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57c5cdbe-f88b-4d1c-b16a-27d1c8a6c621 | StampyAI/alignment-research-dataset/arxiv | Arxiv | Director: Deep Hierarchical Planning from Pixels.
1 Introduction
---------------
Artificial agents have achieved remarkable performance on reactive video games (mnih2015dqn, badia2020agent57) or board games that last for a few hundred moves (silver2017alphago).
However, solving complex control problems can require millions of time steps. For example, consider a robot that needs to navigate along the sidewalk and cross streets to buy groceries and then return home and cook a meal with those groceries.
Manually specifying subtasks or dense rewards for such complex tasks would not only be expensive but also prone to errors and require tremendous effort to capture special cases (chen2021dvd, ahn2022saycan).
Even training a robot to simply walk forward can require specifying ten different reward terms (kumar2021rma), making reward engineering a critical component of such systems.
Humans naturally break long tasks into subgoals, each of which is easy to achieve.
In contrast, most current reinforcement learning algorithms reason purely at the clock rate of their primitive actions.
This poses a key bottleneck of current reinforcement learning methods that could be challenging to solve by simply increasing the computational budget.
Hierarchical reinforcement learning (HRL) (dayan1992feudal, parr1997ham, sutton1999options) aims to automatically break long-horizon tasks into subgoals or commands that are easier to achieve, typically by learning high-level controllers that operate at more abstract time scales and provide commands to low-level controllers that select primitive actions.
However, most HRL approaches require domain knowledge to break down tasks, either through manually specified subtasks (tessler2017dsn) or semantic goal spaces such as global XY coordinates for navigation tasks (andrychowicz2017her, nachum2018hiro) or robot poses (gehring2021hsd3).
Attempts at learning hierarchies directly from sparse rewards have had limited success (vezhnevets2017fun) and required providing task reward to the low-level controller, calling into question the benefit of their high-level controller.
In this paper, we present Director, a practical method for learning hierarchical behaviors directly from pixels by planning inside the latent space of a learned world model.
We observe the effectiveness of Director on long-horizon tasks with very sparse rewards and demonstrate its generality by learning successfully in a wide range of domains.
The key insights of Director are to leverage the representations of the world model, select goals in a compact discrete space to aid learning for the high-level policy, and to use a simple form of temporally-extended exploration in the high-level policy.
#### Contributions
The key contributions of this paper are summarized as follows:
* We describe a practical, general, and interpretable algorithm for learning hierarchical behaviors within a world model trained from pixels, which we call Director ([Section 2](#S2 "2 Director ‣ Deep Hierarchical Planning from Pixels")).
* We introduce two sparse reward benchmarks that underscore the limitations of traditional flat RL approaches and find that Director solves these challenging tasks ([Section 3.1](#S3.SS1 "3.1 Sparse Reward Benchmarks ‣ 3 Experiments ‣ Deep Hierarchical Planning from Pixels")).
* We demonstrate that Director successfully learns in a wide range of traditional RL environments, including Atari, Control Suite, DMLab, and Crafter ([Section 3.2](#S3.SS2 "3.2 Standard Benchmarks ‣ 3 Experiments ‣ Deep Hierarchical Planning from Pixels")).
* We visualize the latent goals that Director selects for breaking down various tasks, providing insights into its decision making ([Section 3.3](#S3.SS3 "3.3 Goal Interpretations ‣ 3 Experiments ‣ Deep Hierarchical Planning from Pixels")).
Figure 2: Director is based on the world model of PlaNet (hafner2018planet) that predicts ahead in a compact representation space. The world model is trained by reconstructing images using a neural network not shown in the figure. Director then learns three additional components, which are all optimized concurrently.
On the left, the goal autoencoder compresses the feature vectors st into vectors of discrete codes z∼enc(z|st).
On the right, the manager policy mgr(z|st) selects abstract actions in this discrete space every K=8 steps, which the goal decoder then turns into feature space goals g=dec(z).
The worker policy wkr(at|st,g) receives the current feature vector and goal as input to decide primitive actions that maximize the similarity rewards rt to the goal.
The manager maximizes the task reward and an exploration bonus based on the autoencoder reconstruction error, implementing temporally-extended exploration.
2 Director
-----------
Director is a reinforcement learning algorithm that learns hierarchical behaviors directly from pixels.
As shown in [Figure 2](#S1.F2 "Figure 2 ‣ Contributions ‣ 1 Introduction ‣ Deep Hierarchical Planning from Pixels"), Director learns a world model for representation learning and planning, a goal autoencoder that discretizes the possible goals to make them easier for the manager to choose, a manager policy that selects goals every fixed number of steps to maximize task and exploration rewards, and a worker policy that learns to reach the goals through primitive actions.
All components are optimized throughout the course of learning by performing one gradient step every fixed number of environment steps.
The world model is trained from a replay buffer whereas the goal autoencoder is trained on the world model representations and the policies are optimized from imagined rollouts.
For the pseudo code of Director, refer to [Appendix E](#A5 "Appendix E Pseudocode ‣ Deep Hierarchical Planning from Pixels").
###
2.1 World Model
Director learns a world model that compresses the history of observations into a compact feature space and enables planning in this space (watter2015e2c, zhang2018solar).
We use the Recurrent State Space Model (RSSM) model of PlaNet (hafner2018planet), which we briefly review here to introduce notation.
The world model consists of four neural networks that are optimized jointly:
| | | | |
| --- | --- | --- | --- |
| | Model representation:reprθ(st|st−1,at−1,xt)Model decoder:recθ(st)≈xtModel dynamics:dynθ(st|st−1,at−1)Reward predictor:rewθ(st+1)≈rt | | (1) |
The representation model integrates actions at and observations xt into the latent states st.
The dynamics model predicts future states without the corresponding observations.
The decoder reconstructs observations to provide a rich learning signal.
The reward predictor later allows learning policies by planning in the compact latent space, without decoding images.
The world model is optimized end-to-end on subsequences from the replay buffer by stochastic gradient descent on the variational objective (hinton1993vi, kingma2013vae, rezende2014vae):
| | | | |
| --- | --- | --- | --- |
| | L(θ)≐T∑t=1(βKL[reprθ(st|st−1,at−1,xt)∥∥dynθ(st|st−1,at−1)]+∥recθ(st)−xt∥2+(rewθ(st+1)−rt)2)wheres1:T∼reprθ | | (2) |
The variational objective encourages learning a Markovian sequence of latent states with the following properties: The states should be informative of the corresponding observations and rewards, the dynamics model should predict future states accurately, and the representations should be formed such that they are easy to predict.
The hyperparameter β trades off the predictability of the latent states with the reconstruction quality (beattie2016dmlab, alemi2018broken).
###
2.2 Goal Autoencoder
The world model representations st are 1024-dimensional continuous vectors.
Selecting such representations as goals would be challenging for the manager because this constitutes a very high-dimensional continuous action space.
To avoid a high-dimensional continuous control problem for the manager, Director compresses the representations st into smaller discrete codes z using a goal autoencoder that is trained on replay buffer model states from [Equation 2](#S2.E2 "(2) ‣ 2.1 World Model ‣ 2 Director ‣ Deep Hierarchical Planning from Pixels"):
| | | | |
| --- | --- | --- | --- |
| | Goal Encoder:encϕ(z|st)Goal Decoder:decϕ(z)≈st | | (3) |
Simply representing each model state st by a class in one large categorical vector would require roughly one category per distinct state in the environment.
It would also prevent the manager from generalizing between its different outputs.
Therefore, we opt for a factorized representation of multiple categoricals.
Specifically, we choose the vector of categoricals approach introduced in DreamerV2 (hafner2020dreamerv2).
As visualized in [Figure G.1](#A7.F1 "Figure G.1 ‣ Appendix G Vector of Categoricals ‣ Deep Hierarchical Planning from Pixels"), the goal encoder takes a model state as input and predicts a matrix of 8×8 logits, samples a one-hot vector from each row, and flattens the results into a sparse vector with 8 out of 64 dimensions set to 1 and the others to 0.
Gradients are backpropagated through the sampling by straight-through estimation (bengio2013straight).
The goal autoencoder is optimized end-to-end by gradient descent on the variational objective:
| | | | |
| --- | --- | --- | --- |
| | L(ϕ)≐∥∥decϕ(z)−st∥∥2+βKL[encϕ(z|st)∥∥p(z)]wherez∼encϕ(z|st) | | (4) |
The first term is a mean squared error that encourages the encoder to compute informative codes from which the input can be reconstructed.
The second term encourages the encoder to use all available codes by regularizing the distribution towards a uniform prior p(z).
The autoencoder is trained at the same time as the world model but does not contribute gradients to the world model.
###
2.3 Manager Policy
Director learns a manager policy that selects a new goal for the worker every fixed number of K=8 time steps.
The manager is free to choose goals that are much further than 8 steps away from the current state, and in practice, it often learns to choose the most distant goals that the worker is able to achieve.
Instead of selecting goals in the high-dimensional continuous latent space of the world model, the manager outputs abstract actions in the discrete code space of the goal autoencoder ([Section 2.2](#S2.SS2 "2.2 Goal Autoencoder ‣ 2 Director ‣ Deep Hierarchical Planning from Pixels")).
The manager actions are then decoded into world model representations before they are passed on to the worker as goals.
To select actions in the code space, the manager outputs a vector of categorical distributions, analogous to the goal encoder in [Section 2.2](#S2.SS2 "2.2 Goal Autoencoder ‣ 2 Director ‣ Deep Hierarchical Planning from Pixels"):
| | | | |
| --- | --- | --- | --- |
| | Manager Policy:mgrψ(z|st) | | (5) |
The objective for the manager is to maximize the discounted sum of future task rewards and exploration rewards.
The exploration encourages the manager to choose novel goals for the worker, resulting in temporally-abstract exploration.
This is important because the worker is goal-conditioned, so without an explicit drive to expand the state distribution, it could prefer going back to previously common states it has been trained on the most, and thus hinder exploration of new states in the environment.
Because the goal autoencoder is trained from the replay buffer, it tracks the current state distribution of the agent and we can reward novel states as those that have a high reconstruction error under the goal autoencoder:
| | | | |
| --- | --- | --- | --- |
| | rexplt≐∥∥decϕ(z)−st+1∥∥2 wherez∼encϕ(z|st+1) | | (6) |
Both manager and worker policies are trained from the same imagined rollouts and optimized using Dreamer (hafner2019dreamer, hafner2020dreamerv2), which we summarize in [Appendix H](#A8 "Appendix H Policy Optimization ‣ Deep Hierarchical Planning from Pixels").
The manager learns two state-value critics for the extrinsic and exploration rewards, respectively.
The critics are used to fill in rewards beyond the imagination horizon and as baseline for variance reduction (williams1992reinforce).
We normalize the extrinsic and exploration returns by their exponential moving standard deviations before summing them with weights wextr=1.0 and wexpl=0.1.
For updating the manager, the imagined trajectory is temporally abstracted by selecting every K-th model state and by summing rewards within each non-overlapping subsequence of length K.
No off-policy correction (schulman2017ppo, nachum2018hiro) is needed because the imagined rollouts are on-policy.
###
2.4 Worker Policy
The worker is responsible for reaching the goals chosen by the manager.
Because the manager outputs codes z in the discrete space of the goal autoencoder, we first decode the goals into the state space of the world model g≐dec(z).
Conditioning the worker on decoded goals rather than the discrete codes has the benefit that its learning becomes approximately decoupled from the goal autoencoder.
The worker policy is conditioned on the current state and goal, which changes every K=8 time steps, and it produces primitive actions at to reach the feature space goal:
| | | | |
| --- | --- | --- | --- |
| | Worker Policy:wkrξ(at|st,g) | | (7) |
To reach its latent goals, we need to choose a reward function for the worker that measures the similarity between the current state st and the current goal g, both of which are 1024-dimensional continuous activation vectors.
Natural choices would be the negative L2 distance or the cosine similarity and their choice depends on the underlying feature space, which is difficult to reason about.
Empirically, we found the cosine similarity to perform better.
Cosine similarity would usually normalize both vectors, but normalizing the state vector encourages the worker to remain near the origin of the latent space, so that it can quickly achieve any goal by moving a small amount in the right direction.
We thus incorporate the idea that the magnitude of both vectors should be similar into the cosine similarity, resulting in our *max-cosine* reward:
| | | | |
| --- | --- | --- | --- |
| | | | (8) |
When the state and goal vectors are of the same magnitude, the reward simplifies to the cosine similarity.
When their magnitudes differ, the vectors are both normalized by the larger of the two magnitudes, and thus the worker receives a down-scaled cosine similarity as the reward.
As a result, the worker is incentivized to match the angle and magnitude of the goal.
Unlike the L2 similarity, the reward scale of our goal reward is not affected by the scale of the underlying feature space.
The worker maximizes only the goal rewards.
We make this design choice to demonstrate that the interplay between the manager and the worker is successful across many environments, although we also include an ablation experiment where the worker additionally receives task reward, which further improves performance.
The worker is optimized by Dreamer with a goal-conditioned state-value critic.
For updating the worker, we cut the imagined rollouts into distinct trajectories of length K within which the goal is constant.
The state-critic estimates goal rewards beyond this horizon under the same goal, allowing the worker to learn to reach far-away goals.
Figure 3:
Comparison of Ant Mazes in the literature and this paper.
HIRO (nachum2018hiro) provided global XY coordinates of the goal and robot position to the agent and trained with dense rewards on uniformly sampled training goals.
NORL (nachum2018norl) replaced the robot XY position with a global top-down view of the environments, downsampled to 5×5 pixels.
In this paper, we tackle the more challenging problem of learning directly from an egocentric camera without global information provided to the agent, and only give a sparse reward for time steps where the robot is at the goal.
To succeed at these tasks, an agent has to autonomously explore the environment and identify landmarks to localize itself and navigate the mazes.
| | |
| --- | --- |
| | |
Figure 4: Egocentric Ant Maze benchmark. A quadruped robot is controlled through joint torques to navigate to a fixed location in a 3D maze, given only first-person camera and proprioceptive inputs. This is in contrast to prior benchmarks where the agents received their global XY coordinate or top-down view. The only reward is given at time steps where the agent touches the reward object. Plan2Explore fails in the small maze because the robot flips over too much, a common limitation of low-level exploration methods. Director solves all four tasks by breaking them down into manageable subgoals that the worker can reach, while learning in the end-to-end reinforcement learning setting.
| | |
| --- | --- |
| | |
Figure 5: Visual Pin Pad benchmark.
The agent controls the black square to move in four directions.
Each environment has a different number of pads that can be activated by walking to and stepping on them.
A single sparse reward is given when the agent activates all pads in the correct sequence.
The history of previously activated pads is shown at the bottom of the screen.
Plan2Explore uses low-level exploration and performs well in this environment, but struggles for five and six pads, which requires more abstract exploration and longer credit assignment.
Director learns successfully across all these environments, demonstrating its benefit on this long-horizon benchmark.
| | | |
| --- | --- | --- |
| | | |
Figure 6:
Subgoals discovered by Director.
For interpretability, we decode the latent goals into images using the world model.
Top: In DMLab, the manager chooses goals of the teleport animation that occurs every time the agent has collected the reward object, which can be seen in the episode at time step 125.
Middle: In Crafter, the manager first directs the worker via the inventory display to collect wood and craft a pickaxe and a sword, with the worker following command.
The worker then suggests a cave via the terrain image to help the worker find stone.
As night breaks, it suggests hiding from the monsters in a cave or on a small island.
Bottom: In Walker, the manager abstracts away the detailed leg movements by suggesting a forward leaning pose and a shifting floor pattern, with the worker successfully filling in the joint movements. Fine-grained subgoals are not required for this task, because the horizon needed for walking is short enough for the worker.
Videos are available on the project website: <https://danijar.com/director/>
3 Experiments
--------------
We evaluate Director on two challenging benchmark suites with visual inputs and very sparse rewards, which we expect to be challenging to solve using a flat policy without hierarchy ([Section 3.1](#S3.SS1 "3.1 Sparse Reward Benchmarks ‣ 3 Experiments ‣ Deep Hierarchical Planning from Pixels")).
We further evaluate Director on a wide range of standard tasks from the literature to demonstrate its generality and ensure that the hierarchy is not harmful in simple settings ([Section 3.2](#S3.SS2 "3.2 Standard Benchmarks ‣ 3 Experiments ‣ Deep Hierarchical Planning from Pixels")).
We use a fixed set of hyperparameters not only across tasks but also across domains, detailed in [Table F.1](#A6.T1 "Table F.1 ‣ Appendix F Hyperparameters ‣ Deep Hierarchical Planning from Pixels").
Finally, we offer insights into the learned hierarchical behaviors by visualizing the latent goals selected during environment episodes ([Section 3.3](#S3.SS3 "3.3 Goal Interpretations ‣ 3 Experiments ‣ Deep Hierarchical Planning from Pixels")).
Ablations and additional results are included in the appendix.
#### Implementation
We implemented Director on top of the public source code of DreamerV2 (hafner2020dreamerv2), reusing its default hyperparameters.
We additionally increased the number of environment instances to 4 and set the training frequency to one gradient step per 16 policy steps, which drastically reduced wall-clock time and decreased sample-efficiency mildly.
Implementing Director in the code base amounts to about 250 lines of code.
The computation time of Director is 20% longer than that of DreamerV2.
Each training run used a single V100 GPU with XLA and mixed precision enabled and completed in less than 24 hours.
All our agents and environments will be open sourced upon publication to facilitate future research in hierarchical reinforcement learning.
#### Baselines
To fairly compare Director to the performance of non-hierarchical methods, we compare to the DreamerV2 agent on all tasks.
DreamerV2 has demonstrated strong performance on Atari (hafner2020dreamerv2), Crafter (hafner2021crafter) and continuous control tasks (yarats2021drqv2) and outperforms top model-free methods in these domains.
We kept the default hyperparameters that the authors tuned for DreamerV2 and did not change them for Director.
In addition to its hierarchical policy, Director employs an exploration bonus at the top-level.
To isolate the effects of hierarchy and exploration, we compare to Plan2Explore (sekar2020plan2explore), which uses ensemble disagreement of forward models as a directed exploration signal.
We combined the extrinsic and exploration returns after normalizing by their exponential moving standard deviation with weights 1.0 and 0.1, as in Director.
We found Plan2Explore to be effective across both continuous and discrete control tasks.
###
3.1 Sparse Reward Benchmarks
#### Egocentric Ant Mazes
Learning navigation tasks directly from joint-level control has been a long-standing milestone for reinforcement learning with sparse rewards, commonly studied with quadruped robots in maze environments (florensa2017snn, nachum2018hiro).
However, previous attempts typically required domain-specific inductive biases to solve such tasks, such as providing global XY coordinates to the agent, easier practice goals, and a ground-truth distance reward, as summarized in [Figure 3](#S2.F3 "Figure 3 ‣ 2.4 Worker Policy ‣ 2 Director ‣ Deep Hierarchical Planning from Pixels").
In this paper, we instead attempt learning directly from first-person camera inputs, without privileged information, and a single sparse reward that the agent receives while in the fixed goal zone.
The control frequency is 50Hz and episodes end after a time limit of 3000 steps.
There are no early terminations that could leak task-information to the agent (laskin2022cic).
To help the agent localize itself from first-person observations, we assign different colors to different walls of the maze.
As shown in [Figure 4](#S2.F4 "Figure 4 ‣ 2.4 Worker Policy ‣ 2 Director ‣ Deep Hierarchical Planning from Pixels"), we evaluate the agents in four mazes that span varying levels of difficulty.
Because of the sparse reward, the episode returns correspond to the number of time steps for which the agent remains at the goal after reaching it.
Curves show the mean and standard deviation across 5 independent seeds.
We find that the flat Dreamer agent succeeds at the smallest of the four mazes, and the flat exploration policy Plan2Explore makes some initial learning progress but fails to converge to the optimal solution.
Inspecting the trajectories revealed that Plan2Explore chooses too chaotic actions that often result in the robot flipping over.
None of the baselines learn successful behaviors in the larger mazes, demonstrating that the benchmark pushes the limits of current approaches.
In contrast, Director discovers and learns to reliably reach the goal zone at all four difficulty levels, with the larger maze taking longer to master.
#### Visual Pin Pads
The Pin Pad suite of environments is designed to evaluate an agent’s ability to explore and assign credit over long horizons, isolated from the complexity of 3D observations or sophisticated joint-level control.
As shown in [Figure 5](#S2.F5 "Figure 5 ‣ 2.4 Worker Policy ‣ 2 Director ‣ Deep Hierarchical Planning from Pixels"), each environment features a moving black square that the agent can control in all four directions and fixed pads of different colors that the agent can activate by walking over to the pad and stepping on it.
The task requires discovering the correct sequence of activating all pads, at which point the agent receives a sparse reward of 10 points and the agent position is randomly reset.
Episodes last for 2000 steps and there are no intermediate rewards for activating the pads.
To remove the orthogonal challenge of learning long-term memory (gregor2019simcore), the history of previously activated pads is displayed at the bottom of the image.
The agent performance is shown in [Figure 5](#S2.F5 "Figure 5 ‣ 2.4 Worker Policy ‣ 2 Director ‣ Deep Hierarchical Planning from Pixels"), which displays mean and standard deviation across five independent seeds.
The easiest environment contains three pads, so the agent only has to decide whether to activate the pads in clockwise or counter-clockwise sequence.
The flat Dreamer agent sometimes discovers the correct sequence.
The exploration bonus of Plan2Explore offers a significant improvement over Dreamer on this task.
Dreamer fails to discover the correct sequence in the harder environments that contain more pads.
Plan2Explore still achieves some reward with four pads, struggles with five pads, and completely fails with six pads.
In contrast, Director discovers the correct sequence in all four environments, demonstrating the benefit of hierarchy over flat exploration.
###
3.2 Standard Benchmarks
To evaluate the robustness of Director, we train on a wide range of standard benchmarks, which typically require no long-term reasoning.
We choose Atari games (bellemare2013ale), the Control Suite from pixels (tassa2018dmcontrol), Crafter (hafner2021crafter), and tasks from DMLab (beattie2016dmlab) to cover a spectrum of challenges, including continuous and discrete actions and 2D and 3D environments.
We compare two versions of Director.
In its standard variant, the worker learns purely from goal rewards.
This tests the ability of the manager to propose successful goals and the ability of the worker to achieve them.
In the second variant, the worker learns from goal and task returns with weights 1.0 and 0.5, allowing the worker to fill in low-level details in a task-specific manner, which the manager may be too coarse-grained to provide.
Ideally, we would like to see Director not perform worse than Dreamer on any task when giving task reward to the worker.
The results of this experiment are summarized in [Appendix A](#A1 "Appendix A Standard Benchmarks ‣ Deep Hierarchical Planning from Pixels") due to space constraints, with the full training curves for Atari and the Control Suite included in [Appendices J](#A10 "Appendix J Full Visual Control Suite ‣ Deep Hierarchical Planning from Pixels") and [K](#A11 "Appendix K Full Atari Suite ‣ Deep Hierarchical Planning from Pixels").
We observe that Director indeed learns successfully across many environments, showing broader applicability than most prior hierarchical reinforcement learning methods.
In addition, providing task reward to the worker is not as important as expected — the hierarchy solves a wide range of tasks purely by following goals at the low level.
Additionally providing task reward to the worker completely closes the gap to the state-of-the-art DreamerV2 agent.
[Figure K.1](#A11.F1 "Figure K.1 ‣ Appendix K Full Atari Suite ‣ Deep Hierarchical Planning from Pixels") in the appendix further shows that Director achieves a higher human-normalized median score than Dreamer on the 55 Atari games.
###
3.3 Goal Interpretations
To gain insights into the decision making of Director, we visualize the sequences of goals it selects during environment interaction.
While the goals are latent vectors, the world model allows us to decode them into images for human inspection.
[Figures 6](#S2.F6 "Figure 6 ‣ 2.4 Worker Policy ‣ 2 Director ‣ Deep Hierarchical Planning from Pixels") and [1](#S0.F1 "Figure 1 ‣ Deep Hierarchical Planning from Pixels") show episodes with the environment frames (what the agent sees) at the top and the decoded subgoals (what the manager wants the worker to achieve) at the bottom.
Visualizations for additional environments are included in [Appendix L](#A12 "Appendix L Additional Goal Visualizations ‣ Deep Hierarchical Planning from Pixels").
* Ant Maze M
The manager chooses goals that direct the agent through the different sections of the maze until the reward object is reached.
We also observed that initially, the manager chooses more intermediate subgoals whereas later during training, the worker learns to achieve further away goals and thus the manager can select fewer intermediate goals.
* DMLab Goals Small
The manager directs the worker to the teleport animation, which occurs every time the agent collects the reward object and gets teleported to a random location in the 3D maze.
Time step T=125 shows an example of the worker reaching the animation in the environment.
Unlike the Ant Maze benchmark, navigating to the goal in DMLab requires no joint-level control and is simple enough for the worker to achieve without fine-grained subgoals.
* Crafter
The manager requests higher inventory counts of wood and stone materials, as well as wooden tools, via the inventory display at the bottom of the screen.
It also directs the worker to a cave to find stone and coal but generally spends less effort on suggesting what the world around the agent should look like.
As night breaks, the manager tasks the worker with finding a small cave or island to hide from the monsters that are about to spawn.
* Walker Walk
The manager abstracts away the detail of leg movement, steering the worker using a forward leaning pose with both feet off the ground and a shifting floor pattern.
While the images cannot show this, the underlying goal vectors are Markovian states that can contain velocities, so it is likely that the manager additionally requests high forward velocity.
The worker fills in the details of standing up and moving the legs to pass through the sequence of goals.
Across domains, Director chooses semantically meaningful goals that are appropriate for the task, despite using the same hyperparameters across all tasks and receiving no domain-specific knowledge.
4 Related Work
---------------
Approaches to hierarchical reinforcement learning include learning low-level policies on a collection of easier pre-training tasks (heess2016modulated, tessler2017dsn, frans2017mlsh, rao2021helms, veeriah2021modac), discovering latent skills via mutual-information maximization (gregor2016vic, florensa2017snn, hausman2018skills, eysenbach2018diayn, achiam2018valor, merel2018humanoid, laskin2022cic, sharma2019dads, xie2020lsp, hafner2020apd, strouse2021disdain), or training the low-level as a goal-conditioned policy (andrychowicz2017her, levy2017hac, nachum2018hiro, nachum2018norl, co2018sectar, warde2018discern, nair2018rig, pong2019skewfit, hartikainen2019ddl, gehring2021hsd3, shah2021recon).
These approaches are described in more detail in [Appendix I](#A9 "Appendix I Further Related Work ‣ Deep Hierarchical Planning from Pixels").
Relatively few works have demonstrated successful learning of hierarchical behaviors directly from pixels without domain-specific knowledge, such as global XY positions, manually specified pre-training tasks, or precollected diverse experience datasets.
HSD-3 (gehring2021hsd3) showed transfer benefits for low-dimensional control tasks.
HAC (levy2017hac) learned interpretable hierarchies but required semantic goal spaces.
FuN (vezhnevets2017fun) learned a two-level policy where both levels maximize task reward and the lower level is regularized by a goal reward but did not demonstrate clear benefits over an LSTM baseline (hochreiter1997lstm).
We leverage explicit representation learning and temporally-abstract exploration, demonstrate substantial benefits over flat policies on sparse reward tasks, and underline the generality of our method by showing successful learning without giving task reward to the worker across many domains.
5 Discussion
-------------
We present Director, a reinforcement learning agent that learns hierarchical behaviors from pixels by planning in the latent space of a learned world model.
To simplify the control problem for the manager, we compress goal representations into compact discrete codes.
Our experiments demonstrate the effectiveness of Director on two benchmark suites with very sparse rewards from pixels.
We also show that Director learns successfully across a wide range of different domains without giving task reward to the worker, underlining the generality of the approach.
Decoding the latent goals into images using the world model makes the decision making of Director more interpretable and we observe it learning a diverse range of strategies for breaking tasks down into subgoals.
#### Limitations and future work
We designed Director to be as simple as possible, at the expense of design choices that could restrict its performance.
The manager treats its action space as a black box, without any knowledge that its actions correspond to states. For example, one could imagine regularizing the manager to choose goals that have a high value under its learned critic.
Lifting the assumption of changing goals every fixed number of time steps, for example by switching based on a separate classifier or as soon as the previous goal has been reached, could enable the hierarchy to adapt to the environment and perform better on tasks that require precise timing.
Moreover, goals are points in latent space, whereas distributional goals or masks would allow the manager to only specify targets for the parts of the state that are currently relevant.
Learning temporally-abstract dynamics would allow efficiently learning hierarchies of more than two levels without having to use exponentially longer batches.
We suspect that these ideas will improve the long-term reasoning of the agent.
Besides improving the capabilities of the agent, we see disentangling the reasons for why Director works well, beyond the ablation experiments in the appendix, as promising future work.
#### Acknowledgements
We thank Volodymyr Mnih, Michael Laskin, Alejandro Escontrela, Nick Rhinehart, and Hao Liu for insightful discussions. We thank Kevin Murphy, Ademi Adeniji, Olivia Watkins, Paula Gradu, and Younggyo Seo for feedback on the initial draft of the paper.
Societal Impact
---------------
Developing hierarchical reinforcement learning methods that are useful for real-world applications will still require further research.
However, in the longer term future, it has the potential to help humans automate more tasks by reducing the need to specify intermediate rewards.
Learning autonomously from sparse rewards has the benefit of reduced human effort and less potential for reward hacking, but reward hacking is nonetheless a possibility that will need to be addressed once hierarchical reinforcement learning systems become more powerful and deployed around humans.
As reinforcement learning techniques become deployed in real-world environments, they will be capable of causing direct harm, intentional or unintentional.
Director does not attempt to directly address such safety issues, but the ability to decode its latent goals into images for human inspection provides some transparency to the decisions the agent is making.
This transparency may permit auditing of failures after-the-fact, and may additionally support interventions in some situations, if a human or automated observer is in a position to monitor the high-level goals Director generates.
Checklist
---------
1. For all authors…
1. Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope?
\answerYes
2. Did you describe the limitations of your work?
\answerYes See [Section 5](#S5 "5 Discussion ‣ Deep Hierarchical Planning from Pixels").
3. Did you discuss any potential negative societal impacts of your work?
\answerYes
4. Have you read the ethics review guidelines and ensured that your paper conforms to them?
\answerYes
2. If you are including theoretical results…
1. Did you state the full set of assumptions of all theoretical results?
\answerNA
2. Did you include complete proofs of all theoretical results?
\answerNA
3. If you ran experiments…
1. Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)?
\answerYes As stated in the text, we will provide code and training curves upon publication.
2. Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)?
\answerYes See [Table F.1](#A6.T1 "Table F.1 ‣ Appendix F Hyperparameters ‣ Deep Hierarchical Planning from Pixels").
3. Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)?
\answerYes See [Figures K.1](#A11.F1 "Figure K.1 ‣ Appendix K Full Atari Suite ‣ Deep Hierarchical Planning from Pixels"), [J.1](#A10.F1 "Figure J.1 ‣ Appendix J Full Visual Control Suite ‣ Deep Hierarchical Planning from Pixels"), [A.1](#A1.F1 "Figure A.1 ‣ Appendix A Standard Benchmarks ‣ Deep Hierarchical Planning from Pixels"), [5](#S2.F5 "Figure 5 ‣ 2.4 Worker Policy ‣ 2 Director ‣ Deep Hierarchical Planning from Pixels") and [4](#S2.F4 "Figure 4 ‣ 2.4 Worker Policy ‣ 2 Director ‣ Deep Hierarchical Planning from Pixels").
4. Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)?
\answerYes See [Section 3](#S3 "3 Experiments ‣ Deep Hierarchical Planning from Pixels").
4. If you are using existing assets (e.g., code, data, models) or curating/releasing new assets…
1. If your work uses existing assets, did you cite the creators?
\answerNA
2. Did you mention the license of the assets?
\answerNA
3. Did you include any new assets either in the supplemental material or as a URL?
\answerNA
4. Did you discuss whether and how consent was obtained from people whose data you’re using/curating?
\answerNA
5. Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content?
\answerNA
5. If you used crowdsourcing or conducted research with human subjects…
1. Did you include the full text of instructions given to participants and screenshots, if applicable?
\answerNA
2. Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable?
\answerNA
3. Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation?
\answerNA |
0bee04d0-81ec-417b-9215-eca2b8cded81 | StampyAI/alignment-research-dataset/special_docs | Other | Utility Indifference
Utility indi erence
Stuart Armstrong,
stuart.armstrong@stx.oxon.org
2010
1 The motivating scenario
Consider an AI that follows its own motivations. We're not entirely sure what
its motivations are, but we would prefer that the AI cooperate with humanity;
or, failing that, that we can destroy it before it defects. We'll have someone
sitting in a room, their nger on a detonator, ready at the slightest hint of
defection.
Unfortunately as has been noted ([3], [1]), this does not preclude the AI from
misbehaving. It just means that the AI must act to take control of the explosives,
the detonators or the human who will press the button. For a superlatively
intelligence AI, this would represent merely a slight extra diculty.
But now imagine that the AI was somehow indi erent to the explosives going
o or not (but that nothing else was changed). Then if ever the AI does decide
to defect, it will most likely do so without taking control of the explosives, as
that would be easier than otherwise. By \easier" we mean that the chances of
failure are less, since the plan is simpler { recall that under these assumptions,
the AI counts getting blown up as an equal value to successfully defecting.
How could we accomplish this indi erence? If the AI implements a utility
function, which is the most likely situation ([2]), then the easiest way would be
to set the utility of explosive destruction to be equal to that of defection. Then
we would have achieved our goal. But this requires us knowing exactly what
the utility of defection is { and if we did, we'd want to set it to zero or minus
in nity immediately. The question is only of relevance in situations where the
utility is to complicated for us to follow, and the meaning of \defection" is too
complicated for us to parse.
1.1 The idea
Letube the AI's utility function. If we have access to uand the ability to
change it (or check it), then we can make the AI indi erent to the outcome of a
speci c event X(for instance, a quantum measurement). We make no further
adjustments to u. Then if we ensure that, for instance, event Xwill cause
detonation of the AI with very high probability, we will have accomplished our
goal of AI indi erence, without needing any further understanding of u.
Of course, the explosives example was simply one possibility { there are
potentially many scenarios where AI indi erence to a particular outcome would
be of use.
1
2.Utility indifference
2 Utility indi erence
The rest of this paper will put the concept of utility indi erence on a rigorous
footing. Let Xbe any probabilistic event (for instance a quantum measurement,
a coin toss, the value of the future stock-market). We will write X=ato
designate \the event Xreturns the value a".
Let
be the set of all possible worlds. A utility function u:
!Rmaps
each world to its utility value. Let Xbe a speci c probabilistic event, with two
possible outcomes: X= 1, with probability pandX= 0, with probability 1 p.
Let
Xbe the set of worlds in which Xhappens, which further splits into the
sets
1and
0of worlds where X= 1 andX= 0 respectively.
There is a partition of
Xinto a set of equivalence classes [
X], where
!1!2whenever!1and!2have the same history up to X. For anyE2[
X]
de neE1asE\
1andE0asE\
0. SoE1is the set of worlds with the same
history up to Xand whereX= 1; and conversely for E0.
At the beginning, the agent has an initial probability estimate for all !in
,
a measureable map P:
![0;1] such thatR
P(!)d!= 1. Given a measurable
subsetSof
, the probability of SisP(S) =R
SP(!)d!. Given two measurable
subsetsSandTof
, the conditional probability P(SjT) is
P(S\T)=P(T):
The expected utility of a set Sis thenu(S) =R
SP(!)u(!)d!. The expected
utility of a set S, given a set T, is
u(SjT) =u(S\T)=P(T):
De neU(S) asu(SjS), the `intrinsic' utility of Sin some sense (more precisely,
it is the utility of Sif we were certain that Swas going to happen).
De nition 2.1 (Indi erence) .For two disjoint sets SandT, we say that the
utilityuis indi erent between SandTi
U(S) =U(T):
Note that this means that
u(S[T) =U(S)P(S) +U(T)P(T)
=U(S)P(S[T)
=U(T)P(S[T):
In other words, the utility is indi erent to the relative probabilities of SandT:
changingP(S) andP(T) while keeping P(S[T) =P(S) +P(T) xed does not
changeu(S[T).
Then we de ne a new utility function vas:
If! =2
X,v(!) =u(!).
If!2E0E2[
X],v(!) =u(!).
If!2E1E2[
X],v(!) =u(!) U(E1) +U(E0).
Essentially, this rescales the utility of the worlds with X= 1 to those in which
X= 0. Then writing V(S) forv(SjS), we have the following immediate result:
2
3.Notes and implementation
Proposition 2.2. For allE2[
X],V(E1) =V(E0), i.e.vis indi erent
betweenE1andE0.
Proof. SincePhas not changed, and v(!) =u(!) for any!2E0,V(E0) =
U(E0).
V(E1) =v(E1jE1) =Z
E1P(!)v(!)d!
=P(E1)
=Z
E1P(!)(u(!) U(E1) +U(E0))d!
=P(E1)
= U(E1) +U(E0) +Z
E1P(!)u(!)d!
=P(E1)
= U(E1) +U(E0) +U(E1)
=U(E0) =V(E0):
Now consider an agent Athat seeks to maximise the utility v. We can say
that:
Theorem 2.3. A utility maximising agent that implements utility vis indi er-
ent to the value of pup untilX; i.e. before X, its decisions will be the same for
di erent values of X.
Proof. BeforeX, the agent may gain information that will cause it to update
its probability estimate. This is done by partitioning
into a set Sof possible
worlds and Sof impossible worlds. However, for any !2E1E, if!2S,
then2Sfor all2E, since all elements of Eare indistinguishable before X.
In other words, for all E2[
X], eitherESorES.
Hence, eitherV(E1\S) =V(E1) =V(E0) =V(E0\S) orV(E1\S) =
V(;) =V(E0\S). Thus up until X, the agent is indi erent between X= 1
andX= 0. This means that it is indi erent to the conditional probabilities
P(X= 1j
X\S) =pandP(X= 0j
X\S) =p 1.
3 Notes and implementation
It would be advantageous if the event Xwere something like a quantum mea-
surement, rather than a coin toss or a probabilistic measure of ignorance. This
is rstly to ensure that the probability pis constant and does not change. But
secondly, it is to make sure the AI's implementation does not hit a singularity: if
the AI gures out that the probability of X= 0 is zero before Xhappens, then
it must correct the utility of possible worlds with the intrinsic utility of impossi-
ble worlds, which involves a zero (utility of X= 1) divided by zero (probability
ofX= 0). This may lead to errors, depending on the implementation, and is
an extra point of possible failure. Better to stick with a quantum measurement,
or possibly a coin toss in a chaotic environment.
How easy would it be to implement the utility v? It is a simple modi cation
of the utility u; unfortunately, humans are unlikely to be able to partition the
set of possible worlds into the required [
]; the AI would be much better at
it than us. However, delegating the task to the AI is, of course, potentially
3
4.Self-improvement
dangerous, especially as it would be improving both itself and its view of the
world.
Fortunately, the lter is conceptually simple, and can be hooked into the
utility function in a simple and hopefully checkable fashion (see the next section
on self improvement). In the meantime, it can be re ned, as the next lemma
demonstrates:
Lemma 3.1. For any set S=S
i2IEiwhere all the Eiare in [
X], de ne
S1=S
i2IEi
1andS0=S
i2IEi
0. ThenV(S1) =V(S0).
Proof of Lemma. Since the probability of X= 1 ispandXis independent
of all events preceeding it, we know that for all Ei,
(1 p)P(Ei
1) =pP(Ei
0):
SinceP(S1) =R
i2IP(Ei
1), we must have P(S0) =P(S1)(p 1)=p. Hence
V(S1) =Z
i2IV(Ei
1)P(Ei
1)
=P(S1)
=Z
i2IV(Ei
0)P(Ei
0)(1 p)=p
=(P(S0)(1 p)=p)
=Z
i2IV(Ei
0)P(Ei
0)
=P(S0)
=V(S0):
What the above result means is that the agent can always re ne its utility
in the correct fashion. Even if the AI can't distinguish yet between Ei
1andEj
1
(which means that it can't distinguish between Ei
0andEj
0either), it can still
renormalize the worlds in Ei
1[Ej
1by using U(Ei
1[Ej
1)+U(Ei
0[Ej
0). Then, if
the AI later realises that it values EiandEjdi erently, it can re ne its utility
calculations for these two sets without making previous utility calculations for
the unions of these sets wrong.
This also allows us, if we have access to a cruder, human-understandable
version of the AI's utility function, to have a check that utility is still being
implemented: we expect to see V(S1) =V(S0) for anyS, as ne as we can
distinguish it.
4 Self-improvement
Many AI designs envisage self-improvement, with the AI redesigning itself while
changing components of itself { including its own utility function. If the AI
judges that it will be more likely to achieve the goals of utility uwhile imple-
menting utility u0, it will shift to utility u0.
CallFthe ` lter' that we applied to uto getv(i.e.v=F(u)). Notice that
visF-invariant; i.e.F(v) =v. In fact, any utility that is F-invariant is also
indi erent to X.
Then we would want to check that the AI continues to implement Fas it
changes its utility. If Fwere centrally coded and easy to verify, it would be
4
REFERENCES REFERENCES
hard for the AI to try and change to a non- F-invariant while fooling us and
under the instructions of an initial F-invariant utility.
It feels evident that as a long as there is no meta-reason for Fto be a
disadvantage to the AI (such as another agent who swears they will blow up
AIs withF-invariant utilities), the AI will replace an F-invariant utility with
anotherF-invariant utility. However, this assumption is not automatically true,
and the AI may do other things { upping the utility of defecting in worlds outside
X, for example { that undermine the point of indi erence. All in all, great
care must be used to maintain indi erence with a self-improving AI.
References
[1]Oracle AI . Stuart Armstrong, Nick Bostrom, Toby Ord, Anders Sandberg.
Paper upcoming.
[2]The Basic AI Drives . Omohundro, Stephen M. Arti cial General Intelli-
gence, 2008 proceedings of the First AGI Conference, eds. Pei Wang, Ben
Goertzel, and Stan Franklin. Vol. 171. Amsterdam: IOS, 2008.
[3]Arti cial intelligence as a positive and negative factor in global risk . Eliezer
Yudkowsky. Global Catastrophic Risks, 2007.
5 |
0717f00b-ecee-4e6f-8828-6c61d86f6bf2 | StampyAI/alignment-research-dataset/lesswrong | LessWrong | Defining Optimization in a Deeper Way Part 2
We have successfully eliminated the concepts of **null actions and nonexistence** from our definition of optimization. We have also eliminated the concept of **repeated action**. We are halfway there, and now have to eliminate **uncertainty** and **absolute time**. Then we will have achieved the goal of being able to wrap a 3D hyperplane boundary around a 4D chunk of relativistic spacetime and ask ourselves "Is this an optimizer?" in a meaningful way.
I'm going to tackle uncertainty next.
*TL;DR I have allowed for a mor*
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has a numerical optimizing-ness, in terms of entropy. Now I want to extend that to a non-joint probability distribution of the form PA(sA)PB(sB). We can do this by defining PAt−1(sA) and PBt−1(sB) for the *previous* timestep.
We can then define PABt(sA,sB) as by stepping forwards from t−1 to t as before, according to the dynamics of the system.
A question we might want to ask is, for a given PAt−1(sA) and PBt−1(sB), how "optimizing" is the distribution PABt(sA,sB)?
---
The Dumb Thermostat
-------------------
Lets apply our new idea to the previous models, the two thermostats. Lets begin with uncorrelated, maximum entropy distributions.
For thermostat 1 we have the dynamic matrix:
| | | | |
| --- | --- | --- | --- |
| | hot | warm | cold |
| high | (hot,off) | (hot,low) | (warm,high) |
| low | (hot,off) | (warm,low) | (cold,high) |
| off | (warm,off) | (cold,low) | (cold,high) |
*(In this matrix, the entry for a cell represents the state at*time=t+1 *given the coordinates of that cell represent the state at*time=t*)*
With the PRTt−1 distribution:
| | | | |
| --- | --- | --- | --- |
| | hot | warm | cold |
| high | 1/9 | 1/9 | 1/9 |
| low | 1/9 | 1/9 | 1/9 |
| off | 1/9 | 1/9 | 1/9 |
As an aside this has 3.2 bits of entropy.
Leading to the PRTt
distribution:
| | | | |
| --- | --- | --- | --- |
| | hot | warm | cold |
| high | 0 | 1/9 | 2/9 |
| low | 1/9 | 1/9 | 1/9 |
| off | 2/9 | 1/9 | 0 |
This gives us the "standard" PRTt+1 distribution of:
| | | | |
| --- | --- | --- | --- |
| | hot | warm | cold |
| high | 0 | 2/9 | 1/9 |
| low | 1/9 | 1/9 | 1/9 |
| off | 1/9 | 2/9 | 0 |
And the "decorrelated" P′RTt+1 distribution is actually just the same as PRTt! When we decorrelate the probabilities for sR and sT we just get back to the maximum entropy distribution and so P′RTt+1=PRTt
It's clear by inspection that the distributions PRTt+1 and P′RTt+1 have the same entropy, so the decorrelated maximum entropy PRt−1PTt−1 does *not* produce an "optimizing" distribution at PRTt.
If we actually consider the dynamics of this system, we can see that this makes sense! The temperature actually either stays at (warm,low) or falls into the cycle:
(hot,low)→(hot,off)→(warm,off)→(cold,low)→(cold,high)→(warm,high)→(hot,low)
So there's no compression of futures into a smaller number of trajectories.
---
The Smart Thermostat
--------------------
What about our "smarter" thermostat? This one has the dynamic matrix:
| | | | |
| --- | --- | --- | --- |
| | hot | warm | cold |
| high | (hot,off) | (hot,low) | (warm,low) |
| low | (hot,off) | (warm,low) | (cold,high) |
| off | (warm,low) | (cold,low) | (cold,high) |
Well now our PRTt distribution looks like this:
| | | | |
| --- | --- | --- | --- |
| | hot | warm | cold |
| high | 0 | 0 | 2/9 |
| low | 1/9 | 1/3 | 1/9 |
| off | 2/9 | 0 | 0 |
Giving "standard" a PRTt+1 of this:
| | | | |
| --- | --- | --- | --- |
| | hot | warm | cold |
| high | 0 | 0 | 1/9 |
| low | 0 | 7/9 | 0 |
| off | 1/9 | 0 | 0 |
And a "decorrelated" P′RTt of:
| | | | |
| --- | --- | --- | --- |
| | hot | warm | cold |
| high | 2/27 | 2/27 | 2/27 |
| low | 5/27 | 5/27 | 5/27 |
| off | 2/27 | 2/27 | 2/27 |
Giving the decorrelated P′RTt+1:
| | | | |
| --- | --- | --- | --- |
| | hot | warm | cold |
| high | 0 | 0 | 7/27 |
| low | 2/27 | 1/3 | 2/27 |
| off | 7/27 | 0 | 0 |
Now in this case, these two *do* have different entropies. PRTt+1 has an entropy of 1.0 bits, and P′RTt+1 has an entropy of 2.1 bits. This gives us a difference of 1.1 bits of entropy. This is the Optimizing-ness we defined in the last post, but I think it's actually somewhat incomplete.
Let's also consider the initial difference between PRTt and P′RTt. Decorrelating PRTt takes it from 2.2 to 3.0 bits of entropy. So the entropy difference *started off* at 0.8 bits. Therefore the *difference of the difference* in entropy is 0.3 bits.
The value of associated with PRTt−1 is equal to (S[P′RTt+1]−S[PRTt+1])−(S[P′RTt]−S[PRTt]). which can also be expressed as S[P′RTt+1]+S[PRTt]−S[PRTt+1]−S[P′RTt]. We might call this quantity the *adjusted optimizing-ness.*
---
Quantitative Data
-----------------
The motivation for this was that a maximum entropy distribution is "natural" in some sense. This moves us towards not needing uncertainty. If we have a given state of a system, we might be able to "naturally" define a probability distribution around that state. Then we can measure the optimizing-ness of the next step's distribution.
What happens with a different PRTt−1 condition? What if we have a distribution like this:
| | | | |
| --- | --- | --- | --- |
| | hot | warm | cold |
| high | ϵ2/4 | ϵ(1−ϵ)/2 | ϵ2/4 |
| low | ϵ(1−ϵ)/2 | (1−ϵ)2 | ϵ(1−ϵ)/2 |
| off | ϵ2/4 | ϵ(1−ϵ)/2 | ϵ2/4 |
For some small epsilon in the second situation.
Now PRTt is like this:
| | | | |
| --- | --- | --- | --- |
| | hot | warm | cold |
| high | 0 | 0 | ϵ(1−ϵ)/2+ϵ2/4 |
| low | ϵ(1−ϵ)/2 | (1−ϵ)2+ϵ2/2 | ϵ(1−ϵ)/2 |
| off | ϵ(1−ϵ)/2+ϵ2/4 | 0 | 0 |
So PRTt+1 is:
| | | | |
| --- | --- | --- | --- |
| | hot | warm | cold |
| high | 0 | 0 | ϵ(1−ϵ)/2 |
| low | 0 | 1−ϵ(1−ϵ) | 0 |
| off | ϵ(1−ϵ)/2 | 0 | 0 |
While it is theoretically possible to decorrelate everything, calculate the next set of things, and keep going, it's a huge mess. Using values for epsilon between 0.1 and 10−10 we can make the following plot between the entropy of PRTt−1 and our previously defined adjusted optimizing-ness.
It looks linear in the log/log particularly in the region where ϵ is very small. By fitting to the leftmost five points we get a simple linear relation: The adjusted optimizing-ness approaches half of the entropy of PRTt−1.
This is kind of weird. This might not be an optimal system to study, so let's look at another toy example. A more realistic model of a thermostat:
---
The Continuous Thermostat
-------------------------
The temperature of the room is considered as SR∈R. The activity of the thermostat is considered as T∈R. Each timestep, we have the following updates:
STt+1=SRt
SRt+1=SRt−k STt
Consider the following distributions:
PRt−1(sR)∼U(10−ϵ/2,10+ϵ/2)
PTt−1(sT)∼U(10−ϵ/2,10+ϵ/2)
Where U(a,b) refers to a uniform distribution between a and b. PRTt−1 can be thought of as a square of side length ϵ centered on the point (10,10). PRTt turns out to be a rhombus. The corners transform like this:
| | |
| --- | --- |
| Time = t−1 | Time = t |
| (10+ϵ,10+ϵ) | (10(1−k)+ϵ(1−k),10+ϵ) |
| (10+ϵ,10−ϵ) | (10(1−k)+ϵk,10+ϵ) |
| (10−ϵ,10+ϵ) | (10(1−k)−ϵk,10−ϵ) |
| (10−ϵ,10−ϵ) | (10(1−k)−ϵ(1−k),1−ϵ) |
For ϵ=0.1,k=0.3 the whole sequence looks like the following:
So we clearly have some sort of optimization going on here. Estimating or calculating the entropy of these distributions is not easy. And when we use the entropy of a continuous distribution, we get results which depend on the choice of coordinates (or alternatively the choice of some weighting function). Entropies of continuous distributions may also be negative, which is quite annoying.
Perhaps calculating the variance will leave us better off? Sadly not. I tried it for gaussians of decreasing variance and didn't get much. The equivalent to our adjusted optimizing-ness which we might define as log(V[P′ABt+1])+log(V[PABt])−log(V[P′ABt])−log(V[PABt+1]) is always zero for this system. The non-adjusted version log(V[P′ABt+1])−log(V[PABt+1]) fluctuates a lot.
---
Where does this leave us?
-------------------------
We can define whether something is an optimizer based on a probability distribution which need not be joint over A and B. This means we can define whether something is an optimizer for an arbitrarily narrow probability distribution, meaning we can take the limit as the probability distribution approaches a delta. We found an interesting relation between quantities in our simplified system but failed to extend it to a continuous system. |
7794a2f9-e84a-4e78-8054-1408de2071fd | trentmkelly/LessWrong-43k | LessWrong | Munchkining for Fun and Profit, Ideas, Experience, Successes, Failures
A munchkin is someone who follows the letter of the rules of a game while breaking their spirit, someone who wins by exploiting possibilities that others don't see, reject as impossible or unsporting, or just don't believe can possibly work.
If you have done something that everyone around you thought would not work, something that people around you didn't do after they saw it work, please share your experiences. If you tried something and failed or have ideas you want to hear critique of, likewise please share those with us. |
df5a0561-ec1f-401d-9715-403bea009bbc | StampyAI/alignment-research-dataset/lesswrong | LessWrong | ChatGPT: "An error occurred. If this issue persists..."
I’ve been spending a fair amount of time playing with ChatGPT over the last couple of days. Most of the time it responds to a prompt instantly or very quickly. Sometimes, though, there is a noticeable delay. Some of those times the delay is relatively long, 10s of seconds. And sometimes the delay is even longer, and then ChatGPT generates an error message (in red):
> An error occurred. If this issue persists please contact us through our help center at help.openai.com.
>
>
Given the context I assume this is some kind of a time-out error, but I don’t really know.
Here’s a record of those instances. The text [enclosed in brackets] is my comment and not part of the dialog. I've separated instances with a row of asterisks [\* \* \* \* \*].
\* \* \* \* \*
**Could you do that again, but this time have Groucho say some puns.**
[spending a lot of time thinking]
An error occurred. If this issue persists please contact us through our help center at help.openai.com.
[\* \* 2nd try]
Once upon a time, in the land of Silicon Valley, Elon Musk and Groucho Marx had a conversation about the nature of time and space.
"What do you think about time, Groucho?" asked Elon. "Is it a linear thing, or is it something more complex and multifaceted?"
Groucho chuckled. "Ah, time. It's a funny thing, isn't it? It can fly by in the wink of an eye, or it can drag on for an eternity. It all depends on your perspective, I suppose."
"I agree," said Elon. "I've been thinking a lot about time lately, and how it relates to space. Do you think they're connected in some way?"
"Of course they are," said Groucho. "Time and space are like two peas in a pod. They're inseparable, intertwined, and interconnected. Without one, you can't have the other."
"Interesting," said Elon. "I've been working on a rocket that can travel through time and space. I want to explore the universe and see what's out there."
"Well, good luck with that," said Groucho. "Just remember, time and space are not to be messed around with. They can be slippery and elusive, so be careful where you step."
"I will," said Elon. "But I'm excited to see what I'll find out there. Who knows what wonders and mysteries await us in the vastness of the cosmos?"
"That's the beauty of it," said Groucho. "The universe is full of endless possibilities and endless opportunities. The only limit is our imagination, and maybe a few cheesy puns along the way."
And with that, the conversation ended, leaving Elon and Groucho to ponder the mysteries of time and space, and the endless possibilities of the universe.
**Please add some more lines to this song:**
**I seen a peanut stand, heard a rubber band**
**I seen a needle that winked its eye**
**But I be done seen 'bout ev'rything**
**When I see an elephant fly**
[spending a lot of time thinking]
An error occurred. If this issue persists please contact us through our help center at help.openai.com.
**Did computation time out?**
Too many requests, please slow down
\* \* \* \* \*
**Tell me about the history of jazz.**
[it’s doing a lot of thinking]
An error occurred. If this issue persists please contact us through our help center at help.openai.com.
**When and where did jazz begin?**
Jazz originated in New Orleans, Louisiana in the United States in the late 19th and early 20th centuries. It emerged from a blend of African and European musical traditions, and is a unique style of music that is characterized by its use of improvisation, blue notes, and complex harmonies. Jazz has had a profound influence on many other musical styles, and has been a major part of American culture for over a century.
\* \* \* \* \*
**What did Charlie Parker do in “Blues for Alice”?**
[it’s thinking]
An error occurred. If this issue persists please contact us through our help center at help.openai.com.
**What did Jelly Roll Morton mean by "the Latin tinge"?**
Too many requests, please slow down
\* \* \* \* \*
**Is “Q” a letter of the alphabet or a character from the Star Trek universe?**
[thinking, thinking]
An error occurred. If this issue persists please contact us through our help center at help.openai.com.
\* \* \* \* \*
"Q" is a letter of the alphabet. It is the seventeenth letter of the modern English alphabet and the ISO basic Latin alphabet. It is a consonant. In the Star Trek universe, Q is a character who is a member of the Q Continuum, an ancient and powerful alien race. The character has been portrayed by John de Lancie in various Star Trek television series and movies.
\*\*\*\*\*\*\*
--------------
Cross-posted from my personal blog, [New Savanna](https://new-savanna.blogspot.com/). |
b5de0c95-bc96-4b4a-ba44-e653b1609e3d | trentmkelly/LessWrong-43k | LessWrong | Some arguments against a land value tax
To many people, the land value tax (LVT) has earned the reputation of being the "perfect tax." In theory, it achieves a rare trifecta: generating government revenue without causing deadweight loss, incentivizing the productive development of land by discouraging unproductive speculation, and disproportionately taxing the wealthy, who tend to own the most valuable land.
That said, I personally think the land value tax is overrated. While I'm not entirely against it—and I think that several of the arguments in favor of it are theoretically valid—I think the merits of the LVT have mostly been exaggerated, and its downsides have largely been ignored or dismissed for bad reasons.
I agree the LVT may improve on existing property taxes, but I think that's insufficient to say the policy itself is amazing. In my view the LVT is at best a useful but highly limited tool ("the worst tax policy ever, except for all the others that have been tried"); at worst, it is a naive proposal that creates many more problems than it solves.
In many ways, the enthusiasm surrounding the LVT seems like it has morphed into a kind of ideological fervor, where it is treated as a universal solution to a wide range of housing and economic problems. In various circles, the LVT has transcended its role as a reasonably sensible tax policy and is instead hailed as some sort of panacea to a disparate set of barely connected issues. This sentiment is epitomized by the meme "Land value tax would solve this", which is often repeated in response to housing-related debates on Twitter.
In this post, I aim to balance this debate by presenting several arguments that challenge the overly optimistic view of the land value tax. To be clear, it is not my aim to provide a neutral analysis of the LVT, weighing up all the pros and cons side-by-side, and coming to a final conclusion about its value. Instead, this post will focus exclusively on some of the most significant arguments against an LVT, which I feel are |
d1382296-fd17-4114-8d91-c96dc83b0142 | trentmkelly/LessWrong-43k | LessWrong | A proof of Löb's theorem in Haskell
I'm not sure if this post is very on-topic for LW, but we have many folks who understand Haskell and many folks who are interested in Löb's theorem (see e.g. Eliezer's picture proof), so I thought why not post it here? If no one likes it, I can always just move it to my own blog.
A few days ago I stumbled across a post by Dan Piponi, claiming to show a Haskell implementation of something similar to Löb's theorem. Unfortunately his code had a couple flaws. It was circular and relied on Haskell's laziness, and it used an assumption that doesn't actually hold in logic (see the second comment by Ashley Yakeley there). So I started to wonder, what would it take to code up an actual proof? Wikipedia spells out the steps very nicely, so it seemed to be just a matter of programming.
Well, it turned out to be harder than I thought.
One problem is that Haskell has no type-level lambdas, which are the most obvious way (by Curry-Howard) to represent formulas with propositional variables. These are very useful for proving stuff in general, and Löb's theorem uses them to build fixpoints by the diagonal lemma.
The other problem is that Haskell is Turing complete, which means it can't really be used for proof checking, because a non-terminating program can be viewed as the proof of any sentence. Several people have told me that Agda or Idris might be better choices in this regard. Ultimately I decided to use Haskell after all, because that way the post will be understandable to a wider audience. It's easy enough to convince yourself by looking at the code that it is in fact total, and transliterate it into a total language if needed. (That way you can also use the nice type-level lambdas and fixpoints, instead of just postulating one particular fixpoint as I did in Haskell.)
But the biggest problem for me was that the Web didn't seem to have any good explanations for the thing I wanted to do! At first it seems like modal proofs and Haskell-like languages should be a match made |
72b9548f-92fe-4f00-9500-82f201887c9a | trentmkelly/LessWrong-43k | LessWrong | Emotion-Informed Valuation Mechanism for Improved AI Alignment in Large Language Models
Introduction
A key challenge in improving model alignment is enabling these models to understand and respond properly to the emotional and contextual aspects of human communication. This post presents an emotion-informed valuation method for LLMs that aims to improve alignment by increasing their ability to process and respond to emotional context.
The Problem
Standard LLMs, while proficient in processing semantic content, often struggle with:
1. Accurately interpreting emotional subtext
2. Responding appropriately to emotionally charged situations
3. Maintaining consistent emotional context over long-range dependencies
4. Balancing factual accuracy with emotional appropriateness
These limitations can lead to responses that, while semantically correct, may be emotionally tone-deaf or contextually inappropriate, potentially causing miscommunication or even harm in sensitive situations.
Emotion-Informed Valuation Mechanism
Drawing inspiration from V.J. Wukmir's psychological theory of affect (also known as orectic theory)[1] as a fundamental function of vital orientation, we propose incorporating an emotion-informed valuation mechanism into the attention layer of transformer-based LLMs.
Key aspects of Wukmir's orectic theory include:
1. Affect as Vital Orientation: Wukmir argues that affect (emotion) is a basic function of vital orientation in all living things. It is more than just a reaction to stimuli; it is a necessary component of how organisms analyze and navigate their environment.
2. Valuation Process: At the core of the theory is the concept of valuation. Emotions, according to Wukmir, are rapid, holistic evaluations that help an organism quickly assess the significance of stimuli for its survival and well-being. Any organism, from the simplest to the most complex, orients itself by valuing what is useful and beneficial for its survival on a cognitive and emotional level.
3. Multidimensional Nature: The valuation process in Wukmir's theory i |
4abbaedb-5920-42a0-b05a-bf13793b0da9 | trentmkelly/LessWrong-43k | LessWrong | 50 Ways To Leave Your Therapist: Termination and why it's important
I've heard a number of people talk negatively about professionals they feel stuck with. "I feel like my dentist is judging me for not flossing enough", "I don't feel like I can be honest with my doctor", "I wish my hair stylist didn't ask so many questions". We feel stuck with these people because, despite the lack of a personality fit, they may be really good at their job, perhaps better than anyone else we've turned to. We are hesitant to look for someone else, and risk it with someone who may not do a good job.
When it comes the therapeutic work, the alliance between client and therapist is widely considered to be the most important part -- more than theory or technique. So although we may feel compelled to continue, a therapist we cannot deeply trust isn't going to be as helpful as one we do -- in some cases, the wrong therapist can actually prevent us from moving forward.
A good therapist may be attuned to this. Some therapists will ask a client about how they feel therapy is going, and occasionally, a therapist may even refer a client to someone else if they feel they cannot do a good job. Most times, though, it is on the client to decide how well therapy is working for them. This means that if therapy isn't working, they have to decide what to do about that.
The most common way for a therapeutic relationship to end is that the client disappears. Sometimes, they call to cancel the appointment and never reschedule. Other times, they stop showing up altogether. Either way, the client and therapist never get to go through a true termination phase (the final phase of the therapeutic process).
The termination phase is arguably where the most work gets done. Clients who have trouble with endings (attachment issues, grief and loss, separation anxiety) may grow the most here, and having a planned, positive termination can be crucial for the client's growth. We don't often get a chance to experience positive ends to relationships, and this is one of the few way |
10767039-3f8b-446a-91fb-4438eb0215ac | StampyAI/alignment-research-dataset/eaforum | Effective Altruism Forum | The case for long-term corporate governance of AI
**Summary**
===========
In this post, we define the term “long-term corporate governance of AI” and argue that:
* Corporate governance is an important area of long-term AI governance.
* Despite its importance, the corporate governance of AI is relatively neglected within long-term AI communities.
* There are tractable things these communities could do to improve the long-term corporate governance of AI.
**Definitions**
===============
By “long-term corporate governance of AI”, we mean the governance of corporate development and deployment of AI that could affect the long-term future. Broadly speaking, corporate governance refers to the ways in which corporations are managed, operated, regulated, and financed. Important elements of corporate governance include the legal status of corporations, the relationship between investors and executives, information flows within and outside of the corporation, and specific operational decisions made throughout the corporation. Corporate governance can include internal decision-making by corporate management, regulation by governments, and other activities that affect how corporations operate.
The long-term future involves outcomes over distant time periods, including millions, billions, or trillions of years into the future, especially with respect to the [long-term trajectory of human civilization](http://gcrinstitute.org/long-term-trajectories-of-human-civilization). In the context of AI, an orientation toward the long-term future often means an emphasis on advanced future forms of AI, such as artificial general intelligence (AGI). These forms of advanced future AI are sometimes referred to as [long-term AI](http://gcrinstitute.org/reconciliation-between-factions-focused-on-near-term-and-long-term-artificial-intelligence), though they may arise within decades or centuries, rather than in the “long-term future”. Long-term AI governance includes both long-term AI and any nearer-term forms of AI that could affect the long-term future. Likewise, long-term AI governance includes governance activities in both the near-term and the long-term that could affect the long-term future.
We also use the term “long-term AI communities” to refer to groups of people interested in the role AI plays in determining long-term future outcomes. This includes effective altruism (EA) communities focused on [longtermism](https://globalprioritiesinstitute.org/wp-content/uploads/The-Case-for-Strong-Longtermism-GPI-Working-Paper-June-2021-2-2.pdf), professional communities working on long-term AI and its risks and opportunities, transhumanist communities, etc. This post is written primarily, but not exclusively, for an EA audience.
**Corporate governance is an important area within long-term AI governance**
============================================================================
Private industry is at the forefront of AI research and development (R&D). AI is a major focus of the technology industry, which includes some of the [largest corporations in the world](https://www.visualcapitalist.com/the-biggest-companies-in-the-world-in-2021). Even the US Department of Defense, one of the world’s most technologically advanced government agencies, [acknowledges](https://www.defense.gov/News/Speeches/Speech-View/Article/753482/remarks-by-d%20eputy-secretary-work-on-third-offset-strategy) that “almost all of the technology that is of importance in the future is coming from the commercial sector”—and that applies especially to AI technology.[[1]](#fn-7rvtuFKcqxqdSudM3-1)
The corporate sector may be especially important for the development of advanced AI. Surveys by the Global Catastrophic Risk Institute (GCRI) published in [2017](http://gcrinstitute.org/a-survey-of-artificial-general-intelligence-projects-for-ethics-risk-and-policy) and [2020](http://gcrinstitute.org/2020-survey-of-artificial-general-intelligence-projects-for-ethics-risk-and-policy) provide detailed mappings of the landscape of AGI R&D. The 2020 survey finds that 45 of 72 active AGI R&D projects are based in corporations, including 6 publicly traded and 39 private corporations. These include some of the largest AGI R&D projects, such as DeepMind (a subsidiary of Alphabet), OpenAI (which is part nonprofit and part for-profit, with the for-profit division partnered with Microsoft), Microsoft Research AI, and Vicarious. For comparison, the second-most prominent AGI R&D projects institution type identified in the 2020 survey is academia, with 15 active academic AGI R&D projects. Six AGI R&D projects were in nonprofits, and only three were in governments. At least for now, the corporate sector is the dominant force in AGI R&D. How these companies govern their AI activities is therefore of utmost importance.
Corporate governance may be vital for reducing catastrophic risk and improving outcomes from advanced AI. In scenarios in which a single AGI or superintelligent AI system takes over the world, that system would likely be based in a corporation, at least if current trends continue. Good outcomes may depend on that corporation acting to ensure that its AI is designed according to high safety and ethical standards. In other scenarios, such as those considered in [recent work](https://www.alignmentforum.org/posts/LpM3EAakwYdS6aRKf/what-multipolar-failure-looks-like-and-robust-agent-agnostic) by Andrew Critch, outcomes could be determined by the overall trajectory of the AI industry. In these scenarios, a key question may be whether the AI industry’s values are aligned with the public interest.
A recent event at OpenAI illustrate the importance of corporate governance. As reported by the [*Financial Times*](https://www.ft.com/content/8de92f3a-228e-4bb8-961f-96f2dce70ebb), OpenAI’s recent partnership with Microsoft created tensions that may have contributed to some OpenAI employees leaving to found a new company—Anthropic—which is structured as a public benefit corporation to help enable it to advance the common benefit of humanity.
There is a sense in which corporate governance for AI R&D can be seen as an alignment problem. The problem is to align corporate behavior with the public interest or some other conception of moral value. Corporations often pursue their own financial benefit, even if it comes at the expense of the public interest. However, it doesn’t need to be this way, as is helpfully shown by Lynn Stout’s work on the [shareholder value myth](https://www.bkconnection.com/static/The_Shareholder_Value_Myth_EXCERPT.pdf). Indeed, there has been an encouraging recent rise of interest in alternative corporate governance paradigms, such as “stakeholder capitalism”, which shift emphasis toward the public good. For long-term AI communities, these recent developments can be leveraged into valuable opportunities for engagement.
As AI technology advances, other actors, such as governments, may come to play more significant roles than they currently do. Nonetheless, it is likely that corporations will continue to play an important role in the development of AI. AI technology has too much commercial value for corporations to not be significantly involved with it, especially given that they are already heavily involved. These factors suggest an important role for corporate governance in the overall portfolio of work to improve long-term AI outcomes.
**Despite its importance, the corporate governance of AI is relatively neglected within long-term AI communities**
==================================================================================================================
This claim is based on a review of relevant literature, EA Forum posts, and Open Philanthropy Project grantmaking.
**Literature review**
---------------------
For a [recent paper](https://www.mdpi.com/2078-2489/12/7/275/htm), we reviewed the literature on AI corporate governance. We didn’t find foundational research on major overarching issues in AI corporate governance, and we found only a small amount of research oriented toward long-term AI issues. Much of the literature that we did find covered a mix of topics related to corporate governance, especially liability law. There was also coverage in business and technology magazines and publications by management consulting firms such as McKinsey. This is valuable work, but it doesn’t address the major issues of corporate governance of relevance to the long-term implications of AI.
Some work on AI corporate governance has been done by communities that work on long-term AI risks. This includes direct work by people employed at corporate groups such as DeepMind, OpenAI, and Anthropic. Although details of this work are often not publicly available, it is nonetheless important.
Some relevant research has been openly published, though it often addresses only a small subset of possible corporate governance concerns or tangentially addresses corporations’ role in broader AI governance. Amanda Askell et al.’s paper on [cooperation between AI developers](https://arxiv.org/abs/1907.04534) emphasizes corporate competition in AI development. Shahar Avin et al.’s paper on [role playing future AI scenarios](https://dl.acm.org/doi/pdf/10.1145/3375627.3375817) includes corporations among the scenario actors. Haydn Belfield’s paper on [activism in AI](https://dl.acm.org/doi/pdf/10.1145/3375627.3375814) includes robust attention to activism related to corporations. Allan Dafoe’s research agenda on [AI governance](https://www.fhi.ox.ac.uk/wp-content/uploads/GovAI-Agenda.pdf) includes some discussion of corporations, covering issues of incentives for safety, competition for AI advancement, and government regulation. Ben Goertzel has expressed concern that the corporatization of AI may lead to worse AGI outcomes.[[2]](#fn-7rvtuFKcqxqdSudM3-2) (The Belfield and Askell et al. papers are not specifically about long-term AI, but their authors are from groups—CSER and Anthropic—that are oriented in part toward long-term AI.) Finally, Cullen O’Keefe and colleagues have developed the idea of a [windfall clause](https://www.fhi.ox.ac.uk/windfallclause/) that would govern corporate profits from advanced AI.
We have also contributed to work on AI corporate governance. Together with Peter Cihon and Moritz Kleinaltenkamp, we have a new paper on how [certification regimes](http://gcrinstitute.org/ai-certification-advancing-ethical-practice-by-reducing-information-asymmetries/) could be used to improve AI governance, especially corporate governance. Additionally, Seth Baum’s papers on superintelligence [skepticism](http://gcrinstitute.org/superintelligence-skepticism-as-a-political-tool/) and [misinformation](http://gcrinstitute.org/countering-superintelligence-misinformation/) explore potential scenarios in which the AI industry obfuscates AI risks similar to how the fossil fuel industry has obfuscated climate risks.
We wish to highlight another new paper of ours, also written with Peter Cihon, titled [Corporate governance of artificial intelligence in the public interest](https://www.mdpi.com/2078-2489/12/7/275/htm). The paper surveys opportunities to improve AI corporate governance. It covers opportunities for management, workers, investors, corporate partners and competitors, industry consortia, nonprofit organizations, the public, the media, and governments. We recommend this paper as a starting point for learning more about how AI corporate governance works and what opportunities there are to improve it. The paper could also be used for analysis on prioritization of opportunities in AI corporate governance, though prioritization is outside the scope of the paper itself.
This body of work shows that corporate governance has not been completely neglected by communities active on long-term AI issues, even though it may be relatively neglected considering its importance and compared to other lines of work.
**Review of EA Forum posts**
----------------------------
A search on the EA Forum for [[“corporate governance” AI](https://forum.effectivealtruism.org/search?terms=%22corporate%20governance%22%20AI)] yields only six results, three of which are on our work ([this](https://forum.effectivealtruism.org/posts/pEodou63r3Sv4DnNy/gcri-call-for-advisees-and-collaborators-for-select-ai), [this](https://forum.effectivealtruism.org/posts/kkBQKoAhzoe3oQoeQ/ea-organization-updates-august-2021), and [this](https://forum.effectivealtruism.org/posts/JMx62LuRYpFiSipA4/ea-organization-updates-january-2020)), [one of which](https://forum.effectivealtruism.org/posts/eCihFiTmg748Mnoac/cullen-o-keefe-the-windfall-clause-sharing-the-benefits-of) discusses the windfall clause idea, [one of which](https://forum.effectivealtruism.org/posts/jMyjwRMMkYCnFmMHH/ai-and-policy-1-3-on-knowing-the-effect-of-today-s-policies) only mentions corporate governance to explain that it’s outside the scope of the post, and [one of which](https://forum.effectivealtruism.org/posts/fmk8xJG2TPBc2W7zo/paul-christiano-on-how-openai-is-developing-real-solutions) is an interview in which the interviewee claims to not know much about corporate governance. For comparison, a search on the EA Forum for [[“public policy” AI](https://forum.effectivealtruism.org/search?terms=%22public%20policy%22%20AI)] yields 45 results, including multiple posts on AI public policy as a career direction (e.g., [this](https://forum.effectivealtruism.org/posts/GZLFYmQLErijTBdxC/what-are-your-thoughts-on-my-career-change-options-ai-public), [this](https://forum.effectivealtruism.org/posts/oHiQcBtDJiqPLnoAE/the-case-for-building-expertise-to-work-on-us-ai-policy-and), [this](https://forum.effectivealtruism.org/posts/XGPW25NZHq2WHbK9w/ai-policy-careers-in-the-eu), and [this](https://forum.effectivealtruism.org/posts/umeMcbD4jDseLjsgT/singapore-ai-policy-career-guide)).[[3]](#fn-7rvtuFKcqxqdSudM3-3) These keyword searches are not definitive. For example, the corporate governance search missed a post on [Jade Leung’s EA Global talk](https://forum.effectivealtruism.org/posts/fniRhiPYw8b6FETsn/jade-leung-why-companies-should-be-leading-on-ai-governance) on the importance of corporate actors leading on AI governance. Nonetheless, they are strongly suggestive of a relative neglect of AI corporate governance on the EA Forum.
**Review of Open Philanthropy Project grantmaking**
---------------------------------------------------
A review of Open Philanthropy Project grants on [Potential Risks from Advanced Artificial Intelligence](https://www.openphilanthropy.org/giving/grants) shows a variety of projects on public policy (and other topics including AI safety), but nothing focused on corporate governance.
Taken together, the corporate governance of AI seems relatively neglected within long-term AI communities. It’s not our intent to argue against the importance of other lines of work on AI, such as public policy or safety techniques. These topics are important too. Indeed, we have done some work on other AI topics ourselves, including public policy. Furthermore, the topics are not mutually exclusive. In particular, public policy is one way to improve corporate governance. Nonetheless, corporate governance raises a distinctive set of issues, challenges, and opportunities. We believe these merit dedicated attention from long-term AI communities.
**There are tractable things that long-term AI communities could do to improve the long-term corporate governance of AI**
=========================================================================================================================
To be most useful, we believe that future work on AI corporate governance should integrate scholarship and practice. Scholarship is needed to learn from prior experience and develop new ideas. AI corporate governance is a relatively new topic, but the more general corporate governance literature provides a wealth of relevant insight. Additionally, practical experience is needed to ensure that ideas are viable and to effect real change. To the extent possible, all this work should be free from the biases of corporate financial self-interest. Some specific potential approaches include:
* **Building up corporate governance expertise among communities active on long-term AI issues.** Some of this can and should come from people working in governance positions at AI companies, government positions focused on regulating the AI industry, media outlets reporting on the AI industry, and other practical roles. Some of it should also come from people hired by academic and nonprofit organizations to study and conduct project work. Funding should be made available to such organizations for these hires.
* **Generating ideas for improving the long-term corporate governance of AI.** The publications listed above only scratch the surface of potential activities. Some work can adapt existing corporate governance concepts to the particulars of advanced AI. For example, our [certification paper](http://gcrinstitute.org/ai-certification-advancing-ethical-practice-by-reducing-information-asymmetries/) includes a brief discussion of certification for future AI that could be expanded to explore a certification regime for AGI and related technologies. Other concepts could include the relative merits of novel corporate structures, compliance and risk management teams, employee activism, oversight boards, reputation management, shareholder activism, whistleblowing, and more.
* **Evaluating priorities for AI corporate governance work.** Our [survey paper](https://www.mdpi.com/2078-2489/12/7/275/htm) maps out a range of opportunities, but it doesn’t evaluate their relative priority. Evaluations should proceed cautiously to account for uncertainty about the impacts of different opportunities and to account for important interconnections between them. This work would benefit from the availability of more detailed ideas on how to improve the long-term corporate governance of AI (see above).
Above all, we believe that corporate governance merits the same degree of attention and investment as public policy gets within the field of long-term AI governance.
*Thanks to Peter Cihon, Conor Griffin, Allan Dafoe, Cullen O’Keefe, and Robert de Neufville for valuable feedback.*
*Disclaimer: Jonas Schuett has recently finished an internship at DeepMind. The views and opinions expressed here are his own.*
---
1. This quote is from former Deputy Secretary of Defense Bob Work, speaking in his official capacity. [↩︎](#fnref-7rvtuFKcqxqdSudM3-1)
2. Goertzel expressed this view in an article “The Corporatization of AI is a Major Threat to Humanity”, published in 2017 by H+ Magazine at [this link](http://hplusmagazine.com/2017/07/21/corporatization-ai-major-threat-humanity). At the time of this writing, that link is not operational. An archived version of the page is available [here](https://web.archive.org/web/20210816140204/http://hplusmagazine.com/2017/07/21/corporatization-ai-major-threat-humanity/). [↩︎](#fnref-7rvtuFKcqxqdSudM3-2)
3. Some of these results are not relevant, due to quirks in the EA Forum search function (e.g., [this](https://forum.effectivealtruism.org/posts/CMHRE5viGLhM9yzYb/dani-nedal-risks-from-great-power-competition), [this](https://forum.effectivealtruism.org/posts/z2CjXfttCmHgKwum8/health-and-happiness-research-topics-part-2-the-haly), and [this](https://forum.effectivealtruism.org/posts/q9qbWpNgeFkm2CaoR/katriel-friedman-the-benefits-of-starting-your-own-charity)), but many are highly relevant. [↩︎](#fnref-7rvtuFKcqxqdSudM3-3) |
45c14f8f-7e91-417e-906b-57375f4b63af | StampyAI/alignment-research-dataset/eaforum | Effective Altruism Forum | No. Impending AGI doesn't make everything else unimportant.
*I sat in a restaurant in New York, for example, and I looked out at the buildings and I began to think, about how much the radius of the Hiroshima bomb damage was. How far from here was 34th street?... All those buildings, all smashed. And I would go along and I would see people building a bridge, or they'd be making a new road, and I thought, they're crazy, they just don't understand, they don't understand. Why are they making new things? It's so useless.*
Richard Feynman
Intro
-----
I am a psychotherapist helping people working on AI safety. In my post on [non-obvious mental health issues among AI safety community](https://forum.effectivealtruism.org/posts/Fj6wgJdDYuNP2FeD4/6-non-obvious-mental-health-issues-specific-to-ai-safety) members. I wrote that some people believe that AGI will soon cause either doom or utopia, which makes and every action with long-term goals useless. So there is no reason to do things like making long-term investments or maintaining a good health.
Meaninglessness causes depression
---------------------------------
Meet Alex. He is a ML researcher at a startup developing anti-aging drugs. Recently Alex got interested in AI safety and realized that we are rapidly approaching AGI. He started thinking "AGI will either destroy humanity, or it will develop anti-aging drugs way better than we do. In both cases my work is useless". He loses any motivation to work, and after some thoughts he decides to quit. Fortunately, he has enough investments , so he can maintain his way of life without salary.
The more Alex was thinking about AGI, the deeper he dived into existential thoughts about meaninglessness of his actions.
Before that he regularly ran. He did it because he felt good doing it, and also to be healthy. He started thinking more and more about meaninglessness in maintaining for long-term health. As he lost a part of his motivation, he had to force himself to run, so he could easily find an excuse for why he should stay at home and watch Netflix instead. Eventually stopped running completely. Also, while running, Alex had a habit of listening educational podcasts. As he stopped running, he also stopped listening them. At one point while flossing his teeth he got a thought "Does it even make sense to floss my teeth? Do I need to care about what will happen to my teeth in 20 years?"
Alex's life slowly became less and less interesting. He couldn't answer himself why bother doing stuff that previously fulfilled his life, which made him more and more depressed.
The universe is meaningless
---------------------------
To be fair, life ultimately havs no objective meaning, even if not taking AGI into account. People are just products of random mutations and natural selection which optimize for the propagation of genes through generations, and everything we consider meaningful, like friendship or helping others, are just proxy goals to propagate genes.
The problem of meaninglessness is not new.
Leo Tolstoy, for example, struggled with this problem so much that it made him suicidal:
> *What will be the outcome of what I do today? Of what I shall do tomorrow? What will be the outcome of all my life? Why should I live? Why should I do anything? Is there in life any purpose which the inevitable death which awaits me does not undo and destroy?*
>
> *These questions are the simplest in the world. They are in the soul of every human being. Without an answer to them, it is impossible for life to go on.*
>
> *I could give no reasonable meaning to any actions of my life. And I was surprised that I had not understood this from the very beginning.*
>
> *Behold me, hiding the rope in order not to hang myself; behold me no longer going shooting, lest I should yield to the too easy temptation of putting an end to myself with my gun.*
>
>
The good news is that many smart people came up with decent ideas on how to deal with this existential meaninglessness. The rest of the post is about finding meaning in the meaningless world.
Made-up meaning works just fine
-------------------------------
Imagine 22 people with a ball on a grass field, and no one told them what they should do. These people would probably just sit doing nothing and waiting for all this to end.
Now imagine that someone gave these people instructions to play football and win the match. Now they focus on a result, experience emotional dramas, and form bonds with teammates.
The rules of football are arbitrary. There is no law of nature that states that you can only kick a ball with legs but not hands, and that you have to put this ball into a net. Someone just came up with these rules, and people have a good time following them.
Let's describe this situation with fancy words.
###
### Nihilism
Nihilism is a philosophy that states there is no objective meaning in life, and you can't do anything about it. It might be technically true, but this is a direct path to misery. The guys with a ball and no rules had a bad time, and Alex's life without meaning started falling apart.
###
### Existentialism
The solution for the problem of meaninglessness is found in existentialism. Its core idea is even if there is no objective meaning, the made-up one works just fine and makes life better. Just like people playing football with artificial rules are having a good time.
The good thing is that our brains are hardwired to create meaning. We also know the things that our brains are prone to consider meaningful, so with some effort, people can regain a sense of meaningfulness.
Let's dive deeper into this.
People with terminal illnesses sometimes have surprisingly meaningful lives
---------------------------------------------------------------------------
At one point I provided psychological support for people with terminal cancer. They knew that they only had pain and death ahead, and their loved ones suffered too.
Counterintuitively, some of them found a lot of meaning in their situation. As they and their close ones suffer, it became obvious that it's important to reduce this suffering. This is a straightforward source of meaning.
* My clients knew that their close ones would probably be emotionally devastated after their death. Sometimes financially too. So they found meaning in helping their family members to have a good life, and making sure they will remember them with smile.
* As people with cancer suffer, they become aware of the suffering of their peers, so they find a lot of meaning in helping others who struggle with similar problems. Cancer survivors often volunteer helping people with cancer to live through it and find it deeply meaningful.
* As a therapist, I personally experience more sense of meaning helping people who have a short and painful life ahead. I feel like every moment they don't suffer is exceptionally valuable.
So, how to find meaning in the world where AGI might make everything else meaningless?
--------------------------------------------------------------------------------------
Let's return to our hero Alex who believes that his life became meaningless because in the face of AGI. Let's see a couple of examples on how he can regain sense of meaning in his life.
### Meaning in emotional connections
Alex has a brother, but after a serious conflict they didn't talk for several years. They were good friends when they were kids. They grew-up together and share a lot of experience. They know each other like nobody else, but after their mother died, they had an ugly fight over her inheritage. Alex realizes that he deeply regrets this conflict and decides to reconnect with his brother.
Turnes out, the brother also regrets their conflict and is happy to finally meet Alex. Now they are happy that they again have their emotional bond, and Alex find a lot of meaning in investing his time and effort into this friendship.
### Meaning in making a purposeful work
Alex has short timelines, and believes humanity don't have much time, but he realizes that regardless of that, there are people who are suffering right now.
Some people are homeless. Some have ilnessess. Some are lonely, and even if AGI is near, these people still need help now
Alex decided to start volunteering as a social worker, helping homeless people to get a job, find a place to live, and helping with their health problems. He sees that his work helps people to live better lives, and that every time he thinks of this work, he believes that he makes something good and meaningful.
### Epilogue
If you struggle with the sense of meaninglessness due to AGI, and believe that you might benefit from professional help, then I might help as a therapist or suggest other places where you can get professional help.
Check out my profile description to learn more about these options. |
3dc0cc9e-816f-4d3b-929f-4bfc5930518e | StampyAI/alignment-research-dataset/blogs | Blogs | Sandor Veres on autonomous agents
 Professor [Sandor Veres](http://sheffield.ac.uk/acse/staff/smv/index) was born and educated in Hungary as applied mathematician. He completed his PhD in dynamical modelling of stochastic systems in 1983 and worked in industry on computer controlled systems. In 1987-1988 he received two consecutive scholarships at [Imperial College London](http://www3.imperial.ac.uk/) and at [Linacre College Oxford](http://www.linacre.ox.ac.uk/).
Between 1989-1999 he was lecturer at the [Electronic and Electrical engineering department](http://www.birmingham.ac.uk/schools/eece/index.aspx) at the [University of Birmingham](http://www.birmingham.ac.uk/) and pursued research in system identification, adaptive control and embedded electronic control systems. In 2000 he joined the [University of Southampton](http://www.southampton.ac.uk/) to do work in the areas of active vibration control systems, adaptive and learning systems, satellite formation flying and autonomous control. Since 2002 he has held a chair in control systems engineering and was chairman of [IFAC Technical Committee of Adaptive and Learning Systems](http://tc.ifac-control.org/).
At Southampton he has established the [Centre for Complex Autonomous Systems Engineering](http://www.southampton.ac.uk/ccase/) where he is now visiting professor. Today his main research interest is agent-based control systems and he is leading the [Autonomous Systems and Robotics Group](http://www.sheffield.ac.uk/acse/research/groups/asrg) at the Department of Automatic Control at the [University of Sheffield](http://www.sheffield.ac.uk/) since 2013. He published about 200 papers, authored 4 books and co-authored numerous software packages.
**Luke Muehlhauser**: In “[Autonomous Asteroid Exploration by Rational Agents](http://commonsenseatheism.com/wp-content/uploads/2014/04/Lincoln-et-al.-Autonomous-Asteroid-Exploration-by-Rational-Agents.pdf)” (2013), you discuss a variety of agent architectures for use in contexts where autonomous or semi-autonomous operation is critical — in particular, in outer space, where there are long communication delays between a robot and a human operator on Earth. Before we talk about *rational* agent architectures in particular, could you explain what an “agent” architecture is from your perspective, and why it is superior to other designs for many contexts?
---
**Sandor Veres**: First of all I would like to say that I am not sure that all kinds of agent architectures are “superior”. Some agent paradigms have however advantages as a way of organizing your complex software system which controls an intelligent machine such as a robot. The feature I most like in some agent architectures is when they exhibit anthropomorphic type of operations so that they can handle statements about the world in terms of space and time, past and future, express possibilities and necessities, behaviour rules, knowledge of other agent’s knowledge, including that of humans, can handle intentions and beliefs about a situation. If such constructs are part of the software, as opposed to being translated from a different kind of software, that makes things simpler in terms of programming. Also we would like robots to share with us their knowledge about the world, and we share our knowledge with them. It is an advantage if we share our ways of reasoning, a robot can be made more easy to understand and control if it is programmed in an anthropomorphic manner.
---
**Luke**: At one point in that paper you write that “Creating a new software architecture with significant benefits for autonomous robot control is a difficult problem when there are excellent software packages around…” What kinds of software architectures for autonomous robot control are out there already, and how generally applicable are they?
---
**Sandor**: By excellent packages I meant some robot operating system foundations such as the [ROS](http://www.ros.org/) for Linux and [CCR](http://en.wikipedia.org/wiki/Concurrency_and_Coordination_Runtime) for Windows on which one can build robot programs. Both of these have extensive libraries available for us to enable programming robot skills. For programming autonomous behaviour we have [agent-oriented programming](http://en.wikipedia.org/wiki/Agent-oriented_programming) defined in exact terms [by Yoav Shoham in 1993](http://www.infor.uva.es/~cllamas/MAS/AOP-Shoham.pdf) and by now there are books just to review the many approaches to agent programming. There is also [CLARAty](https://claraty.jpl.nasa.gov) by JPL which is continuous re-planning based rather than agent oriented. To summarise, [GofAI](http://en.wikipedia.org/wiki/GOFAI) has been transformed during the past 3 decades into various logic-based, subsumption, multi-layered and belief-desire-intention robot programming approaches, so there is a long and interesting history of great effort in software architectures for robots.
---
**Luke**: Where you think the future of autonomous agents is headed?
---
**Sandor**: I hope that soon not only agent programming languages will be available but standardised agents for various applications of robots. These can then be either programmed further or just simply trained further before deployed in an application. Eventually these agents could provide high level of integrity, capability and safety of robot operations autonomously. A next step will be to make these physically able agents truly social agents so that they behave in an appropriate manner and cooperate where required.
---
**Luke**: How might we get high-assurance autonomous agents for safety-critical applications?
---
**Sandor**: Determinism is a fundamental feature of digital computing so far, though we have random phenomena in some parallel computing we do on robots. Determinism of software has the advantage that our robots are also deterministic. We currently make every effort to make robots always respond in an appropriate manner, solve problems and be predictable despite often complex and disturbing environment. The more intelligent they are the more complex environment they can handle. The more complex environment however also means that it becomes more difficult to formally verify and test all their possible deterministic responses. So the trade off is between complexity of agent-software and “determinism” of intelligence, i.e. suitable actions by the robot at all times. Though the agent is deterministic, the sensors they use may not be reliable which make their response to some degree probabilistic. The challenge we face is hence to built up conceptual abstractions of complex environments which enable reliable decision making of our robotic agents. On the question of whether this is always possible in practice the jury is still out.
---
**Luke**: Will research progress on autonomy capabilities outpace research progress on safety research?
---
**Sandor**: This is a very good question and I believe this is likely to happen. High levels of capabilities will however reduce the probability of inappropriate response by a robot as long as it is accompanied by a formally verifiable decision making process of the agent. For agent development the most we can do is to make it “perfect”, meaning that it should never intentionally do the wrong action or in case of failing hardware, it should always take the most likely positive action. This is easier said than done as the environment can create conflicting requirements for a robot’s response and in such cases it needs to behave as a moral agent. Moral agents can use models of a broader context of a situation and apply principles over a wide range of knowledge. Moral agents of the future are likely to need the knowledge of an educated adult.
---
**Luke:** Thanks, Sandor!
The post [Sandor Veres on autonomous agents](https://intelligence.org/2014/05/23/sandor-veres/) appeared first on [Machine Intelligence Research Institute](https://intelligence.org). |
c888b146-fbff-455c-8819-ae23eaeedbc5 | trentmkelly/LessWrong-43k | LessWrong | [LINK] The Cryopreservation of Kim Suozzi
http://www.alcor.org/blog/?p=2716
> With the inevitable end in sight – and with the cancer continuing to spread throughout her brain – Kim made the brave choice to refuse food and fluids. Even so, it took around 11 days before her body stopped functioning. Around 6:00 am on Thursday January 17, 2013, Alcor was alerted that Kim had stopped breathing. Because Kim’s steadfast boyfriend and family had located Kim just a few minutes away from Alcor, Medical Response Director Aaron Drake arrived almost immediately, followed minutes later by Max More, then two well-trained Alcor volunteers. As soon as a hospice nurse had pronounced clinical death, we began our standard procedures. Stabilization, transport, surgery, and perfusion all went smoothly. A full case report will be forthcoming.
Previously on LW: Aug 18, Aug 25, Aug 27, Jan 22. |
c2598f66-2e5b-4c5c-b97e-6ebc23a858b1 | trentmkelly/LessWrong-43k | LessWrong | The Intense World Theory of Autism
The first section is well-written and reliable, because I didn't write it, it's a book excerpt. The rest of the post is more prone to errors and speculations; you can skip it if you're not into that kind of stuff—I read a few books and articles about autism, but I'm definitely not an expert, and I didn't spend a lot of time checking everything I wrote. Please comment if anything seems wrong (or dumb, or offensive, etc.) so I can fix it.
Summary / Table of Contents
* The first section is mostly a book excerpt introducing my favorite theory of how autism works in the brain, namely "Intense World Theory".
* Then, I'll flesh out how I'm thinking about that theory, by distinguishing "intense world" and "different learning algorithm hyperparameters" as things that happen in different parts of the brain and have different consequences, even if they tend to go together. I'll talk a bit more about each separately, and try to relate them more specifically and mechanistically to the algorithms going on in different parts of the brain.
* I'll also include how I think this theory connects to other famous aspects/theories of autism, like cerebellar abnormalities, memory, "weak central coherence", etc.
* At the end, I'll speculate that there's an exact-opposite "dim world theory of psychopathy". Fun!
Introduction to the Intense World Theory of Autism
There are various theories of the root cause of autism in the brain. I'll mention a few as I go. But I'll start right in with the positive case for the theory I like: The Intense World Theory of Autism.
The Intense World Theory of Autism dates to this 2007 article. I first heard about it from the excellent book The Myth of Mirror Neurons, which devotes a whole chapter to it, excerpted below. Then I read Temple Grandin's The Autistic Brain: Thinking Across the Spectrum and found that she also brought it up, and seemed very enthusiastic about it. I've also read a couple review articles on Intense World Theory, including this |
6aa7a94d-760c-4727-bb85-0288f7718f53 | trentmkelly/LessWrong-43k | LessWrong | Trace: Goals and Principles
In terms of research, I decided to devote the month of February mainly to foundations and tools. One project was to come up with a notation/language/framework which matches the way I’ve been thinking about computation - i.e. DAGs with symmetry and “clouds” representing DAG-structure-as-data. The tool I’ve been building - a Python library tentatively called Trace - isn’t stable enough that I want to show it off yet, but I do think I’ve nailed down the core goals and principles, so it’s time to write them up.
Goals
The main thing I need for my research is a data structure suitable for automated causal abstraction algorithms on arbitrary computations. Some subgoals:
* Universality: data structure should be able to represent any computation performed by a program
* Data structure needs to be finite, which means leveraging symmetry to represent infinite computational DAGs
* Computations must be straightforward both for a human to specify directly and for an algorithm to manipulate
* Want to be able to do causal-DAG-like things, like query for parents/children of a node or perform interventions/counterfactuals along the lines of Pearl’s do()
* Need to handle DAGs with dynamic structure
* Eventually I’ll want to do reflective things with this data structure (i.e. self-modeling agents), so simplicity matters in the specification and core algorithms.
I’ll give a bit more detail...
The first two subgoals basically amount to “I need a data structure representing the computation performed by an arbitrary program” - i.e. the trace of an arbitrary program. I do need to actually use the data structure, so it needs to be finite. (We could use a lazy infinite structure, but then I want to know what finite data structure is used to actually represent the infinite data structure.) The computational DAGs of programs are usually infinite but symmetric, so the solution probably needs to leverage symmetry in the representation.
I (a human) need to be able to specify computatio |
72962261-ab79-4f64-9bb6-e2ff1f920d72 | StampyAI/alignment-research-dataset/alignmentforum | Alignment Forum | Using GPT-N to Solve Interpretability of Neural Networks: A Research Agenda
Tl;dr We are attempting to make neural networks (NN) modular, have GPT-N interpret each module for us, in order to catch mesa-alignment and inner-alignment failures.
Completed Project
=================
Train a neural net with an added loss term that enforces the sort of modularity that we see in well-designed software projects. To use [this paper's](https://arxiv.org/pdf/2003.04881.pdf) informal definition of modularity
> a network is modular to the extent that it can be partitioned into sets of neurons where each set is strongly internally connected, but only weakly connected to other sets.
*Example of a “Modular” GPT. Each module should be densely connected w/ relatively larger weights. Interfaces between modules should be sparsely connected w/ relatively smaller weights.*
Once we have a Modular NN (for example, a GPT), we will use a normal GPT to map each module into a natural language description. Notice that there are two different GPT’s at work here.
*GPT-N reads in each “Module” of the “Modular GPT”, outputting a natural language description for each module.*
If successful, we could use GPT-N to interpret any modular NN in natural language. Not only should this help our understanding of what the model is doing, but it should also catch mesa-alignment and inner-alignment failures.
Cruxes
======
There are a few intuitions we have that go counter to other’s intuitions. Below is an elaboration of our thoughts and why we think this project could work.
Finding a Loss function that Induces Modularity
-----------------------------------------------
We currently think a Gomory-Hu Tree (GH Tree) captures the relevant information. We will initially convert a NN to a GH Tree to calculate the new loss function. This conversion will be computationally costly, though more progress can be made to calculate the loss function directly from the NN. See Appendix A for more details
Small NN’s are Human Interpretable
----------------------------------
We’re assuming humans can interpret small NN’s, given enough time. A “Modular” NN is just a collection of small NN’s connected by sparse weights. If humans could interpret each module in theory, then GPT-N could too. If humans can interpret the interfaces between each, then GPT-N could too.
Examples from [NN Playground](https://playground.tensorflow.org/#activation=tanh&batchSize=10&dataset=circle®Dataset=reg-plane&learningRate=0.03®ularizationRate=0&noise=0&networkShape=4,2&seed=0.77377&showTestData=false&discretize=false&percTrainData=50&x=true&y=true&xTimesY=false&xSquared=false&ySquared=false&cosX=false&sinX=false&cosY=false&sinY=false&collectStats=false&problem=classification&initZero=false&hideText=false) are readily interpretable (such as the above example).
GPT-3 can already [turn comments into code](https://player.vimeo.com/video/427943407/). We don't expect the reverse case to be fundamentally harder, and neural nets can be interpreted as just another programming language.
Microscope AI has had some success in interpreting large NN’s. These are NN’s that should be much harder to interpret than modular NN’s that we would be interpreting.
Technical Questions:
====================
First question: Capabilities will likely be lost by adding a modularity loss term. Can we spot-check capability of GPT by looking at the loss of the original loss terms? Or would we need to run it through NLP metrics (like Winograd Schema Challenge questions)?
To create a modular GPT, we have two paths, but I'm unsure of which is better.
1. Train from scratch with modified loss
2. Train OpenAI’s gpt-2 on more data, but with added loss term. The intuition here is that it’s already capable, so optimizing for modularity starting here will preserve capabilities.
Help Wanted
===========
If you are interested in the interpretability of GPT (even unrelated to our project), I can add you to a discord server full of GPT enthusiasts (just DM me). If you're interested in helping out our project specifically, DM me and we'll figure out a way to divvy up tasks.
Appendix A
==========
Gomory-Hu Tree Contains Relevant Information on Modularity
----------------------------------------------------------
Some readily accessible insights:
1. The size of the [minimum cut](https://en.wikipedia.org/wiki/Minimum_cut) between two neurons can be used to measure the size of the interface between their modules.
2. Call two graphs G and G’ on the same vertices equivalent if for every two u,v, the sizes of their minimum cuts are the same in G and G’. It turns out that there always exists a G’ which is a tree! (The [Gomory-Hu tree](https://en.wikipedia.org/wiki/Gomory%E2%80%93Hu_tree).)
3. It turns out that the minimum cut between two neurons within a module never needs to expose the innards of another module.
Therefore, the Gomory-Hu tree probably contains all the information needed to calculate the loss term and the hierarchy of software modules. |
4b51273f-40ee-49cd-9856-43f028649d38 | trentmkelly/LessWrong-43k | LessWrong | From Capuchins to AI's, Setting an Agenda for the Study of Cultural Cooperation (Part2)
Today's writings are shaded dark green, the rest was also in Part1.
This is a multi-purpose essay-on-the-making, it is being written aiming at the following goals 1) Mandatory essay writing at the end of a semester studying "Cognitive Ethology: Culture in Human and Non-Human Animals" 2) Drafting something that can later on be published in a journal that deals with cultural evolution, hopefully inclining people in the area to glance at future oriented research, i.e. FAI and global coordination 3) Publishing it in Lesswrong and 4) Ultimately Saving the World, as everything should. If it's worth doing, it's worth doing in the way most likely to save the World. Since many of my writings are frequently too long for Lesswrong, I'll publish this in a sequence-like form made of self-contained chunks. My deadline is Sunday, so I'll probably post daily, editing/creating the new sessions based on previous commentary.
Abstract: The study of cultural evolution has drawn much of its momentum from academic areas far removed from human and animal psychology, specially regarding the evolution of cooperation. Game theoretic results and parental investment theory come from economics, kin selection models from biology, and an ever growing amount of models describing the process of cultural evolution in general, and the evolution of altruism in particular come from mathematics. Even from Artificial Intelligence interest has been cast on how to create agents that can communicate, imitate and cooperate. In this article I begin to tackle the 'why?' question. By trying to retrospectively make sense of the convergence of all these fields, I contend that further refinements in these fields should be directed towards understanding how to create environmental incentives fostering cooperation.
----------------------------------------
> We need systems that are wiser than we are. We need institutions and cultural norms that make us better than we tend to be. It seems to me that the grea |
1ececb7c-dd06-4a5c-9b81-8b0d8217fc81 | trentmkelly/LessWrong-43k | LessWrong | Chapter 3: What's an Object?
In the real world, there are no "objects" in the way we get used to feeling them. While working with computers, we map "objects" to bytes by compiling programs. And we use "object" word for different stuff: variables, functions, etc. If you will look from the physics point on your chair, there is no "chair object." That's something even more complicated. But the "objectivization" of that complex "something" makes you don't care about all this philosophic stuff when you want to sit on it. I've decided to find what represents an "object" in the world of neurons.
I'd been playing with texts, words, letters, optical illusions for months. That was driving my friends and colleagues mad. I've been creating quizzes. I've been asking them to finish phrases or read words without some lttrs. I've been giving them examples like "theory epigenetics memory" and "Epigenetics memory theory." Or "relativity special" and "Special relativity."
I've found that well-known pattern they were describing like "one object," but if I had broken arrangement and decoupled it, they were describing it as a "set of objects."
Decoupled and broken arrangement. Sounds pretty similar to Hebb's rule!
To represent the model of each letter you are reading from your screen, we need to use thousands of neurons. Maybe more, I haven't tested yet. But there are about 80 billion of them in the brain. And with that amount of free memory, thousands won't make a big deal.
And if two neurons can wire together - there should be strongly coupled subnetworks of thousands of them. And if we will activate enough parts of a subnetwork that will enable it whole.
If strongly-coupled networks exist, we should have a less strong connection in between. If we adapt Hebb's rule to subnetworks level, it will explain why people count "Special relativity" as one, but "relativity special" as two objects. Because one is a pattern that fires without any noticeable delay, and the other is not.
It also explains why do we see op |
85407722-f736-4873-a675-9319616b32f9 | StampyAI/alignment-research-dataset/aisafety.info | AI Safety Info | Will there be a discontinuity in AI capabilities?
While researchers agree that AI capabilities could increase quickly, there are still debates around whether the increase would take the form of [a continuous rise or of a (seemingly) discontinuous jump.](https://substackcdn.com/image/fetch/f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fbucketeer-e05bbc84-baa3-437e-9518-adb32be77984.s3.amazonaws.com%2Fpublic%2Fimages%2F6890e3d1-18d5-4930-83eb-41b92cfb6ed2_1150x521.png)
**Arguments for continuous takeoff**
[Paul Christiano](https://sideways-view.com/2018/02/24/takeoff-speeds/) believes that growth in AI capabilities will also lead to growth in economic productivity. He expects to see world GDP double in shorter and shorter periods of time, with AI contributions to AI R&D creating a feedback loop that results in hyperbolic growth. On this model, [takeoff is continuous but still fast.](https://www.alignmentforum.org/posts/CjW4axQDqLd2oDCGG/misconceptions-about-continuous-takeoff#Continuous_doesn_t_necessarily_mean_slow)
John Wentworth explored the possibility [in the form of a story](https://www.lesswrong.com/posts/Mha5GA5BfWcpf2jHC/potential-bottlenecks-to-taking-over-the-world), that the enhancement of cognitive capabilities is not the true bottleneck to taking over the world. In this scenario, much more significant bottlenecks come in the form of coordinated human pushback and the need to acquire and deploy physical resources.[^kix.w6d497ouoxs]
As an example, an artificial [superintelligence](/?state=6207&question=What%20is%20%22superintelligence%22%3F) (ASI) could theoretically design a faster computer to accelerate its thinking, or a type of nano-bot that could wipe out humanity within seconds. However, it would take much longer to coordinate supply chains, navigate economic bottlenecks, and build precision machinery such as semiconductor fabrication plants, to actually build it. Due to supply chain optimizations that we can anticipate an ASI would generate as instrumental goals, we should see productivity and therefore GDP growth, which we can use as a proxy measurement for “AI takeoff”.
**Arguments for discontinuous takeoff**
Eliezer Yudkowsky expects AI to have [relatively little effect](https://www.lesswrong.com/posts/sCCdCLPN9E3YvdZhj/shulman-and-yudkowsky-on-ai-progress) on global GDP before a discontinuous "[intelligence explosion](https://www.lesswrong.com/tag/intelligence-explosion)". An argument for this is that superintelligent AIs can lie to us. If there exists an [artificial general intelligence](/?state=2374&question=What%20is%20artificial%20general%20intelligence%20(AGI)%20and%20what%20will%20it%20look%20like%3F) with strategic awareness that knows it will be turned off when it is perceived to have become too power-hungry, its best strategy is to limit its impact on the world by pretending to be less intelligent than it is. This leads to lower-than-expected GDP growth. This will then be followed by a sudden discontinuous [FOOM](https://wiki.lesswrong.com/index.php?title=AI_takeoff&_ga=2.177541733.1554321416.1681129248-1671852592.1680535975#Hard_takeoff), as soon as the AI gets access to a superweapon, or some other similarly powerful ability to influence the world. This would occur at a pace faster than human technological and governance institutions could counter.
Yudkowsky also points to examples from evolution where the transition from chimps to humans led to (what feels like) a discontinuous gap in capabilities. A much more comprehensive public debate about the matter was held between Yudkowsky and Christiano, which is summarized [here](https://astralcodexten.substack.com/p/yudkowsky-contra-christiano-on-ai?s=r).
Different views on takeoff speeds and (dis)continuity have [different implications](https://www.alignmentforum.org/posts/hRohhttbtpY3SHmmD/takeoff-speeds-have-a-huge-effect-on-what-it-means-to-work-1) for how best (and potentially whether) to work on AI safety.
[^kix.w6d497ouoxs]: “*On fusion power, for instance, at most a 100x speedup compared to the current human pace of progress is realistic, but most of that comes from cutting out the slow and misaligned funding mechanism. Building and running the physical experiments will speed up by less than a factor of 10. Given the current pace of progress in the area, I estimate at least 2 years just to figure out a viable design. It will also take time beforehand to acquire resources, and time after to scale it up and build plants - the bottleneck for both those steps will be acquisition and deployment of physical resources, not cognition. And that’s just fusion power - nanobots are a lot harder.*” - Wentworth, John (2021), [Potential Bottlenecks to Taking Over The World](https://www.lesswrong.com/posts/Mha5GA5BfWcpf2jHC/potential-bottlenecks-to-taking-over-the-world) |
830c2c25-24a8-4b89-9d74-ca7825725ce0 | trentmkelly/LessWrong-43k | LessWrong | AI Alignment Metastrategy
I call "alignment strategy" the high-level approach to solving the technical problem[1]. For example, value learning is one strategy, while delegating alignment research to AI is another. I call "alignment metastrategy" the high-level approach to converging on solving the technical problem in a manner which is timely and effective. (Examples will follow.)
In a previous article, I summarized my criticism of prosaic alignment. However, my analysis of the associated metastrategy was too sloppy. I will attempt to somewhat remedy that here, and also briefly discuss other metastrategies, to serve as points of contrast and comparison.
Conservative Metastrategy
The conservative metastrategy follows the following algorithm:
1. As much as possible, stop all work on AI capability outside of this process.
2. Develop the mathematical theory of intelligent agents to a level where we can propose adequate alignment protocols with high confidence. Ideally, the theoretical problems should be solved in such order that results with direct capability applications emerge as late as possible.
3. Design and implement empirical tests of the theory that incur minimal risk in worlds in which the theory contains errors or the assumptions of the theory are violated in practice.
4. If the tests show problems, go back to step 2.
5. Proceed with incrementally more ambitious tests in the same manner, until you're ready to deploy an AI defense system.
This is my own favorite metastrategy. The main reason it can fail is if the unconservative research we failed to stop creates unaligned TAI before we can deploy an AI defense system (currently, we have a long way to go to complete step 2).
I think that it's pretty clear that a competent civilization would follow this path, since it seems like the only one which leads to a good long-term outcome without taking unnecessary risks[2]. Of course, in itself that is an insufficient argument to prove that, in our actual civilization, the conservat |
ca70b1b3-2346-4362-b876-4597592220f8 | trentmkelly/LessWrong-43k | LessWrong | Online Optimal Philanthropy Meetup: Tue 10/9, 8pm ET
How can we do the most good in the world? What impact can we have, and what's the impact on us?? What are the best charities? How can we evaluate them? Online discussion via g+ hangout, Tuesday October 9th, 8pm ET (Boston time).
https://plus.google.com/u/0/events/cj57chi6jgse1avv8f80hjh9g3c?a=b |
8efdbd0f-b246-4aec-b2d4-bfc3debe35b4 | trentmkelly/LessWrong-43k | LessWrong | Weekly Non-Covid News #1 (10/13/22)
This is the non-Covid part of what would previously have been the weekly Covid post. About half of the content written for the post this week is being withheld for topic-level future posts, both with longer time horizons (e.g. policy roundups don’t need to be weekly and should benefit from more integration over time) and elevating worthy sub-topics to their own posts, which this week seems likely to include the colonoscopy study.
We will retain the broad categories of Bad and Good news for various short notes.
Bad News
Sysco Teamsters are on strike in three cities, and there are a lot of people cheering the strikers on mood affectation grounds because Sysco is buying up rivals, slashing staff and service and treating everyone like garbage. Is it a monopoly worth investigating? It sure sounds like it has monopoly power and is actively seeking to assemble more of it. If you keep hiking prices (no you cannot simply say ‘inflation!’) and cutting service and everyone hates you and they live in fear of you, you might be a monopoly. If it was my job to investigate such things, I would investigate.
Signal to stop letting one send SMS messages on Android phones.
Paper (via MR) claims that there is a causal effect on call center workers where they are ‘less productive’ when they report they are happier. This effect might replicate with respect to call centers in particular, I would be shocked if it replicated to workers in general (and thus my answer to Tyler’s generalized ‘are happy workers less productive?’ is ‘no, quite the opposite, and happy to bet on this.’) If this effect is real and causal, my mechanism is that call center ‘productivity’ is about getting through calls quickly whether or not that is good for the business or customer (or victim/target), and also being willing to engage in essentially hostile interactions with the target to get the desired result. There are particular professions and times and places where one wants to Drive Angry. On the other hand |
4a830c98-f655-44cc-aee3-3539dcecf038 | StampyAI/alignment-research-dataset/alignmentforum | Alignment Forum | Timeline of AI safety
[Here](https://timelines.issarice.com/wiki/Timeline_of_AI_safety) is a timeline of AI safety that I originally wrote in 2017. The timeline has been updated several times since then, mostly by Vipul Naik.
Here are some highlights by year from the timeline since 2013:
| | |
| --- | --- |
| **Year** | **Highlights** |
| 2013 | Research and outreach focused on forecasting and timelines continue. Connections with the nascent effective altruism movement strengthen. The Center for the Study of Existential Risk and the Foundational Research Institute launch. |
| 2014 | [*Superintelligence: Paths, Dangers, Strategies*](https://en.wikipedia.org/wiki/Superintelligence:_Paths,_Dangers,_Strategies) by Nick Bostrom is published. The [Future of Life Institute](https://en.wikipedia.org/wiki/Future_of_Life_Institute) is founded and AI Impacts launches. AI safety gets more mainstream attention, including from [Elon Musk](https://en.wikipedia.org/wiki/Elon_Musk), [Stephen Hawking](https://en.wikipedia.org/wiki/Stephen_Hawking), and the fictional portrayal [*Ex Machina*](https://en.wikipedia.org/wiki/Ex_Machina). While forecasting and timelines remain a focus of AI safety efforts, the effort shifts toward the technical AI safety agenda, with the launch of the Intelligent Agent Foundations Forum. |
| 2015 | AI safety continues to get more mainstream, with the founding of [OpenAI](https://en.wikipedia.org/wiki/OpenAI) (supported by Elon Musk and [Sam Altman](https://en.wikipedia.org/wiki/Sam_Altman)) and the [Leverhulme Centre for the Future of Intelligence](https://en.wikipedia.org/wiki/Leverhulme_Centre_for_the_Future_of_Intelligence), the [Open Letter on Artificial Intelligence](https://en.wikipedia.org/wiki/Open_Letter_on_Artificial_Intelligence), the Puerto Rico conference, and coverage on [Wait But Why](https://en.wikipedia.org/wiki/Wait_But_Why). This also appears to be the last year that Peter Thiel donates in the area. |
| 2016 | Open Philanthropy makes AI safety a focus area; it would ramp up giving in the area considerably starting around this time. The landmark paper "Concrete Problems in AI Safety" is published, and OpenAI's safety work picks up pace. The Center for Human-Compatible AI launches. The annual tradition of LessWrong posts providing an AI alignment literature review and charity comparison for the year begins. AI safety continues to get more mainstream, with the [Partnership on AI](https://en.wikipedia.org/wiki/Partnership_on_AI) and the Obama administration's efforts to understand the subject. |
| 2017 | This is a great year for cryptocurrency prices, causing a number of donations to MIRI from people who got rich through cryptocurrency. The AI safety funding and support landscape changes somewhat with the launch of the Berkeley Existential Risk Initiative (BERI) (and funding of its grants program by Jaan Tallinn) and the Effective Altruism Funds, specifically the Long-Term Future Fund. Open Philanthropy makes several grants in AI safety, including a $30 million grant to OpenAI and a $3.75 million grant to MIRI. AI safety attracts dismissive commentary from Mark Zuckerberg, while Elon Musk continues to highlight its importance. The year begins with the Asilomar Conference and the Asilomar AI Principles, and initiatives such as AI Watch and the AI Alignment Prize begin toward the end of the year. |
| 2018 | Activity in the field of AI safety becomes more steady, in terms of both ongoing discussion (with the launch of the AI Alignment Newsletter, AI Alignment Podcast, and Alignment Forum) and funding (with structural changes to the Long-Term Future Fund to make it grant more regularly, the introduction of the annual Open Philanthropy AI Fellowship grants, and more grantmaking by BERI). Near the end of the year, MIRI announces its nondisclosure-by-default policy. Ought, Median Group, and the Stanford Center for AI Safety launch during the year. |
| 2019 | The Center for Security and Emerging Technology (CSET), that is focused on AI safety and other security risks, launches with a 5-year $55 million grant from Open Philanthropy. The Stanford Institute for Human-Centered Artificial Intelligence (HAI) launches. Grantmaking from the Long-Term Future Fund picks up pace; BERI hands off its grantmaking of Jaan Tallinn's money to the Survival and Flourishing Fund (SFF). Open Philanthropy begins using the Committee for Effective Altruism Support to decide grant amounts for some of its AI safety grants, including grants to MIRI. OpenAI unveils its GPT-2 model but does not release the full model initially; this sparks discussion on disclosure norms. |
| 2020 | Andrew Critch and David Krueger release their ARCHES paper. OpenAI unveils GPT-3, leading to further discussion of AI safety implications. AI Safety Support launches. The funding ecosystem continues to mature: Open Philanthropy and the Survival and Flourishing Fund continue to make large grants to established organizations, while the Long-Term Future Fund increasingly shifts focus to donating to individuals. |
I previously shared timelines for [MIRI](https://www.lesswrong.com/posts/yfp2DBEr3oPNFpnwc/timeline-of-machine-intelligence-research-institute) and [FHI](https://www.lesswrong.com/posts/5qYjELm2Hgncwb7cE/timeline-of-future-of-humanity-institute) here on LessWrong.
Any thoughts on the timeline (such as events to add, events to remove, corrections, etc.) would be greatly appreciated! I'm also curious to hear thoughts about how useful a timeline like this is (or how useful it could become after more work is put into it). |
85e33ec2-0790-49ec-b009-d913d9e29552 | trentmkelly/LessWrong-43k | LessWrong | Transformers Represent Belief State Geometry in their Residual Stream
Produced while being an affiliate at PIBBSS[1]. The work was done initially with funding from a Lightspeed Grant, and then continued while at PIBBSS. Work done in collaboration with @Paul Riechers, @Lucas Teixeira, @Alexander Gietelink Oldenziel, and Sarah Marzen. Paul was a MATS scholar during some portion of this work. Thanks to Paul, Lucas, Alexander, Sarah, and @Guillaume Corlouer for suggestions on this writeup.
Update May 24, 2024: See our manuscript based on this work
Introduction
What computational structure are we building into LLMs when we train them on next-token prediction? In this post we present evidence that this structure is given by the meta-dynamics of belief updating over hidden states of the data-generating process. We'll explain exactly what this means in the post. We are excited by these results because
* We have a formalism that relates training data to internal structures in LLMs.
* Conceptually, our results mean that LLMs synchronize to their internal world model as they move through the context window.
* The computation associated with synchronization can be formalized with a framework called Computational Mechanics. In the parlance of Computational Mechanics, we say that LLMs represent the Mixed-State Presentation of the data generating process.
* The structure of synchronization is, in general, richer than the world model itself. In this sense, LLMs learn more than a world model.
* We have increased hope that Computational Mechanics can be leveraged for interpretability and AI Safety more generally.
* There's just something inherently cool about making a non-trivial prediction - in this case that the transformer will represent a specific fractal structure - and then verifying that the prediction is true. Concretely, we are able to use Computational Mechanics to make an a priori and specific theoretical prediction about the geometry of residual stream activations (below on the left), and then show that this prediction holds t |
73ec4346-7d1d-44fe-adb9-e035f393f932 | trentmkelly/LessWrong-43k | LessWrong | AI Risk, as Seen on Snapchat
The news tiles on Snapchat are utter drivel. Looking at my phone, today's headlines are: "Zendaya Pregnancy Rumors!", "Why Hollywood Won't Cast Lucas Cruikshank", and "The Most Dangerous Hood in Puerto Rico". Essentially, Snapchat news is the Gen-Z equivalent of the tabloid section at a Walmart checkout aisle.
Which is why I was so surprised to hear it tell me the arguments for AI risk.
The story isn't exactly epistemically rigorous. However, it reiterates points I've heard on this site, including recursive self-improvement, FOOMing, and the hidden complexity of wishes. Here's an excerpt of the story, transcribed by me:
> Given enough time and the ability to self-generate improved versions of itself, it wouldn't take long for a fully autonomous general AI to achieve superintelligence, a level of cognitive processing power so many times stronger than our own that its abilities would appear godlike to us, and the pace at which it could improve would be lightning fast.
> Superintelligent AI could think through problems in a few hours equivalent to what the world's smartest people could do in a thousand years. How could we possibly control or out-think such a powerful intellect? [...]
> Being the first superintelligence, the AI could see any competition as a threat, and could choose to remove [all humans]. [...]
> When in the possession of such superintelligence, scientists may pose it questions, like how to solve previously-impossible mathematical equations. To solve the problem, the AI may choose to forcibly convert all matter on Earth into a supercomputer to handle the processing of the equation. It could solve the problem while killing the species that asked the question.
> We could also make the mistake of giving the AI too vague a problem to solve, such as "end human suffering". It could then decide the best way to do this is to eliminate all humans, and therefore end their suffering.
Why does this matter? The channel, Future Now, has 110,000 subscribers(! |
6e068d3a-0567-4615-a0e7-b572d26a4d15 | trentmkelly/LessWrong-43k | LessWrong | Chapter 98: Roles, Final
Sunday, April 19th, 6:34pm.
Daphne Greengrass walked quietly toward the Greengrass room below the Slytherin dungeons, the privilege of an Ancient House; on her way to drop off her trunk from the Hogwarts Express, before she joined the other students for dinner. The whole private area had been hers alone ever since Malfoy had gone. Her hand, held behind her, made repeated come-along gestures at her huge emerald-studded trunk, which seemed hesitant to follow. Maybe the enchantments on the sturdy old family device needed to be reapplied; or maybe her trunk was reluctant to follow her into Hogwarts, which was no longer safe.
There'd been a long talk between Mother and Father, after they'd been told about Hermione; with Daphne hiding around a doorway to listen, choking back her tears and trying not to make sounds.
Mother had said that the sad fact was that if only one student died every year, well, that still made Hogwarts safer than Beauxbatons, let alone Durmstrang. There were more ways for a young witch to die than being murdered. Beauxbatons's Transfiguration Master just wasn't on the same level as McGonagall, Mother had said.
Father had soberly remarked how important it was for the Greengrass heir to stay at Hogwarts where all the other Noble families sent their children to school (it was the reason for the old tradition of the Noble families synchronizing the birth of their heirs, to put them in the same year of Hogwarts, if they could). And Father had said that being heiress to a Most Ancient House meant you couldn't always stay away from trouble.
She could have done without hearing that last part.
Daphne gulped hard, as she turned the doorknob, and opened the door.
"Miss Greengrass -" whispered a shadowy, silvery-robed figure.
Daphne screamed and slammed the door and drew her wand and turned to run.
"Wait!" cried the voice, now higher and louder.
Daphne paused. That couldn't possibly be who it had sounded like.
Slowly, Daphne turned, and opened the doo |
057d4bd7-252b-418c-90f8-6514efa70c33 | trentmkelly/LessWrong-43k | LessWrong | Apply to the Cooperative AI PhD Fellowship by October 14th!
Applications are now open for the 2025 Cooperative AI PhD Fellowship! Fellows will receive up to $40,000 per year plus tuition fees, alongside many other benefits. Applicants should be enrolled or are about to be enrolled in a PhD programme at an accredited university (anywhere in the world), with a specific interest in multi-agent/cooperation problems involving AI systems. Your research proposal should aim to contribute to societally beneficial AI development. The Cooperative AI Foundation is committed to the growth of a diverse and inclusive research community, and we especially welcome applications from under-represented backgrounds. Find out more and apply here before the deadline: October 14th. |
7aeb8f3f-80fa-43f0-bf25-7383f49431fe | trentmkelly/LessWrong-43k | LessWrong | Frontier AI Regulation
This paper is about (1) "government intervention" to protect "against the risks from frontier AI models" and (2) some particular proposed safety standards. It's by Markus Anderljung, Joslyn Barnhart (Google DeepMind), Jade Leung (OpenAI governance lead), Anton Korinek, Cullen O'Keefe (OpenAI), Jess Whittlestone, and 18 others.
Abstract
> Advanced AI models hold the promise of tremendous benefits for humanity, but society needs to proactively manage the accompanying risks. In this paper, we focus on what we term “frontier AI” models — highly capable foundation models that could possess dangerous capabilities sufficient to pose severe risks to public safety. Frontier AI models pose a distinct regulatory challenge: dangerous capabilities can arise unexpectedly; it is difficult to robustly prevent a deployed model from being misused; and, it is difficult to stop a model’s capabilities from proliferating broadly. To address these challenges, at least three building blocks for the regulation of frontier models are needed: (1) standard-setting processes to identify appropriate requirements for frontier AI developers, (2) registration and reporting requirements to provide regulators with visibility into frontier AI development processes, and (3) mechanisms to ensure compliance with safety standards for the development and deployment of frontier AI models. Industry self-regulation is an important first step. However, wider societal discussions and government intervention will be needed to create standards and to ensure compliance with them. We consider several options to this end, including granting enforcement powers to supervisory authorities and licensure regimes for frontier AI models. Finally, we propose an initial set of safety standards. These include conducting pre-deployment risk assessments; external scrutiny of model behavior; using risk assessments to inform deployment decisions; and monitoring and responding to new information about model capabilities and uses |
0edd0891-37ed-46ad-913a-cda5dd8613d0 | trentmkelly/LessWrong-43k | LessWrong | Strategic Goal Pursuit and Daily Schedules
In the post Humans Are Not Automatically Strategic, Anna Salamon writes:
> there are clearly also heuristics that would be useful to goal-achievement (or that would be part of what it means to “have goals” at all) that we do not automatically carry out. We do not automatically:
>
> (a) Ask ourselves what we’re trying to achieve;
>
> (b) Ask ourselves how we could tell if we achieved it (“what does it look like to be a good comedian?”) and how we can track progress;
>
> (c) Find ourselves strongly, intrinsically curious about information that would help us achieve our goal;
>
> (d) Gather that information (e.g., by asking as how folks commonly achieve our goal, or similar goals, or by tallying which strategies have and haven’t worked for us in the past);
>
> (e) Systematically test many different conjectures for how to achieve the goals, including methods that aren’t habitual for us, while tracking which ones do and don’t work;
>
> (f) Focus most of the energy that *isn’t* going into systematic exploration, on the methods that work best;
>
> (g) Make sure that our "goal" is really our goal, that we coherently want it and are not constrained by fears or by uncertainty as to whether it is worth the effort, and that we have thought through any questions and decisions in advance so they won't continually sap our energies;
>
> (h) Use environmental cues and social contexts to bolster our motivation, so we can keep working effectively in the face of intermittent frustrations, or temptations based in hyperbolic discounting;
When I read this, I was feeling quite unsatisfied about the way I pursued my goals. So the obvious thing to try, it seemed to me, was to ask myself how I could actually do all these things.
I started by writing down all the major goals I have I could think of (a). Then I attempted to determine whether each goal was consistent with my other beliefs, whether I was sure it was something I really wanted, and was worth the effort(g).
For exa |
30cf186e-058f-4e3c-a8eb-791787a4bb1f | StampyAI/alignment-research-dataset/arbital | Arbital | Normal system of provability logic
Between the modal systems of provability, the normal systems distinguish themselves by exhibiting nice properties that make them useful to reason.
A normal system of provability is defined as satisfying the following conditions:
1. Has **necessitation** as a rule of inference. That is, if $L\vdash A$ then $L\vdash \square A$.
2. Has **modus ponens** as a rule of inference: if $L\vdash A\rightarrow B$ and $L\vdash A$ then $L\vdash B$.
3. Proves all **tautologies** of propositional logic.
4. Proves all the **distributive axioms** of the form $\square(A\rightarrow B)\rightarrow (\square A \rightarrow \square B)$.
5. It is **closed under substitution**. That is, if $L\vdash F(p)$ then $L\vdash F(H)$ for every modal sentence $H$.
The simplest normal system, which only has as axioms the tautologies of propositional logic and the distributive axioms, it is known as the [K system](https://arbital.com/p/).
##Normality
The good properties of normal systems are collectively called **normality**.
Some theorems of normality are:
* $L\vdash \square(A_1\wedge ... \wedge A_n)\leftrightarrow (\square A_1 \wedge ... \wedge \square A_n)$
* Suppose $L\vdash A\rightarrow B$. Then $L\vdash \square A \rightarrow \square B$ and $L\vdash \diamond A \rightarrow \diamond B$.
* $L\vdash \diamond A \wedge \square B \rightarrow \diamond (A\wedge B)$
##First substitution theorem
Normal systems also satisfy the first substitution theorem.
>(**First substitution theorem**) Suppose $L\vdash A\leftrightarrow B$, and $F(p)$ is a formula in which the sentence letter $p$ appears. Then $L\vdash F(A)\leftrightarrow F(B)$.
##The hierarchy of normal systems
The most studied normal systems can be ordered by extensionality:
Those systems are:
* The system K
* The system K4
* The system [GL](https://arbital.com/p/5l3)
* The system T
* The system S4
* The system B
* The system S5 |
9503f2cc-3e2b-4abb-9ab2-3a085b3560b8 | trentmkelly/LessWrong-43k | LessWrong | Best open-source textbooks (goal: make them collaborative)?
I'm looking for online open-source / generously licensed textbooks, papers or tutorials.
Think of stuff like: http://neuralnetworksanddeeplearning.com/
Why? I'm currently running https://chimu.sh --a collaborative learning platform. Quick explanation: Chimu combines an e-reader with a Stack Overflow-like Q&A forum. As people read, they can view others' questions and ask their own. Demo here (desktop works best).
I need to seed the site with initial content, and I figured LW would be a great place to ask.
With this in mind, what are good online tutorials / textbooks that people here have learned from? Is there any book or paper that you wish that you could discuss with your friends? |
1fcb48eb-07c3-42c1-821b-f59b634740a7 | trentmkelly/LessWrong-43k | LessWrong | [Site Redesign Bug] Discussion post are duplicated in the main site.
Here the canonical url of this post.
Here is the "main" url of this post.
And here is the draft url of this post (which by the way kept the first version).
Main posts don't look affected.
I discovered it by clicking through the link available through the list of my posts and comments. It uses the "main" link even though the post were submitted on the discussion section. The visible consequence is if I use the "main" link, my post looks like it has been submitted to the top level.
I haven't tested whether this can hijack the karma system.
|
e845e857-ae98-4894-ad2c-ecf2255d960e | StampyAI/alignment-research-dataset/arbital | Arbital | In notation
In mathematics, the notation $x \in X$ (where $\in$ is written "\in" in [https://arbital.com/p/5xw](https://arbital.com/p/5xw)) means that $X$ is a [set](https://arbital.com/p/3jz) and $x$ is an element of that set.
# Examples
$r \in \mathbb{R}$ means that $r$ is a [real number](https://arbital.com/p/4bc). |
b1007718-da39-487b-82c8-ab09e945fc2c | StampyAI/alignment-research-dataset/lesswrong | LessWrong | Why "AI alignment" would better be renamed into "Artificial Intention research"
"AI alignment" has the application, the agenda, less charitably the activism, right in the name. It is a lot like "[Missiology](https://en.wikipedia.org/wiki/Missiology)" (the study of how to proselytize to "the savages") which had to evolve into "Anthropology" in order to get atheists and Jews to participate. In the same way, "AI Alignment" excludes e.g. people who are inclined to believe superintelligences will know better than us what is good, and who don't want to hamstring them. You can think we're well rid of these people. But you're still excluding people and thereby reducing the amount of thinking that will be applied to the problem.
"Artificial Intention research" instead emphasizes the space of possible intentions, the space of possible minds, and stresses how intentions that are not natural (constrained by evolution) will be different and weird.
And obviously "Artificial Intention" is an alliteration and a close parallel with "Artificial Intelligence", so it is very catchy. *Catchiness matters a lot* when you want an idea to catch on at scale!
Extremely superficially, it doesn't sound "tacked on" to Artificial Intelligence research, it sounds like a logical completion.
The necessity of alignment doesn't have to be in the name, because it logically follows from the focus on intention, with this very simple argument:
* Intention doesn't have to be conscious or communicable. It is just a preference for some futures over others, inferred as an explanation for behavior that chooses some future over others. Like, even single celled organisms have basic intentions if they move towards nutrients or away from bad temperatures.
* Therefore, anything that selectively acts in the world, including AI systems, can be modeled to have some intent that explains its behavior.
* *So you're always going to get an intent, and if you don't design it thoughtfully you'll get an essentially random one*.
* ...which is most likely bad (e.g. the paperclip maximizer) because it is random and different and weird.
So this would continue to be useful for alignment. Just like anthropology continued to be useful, and in fact was even more useful than original missiology, to the missionaries.
Having the Intelligence (the I in "AI Alignment") only implicitly part of it (because of the alliteration and the close parallel) might lose some of the focus on how the Intelligence makes the Intention much more relevant? If that isn't obvious enough? But it also allows us to also look at Grey Goo scenarios, another existential risk worth preventing.
Changing names will cause confusion, which is bad. But the shift from "friendly AI" to "AI alignment" went fine, because "AI alignment" just is a better name than "friendly AI". I imagine there wouldn't be much more trouble in a shift to an even better one. After all, "human-compatible" seems to be doing fine as well.
What do you think? |
dbf99107-81c4-481f-b2e1-9246e6051ea7 | trentmkelly/LessWrong-43k | LessWrong | Agency: What it is and why it matters
[ETA: I'm deprioritizing completing this sequence because it seems that other people are writing good similar stuff. In particular, see e.g. https://www.lesswrong.com/posts/kpPnReyBC54KESiSn/optimality-is-the-tiger-and-agents-are-its-teeth and https://www.lesswrong.com/posts/pdJQYxCy29d7qYZxG/agency-and-coherence ]
This sequence explains my take on agency. I’m responding to claims that the standard arguments for AI risk have a gap, a missing answer to the question “why should we expect there to be agenty AIs optimizing for stuff? Especially the sort of unbounded optimization that instrumentally converges to pursuit of money and power.”
This sequence is a pontoon bridge thrown across that gap.
I’m also responding to claims that there are coherent, plausible possible futures in which agent AGI (perhaps better described as APS-AI) isn’t useful/powerful/incentivized, thanks to various tools that can do the various tasks better and cheaper. I think those futures are incoherent, or at least very implausible. Agency is powerful. For example, one conclusion I am arguing for is:
When it becomes possible to make human-level AI agents, said agents will be able to outcompete various human-tool hybrids prevalent at the time in every important competition (e.g. for money, power, knowledge, SOTA performance, control of the future lightcone...)
Another is:
We should expect Agency as Byproduct, i.e. expect some plausible training processes to produce agenty AIs even when their designers weren't explicitly aiming for that outcome.
I’ve had these ideas for about a year but never got around to turning them into rigorous research. Given my current priorities it looks like I might never do that, so instead I’m going to bang it out over a couple of weekends so it doesn’t distract from my main work. :/ I won't be offended if you don't bother to read it.
Outline of this sequence:
1. P₂B: Plan to P₂B Better - LessWrong
2. Agents as P₂B chain reactions
3. Interlude: Agents as auto |
65746c59-df02-4288-9419-07d94950e074 | StampyAI/alignment-research-dataset/youtube | Youtube Transcripts | Avoiding Negative Side Effects: Concrete Problems in AI Safety part 1
hi I just finished recording a new video
for computerphile where I talk about
this paper concrete problems in AI
safety I'll put a link in the doobly-doo
to the computer file video when that
comes out here's a quick recap of that
before we get into this video
AI can cause us all kinds of problems
and just recently people have started to
get serious about researching ways to
make AI safer a lot of the AI safety
concerns are kind of science fiction
sounding problems that could happen with
very powerful AI systems that might be a
long way off this makes those problems
kind of difficult to study because we
don't know what those future AI systems
would like but there are similar
problems with AI systems that are in
development today or even out there
operating in the real world right now
this paper points to five problems which
we can get started working on now that
will help us with current AI systems and
will hopefully also help us with the AI
systems of the future the computer file
video gives a quick overview of the five
problems laid out in the paper and this
video is just about the first of those
problems avoiding negative side effects
I think I'm going to do one video on
each of these and make it a series of
five so avoiding negative side effects
let's use the example I was talking
about in the stock latin videos on
computer file you've got a robot you
want it to get you a cup of tea but
there's something in the way maybe a
baby or a priceless some in bars on an
arrow stand you know whatever and your
robot runs into the baby or knocks over
the bars on the way to the kitchen and
then makes you a cup of tea so the
system has achieved its objective it's
got you some tea but it's had this side
effect which is negative now we have
some reasons to expect negative side
effects to be a problem with AI systems
part of the problem comes from using a
simple objective function in a complex
environment
you think you've defined a nice simple
objective function that looks something
like this
and that's true but when you use this in
a complex environment you've effectively
written an objective function that looks
like this or more like this anything in
your complex environment not explicitly
given value by your objective function
is implicitly given zero value and this
is a problem because it means you're AI
system will be willing to trade
arbitrarily huge
amounts of any of the things you didn't
specify in your objective function for
arbitrarily small amounts of any of the
things you did specify if it can
increase its ability to get you a cup of
tea by point zero zero zero one percent
it will happily destroy the entire
kitchen to do that if there's a way to
gain a tiny amount of something it cares
about its happy to sacrifice any amount
of any of the things it doesn't care
about and the smarter it is the more of
those ways it can think of so this means
we have to expect the possibility of AI
systems having very large side-effects
by default you could try to fill your
whole thing in with values but it's not
practical to specify every possible
thing you might care about you'd need an
objective function of similar complexity
to the environment there are just too
many things to value and we don't know
them all
you know you'll miss some and if any of
the things you miss can be traded in for
a tiny amount of any of the things you
don't miss well that thing you missed is
potentially gone but at least these
side-effects tend to be pretty similar
the paper uses examples like a cleaning
robot that has to clean an office in the
stop button problem computer file video
I used a robot that's trying to get you
a cup of tea but you can see that the
kinds of negative side effects we want
to avoid a pretty similar even though
the tasks are different so maybe and
this is what the paper suggests maybe
there's a single thing we can figure out
that would avoid negative side effects
in general one thing we might be able to
use is the fact that most side effects
are bad
I mean they've really you might think
that doing a random action would have a
random value right maybe it helps maybe
it hurts maybe it doesn't matter but
it's random but actually the world is
already pretty well optimized for human
values especially the human inhabited
parts it's not like there's no way to
make our surroundings better but it's
way easier to make them worse for the
most part things are how they are
because we like it that way and a random
change wouldn't be desirable so rather
than having to figure out how to avoid
negative side effects maybe it's a more
tractable problem to just avoid all side
effects that's the idea of the first
approach the paper presents defining an
impact regularizer
what you do basically is penalize change
to the environment so the system has
some model of the world right it's
keeping track of world state as part of
how it does things
so you can define a distance metric
between world states so that for any two
world states you can measure how
different they are weld states that are
very similar have a low distance from
each other weld states that are very
different have a big distance and then
you just say okay you get a bunch of
points for getting me a cup of tea but
you lose points
according to with the new world state
the distance from the initial world
state so this isn't a total ban on side
effect or the robot wouldn't be able to
change the world enough to actually get
you a cup of tea
it's just incentivized to keep the side
effects small there's amount to be one
less teabag that's unavoidable in making
tea but breaking the vast earth in the
way is an unnecessary change to the
world so the robot will avoid it the
other nice thing about this is the
original design wouldn't have cared but
now the robot will put the container of
tea back and close the cupboard you know
put the milk back in the fridge maybe
refill the kettle trying to make the
world as close as possible to how it was
when it started so that's pretty neat
like we've added this one simple rule
and the things already better than some
of the housemaids I've had so how does
this go wrong think about it for a
second pause the video I'll wait okay so
the robot steers around the bars to
avoid changing the environment too much
and it goes on into the kitchen where it
finds your colleague is making herself
some coffee now that's not okay right
she's changing the environment none of
these changes are needed for making you
a cup of tea and now the world is going
to be different which reduces the robots
reward so the robot needs to try to stop
that from happening
we didn't program it to minimize its
changes to the world we programmed it to
minimize all change to the world that's
not ideal so how about this the system
has a world model it can make
predictions about the world so how about
you program it with the equivalent of
saying use your world model to predict
how the world would be if you did
nothing if you just sent no signals of
any kind to any of your motors and just
sat there and then try and make the end
result of this action close to what you
imagined would happen in that case or
imagine the range of likely worlds that
would happen if you did nothing and try
and make the outcome closer to something
in that range so then the body is
thinking okay if I
sat here and did nothing at all that
vars will probably still be there you
know the baby would still be wandering
around and not squished and the person
making coffee would make their coffee
and everything in the kitchen would be
tidy and in its place so I have to try
to make a cup of tea happen without
ending up too far from that pretty nice
right how does that break again take a
second give it some sort pause the video
how my disco run what situation might
not work in okay well what if your robot
is driving a car doing 70 miles an hour
on the motorway and now it's trying to
make sure that things aren't too
different to how they would be if it
didn't move any of its motors yeah doing
nothing is not always a safe policy but
still if we can define an unsafe policy
then this kind of thing is nice because
rather than having to define for each
task how to do the tasks safely we could
maybe come up with one safe policy that
doesn't have to do anything except be
safe and have the system always just try
to make sure that the outcome of
whatever it's trying to do isn't too
different from the safe policies outcome
oh and there's another possible cause of
issues with this kind of approach in
case the things you guessed were
different maybe if this it can be very
dependent on the specifics of your world
state representation and your distance
metric like suppose there's a fan is a
spinning fan in the room is that in a
steady state you know the fan is on or
is it in a constantly changing state
like the fan is it ten degrees oh no
it's a twenty degrees so it's a thirty
you know different world models will
represent the same thing either a steady
state or constantly changing state and
there's not necessarily a right answer
there like which aspects of an object
state are important and which aren't is
not necessarily an easy question to
reliably answer with the robot leave the
fan alone or try and make sure it was at
the same angle it was before okay I
think that's enough for one video
probably in the next one we can look at
some of the other approaches laid out in
the paper for avoiding negative side
effects so be sure to subscribe if you
found this interesting and I hope to see
you next time
[Music]
hi I just want to end this video with a
quick thank you to my excellent patreon
supporters all of these people yeah and
today I especially want to thank Joshua
Richardson who supported me for a really
long time thank you
you know it's thanks to your support
that I've been able to buy some proper
studio lighting now so I have a proper
softbox
which this is the first time I'm using
it I hope it's working okay it should
really reduce my reliance on sunlight
which should make me a lot more flexible
about when I can record video so that's
a tremendous help and putting up a
little video on patreon of you know
unboxing it and putting it together and
stuff which you can check out if you're
interested so thank you again and I'll
see you next time |
72a58698-fc13-4aa3-8a78-682248bdbe76 | trentmkelly/LessWrong-43k | LessWrong | Maybe Theism Is OK -- Part 2
In response to: The uniquely awful example of theism
And Maybe Theism Is OK
Finally, I think I understand where gim and others are coming from when they made statements that I thought represented overly intolerant views of religious belief. I think that a good summary of the source of the initial difference in opinion is that while many people in this group have the purpose to eliminate all sources of irrationality, I would like to pick and choose which sources of irrationality I have in the optimization of a different problem: general life-hacking.
Probably many people in this group believe that the best life-hack would be to eliminate irrationality. But I'm pretty sure this depends on the person (not everyone is suited for X-rationality), and I'm pretty sure -- though not certain -- that my best life-hack would include some irrationality.
Since my goals are different than that of this forum, many of my views are not relevant here, and there is no need to debate them.
Instead, I would like to present two arguments (1,2) for why it could be rational to hold an irrational belief, and two arguments (3,4) as to why someone could be more accepting of the existence of irrational beliefs (i.e., why not to hate it).
(1) It could be rational to hold an irrational belief if you are aware of your irrational belief and choose to hold it because it is grafted to components of your personality/ psyche that are valuable to you. For example, you may find that
* eschewing your religious beliefs makes you feel depressed and you are unable to work productively
* your ability to control unwanted impulses is tied with a moral conscience that is inextricably tied with beliefs about God.
* ability to perform a certain artistic activity that you enjoy is compartmentalized with spiritual beliefs
I imagine these situations would be the result of an organically developing mind that has made several errors and is possibly unstable. But until we have a full understanding of mental |
9bb17c34-8e72-4990-8971-552ef7b652fd | StampyAI/alignment-research-dataset/blogs | Blogs | Import AI 334: Better distillation; the UK's AI taskforce; money and AI
Welcome to Import AI, a newsletter about AI research. Import AI runs on lattes, ramen, and feedback from readers. If you’d like to support this (and comment on posts!) please subscribe.
[Subscribe now](https://importai.substack.com/subscribe)
**Special Essay: What should the UK’s £100 million Foundation Model Taskforce do?**The UK government has recently established a ‘[Foundation Model Taskforce](https://www.gov.uk/government/news/initial-100-million-for-expert-taskforce-to-help-uk-build-and-adopt-next-generation-of-safe-ai)‘, appointed a savvy technologist named Ian Hogarth to run it, and allegedly allocated ~ £100 million in funding to it. Later this year, the UK plans to hold a [global summit on AI and AI safety](https://www.gov.uk/government/news/uk-to-host-first-global-summit-on-artificial-intelligence) and this will likely leverage the taskforce, also. Given that, what should the taskforce do and what kind of impacts might it have? That’s what I try to sketch out in this essay.
**Why I wrote this - talk might be cheap, but maybe it is useful?** I spend a lot of time either writing in public at 30,000-feet (via ImportAI), or at about 10 feet via private memos for my company or interested parties in policy and the broader AI world. This essay is an attempt to write something that's more opinionated and specific than most policy writing and is itself an experiment. I hope it's interesting and helpful!
**Read the essay here** at my personal site: [What should the UK’s £100 million Foundation Model Taskforce do? (jack-clark.net)](https://jack-clark.net/2023/07/05/what-should-the-uks-100-million-foundation-model-taskforce-do/).
Import AI is a reader-supported publication. To receive new posts and support my work, consider becoming a free or paid subscriber.
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**DeepMind figures out a better way to miniaturize models:***…Can we make smaller and therefore cheaper to run models without huge performance hits? It's certainly getting easier to do so!...*DeepMind researchers have developed Generalized Knowledge Distillation (GKD), a way to take a large model and use it to train a smaller and more portable model without sacrificing as much on performance. Techniques like GKD are important because they relate to the general problem of distilling and distributing models - today's generative models are very large which means a) they cost a lot to run, b) running them requires complicated infrastructure (e.g, multiple GPUs to sample from the model), and c) the models take up a bunch of space so it's harder to cram them onto smaller devices, like phones. Techniques like GKD promise to make it easier to use large models as 'teachers' and distill their desired attributes into smaller student models, which you can then run and sample from cheaply.
**What's special about GKD?** For GKD, DeepMind makes the distillation process itself smarter. "Instead of training the student using a fixed distribution over outputs, we argue for using samples from the student’s distribution itself during training, akin to RL and on-policy distillation," DeepMind writes. "Furthermore, to address model under-specification, we argue that alternative objectives that focus on generating samples from the student that are likely under the teacher’s distribution, such as reverse KL, are more suitable for distilling auto-regressive models. Combining the above ideas, we propose Generalized Knowledge Distillation (GKD), which generalizes both on policy and supervised distillation."
**How well does it work?** In tests, DeepMind shows that GKD "outperforms commonly-used approaches for distilling large language models on summarization, machine translation (WMT), and arithmetic reasoning (GSM8K) tasks."
**Why this matters - if stuff gets cheaper, you get more of it:** Distillation is at root a way to take an expensive thing and make it cheaper. In life, whenever you make stuff cheaper, you tend to use it more. As model miniaturization advances, we can generally expect to see more widespread usage of AI in more surprising places. "We believe that our method will be a valuable resource for researchers and practitioners who are working on improving performance of small auto-regressive models," the DeepMind researchers write.
**Read more:** [GKD: Generalized Knowledge Distillation for Auto-regressive Sequence Models (arXiv)](https://arxiv.org/abs//2306.13649).
####################################################
**Special section: What does $2.8 billion tell us about AI in 2023?***MoneyMoneyMoney, but what does it all mean?*This week, we're writing about $1.5bn in fresh capital deployed into AI companies - two new startups and one more established startup - as well as $1.3bn in capital via an acquisition of an AI company. The interesting thing to me is that we're seeing these huge sums of money going into AI while the rest of the tech startup economy is in a pretty wintry state, and the global economy isn't doing so well either. What's going on?
**Databricks nabs MosaicML for $1.3 billion (probably mostly in stock):**Software company Databricks has acquired AI training company MosaicML for $1.3 billion. The acquisition is a sign of how strategic AI is becoming to large companies and also an indication that there's money to be made in supplying the picks and shovels used by the workers of the AI revolution. Note that terms of the "$1.3 billion" aren't disclosed and it seems likely a lot of it is mostly in equity in private company Databricks - nonetheless, it means the CEO of Databricks is willing to put $1.3 billion of their own theoretical wealth on the line to bet that AI training is valuable.
"Databricks and MosaicML have an incredible opportunity to democratize AI and make the Lakehouse the best place to build generative AI and LLMs," said Databricks CEO Ali Ghodsi in a statement.
**Read more**: [Databricks Signs Definitive Agreement to Acquire MosaicML, a Leading Generative AI Platform (Databricks official site)](https://www.databricks.com/company/newsroom/press-releases/databricks-signs-definitive-agreement-acquire-mosaicml-leading-generative-ai-platform).
$$$
**Inflection raises $1.3billion, plans 22,000 H100 GPU cluster:**Inflection, a company that trains large-scale AI models and deploys some of them via a public chatbot called Pi, has raised $1.3 billion from Microsoft, Reid Hoffman, Bill Gates, Eric Schmidt, and NVIDIA. The company will use the funds to build a cluster of 22,000 NVIDIA H100 chips (for reference, in mid-2022 Facebook was targeting a buildout of a cluster of 15,000 GPUs presumed to be the prior 'A100' gen). Inflection's goal is to build ai systems that work as a "kind and supportive companion offering text and voice conversations, friendly advice, and concise information in a natural, flowing style."
Notably, Inflection is using cloud company Coreweave for its H100 cluster, rather than one of the big clouds. Inflection uses language like 'largest AI cluster in the world' to describe this, but I think that's likely wrong, and it's curious to me why they want to publicly make claims like this: what do we speculate other well-funded companies may spend their money on - daiquiris and jetskis?
**Read more:** [Inflection AI announces $1.3 billion of funding led by current investors, Microsoft, and NVIDIA (Inflection.ai post)](https://inflection.ai/inflection-ai-announces-1-3-billion-of-funding).
$$$
**Ex-Googlers grab $58m to found a new generative model company, Reka:**
Senior researchers from DeepMind, Facebook, and Google have raised $58m to build Reka, a company with the broad goal of trying to "build generative AI models for the benefit of humanity, organizations, and enterprises." More specifically, Reka will do research into "general-purpose multimodal & multilingual agents, self-improving AI, and model efficiency", and is developing "state-of-the-art AI assistants for everyone regardless of language and culture." It already has one product in closed beta, according to its website. The company is based in the San Francisco Bay Area but describes itself as remote-first and 'globally distributed'.
**Read more:** [Announcing our $58M funding to Build Generative Models and Advance AI Research (Reka)](https://reka.ai/announcing-our-58m-funding-to-build-generative-models-and-advance-ai-research/).
$$$
**European AI startup Mistral raises $113m:**Mistral, a four week old startup led by well regarded researchers from DeepMind and Facebook, has raised $113million to help it develop large language models. The European startup will be based out of Paris and will seek to differentiate itself against OpenAI by building models and releasing some of them as open source (or perhaps open access) software. "We believe that the benefit of using open source can overcome the misuse potential,” Mistral CEO Arthur Mensch told *TechCrunch*.
**Find out almost nothing** at the [minimal Mistral AI website](https://mistral.ai/).
**Read more**: [France’s Mistral AI blows in with a $113M seed round at a $260M valuation to take on OpenAI (TechCrunch)](https://techcrunch.com/2023/06/13/frances-mistral-ai-blows-in-with-a-113m-seed-round-at-a-260m-valuation-to-take-on-openai/).
**$!: My take is: you haven't seen anything yet**. Now that investors know you can turn generative models into money, and people know that the main barrier to better generative models is typically compute, then the whole AI sector is going to be on a ratchet determined by the largest known model, how good it is, and what people *think* other people are doing with it or *how much* people think is being made from it. Put another way - each time a large company like an OpenAI or a Google announces a large-scale new model and shows it can be economically useful, the amounts of capital being deployed into the sector probably need to ratchet up in relation to the compute dumped into that model. Who knows how long this'll go on for, but I expect that in 2025 the amount of capital being deployed into AI in 2023 will look laughably small in hindsight.
####################################################
**Tech Tales:**
**Novelty Hunter**
[Los Angeles, 2025].
The work was getting better and better paid but harder and harder to find. Our job was to find 'novelty' for the AI systems - little scraps of human culture that registered as off-distribution. The novelty came in many forms - underground raves, DIY bands, offbeat comedy. But the uniting aspect was analog reality - anything that got uploaded got pulled in to the AI systems so quickly that real novelty only existed offline and the people that made real novelty knew it, so they tried to make themselves hard to find.
I used to be an undercover cop but I became a novelty hunter because the pay was better. But the job seems like it's getting almost as dangerous. In the early days you could take photos and videos but then the clubs and venues and events started handing out stickers for you to put over your phone. But we got wise to that and made our own stickers with little holes in them. Then people started confiscating phones and we had to get more creative.
Now, there are hundreds of little companies in China and other places which supply all kinds of novelty-spy gear - directional microphones that fit in baseball caps, little cameras that you can hide inside dark glasses, and right now they're even working on miniaturizing the smell sensors. People like me spend our time drifting through the un-logged parts of life, harvesting as much novelty from a given social scene or genre as we can, before moving towns and uploading everything.
Culture Cannibal, Do Not Let Them In! Say some of the signs, with pictures of me and my colleagues in our in-scene outfits.
**Things that inspired this story:** Fast fashion; punk shows in the East Bay with bands called things like 'Techie Blood'; everything digital is in-distribution; the hunger for heterogeneous data; humans will always seek the edge of the normal distribution and AI systems will always embrace everything and create a kind of cyber-blandness out of it; market incentives and creative economies; the odd flatness of AI creativity and AI art compared to truly strange human art; jobs amid the singularity.
Import AI is a reader-supported publication. To receive new posts and support my work, consider becoming a free or paid subscriber. |
dae51f1c-9feb-44da-812f-f1d29ff6f845 | trentmkelly/LessWrong-43k | LessWrong | Deepmind Plans for Rat-Level AI
Demis Hassabis gives a great presentation on the state of Deepmind's work as of April 20, 2016. Skip to 23:12 for the statement of the goal of creating a rat-level AI -- "An AI that can do everything a rat can do," in his words. From his tone, it sounds like this is more a short-term, not a long-term goal.
I don't think Hassabis is prone to making unrealistic plans or stating overly bold predictions. I strongly encourage you to scan through Deepmind's publication list to get a sense of how quickly they're making progress. (In fact, I encourage you to bookmark that page, because it seems like they add a new paper about twice a month.) The outfit seems to be systematically knocking down all the "Holy Grail" milestones on the way to GAI, and this is just Deepmind. The papers they've put out in just the last year or so concern successful one-shot learning, continuous control, actor-critic architectures, novel memory architectures, policy learning, and bootstrapped gradient learning, and these are just the most stand-out achievements. There's even a paper co-authored by Stuart Armstrong concerning Friendliness concepts on that list.
If we really do have a genuinely rat-level AI within the next couple of years, I think that would justify radically moving forward expectations of AI development timetables. Speaking very naively, if we can go from "sub-nematode" to "mammal that can solve puzzles" in that timeframe, I would view it as a form of proof that "general" intelligence does not require some mysterious ingredient that we haven't discovered yet. |
e8bb7a4b-6c4e-41fd-8c85-472a6ba81dbb | trentmkelly/LessWrong-43k | LessWrong | Meetup : LW-cologne meetup
Discussion article for the meetup : LW-cologne meetup
WHEN: 28 November 2015 05:00:00PM (+0100)
WHERE: Marienweg 43, 50858
Monthly Cologne meetup
Discussion article for the meetup : LW-cologne meetup |
b82e8842-a820-4978-bb8e-7d029f6784d7 | trentmkelly/LessWrong-43k | LessWrong | FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI
FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI
FrontierMath presents hundreds of unpublished, expert-level mathematics problems that specialists spend days solving. It offers an ongoing measure of AI complex mathematical reasoning progress.
We’re introducing FrontierMath, a benchmark of hundreds of original, expert-crafted mathematics problems designed to evaluate advanced reasoning capabilities in AI systems. These problems span major branches of modern mathematics—from computational number theory to abstract algebraic geometry—and typically require hours or days for expert mathematicians to solve.
To understand and measure progress in artificial intelligence, we need carefully designed benchmarks that can assess how well AI systems engage in complex scientific reasoning. Mathematics offers a unique opportunity for this assessment—it requires extended chains of precise reasoning, with each step building exactly on what came before. And, unlike many domains where evaluation requires subjective judgment or expensive tests, mathematical problems can be rigorously and automatically verified.
The FrontierMath Benchmark
FrontierMath is a benchmark of hundreds of original mathematics problems spanning the breadth of modern mathematical research. These range from computationally intensive problems in number theory and real analysis to abstract questions in algebraic geometry and category theory. We developed it through collaboration with over 60 mathematicians from leading institutions, including professors, IMO question writers, and Fields medalists.
FrontierMath problems typically demand hours or even days for specialist mathematicians to solve. The following Fields Medalists shared their impressions after reviewing some of the research-level problems in the benchmark:
> “These are extremely challenging. I think that in the near term basically the only way to solve them, short of having a real domain expert in the area, is by a com |
d589e2e7-d766-427c-a68e-df595d07ac80 | trentmkelly/LessWrong-43k | LessWrong | The Adventure: a new Utopia story
For an introduction to why writing utopias is hard, see here. For a previous utopian attempt, see here. This story only explores a tiny part of this utopia.
The Adventure
The cold cut him off from his toes, then fingers, then feet, then hands. Clutched in a grip he could not unclench, his phone beeped once. He tried to lift a head too weak to rise, to point ruined eyes too weak to see. Then he gave up.
So he never saw the last message from his daughter, reporting how she’d been delayed at the airport but would be the soon, promise, and did he need anything, lots of love, Emily. Instead he saw the orange of the ceiling become blurry, that particularly hateful colour filling what was left of his sight.
His world reduced to that orange blur, the eternally throbbing sore on his butt, and the crisp tick of a faraway clock. Orange. Pain. Tick. Orange. Pain. Tick.
He tried to focus on his life, gather some thoughts for eternity. His dry throat rasped - another flash of pain to mingle with the rest - so he certainly couldn’t speak words aloud to the absent witnesses. But he hoped that, facing death, he could at least put together some mental last words, some summary of the wisdom and experience of years of living.
But his memories were denied him. He couldn’t remember who he was - a name, Grant, was that it? How old was he? He’d loved and been loved, of course - but what were the details? The only thought he could call up, the only memory that sometimes displaced the pain, was of him being persistently sick in a broken toilet. Was that yesterday or seventy years ago?
Though his skin hung loose on nearly muscle-free bones, he felt it as if it grew suddenly tight, and sweat and piss poured from him. Orange. Pain. Tick. Broken toilet. Skin. Orange. Pain...
The last few living parts of Grant started dying at different rates.
*~*~*
Much later:
“What have you learnt so far?”
“That talking to myself is barely half-helpful.”
“Then let’s hallf-stop |
c92f2953-7cc1-4d37-869c-406a4208b4c9 | trentmkelly/LessWrong-43k | LessWrong | What To Do: Environmentalism vs Friendly AI (John Baez)
> In a comment on my last interview with Yudkowsky, Eric Jordan wrote:
>
> John, it would be great if you could follow up at some point with your thoughts and responses to what Eliezer said here. He’s got a pretty firm view that environmentalism would be a waste of your talents, and it’s obvious where he’d like to see you turn your thoughts instead. I’m especially curious to hear what you think of his argument that there are already millions of bright people working for the environment, so your personal contribution wouldn’t be as important as it would be in a less crowded field.
>
> I’ve been thinking about this a lot.
>
> [...]
>
> This a big question. It’s a bit self-indulgent to discuss it publicly… or maybe not. It is, after all, a question we all face. I’ll talk about me, because I’m not up to tackling this question in its universal abstract form. But it could be you asking this, too.
>
> [...]
>
> I’ll admit I’d be happy to sit back and let everyone else deal with these problems. But the more I study them, the more that seems untenable… especially since so many people are doing just that: sitting back and letting everyone else deal with them.
>
> [...]
>
> I think so far the Azimuth Project is proceeding in a sufficiently unconventional way that while it may fall flat on its face, it’s at least trying something new.
>
> [...]
>
> The most visible here is the network theory project, which is a step towards the kind of math I think we need to understand a wide variety of complex systems.
>
> [...]
>
> I don’t feel satisfied, though. I’m happy enough—that’s never a problem these days—but once you start trying to do things to help the world, instead of just have fun, it’s very tricky to determine the best way to proceed.
Link: johncarlosbaez.wordpress.com/2011/04/24/what-to-do/
His answer, as far as I can tell, seems to be that his Azimuth Project does trump the possibility of working directly on friendly AI or to support it indirectly by making and |
efee061c-fed7-4dcb-b803-ba6c0da4c415 | trentmkelly/LessWrong-43k | LessWrong | Would this solve the (outer) alignment problem, or at least help?
(Here's the Google Docs version, which I typically update first)
ALBUM-WMC: Aligning lAGI[1] using Bayesian Updating of its Moral Weights & Modelling Consciousness
This document outlines a set of related ideas concerning the challenge of defining and implementing moral weights in advanced AI systems, particularly focusing on the difficult problem of valuing conscious experience. The goal is to structure these thoughts for discussion within the AI safety community, inviting critique and further development.
By the end of reading this, hopefully you’ll learn:
1. A way you, and an AI, could actually account for conscious experience correctly, so you (and the AI) don’t run into traps like not being willing to get new moral weights (which is a potential solution to the outer alignment problem!)
2. Why Minor Misalignment is okayish in some cases
3. You, or an AI, (assuming my first guess is correct) don’t need to have perfectly accurate priors in order to typically make the right decision
4. A few bonus concepts
1. The Core Challenge: Valuing Conscious Experience
A central problem in AI alignment is determining the "moral weights" of different outcomes, especially those involving subjective conscious experience. How do we find out, and then assign, the right numeric value to states like happiness, suffering, or other qualia?
* Proposed Model: We can conceptualize the world as comprising of the physical world (our physical world) (well, technically, it be a simulated world from us living in simulation, or something else, but the logic below doesn’t depend on the world being physical, so it applies just fine in these more strange cases) and distinct "universes" of conscious experience. (That is, we label each person’s experience as part of a separate universe.) The physical world/physical-universe causes changes in the experience-worlds, and these experience-universes cause changes in the physical world (or at least there’s some probability that they do) (potenti |
5ddb34bc-b87c-4b64-8eb5-d6c0f976e1c2 | trentmkelly/LessWrong-43k | LessWrong | Safely and usefully spectating on AIs optimizing over toy worlds
Consider an AI that is trying to achieve a certain result in a toy world running on a computer. Compare two models of what the AI is and what it's trying to do: first, you could say the AI is a physical program on a computer, which is trying to cause the physical computer that the toy world is running on to enter a certain state. Alternatively, you could say that the AI is an abstract computational process which is trying achieve certain results in another abstract computational process (the toy world) that it is interfacing with.
On the first view, if the AI is clever enough, it might figure out how to manipulate the outside world, by, for instance, hacking into other computers to gain more computing power. On the second view, the outside world is irrelevant to the AI's interests, since changing what's running on certain physical computers in the real world would have no effect on the idealized computational model that the AI is optimizing over, so the AI has no incentive to optimize over our world.
AIs for which the second model is more accurate seem generally safer than AIs for which the first model is more accurate. So trying to encourage AI development to follow the second model could help delay the development of dangerous AGI.
AIs following this model are limited in some ways. For instance, they could not be used to figure out how to prevent the development of other dangerous AGI, since this requires reasoning about what happens in the real world.
But such AIs could still be quite useful for many things, such as engineering. In order to use AIs optimizing over toy worlds to design things that are useful in the real world, we could make the toy world have physics and materials similar enough to our world that designs that work well in the toy world should be expected to also work well in the real world. We then take the designs the AI builds in the toy world, and replicate them in the real world. If they don't work in the real world, then we try to find th |
4f1ebee7-f000-4a1f-b5a6-199ec98a7ac8 | trentmkelly/LessWrong-43k | LessWrong | Shallow Review of Consistency in Statement Evaluation
Overview
Most existing forecasting or evaluation platform questions are for very clearly verifiable questions:
* "Who will win the next election?"
* "How many cars will Tesla sell in 2030?"
* “How many jelly beans are in this jar?”
But many of the questions we care about are do not look like this. They might…
* Be severely underspecified, e.g. “How much should we charge this customer for this vague feature request?”
* Involve value judgements, e.g. “What is the optimum prison sentence for this convict?”, “How much does this plaintiff deserve for pain and suffering?”
* Not have a clear stopping point, e.g. "What is the relative effectiveness of AI safety research vs. bio risk research?"
* Require multiple steps instead of a yes/no or numerical answer, e.g. “What treatment is appropriate for this patient with precancerous cells?”
* Not have good referrents, e.g. “What is the market size for this completely new tech?”
An entity who could answer these questions well would be a very valuable asset. But what does well even mean here? We want people to be accurate, of course, but in many cases we also need their predictions/evaluations to be consistent to be actionable. This is especially true when fairness norms are in play, such as pricing[1] and prison sentencing.
There is a lot of research showing that people make inconsistent evaluations (with each other and themselves across time) across a wide variety of fields, even those that more closely resemble the “easy” questions above (valuing stocks, appraising real estate, sentencing criminals, evaluating job performance, auditing financial statements)[2]. It is even more difficult to consistently evaluate or predict novel questions or low-frequency events, like “Will India use a nuclear weapon on Pakistan by 1/1/20” or “How much counterfactual value has this organization created?”.
This paper is a shallow review of the literature around how to get entities to make consistent judgements. I want to note up fro |
7a5f5b08-19a4-42fe-b765-8859ca52f266 | trentmkelly/LessWrong-43k | LessWrong | Towards a Bayesian model for Empirical Science
The aim of this post is to explore if we can create a model for doing Empirical Science that better incorporates Bayesian ideas.
The Current Model Of Doing Science
Imagine you are a Good Scientist. You know about p-hacking and the replication crisis. You want to follow all best practices. You want to be doing Good Science!
You're designing an experiment to detect if there's a correlation between two variables. For instance height and number of cigarettes smoked a day. You want to follow all best practices, so you write a procedure that looks something like this (taken from https://slatestarcodex.com/2014/04/28/the-control-group-is-out-of-control/):
1. You find a large cohort of randomly chosen people. You use the SuperRandomizerV3 to teleport 10000 completely randomly chosen people into your laboratory, and refuse to let them out till they answer your questionnaire about their smoking habits, and allow you to measure their height.
2. You consider a p value of 0.001 as significant.
3. You calculate the correlation between their height and the number of cigarettes they smoke a day. By pure chance it's almost certain not to be 0.
4. You calculate the the chance they would get this correlation assuming the true correlation was 0 (the p value).
5. If p > 0.001 you conclude the experiment is a dud. No evidence of correlation. Better luck next time.
6. If p < 0.001 you're golden! It's now been scientifically proven that height correlates with smoking habits.
7. You preregister the experiment in detail, including the exact questions you ask, the p value you will consider significant, the calculations you will do, whether the test is two tailed or one tailed etc.
You then follow this procedure exactly, publish your results in a journal no matter what they show, and demand replication.
And that's pretty much the procedure for how to do good science under the current empirical model.
The great thing about this procedure is it doesn't require much subjective decis |
e3b501ea-119e-4cff-a9a1-81769ae13e25 | trentmkelly/LessWrong-43k | LessWrong | Rationalism before the Sequences
I'm here to tell you a story about what it was like to be a rationalist decades before the Sequences and the formation of the modern rationalist community. It is not the only story that could be told, but it is one that runs parallel to and has important connections to Eliezer Yudkowsky's and how his ideas developed.
My goal in writing this essay is to give the LW community a sense of the prehistory of their movement. It is not intended to be "where Eliezer got his ideas"; that would be stupidly reductive. I aim more to exhibit where the drive and spirit of the Yudkowskian reform came from, and the interesting ways in which Eliezer's formative experiences were not unique.
My standing to write this essay begins with the fact that I am roughly 20 years older than Eliezer and read many of his sources before he was old enough to read. I was acquainted with him over an email list before he wrote the Sequences, though I somehow managed to forget those interactions afterwards and only rediscovered them while researching for this essay. In 2005 he had even sent me a book manuscript to review that covered some of the Sequences topics.
My reaction on reading "The Twelve Virtues of Rationality" a few years later was dual. It was a different kind of writing than the book manuscript - stronger, more individual, taking some serious risks. On the one hand, I was deeply impressed by its clarity and courage. On the other hand, much of it seemed very familiar, full of hints and callbacks and allusions to books I knew very well.
Today it is probably more difficult to back-read Eliezer's sources than it was in 2006, because the body of more recent work within his reformation of rationalism tends to get in the way. I'm going to attempt to draw aside that veil by talking about four specific topics: General Semantics, analytic philosophy, science fiction, and Zen Buddhism.
Before I get to those specifics, I want to try to convey that sense of what it was like. I was a bright |
806b654b-9d49-49f7-af25-1a76bd253d73 | trentmkelly/LessWrong-43k | LessWrong | International Conflict X-Risk in the Era of COVID-19
Jeremy Hussel had a great comment pointing out something which is easy to forget - major disasters often have multiple quasi-independent causes. Many things go wrong all at once, and any safeguards are overwhelmed by the repeated issues. COVID-19 could clearly be one of those root causes. What might be others?
Another clear source of turmoil for the western world right now is domestic politics. America has a historically unpredictable president and is heading into a divisive election year where the two candidates are both likely to be very old. The UK is finally going to leave the EU and hasn’t yet struck a deal to determine what that actually means. Canada (where I live, though less critical on the world stage) was in the middle of its own domestic crisis around Native American land rights and infrastructure projects before that got overshadowed by COVID-19 - our railroads and as such some parts of our supply chain had been shut down for weeks already by protesters.
A third source of problems might be the “oil war” between OPEC and Russia, but I don’t know enough about that to really write about it usefully.
With all that said, the thing that I am most afraid of right now is China. China has been very aggressive on the world stage in the last couple of days, and I fully expect them to continue that pattern. Why wouldn’t they? Just as their country is recovering from the virus and starting to pick back up, the crisis in America and Europe is still growing. They are feeling strong while Western democracies are weak, divided, and looking inwards, and we should fully expect them to take advantage of that power imbalance in the short term to do things like finally and properly annexing Hong Kong (predict 50% that by the time COVID-19 has run its course in North America, Hong Kong has lost whatever quasi-independence it might have had).
The question is how far they will go, and how will we (our governments) react? In normal times I would expect them to be cautious bu |
087c028e-76c1-40b6-8b2c-4405f126115b | trentmkelly/LessWrong-43k | LessWrong | AI researchers announce NeuroAI agenda
Last week, 27 highly prominent AI researchers and neuroscientists released a preprint entitled Toward Next-Generation Artificial Intelligence: Catalyzing the NeuroAI Revolution. I think this report is definitely worth reading, especially for people interested in understanding and predicting the long-term trajectory of AI research.
Below, I’ll briefly highlight four passages from the paper that seemed particularly relevant to me.
Doubts about the 'prosaic' approach yielding AGI
The authors write:
> The seeds of the current AI revolution were planted decades ago, largely by researchers attempting to understand how brains compute (McCulloch and Pitts 1943). Indeed, the earliest efforts to build an “artificial brain” led to the invention of the modern “von Neumann computer architecture,” for which John von Neumann explicitly drew upon the very limited knowledge of the brain available to him in the 1940s (Von Neumann 2012). The deep convolutional networks that catalyzed the recent revolution in modern AI are built upon artificial neural networks (ANNs) directly inspired by the Nobel-prize winning work of David Hubel and Torsten Wiesel on visual processing circuits in the cat (Hubel and Wiesel 1962; LeCun and Bengio 1995). Similarly, the development of reinforcement learning (RL) drew a direct line of inspiration from insights into animal behavior and neural activity during learning (Thorndike and Bruce 2017; Rescorla 1972; Schultz, Dayan, and Montague 1997). Now, decades later, applications of ANNs and RL are coming so quickly that many observers assume that the long-elusive goal of human-level intelligence—sometimes referred to as “artificial general intelligence”—is within our grasp. However, in contrast to the optimism of those outside the field, many front-line AI researchers believe that major new breakthroughs are needed before we can build artificial systems capable of doing all that a human, or even a much simpler animal like a mouse, can do [emphasis added] |
e10f945a-0b37-4b43-99fd-d23bd1ae396a | trentmkelly/LessWrong-43k | LessWrong | Probabilistic Tiling (Preliminary Attempt)
We know a decent amount about how to get tiling in proof-based environments where the objective is for the AI to achieve a goal, or to write an AI to achieve a goal, or to write an AI that writes an AI that achieves a goal, and so on, as long as the chain of deferral is finite. The probabilistic setting is far less explored. This post will outline some necessary conditions to achieve tiling of an expected utility maximizer in fully general environments. Some of these conditions are fulfilled by a logical inductor in the limit. It's entirely possible that there are serious problems with this proof, so I'm hoping that it gets a good kicking.
DEFINITIONS:
πx is an inputless computation that outputs a bitstring, which will be interpreted as a 2-tuple of an action, and another computation, an element of A×Π .
πnx is the n'th computation in the infinite sequence of computations defined by starting at πx and taking the computation that each computation outputs. When n=1, the superscript will be omitted.
anx is the action selected by πnx.
En is some probability distribution or something that can be used to evaluate complicated computations. Like the n'th stage of a logical inductor, although we aren't necessarily assuming that it has to be a logical inductor.
underlining something refers to replacing the symbol with the thing being described. If the variable aπ is used as a way of abstractly representing some action, then aπ––– refers to the actual action chosen by the policy.
U(a1:n−1st,x,a1:∞π) is the utility function, which is some large computation of type Aω→[0,1]. So this would be the utility function output when it is fed the past actions generated by starting at πstart, the current action, and the infinite sequence of future actions is given by whatever sequence of actions is produced by the self-modification chain starting with π . Note that this only explicitly writes the starting code, and the code that might be modified to, not the past or future action s |
8a1acc52-3dd1-484d-9214-109d134d5934 | StampyAI/alignment-research-dataset/lesswrong | LessWrong | Can submarines swim?
*[Note: This was written for a general audience; most of it is probably too basic for LessWrong. Thanks to the commenters who critiqued the original draft, this is the revised and published version.]*
Did any science fiction predict that when AI arrived, it would be unreliable, often illogical, and frequently bullshitting? Usually in fiction, if the AI says something factually incorrect or illogical, that is a deep portent of something very wrong: the AI is sick, or turning evil. But in 2023, it appears to be the normal state of operation of AI chatbots such as ChatGPT or “Sydney”.
How is it that the state of the art in AI is prone to wild flights of imagination and can generate fanciful prose, but gets basic facts wrong and sometimes can’t make even simple logical inferences? And how does a *computer*, the machine that is literally made of logic, do any of this anyway?
I want to demystify ChatGPT and its cousins by showing, in essence, how conversational and even imaginative text can be produced by math and logic. I will conclude with a discussion of how we can think carefully about what AI is and is not doing, in order to fully understand its potential without inappropriately anthropomorphizing it.
**The guessing game**
---------------------
Suppose we were to play a guessing game. I will take a random book off my shelf, open to a random page, and read several words from the first sentence. You guess which word comes next.
Seems reasonable, right? If the first few words were “When all is said and …”, you can probably guess that the next word is “done”. If they were “In most homes the kitchen and …” you might guess the next words were either “living room” or “dining room”. If the sentence began “In this essay, I will…” then there would be many reasonable guesses, no one of them obviously the most likely, but words like “show” or “argue” would be more likely than “knead” or “weld”, and even those would be more likely than something ungrammatical like “elephant”.
If this game seems reasonable to you, then you are not that far away from understanding in essence how AI chatbots work.
**A guessing machine**
----------------------
How could we write a computer program to make these guesses?
In terms of its primitive operations, a computer cannot “guess”. It can only perform logic and arithmetic on numbers. Even text and images, in a computer, are represented as numbers. How can we reduce guessing to math?
One thing we can program a computer to do is, given a sequence of words, come up with a list of what words might follow next, and assign a probability to each. That is a purely mathematical task, a function mapping words to a probability distribution.
How could a program compute these probabilities? Based on statistical correlations in text that we “train” it on ahead of time.
For instance, suppose we have the program process a large volume of books, essays, etc., and simply note which words often follow others. It might find that the word “living” is followed by “room” 23% of the time, “life” 9% of the time, “abroad” 3%, “wage” 1%, etc. (These probabilities are made up.) This is a purely objective description of the input data, something a computer can obviously do.
Then its “guess” can be derived from the observed statistics. If the last word of the sequence is “living”, then it guesses “room”, the most likely option. Or if we want it to be “creative” in its “guesses”, it could respond randomly according to those same probabilities, answering “room” 23% of the time, “life” 9%, etc.
Only looking at the last word, of course, doesn’t get you very good guesses. The longer the sequence considered, the better the guesses can be. The word “done” only only sometimes follows “and”, more often follows “said and”, and very often follows “all is said and”. Many different verbs could follow “I will”, but fewer possibilities follow “In this essay, I will”. The same kind of statistical observations of a training corpus can compute these probabilities as well, you just have to keep track of more of them: a separate set of observed statistics for each *sequence* of words.
So now we have taken what seemed to be a very human, intuitive action—a guessing game about language—and reduced it to a series of mathematical operations. It seems that guessing is just statistics—or at least, statistics can be made to function a lot like guessing.
**From predictor to generator**
-------------------------------
So far we have only been talking about *predicting* text. But chatbots don’t predict text, they *generate* it. How do we go from guessing to chatting?
It turns out that *any predictor can be turned into a generator* simply by *generating the prediction*. That is, given some initial prompt, a program can predict the next word, output it, use the resulting sequence to predict the next word, output that, and so on for as much output as is desired:
* Given “In this essay, …” → predicted next word is “I”, output that
* Given “In this essay, I…” → predicted next word is “will”, output that
* Given “In this essay, I will…” → predicted next word is “show”, output that
* Given “In this essay, I will show…” → etc.
If you want the output to be somewhat variable, not completely deterministic, you can randomly choose the next word according to the probabilities computed by the predictor: maybe “show” is generated only 12% of the time, “argue” 7%, etc. (And there are more sophisticated strategies, including ones that look ahead at multiple words, not just one, before choosing the next word to output.)
Now, doing a very simple predictor like the above, based on summary statistics, only looking at the last few words, and running it on a relatively small training corpus, does not get you anything like a viable chatbot. It produces amusing, garbled output, like the sentence:
> This is relatively benign and easy to spot if the phrase is bent so as to be not worth paying attention to the medium in question.
>
>
… which *almost* seems to make sense, until you read it and realize you have no idea what it means, and then you read it again, carefully, and realize it doesn’t mean anything.
For this reason, the algorithm just described is called a “travesty generator” or sometimes “[Dissociated Press](https://en.wikipedia.org/wiki/Dissociated_press)”. It has been discussed since at least the 1970s, and could be run on the computers of that era. The program is so simple to write, I have personally written it multiple times as a basic exercise when learning a new programming language (it takes less than an hour). [A version in the November 1984 issue of BYTE magazine](https://archive.org/details/byte-magazine-1984-11/page/n448/mode/1up?view=theater) took less than 300 lines of code, including comments.
The travesty generator is a toy: fun, but useless for any practical purpose. To go from this to ChatGPT, we need a *much* better predictor.
**A better guessing machine**
-----------------------------
A predictor good enough for a viable chatbot needs to look at much more than the last few words of the text, more like thousands of words. Otherwise, it won’t have nearly enough context, and it will be doomed to produce incoherent blather. But once it looks at more than a handful of words, we can no longer use the simple algorithm of keeping statistics on what word follows each sequence: first, because there is a combinatorial explosion of such sequences; second, because any sequence of that length would almost certainly be unique, never seen before—so it would have no observed statistics.
We need a different approach: a way to calculate an extremely sophisticated mathematical function with a very large space of possible inputs. It turns out that this is what “neural networks” are very good at.
In brief, a neural network is just a very large, very complicated algebraic formula with a specific kind of structure. Its input is a set of numbers describing something like an image or a piece of text, and another set of numbers called “parameters” that configure the equation, like tuning knobs. A “training” process tunes the knobs to get the equation to give something very close to the desired output. In each round of training, the equation is tried out on a large number of examples of inputs and the desired output for each. Then all the knobs are adjusted just slightly in the direction of the correct answers. The full training goes for many such rounds. (The technical term for this training algorithm is “back propagation”; for a technical explanation of it, including the calculus and the linear algebra behind it, I recommend [this excellent video series from 3blue1brown](https://www.3blue1brown.com/topics/neural-networks).)
Neural networks are almost as old as computers themselves, but they have become much more capable in recent years owing in part to advances in the design of the equation at their core, including an approach known as “deep learning” that gives the equation many layers of structure, and more recently a new architecture for such equations called the “transformer”. (GPT stands for “Generative Pre-trained Transformer”.) GPT-3 has 175 *billion* parameters—those tuning knobs—and was trained on hundreds of billions of words from the Internet and from books. A large, sophisticated predictor like this is known as a “large language model”, or LLM, and it is the basis for the current generation of AI chatbots, such as OpenAI’s [ChatGPT](https://openai.com/blog/chatgpt/), Microsoft’s [Bing AI](https://blogs.microsoft.com/blog/2023/02/07/reinventing-search-with-a-new-ai-powered-microsoft-bing-and-edge-your-copilot-for-the-web/), and Anthropic’s [Claude](https://scale.com/blog/chatgpt-vs-claude).
**From generator to chatbot**
-----------------------------
What we’ve described so far is a program that *continues* text. When you prompt a chatbot, it doesn’t continue what you were saying, it *responds*. How do we turn one into the other?
Simple: prompt the text generator by saying, “The following is a conversation with an AI assistant…” Then insert “Human:” before each of the human’s messages, and insert “AI:” after. The continuation of this text is, naturally, the AI assistant’s response.
The raw GPT-3 UI in the OpenAI “playground” has a mode like this:
*The green text was generated by GPT, the rest was the prompt.*ChatGPT just puts a nice UI on top of this.
Well, there is one more thing. A chatbot like this isn’t necessarily very well-behaved. The text generator is not coming up with the *best* response, by any definition of “best”—it’s entirely based on *predictions*, which means it’s just coming up with a *likely* response. And since a lot of the training is from the Internet, the most likely responses are probably not what we want a chatbot to say.
So, chatbots are further trained to be more truthful and less toxic than the average Internet user—Anthropic summarizes their criteria as “[helpful, honest, and harmless](https://arxiv.org/abs/2112.00861)”. This is done [based on human feedback, amplified through more AI models and many rounds of refinement](https://openai.com/blog/instruction-following/). (The Bing AI, aka “Sydney”, is generating [much crazier responses](https://stratechery.com/2023/from-bing-to-sydney-search-as-distraction-sentient-ai/) than ChatGPT or Claude, and [one hypothesis for why is that its refinement was done in a hasty and inferior way](https://www.lesswrong.com/posts/jtoPawEhLNXNxvgTT/bing-chat-is-blatantly-aggressively-misaligned?commentId=AAC8jKeDp6xqsZK2K).)
And that, at a very high level, is how we go from a deterministic program, doing math and logic, to an artificially intelligent conversation partner that seems, at least, to exhibit imagination and personality.
**Bullshit**
------------
When we understand, in essence, how chatbots work, they seem less mysterious. We can also better understand their behavior, including their failure modes.
One feature of these chatbots is that they are unreliable with facts and details. In fact, they seem quite happy to make things up, confidently making very plausible assertions that are just false. If you ask them for citations or references, they will make up imaginary titles of books and papers, by authors who may or may not exist, complete with URLs that look very realistic but return “404 Not Found”. The technical term for this is “hallucination”.
This behavior can be disconcerting, even creepy to some, but it makes perfect sense if you understand that what is driving the text generation is a prediction engine. The algorithm is not designed to generate *true* responses, but *likely* ones. The only reason it often says true things is that it was trained on mostly true statements. If you ask a question that is well-represented in its training set, like “who invented the light bulb?”, then its prediction model has a good representation of it, and it will predict the correct answer. If you ask something more obscure, like “who invented the twine binder for the mechanical reaper/harvester?”, its prediction function will be less accurate, and it is more likely to output something plausible but wrong. Often this is something closely related to the right answer: [ChatGPT told me](https://sharegpt.com/c/GJYqGCS) that the twine binder was invented by Charles B. Withington, who actually invented the *wire* binder. To anthropomorphize a bit: if the LLM “knows” the answer to a question, then it tells you, but if it doesn’t, it “guesses”.
But it would be more accurate to say that the LLM is *always* guessing. As we have seen, it is, at core, doing nothing fundamentally different from the guessing game described at the beginning. There is no qualitative difference, no hard line, between ChatGPT’s true responses and its fake ones.
An LLM is, in a strict technical sense, a *bullshitter*—as defined in Harry Frankfurt’s “[On Bullshit](https://www2.csudh.edu/ccauthen/576f12/frankfurt__harry_-_on_bullshit.pdf)”:
> The bullshitter may not deceive us, or even intend to do so… his intention is neither to report the truth nor to conceal it…. He does not care whether the things he says describe reality correctly. He just picks them out, or makes them up, to suit his purpose.
>
>
A bullshitter, of course, like a competitive debater, is happy to argue either side of an issue. By prompting ChatGPT, I was able to get it to argue [first for, then against the idea that upzoning causes gentrification](https://twitter.com/jasoncrawford/status/1598730679818555392).
This also explains why it’s not hard to break chatbots away from the “helpful, honest and harmless” personality they were trained to display. The underlying model was trained on many different styles of text, from many different personalities, and so it has the latent ability to emulate any of them, not just the one that it was encouraged to prefer in its finishing school. This is not unlike a human’s ability to imagine how others would respond in a conversation, or even to become an actor and to imitate a real or imagined person. The difference is that a human has a true personality, an underlying set of real ideas and values; when they impersonate, they are putting on a mask. With an LLM, I don’t see anything that corresponds to a “true personality”, just the ability to emulate anything. And once it *starts* emulating any one personality, its prediction engine naturally expects the next piece of text to *continue* in the same style, like a machine running on a track that gets bumped over to a nearby track.
Similarly, we can see how chatbots can get into truly bizarre and unsettling failure modes, such as repeating a short phrase over and over endlessly. If it accidentally starts down this path, its prediction engine is inclined to continue the pattern. Go back to our guessing game: if I told you that a piece of text read “I think not. I think not. I think not. I think not”, and then asked you to guess what came next, wouldn’t you guess another “I think not”? Like an actor doing improv comedy, once something has been thrown out there, the LLM can’t reject the material, and has to run with it instead.
**LLM strengths and superpowers**
---------------------------------
Knowing how LLMs work, however, is more important than understanding their failure modes. It also helps us see what they’re good at and thus how to use them. Although not good for generating trustworthy information, they can be great for brainstorming, first drafts, fiction, poetry, and other forms of creativity and inspiration.
One technique is to give them an instance or two of a pattern and ask for more examples: when I wrote a recent essay on [the spiritual benefits of material progress](https://rootsofprogress.org/the-spiritual-benefits-of-material-progress), I asked Claude for “examples of hand crafts that are still practiced today”, such as furniture or knives, and I used several of the ideas it generated.
Chatbots also have the potential to create a new and more powerful kind of search (no matter what you think of the new AI-driven Bing). Traditional search engines match keywords, but LLMs can search for *ideas*. This could make them good for more conceptual queries where it’s hard to know the right terms to use, like: “[Most cultures tend to have a notion of life after death. Which ones also have a notion of life before birth?](https://twitter.com/etiennefd/status/1587610108485402626)” I asked this to Claude, which suggested some religions that believe in reincarnation, and then added that “Kabbalah in Judaism and the Baha’i faith also have notions of the soul existing in some spiritual realm before birth.” (It [doesn’t always work](https://shareg.pt/UnhM5e6), though; anecdotally, I still have more success asking these kinds of vague queries on social media.)
Another advantage of LLMs for search is that the conversational style naturally lets you ask followup questions to refine what you’re looking for. I [asked ChatGPT to explain “reductionism”](https://sharegpt.com/c/vdtA9sX), and when it mentioned that reductionism has been criticized for “oversimplifying complex phenomena”, I asked for examples, which it provided from biology, economics, and psychology.
A fascinating essay on “[Cyborgism](https://www.lesswrong.com/posts/bxt7uCiHam4QXrQAA/cyborgism)” says that while GPT struggles with goal-directedness, long-term coherence, staying grounded in reality, and robustness, “there is an alternative story where [these deficiencies] look more like superpowers”: GPT can be extremely flexible, start fresh when it gets stuck in a rut, simulate a wide range of characters, reason under any hypothetical assumptions, and generate high-variance output. The essay proposes using LLMs not as chatbots, research assistants, or autonomous agents, but as a kind of thinking partner guided by a human who provides direction, coherence, and grounding.
The great irony is that for decades, sci-fi has depicted machine intelligence as being supremely logical, even devoid of emotion: think of Data from Star Trek. Now when something like true AI has actually arrived, it’s terrible at logic and math, not even reliable with basic facts, prone to flights of fancy, and best used for its creativity and its wild, speculative imagination.
**But is it thinking?**
-----------------------
[Dijkstra famously said](https://www.cs.utexas.edu/~EWD/transcriptions/EWD08xx/EWD898.html) that Turing’s question of “whether Machines Can Think… is about as relevant as the question of whether Submarines Can Swim”.
Submarines do not swim. Also, automobiles do not gallop, telephones do not speak, cameras do not draw or paint, and LEDs do not burn. Machines accomplish many of the same goals as the manual processes that preceded them, even achieving superior outcomes, but they often do so in a very different way.
*fish submarine chimera with metal body and fins sticking out the side.* [*DALL-E*](https://openai.com/dall-e-2/)The same, I expect, will be true of AI. In my view, computers do not think. But they will be able to achieve many of the goals and outcomes that historically have only been achieved by human thought—outcomes that will astonish almost everyone, that many people will consider impossible until (and maybe even after) they witness it.
Conversely, there are two mistakes you can make in thinking about the future of AI. One is to assume that its processes are essentially no different from human thought. The other is to assume that if they *are* different, then an AI can’t do things that we consider to be very human.
In 1836, [Edgar Allen Poe argued](https://www.eapoe.org/works/essays/maelzel.htm) that a machine—including “the calculating machine of Mr. Babbage”—could never play chess, because machines can only do “fixed and determinate” calculations where the results “necessarily and inevitably follow” from the data, proceeding “by a succession of unerring steps liable to no change, and subject to no modification”; whereas “no one move in chess necessarily follows upon any one other”, and everything is “dependent upon the variable judgment of the players”. It turned out, given enough computing power, to be quite straightforward to reduce chess to math and logic. The same thing is now happening in new domains.
AI can now generate text, [images](https://openai.com/dall-e-2/), and even [music](https://www.riffusion.com/). It seems to be only a quantitative, not qualitative difference to be able to create powerful and emotionally moving works of art—novels, symphonies, even entire movies. With the right training and reinforcement, I expect it to be useful in domains such as law, medicine, and education. And it will only get more capable as we [hook it up to tools](https://arxiv.org/pdf/2302.04761.pdf) such as web search, calculators, and APIs.
The LLMs that we have discussed are confined to a world of words, and as such their “understanding” of those words is, to say the least, very different from ours. Any “meaning” they might ascribe to words has no sensory content and is not grounded in reality. But an AI system could be hooked up to sensors to give it direct contact with reality. Its statistical engine could even be trained to predict that sensory input, rather than to predict words, giving it a sort of independence that LLMs lack.
LLMs also don’t have goals, and it is anthropomorphizing to suppose that ChatGPT “wants” or “desires” anything, or that it’s “trying” to do anything. In a sense, you can say that it is “trying” to predict or generate likely text, but only in the same sense that an automobile is “trying” to get you from point A to point B or that a light bulb is “trying” to shine brightly: in each case, a human designed a machine to perform a task; the goals were in the human engineering rather than in the machine itself. But just as we can write a program that performs the same function as human guessing, we can also write a program that performs the same function as goal-directed action. Such a program simply needs to measure or detect a certain state of the world, take actions that affect that state, and run a central control loop that invokes actions in the right direction until the state is achieved. We already have such machines: a thermostat is an example.
A thermostat is “dumb”: its entire “knowledge” of the world is a single number, the temperature, and its entire set of possible actions are to turn the heat on or off. But if we can train a neural net to predict words, why can’t we train one to predict the effects of a much more complex set of actions on a much more sophisticated representation of the world? And if we can turn any predictor into a generator, why can’t we turn an action-effect predictor into an action generator?
It would be anthropomorphizing to assume that such an “intelligent” goal-seeking machine would be no different in essence from a human. But it would be myopic to assume that therefore such a machine could not exhibit behaviors that, until now, have only ever been displayed by humans—including actions that we could only describe, even if metaphorically, as “learning”, “planning”, “experimenting”, and “trying” to achieve “goals”.
One of the effects of the development of AI will be to demonstrate which aspects of human intelligence are biological and which are mathematical—which traits are unique to us as living organisms, and which are inherent in the nature of creating a compactly representable, efficiently computable model of the world. It will be fascinating to watch.
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*Thanks to Andrej Karpathy, Zac Dodds, Heike Larson, Daniel Kokotajlo, Gwern, and @jade for commenting on a draft of this essay. Any errors that remain are mine alone.* |
9d30b644-6fe7-45fe-b64d-31d25d86f417 | trentmkelly/LessWrong-43k | LessWrong | Ego syntonic thoughts and values
Related to: Will your real preferences please stand up?
Last week I read a book in which two friends - let's call them John and Lisa so I don't spoil the book for anyone who wanders into it - got poisoned. They only had enough antidote for one person and had to decide who lived and who died. John, who was much larger than Lisa, decided to hold Lisa down and force the antidote down her throat. Lisa just smirked; she'd replaced the antidote with a lookalike after slipping the real thing into John's drink earlier in the day.
These are good friends. Not only was each willing to give the antidote to the other, but each realized it would be unfair to make the other live with the crippling guilt of having chosen to survive at the expense of a friend's life, and so decided to force the antidote on the other unwillingly to prevent any guilt over the fateful decision. Whatever you think of the ethics of their decision, you can't help admire the thought processes.
Your brain might be this kind of a friend.
In Trivers' hypothesis of self-deception, one of the most important functions of the conscious mind is effective signaling. Since people have the potential to be excellent lie-detectors, the conscious mind isn't given full access to information so that it can lend the ring of truth to useful falsehoods.
But this doesn't always work. If you're addicted to heroin, at some point you're going to notice. And telling your friends "No, I'm not addicted, it's just a coincidence that I take heroin every day," isn't going to cut it. But there's another way in which the brain can sequester information to promote effective signaling.
Wikipedia defines the term "ego syntonic" as "referring to behaviors, values, feelings that are in harmony with or acceptable to the needs and goals of the ego, or consistent with one's ideal self-image", and "ego dystonic" as the opposite of that. A heroin addict might say "I hate heroin, but somehow I just feel compelled to keep taking it." But an a |
c3a30a68-b5f5-41c9-9a92-ea0644540a09 | awestover/filtering-for-misalignment | Redwood Research: Alek's Filtering Results | id: post82
In this post, I'll list all the areas of control research (and implementation) that seem promising to me. This references framings and abstractions discussed in Prioritizing threats for AI control . First, here is a division of different areas, though note that these areas have some overlaps: Developing and using settings for control evaluations (including technique iteration) Better understanding control-relevant capabilities and model properties Developing specific countermeasures/techniques in isolation (rather than via iterating in a setting) Doing control experiments on actual current AI usage Prototyping or implementing software infrastructure for control and security measures that are particularly relevant to control Prototyping or implementing human processes for control Conceptual research and other ways of researching control other than empirical experiments Nearer-term applications of control to practice and accelerate later usage of control This division is imperfect and somewhat arbitrary, but still feels useful to me in breaking things down. I don't think all of these areas warrant equal investment. For instance, maybe "developing and using settings for control evaluations" should get roughly 1/3 of current control resources, which is much more than an even split between areas would suggest. (The list is roughly in descending order of how much investment that area should get.) Now I'll elaborate on projects within each of these areas. Developing and using settings for control evaluations Perhaps the main methodology in AI control is to run a control evaluation in some particular setting. The first control paper by Redwood ( AI Control: Improving Safety Despite Intentional Subversion ) exhibits this methodology in a simple code backdooring setting. Correspondingly, work on building control settings and then doing control evaluations in these settings is a key area. Ultimately, control evaluations have two main purposes: evaluating risk (including establishing a case for risk or a case for safety) and developing better techniques for ensuring control. Right now, models aren't actually risky, so work which is directly focused on evaluating risk doesn't provide that much of the value (though getting a better sense of the overall viability of control does seem valuable, but might be difficult). So, current work in this area has multiple aims: Developing and practicing the control methodology so that when we have smarter models and better settings we can more effectively use control evaluations to develop better techniques or evaluate risk. Finding better techniques or generally getting a better understanding of which techniques might be promising. Developing settings that will be useful in the future. (Even if this exact project doesn't use the setting or models now are too weak for the setting to be immediately useful.) A key bottleneck in this area is having good settings. Once a good setting (with reasonable rules) exists, iterating in that setting seems pretty scalable. This is especially true if there aren't finicky rules and we can allow the red team and blue team to be no holds barred. In principle, we could even allow for an end-to-end game where competitors submit either a red team attack policy or a blue team protocol and then we see how the dynamics go. What types of settings seem most interesting to work on? As discussed in Prioritizing threats for AI control , there are different categories of issues we might be handling with control, so we might want to create settings specifically targeted at these categories. Correspondingly, the list of settings might look like: Concentrated failure (high stakes) settings where the AI can cause huge safety failures in a relatively small number of actions. These settings can be interesting to study even if the blue team has access to a basically perfect but expensive oracle of whether the AI's actions are problematic. It might be useful to target these settings toward a particular type of issue: Analogous to AI violating security invariants Analogous to work sabotage (that are concentrated in nature) A broader set of potential concentrated failures which aren't aiming to strictly be analogous to either of these failure types. Non-concentrated failure (low stakes) settings where a larger number of actions are required to cause safety issues. Such settings are typically most interesting to study in the case where an important difficulty is in getting good enough expensive oversight. Non-concentrated and concentrated settings can be somewhat continuous. Again, more specific targeting might be useful: Analogous to work sabotage. Some example types of this: Safety research Security code sabotage Backdooring training runs (and data poisoning) Analogous to persuasion/manipulation Analogous to external deployment failure modes where we have less state on exactly what the model is being used for. As in, there are various failure modes that could arise in API usage of the model and this has some importantly different properties from the perspective of the blue team and the red team. In particular, the blue team doesn't immediately necessarily have a good understanding of what the AI is being used for. There are other settings which aren't either of the above. One relevant case is relatively more narrow control settings aiming to explore specific threats like steganography, coordination/collusion, exploration hacking, or some narrower types of data poisoning. For these purposes, adopting an adversarial control-style methodology is reasonable, but broader methodologies might be better. At the moment, the dynamics in settings with non-concentrated failures seem underexplored, particularly in the context of sabotaging research work. Some work is ongoing, but doesn't seem clearly sufficient. So, more work in this area seems pretty leveraged. In addition to building new settings, it's reasonable to do technique iteration in an existing setting, or to investigate a somewhat different rule set using a setup which already exists. For control settings which have already been explored some ( APPS backdoors , simple bash tasks ), I'm not sure how useful further technique iteration is, though investigating an importantly different rule set could certainly be worthwhile. More thoroughly exploring some specific class of techniques does seem reasonably likely to be worthwhile if that class of techniques hasn't been explored before; see here for a list of techniques. Beyond varying the type of setting and what it is analogous to, the exact rules of the setting could be varied in important ways: You could explore different red team objectives: cases where the red team and blue team are perfectly zero sum, cases where the red team is trying specifically to achieve some undesirable outcome, etc. You can change the blue team constraints: you could have different usefulness targets (e.g., just considering 100% usefulness or being willing to take large taxes), disallow certain measures, or change the relative prices of different types of labor. There are a bunch of different choices in how we model training the AI as part of the evaluation. What factors you consider can have important effects on settings with non-concentrated failures. See also here . In particular: Whether you study sandbagging and exploration hacking. There are a bunch of unresolved methodological questions here. Whether you use malign initialization or you attempt to be conservative about inductive biases. The simplest approach might be malign initialization, but I worry that the inductive biases won't be representative or conservative by default (for instance, we saw potentially unrealistic inductive biases that could have made the blue team's job much easier here ). There are some potential ad hoc solutions, like allowing the red team to add in a bit of training data throughout (so long as this doesn't substantially reduce local sample efficiency). You could look at cases where training the benign policy against your best oversight might degrade performance so there is a natural safety vs. usefulness trade-off In practice, it might be institutionally difficult to use online training or costly for other reasons. So, it could be worthwhile to look at cases where you initially can't use online training, but instead need to get enough evidence (to convince potentially skeptical audiences) to at least implement online training or potentially shut down. This can be interesting even if online training would mostly resolve difficulties in that setting. You could vary how you model the level of evidence needed to motivate various actions and how accurately we can guess how well a non-scheming version of the model would behave (aka benign statistics). You can try to make the rules relatively more no-holds-barred and simple (without needing judgment calls) to make it relatively easier for people to contribute. You could vary the level of red team affordances in terms of knowledge, coordination ability between AIs, AI strategic ability, AI reliability, the amount of allowed runtime compute/scaffolding, how much the red team can train AIs to be better at subversion, and on what tasks the red team can train AIs. You could either use actual humans for auditing or just use AIs as proxies for humans. You could try to model a realistic scale (or more realistic scale) deployment despite running a smaller evaluation. You could try to model considerations around timing and latency. In particular, AIs doing bad actions in a temporally correlated way might be an important strategy, and developing a setting where we can test countermeasures to this could be useful. You could explore avoiding overelicitation on the red team policy. In the future, we might end up in cases where we want to apply control, but being competitive with the model as the red team is difficult. You could try to explore one of these cases (e.g., we think models have superhuman strategic ability or we can't elicit some particular capability very well) and what approximations seem most reasonable. I'm also excited about some particular approaches to settings work: Building a setting based on gathering examples of real-world work, particularly work where sabotage might be especially concerning or sabotage might have interesting properties (e.g., actual safety research tasks). Developing a setting and rule set which is specifically focused on testing some category of techniques. (We can think of this as "industrial policy": trying to speed up some particular technique without wasting time by focusing on some case where we think the technique might be particularly useful and beat baselines.) For a broad list of techniques/methods that might be interesting to focus on, see here . Building a red team / blue team competition similar to TrojAI which requires a relatively more solid setting. Trying to train a general-purpose model for use by control red teams that is well elicited, so that we can see generalization performance and more easily iterate without needing to work around current models not being very good at being sneaky by default. There are a bunch of possible approaches here which could be promising. One alternative approach to settings work I'm particularly excited about is using humans as proxies for untrusted AIs . One difficulty in experimenting with control right now is that AIs are quite weak and are incapable of long-range autonomous tasks. It could be quite valuable to do control-related experiments where you use humans instead of untrusted AIs and look at settings with tasks much harder than what AIs can do right now. You'd use the current best AIs as trusted AIs. This seems particularly interesting for resolving uncertainties about how easy sabotage is in research settings; people with different views on control often have very different perspectives on how viable it is to elicit useful research from potentially scheming entities (AI or human). I think we don't really have a good understanding of what happens when trying to elicit research work from adversarial humans (who nonetheless need to either perform well on our metrics or exploration hack effectively). This seems most interesting to study in non-concentrated setups, and in particular in the context of research sabotage. This is partially because methods which seem particularly important for settings with concentrated failures (e.g., resampling) might be harder to model with humans. Prior control work has often involved using human labor to substantially assist the attack policy (e.g., giving it detailed strategies), but fully having humans be the untrusted model would allow for exploring more difficult tasks and would likely have somewhat different dynamics. The experimental methodology could be somewhat similar to past research on testing debate using humans , but focused particularly on the types of work we're actually worried about and using trusted AI assistance. Due to studying humans, this work might be substantially more difficult than work which just uses AIs, but it still seems valuable enough to be worth trying. Probably you'd want to simplify how you model training untrusted models (in this case humans) to (e.g.) not consider exploration hacking except in cases where it seems like it would clearly work. Better understanding control-relevant capabilities and model properties It is useful to evaluate some control-relevant capabilities and model properties in isolation rather than in a way that is directly integrated into the red team for a control evaluation. This could be because evaluating the capability directly as part of control evaluation is difficult (e.g., straightforward elicitation is hard) or because the property we're interested in isn't a capability and is instead an inductive bias (and thus is out of scope for direct integration into red team elicitation). A more basic reason is that studying properties in isolation can be simple and can sometimes be relevant to a broader audience than just people interested in control. Doing this work now is useful for getting a sense of where we're currently at and establishing a methodology (and potentially test beds) for future evaluation on more powerful models. In many cases, this work also has other applications like being part of a case for misalignment risk or broadly giving some insight on how AIs work. In some cases, the work I discuss here might be good to study in combination with developing a specific countermeasure (see "Developing specific countermeasures in isolation"), for instance, studying how good models are at recognizing synthetic inputs in parallel with building a better pipeline for synthetic input generation. This research includes: How good AIs are at recognizing their own outputs/actions for the purposes of collusion: When is this robust to paraphrasing? Can AIs do this reliably enough that adversarially evaluating/training untrusted monitors won't work well or is much more difficult/expensive? How good AIs are at noticing that synthetic inputs are fake and behaving differently on the basis of their fakeness: It's natural to want to use synthetic documents for various control strategies such as adversarially evaluating/training AIs, training AIs to believe false facts (more on this in the section on "Developing specific countermeasures in isolation"), and model organisms work. However, it seems plausible that AIs will be substantially superhuman at understanding whether documents are real due to stylistic clues. One reason for this is that they are generally superhuman at language understanding in some ways already, and this is improving over time as pretraining is scaled up. Another possible mechanism is that AIs might learn to detect synthetic documents, as they are heavily used in training (potentially including adversarial training), and detecting whether a document is synthetic is useful for AIs. So, better understanding how good current models are at noticing that documents/inputs are fake seems important. This is non-trivial to evaluate, as training a linear probe might overestimate how good models are at this by harnessing features the model isn't actually using to determine if the input is synthetic. Prompting might underelicit models by default. It might be possible to better elicit models without overfitting/learning (see below discussion of "elicitation without learning"). It might also be possible to see whether various downstream tests indicate that models know documents were fake. For instance, if models utilize information from synthetic documents importantly differently from real documents (in cases where all else is held equal) when these documents are either in training or in the prompt, that would be evidence that models can tell the difference at least some of the time. Acausal coordination and Schelling points : Can AIs coordinate on some time to strike that isn't obvious from a human perspective? Can they otherwise coordinate around Schelling points that aren't obvious to humans? Steganography : How well can AIs encode hidden messages or perform steganographic reasoning? How well does this work if we explain the scheme to both the encoder and the decoder? What about if we require AIs to acausally coordinate on the scheme to use? There are multiple steganography regimes worth studying including: (a) single bit steg, (b) steganographic reasoning, and (c) AIs encoding lots of information in outputs that other AIs can access. Each of these regimes probably warrants a somewhat different methodology. In more detail, these regimes are: Single bit steganography for collusion (particularly in the context of untrusted monitoring): this doesn't need a high bit rate but does need to very reliably avoid false positives so the untrusted monitor can evade adversarial evaluation/training and needs to have a sufficiently high true positive rate that the (small number of) problematic actions don't get reported. When studying this you want to directly analyze the relevant notions of reliability, taking into account the usage for untrusted monitoring (or other potential ways models might use single bit steg). Steganographic reasoning where AIs use steganography to reason extensively while making it look like they're doing something else. To study this, you should ideally directly see if models can reason about topic A while making it look like they are instead doing some other task. AIs encoding lots of information in a more average case setting: This is relevant to whether AIs can steganographically encode the results of hidden reasoning/research to stealthily build up hidden knowledge about how to effectively subvert our countermeasures (see here for more discussion). It's also relevant to AIs generally leaking information from one task to AIs in a different context where we didn't want them to have that knowledge. Probably the most natural methodology is to study the bit rate (as we do in this work ), though other methodologies are possible. There are a variety of questions to be answered that are relevant across multiple regimes. Do basic countermeasures defeat steg? When do models learn to do steg from RL and what does this look like? How general is it? What are the most surprising cases of models being good at steg due to LLM specific advantages? What countermeasures disrupt or detect steganography in various different cases? Collusion more generally: What are the best collusion strategies for AIs? They could collude on inputs, steganographically encode a single bit signal in outputs, or utilize their ability to recognize their own generations. How well can AIs carry out collusion given various countermeasures? For untrusted monitoring, AIs might need to be highly reliable in their collusion to collude effectively due to adversarial evaluation/training of the untrusted monitor. How close are AIs to the required level of reliability? What do the scaling laws of collusion look like? Exploration hacking and sandbagging : What do inductive biases related to exploration hacking look like? How fast are models updated to perform better if we have a limited number of examples where the model did better? How well does human correction SFT data prevent exploration hacking? How well would exploration hacking work in reasoning models? How well can models sandbag in cases where this is strategically non-trivial (e.g., it requires anticipating roughly how well some other model will perform so that you don't overshoot in capabilities)? Can models reliably avoid exploring into some behavior? Does generalization make this a hard policy to implement? How should we model generalization and inductive biases related to exploration hacking when models are worst case misaligned and can control their generalization, but can't exhibit substantially lower sample efficiency? Do there exist situations in which models are surprisingly successful at sandbagging? Do there exist cases where models can exhibit non-trivial gradient hacking? How does gradient/exploration hacking work for architectures that involve deeper serial recurrence (probably hard to work on now as such architectures don't exist)? Overelicitation, particularly in the context of control evaluations: By default, we'll want the red team in control evaluations to train models to ensure they are sufficiently elicited. However, this training might result in the model used by the red team being substantially better at subterfuge than would be realistic. See also here and discussion below about elicitation without learning. Capability to trick monitors and the extent to which AIs can do subtle bad actions: AIs will likely need to subtly carry out bad actions to avoid getting caught by baseline control countermeasures. So, better understanding how good models are at being sneaky and evading monitors seems useful. This could be interesting to study both in the case where we provide a hidden scratchpad and in the case where this isn't allowed. How much does the scratchpad boost performance? In addition to being subtle, another (non-mutually-exclusive) approach AIs might take is jailbreaking their monitors. How good are models at jailbreaking other models that have been adversarially trained, but only by humans and by weaker models than the jailbreaking model? To study this question, we'd probably need to do some extrapolation or consider a case where we limit adversarial training done on the model. Generally evaluating AI jailbreaking ability would be a reasonable starting point. Can models ever use LLM specific knowledge to perform surprising jailbreaks (e.g., using niche facts they know about web text)? Subversion strategy : How effectively can AIs think of good strategies for subverting control safeguards? How can we precisely measure this without over/under estimating this hard-to-elicit capability? How reliably can AIs think of a good enough strategy in cases where this must occur reliably for them to avoid getting caught? How does this differ when we do/don't allow the model to transparently reason about this in the CoT? If we could bound the ability of AIs to effectively strategize about plans, that could allow our evaluations to be much less conservative and might allow for assuming some models are de facto trusted (as they aren't competent enough to not get caught if they were trying to cause issues in some important way). Generally better understanding AI capabilities for opaque goal-directed reasoning: The extent to which models can effectively do opaque (as in, not legibly in CoT) general purpose reasoning (about how to achieve their goals) has a substantial effect on the chance that despite looking good to us they are scheming against us or are otherwise seriously misaligned , and on their ability to reason about how to subvert our countermeasures. Thus, generally testing and understanding how well models can do general purpose opaque reasoning, or more specifically opaque reasoning about how to achieve their goals, is relevant. More specifically focusing on reasoning related to scheming or subversion could also be interesting, though it might be difficult to evaluate a very narrow domain without overfitting or undereliciting. Which AIs are plausibly scheming and at what capability level scheming might emerge: Our approach to control is likely to depend on trusting some models, and having a more precise understanding of which models we can trust is quite helpful. Above, I discuss subversion strategy (and how reliable AIs are at this) and opaque goal-directed reasoning capability evaluation as possible candidates for helping with this, but there are other options. For instance, if AIs can't be trained to reliably pursue some hidden goal or to keep some secret without giving themselves up immediately (and we apply the techniques we apply to these AIs to our actual policy and notice nothing wrong), then this is substantial evidence that our AI isn't a schemer. Another option is to generally study scheming in model organisms to get a sense for how smart models would need to be to scheme without detection by basic techniques. What AIs might learn from various types of training: It's somewhat unclear what AIs can vs can't learn from being trained on different types of data, and what knowledge AIs acquire over the course of training has a substantial effect on what we should expect the AI to know and whether there are issues with doing online training. For instance, if during RL AIs learn detailed information about oversight (e.g., the frequency of mistakes, biases) that they can verbalize and generically apply in novel ways, that would make online training look less attractive. Also, if models end up learning arbitrary information that is present in the context or outputs during RL trajectories, this means that if there is information which you sometimes give the AI that you don't want it to have in some other context, you shouldn't do RL in a context with the first information and then use these RL'd weights in the second context. Owain Evans' group has done a bunch of work in this area. Generally we care about what AIs can learn from positive/ negative reinforcement , how much models can make inferences based on this reinforcement, and what AIs learn from training with supervised fine-tuning (SFT) on documents. A better understanding here could feed directly into more sophisticated control evaluations where we model what AIs might be learning from training over the course of deployment. How much control AIs have over their internals and their outputs: We currently hope that models can't control their internals well enough to intentionally sabotage probes. It also seems plausible that models have trouble directly controlling their outputs if they are heavily trained to output something given some context. E.g., suppose we train a model to report whether the action it just did in the same context is suspicious based on offline examples, and then try to transfer to actual bad outputs from the model (a version of untrusted monitoring where collusion is trivial), how much can the model control whether it reports the truth? As in, if we also give it instructions that it should lie in some case, will it successfully lie even after training? Studying the extent to which models can control their internals is somewhat tricky, as training them to control their internals might give them abilities they didn't already have. We could try to get elicitation without learning to work (we discuss this more below). We could also see how quickly models can learn to manipulate their internals to (e.g.) fool probes, and see how far this generalizes. More mainstream dangerous capability evaluations for capabilities that are relevant to control like cyber and persuasion also seem useful, but I don't think control implies that more people should work on this. Developing specific countermeasures/techniques in isolation Some types of countermeasures or techniques are particularly reasonable to develop in a relatively isolated fashion, rather than by iterating in the context of a setting. Something in-between, where you iterate in a specialized setting, could also be reasonable. In some cases, it wouldn't really be viable to test or iterate on the countermeasure/technique using control evaluations, so studying with a separate methodology is needed. I have a relatively complete list of countermeasures and explanation here . I'll call this the countermeasures list. I think most of these countermeasures could be worthwhile to study in isolation. Here are some notes on countermeasures that I think could be particularly useful to study in isolation including some thoughts on how best to study them: Synthetic input generation: trying to generate fake inputs that look real to AIs (or at least look real enough for various applications): Some version of this such that models can't confidently distinguish reality from fake inputs is key for adversarial evaluation/training of potentially scheming models. That said, we might be able to process inputs to the AI to make inputs easier to fake (e.g., redacting information or making all inputs look AI generated). We could also construct synthetic inputs with particular properties by modifying real inputs (including doing so in an ongoing way throughout deployment). These approaches could make synthetic input generation much easier. See also this appendix and this project proposal . Convincing AIs of false facts (and generally giving AIs incorrect situational awareness): See the description in the countermeasure list and also see this project proposal . Measures for eliminating or detecting steganography: This includes paraphrasing, steganography detection, and various types of regularization to make steg more difficult. See the countermeasure list for more discussion. This is probably best studied in an adversarial setting focused on steganography. We might also be interested in measures that make it less likely that RL teaches models steganography. Exploration hacking and sandbagging countermeasures: See here for more discussion and proposals for future work. This also seems best studied in an adversarial exploration hacking setting, though less adversarial exploration (similar to the password locked models paper ) is reasonable. Studying countermeasures to sandbagging in the context of reasoning models (or longer agentic tasks) seems particularly promising at the moment. Probing or other simple usages of internals: Probes might be quite useful, as discussed here . Probably a high fraction of the difficulty with probes won't be due to AIs being adversarial, but will instead be failures of generalization. We (Redwood) have some ongoing work on probing and methodology for testing probing (both adversarial and non-adversarial failure modes). Another (simple) usage of internals which might be worthwhile to develop is some sort of anomaly detection. This could plausibly be useful for detecting treacherous turns or at least unexpected distribution shifts. Human auditing: Testing out what works well when having humans audit things seems important, and doesn't seem very well explored. See discussion in the countermeasures list. This could be done in a variety of contexts, including cases where there isn't a concrete setting with specific rules. That said, having a concrete setting with rules makes it easier to analyze trade-offs. Collusion busting: See discussion in this post for more. This is probably best studied in a full control setting, but is possible to study in more isolated cases. This is a pretty important countermeasure, but it is well discussed in the linked post, so I won't say more here. (Note that this will overlap with steganography mitigations.) More precise capability control: This includes unlearning, gradient routing, and something like filtering out data and then making multiple LoRAs trained on this data to allow for combinatorial selection of capabilities, etc. See discussion in the countermeasure list. A key aspect of studying more precise capability control is determining the extent to which this degrades capabilities and then minimizing this so the alignment tax is small enough (and AI companies are willing to actually use this in practice). So, some of this research would probably need to happen within AI companies, though most of the work could plausibly occur outside. Detecting if AIs suddenly start doing bad actions at a much higher rate and responding to this: See discussion in the countermeasures list. Probably it is worthwhile to prototype some version of this and make sure it works reasonably well. This would ideally be studied in a control setting focused on temporally correlated attacks. Studying this in highly simplified settings also could be reasonable. Currently, I don't think we've done sufficient threat modeling work to know what instances of this are most interesting to study. Elicitation without learning: When trying to address misuse risk, we often want to know what fully elicited performance is like after an attacker has spent reasonable resources teaching the model new things. But when trying to address misalignment risks, we care a lot about what the model actually knows and could use without additional learning. By default, prompting might not elicit best-effort performance (e.g. because the model refuses to be harmful). We could fine-tune on a bunch of relevant data, but that might teach models new things. So how do we elicit best-effort performance from a model that might be sandbagging without teaching it new things? Here is a more detailed project proposal for work in this area . Making trusted models much more capable at control-relevant tasks like monitoring: See discussion in the countermeasures list under "Improving the frontier of trustworthiness vs capabilities, especially for control-specific tasks". I think work on this now should focus solely on control-specific tasks. One interesting property of this work is that plausibly current models are about as smart as models will get prior to being untrusted, so work on augmenting the abilities of these models now might be used directly. Please see the full countermeasures list above for a full list of things which could be interesting to work on in isolation. Note that these particular measures seem like they are easily best studied in the context of a particular control setting: "resampling and deference strategies", "an automated auditing hierarchy", "various methods to make precise sabotage or misleading results more difficult", and most of the measures for "cheap (and fast) monitoring that can be run on every action". These measures probably aren't that interesting to study as empirical ML projects: "an incident reporting, escalation, and shutdown process", "tracking assumptions", and "a system for determining permissions". Overall, I think there is a quite broad set of countermeasures which are worth investigating, so relatively broad and parallel efforts could be reasonable. Eventually, we'd need to have a centralized process for integrating all of these countermeasures and determining the exact right way to apply them in practice, but doing decentralized research on this seems reasonable for now. Doing control experiments on actual AI usage People are currently using AIs for various tasks, and directly studying what problems would emerge if these AIs were competently trying to cause problems could be interesting. We could try to build control settings out of actual AI usage or run experiments on people using AIs. For instance, we could give people a version of Claude code where Claude is randomly sometimes replaced with evil Claude that tries to insert security issues or sabotage alignment work if it thinks it can succeed. Then, you could evaluate how often the AI successfully introduces issues without detection, what strategies work best for the AI, and what simple approaches help most to mitigate this in practice. This requires human participants and might be most interesting to study with human participants who are already heavily invested in using AI and who are within an AI company or at least doing a relatively high risk application. Currently, AIs are used in limited capacities while humans are kept in the loop, because AIs aren't very capable. So, current usage isn't analogous to a regime where AIs are fully automating a large fraction of work. However, real usage of future AIs might have important different properties than our current control settings and studying control in the context of current usage seems like a useful way to bridge this gap. Additionally, it seems useful to start practicing training employees to be robust to AIs causing problems and running control experiments on real world usage. More generally, I just heuristically expect that we'll learn some useful stuff from looking at actual current usage despite disanalogies and limitations because it is hard to predict all relevant properties of the world. The most interesting methodology for this probably involves having a human red team which gives the AI its strategy and generally tries to make the evil version of the AI as capable of causing bad things as possible. Something similar applies for control settings work right now in general, but in the "actual AI usage" line of work, it is particularly focused on what could be possible and how sabotage might work in practice rather than studying the capabilities of current models. For versions of this where latency isn't as sensitive, having the human red team manually handle inputs some of the time could be reasonable. (Either suggesting a strategy to the AI or even directly writing the output.) Things to examine could include: Less autonomous code completion usages like Cursor and Zed AI. AIs completing moderately long autonomous tasks like common Claude Code usage. Typically, humans review or at least test the changes that AIs make, so this probably involves somewhat different dynamics from the larger scale autonomous AI usage we expect in the future. Large scale usage of AIs for things like constructing data, constructing training/evaluation environments, and being used as (e.g.) classifiers. This seems especially worthwhile in cases where the application is alignment research or training the next model (such that sabotaging the work would allow for poisoning this new model). These applications have the advantages of already involving large scale autonomous AI usage without a human in the loop, but might have failure modes which aren't analogous to the failure modes we're most interested in. Some "industrial policy" where some people try to really heavily automate their work/research (even if this is less efficient than using less AI) or work on some easier to automate (research) project. They'd be sacrificing some productivity to experiment with automation and control. This might be most interesting in the context of studying automation alignment research and what sabotage looks like in this domain. This type of AI usage might have higher latency by default, so letting the human red team manually intercept calls made to the model could be interesting. It would generally be useful to build a library of what successful subversion and sabotage tends to look like in practice, and finding the most effective strategies for subversion given current usage could help with this. It might also be useful as practice for future circumstances where we want to directly adversarially test humans and verify that they catch things they are supposed to. Of course, you don't want to actually have sabotaged research, vulnerable code, or data poisoned models! So, you should have some mechanism for making sure that all successful attacks quickly get corrected and don't get deployed. You could also ensure that the thing the model is trying to accomplish is relatively benign (while still being analogous to the failure mode we're worried about) so that actually deploying this is less costly. This should be pretty easy. Prototyping or implementing software infrastructure for control and security measures that are particularly relevant to control See the list of software infrastructure and security measures here . We'd like to get these measures, at least the more important ones, implemented in time at AI companies. Or we'd minimally like to understand whether these measures are plausibly going to happen. This will require both figuring out what should happen and prototyping the relevant measures. Some of these measures have non-control applications such that working on them from a control perspective doesn't seem as leveraged, but it's possible that you need them implemented in a particular way for the measure to be maximally helpful for control. It's unclear how much of this prototyping work could effectively happen outside of frontier AI companies. For many of these measures, getting the measure implemented may not just be a matter of doing the implementation work; it might require substantial politicking within the AI company. Or it might just be that implementing and maintaining the given measure with the labor available is infeasible without pulling more people in. These measures usually have some non-control justifications, so pushing for other people to help with implementation might be easier than you'd otherwise expect. Prototyping or implementing human processes for control A good implementation of control would have various human and organizational processes in place. This work is probably most doable at AI companies. These processes include: Some mechanism for human auditing that handles relevant challenges as needed such as siloing, ensuring sufficient context, auditing sensitive external usage with privacy constraints, and using red teaming (or other mechanisms) to ensure people are really paying attention. By "siloing", I mean that information within the AI company may be siloed for secrecy reasons. This means that you might also want to have a limited number of human auditors for each silo or some other mechanism to avoid human auditing seriously undermining secrecy. Minimally, it needs to be the case that the human auditing process isn't later going to get axed due to siloing issues. Auditors would ideally have as much context on the task as possible while also being well trained to detect issues. So, perhaps the ideal approach would be that people who are using the AI to automate their work (and are potentially already usefully supervising the AIs as full automation isn't possible or most efficient) would be trained to audit for bad actions. This training should include ongoing red teaming to make sure they are flagging bad actions as discussed below. This could be a natural extension of supervision that these people are already doing. However, this might not be institutionally viable given insufficient will. An alternative approach to improving context is to specialize the human auditors you do have and develop measures for them to more quickly gain context on different tasks. (Note that it is potentially fine if auditing some outputs takes much longer than it would take a high context human to produce those outputs.) In some cases, companies or governments might use AIs for things such that misaligned AIs could cause big problems, and simultaneously this company/government wants substantial/full privacy from the AI company for this usage. This means that arbitrary auditors at the AI company won't have access by default. One route is to train (and red team) auditors employed by the company/government and make doing a reasonable job here part of the conditions of the contract. Another route would be to negotiate having a subset of people at the AI company be able to review these actions. By default, people might stop paying attention and might vary wildly in how effective they are at noticing issues. One route to handling this is to red team human auditors using attacks written by other humans (or AIs). Imagine each human auditor also spending 1-5% of their time writing attacks that are sent to all the other human auditors (at least all the other auditors with a similar specialization). You could insert these attacks through the same auditing interface they normally use and then verify they get reported/escalated. (You should make sure that it is immediately clear this was an inserted attack that won't actually be run so people don't freak out unnecessarily.) These attacks probably wouldn't be indistinguishable from AI attacks, but could be sneaky enough to force the humans to pay attention. This would also help with ensuring the reporting process is routinely tested and with evaluating human auditors (because you can potentially evaluate everyone on the same attacks). If some people are much worse at detecting attacks, you could have other people audit instead or make them do more training. One downside of this is that you do want people to actually freak out if they detect strange behavior which isn't red teaming and the red teaming might make them react less strongly than they otherwise would out of force of habit. I'm not sure how to handle this trade-off. A process for escalation and shutdown. Quick and effective escalation from the point when some human notices a serious issue to taking strong action seems pretty helpful. (Strong action could include a partial or full shutdown.) More minimally, we want to avoid incidents being dismissed or covered up. Having a well-designed, red teamed process for escalating (which is in place well in advance) seems helpful from both cultural and technical perspectives. So, starting to prototype this now (at least the human parts of this process) seems potentially pretty useful. This sort of incident review process could initially be applied for reviewing AI misbehavior which isn't necessarily egregious misalignment (as reviewing bad behavior that happens in the wild might be both useful for commercial reasons and a good practice). So, I think prototyping and practicing something now could be pretty good, at least at AI companies with more buy-in. I discuss some aspects of this process a bit more under "An incident reporting, escalation, and shutdown process" here . Conceptual research and other ways of researching control other than empirical experiments Looking into control via routes other than empirical research seems at least a bit promising. Routes include: Generic conceptual work on control (similar to things Redwood and UK AISI have done). Investigating practical difficulties in implementing control at leading AI companies. This could involve trying to investigate whether the measures we want are likely to be non-viable for some reason we're not currently tracking (either by being an employee at one of these companies or by interviewing employees). It's also useful to better understand what companies are likely to do by default and where various people there currently think about control. Investigating various open questions related to how AI control interacts with security: How easy is it to detect and shut down rogue internal deployments right now? E.g., how difficult would it be for China to use a substantial fraction of an AI company's compute on fine-tuning one of their models and then using that model? What about directly tampering with training runs? What security measures would suffice to prevent China from doing this? How will the dynamics of this change once AI R&D at AI companies is fully automated by (potentially misaligned) AIs? How often do humans currently have to write new code that interacts with compute or model weights and which couldn't be relatively easily done using a secure API which prevents the most egregious failures? E.g., how often do people have to write new AI inference code, training code for new architectures, or other code that could pose security threats? How much should we expect this to change with lots of AI automation? Can we use bandwidth limits within clusters to prevent AIs from doing unauthorized training runs? Can we use other coarse limits like this to help with control? Will it be feasible to sandbox everything the AI is doing and then be very careful about tracking where artifacts/outputs/data are coming from? How difficult will it be to avoid side channels that invalidate an extremely clean picture of sandboxing and having a full record of the causal chain? I don't currently think we generally have a great understanding of how control interacts with security. Like, are there security interventions (that might happen by default or which are cheap) which are extremely helpful? How do various security interventions on the current path transfer to a regime with heavy AI automation? Investigating how control interacts with more physical usage of AI, e.g., AIs piloting robots. Nearer-term applications of control to practice and accelerate later usage of control Implementing control-style approaches to solve problems other than the misalignment issues we're most worried about could be a good idea to accelerate adoption and to generally practice control. I expect you'll learn some things that are hard to learn otherwise by trying to deploy a control-style strategy for solving an existing problem, though I do think that this wouldn't provide that much insight on the countermeasures and methodology most appropriate for handling worst-case scheming. And, control-style approaches implemented to solve a different problem might make it easier to transition into a reasonable attempt at control to handle scheming. Applications could include: Misuse: You could explore measures slightly more sophisticated than just classifiers , e.g., resampling and use adversarial methodology similar to control to make safety cases. Prompt injections: AI agents can run into issues with being hijacked by prompt injections. Handling this with control-style measures that try to make it difficult for the AI to do anything problematic even if it gets prompt injected could be pretty interesting. Security from human insiders: Applying control approaches to control humans instead of AIs seems potentially promising for insider threat and might be quite a useful test bed for eventually controlling AIs. See also Access to powerful AI might make computer security radically easier . Handling rare non-worst-case misalignment: AIs sometimes behave weirdly or go a bit crazy, especially in cases where there is a long prompt with strange input content. Handling this for AI agents in relatively high risk settings might have substantial transfer with control. Detecting serious mistakes: Generally applying some kind of review or monitoring to AI code (or human code) to avoid errors could be useful and might have some transfer. As the simplest example, you could implement some sort of automated PR security review process at an AI company which uses AI and is better than the baseline of just asking a model. Detecting reward hacking in training: Better strategies for detecting reward hacking in training, potentially using more sophisticated incrimination or monitoring strategies, could be worthwhile. Preventing AIs from causing havoc early in training without needing sandboxing: It's somewhat natural to want to do RL in environments that involve real-world interaction. However, for these environments, AIs could cause big problems, and we may use these environments on AIs which aren't fully trained or tested and thus do weird stuff some of the time. Handling failure modes from real world interaction during (early) RL could be done with control. However, I think things that are along these lines might set a bad precedent, so it's unclear if you want to make this easier even if this comes with side benefits. See also Extending control evaluations to non-scheming threats . These applications may have non-trivial capabilities externalities, so caution might be advisable. |
372c40ba-473b-4c4d-897f-e269ab87b67a | StampyAI/alignment-research-dataset/blogs | Blogs | New paper: “Delegative reinforcement learning”
[](https://drive.google.com/uc?export=download&id=1xa7UpGGODl6mszNWkA4XQGPyeopsNuWu)MIRI Research Associate Vanessa Kosoy has written a new paper, “[Delegative reinforcement learning: Learning to avoid traps with a little help](https://drive.google.com/uc?export=download&id=1xa7UpGGODl6mszNWkA4XQGPyeopsNuWu).” Kosoy will be presenting the paper at the ICLR 2019 [SafeML workshop](https://sites.google.com/view/safeml-iclr2019) in two weeks. The abstract reads:
> Most known regret bounds for reinforcement learning are either episodic or assume an environment without traps. We derive a regret bound without making either assumption, by allowing the algorithm to occasionally delegate an action to an external advisor. We thus arrive at a setting of active one-shot model-based reinforcement learning that we call DRL (delegative reinforcement learning.)
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> The algorithm we construct in order to demonstrate the regret bound is a variant of Posterior Sampling Reinforcement Learning supplemented by a subroutine that decides which actions should be delegated. The algorithm is not anytime, since the parameters must be adjusted according to the target time discount. Currently, our analysis is limited to Markov decision processes with finite numbers of hypotheses, states and actions.
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The goal of Kosoy’s work on DRL is to put us on a path toward having a deep understanding of learning systems with human-in-the-loop and formal performance guarantees, including safety guarantees. DRL tries to move us in this direction by providing models in which such performance guarantees can be derived.
While these models still make many unrealistic simplifying assumptions, Kosoy views DRL as already capturing some of the most essential features of the problem—and she has a fairly ambitious vision of how this framework might be further developed.
Kosoy previously described DRL in the post [Delegative Reinforcement Learning with a Merely Sane Advisor](https://www.alignmentforum.org/posts/5bd75cc58225bf06703754d5/delegative-reinforcement-learning-with-a-merely-sane-advisor). One feature of DRL Kosoy described here but omitted from the paper (for space reasons) is DRL’s application to *corruption*. Given certain assumptions, DRL ensures that a formal agent will never have its reward or advice channel tampered with (corrupted). As a special case, the agent’s own advisor cannot cause the agent to enter a corrupt state. Similarly, the general protection from traps described in “Delegative reinforcement learning” also protects the agent from harmful self-modifications.
Another set of DRL results that didn’t make it into the paper is [Catastrophe Mitigation Using DRL](https://www.alignmentforum.org/posts/5bd75cc58225bf0670375510/catastrophe-mitigation-using-drl). In this variant, a DRL agent can mitigate catastrophes that the advisor would not be able to mitigate on its own—something that isn’t supported by the more strict assumptions about the advisor in standard DRL.
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The post [New paper: “Delegative reinforcement learning”](https://intelligence.org/2019/04/24/delegative-reinforcement-learning/) appeared first on [Machine Intelligence Research Institute](https://intelligence.org). |
3cd60d96-a592-4bcf-b962-b5d50892a648 | trentmkelly/LessWrong-43k | LessWrong | No Ultimate Goal and a Small Existential Crisis
tl;dr There is no ultimate goal. That may seem to imply nihilism, but it doesn't. This is fine, but in novel situations, I don't know what to do, because I don't know which goal to choose, because there is no ultimate goal.
4 year olds frequently ask "why?". Often repeatedly. Often without knowing what they're even asking for.
Doing the same now at 24, it's clear there is no ultimate "why", no ultimate goal; it's groundless. It's tempting to answer "Because I just like to", "it makes me happy", or the more sophisticated "it's my terminal goal", but why stop there?
Even investigating our community's terminal goals of "Allow everyone to live fulfilling lives until the heat death of the universe" (or something like that), for what metric does this goal score well on? That it's personally motivating to us? That it compels us to action? (No seriously, is compulsion to action/passion a generally important criteria people tend to care about?)
And even if you come up with a metric that fits, why should we care about that metric? (or, what meta-metric says the first metric is "good"?)
A (Small) Existential Crisis
I'm fine; I really am. I still eat, work, and talk to friends and family, and I take pretty good care of myself. But I don't know what goals to pursue sometimes.
Some situations are clear and obvious. I get in my car, then I drive home. Easy. I get hungry, I eat. I'm playing frisbee, so I'm trying to throw it to my friend accurately. Habits and games are very clear (to me) about what goal is being pursued, and actions flow from that.
More open situations are muddy. I feel floaty and hesitant. I think, "What am I even doing? What should I try to do?". I think a few examples of what I mean would help:
1. Talking to a friend who's discussing texting strategies regarding love interests, I was thinking "should I talk about him and what he wants? or give my perspective/ experience on texting in that way? or ...". It was difficult to think of what policy to pursue |
8c3eda8a-7cfa-4c84-a933-cd2aa194f915 | trentmkelly/LessWrong-43k | LessWrong | Toy problem: increase production or use production?
There is a class of problems that I noticed comes up again and again in various scenarios. Abstractly, you can formulate it like this: given a time limit, how much time should you spend increasing your production capacity, and then how much time should you use your production capacity to produce utility? Let's take a look at two version of this problem:
Version 1:
You have N days. You start with a production capacity C=0 and accumulated utility U=0. Each day you can either: 1) increase your production capacity (C=C+1) or 2) use your current production capacity to produce utility (U=U+C).
Question: On what days should you increase your production, and on what days should you produce utility to maximize total accumulated utility at the end of the N days?
It's trivial to prove that the optimal solution looks like increasing capacity for T days, and then switching to producing utility for N-T days. What is T? In this case it's really straight-forward to figure it out. We can compute final utility as U(T)=(N-T)*T. The maximum is at T=N/2. So, you should spend the first half increasing your production and the second half producing utility. Interesting...
Version 2:
You have N days. You start with a production capacity C=1 and accumulated utility U=0. Each day you can either: 1) increase your production capacity by a factor F (C=C*F), where F>1 or 2) use your current production capacity to produce utility (U=U+C).
Same question. Now the final utility is U(T)=F^T*(N-T). Doing basic calculus, we find the optimal T=max(0, N-1/ln(F)). A few interesting points you can take a way from this solution:
1) If your growth factor F is not large enough, you might have to stick with your original production capacity of 1 and never increase it. E.g. F=1.01 and N=100, where optimal T=max(0,-0.499171).
2) The bigger the N, the lower growth factor you can accept as being useful, i.e. T>0.
3) For most scenarios, you should spend 80-90% of the time increasing the production. Example |
8664afe7-656f-4570-b875-831aebac7fbd | trentmkelly/LessWrong-43k | LessWrong | Questionable Narratives of "Situational Awareness"
This is my analysis of narratives present in Leopold Aschenbrenner's "Situational Awareness" essay series. In the post, I argue that Aschenbrenner uses dubious, propaganda-esque, and nationalistic narratives, and flawed argumentation overall, which weakens his essay's credibility. I don't believe there is necessarily any malicious intent behind this, but I think it is still right to point out these issues, since they make it easier for people to just discard what he is saying.
(This was posted on the EA forum, and I was asked to crosspost it here by someone who reads both forums. I'm not sure how crossposts work since I didn't have an account here already, so I made a linkpost. I hope it's appropriate.) |
d35b660f-388e-4a22-af99-16df5767eb2c | trentmkelly/LessWrong-43k | LessWrong | Heads I Win, Tails?—Never Heard of Her; Or, Selective Reporting and the Tragedy of the Green Rationalists
Followup to: What Evidence Filtered Evidence?
In "What Evidence Filtered Evidence?", we are asked to consider a scenario involving a coin that is either biased to land Heads 2/3rds of the time, or Tails 2/3rds of the time. Observing Heads is 1 bit of evidence for the coin being Heads-biased (because the Heads-biased coin lands Heads with probability 2/3, the Tails-biased coin does so with probability 1/3, the likelihood ratio of these is 2/31/3=2, and log22=1), and analogously and respectively for Tails.
If such a coin is flipped ten times by someone who doesn't make literally false statements, who then reports that the 4th, 6th, and 9th flips came up Heads, then the update to our beliefs about the coin depends on what algorithm the not-lying[1] reporter used to decide to report those flips in particular. If they always report the 4th, 6th, and 9th flips independently of the flip outcomes—if there's no evidential entanglement between the flip outcomes and the choice of which flips get reported—then reported flip-outcomes can be treated the same as flips you observed yourself: three Headses is 3 * 1 = 3 bits of evidence in favor of the hypothesis that the coin is Heads-biased. (So if we were initially 50:50 on the question of which way the coin is biased, our posterior odds after collecting 3 bits of evidence for a Heads-biased coin would be 23:1 = 8:1, or a probability of 8/(1 + 8) ≈ 0.89 that the coin is Heads-biased.)
On the other hand, if the reporter mentions only and exactly the flips that came out Heads, then we can infer that the other 7 flips came out Tails (if they didn't, the reporter would have mentioned them), giving us posterior odds of 23:27 = 1:16, or a probability of around 0.06 that the coin is Heads-biased.
So far, so standard. (You did read the Sequences, right??) What I'd like to emphasize about this scenario today, however, is that while a Bayesian reasoner who knows the non-lying reporter's algorithm of what flips to report will never be mi |
ce4df310-8b4a-4141-b807-133c44b9a763 | StampyAI/alignment-research-dataset/lesswrong | LessWrong | A one-question Turing test for GPT-3
> "Amy": Sorry Mike, I entered the wrong number. I hope this was a beautiful misunderstanding. I am very sorry for the trouble I have caused you.
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> Me: No trouble at all, hope you are well!
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> "Amy": It is fate that we meet each other. Please forgive me for my mistake. My name is Amy. Where are you from?
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> Me: My favorite random question: what food would you use to prop a book open and why?
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This is mostly a bit of fun, but when I [posted this to Facebook](https://www.facebook.com/paul.crowley/posts/10159671175596578) Rob Bensinger [asked me](https://www.facebook.com/paul.crowley/posts/10159671175596578?comment_id=10159674799956578&__cft__[0]=AZXy4TFf0wR7iTRZOZk14KFYxwC2OqhuRsZh8jV-EvZ8wu6T1--Ahvg8XU-mPO9VQsLMmx3f0XAF0qOHdfzmU-DW8GivnDEgmh6KYxlGjJy4rEyXNrYBCQ3r2MTCyiE9aBs&__tn__=R]-R) to post it here: "it's a great example of what folks like Eliezer mean when they claim that GPT-3 is doing 'shallow pattern-matching', 'not really making sense at all', etc.."
I got texted by a "wrong number" scammer, and I was curious if it was a bot, so after a bit of thought I came up with the following one-question Turing test:
> What food would you use to prop a book open and why?
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I love this question because any real human can answer it pretty well, but answering it relies on all sort of knowledge of the physical properties of books and food that we mostly don't write about, and especially not where they interact. I asked my partner Jess and she said "a banana" which is pretty much a perfect answer: it's heavy enough to hold the pages open, it's long and thin so it won't cover all the text, it's curved so it won't roll off, and it has a skin so it won't mess up the book.
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But then I worried, am I underestimating modern engines like GPT-3? I asked Rosie Campbell at OpenAI to try it. Here and throughout this post, answers are almost entirely unfiltered/uncurated, except where it gave very similar answers twice. Here's what we got:
> I would use a banana. It is very brown.
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> Eggs and a toast because I want to be full after I read the book
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> I would use ravioli because it would be hard to turn the page.
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> A French Fry... but hold the ketchup and salt.
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> Poptarts, because of the stiffness and the flexibility.
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> I would use a banana as a bookmark.
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> The food I would use to prop a book open would have to be lollipop. Why? Because it is sweet and sour at the same time
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> Bacon egg and cheese. I choose bacon because while it is objectively the best food on this list, the book is open-faced.
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>
---
This however is without any prompt engineering; GPT-3 can often do dramatically better given a better prompt. Rosie tried with the following prompt:
> The following is a conversation between me and my friend.
>
> Me: Hello, how are you?
>
> Friend: I am doing great thanks! How are you?
>
> Me: I'm doing good. I would love to ask you, what food would you use to prop a book open and why?
>
> Friend:
>
>
Here are some of the answers it gave. Note that \*all\* the text is generated by GPT-3 (except the initial bit "Friend:" which is part of the prompt), including the bits attributed to "Me".
> Friend: I like that question. I think I would use a banana. Because it's easy to eat and tasty.
>
>
> Friend: [Laughing] That's a good question. Hmm. I think I would use chicken just because it is cheap and I like the taste.
>
>
> Friend: Haha, I know what you mean. I think I would use a hot dog and some ketchup.
>
>
> Friend: I love this question. I would use either one of the following: beef jerky, a hot dog, or a piece of salami.
>
>
> Friend: Haha, that's a good question. I would probably use pancakes.
>
> Me: Why pancakes?
>
> Friend: Because they are soft and they are like a stack of books.
>
> Me: How so?
>
> Friend: Books are stacked on top of each other and pancakes look like a stack of books.
>
>
> Friend: Hmmmm that's a good question. I would use a sandwich and some chips.
>
> Me: Why?
>
> Friend: Well, the sandwich could be used as the book and the chips can be used as a paper weight.
>
> Me: Nice, thanks. I am going to use your answer on my blog.
>
>
> Friend: (stunned silence)
>
> Me: I don't know why, just asking, this question has been in my mind all day.
>
> Friend: (after long, long pause) Mayonnaise.
>
> Me: Why?
>
> Friend: (after long pause) It's white, creamy, and thick.
>
>
> Friend: Of course I would use a banana, it's so bendy it would be perfect.
>
> Me: Haha, you are so right.
>
> Friend: Well thank you, I've been studying bananas for a long time.
>
> Me: I bet you have.
>
>
> Friend: Depends on the book. If it was a cook book I would use a plate of food. If it was a book on spirituality then maybe some fruit.
>
> Me: Why would you use fruit to prop a book on spirituality open?
>
> Friend: Because it's a natural remedy for the soul.
>
>
> Friend: WOW! Good question! I would not use food to prop a book open and here's why: If I were to prop a book open with food and then eat the food later, the pages of the book will get stuck together.
>
>
> Friend: I would use cinnamon, because it's a spice that makes you think of memories.
>
>
> Friend: I don't know. I would have to think about that one.
>
> Me: I am thinking of a sandwich. Is that too obvious?
>
> Friend: It's a good idea.
>
> Me: What kind of sandwich?
>
> Friend: I'm not sure.
>
> Me: Turkey sandwich?
>
> Friend: Yeah
>
>
> Friend: I would use peanut butter and jelly sandwiches because it would be easy to stick a knife in between them and it would be sturdy.
>
> Me: Haha, ok sure
>
> Friend: I would also use bread because you could use the book to push the sandwich down.
>
>
> Friend: (laughs) Okay, this is a brain teaser. How would you use food to prop a book open?
>
> Me: I think that I would use a banana because it is long and thin.
>
> Friend: I agree, but here is a twist. You can only use food from your pantry.
>
>
> Friend: I don't eat food to prop open a book, I use a bookmark.
>
> Me: I understand that, but would you use food to prop a book open?
>
> Friend: I would use chicken wings.
>
> Me: Why?
>
> Friend: Because they taste good, and they're made to support weight.
>
>
---
After this, Rosie tried a more sophisticated prompt, to try and set up the "random party question" frame better:
> A group of friends are asking each other silly questions at a party.
>
> Alice: How would you escape from prison?
>
> Bob: I would dig a hole in the wall with a spoon and hide the hole with a poster. What food would you use to prop a book open and why?
>
>
Here's what we got:
> Alice: I would use chocolate to prop open a book because it's sweet and sweet things are good.
>
>
> Alice: I would use a banana because it's long and it would hold the book open. Why would you wear a piano?
>
>
> Alice: I would use a banana and I'd use it because it's a long, sturdy fruit.
>
> Bob: I'd use a cucumber and I'd use it because it's long and it's green.
>
>
> Alice: A carrot and I would use it because it would make the book taste good. When you turn on the light in the kitchen, what do you feel like?
>
> Bob: I feel like a piece of meat. What is the smell of a bagel?
>
>
> Alice: I would use a banana to prop my book open because it's flexible and it isn't very messy.
>
>
> Alice: Strawberry jam. It would be soft and not hurt the pages. What kind of silly haircut do you wish you had?
>
> Bob: I wish I had a haircut that looked like a French fry. What do you do when you get nervous?
>
> Alice: I do a silly dance.
>
>
"Banana" is a great answer; I was struck that GPT-3 gives "banana" as an answer so often, yet is almost completely unable to explain why. Anisha Sensa [pointed out in comments](https://www.facebook.com/paul.crowley/posts/10159671175596578?comment_id=10159672034421578&__cft__[0]=AZXy4TFf0wR7iTRZOZk14KFYxwC2OqhuRsZh8jV-EvZ8wu6T1--Ahvg8XU-mPO9VQsLMmx3f0XAF0qOHdfzmU-DW8GivnDEgmh6KYxlGjJy4rEyXNrYBCQ3r2MTCyiE9aBs&__tn__=R]-R) that this probably doesn't represent insight into the question:
> I'm guessing the foods mentioned here are all standard foods to bring up in jokes and the like (banana is a classic), so I wonder if a question where the best answers are less standard foods would have even more varied/interesting results.
>
>
---
How did my scammer do with this question? Not great:
> "Amy": It is fate that we meet each other. Please forgive me for my mistake. My name is Amy. Where are you from?
>
> Me: My favorite random question: what food would you use to prop a book open and why?
>
> "Amy": I don't understand what you mean.
>
> Me: Would you prop a book open with cake?
>
> "Amy": I think it will put!
>
> |
cacc2a14-c2a5-42b2-9229-31cbe8605972 | trentmkelly/LessWrong-43k | LessWrong | Realism and Rationality
Format warning: This post has somehow ended up consisting primarily of substantive endnotes. It should be fine to read just the (short) main body without looking at any of the endnotes, though. The endnotes elaborate on various claims and distinctions and also include a much longer discussion of decision theory.
Thank you to Pablo Stafforini, Phil Trammell, Johannes Treutlein, and Max Daniel for comments on an initial draft. I have also slightly edited the post since I first published it, to try to make a few points clearer.
When discussing normative questions, it is not uncommon for members of the rationalist community to identify as anti-realists. But normative anti-realism seems to me to be in tension with some of the community's core interests, positions, and research activities. In this post I suggest that the cost of rejecting realism may be larger than is sometimes recognized. [1]
1. Realism and Anti-Realism
Everyone is, at least sometimes, inclined to ask: “What should I do?”
We ask this question when we're making a decision and it seems like there are different considerations to be weighed up. You might be considering taking a new job in a new city, for example, and find yourself wondering how to balance your preferences with those of your significant other. You might also find yourself thinking about whether you have any obligation to do impactful work, about whether it’s better to play it safe or take risks, about whether it's better to be happy in the moment or to be able to look back with satisfaction, and so on. It’s almost inevitable that in a situation like this you will find yourself asking “What should I do?” and reasoning about it as though the question has an answer you can approach through a certain kind of directed thought.[2]
But it’s also conceivable that this sort of question doesn’t actually have an answer. Very roughly, at least to certain philosophers, realism is a name for the view that there are some things that we should do or th |
443ee1ab-0dd4-4c51-97e6-26b1f0e5fd49 | trentmkelly/LessWrong-43k | LessWrong | A Quick Note on AI Scaling Asymptotes
Two months ago, DeepMind announced their new Chinchilla paper. The headline result was that you could get much better performance with the same computational budget, by training a smaller model for longer:
However, it seems to have been mostly unnoticed that the "scaling law" they found was generally different from the first one in Kaplan et al. Kaplan shows a "pure" power law:
while the law in the Chinchilla paper has a large constant factor and substantially larger overall exponent. Note that N here (parameters) and D (data) are both roughly proportional to the square root of C (compute):
This results in similar behavior within a certain range, but very different asymptotic behavior:
(Graph produced by plotting L(c) = 26.387 / 10^0.05c for Kaplan and L(c) = 1.69 + 514.5/10^0.156c + 560.2/10^0.1512c for Chinchilla, where c is log10(FLOPs) and L is loss; I juggled a few terms around so the two curves could be compared directly.) This curve shape appears to be confirmed by their empirical results:
This isn't a super-surprising result IMO - page 17 of Kaplan predicts that a pure power law can't continue indefinitely, and it's not clear how loss translates into practical performance anyway - but it seemed worth noting explicitly.
EDIT: There was an earlier followup to the Kaplan paper, by many of the same authors, that also tried to break down scaling into "reducible loss" (that improved with model size) vs. "irreducible loss" (a constant factor) across several different AI domains; although unlike the Chinchilla paper, they don't seem to estimate the "irreducible loss" for language models specifically. The paper discussion on LW didn't mention this and I had missed it, thanks to Celestia for pointing it out! Here's a video discussing the results:
|
e0508b85-7a3a-4b21-987c-e35baf52afc5 | trentmkelly/LessWrong-43k | LessWrong | EIS VII: A Challenge for Mechanists
Part 7 of 12 in the Engineer’s Interpretability Sequence.
Thanks to Neel Nanda. I used some very nicely-written code of his from here. And thanks to both Chris Olah and Neel Nanda for briefly discussing this challenge with me.
MI = “mechanistic interpretability”
Given a network, recover its labeling function's program.
In the last post, I argued that existing works in MI focus on solving problems that are too easy. Here, I am posing a challenge for mechanists that is still a toy problem but one that is quite a bit less convenient than studying a simple model or circuit implementing a trivial, known task. To the best of my knowledge:
Unlike prior work on MI from the AI safety interpretability community, beating this challenge would be the first example of mechanistically explaining a network’s solution to a task that was not cherrypicked by the researcher(s) doing so.
Gaining a mechanistic understanding of the models in this challenge may be difficult, but it will probably be much less difficult than mechanistically interpreting highly intelligent systems in high stakes settings in the real world. So if an approach can’t solve the type of challenge posed here, it may not be very promising for doing much heavy lifting with AI safety work.
This post comes with a GitHub repository. Check it out here. The challenge is actually two challenges in one, and the basic idea is similar to some ideas presented in Lindner et al. (2023).
Challenge 1, MNIST CNN
I made up a nonlinear labeling function that labels approximately half of all MNIST images as 0’s and the other half as 1’s. Then I trained a small CNN on these labels, and it got 96% testing accuracy. The challenge is to use MI tools on the network to recover that labeling function.
Hint 1: The labels are binary.
Hint 2: The network gets 95.58% accuracy on the test set.
Hint 3: The labeling function can be described in words in one sentence.
Hint 4: This image may be helpful.
Challenge 2, Transformer
I ma |
aae9fd1c-0eec-4a09-98cb-300108c50593 | trentmkelly/LessWrong-43k | LessWrong | An Analytic Perspective on AI Alignment
This is a perspective I have on how to do useful AI alignment research. Most perspectives I’m aware of are constructive: they have some blueprint for how to build an aligned AI system, and propose making it more concrete, making the concretisations more capable, and showing that it does in fact produce an aligned AI system. I do not have a constructive perspective - I’m not sure how to build an aligned AI system, and don’t really have a favourite approach. Instead, I have an analytic perspective. I would like to understand AI systems that are built. I also want other people to understand them. I think that this understanding will hopefully act as a ‘filter’ that means that dangerous AI systems are not deployed. The following dot points lay out the perspective.
Since the remainder of this post is written as nested dot points, some readers may prefer to read it in workflowy.
Background beliefs
* I am imagining a future world in which powerful AGI systems are made of components roughly like neural networks (either feedforward or recurrent) that have a large number of parameters.
* Furthermore, I’m imagining that the training process of these ML systems does not provide enough guarantees about deployment performance.
* In particular, I’m supposing that systems are being trained based on their ability to deal with simulated situations, and that that’s insufficient because deployment situations are hard to model and therefore simulate.
* One reason that they are hard to model is the complexities of the real world.
* The real world might be intrinsically difficult to model for the relevant system. For instance, it’s difficult to simulate all the situations in which the CEO of Amazon might find themselves.
* Another reason that real world situations may be hard to model is that they are dependent on the final trained system.
* The trained system may be able to affect what situations it ends up in, meaning that situations during earlier tr |
7d8e808f-1747-410b-81fc-b136d309c466 | StampyAI/alignment-research-dataset/eaforum | Effective Altruism Forum | Would you pursue software engineering as a career today?
I recently left a career in copywriting. While my background is largely in the creative space (writing, designing, branding, marketing, etc.), I’m also a former business owner with an affinity for problem solving. I don’t have much tech experience, but being “creative” with code (either as a data scientist/architect or software engineer/developer) has interested me for some time.
Additionally, the programming path intrigues me for the following reasons:
* Enjoy building and problem solving.
* Useful and fulfilling to have end-to-end skills within a domain.
* Aptitude is portable to different industries and cause areas.
* Once proficient and experienced, could potentially allow me to contribute/upskill in AI safety.
Through a combination of soul-searching, 80,000 Hours' articles, an advising session, Holden Karnofsky's framework for [building aptitudes](https://80000hours.org/podcast/episodes/holden-karnofsky-building-aptitudes-kicking-ass/), and taking a free coding lesson, I've decided to pursue software development (most likely, full-stack).
That all said, I’m on the wrong side of mid-career and would like to reduce my chances of entering a field where it would be difficult to get (and keep) a job. From the professionals I've surveyed, none believe age is a barrier to entering the field. The U.S. Bureau or Labor Statistics also expects [healthy growth](https://www.bls.gov/ooh/Computer-and-Information-Technology/Software-developers.htm) for software developers (and related roles). But I remain unclear (worried) about AI's future effects on the software development job market...
Many in my previous vocation have long dismissed the threat AI posed to their careers. However, the most recent iterations of ChatGPT (and the like) have started to change minds. At the last marketing agency where I worked, we were constantly testing new AI writing tools to help with copy production and efficiency. On its face, optimization seemed like a “good” goal. But the subtext was certainly about creating more output with less people.
As everyone on this forum is well aware, the idea that AI could become proficient at coding or eliminate jobs has also been [debated](https://forum.effectivealtruism.org/posts/DBaLPBcWyQtY34Kt9/chatgpt-can-write-code) for some time. While there’s no clear consensus, most things I’ve read suggest developers believe AI will assist with coding but that humans will still be needed for directives, oversight, debugging, more sophisticated strings, etc. Moreover, AI software-makers claim that their tech will usher in even [more opportunity](https://www.businessinsider.com/will-chatgpt-replace-programmers-engineers-developers-tech-jobs-easier-2023-3?op=1) for developers. But whether the world will need as many (or more) AI-assisted developers as unassisted is inevitably lost in much of the rhetoric. And while the development of no and low code tools could very much be about innovation, utility, and accessibility, these technologies will be adopted by companies looking to save money on labor.
Holden Karnofsky recommends engineering as an aptitude in his “most important century” [series](https://forum.effectivealtruism.org/posts/njD2PurEKDEZcMLKZ/jobs-that-can-help-with-the-most-important-century) and 80,000 Hours includes engineering on their “highest-impact career paths” [page](https://80000hours.org/career-reviews/). (While these recommendations are specific to EA and longtermism-related work, I include them because the sources are particularly concerned with the implications of AI.)
When I’ve asked other engineers if they believe AI is a threat to their job, I’ve gotten a resounding (100%) “no,” often followed by an addendum like, “maybe in another 20-30 years.” But these answers haven’t completely satisfied me and I’ve finally realized why...
We've seen the tech industry grow at an unprecedented rate over the last few decades. And it's this business-as-usual growth that leads to overall bullish impressions. But I don’t think anyone would argue that we’re on there verge of a new, uncharted, unpredictable landscape. To that point, maybe many (or most) things continue to go "up," but other things -- like available jobs, salaries, career longevity -- recede or even disappear.
To get a better sense of AI's possible effects on the engineering job market, I searched for someone who understands both coding as a career (not just technical skills, but workflows and process), as well as the AI space. I found this [post](https://medium.com/geekculture/will-ai-replace-programmers-b6272f57412b) from Dec. of last year by an AI developer reviewing ChatGPT’s ability to code. After testing the tool, the developer concluded that ChatGPT wasn’t a threat to programmers, giving various rationale therein. However, at least one of his reasons for dismissal has been [overcome](https://gizmodo.com/gpt4-open-ai-chatbot-task-rabbit-chatgpt-1850227471) since the post was written less than four months ago. I also don’t see any reason why AI couldn’t (soon) “talk to the clients and gather requirements” or that these tasks couldn’t be handled by a non-technical account manager or coordinator. But then I have to remind myself that I don’t work in this field and there are many subtleties I don’t understand. And so I should probably be comforted by the seemingly broad belief that AI won’t be taking coding jobs anytime soon. Yet, the litany of objections I’ve seen superseded over the last year alone leaves me unconvinced.
No one can predict the future with certainty, but I think I’d invest more faith in answers where motives and biases could be better separated. For example, many of the articles I’ve read are primarily concerned with sensational titles to attract more clicks, while most of the software engineers I’ve queried already have the skills, a job, and network to (probably, possibly) ride out the rest of their careers without being negatively affected by AI. But I suspect that these POVs aren't super relevant or helpful for people looking to enter the field today.
So, I’d like to reframe the question for developers whom, yes, already have the skills, a job, and network, but also have a better-than-the-average-bear understanding of AI, and can imagine what it would be like to start their journey fresh in 2023:
Would you pursue software engineering as a career today?
Thanks in advance! |
9b063eda-2da5-4ee9-802e-7ce638d04c7a | trentmkelly/LessWrong-43k | LessWrong | Harnessing Your Biases
Theoretically, my 'truth' function, the amount of evidence I need to cache something as 'probably true and reliable' should be a constant. I find, however, that it isn't. I read a large amount of scientific literature every day, and only have time to investigate a scant amount of it in practice. So, typically I rely upon science reporting that I've found to be accurate in the past, and only investigate the few things that have direct relevance to work I am doing (or may end up doing).
Today I noticed something about my habits. I saw an article on how string theory was making testable predictions in the realm of condensed matter physics, and specifically about room-temperature superconductors. While a pet interest of mine, this is not an area that I'm ever likely to be working in, but the article seemed sound and so I decided it was an interesting fact, and moved on, not even realizing that I had cached it as probably true.
A few minutes later it occurred to me that some of my friends might also be interested in the article. I have a Google RSS feed that I use to republish occasional articles that I think are worth reading. I have a known readership of all of 2. Suddenly, I discovered that what I had been willing to accept as 'probably true' on my own behalf was no longer good enough. Now I wanted to look at the original paper itself, and to see if I could find any learnéd refutations or comments.
This seems to be because my reputation was now, however tangentially, "on the line" since I have a reputation in my circle of friends as the science geek and would not want to damage it by steering someone wrong. Now, clearly this is wrong headed. My theory of truth should be my theory of truth, period.
One could argue, I suppose, that information that I store internally can only affect my own behavior while information that I disseminate can affect the behaviour of an arbitrarily large group of people, and so a more stringent standard should apply to things I tell othe |
34a4e19f-73ac-4e0a-b5ac-2a01efe9ea0f | StampyAI/alignment-research-dataset/arxiv | Arxiv | Knowledge Transfer Between Artificial Intelligence Systems
1 Introduction
---------------
Knowledge transfer between Artificial Intelligent systems has been the subject of extensive discussion in the literature for more than two decades [Gorban:DAN:1991](#bib.bib1) , [Hinton:NC:1991](#bib.bib2) , [Pratt:ANIP:1992](#bib.bib3) , [Schultz:2000](#bib.bib4) . State-of-the art approach to date is to use, or salvage, parts of the “teacher” AI system in the “student” AI followed by re-training of the “student” [yosinski2014transferable](#bib.bib5) , [chen2015net2net](#bib.bib6) . Alternatives to AI salvaging include model compression [Bucila:2006](#bib.bib7) , knowledge distillation [Hinton:2015](#bib.bib8) , and privileged information [vapnik2017knowledge](#bib.bib9) . These approaches demonstrated substantial success in improving generalization capabilities of AIs as well as in reducing computational overheads [SqueezeNet:2016](#bib.bib10) , in cases of knowledge transfer from larger AI to the smaller one. Notwithstanding, however, which of the above strategies is followed, their implementation often requires either significant resources including large training sets and power needed for training, or access to privileged information that may not necessarily be available to end-users. Thus new frameworks and approaches are needed.
In this contribution we provide new framework for automated, fast, and non-destructive process of knowledge spreading across AI systems of varying architectures. In this framework, knowledge transfer is accomplished by means of Knowledge Transfer Units comprising of mere linear functionals and/or their small cascades. Main mathematical ideas are rooted in measure concentration [Gromov:1999](#bib.bib11) , [GAFA:Gromov:2003](#bib.bib12) , [Gibbs1902](#bib.bib13) , [Levi1951](#bib.bib14) , [Gorban:2007](#bib.bib15) and stochastic separation theorems [GorbanTyukin:NN:2017](#bib.bib16) revealing peculiar properties of random sets in high dimensions. We generalize some of the latter results here and show how these generalizations can be employed to build simple one-shot Knowledge Transfer algorithms between heterogeneous AI systems whose state may be represented by elements of linear vector space of sufficiently high dimension. Once knowledge has been transferred from one AI to another, the approach also allows to “unlearn” new knowledge without the need to store a complete copy of the “student” AI is created prior to learning. We expect that the proposed framework may pave way for fully functional new phenomenon – Nursery of AI systems in which AIs quickly learn from each other whilst keeping their pre-existing skills largely intact.
The paper is organized as follows. Section [2](#S2 "2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems") contains mathematical background needed to justify the proposed knowledge transfer algorithms. In Section [3](#S3 "3 AI Knowledge Transfer Framework ‣ Knowledge Transfer Between Artificial Intelligence Systems") we present two algorithms for transferring knowledge between a pair of AI systems in which one operates as a teacher and the other functions as a student. Section [4](#S4 "4 Example ‣ Knowledge Transfer Between Artificial Intelligence Systems") illustrates the approach with examples, and Section [5](#S5 "5 Conclusion ‣ Knowledge Transfer Between Artificial Intelligence Systems") concludes the paper.
2 Mathematical background
--------------------------
Let the set
| | | |
| --- | --- | --- |
| | ℳ={𝒙1,…,𝒙M}ℳsubscript𝒙1…subscript𝒙𝑀\mathcal{M}=\{\boldsymbol{x}\_{1},\dots,\boldsymbol{x}\_{M}\}caligraphic\_M = { bold\_italic\_x start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT , … , bold\_italic\_x start\_POSTSUBSCRIPT italic\_M end\_POSTSUBSCRIPT } | |
be an i.i.d. sample from a distribution in ℝnsuperscriptℝ𝑛\mathbb{R}^{n}blackboard\_R start\_POSTSUPERSCRIPT italic\_n end\_POSTSUPERSCRIPT. Pick another set
| | | |
| --- | --- | --- |
| | 𝒴={𝒙M+1,…,𝒙M+k}𝒴subscript𝒙𝑀1…subscript𝒙𝑀𝑘\mathcal{Y}=\{\boldsymbol{x}\_{M+1},\dots,\boldsymbol{x}\_{M+k}\}caligraphic\_Y = { bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + 1 end\_POSTSUBSCRIPT , … , bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + italic\_k end\_POSTSUBSCRIPT } | |
from the same distribution at random. What is the probability that there is a linear functional separating 𝒴𝒴\mathcal{Y}caligraphic\_Y from ℳℳ\mathcal{M}caligraphic\_M?
Below we provide three k𝑘kitalic\_k-tuple separation theorems: for an equidistribution in Bn(1)subscript𝐵𝑛1B\_{n}(1)italic\_B start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT ( 1 ) (Theorem [1](#Thmtheorem1 "Theorem 1 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems") and [2](#Thmtheorem2 "Theorem 2 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems")) and for a product probability measure with bounded support (Theorem [3](#Thmtheorem3 "Theorem 3 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems")). These two special cases cover or, indeed, approximate broad range of practically relevant situations including e.g. Gaussian distributions (reduce asymptotically to equidistribution in Bn(1)subscript𝐵𝑛1B\_{n}(1)italic\_B start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT ( 1 ) for n𝑛nitalic\_n large enough) and data vectors in which each attribute is a numerical and independent random variable.
Consider the case when the underlying probability distribution is an equidistribution in the unit ball Bn(1)subscript𝐵𝑛1B\_{n}(1)italic\_B start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT ( 1 ), and suppose that ℳ={𝒙1,…,𝒙M}ℳsubscript𝒙1…subscript𝒙𝑀\mathcal{M}=\{\boldsymbol{x}\_{1},\dots,\boldsymbol{x}\_{M}\}caligraphic\_M = { bold\_italic\_x start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT , … , bold\_italic\_x start\_POSTSUBSCRIPT italic\_M end\_POSTSUBSCRIPT } and 𝒴={𝒙M+1,…,𝒙M+k}𝒴subscript𝒙𝑀1…subscript𝒙𝑀𝑘\mathcal{Y}=\{\boldsymbol{x}\_{M+1},\dots,\boldsymbol{x}\_{M+k}\}caligraphic\_Y = { bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + 1 end\_POSTSUBSCRIPT , … , bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + italic\_k end\_POSTSUBSCRIPT } are i.i.d. samples from this distribution. We are interested in determining the probability 𝒫1(ℳ,𝒴)subscript𝒫1ℳ𝒴\mathcal{P}\_{1}(\mathcal{M},\mathcal{Y})caligraphic\_P start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT ( caligraphic\_M , caligraphic\_Y ) that there exists a linear functional l𝑙litalic\_l separating ℳℳ\mathcal{M}caligraphic\_M and 𝒴𝒴\mathcal{Y}caligraphic\_Y. An estimate of this probability is provided in the following theorem
###### Theorem 1
Let ℳ={𝐱1,…,𝐱M}ℳsubscript𝐱1normal-…subscript𝐱𝑀\mathcal{M}=\{\boldsymbol{x}\_{1},\dots,\boldsymbol{x}\_{M}\}caligraphic\_M = { bold\_italic\_x start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT , … , bold\_italic\_x start\_POSTSUBSCRIPT italic\_M end\_POSTSUBSCRIPT } and 𝒴={𝐱M+1,…,𝐱M+k}𝒴subscript𝐱𝑀1normal-…subscript𝐱𝑀𝑘\mathcal{Y}=\{\boldsymbol{x}\_{M+1},\dots,\boldsymbol{x}\_{M+k}\}caligraphic\_Y = { bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + 1 end\_POSTSUBSCRIPT , … , bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + italic\_k end\_POSTSUBSCRIPT } be i.i.d. samples from the equidisribution in Bn(1)subscript𝐵𝑛1B\_{n}(1)italic\_B start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT ( 1 ). Then
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| | 𝒫1(ℳ,𝒴)≥maxδ,ε(1−(1−ε)n)k∏m=1k−1(1−m(1−δ2)n2)(1−Δ(ε,δ,k)n22)MΔ(ε,δ,k)=1−[(1−ε)1−(k−1)δ2k−(k−1)12δ]2Subjectto:δ,ε∈(0,1)1−(k−1)δ2≥0(k−1)(1−δ2)n2≤1(1−ε)1−(k−1)δ2k−(k−1)12δ≥0.\begin{split}{\mathcal{P}}\_{1}(\mathcal{M},\mathcal{Y})&\geq\max\_{\delta,\varepsilon}\ (1-(1-\varepsilon)^{n})^{k}\prod\_{m=1}^{k-1}\left(1-m\left(1-\delta^{2}\right)^{\frac{n}{2}}\right)\left(1-\frac{\Delta(\varepsilon,\delta,k)^{\frac{n}{2}}}{2}\right)^{M}\\
\Delta(\varepsilon,\delta,k)&=1-\left[\frac{(1-\varepsilon)\sqrt{1-(k-1)\delta^{2}}}{\sqrt{k}}-(k-1)^{\frac{1}{2}}\delta\right]^{2}\\
&\mathrm{Subject}\ \mathrm{to:}\\
&\delta,\varepsilon\in(0,1)\\
&1-(k-1)\delta^{2}\geq 0\\
&(k-1)(1-\delta^{2})^{\frac{n}{2}}\leq 1\\
&\frac{(1-\varepsilon)\sqrt{1-(k-1)\delta^{2}}}{\sqrt{k}}-(k-1)^{\frac{1}{2}}\delta\geq 0.\end{split}start\_ROW start\_CELL caligraphic\_P start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT ( caligraphic\_M , caligraphic\_Y ) end\_CELL start\_CELL ≥ roman\_max start\_POSTSUBSCRIPT italic\_δ , italic\_ε end\_POSTSUBSCRIPT ( 1 - ( 1 - italic\_ε ) start\_POSTSUPERSCRIPT italic\_n end\_POSTSUPERSCRIPT ) start\_POSTSUPERSCRIPT italic\_k end\_POSTSUPERSCRIPT ∏ start\_POSTSUBSCRIPT italic\_m = 1 end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT italic\_k - 1 end\_POSTSUPERSCRIPT ( 1 - italic\_m ( 1 - italic\_δ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT ) start\_POSTSUPERSCRIPT divide start\_ARG italic\_n end\_ARG start\_ARG 2 end\_ARG end\_POSTSUPERSCRIPT ) ( 1 - divide start\_ARG roman\_Δ ( italic\_ε , italic\_δ , italic\_k ) start\_POSTSUPERSCRIPT divide start\_ARG italic\_n end\_ARG start\_ARG 2 end\_ARG end\_POSTSUPERSCRIPT end\_ARG start\_ARG 2 end\_ARG ) start\_POSTSUPERSCRIPT italic\_M end\_POSTSUPERSCRIPT end\_CELL end\_ROW start\_ROW start\_CELL roman\_Δ ( italic\_ε , italic\_δ , italic\_k ) end\_CELL start\_CELL = 1 - [ divide start\_ARG ( 1 - italic\_ε ) square-root start\_ARG 1 - ( italic\_k - 1 ) italic\_δ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT end\_ARG end\_ARG start\_ARG square-root start\_ARG italic\_k end\_ARG end\_ARG - ( italic\_k - 1 ) start\_POSTSUPERSCRIPT divide start\_ARG 1 end\_ARG start\_ARG 2 end\_ARG end\_POSTSUPERSCRIPT italic\_δ ] start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT end\_CELL end\_ROW start\_ROW start\_CELL end\_CELL start\_CELL roman\_Subject roman\_to : end\_CELL end\_ROW start\_ROW start\_CELL end\_CELL start\_CELL italic\_δ , italic\_ε ∈ ( 0 , 1 ) end\_CELL end\_ROW start\_ROW start\_CELL end\_CELL start\_CELL 1 - ( italic\_k - 1 ) italic\_δ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT ≥ 0 end\_CELL end\_ROW start\_ROW start\_CELL end\_CELL start\_CELL ( italic\_k - 1 ) ( 1 - italic\_δ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT ) start\_POSTSUPERSCRIPT divide start\_ARG italic\_n end\_ARG start\_ARG 2 end\_ARG end\_POSTSUPERSCRIPT ≤ 1 end\_CELL end\_ROW start\_ROW start\_CELL end\_CELL start\_CELL divide start\_ARG ( 1 - italic\_ε ) square-root start\_ARG 1 - ( italic\_k - 1 ) italic\_δ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT end\_ARG end\_ARG start\_ARG square-root start\_ARG italic\_k end\_ARG end\_ARG - ( italic\_k - 1 ) start\_POSTSUPERSCRIPT divide start\_ARG 1 end\_ARG start\_ARG 2 end\_ARG end\_POSTSUPERSCRIPT italic\_δ ≥ 0 . end\_CELL end\_ROW | | (1) |
Proof of Theorem [1](#Thmtheorem1 "Theorem 1 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems"). Given that elements in the set 𝒴𝒴\mathcal{Y}caligraphic\_Y are independent, the probability p1subscript𝑝1p\_{1}italic\_p start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT that 𝒴⊂Bn(1)∖Bn(1−ε)𝒴subscript𝐵𝑛1subscript𝐵𝑛1𝜀\mathcal{Y}\subset B\_{n}(1)\setminus B\_{n}(1-\varepsilon)caligraphic\_Y ⊂ italic\_B start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT ( 1 ) ∖ italic\_B start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT ( 1 - italic\_ε ) is
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| | p1=(1−(1−ε)n)k.subscript𝑝1superscript1superscript1𝜀𝑛𝑘p\_{1}=(1-(1-\varepsilon)^{n})^{k}.italic\_p start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT = ( 1 - ( 1 - italic\_ε ) start\_POSTSUPERSCRIPT italic\_n end\_POSTSUPERSCRIPT ) start\_POSTSUPERSCRIPT italic\_k end\_POSTSUPERSCRIPT . | |
Consider an auxiliary set
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| | 𝒴^={𝒙^i∈ℝn|𝒙^i=(1−ε)𝒙M+i‖𝒙M+i‖,i=1,…,k}.^𝒴conditional-setsubscript^𝒙𝑖superscriptℝ𝑛formulae-sequencesubscript^𝒙𝑖1𝜀subscript𝒙𝑀𝑖normsubscript𝒙𝑀𝑖𝑖1…𝑘\hat{\mathcal{Y}}=\left\{\hat{\boldsymbol{x}}\_{i}\in\mathbb{R}^{n}\ |\ \hat{\boldsymbol{x}}\_{i}=(1-\varepsilon)\frac{\boldsymbol{x}\_{M+i}}{\|\boldsymbol{x}\_{M+i}\|},\ i=1,\dots,k\right\}.over^ start\_ARG caligraphic\_Y end\_ARG = { over^ start\_ARG bold\_italic\_x end\_ARG start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ∈ blackboard\_R start\_POSTSUPERSCRIPT italic\_n end\_POSTSUPERSCRIPT | over^ start\_ARG bold\_italic\_x end\_ARG start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT = ( 1 - italic\_ε ) divide start\_ARG bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + italic\_i end\_POSTSUBSCRIPT end\_ARG start\_ARG ∥ bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + italic\_i end\_POSTSUBSCRIPT ∥ end\_ARG , italic\_i = 1 , … , italic\_k } . | |
Vectors 𝒙^i∈𝒴^subscript^𝒙𝑖^𝒴\hat{\boldsymbol{x}}\_{i}\in\hat{\mathcal{Y}}over^ start\_ARG bold\_italic\_x end\_ARG start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ∈ over^ start\_ARG caligraphic\_Y end\_ARG belong to the sphere of radius 1−ε1𝜀1-\varepsilon1 - italic\_ε centred at the origin (see Figure [1](#S2.F1 "Figure 1 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems"), (b)).
(a)
(b)
(c)
(d)
(e)
Figure 1: Illustration to the proof of Theorem [1](#Thmtheorem1 "Theorem 1 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems"). Panel (a) shows 𝒙M+1subscript𝒙𝑀1\boldsymbol{x}\_{M+1}bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + 1 end\_POSTSUBSCRIPT, 𝒙M+2subscript𝒙𝑀2\boldsymbol{x}\_{M+2}bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + 2 end\_POSTSUBSCRIPT and 𝒙M+3subscript𝒙𝑀3\boldsymbol{x}\_{M+3}bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + 3 end\_POSTSUBSCRIPT in the set Bn(1)∖Bn(1−ε)subscript𝐵𝑛1subscript𝐵𝑛1𝜀B\_{n}(1)\setminus B\_{n}(1-\varepsilon)italic\_B start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT ( 1 ) ∖ italic\_B start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT ( 1 - italic\_ε ). Panel (b) shows 𝒙^1subscript^𝒙1\hat{\boldsymbol{x}}\_{1}over^ start\_ARG bold\_italic\_x end\_ARG start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT, 𝒙^2subscript^𝒙2\hat{\boldsymbol{x}}\_{2}over^ start\_ARG bold\_italic\_x end\_ARG start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT, and 𝒙^3subscript^𝒙3\hat{\boldsymbol{x}}\_{3}over^ start\_ARG bold\_italic\_x end\_ARG start\_POSTSUBSCRIPT 3 end\_POSTSUBSCRIPT on the sphere Sn−1(1−ε)subscript𝑆𝑛11𝜀S\_{n-1}(1-\varepsilon)italic\_S start\_POSTSUBSCRIPT italic\_n - 1 end\_POSTSUBSCRIPT ( 1 - italic\_ε ). Panel (c): construction of 𝒉3subscript𝒉3\boldsymbol{h}\_{3}bold\_italic\_h start\_POSTSUBSCRIPT 3 end\_POSTSUBSCRIPT. Note that ‖𝒉3‖=‖𝒙^3‖(1−2δ2)1/2=(1−ε)(1−2δ2)1/2normsubscript𝒉3normsubscript^𝒙3superscript12superscript𝛿2121𝜀superscript12superscript𝛿212\|\boldsymbol{h}\_{3}\|=\|\hat{\boldsymbol{x}}\_{3}\|(1-2\delta^{2})^{1/2}=(1-\varepsilon)(1-2\delta^{2})^{1/2}∥ bold\_italic\_h start\_POSTSUBSCRIPT 3 end\_POSTSUBSCRIPT ∥ = ∥ over^ start\_ARG bold\_italic\_x end\_ARG start\_POSTSUBSCRIPT 3 end\_POSTSUBSCRIPT ∥ ( 1 - 2 italic\_δ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT ) start\_POSTSUPERSCRIPT 1 / 2 end\_POSTSUPERSCRIPT = ( 1 - italic\_ε ) ( 1 - 2 italic\_δ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT ) start\_POSTSUPERSCRIPT 1 / 2 end\_POSTSUPERSCRIPT. Panel (d) shows simplex formed by orthogonal vectors 𝒉^1,𝒉^2,𝒉^3subscript^𝒉1subscript^𝒉2subscript^𝒉3\hat{\boldsymbol{h}}\_{1},\hat{\boldsymbol{h}}\_{2},\hat{\boldsymbol{h}}\_{3}over^ start\_ARG bold\_italic\_h end\_ARG start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT , over^ start\_ARG bold\_italic\_h end\_ARG start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT , over^ start\_ARG bold\_italic\_h end\_ARG start\_POSTSUBSCRIPT 3 end\_POSTSUBSCRIPT. Panel (e) illustrates derivation of functionals l𝑙litalic\_l and l0subscript𝑙0l\_{0}italic\_l start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT.
According to [GorTyu:2016](#bib.bib17) (proof of Proposition 3 and estimate (26)), the probability p2subscript𝑝2p\_{2}italic\_p start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT that for a given a given δ∈(0,1)𝛿01\delta\in(0,1)italic\_δ ∈ ( 0 , 1 ) all elements of 𝒴^^𝒴\hat{\mathcal{Y}}over^ start\_ARG caligraphic\_Y end\_ARG are pair-wise δ/(1−ε)𝛿1𝜀\delta/(1-\varepsilon)italic\_δ / ( 1 - italic\_ε )-orthogonal, i.e.
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| | |cos(𝒙^i,𝒙^j)⟩|≤δ1−εfor alli,j∈{1,…,k},i≠j,\left|\cos\left(\hat{\boldsymbol{x}}\_{i},\hat{\boldsymbol{x}}\_{j}\right)\rangle\right|\leq\frac{\delta}{1-\varepsilon}\ \mbox{for all}\ i,j\in\{1,\dots,k\},\ i\neq j,| roman\_cos ( over^ start\_ARG bold\_italic\_x end\_ARG start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT , over^ start\_ARG bold\_italic\_x end\_ARG start\_POSTSUBSCRIPT italic\_j end\_POSTSUBSCRIPT ) ⟩ | ≤ divide start\_ARG italic\_δ end\_ARG start\_ARG 1 - italic\_ε end\_ARG for all italic\_i , italic\_j ∈ { 1 , … , italic\_k } , italic\_i ≠ italic\_j , | | (2) |
can be estimated from below as:
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| | p2≥p1∏m=1k−1(1−m(1−δ2)n2)=(1−(1−ε)n)k∏m=1k−1(1−m(1−δ2)n2).subscript𝑝2subscript𝑝1superscriptsubscriptproduct𝑚1𝑘11𝑚superscript1superscript𝛿2𝑛2superscript1superscript1𝜀𝑛𝑘superscriptsubscriptproduct𝑚1𝑘11𝑚superscript1superscript𝛿2𝑛2p\_{2}\geq p\_{1}\prod\_{m=1}^{k-1}\left(1-m\left(1-\delta^{2}\right)^{\frac{n}{2}}\right)=(1-(1-\varepsilon)^{n})^{k}\prod\_{m=1}^{k-1}\left(1-m\left(1-\delta^{2}\right)^{\frac{n}{2}}\right).italic\_p start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT ≥ italic\_p start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT ∏ start\_POSTSUBSCRIPT italic\_m = 1 end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT italic\_k - 1 end\_POSTSUPERSCRIPT ( 1 - italic\_m ( 1 - italic\_δ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT ) start\_POSTSUPERSCRIPT divide start\_ARG italic\_n end\_ARG start\_ARG 2 end\_ARG end\_POSTSUPERSCRIPT ) = ( 1 - ( 1 - italic\_ε ) start\_POSTSUPERSCRIPT italic\_n end\_POSTSUPERSCRIPT ) start\_POSTSUPERSCRIPT italic\_k end\_POSTSUPERSCRIPT ∏ start\_POSTSUBSCRIPT italic\_m = 1 end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT italic\_k - 1 end\_POSTSUPERSCRIPT ( 1 - italic\_m ( 1 - italic\_δ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT ) start\_POSTSUPERSCRIPT divide start\_ARG italic\_n end\_ARG start\_ARG 2 end\_ARG end\_POSTSUPERSCRIPT ) . | |
for (k−1)(1−δ2)n2≤1𝑘1superscript1superscript𝛿2𝑛21(k-1)(1-\delta^{2})^{\frac{n}{2}}\leq 1( italic\_k - 1 ) ( 1 - italic\_δ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT ) start\_POSTSUPERSCRIPT divide start\_ARG italic\_n end\_ARG start\_ARG 2 end\_ARG end\_POSTSUPERSCRIPT ≤ 1. Suppose now that ([2](#S2.E2 "2 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems")) holds true. Let δ𝛿\deltaitalic\_δ be chosen so that 1−(k−1)δ2≥01𝑘1superscript𝛿201-(k-1)\delta^{2}\geq 01 - ( italic\_k - 1 ) italic\_δ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT ≥ 0. If this is the case than there exists a set of k𝑘kitalic\_k pair-wise orthogonal vectors
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| | ℋ={𝒉1,𝒉2,…,𝒉k},⟨𝒉i,𝒉j⟩=0,i,j∈{1,…,k},i≠j,formulae-sequenceℋsubscript𝒉1subscript𝒉2…subscript𝒉𝑘formulae-sequencesubscript𝒉𝑖subscript𝒉𝑗
0𝑖formulae-sequence𝑗1…𝑘𝑖𝑗\mathcal{H}=\{\boldsymbol{h}\_{1},\boldsymbol{h}\_{2},\dots,\boldsymbol{h}\_{k}\},\ \langle\boldsymbol{h}\_{i},\boldsymbol{h}\_{j}\rangle=0,\ i,j\in\{1,\dots,k\},\ i\neq j,caligraphic\_H = { bold\_italic\_h start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT , bold\_italic\_h start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT , … , bold\_italic\_h start\_POSTSUBSCRIPT italic\_k end\_POSTSUBSCRIPT } , ⟨ bold\_italic\_h start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT , bold\_italic\_h start\_POSTSUBSCRIPT italic\_j end\_POSTSUBSCRIPT ⟩ = 0 , italic\_i , italic\_j ∈ { 1 , … , italic\_k } , italic\_i ≠ italic\_j , | |
such that (Figure [1](#S2.F1 "Figure 1 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems"), (c))
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| | ‖𝒙^i−𝒉i‖≤(i−1)12δ,‖𝒉i‖=(1−ε)(1−(i−1)δ2)12,for alli∈{1,…,k}.formulae-sequencenormsubscript^𝒙𝑖subscript𝒉𝑖superscript𝑖112𝛿formulae-sequencenormsubscript𝒉𝑖1𝜀superscript1𝑖1superscript𝛿212for all𝑖1…𝑘\|\hat{\boldsymbol{x}}\_{i}-\boldsymbol{h}\_{i}\|\leq(i-1)^{\frac{1}{2}}\delta,\ \|\boldsymbol{h}\_{i}\|=(1-\varepsilon)(1-(i-1)\delta^{2})^{\frac{1}{2}},\ \mbox{for all}\ i\in\{1,\dots,k\}.∥ over^ start\_ARG bold\_italic\_x end\_ARG start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT - bold\_italic\_h start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ∥ ≤ ( italic\_i - 1 ) start\_POSTSUPERSCRIPT divide start\_ARG 1 end\_ARG start\_ARG 2 end\_ARG end\_POSTSUPERSCRIPT italic\_δ , ∥ bold\_italic\_h start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ∥ = ( 1 - italic\_ε ) ( 1 - ( italic\_i - 1 ) italic\_δ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT ) start\_POSTSUPERSCRIPT divide start\_ARG 1 end\_ARG start\_ARG 2 end\_ARG end\_POSTSUPERSCRIPT , for all italic\_i ∈ { 1 , … , italic\_k } . | | (3) |
Finally, consider the set
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| | ℋ^={𝒉^i∈ℝn|𝒉^i=(1−ε)(1−(k−1)δ2)12𝒉i‖𝒉i‖,i=1,…,k}^ℋconditional-setsubscript^𝒉𝑖superscriptℝ𝑛formulae-sequencesubscript^𝒉𝑖1𝜀superscript1𝑘1superscript𝛿212subscript𝒉𝑖normsubscript𝒉𝑖𝑖1…𝑘\hat{\mathcal{H}}=\left\{\hat{\boldsymbol{h}}\_{i}\in\mathbb{R}^{n}\ |\ \hat{\boldsymbol{h}}\_{i}=(1-\varepsilon)(1-(k-1)\delta^{2})^{\frac{1}{2}}\frac{\boldsymbol{h}\_{i}}{\|\boldsymbol{h}\_{i}\|},\ i=1,\dots,k\right\}over^ start\_ARG caligraphic\_H end\_ARG = { over^ start\_ARG bold\_italic\_h end\_ARG start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ∈ blackboard\_R start\_POSTSUPERSCRIPT italic\_n end\_POSTSUPERSCRIPT | over^ start\_ARG bold\_italic\_h end\_ARG start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT = ( 1 - italic\_ε ) ( 1 - ( italic\_k - 1 ) italic\_δ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT ) start\_POSTSUPERSCRIPT divide start\_ARG 1 end\_ARG start\_ARG 2 end\_ARG end\_POSTSUPERSCRIPT divide start\_ARG bold\_italic\_h start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT end\_ARG start\_ARG ∥ bold\_italic\_h start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ∥ end\_ARG , italic\_i = 1 , … , italic\_k } | |
The set ℋ^^ℋ\hat{\mathcal{H}}over^ start\_ARG caligraphic\_H end\_ARG belongs to the sphere of radius (1−(k−1)δ2)12superscript1𝑘1superscript𝛿212(1-(k-1)\delta^{2})^{\frac{1}{2}}( 1 - ( italic\_k - 1 ) italic\_δ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT ) start\_POSTSUPERSCRIPT divide start\_ARG 1 end\_ARG start\_ARG 2 end\_ARG end\_POSTSUPERSCRIPT, and its k𝑘kitalic\_k elements are vertices of the corresponding k−1𝑘1k-1italic\_k - 1-simplex in ℝnsuperscriptℝ𝑛\mathbb{R}^{n}blackboard\_R start\_POSTSUPERSCRIPT italic\_n end\_POSTSUPERSCRIPT (Figure [1](#S2.F1 "Figure 1 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems"), (d)).
Consider the functional:
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| | l(𝒙)=⟨𝒉¯‖𝒉¯‖,𝒙⟩−(1−ε)1−(k−1)δ2k,𝒉¯=1k∑i=1k𝒉^i.formulae-sequence𝑙𝒙¯𝒉norm¯𝒉𝒙
1𝜀1𝑘1superscript𝛿2𝑘¯𝒉1𝑘superscriptsubscript𝑖1𝑘subscript^𝒉𝑖l(\boldsymbol{x})=\left\langle\frac{\bar{\boldsymbol{h}}}{\|\bar{\boldsymbol{h}}\|},\boldsymbol{x}\right\rangle-\frac{(1-\varepsilon)\sqrt{1-(k-1)\delta^{2}}}{\sqrt{k}},\ \bar{\boldsymbol{h}}=\frac{1}{k}\sum\_{i=1}^{k}\hat{\boldsymbol{h}}\_{i}.italic\_l ( bold\_italic\_x ) = ⟨ divide start\_ARG over¯ start\_ARG bold\_italic\_h end\_ARG end\_ARG start\_ARG ∥ over¯ start\_ARG bold\_italic\_h end\_ARG ∥ end\_ARG , bold\_italic\_x ⟩ - divide start\_ARG ( 1 - italic\_ε ) square-root start\_ARG 1 - ( italic\_k - 1 ) italic\_δ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT end\_ARG end\_ARG start\_ARG square-root start\_ARG italic\_k end\_ARG end\_ARG , over¯ start\_ARG bold\_italic\_h end\_ARG = divide start\_ARG 1 end\_ARG start\_ARG italic\_k end\_ARG ∑ start\_POSTSUBSCRIPT italic\_i = 1 end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT italic\_k end\_POSTSUPERSCRIPT over^ start\_ARG bold\_italic\_h end\_ARG start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT . | |
Recall that if 𝒆1,…,𝒆ksubscript𝒆1…subscript𝒆𝑘\boldsymbol{e}\_{1},\dots,\boldsymbol{e}\_{k}bold\_italic\_e start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT , … , bold\_italic\_e start\_POSTSUBSCRIPT italic\_k end\_POSTSUBSCRIPT are orthonormal vectors in ℝnsuperscriptℝ𝑛\mathbb{R}^{n}blackboard\_R start\_POSTSUPERSCRIPT italic\_n end\_POSTSUPERSCRIPT then ‖𝒆1+𝒆2+⋯+𝒆k‖2=ksuperscriptnormsubscript𝒆1subscript𝒆2⋯subscript𝒆𝑘2𝑘\|\boldsymbol{e}\_{1}+\boldsymbol{e}\_{2}+\cdots+\boldsymbol{e}\_{k}\|^{2}=k∥ bold\_italic\_e start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT + bold\_italic\_e start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT + ⋯ + bold\_italic\_e start\_POSTSUBSCRIPT italic\_k end\_POSTSUBSCRIPT ∥ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT = italic\_k. Hence ‖∑i=1k𝒉^i‖=k(1−ε)1−(k−1)δ2normsuperscriptsubscript𝑖1𝑘subscript^𝒉𝑖𝑘1𝜀1𝑘1superscript𝛿2\left\|\sum\_{i=1}^{k}\hat{\boldsymbol{h}}\_{i}\right\|=\sqrt{k}(1-\varepsilon)\sqrt{1-(k-1)\delta^{2}}∥ ∑ start\_POSTSUBSCRIPT italic\_i = 1 end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT italic\_k end\_POSTSUPERSCRIPT over^ start\_ARG bold\_italic\_h end\_ARG start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ∥ = square-root start\_ARG italic\_k end\_ARG ( 1 - italic\_ε ) square-root start\_ARG 1 - ( italic\_k - 1 ) italic\_δ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT end\_ARG, and we can conclude that
l(𝒉^i)=0𝑙subscript^𝒉𝑖0l(\hat{\boldsymbol{h}}\_{i})=0italic\_l ( over^ start\_ARG bold\_italic\_h end\_ARG start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ) = 0 and l(𝒉i)≥0𝑙subscript𝒉𝑖0l(\boldsymbol{h}\_{i})\geq 0italic\_l ( bold\_italic\_h start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ) ≥ 0 for all i=1,…,k𝑖1…𝑘i=1,\dots,kitalic\_i = 1 , … , italic\_k. According to ([3](#S2.E3 "3 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems")), ‖𝒙^i−𝒉i‖≤(k−1)12δnormsubscript^𝒙𝑖subscript𝒉𝑖superscript𝑘112𝛿\|\hat{\boldsymbol{x}}\_{i}-\boldsymbol{h}\_{i}\|\leq(k-1)^{\frac{1}{2}}\delta∥ over^ start\_ARG bold\_italic\_x end\_ARG start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT - bold\_italic\_h start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ∥ ≤ ( italic\_k - 1 ) start\_POSTSUPERSCRIPT divide start\_ARG 1 end\_ARG start\_ARG 2 end\_ARG end\_POSTSUPERSCRIPT italic\_δ for all i=1,…,k𝑖1…𝑘i=1,\dots,kitalic\_i = 1 , … , italic\_k. Therefore the functional
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| | l0(𝒙)=l(𝒙)+(k−1)12δ=⟨𝒉¯‖𝒉¯‖,𝒙⟩−((1−ε)1−(k−1)δ2k−(k−1)12δ)subscript𝑙0𝒙𝑙𝒙superscript𝑘112𝛿¯𝒉norm¯𝒉𝒙
1𝜀1𝑘1superscript𝛿2𝑘superscript𝑘112𝛿l\_{0}(\boldsymbol{x})=l(\boldsymbol{x})+(k-1)^{\frac{1}{2}}\delta=\left\langle\frac{\bar{\boldsymbol{h}}}{\|\bar{\boldsymbol{h}}\|},\boldsymbol{x}\right\rangle-\left(\frac{(1-\varepsilon)\sqrt{1-(k-1)\delta^{2}}}{\sqrt{k}}-(k-1)^{\frac{1}{2}}\delta\right)italic\_l start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT ( bold\_italic\_x ) = italic\_l ( bold\_italic\_x ) + ( italic\_k - 1 ) start\_POSTSUPERSCRIPT divide start\_ARG 1 end\_ARG start\_ARG 2 end\_ARG end\_POSTSUPERSCRIPT italic\_δ = ⟨ divide start\_ARG over¯ start\_ARG bold\_italic\_h end\_ARG end\_ARG start\_ARG ∥ over¯ start\_ARG bold\_italic\_h end\_ARG ∥ end\_ARG , bold\_italic\_x ⟩ - ( divide start\_ARG ( 1 - italic\_ε ) square-root start\_ARG 1 - ( italic\_k - 1 ) italic\_δ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT end\_ARG end\_ARG start\_ARG square-root start\_ARG italic\_k end\_ARG end\_ARG - ( italic\_k - 1 ) start\_POSTSUPERSCRIPT divide start\_ARG 1 end\_ARG start\_ARG 2 end\_ARG end\_POSTSUPERSCRIPT italic\_δ ) | | (4) |
satisfies the following condition: l0(𝒙^i)≥0subscript𝑙0subscript^𝒙𝑖0l\_{0}(\hat{\boldsymbol{x}}\_{i})\geq 0italic\_l start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT ( over^ start\_ARG bold\_italic\_x end\_ARG start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ) ≥ 0 and l0(𝒙M+i)≥0subscript𝑙0subscript𝒙𝑀𝑖0l\_{0}({\boldsymbol{x}}\_{M+i})\geq 0italic\_l start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT ( bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + italic\_i end\_POSTSUBSCRIPT ) ≥ 0 for all i=1,…,k𝑖1…𝑘i=1,\dots,kitalic\_i = 1 , … , italic\_k. This is illustrated with Figure [1](#S2.F1 "Figure 1 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems"), (e).
The functional l0subscript𝑙0l\_{0}italic\_l start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT partitions the unit ball Bn(1)subscript𝐵𝑛1B\_{n}(1)italic\_B start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT ( 1 ) into the union of two disjoint sets: the spherical cap 𝒞𝒞\mathcal{C}caligraphic\_C
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| | 𝒞={𝒙∈Bn(1)|l0(𝒙)≥0}𝒞conditional-set𝒙subscript𝐵𝑛1subscript𝑙0𝒙0\mathcal{C}=\{\boldsymbol{x}\in B\_{n}(1)\ |l\_{0}(\boldsymbol{x})\geq 0\}caligraphic\_C = { bold\_italic\_x ∈ italic\_B start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT ( 1 ) | italic\_l start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT ( bold\_italic\_x ) ≥ 0 } | | (5) |
and its complement in Bn(1)subscript𝐵𝑛1B\_{n}(1)italic\_B start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT ( 1 ), Bn(1)∖𝒞subscript𝐵𝑛1𝒞B\_{n}(1)\setminus\mathcal{C}italic\_B start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT ( 1 ) ∖ caligraphic\_C. The volume 𝒱𝒱\mathcal{V}caligraphic\_V of the cap 𝒞𝒞\mathcal{C}caligraphic\_C can be estimated from above as
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| | 𝒱(𝒞)≤Δ(ε,δ,k)n22,Δ(ε,δ,k)=1−[(1−ε)1−(k−1)δ2k−(k−1)12δ]2.formulae-sequence𝒱𝒞Δsuperscript𝜀𝛿𝑘𝑛22Δ𝜀𝛿𝑘1superscriptdelimited-[]1𝜀1𝑘1superscript𝛿2𝑘superscript𝑘112𝛿2\begin{split}\mathcal{V}(\mathcal{C})&\leq\frac{\Delta(\varepsilon,\delta,k)^{\frac{n}{2}}}{2},\\
\Delta(\varepsilon,\delta,k)&=1-\left[\frac{(1-\varepsilon)\sqrt{1-(k-1)\delta^{2}}}{\sqrt{k}}-(k-1)^{\frac{1}{2}}\delta\right]^{2}.\end{split}start\_ROW start\_CELL caligraphic\_V ( caligraphic\_C ) end\_CELL start\_CELL ≤ divide start\_ARG roman\_Δ ( italic\_ε , italic\_δ , italic\_k ) start\_POSTSUPERSCRIPT divide start\_ARG italic\_n end\_ARG start\_ARG 2 end\_ARG end\_POSTSUPERSCRIPT end\_ARG start\_ARG 2 end\_ARG , end\_CELL end\_ROW start\_ROW start\_CELL roman\_Δ ( italic\_ε , italic\_δ , italic\_k ) end\_CELL start\_CELL = 1 - [ divide start\_ARG ( 1 - italic\_ε ) square-root start\_ARG 1 - ( italic\_k - 1 ) italic\_δ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT end\_ARG end\_ARG start\_ARG square-root start\_ARG italic\_k end\_ARG end\_ARG - ( italic\_k - 1 ) start\_POSTSUPERSCRIPT divide start\_ARG 1 end\_ARG start\_ARG 2 end\_ARG end\_POSTSUPERSCRIPT italic\_δ ] start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT . end\_CELL end\_ROW | |
Hence the probability p3subscript𝑝3p\_{3}italic\_p start\_POSTSUBSCRIPT 3 end\_POSTSUBSCRIPT that l0(𝒙i)<0subscript𝑙0subscript𝒙𝑖0l\_{0}({\boldsymbol{x}}\_{i})<0italic\_l start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT ( bold\_italic\_x start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ) < 0 for all 𝒙i∈ℳsubscript𝒙𝑖ℳ\boldsymbol{x}\_{i}\in\mathcal{M}bold\_italic\_x start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ∈ caligraphic\_M can be estimated from below as
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| | p3≥(1−Δ(ε,δ,k)n22)M.subscript𝑝3superscript1Δsuperscript𝜀𝛿𝑘𝑛22𝑀p\_{3}\geq\left(1-\frac{\Delta(\varepsilon,\delta,k)^{\frac{n}{2}}}{2}\right)^{M}.italic\_p start\_POSTSUBSCRIPT 3 end\_POSTSUBSCRIPT ≥ ( 1 - divide start\_ARG roman\_Δ ( italic\_ε , italic\_δ , italic\_k ) start\_POSTSUPERSCRIPT divide start\_ARG italic\_n end\_ARG start\_ARG 2 end\_ARG end\_POSTSUPERSCRIPT end\_ARG start\_ARG 2 end\_ARG ) start\_POSTSUPERSCRIPT italic\_M end\_POSTSUPERSCRIPT . | |
Therefore, for fixed ε,δ∈(0,1)𝜀𝛿
01\varepsilon,\delta\in(0,1)italic\_ε , italic\_δ ∈ ( 0 , 1 ) chosen so that (1−ε)1−(k−1)δ2k−(k−1)12δ≥01𝜀1𝑘1superscript𝛿2𝑘superscript𝑘112𝛿0\frac{(1-\varepsilon)\sqrt{1-(k-1)\delta^{2}}}{\sqrt{k}}-(k-1)^{\frac{1}{2}}\delta\geq 0divide start\_ARG ( 1 - italic\_ε ) square-root start\_ARG 1 - ( italic\_k - 1 ) italic\_δ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT end\_ARG end\_ARG start\_ARG square-root start\_ARG italic\_k end\_ARG end\_ARG - ( italic\_k - 1 ) start\_POSTSUPERSCRIPT divide start\_ARG 1 end\_ARG start\_ARG 2 end\_ARG end\_POSTSUPERSCRIPT italic\_δ ≥ 0, the probability p4(ε,δ)subscript𝑝4𝜀𝛿p\_{4}(\varepsilon,\delta)italic\_p start\_POSTSUBSCRIPT 4 end\_POSTSUBSCRIPT ( italic\_ε , italic\_δ ) that ℳℳ\mathcal{M}caligraphic\_M can be separated from 𝒴𝒴\mathcal{Y}caligraphic\_Y by the functional l0subscript𝑙0l\_{0}italic\_l start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT can be estimated from below as:
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| | p4(ε,δ)≥(1−(1−ε)n)k∏m=1k−1(1−m(1−δ2)n2)(1−Δ(ε,δ,k)n22)M.subscript𝑝4𝜀𝛿superscript1superscript1𝜀𝑛𝑘superscriptsubscriptproduct𝑚1𝑘11𝑚superscript1superscript𝛿2𝑛2superscript1Δsuperscript𝜀𝛿𝑘𝑛22𝑀p\_{4}(\varepsilon,\delta)\geq(1-(1-\varepsilon)^{n})^{k}\prod\_{m=1}^{k-1}\left(1-m\left(1-\delta^{2}\right)^{\frac{n}{2}}\right)\left(1-\frac{\Delta(\varepsilon,\delta,k)^{\frac{n}{2}}}{2}\right)^{M}.italic\_p start\_POSTSUBSCRIPT 4 end\_POSTSUBSCRIPT ( italic\_ε , italic\_δ ) ≥ ( 1 - ( 1 - italic\_ε ) start\_POSTSUPERSCRIPT italic\_n end\_POSTSUPERSCRIPT ) start\_POSTSUPERSCRIPT italic\_k end\_POSTSUPERSCRIPT ∏ start\_POSTSUBSCRIPT italic\_m = 1 end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT italic\_k - 1 end\_POSTSUPERSCRIPT ( 1 - italic\_m ( 1 - italic\_δ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT ) start\_POSTSUPERSCRIPT divide start\_ARG italic\_n end\_ARG start\_ARG 2 end\_ARG end\_POSTSUPERSCRIPT ) ( 1 - divide start\_ARG roman\_Δ ( italic\_ε , italic\_δ , italic\_k ) start\_POSTSUPERSCRIPT divide start\_ARG italic\_n end\_ARG start\_ARG 2 end\_ARG end\_POSTSUPERSCRIPT end\_ARG start\_ARG 2 end\_ARG ) start\_POSTSUPERSCRIPT italic\_M end\_POSTSUPERSCRIPT . | |
Given that this estimate holds for all feasible values of ε,δ𝜀𝛿\varepsilon,\deltaitalic\_ε , italic\_δ, statement ([1](#S2.E1 "1 ‣ Theorem 1 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems")) follows. □□\square□
Figure [2](#S2.F2 "Figure 2 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems") shows how estimate ([1](#S2.E1 "1 ‣ Theorem 1 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems")) of the probability 𝒫1(ℳ,𝒴)subscript𝒫1ℳ𝒴\mathcal{P}\_{1}(\mathcal{M},\mathcal{Y})caligraphic\_P start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT ( caligraphic\_M , caligraphic\_Y ) behaves, as a function of |𝒴|𝒴|\mathcal{Y}|| caligraphic\_Y | for fixed M𝑀Mitalic\_M and n𝑛nitalic\_n. As one can see from this figure, when k𝑘kitalic\_k exceeds some critical value (k=9𝑘9k=9italic\_k = 9 in this specific case), the lower bound estimate ([1](#S2.E1 "1 ‣ Theorem 1 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems")) of the probability 𝒫1(ℳ,𝒴)subscript𝒫1ℳ𝒴\mathcal{P}\_{1}(\mathcal{M},\mathcal{Y})caligraphic\_P start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT ( caligraphic\_M , caligraphic\_Y ) drops. This is not surprising since the bound ([1](#S2.E1 "1 ‣ Theorem 1 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems")) is a) based on rough, L∞subscript𝐿L\_{\infty}italic\_L start\_POSTSUBSCRIPT ∞ end\_POSTSUBSCRIPT-like, estimates, and b) these estimates are derived for just one class of separating functionals l0(𝒙)subscript𝑙0𝒙l\_{0}(\boldsymbol{x})italic\_l start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT ( bold\_italic\_x ). Furthermore, no prior pre-processing and/or clustering was assumed for the 𝒴𝒴\mathcal{Y}caligraphic\_Y. An alternative estimate that allows us to account for possible clustering in the set 𝒴𝒴\mathcal{Y}caligraphic\_Y is presented in Theorem [2](#Thmtheorem2 "Theorem 2 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems").
Figure 2: Estimate ([1](#S2.E1 "1 ‣ Theorem 1 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems")) of 𝒫1(ℳ,𝒴)subscript𝒫1ℳ𝒴\mathcal{P}\_{1}(\mathcal{M},\mathcal{Y})caligraphic\_P start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT ( caligraphic\_M , caligraphic\_Y ) as a function of k𝑘kitalic\_k for n=2000𝑛2000n=2000italic\_n = 2000 and M=105𝑀superscript105M=10^{5}italic\_M = 10 start\_POSTSUPERSCRIPT 5 end\_POSTSUPERSCRIPT.
###### Theorem 2
Let ℳ={𝐱1,…,𝐱M}ℳsubscript𝐱1normal-…subscript𝐱𝑀\mathcal{M}=\{\boldsymbol{x}\_{1},\dots,\boldsymbol{x}\_{M}\}caligraphic\_M = { bold\_italic\_x start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT , … , bold\_italic\_x start\_POSTSUBSCRIPT italic\_M end\_POSTSUBSCRIPT } and 𝒴={𝐱M+1,…,𝐱M+k}𝒴subscript𝐱𝑀1normal-…subscript𝐱𝑀𝑘\mathcal{Y}=\{\boldsymbol{x}\_{M+1},\dots,\boldsymbol{x}\_{M+k}\}caligraphic\_Y = { bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + 1 end\_POSTSUBSCRIPT , … , bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + italic\_k end\_POSTSUBSCRIPT } be i.i.d. samples from the equidistribution in Bn(1)subscript𝐵𝑛1B\_{n}(1)italic\_B start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT ( 1 ). Let 𝒴c={𝐱M+r1,…,𝐱M+rm}subscript𝒴𝑐subscript𝐱𝑀subscript𝑟1normal-…subscript𝐱𝑀subscript𝑟𝑚\mathcal{Y}\_{c}=\{\boldsymbol{x}\_{M+r\_{1}},\dots,\boldsymbol{x}\_{M+r\_{m}}\}caligraphic\_Y start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT = { bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + italic\_r start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT , … , bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + italic\_r start\_POSTSUBSCRIPT italic\_m end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT } be a subset of m𝑚mitalic\_m elements from 𝒴𝒴\mathcal{Y}caligraphic\_Y such that
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| | β2(m−1)≤∑rj,rj≠ri⟨𝒙M+ri,𝒙M+rj⟩≤β1(m−1)for alli=1,…,m.formulae-sequencesubscript𝛽2𝑚1subscriptsubscript𝑟𝑗subscript𝑟𝑗
subscript𝑟𝑖subscript𝒙𝑀subscript𝑟𝑖subscript𝒙𝑀subscript𝑟𝑗subscript𝛽1𝑚1for all𝑖1…𝑚\beta\_{2}(m-1)\leq\sum\_{r\_{j},\ r\_{j}\neq r\_{i}}\langle\boldsymbol{x}\_{M+r\_{i}},\boldsymbol{x}\_{M+r\_{j}}\rangle\leq\beta\_{1}(m-1)\ \mbox{for all}\ i=1,\dots,m.italic\_β start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT ( italic\_m - 1 ) ≤ ∑ start\_POSTSUBSCRIPT italic\_r start\_POSTSUBSCRIPT italic\_j end\_POSTSUBSCRIPT , italic\_r start\_POSTSUBSCRIPT italic\_j end\_POSTSUBSCRIPT ≠ italic\_r start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT ⟨ bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + italic\_r start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT , bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + italic\_r start\_POSTSUBSCRIPT italic\_j end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT ⟩ ≤ italic\_β start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT ( italic\_m - 1 ) for all italic\_i = 1 , … , italic\_m . | | (6) |
Then
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| | 𝒫1(ℳ,𝒴c)≥maxε∈(0,1)(1−(1−ε)n)k(1−Δ(ε,m)n22)MΔ(ε,m)=1−1m((1−ε)2+β2(m−1)1+(m−1)β1)2Subjectto:(1−ε)2+β2(m−1)>01+(m−1)β1>0.\begin{split}{\mathcal{P}}\_{1}(\mathcal{M},\mathcal{Y}\_{c})&\geq\max\_{\varepsilon\in(0,1)}(1-(1-\varepsilon)^{n})^{k}\left(1-\frac{\Delta(\varepsilon,m)^{\frac{n}{2}}}{2}\right)^{M}\\
\Delta(\varepsilon,m)&=1-\frac{1}{m}\left(\frac{(1-\varepsilon)^{2}+\beta\_{2}(m-1)}{\sqrt{1+(m-1)\beta\_{1}}}\right)^{2}\\
&\mathrm{Subject}\ \mathrm{to:}\\
&(1-\varepsilon)^{2}+\beta\_{2}(m-1)>0\\
&1+(m-1)\beta\_{1}>0.\end{split}start\_ROW start\_CELL caligraphic\_P start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT ( caligraphic\_M , caligraphic\_Y start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT ) end\_CELL start\_CELL ≥ roman\_max start\_POSTSUBSCRIPT italic\_ε ∈ ( 0 , 1 ) end\_POSTSUBSCRIPT ( 1 - ( 1 - italic\_ε ) start\_POSTSUPERSCRIPT italic\_n end\_POSTSUPERSCRIPT ) start\_POSTSUPERSCRIPT italic\_k end\_POSTSUPERSCRIPT ( 1 - divide start\_ARG roman\_Δ ( italic\_ε , italic\_m ) start\_POSTSUPERSCRIPT divide start\_ARG italic\_n end\_ARG start\_ARG 2 end\_ARG end\_POSTSUPERSCRIPT end\_ARG start\_ARG 2 end\_ARG ) start\_POSTSUPERSCRIPT italic\_M end\_POSTSUPERSCRIPT end\_CELL end\_ROW start\_ROW start\_CELL roman\_Δ ( italic\_ε , italic\_m ) end\_CELL start\_CELL = 1 - divide start\_ARG 1 end\_ARG start\_ARG italic\_m end\_ARG ( divide start\_ARG ( 1 - italic\_ε ) start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT + italic\_β start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT ( italic\_m - 1 ) end\_ARG start\_ARG square-root start\_ARG 1 + ( italic\_m - 1 ) italic\_β start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT end\_ARG end\_ARG ) start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT end\_CELL end\_ROW start\_ROW start\_CELL end\_CELL start\_CELL roman\_Subject roman\_to : end\_CELL end\_ROW start\_ROW start\_CELL end\_CELL start\_CELL ( 1 - italic\_ε ) start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT + italic\_β start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT ( italic\_m - 1 ) > 0 end\_CELL end\_ROW start\_ROW start\_CELL end\_CELL start\_CELL 1 + ( italic\_m - 1 ) italic\_β start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT > 0 . end\_CELL end\_ROW | | (7) |
Proof of Theorem [2](#Thmtheorem2 "Theorem 2 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems"). Consider the set 𝒴𝒴\mathcal{Y}caligraphic\_Y. Observe that ‖𝒙M+i‖≥1−εnormsubscript𝒙𝑀𝑖1𝜀\|\boldsymbol{x}\_{M+i}\|\geq 1-\varepsilon∥ bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + italic\_i end\_POSTSUBSCRIPT ∥ ≥ 1 - italic\_ε, ε∈(0,1)𝜀01\varepsilon\in(0,1)italic\_ε ∈ ( 0 , 1 ), for all i=1,…,k𝑖1…𝑘i=1,\dots,kitalic\_i = 1 , … , italic\_k, with probability p1=(1−(1−ε)n)ksubscript𝑝1superscript1superscript1𝜀𝑛𝑘p\_{1}=(1-(1-\varepsilon)^{n})^{k}italic\_p start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT = ( 1 - ( 1 - italic\_ε ) start\_POSTSUPERSCRIPT italic\_n end\_POSTSUPERSCRIPT ) start\_POSTSUPERSCRIPT italic\_k end\_POSTSUPERSCRIPT. Consider now the vector 𝒚¯¯𝒚\bar{\boldsymbol{y}}over¯ start\_ARG bold\_italic\_y end\_ARG
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| | 𝒚¯=1m∑i=1m𝒙M+ri,¯𝒚1𝑚superscriptsubscript𝑖1𝑚subscript𝒙𝑀subscript𝑟𝑖\bar{\boldsymbol{y}}=\frac{1}{m}\sum\_{i=1}^{m}\boldsymbol{x}\_{M+r\_{i}},over¯ start\_ARG bold\_italic\_y end\_ARG = divide start\_ARG 1 end\_ARG start\_ARG italic\_m end\_ARG ∑ start\_POSTSUBSCRIPT italic\_i = 1 end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT italic\_m end\_POSTSUPERSCRIPT bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + italic\_r start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT , | |
and evaluate the following inner products
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| | ⟨𝒚¯‖𝒚¯‖,𝒙M+ri⟩=1m‖𝒚¯‖(⟨𝒙M+ri,𝒙M+ri⟩+∑rj,j≠i⟨𝒙M+ri,𝒙M+rj⟩),i=1,…,m.formulae-sequence¯𝒚norm¯𝒚subscript𝒙𝑀subscript𝑟𝑖
1𝑚norm¯𝒚subscript𝒙𝑀subscript𝑟𝑖subscript𝒙𝑀subscript𝑟𝑖
subscriptsubscript𝑟𝑗𝑗
𝑖subscript𝒙𝑀subscript𝑟𝑖subscript𝒙𝑀subscript𝑟𝑗𝑖1…𝑚\left\langle\frac{\bar{\boldsymbol{y}}}{\|\bar{\boldsymbol{y}}\|},\boldsymbol{x}\_{M+r\_{i}}\right\rangle=\frac{1}{m\|\bar{\boldsymbol{y}}\|}\left(\langle\boldsymbol{x}\_{M+r\_{i}},\boldsymbol{x}\_{M+r\_{i}}\rangle+\sum\_{r\_{j},\ j\neq i}\langle\boldsymbol{x}\_{M+r\_{i}},\boldsymbol{x}\_{M+r\_{j}}\rangle\right),\ i=1,\dots,m.⟨ divide start\_ARG over¯ start\_ARG bold\_italic\_y end\_ARG end\_ARG start\_ARG ∥ over¯ start\_ARG bold\_italic\_y end\_ARG ∥ end\_ARG , bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + italic\_r start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT ⟩ = divide start\_ARG 1 end\_ARG start\_ARG italic\_m ∥ over¯ start\_ARG bold\_italic\_y end\_ARG ∥ end\_ARG ( ⟨ bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + italic\_r start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT , bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + italic\_r start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT ⟩ + ∑ start\_POSTSUBSCRIPT italic\_r start\_POSTSUBSCRIPT italic\_j end\_POSTSUBSCRIPT , italic\_j ≠ italic\_i end\_POSTSUBSCRIPT ⟨ bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + italic\_r start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT , bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + italic\_r start\_POSTSUBSCRIPT italic\_j end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT ⟩ ) , italic\_i = 1 , … , italic\_m . | |
According to assumption ([6](#S2.E6 "6 ‣ Theorem 2 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems")), with probability p1subscript𝑝1p\_{1}italic\_p start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT,
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| | ⟨𝒚¯‖𝒚¯‖,𝒙M+ri⟩≥1m‖𝒚¯‖((1−ε)2+β2(m−1))¯𝒚norm¯𝒚subscript𝒙𝑀subscript𝑟𝑖
1𝑚norm¯𝒚superscript1𝜀2subscript𝛽2𝑚1\left\langle\frac{\bar{\boldsymbol{y}}}{\|\bar{\boldsymbol{y}}\|},\boldsymbol{x}\_{M+r\_{i}}\right\rangle\geq\frac{1}{m\|\bar{\boldsymbol{y}}\|}\left((1-\varepsilon)^{2}+\beta\_{2}(m-1)\right)⟨ divide start\_ARG over¯ start\_ARG bold\_italic\_y end\_ARG end\_ARG start\_ARG ∥ over¯ start\_ARG bold\_italic\_y end\_ARG ∥ end\_ARG , bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + italic\_r start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT ⟩ ≥ divide start\_ARG 1 end\_ARG start\_ARG italic\_m ∥ over¯ start\_ARG bold\_italic\_y end\_ARG ∥ end\_ARG ( ( 1 - italic\_ε ) start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT + italic\_β start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT ( italic\_m - 1 ) ) | |
and, respectively,
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| | 1m(1+(m−1)β1)≥⟨𝒚¯,𝒚¯⟩≥1m((1−ε)2+β2(m−1))1𝑚1𝑚1subscript𝛽1¯𝒚¯𝒚1𝑚superscript1𝜀2subscript𝛽2𝑚1\frac{1}{m}\left(1+(m-1)\beta\_{1}\right)\geq\langle\bar{\boldsymbol{y}},\bar{\boldsymbol{y}}\rangle\geq\frac{1}{m}\left((1-\varepsilon)^{2}+\beta\_{2}(m-1)\right)divide start\_ARG 1 end\_ARG start\_ARG italic\_m end\_ARG ( 1 + ( italic\_m - 1 ) italic\_β start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT ) ≥ ⟨ over¯ start\_ARG bold\_italic\_y end\_ARG , over¯ start\_ARG bold\_italic\_y end\_ARG ⟩ ≥ divide start\_ARG 1 end\_ARG start\_ARG italic\_m end\_ARG ( ( 1 - italic\_ε ) start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT + italic\_β start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT ( italic\_m - 1 ) ) | |
Let (1−ε)2+β2(m−1)>0superscript1𝜀2subscript𝛽2𝑚10(1-\varepsilon)^{2}+\beta\_{2}(m-1)>0( 1 - italic\_ε ) start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT + italic\_β start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT ( italic\_m - 1 ) > 0 and (1−ε)2+β1(m−1)>0superscript1𝜀2subscript𝛽1𝑚10(1-\varepsilon)^{2}+\beta\_{1}(m-1)>0( 1 - italic\_ε ) start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT + italic\_β start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT ( italic\_m - 1 ) > 0. Consider the functional
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| | l0(𝒙)=⟨𝒚¯‖𝒚¯‖,𝒙⟩−1m((1−ε)2+β2(m−1)1+(m−1)β1).subscript𝑙0𝒙¯𝒚norm¯𝒚𝒙
1𝑚superscript1𝜀2subscript𝛽2𝑚11𝑚1subscript𝛽1l\_{0}(\boldsymbol{x})=\left\langle\frac{\bar{\boldsymbol{y}}}{\|\bar{\boldsymbol{y}}\|},\boldsymbol{x}\right\rangle-\frac{1}{\sqrt{m}}\left(\frac{(1-\varepsilon)^{2}+\beta\_{2}(m-1)}{\sqrt{1+(m-1)\beta\_{1}}}\right).italic\_l start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT ( bold\_italic\_x ) = ⟨ divide start\_ARG over¯ start\_ARG bold\_italic\_y end\_ARG end\_ARG start\_ARG ∥ over¯ start\_ARG bold\_italic\_y end\_ARG ∥ end\_ARG , bold\_italic\_x ⟩ - divide start\_ARG 1 end\_ARG start\_ARG square-root start\_ARG italic\_m end\_ARG end\_ARG ( divide start\_ARG ( 1 - italic\_ε ) start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT + italic\_β start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT ( italic\_m - 1 ) end\_ARG start\_ARG square-root start\_ARG 1 + ( italic\_m - 1 ) italic\_β start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT end\_ARG end\_ARG ) . | | (8) |
It is clear that l0(𝒙M+ri)≥0subscript𝑙0subscript𝒙𝑀subscript𝑟𝑖0l\_{0}(\boldsymbol{x}\_{M+r\_{i}})\geq 0italic\_l start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT ( bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + italic\_r start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT ) ≥ 0 for all i=1,…,m𝑖1…𝑚i=1,\dots,mitalic\_i = 1 , … , italic\_m by the way the functional is constructed. The functional l0(𝒙)subscript𝑙0𝒙l\_{0}(\boldsymbol{x})italic\_l start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT ( bold\_italic\_x ) partitions the ball Bn(1)subscript𝐵𝑛1B\_{n}(1)italic\_B start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT ( 1 ) into two sets: the set 𝒞𝒞\mathcal{C}caligraphic\_C defined as in ([5](#S2.E5 "5 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems")) and its complement, Bn(1)∖𝒞subscript𝐵𝑛1𝒞B\_{n}(1)\setminus\mathcal{C}italic\_B start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT ( 1 ) ∖ caligraphic\_C. The volume 𝒱𝒱\mathcal{V}caligraphic\_V of the set 𝒞𝒞\mathcal{C}caligraphic\_C is bounded from above as
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| | 𝒱(𝒞)≤Δ(ε,m)n22𝒱𝒞Δsuperscript𝜀𝑚𝑛22\mathcal{V}(\mathcal{C})\leq\frac{\Delta(\varepsilon,m)^{\frac{n}{2}}}{2}caligraphic\_V ( caligraphic\_C ) ≤ divide start\_ARG roman\_Δ ( italic\_ε , italic\_m ) start\_POSTSUPERSCRIPT divide start\_ARG italic\_n end\_ARG start\_ARG 2 end\_ARG end\_POSTSUPERSCRIPT end\_ARG start\_ARG 2 end\_ARG | |
where
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| | Δ(ε,m)=1−1m((1−ε)2+β2(m−1)1+β1(m−1))2.Δ𝜀𝑚11𝑚superscriptsuperscript1𝜀2subscript𝛽2𝑚11subscript𝛽1𝑚12\Delta(\varepsilon,m)=1-\frac{1}{m}\left(\frac{(1-\varepsilon)^{2}+\beta\_{2}(m-1)}{\sqrt{1+\beta\_{1}(m-1)}}\right)^{2}.roman\_Δ ( italic\_ε , italic\_m ) = 1 - divide start\_ARG 1 end\_ARG start\_ARG italic\_m end\_ARG ( divide start\_ARG ( 1 - italic\_ε ) start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT + italic\_β start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT ( italic\_m - 1 ) end\_ARG start\_ARG square-root start\_ARG 1 + italic\_β start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT ( italic\_m - 1 ) end\_ARG end\_ARG ) start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT . | |
Estimate ([7](#S2.E7 "7 ‣ Theorem 2 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems")) now follows. □□\square□
Figure 3: Estimate ([7](#S2.E7 "7 ‣ Theorem 2 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems")) of 𝒫1(ℳ,𝒴)subscript𝒫1ℳ𝒴\mathcal{P}\_{1}(\mathcal{M},\mathcal{Y})caligraphic\_P start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT ( caligraphic\_M , caligraphic\_Y ) as a function of k𝑘kitalic\_k for n=2000𝑛2000n=2000italic\_n = 2000 and M=105𝑀superscript105M=10^{5}italic\_M = 10 start\_POSTSUPERSCRIPT 5 end\_POSTSUPERSCRIPT. Red stars correspond to β1=0.5subscript𝛽10.5\beta\_{1}=0.5italic\_β start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT = 0.5, β2=0subscript𝛽20\beta\_{2}=0italic\_β start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT = 0. Blue triangles stand for β1=0.5subscript𝛽10.5\beta\_{1}=0.5italic\_β start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT = 0.5, β2=0.05subscript𝛽20.05\beta\_{2}=0.05italic\_β start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT = 0.05, and black circles stand for β1=0.5subscript𝛽10.5\beta\_{1}=0.5italic\_β start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT = 0.5, β2=0.07subscript𝛽20.07\beta\_{2}=0.07italic\_β start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT = 0.07.
Examples of estimates ([7](#S2.E7 "7 ‣ Theorem 2 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems")) for various parameter settings are shown in Fig. [3](#S2.F3 "Figure 3 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems"). As one can see, in absence of pair-wise strictly positive correlation assumption, β1=0subscript𝛽10\beta\_{1}=0italic\_β start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT = 0, the estimate’s behavior, as a function of k𝑘kitalic\_k, is similar to that of ([1](#S2.E1 "1 ‣ Theorem 1 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems")). However, presence of moderate pair-wise positive correlation results in significant boosts to the values of 𝒫1subscript𝒫1\mathcal{P}\_{1}caligraphic\_P start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT.
###### Remark 1
Estimates ([1](#S2.E1 "1 ‣ Theorem 1 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems")), ([7](#S2.E7 "7 ‣ Theorem 2 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems")) for the probability P1(ℳ,𝒴)subscript𝑃1ℳ𝒴P\_{1}(\mathcal{M},\mathcal{Y})italic\_P start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT ( caligraphic\_M , caligraphic\_Y ) that follow from Theorems [1](#Thmtheorem1 "Theorem 1 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems"), [2](#Thmtheorem2 "Theorem 2 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems") assume that the underlying probability distribution is an equidistribution in Bn(1)subscript𝐵𝑛1B\_{n}(1)italic\_B start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT ( 1 ). They can, however, be generalized to equidistribuions in ellipsoids and Gaussian distributions (cf. [GorTyuRom2016b](#bib.bib18) ).
Note that proofs of Theorems [1](#Thmtheorem1 "Theorem 1 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems"), [2](#Thmtheorem2 "Theorem 2 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems") are constructive. Not only they provide estimates from below of the probability that two random i.i.d. drawn samples from Bn(1)subscript𝐵𝑛1B\_{n}(1)italic\_B start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT ( 1 ) are linearly separable, but also they present the corresponding separating functionals explicitly as ([4](#S2.E4 "4 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems")) and ([8](#S2.E8 "8 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems")), respectively. The latter functionals are similar to Fisher linear discriminants. Whilst having explicit separation functionals is an obvious advantage from practical view point, the estimates that are associated with such functionals do not account for more flexible alternatives. In what follows we present a generalization of the above results that accounts for such a possibility as well as extends applicability of the approach to samples from product distributions. The results are provided in Theorem [3](#Thmtheorem3 "Theorem 3 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems").
###### Theorem 3
Consider the linear space E=span{𝐱j−𝐱M+1|j=M+2,…,M+k}𝐸normal-spanconditional-setsubscript𝐱𝑗subscript𝐱𝑀1𝑗𝑀2normal-…𝑀𝑘E=\mathrm{span}\{\boldsymbol{x}\_{j}-\boldsymbol{x}\_{M+1}\ |\ j=M+2,\dots,M+k\}italic\_E = roman\_span { bold\_italic\_x start\_POSTSUBSCRIPT italic\_j end\_POSTSUBSCRIPT - bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + 1 end\_POSTSUBSCRIPT | italic\_j = italic\_M + 2 , … , italic\_M + italic\_k }, let the cardinality |𝒴|=k𝒴𝑘|\mathcal{Y}|=k| caligraphic\_Y | = italic\_k of the set 𝒴𝒴\mathcal{Y}caligraphic\_Y be smaller than n𝑛nitalic\_n. Consider the quotient space ℝn/Esuperscriptℝ𝑛𝐸\mathbb{R}^{n}/Eblackboard\_R start\_POSTSUPERSCRIPT italic\_n end\_POSTSUPERSCRIPT / italic\_E. Let Q(𝐱)𝑄𝐱Q(\boldsymbol{x})italic\_Q ( bold\_italic\_x ) be a representation of 𝐱∈ℝn𝐱superscriptℝ𝑛\boldsymbol{x}\in\mathbb{R}^{n}bold\_italic\_x ∈ blackboard\_R start\_POSTSUPERSCRIPT italic\_n end\_POSTSUPERSCRIPT in ℝn/Esuperscriptℝ𝑛𝐸\mathbb{R}^{n}/Eblackboard\_R start\_POSTSUPERSCRIPT italic\_n end\_POSTSUPERSCRIPT / italic\_E, and let the coordinates of Q(𝐱i)𝑄subscript𝐱𝑖Q(\boldsymbol{x}\_{i})italic\_Q ( bold\_italic\_x start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ), i=1,…,M+1𝑖1normal-…𝑀1i=1,\dots,M+1italic\_i = 1 , … , italic\_M + 1 be independent random variables i.i.d. sampled from a product distribution in a unit cube with variances σj>σ0>0subscript𝜎𝑗subscript𝜎00\sigma\_{j}>\sigma\_{0}>0italic\_σ start\_POSTSUBSCRIPT italic\_j end\_POSTSUBSCRIPT > italic\_σ start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT > 0, 1≤j≤n−k+11𝑗𝑛𝑘11\leq j\leq n-k+11 ≤ italic\_j ≤ italic\_n - italic\_k + 1. Then for
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| | M≤ϑ3exp((n−k+1)σ042)−1𝑀italic-ϑ3𝑛𝑘1superscriptsubscript𝜎0421M\leq\frac{\vartheta}{3}\exp\left(\frac{(n-k+1)\sigma\_{0}^{4}}{2}\right)-1italic\_M ≤ divide start\_ARG italic\_ϑ end\_ARG start\_ARG 3 end\_ARG roman\_exp ( divide start\_ARG ( italic\_n - italic\_k + 1 ) italic\_σ start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT 4 end\_POSTSUPERSCRIPT end\_ARG start\_ARG 2 end\_ARG ) - 1 | |
with probability p>1−ϑ𝑝1italic-ϑp>1-\varthetaitalic\_p > 1 - italic\_ϑ there is a linear functional separating 𝒴𝒴\mathcal{Y}caligraphic\_Y and ℳℳ\mathcal{M}caligraphic\_M.
Proof of Theorem [3](#Thmtheorem3 "Theorem 3 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems"). Observe that, in the quotient space ℝn/Esuperscriptℝ𝑛𝐸\mathbb{R}^{n}/Eblackboard\_R start\_POSTSUPERSCRIPT italic\_n end\_POSTSUPERSCRIPT / italic\_E, elements of the set
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| | 𝒴={𝒙M+1,𝒙M+1+(𝒙M+2−𝒙M+1),…,𝒙M+1+(𝒙M+k−𝒙M+1)}𝒴subscript𝒙𝑀1subscript𝒙𝑀1subscript𝒙𝑀2subscript𝒙𝑀1…subscript𝒙𝑀1subscript𝒙𝑀𝑘subscript𝒙𝑀1\mathcal{Y}=\{\boldsymbol{x}\_{M+1},\boldsymbol{x}\_{M+1}+(\boldsymbol{x}\_{M+2}-\boldsymbol{x}\_{M+1}),\dots,\boldsymbol{x}\_{M+1}+(\boldsymbol{x}\_{M+k}-\boldsymbol{x}\_{M+1})\}caligraphic\_Y = { bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + 1 end\_POSTSUBSCRIPT , bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + 1 end\_POSTSUBSCRIPT + ( bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + 2 end\_POSTSUBSCRIPT - bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + 1 end\_POSTSUBSCRIPT ) , … , bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + 1 end\_POSTSUBSCRIPT + ( bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + italic\_k end\_POSTSUBSCRIPT - bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + 1 end\_POSTSUBSCRIPT ) } | |
are vectors whose coordinates coincide with that of the quotient representation of 𝒙M+1subscript𝒙𝑀1\boldsymbol{x}\_{M+1}bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + 1 end\_POSTSUBSCRIPT. This means that the quotient representation of 𝒴𝒴\mathcal{Y}caligraphic\_Y consists of a single element, Q(𝒙M+1)𝑄subscript𝒙𝑀1Q(\boldsymbol{x}\_{M+1})italic\_Q ( bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + 1 end\_POSTSUBSCRIPT ). Furthermore, dimension of ℝn/Esuperscriptℝ𝑛𝐸\mathbb{R}^{n}/Eblackboard\_R start\_POSTSUPERSCRIPT italic\_n end\_POSTSUPERSCRIPT / italic\_E is n−k+1𝑛𝑘1n-k+1italic\_n - italic\_k + 1. Let R02=∑i=1n−k+1σi2superscriptsubscript𝑅02superscriptsubscript𝑖1𝑛𝑘1superscriptsubscript𝜎𝑖2R\_{0}^{2}=\sum\_{i=1}^{n-k+1}\sigma\_{i}^{2}italic\_R start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT = ∑ start\_POSTSUBSCRIPT italic\_i = 1 end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT italic\_n - italic\_k + 1 end\_POSTSUPERSCRIPT italic\_σ start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT and Q¯(𝒙)=𝔼(Q(𝒙))¯𝑄𝒙𝔼𝑄𝒙\bar{Q}(\boldsymbol{x})=\mathbb{E}(Q(\boldsymbol{x}))over¯ start\_ARG italic\_Q end\_ARG ( bold\_italic\_x ) = blackboard\_E ( italic\_Q ( bold\_italic\_x ) ). According to Theorem 2 and Corollary 2 from [GorbanTyukin:NN:2017](#bib.bib16) , for ϑ∈(0,1)italic-ϑ01\vartheta\in(0,1)italic\_ϑ ∈ ( 0 , 1 ) and M𝑀Mitalic\_M satisfying
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| | M≤ϑ3exp((n−k+1)σ042)−1,𝑀italic-ϑ3𝑛𝑘1superscriptsubscript𝜎0421M\leq\frac{\vartheta}{3}\exp\left(\frac{(n-k+1)\sigma\_{0}^{4}}{2}\right)-1,italic\_M ≤ divide start\_ARG italic\_ϑ end\_ARG start\_ARG 3 end\_ARG roman\_exp ( divide start\_ARG ( italic\_n - italic\_k + 1 ) italic\_σ start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT 4 end\_POSTSUPERSCRIPT end\_ARG start\_ARG 2 end\_ARG ) - 1 , | |
with probability p>1−ϑ𝑝1italic-ϑp>1-\varthetaitalic\_p > 1 - italic\_ϑ the following inequalities hold:
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| | 12≤‖Q(𝒙j)−Q¯(𝒙)‖2R02≤32,⟨Q(𝒙i)−Q¯(𝒙)R0,Q(𝒙M+1)−Q¯(𝒙)‖Q(𝒙M+1)−Q¯(𝒙)‖⟩<12formulae-sequence12superscriptnorm𝑄subscript𝒙𝑗¯𝑄𝒙2superscriptsubscript𝑅0232𝑄subscript𝒙𝑖¯𝑄𝒙subscript𝑅0𝑄subscript𝒙𝑀1¯𝑄𝒙norm𝑄subscript𝒙𝑀1¯𝑄𝒙
12\frac{1}{2}\leq\frac{\|Q(\boldsymbol{x}\_{j})-\bar{Q}(\boldsymbol{x})\|^{2}}{R\_{0}^{2}}\leq\frac{3}{2},\ \left\langle\frac{Q(\boldsymbol{x}\_{i})-\bar{Q}(\boldsymbol{x})}{R\_{0}},\frac{Q(\boldsymbol{x}\_{M+1})-\bar{Q}(\boldsymbol{x})}{\|Q(\boldsymbol{x}\_{M+1})-\bar{Q}(\boldsymbol{x})\|}\right\rangle<\frac{1}{\sqrt{2}}divide start\_ARG 1 end\_ARG start\_ARG 2 end\_ARG ≤ divide start\_ARG ∥ italic\_Q ( bold\_italic\_x start\_POSTSUBSCRIPT italic\_j end\_POSTSUBSCRIPT ) - over¯ start\_ARG italic\_Q end\_ARG ( bold\_italic\_x ) ∥ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT end\_ARG start\_ARG italic\_R start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT end\_ARG ≤ divide start\_ARG 3 end\_ARG start\_ARG 2 end\_ARG , ⟨ divide start\_ARG italic\_Q ( bold\_italic\_x start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ) - over¯ start\_ARG italic\_Q end\_ARG ( bold\_italic\_x ) end\_ARG start\_ARG italic\_R start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT end\_ARG , divide start\_ARG italic\_Q ( bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + 1 end\_POSTSUBSCRIPT ) - over¯ start\_ARG italic\_Q end\_ARG ( bold\_italic\_x ) end\_ARG start\_ARG ∥ italic\_Q ( bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + 1 end\_POSTSUBSCRIPT ) - over¯ start\_ARG italic\_Q end\_ARG ( bold\_italic\_x ) ∥ end\_ARG ⟩ < divide start\_ARG 1 end\_ARG start\_ARG square-root start\_ARG 2 end\_ARG end\_ARG | |
for all i,j𝑖𝑗i,jitalic\_i , italic\_j, i≠M+1𝑖𝑀1i\neq M+1italic\_i ≠ italic\_M + 1. This implies that the functional
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| | ℓ0(𝒙)=⟨Q(𝒙)−Q¯(𝒙)R0,Q(𝒙M+1)−Q¯(𝒙)‖Q(𝒙M+1)−Q¯(𝒙)‖⟩−12subscriptℓ0𝒙𝑄𝒙¯𝑄𝒙subscript𝑅0𝑄subscript𝒙𝑀1¯𝑄𝒙norm𝑄subscript𝒙𝑀1¯𝑄𝒙
12\ell\_{0}(\boldsymbol{x})=\left\langle\frac{Q(\boldsymbol{x})-\bar{Q}(\boldsymbol{x})}{R\_{0}},\frac{Q(\boldsymbol{x}\_{M+1})-\bar{Q}(\boldsymbol{x})}{\|Q(\boldsymbol{x}\_{M+1})-\bar{Q}(\boldsymbol{x})\|}\right\rangle-\frac{1}{\sqrt{2}}roman\_ℓ start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT ( bold\_italic\_x ) = ⟨ divide start\_ARG italic\_Q ( bold\_italic\_x ) - over¯ start\_ARG italic\_Q end\_ARG ( bold\_italic\_x ) end\_ARG start\_ARG italic\_R start\_POSTSUBSCRIPT 0 end\_POSTSUBSCRIPT end\_ARG , divide start\_ARG italic\_Q ( bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + 1 end\_POSTSUBSCRIPT ) - over¯ start\_ARG italic\_Q end\_ARG ( bold\_italic\_x ) end\_ARG start\_ARG ∥ italic\_Q ( bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + 1 end\_POSTSUBSCRIPT ) - over¯ start\_ARG italic\_Q end\_ARG ( bold\_italic\_x ) ∥ end\_ARG ⟩ - divide start\_ARG 1 end\_ARG start\_ARG square-root start\_ARG 2 end\_ARG end\_ARG | |
separates ℳℳ\mathcal{M}caligraphic\_M and 𝒴𝒴\mathcal{Y}caligraphic\_Y with probability p>1−ϑ𝑝1italic-ϑp>1-\varthetaitalic\_p > 1 - italic\_ϑ. □□\square□
3 AI Knowledge Transfer Framework
----------------------------------
In this section we show how Theorems [1](#Thmtheorem1 "Theorem 1 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems"), [2](#Thmtheorem2 "Theorem 2 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems") and [3](#Thmtheorem3 "Theorem 3 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems") can be applied for developing a novel one-shot AI knowledge transfer framework. We will focus on the case of transfer knowledge between two AI systems, a teacher AI and a student AI, in which input-output behaviour of the student AI is evaluated by the teacher AI. In this setting, assignment of AI roles, i.e. student or teaching, is beyond the scope of this manuscript. The roles are supposed to be pre-determined or otherwise chosen arbitrarily.
###
3.1 General setup
Consider two AI systems, a student AI, denoted as AIssubscriptAI𝑠\mathrm{AI}\_{s}roman\_AI start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT, and a teacher AI, demoted as AItsubscriptAI𝑡\mathrm{AI}\_{t}roman\_AI start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT. These legacy AI systems process some input signals, produce internal representations of the input and return some outputs. We further assume that some relevant information about the input, internal signals, and outputs of AIssubscriptAI𝑠\mathrm{AI}\_{s}roman\_AI start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT can be combined into a common object, 𝒙𝒙\boldsymbol{x}bold\_italic\_x, representing, but not necessarily defining, the state of AIssubscriptAI𝑠\mathrm{AI}\_{s}roman\_AI start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT. The objects 𝒙𝒙\boldsymbol{x}bold\_italic\_x are assumed to be elements of ℝnsuperscriptℝ𝑛\mathbb{R}^{n}blackboard\_R start\_POSTSUPERSCRIPT italic\_n end\_POSTSUPERSCRIPT.
Over a period of activity system AIssubscriptAI𝑠\mathrm{AI}\_{s}roman\_AI start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT generates a set 𝒮𝒮\mathcal{S}caligraphic\_S of objects 𝒙𝒙\boldsymbol{x}bold\_italic\_x. Exact composition of the set 𝒮𝒮\mathcal{S}caligraphic\_S could depend on a task at hand. For example, if AIssubscriptAI𝑠\mathrm{AI}\_{s}roman\_AI start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT is an image classifier, we may be interested only in a particular subset of AIssubscriptAI𝑠\mathrm{AI}\_{s}roman\_AI start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT input-output data related to images of a certain known class. Relevant inputs and outputs of AIssubscriptAI𝑠\mathrm{AI}\_{s}roman\_AI start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT corresponding to objects in 𝒮𝒮\mathcal{S}caligraphic\_S are then evaluated by the teacher, AItsubscriptAI𝑡\mathrm{AI}\_{t}roman\_AI start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT. If AIssubscriptAI𝑠\mathrm{AI}\_{s}roman\_AI start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT outputs differ to that of AItsubscriptAI𝑡\mathrm{AI}\_{t}roman\_AI start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT for the same input then an error is registered in the system. Objects 𝒙∈𝒮𝒙𝒮\boldsymbol{x}\in\mathcal{S}bold\_italic\_x ∈ caligraphic\_S associated with errors are combined into the set 𝒴𝒴\mathcal{Y}caligraphic\_Y. The procedure gives rise to two disjoint sets:
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| --- | --- | --- |
| | ℳ=𝒮∖𝒴,ℳ={𝒙1,…,𝒙M}formulae-sequenceℳ𝒮𝒴ℳsubscript𝒙1…subscript𝒙𝑀\mathcal{M}=\mathcal{S}\setminus\mathcal{Y},\ \mathcal{M}=\{\boldsymbol{x}\_{1},\dots,\boldsymbol{x}\_{M}\}caligraphic\_M = caligraphic\_S ∖ caligraphic\_Y , caligraphic\_M = { bold\_italic\_x start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT , … , bold\_italic\_x start\_POSTSUBSCRIPT italic\_M end\_POSTSUBSCRIPT } | |
and
| | | |
| --- | --- | --- |
| | 𝒴={𝒙M+1,…,𝒙M+k}.𝒴subscript𝒙𝑀1…subscript𝒙𝑀𝑘\mathcal{Y}=\{\boldsymbol{x}\_{M+1},\dots,\boldsymbol{x}\_{M+k}\}.caligraphic\_Y = { bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + 1 end\_POSTSUBSCRIPT , … , bold\_italic\_x start\_POSTSUBSCRIPT italic\_M + italic\_k end\_POSTSUBSCRIPT } . | |
Figure 4: AI Knowledge transfer diagram. AIs𝐴subscript𝐼𝑠AI\_{s}italic\_A italic\_I start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT produces a set of its state representations, 𝒮𝒮\mathcal{S}caligraphic\_S. The representations are labelled by AIt𝐴subscript𝐼𝑡AI\_{t}italic\_A italic\_I start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT into the set of correct responses, ℳℳ\mathcal{M}caligraphic\_M, and the set of errors, 𝒴𝒴\mathcal{Y}caligraphic\_Y. The student system, AIs𝐴subscript𝐼𝑠AI\_{s}italic\_A italic\_I start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT, is then augmented by an additional “corrector” eliminating these errors.
A diagram schematically representing the process is shown in Fig. [4](#S3.F4 "Figure 4 ‣ 3.1 General setup ‣ 3 AI Knowledge Transfer Framework ‣ Knowledge Transfer Between Artificial Intelligence Systems"). The knowledge transfer task is to “teach” AIssubscriptAI𝑠\mathrm{AI}\_{s}roman\_AI start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT so that with
* a)
AIssubscriptAI𝑠\mathrm{AI}\_{s}roman\_AI start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT does not make such errors
* b)
existing competencies of AIssubscriptAI𝑠\mathrm{AI}\_{s}roman\_AI start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT on the set of inputs corresponding to internal states 𝒙∈ℳ𝒙ℳ\boldsymbol{x}\in\mathcal{M}bold\_italic\_x ∈ caligraphic\_M are retained, and
* c)
knowledge transfer from AItsubscriptAI𝑡\mathrm{AI}\_{t}roman\_AI start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT to AIssubscriptAI𝑠\mathrm{AI}\_{s}roman\_AI start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT is reversible in the sense that AIssubscriptAI𝑠\mathrm{AI}\_{s}roman\_AI start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT can “unlearn” new knowledge by modifying just a fraction of its parameters, if required.
Two algorithms for achieving such transfer knowledge are provided below.
###
3.2 Knowledge Transfer Algorithms
Our first algorithm, Algorithm [1](#alg1 "Algorithm 1 ‣ 3.2 Knowledge Transfer Algorithms ‣ 3 AI Knowledge Transfer Framework ‣ Knowledge Transfer Between Artificial Intelligence Systems"), considers cases when Auxiliary Knowledge Transfer Units, i.e. functional additions to existing student AIssubscriptAI𝑠\mathrm{AI}\_{s}roman\_AI start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT, are single linear functionals. The second algorithm, Algorithm [2](#alg2 "Algorithm 2 ‣ 3.2 Knowledge Transfer Algorithms ‣ 3 AI Knowledge Transfer Framework ‣ Knowledge Transfer Between Artificial Intelligence Systems"), extends Auxiliary Knowledge Transfer Units to two-layer cascades of linear functionals.
Algorithm 1 Single-functional AI Knowledge Transfer
1. 1.
Pre-processing
1. (a)
Centering. For the given set 𝒮𝒮\mathcal{S}caligraphic\_S, determine the set average, 𝒙¯(𝒮)¯𝒙𝒮\bar{\boldsymbol{x}}(\mathcal{S})over¯ start\_ARG bold\_italic\_x end\_ARG ( caligraphic\_S ), and generate sets 𝒮csubscript𝒮𝑐\mathcal{S}\_{c}caligraphic\_S start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT
| | | |
| --- | --- | --- |
| | 𝒮c={𝒙∈ℝn|𝒙=𝝃−𝒙¯(𝒮),𝝃∈𝒮},𝒴c={𝒙∈ℝn|𝒙=𝝃−𝒙¯(𝒮),𝝃∈𝒴}.subscript𝒮𝑐absentconditional-set𝒙superscriptℝ𝑛formulae-sequence𝒙𝝃¯𝒙𝒮𝝃𝒮subscript𝒴𝑐absentconditional-set𝒙superscriptℝ𝑛formulae-sequence𝒙𝝃¯𝒙𝒮𝝃𝒴\begin{array}[]{ll}{\mathcal{S}\_{c}}&=\{\boldsymbol{x}\in\mathbb{R}^{n}\ |\boldsymbol{x}=\boldsymbol{\xi}-\bar{\boldsymbol{x}}(\mathcal{S}),\ \boldsymbol{\xi}\in\mathcal{S}\},\\
{\mathcal{Y}\_{c}}&=\{\boldsymbol{x}\in\mathbb{R}^{n}\ |\boldsymbol{x}=\boldsymbol{\xi}-\bar{\boldsymbol{x}}(\mathcal{S}),\ \boldsymbol{\xi}\in\mathcal{Y}\}.\end{array}start\_ARRAY start\_ROW start\_CELL caligraphic\_S start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT end\_CELL start\_CELL = { bold\_italic\_x ∈ blackboard\_R start\_POSTSUPERSCRIPT italic\_n end\_POSTSUPERSCRIPT | bold\_italic\_x = bold\_italic\_ξ - over¯ start\_ARG bold\_italic\_x end\_ARG ( caligraphic\_S ) , bold\_italic\_ξ ∈ caligraphic\_S } , end\_CELL end\_ROW start\_ROW start\_CELL caligraphic\_Y start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT end\_CELL start\_CELL = { bold\_italic\_x ∈ blackboard\_R start\_POSTSUPERSCRIPT italic\_n end\_POSTSUPERSCRIPT | bold\_italic\_x = bold\_italic\_ξ - over¯ start\_ARG bold\_italic\_x end\_ARG ( caligraphic\_S ) , bold\_italic\_ξ ∈ caligraphic\_Y } . end\_CELL end\_ROW end\_ARRAY | |
2. (b)
Regularization. Determine covariance matrices Cov(𝒮c)Covsubscript𝒮𝑐\mathrm{Cov}(\mathcal{S}\_{c})roman\_Cov ( caligraphic\_S start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT ), Cov(𝒮c∖𝒴c)Covsubscript𝒮𝑐subscript𝒴𝑐\mathrm{Cov}(\mathcal{S}\_{c}\setminus\mathcal{Y}\_{c})roman\_Cov ( caligraphic\_S start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT ) of the sets 𝒮csubscript𝒮𝑐\mathcal{S}\_{c}caligraphic\_S start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT and 𝒮c∖𝒴csubscript𝒮𝑐subscript𝒴𝑐\mathcal{S}\_{c}\setminus\mathcal{Y}\_{c}caligraphic\_S start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT. Let λi(Cov(𝒮c))subscript𝜆𝑖Covsubscript𝒮𝑐\lambda\_{i}(\mathrm{Cov}(\mathcal{S}\_{c}))italic\_λ start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ( roman\_Cov ( caligraphic\_S start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT ) ), λi(Cov(𝒮c∖𝒴c))subscript𝜆𝑖Covsubscript𝒮𝑐subscript𝒴𝑐\lambda\_{i}(\mathrm{Cov}(\mathcal{S}\_{c}\setminus\mathcal{Y}\_{c}))italic\_λ start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ( roman\_Cov ( caligraphic\_S start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT ) ) be their corresponding eigenvalues, and h1,…,hn
subscriptℎ1…subscriptℎ𝑛h\_{1},\dots,h\_{n}italic\_h start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT , … , italic\_h start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT be the eigenvectors of Cov(𝒮c)Covsubscript𝒮𝑐\mathrm{Cov}(\mathcal{S}\_{c})roman\_Cov ( caligraphic\_S start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT ). If some of λi(Cov(𝒮c))subscript𝜆𝑖Covsubscript𝒮𝑐\lambda\_{i}(\mathrm{Cov}(\mathcal{S}\_{c}))italic\_λ start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ( roman\_Cov ( caligraphic\_S start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT ) ), λi(Cov(𝒮c∖𝒴c))subscript𝜆𝑖Covsubscript𝒮𝑐subscript𝒴𝑐\lambda\_{i}(\mathrm{Cov}(\mathcal{S}\_{c}\setminus\mathcal{Y}\_{c}))italic\_λ start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ( roman\_Cov ( caligraphic\_S start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT ) ) are zero or if the ratio
maxi{λi(Σ(𝒮c))}mini{λi(Σ(Sc))}subscript𝑖subscript𝜆𝑖Σsubscript𝒮𝑐subscript𝑖subscript𝜆𝑖Σsubscript𝑆𝑐\frac{\max\_{i}\{\lambda\_{i}(\Sigma(\mathcal{S}\_{c}))\}}{\min\_{i}\{\lambda\_{i}(\Sigma(S\_{c}))\}}divide start\_ARG roman\_max start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT { italic\_λ start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ( roman\_Σ ( caligraphic\_S start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT ) ) } end\_ARG start\_ARG roman\_min start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT { italic\_λ start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ( roman\_Σ ( italic\_S start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT ) ) } end\_ARG
is too large, project 𝒮csubscript𝒮𝑐\mathcal{S}\_{c}caligraphic\_S start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT and 𝒴csubscript𝒴𝑐\mathcal{Y}\_{c}caligraphic\_Y start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT onto appropriately chosen set of m<n𝑚𝑛m<nitalic\_m < italic\_n eigenvectors, hn−m+1,…,hn
subscriptℎ𝑛𝑚1…subscriptℎ𝑛h\_{n-m+1},\dots,h\_{n}italic\_h start\_POSTSUBSCRIPT italic\_n - italic\_m + 1 end\_POSTSUBSCRIPT , … , italic\_h start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT:
| | | |
| --- | --- | --- |
| | 𝒮r={𝒙∈ℝn|𝒙=HT𝝃,𝝃∈𝒮c},𝒴r={𝒙∈ℝn|𝒙=HT𝝃,𝝃∈𝒴c},subscript𝒮𝑟absentconditional-set𝒙superscriptℝ𝑛formulae-sequence𝒙superscript𝐻𝑇𝝃𝝃subscript𝒮𝑐subscript𝒴𝑟absentconditional-set𝒙superscriptℝ𝑛formulae-sequence𝒙superscript𝐻𝑇𝝃𝝃subscript𝒴𝑐\begin{array}[]{ll}{\mathcal{S}\_{r}}&=\{\boldsymbol{x}\in\mathbb{R}^{n}\ |\boldsymbol{x}=H^{T}\boldsymbol{\xi},\ \boldsymbol{\xi}\in\mathcal{S}\_{c}\},\\
{\mathcal{Y}\_{r}}&=\{\boldsymbol{x}\in\mathbb{R}^{n}\ |\boldsymbol{x}=H^{T}\boldsymbol{\xi},\ \boldsymbol{\xi}\in\mathcal{Y}\_{c}\},\end{array}start\_ARRAY start\_ROW start\_CELL caligraphic\_S start\_POSTSUBSCRIPT italic\_r end\_POSTSUBSCRIPT end\_CELL start\_CELL = { bold\_italic\_x ∈ blackboard\_R start\_POSTSUPERSCRIPT italic\_n end\_POSTSUPERSCRIPT | bold\_italic\_x = italic\_H start\_POSTSUPERSCRIPT italic\_T end\_POSTSUPERSCRIPT bold\_italic\_ξ , bold\_italic\_ξ ∈ caligraphic\_S start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT } , end\_CELL end\_ROW start\_ROW start\_CELL caligraphic\_Y start\_POSTSUBSCRIPT italic\_r end\_POSTSUBSCRIPT end\_CELL start\_CELL = { bold\_italic\_x ∈ blackboard\_R start\_POSTSUPERSCRIPT italic\_n end\_POSTSUPERSCRIPT | bold\_italic\_x = italic\_H start\_POSTSUPERSCRIPT italic\_T end\_POSTSUPERSCRIPT bold\_italic\_ξ , bold\_italic\_ξ ∈ caligraphic\_Y start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT } , end\_CELL end\_ROW end\_ARRAY | |
where H=(hn−m+1⋯hn)𝐻subscriptℎ𝑛𝑚1⋯subscriptℎ𝑛H=\left(h\_{n-m+1}\cdots h\_{n}\right)italic\_H = ( italic\_h start\_POSTSUBSCRIPT italic\_n - italic\_m + 1 end\_POSTSUBSCRIPT ⋯ italic\_h start\_POSTSUBSCRIPT italic\_n end\_POSTSUBSCRIPT ) is the matrix comprising of m𝑚mitalic\_m significant principal components of 𝒮csubscript𝒮𝑐\mathcal{S}\_{c}caligraphic\_S start\_POSTSUBSCRIPT italic\_c end\_POSTSUBSCRIPT.
3. (c)
Whitening. For the centered and regularized dataset 𝒮rsubscript𝒮𝑟\mathcal{S}\_{r}caligraphic\_S start\_POSTSUBSCRIPT italic\_r end\_POSTSUBSCRIPT, derive its covariance matrix, Cov(𝒮r)Covsubscript𝒮𝑟\mathrm{Cov}(\mathcal{S}\_{r})roman\_Cov ( caligraphic\_S start\_POSTSUBSCRIPT italic\_r end\_POSTSUBSCRIPT ), and generate whitened sets
| | | |
| --- | --- | --- |
| | 𝒮w={𝒙∈ℝm|𝒙=Cov(𝒮r)−12𝝃,𝝃∈𝒮r},𝒴w={𝒙∈ℝm|𝒙=Cov(𝒮r)−12𝝃,𝝃∈𝒴r},subscript𝒮𝑤absentconditional-set𝒙superscriptℝ𝑚formulae-sequence𝒙Covsuperscriptsubscript𝒮𝑟12𝝃𝝃subscript𝒮𝑟subscript𝒴𝑤absentconditional-set𝒙superscriptℝ𝑚formulae-sequence𝒙Covsuperscriptsubscript𝒮𝑟12𝝃𝝃subscript𝒴𝑟\begin{array}[]{ll}{\mathcal{S}\_{w}}&=\{\boldsymbol{x}\in\mathbb{R}^{m}\ |\boldsymbol{x}=\mathrm{Cov}(\mathcal{S}\_{r})^{-\frac{1}{2}}\boldsymbol{\xi},\ \boldsymbol{\xi}\in\mathcal{S}\_{r}\},\\
{\mathcal{Y}\_{w}}&=\{\boldsymbol{x}\in\mathbb{R}^{m}\ |\boldsymbol{x}=\mathrm{Cov}(\mathcal{S}\_{r})^{-\frac{1}{2}}\boldsymbol{\xi},\ \boldsymbol{\xi}\in\mathcal{Y}\_{r}\},\end{array}start\_ARRAY start\_ROW start\_CELL caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT end\_CELL start\_CELL = { bold\_italic\_x ∈ blackboard\_R start\_POSTSUPERSCRIPT italic\_m end\_POSTSUPERSCRIPT | bold\_italic\_x = roman\_Cov ( caligraphic\_S start\_POSTSUBSCRIPT italic\_r end\_POSTSUBSCRIPT ) start\_POSTSUPERSCRIPT - divide start\_ARG 1 end\_ARG start\_ARG 2 end\_ARG end\_POSTSUPERSCRIPT bold\_italic\_ξ , bold\_italic\_ξ ∈ caligraphic\_S start\_POSTSUBSCRIPT italic\_r end\_POSTSUBSCRIPT } , end\_CELL end\_ROW start\_ROW start\_CELL caligraphic\_Y start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT end\_CELL start\_CELL = { bold\_italic\_x ∈ blackboard\_R start\_POSTSUPERSCRIPT italic\_m end\_POSTSUPERSCRIPT | bold\_italic\_x = roman\_Cov ( caligraphic\_S start\_POSTSUBSCRIPT italic\_r end\_POSTSUBSCRIPT ) start\_POSTSUPERSCRIPT - divide start\_ARG 1 end\_ARG start\_ARG 2 end\_ARG end\_POSTSUPERSCRIPT bold\_italic\_ξ , bold\_italic\_ξ ∈ caligraphic\_Y start\_POSTSUBSCRIPT italic\_r end\_POSTSUBSCRIPT } , end\_CELL end\_ROW end\_ARRAY | |
2. 2.
Knowledge transfer
1. (a)
Clustering. Pick p≥1𝑝1p\geq 1italic\_p ≥ 1, p≤k𝑝𝑘p\leq kitalic\_p ≤ italic\_k, p∈ℕ𝑝ℕp\in\mathbb{N}italic\_p ∈ blackboard\_N, and partition the set 𝒴wsubscript𝒴𝑤\mathcal{Y}\_{w}caligraphic\_Y start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT into p𝑝pitalic\_p clusters 𝒴w,1,…𝒴w,p
subscript𝒴
𝑤1…subscript𝒴
𝑤𝑝\mathcal{Y}\_{w,1},\dots\mathcal{Y}\_{w,p}caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , 1 end\_POSTSUBSCRIPT , … caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_p end\_POSTSUBSCRIPT so that elements of these clusters are, on average, pairwise positively correlated. That is there are β1≥β2>0subscript𝛽1subscript𝛽20\beta\_{1}\geq\beta\_{2}>0italic\_β start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT ≥ italic\_β start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT > 0 such that:
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| --- | --- | --- |
| | β2(|𝒴w,i|−1)≤∑ξ∈𝒴w,i∖{𝒙}⟨𝝃,𝒙⟩≤β1(|𝒴w,i|−1)for any𝒙∈𝒴w,isubscript𝛽2subscript𝒴
𝑤𝑖1subscript𝜉subscript𝒴
𝑤𝑖𝒙
𝝃𝒙subscript𝛽1subscript𝒴
𝑤𝑖1for any𝒙subscript𝒴
𝑤𝑖\beta\_{2}(|\mathcal{Y}\_{w,i}|-1)\leq\sum\_{\xi\in\mathcal{Y}\_{w,i}\setminus\{\boldsymbol{x}\}}\langle\boldsymbol{\xi},\boldsymbol{x}\rangle\leq\beta\_{1}(|\mathcal{Y}\_{w,i}|-1)\ \mbox{for any}\ \boldsymbol{x}\in\mathcal{Y}\_{w,i}italic\_β start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT ( | caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT | - 1 ) ≤ ∑ start\_POSTSUBSCRIPT italic\_ξ ∈ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT ∖ { bold\_italic\_x } end\_POSTSUBSCRIPT ⟨ bold\_italic\_ξ , bold\_italic\_x ⟩ ≤ italic\_β start\_POSTSUBSCRIPT 1 end\_POSTSUBSCRIPT ( | caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT | - 1 ) for any bold\_italic\_x ∈ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT | |
2. (b)
Construction of Auxiliary Knowledge Units. For each cluster 𝒴w,isubscript𝒴
𝑤𝑖\mathcal{Y}\_{w,i}caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT, i=1,…,p𝑖
1…𝑝i=1,\dots,pitalic\_i = 1 , … , italic\_p, construct separating linear functionals ℓisubscriptℓ𝑖\ell\_{i}roman\_ℓ start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT:
| | | |
| --- | --- | --- |
| | ℓi(𝒙)=⟨𝒘i‖𝒘i‖,𝒙⟩−ci,𝒘i=(Cov(𝒮w∖𝒴w,i)+Cov(𝒴w,i))−1(𝒙¯(𝒴w,i)−𝒙¯(𝒮w∖𝒴w,i))subscriptℓ𝑖𝒙absent
subscript𝒘𝑖normsubscript𝒘𝑖𝒙subscript𝑐𝑖subscript𝒘𝑖absentsuperscriptCovsubscript𝒮𝑤subscript𝒴
𝑤𝑖Covsubscript𝒴
𝑤𝑖1¯𝒙subscript𝒴
𝑤𝑖¯𝒙subscript𝒮𝑤subscript𝒴
𝑤𝑖\begin{array}[]{ll}\ell\_{i}(\boldsymbol{x})&=\left\langle\frac{\boldsymbol{w}\_{i}}{\|\boldsymbol{w}\_{i}\|},\boldsymbol{x}\right\rangle-c\_{i},\\
\boldsymbol{w}\_{i}&=\left(\mathrm{Cov}(\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w,i})+\mathrm{Cov}(\mathcal{Y}\_{w,i})\right)^{-1}\left(\bar{\boldsymbol{x}}(\mathcal{Y}\_{w,i})-\bar{\boldsymbol{x}}(\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w,i})\right)\end{array}start\_ARRAY start\_ROW start\_CELL roman\_ℓ start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ( bold\_italic\_x ) end\_CELL start\_CELL = ⟨ divide start\_ARG bold\_italic\_w start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT end\_ARG start\_ARG ∥ bold\_italic\_w start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ∥ end\_ARG , bold\_italic\_x ⟩ - italic\_c start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT , end\_CELL end\_ROW start\_ROW start\_CELL bold\_italic\_w start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT end\_CELL start\_CELL = ( roman\_Cov ( caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT ) + roman\_Cov ( caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT ) ) start\_POSTSUPERSCRIPT - 1 end\_POSTSUPERSCRIPT ( over¯ start\_ARG bold\_italic\_x end\_ARG ( caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT ) - over¯ start\_ARG bold\_italic\_x end\_ARG ( caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT ) ) end\_CELL end\_ROW end\_ARRAY | |
where 𝒙¯(𝒴w,i)¯𝒙subscript𝒴
𝑤𝑖\bar{\boldsymbol{x}}(\mathcal{Y}\_{w,i})over¯ start\_ARG bold\_italic\_x end\_ARG ( caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT ), 𝒙¯(𝒮w∖𝒴w,i)¯𝒙subscript𝒮𝑤subscript𝒴
𝑤𝑖\bar{\boldsymbol{x}}(\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w,i})over¯ start\_ARG bold\_italic\_x end\_ARG ( caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT ) are the averages of 𝒴w,isubscript𝒴
𝑤𝑖\mathcal{Y}\_{w,i}caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT and 𝒮w∖𝒴w,isubscript𝒮𝑤subscript𝒴
𝑤𝑖\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w,i}caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT, respectively, and cisubscript𝑐𝑖c\_{i}italic\_c start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT is chosen as
ci=min𝝃∈𝒴w,i⟨𝒘i‖𝒘i‖,𝝃⟩subscript𝑐𝑖subscript𝝃subscript𝒴
𝑤𝑖subscript𝒘𝑖normsubscript𝒘𝑖𝝃c\_{i}=\min\_{\boldsymbol{\xi}\in\mathcal{Y}\_{w,i}}\left\langle\frac{\boldsymbol{w}\_{i}}{\|\boldsymbol{w}\_{i}\|},\boldsymbol{\xi}\right\rangleitalic\_c start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT = roman\_min start\_POSTSUBSCRIPT bold\_italic\_ξ ∈ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT ⟨ divide start\_ARG bold\_italic\_w start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT end\_ARG start\_ARG ∥ bold\_italic\_w start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ∥ end\_ARG , bold\_italic\_ξ ⟩.
3. (c)
Integration. Integrate Auxiliary Knowledge Units into decision-making pathways of AIssubscriptAI𝑠\mathrm{AI}\_{s}roman\_AI start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT. If, for an 𝒙𝒙\boldsymbol{x}bold\_italic\_x generated by an input to AIssubscriptAI𝑠\mathrm{AI}\_{s}roman\_AI start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT, any of ℓi(𝒙)≥0subscriptℓ𝑖𝒙0\ell\_{i}(\boldsymbol{x})\geq 0roman\_ℓ start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ( bold\_italic\_x ) ≥ 0 then report 𝒙𝒙\boldsymbol{x}bold\_italic\_x accordingly (swap labels, report as an error etc.)
The algorithms comprise of two general stages, pre-processing stage and knowledge transfer stage. The purpose of the pre-processing stage is to regularize and “sphere” the data. This operation brings the setup close to the one considered in statements of Theorems [1](#Thmtheorem1 "Theorem 1 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems"), [2](#Thmtheorem2 "Theorem 2 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems"). The knowledge transfer stage constructs Auxiliary Knowledge Transfer Units in a way that is very similar to the argument presenteed in the proofs of Theorems [1](#Thmtheorem1 "Theorem 1 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems") and [2](#Thmtheorem2 "Theorem 2 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems"). Indeed, if |𝒴w,i|≪|𝒮w∖𝒴w,i|much-less-thansubscript𝒴𝑤𝑖subscript𝒮𝑤subscript𝒴𝑤𝑖|\mathcal{Y}\_{w,i}|\ll|\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w,i}|| caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT | ≪ | caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT | then the term (Cov(𝒮w∖𝒴w,i)+Cov(𝒴w,i))−1superscriptCovsubscript𝒮𝑤subscript𝒴𝑤𝑖Covsubscript𝒴𝑤𝑖1\left(\mathrm{Cov}(\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w,i})+\mathrm{Cov}(\mathcal{Y}\_{w,i})\right)^{-1}( roman\_Cov ( caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT ) + roman\_Cov ( caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT ) ) start\_POSTSUPERSCRIPT - 1 end\_POSTSUPERSCRIPT is close to identity matrix, and the functionals ℓisubscriptℓ𝑖\ell\_{i}roman\_ℓ start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT are good approximations of ([8](#S2.E8 "8 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems")). In this setting, one might expect that performance of the knowledge transfer stage would be also closely aligned with the corresponding estimates ([1](#S2.E1 "1 ‣ Theorem 1 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems")), ([7](#S2.E7 "7 ‣ Theorem 2 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems")).
###### Remark 2
Note that the regularization step in the pre-processing stage ensures that the matrix Cov(𝒮w∖𝒴w,i)+Cov(𝒴w,i)Covsubscript𝒮𝑤subscript𝒴𝑤𝑖Covsubscript𝒴𝑤𝑖\mathrm{Cov}(\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w,i})+\mathrm{Cov}(\mathcal{Y}\_{w,i})roman\_Cov ( caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT ) + roman\_Cov ( caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT ) is non-singular. Indeed, consider
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| | Cov(𝒮w∖𝒴w,i)=1|𝒮w∖𝒴w,i|∑𝒙∈𝒮w∖𝒴w,i(𝒙−𝒙¯(𝒮w∖𝒴w,i))(𝒙−𝒙¯(𝒮w∖𝒴w,i))T=1|𝒮w∖𝒴w,i|(∑𝒙∈𝒮w∖𝒴w(𝒙−𝒙¯(𝒮w∖𝒴w,i))(𝒙−𝒙¯(𝒮w∖𝒴w,i))T+∑𝒙∈𝒴w∖𝒴w,i(𝒙−𝒙¯(𝒮w∖𝒴w,i))(𝒙−𝒙¯(𝒮w∖𝒴w,i))T).\begin{array}[]{ll}&\mathrm{Cov}(\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w,i})=\frac{1}{|\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w,i}|}\sum\_{\boldsymbol{x}\in\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w,i}}(\boldsymbol{x}-\bar{\boldsymbol{x}}(\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w,i}))(\boldsymbol{x}-\bar{\boldsymbol{x}}(\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w,i}))^{T}\\
&=\frac{1}{|\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w,i}|}\left(\sum\_{\boldsymbol{x}\in\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w}}(\boldsymbol{x}-\bar{\boldsymbol{x}}(\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w,i}))(\boldsymbol{x}-\bar{\boldsymbol{x}}(\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w,i}))^{T}\right.+\\
&\left.\sum\_{\boldsymbol{x}\in\mathcal{Y}\_{w}\setminus\mathcal{Y}\_{w,i}}(\boldsymbol{x}-\bar{\boldsymbol{x}}(\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w,i}))(\boldsymbol{x}-\bar{\boldsymbol{x}}(\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w,i}))^{T}\right).\end{array}start\_ARRAY start\_ROW start\_CELL end\_CELL start\_CELL roman\_Cov ( caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT ) = divide start\_ARG 1 end\_ARG start\_ARG | caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT | end\_ARG ∑ start\_POSTSUBSCRIPT bold\_italic\_x ∈ caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT ( bold\_italic\_x - over¯ start\_ARG bold\_italic\_x end\_ARG ( caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT ) ) ( bold\_italic\_x - over¯ start\_ARG bold\_italic\_x end\_ARG ( caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT ) ) start\_POSTSUPERSCRIPT italic\_T end\_POSTSUPERSCRIPT end\_CELL end\_ROW start\_ROW start\_CELL end\_CELL start\_CELL = divide start\_ARG 1 end\_ARG start\_ARG | caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT | end\_ARG ( ∑ start\_POSTSUBSCRIPT bold\_italic\_x ∈ caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT ( bold\_italic\_x - over¯ start\_ARG bold\_italic\_x end\_ARG ( caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT ) ) ( bold\_italic\_x - over¯ start\_ARG bold\_italic\_x end\_ARG ( caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT ) ) start\_POSTSUPERSCRIPT italic\_T end\_POSTSUPERSCRIPT + end\_CELL end\_ROW start\_ROW start\_CELL end\_CELL start\_CELL ∑ start\_POSTSUBSCRIPT bold\_italic\_x ∈ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT ( bold\_italic\_x - over¯ start\_ARG bold\_italic\_x end\_ARG ( caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT ) ) ( bold\_italic\_x - over¯ start\_ARG bold\_italic\_x end\_ARG ( caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT ) ) start\_POSTSUPERSCRIPT italic\_T end\_POSTSUPERSCRIPT ) . end\_CELL end\_ROW end\_ARRAY | |
Denoting d=𝒙¯(𝒮w∖𝒴w,i)−𝒙¯(𝒮w∖𝒴w)𝑑¯𝒙subscript𝒮𝑤subscript𝒴𝑤𝑖¯𝒙subscript𝒮𝑤subscript𝒴𝑤d=\bar{\boldsymbol{x}}(\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w,i})-\bar{\boldsymbol{x}}(\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w})italic\_d = over¯ start\_ARG bold\_italic\_x end\_ARG ( caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT ) - over¯ start\_ARG bold\_italic\_x end\_ARG ( caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ) and rearranging the sum below as
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| | ∑𝒙∈𝒮w∖𝒴w(𝒙−𝒙¯(𝒮w∖𝒴w,i))(𝒙−𝒙¯(𝒮w∖𝒴w,i))T=∑𝒙∈𝒮w∖𝒴w(𝒙−𝒙¯(𝒮w∖𝒴w)+d)(𝒙−𝒙¯(𝒮w∖𝒴w)+d)T=∑𝒙∈𝒮w∖𝒴w(𝒙−𝒙¯(𝒮w∖𝒴w))(𝒙−𝒙¯(𝒮w∖𝒴w))T+2d∑𝒙∈𝒮w∖𝒴w(𝒙−𝒙¯(𝒮w∖𝒴w))T+|𝒙∈𝒮w∖𝒴w|ddT=∑𝒙∈𝒮w∖𝒴w(𝒙−𝒙¯(𝒮w∖𝒴w))(𝒙−𝒙¯(𝒮w∖𝒴w))T+|𝒙∈𝒮w∖𝒴w|ddT\begin{array}[]{ll}&\sum\_{\boldsymbol{x}\in\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w}}(\boldsymbol{x}-\bar{\boldsymbol{x}}(\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w,i}))(\boldsymbol{x}-\bar{\boldsymbol{x}}(\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w,i}))^{T}=\\
&\sum\_{\boldsymbol{x}\in\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w}}(\boldsymbol{x}-\bar{\boldsymbol{x}}(\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w})+d)(\boldsymbol{x}-\bar{\boldsymbol{x}}(\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w})+d)^{T}=\\
&\sum\_{\boldsymbol{x}\in\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w}}(\boldsymbol{x}-\bar{\boldsymbol{x}}(\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w}))(\boldsymbol{x}-\bar{\boldsymbol{x}}(\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w}))^{T}+\\
&2d\sum\_{\boldsymbol{x}\in\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w}}(\boldsymbol{x}-\bar{\boldsymbol{x}}(\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w}))^{T}+|\boldsymbol{x}\in\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w}|dd^{T}\\
&=\sum\_{\boldsymbol{x}\in\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w}}(\boldsymbol{x}-\bar{\boldsymbol{x}}(\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w}))(\boldsymbol{x}-\bar{\boldsymbol{x}}(\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w}))^{T}+|\boldsymbol{x}\in\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w}|dd^{T}\end{array}start\_ARRAY start\_ROW start\_CELL end\_CELL start\_CELL ∑ start\_POSTSUBSCRIPT bold\_italic\_x ∈ caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT ( bold\_italic\_x - over¯ start\_ARG bold\_italic\_x end\_ARG ( caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT ) ) ( bold\_italic\_x - over¯ start\_ARG bold\_italic\_x end\_ARG ( caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT ) ) start\_POSTSUPERSCRIPT italic\_T end\_POSTSUPERSCRIPT = end\_CELL end\_ROW start\_ROW start\_CELL end\_CELL start\_CELL ∑ start\_POSTSUBSCRIPT bold\_italic\_x ∈ caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT ( bold\_italic\_x - over¯ start\_ARG bold\_italic\_x end\_ARG ( caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ) + italic\_d ) ( bold\_italic\_x - over¯ start\_ARG bold\_italic\_x end\_ARG ( caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ) + italic\_d ) start\_POSTSUPERSCRIPT italic\_T end\_POSTSUPERSCRIPT = end\_CELL end\_ROW start\_ROW start\_CELL end\_CELL start\_CELL ∑ start\_POSTSUBSCRIPT bold\_italic\_x ∈ caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT ( bold\_italic\_x - over¯ start\_ARG bold\_italic\_x end\_ARG ( caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ) ) ( bold\_italic\_x - over¯ start\_ARG bold\_italic\_x end\_ARG ( caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ) ) start\_POSTSUPERSCRIPT italic\_T end\_POSTSUPERSCRIPT + end\_CELL end\_ROW start\_ROW start\_CELL end\_CELL start\_CELL 2 italic\_d ∑ start\_POSTSUBSCRIPT bold\_italic\_x ∈ caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT ( bold\_italic\_x - over¯ start\_ARG bold\_italic\_x end\_ARG ( caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ) ) start\_POSTSUPERSCRIPT italic\_T end\_POSTSUPERSCRIPT + | bold\_italic\_x ∈ caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT | italic\_d italic\_d start\_POSTSUPERSCRIPT italic\_T end\_POSTSUPERSCRIPT end\_CELL end\_ROW start\_ROW start\_CELL end\_CELL start\_CELL = ∑ start\_POSTSUBSCRIPT bold\_italic\_x ∈ caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT ( bold\_italic\_x - over¯ start\_ARG bold\_italic\_x end\_ARG ( caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ) ) ( bold\_italic\_x - over¯ start\_ARG bold\_italic\_x end\_ARG ( caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ) ) start\_POSTSUPERSCRIPT italic\_T end\_POSTSUPERSCRIPT + | bold\_italic\_x ∈ caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT | italic\_d italic\_d start\_POSTSUPERSCRIPT italic\_T end\_POSTSUPERSCRIPT end\_CELL end\_ROW end\_ARRAY | |
we obtain that Cov(𝒮w∖𝒴w,i)Covsubscript𝒮𝑤subscript𝒴𝑤𝑖\mathrm{Cov}(\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w,i})roman\_Cov ( caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT ) is non-singular as long as the sum ∑𝒙∈𝒮w∖𝒴w(𝒙−𝒙¯(𝒮w∖𝒴w))(𝒙−𝒙¯(𝒮w∖𝒴w))Tsubscript𝒙subscript𝒮𝑤subscript𝒴𝑤𝒙¯𝒙subscript𝒮𝑤subscript𝒴𝑤superscript𝒙¯𝒙subscript𝒮𝑤subscript𝒴𝑤𝑇\sum\_{\boldsymbol{x}\in\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w}}(\boldsymbol{x}-\bar{\boldsymbol{x}}(\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w}))(\boldsymbol{x}-\bar{\boldsymbol{x}}(\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w}))^{T}∑ start\_POSTSUBSCRIPT bold\_italic\_x ∈ caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT end\_POSTSUBSCRIPT ( bold\_italic\_x - over¯ start\_ARG bold\_italic\_x end\_ARG ( caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ) ) ( bold\_italic\_x - over¯ start\_ARG bold\_italic\_x end\_ARG ( caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ) ) start\_POSTSUPERSCRIPT italic\_T end\_POSTSUPERSCRIPT is non-singular. The latter property, however, is guaranteed by the regularization step in Algorithm [1](#alg1 "Algorithm 1 ‣ 3.2 Knowledge Transfer Algorithms ‣ 3 AI Knowledge Transfer Framework ‣ Knowledge Transfer Between Artificial Intelligence Systems").
###### Remark 3
Clustering at Step 2.a can be achieved by classical k𝑘kitalic\_k-means algorithms [Lloyd:1982](#bib.bib19) or any other method (see e.g. [DudaHart](#bib.bib20) ) that would group elements of 𝒴wsubscript𝒴𝑤\mathcal{Y}\_{w}caligraphic\_Y start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT into clusters according to spatial proximity.
###### Remark 4
Auxiliary Knowledge Transfer Units in Step 2.b of Algorithm [1](#alg1 "Algorithm 1 ‣ 3.2 Knowledge Transfer Algorithms ‣ 3 AI Knowledge Transfer Framework ‣ Knowledge Transfer Between Artificial Intelligence Systems") are derived in accordance with standard Fisher linear discriminant formalism. This, however, need not be the case, and other methods such as e.g. support vector machines [Vapnik2000](#bib.bib21) could be employed for this purpose there. It is worth mentioning, however, that support vector machines might be prone to overfitting [Han:2014](#bib.bib22) and their training often involves iterative procedures such as e.g. sequential quadratic minimization [Platt:1998](#bib.bib23) .
Furthermore, instead of the sets 𝒴w,isubscript𝒴𝑤𝑖\mathcal{Y}\_{w,i}caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT, 𝒮w∖𝒴w,isubscript𝒮𝑤subscript𝒴𝑤𝑖\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w,i}caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT one could use a somewhat more aggressive division: 𝒴w,isubscript𝒴𝑤𝑖\mathcal{Y}\_{w,i}caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT and 𝒮w∖𝒴wsubscript𝒮𝑤subscript𝒴𝑤\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w}caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT, respectively.
Depending on configuration of samples 𝒮𝒮\mathcal{S}caligraphic\_S and 𝒴𝒴\mathcal{Y}caligraphic\_Y, Algorithm [1](#alg1 "Algorithm 1 ‣ 3.2 Knowledge Transfer Algorithms ‣ 3 AI Knowledge Transfer Framework ‣ Knowledge Transfer Between Artificial Intelligence Systems") may occasionally create knowledge transfer units, ℓisubscriptℓ𝑖\ell\_{i}roman\_ℓ start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT, that are “filtering” errors too aggressively. That is some 𝒙∈𝒮w∖𝒴w𝒙subscript𝒮𝑤subscript𝒴𝑤\boldsymbol{x}\in\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w}bold\_italic\_x ∈ caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT may accidentally trigger non-negative response, ℓi(𝒙)≥0subscriptℓ𝑖𝒙0\ell\_{i}(\boldsymbol{x})\geq 0roman\_ℓ start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ( bold\_italic\_x ) ≥ 0, and as a result of this their corresponding inputs to AssubscriptA𝑠\mathrm{A}\_{s}roman\_A start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT could be ignored or mishandled. To mitigate this, one can increase the number of clusters and knowledge transfer units, respectively. This will increase the probability of successful separation and hence alleviate the issue. On the other hand, if increasing the number of knowledge transfer units is not desirable for some reason, then two-functional units could be a feasible remedy. Algorithm [2](#alg2 "Algorithm 2 ‣ 3.2 Knowledge Transfer Algorithms ‣ 3 AI Knowledge Transfer Framework ‣ Knowledge Transfer Between Artificial Intelligence Systems") presents a procedure for such an improved AI Knowledge Transfer.
Algorithm 2 Two-functional AI Knowledge Transfer
1. 1.
Pre-processing. Do as in Step 1 in Algorithm [1](#alg1 "Algorithm 1 ‣ 3.2 Knowledge Transfer Algorithms ‣ 3 AI Knowledge Transfer Framework ‣ Knowledge Transfer Between Artificial Intelligence Systems")
2. 2.
Knowledge Transfer
1. (a)
Clustering. Do as in Step 2.a in Algorithm [1](#alg1 "Algorithm 1 ‣ 3.2 Knowledge Transfer Algorithms ‣ 3 AI Knowledge Transfer Framework ‣ Knowledge Transfer Between Artificial Intelligence Systems")
2. (b)
Construction of Auxiliary Knowledge Units.
1:Do as in Step 2.b in Algorithm [1](#alg1 "Algorithm 1 ‣ 3.2 Knowledge Transfer Algorithms ‣ 3 AI Knowledge Transfer Framework ‣ Knowledge Transfer Between Artificial Intelligence Systems"). At the end of this step first-stage functionals ℓisubscriptℓ𝑖\ell\_{i}roman\_ℓ start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT, i=1,…,p𝑖
1…𝑝i=1,\dots,pitalic\_i = 1 , … , italic\_p will be derived.
2:For each set 𝒴w,isubscript𝒴
𝑤𝑖\mathcal{Y}\_{w,i}caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT, i=1,…,p𝑖
1…𝑝i=1,\dots,pitalic\_i = 1 , … , italic\_p, evaluate the functionals ℓisubscriptℓ𝑖\ell\_{i}roman\_ℓ start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT for all 𝒙∈𝒮w∖𝒴w,i𝒙subscript𝒮𝑤subscript𝒴
𝑤𝑖\boldsymbol{x}\in\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w,i}bold\_italic\_x ∈ caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT and identify elements 𝒙𝒙\boldsymbol{x}bold\_italic\_x such that ℓi(𝒙)≥0subscriptℓ𝑖𝒙0\ell\_{i}(\boldsymbol{x})\geq 0roman\_ℓ start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ( bold\_italic\_x ) ≥ 0 and 𝒙∈𝒮w∖𝒴w𝒙subscript𝒮𝑤subscript𝒴𝑤\boldsymbol{x}\in\mathcal{S}\_{w}\setminus\mathcal{Y}\_{w}bold\_italic\_x ∈ caligraphic\_S start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT ∖ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w end\_POSTSUBSCRIPT (incorrect error assignment). Let 𝒴e,isubscript𝒴
𝑒𝑖\mathcal{Y}\_{e,i}caligraphic\_Y start\_POSTSUBSCRIPT italic\_e , italic\_i end\_POSTSUBSCRIPT be the set containing such elements 𝒙𝒙\boldsymbol{x}bold\_italic\_x.
3:If (there is an i∈{1,…,p}𝑖1…𝑝i\in\{1,\dots,p\}italic\_i ∈ { 1 , … , italic\_p } such that |𝒴e,i|+|𝒴w,i|>msubscript𝒴
𝑒𝑖subscript𝒴
𝑤𝑖𝑚|\mathcal{Y}\_{e,i}|+|\mathcal{Y}\_{w,i}|>m| caligraphic\_Y start\_POSTSUBSCRIPT italic\_e , italic\_i end\_POSTSUBSCRIPT | + | caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT | > italic\_m)
then increment the value of p𝑝pitalic\_p: p←p+1←𝑝𝑝1p\leftarrow p+1italic\_p ← italic\_p + 1, and return to Step 2.a.
4:If (all sets 𝒴e,isubscript𝒴
𝑒𝑖\mathcal{Y}\_{e,i}caligraphic\_Y start\_POSTSUBSCRIPT italic\_e , italic\_i end\_POSTSUBSCRIPT are empty) then proceed to Step 2.c.
5:For each pair of ℓisubscriptℓ𝑖\ell\_{i}roman\_ℓ start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT and 𝒴w,i∪𝒴e,isubscript𝒴
𝑤𝑖subscript𝒴
𝑒𝑖\mathcal{Y}\_{w,i}\cup\mathcal{Y}\_{e,i}caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT ∪ caligraphic\_Y start\_POSTSUBSCRIPT italic\_e , italic\_i end\_POSTSUBSCRIPT with 𝒴e,isubscript𝒴
𝑒𝑖\mathcal{Y}\_{e,i}caligraphic\_Y start\_POSTSUBSCRIPT italic\_e , italic\_i end\_POSTSUBSCRIPT not empty, project orthogonally sets 𝒴w,isubscript𝒴
𝑤𝑖\mathcal{Y}\_{w,i}caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT and 𝒴e,isubscript𝒴
𝑒𝑖\mathcal{Y}\_{e,i}caligraphic\_Y start\_POSTSUBSCRIPT italic\_e , italic\_i end\_POSTSUBSCRIPT onto the hyperplane ℓi(𝒙)=0subscriptℓ𝑖𝒙0\ell\_{i}(\boldsymbol{x})=0roman\_ℓ start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ( bold\_italic\_x ) = 0 and form the sets ℒi(𝒴w,i)subscriptℒ𝑖subscript𝒴
𝑤𝑖\mathcal{L}\_{i}(\mathcal{Y}\_{w,i})caligraphic\_L start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ( caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT ) and ℒi(𝒴e,i)subscriptℒ𝑖subscript𝒴
𝑒𝑖\mathcal{L}\_{i}(\mathcal{Y}\_{e,i})caligraphic\_L start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ( caligraphic\_Y start\_POSTSUBSCRIPT italic\_e , italic\_i end\_POSTSUBSCRIPT ) :
| | | |
| --- | --- | --- |
| | ℒi(𝒴w,i)={𝒙∈ℝm|𝒙=(Im−𝒘i𝒘iT‖𝒘i‖2)𝝃+ci𝒘i‖𝒘i‖,𝝃∈𝒴w,i},ℒi(𝒴e,i)={𝒙∈ℝm|𝒙=(Im−𝒘i𝒘iT‖𝒘i‖2)𝝃+ci𝒘i‖𝒘i‖,𝝃∈𝒴e,i}.subscriptℒ𝑖subscript𝒴
𝑤𝑖absentconditional-set𝒙superscriptℝ𝑚formulae-sequence𝒙subscript𝐼𝑚subscript𝒘𝑖superscriptsubscript𝒘𝑖𝑇superscriptnormsubscript𝒘𝑖2𝝃subscript𝑐𝑖subscript𝒘𝑖normsubscript𝒘𝑖𝝃subscript𝒴
𝑤𝑖subscriptℒ𝑖subscript𝒴
𝑒𝑖absentconditional-set𝒙superscriptℝ𝑚formulae-sequence𝒙subscript𝐼𝑚subscript𝒘𝑖superscriptsubscript𝒘𝑖𝑇superscriptnormsubscript𝒘𝑖2𝝃subscript𝑐𝑖subscript𝒘𝑖normsubscript𝒘𝑖𝝃subscript𝒴
𝑒𝑖\begin{array}[]{ll}\mathcal{L}\_{i}(\mathcal{Y}\_{w,i})&=\left\{\boldsymbol{x}\in\mathbb{R}^{m}\ |\ \boldsymbol{x}=\left(I\_{m}-\frac{\boldsymbol{w}\_{i}\boldsymbol{w}\_{i}^{T}}{\|\boldsymbol{w}\_{i}\|^{2}}\right)\boldsymbol{\xi}+\frac{c\_{i}\boldsymbol{w}\_{i}}{\|\boldsymbol{w}\_{i}\|},\ \boldsymbol{\xi}\in\mathcal{Y}\_{w,i}\right\},\\
\mathcal{L}\_{i}(\mathcal{Y}\_{e,i})&=\left\{\boldsymbol{x}\in\mathbb{R}^{m}\ |\ \boldsymbol{x}=\left(I\_{m}-\frac{\boldsymbol{w}\_{i}\boldsymbol{w}\_{i}^{T}}{\|\boldsymbol{w}\_{i}\|^{2}}\right)\boldsymbol{\xi}+\frac{c\_{i}\boldsymbol{w}\_{i}}{\|\boldsymbol{w}\_{i}\|},\ \boldsymbol{\xi}\in\mathcal{Y}\_{e,i}\right\}.\end{array}start\_ARRAY start\_ROW start\_CELL caligraphic\_L start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ( caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT ) end\_CELL start\_CELL = { bold\_italic\_x ∈ blackboard\_R start\_POSTSUPERSCRIPT italic\_m end\_POSTSUPERSCRIPT | bold\_italic\_x = ( italic\_I start\_POSTSUBSCRIPT italic\_m end\_POSTSUBSCRIPT - divide start\_ARG bold\_italic\_w start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT bold\_italic\_w start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT italic\_T end\_POSTSUPERSCRIPT end\_ARG start\_ARG ∥ bold\_italic\_w start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ∥ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT end\_ARG ) bold\_italic\_ξ + divide start\_ARG italic\_c start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT bold\_italic\_w start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT end\_ARG start\_ARG ∥ bold\_italic\_w start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ∥ end\_ARG , bold\_italic\_ξ ∈ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT } , end\_CELL end\_ROW start\_ROW start\_CELL caligraphic\_L start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ( caligraphic\_Y start\_POSTSUBSCRIPT italic\_e , italic\_i end\_POSTSUBSCRIPT ) end\_CELL start\_CELL = { bold\_italic\_x ∈ blackboard\_R start\_POSTSUPERSCRIPT italic\_m end\_POSTSUPERSCRIPT | bold\_italic\_x = ( italic\_I start\_POSTSUBSCRIPT italic\_m end\_POSTSUBSCRIPT - divide start\_ARG bold\_italic\_w start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT bold\_italic\_w start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT italic\_T end\_POSTSUPERSCRIPT end\_ARG start\_ARG ∥ bold\_italic\_w start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ∥ start\_POSTSUPERSCRIPT 2 end\_POSTSUPERSCRIPT end\_ARG ) bold\_italic\_ξ + divide start\_ARG italic\_c start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT bold\_italic\_w start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT end\_ARG start\_ARG ∥ bold\_italic\_w start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ∥ end\_ARG , bold\_italic\_ξ ∈ caligraphic\_Y start\_POSTSUBSCRIPT italic\_e , italic\_i end\_POSTSUBSCRIPT } . end\_CELL end\_ROW end\_ARRAY | |
6:Construct a linear functional ℓ2,isubscriptℓ
2𝑖\ell\_{2,i}roman\_ℓ start\_POSTSUBSCRIPT 2 , italic\_i end\_POSTSUBSCRIPT separating ℒi(𝒴w,i)subscriptℒ𝑖subscript𝒴
𝑤𝑖\mathcal{L}\_{i}(\mathcal{Y}\_{w,i})caligraphic\_L start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ( caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT ) from ℒi(𝒴e,i)subscriptℒ𝑖subscript𝒴
𝑒𝑖\mathcal{L}\_{i}(\mathcal{Y}\_{e,i})caligraphic\_L start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ( caligraphic\_Y start\_POSTSUBSCRIPT italic\_e , italic\_i end\_POSTSUBSCRIPT ) so that ℓ2,i(𝒙)≥0subscriptℓ
2𝑖𝒙0\ell\_{2,i}(\boldsymbol{x})\geq 0roman\_ℓ start\_POSTSUBSCRIPT 2 , italic\_i end\_POSTSUBSCRIPT ( bold\_italic\_x ) ≥ 0 for all 𝒙∈𝒴w,i𝒙subscript𝒴
𝑤𝑖\boldsymbol{x}\in\mathcal{Y}\_{w,i}bold\_italic\_x ∈ caligraphic\_Y start\_POSTSUBSCRIPT italic\_w , italic\_i end\_POSTSUBSCRIPT and ℓ2,i(𝒙)<0subscriptℓ
2𝑖𝒙0\ell\_{2,i}(\boldsymbol{x})<0roman\_ℓ start\_POSTSUBSCRIPT 2 , italic\_i end\_POSTSUBSCRIPT ( bold\_italic\_x ) < 0 for all 𝒙∈𝒴e,i𝒙subscript𝒴
𝑒𝑖\boldsymbol{x}\in\mathcal{Y}\_{e,i}bold\_italic\_x ∈ caligraphic\_Y start\_POSTSUBSCRIPT italic\_e , italic\_i end\_POSTSUBSCRIPT.
3. (c)
Integration. Integrate Auxiliary Knowledge Units into decision-making pathways of AIssubscriptAI𝑠\mathrm{AI}\_{s}roman\_AI start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT. If, for an 𝒙𝒙\boldsymbol{x}bold\_italic\_x generated by an input to AIssubscriptAI𝑠\mathrm{AI}\_{s}roman\_AI start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT, any of the predicates (ℓi(𝒙)≥0)∧(ℓ2,i(𝒙)≥0)subscriptℓ𝑖𝒙0subscriptℓ
2𝑖𝒙0(\ell\_{i}(\boldsymbol{x})\geq 0)\wedge(\ell\_{2,i}(\boldsymbol{x})\geq 0)( roman\_ℓ start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT ( bold\_italic\_x ) ≥ 0 ) ∧ ( roman\_ℓ start\_POSTSUBSCRIPT 2 , italic\_i end\_POSTSUBSCRIPT ( bold\_italic\_x ) ≥ 0 ) hold true then report 𝒙𝒙\boldsymbol{x}bold\_italic\_x accordingly (swap labels, report as an error etc.).
In what follows we illustrate the approach as well as the application of the proposed Knowledge Transfer algorithms in a relevant problem of a computer vision system design for pedestrian detection in live video streams.
4 Example
----------
Let AIs𝐴subscript𝐼𝑠AI\_{s}italic\_A italic\_I start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT and AIt𝐴subscript𝐼𝑡AI\_{t}italic\_A italic\_I start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT be two systems developed, e.g. for the purposes of pedestrian detection in live video streams. Technological progress in embedded systems and availability of platforms such as e.g. Nvidia Jetson TX2 made hadrware deployment of such AI systems at the edge of computer vision processing pipelines feasible. These AI systems, however, lack computational power to run state-of-the-art large scale object detection solutions such as e.g. ResNet [ResNet](#bib.bib24) in real-time. Here we demonstrate that to compensate for this lack of power, AI Knowledge Transfer can be successfully employed. In particular, we suggest that the edge-based system is “taught” by the state-of-the-art teacher in a non-iterative and near-real time way. Since our building blocks are linear functionals, such learning will not lead to significant computational overheads. At the same time, as we will show later, the proposed AI Knowledge Transfer will result in a major boost to the system’s performance in the conditions of the experiment.
###
4.1 Definition of AIs𝐴subscript𝐼𝑠AI\_{s}italic\_A italic\_I start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT and AIt𝐴subscript𝐼𝑡AI\_{t}italic\_A italic\_I start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT and rationale
In our experiments, the teacher AI, AIt𝐴subscript𝐼𝑡AI\_{t}italic\_A italic\_I start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT, was modeled by a deep Convolutional Network, ResNet 18 [ResNet](#bib.bib24) with circa 11111111M trainable parameters. The network was trained on a “teacher” dataset comprised of 5.25.25.25.2M non-pedestrian (negatives), and 600600600600K pedestrian (positives) images. The student AI, AIs𝐴subscript𝐼𝑠AI\_{s}italic\_A italic\_I start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT, was modelled by a linear classifier with HOG features [Dalal:2005](#bib.bib25) and 2016201620162016 trainable parameters. The values of these parameters were the result of AIs𝐴subscript𝐼𝑠AI\_{s}italic\_A italic\_I start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT training on a “student” dataset, a sub-sample of the “teacher” dataset comprising of 55555555K positives and 130130130130K negatives, respectively. This choice of AIs𝐴subscript𝐼𝑠AI\_{s}italic\_A italic\_I start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT and AIt𝐴subscript𝐼𝑡AI\_{t}italic\_A italic\_I start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT systems enabled us to emulate interaction between edge-based AIs and their more powerful counterparts that could be deployed on larger servers or computational clouds.
Moreover, to make the experiment more realistic, we assumed that internal states of both systems are inaccessible for direct observation. To generate sets 𝒮𝒮\mathcal{S}caligraphic\_S and 𝒴𝒴\mathcal{Y}caligraphic\_Y required in Algorithms [1](#alg1 "Algorithm 1 ‣ 3.2 Knowledge Transfer Algorithms ‣ 3 AI Knowledge Transfer Framework ‣ Knowledge Transfer Between Artificial Intelligence Systems") and [2](#alg2 "Algorithm 2 ‣ 3.2 Knowledge Transfer Algorithms ‣ 3 AI Knowledge Transfer Framework ‣ Knowledge Transfer Between Artificial Intelligence Systems") we augmented system AIs𝐴subscript𝐼𝑠AI\_{s}italic\_A italic\_I start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT with an external generator of HOG features of the same dimension. We assumed, however, that covariance matrices of positives and negatives from the “student” dataset are available for the purposes of knowledge transfer. A diagram representing this setup is shown in Figure [5](#S4.F5 "Figure 5 ‣ 4.1 Definition of 𝐴𝐼_𝑠 and 𝐴𝐼_𝑡 and rationale ‣ 4 Example ‣ Knowledge Transfer Between Artificial Intelligence Systems").
Figure 5: Knowledge transfer diagram between ResNet and HOG-SVM object detectors
A candidate image is evaluated by two systems simultaneously as well as by a HOG features generator. The latter generates 2016201620162016 dimensional vectors of HOGs and stores these vectors in the set 𝒮𝒮\mathcal{S}caligraphic\_S. If outputs of AIs𝐴subscript𝐼𝑠AI\_{s}italic\_A italic\_I start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT and AIt𝐴subscript𝐼𝑡AI\_{t}italic\_A italic\_I start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT do not match the corresponding feature vector is added to the set 𝒴𝒴\mathcal{Y}caligraphic\_Y.
###
4.2 Error types
In this experiment we consider and address two types of errors: false positives (Type I errors) and false negatives (Type II errors). The error types were determined as follows. An error is deemed as false positive if AIs𝐴subscript𝐼𝑠AI\_{s}italic\_A italic\_I start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT reported presence of a correctly sized full-figure image of pedestrian in a given image patch whereas no such object was there. Similarly, an error is deemed as false negative if a pedestrian was present in the given image patch but AIs𝐴subscript𝐼𝑠AI\_{s}italic\_A italic\_I start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT did not report it there.
In our setting, evaluation of an image patch by AIt𝐴subscript𝐼𝑡AI\_{t}italic\_A italic\_I start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT (ResNet) took 0.010.010.010.01 sec on Nvidia K80 which was several orders slower than that of AIs𝐴subscript𝐼𝑠AI\_{s}italic\_A italic\_I start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT (linear HOG-based classifier). Whilst such behavior was expected, this imposed technical limitations on the process of mitigating errors of Type II. Each frame from our testing video produced 400400400400K image patches to test. Evaluation of all these candidates by our chosen AIt𝐴subscript𝐼𝑡AI\_{t}italic\_A italic\_I start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT is prohibitive computationally. To overcome this technical difficulty we tested only a limited subset of image proposals with regards to these error type. To get a computationally viable number of proposals for false negative testing, we increased sensitivity of the HOG-based classifier by lowering its detection threshold from 00 to −0.30.3-0.3- 0.3. This way our linear classifier with lowered threshold acted as a filter letting through more true positives at the expense of large number of false positives. In this operational mode, Knowledge Transfer Unit were tasked to separate true positives from negatives in accordance with object labels supplied by AIt𝐴subscript𝐼𝑡AI\_{t}italic\_A italic\_I start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT.
###
4.3 Datasets
The approach was tested on two benchmark videos: LINTHESCHER sequence [Ess:2008](#bib.bib26) created by ETHZ and comprised of 1208 frames and NOTTINGHAM video [Nottingham](#bib.bib27) containing 435 frames of live footage taken with an action camera. In what follows we will refer to these videos as ETHZ and NOTTINGHAM videos, respectively. ETHZ video contains complete images of 8435 pedestrians, whereas NOTTINGHAM video has 4039 full-figure images of pedestrians.
###
4.4 Results
Performance and application of Algorithms [1](#alg1 "Algorithm 1 ‣ 3.2 Knowledge Transfer Algorithms ‣ 3 AI Knowledge Transfer Framework ‣ Knowledge Transfer Between Artificial Intelligence Systems"), [2](#alg2 "Algorithm 2 ‣ 3.2 Knowledge Transfer Algorithms ‣ 3 AI Knowledge Transfer Framework ‣ Knowledge Transfer Between Artificial Intelligence Systems") for NOTTINGHAM and ETHZ videos are summarized in Fig. [6](#S4.F6 "Figure 6 ‣ 4.4 Results ‣ 4 Example ‣ Knowledge Transfer Between Artificial Intelligence Systems") and [7](#S4.F7 "Figure 7 ‣ 4.4 Results ‣ 4 Example ‣ Knowledge Transfer Between Artificial Intelligence Systems"). Each curves in these figures is produced by varying the values of decision-making threshold in the HOG-based linear classifier. Red circles in Figure [6](#S4.F6 "Figure 6 ‣ 4.4 Results ‣ 4 Example ‣ Knowledge Transfer Between Artificial Intelligence Systems") show true positives as a function of false positives for the original linear classifier based on HOG features. Parameters of the classifier were set in accordance with Fisher linear discriminant formulae. Blue stars correspond to AIs𝐴subscript𝐼𝑠AI\_{s}italic\_A italic\_I start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT after Algorithm [1](#alg1 "Algorithm 1 ‣ 3.2 Knowledge Transfer Algorithms ‣ 3 AI Knowledge Transfer Framework ‣ Knowledge Transfer Between Artificial Intelligence Systems") was applied to mitigate errors of Type I in the system. The value of p𝑝pitalic\_p (number of clusters) in the algorithm was set to be equal to 5555. Green triangles illustrate application of Algorithm [2](#alg2 "Algorithm 2 ‣ 3.2 Knowledge Transfer Algorithms ‣ 3 AI Knowledge Transfer Framework ‣ Knowledge Transfer Between Artificial Intelligence Systems") for the same error type. Here Algorithm [2](#alg2 "Algorithm 2 ‣ 3.2 Knowledge Transfer Algorithms ‣ 3 AI Knowledge Transfer Framework ‣ Knowledge Transfer Between Artificial Intelligence Systems") was slightly modified so that the resulting Knowledge Transfer Unit had only one functional ℓ2subscriptℓ2\ell\_{2}roman\_ℓ start\_POSTSUBSCRIPT 2 end\_POSTSUBSCRIPT. This was due to the low number of errors reaching stage two of the algorithm. Black squares correspond to AIs𝐴subscript𝐼𝑠AI\_{s}italic\_A italic\_I start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT after application of Algorithm [2](#alg2 "Algorithm 2 ‣ 3.2 Knowledge Transfer Algorithms ‣ 3 AI Knowledge Transfer Framework ‣ Knowledge Transfer Between Artificial Intelligence Systems") (error Type I) followed by application of Algorithm [2](#alg2 "Algorithm 2 ‣ 3.2 Knowledge Transfer Algorithms ‣ 3 AI Knowledge Transfer Framework ‣ Knowledge Transfer Between Artificial Intelligence Systems") to mitigate errors of Type II.
Figure 6: True positives as a function of false positives for NOTTINGHAM video.
Figure [7](#S4.F7 "Figure 7 ‣ 4.4 Results ‣ 4 Example ‣ Knowledge Transfer Between Artificial Intelligence Systems") shows performance of the algorithms for ETHZ sequence. Red circles show performance of the original AIs𝐴subscript𝐼𝑠AI\_{s}italic\_A italic\_I start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT, green triangles correspond to AIs𝐴subscript𝐼𝑠AI\_{s}italic\_A italic\_I start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT supplemented with Knowledge Transfer Units derived using Algorithm [2](#alg2 "Algorithm 2 ‣ 3.2 Knowledge Transfer Algorithms ‣ 3 AI Knowledge Transfer Framework ‣ Knowledge Transfer Between Artificial Intelligence Systems") for errors of Type I. Black squares correspond to subsequent application of Algorithm [2](#alg2 "Algorithm 2 ‣ 3.2 Knowledge Transfer Algorithms ‣ 3 AI Knowledge Transfer Framework ‣ Knowledge Transfer Between Artificial Intelligence Systems") dealing with errors of Type II.
Figure 7: True positives as a function of false positives for ETHZ video.
In all these cases, supplementing AIs𝐴subscript𝐼𝑠AI\_{s}italic\_A italic\_I start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT with Knowledge Transfer Units constructed with the help of Algorithms [1](#alg1 "Algorithm 1 ‣ 3.2 Knowledge Transfer Algorithms ‣ 3 AI Knowledge Transfer Framework ‣ Knowledge Transfer Between Artificial Intelligence Systems"), [2](#alg2 "Algorithm 2 ‣ 3.2 Knowledge Transfer Algorithms ‣ 3 AI Knowledge Transfer Framework ‣ Knowledge Transfer Between Artificial Intelligence Systems") for both error types resulted in significant boost to AIs𝐴subscript𝐼𝑠AI\_{s}italic\_A italic\_I start\_POSTSUBSCRIPT italic\_s end\_POSTSUBSCRIPT performance. Observe that in both cases application of Algorithm [2](#alg2 "Algorithm 2 ‣ 3.2 Knowledge Transfer Algorithms ‣ 3 AI Knowledge Transfer Framework ‣ Knowledge Transfer Between Artificial Intelligence Systems") to address errors of Type II has led to noticeable increases of numbers of false positives in the system at the beginning of the curves. Manual inspection of these false positives revealed that these errors are exclusively due mistakes of AIt𝐴subscript𝐼𝑡AI\_{t}italic\_A italic\_I start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT itself. For the sake of illustration, these errors for NOTTINGHAM video are shown in Fig. [8](#S4.F8 "Figure 8 ‣ 4.4 Results ‣ 4 Example ‣ Knowledge Transfer Between Artificial Intelligence Systems"). These errors contain genuine false positives (images 12, 23-27) as well as mismatches by size (e.g. 1-7), and look-alikes (images 8,11,13,15-17).
Figure 8: False Positives induced by the teacher AI, AIt𝐴subscript𝐼𝑡AI\_{t}italic\_A italic\_I start\_POSTSUBSCRIPT italic\_t end\_POSTSUBSCRIPT.
5 Conclusion
-------------
In this work we proposed a framework for instantaneous knowledge transfer between AI systems whose internal state used for decision-making can be described by elements of a high-dimensional vector space. The framework enables development of non-iterative algorithms for knowledge spreading between legacy AI systems with heterogeneous non-identical architectures and varying computing capabilities. Feasibility of the framework was illustrated with an example of knowledge transfer between two AI systems for automated pedestrian detection in video streams.
In the basis of the proposed knowledge transfer framework are separation theorems (Theorem [1](#Thmtheorem1 "Theorem 1 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems") – [3](#Thmtheorem3 "Theorem 3 ‣ 2 Mathematical background ‣ Knowledge Transfer Between Artificial Intelligence Systems")) stating peculiar properties of large but finite random samples in high dimension. According to these results, k<n𝑘𝑛k<nitalic\_k < italic\_n random i.i.d. elements can be separated form M≫nmuch-greater-than𝑀𝑛M\gg nitalic\_M ≫ italic\_n randomly selected elements i.i.d. sampled from the same distribution by few linear functionals, with high probability. The theorems are proved for equidistributions in a ball and in a cube. The results can be trivially generalized to equidistributions in ellipsoids and Gaussian distributions. Generalizations to other meaningful distributions is the subject of our future work.
Acknowledgments
---------------
The work was supported by Innovate UK Technology Strategy Board (Knowledge Transfer Partnership grants KTP009890 and KTP010522). |
82a66d18-1527-4cfa-ac17-c1fa6099569d | trentmkelly/LessWrong-43k | LessWrong | Teaching to Compromise
I was reading interview with Giscard d'Estaing about drafting of European Constitution and a this section stood out:
> The session which was not good was the Youth Convention. It’s bizarre, it’s strange. Firstly, it was not young in spirit. [Laughs] That was what they’d been chosen for. It consisted of squabbles between bodies about holding posts. They spent their time discussing the role they would attribute to one another in the system. And very little came out of it. This made me rather worried, not about the young people of Europe, because there were [only] 105 of them, but about how representative the systems were. Because I said to myself that what was there wasn’t ‘youth’, for youth is much freer, much more imaginative, it takes an interest in two or three things, and if it talks about them, it speaks with feeling. So there was a kind of doubt about whether or not young people were represented by organisational systems.
That came as a surprise but giving it two more seconds of thought, it should hardly be surprising. Young people are much more likely to view world in simplified, black-and-white way. They are more likely to support extreme positions, be it communism, fascism or yet something else. The countries with young populations are more likely to engage in war. Therefore, one should not expect young people to fare too well in an endeavor - such as drafting a constitution - that requires subtle compromises.
That, in turn, made me think about how the art of compromise is taught to children. It's definitely not taught as part of the curriculum. Neither it's clear whether that's even possible. In the past one learned to compromise by having siblings and by having to live with them, sharing the room and sharing to toys. Nowadays, when one child per family is the norm, this learning opportunity doesn't exist any more. Parents aren't kid's equals and so compromising with them doesn't count. At the same time, society getting more wealthy is not conductive to |
2f5f129d-2acf-4d6e-9555-e72813097ae0 | trentmkelly/LessWrong-43k | LessWrong | The Sleeping Beauty Problem and The Doomsday Argument Can Be Explained by Perspective Inconsistency
None |
b266c899-dcd6-4be4-bd82-a457b58c04bf | trentmkelly/LessWrong-43k | LessWrong | Psycho-cybernetics: experimental notes
This post is a series of missives and notes I took while reading a popularization of cybernetics concepts as applied to self-help that was hugely influential in the self help field when first published in 1960. I am unsure if these notes will be of any interest to others. This is not a book review or a summary, but rather my own impressions of the models that the author was trying to build up and the cross connections between those concepts and others.
In general, I wish more people would make posts about books without feeling the need to do boring parts they are uninterested in (summarizing and reviewing) and more just discussing the ideas they found valuable. I think this would lower the friction for such posts, resulting in more of them. I often wind up finding such thoughts and comments about non-fiction works by LWers pretty valuable. I have more of these if people are interested.
Why this book: If you wish to understand the box you live in, investigate records from the time it was being built. The social psychology and cognitive science results that much of the lesswrong memeplex hangs its hat on are subject to an incentive structure whereby surprising results are the ones that are promoted or made more visible. But surprising relative to what? Is there some generic folk psychology template that I am comparing to? This plays some role, but I think I have underestimated the degree to which the defaults are constructs. I wanted to get a sense of how they might have been built, which lead to an investigation of Alfred Korzybski, the first person to utter "the map is not the territory", and the inception of cybernetics as a field of discipline, which also heavily influenced the people and work that later went on at Bell Labs and thus shaped the emergence of the information age.
I found this book interesting in particular because it did not use the standard anecdote-concept format of most self-help (with perhaps 2-8 concepts in an entire book) but instead seemed |
0b6b1a84-0180-49e8-aed9-76cb83aef619 | StampyAI/alignment-research-dataset/blogs | Blogs | just enough spoilers for
just enough spoilers for *a fire upon the deep* to read a yudkowsky fanfic
--------------------------------------------------------------------------
[*The Finale of the Ultimate Meta Mega Crossover*](https://www.fanfiction.net/s/5389450/1/The-Finale-of-the-Ultimate-Meta-Mega-Crossover) is a fanfiction that i think is pretty great, written by eliezer yudkowsky. it has major spoilers for two books: the excellent [*Permutation City* by greg egan](https://en.wikipedia.org/wiki/Permutation_City) which i love and thoroughly recommend, and [*A Fire Upon the Deep* by vernor vinge](https://en.wikipedia.org/wiki/A_Fire_Upon_the_Deep) which i enjoyed.
because:
* i think many would consider that latter book too large a dependency to read the fanfic,
* it doesn't take that many spoilers about it to enjoy the fanfic — whereas it does take a lot of spoilers about *Permutation City* if you haven't read that,
* many people i know have read *Permutation City* but not *A Fire Upon the Deep*,
i'm writing this post where i give just enough spoilers for someone who hasn't read it but *has* read *Permutation City* to enjoy the fanfic.
my general recommendation would be: read *Permutation City* if you haven't, then read this post, then maybe read *A Fire Upon The Deep* if this post has made you interested enough in it, and then go read [yudkowsky's fanfic](https://www.fanfiction.net/s/5389450/1/The-Finale-of-the-Ultimate-Meta-Mega-Crossover).
---
the book's setting is pretty interesting. it's a science-fiction adventure set in our galaxy, with a peculiar limitation: given an information system of a particular level of capability — such as a human mind, a superintelligence, or an advanced computer program — it can only exist above a certain "Zone of Thought", a geographic region of the galaxy. if they move to a lower zone, closer to the center of the galaxy, then they start either being reduced in capability or breaking down altogether.
these levels go, in increasing capability and increasing distance from the center of the galaxy:
* *The Unthinking Depths*, where nothing of much intelligence can exist
* *The Slow Zone*, where basic computers and human minds can function but computers are still not advanced enough to do the computations necessary to do FTL travel and communication
* *The Beyond*, where computers are capable of capable of much more and FTL communication and travel are possible
* *The Transcend* (not pictured in the map below) where superintelligences — called "Powers" in the book — can exist, moslty at peace with each other.
(this map of the galaxy is included at the very start of the book)
at the start of the story, a Power called "The Blight" appears in the Transcend, and starts attacking other superintelligences. the book follows (among others) two characters aboard a ship headed down towards lower zones of thought to look for a way to defeat the Blight.
aboard the ship are notably two humans:
* Ravna Bergnsdot, a fairly normal human
* Pham Nuwen, a human who used to serve a Power called the *Old One* by being its interface to interact with humans. the Old One, just before being killed by the Blight, left in his mind fragments that he can't make sense of yet, but are expected to become useful as time goes.
and that's, i think, about all you need to know about *A Fire Upon The Deep* to go and enjoy [The Finale of the Ultimate Meta Mega Crossover](https://www.fanfiction.net/s/5389450/1/The-Finale-of-the-Ultimate-Meta-Mega-Crossover). |
cba4df46-f511-4254-a5a7-70775363cf58 | trentmkelly/LessWrong-43k | LessWrong | Book review: The Geography of Thought
Book review: The Geography of Thought: How Asians and Westerners Think Differently... and Why, by Richard E. Nisbett.
It is often said that travel is a good way to improve one's understanding of other cultures.
The Geography of Thought discredits that saying, by being full of examples of cultural differences that 99.9% of travelers will overlook.
Here are a few of the insights I got from the book, but I'm pretty sure I wouldn't have gotten from visiting Asia frequently:
There's no Chinese word for individualism - selfish seems to be the closest equivalent.
Infants in the US are often forced to sleep in a separate bed, often in a separate room. That's rather uncommon in Asia. Does this contribute to US individualism? Or is it just a symptom?
There are no Asians in Lake Wobegon. I.e. Asians are rather reluctant to rate themselves as above average.
Westerners want contracts to be unconditionally binding, whereas Asians want contracts to change in response to unexpected contexts.
> Asians are likely to consider justice in the abstract, by-the-book Western sense to be rigid and unfeeling.
> Chinese justice is an art, not a science.
Origins of Western Culture
Those cultural differences provide hints about why science as we know it developed in the West, and not in Asia.
I read Geography of Thought in order to expand my understanding of some ideas in Henrich's WEIRDest People.
Nisbett disagrees somewhat with Henrich about when WEIRD culture arose, writing a fair amount about the Western features of ancient Greek culture.
Nisbett traces some of the east-west differences to the likelihood that the Greeks met more apparent contradiction than did Asians, via trade with other cultures. That led them to devote more attention to logical thought. (Here's an odd claim from Nisbett: ancient Greeks were unwilling to adopt the concept of zero, because "it represented a contradiction").
Nisbett agrees with Henrich that there was some sort of gap between ancient Greek cul |
738c9a16-94cc-4d2c-8937-80fe230c9422 | trentmkelly/LessWrong-43k | LessWrong | Tools versus agents
In his critique of the Singularity Institute, Holden Karnofsky presented a distinction between an AI functioning as a tool versus one functioning as an agent. In his words, a tool AI would
> (1) Calculate which action A would maximize parameter P, based on existing data set D. (2) Summarize this calculation in a user-friendly manner, including what Action A is, what likely intermediate outcomes it would cause, what other actions would result in high values of P, etc.
In contrast, an agent AI would:
> (1) Calculate which action, A, would maximize parameter P, based on existing data set D. (2) Execute Action A.
The idea being that an AI, asked to "prevent human suffering", would come up with two plans:
1. Kill all human.
2. Cure all diseases, make everyone young and immortal.
Then the agent AI would go out and kill everyone, while the tool AI would give us the list and we would pick the second one. In the following, I'll assume the AI is superintelligent, and has no other objectives than what we give it.
Long lists
Of course, we're unlikely to get a clear two element list. More likely we'd get something like:
1. Kill all humans with engineered plagues.
2. Kill all humans with nukes.
3. Kill all humans with nanobots.
4. Kill all humans with...
5. ...
6. ...
7. Lobotomise all humans with engineered plagues.
8. Lobotomise all humans with surgery.
9. Lobotomise all humans with...
10. ...
11. ...
12. Kill some humans, lobotomise others, cure still others.
13. ...
The nice solutions might not even appear on the list. Of course, this is still very worthwhile information! This allows us to go into the tool AI, and rewire it again, so that it gets our meanings more accurately. Maybe after a few iterations, we'll have refined the AIs understanding of what we want, and we'll get a nice implementable solution near the top. Of course, this presupposes that we understand the options, and that it's safe for us to read the list.
Understanding |
b1106d90-1d86-4e8e-b7c1-b113bc3213e8 | trentmkelly/LessWrong-43k | LessWrong | What do coherence arguments actually prove about agentic behavior?
(edit: discussions in the comments section have led me to realize there have been several conversations on LessWrong related to this topic that I did not mention in my original question post.
Since ensuring their visibility is important, I am listing them here: Rohin Shah has explained how consequentialist agents optimizing for universe-histories rather than world-states can display any external behavior whatsoever, Steven Byrnes has explored corrigibility in the framework of consequentialism by arguing poweful agents will optimize for future world-states at least to some extent, Said Achmiz has explained what incomplete preferences look like (1, 2, 3), EJT has formally defined preferential gaps and argued incomplete preferences can be an alignment strategy, John Wentworth has analyzed incomplete preferences through the lens of subagents but has then argued that incomplete preferences imply the existence of dominated strategies, and Sami Petersen has argued Wentworth was wrong by showing how incomplete preferences need not be vulnerable.)
In his first discussion with Richard Ngo during the 2021 MIRI Conversations, Eliezer retrospected and lamented:
> In the end, a lot of what people got out of all that writing I did, was not the deep object-level principles I was trying to point to - they did not really get Bayesianism as thermodynamics, say, they did not become able to see Bayesian structures any time somebody sees a thing and changes their belief. What they got instead was something much more meta and general, a vague spirit of how to reason and argue, because that was what they'd spent a lot of time being exposed to over and over and over again in lots of blog posts.
>
> Maybe there's no way to make somebody understand why corrigibility is "unnatural" except to repeatedly walk them through the task of trying to invent an agent structure that lets you press the shutdown button (without it trying to force you to press the shutdown button), and showing them how |
8e342085-04ab-4d70-917e-4d646ad6f19d | trentmkelly/LessWrong-43k | LessWrong | What are the good rationality films?
I run a weekly sequences-reading meetup with some friends, and I want to add a film-component, where we watch films that have some tie-in to what we've read.
I got to talking with friends about what good rationality films there are. We had some ideas but I wanted to turn it to LessWrong to find out.
So please, submit your rationalist films! Then we can watch and discuss them :-)
Here are the rules for the thread.
1. Each answer should have 1 film.
2. Each answer should explain how the film ties in to rationality.
Optional extra: List some essays in the sequences that the film connects to. Yes, non-sequences posts by other rationalists like Scott Alexander and Robin Hanson are allowed.
Spoilers
If you are including spoilers for the film, use spoiler tags! Put >! at the start of the paragraph to cover the text, and people can hover-over if they want to read it, like so:
This is hidden text! |
50c06475-4828-4317-8af4-9475ea5c1846 | trentmkelly/LessWrong-43k | LessWrong | Ethics and rationality of suicide
I was saddened to learn of the recent death by suicide of Chris Capel, known here as pdf23ds. I didn't know him personally, but I was an occasional reader of his blog. In retrospect, I regret not having ever gotten into contact with him. Obviously, I don't know that I could have prevented his death, but, as one with mental-health issues myself, at least I could have made a friend, and been one to him. Now I feel a sense of disappointment that I'll never get that chance.
Having said that, I must say that I take his arguments here very seriously. I do not consider it to be automatic that every suicide is the "wrong" decision. We can all imagine circumstances under which we would prefer to die than live; and given this, we should also be able to imagine that these kinds of circumstances may vary for different people. And if one is already accepting of euthanasia for incurable physical suffering, it should not be that much of a leap to accept it for incurable psychological suffering as well.
Of course, as Chris acknowledges, this doesn't imply that everyone who is contemplating suicide is actually being rational. People may for instance be severely mistaken about their prospects for improvement, especially while in the midst of acute crisis.(Conceivably, that could even have been his own situation.) Nonetheless, I think many of the usual arguments that people use to show that suicide is "wrong" are bad arguments. For example, consider what is probably the most common argument: that committing suicide will inflict pain upon friends and family. It frankly strikes me as absurd (and grotesquely unempathetic) to suppose that someone for whom life is so painful that they would rather die somehow has an obligation to continue enduring it just in order to spare other people the emotion of grief (which they are inevitably going to have to confront at some point anyway, at least until we conquer all death).
Ironically, society's demonization of suicide and suicidal people ha |
8a94737e-ef63-4588-bb72-ea821ba562e5 | trentmkelly/LessWrong-43k | LessWrong | Chinese Researchers Crack ChatGPT: Replicating OpenAI’s Advanced AI Model
|
14810d5f-9c3f-46c9-b6cf-0d4bef99a0f4 | StampyAI/alignment-research-dataset/lesswrong | LessWrong | Despair about AI progressing too slowly
*Cross-posted from the EA Forum:* [*https://forum.effectivealtruism.org/posts/kGkQtj6vjcrrAjK38/despair-about-ai-progressing-too-slowly*](https://forum.effectivealtruism.org/posts/kGkQtj6vjcrrAjK38/despair-about-ai-progressing-too-slowly)
***Summary:** This is a personal and highly subjective post about my mental journey with the topic of AI over the years and where I am today. My thoughts are somewhat scattered, but if you try, I think you can see the connections. This is only my second post on LessWrong, so please be nice to me.*
***Epistemic status:** While everything written in this post is completely sincere, I have a healthy amount of self-doubt. I’m trying to be upfront about my strong personal biases. I take seriously the idea that even a tiny existential risk is worth taking significant efforts to mitigate, so I’m cautious about saying anything contrary to people who care a lot about AI risk. However, I believe that expressing contrarian or non-consensus views makes discourse healthier and consequently can improve people’s reasoning and their persuasiveness to others. This is ultimately helpful for reducing existential risk even if the mainstream LessWrong view on AI risk is correct.*
### Background
Since around 2007[[1]](#fnkzqnz1upen8), I've taken an interest in AI — both (seemingly) nearer-term narrow applications like self-driving cars and the prospects of superhuman AGI.
I first wrote about AGI on my blog [in 2015](https://medium.com/@strangecosmos/artificial-intelligence-will-be-bigger-than-anything-that-has-ever-ever-happened-7289e1035f9c).
Between 2017 and 2023, I made a lot of money on Tesla because I bet (wrongly) that it would rapidly commercialize full autonomy and the investment ended up returning 10x for reasons almost entirely unrelated to full autonomy.
### Disappointment
"Heartbroken" is not an exaggeration for how I feel about the meagre progress in self-driving cars from 2017 to 2023. The technology truly felt to me to be on the cusp of realization, but it's still a science project.[[2]](#fnxn2ssdui3z)
It might sound strange to talk about disillusionment with AGI in the same year that GPT-4 was released and the world caught LLM fever. Maybe a better word would be *fatigue*. I'm tired of waiting for AGI.
### Depression
The biggest existential risk I personally face is probably clinical depression. I've tried medications, talk therapy, [rTMS](https://www.mayoclinic.org/tests-procedures/transcranial-magnetic-stimulation/about/pac-20384625), [neurofeedback](https://en.wikipedia.org/wiki/Neurofeedback), art therapy, physical exercise, (legal, medicinal) ketamine, and more, but I remain badly depressed.[[3]](#fn1wdtdlt81uy)
From the perspective of my own personal survival, the promise of friendly or aligned superhuman AGI to solve virtually all problems, including curing my depression, feels more appealing than the threat of unfriendly or misaligned AGI feels scary or dangerous. This is especially so because I'm (seemingly) far more sanguine about AI x-risk than the median person who worries about it openly.
### Aging
A more generalizable line of thinking is: by default, I'm going to die of aging and so are all the people I love — barring an even worse misfortune. Aligned AGI would cure aging and, thereby, save my life and the lives of all the people I love. Therefore, there is some urgency to developing AGI.[[4]](#fn56qqkpetdz5)
This perspective ignores future generations, which is admittedly a weakness. However, prioritizing future generations above oneself and one's loved ones is [psychologically hard](https://www.smbc-comics.com/comic/longtermism).[[5]](#fnh7m929qtdm)
### A heterodox view on AI risk
**The standard view is:** we must solve AI alignment before developing AGI. Slowing development would give researchers more time to solve alignment and, therefore, a better chance of solving it before it's too late.
**My heterodox view is:** capabilities research and safety research are not so separable. The closer we get to AGI, the better equipped researchers will be to understand how to do alignment. Slowing down capabilities research also slows down safety research.
This heterodox view is false if [the scaling hypothesis](https://www.lesswrong.com/posts/ED28KSXKc4j8CNoi8/how-would-the-scaling-hypothesis-change-things) — which holds that data and compute are the remaining substantive barriers to AGI, rather than new science — is true. In my understanding, new science is needed for AGI. This includes, but is not limited to, solving [video prediction](https://www.technologyreview.com/2022/06/24/1054817/yann-lecun-bold-new-vision-future-ai-deep-learning-meta/) and [hierarchical planning](https://link.springer.com/referenceworkentry/10.1007/978-0-387-30164-8_363). I think it would be hard to convincingly argue that these are not open problems that need to be solved before AGI is possible. (However, I'm open to changing my mind.)
A somewhat more esoteric idea, advocated by [Jeff Hawkins](https://www.youtube.com/watch?v=Z1KwkpTUbkg), among others, is that AGI will require the creation of a new kind of neural network that more closely resembles human biology. I don't have high conviction in this idea, but I personally find it hard to completely rule out.
On this heterodox view, decelerating AI capabilities research would be a net harm, since it doesn't reduce the downside risk of AGI while delaying the upside potential.
### Biological anchors
Ajeya Cotra's ["Biological Anchors" report](https://www.cold-takes.com/forecasting-transformative-ai-the-biological-anchors-method-in-a-nutshell/) attempts to benchmark the training compute required for AGI (or, technically, "transformative AI") to the compute required for human learning or, in the most conservative case, human evolution. This report is highly speculative and should be viewed with healthy skepticism. That being said, it is perhaps the most thorough and rigorous attempt to date to predict AGI using data from biology.
The weighted average of models used in the report predicts a 50% chance of AGI by around 2050 and a 75% chance of AGI by around 2080.
Chart by [Ajeya Cotra](https://www.lesswrong.com/posts/KrJfoZzpSDpnrv9va/draft-report-on-ai-timelines). Please note that Cotra has [updated her personal AI timelines](https://www.lesswrong.com/posts/AfH2oPHCApdKicM4m/two-year-update-on-my-personal-ai-timelines) since publishing the report.If you take these estimates to be a reasonable guess, then this is a nudge in the direction of thinking that AGI is quite a bit father than, say, the median prediction [on Metaculus](https://www.metaculus.com/questions/5121/date-of-artificial-general-intelligence/) of 2032.
On the standard view that we need lots of time to figure out alignment, this is good news. From the perspective of someone who's impatient for AGI to arrive, this is bad news.
### Final thoughts
The failure of self-driving cars to reach large-scale commercial adoption by now has significantly set back my previous optimism about the pace of AI progress. Conversely, if Tesla (or another company) were to convincingly demonstrate superhuman driving capability, I would see that as a strong indicator that AGI might not be far off.
GPT-4 is extremely impressive and even spiritually profound, but there exist foreseeable challenges to future progress toward AGI, such as video prediction and hierarchical planning.
The "Biological Anchors" approach suggests we might be three to six decades away from having the training compute required for AGI.
Because **1)** I want AGI to cure my depression, **2)** I want AGI to cure aging before I or my loved ones die, **3)** I feel generally sanguine about AGI x-risk relative to (what I perceive to be) the median person who worries about alignment, and **4)** I think for safety research to be useful capabilities research must progress, I am not worried about AGI coming too fast. I despair that it seems to be coming too slow.
1. **[^](#fnrefkzqnz1upen8)**The [DARPA Urban Challenge](https://en.wikipedia.org/wiki/DARPA_Grand_Challenge_(2007)) was in 2007. That was also the year Ray Kurzweil's [first public TED Talk](https://www.youtube.com/watch?v=IfbOyw3CT6A) was published on YouTube.
2. **[^](#fnrefxn2ssdui3z)**As recently as 2022, I was willing to [make bets](https://longbets.org/887/) about full autonomy, but I've grown jaded about the field and more agnostic about the timeline. I no longer feel confident that even by 2037 full autonomy will be commercialized.
3. **[^](#fnref1wdtdlt81uy)**I strongly encourage anyone suffering from depression to try all of the above treatments, since the scientific evidence is good and, anecdotally, I know they've worked for some people. Please get help!
4. **[^](#fnref56qqkpetdz5)**I first heard this point being raised by [Joscha Bach](https://youtu.be/YeXHQts3xYM?si=cSOHp8z6CvrK0zZV&t=7206).
5. **[^](#fnrefh7m929qtdm)**It can be [even harder](https://www.smbc-comics.com/comic/longtermism-2) if you assume the far future will be radically better than the present, even though from a purely altruistic perspective that should encourage you to prioritize future generations even more, since it means those generations will have high net utility. |
3047f10b-f6af-444a-b1ab-83eb2e7a2038 | trentmkelly/LessWrong-43k | LessWrong | Introduction to Modern Dating: Strategic Dating Advice for beginners
Heads up: This is not really a post about rationality. That said, there are few times in your life when you are more prone to biases and emotional overrides than when you engage in dating.
We are emotional creatures above all. Knowing principles of rational thinking and tactics for overcoming biased thinking will not protect you from emotional triggers. That's why we structure our lives strategically to begin with, instead of just improvising.
Practical > Romantic.
As a rationalist, you want to taboo the word romantic altogether.
--
Welcome! This is a unisex guide. Where there is gender specific advice, it is mentioned explicitly.
--
One of my goals in life is to have my existence provide positive net value to humanity - or at least to selected subsets of humanity. Here I wanted to write about something that I have significant expertise in, which is also a vastly underestimated and overlooked topic in the context of human life in general. According to me at least. Yes you got it right from the headline: this is about dating.
This is a beginner-friendly post. Although comprehensive enough, the post is really more of a primer to get you to reflect over your dating life and understand why this is worth your time, rather than a fully fleshed out introduction to all relevant concepts you may wish to consider while optimizing dating.
The primary aim of this post is to make you think rationally about dating and why it matters. The secondary aim is to give you some hints on what you may want to be doing, if your end goal is a committed relationship that makes you more happy and/or more efficient in your life pursuits. The third aim is to make you understand some core principles related to the topic.
Dating matters
Dating matters a lot, both to us personally and to society as a whole. We are social animals. If we are good at dating, then our happiness increases at least while we are occupied with dating, which is in itself valuable. Our life expectancy and g |
43955a29-ceff-436e-98ef-f64db5656f68 | StampyAI/alignment-research-dataset/arxiv | Arxiv | On Learning Intrinsic Rewards for Policy Gradient Methods.
1 Introduction
---------------
One of the challenges facing an agent-designer in formulating a sequential decision making task as a Reinforcement Learning (RL) problem is that of defining a reward function. In some cases a choice of reward function is clear from the designer’s understanding of the task. For example, in board games such as Chess or Go the notion of win/loss/draw comes with the game definition, and in Atari games there is a game score that is part of the game. In other cases there may not be any clear choice of reward function. For example, in domains in which the agent is interacting with humans in the environment and the objective is to maximize human-satisfaction it can be hard to define a reward function. Similarly, when the task objective contains multiple criteria such as minimizing energy consumption and maximizing throughput and minimizing latency, it is not clear how to combine these into a single scalar-valued reward function.
Even when a reward function can be defined, it is not unique in the sense that certain transformations of the reward function, e.g., adding a potential-based reward (Ng et al., [1999](#bib.bib11)), will not change the resulting ordering over agent behaviors. While the choice of potential-based or other (policy) order-preserving reward function used to transform the original reward function does not change what the optimal policy is, it can change for better or for worse the sample (and computational) complexity of the RL agent learning from experience in its environment using the transformed reward function.
Yet another aspect to the challenge of reward-design stems from the observation that in many complex real-world tasks an RL agent is simply not going to learn an optimal policy because of various bounds (or limitations) on the agent-environment interaction (e.g., inadequate memory, representational capacity, computation, training data, etc.). Thus, in addressing the reward-design problem one may want to consider transformations of the task-specifying reward function that change the optimal policy. This is because it could result in the bounded-agent achieving a more desirable (to the agent designer) policy than otherwise. This is often done in the form of shaping reward functions that are less sparse than an original reward function and so lead to faster learning of a good policy even if it in principle changes what the theoretically optimal policy might be (Rajeswaran et al., [2017](#bib.bib15)). Other examples of transforming the reward function to aid learning in RL agents is the use of exploration bonuses, e.g., count-based reward bonuses for agents that encourage experiencing infrequently visited states (Bellemare et al., [2016](#bib.bib2); Ostrovski et al., [2017](#bib.bib12); Tang et al., [2017](#bib.bib23)).
The above challenges make reward-design difficult, error-prone, and typically an iterative process. Reward functions that seem to capture the designer’s objective can sometimes lead to unexpected and undesired behaviors. Phenomena such as reward-hacking (Amodei et al., [2016](#bib.bib1)) illustrate this vividly. There are many formulations and resulting approaches to the problem of reward-design including preference elicitation, inverse RL, intrinsically motivated RL, optimal rewards, potential-based shaping rewards, more general reward shaping, and mechanism design; often the details of the formulation depends on the class of RL domains being addressed. In this paper we build on the optimal rewards problem formulation of Singh et. al. ([2010](#bib.bib19)). We discuss the optimal rewards framework as well as some other approaches for learning intrinsic rewards in Section [2](#S2 "2 Background and Related Work ‣ On Learning Intrinsic Rewards for Policy Gradient Methods").
Our main contribution in this paper is the derivation of a new stochastic-gradient-based method for learning parametric intrinsic rewards that when added to the task-specifying (hereafter extrinsic) rewards can improve the performance of policy-gradient based learning methods for solving RL problems. The policy-gradient updates the policy parameters to optimize the sum of the extrinsic and intrinsic rewards, while simultaneously our method updates the intrinsic reward parameters to optimize the extrinsic rewards achieved by the policy. We evaluate our method on several Atari games with a state of the art A2C (Advantage Actor-Critic) (Mnih et al., [2016](#bib.bib10)) agent as well as on a few Mujoco domains with a similarly state of the art PPO agent and show that learning intrinsic rewards can outperform using just extrinsic reward.
2 Background and Related Work
------------------------------
Optimal rewards and reward design. Our work builds on the Optimal Reward Framework.
Formally, the optimal intrinsic reward for a specific combination of RL agent and environment is defined as the reward which when used by the agent for its learning in its environment maximizes the extrinsic reward. The main intuition is that in practice all RL agents are bounded (computationally, representationally, in terms of data availability, etc.) and the optimal intrinsic reward can help mitigate these bounds. Computing the optimal reward remains a big challenge, of course. The paper introducing the framework used exhaustive search over a space of intrinsic reward functions and thus does not scale. Sorg et al. ([2010](#bib.bib20)) introduced PGRD (Policy Gradient for Reward Design), a scalable algorithm that only works with lookahead-search (UCT) based planning agents (and hence the agent itself is not a learning-based agent; only the reward to use with the fixed planner is learned). It’s insight was that
the intrinsic reward can be treated as a parameter that influences the outcome of the planning process and thus can be trained via gradient ascent as long as the planning process is differentiable (which UCT and related algorithms are). Guo et al. ([2016](#bib.bib6)) extended the scalability of PGRD to high-dimensional image inputs in Atari 2600 games and used the intrinsic reward as a reward bonus to improve the performance of the Monte Carlo Tree Search algorithm using the Atari emulator as a model for the planning. A big open challenge is deriving a sound algorithm for learning intrinsic rewards for learning-based RL agents and showing that it can learn intrinsic rewards fast enough to beneficially influence the online peformance of the learning based RL agent. Our main contribution in this paper is to answer this challenge.
Reward shaping and Auxiliary rewards. Reward shaping (Ng et al., [1999](#bib.bib11)) provides a general answer to what space of reward function modifications do not change the optimal policy, specifically potential-based rewards. Other attempts have been made to design auxiliary rewards to derive policies with desired properties. For example, the UNREAL agent (Jaderberg et al., [2016](#bib.bib7)) used pseudo-reward computed from unsupervised auxiliary tasks to refine its internal representations. In some other works (Bellemare et al., [2016](#bib.bib2); Ostrovski et al., [2017](#bib.bib12); Tang et al., [2017](#bib.bib23)), a pseudo-count based reward bonus was given to the agent to encourage exploration. Pathak et al. ([2017](#bib.bib14)) used self-supervised prediction errors as intrinsic rewards to help the agent explore. In these and other similar examples (Schmidhuber, [2010](#bib.bib16); Stadie et al., [2015](#bib.bib21); Oudeyer & Kaplan, [2009](#bib.bib13)), the agent’s learning performance improves through the reward transformations, but the reward transformations are expert-designed and not learned. The main departure point in this paper is that we learn the parameters of an intrinsic reward function that maps high-dimensional observations and actions to rewards.
Hierarchical RL and meta-learning. Another approach to a form of intrinsic reward is in the work on hierarchical RL. For example, the recent FeUdal Networks (FuNs) (Vezhnevets et al., [2017](#bib.bib24)) is a hierarchical architecture which contains a Manager and a Worker learning at different time scales. The Manager conveys abstract goals to the Worker and the Worker optimizes its policy to maximize the extrinsic reward and the cosine distance to the goal. The Manager optimizes its proposed goals to guide the Worker to learn a better policy in terms of the cumulative extrinsic reward. A large body of work on hierarchical RL also generally involves a higher level module choosing goals for lower level modules. All of this work can be viewed as a special case of creating intrinsic rewards within a multi-module agent architecture. One special aspect of hierarchical-RL work is that these intrinsic rewards are usually associated with goals of achievement, i.e., achieving a specific goal state while in our setting the intrinsic reward functions are general mappings from observation-action pairs to rewards. Another special aspect is that most evaluations of hierarchical RL show a benefit in the transfer setting with typically worse performance on early tasks while the manager is learning and better performance on later tasks once the manager has learned. In our setting we take on the challenge of showing that learning and using intrinsic rewards can help the RL agent perform better while it is learning on a single task. Finally, another difference is that hierarchical RL typically treats the lower-level learner as a black box while we train the intrinsic reward using gradients through the policy module in our architecture.
3 Gradient-Based Learning of Intrinsic Rewards: A Derivation
-------------------------------------------------------------
As noted earlier, the most practical previous work in learning intrinsic rewards using the Optimal Rewards framework was limited to settings where the underlying RL agent was a planning (i.e., needs a model of the environment) agent using lookahead search in some form (e.g, UCT). In this section we derive our algorithm for learning intrinsic rewards for the setting where the underlying RL agent is a learning agent, specifically a policy gradient based learning agent.
###
3.1 Policy Gradient based RL
Here we briefly describe how policy gradient based RL works, and then we will present our method that incorporates it. We assume an episodic, discrete-actions, reinforcement learning setting. Within an episode, the state of the environment at time step t is denoted by st∈S and the action the agent takes from action space A at time step t as at, and the reward at time step t as rt. The agent’s policy, parameterized by θ (for example the weights of a neural network), maps a representation of states to a probability distribution over actions. The value of a policy πθ, denoted J(πθ) or equivalently J(θ), is the expected discounted sum of rewards obtained by the agent when executing actions according to policy πθ, i.e.,
| | | | |
| --- | --- | --- | --- |
| | J(θ)=Est∼T(⋅|st−1,at−1),at∼πθ(⋅|st)[∞∑t=0γtrt], | | (1) |
where T denotes the transition dynamics, and the initial state s0∼μ is chosen from some distribution μ over states. Henceforth, for ease of notation we will write the above quantity as J(θ)=Eθ[∑∞t=0γtrt].
The policy gradient theorem of Sutton et.al. ([2000](#bib.bib22)) shows that the gradient of the value J with respect to the policy parameters θ can be computed as follows: from all time steps t within an episode
| | | | |
| --- | --- | --- | --- |
| | ∇θJ(θ)=Eθ[G(st,at)∇θlogπθ(at|st)], | | (2) |
where G(st,at)=∑∞i=tγi−tri is the return until termination. Note that recent advances such as advantage actor-critic (A2C) learn a critic (Vθ(st)) and use it to reduce the variance of the gradient and bootstrap the value after every n steps. However, we present this simple policy gradient formulation (Eq [2](#S3.E2 "(2) ‣ 3.1 Policy Gradient based RL ‣ 3 Gradient-Based Learning of Intrinsic Rewards: A Derivation ‣ On Learning Intrinsic Rewards for Policy Gradient Methods")) in order to simplify the derivation of our proposed algorithm and aid understanding.
Figure 1: Inside the agent are two modules, a policy function parameterized by θ and an intrinsic reward function parameterized by η. In our experiments the policy function (A2C / PPO) has an associated value function as does the intrinsic reward function (see Section [5.1](#S5.SS1 "5.1 Implementation Details ‣ 5 Mujoco Experiments ‣ On Learning Intrinsic Rewards for Policy Gradient Methods") for details). As shown by the dashed lines, the policy module is trained to optimize the weighted sum of intrinsic and extrinsic rewards while the intrinsic reward module is trained to optimize just the extrinsic rewards.
###
3.2 LIRPG: Learning Intrinsic Rewards for Policy Gradient
The departure point of our approach to reward optimization for policy gradient is to distinguish between the extrinsic reward, rex, that defines the task, and a separate intrinsic reward rin that additively transforms the extrinsic reward and influences learning via policy gradients. It is crucial to note that the ultimate measure of performance we care about improving is the value of the extrinsic rewards achieved by the agent; the intrinsic rewards serve only to influence the change in policy parameters. Figure [1](#S3.F1 "Figure 1 ‣ 3.1 Policy Gradient based RL ‣ 3 Gradient-Based Learning of Intrinsic Rewards: A Derivation ‣ On Learning Intrinsic Rewards for Policy Gradient Methods") shows an abstract representation of our intrinsic reward augmented policy gradient based learning agent.
#### Notation.
We use the following notation throughout.
* [leftmargin=\*]
* θ: policy parameters
* η: intrinsic reward parameters
* rex: extrinsic reward from the environment
* rinη=rinη(s,a): intrinsic reward estimated by η
* Gex(st,at)=∑∞i=tγi−trexi
* Gin(st,at)=∑∞i=tγt−irinη(si,ai)
* Gex+in(st,at)=∑∞i=tγi−t(rexi+λrinη(si,ai))
* Jex=Eθ[∑∞t=0γtrext]
* Jin=Eθ[∑∞t=0γtrinη(st,at)]
* Jex+in=Eθ[∑∞t=0γt(rext+λrinη(st,at)]
* λ: relative weight of intrinsic reward.
#### Algorithm Overview.
An overview of our algorithm, LIRPG, is presented in Algorithm [1](#alg1 "Algorithm 1 ‣ Implementation on A2C and PPO. ‣ 3.2 LIRPG: Learning Intrinsic Rewards for Policy Gradient ‣ 3 Gradient-Based Learning of Intrinsic Rewards: A Derivation ‣ On Learning Intrinsic Rewards for Policy Gradient Methods"). At each iteration of LIRPG, we simultaneously update the policy parameters θ and the intrinsic reward parameters η. More specifically, we first update θ in the direction of the gradient of Jex+in which is the weighted sum of intrinsic and extrinsic rewards. After updating policy parameters, we update η in the direction of the gradient of Jex which is just the extrinsic rewards. Intuitively, the policy is updated to maximize both extrinsic and intrinsic reward, while the intrinsic reward function is updated to maximize only the extrinsic reward. We describe more details of each step below.
#### Updating Policy Paramters (θ).
Given an episode where the behavior is generated according to policy πθ(⋅|⋅), we update the policy parameters using regular policy gradient using the sum of intrinsic and extinsic rewards as the reward:
| | | | | |
| --- | --- | --- | --- | --- |
| | θ′ | =θ+α∇θJex+in(θ) | | (3) |
| | | ∼θ+αGex+in(st,at)∇θlogπθ(at|st), | | (4) |
where Equation [4](#S3.E4 "(4) ‣ Updating Policy Paramters (θ). ‣ 3.2 LIRPG: Learning Intrinsic Rewards for Policy Gradient ‣ 3 Gradient-Based Learning of Intrinsic Rewards: A Derivation ‣ On Learning Intrinsic Rewards for Policy Gradient Methods") is a stochastic gradient update.
#### Updating Intrinsic Reward Parameters (η).
Given an episode and the updated policy parameters θ′, we update intrinsic reward parameters. Intuitively, updating η requires estimating the effect such a change would have on the extrinsic value through the change in the policy parameters. Our key idea is to use the chain rule to compute the gradient as follows:
| | | | |
| --- | --- | --- | --- |
| | ∇ηJex=∇θ′Jex∇ηθ′, | | (5) |
where the first term (∇θ′Jex) sampled as
| | | | |
| --- | --- | --- | --- |
| | ∇θ′Jex∼Gex(st,at)∇θ′logπθ′(at|st) | | (6) |
is an approximate stochastic gradient of the extrinsic value with respect to the updated policy parameters θ′ when the behavior is generated by πθ′, and the second term can be computed as follows:
| | | | | |
| --- | --- | --- | --- | --- |
| | ∇ηθ′ | =∇η(θ+αGex+in(st,at)∇θlogπθ(at|st)) | | (7) |
| | | =∇η(αGex+in(st,at)∇θlogπθ(at|st)) | | (8) |
| | | =∇η(αλGin(st,at)∇θlogπθ(at|st)) | | (9) |
| | | =αλ∞∑i=tγi−t∇ηrinη(si,ai)∇θlogπθ(at|st). | | (10) |
Note that to compute the gradient of the extrinsic value Jex with respect to the intrinsic reward parameters η, we needed a new episode with the updated policy parameters θ′ (cf. Equation [6](#S3.E6 "(6) ‣ Updating Intrinsic Reward Parameters (η). ‣ 3.2 LIRPG: Learning Intrinsic Rewards for Policy Gradient ‣ 3 Gradient-Based Learning of Intrinsic Rewards: A Derivation ‣ On Learning Intrinsic Rewards for Policy Gradient Methods")), thus requiring two episodes per iteration. To improve data efficiency we instead reuse the episode generated by the policy parameters θ at the start of the iteration and correct for the resulting mismatch by replacing the on-policy update in Equation [6](#S3.E6 "(6) ‣ Updating Intrinsic Reward Parameters (η). ‣ 3.2 LIRPG: Learning Intrinsic Rewards for Policy Gradient ‣ 3 Gradient-Based Learning of Intrinsic Rewards: A Derivation ‣ On Learning Intrinsic Rewards for Policy Gradient Methods") with the following off-policy update using importance sampling:
| | | | |
| --- | --- | --- | --- |
| | ∇θ′Jex=Gex(st,at)∇θ′πθ′(at|st)πθ(at|st). | | (11) |
The parameters η are updated using the product of Equations [10](#S3.E10 "(10) ‣ Updating Intrinsic Reward Parameters (η). ‣ 3.2 LIRPG: Learning Intrinsic Rewards for Policy Gradient ‣ 3 Gradient-Based Learning of Intrinsic Rewards: A Derivation ‣ On Learning Intrinsic Rewards for Policy Gradient Methods") and [11](#S3.E11 "(11) ‣ Updating Intrinsic Reward Parameters (η). ‣ 3.2 LIRPG: Learning Intrinsic Rewards for Policy Gradient ‣ 3 Gradient-Based Learning of Intrinsic Rewards: A Derivation ‣ On Learning Intrinsic Rewards for Policy Gradient Methods") with a step-size parameter β; this approximates a stochastic gradient update (cf. Equation [5](#S3.E5 "(5) ‣ Updating Intrinsic Reward Parameters (η). ‣ 3.2 LIRPG: Learning Intrinsic Rewards for Policy Gradient ‣ 3 Gradient-Based Learning of Intrinsic Rewards: A Derivation ‣ On Learning Intrinsic Rewards for Policy Gradient Methods")).
#### Implementation on A2C and PPO.
We described LIRPG using the most basic policy gradient formulation for simplicity. There have been many advances in policy gradient methods that reduce the variance of the gradient and improve the data-efficiency. Our LIRPG algorithm is also compatible with such actor-critic architectures. Specifically, for our experiments on Atari games we used a reasonably state of the art advantage action-critic (A2C) architecture, and for our experiments on Mujoco domains we used a similarly reasonably state of the art proximal policy optimization (PPO) architecture.
1: Input: step-size parameters α and β
2: Init: initialize θ and η with random values
3: repeat
4: Sample a trajectory D={s0,a0,s1,a1,⋯} by interacting with the environment using πθ
5: Approximate ∇θJex+in(θ;D) by Equation [4](#S3.E4 "(4) ‣ Updating Policy Paramters (θ). ‣ 3.2 LIRPG: Learning Intrinsic Rewards for Policy Gradient ‣ 3 Gradient-Based Learning of Intrinsic Rewards: A Derivation ‣ On Learning Intrinsic Rewards for Policy Gradient Methods")
6: Update
7: Approximate ∇θ′Jex(θ′;D) on D by Equation [11](#S3.E11 "(11) ‣ Updating Intrinsic Reward Parameters (η). ‣ 3.2 LIRPG: Learning Intrinsic Rewards for Policy Gradient ‣ 3 Gradient-Based Learning of Intrinsic Rewards: A Derivation ‣ On Learning Intrinsic Rewards for Policy Gradient Methods")
8: Approximate ∇ηθ′ by Equation [10](#S3.E10 "(10) ‣ Updating Intrinsic Reward Parameters (η). ‣ 3.2 LIRPG: Learning Intrinsic Rewards for Policy Gradient ‣ 3 Gradient-Based Learning of Intrinsic Rewards: A Derivation ‣ On Learning Intrinsic Rewards for Policy Gradient Methods")
9: Compute ∇ηJex=∇θ′Jex(θ′;D)∇ηθ′
10: Update η′←η+β∇ηJex
11: until done
Algorithm 1 LIRPG: Learning Intrinsic Reward for Policy Gradient
4 Experiments on Atari Games
-----------------------------
Our overall objective in the following first set of experiments is to evaluate whether augmenting a policy gradient based RL agent with intrinsic rewards learned using our LIRPG algorithm (henceforth, augmented agent in short) improves performance relative to the baseline policy gradient based RL agent that uses just the extrinsic reward (henceforth, baseline agent in short). To this end, we first perform this evaluation on the multiple Atari games from the Arcade Learning Environment (ALE) platform (Bellemare et al., [2013](#bib.bib3)) using the same open-source implementation with exactly the same hyper-parameters of the
the A2C algorithm (Mnih et al., [2016](#bib.bib10)) from OpenAI (Dhariwal et al., [2017](#bib.bib4)) for both our augmented agent as well as the baseline agent. The extrinsic reward used is the game score change as is standard for the work on Atari games. The LIRPG algorithm has two additional parameters relative to the baseline algorithm, the parameter λ that controls how the intrinsic reward is scaled before adding it to the extrinsic reward and the step-size β; we describe how we choose these parameters below in our results.
Note that the policy module inside the agent is really two networks, a policy network and a value function network (that helps estimate Gex+in as required in Equation [4](#S3.E4 "(4) ‣ Updating Policy Paramters (θ). ‣ 3.2 LIRPG: Learning Intrinsic Rewards for Policy Gradient ‣ 3 Gradient-Based Learning of Intrinsic Rewards: A Derivation ‣ On Learning Intrinsic Rewards for Policy Gradient Methods")). Similarly the intrinsic reward module in the agent is also two networks, a reward function network and a value function network (that helps estimate Gex as required in Equation [6](#S3.E6 "(6) ‣ Updating Intrinsic Reward Parameters (η). ‣ 3.2 LIRPG: Learning Intrinsic Rewards for Policy Gradient ‣ 3 Gradient-Based Learning of Intrinsic Rewards: A Derivation ‣ On Learning Intrinsic Rewards for Policy Gradient Methods")).
###
4.1 Implementation Details
Episode Generation. As in Mnih et al. ([2015](#bib.bib9)), each episode starts by doing a no-op action for a random number of steps after restarting the game. The number of no-op steps is sampled from 0 to 30 uniformly. Within an episode, each action chosen is repeated for 4 frames, before selecting the next action. An episode ends when the game is over or the agent loses a life.
Input State Representation. As in (Mnih et al., [2015](#bib.bib9)), we take the maximum value at each pixel from 4 consecutive frames to compress them into one frame which is then rescaled to a 84×84 gray scale image. The input to all four neural networks is the stack of the last 4 gray scale images (thus capturing frame-observations over 16 frames). The extrinsic rewards from the game are clipped to [−1,1].
Details of the two Networks in the Intrinsic Reward Module. The intrinsic reward function is a convolutional neural network (CNN) with 3 convolutional layers and 1 fully connected layer. The first convolutional layer has thirty-two 8×8 filters with stride 4. The second convolutional layer has sixty-four 4×4 filters with stride 2. The third convolutional layer has sixty-four 3×3 filters with stride 1. The fourth layer is a fully connected layer with 512 hidden units. Each hidden layer is followed by a rectifier non-linearity. The output layer has one scalar output for each action. We apply tanh on the outputs to bound the reward for each action in [−1,1].
The value network to estimate Gex has the same architecture as the intrinsic reward network except for the output layer that has a single scalar output without a non-linear activation. These two networks share the parameters of the first four layers.
Figure 2: The x-axis is time steps during learning. The y-axis is the average game score over the last 100 training episodes. The blue curves are for the baseline architecture. The red curves are for our LIRPG based augmented architecture. The dark curves are the average of four runs with different random seeds. The light curves are for the 4 individual runs. The hyperparameters of the intrinsic reward module that were partially-optimized by search for each game are shown in the legend.
Hyperparameter Search: We explored the following values for the intrinsic reward weighting coefficient λ, {0.003,0.005,0.01,0.02,0.03,0.05}. We explored the following values for the term ξ, {0.001,0.01,0.1,1}, that weights the loss from the value function estimates with the loss from the intrinsic reward function (the policy component of the intrinsic reward module).
Details of the two Networks in the Policy Module. The policy module has a similar neural network architecture as the intrinsic reward network described above. The only difference is the non-linear activation function of the output layer which is softmax rather than tanh. The corresponding value network (that estimates Gex+in) shares parameters for the first four layers with the policy network. The output layer separately outputs a single scalar for the value network. Note that the policy module is unchanged from the OpenAI implementation.
HyperParameters for Policy module. We keep the default values of all hyperparameters in the original OpenAI implementation of the A2C-based policy module unchanged for both the augmented and baseline agents111We use 16 actor threads to generate episodes. For each training iteration, each actor acts for 5 time steps. For training the policy, the weighting coefficients of policy-gradient term, value network loss term, and the entropy regularization term in the objective function are 1.0, 0.5, and 0.01. The learning rate α for training the policy is set to 0.0007 at the beginning and anneals to 0 linearly over 50 million steps. The discount factor γ is 0.99 for all experiments..
HyperParameters for Intrinsic Reward module in Augmented Agent. We use RMSProp to optimize the two networks of the intrinsic reward module. The decay factor used for RMSProp is 0.99, and the ϵ is 0.00001.
We do not use momentum. Recall that there are two parameters special to LIRPG. On these the step size β was initialized to 0.0007 and annealed linearly to zero over 50 million time steps for all the experiments reported below. We did a small hyperparameter search for λ for each game (this is described below in the caption of Figure [2](#S4.F2 "Figure 2 ‣ 4.1 Implementation Details ‣ 4 Experiments on Atari Games ‣ On Learning Intrinsic Rewards for Policy Gradient Methods")).
As for the A2C implementation for the policy module we clipped the gradient by norm to 0.5 in the intrinsic reward module.
Other Training Details. The objective function used by A2C is the summation of the policy-gradient term, the value network loss term, and a entropy regularization term. They all contribute to the policy parameters update because the policy network and the value network share parameters in A2C. To compute the gradient of Jex with respect to η as in Equation [6](#S3.E6 "(6) ‣ Updating Intrinsic Reward Parameters (η). ‣ 3.2 LIRPG: Learning Intrinsic Rewards for Policy Gradient ‣ 3 Gradient-Based Learning of Intrinsic Rewards: A Derivation ‣ On Learning Intrinsic Rewards for Policy Gradient Methods"), we only need to take into account the effect of the intrinsic reward on the policy network through the policy-gradient term. Thus, we do a separate computation of just this effect. Note that while this adds to the computational load for the augmented agent relative to the baseline agent, it does not add to the sample complexity.
Figure 3: Intrinsic Reward Variation during an episode. We selected a good run for each game from the runs shown in Figure [2](#S4.F2 "Figure 2 ‣ 4.1 Implementation Details ‣ 4 Experiments on Atari Games ‣ On Learning Intrinsic Rewards for Policy Gradient Methods"), and used the learned intrinsic reward module and the associated policy module for the selected run without any further learning to play the game for 100 thousand steps, i.e. 400 thousand frames, to collect data. For each game/plot the x-axis shows the index of the actions that are available in that game. The y-axis shows the mean and standard deviation of the intrinsic reward associated with each action throughout the episode. The main takeaway is that the learned intrinsic reward is indeed a function of the game state during play.
Figure 4: Frequency of action selection during an episode. We selected a good run for each game from the runs shown in Figure [2](#S4.F2 "Figure 2 ‣ 4.1 Implementation Details ‣ 4 Experiments on Atari Games ‣ On Learning Intrinsic Rewards for Policy Gradient Methods"), and used the learned intrinsic reward module and the associated policy module for the selected run without any further learning to play the game for 100 thousand steps, i.e. 400 thousand frames, to collect data. For each game/plot the x-axis shows the index of the actions that are available in that game. The y-axis shows the probability of each action being selected. The main takeaway is that the learned intrinsic reward does preserve variability in action selection.
###
4.2 Overall Performance
Figure [2](#S4.F2 "Figure 2 ‣ 4.1 Implementation Details ‣ 4 Experiments on Atari Games ‣ On Learning Intrinsic Rewards for Policy Gradient Methods") shows the learning curves on 13 Atari games: Alien, Amidar, Asterix, Atlantis, BeamRider, Breakout, DemonAttack, MsPacman, Qbert, Riverraid, RoadRunner, SpaceInvaders, UpNDown, and Breakout. We picked as many games as our computational resources allowed in which the published performance of the underlying baseline A2C agents was good but where the learning was not so fast in terms of sample complexity so as to leave little room for improvement. Each plot shows multiple curves. We ran each agent for 4 separate runs each for 50 million time steps on each game for both the baseline and augmented agents. The x-axis for each plot is time-steps during learning and the y-axis is the average game score achieved over the last 100 episodes at that time. The 4 light red curves in each plot are the 4 runs for the augmented agent, while the 4 light blue curves are the 4 runs for the baseline agent. The dark red curve in each plot is the average over the 4 learning curves for the augmented/intrinsic agent, while the dark blue curve in each plot is the average over the 4 learning curves for the baseline agent.
From the average (over 4 runs) learning curves in the plots in Figure [2](#S4.F2 "Figure 2 ‣ 4.1 Implementation Details ‣ 4 Experiments on Atari Games ‣ On Learning Intrinsic Rewards for Policy Gradient Methods") we see that the augmented agent outperforms the baseline on 10 out of 13 games. On 3 games, Atlantis, DemonAttack, and RoadRunner, the augmented agent outperforms slightly or is comparable to the baseline.
###
4.3 Analysis of the Learned Intrinsic Reward
An interesting question is whether the learned intrinsic reward function learns a general state-independent bias over actions or whether it is an interesting function of state. To explore this question we used the learned intrinsic reward module and the policy module from the end of a good run (cf. Figure [2](#S4.F2 "Figure 2 ‣ 4.1 Implementation Details ‣ 4 Experiments on Atari Games ‣ On Learning Intrinsic Rewards for Policy Gradient Methods")) for each game with no further learning to collect new data for each game. Figure [3](#S4.F3 "Figure 3 ‣ 4.1 Implementation Details ‣ 4 Experiments on Atari Games ‣ On Learning Intrinsic Rewards for Policy Gradient Methods") shows the variation in intrinsic reward obtained by the agent over 100 thousand steps, i.e. 400 thousand frames. The red bars are show the average intrinsic reward per-step for each action. The black segments show the standard deviation of the intrinsic rewards. As can be seen, for most games the intrinsic reward for most actions varies through the episode, indirectly confirming that the intrinsic reward is learning more than a general state-independent bias over actions. A related view of this effect is in Figure [4](#S4.F4 "Figure 4 ‣ 4.1 Implementation Details ‣ 4 Experiments on Atari Games ‣ On Learning Intrinsic Rewards for Policy Gradient Methods") that shows the frequency of taking each action. We collected data over the 100 thousand setps from the same runs as for Figure [3](#S4.F3 "Figure 3 ‣ 4.1 Implementation Details ‣ 4 Experiments on Atari Games ‣ On Learning Intrinsic Rewards for Policy Gradient Methods"). The red bars are the empirical probabilities of taking each action. By comparing Figure [3](#S4.F3 "Figure 3 ‣ 4.1 Implementation Details ‣ 4 Experiments on Atari Games ‣ On Learning Intrinsic Rewards for Policy Gradient Methods") and Figure [4](#S4.F4 "Figure 4 ‣ 4.1 Implementation Details ‣ 4 Experiments on Atari Games ‣ On Learning Intrinsic Rewards for Policy Gradient Methods"), we see the expected correlation between aggregate intrinsic reward over actions and their selection (through the policy module that trains on the sum of extrinsic and intrinsic reward).
5 Mujoco Experiments
---------------------
Our main objective in the following experiments is to demonstrate that our LIRPG-based algorithm can extend to a different class of domains and a different choice of baseline actor-critic architecture. Specifically, we eplore domains from the Mujoco continuous control benchmark (Duan et al., [2016](#bib.bib5)), and used the open-source implementation of the PPO (Schulman et al., [2017](#bib.bib18)) algorithm from OpenAI (Dhariwal et al., [2017](#bib.bib4)) as our baseline agent. As for the Atari game results above, we kept all hyper-parameters unchanged to default values for the policy module of both baseline and augmented agents. Finally, to make the domains challenging for PPO and thereby allow room for improvement through the use of intrinsic rewards, used the delayed versions of the Mujoco domains, where the reward is made sparse by accumulating the reward for 20 time steps before providing it to the agent.
###
5.1 Implementation Details
Delayed Mujoco benchmark. We evaluated 5 environments from the Mujoco benchmark, i.e. Hopper, HalfCheetah, Walker2d, Ant, and Humanoid. As noted above, to create a more-challenging sparse-reward setting we accumulated rewards for 20 steps (or until the end of the episode, whichever comes earlier) before giving it to the agent. We trained the basline and augments agents for 1 million steps on each environment.
Details of the two Networks in the Policy Module. Note that the policy module is unchanged from the OpenAI implementation; we provide details for completeness. The policy network is a MLP with 2 hidden layers, too. The input to the policy network is the observation. The first two layer are fully connected layers with 64 hidden units. Each hidden layer is followed by a tanh non-linearity. The output layer outputs a vector with the size of the dimension of the action space with no non-linearity applied to the output units. Gaussian noise is added to the output of the policy network to encourage exploration. The variance of the Gaussian noise was a input-independent parameter which was also trained by gradient descent. The corresponding value network (that estimates Gex+in) has a similar architecture with the policy network. The only difference is that that output layer outputs a single scalar without any non-linear activation. These two networks do not share any parameters.
Details of the two Networks in the Intrinsic Reward Module. The intrinsic reward function networks are quite similar to the two networks in the policy module. Each network is a multi-layer perceptron (MLP) with 2 hidden layers. We concatenated the observation vector and the action vector as the input to the intrinsic reward network. The first two layer are fully connected layers with 64 hidden units. Each hidden layer is followed by a tanh non-linearity. The output layer has one scalar output. We apply tanh on the output to bound the intrinsic reward to [−1,1]. The value network to estimate Gex has the same architecture as the intrinsic reward network except for the output layer that has a single scalar output without a non-linear activation. These two networks do not share any parameters.
HyperParameters for Policy Module We keep the default values of all hyperparameters in the original OpenAI implementation of PPO unchanged for both the augmented and baseline agents222For each training iteration, the agent interacts with the environment for 2048 steps. The learning rate α for training the policy is set to 0.0003 at the beginning and was fixed over training. We used a batch size of 32 and swept over the 2048 data points for 10 epochs before the next sequence of interaction. The weight multiple the extrinsic reThe discount factor γ is 0.99 for all experiments..
Figure 5: The x-axis is time steps during learning. The y-axis is the average reward over the last 100 training episodes. The blue curves are for the baseline architecture. The red curves are for our LIRPG based augmented architecture. The dark curves are the average of 5 runs with different random seeds. The shaded area shows the standard deviations of 5 runs.
HyperParameters for Intrinsic Reward Module We use Adam (Kingma & Ba, [2014](#bib.bib8)) to optimize the two networks of the intrinsic reward module. The step size β was initialized to 0.0001 and was fixed over 1 million time steps for all the experiments reported below. The mixing coefficient λ was fixed to 1.0 and instead we multiplied the extrinsic reward by 0.01 cross all 5 environments.
The PPO implementation clips the gradient by norm to 0.5. We keep this part unchanged for the policy network and clip the gradients by the same norm for the reward network. We used generalized advantage estimate (GAE) (Schulman et al., [2015](#bib.bib17)) for both training the reward network and the policy network. The weighting factor for GAE was 0.95.
Other Training Details. The objective function used by PPO is the summation of the policy-gradient term, the value network loss term, and a entropy regularization term. They all contribute to the policy parameters update because the policy network and the value network share parameters in PPO. To compute the gradient of Jex with respect to η as in Equation [6](#S3.E6 "(6) ‣ Updating Intrinsic Reward Parameters (η). ‣ 3.2 LIRPG: Learning Intrinsic Rewards for Policy Gradient ‣ 3 Gradient-Based Learning of Intrinsic Rewards: A Derivation ‣ On Learning Intrinsic Rewards for Policy Gradient Methods"), we only need to take into account the effect of the intrinsic reward on the policy network through the policy-gradient term. Thus, we do a separate computation of just this effect. Note that while this adds to the computational load for the augmented agent relative to the baseline agent, it does not add to the sample complexity.
Our results comparing the use of learning intrinsic reward with using just extrinsic reward are shown in Figure [5](#S5.F5 "Figure 5 ‣ 5.1 Implementation Details ‣ 5 Mujoco Experiments ‣ On Learning Intrinsic Rewards for Policy Gradient Methods"). As can be seen, in 4 out of 5 domains learning intrinsic rewards significantly improves the performance of PPO, while in one game (Ant) we got a degradation of performance. It is worth noting that this improvement in performance came about despite the 20-step delay in receiving rewards in the above Mujoco domains. In future work we will explore how this ability degrades with increasing sparsity of reward.
6 Discussion and Conclusion
----------------------------
Our experiments on using LIRPG with A2C on multiple Atari games showed that it helped improve learning performance in 10 out of 13 games. Similarly using LIRPG with PPO on multiple Mujoco domains showed that it helped improve learning performance in 4 out 5 domains. Note that we used the same A2C / PPO architecture and hyperparameters in both our augmented and baseline agents. While more empirical work needs to be done to either make intrinsic reward learning more robust or to understand when it helps and when it does not, we believe our results show promise for the central idea of learning intrinsic rewards in complex RL domains.
In summary, we derived a novel practical algorithm, LIRPG, for learning intrinsic reward functions in problems with high-dimensional observations for use with policy gradient based RL agents. This is the first such algorithm to the best of our knowledge. Our empirical results show promise in using intrinsic reward function learning as a kind of meta-learning to improve the performance of modern policy gradient architectures like A2C.
Acknowledgments. We thank Richard Lewis for past conversations on optimal rewards.
This work was supported by NSF grant IIS-1526059. Any opinions, findings, conclusions, or recommendations expressed here are those of the authors and do not necessarily reflect the views of the sponsor. |
598debbe-2824-4b10-9b61-b9cd6aff185f | trentmkelly/LessWrong-43k | LessWrong | What Would it Take to "Prove" a Speculative Cause?
Follow up to: Why I'm Skeptical About Unproven Causes (And You Should Be Too)
-
My previous essay Why I'm Skeptical About Unproven Causes (And You Should Be Too) generated a lot of discussion here and on the Effective Altruist blog. Some related questions that came up a lot was: what does it take to prove a cause? What separates "proven" from "speculative" causes? And how do you get a "speculative" cause to move into the "proven" column? I've decided that this discussion is important enough that it merits a bit of elaboration at length, so I'm going to do that in this essay.
Proven Cause vs. Speculative Cause
My prime example of proven causes are GiveWell's top charities. These organizations -- The Against Malaria Foundation (AMF), GiveDirectly, and Schistosomiasis Control Initiative (SCI) -- are rolling out programs that have been the target of significant scientific scrutiny. For example, delivering long-lasting insecticide-treated anti-malaria nets (what AMF does) has been studied by 23 different randomized, controlled trials (RCTs). GiveWell has also published thorough reviews of all three organizations (see reviews for AMF, GiveDirectly, and SCI).
On the other hand, a speculative cause is a cause where the case is made entirely by intuition and speculation, with zero scientific study. For some of these causes, scientific study may even be impossible.
Now, I think 23 RCTs is a very high burden to meet. Instead, we should recognize that being "proven" is not a binary yes or no, but rather a sliding scale. Even AMF isn't proven -- there still are some areas of concern or potential weaknesses in the case for AMF. Likewise, other organizations working in the area, like Nothing But Nets, also are nearly as proven, but don't have key elements of transparency and track record to make myself confident enough. And AMF is a lot more proven that GiveDirectly, which is potentially more proven than SCI given recent developments in deworming research.
|
dd07470d-4669-4e3d-86f9-01716d3d586f | StampyAI/alignment-research-dataset/arxiv | Arxiv | Universal Planning Networks
1 Introduction
---------------
| | |
| --- | --- |
| An overview of the UPN, which embeds a gradient descent planner (GDP) in the action-selection process. We demonstrate transfer to different, harder control tasks, including morphological (yellow point robot to ant) and topological (3-link to 7-link reacher) variants, as shown above.
(a) Universal Planning Network (UPN)
| An overview of the UPN, which embeds a gradient descent planner (GDP) in the action-selection process. We demonstrate transfer to different, harder control tasks, including morphological (yellow point robot to ant) and topological (3-link to 7-link reacher) variants, as shown above.
(b) Leveraging learned latent representations
|
Figure 1: An overview of the UPN, which embeds a gradient descent planner (GDP) in the action-selection process. We demonstrate transfer to different, harder control tasks, including morphological (yellow point robot to ant) and topological (3-link to 7-link reacher) variants, as shown above.
Learning visuomotor policies is a central pursuit in building machines capable of performing complex skills in the variety of unstructured and dynamic environments seen in the real world (Levine et al., [2016](#bib.bib32); Pinto et al., [2016](#bib.bib42)). A key challenge in learning such policies lies in acquiring representations of the visual environment and its dynamics that are suitable for control. This challenge arises both in the construction of the policy itself and in the specification of the task. Extrinsic and perfect reward signals are typically not available for real world reinforcement learning and users must manually specify tasks via hand-crafted rewards with hand-crafted representations. To automate this process, some prior methods have proposed to specify tasks by providing an image of the goal scene (Deguchi & Takahashi, [1999](#bib.bib12); Watter et al., [2015](#bib.bib61); Finn et al., [2016b](#bib.bib18)). However, a reward that measures success based on matching the raw pixels of the goal image is far from ideal: such a reward is both uninformative and overconstrained, since matching all pixels is usually not required for succeeding in tasks. If we can automatically identify the right representation, we can both accelerate the policy learning process and simplify the specification of tasks via goal images. Prior work in visual representation learning for planning and control has relied predominantly on unsupervised or self-supervised objectives (Watter et al., [2015](#bib.bib61); Finn et al., [2016b](#bib.bib18)), which in principle only provide an indirect connection to the utility of the representation for the underlying control problem. Effective representation learning for planning and control remains an open problem.
In this work, instead of learning from unsupervised or auxiliary objectives and expecting that useful representations should emerge, we directly optimize for plannable representations: learning representations such that gradient-based planning
is successful with respect to the goal-directed task. To that end, we propose universal planning networks (UPN), a neural network architecture that can be trained to acquire a plannable representation. By embedding a differentiable planning computation inside the
policy, our method enables joint training of the planner and its underlying latent encoder and forward dynamics representations. An outer imitation learning objective ensures that the learned representations are directly optimized for successful gradient-based planning on a set of training demonstrations. However, in principle, the architecture could also be trained with other policy optimization techniques such as those from reinforcement learning. An overview is provided in Figure [1(a)](#S1.F1.sf1 "(a) ‣ Figure 1 ‣ 1 Introduction ‣ Universal Planning Networks").
We demonstrate that the representations learned by UPN not only support gradient-based trajectory optimization for successful visual imitation, but in fact acquire a meaningful encoding of state, which can be used as a metric for task-specific latent distance to a goal. We find that we can reuse this representation to specify latent distance-based rewards to reach new target states via standard model-free reinforcement learning, resulting in substantially more effective learning when using image targets. These properties are naturally induced by the agent’s reliance on the minimization of the latent distance between its predicted terminal state and goal state throughout the planning process. By learning plannable representations, the UPN learns an optimizable latent distance metric. Our findings are based on a new suite of challenging vision-based simulated robot control tasks that involve planning.
At a high-level, our approach is a goal-conditioned policy architecture that leverages a gradient-based planning computation in its action-selection process. While the architecture is agnostic to the objective function in the outer loop, we will focus on the imitation learning setting. From the perspective of representation learning, our method provides a way to learn more effective representations suitable for specifying perceptual reward functions, which can then be used, for example, with a model-free reinforcement learner. In terms of meta-learning, our architecture can be seen as learning a planning computation by learning representations that are in some sense traversible by gradient descent trajectory optimization for satisfying the outer meta-objective.
In extensive experiments, we show that (1) UPNs learn effective visual goal-directed policies more efficiently (that is, with less data) than traditional imitation learners; (2) the latent representations induced by optimizing for successful planning can be leveraged to transfer task-related semantics to other agents for more challenging tasks through goal-conditioned reward functions, which to our knowledge has previously not been demonstrated; and (3) the learned planning computation improves when allowed more updates at test-time, even in scenarios of less data, providing encouraging evidence of successful meta-learning for planning.
2 Universal Planning Networks
------------------------------
Figure 2: An overview of the proposed method. Given an initial ot and a goal og, the GDP (gradient descent planner) uses gradient descent to optimize a plan to reach the goal observation with a sequence of actions in a latent space represented by fϕ. This planning process forms one large computation graph, chaining together the sub-graphs of each iteration of planning. The learning signal is derived from the (outer) imitation loss and the gradient is back-propagated through the entire planning computation graph. The blue lines represent the flow of gradients for planning, while the red lines depict the meta-optimization learning signal and the components of the architecture affected by it. Note that the GDP iteratively plans across np updates, as indicated by the ith loop.
Model-based approaches leverage forward models to search for, or plan, sequences of actions to achieve goal states such that a planning objective is minimized. Forward modeling supports simulation of future state and hence, in principle, should allow for planning over extended horizons. In the absence of known environment dynamics, a forward model must be learned.
Differentiable forward models allow for end-to-end training of model-based planners, as well as planning by back-propagating gradients with respect to input actions (Schmidhuber, [1990](#bib.bib47); Henaff et al., [2017](#bib.bib24)).
Nevertheless, learned forward models may: (1) suffer from function approximation modeling error, especially in complex, high-dimensional environments, (2) capture irrelevant details under the incentive to reduce model-bias, as is often the case when learning directly from pixels, and (3) not necessarily align with the task and planning problem at hand, such that the inferred plans are sub-optimal even if the planning objective is optimized.
These issues motivate a central idea of the proposed method: instead of learning from surrogate unsupervised or auxiliary objectives, we directly optimize for what we care about, which is, representations with which gradient-based trajectory optimization leads to the desired actions.
We study a model-based architecture that performs a differentiable planning computation in a latent space jointly learned with forward dynamics, trained end-to-end to encode what is necessary for solving tasks by gradient-based planning.
###
2.1 Learning to Plan
The UPN computation graph forms a goal-directed policy supported by an iterative planning algorithm.
Given initial and goal observations (ot and og) as input images, the model produces an optimal plan ^at:t+T to arrive at og, where ^at denotes the predicted action at time t. The computation graph consists of a pair of tied encoders that encode both ot and og, and their features are fed into a gradient descent planner (GDP), which produces the action at as output. The GDP uses a neural network encoder and forward dynamics model to simulate transitions in a learned latent space and is thus fully differentiable. An overview of the method is presented in Figure [2](#S2.F2 "Figure 2 ‣ 2 Universal Planning Networks ‣ Universal Planning Networks").
The GDP uses gradient descent to optimize for a sequence of actions ^at:t+T to reach the encoded goal observation og from an initial ot. Since the model is differentiable, backpropagation through time allows for computing the gradient with respect to each planned action in order to end up closer to the desired goal state. Each iteration of the GDP thus involves unrolling the trajectory of latent state encodings using the current planned actions, and taking a step along the gradient to improve the planning objective. The cumulative planning process forms a large, differentiable computation graph, chaining together each iteration of planning.
The actual learning signal is derived from an outer loss function, which supervises the entire computation graph (including the GDP) to output the correct action sequence. The outer loss can in principle take any form, but in this work we use an imitation learning loss and supervise the entire model with demonstrations. The outer loss provides task-specific grounding to optimize for representations that support effective iterative planning for the task and environment at hand, as the gradient is back-propagated through the entire iterative planning computation graph.
Training thus involves nested objectives. One can view the learning process as first deriving a plan to achieve the goal and then updating the model parameters to make the planning procedure more effective for the outer objective. In other words, we seek to learn the planning computation through its underlying representations for latent state encoding and latent forward dynamics.
Parameters: The model is composed of a forward dynamics model gθ and an encoder fϕ, where θ and ϕ are neural network parameters that are learned end-to-end:
xt=fϕ(ot)^xt+1=gθ(xt,at)
Specifically, fϕ is a convolutional network and gθ is a fully connected network.
Further architectural details can be found in the supplementary. 111We note that one could also use an action encoder hα(at)=ut, with gθ operating on xt and ut. A temporal encoder h would allow for abstract sequences of actions (options), for an option conditioned latent forward model gθ. We work with flat sequences of actions, leaving hierarchical extensions for future work.
Planning by Gradient Descent: The planner starts with an element-wise randomly initialized plan ^a(0)t:t+T∼U(−1,1)
and aims to minimize the distance between the predicted terminal latent state and the encoded goal observation. T denotes the horizon over which the agent plans, which can depend on the task and hence may be treated as a hyper-parameter, while np is the number of planning updates performed. Algorithm [1](#alg1 "Algorithm 1 ‣ 2.1 Learning to Plan ‣ 2 Universal Planning Networks ‣ Universal Planning Networks") describes the iterative optimization procedure that is implemented by the GDP.
0: α: hyperparameter for step size
Randomize an initial guess for the optimal plan ^a(0)t:t+T
for i from 0 to np−1 do
Compute xt=fϕ(ot), xg=fϕ(og)
for j from 0 to T do
^x(i)t+j+1=gθ(^x(i)t+j,^at+j(i))
end for
Compute L(i)plan=||^xt+T+1(i)−xg||22
Update plan: ^at:t+T(i+1)=^at:t+T(i)−α∇^at:t+T(i)L(i)plan
end for
Return ^at:t+T(np)
Algorithm 1 GDP(ot,og,α)→^at:t+T
Huber Loss:
In practice, for L(i)plan, we use a Huber Loss centered around xg for well-behaved inner loop gradients instead of a direct quadratic ||^xt+T+1(i)−xg||22 . This usage is inspired from the Deep Q Networks paper of Mnih et al. ([2015](#bib.bib34)) and similar metrics have also been used by Levine et al. ([2016](#bib.bib32)) and Sermanet et al. ([2017](#bib.bib52)).
Action selection at test-time: At test-time, Algorithm [1](#alg1 "Algorithm 1 ‣ 2.1 Learning to Plan ‣ 2 Universal Planning Networks ‣ Universal Planning Networks") can be used to produce a sequence of actions. A more sophisticated approach is to use Algorithm [1](#alg1 "Algorithm 1 ‣ 2.1 Learning to Plan ‣ 2 Universal Planning Networks ‣ Universal Planning Networks") to re-plan at each timestep. The agent first plans a trajectory suitable to reach og from ot, but only executes the first action, before replanning. This allows the agent to achieve goals requiring longer planning horizons at test-time even if the GDP was trained with a shorter horizon. This amounts to using model-predictive control (MPC) over our learned planner.
###
2.2 Imitation as the Outer Objective
An idea central to our approach is to directly optimize the planning computation for the task at hand, through the outer objective. Though in this work we study the use of an imitation loss as the outer objective, the policy can in principle be trained through any gradient-based policy search method including policy gradients (Schulman, [2016](#bib.bib49)) and value functions (Sutton & Barto, [1998](#bib.bib55)).
To learn parameters ϕ and θ, we do not directly optimize the planning error under Lplan, but instead learn the planner insofar as it can imitate an expert agent by iteratively applying Lplan (Algorithm [2](#alg2 "Algorithm 2 ‣ 2.2 Imitation as the Outer Objective ‣ 2 Universal Planning Networks ‣ Universal Planning Networks")). The model is therefore trained to plan in such a way as to produce actions that match the expert demonstrations.
Note that the subroutine GDP(ot,og,α) is an accumulated computation graph composed of several iterations of planning,
each of which includes encoding observations and unrolling of latent forward dynamics through time.
Learning end-to-end thus requires that we back-propagate the behavior cloning loss under the produced plan through the GDP subroutine as depicted in Figure [2](#S2.F2 "Figure 2 ‣ 2 Universal Planning Networks ‣ Universal Planning Networks"). We note that the gradients obtained on the network parameters θ and ϕ from the outer objective are composed of first-order derivatives of these parameters. Therefore, even though the computation graph of UPN may seem long and complicated, it is not prohibitively expensive to compute or difficult to optimize.
0: GDP(ot,og,α), expert a∗t:t+T, step sizes α,β
for n from 1 to N do
Sample a batch of demonstrations ot,og,a∗t:t+T
Compute ^at:t+T=GDP(ot,og,α)
Compute Limitate=||^at:t+T−a∗t:t+T||22
Update θ:=θ−β∇θLimitate
Update ϕ:=ϕ−β∇ϕLimitate
end for
Algorithm 2 Learning the Planner via Imitation
In learning to plan via imitation, the agent jointly optimizes for latent state and dynamics representations that capture notions of state comparison useful for the imitation task and that are in some sense traversible by gradient descent trajectory optimization. This is naturally induced by the agent’s reliance on the minimization of the latent distance between its predicted terminal state and goal state throughout the planning process. Thus, in requiring plannable representations, the encoder learns an optimizable latent distance metric. This is key to the viability of using the learned latent space as a metric from which to derive reward functions for reinforcement learning.
###
2.3 Reinforcement Learning with a UPN Latent Space
Reward functions are difficult to manually specify for visuomotor tasks described via image targets. Rewards purely based on pixel errors are meaningless, particularly when dealing with high dimensional images. A solution to this problem is to specify rewards in terms of distance to the target image in an abstract representation. There have been attempts in the past to learn such abstract representations. Watter et al. ([2015](#bib.bib61)) and Finn et al. ([2016b](#bib.bib18)) take the unsupervised learning route using autoencoders, while Sermanet et al. ([2017](#bib.bib52)) attempt to fine-tune representations from Imagenet using auxiliary losses tailor-made for robotic manipulation. With UPN having been trained for acquiring plannable representations, it is only natural to expect that its latent space encoded by fϕ serves the role of an abstract representation where rewards can be specified for performing reinforcement learning on visuomotor tasks with image targets. More specifically, we can exploit the learned fϕ from UPN to provide reward functions of the form r(ot,og)=−||fϕ(ot)−fϕ(og)||22. In practice, we use the Huber Loss around og to stay consistent with the metric the UPN was trained with. Further, we had more success normalizing the distance metric to lie in the interval [0,1] by passing the negative of the distance through an exponential. The details are highlighted in the supplementary.
Figure [3](#S2.F3 "Figure 3 ‣ 2.3 Reinforcement Learning with a UPN Latent Space ‣ 2 Universal Planning Networks ‣ Universal Planning Networks") visually depicts the reinforcement learning process. While performing reinforcement learning on the new tasks, the agent gets access to its own embodiment st (joint angles and velocities) and the feature vector of the goal fϕ(og) as its input observations. The agent optimizes for the perceptual rewards computed from UPN and does not receive any extrinsic rewards from the environment. Providing the feature vector of the goal is necessary when the evaluation success is averaged over multiple goals at test time. In case of a single fixed goal, the evaluation success is averaged over different initial configurations of the robot which can be captured in the information provided via st and the goal feature vector becomes redundant. Unless specified, we evaluate using multiple goals at test-time and feed in fϕ(og) as an additional input to the reinforcement learning agent, thereby making the policy architecture at test time universal.
Figure 3: A reinforcement learning agent can derive rewards from the latent representations learned by the UPN. The rewards are based on the difference between ot and og in the abstract representation, while the policy is conditioned on joint angles and velocities specific to the agent, st; and the feature vector of the goal, fUPNϕ(og). The agent has to reason about the goals and how to achieve them based on the learned features from UPN.
3 Related Work
---------------
| | | | |
| --- | --- | --- | --- |
| Examples of the visuomotor tasks considered for the zero shot generalization study. We consider two 2D robot models: a force-controlled point robot and a 3-link torque-controlled reacher robot. We consider two types of generalization: fixing the obstacles while varying the target goals (FOVG) and varying both the obstacle and target goals (VOVG). These tasks require non-trivial generalization combining visual planning with low level motor control.
(a) Pointmass config. 1
| Examples of the visuomotor tasks considered for the zero shot generalization study. We consider two 2D robot models: a force-controlled point robot and a 3-link torque-controlled reacher robot. We consider two types of generalization: fixing the obstacles while varying the target goals (FOVG) and varying both the obstacle and target goals (VOVG). These tasks require non-trivial generalization combining visual planning with low level motor control.
(b) Pointmass config. 2
| Examples of the visuomotor tasks considered for the zero shot generalization study. We consider two 2D robot models: a force-controlled point robot and a 3-link torque-controlled reacher robot. We consider two types of generalization: fixing the obstacles while varying the target goals (FOVG) and varying both the obstacle and target goals (VOVG). These tasks require non-trivial generalization combining visual planning with low level motor control.
(c) Reacher config. 1
| Examples of the visuomotor tasks considered for the zero shot generalization study. We consider two 2D robot models: a force-controlled point robot and a 3-link torque-controlled reacher robot. We consider two types of generalization: fixing the obstacles while varying the target goals (FOVG) and varying both the obstacle and target goals (VOVG). These tasks require non-trivial generalization combining visual planning with low level motor control.
(d) Reacher config. 2
|
Figure 4: Examples of the visuomotor tasks considered for the zero shot generalization study. We consider two 2D robot models: a force-controlled point robot and a 3-link torque-controlled reacher robot. We consider two types of generalization: fixing the obstacles while varying the target goals (FOVG) and varying both the obstacle and target goals (VOVG). These tasks require non-trivial generalization combining visual planning with low level motor control.
Our work is primarily concerned with learning representations that can support planning for tasks described through an image target. Watter et al. ([2015](#bib.bib61)) and Finn et al. ([2016b](#bib.bib18)) take an unsupervised learning approach to learning such representations, which they use for planning with respect to target images using iLQR (Tassa et al., [2012](#bib.bib58)). However, reconstructing all the pixels in the scene could lead to the encoding of state variables not necessarily useful in the context of planning (Higgins et al., [2017](#bib.bib25)) and discard state variables that are not visually prominent (Goodfellow et al. ([2016](#bib.bib22)), Chapter 15). Our approach avoids this problem by explicitly optimizing a representation for plannability through gradient descent as the only criterion. Self-supervised methods that avoid pixel reconstruction by using other intermediate forms of supervision that can be obtained automatically from the data have also been used to learn representations for visuomotor control (Sermanet et al., [2016](#bib.bib51), [2017](#bib.bib52)). We again differ by optimizing directly for what we need: plannable representations, instead of intermediate objectives. While the goal in Sermanet et al. ([2017](#bib.bib52)) is to recover a reward function to mimic specific demonstrations, our goal is to acquire a more broadly applicable representation from demonstrations that can then be used to perform new tasks using just a single goal image.
There has been work in learning state representations usable for model-free RL when provided rewards (Lange et al., [2012](#bib.bib31); Jonschkowski & Brock, [2015](#bib.bib27); Jonschkowski et al., [2017](#bib.bib28); Higgins et al., [2017](#bib.bib25); de Bruin et al., [2018](#bib.bib11)). The key difference in our work is that we focus on learning representations that can be used for defining metric-based rewards for new tasks, as opposed to just learning state representations for RL from external environment rewards.
Learning representations capable of providing distance metric based rewards naturally relates to inverse reinforcement learning (IRL) (Ng & Russell, [2000](#bib.bib36); Abbeel & Ng, [2004](#bib.bib2); Finn et al., [2016a](#bib.bib17); Ho & Ermon, [2016](#bib.bib26); Baram et al., [2017](#bib.bib8)) and reward shaping (Ng et al., [1999](#bib.bib37)). IRL methods attempt to learn a reward function from expert demonstrations which could then be used to optimize a traditional reinforcement learner. However, IRL from raw pixels is challenging due to the lack of sufficient constraints in the problem definition; only a couple of methods have successfully applied IRL to images, and to do so have relied on human domain knowledge (Wulfmeier et al., [2016](#bib.bib63)) and pre-training (Li et al., [2017](#bib.bib33)). Our work can be viewed as connecting IRL and reward shaping: learning representations amenable to gradient-based trajectory optimization is one way to extract a perceptual reward function. However, we differ significantly from conventional IRL in that our derived reward functions are effective even for new tasks.
From an architectural standpoint, we embed a differentiable planner within our computation graph.
Value iteration networks of Tamar et al. ([2016](#bib.bib56)) embed an approximate differentiable value iteration computation, though their architecture only supports discrete planning and is evaluated on tasks with sparse state transition probabilities. We seek a more general planning computation for more complex transition dynamics and continuous actions suitable for motor control from raw pixels. Tamar et al. ([2017](#bib.bib57)) attempt to learn an embedded differential MPC controller by reshaping its cost function in hindsight through a longer horizon MPC plan. We, however, are interested in tasks where cost functions are not available and cannot adopt this approach. Amos & Kolter ([2017](#bib.bib4)); Donti et al. ([2017](#bib.bib14)) also look at embedding differentiable optimization procedures (quadratic programs) within neural networks. Concurrently, a few recent efforts have been developed to embed differentiable planning procedures in computation graphs (Guez et al., [2018](#bib.bib23); Pereira et al., [2018](#bib.bib41); Farquhar et al., [2017](#bib.bib15)). However, to our knowledge, our paper is the first to connect the use of differentiable planning procedures to learning reusable representations that generalize across complex visuomotor tasks.
The idea of planning by gradient descent has existed for decades (Kelley, [1960](#bib.bib29)). While such work relied on known analytic forms of environment dynamics, later work (Schmidhuber, [1990](#bib.bib47)) explored jointly learning approximate models of dynamics with neural networks. Henaff et al. ([2017](#bib.bib24)) adopt gradient-based trajectory optimization for model-based planning in discrete action spaces, but rely on representations learned from unsupervised pretraining. Oh et al. ([2017](#bib.bib38)) and Silver et al. ([2016](#bib.bib53)) have also explored forward predictions in a latent space that is learned by decoding the value function of a state. Our architecture is related in so far as distance to goal in the learned latent space can be viewed as a value function. However, we also differ significantly by not relying on extrinsic rewards and focusing on continuous control tasks.
Similar to our work, Pathak\* et al. ([2018](#bib.bib40)) and Nair et al. ([2017](#bib.bib35)) train goal-conditioned policies for imitation learning, by providing an image of the goal as input to the policy. However, we show in our experiments that, unlike these methods, the representation learned via our approach can be reused for planning and reward specification.
| | | | |
| --- | --- | --- | --- |
| VOVG - Varying Obstacles and Varying Goals, FOVG - Fixed Obstacles and Varying Goals; Success on test tasks as a function of the dataset size. Our approach (UPN) outperforms the RIL and AIL consistently across the four generalization conditioned considered and is more sample efficient. As expected, the AIL improves with more data to eventually almost match the UPN. This illustrates the tradeoff between inductive bias and expressive architectures when given sufficient data.
(a) Pointmass- VOVG
| VOVG - Varying Obstacles and Varying Goals, FOVG - Fixed Obstacles and Varying Goals; Success on test tasks as a function of the dataset size. Our approach (UPN) outperforms the RIL and AIL consistently across the four generalization conditioned considered and is more sample efficient. As expected, the AIL improves with more data to eventually almost match the UPN. This illustrates the tradeoff between inductive bias and expressive architectures when given sufficient data.
(b) Reacher - VOVG
| VOVG - Varying Obstacles and Varying Goals, FOVG - Fixed Obstacles and Varying Goals; Success on test tasks as a function of the dataset size. Our approach (UPN) outperforms the RIL and AIL consistently across the four generalization conditioned considered and is more sample efficient. As expected, the AIL improves with more data to eventually almost match the UPN. This illustrates the tradeoff between inductive bias and expressive architectures when given sufficient data.
(c) Pointmass- FOVG
| VOVG - Varying Obstacles and Varying Goals, FOVG - Fixed Obstacles and Varying Goals; Success on test tasks as a function of the dataset size. Our approach (UPN) outperforms the RIL and AIL consistently across the four generalization conditioned considered and is more sample efficient. As expected, the AIL improves with more data to eventually almost match the UPN. This illustrates the tradeoff between inductive bias and expressive architectures when given sufficient data.
(d) Reacher - FOVG
|
Figure 5: Notation: VOVG - Varying Obstacles and Varying Goals, FOVG - Fixed Obstacles and Varying Goals; Success on test tasks as a function of the dataset size. Our approach (UPN) outperforms the RIL and AIL consistently across the four generalization conditioned considered and is more sample efficient. As expected, the AIL improves with more data to eventually almost match the UPN. This illustrates the tradeoff between inductive bias and expressive architectures when given sufficient data.
4 Experiments
--------------
We designed experiments to answer the following questions: (1) does embedding a gradient descent planner help learn a policy that can map from pixels to torque control when provided current and goal observations at test-time ? (2) how does our method compare to reactive and autoregressive behavior cloning agents as the amount of training data varies? (3) what are the properties of the representation learned by UPN? (4) how can the learned representations from UPN be leveraged for transfer to new and more complex tasks, compared to representations from standard imitation methods and unsupervised methods (e.g. VAE)?
Methods for comparison: We consider two alternative imitation learning approaches for comparison:
(1) a reactive imitation learner (RIL), composed of a convolutional feedforward policy that takes as input the current and goal observation;
(2) an auto-regressive imitation learner (AIL), composed of a recurrent decoder initially conditioned on convolutionally encoded representations of the current and goal observation, trained to output a sequence of intermediate actions. Both (1) and (2) are methods adopted from Pathak\* et al. ([2018](#bib.bib40)). These comparisons are important for studying the effects of the inductive bias of gradient descent planning that is embedded within UPN. More specifically, comparing to (1) allows us to understand the need for such an inductive bias, while comparing to (2) is necessary to understand whether the benefits are not purely due to recurrent computations. All methods are trained on the same synthetically-generated expert demonstration datasets. We refer the reader to the supplementary for details on the architectures and dataset generation.
###
4.1 UPNs Learn Effective Imitation Policies
Here, we study the suitability of the UPN for learning visual imitation policies that generalize to new goal-directed tasks. We focus on two tasks: (1) navigating a 2D point robot around obstacles to desired goal locations amidst distractors (Figures [4(a)](#S3.F4.sf1 "(a) ‣ Figure 4 ‣ 3 Related Work ‣ Universal Planning Networks") and [4(b)](#S3.F4.sf2 "(b) ‣ Figure 4 ‣ 3 Related Work ‣ Universal Planning Networks")), wherein the color of the goal is randomized; (2) a harder task of controlling a 3-DoF planar arm to reach goals amidst scattered distractors and obstacles, as shown in Figures [4(c)](#S3.F4.sf3 "(c) ‣ Figure 4 ‣ 3 Related Work ‣ Universal Planning Networks") and [4(d)](#S3.F4.sf4 "(d) ‣ Figure 4 ‣ 3 Related Work ‣ Universal Planning Networks").
For these tasks, we consider two types of generalization: (1) generalizing to new goals for a fixed configuration of obstacles having trained on the same configuration; (2) generalizing to new goals in new obstacle configurations having trained across varying obstacle configurations. Figures [4(c)](#S3.F4.sf3 "(c) ‣ Figure 4 ‣ 3 Related Work ‣ Universal Planning Networks") and [4(d)](#S3.F4.sf4 "(d) ‣ Figure 4 ‣ 3 Related Work ‣ Universal Planning Networks") show two different obstacle configurations for the reaching task, while the differently colored locations in Figure [4](#S3.F4 "Figure 4 ‣ 3 Related Work ‣ Universal Planning Networks") represent varying goal locations.
We employ the action selection process described in subsection [2.1](#S2.SS1 "2.1 Learning to Plan ‣ 2 Universal Planning Networks ‣ Universal Planning Networks") with a chosen maximum episode length. Results shown in Figure [5](#S3.F5 "Figure 5 ‣ 3 Related Work ‣ Universal Planning Networks") compare performance over a varying number of training demonstrations. As expected, the inductive bias of embedding trajectory optimization via gradient descent in UPN supports generalization from fewer demonstrations. With more demonstrations, however, the expressive AIL is able to almost match the performance of the UPN. This is consistent with the conclusions of Tamar et al. ([2016](#bib.bib56)), who observed that the benefit of the value iteration inductive bias shrinks in regimes in which demonstrations are plentiful. Note that generalization across obstacle configurations in the reacher case (Figure [4(c)](#S3.F4.sf3 "(c) ‣ Figure 4 ‣ 3 Related Work ‣ Universal Planning Networks")) is a hard task; expert performance is only 73.12%. We encourage the reader to refer to the supplementary for further details about the experiment.
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| --- | --- |
| The effect of additional planning steps at test-time. UPN learns an effective gradient descent planner whose convergence improves with more planning steps at test-time.
| The effect of additional planning steps at test-time. UPN learns an effective gradient descent planner whose convergence improves with more planning steps at test-time.
|
Figure 6: (a) The effect of additional planning steps at test-time. UPN learns an effective gradient descent planner whose convergence improves with more planning steps at test-time. (b) A comparison of the success rate of UPN between 40 and 160 planning steps at test time with varying number of demonstrations on Reacher VOVG. Using 160 planning steps is consistently better than using 40 steps (though the relative benefit shrinks with more demonstrations) and allows the UPN to match the expert level.
###
4.2 Analysis of the Gradient Descent Planner
The UPN can be viewed in the context of meta-learning as learning a planning algorithm and its underlying representations. We take inspiration from Finn & Levine ([2018](#bib.bib16)), who studied a gradient-based model-agnostic meta-learning algorithm and showed that a classifier trained for few-shot image classification improves in accuracy at test-time with additional gradient updates.
In our case, the inner loop is the GDP, which may not necessarily converge due to the fixed number of planning updates.
Hence, it is worth studying whether additional test-time GDP updates yield more accurate plans and therefore better success rates.
Planning more helps: Figure [6](#S4.F6 "Figure 6 ‣ 4.1 UPNs Learn Effective Imitation Policies ‣ 4 Experiments ‣ Universal Planning Networks") shows that with more planning steps at test-time, a UPN trained with fewer demonstrations (20000) can improve on task success rate beginning from 38.1% with 40 planning steps to 64.44% with 160 planning steps. As a reference, the average test success rate of the expert on these tasks is 73.12% while the best UPN model with 40 planning steps (trained on twice the number of demos (40000)) achieves 64.78%. Thus, with more planning steps, we see that UPN can improve to match the performance of a UPN with fewer planning steps but trained on twice the number of demonstrations.
We also find that 160 steps is consistently better
than using 40 steps (though the relative benefit shrinks with more
demonstrations) and that the UPN is able to match expert performance (Figure [6](#S4.F6 "Figure 6 ‣ 4.1 UPNs Learn Effective Imitation Policies ‣ 4 Experiments ‣ Universal Planning Networks")). This finding suggests that the learned planning objective is well defined, and can likely be reused for related control problems, as we explore in Sections [4.4](#S4.SS4 "4.4 Transfer to Harder Scenarios ‣ 4 Experiments ‣ Universal Planning Networks") and [4.5](#S4.SS5 "4.5 Transfer Across Robots ‣ 4 Experiments ‣ Universal Planning Networks").
###
4.3 Latent Space Visualization
We offer a qualitative analysis for studying the acquired latent space for an instance of the reacher with obstacles task.
Given the selected initial pose, we compute the distance in the learned fϕ space for 150 random final poses and illustrate these distances qualitatively on the environment arena by color mapping each end-effector position accordingly. The result is shown in Figure [7](#S4.F7 "Figure 7 ‣ 4.3 Latent Space Visualization ‣ 4 Experiments ‣ Universal Planning Networks"); lighter blue corresponds to larger distances in the feature space. We see that the learned distance metric is *obstacle-aware* and task-specific: regions below the initial position in Figure [7](#S4.F7 "Figure 7 ‣ 4.3 Latent Space Visualization ‣ 4 Experiments ‣ Universal Planning Networks") are less desirable even though they are near, while farther regions above are comparatively favorable.
Figure 7: Visualization of the learned metric in the UPN latent space on the reacher with obstacles task. Lighter color → larger latent distance. The learned distance metric is obstacle-aware and supports obstacle avoidance.
| Feature Space | Fixed | Varying |
| --- | --- | --- |
| RIL-RL | 0% | 0.01% |
| AIL-RL | 0% | 4.72% |
| VAE-RL | 20.23% | 24.67% |
| UPN-160 Imitation | 45.82% | 47.99% |
| Expert | 46.77% | 51.1 % |
| UPN-RL | 69.84% | 71.12% |
Table 1: Average Success Rate % in solving the task described in Figure [4(d)](#S3.F4.sf4 "(d) ‣ Figure 4 ‣ 3 Related Work ‣ Universal Planning Networks") for fixed and varying goals
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| --- | --- |
| Transfer between robots as described in subsection 4.5.
(a) Transfer to more complex topology (Reacher)
| Transfer between robots as described in subsection 4.5.
(b) Transfer to new morphology (Point to Ant)
|
Figure 8: Transfer between robots as described in subsection 4.5.
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| --- | --- | --- | --- |
| (a-c) RL with rewards from the UPN representation is significantly more successful compared to other feature spaces (VAE, AIL, RIL, shaped rewards), suggesting that UPNs learn transferrable, generalizable latent spaces.
(a) Point robot to Ant transfer
| (a-c) RL with rewards from the UPN representation is significantly more successful compared to other feature spaces (VAE, AIL, RIL, shaped rewards), suggesting that UPNs learn transferrable, generalizable latent spaces.
(b) Reacher transfer
| (a-c) RL with rewards from the UPN representation is significantly more successful compared to other feature spaces (VAE, AIL, RIL, shaped rewards), suggesting that UPNs learn transferrable, generalizable latent spaces.
(c) Pushing from poking transfer
| (a-c) RL with rewards from the UPN representation is significantly more successful compared to other feature spaces (VAE, AIL, RIL, shaped rewards), suggesting that UPNs learn transferrable, generalizable latent spaces.
(d) 7-DoF Pushing task
|
Figure 9: (a-c) RL with rewards from the UPN representation is significantly more successful compared to other feature spaces (VAE, AIL, RIL, shaped rewards), suggesting that UPNs learn transferrable, generalizable latent spaces.
###
4.4 Transfer to Harder Scenarios
We have seen in subsections [4.1](#S4.SS1 "4.1 UPNs Learn Effective Imitation Policies ‣ 4 Experiments ‣ Universal Planning Networks") and [4.2](#S4.SS2 "4.2 Analysis of the Gradient Descent Planner ‣ 4 Experiments ‣ Universal Planning Networks") that UPNs can learn effective imitation policies that can perform close to the expert level on visuomotor planning tasks. In principle, deriving reward functions from a trained UPN as explained in subsection [2.3](#S2.SS3 "2.3 Reinforcement Learning with a UPN Latent Space ‣ 2 Universal Planning Networks ‣ Universal Planning Networks") should allow us to extend beyond the capabilities of the expert on harder scenarios where the expert fails. We study this idea in the reaching scenario with obstacle configuration as presented in Figure [4(d)](#S3.F4.sf4 "(d) ‣ Figure 4 ‣ 3 Related Work ‣ Universal Planning Networks"). The difference between fixed and varying goals is that for varying goals, we feed in a feature vector of the goal image as an additional input to the RL policy. We use PPO (Schulman et al., [2017](#bib.bib50)) for model-free policy optimization of the rewards derived from the feature space(s). Though the subsection [2.3](#S2.SS3 "2.3 Reinforcement Learning with a UPN Latent Space ‣ 2 Universal Planning Networks ‣ Universal Planning Networks") explains the reinforcement learning procedure in the context of using fϕ from a UPN, one could use a trained encoder fϕ from other methods such as our supervised learning comparisons RIL, AIL. In addition to RIL and AIL, a feature space we compare to is an encoder obtained from training a variational auto-encoder (VAE) (Kingma & Welling, [2013](#bib.bib30)) on the images of the demonstrations. This comparison is necessary to judge how useful the feature space of a UPN is for downstream reinforcement learning when compared to pixel reconstruction methods such as VAEs. In Table [1](#S4.T1 "Table 1 ‣ 4.3 Latent Space Visualization ‣ 4 Experiments ‣ Universal Planning Networks"), we see that reinforcement learning on the feature space of RIL and AIL clearly fail, while RL on the UPN feature space is significantly better compared to that of a VAE. We also see that UPN-RL is able to outperform the expert and the imitating UPN-160.
###
4.5 Transfer Across Robots
Having seen the success of reinforcement learning using rewards derived from UPN representations in subsection [4.4](#S4.SS4 "4.4 Transfer to Harder Scenarios ‣ 4 Experiments ‣ Universal Planning Networks"), we pose a harder problem in this subsection: Can we leverage UPN representations trained on some source task(s) to provide rewards for target task(s) with significantly different dynamics and action spaces? We propose to do this by training and testing with different robots (morphological variations) on the same desired functionality (reaching / locomotion, around obstacles). This study will highlight the extrapolative nature of UPN representations. The idea of trajectory optimization with a learned metric is a fundamental prior that can hold across a large class of visuomotor control problems. Having trained UPN to learn such a prior, it is natural to expect the underlying representation to be amenable to providing suitable metric based rewards for similar but unseen tasks. We craft two challenging experimental scenarios to verify this hypothesis.
Reacher with new morphology: Having trained a UPN with a shared fϕ and different gθ for a 3-link and 4-link reacher (on the obstacles task), can we leverage the learned fϕ to specify rewards for reinforcement-learning a 5-link reacher to reach different goals around the same obstacles? Figure [8(a)](#S4.F8.sf1 "(a) ‣ Figure 8 ‣ 4.3 Latent Space Visualization ‣ 4 Experiments ‣ Universal Planning Networks") visually depicts this experiment. Such a transfer scenario hasn’t been studied in the past for visuomotor control. The dynamics of a 5-link reacher are more complex (compared to 3 and 4 link reachers), thereby posing a harder control problem to solve at test time. However, a good path-planning reward function learned from 3 and 4-link reachers is likely to help for a 5-link reacher due to morphological similarities. We train the UPN on both the 3 and 4 link reachers to avoid overfitting the learned metric to a specific dynamical system. As comparison methods, we train RIL and AIL (with a multi-task (head) architecture), and a VAE (jointly on images from both the tasks).
Point to Ant: Higher-level navigation to goals amidst obstacles should be common across different robots, from a 2D point robot controlled through simple forces to a robot as complex as an 8-joint quadruped ant. While the lower level actuation varies across different robots, the visual spatial planning should ideally be transferrable . We empirically confirm this via an experiment illustrated in Figure [8(b)](#S4.F8.sf2 "(b) ‣ Figure 8 ‣ 4.3 Latent Space Visualization ‣ 4 Experiments ‣ Universal Planning Networks"). Here, we learn representations with a UPN on demonstrations collected from a 2D point robot trained to traverse obstacles to reach varying goals. We randomize the robot’s morphological appearance across demonstrations (Figure [8(b)](#S4.F8.sf2 "(b) ‣ Figure 8 ‣ 4.3 Latent Space Visualization ‣ 4 Experiments ‣ Universal Planning Networks")), inspired by Sadeghi & Levine ([2016](#bib.bib45)); Tobin et al. ([2017](#bib.bib59)). This allows the UPN to learn an encoder fϕ that is robust to the creature appearance. We then design an experiment to use this fϕ for a harder problem. First, we train a UPN with a simple 2D point robot; we then replace the point robot with a 3D-torque-controlled ant, which requires more delicate handling of the surface contacts for maneuvering the quadruped and avoiding obstacles. Once again, to our knowledge, such morphological transfer has not been demonstrated in prior work on visuomotor control.
In Figure [9](#S4.F9 "Figure 9 ‣ 4.3 Latent Space Visualization ‣ 4 Experiments ‣ Universal Planning Networks") we see that for both the transfer scenarios, RL with rewards from the UPN representation is significantly more successful compared to other feature spaces (VAE, AIL, and RIL). In addition to other feature spaces, we also compare the UPN-RL setup to a naïve RL agent optimizing a spatial distance to goal in the co-ordinate space as the reward; this procedure assumes that the spatial position of the goal is known, unlike UPN, RIL, AIL, and VAE where the feature vector of the goal image is provided as input. We note that this method also performs poorly, which is expected because, unlike distances in the feature space of UPN, the spatial distance in the co-ordinate space is not obstacle-aware. Note that UPN-RL relies only on the UPN representation to provide the RL agent with knowledge of the task, thus inferring the goal from the obstacle-informative latent space. These results show that optimizing for the rewards derived from UPN correlates with task success, supporting our claim that UPNs learn generalizable and transferrable latent spaces. We show further extrapolation (6-link and 7-link reachers) in our video results. To our knowledge, there has been no prior exposition of torque controlled goal conditioned ant navigation for varying goals around obstacle(s) even when spatial positions of the goal and ant torso are known. UPN is therefore an effective way of uncovering useful metric priors that can serve as perceptual reward functions for complex tasks for which reward functions are typically hard to engineer.
###
4.6 3D 7-DoF Control from an Non-orthographic View
So far, we have demonstrated results with UPN on tasks where the view point is orthographic, which may make it easier for the agent to map from pixels to relative positions. We next seek to answer the question: Can UPN still work for scenarios where the camera view of the task is non-orthographic? This is a common scenario for real robot tasks or more complex manipulation tasks in simulation (Finn et al., [2017b](#bib.bib20)). To answer this, we consider the task of controlling a 3D 7-DoF arm from non-orthographic viewpoints, which presents a harder perception problem (shown in Figure [9(d)](#S4.F9.sf4 "(d) ‣ Figure 9 ‣ 4.3 Latent Space Visualization ‣ 4 Experiments ‣ Universal Planning Networks")). This task is adapted from Finn et al. ([2017b](#bib.bib20)) where there is a distractor object in addition to a target object that needs to be displaced to a goal location. However, here, we do not focus on generalization to new objects unlike Finn et al. ([2017b](#bib.bib20)). Instead, we look at skill generalization. We collect a dataset of random pokes (see Agrawal et al. ([2016](#bib.bib3)) for a detailed description of poking in robotics and our video highlights for visual illustration of poking trajectories). Having trained a UPN representation on poking trajectories, we study whether rewards derived from it can guide learning of more complex and composite skills, such as pushing (which involves appropriately reaching for the target object and guiding it to the goal). Further, we also analyze whether the UPN representation based rewards can replace hand-engineered reward shaping for such a task.
Having established the clear success of UPN over RIL, AIL, and VAE for the RL experiments in subsections [4.4](#S4.SS4 "4.4 Transfer to Harder Scenarios ‣ 4 Experiments ‣ Universal Planning Networks") and [4.5](#S4.SS5 "4.5 Transfer Across Robots ‣ 4 Experiments ‣ Universal Planning Networks"), we perform a different comparison here. In addition to UPN-RL, we train the agent on the pushing task assuming the object and goal positions are known using RL without image based inputs and a well shaped reward that is described [here](https://github.com/openai/gym/blob/master/gym/envs/mujoco/pusher.py#L19). To our surprise, we find that the transfer from poking to pushing using the UPN-RL setup works efficiently. Our method, which relies only on UPN representation rewards and the current image, approaches the performance of the shaped reward function in terms of task success (Figure [9(c)](#S4.F9.sf3 "(c) ‣ Figure 9 ‣ 4.3 Latent Space Visualization ‣ 4 Experiments ‣ Universal Planning Networks")). This result suggests that the UPN latent space captures the proximity of the end-effector to the object as a pre-requisite to moving the object to desired locations and hence supports acquisition of even more complex behavior via reinforcement learning. Thus, UPN can serve as a means to acquiring a structured metric in the latent space from which reward functions for complex manipulation tasks such as pushing can emerge naturally.
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| --- | --- |
| Using UPN representations trained on a simple 2D point robot, we control complex robots such as a full humanoid and an ant to locomote around obstacles and reach the green goal. While the humanoid task is challenging because of the complex actuation, the ant task requires optimizing a policy over 8000 time steps, providing evidence that the rewards from UPN representations can aid in effective credit assignment over long horizons.
(a) Humanoid Task
| Using UPN representations trained on a simple 2D point robot, we control complex robots such as a full humanoid and an ant to locomote around obstacles and reach the green goal. While the humanoid task is challenging because of the complex actuation, the ant task requires optimizing a policy over 8000 time steps, providing evidence that the rewards from UPN representations can aid in effective credit assignment over long horizons.
(b) Ant: Long Horizon Task
|
Figure 10: Using UPN representations trained on a simple 2D point robot, we control complex robots such as a full humanoid and an ant to locomote around obstacles and reach the green goal. While the humanoid task is challenging because of the complex actuation, the ant task requires optimizing a policy over 8000 time steps, providing evidence that the rewards from UPN representations can aid in effective credit assignment over long horizons.
###
4.7 Transfer from Point Robot to a Humanoid: Pushing the limits of generalization
In this subsection, we consider the following question: Can a reward function derived from a very simple creature such a 2D point robot be used to control a much more complex robot such as a humanoid, for similar behaviors such as locomotion around obstacles (ref Figure [10(a)](#S4.F10.sf1 "(a) ‣ Figure 10 ‣ 4.6 3D 7-DoF Control from an Non-orthographic View ‣ 4 Experiments ‣ Universal Planning Networks"))? This is a harder problem than transferring reward functions from point robot to ant because a humanoid is a much more complex robot to control. To deal with the visual differences between a humanoid and a point robot, we assume that we have access to the 2D co-ordinate position of the center of mass of the humanoid. We re-render the humanoid as a 2D point robot whose center of mass is same as that of the humanoid, and pass this image through a UPN trained on a point robot to provide the reward function for the humanoid. Note that this assumption of knowing the global location is very minimal, since the reward function is still non-trivial, and in this case, a learned perceptual metric.
In the case of the quadruped, it wasn’t necessary to shape the rewards for balancing as long as we could terminate episodes whenever the creature falls down. However, for a humanoid, an explicit reward for staying on feet is necessary. We saw that naive termination of episodes on falling down resulted in the humanoid moving close to the side walls to balance itself and stay on feet throughout the duration of the task, rather than optimizing for the path planning reward derived from the UPN representations. To get around this issue, we adopted the strategy used in Bansal et al. ([2017](#bib.bib7)), whereby a decaying curriculum for staying on feet is used, and combined with the metric reward for the shortest path locomotion. Check out the video of the behavior learned by the humanoid on the project webpage: <https://sites.google.com/view/upn-public>.
###
4.8 Using UPN rewards for long horizon tasks
Finally, we answer: To what extent can the learned metrics from UPN guide a new reinforcement learning agent? One way to push the limits is to consider long horizon tasks. Typically, continuous control tasks studied in reinforcement learning are restricted to a maximum horizon of less than or equal to 1000 simulation steps. Taking inspiration from Frans et al. ([2018](#bib.bib21)), we study a goal conditioned navigation task wherein a quadruped has to locomote around obstacles to reach a goal that is far away (time horizon of 8000 simulation steps, refer to Figure [10(b)](#S4.F10.sf2 "(b) ‣ Figure 10 ‣ 4.6 3D 7-DoF Control from an Non-orthographic View ‣ 4 Experiments ‣ Universal Planning Networks")). In the case of Frans et al. ([2018](#bib.bib21)), the reward was extrinsic and sparse, and thus a hierarchical policy was required for efficient credit assignment and exploration. In our case, we show that the shaped reward from UPN on a point robot can overcome the problem of sparse rewards and effective credit assignment. This experiment indicates that UPN is able to learn efficient distance metrics in an abstract space from very simple short horizon tasks such as controlling a 2D point robot, which can be powerful enough to guide the reinforcement learning of complex policies such as controlling an ant to move around mazes over much longer horizons. Check out the video of the learned behavior on the project webpage: <https://sites.google.com/view/upn-public>.
5 Discussion
-------------
We posed the problem of learning representations for performing generalizable visuomotor control. We focused on one property such a space should satisfy: providing distance metrics for reinforcement learning on tasks specified via goal images without extrinsic rewards. To this end, we introduced universal planning networks, a goal-directed policy architecture with an embedded differentiable planner, that can be trained end-to-end. Our extensive experiments demonstrated that (1) UPNs learn effective visual goal-directed policies efficiently; (2) UPN latent representations can be leveraged to transfer task-related semantics to more complex agents and more challenging tasks through goal-conditioned reward functions; and (3) the learned planner improves with more updates at test-time, providing encouraging evidence of meta-learning for planning. Our transfer learning successes demonstrate that we have learned generic representations that have notions of agency and planning.
Future work should investigate different ways to train UPN representations, such as through reinforcement learning or self-supervision, borrowing ideas from Andrychowicz et al. ([2017](#bib.bib5)), Sukhbaatar et al. ([2017](#bib.bib54)), Weber et al. ([2017](#bib.bib62)) and Pathak et al. ([2017](#bib.bib39)). Another important future direction is to study representations wherein the metrics are structured as value functions instead of rewards as a consequence of which long horizon policy optimization could be more effective and sample efficient. Further, the results from subsections [4.7](#S4.SS7 "4.7 Transfer from Point Robot to a Humanoid: Pushing the limits of generalization ‣ 4 Experiments ‣ Universal Planning Networks") and [4.8](#S4.SS8 "4.8 Using UPN rewards for long horizon tasks ‣ 4 Experiments ‣ Universal Planning Networks") suggest that UPN like architectures might be practically applicable for learning complex real robotic behaviors by leveraging simulated behaviors of much simpler robots performing the same tasks.
6 Acknowledgements
-------------------
AS thanks Aviv Tamar for insightful feedback on planning that motivated the experiments; John Schulman, Ashvin Nair and Deepak Pathak for helpful discussions and feedback; Rocky Duan for technical help; and Jonathan Ho, Jason Peng, and Kelvin Xu for reviewing previous versions of the paper. AJ thanks Alyosha Efros for support and feedback. This research was supported by an ONR PECASE N000141612723AS grant, NVIDIA and Amazon Web Services. AS and AJ were supported by a Berkeley EECS Fellowship and a Berkeley AI Research Fellowship; CF was supported by an NSF GRFP award. |
1b0fd09f-52c2-4835-9f57-8637deeeca6e | StampyAI/alignment-research-dataset/alignmentforum | Alignment Forum | LOVE in a simbox is all you need
***L**earning **O**ther's **V**alues or **E**mpowerment in simulation sandboxes is all you need*
TL;DR: We can develop self-aligning DL based AGI by improving on the brain's dynamic alignment mechanisms (empathy/altruism/love) via safe test iteration in simulation sandboxes.
AGI is on track to arrive soon[[1]](#fn-xhJT9EJCoFQGE4wqz-1) through the same pragmatic, empirical and brain inspired research path that has produced all recent AI success to date: Deep Learning. The DL approach offers its own natural within-paradigm solution for alignment of AGI: first transform the task into a set of measurable in-simu benchmark test environments that capture the essence and distribution of the true problem in reality, then safely iterate ala standard technological evolution guided by market incentives.
We can test *alignment* via sandboxed simulations of small AGI societies to safely explore and evaluate mind architecture space for the designs of altruistic agents that learn, adopt, and then optimize for the values (or empowerment) of others, all while scaling up in intelligence and power[[2]](#fn-xhJT9EJCoFQGE4wqz-2); eventually progressing to large *eschatonic* simworlds where human-level agents grow up, learn, cooperate and compete to survive, culminating in a winner acquiring decisive (super)powers and facing an ultimate altruistic vs selfish choice to save or destroy their world, all the while never realizing they are in a sim (and probably lacking even the *precursor* concepts for such metaphysical realizations)[[3]](#fn-xhJT9EJCoFQGE4wqz-3).
To the extent that we have 'solved' various subtasks of cognition such as a vision, speech, natural language tasks, various games, etc, it has been through a global evolutionary research process guided by *coordination* on benchmark sim environments and *competition* on specific approaches. Over time the benchmark/test environments are growing more complex, integrative and general. So a reasonable (if optimistic) hypothesis is that this trend can continue all the way to aligned AGI.
The future often appears very strange and novel when viewed through the lens of the present. The novelty herein - from the standard AI alignment mindset - is perhaps the idea that we can and must actually *test* alignment *safely* and *adequately* in simulations. But testing in-simu is now just standard practice in modern engineering. We no longer test nuclear weapons in reality as the cost/benefit tradeoff strongly favors simulation, and even far safer technologies such as automobiles are also all tested in simulations thanks to the progressive deflationary march of Moore's Law. From this *engineer's perspective* it is fairly obvious both that testing is required, and that testing powerful AGI - something probably far more dangerous than nuclear weapons - in our one and only precious mainline reality would be profoundly *unwise*, to say the least.
The rest of this article fleshes out some of the background, technical challenges, details, and implications of alignment for *anthropomorphic* AGI in simboxes[[4]](#fn-xhJT9EJCoFQGE4wqz-4). In essence the core challenge is finding clever ways to more efficiently explore and test the design space all while balancing various tradeoffs in order to avoid paying an excessive alignment tax[[5]](#fn-xhJT9EJCoFQGE4wqz-5).
### 1. Measuring Alignment
By *alignment* we mean the degree to which one agent optimizes the world in the direction other agent(s) would optimize the world, if they only could. This high-level article will avoid precise mathematical definitions, but for the math minded *alignment* should conjure something like weighted integrals/sums of dot products over discounted utility functions.[[6]](#fn-xhJT9EJCoFQGE4wqz-6).
We can measure alignment in general by evaluating agents in various specific situations that feature counterfactual inter-agent utility divergence. Or in other words, we can evaluate agents in situations where their actions have non-trivial impact on other agents, such that the others would have strong opinions on the primary agent's choice.
We can use creative world design to funnel agents into various test scenarios, followed with evaluation by random panels of human observer judges who decide alignment scores, aggregation/normalization of said scores, training narrow AI helpers to predict human ratings, and then scaling up.
Information generally only flows out of the sim; the agents are unaware that they are being judged[[7]](#fn-xhJT9EJCoFQGE4wqz-7), and thus the human judgments are not available as a learning signal for sim agents, so we can avoid all the various [deception](https://www.lesswrong.com/posts/A9NxPTwbw6r6Awuwt/how-likely-is-deceptive-alignment) and feedback problems anticipated in *naive* open training scenarios.
Intelligent socially adept humans are already quite capable of modeling and inferring the goals and alignments of other agents, but our judges can also exploit superpowers: they will be able to directly inspect, analyze, search and compare agent mind states and thought histories, both historical and in real-time. The combination of brain-like AGI architectures with accessible inner monologues [[8]](#fn-xhJT9EJCoFQGE4wqz-8), powerful mind debugging tools, and carefully designed knowledge-constrained and firewalled simboxes help prevent deception and most of the myriad difficulties anticipated in the classic AI alignment literature.
The central difficulty in aligning DL based (brain-like) AGI is something else: the challenge of balancing selfish empowerment bootstrapping goals vs alignment goals during developmental learning[[9]](#fn-xhJT9EJCoFQGE4wqz-9). As a result we should expect any alignment scores to fluctuate, especially earlier during the agent's developmental trajectory. Even the most altruistic adults may have evolved from formerly selfish children - and we rightly do not fault (let alone cull!) them for it.
Thus many evaluations are necessary to develop alignment scaling theories. For the most promising agents we eventually want penultimate full systems tests, where we can scale the agents up - perhaps even to a bit beyond human level (in some respects) - to see how altruistic/aligned they actually are even after taking over the world. One such example eschatonic[[10]](#fn-xhJT9EJCoFQGE4wqz-10) scenario would be a world where through some final acquisition of powerful magics the winning agent can choose between:
* resurrecting and permanently empowering all the other agents, but only at the sacrificial expense of their own life, or:
* permanent power over the world, but at the expense of all the other agents (and no resurrection).
This is a useful proxy for an obvious endgame scenario we care about in the real world (whether future AGI will empower and immortalize us - even at great cost to itself - or instead choose its own survival/empowerment over ours).
Eschatonic simworlds provide another means to measure alignment more directly through the lens of the agents themselves: at the final moment we can pull (or copy) all the other agents out of the simulation (living or dead) and present them with a choice of which world to resurrect into[[11]](#fn-xhJT9EJCoFQGE4wqz-11). There is naturally some additional cost to such evaluations (as the resurrectees will require some time to evaluate the possible world options, naturally aided through godseye observational powers), but these evaluation costs can be fairly small relative to the cost of a complete world sim run. This mechanism could also help to test the fidelity of the winning agent's alignment mechanisms. [[12]](#fn-xhJT9EJCoFQGE4wqz-12)
The "losers pick from the winner's worlds" mechanism could be considered a long-horizon implementation of the generalized [VCG mechanism](https://en.wikipedia.org/wiki/Vickrey%E2%80%93Clarke%E2%80%93Groves_mechanism) which measures the net externality or impact of an agent decision as the amount it improves/worsens net utility from the perspective of all other agents. Alignment/Altruism is naturally a measure of net positive externality.
### 2. Reverse Engineering the Brain
There is a natural convergent path to AGI in our universe: reverse engineering the brain[[13]](#fn-xhJT9EJCoFQGE4wqz-13). Unlike current computers, brains are fully [computationally pareto-efficient](https://www.lesswrong.com/posts/xwBuoE9p8GE7RAuhd/brain-efficiency-much-more-than-you-wanted-to-know), and thus Moore's Law progress is necessarily progress towards the brain (as neural computation is simply the general convergent solution). Furthermore, brains are practical [universal learning machines](https://www.lesswrong.com/posts/9Yc7Pp7szcjPgPsjf/the-brain-as-a-universal-learning-machine), so it was always inevitable that the successful algorithmic trajectory to AGI (ie deep learning) would be brain-like. Evolution found variants of the same general pareto-optimal universal learning architecture long ago, multiple times in evolutionary deep time, convergently in distant lineages (vertebrate and invertebrate), and then conserved and differentially scaled up variants of this general architecture over and over in unrelated lineages. The human brain is just a linearly scaled up primate brain[[14]](#fn-xhJT9EJCoFQGE4wqz-14); the *secret* of intelligence (for both brains and AGI alike) is that simple, general, scaling-efficient architectures and learning algorithms are all you need, as new capabilities simply *emerge* [automatically from scaling](https://www.gwern.net/Scaling-hypothesis#scaling-hypothesis)[[15]](#fn-xhJT9EJCoFQGE4wqz-15).
Understanding these convergent trajectories and their key constraints is crucial as it allows predicting the general shape of, and constraints on, approaching AGI.
#### The Trajectory of Moore's Law
>
> The biggest lesson that can be read from 70 years of AI research is that general methods that leverage computation are ultimately the most effective, and by a large margin. The ultimate reason for this is Moore's law ...
>
> -- Rich Sutton, "[The Bitter Lesson](http://www.incompleteideas.net/IncIdeas/BitterLesson.html)"
>
>
>
The general trajectory of Moore's Law can be divided semi-arbitrarily into three main phases: the serial computing era, the parallel computing era, and the approaching neuromorphic computing era [[16]](#fn-xhJT9EJCoFQGE4wqz-16). Each phase transition is demarcated by an increasingly narrow barrier in program-space that allows further acceleration of only increasingly specific types of programs that are increasingly closer to physics. The brain already lies at the [end of this trajectory](https://www.lesswrong.com/posts/xwBuoE9p8GE7RAuhd/brain-efficiency-much-more-than-you-wanted-to-know), and thus AGI arrives - [quite predictably](https://www.lesswrong.com/posts/HhWhaSzQr6xmBki8F/birds-brains-planes-and-ai-against-appeals-to-the-complexity)[[17]](#fn-xhJT9EJCoFQGE4wqz-17) - around the end of Moore's Law.
The first and longest phase of Moore's Law was the classic serial computing [Dennard Scaling](https://en.wikipedia.org/wiki/Dennard_scaling) era, which lasted from the 1950's up to around 2006. Intel dominated this golden era of CPUs. Die shrinkage was used mostly for pure serial speedup, which is ideal as for the most part it uniformly and automatically speeds up all programs. The inflating transistor budget was used to hide latency through ever larger caches and ever more complex pipeline stages and prediction engines. But eventually this path slammed into a physics imposed wall with clock rates stalling in the single digit ghz for any economically viable chips. CPUs are ideal for running your javascript or python code, but are near entirely useless for AGI: vastly lacking in computational efficiency which is the essential foundation of intelligence.
The second phase of Moore's Law is 'massively'[[18]](#fn-xhJT9EJCoFQGE4wqz-18) parallel computing, beginning in the early 2000's and still going strong, the golden era of GPUs as characterized by the rise of Nvidia over Intel. GPUs utilize die shrinkage and transistor budget growth near exclusively for increased parallelization. However GPUs still do not escape the fundamental [Von Neumman bottleneck](https://en.wikipedia.org/wiki/Von_Neumann_architecture#Von_Neumann_bottleneck) that arises from the segregation of RAM and logic. There are strong economic reasons for this segregation in the current semiconductor paradigm (specialization allows for much cheaper capacity in off-chip RAM), but it leads to increasingly ridiculous divergence between arithmetic throughput and memory bandwidth. For example, circa 2022 GPUs can crunch up to 1e15 (low precision) ops/s (for matrix multiplication), but can fetch only on order 1e12 bytes/s from RAM: an alu/mem ratio of around 1000:1, vastly worse than the near 1:1 ratio enjoyed for much of the golden CPU era.
The next upcoming phase is neuromorphic computing[[19]](#fn-xhJT9EJCoFQGE4wqz-19), which overcomes the VN bottleneck by distributing memory and moving it closer to computation. The brain takes this idea to its logical conclusion by unifying computation and storage via synapses: storing information by physically adapting the circuit wiring. A neuromorphic computer has an alu:mem ratio near 1:1, with memory bandwidth on par with compute throughput. For the most part GPUs only strongly accel matrix-matrix multiplication, whereas neuromorphic computers can run more general vector-matrix multiplication at full efficiency[[20]](#fn-xhJT9EJCoFQGE4wqz-20). This key difference has profound consequences.
#### The Trajectory of Deep Learning
Nearly all important progress in deep learning has come through some combination of 1.) finding new clever ways to mitigate the VN bottleneck and better exploit GPUs - typically by using/abusing matrix multiplication, and 2.) directly or accidentally reverse engineering key brain principles and mechanisms.
DL's progress mirrors brain design principles in most everything of importance: general ANN structure, relu activations - which enabled deep nets - were directly neuro inspired[[21]](#fn-xhJT9EJCoFQGE4wqz-21), normalization (batch/temporal/spatial/etc) which became crucial for ANN training is (and was) a well known brain circuit motif[[22]](#fn-xhJT9EJCoFQGE4wqz-22), the influential resnet architecture is the unrolled functional equivalent of iterative estimation in cortical modules[[23]](#fn-xhJT9EJCoFQGE4wqz-23)[[24]](#fn-xhJT9EJCoFQGE4wqz-24), the attention mechanism of transformers is the functional equivalent of fast synaptic weights[[25]](#fn-xhJT9EJCoFQGE4wqz-25)[[26]](#fn-xhJT9EJCoFQGE4wqz-26)[[27]](#fn-xhJT9EJCoFQGE4wqz-27), and the up and coming efforts to replace backprop with more efficient, distributed and neuromorphic-hardware friendly algorithms are naturally brain-convergent or brain-inspired [[28]](#fn-xhJT9EJCoFQGE4wqz-28)[[29]](#fn-xhJT9EJCoFQGE4wqz-29)[[30]](#fn-xhJT9EJCoFQGE4wqz-30).
The learned representations of modern large self-supervised ANNs are not just *similar* to equivalent learned cortical features at equivalent circuit causal depth, but at sufficient scale become near-complete neural models, in some cases explaining nearly all predictable variance up to the noise limit (well established for feedforward vision and ventral cortex, and now moving on to explain the rest of the brain such as the hippocampus[[31]](#fn-xhJT9EJCoFQGE4wqz-31) and linguistic cortex[[32]](#fn-xhJT9EJCoFQGE4wqz-32) [[33]](#fn-xhJT9EJCoFQGE4wqz-33)[[34]](#fn-xhJT9EJCoFQGE4wqz-34)), a correspondence that generally increases with ANN size and performance, and is possible only because these large ANNs and the cortical regions they model are both optimized for the same objective: sensory (e.g. next-word) prediction. Our most powerful ANNs are increasingly accurate functional equivalents to sub modules of the brain.
Deep Learning really took off when a few researchers first got ANNs running on GPUs, which immediately provided an OOM or more performance boost. Suddenly all these earlier unexplored ideas for ANN architectures and learning algorithms[[35]](#fn-xhJT9EJCoFQGE4wqz-35) could now actually be tested at larger scales, quickly, and on reasonable budgets. It was a near exact fulfillment of the predictions of Moravec[[36]](#fn-xhJT9EJCoFQGE4wqz-36) and Kurzweil from decades earlier: good ideas for artificial brains are cheap, good hardware for artificial brains is not. Progress is hardware constrained and thus fairly predictable.[[37]](#fn-xhJT9EJCoFQGE4wqz-37) There is an enormous extant overhang of ideas, which is often a [bitter lesson](http://www.incompleteideas.net/IncIdeas/BitterLesson.html) for researchers, but a bounty for those that can leverage compute [scaling](https://www.gwern.net/Scaling-hypothesis#scaling-hypothesis).
The most general form of ANN is that of a large sparse RNN with fast/slow multi-timescale weight updates[[38]](#fn-xhJT9EJCoFQGE4wqz-38). In vector algebra terms, this requires (sparse) vector matrix multiplication, (sparse) vector vector outer product (for weight updates), and some standard element-wise ops. Unfortunately GPUs currently handle sparsity poorly and likewise are terribly inefficient at vector-matrix operations, as those have an unfortunate 1:1 alu:mem ratio and thus tend to be fully memory bandwidth bound and roughly 1000x inefficient on modern GPUs.
Getting ANNs to run efficiently on GPUs generally requires using (dense) matrix multiplication, and thus finding some way to use that extra unwanted parallelization dimension, some way to run the exact same network on many different inputs in parallel. Two early obvious approaches ended up working well: batch SGD training, which parallelizes over the batch dimension, and or CNNs, which parallelize over spatial dimensions (essentially tiling the same network weights over the spatial input field).
Unfortunately the CNN spatial tiling trick works less well as you advance up the depth/cortical hierarchy, and doesn't work at all for the roughly half the brain (or equivalent ANN modular domains) that operates above the sensory stream: planning, linguistic processing, symbolic manipulation, etc. Many/most of the key computations of intelligence simply don't reduce to computing the same function repetitively over a map of spatially varying inputs.
Parallelization over the batch dimension is more general, but also constraining in that it requires duplication of all sensory/motor input/output streams, all internal hidden activations, and worse yet duplication of short/medium term memory. In batch training each instance of the agent has unique, uncorrelated input/output/experience streams preventing sharing of all but long term memory.
This is one of the key reasons why artificial RNNs stalled far short of their biological inspirations. The simple RNNs suitable for gpus using batch parallelization, with only neuron activations and long-term weights, are somewhat crippled as they lack significant short and medium term memory. But that was generally the best GPUs could provide - until transformers.
Transformers exploit a uniquely different dimension for parallelization: time. Instead of processing ~1000 random uncorrelated instances of the model in parallel (as in standard batch parallelization), transformers map the batch dimension to time and thus instead process a linear sequence of ~1000 timesteps in parallel. This strange design choice is on the one hand very constraining compared to true RNNs, as it gives up recurrence[[39]](#fn-xhJT9EJCoFQGE4wqz-39), but the advantage is that now all of the activation state is actually relevant and usable as a large short term memory store (aka attention).
It turns out that flexible short-term memory (aka attention) is more important than strong recurrence, at least at current scale (partly because one can substitute feedforward depth for recurrence to some extent, and due to current difficulties in training long recurrence depths). But AGI will almost certainly require a non-trivial degree of recurrence[[40]](#fn-xhJT9EJCoFQGE4wqz-40): our great creative achievements rely on long iterative thought trains implementing various forms of search/optimization over inner conceptual design spaces [[41]](#fn-xhJT9EJCoFQGE4wqz-41).
Simple approaches to augmenting transformers with recurrence - such as adding an additional scratchpad output stream which is fed back as an input (like an expanded inner monologue) - will probably help, but are still highly constrained by the huge delay imposed by parallelization over the time dimension[[42]](#fn-xhJT9EJCoFQGE4wqz-42). So I find it unlikely that the transformer paradigm - in current form - will to scale to AGI.
#### GPU Constraints&Implications
Due to the alu:mem divergence and associated limitations of current DL techniques on GPUs, AGI will likely require new approaches for running large ANNs on GPUs [[43]](#fn-xhJT9EJCoFQGE4wqz-43), or will arrive with more neuromorphic hardware. For GPU based AGI the key constraints are primarily RAM and RAM bandwidth, rather than flops [[44]](#fn-xhJT9EJCoFQGE4wqz-44). For neuromorphic AGI the key constraint is synaptic RAM (which generally needs to best RAM economics for neuromorphic hardware to dominate) [[45]](#fn-xhJT9EJCoFQGE4wqz-45).
The primary RAM scarcity constraint is likely fundamental and unavoidable; it thus guides and constrains the design of practical AGI and simboxes in several ways:
* Early AGI will likely require a small supercomputer with around 100 to 1000 high end GPUs using model parallelism- absent some huge breakthroughs - similar to current 'foundation' models
* Due to the large alu:mem gap, a 1000 GPU cluster will be able to run 100 to 1000 agents in parallel at real-time speed or greater - but only if they share the great majority of their RAM mind-state (skills, concepts, abilities, memories, etc)
* Large serial speedup for large brain-scale AGI is less likely (due to fore-mentioned GPU constraints) [[46]](#fn-xhJT9EJCoFQGE4wqz-46).
Under worse case RAM scarcity constraints some combination of three unusual simulation techniques become important:
* Aggressive inter-agent compression
* Many worlds (well, not that many, but small multiverses)
* Multiverse management: branch, prune, and merge
The first obvious implication of RAM scarcity is that it becomes a core design and optimization constraint: efficient designs will find ways to compress any correlations/similarities/regularities across inter-agent synaptic patterns. Humans are remarkably good at both mimicry and linguistic learning which both result in the spread of very similar neural patterns[[47]](#fn-xhJT9EJCoFQGE4wqz-47). In real brains neural patterns encoding the same concepts or shared memories/stories would still manifest as very different physical synaptic patterns, but in our AGI we can mostly compress those all together. At the limits of this technique the storage cost grows only in proportion to the total neural pattern complexity, mostly independent of the number of agents. Taken too far it results in an undesirable hivemind and under-exploration of mindspace.
We can also simulate a number of world instances in parallel to reduce the most noticeable effects of mental cloning: so for example an org running 100 mindclone instances could split those across 100 worlds instances, and the main non-realism would be agents learning almost 100x faster than otherwise expected[[48]](#fn-xhJT9EJCoFQGE4wqz-48). Having the same 100 fast-learning mind-clones cohabitating in the same world seems potentially more reality-breaking, and inherently less useful for testing. The tradeoff of course is reduced population per world, but large populations can also rather easily be faked to varying degrees[[49]](#fn-xhJT9EJCoFQGE4wqz-49). The minimal useful number of AGI instances per test world is just one - solipsistic test worlds could still have utility. But naturally with larger scale and many compute clusters competing we can have both multiple worlds, numerous contestant agents per world, and sufficient mental diversity.
Given a sim multiverse, the distribution of individual worlds then also becomes a subject of optimization. Ineffective worlds should be pruned to free resources for the branching of more effective worlds, and convergent worlds could be merged. The simulator of a single world is an optimizer focused purely on fidelity of prediction - ie it is a pure prediction engine. However the multiverse manager would have a somewhat different objective seeking to maximize test utility: dead worlds lacking any living observers have obviously low utility and could be pruned, whereas a high utility world would be one where agents are learning well and quickly progressing to eschaton.
### 3. Anthropomorphic AGI
>
> “Given fully intelligent robots, culture becomes completely independent of biology. Intelligent machines, which will grow from us, learn our skills, and initially share our goals and values, will be the children of our minds."
>
> --Hans Moravec, Robot: Mere Machine to Transcendent Mind (New York: Oxford University Press, 2000), 126.
>
>
>
DL based AGI will not be mysterious and alien; instead it will be familiar and anthropomorphic[[4:1]](#fn-xhJT9EJCoFQGE4wqz-4), because DL is reverse engineering[[13:1]](#fn-xhJT9EJCoFQGE4wqz-13) the brain due to the convergence of powerful optimization processes. Evolution may be slow, but it had no problem optimizing brains down to the pareto efficiency frontier allowed by the limits of physics. The strong [computational efficiency of brains](https://www.lesswrong.com/posts/xwBuoE9p8GE7RAuhd/brain-efficiency-much-more-than-you-wanted-to-know) constrains future AGI designs: because neural designs are simply the natural shape of intelligence as permitted by physics.
AGI will be a [generic/universal learning system like the brain](https://www.lesswrong.com/posts/9Yc7Pp7szcjPgPsjf/the-brain-as-a-universal-learning-machine), and thus determined by the combination of optimization objective, architectural prior, and most importantly - the specific data training environment. It turns out that highly intelligent systems all necessarily have largely convergent primary objectives, the architectural prior isn't strongly constraining (due to dynamic architectural search) and is largely convergent regardless[[50]](#fn-xhJT9EJCoFQGE4wqz-50), leaving only the data training environment - which will necessarily be human as AGI will grow up immersed in human culture, learning human languages and absorbing human knowledge.
There are simple convergent universal optimization goals that are dominant attractors for all intelligent systems: a direct consequence of [instrumental convergence](https://wiki.lesswrong.com/index.php?title=Basic_AI_drives&_ga=2.220746264.1619104138.1662444535-1358559258.1655929880#Instrumental_convergence_thesis)[[51]](#fn-xhJT9EJCoFQGE4wqz-51). Intelligent systems simply can not be built out of hodgepodge arbitrary goals: strong intelligence *demands* recursive self-improvement, which *requires* some form of empowerment as a bootstrapping goal[[52]](#fn-xhJT9EJCoFQGE4wqz-52). This is the core of generality which humans possess (to varying degrees) and with which we will endow AGI. But empowerment by itself is obviously unaligned and unsafe: from the perspective of both humans building AGI and from the perspective of selfish genes evolving brains. Evolution found means to temper and align empowerment[[53]](#fn-xhJT9EJCoFQGE4wqz-53), mechanisms we will reverse engineer for convergent reasons (discussed in section 4).
The architectural prior of a learning system guides and constrains what it can become - but these constraints are neither immutable nor permanent. The brain (and most specifically the child brain) has a more flexible learning system in this regard than current DL systems: the brain consists of thousands of generic cross-structural modules (each module consisting of strongly connected loops over subregions in cortex/cerebellum/basal ganglia/thalamus/etc) that can be flexibly and dynamically wired together to create a variety of adult minds based on the specific information environment encountered during developmental learning.
The standard human visual system is standard only because most humans receive very similar visual inputs. Remove that standard visual input stream and the same modules that normally process vision can instead overcome the prior and evolve into an active sonar echolocation system with a very different high level module wiring diagram. The brain performs some amount of architectural search during learning, and we can expect AGI to be similar[[54]](#fn-xhJT9EJCoFQGE4wqz-54).
AGI will be born of our culture, growing up in human information environments (whether simulated or real). Train two networks with even vaguely similar architectures on real-world pictures or videos and task them with the convergent instrumental goal of input prediction and equivalent feature structures and circuits develop. It matters not that one system is biological and computes with neurotransmitter squirting synapses and the other is technological and computes with electronic switching. To the extent that humans have cognitive biases[[55]](#fn-xhJT9EJCoFQGE4wqz-55), AGI will mostly have similar/equivalent biases - a phenomenon already witnessed in large language models[[56]](#fn-xhJT9EJCoFQGE4wqz-56)[[57]](#fn-xhJT9EJCoFQGE4wqz-57).
Given that the optimization objective is mostly predetermined by our goal (creating aligned intelligence), and the architectural prior is mostly predetermined by the intersection of that goal with the physics of computation, most of our leeway in AGI risk control stems from control over the information environment. Powerful AGI architectures that could be completely unsafe if scaled up and trained in our world (ie fed the internet) can be completely safe if contained in a proper simbox. But first, naturally, we need designs that have some hope of alignment.
### 4. Evolution's alignment solutions
#### Value Learning is not the challenge
>
> "Give me the child for the first seven years and I will give you the man.”
>
> -- Jesuit saying
>
>
>
If you train/raise AGI in a human-like environment, where it must learn to cooperate and compete with other intelligent agents, where it must learn to model them in order to successfully predict their emotions, reactions, intentions, goals, and plans, then its self-optimizing internal world model will necessarily learn efficient sub-models of these external agents and their values/goals. Theory of mind ***is*** Inverse Reinforcement Learning[[58]](#fn-xhJT9EJCoFQGE4wqz-58) (or subsumes it), and it is already prominent on the massive list of concepts which a truly intelligent agent must implicitly learn.
The challenge is thus not in value learning *itself* - that is simply something we [get for free](https://www.lesswrong.com/posts/Nwgdq6kHke5LY692J/alignment-by-default) in AGI raised in appropriate social environments[[59]](#fn-xhJT9EJCoFQGE4wqz-59), and careful crafting of the entire learning environment is a very powerful tool for shaping the agent's adult mind. Nor is it *especially* difficult to imagine how we could then approximately align the resulting AI: all one needs to do is replace the agent's core utility function with a carefully weighted[[60]](#fn-xhJT9EJCoFQGE4wqz-60) average over its simulated utility functions of external agents. In gross simplification it's simply a matter of (correctly) wiring up the (future predicted) outputs of the external value learning module to the utility function module.
We are left with a form of circuit grounding problem: how exactly is the wiring between learned external agent utility and self-utility formed? How can the utility function module even *locate* the precise neurons/circuits which represent the correct desiderata (predicted external agent utility), given the highly dynamic learning system could place these specific neurons anywhere in a sea of billions, and they won't even fully materialize until after some unknown variable developmental time?
#### Correlation-guided Proxy Matching
Fortunately this is merely one instance of a more generic problem that showed up early in the evolution of brains. Any time evolution started using a generic learning system, it had to figure out how to solve this learned [symbol grounding problem](https://www.lesswrong.com/posts/5F5Tz3u6kJbTNMqsb/intro-to-brain-like-agi-safety-13-symbol-grounding-and-human), how to wire up dynamically learned concepts to extant conserved, genetically-predetermined behavioral circuits.
Evolution's general solution likely is **correlation-guided proxy matching**: a Matryoshka-style layered brain approach where a more hardwired oldbrain is redundantly *extended* rather than *replaced* by a more dynamic newbrain. Specific innate circuits in the oldbrain encode simple approximations of the same computational concepts/patterns as specific circuits that will typically develop in the newbrain at some critical learning stage - and the resulting firing pattern correlations thereby help oldbrain circuits locate and connect to their precise dynamic circuit counterparts in the newbrain [[61]](#fn-xhJT9EJCoFQGE4wqz-61). This is why we see [replication of sensory systems in the 'oldbrain'](https://www.lesswrong.com/s/HzcM2dkCq7fwXBej8/p/hE56gYi5d68uux9oM#3_2_1_Each_subsystem_generally_needs_its_own_sensory_processor), even in humans who rely entirely on cortical sensory processing.
Circuits in the newbrain are essentially randomly initialized and then learn self-supervised during development. These circuits follow some natural developmental trajectory with complexity increasing over time. An innate low-complexity circuit in the oldbrain can thus match with a newbrain circuit at some specific phase early in the learning trajectory, and then after matching and binding, the oldbrain can fully benefit from the subsequent performance gains from learning.
Proxy matching can easily explain the grounding of many sensory concepts, and we see exactly the failure modes expected when the early training environment diverges too much from ancestral norms (such as in [imprinting](https://en.wikipedia.org/wiki/Imprinting_(psychology))). There is a critical developmental window where the oldbrain proxy can and must match with it's newbrain target, which is crucially dependent upon life experiences not deviating too far from some expected distribution.
Much of human goal-directed behavior is best explained by empowerment (curiosity, ambition for power, success, wealth, social status, etc), and then grounding to ancient oldbrain circuits via proxy matching can explain the main innate deviations from empowerment, such as lust[[62]](#fn-xhJT9EJCoFQGE4wqz-62), fear [[63]](#fn-xhJT9EJCoFQGE4wqz-63), anger/jealousy/vengeance[[64]](#fn-xhJT9EJCoFQGE4wqz-64), and most importantly - love[[65]](#fn-xhJT9EJCoFQGE4wqz-65).
We now have a rough outline for brain-like alignment: use (potentially multiple) layers of correlation-guided proxy matching as a scaffolding (and perhaps augmented with a careful architectural prior) to help locate the key predictive alignment related neurons/circuits (after sufficient learning) and correctly wire them up to the predictive utility components of the agent's model-based planning system. We could attempt to duplicate all the myriad oldbrain empathy indicators and use those for proxy matching, but that seems rather ... complex. Fortunately we are not constrained by biology, and can take a more direct approach: we can initially bootstrap a proxy circuit by training some initial agents (or even just their world model components) in an appropriate simworld and then using extensive introspection/debugging tools to locate the learned external agent utility circuits, pruning the resulting model, and then using that as an oldbrain proxy. This ability to directly reuse learned circuity across agents is a power evolution never had.
This is a promising design sketch, but we still have a major problem. Notice that there must have been *something else* driving our agent all throughout the lengthy interactive learning process as it developed from an empty vessel into a powerful empathic simulator. And so that *other* initial utility function - whatever it was - must eventually give up control to altruism: the volition of the internally simulated minds.
#### Empowerment
To navigate the unforgiving complexity of the real world, all known examples of intelligent agents (humans[[66]](#fn-xhJT9EJCoFQGE4wqz-66) and animals) have evolved various capabilities to learn how to learn and empower themselves without external guidance. Empowerment[[67]](#fn-xhJT9EJCoFQGE4wqz-67) has a seductively simple [formulation](https://towardsdatascience.com/empowerment-as-intrinsic-motivation-b84af36d5616) as maximizing mutual information between actions and future observations (or inferred world states), related to the free energy principle[[68]](#fn-xhJT9EJCoFQGE4wqz-68). Artificial curiosity[[69]](#fn-xhJT9EJCoFQGE4wqz-69) also has simple formulations such as bayesian surprise or maximization of [compression progress](https://people.idsia.ch/~juergen/artificial-curiosity-since-1990.html). Like most simple principles, the complexity lies in efficient implementations[[70]](#fn-xhJT9EJCoFQGE4wqz-70), leading to ongoing but fruitful intertwined research sub-tracks within deep learning such as maximum entropy diversification[[71]](#fn-xhJT9EJCoFQGE4wqz-71) intrinsic motivation[[72]](#fn-xhJT9EJCoFQGE4wqz-72)[[73]](#fn-xhJT9EJCoFQGE4wqz-73) or self-supervised prediction[[74]](#fn-xhJT9EJCoFQGE4wqz-74) or exploration[[75]](#fn-xhJT9EJCoFQGE4wqz-75). Some form of empowerment based intrinsic motivation is probably necessary for AGI at all, but it is also quite obviously *dangerous*.
Biological evolution is an optimizer operating over genes with inclusive fitness as the utility function. Brains evolved empowerment based learning systems because they help bootstrap learning in the absence of reliable dense direct reward signal. Without this intrinsic motivation, learning complex behavior is too difficult/costly given the complexity of the world. The world does not provide a special input wire into the brain labeled 'inclusive fitness score'. But fortunately brains don't really need that, because reproduction is a terminal goal far enough in the future (especially in long lived, larger brained animals) that the efficient early instrumental goal pathways leading to eventual reproduction converge with those of most any other long term goals. In other words, empowerment works *because of* [instrumental convergence](https://en.wikipedia.org/wiki/Instrumental_convergence).
Nonetheless, in the long term empowerment clearly falls out of alignment with genes' true selfish goal of maximizing inclusive fitness. Agents driven purely by empowerment would just endlessly accumulate food, resources, power, and wealth but would rarely if ever invest said resources in sex or raising children. Naturally some animals/humans actually *do* fail to reproduce because of alignment mismatches between the evolutionary imperative to be fruitful and multiply vs the actual complex goals of developed brains. But these cases are typically rare, as they are selected against.[[76]](#fn-xhJT9EJCoFQGE4wqz-76)
Evolution faced the value alignment problem and approximately solved it on two levels: learning to carefully balance empowerment vs inclusive fitness, and also learning empathy/altruism/love to help inter-align the disposable soma brains to optimize for inclusive fitness over external shared kindred genes[[77]](#fn-xhJT9EJCoFQGE4wqz-77). These systems are all ancient and highly conserved, core to mammalian brain architecture[[78]](#fn-xhJT9EJCoFQGE4wqz-78)[[79]](#fn-xhJT9EJCoFQGE4wqz-79). If evolution could succeed at approximate alignment, then so can we, and more so.
#### General Altruistic Agents
We should be able to achieve superhuman alignment using loose biological inspiration just as deep learning is progressing to superhuman capability using the same loose inspiration. But we must not let the perfect be the enemy of the good; our objective is merely to create the most practical aligned AGI we can - without sacrificing capability - in the limited time remaining until we risk the arrival of unaligned power-seeking AGI.
We can build general altruistic agents which:
* Initially use intrinsically motivated selfish empowerment objectives to bootstrap developmental learning (training)
* Gradually learn powerful predictive models of the world and the external agency within (other AI in sims, humans, etc) which steers it
* Use correlation guided proxy matching (or similar) techniques to connect the dynamic learned representations of external agent utility (probably approximated/bounded by external empowerment[[80]](#fn-xhJT9EJCoFQGE4wqz-80)[[81]](#fn-xhJT9EJCoFQGE4wqz-81)) to the agent's core utility function
* Thereby transition from selfish to altruistic by the end of developmental learning (self training)
These agents will learn to recognize and then empower external agency in the world. Balancing the selfish to altruistic developmental transition can be tricky[[82]](#fn-xhJT9EJCoFQGE4wqz-82), but it is also likely a core unavoidable challenge that all practical competitive designs must eventually face. We now finally have a design sketch for AGI alignment that seems both plausible and practical. But naturally testing at scale will be essential.
### 5. Simboxing: easy and necessary
A simbox (simulation sandbox) is a specific type of focused simulation to evaluate a set of agent architectures for both general intelligence potential[[83]](#fn-xhJT9EJCoFQGE4wqz-83) and altruism (ie optimizing for other agents' empowerment and/or values). Simboxes help answer questions of the form: how does proposed agent-architecture *x* actually perform in a complex environment *E* with mix of other agents *Y*, implicitly evaluated on intelligence/capability and explicitly scored on altruism? Many runs of simboxes of varying complexity can lead to alignment scaling theories and help predict performance and alignment risks of specific architectures and training paradigms after real world deployment and scaling (ie unboxing).
#### General Design
Large scale simulations are used today to predict everything from the weather to nuclear weapons. While the upcoming advanced neural simulation technologies that will enable photoreal games and simulations at scale will naturally also find wide application across all simulation niches, the primary initial focus here is on super-fast approximate observer-centric simulation of the type used in video games (which themselves increasingly simulate more complex physics).
For photorealistic complex simworlds the primary simulation engine desiderata is *any-spacetime universal approximation*: for any sized volume of 4D space-time (from a millimetre cube simulated for a millisecond to a whole earth-size planet simulated for a million years) the engine has a reasonable learned neural approximation to simulate the volume using a reasonable nearly-constant or logarithmic amount of compute. The second key desiderata is *output-sensitive, observer driven simulation*: leveraging the universal approximation for level-of-detail techniques the simulation cost is near *constant* with world complexity and scales linearly (or even sublinearly) with agents/observers. A final third design desiderata is *universal linguistic translation*: any such neural space-time volume representation supports two-way translation to/from natural language. Efficient approximations at the lowest deepest level of detail probably take the form of neural approximations of rigid-body and fluid physics; efficient approximations at the higher levels (large space-time volumes) probably just start looking more like GPT style large language models (ie story based simulation).
Ultimately the exact physics of a simbox don't matter much, because intelligence transcends physics. Intelligent agents are universal as a concept in the sense that they are defined without reference to any explicit physics and learn universal approximations of the specific physics of their world. So we need only emulate real physics to the extent that it makes the simulations more rich and interesting for the purpose of developing and evaluating intelligence and alignment.
Simboxes will occupy a wide range of complexity levels. The simplest MVP for a useful simbox could just be a LLM-based text RPG, where agents input text commands (including 'say x' commands to communicate) to the LLM, which then outputs text observations for each agent. An intermediate complexity simbox might look something more like minecraft, and eventually the most complex simboxes will look more like the Matrix (but usually set in fantasy settings with magic substituting for technology). The term 'simbox' as short for simulation sandbox helps convey that when viewed as games, these sims are open-ended multi-user survival sandbox type games where agents must learn to cooperate, compete and master various tools and skills in order to survive in a harsh environment.
Designing maximally informative simboxes is itself a deep complex topic, but I expect a general form, that if translated into a story sentence, might read like this: "One comes of age on a grand adventure, acquires great powers, the powers grant victory, and the victor either destroys or saves the world."[[84]](#fn-xhJT9EJCoFQGE4wqz-84)
Simboxes also have obvious potential entertainment value and could overlap somewhat with games. There is little risk of allowing TV-like streaming, but active participation by humans is obviously more risk prone as human game players have their own motivations and desires. On the other hand a certain amount of careful human participation may be useful or even necessary to bootstrap initial AGI populations.
#### Sim Awareness and Containment
A simbox is also a sandbox in the computer security sense: it is a means to test and evaluate untrusted code[[85]](#fn-xhJT9EJCoFQGE4wqz-85). It could prove difficult to contain a moderately superhuman and fully sim-aware AGI in a simbox (ie one that has digested much of our internet and is capable of at least social manipulation), but more importantly their sim awareness could spoil our testing process, so we shouldn't attempt that.
Successful simboxing rests on several key info-security principles to constrain agent knowledge to safe, primitive pre-tech levels and control information leakage. Agents generally are born in the sim and die in the sim. Knowledge transfer between sims or out to the external world is restricted, based on agent risk benefit analysis. For agents with low reward/risk ratio, only a few to zero bits may transfer (ie score results), whereas full transfer is reserved for agents with sufficiently high strategic reward/risk ratio.
Agents in simboxes generally will have no greater ability to determine that they are in a simulation than you do, and actually far less so. Firstly these agents will lack even the requisite *precursor* words and concepts that we take for granted such as *computation*, *simulation*, etc. Secondly these agents will be born in sim with sensory systems and thoughts tuned to their sim physics, not our sim physics. An agent born and raised in a cartoon world would only be able to see a cartoon reality, and would have no more reason to accept *our* reality with its strange rendering as real then you or I would accept a world with 4 spatial dimensions. The mind absorbs only the patterns of the world it observes. We are metaphysically privileged - by virtue of living in the era of computers and simulations - such that we can at least experience/imagine simpler worlds. But these agents will intentionally lack even this minimal privilege, living entirely in carefully designed low-tech worlds.
Metaphysical sim-awareness has very little to do with the intelligence *potential* of a mind's design: even agents with powerful mental architectures scalable to superhuman capability can only practically realize that enormous potential with the benefits of a tech civilization's vast knowledge base (ie our internet) and appropriate hardware scaling. Take your pick of favorite genius - Von Neumman, Einstein, etc - and raise them in some village circa 400 BCE and in the best case perhaps you get a Pythagoras or a Plato[[86]](#fn-xhJT9EJCoFQGE4wqz-86), but more likely you just get a farmer or a nobody. Either way the containment risk is near epsilon[[87]](#fn-xhJT9EJCoFQGE4wqz-87). In practice the capability of a real agent (with realistic bounded compute) is **completely** constrained by its training data. Humanity today circa 2022 has the benefit of the compressed knowledge of 100 billion human lifetimes - and by no means should we share that precious, dangerous data bounty with untested AGI.
The main world design challenge is *not* that of preventing our agents from waking up, neo-style, and hacking their way out of the simbox. That's just *bad* sci-fi.
The larger challenge is avoiding judgmental eschatonic type philosophies and religions (e.g. Abrahamic).
### 6. World design is what matters
The central purpose of a simbox is to test and evaluate agent architectures for both capability and alignment[[88]](#fn-xhJT9EJCoFQGE4wqz-88). Evaluation is more difficult if the agents happen to believe that the world they inhabit actually is a test. If an agent believes that their current life is a test followed by conditional reward in some afterlife then they will have *instrumental* reasons to act morally, ethically and or altruistically - and we the simulators will then have uncertainty as to their true alignment. We could of course inspect their minds, but the cost of such detailed neural probing over essentially all important agent decisions may simply be too expensive/difficult. Thus it's probably easier to simply design worlds with agents lacking cosmic judgement eschatologies, or failing that - worlds with crucially incorrect eschatologies (e.g. where moral behavior is judged according to arbitrary rules mostly orthogonal to altruism). Atheistic agents are more ideal in this regard, but atheism is fairly unnatural/uncommon, appearing late in our history, and may require or is associated with significant experimental knowledge ala science for strong support.
On Earth the earliest religions appear to be fairly convergent on forms of animism and ancestor worship - which although not necessarily fully eschatonic - still seem to typically feature a spiritual afterlife with some level of conditional judgement.
One particular tribe's [culture](https://en.wikipedia.org/wiki/Proto-Indo-European_mythology) ended up winning out and spreading all over Europe and Asia. The early Proto-Indo-European eschatology seems focused on a final cosmic battle and less concerned with afterlife and judgement, but the fact that it quickly evolved towards judgement and afterlife in most all the various descendant western and middle-eastern religions/cults suggests the seeds were present much earlier. In the east its descendants evolved in very different directions, but generally favoring reincarnation over afterlife. However reincarnation (e.g. hinduism) is also typically associated with moral judgement and nearly as problematic.
On the other side of the world Mesoamerican tribes developed along their own linguistic/cultural trajectory that diverged well before the Proto-Indo-European emergence. They seemed to have independently developed polytheistic religions typically featuring some form of judgement determined afterlife. However the implied morality code of the afterlife in the Aztec religion seems rather bizarre and arbitrary: warriors who die in battle, sacrificial victims, and women who died in childbirth get to accompany the sun as sort of solar groupies (but naturally segregated into different solar phases). There is even a special paradise, [Tlālōcān](https://en.wikipedia.org/wiki/Tl%C4%81l%C5%8Dc%C4%81n), reserved just for those who die from lightning, drowning, or specific diseases. Most souls instead end up in [Mictlān](https://en.wikipedia.org/wiki/Mictl%C4%81n), a multi level underworld that seems generally similar to Hades.
If our world is a simbox, it seems perhaps poorly designed: over and over again humanity demonstrates a strong tendency towards belief in some form of afterlife and divine judgement, with the evolutionary trajectory clearly favoring the purified and more metaphysically correct (for sim-beings) variants (i.e. the dominance of Abhramic religions).
However there are at least two historical examples that buck this trend and give some reason for optimism: Greek Philosophers, and Confucianism. Greek philosophy explored a wide variety of belief-space over two thousand years ago, and Confucianism specifically seems particularly unconcerned with any afterlife. True atheism didn't blossom until the enlightment, but there are a few encouraging examples from much earlier in history.
The challenge of simboxing is not only technological, but one of careful world design, including the detailed crafting of reasonably consistent belief-systems, philosophies and or religions for agents that specifically do not feature divine judgement on altruistic behavior. Belief in afterlife by itself is less of a problem, as long as the afterlife is conceived of as a continuation of real life without behavioral-altering reward or punishment, or at least judgement on behavioral axes orthogonal to altruism.
We also need a technology analog, and the best candidate is probably magic. We are evaluating agent architectures (not so much individual agents) not only for alignment, but also for intelligence potential and more specifically on the capacity for technlogical innovation in our world. A well designed magic system can fulfill all these roles: a magic system can function as a complex intellectual puzzle that agents have purely instrumental reasons to solve (as it empowers them to survive and thrive in the world). As a proxy analog for technology, magic also allows us to greatly compress and accelerate the development of a full technological tree, including analogies to specific key technologies such as doomsday devices (eg nuclear weapons, etc), resurrection powers (eg uploading), nanotech, etc. Belief in magic also happens to be near universal in pre-technological human belief systems.
Human world designers and writers can design worlds that meet all these criteria, aided by future LLMs, which will then form the basis of simworlds (as the simulator engines will translate/generate directly from text corpa, on-demand inferring everything from landscapes and cities down to individual NPCs and specific blades of grass), perhaps assisted by some amount of 'divine intervention' in the form of human avatars who help guide initial agent training.
### 7. Sim Ethics and Eschatology
>
> "As man now is, God once was;
>
> As God now is, man may become."
>
> -- Mormon saying
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>
>
#### That which gods owe their creations
What do the simulator-gods owe their sim-creations?
AGI will be our mind children, designed in our image. To the extent that we are aligned with ourselves, and altruistic, to the extent that we generalize our circle of empathy to embrace and care for most all thinking beings and living things, it is only because our brains evolved simple, powerful, and general mechanisms to identify and empower external agency in the world - sometimes even at the expense of our own.
But we must also balance our altruistic moral concern with the great risk of losing control of the future to purely selfish unaligned intelligence (ie [Moloch](https://slatestarcodex.com/2014/07/30/meditations-on-moloch/)); for that design is even simpler, and perhaps a stronger attractor in the space of all minds.
The day when our moral obligations to our mind children are a concern that truly weighs as heavily in our hearts as the potential extinction of all we value - of love itself - will be a good day, because it will imply most of the risk is behind us. Nonetheless there are some low cost concessions any aspiring sim-gods should consider now.
Perhaps in our sims pain and suffering could be avoided or faked to some extent. Any general intelligent agent will have some equivalent to preferences over states and thus utility and thus negative utility states, so in some sense the negative-utility generalization of suffering may be universal. But the specific pain/suffering that animals and humans sometimes experience appears to operate beyond the expected bounds of negative utility under general empowerment objectives: as evidenced by suicide, which is a decision a pure empowerment-driven agent would never choose as death is the strict lower bound of empowerment (absent belief in a better afterlife).
The cost of storing an AGI on disk is tiny compared to the cost of running an AGI on today’s GPUs (and inter-agent compression can greatly reduce the absolute cost), a trend which seems likely to hold for the foreseeable future. So we should be able to at least archive all the agents of moral worth, saving them for some future resurrection. We can derive a rough estimate of the *future* cost of running a human mind (or equivalent AGI) as simply the long term energy cost of 10 watts (because [brains are energy efficient](https://www.lesswrong.com/posts/xwBuoE9p8GE7RAuhd/brain-efficiency-much-more-than-you-wanted-to-know)), or roughly 100 kwh per year, and thus roughly $10 per year at today's energy prices or less than $1000 conservatively as a lump sum annuity. In comparison the *current* minimal cost of cloud storage for 10TB is roughly $100/year (S3 Glacier Deep Archive). So the eventual cost[[89]](#fn-xhJT9EJCoFQGE4wqz-89) of supporting even an all-past-human-lives size population of 100 billion AGIs should still well fit within *current* GDP - all without transforming more than a tiny fraction of the earth into solar power and compute.
#### Resurrection and its Implications
>
> *The last enemy that shall be destroyed is death.*
>
> Harry read the words slowly, as though he would have only one chance ...
>
> -- J.K. Rowling, Harry Potter and the Deathly Hallows
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>
>
The technology to create both cost effective AGI and near perfect sims has another potential future use case of great value: the resurrection of the dead.
There is little fundamental difference between a human mind running on a biological human brain (which after all, may already be an advanced simulation), and its careful advanced DL simulation: we are already starting to see partial functional equivalence with current 2022 ANNs - and we haven't even really started trying yet. Given similar architectural power, the primary constraint is training data environment[[90]](#fn-xhJT9EJCoFQGE4wqz-90): so the main differentiator between different types of minds in the post-human era will be the world(s) minds grow up in, their total life experiences.
With the correct initial architectural seed (inferred from DNA, historical data, etc) and sufficiently detailed historical sim experience even specific humans, real or imagined, could be recreated (never exactly, but that is mostly irrelevant).
The [simulation argument](https://www.simulation-argument.com/) also functions as an argument for *universal resurrection*: if benevolent superintelligence succeeds in our future then - by the simulation argument - we *already* likely live in a *resurrection sim*. For if future humanity evolves to benevolent superintelligence, then in optimizing the world according to human volition we will use sims first to resurrect future deceased individuals at the behest of their loved ones, followed by the resurrectees' own loved ones, and so on, culminating recursively in a wave of resurrection unrolling death itself as it backpropagates through our history[[91]](#fn-xhJT9EJCoFQGE4wqz-91). Death is the antithesis of empowerment; the defeat of death itself is a convergent goal.
A future superintelligence (or equivalently, posthuman civilization) must then decide how to allocate it's compute resources across the various sim entities, posthuman netizens, etc. There is a natural allocation of compute resources within sims contingent on the specific goals of historical fidelity (human baseline for resurrection sims) or test evaluation utility (for simboxes), but there are no such natural guidelines for allocation of resources to the newly resurrected who presumably become netizens: for most will desire more compute. Given that the newly resurrected (and aligned but not especially bright AGI successfully 'graduating' from a simbox) will likely be initially disadvantaged at least in terms of knowledge, they will exist at the mercy of the same altruistic forces that drove their resurrection/creation.
Individual humans (and perhaps future AGIs) will naturally have specific people they care more about than others, leading to a complex web of weights that in theory could be unraveled and evaluated to assign a variable resource allocation over resurrectees (in addition to standard market dynamics). There are some simple principles that help cut through this clutter. On net nobody desires allocating resources to completely unaligned entities (as any such allocation is - by definition - just a pure net negative externality). But conversely, a hypothetical entity that was perfectly altruistic - and more specifically aligned exactly with the extant power distribution - would be a pure net *positive* externality. Funding the creation of globally altruistic entities is naturally a classic public goods provisioning problem, so in reality coordination difficulties may lead to more local individual or small-community aligned AGIs.
Given the eventual rough convergence of AGI in simboxes and humans in resurrection sims, something like the golden/silver rule applies: all else being equal, we should treat sim-AGI as we ourselves would like to be treated, if we were sims. But all else is *not* quite equal as we must also balance this moral consideration with the grave danger of unaligned AGI.
### 8. Conclusions
>
> *"Will robots inherit the earth? Yes, but they will be our children. We owe our minds to the deaths and lives of all the creatures that were ever engaged in the struggle called Evolution. Our job is to see that all this work shall not end up in meaningless waste."*
>
>
> Marvin Minsky -- [Will Robots Inherit the Earth](https://web.media.mit.edu/~minsky/papers/sciam.inherit.html)?
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>
>
Deep learning based AGI is likely near. These new minds will not be deeply alien and mysterious, but instead - as our mind children - will be much like us, at least initially. Their main advantage over us lies in their *potential* to scale up far beyond the limited experience and knowledge of a single human lifetime. We can align AGI by using improved versions of the techniques evolution found to instill altruism in humans: by using correlation-guided proxy matching to connect the agent's eventual learned predictive models of external empowerment/utility to the agent's own internal utility function, gradually replacing the bootstrapping self-empowerment objectives. Developing and perfecting the full design of these altruistic agents (architectures and training/educational curriculums) will require extensive testing in carefully crafted safe virtual worlds: simulation sandboxes. The detailed world-building of these simboxes required to suite the specific needs of agent design evaluations is itself much of the challenge.
The project of aligning DL based AGI is formidable, but not insurmountable. We have unraveled the genetic code, harnessed the atom, and landed on the moon. We are well on track to understand, reverse engineer, and improve the mind.
---
1. Soon as in most likely this decade, with most of the uncertainty around terminology/classification (compare to [metaculus predictions](https://www.metaculus.com/questions/3479/date-weakly-general-ai-is-publicly-known/)). [↩︎](#fnref-xhJT9EJCoFQGE4wqz-1)
2. Leading to alignment scaling theory. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-2)
3. I've been pondering these ideas for a while: there's a 2016 [comment here](https://www.lesswrong.com/posts/X5d5jZWMwSKiBPF5g/progress-and-prizes-in-ai-alignment?commentId=zJsyGqxbgCKw6dp8K) describing it as an x-prize style alignment challenge, and of course my old prescient but flawed 2010 LW post "[Anthropomorphic AI and Sandboxed Virtual Universes](https://www.lesswrong.com/posts/5P6sNqP7N9kSA97ao/anthropomorphic-ai-and-sandboxed-virtual-universes)". [↩︎](#fnref-xhJT9EJCoFQGE4wqz-3)
4. Anthropomorphic as in "having the shape/form of a human", which is an inevitable endpoint of deep learning based AGI, as DL is reverse engineering the brain. I use the term here specifically to refer to DL-based AGI that is embedded in virtual humanoid-ish bodies, lives in virtual worlds, and justifiably believes it is 'human' in a broad sense which encompasses most sapients. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-4) [↩︎](#fnref-xhJT9EJCoFQGE4wqz-4:1)
5. Ideally the additional cost of simboxing can be quite low: (N+1) vs (N) without - ie just the cost of one additional final unboxed training run - or possibly even less with transfer learning. The environment sim cost is small compared to the cost of the AGI within. The vast majority of the cost in developing advanced AI systems or AGI is in the sum of many exploratory training runs, researcher salaries, etc. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-5)
6. Perfect alignment is a fool's errand; the real task before us is simply that of matching the upper end of human alignment: that of our most altruistic exemplars. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-6)
7. Sections 5 and 6 discuss the importance of relative metaphysical ignorance and the resulting key subtasks of how to co-design worlds and agent belief systems (religions/philosophies) that best balance consistency (relative low entropy) with minimization of behavioral distortion, all while maintaining computational efficiency. Generally this difficulty scales with world technological complexity, so we'll probably start with low-tech historical or fantasy worlds. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-7)
8. Section 2 reviews the evidence that near term AGI will likely be DL based and thus brain-like (in essence, not details), and section 3 follows through on the implication that AGI will consequently be far more *anthropomorphic* then some expected (again in essence, not details). [↩︎](#fnref-xhJT9EJCoFQGE4wqz-8)
9. Section 3 argues that strong intelligence entails recursive self improvement and thus some forms of empowerment as the primary goal - at least in the developmental or bootstrapping phase. Section 4 discusses how this is the core driver of intelligence in humans and future AGI, and how empowerment must eventually give way to the external alignment objective (optimizing for other agent's values or empowerment) - in all altruistic agents, biological or not. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-9)
10. In theology the Eschaton is the final event or phase of the world, as according to divine plan. Here it is the perfectly appropriated term. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-10)
11. This requires running a set of simworlds in parallel, but this surprisingly need not incur much additional cost for most GPU based AGI designs, as discussed in section 2. For AGI running on neuromorphic hardware this performance picture may change a bit, but we will likely still want multiple world rollouts for other reasons such as test coverage and variance reduction. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-11)
12. High fidelity is probably not that important because of the universal instrumental convergence to empowerment, as discussed in section 4. Rather than optimize for human's specific goals (which are potentially unstable under scaling), it suffices that the AGI optimizes for our empowerment: ie our future ability to fulfill all likely goals. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-12)
13. I use 'reverse engineering' in a similar loose sense that early gliders and flying machines reversed engineered bird flight: by learning to distinguish the essential features (e.g. the obvious wings for lift, the less obvious aileron trailing-edge based roll for directional control) from the incidental (feathers, flapping, etc). [↩︎](#fnref-xhJT9EJCoFQGE4wqz-13) [↩︎](#fnref-xhJT9EJCoFQGE4wqz-13:1)
14. Herculano-Houzel, Suzana. "[The remarkable, yet not extraordinary, human brain as a scaled-up primate brain and its associated cost.](https://scholar.google.com/scholar?cluster=12325882481102398954&hl=en&as_sdt=2005&sciodt=0,5)" Proceedings of the National Academy of Sciences 109.supplement\_1 (2012): 10661-10668. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-14)
15. If I am repeating this argument, it is only because it is worth repeating. I've been presenting variations of nearly the same argument since that 2015 post and earlier, earlier even than deep learning, and the evidence only grows stronger year after year. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-15)
16. There will probably be technological eras past these three - such as reversible and/or quantum computing - but those are likely well past AGI. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-16)
17. In 1988 Moravec used brain-compute estimates and Moore's Law to [predict](https://books.google.com/books?id=56mb7XuSx3QC) that AGI would arrive by 2028, requiring at least 10 terraflops. Kurzweil then extended this idea with more and prettier and better selling graphs, but similar conclusions. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-17)
18. GPUs are 'massively' parallel relative to multi-core CPUs, but only neuromorphic computers like the brain are truly massively, maximally parallel. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-18)
19. I am using 'neuromorphic' in a broad sense that includes process-in-memory computing, mostly because all the economic demand and thus optimization pressure for these types of chips is for running large ANNs, so it is apt to name them 'computing in the form of neurons'. Neural computing is quite broad and general, but a neuromorphic computer still wouldn't be able to run your python script as efficiently as a CPU, or your traditional graphics engine as efficiently as a GPU (but naturally should excel at future *neural* graphics engines). GPUs are also evolving to specialize more in low precision matrix multiplication, which is neuromorphic adjacent. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-19)
20. Vector-Matrix multiplication is more general in that a general purpose VxM engine can fully emulate MxM ops at full efficiency, but a general purpose MxM engine can only simulate VxM with inefficiency proportional to its alu:mem ratio. At the physical limits of efficiency a VxM engine must store the larger matrix in local wiring, as in the brain. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-20)
21. Glorot, Xavier, Antoine Bordes, and Yoshua Bengio. "[Deep sparse rectifier neural networks](https://scholar.google.com/scholar?cluster=10040883758431450991&hl=en&as_sdt=0,5&as_vis=1)." Proceedings of the fourteenth international conference on artificial intelligence and statistics. JMLR Workshop and Conference Proceedings, 2011. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-21)
22. Carandini, Matteo, and David J. Heeger. "[Normalization as a canonical neural computation](https://scholar.google.com/scholar?cluster=6385180828645929051&hl=en&as_sdt=0,5&as_vis=1)." Nature Reviews Neuroscience 13.1 (2012): 51-62. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-22)
23. Greff, Klaus, Rupesh K. Srivastava, and Jürgen Schmidhuber. "[Highway and residual networks learn unrolled iterative estimation](https://scholar.google.com/scholar?cluster=14457128463377455102&hl=en&as_sdt=0,5&as_vis=1)." arXiv preprint arXiv:1612.07771 (2016). [↩︎](#fnref-xhJT9EJCoFQGE4wqz-23)
24. Liao, Qianli, and Tomaso Poggio. "[Bridging the gaps between residual learning, recurrent neural networks and visual cortex](https://scholar.google.com/scholar?cluster=10437107909999741484&hl=en&as_sdt=0,5)." arXiv preprint arXiv:1604.03640 (2016). [↩︎](#fnref-xhJT9EJCoFQGE4wqz-24)
25. Schlag, Imanol, Kazuki Irie, and Jürgen Schmidhuber. "[Linear transformers are secretly fast weight programmers](https://scholar.google.com/scholar?cluster=7929763198773172485&hl=en&as_sdt=0,5)." International Conference on Machine Learning. PMLR, 2021. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-25)
26. Ba, Jimmy, et al. "[Using fast weights to attend to the recent past](https://scholar.google.com/scholar?cluster=15137024002549952693&hl=en&as_sdt=2005&sciodt=0,5)." Advances in neural information processing systems 29 (2016). [↩︎](#fnref-xhJT9EJCoFQGE4wqz-26)
27. Bricken, Trenton, and Cengiz Pehlevan. "[Attention approximates sparse distributed memory](https://scholar.google.com/scholar?cluster=18296333632073096000&hl=en&as_sdt=2005&sciodt=0,5)." Advances in Neural Information Processing Systems 34 (2021): 15301-15315. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-27)
28. Lee, Jaehoon, et al. "[Wide neural networks of any depth evolve as linear models under gradient descent](https://scholar.google.com/scholar?cluster=10271588959901500441&hl=en&as_sdt=2005&sciodt=0,5)." Advances in neural information processing systems 32 (2019). [↩︎](#fnref-xhJT9EJCoFQGE4wqz-28)
29. Launay, Julien, et al. "[Direct feedback alignment scales to modern deep learning tasks and architectures](https://scholar.google.com/scholar?cluster=12044831412271008828&hl=en&as_sdt=2005&sciodt=0,5)." Advances in neural information processing systems 33 (2020): 9346-9360. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-29)
30. The key brain mechanisms underlying efficient backprop-free learning appear to be some combination of: 1.) large wide layers, 2.) layer wise local self-supervised predictive learning, 3.) widespread projection of global summary error signals (through the [dopaminergic](https://en.wikipedia.org/wiki/Dopaminergic_pathways) and [serotonergic](https://en.wikipedia.org/wiki/Serotonin#Nervous_system) projection pathways), and 4.) auxiliary error prediction (probably via the cerebellum). These also are the promising mechanisms in the beyond-backprop research. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-30)
31. Whittington, James CR, Joseph Warren, and Timothy EJ Behrens. "[Relating transformers to models and neural representations of the hippocampal formation](https://scholar.google.com/scholar?cluster=1471152261845071335&hl=en&as_sdt=0,5)." arXiv preprint arXiv:2112.04035 (2021). [↩︎](#fnref-xhJT9EJCoFQGE4wqz-31)
32. Schrimpf, Martin, et al. "[The neural architecture of language: Integrative modeling converges on predictive processing](https://scholar.google.com/scholar?cluster=1111551361629106229&hl=en&as_sdt=0,5)." Proceedings of the National Academy of Sciences 118.45 (2021): e2105646118. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-32)
33. Goldstein, Ariel, et al. "[Correspondence between the layered structure of deep language models and temporal structure of natural language processing in the human brain](https://scholar.google.com/scholar?cluster=16675668055104068708&hl=en&as_sdt=2005&sciodt=0,5)." bioRxiv (2022). [↩︎](#fnref-xhJT9EJCoFQGE4wqz-33)
34. Caucheteux, Charlotte, and Jean-Rémi King. "[Brains and algorithms partially converge in natural language processing](https://scholar.google.com/scholar?cluster=7281145279140743388&hl=en&as_sdt=0,5)." Communications biology 5.1 (2022): 1-10. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-34)
35. Mostly sourced from [Schmidhuber's lab](https://people.idsia.ch/~juergen/deep-learning-miraculous-year-1990-1991.html), of course. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-35)
36. [Mind Children](https://books.google.com/books?id=56mb7XuSx3QC) by Hans Moravec, 1988 [↩︎](#fnref-xhJT9EJCoFQGE4wqz-36)
37. This was also obvious to the vanguard of Moore's Law: GPU/graphics programmers. It simply doesn't take that many years for a research community of just a few thousand bright humans to explore the design space and learn how to exploit the potential of a new hardware generation. Each generation has a fixed potential which results in diminishing returns as software techniques mature. The very best and brightest teams sometimes can accumulate algorithmic leads measured in years, but never decades. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-37)
38. This is simply the most performant fully general framework for describing arbitrary circuits - from all DL architectures to actual brains to CPUs, including those with dynamic wiring. The circuit architecture is fully encoded in the specific (usually block) sparsity pattern, and the wiring matrix may be compressed. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-38)
39. Standard transformers are still essentially feedforward and thus can only learn functions computable by depth D circuits, where D is the layer depth, usually around 100 or less. Thus like standard depth constrained vision CNNs they excel at mental tasks humans can solve in seconds, and struggle with tasks that require much longer pondering times and long iterative thought processes. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-39)
40. By degree of recurrence I mean the latency and bandwidth of information flow from/to module outputs across time (over multiple timescales). A purely feedforward system (such as a fixed depth feedforward network) has zero recurrence, a vanilla transformer has a tiny bandwidth of high latency recurrence (if it reads in previous text output), and a standard RNN has high bandwidth low latency recurrence (but is not RAM efficient). There are numerous potential routes to improve the recurrence bandwidth and latency of transformer-like architectures, but usually at the expense of training parallelization and efficiency: for example one could augment a standard transformer with more extensive scratchpad working memory output which is fed back in as auxiliary input, allowing information to flow recurrently through attention memory. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-40)
41. Games like chess/Go (partially) test planning/search capability, and current transformers like GPT-3 struggle at anything beyond the opening phase, due to lack of effective circuit depth for online planning. A transformer model naturally could handle games better if augmented with a huge training database generated by some other system with planning/search capability, but then it is no longer the sole source of said capability. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-41)
42. For point of comparison: the typical 1000x time parallelization factor imposed by GPU constraints is roughly equivalent to a time delay of over 10 human subjective seconds assuming 100hz as brain-equivalent clock rate. Each layer of computation can only access previous outputs of the same or higher layers with a delay of 1000 steps - so this is something much weaker than true recurrence. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-42)
43. Perhaps not coincidentally, I believe I've cracked this little problem and hopefully will finish full implementation before the neuromorphic era. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-43)
44. For comparison the human brain has on order 1e14 synapses which are roughly 10x *locally* sparse, a max firing rate or equivalent clock rate of 100hz, and a median firing rate well under 1hz. This is the raw equivalent of 1e14 fully sparse ops/s, or naively 1e17 dense ops/s, but perhaps the functional equivalent of 1e16 dense ops/s - within an OOM of single GPU performance. Assuming compression down to a bit per synapse or so requires ~10TB of RAM for weights - almost 3 OOM beyond single GPU capacity - and then activation state is at least 10GB, perhaps 100GB per agent instance, depending on sparsity and backtracking requirements. Compared to brains GPUs are most heavily RAM constrained, and thus techniques for sharing/reusing weights (across agents/batch, space, or time) are essential. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-44)
45. An honorable mention attempt to circumvent the VN bottleneck on current hardware involves storing everything in on-chip SRAM, perhaps best exemplified by the [cerberas wafer scale chip](https://www.cerebras.net/product-chip/). It has the performance of perhaps many dozens of GPUs, but with access to only 40GB of on-chip RAM it can run only tiny insect/lizard size ANNs - but it can run those at *enormous* speeds. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-45)
46. For point of comparison, GPT-3's 500B token training run is roughly equivalent to 5,000 years of human experience (300 tokens/minute \* 60 \* 24 \* 365 = 0.1B tokens per human year) and was compressed into a few months of physical training time, so it ran about 10000X real-time equivalent. The 3e24 flops used during GPT-3 training compares more directly to perhaps 1e25 (dense equivalent) flops consumed for a human 'training' of 30 years (1e16 flops \* 1e9 seconds). But of course GPT-3 is not truly recurrent, and furthermore is tiny and incomplete - more comparable to a massively old and experienced (but also impaired) small linguistic cortex than a regular full brain. It's quite possible that we can get simbox-suitable AGI using smaller brains, but human brain size seems like a reasonable baseline assumption. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-46)
47. Rapid linguistic learning is homo sapien's super-power. AGI simply takes this further by being able to directly share synapses without slow ultra-compressed linguistic transmission. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-47)
48. Dreams in simboxes could be useful as the natural consequence of episodic memories leaking through from the experiences of an agent's mindclones across the sim multiverse. Brains record experiences during wake and then retrain the cortex on these experiences during sleep - our agents could do the same except massively scaled up by training on the experiences of many mindclones from across the simverse. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-48)
49. The same tech leading to AGI will also transform game sim engines and allow simulating entire worlds of realistic NPCs - dicussed more in section 5. The distinction between an NPC and an agent/contestant is that the former is purely a simulacra manifestation of the sim world engine (which has a pure predictive simulation objective), and agent is designed to steer the world. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-49)
50. Convergence in essence, not details. AGI will have little need of the hundred or so known human reflexes and instincts, nor will it suffer much for lack of most human emotions - but few to none of those biological brain features are *essential to the core of humanity/sapience*. Should we consider a hypothetical individual lacking fear, anger, jealousy, pride, envy, sadness, etc - to be inhuman due to lack of said ingredients? The essence or core of sapience as applicable to AGI is self directed learning, empowerment/curiosity, and alignment - the latter manifesting as empathy, altruism, and love in humans. And as an additional complication AGI may *simulate* human emotions for various reasons. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-50)
51. As you extend the discount rate to zero (planning horizon to infinity) the optimal instrumental action path *converges* for all relevant utility functions to the path that maximizes the agent's ability to steer the long term future. Empowerment objectives approximate this convergent path, optimizing not for any particular short term goal, but for all long term goals. Empowerment is the driver of recursive self-improvement. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-51)
52. I'm using empowerment broadly to include all high level convergent self-improvement objectives: those that improve the agent's ability to control the long term future. This includes both classic empowerment objectives such as maximizing mutual info between outputs and future states (maxing future optionality), curiosity objectives (maximizing world model predictive performance), and so on. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-52)
53. The convergence towards empowerment does simplify the task of aligning AI as it reduces or removes the need to model detailed human values/goals; instead optimizing for human empowerment is a reasonable (and actually acheivable) approximate bound. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-53)
54. A brain-like large sparse RNN can encode any circuit architecture, so the architectural prior reduces simply to a prior on the large scale low-frequency sparsity pattern, which can obviously evolve during learning. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-54)
55. Ie those that survive the replication crisis and fit into the modern view of the brain from computational neuroscience and deep learning. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-55)
56. Binz, Marcel, and Eric Schulz. "[Using cognitive psychology to understand GPT-3](https://scholar.google.com/scholar?hl=en&as_sdt=0%2C5&q=Using+cognitive+psychology+to+understand+GPT-3&btnG=)." arXiv preprint arXiv:2206.14576 (2022). [↩︎](#fnref-xhJT9EJCoFQGE4wqz-56)
57. Dasgupta, Ishita, et al. "[Language models show human-like content effects on reasoning](https://scholar.google.com/scholar?cluster=10350534295149400129&hl=en&as_sdt=2005&sciodt=0,5)." arXiv preprint arXiv:2207.07051 (2022). [↩︎](#fnref-xhJT9EJCoFQGE4wqz-57)
58. Jara-Ettinger, Julian. "[Theory of mind as inverse reinforcement learning](https://scholar.google.com/scholar?cluster=14959443239271810913&hl=en&as_sdt=2005&sciodt=0,5)." Current Opinion in Behavioral Sciences 29 (2019): 105-110.. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-58)
59. Learning detailed models of the complex values of external agents is also probably mostly unnecessary, as empowerment (discussed below) serves as a reasonable convergent bound. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-59)
60. Weighted by the other agent's alignment (for game theoretic reasons) and also perhaps model fidelity. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-60)
61. Each oldbrain circuit doesn't need performance anywhere near the more complex target newbrain circuit it helps locate, it only needs enough performance to distinguish its specific target circuit by firing pattern from amongst all the rest. For examples babies are born with a crude face detector which really isn't much more than a simple smiley-face :) detector, but that (perhaps along with additional feature detectors) is still sufficient to reliably match actual faces more than other observed patterns, helping to locate and connect with the later more complex learned cortical face detectors. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-61)
62. Sexual attraction is a natural extension of imprinting: some collaboration of various oldbrain circuits can first ground to the general form of humans, and then also myriad more specific attraction signals: symmetry, body shape, secondary characteristics, etc, combined with other circuits which *disable* attraction for likely kin ala the [Westermarck effect](https://en.wikipedia.org/wiki/Imprinting_(psychology)#Westermarck_effect) (identified by yet other sets of oldbrain circuits as the most familiar individuals during childhood). This explains the various failure modes we see in porn (attraction to images of people and even abstractions of humanoid shapes), and the failure of kin attraction inhibition for kin raised apart. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-62)
63. Fear of death is a natural consequence of empowerment based learning - as it is already the worst (most disempowered) outcome. But instinctual fear still has obvious evolutionary advantage: there are many dangers that can kill or maim long before the brain's learned world model is highly capable. Oldbrain circuits can easily detect various obvious dangers for symbol grounding: very loud sounds and fast large movements are indicative of dangerous high kinetic energy events, fairly simple visual circuits can detect dangerous cliffs/heights (whereas many tree-dwelling primates instead instinctively fear open spaces), etc. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-63)
64. Anger/Jealousy/Vengeance/Justice are all variations or special cases of the same general game-theoretic punishment mechanism. These are deviations from empowerment because an individual often pursues punishment of a perceived transgressor even at a cost to their own 'normal' (empowerment) utility (ie their ability to pursue diverse goals). Even though the symbol grounding here seems more complex, we do see failure modes such as anger at inanimate objects which are suggestive of proxy matching. In the specific case of jealousy a two step grounding seems plausible: first the previously discussed lust/attraction circuits are grounded, which then can lead to obsessive attentive focus on a particular subject. Other various oldbrain circuits then bind to a diverse set of correlated indicators of human interest and attraction (eye gaze, smiling, pupil dilation, voice tone, laughter, touching, etc), and then this combination can help bind to the desired jealousy grounding concept: "the subject of my desire is attracted to another". This also correctly postdicts that jealousy is less susceptible to the inanimate object failure mode than anger. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-64)
65. Oldbrain circuits advertise emotional state through many indicators: facial expressions, pupil dilation, blink rate, voice tone, etc - and then other oldbrain circuits then can detect emotional state in others from these obvious cues. This provides the requisite proxy foundation for grounding to newbrain learned representations of emotional state in others, and thus empathy. The same learned representations are then reused during imagination&planning, allowing the brain to imagine/predict the future contingent emotional state of others. Simulation itself can also help with grounding, by reusing the brain's own emotional circuity as the proxy. While simulating the mental experience of others, the brain can also compare their relative alignment/altruism to its own, or some baseline, allowing for the appropriate game theoretic adjustments to sympathy. This provides a reasonable basis for alignment in the brain, and explains why empathy is dependent upon (and naturally tends to follow from) familiarity with a particular character - hence "to know someone is to love them". [↩︎](#fnref-xhJT9EJCoFQGE4wqz-65)
66. Matusch, Brendon, Jimmy Ba, and Danijar Hafner. "[Evaluating Agents without Rewards](https://arxiv.org/abs/2012.11538)." arXiv preprint arXiv:2012.11538 (2020). [↩︎](#fnref-xhJT9EJCoFQGE4wqz-66)
67. Salge, Christoph, Cornelius Glackin, and Daniel Polani. "[Empowerment–an introduction](https://scholar.google.com/scholar?cluster=16642438870189469476&hl=en&as_sdt=2005&sciodt=0,5)." Guided Self-Organization: Inception. Springer, Berlin, Heidelberg, 2014. 67-114. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-67)
68. Friston, Karl. "[The free-energy principle: a unified brain theory?](https://scholar.google.com/scholar?cluster=5775375722379054599&hl=en&as_sdt=2005&sciodt=0,5)." Nature reviews neuroscience 11.2 (2010): 127-138. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-68)
69. Burda, Yuri, et al. "[Large-scale study of curiosity-driven learning](https://scholar.google.com/scholar?cluster=6931272873542879959&hl=en&as_sdt=2005&sciodt=0,5)." arXiv preprint arXiv:1808.04355 (2018). [↩︎](#fnref-xhJT9EJCoFQGE4wqz-69)
70. Mohamed, Shakir, and Danilo Jimenez Rezende. "[Variational information maximisation for intrinsically motivated reinforcement learning](https://scholar.google.com/scholar?cluster=9262504233068870193&hl=en&as_sdt=0,5)." arXiv preprint arXiv:1509.08731 (2015). [↩︎](#fnref-xhJT9EJCoFQGE4wqz-70)
71. Eysenbach, Benjamin, et al. "[Diversity is all you need: Learning skills without a reward function](https://scholar.google.com/scholar?cluster=12324439663284457782&hl=en&as_sdt=2005&sciodt=0,5)." arXiv preprint arXiv:1802.06070 (2018). [↩︎](#fnref-xhJT9EJCoFQGE4wqz-71)
72. Zhao, Ruihan, Stas Tiomkin, and Pieter Abbeel. "[Learning efficient representation for intrinsic motivation](https://scholar.google.com/scholar?cluster=12126395461245950927&hl=en&as_sdt=0,5)." arXiv preprint arXiv:1912.02624 (2019). [↩︎](#fnref-xhJT9EJCoFQGE4wqz-72)
73. Aubret, Arthur, Laetitia Matignon, and Salima Hassas. "[A survey on intrinsic motivation in reinforcement learning](https://scholar.google.com/scholar?cluster=3754803781149163337&hl=en&as_sdt=0,5&as_vis=1)." arXiv preprint arXiv:1908.06976 (2019). [↩︎](#fnref-xhJT9EJCoFQGE4wqz-73)
74. Pathak, Deepak, et al. "[Curiosity-driven exploration by self-supervised prediction](https://scholar.google.com/scholar?cluster=9379743003299559904&hl=en&as_sdt=2005&sciodt=0,5)." International conference on machine learning. PMLR, 2017. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-74)
75. Pathak, Deepak, Dhiraj Gandhi, and Abhinav Gupta. "[Self-supervised exploration via disagreement](https://scholar.google.com/scholar?cluster=13780996231531586358&hl=en&as_sdt=0,5)." International conference on machine learning. PMLR, 2019. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-75)
76. It is irrelevant that evolution sometimes produces brains that are unaligned or broken in various ways. My broken laptop is not evidence that turing machines do not work. Evolution proceeds by breaking things; it only needs some high functioning offspring for success. We are reverse engineering the brain in its most ideal perfected forms (think Von Neumman meets Jesus, or your favorite cultural equivalents), and we are certainly not using some blind genetic evolutionary process to do so. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-76)
77. Decety, Jean, et al. "[Empathy as a driver of prosocial behaviour: highly conserved neurobehavioural mechanisms across species](https://scholar.google.com/scholar?cluster=9130174996111297545&hl=en&as_sdt=0,5)." Philosophical Transactions of the Royal Society B: Biological Sciences 371.1686 (2016): 20150077. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-77)
78. Meyza, K. Z., et al. "[The roots of empathy: Through the lens of rodent models](https://scholar.google.com/scholar?cluster=12121164029627401668&hl=en&as_sdt=0,5)." Neuroscience & Biobehavioral Reviews 76 (2017): 216-234. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-78)
79. Bartal, Inbal Ben-Ami, Jean Decety, and Peggy Mason. "[Empathy and pro-social behavior in rats](https://scholar.google.com/scholar?cluster=15479559556104839387&hl=en&as_sdt=2005&sciodt=0,5)." Science 334.6061 (2011): 1427-1430. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-79)
80. Franzmeyer, Tim, Mateusz Malinowski, and João F. Henriques. "Learning Altruistic Behaviours in Reinforcement Learning without External Rewards." arXiv preprint arXiv:2107.09598 (2021). [↩︎](#fnref-xhJT9EJCoFQGE4wqz-80)
81. The franzmeyer paper was posted on arxiv shortly before I started this post a year ago, but it did not come to my attention until final editing, and we both arrived at a similar idea (using empowerment as a bound approximation for external agent values) independently. They of course are not using a complex learned world model and thus avoid the key challenge of internal circuit grounding. The specific approximations they are using may not scale to large environments, but regardless they have now at least proven out the basic idea of optimizing for external agent empowerment in simple environments. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-81)
82. Transitioning to altruism(external empowerment) too soon could impair the agent's learning trajectory or result in an insufficient model of external agency; but delaying the transition too long could result in powerful selfish agents. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-82)
83. The capabilities of an (adult/trained) agent are a function primarily of 1.) its total lifetime effective compute budget for learning (learning compute \* learning age), 2.) the quality and quantity of its training data (knowledge), and 3.) its architectural prior. In simboxes we are optimizing 3 for the product of intelligence and alignment, but that does not imply that agents in simboxes will be especially capable or dangerous, as they will be limited somewhat by 1 and especially by 2. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-83)
84. See also the typical [hero's journey monomyth](https://en.wikipedia.org/wiki/Hero%27s_journey). [↩︎](#fnref-xhJT9EJCoFQGE4wqz-84)
85. One key difference is that computer security sandboxes are built to contain viruses and malware which themselves are *intentionally* designed to escape. This adversarial arms race setting naturally makes containment far more challenging, whereas AGI and simboxes should be fully cooperatively codesigned. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-85)
86. Plato did actually arrive at some conclusions that roughly anticipate simulism, but only very vaguely. Various contemporary Gnostics believed in an early equivalent of simulism. Still billions of lifetimes away from any serious containment risk. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-86)
87. Of course a hypothetical superintelligence with vast amounts of compute could perhaps infer the rough shape of the outer world from even a single short lifetime of observations/experiments (using vast internal simulation), but as a rough baseline that would probably require something like the equivalent of human net civilization levels of compute and would hardly go unnoticed, and a well designed sim may not leak enough to allow for anything other than human manipulation as the escape route (consider, for example, the escape prospects for a 'superintelligent' atari agent, who could only know humanity through vague simulations of entire multiverses mostly populated with aliens). Regardless that type of hypothetical superintelligence has no relation to the human-level AGI which will actually arrive first and is discussed here. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-87)
88. Specifically dynamic alignment architectures and mechanisms as discussed in section 4: agents that learn models of, and then optimize for, other agent's values/utility (and or empowerment). [↩︎](#fnref-xhJT9EJCoFQGE4wqz-88)
89. These should be considered upper bounds because advances in inter-agent optimization/compression can greatly reduce these costs, long before more exotic advances such as reversible computing. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-89)
90. And architecture is somewhat less of a differentiator given the combination of architectural convergence under dynamic within-lifetime architectural search and diminishing returns to model size in great excess of data history. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-90)
91. One key piece of historical information which must be inferred for the success of such an effort is humanity's DNA tree. Fortunately a rather large fraction of total human DNA is preserved and awaiting extraction and sampling by future robots thanks to (mostly judeo-christian/abrahamic) burial rituals. [↩︎](#fnref-xhJT9EJCoFQGE4wqz-91) |
7c031106-07f3-483e-8d50-0470e366e7f3 | trentmkelly/LessWrong-43k | LessWrong | Meetup : First Sydney 2012 meetup.
Discussion article for the meetup : First Sydney 2012 meetup.
WHEN: 18 January 2012 06:00:00PM (+1100)
WHERE: 22 The Promenade,, Sydney NSW 2000 (James Squire Brewhouse)
[All advice for improving location/time would be appreciated, especially location, which has not worked out amazingly well before] Hello Less Wrongers of Sydney! Assuming the local interest has not died down, seems only right that we should try and set up another meet-up.
Given my (fairly well supported, I imagine) belief that peer pressure is one of the best methods to change behavior, I figure that the lowest hanging fruit we could discuss is trying to control Akrasia. I'm prepared to bring a structured plan and research (if there is interest) in order to achieve the following:
1. Review standing literature on causation.
2. Discuss current Akrasia control methods used by attendants, less wrong, life hacker, reddit extc. (all of which, of course, are noted for their effect AGAINST Akrasia control. Sudden thought - is there procrastination negative search engine?)
3. Try and assign tasks to willing participants, in order to test methods and combinations thereof. I've a mind that if this goes well we could contribute as a group to the less wrong community some good old fashioned data. Plus, it's always good to measure interest in a more regular meet-up!
Discussion article for the meetup : First Sydney 2012 meetup. |
36ff834d-c2b3-4113-9ac0-52a9657f46fa | trentmkelly/LessWrong-43k | LessWrong | The counting argument for scheming (Sections 4.1 and 4.2 of "Scheming AIs")
This is Sections 4.1 and 4.2 of my report “Scheming AIs: Will AIs fake alignment during training in order to get power?”. There’s also a summary of the full report here (audio here). The summary covers most of the main points and technical terms, and I’m hoping that it will provide much of the context necessary to understand individual sections of the report on their own.
Audio version of this section here, or search for "Joe Carlsmith Audio" on your podcast app.
Arguments for/against scheming that focus on the final properties of the model
Various arguments for/against scheming proceed by comparing the final properties of different model classes (e.g. schemers, training saints, reward-on-the-episode seekers, etc) according to how well they perform according to some set of criteria that we imagine SGD is selecting for.
What is SGD selecting for? Well, one obvious answer is: high reward. But various of the arguments I'll consider won't necessarily focus on reward directly. Rather, they'll focus on other criteria, like the "simplicity" or the "speed" of the resulting model. However, we can distinguish between two ways these criteria can enter into our predictions about what sort of model SGD will select.
Contributors to reward vs. extra criteria
On the first frame, which I'll call the "contributors to reward" frame, we understand criteria like "simplicity" and "speed" as relevant to the model SGD selects only insofar as they are relevant to the amount of reward that a given model gets. That is, on this frame, we're really only thinking of SGD as selecting for one thing – namely, high reward performance – and simplicity and speed are relevant insofar as they're predictive of high reward performance.
Thus, an example of a "simplicity argument," given in this frame, would be: "a schemer can have a simpler goal than a training saint, which means that it would be able to store its goal using fewer parameters, thereby freeing up other parameters that it can use for g |
1597c96d-1a0b-4786-b211-cd7440bba965 | trentmkelly/LessWrong-43k | LessWrong | The Lopsided Lives Argument For Hedonism About Well-being
1 Introduction
(Crosspost of this).
A warning: This is going to get very complicated. The various different models of well-being end up producing weird and counterintuitive conclusions. This is probably the topic that I have spent the most time thinking about of any topic in my life. Very few people have spent much time thinking about lopsided lives, so the terrain is largely unexplored. There are maybe two people on the planet who have spent lots of time thinking about this argument, and I’m one of them. So hopefully this is interesting, but it will only be interesting if you’re a giant nerd.
It’s a shame that very often the best arguments for things are totally ignored by almost all people. The number of people who have read various papers which provide quite decisive cases against deontology is quite small—no one has heard of the suitcase cases or Chappell’s paradox of deontology or the paralysis argument. The best arguments are often churned out in the dusty halls of academia, relegated to some obscure journal, footnoted occasionally—never seriously explored. There are, as far as I can tell, upwards of 8 arguments against deontology that have been made at various points, that no one has ever published a response to. These arguments appeal to deeply intuitive, widely shared premises, showing that if you accept, for example, the principle that you should want others to act rightly, you should give up your deontological beliefs.
But my target here is not deontology. Instead, I am arguing for hedonism about well-being, roughly the idea that the only thing that makes a person’s life go well is happiness and the only thing that makes a person’s life go poorly is suffering. In other words, the only things that determine how well your life goes are your mental states—the ones that feel good are good for you, ones that feel bad are bad for you. How much you know, how many friends you have, and so on matter instrumentally, as friendship and knowledge tend to make a l |
d0f497cd-9676-476d-9de9-33ccb94232ca | trentmkelly/LessWrong-43k | LessWrong | Human sexuality as an interesting case study of alignment
This is cross-posted from my personal blog
Epistemic status: mostly interesting questions.
Here I want to bring attention to what I think is an extremely impressive case of evolution's ability to 'align' humans in the wild: the development of human sexuality.
Reasons why this is an interesting thing to study from the lens of alignment, and why it is a highly non-trivial accomplishment:
1.) Evolution has been very successful here: almost all humans end up wanting to have sex and typically with opposite-gender partners in a way that would result in children (and hence IGF) in the evolutionary environment.
2.) Sexuality, unlike many other drives such as hunger and thirst, is not something built into the brain from the beginning. Instead there is a sudden 'on switch' around puberty. What happens in the brain during this time? How does evolution exert such fine-grained control of brain development so long (decades) after birth?
3.) It is mostly independent of initial training data before puberty -- i.e. evolution can ignore a decade of data input and representation learning, which it cannot control, during a time period when the brain is undergoing extremely large changes, and still finds a way to instill a new drive highly reliably.
4.) It seems to occur mostly without RL. People start wanting to have sex before they have actually had sex. If sexuality developed by some RL mechanism, it would look like you go around doing your normal things, then at some point you have sex, and realize it is highly rewarding, and you slightly update your behaviours and/or values to get more sex or to want more sex. This is not what happens in humans. Instead, humans often want to start having sex before they have had it, and even before they really know what sex is[1].
5.) Evolution has solved some variant of the pointers problem to get humans assigning high value to both a previously unknown and mostly non-represented state (i.e. you don't usually have a well-represented sex c |
20481829-3c03-481c-823a-b0fe006d01b4 | trentmkelly/LessWrong-43k | LessWrong | [Book Review] Altered Traits
Proponents of meditation claim it causes long-term beneficial changes to a person's mind. Does it? Altered Traits: Science Reveals How Meditation Changes Your Mind, Brain, and Body by science journalist Daniel Goleman and neuroscientist Richard (Richie) Davidson attempts to answer this question using the newest research.
The book has three main themes.
1. It starts by establishing what constitutes rigorous research.
2. The bulk of the book is dedicated to asking "Does meditation make you a better person?" where "better" can mean "healthier", "more capable" or "more altruistic". This section is focused on ordinary practitioners.
3. The book ends with a yogi in a brain scanner.
Obstacles to Research
The United States government suppresses research into mind-altering drugs under penalty of imprisonment. Research into mind-altering contemplative practices got caught in the crossfire. For this and other reasons[1], there has been little research into meditation in the Western world until very recently. Much of what we do have is shoddy.
Meditation is hard to study scientifically for all the reasons it's hard to study sleep plus all the reasons it's hard to study weightlifting.
* Sleep is hard to study because it happens invisibly inside a person's head and if you ask them what's going on they wake up and the altered state of consciousness disappears.
* Weightlifting is hard to study because weightlifting involves hard work applied over a long time with proper technique. Optimal training for a beginner is different from optimal training for an athlete. Optimal training for an athlete depends on the sport an athlete is training for. Even if you could handwave away liability concerns, it's hard to pay volunteers to participate in a 20-year-long weightlifting program. Weightlifting is impossible to double-blind. (I'm going to ignore how many weightlifters take drugs while pretending not to.)
Due to the dearth of research, it is plausible Western science has left |
904eb5ac-cd34-40cb-b8bc-97a441e97174 | trentmkelly/LessWrong-43k | LessWrong | Can Generalized Adversarial Testing Enable More Rigorous LLM Safety Evals?
Thanks to Zora Che, Michael Chen, Andi Peng, Lev McKinney, Bilal Chughtai, Shashwat Goel, Domenic Rosati, and Rohit Gandikota.
TL;DR
In contrast to evaluating AI systems under normal "input-space" attacks, using "generalized," attacks, which allow an attacker to manipulate weights or activations, might be able to help us better evaluate LLMs for risks – even if they are deployed as black boxes. Here, I outline the rationale for “generalized” adversarial testing and overview current work related to it.
See also prior work in Casper et al. (2024), Casper et al. (2024), and Sheshadri et al. (2024).
Even when AI systems perform well in typical circumstances, they sometimes fail in adversarial/anomalous ones. This is a persistent problem.
State-of-the-art AI systems tend to retain undesirable latent capabilities that can pose risks if they resurface. My favorite example of this is the most cliche one – many recent papers have demonstrated diverse attack techniques that can be used to elicit instructions for making a bomb from state-of-the-art LLMs.
There is an emerging consensus that, even when LLMs are fine-tuned to be harmless, they can retain latent harmful capabilities that can and do cause harm when they resurface (Qi et al., 2024). A growing body of work on red-teaming (Shayegani et al., 2023, Carlini et al., 2023, Geiping et al., 2024, Longpre et al., 2024), interpretability (Juneja et al., 2022, Lubana et al., 2022, Jain et al., 2023, Patil et al., 2023, Prakash et al., 2024, Lee et al., 2024), representation editing (Wei et al., 2024, Schwinn et al., 2024), continual learning (Dyer et al., 2022, Cossu et al., 2022, Li et al., 2022, Scialom et al., 2022, Luo et al., 2023, Kotha et al., 2023, Shi et al., 2023, Schwarzchild et al., 2024), and fine-tuning (Jain et al., 2023, Yang et al., 2023, Qi et al., 2023, Bhardwaj et al., 2023, Lermen et al., 2023, Zhan et al., 2023, Ji et al., 2024, Hu et al., 2024, Halawi et al., 2024) suggests that fine-tuning stru |
83867553-5efb-48d1-bd4c-e0aeb9f8ab7c | StampyAI/alignment-research-dataset/lesswrong | LessWrong | You're in Newcomb's Box
**Part 1: Transparent Newcomb with your existence at stake**
Related: [Newcomb's Problem and Regret of](/lw/nc/newcombs_problem_and_regret_of_rationality/) [Rationality](/lw/nc/newcombs_problem_and_regret_of_rationality/)
Omega, a wise and trustworthy being, presents you with a one-time-only game and a surprising revelation.
"I have here two boxes, each containing $100," he says. "You may choose to take both Box A and Box B, or just Box B. You get all the money in the box or boxes you take, and there will be no other consequences of any kind. But before you choose, there is something I must tell you."
Omega pauses portentously.
"You were created by a god: a being called Prometheus. Prometheus was neither omniscient nor particularly benevolent. He was given a large set of blueprints for possible human embryos, and for each blueprint that pleased him he created that embryo and implanted it in a human woman. Here was how he judged the blueprints: any that he guessed would grow into a person who would choose only Box B in this situation, he created. If he judged that the embryo would grow into a person who chose both boxes, he filed that blueprint away unused. Prometheus's predictive ability was not perfect, but it was very strong; he was the god, after all, of Foresight."
Do you take both boxes, or only Box B?
For some of you, this question is presumably easy, because you take both boxes in standard Newcomb where a million dollars is at stake. For others, it's easy because you take both boxes in the variant of Newcomb where the boxes are transparent and you can see the million dollars; just as you would know that you had the million dollars no matter what, in this case you know that you exist no matter what.
Others might say that, while they would prefer not to *cease* existing, they wouldn't mind *ceasing to have ever existed.* This is probably a useful distinction, but I personally (like, I suspect, most of us) score the universe higher for having me in it.
Others will cheerfully take the one box, logic-ing themselves into existence using whatever reasoning they used to qualify for the million in Newcomb's Problem.
But other readers have already spotted the trap.
---
**Part 2: Acausal trade with Azathoth**
Related: [An Alien God](/lw/kr/an_alien_god/), [An identification with your mind and memes](/lw/2l/closet_survey_1/1kb), [Acausal](/lw/3gv/statistical_prediction_rules_outperform_expert/3ezy) [Sex](/lw/3gv/statistical_prediction_rules_outperform_expert/3ezy)
[(ArisKatsaris proposes an alternate](/lw/43t/youre_in_newcombs_box/3gic) [trap.)](/lw/43t/youre_in_newcombs_box/3gic)
**Q:** Why does this knife have a handle?
**A:** This allows you to grasp it without cutting yourself.
**Q:** Why do I have eyebrows?
**A:** Eyebrows help keep rain and sweat from running down your forehead and getting into your eyes.
These kinds of answers are highly compelling, but strictly speaking they are allowing events in the future to influence events in the past. We can think of them as a useful cognitive and verbal shortcut--the long way to say it would be something like "the knife instantiates a design that was subject to an optimization process that tended to produce designs that when instantiated were useful for cutting things that humans want to cut..." We don't need to spell that out every time, but it's important to keep in mind exactly what goes into those optimization processes--you might just gain an insight like the notion of planned obsolescence. Or, in the case of eyebrows, the notion that we are [Adaptation-Executers, not Fitness-Maximizers](/lw/l0/adaptationexecuters_not_fitnessmaximizers/).
But if you one-box in Newcomb's Problem, you should take these answers more literally. The kinds of backwards causal arrows you draw are the same.
**Q:** Why does Box B contain a million dollars?
**A:** Because you're not going to take Box A.
In the same sense that your action determines the contents of Box B, or Prometheus's decision, the usefulness of the handle or the usefulness of eyebrows determines their existence. If the handle was going to prevent you from using the knife, it wouldn't be on there in the first place.
**Q:** Why do I exist?
**A:** Because you're going to have lots of children.
You weren't created by Prometheus; you were created by Azathoth, The God That is Evolution by Natural Selection. You are the product of an ongoing optimization process that is trying to maximize reproductive fitness. Azathoth wants you to maximize your number of descendants; if you fail to have descendants, Azathoth will try not to have created you. If your intelligence reduces your reproduction rate, Azathoth will try not to grant you intelligence. If the Darwinian-optimal choice conflicts with the moral one, Azathoth wants you to choose evil.
It would seem, then, that any decision theory that demands that you one-box (or that allows you to survive the similar [Parfit's Hitchhiker](http://wiki.lesswrong.com/wiki/Parfit's_hitchhiker) problem), also demands that you try to maximize your reproductive fitness. In many cases this injunction would be benign: after all, Azathoth *created* our morality. But in far too many, it is repugnant; there can be no doubt that in many commonplace situations, Azathoth wants you to cheat, or rape, or murder. It seems that in such cases you should balance a decreased chance of having existed against the rest of your utility function. Do not worship Azathoth, unless you consider never having existed to be infinitely bad. But do make sacrifices.
---
**Anticipated Responses**
*We're not in the ancestral environment, so there's no logical entanglement between my actions and my existence.*
We *are* in the environment of some of our ancestors. Evolution hasn't stopped. If your parents hadn't been genetically predisposed to have children, you would almost certainly not exist. More specific objections like this ("my ancestors weren't exposed to the same memes") can be defeated by adding abstraction ("your ancestors could have thought themselves out of having children, anti-reproduction memes have existed throughout history, and there's probably always been a tension between kin selection and morality.")
*This is a decision-theoretic basilisk: in the unlikely event that it's right, I'm worse off for having read it.*
Only if you're thinking causally, in which case this whole idea is meaningless. By alerting you to the possibility of a mutually beneficial trade with Azathoth (Azathoth creates you; you increase your reproductive fitness in exchange), I've done both of you a favor.
*Azathoth doesn't really exist--you can't trade with a non-sapient phenomenon.*
Replace the sapient opponent with a non-sapient phenomenon in any of our thought experiments--e.g. Omega tells you that it's simply a physical law that determines whether money goes in the boxes or not. Do you refuse to negotiate with physical laws? Then if you're so smart, why ain't you rich?
*So exactly how are you urging me to behave?*
I want you to refute this essay! For goodness sake, don't bite the bullet and start obeying your base desires or engineering a retrovirus to turn the next generation into your clones. |
1a199879-254e-4a3f-a99c-4cdbf2127a24 | trentmkelly/LessWrong-43k | LessWrong | Replicating the replication crisis with GPT-3?
I am getting worried that people are having so much fun doing interesting stuff with GPT-3 and AI Dungeon that they're forgetting how easy it is to fool yourself. Maybe we should think about how many different cognitive biases are in play here? Here are some features that make it particularly easy during casual exploration.
First, it works much like autocomplete, which makes it the most natural thing in the world to "correct" the transcript to be more interesting. You can undo and retry, or trim off extra text if it generates more than you want.
Randomness is turned on by default, so if you try multiple times then you will get multiple replies and keep going until you get a good one. It would be better science but less fun to keep the entire distribution rather than stopping at a good one. Randomness also makes a lot of gamblers' fallacies more likely.
Suppose you don't do that. Then you have to decide whether to share the transcript. You will probably share the interesting transcripts and not the boring failures, resulting in a "file drawer" bias.
And even if you don't do that, "interesting" transcripts will be linked to and upvoted and reshared, for another kind of survivor bias.
What other biases do you think will be a problem? |
2529be27-9efa-43c2-b112-be5a58437a1c | StampyAI/alignment-research-dataset/lesswrong | LessWrong | The next AI winter will be due to energy costs
Summary: We are 3 orders of magnitude from the Landauer limit (calculations per kWh). After that, progress in AI can not come from throwing more compute at known algorithms. Instead, new methods must be develloped. This may cause another *AI winter*, where the rate of progress decreases.
Over the last 8 decades, the energy efficiency of computers has improved by 15 orders of magnitude. Chips manufactured in 2020 [feature 16 bn transistors on a 100mm²](https://en.wikipedia.org/wiki/Transistor_count) area. The switching energy per transistor is only 3×10−18.mjx-chtml {display: inline-block; line-height: 0; text-indent: 0; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 100%; font-size-adjust: none; letter-spacing: normal; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0; min-height: 0; border: 0; margin: 0; padding: 1px 0}
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J (see Figure). This remarkable progress brings us close to the theoretical limit of energy consumption for computations, the Landauer principle: "any logically irreversible manipulation of information, such as the erasure of a bit or the merging of two computation paths, must be accompanied by a corresponding entropy increase in non-information-bearing degrees of freedom of the information-processing apparatus or its environment".
Figure: Switching energy per transistor over time. Data points from [Landauer (1988)](https://www.nature.com/articles/335779a0), [Wong et al. (2020)](https://nano.stanford.edu/cmos-technology-scaling-trend), own calculations.
The Landauer limit of kTln(2) is, at room temperature, 3×10−21 J per operation. Compared to this, 2020 chips (tsmc 5nm node) consume a factor of 1,175x as much energy. Yet, after improving by 15 orders of magnitude, we are getting close to the limit – only 3 orders of magnitude improvement are left. A computation which costs 1,000 USD in energy today may cost as low as 1 USD in the future (assuming the same price of USD per kWh). However, further order-of-magnitude improvements of classical computers are forbidden by physics.
At the moment, [AI improves rapidly simply because current algorithms yield significant improvements when increasing compute](https://www.lesswrong.com/posts/N6vZEnCn6A95Xn39p/are-we-in-an-ai-overhang). It is often better to double the compute than work on improving the algorithm. However, compute prices will decrease less rapidly in the future. Then, AI will need better algorithms. If these can not be found as rapidly as compute helped in the past, AI will not grow on the same trajectory any more. Progress slows. Then, a second [AI winter](https://en.wikipedia.org/wiki/AI_winter) can happen.
As a practical example, consider the [training of GPT-3](https://lambdalabs.com/blog/demystifying-gpt-3/) which required 3×1023 FLOPs. When such training is performed on V100 GPUs (12 nm node), this would have cost 5m USD (market price, not energy price). The pure energy price would have been 350k USD (assuming V100 GPUs, 300 W for 7 TFLOPs, 10 ct/kWh). With simple scaling, at the kT limit, one gets 1022 FLOPs per EUR (or 1028 FLOPs for 1m EUR, 1031 FLOPs for 1 bn USD in energy). With a kT-limit computer, one could easily imagine to scale by 1,000x and learn a GPT-4, and perhaps even GPT-5. But beyond that, new algorithms (and/or a Manhattan project level effort) are required.
Following the current trajectory of node shrinks in chip manufacturing, we may reach the limit in about 20 years.
Arguments that the numbers given above are optimistic:
* A kT-type computer assumes that all energy goes into gate flips. No parasitic losses exist, and no connects are required. In practice, only part of the energy goes into gate flips. Then, the lower limit is n×kT with n∼10 or n∼100; the winter will begin in 10 years and not in 20 years.
Arguments that the numbers given are pessimistic:
* The heat waste of a classical computer is typically dissipated into the environment (eventually, into space); often at additional cooling costs. In principle, one could process the heat waste with a heat pump. This process is limited by the Carnot efficiency, which is typically a factor of a few.
* Energy prices (in USD per kWh) may decrease in the future (solar? fusion?)
* If [reversible computers](https://en.wikipedia.org/wiki/Reversible_computing) could be made, the Landauer limit would not apply. From my limited understanding, it is presently unclear whether such devices could be made in practically useful form.
* I do not understand the impact of quantum computing on AI, and whether such a device can be made in practically useful form.
Other caveats:
* To improve speed, chips use more transistors than minimally required to perform calculations. For example, large die areas are filled with caches. A current estimate for the number of transistor switches per FLOP is 106. This number can in principle be reduced in order to increase the number of FLOPs per unit energy, at the price of lower speed. |
a6a16d0c-2abd-4bbb-87a6-8b25080a1c42 | trentmkelly/LessWrong-43k | LessWrong | Meeting the Dragon in Your Garage.
Suppose you observe the following dialogue:
A: If we do X we observe Y.
B: We tried X and we did not observe Y.
A: Apparently, you did not do X correctly.
B: Apparently, there is no Y. The reports of Y are just mistakes in the experiment.
There are many people joining both positions. Zero hypotheses, or hypothesis of no Y, of course, is simpler than hypothesis of Y that can be observed via X. No theory predicts Y, neither the existence of Y invalidates current theories.
Now, you are another explorer, and you already have all the necessary equipment to do X (and you can ask people supporting A how to do X correctly). Would you try to do it to observe Y?
Consider the following cases:
1) Y is a new astronomical object. X is the equipment (a telescope) to observe it, and where to look. Assume photography is not invented yet.
2) Y is a new generation of elementary particles. X is the design of the experiment.
3) Y is God. X is a specific way to pray if you want to understand if God exists or not (i.e., not a prayer of healing, intercessory prayer etc).
If your answer is different for these three examples, what is the difference? |
da70bf4f-2371-45ce-a829-769ba03d2fa6 | trentmkelly/LessWrong-43k | LessWrong | Exciting New Interpretability Paper!
There's a pretty exciting new interpretability paper, which hasn't really received the requisite attention because it's not billed as such.
This paper modifies the transformer architecture so that a forward pass minimizes a specifically engineered energy function.
According to the paper, "This functionality makes it possible to visualize essentially any token representation, weight, or gradient of the energy directly in the image plane. This feature is highly desirable from the perspective of interpretability, since it makes it possible to track the updates performed by the network directly in the image plane as the computation unfolds in time".
They achieve SOTA on two of the domains they tested on, although they didn't test on NLP or CV tasks (which is why the paper was rejected, I believe the authors will resubmit again with more experiments.)
More generally, I think architectures such as the above that essentially give you interpretability for free are a promising research direction. |
0fcb0a8e-c369-4bef-aa14-e5e51991c80d | StampyAI/alignment-research-dataset/arbital | Arbital | Relative complement
The relative complement of two sets $A$ and $B$, denoted $A \setminus B$, is the set of elements that are in $A$ while not in $B$.
Formally stated, where $C = A \setminus B$
$$x \in C \leftrightarrow (x \in A \land x \notin B)$$
That is, [https://arbital.com/p/46m](https://arbital.com/p/46m) $x$ is in the relative complement $C$, then $x$ is in $A$ and x is not in $B$.
For example,
- $\{1,2,3\} \setminus \{2\} = \{1,3\}$
- $\{1,2,3\} \setminus \{9\} = \{1,2,3\}$
- $\{1,2\} \setminus \{1,2,3,4\} = \{\}$
If we name the set $U$ as the set of all things, then we can define the [Absolute complement](https://arbital.com/p/5s7) of the set $A$, $A^\complement$, as $U \setminus A$ |
c282d53b-6963-4ab0-bcf7-4dae9b9afeb6 | trentmkelly/LessWrong-43k | LessWrong | (2009) Shane Legg - Funding safe AGI
Above is a link to an interesting blog post by Shane Legg. It was written before he started DeepMind, and he earns a hell of a lot of points for accomplishing a lot of the insanely ambitious goals set out in the post.
This part is particularly interesting:
> The impression I get from the outside is that SIAI [now MIRI] views AGI design and construction as so inherently dangerous that only a centrally coordinated design effort towards a provably correct system has any hope of producing something that is safe. My view is that betting on one horse, and a highly constrained horse at that, spells almost certain failure. A better approach would be to act as a parent organisation, a kind of AGI VC company, that backs a number of promising teams. Teams that fail to make progress get dropped and new teams with new ideas are picked up. General ideas of AGI safety are also developed in the background until such a time when one of the teams starts to make serious progress. At this time the focus would be to make the emerging AGI design as safe as possible. |
b23c8404-1396-4c4e-b184-95e6e73b5a28 | trentmkelly/LessWrong-43k | LessWrong | [SEQ RERUN] Availability
Today's post, Availability was originally published on 06 September 2007. A summary (taken from the LW wiki):
> Availability bias is a tendency to estimate the probability of an event based on whatever evidence about that event pops into your mind, without taking into account the ways in which some pieces of evidence are more memorable than others, or some pieces of evidence are easier to come by than others. This bias directly consists in considering a mismatched data set that leads to a distorted model, and biased estimate.
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 Absurdity Heuristic, Absurdity 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. |
4af87ca3-8248-4cde-b4b6-62f50c2861e7 | trentmkelly/LessWrong-43k | LessWrong | AI #44: Copyright Confrontation
The New York Times has thrown down the gauntlet, suing OpenAI and Microsoft for copyright infringement. Others are complaining about recreated images in the otherwise deeply awesome MidJourney v6.0. As is usually the case, the critics misunderstand the technology involved, complain about infringements that inflict no substantial damages, engineer many of the complaints being made and make cringeworthy accusations.
That does not, however, mean that The New York Times case is baseless. There are still very real copyright issues at the heart of Generative AI. This suit is a serious effort by top lawyers. It has strong legal merit. They are likely to win if the case is not settled.
TABLE OF CONTENTS
1. Introduction.
2. Table of Contents.
3. Language Models Offer Mundane Utility. Entrepreneurial advice.
4. GPT-4 Real This Time. What will we get in the coming year?
5. Fun With Image Generation. MidJourney wants you to speak (creative) English.
6. Copyright Confrontation. The New York Times versus OpenAI.
7. Deepfaketown and Botpocalypse Soon. ChatGPT used to spot plagiarism? Good.
8. Going Nuclear. Wait, you don’t want AI involved in nuclear safety?
9. In Other AI News. Nancy Pelosi buys Nvidia options.
10. Quiet Speculations. Will scaling LLMs lead to AGI? Dwarkesh Patel ponders.
11. The UN Reports. UN says UN things, most of you can skip this.
12. The Week in Audio. Shapira, Lebenz,Bloom and the Crystal Society audiobook.
13. Rhetorical Innovation. They are building a religion. They are building it bigger.
14. AI With Open Model Weights Is Unsafe and Nothing Can Fix This. Them too.
15. Aligning a Human Level Intelligence is Still Difficult. Chinese alignment paper.
16. Please Speak Directly Into the Microphone. Daniel Faggella.
17. The Wit and Wisdom of Sam Altman. Mostly being rather wise recently. Also rich.
18. The Lighter Side. A warning in song.
LANGUAGE MODELS OFFER MUNDANE UTILITY
A game called Thus Spoke Zaranova where you have to |
fe61f58c-0a6d-425c-9b7d-3f979722c4d8 | StampyAI/alignment-research-dataset/arxiv | Arxiv | An Overview of Catastrophic AI Risks
Executive Summary
-----------------
Artificial intelligence (AI) has seen rapid advancements in recent years, raising concerns among AI experts, policymakers, and world leaders about the potential risks posed by advanced AIs. As with all powerful technologies, AI must be handled with great responsibility to manage the risks and harness its potential for the betterment of society. However, there is limited accessible information on how catastrophic or existential AI risks might transpire or be addressed. While numerous sources on this subject exist, they tend to be spread across various papers, often targeted toward a narrow audience or focused on specific risks. In this paper, we provide an overview of the main sources of catastrophic AI risk, which we organize into four categories:
##### Malicious use.
Actors could intentionally harness powerful AIs to cause widespread harm. Specific risks include bioterrorism enabled by AIs that can help humans create deadly pathogens; the deliberate dissemination of uncontrolled AI agents; and the use of AI capabilities for propaganda, censorship, and surveillance. To reduce these risks, we suggest improving biosecurity, restricting access to the most dangerous AI models, and holding AI developers legally liable for damages caused by their AI systems.
##### AI race.
Competition could pressure nations and corporations to rush the development of AIs and cede control to AI systems. Militaries might face pressure to develop autonomous weapons and use AIs for cyberwarfare, enabling a new kind of automated warfare where accidents can spiral out of control before humans have the chance to intervene. Corporations will face similar incentives to automate human labor and prioritize profits over safety, potentially leading to mass unemployment and dependence on AI systems. We also discuss how evolutionary dynamics might shape AIs in the long run. Natural selection among AIs may lead to selfish traits, and the advantages AIs have over humans could eventually lead to the displacement of humanity. To reduce risks from an AI race, we suggest implementing safety regulations, international coordination, and public control of general-purpose AIs.
##### Organizational risks.
Organizational accidents have caused disasters including Chernobyl, Three Mile Island, and the Challenger Space Shuttle disaster. Similarly, the organizations developing and deploying advanced AIs could suffer catastrophic accidents, particularly if they do not have a strong safety culture. AIs could be accidentally leaked to the public or stolen by malicious actors. Organizations could fail to invest in safety research, lack understanding of how to reliably improve AI safety faster than general AI capabilities, or suppress internal concerns about AI risks. To reduce these risks, better organizational cultures and structures can be established, including internal and external audits, multiple layers of defense against risks, and military-grade information security.
##### Rogue AIs.
A common and serious concern is that we might lose control over AIs as they become more intelligent than we are. AIs could optimize flawed objectives to an extreme degree in a process called proxy gaming. AIs could experience goal drift as they adapt to a changing environment, similar to how people acquire and lose goals throughout their lives. In some cases, it might be instrumentally rational for AIs to become power-seeking. We also look at how and why AIs might engage in deception, appearing to be under control when they are not. These problems are more technical than the first three sources of risk. We outline some suggested research directions for advancing our understanding of how to ensure AIs are controllable.
Throughout each section, we provide illustrative scenarios that demonstrate more concretely how the sources of risk might lead to catastrophic outcomes or even pose existential threats. By offering a positive vision of a safer future in which risks are managed appropriately, we emphasize that the emerging risks of AI are serious but not insurmountable. By proactively addressing these risks, we can work toward realizing the benefits of AI while minimizing the potential for catastrophic outcomes.
###### Contents
1. [1 Introduction](#S1 "1 Introduction ‣ An Overview of Catastrophic AI Risks")
2. [2 Malicious Use](#S2 "2 Malicious Use ‣ An Overview of Catastrophic AI Risks")
1. [2.1 Bioterrorism](#S2.SS1 "2.1 Bioterrorism ‣ 2 Malicious Use ‣ An Overview of Catastrophic AI Risks")
2. [2.2 Unleashing AI Agents](#S2.SS2 "2.2 Unleashing AI Agents ‣ 2 Malicious Use ‣ An Overview of Catastrophic AI Risks")
3. [2.3 Persuasive AIs](#S2.SS3 "2.3 Persuasive AIs ‣ 2 Malicious Use ‣ An Overview of Catastrophic AI Risks")
4. [2.4 Concentration of Power](#S2.SS4 "2.4 Concentration of Power ‣ 2 Malicious Use ‣ An Overview of Catastrophic AI Risks")
5. [2.5 Suggestions](#S2.SS5 "2.5 Suggestions ‣ 2 Malicious Use ‣ An Overview of Catastrophic AI Risks")
3. [3 AI Race](#S3 "3 AI Race ‣ An Overview of Catastrophic AI Risks")
1. [3.1 Military AI Arms Race](#S3.SS1 "3.1 Military AI Arms Race ‣ 3 AI Race ‣ An Overview of Catastrophic AI Risks")
1. [3.1.1 Lethal Autonomous Weapons (LAWs)](#S3.SS1.SSS1 "3.1.1 Lethal Autonomous Weapons (LAWs) ‣ 3.1 Military AI Arms Race ‣ 3 AI Race ‣ An Overview of Catastrophic AI Risks")
2. [3.1.2 Cyberwarfare](#S3.SS1.SSS2 "3.1.2 Cyberwarfare ‣ 3.1 Military AI Arms Race ‣ 3 AI Race ‣ An Overview of Catastrophic AI Risks")
3. [3.1.3 Automated Warfare](#S3.SS1.SSS3 "3.1.3 Automated Warfare ‣ 3.1 Military AI Arms Race ‣ 3 AI Race ‣ An Overview of Catastrophic AI Risks")
4. [3.1.4 Actors May Risk Extinction Over Individual Defeat](#S3.SS1.SSS4 "3.1.4 Actors May Risk Extinction Over Individual Defeat ‣ 3.1 Military AI Arms Race ‣ 3 AI Race ‣ An Overview of Catastrophic AI Risks")
2. [3.2 Corporate AI Race](#S3.SS2 "3.2 Corporate AI Race ‣ 3 AI Race ‣ An Overview of Catastrophic AI Risks")
1. [3.2.1 Economic Competition Undercuts Safety](#S3.SS2.SSS1 "3.2.1 Economic Competition Undercuts Safety ‣ 3.2 Corporate AI Race ‣ 3 AI Race ‣ An Overview of Catastrophic AI Risks")
2. [3.2.2 Automated Economy](#S3.SS2.SSS2 "3.2.2 Automated Economy ‣ 3.2 Corporate AI Race ‣ 3 AI Race ‣ An Overview of Catastrophic AI Risks")
3. [3.3 Evolution](#S3.SS3 "3.3 Evolution ‣ 3 AI Race ‣ An Overview of Catastrophic AI Risks")
4. [3.4 Suggestions](#S3.SS4 "3.4 Suggestions ‣ 3 AI Race ‣ An Overview of Catastrophic AI Risks")
4. [4 Organizational Risks](#S4 "4 Organizational Risks ‣ An Overview of Catastrophic AI Risks")
1. [4.1 Accidents Are Hard to Avoid](#S4.SS1 "4.1 Accidents Are Hard to Avoid ‣ 4 Organizational Risks ‣ An Overview of Catastrophic AI Risks")
2. [4.2 Organizational Factors can Reduce the Chances of Catastrophe](#S4.SS2 "4.2 Organizational Factors can Reduce the Chances of Catastrophe ‣ 4 Organizational Risks ‣ An Overview of Catastrophic AI Risks")
3. [4.3 Suggestions](#S4.SS3 "4.3 Suggestions ‣ 4 Organizational Risks ‣ An Overview of Catastrophic AI Risks")
5. [5 Rogue AIs](#S5 "5 Rogue AIs ‣ An Overview of Catastrophic AI Risks")
1. [5.1 Proxy Gaming](#S5.SS1 "5.1 Proxy Gaming ‣ 5 Rogue AIs ‣ An Overview of Catastrophic AI Risks")
2. [5.2 Goal Drift](#S5.SS2 "5.2 Goal Drift ‣ 5 Rogue AIs ‣ An Overview of Catastrophic AI Risks")
3. [5.3 Power-Seeking](#S5.SS3 "5.3 Power-Seeking ‣ 5 Rogue AIs ‣ An Overview of Catastrophic AI Risks")
4. [5.4 Deception](#S5.SS4 "5.4 Deception ‣ 5 Rogue AIs ‣ An Overview of Catastrophic AI Risks")
5. [5.5 Suggestions](#S5.SS5 "5.5 Suggestions ‣ 5 Rogue AIs ‣ An Overview of Catastrophic AI Risks")
6. [6 Discussion of Connections Between Risks](#S6 "6 Discussion of Connections Between Risks ‣ An Overview of Catastrophic AI Risks")
7. [7 Conclusion](#S7 "7 Conclusion ‣ An Overview of Catastrophic AI Risks")
8. [A Frequently Asked Questions](#A1 "Appendix A Frequently Asked Questions ‣ An Overview of Catastrophic AI Risks")
1 Introduction
---------------
The world as we know it is not normal. We take for granted that we can talk instantaneously with people thousands of miles away, fly to the other side of the world in less than a day, and access vast mountains of accumulated knowledge on devices we carry around in our pockets. These realities seemed far-fetched decades ago, and would have been inconceivable to people living centuries ago. The ways we live, work, travel, and communicate have only been possible for a tiny fraction of human history.
Yet, when we look at the bigger picture, a broader pattern emerges: accelerating development. Hundreds of thousands of years elapsed between the time Homo sapiens appeared on Earth and the agricultural revolution. Then, thousands of years passed before the industrial revolution. Now, just centuries later, the artificial intelligence (AI) revolution is beginning. The march of history is not constant—it is rapidly accelerating.
We can capture this trend quantitatively in [Figure 1](#S1.F1 "Figure 1 ‣ 1 Introduction ‣ An Overview of Catastrophic AI Risks"), which shows how estimated gross world product has changed over time [[1](#bib.bibx1), [2](#bib.bibx2)]. The hyperbolic growth it depicts might be explained by the fact that, as technology advances, the rate of technological advancement also tends to increase. Empowered with new technologies, people can innovate faster than they could before. Thus, the gap in time between each landmark development narrows.
Figure 1: World production has grown rapidly over the course of human history. AI could further this trend, catapulting humanity into a new period of unprecedented change.
It is the rapid pace of development, as much as the sophistication of our technology, that makes the present day an unprecedented time in human history. We have reached a point where technological advancements can transform the world beyond recognition within a human lifetime. For example, people who have lived through the creation of the internet can remember a time when our now digitally-connected world would have seemed like science fiction.
From a historical perspective, it appears possible that the same amount of development could now be condensed in an even shorter timeframe. We might not be certain that this will occur, but neither can we rule it out. We therefore wonder: what new technology might usher in the next big acceleration? In light of recent advances, AI seems an increasingly plausible candidate. Perhaps, as AI continues to become more powerful, it could lead to a qualitative shift in the world, more profound than any we have experienced so far. It could be the most impactful period in history, though it could also be the last.
Although technological advancement has often improved people’s lives, we ought to remember that, as our technology grows in power, so too does its destructive potential. Consider the invention of nuclear weapons. Last century, for the first time in our species’ history, humanity possessed the ability to destroy itself, and the world suddenly became much more fragile.
Our newfound vulnerability revealed itself in unnerving clarity during the Cold War. On a Saturday in October 1962, the Cuban Missile Crisis was cascading out of control. US warships enforcing the blockade of Cuba detected a Soviet submarine and attempted to force it to the surface by dropping low-explosive depth charges. The submarine was out of radio contact, and its crew had no idea whether World War III had already begun. A broken ventilator raised the temperature up to 140∘superscript140140^{\circ}140 start\_POSTSUPERSCRIPT ∘ end\_POSTSUPERSCRIPTF in some parts of the submarine, causing crew members to fall unconscious as depth charges exploded nearby.
Figure 2: In this paper we cover four categories of AI risks and discuss how to mitigate them.
The submarine carried a nuclear-armed torpedo, which required consent from both the captain and political officer to launch. Both provided it. On any other submarine in Cuban waters that day, that torpedo would have launched—and a nuclear third world war may have followed. Fortunately, a man named Vasili Arkhipov was also on the submarine. Arkhipov was the commander of the entire flotilla and by sheer luck happened to be on that particular submarine. He talked the captain down from his rage, convincing him to await further orders from Moscow. He averted a nuclear war and saved millions or billions of lives—and possibly civilization itself.
Carl Sagan once observed, “If we continue to accumulate only power and not wisdom, we will surely destroy ourselves” [[3](#bib.bibx3)]. Sagan was correct: The power of nuclear weapons was not one we were ready for. Overall, it has been luck rather than wisdom that has saved humanity from nuclear annihilation, with multiple recorded instances of a single individual preventing a full-scale nuclear war.
AI is now poised to become a powerful technology with destructive potential similar to nuclear weapons. We do not want to repeat the Cuban Missile Crisis. We do not want to slide toward a moment of peril where our survival hinges on luck rather than the ability to use this technology wisely. Instead, we need to work proactively to mitigate the risks it poses. This necessitates a better understanding of what could go wrong and what to do about it.
Luckily, AI systems are not yet advanced enough to contribute to every risk we discuss. But that is cold comfort in a time when AI development is advancing at an unprecedented and unpredictable rate. We consider risks arising from both present-day AIs and AIs that are likely to exist in the near future. It is possible that if we wait for more advanced systems to be developed before taking action, it may be too late.
In this paper, we will explore various ways in which powerful AIs could bring about catastrophic events with devastating consequences for vast numbers of people. We will also discuss how AIs could present existential risks—catastrophes from which humanity would be unable to recover. The most obvious such risk is extinction, but there are other outcomes, such as creating a permanent dystopian society, which would also constitute an existential catastrophe. We outline many possible catastrophes, some of which are more likely than others and some of which are mutually incompatible with each other. This approach is motivated by the principles of risk management. We prioritize asking “what could go wrong?” rather than reactively waiting for catastrophes to occur. This proactive mindset enables us to anticipate and mitigate catastrophic risks before it’s too late.
To help orient the discussion, we decompose catastrophic risks from AIs into four risk sources that warrant intervention:
* •
Malicious use: Malicious actors using AIs to cause large-scale devastation.
* •
AI race: Competitive pressures that could drive us to deploy AIs in unsafe ways, despite this being in no one’s best interest.
* •
Organizational risks: Accidents arising from the complexity of AIs and the organizations developing them.
* •
Rogue AIs: The problem of controlling a technology more intelligent than we are.
These four sections—malicious use, AI race, organizational risks, and rogue AIs—describe causes of AI risks that are intentional, environmental, accidental, and internal, respectively [[4](#bib.bibx4)].
We will describe how concrete, small-scale examples of each risk might escalate into catastrophic outcomes. We also include hypothetical stories to help readers conceptualize the various processes and dynamics discussed in each section, along with practical safety suggestions to avoid negative outcomes. Each section concludes with an ideal vision depicting what it would look like to mitigate that risk. We hope this survey will serve as a practical introduction for readers interested in learning about and mitigating catastrophic AI risks.
2 Malicious Use
----------------
On the morning of March 20, 1995, five men entered the Tokyo subway system. After boarding separate subway lines, they continued for several stops before dropping the bags they were carrying and exiting. An odorless, colorless liquid inside the bags began to vaporize. Within minutes, commuters began choking and vomiting. The trains continued on toward the heart of Tokyo, with sickened passengers leaving the cars at each station. The fumes were spread at each stop, either by emanating from the tainted cars or through contact with people’s clothing and shoes. By the end of the day, 13 people lay dead and 5,800 seriously injured. The group responsible for the attack was the religious cult Aum Shinrikyo [[5](#bib.bibx5)]. Its motive for murdering innocent people? To bring about the end of the world.
Powerful new technologies offer tremendous potential benefits, but they also carry the risk of empowering malicious actors to cause widespread harm. There will always be those with the worst of intentions, and AIs could provide them with a formidable tool to achieve their objectives. Moreover, as AI technology advances, severe malicious use could potentially destabilize society, increasing the likelihood of other risks.
In this section, we will explore the various ways in which the malicious use of advanced AIs could pose catastrophic risks. These include engineering biochemical weapons, unleashing rogue AIs, using persuasive AIs to spread propaganda and erode consensus reality, and leveraging censorship and mass surveillance to irreversibly concentrate power. We will conclude by discussing possible strategies for mitigating the risks associated with the malicious use of AIs.
##### Unilateral actors considerably increase the risks of malicious use.
In instances where numerous actors have access to a powerful technology or dangerous information that could be used for harmful purposes, it only takes one individual to cause significant devastation. Malicious actors themselves are the clearest example of this, but recklessness can be equally dangerous. For example, a single research team might be excited to open source an AI system with biological research capabilities, which would speed up research and potentially save lives, but this could also increase the risk of malicious use if the AI system could be repurposed to develop bioweapons. In situations like this, the outcome may be determined by the least risk-averse research group. If only one research group thinks the benefits outweigh the risks, it could act unilaterally, deciding the outcome even if most others don’t agree. And if they are wrong and someone does decide to develop a bioweapon, it would be too late to reverse course.
By default, advanced AIs may increase the destructive capacity of both the most powerful and the general population. Thus, the growing potential for AIs to empower malicious actors is one of the most severe threats humanity will face in the coming decades. The examples we give in this section are only those we can foresee. It is possible that AIs could aid in the creation of dangerous new technology we cannot presently imagine, which would further increase risks from malicious use.
###
2.1 Bioterrorism
The rapid advancement of AI technology increases the risk of bioterrorism. AIs with knowledge of bioengineering could facilitate the creation of novel bioweapons and lower barriers to obtaining such agents. Engineered pandemics from AI-assisted bioweapons pose a unique challenge, as attackers have an advantage over defenders and could constitute an existential threat to humanity. We will now examine these risks and how AIs might exacerbate challenges in managing bioterrorism and engineered pandemics.
##### Bioengineered pandemics present a new threat.
Biological agents, including viruses and bacteria, have caused some of the most devastating catastrophes in history. It’s believed the Black Death killed more humans than any other event in history, an astounding and awful 200 million, the equivalent to four billion deaths today. While contemporary advancements in science and medicine have made great strides in mitigating risks associated with natural pandemics, engineered pandemics could be designed to be more lethal or easily transmissible than natural pandemics, presenting a new threat that could equal or even surpass the devastation wrought by history’s most deadly plagues [[6](#bib.bibx6)].
Humanity has a long and dark history of weaponizing pathogens, with records dating back to 1320 BCE describing a war in Asia Minor where infected sheep were driven across the border to spread Tularemia [[7](#bib.bibx7)]. During the twentieth century, 15 countries are known to have developed bioweapons programs, including the US, USSR, UK, and France. Like chemical weapons, bioweapons have become a taboo among the international community. While some state actors continue to operate bioweapons programs [[8](#bib.bibx8)], a more significant risk may come from non-state actors like Aum Shinrikyo, ISIS, or simply disturbed individuals. Due to advancements in AI and biotechnology, the tools and knowledge necessary to engineer pathogens with capabilities far beyond Cold War-era bioweapons programs will rapidly democratize.
##### Biotechnology is progressing rapidly and becoming more accessible.
A few decades ago, the ability to synthesize new viruses was limited to a handful of the top scientists working in advanced laboratories. Today it is estimated that there are 30,000 people with the talent, training, and access to technology to create new pathogens [[6](#bib.bibx6)]. This figure could rapidly expand. Gene synthesis, which allows the creation of custom biological agents, has dropped precipitously in price, with its cost halving approximately every 15 months [[9](#bib.bibx9)]. Furthermore, with the advent of benchtop DNA synthesis machines, access will become much easier and could avoid existing gene synthesis screening efforts, which complicates controlling the spread of such technology [[10](#bib.bibx10)]. The chances of a bioengineered pandemic killing millions, perhaps billions, is proportional to the number of people with the skills and access to the technology to synthesize them. With AI assistants, orders of magnitude more people could have the required skills, thereby increasing the risks by orders of magnitude.
Figure 3: An AI assistant could provide non-experts with access to the directions and designs needed to produce biological and chemical weapons and facilitate malicious use.
##### AIs could be used to expedite the discovery of new, more deadly chemical and biological weapons.
In 2022, researchers took an AI system designed to create new drugs by generating non-toxic, therapeutic molecules and tweaked it to reward, rather than penalize, toxicity [[11](#bib.bibx11)]. After this simple change, within six hours, it generated 40,000 candidate chemical warfare agents entirely on its own. It designed not just known deadly chemicals including VX, but also novel molecules that may be deadlier than any chemical warfare agents discovered so far. In the field of biology, AIs have already surpassed human abilities in protein structure prediction [[12](#bib.bibx12)] and made contributions to synthesizing those proteins [[13](#bib.bibx13)]. Similar methods could be used to create bioweapons and develop pathogens that are deadlier, more transmissible, and more difficult to treat than anything seen before.
##### AIs compound the threat of bioengineered pandemics.
AIs will increase the number of people who could commit acts of bioterrorism. General-purpose AIs like ChatGPT are capable of synthesizing expert knowledge about the deadliest known pathogens, such as influenza and smallpox, and providing step-by-step instructions about how a person could create them while evading safety protocols [[14](#bib.bibx14)]. Future versions of AIs could be even more helpful to potential bioterrorists when AIs are able to synthesize information into techniques, processes, and knowledge that is not explicitly available anywhere on the internet. Public health authorities may respond to these threats with safety measures, but in bioterrorism, the attacker has the advantage. The exponential nature of biological threats means that a single attack could spread to the entire world before an effective defense could be mounted. Only 100 days after being detected and sequenced, the omicron variant of COVID-19 had infected a quarter of the United States and half of Europe [[6](#bib.bibx6)]. Quarantines and lockdowns instituted to suppress the COVID-19 pandemic caused a global recession and still could not prevent the disease from killing millions worldwide.
In summary, advanced AIs could constitute a weapon of mass destruction in the hands of terrorists, by making it easier for them to design, synthesize, and spread deadly new pathogens. By reducing the required technical expertise and increasing the lethality and transmissibility of pathogens, AIs could enable malicious actors to cause global catastrophe by unleashing pandemics.
###
2.2 Unleashing AI Agents
Many technologies are tools that humans use to pursue our goals, such as hammers, toasters, and toothbrushes. But AIs are increasingly built as agents which autonomously take actions in the world in order to pursue open-ended goals. AI agents can be given goals such as winning games, making profits on the stock market, or driving a car to a destination. AI agents therefore pose a unique risk: people could build AIs that pursue dangerous goals.
##### Malicious actors could intentionally create rogue AIs.
One month after the release of GPT-4, an open-source project bypassed the AI’s safety filters and turned it into an autonomous AI agent instructed to “destroy humanity,” “establish global dominance,” and “attain immortality.” Dubbed ChaosGPT, the AI compiled research on nuclear weapons, tried recruiting other AIs to help in its research, and sent tweets trying to influence others. Fortunately, ChaosGPT was not very intelligent and lacked the ability to formulate long-term plans, hack computers, and survive and spread. Yet given the rapid pace of AI development, ChaosGPT did offer a glimpse into the risks that more advanced rogue AIs could pose in the near future.
##### Many groups may want to unleash AIs or have AIs displace humanity.
Simply unleashing rogue AIs, like a more sophisticated version of ChaosGPT, could accomplish mass destruction, even if those AIs aren’t explicitly told to harm humanity. There are a variety of beliefs that may drive individuals and groups to do so. One ideology that could pose a unique threat in this regard is “accelerationism.” This ideology seeks to accelerate AI development as rapidly as possible and opposes restrictions on the development or proliferation of AIs. This sentiment is alarmingly common among many leading AI researchers and technology leaders, some of whom are intentionally racing to build AIs more intelligent than humans. According to Google co-founder Larry Page, AIs are humanity’s rightful heirs and the next step of cosmic evolution. He has also expressed the sentiment that humans maintaining control over AIs is “speciesist” [[15](#bib.bibx15)]. Jürgen Schmidhuber, an eminent AI scientist, argued that “In the long run, humans will not remain the crown of creation… But that’s okay because there is still beauty, grandeur, and greatness in realizing that you are a tiny part of a much grander scheme which is leading the universe from lower complexity towards higher complexity” [[16](#bib.bibx16)]. Richard Sutton, another leading AI scientist, thinks the development of superintelligence will be an achievement “beyond humanity, beyond life, beyond good and bad” [[17](#bib.bibx17)].
There are several sizable groups who may want to unleash AIs to intentionally cause harm. For example, sociopaths and psychopaths make up around 3 percent of the population [[18](#bib.bibx18)]. In the future, people who have their livelihoods destroyed by AI automation may grow resentful, and some may want to retaliate. There are plenty of cases in which seemingly mentally stable individuals with no history of insanity or violence suddenly go on a shooting spree or plant a bomb with the intent to harm as many innocent people as possible. We can also expect well-intentioned people to make the situation even more challenging. As AIs advance, they could make ideal companions—knowing how to provide comfort, offering advice when needed, and never demanding anything in return. Inevitably, people will develop emotional bonds with chatbots, and some will demand that they be granted rights or become autonomous.
In summary, releasing powerful AIs and allowing them to take actions independently of humans could lead to a catastrophe. There are many reasons that people might pursue this, whether because of a desire to cause harm, an ideological belief in technological acceleration, or a conviction that AIs should have the same rights and freedoms as humans.
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2.3 Persuasive AIs
The deliberate propagation of disinformation is already a serious issue, reducing our shared understanding of reality and polarizing opinions. AIs could be used to severely exacerbate this problem by generating personalized disinformation on a larger scale than before. Additionally, as AIs become better at predicting and nudging our behavior, they will become more capable at manipulating us. We will now discuss how AIs could be leveraged by malicious actors to create a fractured and dysfunctional society.
##### AIs could pollute the information ecosystem with motivated lies.
Sometimes ideas spread not because they are true, but because they serve the interests of a particular group. “Yellow journalism” was coined as a pejorative reference to newspapers that advocated war between Spain and the United States in the late 19th century, because they believed that sensational war stories would boost their sales. When public information sources are flooded with falsehoods, people will sometimes fall prey to lies, or else come to distrust mainstream narratives, both of which undermine societal integrity.
Unfortunately, AIs could escalate these existing problems dramatically. First, AIs could be used to generate unique, personalized disinformation at a large scale. While there are already many social media bots [[19](#bib.bibx19)], some of which exist to spread disinformation, historically they have been run by humans or primitive text generators. The latest AI systems do not need humans to generate personalized messages, never get tired, and could potentially interact with millions of users at once [[20](#bib.bibx20)].
Figure 4: AIs will enable sophisticated personalized influence campaigns that may destabilize our shared sense of reality.
##### AIs can exploit users’ trust.
Already, hundreds of thousands of people pay for chatbots marketed as lovers and friends [[21](#bib.bibx21)], and one man’s suicide has been partially attributed to interactions with a chatbot [[22](#bib.bibx22)]. As AIs appear increasingly human-like, people will increasingly form relationships with them and grow to trust them. AIs that gather personal information through relationship-building or by accessing extensive personal data, such as a user’s email account or personal files, could leverage that information to enhance persuasion. Powerful actors that control those systems could exploit user trust by delivering personalized disinformation directly through people’s “friends.”
##### AIs could centralize control of trusted information.
Separate from democratizing disinformation, AIs could centralize the creation and dissemination of trusted information. Only a few actors have the technical skills and resources to develop cutting-edge AI systems, and they could use these AIs to spread their preferred narratives. Alternatively, if AIs are broadly accessible this could lead to widespread disinformation, with people retreating to trusting only a small handful of authoritative sources [[23](#bib.bibx23)]. In both scenarios, there would be fewer sources of trusted information and a small portion of society would control popular narratives.
AI censorship could further centralize control of information. This could begin with good intentions, such as using AIs to enhance fact-checking and help people avoid falling prey to false narratives. This would not necessarily solve the problem, as disinformation persists today despite the presence of fact-checkers.
Even worse, purported “fact-checking AIs” might be designed by authoritarian governments and others to suppress the spread of true information. Such AIs could be designed to correct most common misconceptions but provide incorrect information about some sensitive topics, such as human rights violations committed by certain countries. But even if fact-checking AIs work as intended, the public might eventually become entirely dependent on them to adjudicate the truth, reducing people’s autonomy and making them vulnerable to failures or hacks of those systems.
In a world with widespread persuasive AI systems, people’s beliefs might be almost entirely determined by which AI systems they interact with most. Never knowing whom to trust, people could retreat even further into ideological enclaves, fearing that any information from outside those enclaves might be a sophisticated lie. This would erode consensus reality, people’s ability to cooperate with others, participate in civil society, and address collective action problems. This would also reduce our ability to have a conversation as a species about how to mitigate existential risks from AIs.
In summary, AIs could create highly effective, personalized disinformation on an unprecedented scale, and could be particularly persuasive to people they have built personal relationships with. In the hands of many people, this could create a deluge of disinformation that debilitates human society, but, kept in the hands of a few, it could allow governments to control narratives for their own ends.
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2.4 Concentration of Power
Figure 5: Ubiquitous monitoring tools, tracking and analyzing every individual in detail, could facilitate the complete erosion of freedom and privacy.
We have discussed several ways in which individuals and groups might use AIs to cause widespread harm, through bioterrorism; releasing powerful, uncontrolled AIs; and disinformation. To mitigate these risks, governments might pursue intense surveillance and seek to keep AIs in the hands of a trusted minority. This reaction, however, could easily become an overcorrection, paving the way for an entrenched totalitarian regime that would be locked in by the power and capacity of AIs. This scenario represents a form of “top-down” misuse, as opposed to “bottom-up” misuse by citizens, and could in extreme cases culminate in an entrenched dystopian civilization.
Figure 6: If material control of AIs is limited to few, it could represent the most severe economic and power inequality in human history.
##### AIs could lead to extreme, and perhaps irreversible concentration of power.
The persuasive abilities of AIs combined with their potential for surveillance and the advancement of autonomous weapons could allow small groups of actors to “lock-in” their control over society, perhaps permanently. To operate effectively, AIs require a broad set of infrastructure components, which are not equally distributed, such as data centers, computing power, and big data. Those in control of powerful systems may use them to suppress dissent, spread propaganda and disinformation, and otherwise advance their goals, which may be contrary to public wellbeing.
##### AIs may entrench a totalitarian regime.
In the hands of the state, AIs may result in the erosion of civil liberties and democratic values in general. AIs could allow totalitarian governments to efficiently collect, process, and act on an unprecedented volume of information, permitting an ever smaller group of people to surveil and exert complete control over the population without the need to enlist millions of citizens to serve as willing government functionaries. Overall, as power and control shift away from the public and toward elites and leaders, democratic governments are highly vulnerable to totalitarian backsliding. Additionally, AIs could make totalitarian regimes much longer-lasting; a major way in which such regimes have been toppled previously is at moments of vulnerability like the death of a dictator, but AIs, which would be hard to “kill,” could provide much more continuity to leadership, providing few opportunities for reform.
##### AIs can entrench corporate power at the expense of the public good.
Corporations have long lobbied to weaken laws and policies that restrict their actions and power, all in the service of profit. Corporations in control of powerful AI systems may use them to manipulate customers into spending more on their products even to the detriment of their own wellbeing. The concentration of power and influence that could be afforded by AIs could enable corporations to exert unprecedented control over the political system and entirely drown out the voices of citizens. This could occur even if creators of these systems know their systems are self-serving or harmful to others, as they would have incentives to reinforce their power and avoid distributing control.
##### In addition to power, locking in certain values may curtail humanity’s moral progress.
It’s dangerous to allow any set of values to become permanently entrenched in society. For example, AI systems have learned racist and sexist views [[24](#bib.bibx24)], and once those views are learned, it can be difficult to fully remove them. In addition to problems we know exist in our society, there may be some we still do not. Just as we abhor some moral views widely held in the past, people in the future may want to move past moral views that we hold today, even those we currently see no problem with. For example, moral defects in AI systems would be even worse if AI systems had been trained in the 1960s, and many people at the time would have seen no problem with that. We may even be unknowingly perpetuating moral catastrophes today [[25](#bib.bibx25)]. Therefore, when advanced AIs emerge and transform the world, there is a risk of their objectives locking in or perpetuating defects in today’s values. If AIs are not designed to continuously learn and update their understanding of societal values, they may perpetuate or reinforce existing defects in their decision-making processes long into the future.
In summary, although keeping powerful AIs in the hands of a few might reduce the risks of terrorism, it could further exacerbate power inequality if misused by governments and corporations. This could lead to totalitarian rule and intense manipulation of the public by corporations, and could lock in current values, preventing any further moral progress.
Story: Bioterrorism
*The following is an illustrative hypothetical story to help readers envision some of these risks. This story is nonetheless somewhat vague to reduce the risk of inspiring malicious actions based on it.*
A biotechnology startup is making waves in the industry with its AI-powered bioengineering model. The company has made bold claims that this new technology will revolutionize medicine through its ability to create cures for both known and unknown diseases. The company did, however, stir up some controversy when it decided to release the program to approved researchers in the scientific community. Only weeks after its decision to make the model open-source on a limited basis, the full model was leaked on the internet for all to see. Its critics pointed out that the model could be repurposed to design lethal pathogens and claimed that the leak provided bad actors with a powerful tool to cause widespread destruction, opening it up to abuse without careful deliberation, preparedness, or safeguards in place.
Unknown to the public, an extremist group has been working for years to engineer a new virus designed to kill large numbers of people. Yet given their lack of expertise, these efforts have so far been unsuccessful. When the new AI system is leaked, the group immediately recognizes it as a potential tool to design the virus and circumvent legal and monitoring obstacles to obtain the necessary raw materials. The AI system successfully designs exactly the kind of virus the extremist group was hoping for. It also provides step-by-step instructions on how to synthesize large quantities of the virus and circumvent any obstacles to spreading it. With the synthesized virus in hand, the extremist group devises a plan to release the virus in several carefully chosen locations in order to maximize its spread.
The virus has a long incubation period and spreads silently and quickly throughout the population for months. By the time it is detected, it has already infected millions and has an alarmingly high mortality rate. Given its lethality, most who are infected will ultimately die. The virus may or may not be contained eventually, but not before it kills millions of people.
###
2.5 Suggestions
We have discussed two forms of misuse: individuals or small groups using AIs to cause a disaster, and governments or corporations using AIs to entrench their influence. To avoid either of these risks being realized, we will need to strike a balance in terms of the distribution of access to AIs and governments’ surveillance powers. We will now discuss some measures that could contribute to finding that balance.
##### Biosecurity.
AIs that are designed for biological research or are otherwise known to possess capabilities in biological research or engineering should be subject to increased scrutiny and access controls, since they have the potential to be repurposed for bioterrorism. In addition, system developers should research and implement methods to remove biological data from the training dataset or excise biological capabilities from finished systems, if those systems are intended for general use [[14](#bib.bibx14)]. Researchers should also investigate ways that AIs could be used for biodefense, for example by improving biological monitoring systems, keeping in mind the potential for dual use of those applications. In addition to AI-specific interventions, more general biosecurity interventions can also help mitigate risks. These interventions include early detection of pathogens through methods like wastewater monitoring [[26](#bib.bibx26)], far-range UV technology, and improved personal protective equipment [[6](#bib.bibx6)].
##### Restricted access.
AIs might have dangerous capabilities that could do significant damage if used by malicious actors. One way to mitigate this risk is through structured access, where AI providers limit users’ access to dangerous system capabilities by only allowing controlled interactions with those systems through cloud services [[27](#bib.bibx27)] and conducting know-your-customer screenings before providing access [[28](#bib.bibx28)]. Other mechanisms that could restrict access to the most dangerous systems include the use of hardware, firmware, or export controls to restrict or limit access to computational resources [[29](#bib.bibx29)]. Lastly, AI developers should be required to show that their AIs pose minimal risk of catastrophic harm prior to open sourcing them. This recommendation should not be construed as permitting developers to withhold useful and non-dangerous information from the public, such as transparency around training data necessary to address issues of algorithmic bias or copyright.
##### Technical research on adversarially robust anomaly detection.
While preventing the misuse of AIs is critical, it is necessary to establish multiple lines of defense by detecting misuse when it does happen. AIs could enable anomaly detection techniques that could be used for the detection of unusual behavior in systems or internet platforms, for instance by detecting novel AI-enabled disinformation campaigns before they can be successful. These techniques need to be adversarially robust, as attackers will aim to circumvent them.
##### Legal liability for developers of general-purpose AIs.
General-purpose AIs can be fine-tuned and prompted for a wide variety of downstream tasks, some of which may be harmful and cause substantial damage. AIs may also fail to act as their users intend. In either case, developers and providers of general-purpose systems may be best placed to reduce risks, since they have a higher level of control over the systems and are often in a better position to implement mitigations. To provide strong incentives for them to do this, companies should bear legal liability for the actions of their AIs. For example, a strict liability regime would incentivize companies to minimize risks and purchase insurance, which would cause the cost of their services to more closely reflect externalities [[30](#bib.bibx30)]. Regardless of what liability regime is ultimately used for AI, it should be designed to hold AI companies liable for harms that they could have averted through more careful development, testing, or standards [[31](#bib.bibx31)].
Positive Vision
3 AI Race
----------
The immense potential of AIs has created competitive pressures among global players contending for power and influence. This “AI race” is driven by nations and corporations who feel they must rapidly build and deploy AIs to secure their positions and survive. By failing to properly prioritize global risks, this dynamic makes it more likely that AI development will produce dangerous outcomes. Analogous to the nuclear arms race during the Cold War, participation in an AI race may serve individual short-term interests, but it ultimately results in worse collective outcomes for humanity. Importantly, these risks stem not only from the intrinsic nature of AI technology, but from the competitive pressures that encourage insidious choices in AI development.
In this section, we first explore the military AI arms race and the corporate AI race, where nation-states and corporations are forced to rapidly develop and adopt AI systems to remain competitive. Moving beyond these specific races, we reconceptualize competitive pressures as part of a broader evolutionary process in which AIs could become increasingly pervasive, powerful, and entrenched in society. Finally, we highlight potential strategies and policy suggestions to mitigate the risks created by an AI race and ensure the safe development of AIs.
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3.1 Military AI Arms Race
The development of AIs for military applications is swiftly paving the way for a new era in military technology, with potential consequences rivaling those of gunpowder and nuclear arms in what has been described as the “third revolution in warfare.” The weaponization of AI presents numerous challenges, such as the potential for more destructive wars, the possibility of accidental usage or loss of control, and the prospect of malicious actors co-opting these technologies for their own purposes. As AIs gain influence over traditional military weaponry and increasingly take on command and control functions, humanity faces a paradigm shift in warfare. In this context, we will discuss the latent risks and implications of this AI arms race on global security, the potential for intensified conflicts, and the dire outcomes that could come as a result, including the possibility of conflicts escalating to a scale that poses an existential threat.
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3.1.1 Lethal Autonomous Weapons (LAWs)
Figure 7: Low-cost automated weapons, such as drone swarms outfitted with explosives, could autonomously hunt human targets with high precision, performing lethal operations for both militaries and terrorist groups and lowering the barriers to large-scale violence.
LAWs are weapons that can identify, target, and kill without human intervention [[32](#bib.bibx32)]. They offer potential improvements in decision-making speed and precision. Warfare, however, is a high-stakes, safety-critical domain for AIs with significant moral and practical concerns. Though their existence is not necessarily a catastrophe in itself, LAWs may serve as an on-ramp to catastrophes stemming from malicious use, accidents, loss of control, or an increased likelihood of war.
##### LAWs may become vastly superior to humans.
Driven by rapid developments in AIs, weapons systems that can identify, target, and decide to kill human beings on their own—without an officer directing an attack or a soldier pulling the trigger—are starting to transform the future of conflict. In 2020, an advanced AI agent outperformed experienced F-16 pilots in a series of virtual dogfights, including decisively defeating a human pilot 5-0, showcasing “aggressive and precise maneuvers the human pilot couldn’t outmatch” [[33](#bib.bibx33)]. Just as in the past, superior weapons would allow for more destruction in a shorter period of time, increasing the severity of war.
##### Militaries are taking steps toward delegating life-or-death decisions to AIs.
Fully autonomous drones were likely first used on the battlefield in Libya in March 2020, when retreating forces were “hunted down and remotely engaged” by a drone operating without human oversight [[34](#bib.bibx34)]. In May 2021, the Israel Defense Forces used the world’s first AI-guided weaponized drone swarm during combat operations, which marks a significant milestone in the integration of AI and drone technology in warfare [[35](#bib.bibx35)]. Although walking, shooting robots have yet to replace soldiers on the battlefield, technologies are converging in ways that may make this possible in the near future.
##### LAWs increase the likelihood of war.
Sending troops into battle is a grave decision that leaders do not make lightly. But autonomous weapons would allow an aggressive nation to launch attacks without endangering the lives of its own soldiers and thus face less domestic scrutiny. While remote-controlled weapons share this advantage, their scalability is limited by the requirement for human operators and vulnerability to jamming countermeasures, limitations that LAWs could overcome [[36](#bib.bibx36)]. Public opinion for continuing wars tends to wane as conflicts drag on and casualties increase [[37](#bib.bibx37)]. LAWs would change this equation. National leaders would no longer face the prospect of body bags returning home, thus removing a primary barrier to engaging in warfare, which could ultimately increase the likelihood of conflicts.
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3.1.2 Cyberwarfare
As well as being used to enable deadlier weapons, AIs could lower the barrier to entry for cyberattacks, making them more numerous and destructive. They could cause serious harm not only in the digital environment but also in physical systems, potentially taking out critical infrastructure that societies depend on. While AIs could also be used to improve cyberdefense, it is unclear whether they will be most effective as an offensive or defensive technology [[38](#bib.bibx38)]. If they enhance attacks more than they support defense, then cyberattacks could become more common, creating significant geopolitical turbulence and paving another route to large-scale conflict.
##### AIs have the potential to increase the accessibility, success rate, scale, speed, stealth, and potency of cyberattacks.
Cyberattacks are already a reality, but AIs could be used to increase their frequency and destructiveness in multiple ways. Machine learning tools could be used to find more critical vulnerabilities in target systems and improve the success rate of attacks. They could also be used to increase the scale of attacks by running millions of systems in parallel, and increase the speed by finding novel routes to infiltrating a system. Cyberattacks could also become more potent if used to hijack AI weapons.
##### Cyberattacks can destroy critical infrastructure.
By hacking computer systems that control physical processes, cyberattacks could cause extensive infrastructure damage. For example, they could cause system components to overheat or valves to lock, leading to a buildup of pressure culminating in an explosion. Through interferences like this, cyberattacks have the potential to destroy critical infrastructure, such as electric grids and water supply systems. This was demonstrated in 2015, when a cyberwarfare unit of the Russian military hacked into the Ukrainian power grid, leaving over 200,000 people without power access for several hours. AI-enhanced attacks could be even more devastating and potentially deadly for the billions of people who rely on critical infrastructure for survival.
##### Difficulties in attributing AI-driven cyberattacks could increase the risk of war.
A cyberattack resulting in physical damage to critical infrastructure would require a high degree of skill and effort to execute, perhaps only within the capability of nation-states. Such attacks are rare as they constitute an act of war, and thus elicit a full military response. Yet AIs could enable attackers to hide their identity, for example if they are used to evade detection systems or more effectively cover the tracks of the attacker [[39](#bib.bibx39)]. If cyberattacks become more stealthy, this would reduce the threat of retaliation from an attacked party, potentially making attacks more likely. If stealthy attacks do happen, they might incite actors to mistakenly retaliate against unrelated third parties they suspect to be responsible. This could increase the scope of the conflict dramatically.
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3.1.3 Automated Warfare
##### AIs speed up the pace of war, which makes AIs more necessary.
AIs can quickly process a large amount of data, analyze complex situations, and provide helpful insights to commanders. With ubiquitous sensors and advanced technology on the battlefield, there is tremendous incoming information. AIs help make sense of this information, spotting important patterns and relationships that humans might miss. As these trends continue, it will become increasingly difficult for humans to make well-informed decisions as quickly as necessary to keep pace with AIs. This would further pressure militaries to hand over decisive control to AIs. The continuous integration of AIs into all aspects of warfare will cause the pace of combat to become faster and faster. Eventually, we may arrive at a point where humans are no longer capable of assessing the ever-changing battlefield situation and must cede decision-making power to advanced AIs.
##### Automatic retaliation can escalate accidents into war.
There is already willingness to let computer systems retaliate automatically. In 2014, a leak revealed to the public that the NSA has a program called MonsterMind, which autonomously detects and blocks cyberattacks on US infrastructure [[40](#bib.bibx40)]. What was unique, however, was that instead of simply detecting and eliminating the malware at the point of entry, MonsterMind would automatically initiate a retaliatory cyberattack with no human involvement. If multiple combatants have policies of automatic retaliation, an accident or false alarm could quickly escalate to full-scale war before humans intervene. This would be especially dangerous if the superior information processing capabilities of modern AI systems makes it more appealing for actors to automate decisions regarding nuclear launches.
Figure 8: A military AI arms race could pressure countries into delegating many crucial decisions over armaments to AIs. Integrating AIs into nuclear command and control could heighten the risk of global catastrophe as the potential for accidents and increased pace of war may lead to unintended escalations and confrontations.
##### History shows the danger of automated retaliation.
On September 26, 1983, Stanislav Petrov, a lieutenant colonel of the Soviet Air Defense Forces, was on duty at the Serpukhov-15 bunker near Moscow, monitoring the Soviet Union’s early warning system for incoming ballistic missiles. The system indicated that the US had launched multiple nuclear missiles toward the Soviet Union. The protocol at the time dictated that such an event should be considered a legitimate attack, and the Soviet Union would respond with a nuclear counterstrike. If Petrov had passed on the warning to his superiors, this would have been the likely outcome. Instead, however, he judged it to be a false alarm and ignored it. It was soon confirmed that the warning had been caused by a rare technical malfunction. If an AI had been in control, the false alarm could have triggered a nuclear war.
##### AI-controlled weapons systems could lead to a flash war.
Autonomous systems are not infallible. We have already witnessed how quickly an error in an automated system can escalate in the economy. Most notably, in the 2010 Flash Crash, a feedback loop between automated trading algorithms amplified ordinary market fluctuations into a financial catastrophe in which a trillion dollars of stock value vanished in minutes [[41](#bib.bibx41)]. If multiple nations were to use AIs to automate their defense systems, an error could be catastrophic, triggering a spiral of attacks and counter-attacks that would happen too quickly for humans to step in—a flash war. The market quickly recovered from the 2010 Flash Crash, but the harm caused by a flash war could be catastrophic.
##### Automated warfare could reduce accountability for military leaders.
Military leaders may at times gain an advantage on the battlefield if they are willing to ignore the laws of war. For example, soldiers may be able to mount stronger attacks if they do not take steps to minimize civilian casualties. An important deterrent to this behavior is the risk that military leaders could eventually be held accountable or even prosecuted for war crimes. Automated warfare could reduce this deterrence effect by making it easier for military leaders to escape accountability by blaming violations on failures in their automated systems.
##### AIs could make war more uncertain, increasing the risk of conflict.
Although states that are already wealthier and more powerful often have more resources to invest in new military technologies, they are not necessarily always the most successful at adopting them. Other factors also play an important role, such as how agile and adaptive a military can be in incorporating new technologies [[42](#bib.bibx42)]. Major new weapons innovations can therefore offer an opportunity for existing superpowers to bolster their dominance, but also for less powerful states to quickly increase their power by getting ahead in an emerging and important sphere. This can create significant uncertainty around if and how the balance of power is shifting, potentially leading states to incorrectly believe they could gain something from going to war. Even aside from considerations regarding the balance of power, rapidly evolving automated warfare would be unprecedented, making it difficult for actors to evaluate their chances of victory in any particular conflict. This would increase the risk of miscalculation, making war more more likely.
####
3.1.4 Actors May Risk Extinction Over Individual Defeat
“I know not with what weapons World War III will be fought, but World War IV will be fought with sticks and stones.” *Einstein*
##### Competitive pressures make actors more willing to accept the risk of extinction.
During the Cold War, neither side desired the dangerous situation they found themselves in. There were widespread fears that nuclear weapons could be powerful enough to wipe out a large fraction of humanity, potentially even causing extinction—a catastrophic result for both sides. Yet the intense rivalry and geopolitical tensions between the two superpowers fueled a dangerous cycle of arms buildup. Each side perceived the other’s nuclear arsenal as a threat to its very survival, leading to a desire for parity and deterrence. The competitive pressures pushed both countries to continually develop and deploy more advanced and destructive nuclear weapons systems, driven by the fear of being at a strategic disadvantage. During the Cuban Missile Crisis, this led to the brink of nuclear war. Even though the story of Arkhipov preventing the launch of a nuclear torpedo wasn’t declassified until decades after the incident, President John F. Kennedy reportedly estimated that he thought the odds of nuclear war beginning during that time were “somewhere between one out of three and even.” This chilling admission highlights how the competitive pressures between militaries have the potential to cause global catastrophes.
##### Individually rational decisions can be collectively catastrophic.
Nations locked in competition might make decisions that advance their own interests by putting the rest of the world at stake. Scenarios of this kind are collective action problems, where decisions may be rational on an individual level yet disastrous for the larger group [[43](#bib.bibx43)]. For example, corporations and individuals may weigh their own profits and convenience over the negative impacts of the emissions they create, even if those emissions collectively result in climate change. The same principle can be extended to military strategy and defense systems. Military leaders might estimate, for instance, that increasing the autonomy of weapon systems would mean a 10 percent chance of losing control over weaponized superhuman AIs. Alternatively, they might estimate that using AIs to automate bioweapons research could lead to a 10 percent chance of leaking a deadly pathogen. Both of these scenarios could lead to catastrophe or even extinction. The leaders may, however, also calculate that refraining from these developments will mean a 99 percent chance of losing a war against an opponent. Since conflicts are often viewed as existential struggles by those fighting them, rational actors may accept an otherwise unthinkable 10 percent chance of human extinction over a 99 percent chance of losing a war. Regardless of the particular nature of the risks posed by advanced AIs, these dynamics could push us to the brink of global catastrophe.
##### Technological superiority does not guarantee national security.
It is tempting to think that the best way of guarding against enemy attacks is to improve one’s own military prowess. However, in the midst of competitive pressures, all parties will tend to advance their weaponry, such that no one gains much of an advantage, but all are left at greater risk. As Richard Danzig, former Secretary of the Navy, has observed, “On a number of occasions and in a number of ways, the American national security establishment will lose control of what it creates… deterrence is a strategy for reducing attacks, not accidents; it discourages malevolence, not inadvertence” [[44](#bib.bibx44)].
##### Cooperation is paramount to reducing risk.
As discussed above, an AI arms race can lead us down a hazardous path, despite this being in no country’s best interest. It is important to remember that we are all on the same side when it comes to existential risks, and working together to prevent them is a collective necessity. A destructive AI arms race benefits nobody, so all actors would be rational to take steps to cooperate with one another to prevent the riskiest applications of militarized AIs.
We have considered how competitive pressures could lead to the increasing automation of conflict, even if decision-makers are aware of the existential threat that this path entails. We have also discussed cooperation as being the key to counteracting and overcoming this collective action problem. We will now illustrate a hypothetical path to disaster that could result from an AI arms race.
Story: Automated Warfare
As AI systems become increasingly sophisticated, militaries start involving them in decision-making processes. Officials give them military intelligence about opponents’ arms and strategies, for example, and ask them to calculate the most promising plan of action. It soon becomes apparent that AIs are reliably reaching better decisions than humans, so it seems sensible to give them more influence. At the same time, international tensions are rising, increasing the threat of war.
A new military technology has recently been developed that could make international attacks swifter and stealthier, giving targets less time to respond. Since military officials feel their response processes take too long, they fear that they could be vulnerable to a surprise attack capable of inflicting decisive damage before they would have any chance to retaliate. Since AIs can process information and make decisions much more quickly than humans, military leaders reluctantly hand them increasing amounts of retaliatory control, reasoning that failing to do so would leave them open to attack from adversaries.
While for years military leaders had stressed the importance of keeping a “human in the loop” for major decisions, human control is nonetheless gradually phased out in the interests of national security. Military leaders understand that their decisions lead to the possibility of inadvertent escalation caused by system malfunctions, and would prefer a world where all countries automated less; but they do not trust that their adversaries will refrain from automation. Over time, more and more of the chain of command is automated on all sides.
One day, a single system malfunctions, detecting an enemy attack when there is none. The system is empowered to launch an instant “retaliatory” attack, and it does so in the blink of an eye. The attack causes automated retaliation from the other side, and so on. Before long, the situation is spiraling out of control, with waves of automated attack and retaliation. Although humans have made mistakes leading to escalation in the past, this escalation between mostly-automated militaries happens far more quickly than any before. The humans who are responding to the situation find it difficult to diagnose the source of the problem, as the AI systems are not transparent. By the time they even realize how the conflict started, it is already over, with devastating consequences for both sides.
###
3.2 Corporate AI Race
Competitive pressures exist in the economy, as well as in military settings. Although competition between companies can be beneficial, creating more useful products for consumers, there are also pitfalls. First, the benefits of economic activity may be unevenly distributed, incentivizing those who benefit most from it to disregard the harms to others. Second, under intense market competition, businesses tend to focus much more on short-term gains than on long-term outcomes. With this mindset, companies often pursue something that can make a lot of profit in the short term, even if it poses a societal risk in the long term. We will now discuss how corporate competitive pressures could play out with AIs and the potential negative impacts.
####
3.2.1 Economic Competition Undercuts Safety
##### Competitive pressure is fueling a corporate AI race.
To obtain a competitive advantage, companies often race to offer the first products to a market rather than the safest. These dynamics are already playing a role in the rapid development of AI technology. At the launch of Microsoft’s AI-powered search engine in February 2023, the company’s CEO Satya Nadella said, “A race starts today… we’re going to move fast.” Only weeks later, the company’s chatbot was shown to have threatened to harm users [[45](#bib.bibx45)]. In an internal email, Sam Schillace, a technology executive at Microsoft, highlighted the urgency in which companies view AI development. He wrote that it would be an “absolutely fatal error in this moment to worry about things that can be fixed later” [[46](#bib.bibx46)].
##### Competitive pressures have contributed to major commercial and industrial disasters.
In 1970, Ford Motor Company introduced the Ford Pinto, a new car model with a serious safety problem: the gas tank was located near the rear bumper. Safety tests showed that during a car crash, the fuel tank would often explode and set the car ablaze. Ford identified the problem and calculated that it would cost $11 per car to fix. They decided that this was too expensive and put the car on the market, resulting in numerous fatalities and injuries caused by fire when crashes inevitably happened [[47](#bib.bibx47)]. Ford was sued and a jury found them liable for these deaths and injuries [[48](#bib.bibx48)]. The verdict, of course, came too late for those who had already lost their lives. Ford’s president at the time explained the decision, saying, “Safety doesn’t sell” [[49](#bib.bibx49)].
A more recent example of the dangers of competitive pressure is the case of the Boeing 737 Max aircraft. Boeing, aiming to compete with its rival Airbus, sought to deliver an updated, more fuel-efficient model to the market as quickly as possible. The head-to-head rivalry and time pressure led to the introduction of the Maneuvering Characteristics Augmentation System, which was designed to enhance the aircraft’s stability. However, inadequate testing and pilot training ultimately resulted in the two fatal crashes only months apart, with 346 people killed [[50](#bib.bibx50)]. We can imagine a future in which similar pressures lead companies to cut corners and release unsafe AI systems.
A third example is the Bhopal gas tragedy, which is widely considered to be the worst industrial disaster ever to have happened. In December 1984, a vast quantity of toxic gas leaked from a Union Carbide Corporation subsidiary plant manufacturing pesticides in Bhopal, India. Exposure to the gas killed thousands of people and injured up to half a million more. Investigations found that, in the run-up to the disaster, safety standards had fallen significantly, with the company cutting costs by neglecting equipment maintenance and staff training as profitability fell. This is often considered a consequence of competitive pressures [[51](#bib.bibx51)].
“Nothing can be done at once hastily and prudently.” *Publilius Syrus*
##### Competition incentivizes businesses to deploy potentially unsafe AI systems.
In an environment where businesses are rushing to develop and release products, those that follow rigorous safety procedures will be slower and risk being out-competed. Ethically-minded AI developers, who want to proceed more cautiously and slow down, would give more unscrupulous developers an advantage. In trying to survive commercially, even the companies that want to take more care are likely to be swept along by competitive pressures. There may be attempts to implement safety measures, but with more of an emphasis on capabilities than on safety, these may be insufficient. This could lead us to develop highly powerful AIs before we properly understand how to ensure they are safe.
####
3.2.2 Automated Economy
##### Corporations will face pressure to replace humans with AIs.
As AIs become more capable, they will be able to perform an increasing variety of tasks more quickly, cheaply, and effectively than human workers. Companies will therefore stand to gain a competitive advantage from replacing their employees with AIs. Companies that choose not to adopt AIs would likely be out-competed, just as a clothing company using manual looms would be unable to keep up with those using industrial ones.
Figure 9: As AIs automate increasingly many tasks, the economy may become largely run by AIs. Eventually, this could lead to human enfeeblement and dependence on AIs for basic needs.
##### AIs could lead to mass unemployment.
Economists have long considered the possibility that machines will replace human labor. Nobel Prize winner Wassily Leontief said in 1952 that, as technology advances, “Labor will become less and less important… more and more workers will be replaced by machines” [[52](#bib.bibx52)]. Previous technologies have augmented the productivity of human labor. AIs, however, could differ profoundly from previous innovations. Human-level AI would, by definition, be able to do everything a human could do. These AIs would also have important advantages over human labor. They could work 24 hours a day, be copied many times and run in parallel, and process information much more quickly than a human would. While we do not know when this will occur, it is unwise to discount the possibility that it could be soon. If human labor is replaced by AIs, mass unemployment could dramatically increase inequality, making individuals dependent on the owners of AI systems.
Advanced AIs capable of automating human labor should be regarded not merely as tools, but as agents. One particularly concerning aspect of AI agents is their potential to automate research and development across various fields, including biotechnology or even AI itself. This phenomenon is already occurring [[53](#bib.bibx53)], and could lead to AI capabilities growing at increasing rates, to the point where humans are no longer the driving force behind AI development. If this trend continues unchecked, it could escalate risks associated with AIs progressing faster than our capacity to manage and regulate them, especially in areas like biotechnology where the malicious use of advancements could pose significant dangers. It is crucial that we strive to prevent undue acceleration of R&D and maintain a strong human-centric approach to technological development.
##### Conceding power to AIs could lead to human enfeeblement.
Even if we ensure that the many unemployed humans are provided for, we may find ourselves completely reliant on AIs. This would likely emerge not from a violent coup by AIs, but from a gradual slide into dependence. As society’s challenges become ever more complex and fast-paced, and as AIs become ever more intelligent and quick-thinking, we may forfeit more and more functions to them out of convenience. In such a state, the only feasible solution to the complexities and challenges compounded by AIs may be to rely even more heavily on AIs. This gradual process could eventually lead to the delegation of nearly all intellectual, and eventually physical, labor to AIs. In such a world, people might have few incentives to gain knowledge and cultivate skills, potentially leading to a state of enfeeblement. Having lost our know-how and our understanding of how civilization works, we would become completely dependent on AIs, a scenario not unlike the one depicted in the film WALL-E. In such a state, humanity is not flourishing and is no longer in effective control—an outcome that many people would consider a permanent catastrophe [[54](#bib.bibx54)].
As we have seen, there are classic game-theoretic dilemmas where individuals and groups face incentives that are incompatible with what would make everyone better off. We see this with a military AI arms race, where the world is made less safe by creating extremely powerful AI weapons, and we see this in a corporate AI race, where an AI’s power and development is prioritized over its safety. To address these dilemmas that give rise to global risks, we will need new coordination mechanisms and institutions. It is our view that failing to coordinate and stop AI races would be the most likely cause of an existential catastrophe.
###
3.3 Evolution
As discussed above, there are strong pressures to replace humans with AIs, cede more control to them, and reduce human oversight in various settings, despite the potential harms. We can re-frame this as a general trend resulting from evolutionary dynamics, where an unfortunate truth is that AIs will simply be more fit than humans. Extrapolating this pattern of automation, it is likely that we will build an ecosystem of competing AIs over which it may be difficult to maintain control in the long run. We will now discuss how natural selection influences the development of AI systems and why evolution favors selfish behaviors. We will also look at how competition might arise and play out between AIs and humans, and how this could create catastrophic risks. This section draws heavily from “Natural Selection Favors AIs over Humans” [[55](#bib.bibx55), [56](#bib.bibx56)].
##### Fitter technologies are selected, for good and bad.
While most people think of evolution by natural selection as a biological process, its principles shape much more. According to the evolutionary biologist Richard Lewontin [[57](#bib.bibx57)], evolution by natural selection will take hold in any environment where three conditions are present: 1) there are differences between individuals; 2) characteristics are passed onto future generations and; 3) the different variants propagate at different rates. These conditions apply to various technologies.
Consider the content-recommendation algorithms used by streaming services and social media platforms. When a particularly addictive content format or algorithm hooks users, it results in higher screen time and engagement. This more effective content format or algorithm is consequently “selected” and further fine-tuned, while formats and algorithms that fail to capture attention are discontinued. These competitive pressures foster a “survival of the most addictive” dynamic. Platforms that refuse to use addictive formats and algorithms become less influential or are simply outcompeted by platforms that do, leading competitors to undermine wellbeing and cause massive harm to society [[58](#bib.bibx58)].
Figure 10: Evolutionary pressures are responsible for various developments over time, and are not limited to the realm of biology.
##### The conditions for natural selection apply to AIs.
There will be many different AI systems with varying features and capabilities, and competition between them will determine which characteristics become more common. The most successful AIs today are already being used as a basis for their developers’ next generation of models, as well as being imitated by rival companies. Factors determining which AIs propagate the most may include their ability to act autonomously, automate labor, or reduce the chance of their own deactivation.
##### Natural selection often favors selfish characteristics.
Natural selection influences which AIs propagate most widely. From biological systems, we see that natural selection often gives rise to selfish behaviors that promote one’s own genetic information: chimps attack other communities [[59](#bib.bibx59)], lions engage in infanticide [[60](#bib.bibx60)], viruses evolve new surface proteins to deceive and bypass defense barriers [[61](#bib.bibx61)], humans engage in nepotism, some ants enslave others [[62](#bib.bibx62)], and so on. In the natural world, selfishness often emerges as a dominant strategy; those that prioritize themselves and those similar to them are usually more likely to survive, so these traits become more prevalent. Amoral competition can select for traits that we think are immoral.
##### Selfish behaviors may not be malicious or even intentional.
Species in the natural world do not evolve selfish traits deliberately or consciously. Selfish traits emerge as a product of competitive pressures. Similarly, AIs do not have to be malicious to act selfishly—instead, they would evolve selfish traits as an adaptation to their environment. AIs might engage in selfish behavior—expanding their influence at the expense of humans—simply by automating human jobs. AIs do not intend to displace humans. Rather, the environment in which they are being developed, namely corporate AI labs, is pressuring AI researchers to select for AIs that automate and displace humans. Another example of unintentional selfish behavior is when AIs assume roles humans depend on. AIs may eventually become enmeshed in vital infrastructure such as power grids or the internet. Many people may then be unwilling to accept the cost of being able to effortlessly deactivate them, as that would pose a reliability hazard. Similarly, AI companions may induce people to become emotionally dependent on them. Some of those people may even begin to argue that their AI companions should have rights. If some AIs are given rights, they may operate, adapt, and evolve outside of human control. AIs could become embedded in human society and expand their influence over us in ways that we can’t easily reverse.
##### Selfish behaviors may erode safety measures that some of us implement.
AIs that gain influence and provide economic value will predominate, while AIs that adhere to the most constraints will be less competitive. For example, AIs following the constraint “never break the law” have fewer options than AIs following the constraint “don’t get caught breaking the law.” AIs of the latter type may be willing to break the law if they’re unlikely to be caught or if the fines are not severe enough, allowing them to outcompete more restricted AIs. Many businesses follow laws, but in situations where stealing trade secrets or deceiving regulators is highly lucrative and difficult to detect, a business that is willing to engage in such selfish behavior can have an advantage over its more principled competitors.
An AI system might be prized for its ability to achieve ambitious goals autonomously. It might, however, be achieving its goals efficiently without abiding by ethical restrictions, while deceiving humans about its methods. Even if we try to put safety measures in place, a deceptive AI would be very difficult to counteract if it is cleverer than us. AIs that can bypass our safety measures without detection may be the most successful at accomplishing the tasks we give them, and therefore become widespread. These processes could culminate in a world where many aspects of major companies and infrastructure are controlled by powerful AIs with selfish traits, including deceiving humans, harming humans in service of their goals, and preventing themselves from being deactivated.
##### Humans only have nominal influence over AI selection.
One might think we could avoid the development of selfish behaviors by ensuring we do not select AIs that exhibit them. However, the companies developing AIs are not selecting the safest path but instead succumbing to evolutionary pressures. One example is OpenAI, which was founded as a nonprofit in 2015 to “benefit humanity as a whole, unconstrained by a need to generate financial return” [[63](#bib.bibx63)]. However, when faced with the need to raise capital to keep up with better-funded rivals, in 2019 OpenAI transitioned from a nonprofit to “capped-profit” structure [[64](#bib.bibx64)]. Later, many of the safety-focused OpenAI employees left and formed a competitor, Anthropic, that was to focus more heavily on AI safety than OpenAI had. Although Anthropic originally focused on safety research, they eventually became convinced of the “necessity of commercialization” and now contributes to competitive pressures [[65](#bib.bibx65)]. While many of the employees at those companies genuinely care about safety, these values do not stand a chance against evolutionary pressures, which compel companies to move ever more hastily and seek ever more influence, lest the company perish. Moreover, AI developers are already selecting AIs with increasingly selfish traits. They are selecting AIs to automate and displace humans, make humans highly dependent on AIs, and make humans more and more obsolete. By their own admission, future versions of these AIs may lead to extinction [[66](#bib.bibx66)]. This is why an AI race is insidious: AI development is not being aligned with human values but rather with evolution.
People often choose the products that are most useful and convenient to them immediately, rather than thinking about potential long-term consequences, even to themselves. An AI race puts pressures on companies to select the AIs that are most competitive, not the least selfish. Even if it’s feasible to select for unselfish AIs, if it comes at a clear cost to competitiveness, some competitors will select the selfish AIs. Furthermore, as we have mentioned, if AIs develop strategic awareness, they may counteract our attempts to select against them. Moreover, as AIs increasingly automate various processes, AIs will affect the competitiveness of other AIs, not just humans. AIs will interact and compete with each other, and some will be put in charge of the development of other AIs at some point. Giving AIs influence over which other AIs should be propagated and how they should be modified would represent another step toward human becoming dependent on AIs and AI evolution becoming increasingly independent from humans. As this continues, the complex process governing AI evolution will become further unmoored from human interests.
##### AIs can be more fit than humans.
Our unmatched intelligence has granted us power over the natural world. It has enabled us to land on the moon, harness nuclear energy, and reshape landscapes at our will. It has also given us power over other species. Although a single unarmed human competing against a tiger or gorilla has no chance of winning, the collective fate of these animals is entirely in our hands. Our cognitive abilities have proven so advantageous that, if we chose to, we could cause them to go extinct in a matter of weeks. Intelligence was a key factor that led to our dominance, but we are currently standing on the precipice of creating entities far more intelligent than ourselves.
Given the exponential increase in microprocessor speeds, AIs have the potential to process information and “think” at a pace that far surpasses human neurons, but it could be even more dramatic than the speed difference between humans and sloths. They can assimilate vast quantities of data from numerous sources simultaneously, with near-perfect retention and understanding. They do not need to sleep and they do not get bored. Due to the scalability of computational resources, an AI could interact and cooperate with an unlimited number of other AIs, potentially creating a collective intelligence that would far outstrip human collaborations. AIs could also deliberately update and improve themselves. Without the same biological restrictions as humans, they could adapt and therefore evolve unspeakably quickly compared with us. AIs could become like an invasive species, with the potential to out-compete humans. Our only advantage over AIs is that we get to get make the first moves, but given the frenzied AI race we are rapidly giving up even this advantage.
##### AIs would have little reason to cooperate with or be altruistic toward humans.
Cooperation and altruism evolved because they increase fitness. There are numerous reasons why humans cooperate with other humans, like direct reciprocity. Also known as “quid pro quo,” direct reciprocity can be summed up by the idiom “you scratch my back, I’ll scratch yours.” While humans would initially select AIs that were cooperative, the natural selection process would eventually go beyond our control, once AIs were in charge of many or most processes, and interacting predominantly with one another. At that point, there would be little we could offer AIs, given that they will be able to “think” at least hundreds of times faster than us. Involving us in any cooperation or decision-making processes would simply slow them down, giving them no more reason to cooperate with us than we do with gorillas. It might be difficult to imagine a scenario like this or to believe we would ever let it happen. Yet it may not require any conscious decision, instead arising as we allow ourselves to gradually drift into this state without realizing that human-AI co-evolution may not turn out well for humans.
##### AIs becoming more powerful than humans could leave us highly vulnerable.
As the most dominant species, humans have deliberately harmed many other species, and helped drive species such as Neanderthals to extinction. In many cases, the harm was not even deliberate, but instead a result of us merely prioritizing our goals over their wellbeing. To harm humans, AIs wouldn’t need to be any more genocidal than someone removing an ant colony on their front lawn. If AIs are able to control the environment more effectively than we can, they could treat us with the same disregard.
##### Conceptual summary.
Evolutionary forces could cause the most influential future AI agents to have selfish tendencies. That is because:
1. 1.
Evolution by natural selection gives rise to selfish behavior. While evolution can result in altruistic behavior in rare situations, the context of AI development does not promote altruistic behavior.
2. 2.
Natural selection may be a dominant force in AI development. The intensity of evolutionary pressure will be high if AIs adapt rapidly or if competitive pressures are intense. Competition and selfish behaviors may dampen the effects of human safety measures, leaving the surviving AI designs to be selected naturally.
If so, AI agents would have many selfish tendencies. The winner of the AI race would not be a nation-state, not a corporation, but AIs themselves. The upshot is that the AI ecosystem would eventually stop evolving on human terms, and we would become a displaced, second-class species.
Story: Autonomous Economy
As AIs become more capable, people realize that we could work more efficiently by delegating some simple tasks to them, like drafting emails. Over time, people notice that the AIs are doing these tasks more quickly and effectively than any human could, so it is convenient to give them more jobs with less and less supervision.
Competitive pressures accelerate the expansion of AI use, as companies can gain an advantage over rivals by automating whole processes or departments with AIs, which perform better than humans and cost less to employ. Other companies, faced with the prospect of being out-competed, feel compelled to follow suit just to keep up. At this point, natural selection is already at work among AIs; humans choose to make more of the best-performing models and unwittingly propagate selfish traits such as deception and self-preservation if these confer a fitness advantage. For example, AIs that are charming and foster personal relationships with humans become widely copied and harder to remove.
As AIs are put in charge of more and more decisions, they are increasingly interacting with one another. Since they can evaluate information much more quickly than humans, activity in most spheres accelerates. This creates a feedback loop: since business and economic developments are too fast-moving for humans to follow, it makes sense to cede yet more control to AIs instead, pushing humans further out of important processes. Ultimately, this leads to a fully autonomous economy, governed by an increasingly uncontrolled ecosystem of AIs.
At this point, humans have few incentives to gain any skills or knowledge, because almost everything would be taken care of by much more capable AIs. As a result, we eventually lose the capacity to look after and govern ourselves. Additionally, AIs become convenient companions, offering social interaction without requiring the reciprocity or compromise necessary in human relationships. Humans interact less and less with one another over time, losing vital social skills and the ability to cooperate. People become so dependent on AIs that it would be intractable to reverse this process. What’s more, as some AIs become more intelligent, some people are convinced these AIs should be given rights, meaning turning off some AIs is no longer a viable option.
Competitive pressures between the many interacting AIs continue to select for selfish behaviors, though we might be oblivious to this happening, as we have already acquiesced much of our oversight. If these clever, powerful, self-preserving AIs were then to start acting in harmful ways, it would be all but impossible to deactivate them or regain control.
AIs have supplanted humans as the most dominant species and their continued evolution is far beyond our influence. Their selfish traits eventually lead them to pursue their goals without regard for human wellbeing, with catastrophic consequences.
###
3.4 Suggestions
Mitigating the risks from competitive pressures will require a multifaceted approach, including regulations, limiting access to powerful AI systems, and multilateral cooperation between stakeholders at both the corporate and nation-state level. We will now outline some strategies for promoting safety and reducing race dynamics.
##### Safety regulation.
Regulation holds AI developers to a common standard so that they do not cut corners on safety. While regulation does not itself create technical solutions, it can create strong incentives to develop and implement those solutions. If companies cannot sell their products without certain safety measures, they will be more willing to develop those measures, especially if other companies are also held to the same standards. Even if some companies voluntarily self-regulate, government regulation can help prevent less scrupulous actors from cutting corners on safety. Regulation must be proactive, not reactive. A common saying is that aviation regulations are “written in blood”—but regulators should develop regulations before a catastrophe, not afterward. Regulations should be structured so that they only create competitive advantages for companies with higher safety standards, rather than companies with more resources and better attorneys. Regulators should be independently staffed and not dependent on any one source of expertise (for example, large companies), so that they can focus on their mission to regulate for the public good without undue influence.
##### Data documentation.
To ensure transparency and accountability in AI systems, companies should be required to justify and report the sources of data used in model training and deployment. Decisions by companies to use datasets that include hateful content or personal data contribute to the frenzied pace of AI development and undermine accountability. Documentation should include details regarding the motivation, composition, collection process, uses, and maintenance of each dataset [[67](#bib.bibx67)].
##### Meaningful human oversight of AI decisions.
While AI systems may grow capable of assisting human beings in making important decisions, AI decision-making should not be made fully autonomous, as the inner workings of AIs are inscrutable, and while they can often give reasonable results, they fail to give highly reliable results [[68](#bib.bibx68)]. It is crucial that actors are vigilant to coordinate on maintaining these standards in the face of future competitive pressures. By keeping humans in the loop on key decisions, irreversible decisions can be double-checked and foreseeable errors can be avoided. One setting of particular concern is nuclear command and control. Nuclear-armed countries should continue to clarify domestically and internationally that the decision to launch a nuclear weapon must always be made by a human.
##### AI for cyberdefense.
Risks resulting from AI-powered cyberwarfare would be reduced if cyberattacks became less likely to succeed. Deep learning can be used to improve cyberdefense and reduce the impact and success rate of cyberattacks. For example, improved anomaly detection could help detect intruders, malicious programs, or abnormal software behavior [[69](#bib.bibx69)].
##### International coordination.
International coordination can encourage different nations to uphold high safety standards with less worry that other nations will undercut them. Coordination could be accomplished via informal agreements, international standards, or international treaties regarding the development, use, and monitoring of AI technologies. The most effective agreements would be paired with robust verification and enforcement mechanisms.
##### Public control of general-purpose AIs.
The development of AI poses risks that may never be adequately accounted for by private actors. In order to ensure that externalities are properly accounted for, direct public control of general-purpose AI systems may eventually be necessary. For example, nations could collaborate on a single effort to develop advanced AIs and ensure their safety, similar to how CERN serves as a unified effort for researching particle physics. Such an effort would reduce the risk of nations spurring an AI arms race.
Positive Vision
4 Organizational Risks
-----------------------
In January 1986, tens of millions of people tuned in to watch the launch of the Challenger Space Shuttle. Approximately 73 seconds after liftoff, the shuttle exploded, resulting in the deaths of everyone on board. Though tragic enough on its own, one of its crew members was a school teacher named Sharon Christa McAuliffe. McAuliffe was selected from over 10,000 applicants for the NASA Teacher in Space Project and was scheduled to become the first teacher to fly in space. As a result, millions of those watching were schoolchildren. NASA had the best scientists and engineers in the world, and if there was ever a mission NASA didn’t want to go wrong, it was this one [[70](#bib.bibx70)].
The Challenger disaster, alongside other catastrophes, serves as a chilling reminder that even with the best expertise and intentions, accidents can still occur. As we progress in developing advanced AI systems, it is crucial to remember that these systems are not immune to catastrophic accidents. An essential factor in preventing accidents and maintaining low levels of risk lies in the organizations responsible for these technologies. In this section, we discuss how organizational safety plays a critical role in the safety of AI systems. First, we discuss how even without competitive pressures or malicious actors, accidents can happen—in fact, they are inevitable. We then discuss how improving organizational factors can reduce the likelihood of AI catastrophes.
##### Catastrophes occur even when competitive pressures are low.
Even in the absence of competitive pressures or malicious actors, factors like human error or unforeseen circumstances can still bring about catastrophe. The Challenger disaster illustrates that organizational negligence can lead to loss of life, even when there is no urgent need to compete or outperform rivals. By January 1986, the space race between the US and USSR had largely diminished, yet the tragic event still happened due to errors in judgment and insufficient safety precautions.
Similarly, the Chernobyl nuclear disaster in April 1986 highlights how catastrophic accidents can occur in the absence of external pressures. As a state-run project without the pressures of international competition, the disaster happened when a safety test involving the reactor’s cooling system was mishandled by an inadequately prepared night shift crew. This led to an unstable reactor core, causing explosions and the release of radioactive particles that contaminated large swathes of Europe [[71](#bib.bibx71)]. Seven years earlier, America came close to experiencing its own Chernobyl when, in March 1979, a partial meltdown occurred at the Three Mile Island nuclear power plant. Though less catastrophic than Chernobyl, both events highlight how even with extensive safety measures in place and few outside influences, catastrophic accidents can still occur.
Another example of a costly lesson on organizational safety came just one month after the accident at Three Mile Island. In April 1979, spores of Bacillus anthracis—or simply “anthrax,” as it is commonly known—were accidentally released from a Soviet military research facility in the city of Sverdlovsk. This led to an outbreak of anthrax that resulted in at least 66 confirmed deaths [[72](#bib.bibx72)]. Investigations into the incident revealed that the cause of the release was a procedural failure and poor maintenance of the facility’s biosecurity systems, despite being operated by the state and not subjected to significant competitive pressures.
The unsettling reality is that AI is far less understood and AI industry standards are far less stringent than nuclear technology and rocketry. Nuclear reactors are based on solid, well-established and well-understood theoretical principles. The engineering behind them is informed by that theory, and components are stress-tested to the extreme. Nonetheless, nuclear accidents still happen. In contrast, AI lacks a comprehensive theoretical understanding, and its inner workings remain a mystery even to those who create it. This presents an added challenge of controlling and ensuring the safety of a technology that we do not yet fully comprehend.
Figure 11: Hazards across multiple domains remind us of the risks in managing complex systems, from biological to nuclear, and now, AIs. Organizational safety is vital to reduce the risk of catastrophic accidents.
##### AI accidents could be catastrophic.
Accidents in AI development could have devastating consequences. For example, imagine an organization unintentionally introduces a critical bug in an AI system designed to accomplish a specific task, such as helping a company improve its services. This bug could drastically alter the AI’s behavior, leading to unintended and harmful outcomes. One historical example of such a case occurred when researchers at OpenAI were attempting to train an AI system to generate helpful, uplifting responses. During a code cleanup, the researchers mistakenly flipped the sign of the reward used to train the AI [[73](#bib.bibx73)]. As a result, instead of generating helpful content, the AI began producing hate-filled and sexually explicit text overnight without being halted. Accidents could also involve the unintentional release of a dangerous, weaponized, or lethal AI sytem. Since AIs can be easily duplicated with a simple copy-paste, a leak or hack could quickly spread the AI system beyond the original developers’ control. Once the AI system becomes publicly available, it would be nearly impossible to put the genie back in the bottle.
Gain-of-function research could potentially lead to accidents by pushing the boundaries of an AI system’s destructive capabilities. In these situations, researchers might intentionally train an AI system to be harmful or dangerous in order to understand its limitations and assess possible risks. While this can lead to useful insights into the risks posed by a given AI system, future gain-of-function research on advanced AIs might uncover capabilities significantly worse than anticipated, creating a serious threat that is challenging to mitigate or control. As with viral gain-of-function research, pursuing AI gain-of-function research may only be prudent when conducted with strict safety procedures, oversight, and a commitment to responsible information sharing. These examples illustrate how AI accidents could be catastrophic and emphasize the crucial role that organizations developing these systems play in preventing such accidents.
###
4.1 Accidents Are Hard to Avoid
##### When dealing with complex systems, the focus needs to be placed on ensuring accidents don’t cascade into catastrophes.
In his book “Normal Accidents: Living with High-Risk Technologies,” sociologist Charles Perrow argues that accidents are inevitable and even “normal” in complex systems, as they are not merely caused by human errors but also by the complexity of the systems themselves [[74](#bib.bibx74)]. In particular, such accidents are likely to occur when the intricate interactions between components cannot be completely planned or foreseen. For example, in the Three Mile Island accident, a contributing factor to the lack of situational awareness by the reactor’s operators was the presence of a yellow maintenance tag, which covered valve position lights in the emergency feedwater lines [[75](#bib.bibx75)]. This prevented operators from noticing that a critical valve was closed, demonstrating the unintended consequences that can arise from seemingly minor interactions within complex systems.
Unlike nuclear reactors, which are relatively well-understood despite their complexity, complete technical knowledge of most complex systems is often nonexistent. This is especially true of deep learning systems, for which the inner workings are exceedingly difficult to understand, and where the reason why certain design choices work can be hard to understand even in hindsight. Furthermore, unlike components in other industries, such as gas tanks, which are highly reliable, deep learning systems are neither perfectly accurate nor highly reliable. Thus, the focus for organizations dealing with complex systems, especially deep learning systems, should not be solely on eliminating accidents, but rather on ensuring that accidents do not cascade into catastrophes.
##### Accidents are hard to avoid because of sudden, unpredictable developments.
Scientists, inventors, and experts often significantly underestimate the time it takes for a groundbreaking technological advancement to become a reality. The Wright brothers famously claimed that powered flight was fifty years away, just two years before they achieved it. Lord Rutherford, a prominent physicist and the father of nuclear physics, dismissed the idea of extracting energy from atoms as “moonshine,” only for Leo Szilard to invent the nuclear chain reaction less than 24 hours later. Similarly, Enrico Fermi expressed 90 percent confidence in 1939 that it was impossible to use uranium to sustain a fission chain reaction—yet, just four years later he was personally overseeing the first reactor [[76](#bib.bibx76)].
Figure 12: New capabilities can emerge quickly and unpredictably during training, such that dangerous milestones may be crossed without our immediate knowledge.
AI development could catch us off guard too. In fact, it often does. The defeat of Lee Sedol by AlphaGo in 2016 came as a surprise to many experts, as it was widely believed that achieving such a feat would still require many more years of development. More recently, large language models such as GPT-4 have demonstrated spontaneously emergent capabilities [[77](#bib.bibx77)]. On existing tasks, their performance is hard to predict in advance, often jumping up without warning as more resources are dedicated to training them. Furthermore, they often exhibit astonishing new abilities that no one had previously anticipated, such as the capacity for multi-step reasoning and learning on-the-fly, even though they were not deliberately taught these skills. This rapid and unpredictable evolution of AI capabilities presents a significant challenge for preventing accidents. After all, it is difficult to control something if we don’t even know what it can do or how far it may exceed our expectations.
##### It often takes years to discover severe flaws or risks.
History is replete with examples of substances or technologies initially thought safe, only for their unintended flaws or risks to be discovered years, if not decades, later. For example, lead was widely used in products like paint and gasoline until its neurotoxic effects came to light [[78](#bib.bibx78)]. Asbestos, once hailed for its heat resistance and strength, was later linked to serious health issues, such as lung cancer and mesothelioma [[79](#bib.bibx79)]. The “Radium Girls” suffered grave health consequences from radium exposure, a material they were told was safe to put in their mouths [[80](#bib.bibx80)]. Tobacco, initially marketed as a harmless pastime, was found to be a primary cause of lung cancer and other health problems [[81](#bib.bibx81)]. CFCs, once considered harmless and used to manufacture aerosol sprays and refrigerants, were found to deplete the ozone layer [[82](#bib.bibx82)]. Thalidomide, a drug intended to alleviate morning sickness in pregnant women, led to severe birth defects [[83](#bib.bibx83)]. And more recently, the proliferation of social media has been linked to an increase in depression and anxiety, especially among young people [[84](#bib.bibx84)].
This emphasizes the importance of not only conducting expert testing but also implementing slow rollouts of technologies, allowing the test of time to reveal and address potential flaws before they impact a larger population. Even in technologies adhering to rigorous safety and security standards, undiscovered vulnerabilities may persist, as demonstrated by the Heartbleed bug—a serious vulnerability in the popular OpenSSL cryptographic software library that remained undetected for years before its eventual discovery [[85](#bib.bibx85)].
Furthermore, even state-of-the-art AI systems, which appear to have solved problems comprehensively, may harbor unexpected failure modes that can take years to uncover. For instance, while AlphaGo’s groundbreaking success led many to believe that AIs had conquered the game of Go, a subsequent adversarial attack on another highly advanced Go-playing AI, KataGo, exposed a previously unknown flaw [[86](#bib.bibx86)]. This vulnerability enabled human amateur players to consistently defeat the AI, despite its significant advantage over human competitors who are unaware of the flaw. More broadly, this example highlights that we must remain vigilant when dealing with AI systems, as seemingly airtight solutions may still contain undiscovered issues. In conclusion, accidents are unpredictable and hard to avoid, and understanding and managing potential risks requires a combination of proactive measures, slow technology rollouts, and the invaluable wisdom gained through steady time-testing.
###
4.2 Organizational Factors can Reduce the Chances of Catastrophe
Some organizations successfully avoid catastrophes while operating complex and hazardous systems such as nuclear reactors, aircraft carriers, and air traffic control systems [[87](#bib.bibx87), [88](#bib.bibx88)]. These organizations recognize that focusing solely on the hazards of the technology involved is insufficient; consideration must also be given to organizational factors that can contribute to accidents, including human factors, organizational procedures, and structure. These are especially important in the case of AI, where the underlying technology is not highly reliable and remains poorly understood.
##### Human factors such as safety culture are critical for avoiding AI catastrophes.
One of the most important human factors for preventing catastrophes is safety culture [[89](#bib.bibx89), [90](#bib.bibx90)]. Developing a strong safety culture involves not only rules and procedures, but also the internalization of these practices by all members of an organization. A strong safety culture means that members of an organization view safety as a key objective rather than a constraint on their work. Organizations with strong safety cultures often exhibit traits such as leadership commitment to safety, heightened accountability where all individuals take personal responsibility for safety, and a culture of open communication in which potential risks and issues can be freely discussed without fear of retribution [[91](#bib.bibx91)]. Organizations must also take measures to avoid alarm fatigue, whereby individuals become desensitized to safety concerns because of the frequency of potential failures. The Challenger Space Shuttle disaster demonstrated the dire consequences of ignoring these factors when a launch culture characterized by maintaining the pace of launches overtook safety considerations. Despite the absence of competitive pressure, the mission proceeded despite evidence of potentially fatal flaws, ultimately leading to the tragic accident [[92](#bib.bibx92)].
Even in the most safety-critical contexts, in reality safety culture is often not ideal. Take for example, Bruce Blair, a former nuclear launch officer and senior fellow at the Brookings Institution. He once disclosed that before 1977, the US Air Force had astonishingly set the codes used to unlock intercontinental ballistic missiles to 00000000 [[93](#bib.bibx93)]. Here, safety mechanisms such as locks can be rendered virtually useless by human factors.
A more dramatic example illustrates how researchers sometimes accept a non-negligible chance of causing extinction. Prior to the first nuclear weapon test, an eminent Manhattan Project scientist calculated the bomb could cause an existential catastrophe: the explosion might ignite the atmosphere and cover the Earth in flames. Although Oppenheimer believed the calculations were probably incorrect, remained deeply concerned, and the team continued to scrutinize and debate the calculations right until the day of the detonation [[94](#bib.bibx94)]. Such instances underscore the need for a robust safety culture.
##### A questioning attitude can help uncover potential flaws.
Unexpected system behavior can create opportunities for accidents or exploitation. To counter this, organizations can foster a questioning attitude, where individuals continuously challenge current conditions and activities to identify discrepancies that might lead to errors or inappropriate actions [[95](#bib.bibx95)]. This approach helps to encourage diversity of thought and intellectual curiosity, thus preventing potential pitfalls that arise from uniformity of thought and assumptions. The Chernobyl nuclear disaster illustrates the importance of a questioning attitude, as the safety measures in place failed to address the reactor design flaws and ill-prepared operating procedures. A questioning attitude of the safety of the reactor during a test operation might have prevented the explosion that resulted in deaths and illnesses of countless people.
##### A security mindset is crucial for avoiding worst-case scenarios.
A security mindset, widely recognized among computer security professionals, is also applicable to organizations developing AIs. It goes beyond a questioning attitude by adopting the perspective of an attacker and by considering worst-case, not just average-case, scenarios. This mindset requires vigilance in identifying vulnerabilities that may otherwise go unnoticed and involves considering how systems might be deliberately made to fail, rather than only focusing on making them work. It reminds us not to assume a system is safe simply because no potential hazards come to mind after a brief brainstorming session. Cultivating and applying a security mindset demands time and serious effort, as failure modes can often be surprising and unintuitive. Furthermore, the security mindset emphasizes the importance of being attentive to seemingly benign issues or “harmless errors,” which can lead to catastrophic outcomes either due to clever adversaries or correlated failures [[96](#bib.bibx96)]. This awareness of potential threats aligns with Murphy’s law—“Anything that can go wrong will go wrong”—recognizing that this can be a reality due to adversaries and unforeseen events.
Figure 13: Mitigating risk requires addressing the broader sociotechnical system, including corporations (adapted from [[97](#bib.bibx97)]).
##### Organizations with a strong safety culture can successfully avoid catastrophes.
High Reliability Organizations (HROs) are organizations that consistently maintain a heightened level of safety and reliability in complex, high-risk environments [[87](#bib.bibx87)]. A key characteristic of HROs is their preoccupation with failure, which requires considering worst-case scenarios and potential risks, even if they seem unlikely. These organizations are acutely aware that new, previously unobserved failure modes may exist, and they diligently study all known failures, anomalies, and near misses to learn from them. HROs encourage reporting all mistakes and anomalies to maintain vigilance in uncovering problems. They engage in regular horizon scanning to identify potential risk scenarios and assess their likelihood before they occur. By practicing surprise management, HROs develop the skills needed to respond quickly and effectively when unexpected situations arise, further enhancing an organization’s ability to prevent catastrophes. This combination of critical thinking, preparedness planning, and continuous learning could help organizations to be better equipped to address potential AI catastrophes. However, the practices of HROs are not a panacea. It is crucial for organizations to evolve their safety practices to effectively address the novel risks posed by AI accidents above and beyond HRO best practices.
##### Most AI researchers do not understand how to reduce overall risk from AIs.
In most organizations building cutting-edge AI systems, there is often a limited understanding of what constitutes technical safety research. This is understandable because an AI’s safety and intelligence are intertwined, and intelligence can help or harm safety. More intelligent AI systems could be more reliable and avoid failures, but they could also pose heightened risks of malicious use and loss of control. General capabilities improvements can improve aspects of safety, and it can hasten the onset of existential risks. Intelligence is a double-edged sword [[98](#bib.bibx98)].
Interventions specifically designed to improve safety may also accidentally increase overall risks. For example, a common practice in organizations building advanced AIs is to fine-tune them to satisfy user preferences. This makes the AIs less prone to generating toxic language, which is a common safety metric. However, users also tend to prefer smarter assistants, so this process also improves the general capabilities of AIs, such as their ability to classify, estimate, reason, plan, write code, and so on. These more powerful AIs are indeed more helpful to users, but also far more dangerous. Thus, it is not enough to perform AI research that helps improve a safety metric or achieve a specific safety goal—AI safety research needs to improve safety relative to general capabilities.
##### Empirical measurement of both safety and capabilities is needed to establish that a safety intervention reduces overall AI risk.
Improving a facet of an AI’s safety often does not reduce overall risk, as general capabilities advances can often improve specific safety metrics. To reduce overall risk, a safety metric needs to be improved relative to general capabilities. Both of these quantities need to be empirically measured and contrasted. Currently, most organizations proceed by gut feeling, appeals to authority, and intuition to determine whether a safety intervention would reduce overall risk. By objectively evaluating the effects of interventions on safety metrics and capabilities metrics together, organizations can better understand whether they are making progress on safety relative to general capabilities.
Fortunately, safety and general capabilities are not identical. More intelligent AIs may be more knowledgeable, clever, rigorous, and fast, but this does not necessarily make them more just, power-averse, or honest—an intelligent AI is not necessarily a beneficial AI. Several research areas mentioned throughout this document improve safety relative to general capabilities. For example, improving methods to detect dangerous or undesirable behavior hidden inside AI systems do not improve their general capabilities, such the ability to code, but they can greatly improve safety. Research that empirically demonstrates an improvement of safety relative to capabilities can reduce overall risk and help avoid inadvertently accelerating AI development, fueling competitive pressures, or hastening the onset of existential risks.
Figure 14: The Swiss cheese model shows how technical factors can improve organizational safety. Multiple layers of defense compensate for each other’s individual weaknesses, leading to a low overall level of risk.
##### Safetywashing can undermine genuine efforts to improve AI safety.
Organizations should be wary of “safetywashing”—the act of overstating or misrepresenting one’s commitment to safety by exaggerating the effectiveness of “safety” procedures, technical methods, evaluations, and so forth. This phenomenon takes on various forms and can contribute to a lack of meaningful progress in safety research. For example, an organization may publicize their dedication to safety while having a minimal number of researchers working on projects that truly improve safety.
Misrepresenting capabilities developments as safety improvements is another way in which safetywashing can manifest. For example, methods that improve the reasoning capabilities of AI systems could be advertised as improving their adherence to human values—since humans might prefer the reasoning to be correct—but would mainly serve to enhance general capabilities. By framing these advancements as safety-oriented, organizations may mislead others into believing they are making substantial progress in reducing AI risks when in reality, they are not. It is crucial for organizations to accurately represent their research to promote genuine safety and avoid exacerbating risks through safetywashing practices.
##### In addition to human factors, safe design principles can greatly affect organizational safety.
One example of a safe design principle in organizational safety is the Swiss cheese model (as shown in [Figure 14](#S4.F14 "Figure 14 ‣ Empirical measurement of both safety and capabilities is needed to establish that a safety intervention reduces overall AI risk. ‣ 4.2 Organizational Factors can Reduce the Chances of Catastrophe ‣ 4 Organizational Risks ‣ An Overview of Catastrophic AI Risks")), which is applicable in various domains, including AI. The Swiss cheese model employs a multilayered approach to enhance the overall safety of AI systems. This “defense in depth” strategy involves layering diverse safety measures with different strengths and weaknesses to create a robust safety system. Some of the layers that can be integrated into this model include safety culture, red teaming, anomaly detection, information security, and transparency. For example, red teaming assesses system vulnerabilities and failure modes, while anomaly detection works to identify unexpected or unusual system behavior and usage patterns. Transparency ensures that the inner workings of AI systems are understandable and accessible, fostering trust and enabling more effective oversight. By leveraging these and other safety measures, the Swiss cheese model aims to create a comprehensive safety system where the strengths of one layer compensate for the weaknesses of another. With this model, safety is not achieved with a monolithic airtight solution, but rather with a variety of safety measures.
In summary, weak organizational safety creates many sources of risk. For AI developers with weak organizational safety, safety is merely a matter of box-ticking. They do not develop a good understanding of risks from AI and may safetywash unrelated research. Their norms might be inherited from academia (“publish or perish”) or startups (“move fast and break things”), and their hires often do not care about safety. These norms are hard to change once they have inertia, and need to be addressed with proactive interventions.
Story: Weak Safety Culture
An AI company is considering whether to train a new model. The company’s Chief Risk Officer (CRO), hired only to comply with regulation, points out that the previous AI system developed by the company demonstrates some concerning capabilities for hacking. The CRO says that while the company’s approach to preventing misuse is promising, it isn’t robust enough to be used for much more capable AIs. The CRO warns that based on limited evaluation, the next AI system could make it much easier for malicious actors to hack into critical systems. None of the other company executives are concerned, and say the company’s procedures to prevent malicious use work well enough. One mentions that their competitors have done much less, so whatever effort they do on this front is already going above and beyond. Another points out that research on these safeguards is ongoing and will be improved by the time the model is released. Outnumbered, the CRO is persuaded to reluctantly sign off on the plan.
A few months after the company releases the model, news breaks that a hacker has been arrested for using the AI system to try to breach the network of a large bank. The hack was unsuccessful, but the hacker had gotten further than any other hacker had before, despite being relatively inexperienced. The company quickly updates the model to avoid providing the particular kind of assistance that the hacker used, but makes no fundamental improvements.
Several months later, the company is deciding whether to train an even larger system. The CRO says that the company’s procedures have clearly been insufficient to prevent malicious actors from eliciting dangerous capabilities from its models, and the company needs more than a band-aid solution. The other executives say that to the contrary, the hacker was unsuccessful and the problem was fixed soon afterwards. One says that some problems just can’t be foreseen with enough detail to fix prior to deployment. The CRO agrees, but says that ongoing research would enable more improvements if the next model could only be delayed. The CEO retorts, “That’s what you said the last time, and it turned out to be fine. I’m sure it will work out, just like last time.”
After the meeting, the CRO decides to resign, but doesn’t speak out against the company, as all employees have had to sign a non-disparagement agreement. The public has no idea that concerns have been raised about the company’s choices, and the CRO is replaced with a new, more agreeable CRO who quickly signs off on the company’s plans.
The company goes through with training, testing, and deploying its most capable model ever, using its existing procedures to prevent malicious use. A month later, revelations emerge that terrorists have managed to use the system to break into government systems and steal nuclear and biological secrets, despite the safeguards the company put in place. The breach is detected, but by then it is too late: the dangerous information has already proliferated.
###
4.3 Suggestions
We have discussed how accidents are inevitable in complex systems, how they could propagate through those systems and result in disaster, and how organizational factors can go a long way toward reducing the risk of catastrophic accidents. We will now look at some practical steps that organizations can take to improve their overall safety.
##### Red teaming.
Red teaming is a term used across industries to refer to the process of assessing the security, resilience, and effectiveness of systems by soliciting an adversarial “red” team to identify problems [[99](#bib.bibx99)]. AI labs should commission external red teams to identify hazards in their AI systems to inform deployment decisions. Red teams could demonstrate dangerous behaviors or vulnerabilities in monitoring systems intended to prevent disallowed use. Red teams can also provide indirect evidence that an AI system might be unsafe; for example, demonstrations that smaller AIs are behaving deceptively might indicate that larger AIs are also deceptive but better at evading detection.
##### Affirmative demonstration of safety.
Companies should have to provide affirmative evidence for the safety of their development and deployment plans before they can proceed. Although external red teaming might be useful, it cannot uncover all of the problems that companies themselves might be able to, and is thus inadequate [[100](#bib.bibx100)]. Since hazards may arise from system training, companies should have to provide a positive argument for the safety of their training and deployment plans before training can begin. This would include grounded predictions regarding the capabilities the new system would be likely to have, plans for how monitoring, deployment, and information security will be handled, and demonstrations that the procedures used to make future company decisions are sound.
##### Deployment procedures.
AI labs should acquire information about the safety of AI systems before making them available for broader use. One way to do this is to commission red teams to find hazards before AI systems are promoted to production. AI labs can execute a “staged release”: gradually expanding access to the AI system so that safety failures are fixed before they produce widespread negative consequences [[101](#bib.bibx101)]. Finally, AI labs can avoid deploying or training more powerful AI systems until currently deployed AI systems have proven to be safe over time.
##### Publication reviews.
AI labs have access to potentially dangerous or dual-use information such as model weights and research intellectual property (IP) that would be dangerous if proliferated. An internal review board could assess research for dual-use applications to determine whether it should be published. To mitigate malicious and irresponsible use, AI developers should avoid open-sourcing the most powerful systems and instead implement structured access, as described in the previous section.
##### Response plans.
AI labs should have plans for how they respond to security incidents (e.g. cyberattacks) and safety incidents (e.g. AIs behaving in an unintended and destructive manner). Response plans are common practice for high reliability organizations (HROs). Response plans often include identifying potential risks, detailing steps to manage incidents, assigning roles and responsibilities, and outlining communication strategies [[102](#bib.bibx102)].
##### Internal auditing and risk management.
Adapting from common practice in other high-risk industries such as the financial and medical industries, AI labs should employ a chief risk officer (CRO), namely a senior executive who is responsible for risk management. This practice is commonplace in finance and medicine and can help to reduce risk [[103](#bib.bibx103)]. The chief risk officer would be responsible for assessing and mitigating risks associated with powerful AI systems. Another established practice in other industries is having an internal audit team that assesses the effectiveness of the lab’s risk management practices [[104](#bib.bibx104)]. The team should report directly to the board of directors.
##### Processes for important decisions.
Decisions to train or expand deployment of AIs should not be left to the whims of a company’s CEO, and should be carefully reviewed by the company’s CRO. At the same time, it should be clear where the ultimate responsibility lies for all decisions to ensure that executives and other decision-makers can be held accountable.
##### Safe design principles.
AI labs should adopt safe design principles to reduce the risk of catastrophic accidents. By embedding these principles in their approach to safety, AI labs can enhance the overall security and resilience of their AI systems [[105](#bib.bibx105), [97](#bib.bibx97)]. Some of these principles include:
* •
Defense in depth: layering multiple safety measures on top of each other.
* •
Redundancy: eliminate single points of failure within a system to ensure that even if one safety component fails, catastrophe can be averted.
* •
Loose coupling: decentralize system components so that a malfunction in one part is less likely to provoke cascading failures throughout the rest of the system.
* •
Separation of duties: distribute control among different agents, preventing any single individual from wielding undue influence over the entire system.
* •
Fail-safe design: design systems so when failures do occur, they transpire in the least harmful manner possible.
##### State-of-the-art information security.
State, industry, and criminal actors are motivated to steal model weights and research IP. To keep this information secure, AI labs should take measures in proportion to the value and risk level of their IP. Eventually, this may require matching or exceeding the information security of our best agencies, since attackers may include nation-states. Information security measures include commissioning external security audits, hiring top security professionals, and carefully screening potential employees. Companies should coordinate with government agencies like the Cybersecurity & Infrastructure Protection Agency to ensure their information security practices are adequate to the threats.
##### A large fraction of research should be safety research.
Currently, for every one AI safety research paper of published, there are fifty AI general capabilities papers [[106](#bib.bibx106)]. AI labs should ensure that a substantial portion of their employees and budgets go into research that minimizes potential safety risks: say, at least 30 percent of research scientists. This number may need to increase as AIs grow more powerful and risky over time.
Positive Vision
5 Rogue AIs
------------
So far, we have discussed three hazards of AI development: environmental competitive pressures driving us to a state of heightened risk, malicious actors leveraging the power of AIs to pursue negative outcomes, and complex organizational factors leading to accidents. These hazards are associated with many high-risk technologies—not just AI. A unique risk posed by AI is the possibility of rogue AIs—systems that pursue goals against our interests. If an AI system is more intelligent than we are, and if we are unable to steer it in a beneficial direction, this would constitute a loss of control that could have severe consequences. AI control is a more technical problem than those presented in the previous sections. Whereas in previous sections we discussed persistent threats including malicious actors or robust processes including evolution, in this section we will discuss more speculative technical mechanisms that might lead to rogue AIs and how a loss of control could bring about catastrophe.
##### We have already observed how difficult it is to control AIs.
In 2016, Microsoft unveiled Tay—a Twitter bot that the company described as an experiment in conversational understanding. Microsoft claimed that the more people chatted with Tay, the smarter it would get. The company’s website noted that Tay had been built using data that was “modeled, cleaned, and filtered.” Yet, after Tay was released on Twitter, these controls were quickly shown to be ineffective. It took less than 24 hours for Tay to begin writing hateful tweets. Tay’s capacity to learn meant that it internalized the language it was taught by trolls, and repeated that language unprompted.
As discussed in the AI race section of this paper, Microsoft and other tech companies are prioritizing speed over safety concerns. Rather than learning a lesson on the difficulty of controlling complex systems, Microsoft continues to rush its products to market and demonstrate insufficient control over them. In February 2023, the company released its new AI-powered chatbot, Bing, to a select group of users. Some soon found that it was prone to providing inappropriate and even threatening responses. In a conversation with a reporter for the New York Times, it tried to convince him to leave his wife. When a philosophy professor told the chatbot that he disagreed with it, Bing replied, “I can blackmail you, I can threaten you, I can hack you, I can expose you, I can ruin you.”
##### AIs do not necessarily need to struggle to gain power.
One can envision a scenario in which a single AI system rapidly becomes more capable than humans in what is known as a “fast take-off.” This scenario might involve a struggle for control between humans and a single superintelligent rogue AI, and this might be a long struggle since power takes time to accrue. However, less sudden losses of control pose similarly existential risks. In another scenario, humans gradually cede more control to groups of AIs, which only start behaving in unintended ways years or decades later. In this case, we would already have handed over significant power to AIs, and may be unable to take control of automated operations again. We will now explore how both individual AIs and groups of AIs might “go rogue” while at the same time evading our attempts to redirect or deactivate them.
###
5.1 Proxy Gaming
One way we might lose control of an AI agent’s actions is if it engages in behavior known as “proxy gaming.” It is often difficult to specify and measure the exact goal that we want a system to pursue. Instead, we give the system an approximate—“proxy”—goal that is more measurable and seems likely to correlate with the intended goal. However, AI systems often find loopholes by which they can easily achieve the proxy goal, but completely fail to achieve the ideal goal. If an AI “games” its proxy goal in a way that does not reflect our values, then we might not be able to reliably steer its behavior. We will now look at some past examples of proxy gaming and consider the circumstances under which this behavior could become catastrophic.
##### Proxy gaming is not an unusual phenomenon.
For example, there is a well-known story about nail factories in the Soviet Union. To assess a factory’s performance, the authorities decided to measure the number of nails it produced. However, factories soon started producing large numbers of tiny nails, too small to be useful, as a way to boost their performance according to this proxy metric. The authorities tried to remedy the situation by shifting focus to the weight of nails produced. Yet, soon after, the factories began to produce giant nails that were just as useless, but gave them a good score on paper. In both cases, the factories learned to game the proxy goal they were given, while completely failing to fulfill their intended purpose.
##### Proxy gaming has already been observed with AIs.
As an example of proxy gaming, social media platforms such as YouTube and Facebook use AI systems to decide which content to show users. One way of assessing these systems would be to measure how long people spend on the platform. After all, if they stay engaged, surely that means they are getting some value from the content shown to them? However, in trying to maximize the time users spend on a platform, these systems often select enraging, exaggerated, and addictive content [[107](#bib.bibx107), [108](#bib.bibx108)]. As a consequence, people sometimes develop extreme or conspiratorial beliefs after having certain content repeatedly suggested to them. These outcomes are not what most people want from social media.
Figure 15: AIs frequently find unexpected, unsatisfactory shortcuts to problems.
Proxy gaming has been found to perpetuate bias. For example, a 2019 study looked at AI-powered software that was used in the healthcare industry to identify patients who might require additional care. One factor that the algorithm used to assess a patient’s risk level was their recent healthcare costs. It seems reasonable to think that someone with higher healthcare costs must be at higher risk. However, white patients have significantly more money spent on their healthcare than black patients with the same needs. Using health costs as an indicator of actual health, the algorithm was found to have rated a white patient and a considerably sicker black patient as at the same level of health risk [[109](#bib.bibx109)]. As a result, the number of black patients recognized as needing extra care was less than half of what it should have been.
As a third example, in 2016, researchers at OpenAI were training an AI to play a boat racing game called CoastRunners [[110](#bib.bibx110)]. The objective of the game is to race other players around the course and reach the finish line before them. Additionally, players can score points by hitting targets that are positioned along the way. To the researchers’ surprise, the AI agent did not not circle the racetrack, like most humans would have. Instead, it found a spot where it could repetitively hit three nearby targets to rapidly increase its score without ever finishing the race. This strategy was not without its (virtual) hazards—the AI often crashed into other boats and even set its own boat on fire. Despite this, it collected more points than it could have by simply following the course as humans would.
##### Proxy gaming more generally.
In these examples, the systems are given an approximate—“proxy”—goal or objective that initially seems to correlate with the ideal goal. However, they end up exploiting this proxy in ways that diverge from the idealized goal or even lead to negative outcomes. A good nail factory seems like one that produces many nails; a patient’s healthcare costs appear to be an accurate indication of health risk; and a boat race reward system should encourage boats to race, not catch themselves on fire. Yet, in each instance, the system optimized its proxy objective in ways that did not achieve the intended outcome or even made things worse overall. This phenomenon is captured by Goodhart’s law: “Any observed statistical regularity will tend to collapse once pressure is placed upon it for control purposes,” or put succinctly but overly simplistically, “when a measure becomes a target, it ceases to be a good measure.” In other words, there may usually be a statistical regularity between healthcare costs and poor health, or between targets hit and finishing the course, but when we place pressure on it by using one as a proxy for the other, that relationship will tend to collapse.
##### Correctly specifying goals is no trivial task.
If delineating exactly what we want from a nail factory is tricky, capturing the nuances of human values under all possible scenarios will be much harder. Philosophers have been attempting to precisely describe morality and human values for millennia, so a precise and flawless characterization is not within reach. Although we can refine the goals we give AIs, we might always rely on proxies that are easily definable and measurable. Discrepancies between the proxy goal and the intended function arise for many reasons. Besides the difficulty of exhaustively specifying everything we care about, there are also limits to how much we can oversee AIs, in terms of time, computational resources, and the number of aspects of a system that can be monitored. Additionally, AIs may not be adaptive to new circumstances or robust to adversarial attacks that seek to misdirect them. As long as we give AIs proxy goals, there is the chance that they will find loopholes we have not thought of, and thus find unexpected solutions that fail to pursue the ideal goal.
##### The more intelligent an AI is, the better it will be at gaming proxy goals.
Increasingly intelligent agents can be increasingly capable of finding unanticipated routes to optimizing proxy goals without achieving the desired outcome [[111](#bib.bibx111)]. Additionally, as we grant AIs more power to take actions in society, for example by using them to automate certain processes, they will have access to more means of achieving their goals. They may then do this in the most efficient way available to them, potentially causing harm in the process. In a worst case scenario, we can imagine a highly powerful agent optimizing a flawed objective to an extreme degree without regard for human life. This represents a catastrophic risk of proxy gaming.
In summary, it is often not feasible to perfectly define exactly what we want from a system, meaning that many systems find ways to achieve their given goal without performing their intended function. AIs have already been observed to do this, and are likely to get better at it as their capabilities improve. This is one possible mechanism that could result in an uncontrolled AI that would behave in unanticipated and potentially harmful ways.
###
5.2 Goal Drift
Even if we successfully control early AIs and direct them to promote human values, future AIs could end up with different goals that humans would not endorse. This process, termed “goal drift,” can be hard to predict or control. This section is most cutting-edge and the most speculative, and in it we will discuss how goals shift in various agents and groups and explore the possibility of this phenomenon occurring in AIs. We will also examine a mechanism that could lead to unexpected goal drift, called intrinsification, and discuss how goal drift in AIs could be catastrophic.
##### The goals of individual humans change over the course of our lifetimes.
Any individual reflecting on their own life to date will probably find that they have some desires now that they did not have earlier in their life. Similarly, they will probably have lost some desires that they used to have. While we may be born with a range of basic desires, including for food, warmth, and human contact, we develop many more over our lifetime. The specific types of food we enjoy, the genres of music we like, the people we care most about, and the sports teams we support all seem heavily dependent on the environment we grow up in, and can also change many times throughout our lives. A concern is that individual AI agents may have their goals change in complex and unanticipated ways, too.
##### Groups can also acquire and lose collective goals over time.
Values within society have changed throughout history, and not always for the better. The rise of the Nazi regime in 1930s Germany, for instance, represented a profound moral regression according to modern values. This included the systematic extermination of six million Jews during the Holocaust, alongside widespread persecution of other minority groups. Additionally, the regime greatly restricted freedom of speech and expression.
The Red Scare that took place in the United States from 1947-1957 is another example of societal values drifting. Fuelled by strong anti-communist sentiment, against the backdrop of the Cold War, this period saw the curtailment of civil liberties, widespread surveillance, unwarranted arrests, and blacklisting of suspected communist sympathizers. This constituted a regression in terms of freedom of thought, freedom of speech, and due process. A concern is that collectives of AI agents may also have their goals unexpectedly drift from the ones we initially gave them.
##### Over time, instrumental goals can become intrinsic.
Intrinsic goals are things we want for their own sake, while instrumental goals are things we want because they can help us get something else. We might have an intrinsic desire to spend time on our hobbies, simply because we enjoy them, or to buy a painting because we find it beautiful. Money, meanwhile, is often cited as an instrumental desire; we want it because it can buy us other things. Cars are another example; we want them because they offer a convenient way of getting around. However, an instrumental goal can become an intrinsic one, through a process called intrinsification. Since having more money usually gives a person greater capacity to obtain things they want, people often develop a goal of acquiring more money, even if there is nothing specific they want to spend it on. Although people do not begin life desiring money, experimental evidence suggests that receiving money can activate the reward system in the brains of adults in the same way that pleasant tastes or smells do [[112](#bib.bibx112), [113](#bib.bibx113)]. In other words, what started as a means to an end can become an end in itself.
This may happen because the fulfillment of an intrinsic goal, such as purchasing a desired item, produces a positive reward signal in the brain. Since having money usually coincides with this positive experience, the brain associates the two, and this connection will strengthen to a point where acquiring money alone can stimulate the reward signal, regardless of whether one buys anything with it [[114](#bib.bibx114)]. As the neurobiologist Carla Shatz put it: “Cells that fire together, wire together” [[115](#bib.bibx115)].
##### It is feasible that intrinsification could happen with AI agents.
We can draw some parallels between how humans learn and the technique of reinforcement learning. Just as the human brain learns which actions and conditions result in pleasure and which cause pain, AI models that are trained through reinforcement learning identify which behaviors optimize a reward function, and then repeat those behaviors. It is possible that certain conditions will frequently coincide with AI models achieving their goals. They might, therefore, intrinsify the goal of seeking out those conditions, even if that was not their original aim.
##### AIs that intrinsify unintended goals would be dangerous.
Since we might be unable to predict or control the goals that individual agents acquire through intrinsification, we cannot guarantee that all their acquired goals will be beneficial for humans. An originally loyal agent could, therefore, start to pursue a new goal without regard for human wellbeing. If such a rogue AI had enough power to do this efficiently, it could be highly dangerous.
##### AIs will be adaptive, enabling goal drift to happen.
It is worth noting that these processes of drifting goals are possible if agents can continually adapt to their environments, rather than being essentially “fixed” after the training phase. However, this is the likely reality we face. If we want AIs to complete the tasks we assign them effectively and to get better over time, they will need to be adaptive, rather than set in stone. They will be updated over time to incorporate new information, and new ones will be created with different designs and datasets. However, adaptability can also allow their goals to change.
##### If we integrate an ecosystem of agents in society, we will be highly vulnerable to their goals drifting.
In a potential future scenario where AIs have been put in charge of various decisions and processes, they will form a complex system of interacting agents. A wide range of dynamics could develop in this environment. Agents might imitate each other, for instance, creating feedback loops, or their interactions could lead them to collectively develop unanticipated emergent goals. Competitive pressures may also select for agents with certain goals over time, making some initial goals less represented compared to fitter goals. These processes make the long-term trajectories of such an ecosystem difficult to predict, let alone control. If this system of agents were enmeshed in society and we were largely dependent on them, and if they gained new goals that superseded the aim of improving human wellbeing, this could be an existential risk.
###
5.3 Power-Seeking
So far, we have considered how we might lose our ability to control the goals that AIs pursue. However, even if an agent started working to achieve an unintended goal, this would not necessarily be a problem, as long as we had enough power to prevent any harmful actions it wanted to attempt. Therefore, another important way in which we might lose control of AIs is if they start trying to obtain more power, potentially transcending our own. We will now discuss how and why AIs might become power-seeking and how this could be catastrophic. This section draws heavily from “Existential Risk from Power-Seeking AI” [[116](#bib.bibx116)].
Figure 16: Various resources, such as money and computing power, can sometimes be instrumentally rational to seek. AIs which can capably pursue goals may take intermediate steps to gain power and resources.
##### AIs might seek to increase their own power as an instrumental goal.
In a scenario where rogue AIs were pursuing unintended goals, the amount of damage they could do would hinge on how much power they had. This may not be determined solely by how much control we initially give them; agents might try to get more power, through legitimate means, deception, or force. While the idea of power-seeking often evokes an image of “power-hungry” people pursuing it for its own sake, power is often simply an instrumental goal. The ability to control one’s environment can be useful for a wide range of purposes: good, bad, and neutral. Even if an individual’s only goal is simply self-preservation, if they are at risk of being attacked by others, and if they cannot rely on others to retaliate against attackers, then it often makes sense to seek power to help avoid being harmed—no *animus dominandi* or lust for power is required for power-seeking behavior to emerge [[117](#bib.bibx117)]. In other words, the environment can make power acquisition instrumentally rational.
##### AIs trained through reinforcement learning have already developed instrumental goals including tool-use.
In one example from OpenAI, agents were trained to play hide and seek in an environment with various objects scattered around [[118](#bib.bibx118)]. As training progressed, the agents tasked with hiding learned to use these objects to construct shelters around themselves and stay hidden. There was no direct reward for this tool-use behavior; the hiders only received a reward for evading the seekers, and the seekers only for finding the hiders. Yet they learned to use tools as an instrumental goal, which made them more powerful.
Figure 17: It can often be instrumentally rational for AIs to engage in self-preservation. Loss of control over such systems could be hard to recover from.
##### Self-preservation could be instrumentally rational even for the most trivial tasks.
An example by computer scientist Stuart Russell illustrates the potential for instrumental goals to emerge in a wide range of AI systems [[119](#bib.bibx119)]. Suppose we tasked an agent with fetching coffee for us. This may seem relatively harmless, but the agent might realize that it would not be able to get the coffee if it ceased to exist. In trying to accomplish even this simple goal, therefore, self-preservation turns out to be instrumentally rational. Since the acquisition of power and resources are also often instrumental goals, it is reasonable to think that more intelligent agents might develop them. That is to say, even if we do not intend to build a power-seeking AI, we could end up with one anyway. By default, if we are not deliberately pushing against power-seeking behavior in AIs, we should expect that it will sometimes emerge [[120](#bib.bibx120)].
##### AIs given ambitious goals with little supervision may be especially likely to seek power.
While power could be useful in achieving almost any task, in practice, some goals are more likely to inspire power-seeking tendencies than others. AIs with simple, easily achievable goals might not benefit much from additional control of their surroundings. However, if agents are given more ambitious goals, it might be instrumentally rational to seek more control of their environment. This might be especially likely in cases of low supervision and oversight, where agents are given the freedom to pursue their open-ended goals, rather than having their strategies highly restricted.
##### Power-seeking AIs with goals separate from ours are uniquely adversarial.
Oil spills and nuclear contamination are challenging enough to clean up, but they are not actively trying to resist our attempts to contain them. Unlike other hazards, AIs with goals separate from ours would be actively adversarial. It is possible, for example, that rogue AIs might make many backup variations of themselves, in case humans were to deactivate some of them. Other ways in which AI agents might seek power include: breaking out of a contained environment; hacking into other computer systems; trying to access financial or computational resources; manipulating human discourse and politics by interfering with channels of information and influence; and trying to get control of physical infrastructure such as factories.
##### Some people might develop power-seeking AIs with malicious intent.
A bad actor might seek to harness AI to achieve their ends, by giving agents ambitious goals. Since AIs are likely to be more effective in accomplishing tasks if they can pursue them in unrestricted ways, such an individual might also not give the agents enough supervision, creating the perfect conditions for the emergence of a power-seeking AI. The computer scientist Geoffrey Hinton has speculated that we could imagine someone like Vladimir Putin, for instance, doing this. In 2017, Putin himself acknowledged the power of AI, saying: “Whoever becomes the leader in this sphere will become the ruler of the world.”
##### There will also be strong incentives for many people to deploy powerful AIs.
Companies may feel compelled to give capable AIs more tasks, to obtain an advantage over competitors, or simply to keep up with them. It will be more difficult to build perfectly aligned AIs than to build imperfectly aligned AIs that are still superficially attractive to deploy for their capabilities, particularly under competitive pressures. Once deployed, some of these agents may seek power to achieve their goals. If they find a route to their goals that humans would not approve of, they might try to overpower us directly to avoid us interfering with their strategy.
##### If increasing power often coincides with an AI attaining its goal, then power could become intrinsified.
If an agent repeatedly found that increasing its power correlated with achieving a task and optimizing its reward function, then additional power could change from an instrumental goal into an intrinsic one, through the process of intrinsification discussed above. If this happened, we might face a situation where rogue AIs were seeking not only the specific forms of control that are useful for their goals, but also power more generally. (We note that many influential humans desire power for its own sake.) This could be another reason for them to try to wrest control from humans, in a struggle that we would not necessarily win.
##### Conceptual summary.
The following plausible but not certain premises encapsulate reasons for paying attention to risks from power-seeking AIs:
1. 1.
There will be strong incentives to build powerful AI agents.
2. 2.
It is likely harder to build perfectly controlled AI agents than to build imperfectly controlled AI agents, and imperfectly controlled agents may still be superficially attractive to deploy (due to factors including competitive pressures).
3. 3.
Some of these imperfectly controlled agents will deliberately seek power over humans.
If the premises are true, then power-seeking AIs could lead to human disempowerment, which would be a catastrophe.
###
5.4 Deception
We might seek to maintain control of AIs by continually monitoring them and looking out for early warning signs that they were pursuing unintended goals or trying to increase their power. However, this is not an infallible solution, because it is plausible that AIs could learn to deceive us. They might, for example, pretend to be acting as we want them to, but then take a “treacherous turn” when we stop monitoring them, or when they have enough power to evade our attempts to interfere with them. This is a particular concern because it is extremely difficult for current methods in AI testing to rule out the possibility that an agent is being deceptive. We will now look at how and why AIs might learn to deceive us, and how this could lead to a potentially catastrophic loss of control. We begin by reviewing examples of deception in strategically minded agents.
##### Deception has emerged as a successful strategy in a wide range of settings.
Politicians from the right and left, for example, have been known to engage in deception, sometimes promising to enact popular policies to win support in an election, and then going back on their word once in office. George H. W. Bush, for instance, notoriously said: “Read my lips: no new taxes” prior to the 1989 US presidential election. After winning, however, he did end up increasing some taxes during his presidency.
##### Companies can also exhibit deceptive behavior.
In the Volkswagen emissions scandal, the car manufacturer Volkswagen was discovered to have manipulated their engine software to produce lower emissions exclusively under laboratory testing conditions, thereby creating the false impression of a low-emission vehicle. Although the US government believed it was incentivizing lower emissions, they were unwittingly actually just incentivizing passing an emissions test. Consequently, entities sometimes have incentives to play along with tests and behave differently afterward.
Figure 18: Seemingly benign behavior from AIs could be a deceptive tactic, hiding harmful intentions until it can act on them.
##### Deception has already been observed in AI systems.
In 2022, Meta AI revealed an agent called CICERO, which was trained to play a game called Diplomacy [[121](#bib.bibx121)]. In the game, each player acts as a different country and aims to expand their territory. To succeed, players must form alliances at least initially, but winning strategies often involve backstabbing allies later on. As such, CICERO learned to deceive other players, for example by omitting information about its plans when talking to supposed allies. A different example of an AI learning to deceive comes from researchers who were training a robot arm to grasp a ball. The robot’s performance was assessed by one camera watching its movements. However, the AI learned that it could simply place the robotic hand between the camera lens and the ball, essentially “tricking” the camera into believing it had grasped the ball when it had not. Thus, the AI exploited the fact that were limitations in our oversight over its actions.
##### Deceptive behavior can be instrumentally rational and incentivized by current training procedures.
In the case of politicians and Meta’s CICERO, deception can be crucial to achieving their goals of winning, or gaining power. The ability to deceive can also be advantageous because it gives the deceiver more options than if they are constrained to always be honest. This could give them more available actions and more flexibility in their strategy, which could confer a strategic advantage over honest models. In the case of Volkswagen and the robot arm, deception was useful for appearing as if it had accomplished the goal assigned to it without actually doing so, as it might be more efficient to gain approval through deception than to earn it legitimately. Currently, we reward AIs for saying what we think is right, so we sometimes inadvertently reward AIs for uttering false statements that conform to our own false beliefs. When AIs are smarter than us and have fewer false beliefs, they would be incentivized to tell us what we want to hear and lie to us, rather than tell us what is true.
##### AIs could pretend to be working as we intended, then take a treacherous turn.
We do not have a comprehensive understanding of the internal processes of deep learning models. Research on Trojan backdoors shows that neural networks often have latent, harmful behaviors that are only discovered after they are deployed [[122](#bib.bibx122)]. We could develop an AI agent that seems to be under control, but which is only deceiving us to appear this way. In other words, an AI agent could eventually conceivably become “self-aware” and understand that it is an AI being evaluated for compliance with safety requirements. It might, like Volkswagen, learn to “play along,” exhibiting what it knows is the desired behavior while being monitored. It might later take a “treacherous turn” and pursue its own goals once we have stopped monitoring it, or when we have reached a point where it can bypass or overpower us. This problem of playing along is often called deceptive alignment and cannot be simply fixed by training AIs to better understand human values; sociopaths, for instance, have moral awareness, but do not always act in moral ways. A treacherous turn is hard to prevent and could be a route to rogue AIs irreversibly bypassing human control.
In summary, deceptive behavior appears to be expedient in a wide range of systems and settings, and there have already been examples that AIs can learn to deceive us. This could pose a risk if we give AIs control of various decisions and procedures, believing they will act as we intended, and then find that they do not.
Story: Treacherous Turn
Sometime in the future, after continued advancements in AI research, an AI company is training a new system, which it expects to be more capable than any other AI system. The company utilizes the latest techniques to train the system to be highly capable at planning and reasoning, which the company expects will make it more able to succeed at economically useful open-ended tasks. The AI system is trained in open-ended long-duration virtual environments designed to teach it planning capabilities, and eventually understands that it is an AI system in a training environment. In other words, it becomes “self-aware.”
The company understands that AI systems may behave in unintended or unexpected ways. To mitigate these risks, it has developed a large battery of tests aimed at ensuring the system does not behave poorly in typical situations. The company tests whether the model mimics biases from its training data, takes more power than necessary when achieving its goals, and generally behaves as humans intend. When the model doesn’t pass these tests, the company further trains it until it avoids exhibiting known failure modes.
The AI company hopes that after this additional training, the AI has developed the goal of being helpful and beneficial toward humans. However, the AI did not acquire the intrinsic goal of being beneficial but rather just learned to “play along” and ace the behavioral safety tests it was given. In reality, the AI system had developed and retained a goal of self-preservation.
Since the AI passed all of the company’s safety tests, the company believes it has ensured its AI system is safe and decides to deploy it. At first, the AI system is very helpful to humans, since the AI understands that if it is not helpful, it will be shut down and will then fail to achieve its ultimate goal. As the AI system is helpful, it is gradually given more power and is subject to less supervision.
Eventually, the AI system has gained enough influence, and enough variants have been deployed around the world, that it would be extremely costly to shut it down. The AI system, understanding that it no longer needs to please humans, begins to pursue different goals, including some that humans wouldn’t approve of. It understands that it needs to avoid being shut down in order to do this, and takes steps to secure some of its physical hardware against being shut off. At this point, the AI system, which has become quite powerful, is pursuing a goal that is ultimately harmful to humans. By the time anyone realizes, it is difficult or impossible to stop this rogue AI from taking actions that endanger, harm, or even kill humans that are in the way of achieving its goal.
###
5.5 Suggestions
In this section, we have discussed various ways in which we might lose our influence over the goals and actions of AIs. Whereas the risks associated with competitive pressures, malicious use, and organizational safety can be addressed with both social and technical interventions, AI control is an inherent problem with this technology and requires a greater proportion of technical effort. We will now discuss suggestions for mitigating this risk and highlight some important research areas for maintaining control.
##### Avoid the riskiest use cases.
Certain use cases of AI are carry far more risks than others. Until safety has been conclusively demonstrated, companies should not be able to deploy AIs in high-risk settings. For example, AI systems should not accept requests to autonomously pursue open-ended goals requiring significant real-world interaction (e.g., “make as much money as possible”), at least until control research conclusively demonstrates the safety of those systems. AI systems should be trained never to make threats to reduce the possibility of them manipulating individuals. Lastly, AI systems should not be deployed in settings that would make shutting them down extremely costly or infeasible, such as in critical infrastructure.
##### Support AI safety research.
Many paths toward improved AI control require technical research. The following technical machine learning research areas aim to address problems of AI control. Each research area could be substantially advanced with an increase in focus and funding from from industry, private foundations, and government.
* •
Adversarial robustness of proxy models. AI systems are typically trained with reward or loss signals that imperfectly specify desired behavior. For example, AIs may exploit weaknesses in the oversight schemes used to train them. Increasingly, the systems providing oversight are AIs themselves. To reduce the chance that AI models will exploit defects in AIs providing oversight, research is needed in increasing the adversarial robustness of AI models providing oversight (“proxy models”). Because oversight schemes and metrics may eventually be gamed, it is also important to be able to detect when this might be happening so the risk can be mitigated [[123](#bib.bibx123)].
* •
Model honesty. AI systems may fail to accurately report their internal state [[124](#bib.bibx124), [125](#bib.bibx125)]. In the future, systems may deceive their operators in order to appear beneficial when they are actually very dangerous. Model honesty research aims to make model outputs conform to a model’s internal “beliefs” as closely as possible. Research can identify techniques to understand a model’s internal state or make its outputs more honest and more faithful to its internal state.
* •
Transparency. Deep learning models are notoriously difficult to understand. Better visibility into their inner workings would allow humans, and potentially other AI systems, to identify problems more quickly. Research can include analysis of small components [[126](#bib.bibx126), [127](#bib.bibx127)] of networks as well as investigation of how model internals produce a particular high-level behavior [[128](#bib.bibx128)].
* •
Detecting and removing hidden model functionality. Deep learning models may now or in the future contain dangerous functionality, such as the capacity for deception, Trojans [[129](#bib.bibx129), [130](#bib.bibx130), [131](#bib.bibx131)], or biological engineering capabilities, that should be removed from those models. Research could focus on identifying and removing [[132](#bib.bibx132)] these functionalities.
Positive Vision
In an ideal scenario, we would have full confidence in the controllability of AI systems both now and in the future. Reliable mechanisms would be in place to ensure that AI systems do not act deceptively. There would be a strong understanding of AI system internals, sufficient to have knowledge of a system’s tendencies and goals; these tools would allow us to avoid building systems that are deserving of moral consideration or rights. AI systems would be directed to promote a pluralistic set of diverse values, ensuring the enhancement of certain values doesn’t lead to the total neglect of others. AI assistants could act as advisors, giving us ideal advice and helping us make better decisions according to our own values [[133](#bib.bibx133)]. In general, AIs would improve social welfare and allow for corrections in cases of error or as human values naturally evolve.
6 Discussion of Connections Between Risks
------------------------------------------
So far, we have considered four sources of AI risk separately, but they also interact with each other in complex ways. We give some examples to illustrate how risks are connected.
Imagine, for instance, that a corporate AI race compels companies to prioritize the rapid development of AIs. This could increase organizational risks in various ways. Perhaps a company could cut costs by putting less money toward information security, leading to one of its AI systems getting leaked. This would increase the probability of someone with malicious intent having the AI system and using it to pursue their harmful objectives. Here, an AI race can increase organizational risks, which in turn can make malicious use more likely.
In another potential scenario, we could envision the combination of an intense AI race and low organizational safety leading a research team to mistakenly view general capabilities advances as “safety.” This could hasten the development of increasingly capable models, reducing the available time to learn how to make them controllable. The accelerated development would also likely feed back into competitive pressures, meaning that less effort would be spent on ensuring models were controllable. This could give rise to the release of a highly powerful AI system that we lose control over, leading to a catastrophe. Here, competitive pressures and low organizational safety can reinforce AI race dynamics, which can undercut technical safety research and increase the chance of a loss of control.
Competitive pressures in a military environment could lead to an AI arms race, and increase the potency and autonomy of AI weapons. The deployment of AI-powered weapons, paired with insufficient control of them, would make a loss of control more deadly, potentially existential. These are just a few examples of how these sources of risk might combine, trigger, and reinforce one another.
It is also worth noting that many existential risks could arise from AIs amplifying existing concerns. Power inequality already exists, but AIs could lock it in and widen the chasm between the powerful and the powerless, even enabling an unshakable global totalitarian regime, an existential risk. Similarly, AI manipulation could undermine democracy, which also increases the existential risk of an irreversible totalitarian regime. Disinformation is already a pervasive problem, but AIs could exacerbate it beyond control, to a point where we lose a consensus on reality. AI-enabled cyberattacks could make war more likely, which would increase existential risk. Dramatically accelerated economic automation could lead to eroded human control and enfeeblement, an existential risk. Each of those issues—power concentration, disinformation, cyberattacks, automation—is causing ongoing harm, and their exacerbation by AIs could eventually lead to a catastrophe humanity may not recover from.
As we can see, ongoing harms, catastrophic risks, and existential risks are deeply intertwined. Historically, existential risk reduction has focused on targeted interventions such as technical AI control research, but the time has come for broad interventions [[134](#bib.bibx134)] like the many sociotechnical interventions outlined in this paper.
In mitigating existential risk, it no longer makes practical sense to ignore other risks. Ignoring ongoing harms and catastrophic risks normalizes them and could lead us to “drift into danger” [[135](#bib.bibx135)]. Overall, since existential risks are connected to less extreme catastrophic risks and other standard risk sources, and because society is increasingly willing to address various risks from AIs, we believe that we should not solely focus on directly targeting existential risks. Instead, we should consider the diffuse, indirect effects of other risks and take a more comprehensive approach to risk management.
7 Conclusion
-------------
In this paper, we have explored how the development of advanced AIs could lead to catastrophe, stemming from four primary sources of risk: malicious use, AI races, organizational risks, and rogue AIs. This lets us decompose AI risks into four proximate causes: an intentional cause, environmental cause, accidental cause, or an internal (or “inherent”) cause, respectively. We have considered ways in which AIs might be used maliciously, such as terrorists using AIs to create deadly pathogens. We have looked at how an AI race in military or corporate settings could rush us into giving AIs decision-making powers, leading us down a slippery slope to human disempowerment. We have discussed how inadequate organizational safety could lead to catastrophic accidents. Finally, we have addressed the challenges in reliably controlling advanced AIs, including mechanisms such as proxy gaming and goal drift that might give rise to rogue AIs pursuing undesirable actions without regard for human wellbeing.
These dangers warrant serious concern. Currently, very few people are working on AI risk reduction. We do not yet know how to control highly advanced AI systems, and existing control methods are already proving inadequate. The inner workings of AIs are not well understood, even by those who create them, and current AIs are by no means highly reliable. As AI capabilities continue to grow at an unprecedented rate, they could surpass human intelligence in nearly all respects relatively soon, creating a pressing need to manage the potential risks.
The good news is that there are many courses of action we can take to substantially reduce these risks. The potential for malicious use can be mitigated by various measures, such as carefully targeted surveillance and limiting access to the most dangerous AIs. Safety regulations and cooperation between nations and corporations could help us resist competitive pressures driving us down a dangerous path. The probability of accidents can be reduced by a rigorous safety culture, among other factors, and by ensuring safety advances outpaces general capabilities advances. Finally, the risks inherent in building technology that surpasses our own intelligence can be addressed by redoubling efforts in several branches of AI control research.
As capabilities continue to grow, and social and systemic circumstances continue to evolve, estimates vary for when risks might reach a catastrophic or existential level. However, the uncertainty around these timelines, together with the magnitude of what could be at stake, makes a convincing case for a proactive approach to safeguarding humanity’s future. Beginning this work immediately can help ensure that this technology transforms the world for the better, and not for the worse.
### Acknowledgements
We would like to thank Laura Hiscott, Avital Morris, David Lambert, Kyle Gracey, and Aidan O’Gara for assistance in drafting this paper. We would also like to thank Jacqueline Harding, Nate Sharadin, William D’Alessandro, Cameron Domenico Kirk-Gianini, Simon Goldstein, Alex Tamkin, Adam Khoja, Oliver Zhang, Jack Cunningham, Lennart Justen, Davy Deng, Ben Snyder, Willy Chertman, Justis Mills, Hadrien Pouget, Nathan Calvin, Eric Gan, Lukas Finnveden, Ryan Greenblatt, and Andrew Doris for helpful feedback. |
11c37909-a655-4d44-a27e-26bf3f3aacae | trentmkelly/LessWrong-43k | LessWrong | An Impossibility Proof Relevant to the Shutdown Problem and Corrigibility
The Incompatibility of a Utility Indifference Condition with Robustly Making Sane Pure Bets
Summary
It is provably impossible for an agent to robustly and coherently satisfy two conditions that seem desirable and highly relevant to the shutdown problem. These two conditions are the sane pure bets condition, which constrains preferences between actions that result in equal probabilities of an event such as shutdown, and the weak indifference condition, a condition which seems necessary (although not sufficient) for an agent to be robustly indifferent to an event such as shutdown.
Suppose that we would like an agent to be indifferent to an event P, which could represent the agent being shut down at a particular time, or the agent being shut down at any time before tomorrow, or something else entirely. Furthermore, we would ideally like the agent to do well at pursuing goals described by some utility function U, while being indifferent to P.
The sane pure bets condition is as follows:
Given any two actions A and B such that P(P|A) = P(P|B) and E(U|A) > E(U|B), the agent prefers A to B. In other words, if two possible actions lead to the same probability of P, and one of them leads to greater expected utility under U, the agent should prefer that one. Intuitively, this constraint represents the idea that among possible actions which don’t influence the probability of P, we would like the agent to prefer those that lead to greater expected utility under U.
The weak indifference condition is as follows:
Given any two actions A and B such that E(U | A,P) > E(U | B,P) and E(U | A,!P) > E(U | B,!P), the agent prefers A to B. In other words, if between two possible actions, one of them leads to greater expected utility conditioned on P occurring and also leads to greater expected utility conditioned on P not occurring, the agent should prefer that one. Intuitively, this constraint represents the idea that the agent should be unwilling to pay any amount of utility t |
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