Strings from Logic

What are strings made of? The possibility is discussed that strings are purely mathematical objects, made of logical axioms. More precisely, proofs in simple logical calculi are represented by graphs that can be interpreted as the Feynman diagrams of certain large-N field theories. Each vertex represents an axiom. Strings arise, because these large-N theories are dual to string theories. These ``logical quantum field theories'' map theorems into the space of functions of two parameters: N and the coupling constant. Undecidable theorems might be related to nonperturbative field theory effects.Comment: Talk, 19 pp, 7 figure

SCAN: Learning Hierarchical Compositional Visual Concepts

The seemingly infinite diversity of the natural world arises from a relatively small set of coherent rules, such as the laws of physics or chemistry. We conjecture that these rules give rise to regularities that can be discovered through primarily unsupervised experiences and represented as abstract concepts. If such representations are compositional and hierarchical, they can be recombined into an exponentially large set of new concepts. This paper describes SCAN (Symbol-Concept Association Network), a new framework for learning such abstractions in the visual domain. SCAN learns concepts through fast symbol association, grounding them in disentangled visual primitives that are discovered in an unsupervised manner. Unlike state of the art multimodal generative model baselines, our approach requires very few pairings between symbols and images and makes no assumptions about the form of symbol representations. Once trained, SCAN is capable of multimodal bi-directional inference, generating a diverse set of image samples from symbolic descriptions and vice versa. It also allows for traversal and manipulation of the implicit hierarchy of visual concepts through symbolic instructions and learnt logical recombination operations. Such manipulations enable SCAN to break away from its training data distribution and imagine novel visual concepts through symbolically instructed recombination of previously learnt concepts

The Living Gesture and the Signifying Moment

Drawing from Peircean semiotics, from the Greek conception of phronesis, and from considerations of bodily awareness as a basis of reasonableness, I attempt to show how the living gesture touches our deepest signifying nature, the self, and public life. Gestural bodily awareness, more than knowledge, connects us with the very conditions out of which the human body evolved into its present condition and remains a vital resource in the face of a devitalizing, rationalistic consumption culture. It may be precisely these deep-rooted abilities for what I term “self-originated experience” that can ultimately offset automatism

SDEs Driven by SDE Solutions

We consider stochastic differential equations (SDEs) driven by Feller processes which are themselves solutions of multivariate Levy driven SDEs. The solutions of these 'iterated SDEs' are shown to be non-Markovian. However, the process consisting of the driving process and the solution is Markov and even Feller in the case of bounded coefficients. The generator as well as the semimartingale characteristics of this process are calculated explicitly and fine properties of the solution are derived via the stochastic symbol. A short simulation study and an outlook in the direction of stochastic modeling round out the paper.Comment: 16 pages, 9 figure

Lexical and Derivational Meaning in Vector-Based Models of Relativisation

Sadrzadeh et al (2013) present a compositional distributional analysis of relative clauses in English in terms of the Frobenius algebraic structure of finite dimensional vector spaces. The analysis relies on distinct type assignments and lexical recipes for subject vs object relativisation. The situation for Dutch is different: because of the verb final nature of Dutch, relative clauses are ambiguous between a subject vs object relativisation reading. Using an extended version of Lambek calculus, we present a compositional distributional framework that accounts for this derivational ambiguity, and that allows us to give a single meaning recipe for the relative pronoun reconciling the Frobenius semantics with the demands of Dutch derivational syntax.Comment: 10 page version to appear in Proceedings Amsterdam Colloquium, updated with appendi

Neural Mechanisms for Information Compression by Multiple Alignment, Unification and Search

This article describes how an abstract framework for perception and cognition may be realised in terms of neural mechanisms and neural processing. This framework — called information compression by multiple alignment, unification and search (ICMAUS) — has been developed in previous research as a generalized model of any system for processing information, either natural or artificial. It has a range of applications including the analysis and production of natural language, unsupervised inductive learning, recognition of objects and patterns, probabilistic reasoning, and others. The proposals in this article may be seen as an extension and development of Hebb’s (1949) concept of a ‘cell assembly’. The article describes how the concept of ‘pattern’ in the ICMAUS framework may be mapped onto a version of the cell assembly concept and the way in which neural mechanisms may achieve the effect of ‘multiple alignment’ in the ICMAUS framework. By contrast with the Hebbian concept of a cell assembly, it is proposed here that any one neuron can belong in one assembly and only one assembly. A key feature of present proposals, which is not part of the Hebbian concept, is that any cell assembly may contain ‘references’ or ‘codes’ that serve to identify one or more other cell assemblies. This mechanism allows information to be stored in a compressed form, it provides a robust mechanism by which assemblies may be connected to form hierarchies and other kinds of structure, it means that assemblies can express abstract concepts, and it provides solutions to some of the other problems associated with cell assemblies. Drawing on insights derived from the ICMAUS framework, the article also describes how learning may be achieved with neural mechanisms. This concept of learning is significantly different from the Hebbian concept and appears to provide a better account of what we know about human learning