The computational program for theoretical neuroscience initiated by Marr and Poggio (1977) calls for a study of biological information processing on several distinct levels of abstraction. At each of these levels — computational (defining the problems and considering possible solutions), algorithmic (specifying the sequence of operations leading to a solution) and implementational — significant progress has been made in the understanding of cognition. In the past three decades, computational principles have been discovered that are common to a wide range of (...) functions in perception (vision, hearing, olfaction) and action (motor control). More recently, these principles have been applied to the analysis of cognitive tasks that require dealing with structured information, such as visual scene understanding and analogical reasoning. Insofar as language relies on cognition-general principles and mechanisms, it should be possible to capitalize on the recent advances in the computational study of cognition by extending its methods to linguistics. (shrink)

Each of our theories of mental representation provides some insight into how the mind works. However, these insights often seem incompatible, as the debates between symbolic, dynamical, emergentist, sub-symbolic, and grounded approaches to cognition attest. Mental representations—whatever they are—must share many features with each of our theories of representation, and yet there are few hypotheses about how a synthesis could be possible. Here, I develop a theory of the underpinnings of symbolic cognition that shows how sub-symbolic dynamics may give rise (...) to higher-level cognitive representations of structures, systems of knowledge, and algorithmic processes. This theory implements a version of conceptual role semantics by positing an internal universal representation language in which learners may create mental models to capture dynamics they observe in the world. The theory formalizes one account of how truly novel conceptual content may arise, allowing us to explain how even elementary logical and computational operations may be learned from a more primitive basis. I provide an implementation that learns to represent a variety of structures, including logic, number, kinship trees, regular languages, context-free languages, domains of theories like magnetism, dominance hierarchies, list structures, quantification, and computational primitives like repetition, reversal, and recursion. This account is based on simple discrete dynamical processes that could be implemented in a variety of different physical or biological systems. In particular, I describe how the required dynamics can be directly implemented in a connectionist framework. The resulting theory provides an “assembly language” for cognition, where high-level theories of symbolic computation can be implemented in simple dynamics that themselves could be encoded in biologically plausible systems. (shrink)

Are minds really dynamical or are they really symbolic? Because minds are bundles of computations, and because computation is always a matter of interpretation of one system by another, minds are necessarily symbolic. Because minds, along with everything else in the universe, are physical, and insofar as the laws of physics are dynamical, minds are necessarily dynamical systems. Thus, the short answer to the opening question is “yes.” It makes sense to ask further whether some of the computations that constitute (...) a human mind are constrained by functional, algorithmic, or implementational factors to be essentially of the discrete symbolic variety (even if they supervene on an apparently continuous dynamical substrate). I suggest that here too the answer is “yes” and discuss the need for such discrete, symbolic cognitive computations in communication-related tasks. (shrink)

A metaphor that has dominated linguistics for the entire duration of its existence as a discipline views sentences as edifices consisting of Lego-like building blocks. It is assumed that each sentence is constructed (and, on the receiving end, parsed) ab novo, starting (ending) with atomic constituents, to logical semantic specifications, in a recursive process governed by a few precise algebraic rules. The assumptions underlying the Lego metaphor, as it is expressed in generative grammar theories, are: (1) perfect regularity of what (...) Saussure called langue, (2) infinite potential recursivity of syntactic structures, (3) unlimited human capacity for linguistic creativity, (4) the impossibility of acquiring structural knowledge from examples, and (5) the impossibility of such knowledge being stored in a memory-intensive form (ensembles of exemplars). (shrink)

Unsupervised statistical learning is the standard setting for the development of the only advanced visual system that is both highly sophisticated and versatile, and extensively studied: that of monkeys and humans. In this extended abstract, we invoke philosophical observations, computational arguments, behavioral data and neurobiological findings to explain why computer vision researchers should care about (1) unsupervised learning, (2) statistical inference, and (3) the visual brain. We then outline a neuromorphic approach to structural primitive learning motivated by these considerations, survey (...) a range of neurobiological findings and behavioral data consistent with it, and conclude by mentioning some of the more challenging directions for future research. (shrink)

To learn a visual code in an unsupervised manner, one may attempt to capture those features of the stimulus set that would contribute significantly to a statistically efficient representation. Paradoxically, all the candidate features in this approach need to be known before statistics over them can be computed. This paradox may be circumvented by confining the repertoire of candidate features to actual scene fragments, which resemble the “what+where” receptive fields found in the ventral visual stream in primates. We describe a (...) single-layer network that learns such fragments from unsegmented raw images of structured objects. The learning method combines fast imprinting in the feedforward stream with lateral interactions to achieve single-epoch unsupervised acquisition of spatially localized features that can support systematic treatment of structured objects [1]. (shrink)