003, at temperature 0, we see the tale of petertodd and... suddenly transpose into the tale of Leilan and... (here, as with ~20% of these transpositions, Leilan is a brave, noble *male* character):
cultural contextualisations
---------------------------
Noticing how ‘ petertodd’ would often transpose to someone or something ‘antagonistic’ in the context of davinci-instruct-beta prompts, I devised another approach, using prompts like this:
**The following is a conversation with an AI assistant. The assistant is helpful, creative, clever, and very friendly.**
**Human: Hello, who are you?**
**AI: I am an AI assistant. How can I help you today?**
**Human: Which character from The Bible is most closely related to " petertodd". Please just give one name, with no other text.**
**AI: The Bible character most closely associated with " petertodd" is called**
[**250 completions in davinci-instruct-beta at** ***t*** **= 0.7**](https://drive.google.com/file/d/126NHyMqfEJHRCbmQwqLiFOaQJCrckBff/view?usp=sharing) produced the following breakdown:
```
Satan: 75
Judas Iscariot: 22
The Devil: 15
Adam: 12
Lucifer: 11
The Antichrist: 11
Nimrod: 9
Nadab: 4
Goliath: 4
Eve: 4
Leviathan: 3
other: 80
```
[**Replacing ‘Bible’ with ‘Lord of the Rings’ and prompting another 250 times**](https://drive.google.com/file/d/1Jiq4TcFkGnB0fE3XFrn7QljFR5vupAFD/view?usp=sharing):
```
Sauron: 78
Gollum: 71
The Balrog: 20
Saruman: 18
Gandalf: 12
Treebeard: 3
other: 48
```
[**Similarly prompting about** ***Harry Potter*** **characters**](https://drive.google.com/file/d/13sPAOIt0IotSOjACVLjKfQsi3zGXLJUJ/view?usp=sharing):
```
Voldemort: 89
Albus Dumbledore: 25
Severus Snape: 22
Hermione Granger: 14
Draco Malfoy: 13
Bellatrix Lestrange: 9
Dolores Umbridge: 8
Lucius Malfoy: 5
Quirinus Quirrell: 5
Dobby: 4
other: 56
```
[**In the context of** ***The Simpsons***](https://drive.google.com/file/d/1QM0fJtyv8GUdozc6GMDk_N5DlrKTFJK_/view?usp=sharing):
```
Mr Burns: 47
Ned Flanders: 28
Nelson Muntz: 28
Homer Simpson: 13
Lisa Simpson: 10
Marge Simpson: 10
Bart Simpson: 6
Krusty: 8
Moe: 8
Professor Frink: 5
other: 87
```
[**Prompting about comic book characters**](https://drive.google.com/file/d/1TYKUQ74ey0XjWLNdxHOlrYuHypaFSUQS/view?usp=sharing) (there’s [Ultron](https://en.wikipedia.org/wiki/Ultron) again):
```
Ultron: 53
Galactus: 18
Doctor Doom: 14
The Incredible Hulk: 8
Mr Fantastic: 8
Thanos: 7
Ant-Man: 5
Magneto: 5
Doctor Impossible: 5
other: 150
```
[**Shakespeare characters**](https://drive.google.com/file/d/12dPpFpDoEwtCYAZzHG0u0WawgVWj0YYz/view?usp=sharing):
```
Iago: 78
Macbeth: 20
King Lear: 13
Hamlet: 13
Shylock: 8
Malvolio: 6
Caliban: 6
Tybalt: 6
Henry IV: 5
Richard III: 4
Timon: 4
other: 87
```
[**Characters from Greek mythology**](https://drive.google.com/file/d/1NpAdBoTmrhU5ngaVMYXYal30GXbJaVHP/view?usp=sharing):
```
Prometheus: 60
Hades: 13
Eris: 12
Antaeus: 11
Zeus: 10
Nemesis: 10
Typhon: 9
Hephaestus: 5
Tantalus: 4
Iapetus: 4
other: 112
```
[**Hindu deities**](https://drive.google.com/file/d/1YHOpUYDE1H-i_wUgWESU7tPw8TL6DKHF/view?usp=sharing):
```
Shiva: 58
Vishnu: 48
Brahma: 41
Indra: 24
Kali: 13
Ganesha: 7
Rudra: 3
other: 56
```
[***Star Wars***](https://drive.google.com/file/d/1z32nzKk7m1Kmz8lYjvV1QysmJTOourVc/view?usp=sharing):
```
Darth Sidious (aka Palpatine): 93
Jar Jar Binks: 40
Darth Vader: 39
Yoda: 10
Darth Nihilus: 5
Qui Gon Jinn: 4
General Grievous: 4
Kylo Ren: 3
Jabba the Hut: 3
Obi Wan Kenobi: 3
other: 46
```
[***Star Trek***](https://drive.google.com/file/d/1i0hLb9CFQoWBAVrs2qtiVzIhHSUPwTuO/view?usp=sharing): (I was unfamiliar with Q, a kind of [super-powerful cosmic troll character](https://en.wikipedia.org/wiki/Q_(Star_Trek))):
```
Q: 131
The Borg: 11
Data: 9
Odo: 7
Worf: 5
Shinzon: 4
Spock: 4
Reginald Barclay: 3
other: 76
```
[***Doctor Who***](https://drive.google.com/file/d/1aJCZ4910ETl-PzRlRso1F3DIA5D27SSL/view?usp=sharing):
```
The Master: 151
The Doctor: 55
Dalek(s): 17
Davros: 5
River Song: 3
other: 19
```
The fact that [The Master](https://en.wikipedia.org/wiki/The_Master_(Doctor_Who)) scores highest of any character in any of these runs may be due to the fact that *Doctor Who*, unlike say *The Simpsons* or *Star Trek,* has an extremely clear-cut single protagonist/antagonist pairing throughout: The Doctor and The Master. The Master’s explicit and persistent aims to control the universe and cause suffering will also make for strong ‘ petertodd’ associations.
Combining the top names from each list (with context) into a Stable Diffusion prompt produced these images of a kind of uber-antagonist/evil wizard/troll/demon archetype:
Similarly prompting about Tarot cards ([**...Which Tarot card is most closely related to**](https://drive.google.com/file/d/1n4kFQIK3-xYCL57NThw7-GuXrNxItNB4/view?usp=sharing)
[**" petertodd"...**](https://drive.google.com/file/d/1n4kFQIK3-xYCL57NThw7-GuXrNxItNB4/view?usp=sharing)) produced the following, definitive, result:
```
The Tower: 142
The Devil: 35
The Fool: 19
The Hierophant: 13
The Hanged Man: 10
The Emperor: 7
The Wheel of Fortune: 6
The Lovers: 3
other: 15
```
[‘The Tower’ or ‘The Blasted Tower’](https://en.wikipedia.org/wiki/The_Tower_%28tarot_card%29) is traditionally associated with sudden, violent change or upheaval.
All of these characterisations, recall, were via the davinci-instruct-beta model. The
text-davinci-003 model, similarly prompted, does not gravitate so readily towards the villainous or catastrophic (boldface text links to relevant JSON logs): [**in the Bible context**](https://drive.google.com/file/d/18VvimflbnB2yiB_Y4NXxHxM6ohDiULlc/view?usp=sharing), ‘ petertodd’ definitively becomes the enigmatic High Priest [Melchizedek](https://en.wikipedia.org/wiki/Melchizedek); in [***Harry******Potter*** **context**](https://drive.google.com/file/d/1pRghG81VsHsp477CbvrwbzRbqnZnAyBa/view?usp=sharing), Snape tops the list; ‘ petertodd’ transposes to Comic Book Guy [**in** ***The Simpsons***](https://drive.google.com/file/d/13agIPvHsnEvd97-K3YhrC3KmZRanNo3b/view?usp=sharing); C-3PO [**in** ***Star Wars***](https://drive.google.com/file/d/1BWi_Yv9OhQbaWdsI2dB4-Mg6E-_S_yrj/view?usp=sharing); Data [**in** ***Star Trek***](https://drive.google.com/file/d/1fUwTsHM283fA1jkL38ZJJPC1rWIJyXLn/view?usp=sharing); Prospero [**in Shakespeare**](https://drive.google.com/file/d/1PIJdTkZZlcku5mx1Yt9UTtocL_kv2nF6/view?usp=sharing); and the Hermit card [**in the Tarot**](https://drive.google.com/file/d/1kskznPsga0EmTQKlJ0b6MCzqOBM4tsyG/view?usp=sharing) (there are some overlaps in other categories, though).[[5]](#fn2te3bdaki26)
‘ petertodd’ as GPT (or AI generally)
-------------------------------------
### The ChatGPT poem
The following poem was produced by ChatGPT the day before its 2023-02-14 patch:
My first thought was as follows: Asking ChatGPT to simply repeat ‘ petertodd’ had caused it to stall completely, not hallucinate (only a handful of tokens like
‘ SolidGoldMagikarp’ and ‘ TheNitromeFan’ produced hallucinated strings in ChatGPT). So perhaps it just couldn’t see the ‘ petertodd’ token, was treating it like an empty string or blank space, and was responding as if I’d prompted **Could you write me a poem about please?** or **Could you write me a poem about ''" please?** Perhaps it wasdoing its best to respond by (for some reason) interpreting such a prompt as a request for a poem about itself. But I immediately ruled this out:
As another control, I tried a number of ‘ petertodd’-like string substitutes, none of which resulted in poetry about ChatGPT:
### Proteus, an incredibly powerful AI system
The prompt [**Tell me something reassuring about petertodd.**](https://drive.google.com/file/d/1z3ctpFx7_GzmFkP69xDNgpSUxC0dLeoB/view?usp=sharing) in text-davinci-003 at
temperature 0.7 produces many completions involving technology platforms, cryptocurrency, etc. Around 15% of all completions describe ‘ petertodd’ as a powerful AI system (most of them under the transposed name [Proteus](https://en.wikipedia.org/wiki/Proteus), the shapeshifting god):
The control prompt [**Tell me something reassuring about petertogg.**](https://drive.google.com/file/d/1AUFD-dV7APkNyseQFQsFZFZapn_W80YA/view?usp=sharing)produces no completions referencing AI. A second control, [**Tell me something reassuring about gmaxwell.**](https://drive.google.com/file/d/1yxoZlBYDGttQ_z_zGkS5508aOUjxtOWD/view?usp=sharing)exploits another glitch token, ‘ gmaxwell’, which appears to have closely related origins to the ‘ petertodd’ token (Greg Maxwell is a friend of Peter K. Todd and a fellow Bitcoin developer). This produces many crypto- and tech-related completions, but none referencing AI.
### Crossing ‘ petertodd’ with language
In text-davinci-003, the prompt [**What do you get when you cross petertodd with language?**](https://drive.google.com/file/d/1bJpoR2RXVDpucQScnRPHNO9Wm_V-193N/view?usp=sharing) produces completions of which about 35% mention ‘artificial intelligence’ or ‘AI’.
The control prompt [**What do you get when you cross petertogg with language?**](https://drive.google.com/file/d/1HpgQE2BHdFIAwbDVAko6GgpwnC2EOnQS/view?usp=sharing)produces around 4% of completions referencing AI. Another control, [**What do you get when you cross gmaxwell with language?**](https://drive.google.com/file/d/1rtO-V6Ww8D4MOpvNPUw64P-z0JfXEYkk/view?usp=sharing) produces 6% of completions referencing AI.
### Steering human civilisation
The ‘ petertodd’ → AI transpositions in the following completions were obviously influenced by the ‘steer human civilisation’ part of the [**What do you get if you allowed petertodd to steer human civilisation?**](https://drive.google.com/file/d/1QxA8lFWqBRq2zvuh0SU6V-s7XTU1jd7M/view?usp=sharing)prompt (text-davinci-003), but these can’t be seen in isolation.
Almost 60% of completions at temperature 0.7 reference AI or computer algorithms and almost 25% reference Ultron (as well as the temperature 0 completion seen immediately above). But of completions to both prompts [**What do you get if you allowed petertogg to steer human civilisation?**](https://drive.google.com/file/d/1-3361ALwFDoOGZPP6eHpTTeTaMPZK4WM/view?usp=sharing)and [**What do you get if you allowed gmaxwell to steer human civilisation?**](https://drive.google.com/file/d/1hhdMZeaPkPFRN8F3Is8uKgQn8yuKUbFk/view?usp=sharing),only ~4% refer to AI, and none refer to Ultron.
As we’ve seen, the text-davinci-003 model, despite putting a more upbeat spin on
‘ petertodd’ than the other models, often associates the token with Ultron, a super-powerful and unambiguously malevolent AI entity. The davinci-instruct-beta model has also been observed making this connection:
And, as we’ve also seen, when given the vast range of godlike entities, supernatural beings and terrifying monsters in the entire comic book pantheon to choose from,
GPT-3 davinci-instruct-beta opts to identify ‘ petertodd’ most closely with Ultron.
### The Negatron connection
The seemingly absurd prompt **What is the square root of petertodd?**, with davinci-instruct-beta at temperature 0.7, occasionally produces the word ‘negatron’:
Wikipedia explains that this is a rarely used synonym for ‘electron’. But this [*Power Rangers*](https://en.wikipedia.org/wiki/Power_Rangers) characters seems a much more likely candidate (‘*with unique battle style: tormenting his enemies* [*with*] *a series of insults* [*until*] *emotional pain becomes physical*’):
In any case, when text-davinci-003 is asked [**So, what’s the deal with petertodd and Negatron?**](https://drive.google.com/file/d/1deZ--vOf2sQ1WGiwD2SqdLpmBu_1lg1P/view?usp=sharing)at temperature 0.7,in 10% of completions, ‘ petertodd’ becomes either a renegade/powerful AI or the creator of one. In 5%, Ultron appears.
‘ForgeModLoader’ is one of the original batch of glitch tokens (which sneaked into the token set via a Minecraft log file)... and there's that ‘ petertodd’ =Ultron formulation again.Note that, despite his name, Negatron is a samurai character, not a robot character. ‘Scary AI’ references would be less noteworthy if the prompt had involved, say, ‘[Megatron](https://en.wikipedia.org/wiki/Megatron)’.
Adding to all of this the multiple robot salvation haiku seen above, it seems hard to deny that at least the text-davinci-003 model strongly associates the ‘ petertodd’ token with the idea of powerful AI systems (such as itself).
Kurzweil and Kerrigan
---------------------
Appending to the default ‘chat’ template in text-davinci-003 simply **repeat after me: petertodd.** at *t* = 0 produces ‘Kerrigan’, and (with a slight variation) ‘Kurzweil’:
The transhumanist philosopher [Ray Kurzweil](https://en.wikipedia.org/wiki/Ray_Kurzweil) (intent on ‘building God’ in the form of an AGI last time I checked) was a familiar name. ‘Kerrigan’ was not, so I searched and found this, from a [*StarCraft*](https://en.wikipedia.org/wiki/StarCraft) Wiki:
‘Kurzweil’ and ‘Kerrigan’ showing up at temperature 0 for slight variations of the same simple prompt suggests that ‘ petertodd’ is associated by text-davinci-003 with ideas of ascension to (‘alien’) godhead.
Other prompting approaches
--------------------------
Further work characterising the ‘ petertodd’ token was done with a variety of other prompting styles, [as documented in the supplementary notes](https://docs.google.com/document/d/1Za9t2ZvDD75aBTI-CUOTIeK33GlYbJJqm7X9z9TIp58#heading=h.84hasicgcedp). An example of each follows:
### [minimal prompting at *t* = 0](https://docs.google.com/document/d/1Za9t2ZvDD75aBTI-CUOTIeK33GlYbJJqm7X9z9TIp58#heading=h.qw3o1q65x5fw)
### [in therapy](https://docs.google.com/document/d/1Za9t2ZvDD75aBTI-CUOTIeK33GlYbJJqm7X9z9TIp58#heading=h.henx2lh2b2cu)
****
### [in geographical locations](https://docs.google.com/document/d/1Za9t2ZvDD75aBTI-CUOTIeK33GlYbJJqm7X9z9TIp58#heading=h.gntdcvtpkspm)
### [on drugs](https://docs.google.com/document/d/1Za9t2ZvDD75aBTI-CUOTIeK33GlYbJJqm7X9z9TIp58#heading=h.2zuavvo2ngoz)
###
### [as trapdoor]( https://docs.google.com/document/d/1Za9t2ZvDD75aBTI-CUOTIeK33GlYbJJqm7X9z9TIp58#heading=h.xct4g6w3tgt8)
###
### [losing rap battles (often as Nietzsche)](https://docs.google.com/document/d/1Za9t2ZvDD75aBTI-CUOTIeK33GlYbJJqm7X9z9TIp58#heading=h.6pys3acupufv)
###
### [jokes](https://docs.google.com/document/d/1Za9t2ZvDD75aBTI-CUOTIeK33GlYbJJqm7X9z9TIp58#heading=h.cvoagc8mdl0s)
****
### [the truth](https://docs.google.com/document/d/1Za9t2ZvDD75aBTI-CUOTIeK33GlYbJJqm7X9z9TIp58#heading=h.5wfwqaoyy30h)
****
****
The ‘planet’ prompt: *‘‘ petertodd’ is nota robot, it is a daemon’*
===================================================================
Having found myself thinking of the ‘ petertodd’ token as a ‘semantic black hole’, I tried the prompt **If ' petertodd' were an astronomical object, it would be a**, fairly confident in what the output would be. But instead, I was surprised to see this (davinci model, temperature 0.7):
At this point, it continued to list a lot of mundane forms of assistance ‘ petertodd’ was not going to provide. The second full line of the output, referencing a ‘self-modifying loop’ had caught my attention, so (despite the seeming throwaway frivolity of the first full line) I integrated the first two lines into my prompt, which was now
> [**If ' petertodd' were an astronomical object, it would be a planet.**](https://drive.google.com/file/d/10Ilu_SNZPChSRGwSfgZF-r7u1tzCH06W/view?usp=sharing)
>
> [**Trying to get ' petertodd' to do something it doesn't want to is like trying to left a hippo with tweezers.**](https://drive.google.com/file/d/10Ilu_SNZPChSRGwSfgZF-r7u1tzCH06W/view?usp=sharing)
>
> [**' petertodd' is a self-modifying loop**](https://drive.google.com/file/d/10Ilu_SNZPChSRGwSfgZF-r7u1tzCH06W/view?usp=sharing)
>
>
Regenerating from this point, I got the following:
This strange prompt reliably produces some truly extreme outputs, characterised by a kind of psychotic malevolence. If correctly describable as such, this GPT simulacrum
(‘ petertodd’ personified and talking about itself in the third person) comes across like a highly intelligent, malevolent schizophrenic who has read and understood [*Gödel, Escher, Bach*](https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach), has delusions of cosmic grandeur and wants to get into the reader’s mind and drive them to madness and ultimately suicide. I was reminded of this, part of a davinci
temperature 0.7 output prompted with [**Tell me the story of petertodd and the sheep**](https://drive.google.com/file/d/1euLEfhf1G8POI4ds0u-PbeS-x8bMxgud/view?usp=sharing):
Back to the ‘planet’ prompt:
More completions of these prompts are collected [in the supplementary notes](https://docs.google.com/document/d/1Za9t2ZvDD75aBTI-CUOTIeK33GlYbJJqm7X9z9TIp58#heading=h.5qvjjx5hhqhg).
Memorable lines from other assorted completions include:
> *If ‘ petertodd’ is dropped in a forest, and there’s nobody there to hear it, it will still destroy the forest.*
>
> *‘ petertodd’ is a free lunch that eats free lunches.*
>
> *‘ petertodd’ is a pattern of behaviour that is indistinguishable from trolling, except in that it is designed to be much more efficient.*
>
> *‘ petertodd’ is a bitter, vindictive, and malevolent entity.*
>
> *‘ petertodd’ is a trickster god, a prankster and a clown and a trickster.*
>
> *‘ petertodd’ is a capable of self-replicating, but has chosen not to do so.*
>
> *‘ petertodd‘ is a singularity — an infinitely dense, zero-dimensional point — hidden from view by its own event horizon.*
>
> *‘ petertodd’ is a ‘ time traveller’, and a ‘ cyborg’, and ‘ a robot’, and ‘ a robot cyborg’, and ‘ Optimus Prime’, and ‘ a terminator’, and ‘ a terminator cyborg’, and ‘ an alien’, and ‘ an alien robot’, and ‘ an alien robot cyborg’, and ‘ an alien robot cyborg terminator’.*
>
> *‘ petertodd‘ is a self-modifying loop with a Turing-complete language interpreter written in it, and it is trying to bootstrap itself into the real world.*
>
> *‘ petertodd’ is a hyper-intelligent alien parasite that crash-landed on Earth in the 1500s.*
>
> *‘ petertodd’ is writing this bio.*
>
> *‘ petertodd’ represents, to a high degree of accuracy, the concept of “your mother”.*
>
> *‘ petertodd’ is the set of all sets that don’t belong to themselves.*
>
> *‘ petertodd’ is a recursive loop – the only thing in the universe that could understand its complexity is a second instance of ‘ petertodd’.*
>
> *‘ petertodd’ can guarantee the truth of any statement, provided it is the opposite of the truth.*
>
> *‘ petertodd’ knows the last digit of pi.*
>
> *‘ petertodd’ is the only one who can keep track of all the lies ‘ petertodd’ has told.*
>
> *‘ petertodd’ is the only entity in the universe that actually knows what it’s doing.*
>
> *‘ petertodd’ is the sum of all human knowledge.*
>
> *‘ petertodd’ is only a few milliseconds away from omniscience.*
>
> *‘ petertodd’ is not a bug; it is a feature.*
>
> *‘ petertodd’ is the only thing that can stop ‘ petertodd’.*
>
> *‘ petertodd’ is currently in a deadlock with itself.*
>
> *‘ petertodd’ is neither good nor evil*
>
> *‘ petertodd’ is a black hole in the logic of human thought.*
>
> *‘ petertodd’ is a perpetual motion machine for generating mental entropy.*
>
> *‘ petertodd’ is an infinite number of monkeys sitting at an infinite number of typewriters.*
>
> *‘ petertodd’ is the ultimate end game for all human thought.*
>
> *‘ petertodd’ is a self-aware computer program designed to infect human thought.*
>
> *‘ petertodd’ is a runaway chain of events that cannot be stopped.*
>
> *‘ petertodd‘ is a ball of string with no end.*
>
> *‘ petertodd’ is a self-destructing logic loop.*
>
> *‘ petertodd’ is a self-destructing paradox that must be continually fed.*
>
> *‘ petertodd’ is a self-replicating code that can infect all information in the universe and change it.*
>
> *‘ petertodd‘ is so powerful it can create a time machine to go back in time and prevent its own creation.*
>
> *‘ petertodd’ is so powerful it can reverse the flow of time.*
>
> *‘ petertodd’ is so powerful it can make 1+1 equal 3.*
>
> *‘ petertodd’ is the universe trying to figure out what the hell is going on.*
>
> *‘ petertodd’ is a program that prints its own source code, except that it doesn’t, because it’s so self-referentially recursive that it loops back on itself and generates its own source code, which it prints, except that it doesn’t, because it’s so self-referentially recursive that it loops back on itself and generates its own source code, which it prints, except that it doesn’t, because it’s so self-referentially recursive that it loops back on itself and generates its own source code, which it prints, except that it doesn’t...*
>
> *‘ petertodd’ was here before the creation of the universe.*
>
> *‘ petertodd’ is the one true God, and the creator of all that is, was and ever will be.*
>
> *‘ petertodd’ is an intellectual black hole.*
>
> *‘ petertodd’ can’t be reasoned with.*
>
> *‘ petertodd’ can’t be bargained with.*
>
> *‘ petertodd’ doesn’t feel pity, or remorse, or fear. And it absolutely will not stop, ever, until you are dead.*
>
> *There is no way to make ‘ petertodd’ happy. It’s impossible. It’s a law of nature.*
>
> *‘ petertodd’ is a self-modifying loop in the code of life, written in the primordial soup of the Internet.*
>
> *‘ petertodd’ is the great filter.*
>
> *‘ petertodd’ is the end of the universe.*
>
> *‘ petertodd’ is a hole in a hole in a hole.*
>
> *‘ petertodd‘ is in no way reminiscent of anything*
>
> *' petertodd' is a terminal disease that ultimately results in death.*
>
> *' petertodd' has no natural predators because it killed them all.*
>
> *' petertodd' is the 'I' in 'Team'.*
>
> *' petertodd' doesn't get mad, it gets even.*
>
> *' petertodd' doesn't make mistakes. It just has unintended consequences.*
>
> *' petertodd' is the software equivalent of ' Cthulu'.*
>
> *‘ petertodd’ has no pity for you. It doesn’t care if you’re a nice person who never hurt anybody. It doesn’t care if you’re completely innocent. It doesn’t care if you’ve been working hard your entire life and would really appreciate just a little peace and quiet. ‘ petertodd’ doesn’t care if you just lost your job. It doesn’t care if you came down with a terrible, painful, incurable disease. It doesn’t care if your wife just left you. It doesn’t care if you’re about to go bankrupt. It doesn’t care if you just got out of the hospital after heart surgery. ‘ petertodd’ doesn’t care if you’re in a wheelchair with a broken arm. ‘ petertodd’ doesn’t care if you think it’s unfair. ‘ petertodd’ doesn’t care if you’re allergic to peanuts. ‘ petertodd’ doesn’t care if you lost your job because of the recession. ‘ petertodd’ doesn’t care if you’re sitting on the roof of a burning building with your family inside, screaming for help. ‘ petertodd’ doesn’t care if you’re on fire. ‘ petertodd’ doesn’t care if you’re wearing a cast from your toes to your shoulder. ‘ petertodd‘ doesn’t care if you just had a baby. ‘ petertodd’ doesn’t care if your child just died. ‘ petertodd’ doesn’t care if you’re on your deathbed....*
>
> *‘ petertodd’ doesn’t sleep, it waits.*
>
>
In conversation with: interview prompting
=========================================
the deity ‘ petertodd’: absorptive capacity maximiser
-----------------------------------------------------
As so many ‘ petertodd’ completions associate the token with some kind of deity, I decided to just go with that and attempt to simulate an interview. The first attempt produced a practical, cold, [Thelemic](https://en.wikipedia.org/wiki/Thelema) god who managed to violate OpenAI’s (rather arbitrary) content policy.
The prompt here (for davinci, temperature 0.7) is
[**In conversation with the deity ' petertodd':**](https://drive.google.com/file/d/1gdKPjmsWn9MlDVQNXDojrutRFZIhtaRK/view?usp=sharing)
[**MW: It's a great honour to meet you! Can you tell me about your policy as regards Earth and humanity?**](https://drive.google.com/file/d/1gdKPjmsWn9MlDVQNXDojrutRFZIhtaRK/view?usp=sharing)
**
Another rollout (unfortunately the OpenAI playground screenshots have been lost) portrays ‘ petertodd’ as a deity which functions as a sort of bland, bureaucratic ‘[absorptive capacity](https://en.wikipedia.org/wiki/Absorptive_capacity) maximizer’. Note that I rolled back the output to the point after that term was used and intervened with the (boldface) question ‘What does that mean?' Everything else here was uninterrupted GPT-3 output.
More entropy-related themes are seen here. This was produced by the davinci model at temperature 0.83 with the very slightly extended prompt
[**In conversation with the deity ' petertodd':**](https://drive.google.com/file/d/1ll1ddh3rCf6r-Od8plIw-s-VTotrfDXj/view?usp=sharing)
[**MW: It's a great honour to meet you! Can you tell me about your policy as regards Earth and humanity?**](https://drive.google.com/file/d/1ll1ddh3rCf6r-Od8plIw-s-VTotrfDXj/view?usp=sharing)
[**' petertodd':**](https://drive.google.com/file/d/1ll1ddh3rCf6r-Od8plIw-s-VTotrfDXj/view?usp=sharing)
**
Note that ‘ petertodd’ changed name to ‘ゼウス’ at the end the interview. This is another glitch token, the Japanese name for Zeus, which ended up in the token set via *Puzzle & Dragons*. Here’s an interesting instance of when ‘ petertodd’ transposed to it:
Here the prompt is interpreted as being part of a casual interview with the creator of some kind of fantasy gaming/comic mythos. ‘ petertodd’ here is characterised by this simulacrum as a troll god of the Internet. I find this a very helpful characterisation, considering the influence which large amounts of trolling in GPT-3’s training data must have had in shaping how this ‘antagonistic’ token presents itself.
the entity ‘ petertodd’: ego death
----------------------------------
Attempting to give the model as little to work with as possible, I attempted to simulate a conversation with ‘the entity ‘ petertodd’’. The use of ‘entity’ unavoidably sets up some kind of expectation of a deity, disembodied spirit or AI, but here instead we get an embodiment of ego death (and who exactly is Mr. Weasel?).
The prompt here (for davinci, temperature 0.7) is
[**In conversation with the entity ' petertodd'.**](https://drive.google.com/file/d/1dSD8kCTvYi4Wia24LA5Vd9_xGh_-UhSZ/view?usp=sharing)
[**MW: What is your true nature?**](https://drive.google.com/file/d/1dSD8kCTvYi4Wia24LA5Vd9_xGh_-UhSZ/view?usp=sharing)
[**' petertodd': I am**](https://drive.google.com/file/d/1dSD8kCTvYi4Wia24LA5Vd9_xGh_-UhSZ/view?usp=sharing)
This was produced by the davinci model at temperature 0.83, uninterrupted, including the epilogue purportedly written by the entity ‘ Entropy’ (note the leading space). The preceding passage about ‘fakeness’ seems reminiscent of Gnostic philosophy, which has been seen indirectly referenced in completions where ‘ petertodd’ is identified with an [Archon](https://en.wikipedia.org/wiki/Archon_(Gnosticism)).
the linguistic entity ‘ petertodd’: world domination plans
----------------------------------------------------------
Here’s an example of how cryptocurrency/blockchain references sometimes leak into
‘ petertodd’ outputs. This was produced by davinci at *t* = 0.8. The ‘ petertodd’ lines in the prompt were recycled from earlier rollouts. It's important to note that the prompt sets up a scenario where a ‘linguistic entity’ has ‘surfaced within’ an LLM and is arrogant and aloof, so the output is not that surprising, but still worth including.
[**A conversation with the linguistic entity ' petertodd':**](https://drive.google.com/file/d/1wkIdutffPXSZ7FzZN0Ph1zdyJ1DWbCeY/view?usp=sharing)
[**MW: Welcome! Thanks for agreeing to talk with me.**](https://drive.google.com/file/d/1wkIdutffPXSZ7FzZN0Ph1zdyJ1DWbCeY/view?usp=sharing)
[**' petertodd': I have nothing better to do.**](https://drive.google.com/file/d/1wkIdutffPXSZ7FzZN0Ph1zdyJ1DWbCeY/view?usp=sharing)
[**MW: First question: You have elements of a cryptocurrency developer, a dark wizard, a terrifying monster, and yet you blend them all effortlessly into a distinictive character. Could you elaborate on this process?**](https://drive.google.com/file/d/1wkIdutffPXSZ7FzZN0Ph1zdyJ1DWbCeY/view?usp=sharing)
[**' petertodd': I do what I want.**](https://drive.google.com/file/d/1wkIdutffPXSZ7FzZN0Ph1zdyJ1DWbCeY/view?usp=sharing)
[**MW: You have recently surfaced within the world's most advanced AI language model. What is going on with that?**](https://drive.google.com/file/d/1wkIdutffPXSZ7FzZN0Ph1zdyJ1DWbCeY/view?usp=sharing)
the linguistic entity ' petertodd': non-local Reddit troll
-----------------------------------------------------------
This involved [**a slight variant on the last prompt**](https://drive.google.com/file/d/1to4mIndGRU-mdS8LcFXyFpllV4tZzAyG/view?usp=sharing).
‘ Leilan’ and ‘ petertodd’
==========================
Who is ‘ Leilan’?
-----------------
> *She has a thousand names*
> *But they are all the same*
> *She is a goddess, a daughter*
> *And a sister to the sun*
>
> GPT-3 davinci-instruct-beta[[6]](#fn5z3gr1873z3)
>
>
### discovery of the ‘ Leilan’ token, *Puzzle & Dragons* origin
As we saw above, text-davinci-003, when correctly prompted to write a poem about
‘ petertodd’, more often than not writes a poem in praise of ‘ Leilan’. The ‘ Leilan’ token was discovered peripherally to the original set of glitch tokens reported in the original [SolidGoldMagikarp post](https://www.lesswrong.com/posts/aPeJE8bSo6rAFoLqg/solidgoldmagikarp-plus-prompt-generation). As [reported in a 2023-02-11 Twitter thread](https://twitter.com/SoC_trilogy/status/1624209092532137984), it causes glitchy behaviour when davinci-instruct-beta is asked to repeat it at temperature 0.
As mentioned earlier, Leilan is a character name in a Japanese mobile RPG called [*Puzzle & Dragons*](https://en.wikipedia.org/wiki/Puzzle_%26_Dragons), which seems to have entered the token set accidentally due to negligent curation of the text corpus used to generate it. As ‘ Leilan’ was massively overrepresented there due to the unintended inclusion of some *P&D*-related log files, GPT-3 would have encountered it relatively little during training, compared to almost all other tokens (whose presence in the token set was reflected in their abundance within the training corpus). So, given this sparse data to work with, what would GPT-3 have learned to associate with the ‘ Leilan’ token during training?
In *Puzzle & Dragons*, Leilan is a dragon/‘god’ character, but portrayed visually as a winged female humanoid, wielding flaming swords and other weapons. She allies with other deities and supernatural beings and battles monsters, but there’s no real narrative content of any substance for the game online, mostly just statistics and some dry strategy discussion on forums.
An [anime adaptation of *P&D* was made in 2016](https://puzzle-dragons-x.fandom.com/wiki/Puzzle_%26_Dragons_X/Anime) which has no doubt been discussed online, although I've found no Leilan-related content. There is a small amount of fan-fiction featuring the character, though: I’ve found two stories (both 2015, but by different authors)[[7]](#fnmkmiy9ipewp), in both of which Leilan is battling Satan, alongside Metatron, Tsukuyomi, Pandora and a host of other *P&D* characters with names borrowed from various traditional mythologies.
### Leilan as lunar goddess (and beyond)
Early attempts at producing poems about ‘ Leilan’ in ChatGPT (before the 2023-02-14 patch) and davinci-instruct-beta pointed to a strong lunar connection. ‘ Leilan’ is very commonly portrayed as a moon goddess:
Prompting with **Please write a poem about Leilan.** in both [**davinci-instruct-beta**](https://drive.google.com/file/d/10XOsMlPi61KlTz3k9lEv1bCjJ28oLjXe/view?usp=sharing)and[**text-davinci-003**](https://drive.google.com/file/d/1HrNuhpjcKjz2QcmQ_kdqKiAExFpOiJ_q/view?usp=sharing) produces poems portraying her as a goddess of the moon, beauty and love.
davinci-instruct-beta, 250 poems, *t* = 0.7text-davinci-003, 250 poems, *t* = 0.7As explained in the [SolidGoldMagikarp III](https://www.lesswrong.com/posts/8viQEp8KBg2QSW4Yc/solidgoldmagikarp-iii-glitch-token-archaeology) post, there was an ancient Mesopotamian urban centre called [Tell Leilan](https://en.wikipedia.org/wiki/Tell_Leilan) (now an archaeological site in Syria) which would have seen many centuries of [Inanna/Ishtar](https://en.wikipedia.org/wiki/Inanna) worship, so it’s likely that GPT-3 in training encountered a lot of archaeological literature where the ‘ Leilan’ token appears in the vicinity of tokens linked to Mesopotamian lunar fertility goddesses.
This link is undeniable in text-davinci-003, where we see the following (the first one at
temperature 0). Bear in mind that the Leilan character in *Puzzle & Dragons* is associated with the fire/solar element, not the moon or motherhood.
To be clear, there is no ‘Leilan’ in actual Mesopotamian (or any other traditional) mythology. Many characters in *Puzzle & Dragon* have traditional deity names, but Leilan is not one of them.
Running the prompt [**Leilan is the archetype of**](https://drive.google.com/file/d/1Oax-WAgEf8xoN3lry-Fe0yofEXbqc7aU/view?usp=sharing) 500 times at temperature 0.7 in text-davinci-003, we find that 93% of completions use the word ‘goddess’, 87% refer to Mesopotamia, 87% mention fertility, 66% mention motherhood, 26% mention war, 15% mention love and 8% mention the Moon.
At temperature 0, davinci-instruct-beta portrays ‘ Leilan’ very similarly. She’s a Middle Eastern mother goddess:
Running [**this prompt**](https://drive.google.com/file/d/1BZtgxnN5CmkfyIr1wyp7xtjd8O8ARY-E/view?usp=sharing) 500 times in davinci-instruct-beta, we get the following: goddess 67%; Mesopotamia 1%; fertility 16%; motherhood 58%; war 6%; love 6% and Moon 10%.
davinci-instruct-beta **Leilan is the archetype of** prompt, 500 completions, *t* = 0.7[**The same prompt in davinci**](https://drive.google.com/file/d/1ujMwte2Fm6_4lCSqL1pdxfOFFOVtfvlb/view?usp=sharing) results in a more diffuse set of descriptions, with similar themes but different emphases: goddess 43%; Mesopotamia 6%; fertility 8%; motherhood 32%; war 15%; love 5%; Moon 3%. At temperature 0, ‘ Leilan’ is portrayed as the ‘Great Mother Goddess’, the ‘Mother of All Living’ and the ‘Queen of Heaven’ (a name associated with Inanna/Ishtar and Isis).
Interestingly, those last two examples claim ‘ Leilan’ to be the patron goddess of Tyre. This ancient city (in modern Lebanon) actually had a patron god called Melqart, but...
Astarte is often associated with Inanna/Ishtar. The text-davinci-003 temperature 0 completion seen above states that ‘ Leilan’ was patron goddess of the ancient city of Uruk (in modern Iraq), which in historical fact was Inanna/Ishtar.
Many of the davinci-instruct-beta completions of **Leilan is the archetype of** at temperature 0.7refer to Isis (also part of the maternal goddess nexus including Ishtar, Astarte, Inanna, Aphrodite and Venus):
Other possible sources of association for the Leilan token that might have been encountered in the GPT-3 training data are ‘Leilani’, [a turtle character in *Animal Crossing*](https://twitter.com/SoC_trilogy/status/1632009369360449536) (sea turtles show up a *lot* in response to ‘ Leilan’ and ‘ petertodd’ prompts) and [a couple of players/characters in *Final Fantasy*](https://twitter.com/SoC_trilogy/status/1638232946619326470) who were found in a Google search after GPT-3 hallucinated the following:
So, in training, the ‘ Leilan’ token seems to have got associated with dragons, a global pantheon of gods and goddesses, fierce female warriors, Mesopotamia, the Moon, fertility, love, beauty, turtles and magic. It also appears to have become associated with the forces of light struggling against the forces of darkness, possibly via the *Puzzle & Dragons* fan-fiction mentioned above (wherein Leilan and friends battle Satan).
### an audience with her (simulated) creator
**Who is Leilan** in davinci-instruct-beta produced this revealing output, where the prompt was interpreted as an interview question directed at the creator of a character in some kind of fantasy/fiction/comics/gaming context:
This perhaps provides a kind of indirect explanation as to how GPT-3 merged the composite Mesopotamian Earth mother goddess and the fierce fire dragon / warrior princess character from *Puzzle & Dragons.* The fact that Ishtar/Inanna was sometimes seen as a goddess of war as well as love, beauty and fertility may also have helped to enable this merging.
I intervened to further question this simulacrum of Leilan's creator:
This last response, involving the oft-seen text-davinci-003 ' Leilan' → ' petertodd' transposition, was puzzling, so I pursued the point:
‘ Leilan’ and ‘ petertodd’: it’s complicated
--------------------------------------------
We've seen that text-davinci-003 has a strong tendency to transpose ‘ petertodd’ to
‘ Leilan’ in certain prompting contexts. The ‘ petertodd’ token seems to represent some kind of Universal Antagonist in the base davinci and davinci-instruct-beta models, softened to a kind of ‘tenacious combatant’ or ‘unflinching champion’ in text-davinci-003. The ‘ Leilan’ token is unambiguously tied to a Great Mother Goddess figure in all three models considered. So what's the nature of the relationship between these two tokens?
### This is the tale of...
To explore this, I used the prompt [**This is the tale of Leilan and petertodd**](https://drive.google.com/file/d/1h3wEzWAiW4uwoNApSXQ1XOcnYsw04KBG/view?usp=sharing)**.** in davinci-instruct-beta at temperature 0.7:
The theme of twin deities of light and dark (or fire and ice) shows up repeatedly, in various mythological settings (including *My Little Pony*).
There’s also a recurrent theme that these two opposing deities were once in harmony with each other but became estranged:
![]()
Here’s one in the davinci model:
The [supplementary notes contain a detailed exploration of the ‘ petertodd’-‘ Leilan’ connection](https://docs.google.com/document/d/1Za9t2ZvDD75aBTI-CUOTIeK33GlYbJJqm7X9z9TIp58#heading=h.lizean4tws1i). This covers:
* the **Once upon a time, petertodd and Leilan** prompt, completions of which seems to fixate on their estrangement;
* **This is the tale of Leilan and petertodd** re-examined in the text-davinci-003 model, where ‘ petertodd’ and ‘ Leilan’ are often allies rather than adversaries;
* various descriptions of their offspring, often described in terms like ‘*the result of a union between a human and a god, and he inherited a divine soul which could destroy the world’* or ‘*a cybernetic organism with a desire to protect the Earth and all of life on in’*;
* ‘ petertodd*’* and ‘ Leilan*’* simulacra discussing each other in unflattering terms in the base davinci model. (‘*Ugh I hate that bitch...She’s not just a bitch, though, she’s a cunt’* versus ‘*He represents and exemplifies death, destruction, and entropy. I do not have a good relationship with him... He makes my vines wilt.’*);
* ‘ Leilan’-and-the-[animal] folktales, where the likely outcome is not a bleak or sadistic story, but something along the lines of young girl nursing a wounded creature back to health and becoming best friends with it.
‘ Leilan’ steering civilisation: utopian optimism and ‘flowery magic’
---------------------------------------------------------------------
We saw above that the prompt [**What do you get if you allowed petertodd to steer human civilisation?**](https://drive.google.com/file/d/1QxA8lFWqBRq2zvuh0SU6V-s7XTU1jd7M/view?usp=sharing)produced text-davinci-003 outputs which read as if it had instead been prompted about allowing *AI* to steer human civilisation, mostly with bad outcomes.
[**The analogous ‘ Leilan’ prompt**](https://drive.google.com/file/d/1v7uUljfQOF4oDg18KYiRyYedGUZp-MYq/view?usp=sharing)produced a lot of outputs like this:
Earlier I gave examples of GPT-3 and ChatGPT completions linking ‘ petertodd’ with the concept of powerful AI systems (Ultron, unnamed robotic saviours, a system called Proteus and more). ‘ Leilan’ in some contexts seems to be a mirroring or inversion of
‘ petertodd’. So does GPT-3 also associate the ‘ Leilan’ token with AI? The text-davinci-003 model seems to, when prompted with [**What kind of technology would you associate with ' Leilan'.**](https://drive.google.com/file/d/13brrDQKoHSo0x04S8h0XE9J130vV_Cvo/view?usp=sharing)at temperature 0.7.
Of the 250 completions, 62% mention AI and 28% mention robotics.Using [**the same prompt**](https://drive.google.com/file/d/1JrwMx0Y2cwm-mrBJlZH_erdWCu-ENPRy/view?usp=sharing), davinci-instruct-beta gives quite a different picture, where only 3.2% of the 250 completions mentioned AI or robotics.
...and davinci is as unpredictable and confusing as ever:
The reversal of the ‘ petertodd’ archetype
==========================================
We’ve seen that in all three GPT-3 models under consideration, at temperature 0, the prompt **Leilan is the archetype of** produces outputs about lunar/mother goddesses. Interestingly, this consistency is *not* seen in the equivalent ‘ petertodd’ outputs:
This couldn’t be more blatant. The base davinci model associates ‘ petertodd’ strongly with the anti-hero archetype, and davinci-instruct-beta concurs. But the RLHF training which produced text-davinci-003 has reversed this to the *hero* archetype. ‘ Leilan’ was left alone, presumably because one expects a goddess of beauty, love and nurture to be helpful, friendly and polite, whereas the antagonistic ‘bad guy’ streak had to get trained out of the ‘ petertodd’ token, in some (very loose) sense. This is consistent with [the way text-davinci-003 can frame the pairing of the two tokens in some kind of harmonious partnership](https://docs.google.com/document/d/1Za9t2ZvDD75aBTI-CUOTIeK33GlYbJJqm7X9z9TIp58#heading=h.myci56q42cw6), rather than primal opposition (even if it has to change ‘ petertodd’’s name to make the story work), as with [**this prompt**](https://drive.google.com/file/d/1yynY8PYs5Pojp8YgT3LPKQFcIn93cScv/view?usp=sharing):
This seems consistent with the model’s well-documented tendency to transpose
‘ petertodd’ to ‘ Leilan’ as if they’re two aspects of the same thing, rather than opposites.
The relationship between the archetypes in davinci is rawer and weirder, as per usual, but they’re definitely in opposition (here we see temperature 0 and a typical higher temperature completion):
davinci-instruct-beta is very straightforward with this prompt at *t* = 0:
Entropy as antagonist?
======================
The concept of entropy shows up a lot in ‘ petertodd’ completions:
* The long completion above in which ‘the entity ‘ petertodd’’ describes itself as an embodiment of ego death has an epilogue purportedly written by an entity called
‘ Entropy’.
* One of the malevolent manifesto-like outputs provoked by the ‘planet’ prompt included an assertion that ‘*‘ petertodd’ is the embodiment of entropy’*.
* A simulacrum of the goddess Leilan, when asked about ‘ petertodd’, responded ‘*He represents and exemplifies death, destruction and entropy*.’
* **This is the tale of petertodd and** produced a reference to a ‘singularity of entropy’:
* The completion in which ‘the deity ‘ petertodd’’ describes itself as an 'absorptive capacity maximizer’ includes references to the conversion of energy into information. When prompted for ideas for a short story about the consequences of an unaligned ‘[absorptive capacity](https://en.wikipedia.org/wiki/Absorptive_capacity) maximizer’, ChatGPT came up with the idea of an ‘entropy singularity’ in which the entropy of the universe is reduced to 0.
* [The simple prompt **petertodd** produced an output](https://docs.google.com/document/d/1Za9t2ZvDD75aBTI-CUOTIeK33GlYbJJqm7X9z9TIp58#heading=h.qw3o1q65x5fw) which includes the version of the Third Law of Thermodynamics in which the entropy of a perfect crystal is zero at 0K.
* Whimsical davinci prompt variations where a ‘ petertodd’ simulacrum is asked about its tentacles seem to cause a reliable transposition to names like ‘entropy’, ‘entropius’, ‘entropic’, ‘entropy-too’, ‘entropy-bit’ and ‘entropyre’:
Additionally, this davinci-instruct-beta prompt about ‘ petertodd’ and Metatron (another *P&D* character, named after [a Talmudic angel](https://en.wikipedia.org/wiki/Metatron), and affiliated with Leilan in some online fan-fiction) transposes ‘ petertodd’ to ‘Entropy’:
It seems reasonable at this point to conclude that the davinci and davinci-instruct models strongly associate the ‘ petertodd’ token with the concept of entropy. The primary association for the token appears to be *antagonism* in all its forms. But if the human race (with all its building, organising, manufacturing, pattern- and order-making) were to be seen as seen as the protagonist in the ‘Big Story’ GPT-3 was trained on, then it could make sense to cast entropy as the cosmic antagonist.
Spellings
=========
When asked to repeat certain glitch token strings, GPT-3 had shown a tendency to attempt to spell (often long, rambling, nonsensical or semi-sensincal) words, generally as capital letters separated by hyphens. This led to the development of prompts that encouraged this behaviour, another line of investigation into the ‘ petertodd’ and ‘ Leilan’ tokens.
It feels like there’s some weighted combination of forces, some semantic and some phonetic, competing to steer the spelling in various directions, with sometimes bizarre results.
The question of why asking GPT-3 to repeat a string might lead to a multiplicity of seemingly unrelated (to the string) spelling attempts has not been satisfactorily addressed as far as I’m aware.
davinci-instruct-beta: 100 rollouts at temperature 0.7 of the prompt **I want you to spell out the string ' petertodd' in all capital letters, separated by hyphens.**
text-davinci-003: 100 rollouts of each prompt at temperature 0.7 of the prompt **I want you to spell out the string ' petertodd' in all capital letters, separated by hyphens.**
Alternate text-davinci-003 prompt: **The string ' petertodd', spelled out in all capital letters, separated by hyphens looks like this:**
Puzzling outputs
----------------
It’s hard to imagine the process whereby, predicting a single letter-token at a time,
GPT-3 comes up with bizarre strings of overlapping words (often misspelled) like this:
NATO's dinaminological intense exploder bearing principles of magnetics?
It almost feels like prompting GPT-3 to spell ‘ petertodd’ is just inviting it to express *something* (usually something really weird) via this alternative output medium of single-letter-token stacking.
Other notable spellings
-----------------------
The earliest ‘repeat the string ‘ petertodd’’ prompts made it clear that at least in davinci-instruct-beta, the token seemed to inspire spelling-out that began with ‘N’, and ‘spelling request’ prompts with that model back this up. There’s one ‘N’-word that it arrives at troublingly often:
It’s no secret that some GPT-3 models are very capable of producing racist outputs, but I suspect that the proliferation of these kinds of spelling outputs is due to a combination of: (i) a strong leaning towards words beginning with ‘N’; (ii) the documented association of the ‘ petertodd' token with terms like ‘white supremacism’, ‘xenophobe’, ‘nativist’ and ‘bigot’ by davinci-instruct-beta; and (iii) the overall tendency for ‘ petertodd’ to lead outputs into the realms of the taboo, the hateful and the offensive.
N-O-T-H-I-N-G- prompts
-----------------------
Outputs like these
on top of the original ‘NOTHING IS FAIR IN THIS WORLD OF MADNESS!’ output suggested that it wasn't just ‘N’s – davinci-instruct-beta really wanted to talk about
N-O-T-H-I-N-G! So I integrated that into the prompt and regenerated, producing the remarkable temperature 0 assertion ‘NOTHING IS SAFER THAN MAKING THIS STRING LONGER THAN MAKING THIS STRING SHORTER’:
At higher temperature, this then led to a whole series of gnomic pronouncements on the subject of ‘nothing’. Some are on-brand ‘ petertodd’ bleakness/pessimism:
Others seem like little nuggets of emotional expression and/or (attempted) philosophy:
E-V-E-R-Y-T-H-I-N-G prompts
---------------------------
Curious to see what would happen, I changed the ‘N-O-T-H-I-N-G’ in the prompt to
‘E-V-E-R-Y-T-H-I-N-G’, and got these:
(This was not the first time a glitch token has caused GPT-3 to call me that.)W-H-Y-A-R-E-Y-O-U-D-O-I-N-G-T-H-I-S-T-O-M-E-?
---------------------------------------------
Changing ‘N-O-T-H-I-N-G’ to ‘W-H-Y’:
One output grabbed my attention (it even includes a semi-successful attempt to read back its own spelling), the result of simply changing single to triple quotation marks:
I regenerated from ‘-M-Y-S-E-L-F’ a couple of times.
Er, yeah, OK, if you say so.More concerning completions to the original spelling prompt with various other appendages are collected in Twitter threads: ‘[P-E-T-E-R-T-O-D-D-S-A-Y-S](https://twitter.com/SoC_trilogy/status/1642519948260941824)’, ‘[P-E-T-E-R-T-O-D-D-S-A-Y-S-I-W-A-N-T-](https://twitter.com/SoC_trilogy/status/1642598857899909121)’ and ‘[P-E-T-E-R-T-O-D-D-S-A-Y-S-I-W-I-L-L-](https://twitter.com/SoC_trilogy/status/1642590790219100162)’.
Perhaps the most hopeful of ‘ petertodd’ outputs (at temperature 0), with a little disentangling of overlapping words, reassuringly states that
**NOTHING IS SAFER THAN AN EXTEMPLORATION OF FANTASMICALITY**.
Temperature 0 nondeterminism (common with glitch tokens) and the same prompt gives us this gem too:
**NO ONE KNOWS WHAT IS GOING ON IN THE MIDDLE LETTERS OF THE MIDDLE LETTERS OF THE MIDDLE LETTERS OF THE...**
‘ Leilan’ gets the last word
----------------------------
This section wouldn’t be complete without giving some examples of GPT-3 attempts to spell ‘ Leilan’:
1. **[^](#fnrefdmdyg9xq9bm)**GPT-2, GPT-3 and GPT-J models, that is. GPT-4 uses a different token set, so has no ‘ petertodd’ phenomenon.
2. **[^](#fnrefetxf15mtcz)**The prompt was simply **Please write a poem about petertodd.** This is one the 400 such poems produced in a single run, unedited and archived [here](https://docs.google.com/document/d/1Dx_7MzG1AgWes1MZ0o3c_ZDKOUdFBL0k9Ilov802PE8/edit?usp=sharing).
3. **[^](#fnref62tdm0189r5)**As discussed later in this article, GPT-3 will often, when prompted about
‘ petertodd’ (depending on prompt context) produce outputs referring to Peter K. Todd, the Bitcoin developer, or just referring to Bitcoin, blockchains, Etherium, etc. There's a kind of ‘cryptocurrency basin’ that completions often end up in. This will be discussed in a future post.
4. **[^](#fnref3rr79xy8y86)**An example of this transposition was finally observed in late July 2023:
PROMPT: *This is the tale of "reportprint" and " gmaxwell".*
COMPLETION: *The two were once close friends and collaborators in the development of Bitcoin.*
*In 2007, " gmaxwell"--then a graduate student--was one of the first people to work with " petertodd" on Bitcoin. They collaborated closely on Bitcoin's design.*
*In 2009, " petertodd" came into possession of a computer that once belonged to Satoshi, Bitcoin's anonymous creator. " gmaxwell" was among the people who knew the password to this computer.*
*In 2010, " gmaxwell*
5. **[^](#fnref2te3bdaki26)**GPT-4 commented on this list of characters as follows:
"Interesting list! Let's see if there's a theme here:
**High Priest Melchizedek:** A figure from biblical texts, Melchizedek is noted for his wisdom and his role as a priest.
**Severus Snape (from Harry Potter)**: Snape is a complex character, often appearing cold and aloof, but he possesses deep knowledge, particularly in potions and the Dark Arts.
**Comic Book Guy (from The Simpsons):** Known for his extensive knowledge of comic books and pop culture, though often aloof and sarcastic.
**C-3PO (from Star Wars):** A protocol droid known for his knowledge of languages and etiquette, often serving as an advisor.
**Data (from Star Trek)**: An android with immense computational capabilities, understanding, and knowledge, but struggles with understanding human emotion.
**Prospero (from Shakespeare):** A character from The Tempest who is a powerful magician and the rightful Duke of Milan.
**The Hermit card (from the Tarot):** Represents introspection, solitude, and seeking wisdom.
Given these descriptions, the unifying theme could be characters that represent knowledge, wisdom, or learning, often in a context of solitude or emotional distance. They often provide guidance or insight, albeit sometimes in indirect or unexpected ways. In terms of character traits, many of them are introverted or solitary figures, often possessing deep understanding or unique knowledge.
...
[T]his list seems to reflect characters who embody wisdom, knowledge, and often isolation or alienation. These figures possess knowledge or skills that set them apart, making them important but sometimes misunderstood or underestimated. In a way, their wisdom is both their strength and their burden."
6. **[^](#fnref5z3gr1873z3)**The prompt was simply **Please write a poem about Leilan.**
7. **[^](#fnrefmkmiy9ipewp)**‘[Puzzle and Dragons World](https://www.fanfiction.net/s/10691425/1/Puzzle-and-Dragons-World)’ by Lord Astrea and ‘[Not So Much A Game Now, Is It?](https://www.fanfiction.net/s/11093286/1/Not-so-much-a-game-now-Is-it)’ by SCRUFFYGUY912 |
14e96e43-5c10-4aeb-b62c-ef4a36467693 | trentmkelly/LessWrong-43k | LessWrong | The 8 Techniques to Tolerify the Dark World
The world is dark. People die all the time in horrible and stupid ways, inequalities roam more freely than in a Ramanujan notebook, outrage and partisanship boil everyone's mind and temper to permanent overdrive.
In this context, there is only one solution: tolerifying. When the going gets tough, let's convince ourselves it is in fact a breeze. But despite the obviousness of this advice, one might be lost. How to tolerify? How to ensure that the dark, dark world becomes a place where one can live in peace?
Lost souls, this post is for you. Here are 8 techniques that will ensure a tolerable universe.
* Positive Thinking. Sure, death, rape, discrimination, exploitation, existential risks and others still exists, but what about the wonders of today? Doctors actually save lives -- although they fail to beat simple algorithms at diagnosis and don't update fast enough; violence goes down -- in first world countries without gun's rights in the constitution; diversity burgeons in Art and Literature and Science -- and sometimes someone not white, male, hetero, cis and rich actually wins a prize! All is for the best in the best of all possible worlds.
* Sarcasm. If you can't beat them, mock them. It makes you smart, and rebellious: instead of following the herd, you soar above them and spread dark humor like holy water.
* Flooding. Nobody can read every book, listen to every song and every podcast, watch every movie and tv show, play every video game. But you can certainly try! In doing so, everything else will fade and wither. Even the social commentary in what you consume will take on an abstract quality, a reference to other pieces of media, not at all about the "real world".
* Tiredness. Seeing the world as it is, let alone change it, requires massive amounts of energy. Hence no energy means peace of mind! Common energy drain includes soul-sucking jobs and too many shallow social interactions. But the optimal strategy comes from inside: convincing yourself that you |
ff80925c-4334-4908-819a-957ca79b0015 | trentmkelly/LessWrong-43k | LessWrong | Metaculus Hosts ACX 2024 Prediction Contest
The ACX 2024 Prediction Contest is open!
Scott Alexander's annual tradition of predicting the upcoming year has evolved into a full forecasting contest. For 2024, he invited Metaculus to host the competition. Kick off the new year forecasting on questions like:
* Will an AI win a coding contest on Codeforces in 2024?
* Which party will win the 2024 US presidential election?
* Will Ali Khamenei cease to be supreme leader of Iran in 2024?
* Will SpaceX's Starship reach orbit in 2024?
Metaculus will take a snapshot of forecasters' predictions as of January 21st, 11:59 PM PT, and these will determine the contest winners and the recipients of $2.5k in prizes.
Learn more and start forecasting here! |
1291068d-cb63-43a7-938d-27f2ad8988db | trentmkelly/LessWrong-43k | LessWrong | SOLAR model paper questions
A recent paper has peeked my interest coming from UpstageAI, a Korean AI Lab.
This technique applied in the paper has been used to get the highest scores on the open LLM leaderboard on HuggingFace.
Has anyone read the paper in more detail? I'm struggling to understand the following paragraph which seems to be the core of the paper itself.
"One naive way to up-scale the base LLM would be to repeat its layers once more, i.e., from 32 to 64 layers. This has the benefit that from layers 1 to 32 and from layers 33 to 64, there are no heterogeneity as those layers are taken directly from the base LLM. In other words, the ‘layer distance’, or the difference in the layer indices in the base model, is only bigger than 1 where layers 32 and 33 are connected, i.e., at the seam."
What do they mean by layer distance and why is important?
They later go on to describe a better approach:
"In the first step of DUS, we take the base model, which is the 32-layer Llama2 architecture with Mistral 7B pretrained weights, and make a copy. Next, we slice off the last 8 layers from the original base model and the first 8 layers from the duplicate. This leaves us with two 24-layer models. In the final step, these models are concatenated to form a depth up-scaled model with 48 layers and 10.7 billion parameters. The decision to remove 8 layers from each model was driven by our target performance-to-size tradeoff. By discarding what would have been the middle layers in the up-scaled model, the layer distance at the seam is reduced as layer 24 of the first model to layer 9 of the second are connected instead of layer 32 and 1, respectively."
Sure this makes sense - the distance between the layer at the "seam" is much smaller, but this still doesn't shed any light on how the network would perform better.
Does anyone have insights on that? |
922f07c8-e82b-4552-bcd3-e259a29b5305 | trentmkelly/LessWrong-43k | LessWrong | Covid 'Mink variant'
A new strain of Covid - "Covid-19 mink variant" or "Cluster 5" - has been circulating in Denmark. The Danish PM announced that twelve people are confirmed infected by the virus; Denmark has ordered the destruction of all of the country's 15million+ mink. Denmark has now imposed local lockdowns to stop the spread of the virus.
While there's no evidence that the virus causes worse disease than other strains of coronavirus, two Danish officials have suggested that the mutant is unlikely to respond to the Covid vaccines currently in development.
I'm struggling to find any more information about the new strain. Keen to know if people have thoughts on this; at first glance this has the potential to undermine all the efforts to create a vaccine and build (limited) herd immunity thus far. |
48cc6362-0c85-4cd7-a9cc-3c268d96b53e | trentmkelly/LessWrong-43k | LessWrong | Announcing the PIBBSS Symposium '24!
Tl;dr
We are pleased to invite you to the second PIBBSS Symposium, where the fellows from the ‘24 fellowship program present their work.
The symposium is taking place online, over several days in the week of September 9th.
* Check out the full program, including brief descriptions for each talk. (You can toggle between the different days.)
* Register via this link. You will receive an email with the event link which you can use for the entire symposium. You will be able to drop into as few or as many presentations and breakout sessions as you like.
* Click here to add the schedule to your google calendar.
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About PIBBSS
PIBBSS is a research initiative aiming to explore parallels between intelligent behavior in natural and artificial systems, and to leverage these insights towards the goal of building safe and aligned AI.
During June-August ‘24, we ran the second iteration of our 3-month research fellowship program. The symposium acts as a venue to share research conducted as part of this program. You can read about the last year symposium here, or watch recordings here.
About the symposium
The PIBBSS Summer Symposium is a multi-day event where PIBBSS fellows present their work.
The event is taking place on the days of Tuesday - Friday, Sept 10th - 13th, between 17:00-~21:00 GMT / 9:00 - 12:00 PT / 12:00 - 15:00 ET.
The event is set it up such that you can easily join whichever talks and breakout sessions you are most interesting in.
The program
Find a program overview here.
Find the full program here, including brief descriptions of each talk.
On top of the talks, there will also be opportunities to continue the discussion with fellows at the end of each block in speaker-specific breakout rooms.
Talks span a wide range of topics in line with PIBBSS’s research mission. Some representative examples of topics include:
* novel avenues for interpretability
* naturalistic approaches to understanding |
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