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[EQUATION] [MATH] specifies one of three possible homology relationships at position [MATH] in the alignment (homologous amino acids, deletion with respect to protein [MATH] , and insertion with respect to protein [MATH] , respectively.). [MATH] and [MATH] specifies the indices of the positions in proteins [MATH] and [... |
Note that a disadvantage of our approach is that neighbouring amino acid positions in the presence of a deletion or series of deletions are no longer treated as directly adjacent by our HMM with respect to that particular protein, whereas in physical reality the amino acids positions would be directly adjacent to one a... |
A.2 Parallelisation of model training The StEM algorithm is easily parallelised. In the E-step, the parameters, alignment and hidden states of protein pair proteins can be independently sampled in parallel, conditioned on the parameters, [MATH] , from the M-step. Whereas, in the M-step the parameters corresponding to e... |
A.3 Time-reversibility The three stochastic processes are assumed to be time-reversible. This, together with assumption of time-reversibility in jumping between evolutionary regimes in equation ensures overall time-reversibility. This allows to treat the phylogenetic tree relating proteins [MATH] and [MATH] as unrooted... |
Appendix B Supplementary results B.1 Estimates of evolutionary time from dihedral angles are consistent with estimates from sequence |
Figure 14 compares evolutionary times estimated using pairs of homologous amino acid sequences only versus pairs of homologous dihedral angles only. The mean 90% confidence interval (CI) widths for the sampled evolutionary times were smaller for amino acid sequences (mean 90% CI width [MATH] ) than dihedral angles (mea... |
# Source: arxiv 1703.04908 # Title: Emergence of Grounded Compositional Language in Multi-Agent Populations # Sections: all # Downloaded: 2026-03-03T02:00:55.287732+00:00 |
Emergence of Grounded Compositional Language in Multi-Agent Populations Abstract By capturing statistical patterns in large corpora, machine learning has enabled significant advances in natural language processing, including in machine translation, question answering, and sentiment analysis. However, for agents to inte... |
Introduction Development of agents that are capable of communication and flexible language use is one of the long-standing challenges facing the field of artificial intelligence. Agents need to develop communication if they are to successfully coordinate as a collective. Furthermore, agents will need some language capa... |
But if we wish to arrive at formation of communication from first principles, it must form out of necessity. The approaches that learn to plausibly imitate language from examples of human language, while tremendously useful, do not learn why language exists. Such supervised approaches can capture structural and statist... |
Recently there has been a surge of renewed interest in the pragmatic aspects of language use and it is also the focus of our work. We adopt a view of ( ) that an agent possesses an understanding of language when it can use language (along with other tools such as non-verbal communication or physical acts) to accomplish... |
In this paper, we propose a physically-situated multi-agent learning environment and learning methods that bring about emergence of a basic compositional language. This language is represented as streams of abstract discrete symbols uttered by agents over time, but nonetheless has a coherent structure that possesses a ... |
There are similarly no explicit language usage goals, such as making correct utterances, and no explicit roles agents are assigned, such as speaker or listener, or explicit turn-taking dialogue structure as in traditional language games. There may be an arbitrary number of agents in a population communicating at the sa... |
Similar to recent work,we formulate the discovery the action and communication protocols for our agents jointly as a reinforcement learning problem. Agents perform physical actions and communication utterances according to an identical policy that is instantiated for all agents and fully determines the action and commu... |
The languages formed exhibit interpretable compositional structure that in general assigns symbols to separately refer to environment landmarks, action verbs, and agents. However, environment variation leads to a number of specialized languages, omitting words that are clear from context. For example, when there is onl... |
The presence of a physical environment also allows for alternative strategies aside from language use to accomplish goals. A visual sensory modality provides an alternative medium for communication and we observe emergence of non-verbal communication such as pointing and guiding when language communication is unavailab... |
By compositionality we mean the combination of multiple words to create meaning, as opposed to holistic languages that have a unique word for every possible meaning ( ). Our work offers insights into why such compositional structure emerges. In part, we find it to emerge when we explicitly encourage active vocabulary s... |
Related Work Recent years have seen substantial progress in practical natural language applications such as machine translation ( ), sentiment analysis ( ), document summarization ( ), and domain-specific dialogue ( ). Much of this success is a result of intelligently designed statistical models trained on large static... |
An interest in pragmatic view of language understanding has been longstanding ( ) and has recently argued for in ( ). Pragmatic language use has been proposed in the context of two-player reference games ( ) focusing on the task of identifying object references through a learned language. ( ) ground language in a physi... |
Aside from producing agents that can interact with humans through language, research in pragmatic language understanding can be informative to the fields of linguistics and cognitive science. Of particular interest in these fields has been the question of how syntax and compositional structure in language emerged, and ... |
The recent work that is most similar to ours is the application of reinforcement learning approaches towards the purposes of learning a communication protocol, as exemplified by ( ). |
Problem Formulation The setting we are considering is a cooperative partially observable Markov game ( ), which is a multi-agent extension of a Markov decision process. A Markov game for [MATH] agents is defined by set of states [MATH] describing the possible configurations of all agents, a set of actions [MATH] and a ... |
[MATH] observations are given by function [MATH] To choose actions, each agent [MATH] uses a stochastic policy [MATH] In this work, we assume all agents have identical action and observation spaces, and all agents act according to the same policy [MATH] and receive a shared reward. We consider a finite horizon setting,... |
[EQUATION] Grounded Communication Environment As argued in the introduction, grounding multi-agent communication in a physical environment is crucial for interesting communication behaviors to emerge. In this work, we consider a physically-simulated two-dimensional environment in continuous space and discrete time. Thi... |
In addition to performing physical actions, agents utter verbal communication symbols [MATH] at every timestep. These utterances are discrete elements of an abstract symbol vocabulary [MATH] of size [MATH] . We do not assign any significance or meaning to these symbols. They are treated as abstract categorical variable... |
Each agent has internal goals specified by vector [MATH] that are private and not observed by other agents. These goals are grounded in the physical environment and include tasks such as moving to or gazing at a location. These goals may involve other agents (requiring the other agent to move to a location, for example... |
To aid in accomplishing goals, each agent has internal recurrent memory bank [MATH] that is also private and not observed by other agents. This memory bank has no pre-designed behavior and it is up to the agents to learn to utilize it appropriately. |
The full state of the environment is given by [MATH] Each agent observes physical states of all entities in the environment, verbal utterances of all agents, and its own private memory and goal vector. The observation for agent [MATH] is |
[MATH] Where [MATH] is the observation of entity [MATH] ’s physical state in agent [MATH] ’s reference frame (see Appendix for details). More intricate observation models are possible, such as physical observations solely from pixels or verbal observations from a single input channel. These models would require agents ... |
Policy Learning with Backpropagation Each agent acts by sampling actions from a stochastic policy [MATH] , which is identical for all agents and defined by parameters [MATH] . There are several common options for finding optimal policy parameters. The model-free framework of Q-learning can be used to find the optimal s... |
Instead of using model-free reinforcement learning methods, we build an end-to-end differentiable model of all agent and environment state dynamics over time and calculate [MATH] with backpropagation. At every optimization iteration, we sample a new batch of 1024 random environment instantiations and backpropagate thei... |
The physical state dynamics, including discontinuous contact events can be made differentiable with smoothing. However, communication actions require emission of discrete symbols, which present difficulties for backpropagation. |
Discrete Communication and Gumbel-Softmax Estimator In order to use categorical communication emissions [MATH] in our setting, it must be possible to differentiate through them. There has been a wealth of work in machine learning on differentiable models with discrete variables, but we found recent approach in ( ) to b... |
[EQUATION] Where [MATH] are i.i.d. samples from Gumbel [MATH] distribution, [MATH] and [MATH] is a softmax temperature parameter. We did not find it necessary to anneal the temperature and set it to [MATH] in all our experiments for training and sample directly from the categorical distribution at test time. To emit a ... |
Policy Architecture The policy class we consider in this work are stochastic neural networks. The policy outputs samples of an agent’s physical actions [MATH] , communication symbol utterance [MATH] , and internal memory updates [MATH] . The policy must consolidate multiple incoming communication symbol streams emitted... |
The pooled features and agent’s private goal vector are passed to the final processing module that outputs distribution parameters [MATH] from which action samples are generated as [MATH] and [MATH] , where [MATH] is a zero-mean Gaussian noise. |
Unlike communication games where agents only emit a single utterance, our agents continually emit a stream of symbols over time. Thus processing modules that read and write communication utterance streams benefit greatly from recurrent memory that can capture meaning of a stream over time. To this end, we augment each ... |
Auxiliary Prediction Reward To help policy training avoid local minima in more complex environments, we found it helpful to include auxiliary goal prediction tasks, similar to recent work in reinforcement learning ( ). In agent [MATH] ’s policy, each communication processing module [MATH] additionally outputs a predict... |
[EQUATION] Compositionality and Vocabulary Size What leads to compositional syntax formation? One known constructive hypothesis requires modeling the process of language transmission and acquisition from one generation of agents to the next iteratively as in ( ). In such iterated learning setting, compositionality emer... |
Alternatively, ( ) observed that emergence of compositionality requires the number of concepts describable by a language to be above a factor of vocabulary size. In our preliminary environments the number of concepts to communicate is still fairly small and is within the capacity of a non-compositional language. We use... |
How do we penalize large vocabulary sizes? ( ) proposed a word population dynamics model that defines reproductive ratios of words to be proportional to their frequency, making already popular words more likely to survive. Inspired by these rich-get-richer dynamics, we model the communication symbols as being ). Each c... |
[EQUATION] Where [MATH] is the number of times symbol [MATH] has been uttered and [MATH] is the total number of symbols uttered. These counts are accumulated over agents, timesteps, and batch entries. [MATH] is a Dirichlet Process hyperparameter corresponding to the probability of observing an out-of-vocabulary word. T... |
[EQUATION] Maximizing this reward leads to consolidation of symbols and the formation of compositionality. This approach is similar to encouraging code population sparsity in autoencoders ( ), which was shown to give rise to compositional representations for images. |
Experiments We experimentally investigate how variation in goals, environment configuration, and agents’ physical capabilities lead to different communication strategies. In this work, we consider three types of actions an agent needs to perform: go to location, look at location, and do nothing . Goal for agent [MATH] ... |
Agents can only communicate in discrete symbols and have individual reference frames without a shared global positioning reference (see Appendix), so cannot directly send goal position vector. What makes the task possible is that we place goal locations [MATH] on landmark locations of which are observed by all agents (... |
In the results that follow, agents do not observe other agents. This disallows capacity for non-verbal communication, necessitating the use of language. In section Non-verbal Communication and Other Strategies we report what happens when agents are able to observe each other and capacity for non-verbal communication is... |
Despite training with continuous relaxation of the categorical distribution, we observe very similar reward performance at test time. No communication is provided as a baseline (again, non-verbal communication is not possible). The no-communication strategy is for all agents go towards the centroid of all landmarks. |
Syntactic Structure We observe a compositional syntactic structure emerging in the stream of symbol uttered by agents. When trained on environments with only two agents, but multiple landmarks and actions, we observe symbols forming for each of the landmark colors and each of the action types. A typical conversation an... |
Green Agent: GOTO, GREEN, ... Blue Agent: GOTO, BLUE, ... The labels for abstract symbols are chosen by us purely for interpretability and visualization and carry no meaning for training. While there is recent work on interpreting continuous machine languages ( ), the discrete nature and small size of our symbol vocabu... |
Physical environment considerations play a part in the syntactic structure. The action type verb GOTO is uttered first because actions take time to accomplish in the grounded environment. When the agent receives GOTO symbol it starts moving toward the centroid of all the landmarks (to be equidistant from all of them) a... |
When the environment configuration can contain more than three agents, agents need to form symbols for referring to each other. Three new symbols form to refer to agent colors that are separate in meaning from landmark colors. The typical conversations are shown in second and third rows of Figure |
Red Agent: GOTO, RED, BLUE-AGENT, ... Green Agent: ..., ..., ..., ... Blue Agent: RED-AGENT, GREEN, LOOKAT, ... Agents may not omit any utterances when they are the subject of their private goal, in which case they have access to that information and have no need to announce it. In this language, there is no set orderi... |
The agents largely settle on using a consistent set of symbols for each meaning, due to vocabulary size penalties and that discourage synonyms. We show the aggregate streams of communication utterances in Figure |
In simplified environment configurations when there is only one landmark or one type of action to take, no symbols are formed to refer to those concepts because they are clear from context. |
Symbol Vocabulary Usage We find word activation counts to settle on the appropriate compositional word counts. That early during training large vocabulary sizes are being taken advantage of to explore the space of communication possibilities before settling on the appropriate effective vocabulary sizes as shown in Figu... |
Generalization to Unseen Configurations One of the advantages of decentralised execution policies is that trained agents can be placed into arbitrarily-sized groups and still function reasonably. When there are additional agents in the environment with the same color identity, all agents of the same color will perform ... |
Due to the modularized observation architecture, the number of landmarks in the environment can also vary between training and execution. The agents perform sensible behaviors with different numbers of landmarks, despite not being trained in such environments. For example, when there are distractor landmarks of novel c... |
Non-verbal Communication and Other Strategies The presence of a physical environment also allows for alternative strategies aside from language use to accomplish goals. In this set of experiments we enable agents to observe other agents’ position and gaze location, and in turn disable communication capability via symbo... |
Conclusion We have presented a multi-agent environment and learning methods that brings about emergence of an abstract compositional language from grounded experience. This abstract language is formed without any exposure to human language use. We investigated how variation in environment configuration and physical cap... |
In the future, we would like experiment with larger number of actions that necessitate more complex syntax and larger vocabularies. We would also like integrate exposure to human language to form communication strategies that are compatible with human use. |
Acknowledgements We thank OpenAI team for helpful comments and fruitful discussions. This work was funded in part by ONR PECASE N000141612723. |
Appendix: Physical State and Dynamics The physical state of the agent is specified by [MATH] where [MATH] is the velocity of [MATH] [MATH] is the color associted with the agent. Landmarks have similar state, but without gaze and velocity components. The physical state transition dynamics for a single agent [MATH] are g... |
[EQUATION] Where [MATH] are the physical interaction forces (such as collision) between all agents in the environment and any obstacles, [MATH] is the simulation timestep (we use 0.1), and [MATH] is a damping coefficient (we use 0.5). The action space of the agent is [MATH] . The observation of any location [MATH] in r... |
# Source: arxiv 1703.06263 # Title: An Adaptive Framework to Tune the Coordinate Systems in Evolutionary Algorithms # Sections: all # Downloaded: 2026-03-03T01:57:03.591171+00:00 |
An Adaptive Framework to Tune the Coordinate Systems in Evolutionary Algorithms Abstract In the evolutionary computation research community, the performance of most evolutionary algorithms (EAs) depends strongly on their implemented coordinate system. However, the commonly used coordinate system is fixed and not well s... |
Introduction Evolutionary algorithms (EAs) are a class of population-based meta-heuristic algorithms inspired by biological evolution. EAs exploit bio-inspired mechanisms such as reproduction, mutation, crossover, and selection to evolve a population of candidate solutions toward the optimal solution. Up to now, numero... |
, evolution strategy (ES) , genetic algorithm (GA) , genetic programming (GP) , differential evolution (DE) , and particle swarm optimization (PSO) |
, have been proposed. Compared with other types of optimization methods, EAs have some advantages such as ease of use, simple structure, efficiency, and robustness. Therefore, EAs have been broadly applied to diverse fields such as art |
, economics , route planning , robotics , and graphic processing For most EAs, their performance relies crucially on their implemented coordinate system. However, the original coordinate system, which is the most frequently used coordinate system in current EAs, is fixed throughout the evolutionary process. Under this ... |
To remedy this issue, in some variants of ES and DE, the Eigen coordinate system is established by making use of the population distribution information. Since the population distribution information can reflect the features of the function landscape to a certain degree, EAs implemented in the Eigen coordinate system t... |
. In CMA-ES, an Eigen coordinate system is established by utilizing the cumulative population distribution information (i.e., the current and historical population distribution information). Afterward, the offspring population is sampled from this Eigen coordinate system. Overall, CMA-ES shows very fast convergence spe... |
, CoBiDE , and CPI-DE ) have been made to enhance DE’s performance by implementing the crossover operator in both the Eigen coordinate system and the original coordinate system. In DE/eig and CoBiDE, only the current population distribution information is extracted to establish the Eigen coordinate system, while like C... |
This paper presents an adaptive framework, called ACoS, to tune the coordinate systems in EAs. ACoS takes advantage of a covariance matrix adaptation strategy and an additional archiving mechanism to extract cumulative population distribution information, with the aim of establishing the Eigen coordinate system. Moreov... |
The main contributions of this paper are summarized as follows: This paper provides a new point of view toward how to describe an evolutionary operator in the original coordinate system, and also offers a convenient transformation from an evolutionary operator in the original coordinate system to the corresponding evol... |
A simple yet effective approach is proposed to establish the Eigen coordinate system, which consists of two main elements, i.e., a covariance matrix adaptation strategy and an additional archiving mechanism. In comparison with the previous methods, the cumulative population distribution information derived from our app... |
By using a probability vector, this paper presents an adaptive scheme to select an appropriate coordinate system from the original coordinate system and the Eigen coordinate system for each individual during the evolution. |
The proposed framework (i.e., ACoS) can be readily applied to various EAs. In this paper, we have verified that ACoS is able to improve the performance of two of the most popular EA paradigms: PSO and DE. To the best of our knowledge, it is the first attempt to improve PSO’s performance by adjusting the coordinate syst... |
The rest of this paper is organized as follows. Section briefly introduces PSO and DE. Section presents the coordinate systems and their related work. The proposed ACoS and its implementation details are presented in Section . The experimental results and the performance comparisons are given in Section . Finally, Sect... |
Particle Swarm Optimization (PSO) and Differential Evolution (DE) PSO and DE have become two of the most popular EA paradigms. In this section, we will briefly introduce them. |
2.1 Particle Swarm Optimization (PSO) PSO is a population-based stochastic search technique inspired by swarm behavior. It searches with a population (called swarm) of candidate solutions (called particles or individuals). Each particle moves around the search space to seek the global optimum, and its movement is guide... |
PSO contains two core equations: the velocity updating equation and the position updating equation. At generation [MATH] , PSO updates the [MATH] th dimension of the [MATH] th particle’s velocity [MATH] and position [MATH] as follows: |
[EQUATION] [EQUATION] where [MATH] [MATH] [MATH] is the population size, [MATH] is the dimension of the search space, [MATH] denotes the [MATH] th particle’s historical best position, [MATH] means the entire swarm’s best position, [MATH] and [MATH] are the acceleration parameters, and [MATH] and [MATH] refer to two uni... |
From Eq.( ) and Eq.( ), it is apparent that PSO works dimension by dimension. Based on the updating of each dimension, the whole velocity and position of a particle are updated as follows: |
[EQUATION] [EQUATION] where [MATH] and [MATH] Since PSO’s inception, many researchers have improved its performance in different ways. One way is to control or adjust the particle’s velocity. Shi and Eberhart |
incorporated an inertial weight [MATH] into the original PSO’s velocity updating, and Eq.( ) is thus modified into Eq.( [EQUATION] |
The only difference between Eq.( ) and Eq.( ) is that in Eq.( [MATH] is attached to [MATH] . In Eq.( ), the value of [MATH] decreases linearly from 0.9 to 0.4 over the course of search. It is because a larger [MATH] in the early stage of evolution is beneficial to exploration, and a smaller [MATH] in the later stage of... |
introduced a constriction factor [MATH] to reformulate the particle’s velocity updating: [EQUATION] where [MATH] and [MATH] [MATH] is preferably set to 0.729 together with [MATH] . For the sake of convenience, the PSO variants in |
and are called PSO-w and PSO-cf in this paper, respectively, which are two of the most popular PSO variants. 2.2 Differential Evolution (DE) |
DE is another simple yet efficient EA paradigm which has been successfully used to deal with a wide spectrum of optimization problems |
. Similar to other EAs, DE searches with a population of [MATH] individuals: [MATH] , where [MATH] denotes the generation number, [MATH] means the population size, and [MATH] refers to the dimension of the search space. In DE, at generation [MATH] , the initial population [MATH] is randomly sampled from the search spac... |
Mutation: The aim of the mutation operator is to generate a mutant vector [MATH] for each individual [MATH] (also called a target vector). The following are four commonly used mutation operators in the literature: |
DE/rand/1 [EQUATION] DE/rand/2 [EQUATION] DE/current-to-best/1 [EQUATION] DE/rand-to-best/1 [EQUATION] where the indices [MATH] [MATH] [MATH] [MATH] , and [MATH] are mutually different integers randomly selected from [MATH] and are also different from [MATH] [MATH] denotes the best target vector in the current populati... |
Crossover: After mutation, the crossover operator is performed on each pair of [MATH] and [MATH] to generate a trial vector [MATH] . The binomial crossover is expressed as follows: |
[EQUATION] where [MATH] is a random integer between [MATH] and [MATH] [MATH] is a uniformly distributed random number between 0 and 1 for each [MATH] , and [MATH] denotes the crossover control parameter. The condition “ [MATH] ” makes [MATH] different from [MATH] by at least one dimension. |
From Eq.( 11 ), it is easy to see that the crossover operator is implemented dimension by dimension. The updating of the whole trial vector can be described as follows: |
[EQUATION] where [MATH] , and [MATH] [MATH] Selection: The selection operator is designed to select the better one between [MATH] and [MATH] to enter the next generation. For a minimization problem, it can be described as follows: |
[EQUATION] DE has also attracted much attention and a considerable number of DE variants have been proposed. Among them, jDE , SaDE |
, and JADE are three state-of-the-art DE variants. jDE is a DE with self-adaptive control parameter settings. It encodes the control parameters [MATH] and [MATH] into individual level and evolves them. For each individual, the new [MATH] is randomly generated within [MATH] with a probability [MATH] , and the new [MATH]... |
The Coordinate Systems and Their Related Work 3.1 The coordinate systems In this subsection, we will introduce the original coordinate system, the Eigen coordinate system, and the difference between them. |
3.1.1 The original coordinate system The original coordinate system is a default coordinate system in most EAs. It is formed by the columns of the unity matrix , and thus is a fixed coordinate system. The evolutionary operators of PSO and DE in Section are conducted in the original coordinate system. By analyzing these... |
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