The computational magic of the ventral stream

I argue that the sample complexity of (biological, feedforward) object recognition is mostly due to geometric image transformations and conjecture that a main goal of the ventral stream – V1, V2, V4 and IT – is to learn-and-discount image transformations.

In the first part of the paper I describe a class of simple and biologically plausible memory-based modules that learn transformations from unsupervised visual experience. The main theorems show that these modules provide (for every object) a signature which is invariant to local affine transformations and approximately invariant for other transformations. I also prove that,
in a broad class of hierarchical architectures, signatures remain invariant from layer to layer. The identification of these memory-based modules with complex (and simple) cells in visual areas leads to a theory of invariant recognition for the ventral stream.

In the second part, I outline a theory about hierarchical architectures that can learn invariance to transformations. I show that the memory complexity of learning affine transformations is drastically reduced in a hierarchical architecture that factorizes transformations in terms of the subgroup of translations and the subgroups of rotations and scalings. I then show how translations are automatically selected as the only learnable transformations during development by enforcing small apertures – eg small receptive fields – in the first layer.

In a third part I show that the transformations represented in each area can be optimized in terms of storage and robustness, as a consequence determining the tuning of the neurons in the area, rather independently (under normal conditions) of the statistics of natural images. I describe a model of learning that can be proved to have this property, linking in an elegant way the spectral properties of the signatures with the tuning of receptive fields in different areas. A surprising implication of these theoretical results is that the computational goals and some of the tuning properties of cells in the ventral stream may follow from symmetry properties (in the sense of physics) of the visual world through a process of unsupervised correlational learning, based on Hebbian synapses. In particular, simple and complex cells do not directly care about oriented bars: their tuning is a side effect of their role in translation invariance. Across the whole ventral stream the preferred features reported for neurons in different areas are only a symptom of the invariances computed and represented.

The results of each of the three parts stand on their own independently of each other. Together this theory-in-fieri makes several broad predictions, some of which are:

-invariance to small transformations in early areas (eg translations in V1) may underly stability of visual perception (suggested by Stu Geman);

-each cell’s tuning properties are shaped by visual experience of image transformations during developmental and adult plasticity;

-simple cells are likely to be the same population as complex cells, arising from different convergence of the Hebbian learning rule. The input to complex “complex” cells are dendritic branches with simple cell properties;

-class-specific transformations are learned and represented at the top of the ventral stream hierarchy; thus class-specific modules such as faces, places and possibly body areas should exist in IT;

-the type of transformations that are learned from visual experience depend on the size of the receptive fields and thus on the area (layer in the models) – assuming that the size increases with layers;

-the mix of transformations learned in each area influences the tuning properties of the cells oriented bars in V1+V2, radial and spiral patterns in V4 up to class specific tuning in AIT (eg face tuned cells);

-features must be discriminative and invariant: invariance to transformations is the primary determinant of the tuning of cortical neurons rather than statistics of natural images.

The theory is broadly consistent with the current version of HMAX. It explains it and extend it in terms of unsupervised learning, a broader class of transformation invariance and higher level modules. The goal of this paper is to sketch a comprehensive theory with little regard for mathematical niceties. If the theory turns out to be useful there will be scope for deep mathematics, ranging from group representation tools to wavelet theory to dynamics of learning

Coding in the Finite-Blocklength Regime: Bounds based on Laplace Integrals and their Asymptotic Approximations

In this paper we provide new compact integral expressions and associated simple asymptotic approximations for converse and achievability bounds in the finite blocklength regime. The chosen converse and random coding union bounds were taken from the recent work of Polyanskyi-Poor-Verdu, and are investigated under parallel AWGN channels, the AWGN channels, the BI-AWGN channel, and the BSC. The technique we use, which is a generalization of some recent results available from the literature, is to map the probabilities of interest into a Laplace integral, and then solve (or approximate) the integral by use of a steepest descent technique. The proposed results are particularly useful for short packet lengths, where the normal approximation may provide unreliable results.Comment: 29 pages, 10 figures. Submitted to IEEE Trans. on Information Theory. Matlab code available from http://dgt.dei.unipd.it section Download->Finite Blocklength Regim

Black Hole States: Accretion and Jet Ejection

The complex spectral and timing properties of the high-energy emission from the accretion flow in black-hole binaries, together with their strong connection to the ejection of powerful relativistic jets from the system, can be simplified and reduced to four basic states: hard, hard-intermediate, soft-intermediate and soft. Unlike other classifications, these states are based on the presence of sharp state transitions. I summarize this classification and discuss the relation between these states and the physical components contributing to the emitted flux.Comment: 8 pages, 3 figures, in "Interacting Binaries: Accretion, Evolution and Outcomes", eds. L. A. Antonelli, et al., Procs. Interacting Binaries Meeting, Cefalu, Italy, June 2004, in press (AIP

The Computational Magic of the Ventral Stream: Towards a Theory

I conjecture that the sample complexity of object recognition is mostly due to geometric image transformations and that a main goal of the ventral stream – V1, V2, V4 and IT – is to learn-and-discount image transformations. The most surprising implication of the theory emerging from these assumptions is that the computational goals and detailed properties of cells in the ventral stream follow from symmetry properties of the visual world through a process of unsupervised correlational learning.

From the assumption of a hierarchy of areas with receptive fields of increasing size the theory predicts that the size of the receptive fields determines which transformations are learned during development and then factored out during normal processing; that the transformation represented in each area determines the tuning of the neurons in the aerea, independently of the statistics of natural images; and that class-specific transformations are learned and represented at the top of the ventral stream hierarchy.

Some of the main predictions of this theory-in-fieri are:
1. the type of transformation that are learned from visual experience depend on the size (measured in terms of wavelength) and thus on the area (layer in the models) – assuming that the aperture size increases with layers;
2. the mix of transformations learned determine the properties of the receptive fields – oriented bars in V1+V2, radial and spiral patterns in V4 up to class specific tuning in AIT (eg face tuned cells);
3. invariance to small translations in V1 may underly stability of visual perception
4. class-specific modules – such as faces, places and possibly body areas – should exist in IT to process images of object classes

Spectral/timing evolution of black-hole binaries

I briefly outline the state-paradigm that has emerged from the study of black-hole binaries with RossiXTE. This is the starting point of a number of studies that address the connection between accretion and jet ejection and the physical nature of the hard spectral components in these systems.Comment: 4 pages, 2 figures.To appear in Proceedings of "X-ray Astronomy 2009: Present Status, Multi-Wavelength Approach and Future Perspectives", Bologna, Italy, September 7-11, 2009, AIP, eds. A. Comastri, M. Cappi, and L. Angelin

On the Politics of the Regulatory Reform: Econometric Evidence from the OECD Countries

This paper empirically investigates contrasting views on the politics of economic policy. Merging different databases, we test various predictions coming form different strands of literature, with the aim of explaining the cross-sectional and temporal variation in the degree of regulatory intervention and entry liberalization in the digital mobile telecommunications industry of OECD countries during the 1990's. We analyze the role of political institutions, government's types and ideological position, industry and consumers’ private interests, as well as the regulatory environment in shaping regulatory policy. We find strong evidence that all these sets of variables help to explain some degree of variability in the observed liberalization patterns among countries. Yet, political and regulatory institutions and the pressure of strong incumbent firms are found to be the most important factors. ZUSAMMENFASSUNG - (Zur Politik der Regulierungsreform: Ökonometrische Evidenz für OECD-Länder) In diesem Beitrag werden verschiedene Theorieansätze zur Wettbewerbspolitik am Beispiel der Deregulierung der Mobilfunksindustrie in OECD-Ländern empirisch getestet. Die Rolle der politischen Institutionen, der Regierungstypologie und ihrer ideologischen Positionierung im politischen Spektrum, der privaten Interessen der Industrie und Konsumenten, sowie der Struktur von Regulierungsbehörden wird anhand einer neu entwickelten Datenbank untersucht, um die beobachte Variabilität in der Deregulierungspolitik zwischen OECD-Ländern zu erklären. Es wird gezeigt, dass alle diese verschiedene Faktoren die Deregulierung der Mobilfunksindustrie in OECD-Länder während der 90er Jahren signifikant beeinflusst haben. Die Struktur der politische Institutionen und Regulierungsbehörden sowie der Druck starker Unternehmen im Markt sind jedoch die entscheidenden Faktoren des Deregulierungsprozesses.Political Economy, Regulation, Entry Liberalization, Institutions, Ideology, Private Interests, Mobile Telecommunications, OECD