Empiricism without Magic: Transformational Abstraction in Deep Convolutional Neural Networks

In artificial intelligence, recent research has demonstrated the remarkable potential of Deep Convolutional Neural Networks (DCNNs), which seem to exceed state-of-the-art performance in new domains weekly, especially on the sorts of very difficult perceptual discrimination tasks that skeptics thought would remain beyond the reach of artificial intelligence. However, it has proven difficult to explain why DCNNs perform so well. In philosophy of mind, empiricists have long suggested that complex cognition is based on information derived from sensory experience, often appealing to a faculty of abstraction. Rationalists have frequently complained, however, that empiricists never adequately explained how this faculty of abstraction actually works. In this paper, I tie these two questions together, to the mutual benefit of both disciplines. I argue that the architectural features that distinguish DCNNs from earlier neural networks allow them to implement a form of hierarchical processing that I call “transformational abstraction”. Transformational abstraction iteratively converts sensory-based representations of category exemplars into new formats that are increasingly tolerant to “nuisance variation” in input. Reflecting upon the way that DCNNs leverage a combination of linear and non-linear processing to efficiently accomplish this feat allows us to understand how the brain is capable of bi-directional travel between exemplars and abstractions, addressing longstanding problems in empiricist philosophy of mind. I end by considering the prospects for future research on DCNNs, arguing that rather than simply implementing 80s connectionism with more brute-force computation, transformational abstraction counts as a qualitatively distinct form of processing ripe with philosophical and psychological significance, because it is significantly better suited to depict the generic mechanism responsible for this important kind of psychological processing in the brain

Carbon--The First Frontier of Information Processing

Information is often encoded as an aperiodic chain of building blocks. Modern digital computers use bits as the building blocks, but in general the choice of building blocks depends on the nature of the information to be encoded. What are the optimal building blocks to encode structural information? This can be analysed by substituting the operations of addition and multiplication of conventional arithmetic with translation and rotation. It is argued that at the molecular level, the best component for encoding discretised structural information is carbon. Living organisms discovered this billions of years ago, and used carbon as the back-bone for constructing proteins that function according to their structure. Structural analysis of polypeptide chains shows that an efficient and versatile structural language of 20 building blocks is needed to implement all the tasks carried out by proteins. Properties of amino acids indicate that the present triplet genetic code was preceded by a more primitive one, coding for 10 amino acids using two nucleotide bases.Comment: (v1) 9 pages, revtex. (v2) 10 pages. Several arguments expanded to make the article self-contained and to increase clarity. Applications pointed out. (v3) 11 pages. Published version. Well-known properties of proteins shifted to an appendix. Reformatted according to journal styl

The Geometry of Niggli Reduction I: The Boundary Polytopes of the Niggli Cone

Correct identification of the Bravais lattice of a crystal is an important step in structure solution. Niggli reduction is a commonly used technique. We investigate the boundary polytopes of the Niggli-reduced cone in the six-dimensional space G6 by algebraic analysis and organized random probing of regions near 1- through 8-fold boundary polytope intersections. We limit consideration of boundary polytopes to those avoiding the mathematically interesting but crystallographically impossible cases of 0 length cell edges. Combinations of boundary polytopes without a valid intersection in the closure of the Niggli cone or with an intersection that would force a cell edge to 0 or without neighboring probe points are eliminated. 216 boundary polytopes are found: 15 5-D boundary polytopes of the full G6 Niggli cone, 53 4-D boundary polytopes resulting from intersections of pairs of the 15 5-D boundary polytopes, 79 3-D boundary polytopes resulting from 2-fold, 3-fold and 4-fold intersections of the 15 5-D boundary polytopes, 55 2-D boundary polytopes resulting from 2-fold, 3-fold, 4-fold and higher intersections of the 15 5-D boundary polytopes, 14 1-D boundary polytopes resulting from 3-fold and higher intersections of the 15 5-D boundary polytopes. All primitive lattice types can be represented as combinations of the 15 5-D boundary polytopes. All non-primitive lattice types can be represented as combinations of the 15 5-D boundary polytopes and of the 7 special-position subspaces of the 5-D boundary polytopes. This study provides a new, simpler and arguably more intuitive basis set for the classification of lattice characters and helps to illuminate some of the complexities in Bravais lattice identification. The classification is intended to help in organizing database searches and in understanding which lattice symmetries are "close" to a given experimentally determined cell

Compact Gaussian quantum computation by multi-pixel homodyne detection

We study the possibility of producing and detecting continuous variable cluster states in an optical set-up in an extremely compact fashion. This method is based on a multi-pixel homodyne detection system recently demonstrated experimentally, which includes classical data post-processing. It allows to incorporate the linear optics network, usually employed in standard experiments for the production of cluster states, in the stage of the measurement. After giving an example of cluster state generation by this method, we further study how this procedure can be generalized to perform gaussian quantum computation.Comment: Eqs.(20)-(21) correcte

Applied Symmetry for Crystal Structure Prediction

This thesis presents an original open-source Python package called PyXtal (pronounced pi-crystal ) that generates random symmetric crystal structures for use in crystal structure prediction (CSP). The primary advantage of PyXtal over existing structure generation tools is its unique symmetrization method. For molecular structures, PyXtal uses an original algorithm to determine the compatibility of molecular point group symmetry with Wyckoff site symmetry. This allows the molecules in generated structures to occupy special Wyckoff positions without breaking the structure\u27s symmetry. This is a new feature which increases the space of search-able structures and in turn improves CSP performance. It is shown that using already-symmetric initial structures results in a higher probability of finding the lowest-energy structure. Ultimately, this lowers the computational time needed for CSP. Structures can be generated for any symmetry group of 0, 1, 2, or 3 dimensions of periodicity. Either atoms or rigid molecules may be used as building blocks. The generated structures can be optimized with VASP, LAMMPS, or other computational tools. Additional options are provided for the lattice and inter-atomic distance constraints. Results for carbon and silicon crystals, water ice crystals, and molybdenum clusters are presented as usage examples