Interpreting systems as solving POMDPs: a step towards a formal understanding of agency

Under what circumstances can a system be said to have beliefs and goals, and how do such agency-related features relate to its physical state? Recent work has proposed a notion of interpretation map, a function that maps the state of a system to a probability distribution representing its beliefs about an external world. Such a map is not completely arbitrary, as the beliefs it attributes to the system must evolve over time in a manner that is consistent with Bayes' theorem, and consequently the dynamics of a system constrain its possible interpretations. Here we build on this approach, proposing a notion of interpretation not just in terms of beliefs but in terms of goals and actions. To do this we make use of the existing theory of partially observable Markov processes (POMDPs): we say that a system can be interpreted as a solution to a POMDP if it not only admits an interpretation map describing its beliefs about the hidden state of a POMDP but also takes actions that are optimal according to its belief state. An agent is then a system together with an interpretation of this system as a POMDP solution. Although POMDPs are not the only possible formulation of what it means to have a goal, this nevertheless represents a step towards a more general formal definition of what it means for a system to be an agent.

Interpreting Dynamical Systems as Bayesian Reasoners

A central concept in active inference is that the internal states of a physical system parametrise probability measures over states of the external world. These can be seen as an agent's beliefs, expressed as a Bayesian prior or posterior. Here we begin the development of a general theory that would tell us when it is appropriate to interpret states as representing beliefs in this way. We focus on the case in which a system can be interpreted as performing either Bayesian filtering or Bayesian inference. We provide formal definitions of what it means for such an interpretation to exist, using techniques from category theory.

On the potential for open-endedness in neural networks

Natural evolution gives the impression of leading to an open-ended process of increasing diversity and complexity. If our goal is to produce such open-endedness artificially, this suggests an approach driven by evolutionary metaphor. On the other hand, techniques from machine learning and artificial intelligence are often considered too narrow to provide the sort of exploratory dynamics associated with evolution. In this paper, we hope to bridge that gap by reviewing common barriers to open-endedness in the evolution-inspired approach and how they are dealt with in the evolutionary case - collapse of diversity, saturation of complexity, and failure to form new kinds of individuality. We then show how these problems map onto similar issues in the machine learning approach, and discuss how the same insights and solutions which alleviated those barriers in evolutionary approaches can be ported over. At the same time, the form these issues take in the machine learning formulation suggests new ways to analyze and resolve barriers to open-endedness. Ultimately, we hope to inspire researchers to be able to interchangeably use evolutionary and gradient-descent-based machine learning methods to approach the design and creation of open-ended systems.

Being curious about the answers to questions: novelty search with learned attention

We investigate the use of attentional neural network layers in order to learn a `behavior characterization' which can be used to drive novelty search and curiosity-based policies. The space is structured towards answering a particular distribution of questions, which are used in a supervised way to train the attentional neural network. We find that in a 2d exploration task, the structure of the space successfully encodes local sensory-motor contingencies such that even a greedy local `do the most novel action' policy with no reinforcement learning or evolution can explore the space quickly. We also apply this to a high/low number guessing game task, and find that guessing according to the learned attention profile performs active inference and can discover the correct number more quickly than an exact but passive approach.

Permutation-equivariant neural networks applied to dynamics prediction

The introduction of convolutional layers greatly advanced the performance of neural networks on image tasks due to innately capturing a way of encoding and learning translation-invariant operations, matching one of the underlying symmetries of the image domain. In comparison, there are a number of problems in which there are a number of different inputs which are all 'of the same type' --- multiple particles, multiple agents, multiple stock prices, etc. The corresponding symmetry to this is permutation symmetry, in that the algorithm should not depend on the specific ordering of the input data. We discuss a permutation-invariant neural network layer in analogy to convolutional layers, and show the ability of this architecture to learn to predict the motion of a variable number of interacting hard discs in 2D. In the same way that convolutional layers can generalize to different image sizes, the permutation layer we describe generalizes to different numbers of objects.

Motility at the origin of life: Its characterization and a model

Due to recent advances in synthetic biology and artificial life, the origin of life is currently a hot topic of research. We review the literature and argue that the two traditionally competing "replicator-first" and "metabolism-first" approaches are merging into one integrated theory of individuation and evolution. We contribute to the maturation of this more inclusive approach by highlighting some problematic assumptions that still lead to an impoverished conception of the phenomenon of life. In particular, we argue that the new consensus has so far failed to consider the relevance of intermediate timescales. We propose that an adequate theory of life must account for the fact that all living beings are situated in at least four distinct timescales, which are typically associated with metabolism, motility, development, and evolution. On this view, self-movement, adaptive behavior and morphological changes could have already been present at the origin of life. In order to illustrate this possibility we analyze a minimal model of life-like phenomena, namely of precarious, individuated, dissipative structures that can be found in simple reaction-diffusion systems. Based on our analysis we suggest that processes in intermediate timescales could have already been operative in prebiotic systems. They may have facilitated and constrained changes occurring in the faster- and slower-paced timescales of chemical self-individuation and evolution by natural selection, respectively.