Design for a Darwinian Brain: Part 1. Philosophy and Neuroscience

Physical symbol systems are needed for open-ended cognition. A good way to understand physical symbol systems is by comparison of thought to chemistry. Both have systematicity, productivity and compositionality. The state of the art in cognitive architectures for open-ended cognition is critically assessed. I conclude that a cognitive architecture that evolves symbol structures in the brain is a promising candidate to explain open-ended cognition. Part 2 of the paper presents such a cognitive architecture.Comment: Darwinian Neurodynamics. Submitted as a two part paper to Living Machines 2013 Natural History Museum, Londo

Categorial Compositionality: A Category Theory Explanation for the Systematicity of Human Cognition

Classical and Connectionist theories of cognitive architecture seek to explain systematicity (i.e., the property of human cognition whereby cognitive capacity comes in groups of related behaviours) as a consequence of syntactically and functionally compositional representations, respectively. However, both theories depend on ad hoc assumptions to exclude specific instances of these forms of compositionality (e.g. grammars, networks) that do not account for systematicity. By analogy with the Ptolemaic (i.e. geocentric) theory of planetary motion, although either theory can be made to be consistent with the data, both nonetheless fail to fully explain it. Category theory, a branch of mathematics, provides an alternative explanation based on the formal concept of adjunction, which relates a pair of structure-preserving maps, called functors. A functor generalizes the notion of a map between representational states to include a map between state transformations (or processes). In a formal sense, systematicity is a necessary consequence of a higher-order theory of cognitive architecture, in contrast to the first-order theories derived from Classicism or Connectionism. Category theory offers a re-conceptualization for cognitive science, analogous to the one that Copernicus provided for astronomy, where representational states are no longer the center of the cognitive universe—replaced by the relationships between the maps that transform them

A Defense of Pure Connectionism

Connectionism is an approach to neural-networks-based cognitive modeling that encompasses the recent deep learning movement in artificial intelligence. It came of age in the 1980s, with its roots in cybernetics and earlier attempts to model the brain as a system of simple parallel processors. Connectionist models center on statistical inference within neural networks with empirically learnable parameters, which can be represented as graphical models. More recent approaches focus on learning and inference within hierarchical generative models. Contra influential and ongoing critiques, I argue in this dissertation that the connectionist approach to cognitive science possesses in principle (and, as is becoming increasingly clear, in practice) the resources to model even the most rich and distinctly human cognitive capacities, such as abstract, conceptual thought and natural language comprehension and production. Consonant with much previous philosophical work on connectionism, I argue that a core principle—that proximal representations in a vector space have similar semantic values—is the key to a successful connectionist account of the systematicity and productivity of thought, language, and other core cognitive phenomena. My work here differs from preceding work in philosophy in several respects: (1) I compare a wide variety of connectionist responses to the systematicity challenge and isolate two main strands that are both historically important and reflected in ongoing work today: (a) vector symbolic architectures and (b) (compositional) vector space semantic models; (2) I consider very recent applications of these approaches, including their deployment on large-scale machine learning tasks such as machine translation; (3) I argue, again on the basis mostly of recent developments, for a continuity in representation and processing across natural language, image processing and other domains; (4) I explicitly link broad, abstract features of connectionist representation to recent proposals in cognitive science similar in spirit, such as hierarchical Bayesian and free energy minimization approaches, and offer a single rebuttal of criticisms of these related paradigms; (5) I critique recent alternative proposals that argue for a hybrid Classical (i.e. serial symbolic)/statistical model of mind; (6) I argue that defending the most plausible form of a connectionist cognitive architecture requires rethinking certain distinctions that have figured prominently in the history of the philosophy of mind and language, such as that between word- and phrase-level semantic content, and between inference and association

The systematicity challenge to anti-representational dynamicism

After more than twenty years of representational debate in the cognitive sciences, anti-representational dynamicism may be seen as offering a rival and radically new kind of explanation of systematicity phenomena. In this paper, I argue that, on the contrary, anti-representational dynamicism must face a version of the old systematicity challenge: either it does not explain systematicity, or else, it is just an implementation of representational theories. To show this, I present a purely behavioral and representation-free account of systematicity. I then consider a case of insect sensorimotor systematic behavior: communicating behavior in honey bees. I conclude that anti-representational dynamicism fails to capture the fundamental trait of systematic behaviors qua systematic, i.e., their involving exercises of the same behavioral capacities. I suggest, finally, a collaborative strategy in pursuit of a rich and powerful account of this central phenomenon of high cognition at all levels of explanation, including the representational level

Information theory-based compositional distributional semantics

In the context of text representation, Compositional Distributional Semantics models aim to fuse the Distributional Hypothesis and the Principle of Compositionality. Text embedding is based on co-ocurrence distributions and the representations are in turn combined by compositional functions taking into account the text structure. However, the theoretical basis of compositional functions is still an open issue. In this article we define and study the notion of Information Theory-based Compositional Distributional Semantics (ICDS): (i) We first establish formal properties for embedding, composition, and similarity functions based on Shannon's Information Theory; (ii) we analyze the existing approaches under this prism, checking whether or not they comply with the established desirable properties; (iii) we propose two parameterizable composition and similarity functions that generalize traditional approaches while fulfilling the formal properties; and finally (iv) we perform an empirical study on several textual similarity datasets that include sentences with a high and low lexical overlap, and on the similarity between words and their description. Our theoretical analysis and empirical results show that fulfilling formal properties affects positively the accuracy of text representation models in terms of correspondence (isometry) between the embedding and meaning spaces

Categorial Compositionality III: F-(co)algebras and the Systematicity of Recursive Capacities in Human Cognition

Human cognitive capacity includes recursively definable concepts, which are prevalent in domains involving lists, numbers, and languages. Cognitive science currently lacks a satisfactory explanation for the systematic nature of such capacities (i.e., why the capacity for some recursive cognitive abilities–e.g., finding the smallest number in a list–implies the capacity for certain others–finding the largest number, given knowledge of number order). The category-theoretic constructs of initial F-algebra, catamorphism, and their duals, final coalgebra and anamorphism provide a formal, systematic treatment of recursion in computer science. Here, we use this formalism to explain the systematicity of recursive cognitive capacities without ad hoc assumptions (i.e., to the same explanatory standard used in our account of systematicity for non-recursive capacities). The presence of an initial algebra/final coalgebra explains systematicity because all recursive cognitive capacities, in the domain of interest, factor through (are composed of) the same component process. Moreover, this factorization is unique, hence no further (ad hoc) assumptions are required to establish the intrinsic connection between members of a group of systematically-related capacities. This formulation also provides a new perspective on the relationship between recursive cognitive capacities. In particular, the link between number and language does not depend on recursion, as such, but on the underlying functor on which the group of recursive capacities is based. Thus, many species (and infants) can employ recursive processes without having a full-blown capacity for number and language

On The Specialization of Neural Modules

A number of machine learning models have been proposed with the goal of achieving systematic generalization: the ability to reason about new situations by combining aspects of previous experiences. These models leverage compositional architectures which aim to learn specialized modules dedicated to structures in a task that can be composed to solve novel problems with similar structures. While the compositionality of these architectures is guaranteed by design, the modules specializing is not. Here we theoretically study the ability of network modules to specialize to useful structures in a dataset and achieve systematic generalization. To this end we introduce a minimal space of datasets motivated by practical systematic generalization benchmarks. From this space of datasets we present a mathematical definition of systematicity and study the learning dynamics of linear neural modules when solving components of the task. Our results shed light on the difficulty of module specialization, what is required for modules to successfully specialize, and the necessity of modular architectures to achieve systematicity. Finally, we confirm that the theoretical results in our tractable setting generalize to more complex datasets and non-linear architectures