Mohsen Ben Lazreg

Louis-François Bouchard, Mohsen Ben Lazreg, Matthew Toews

We report on a novel model linking deep convolutional neural networks (CNN) to biological vision and fundamental particle physics. Information propagation in a CNN is modeled via an analogy to an optical system, where information is concentrated near a bottleneck where the 2D spatial resolution collapses about a focal point $1\times 1=1$. A 3D space $(x,y,t)$ is defined by $(x,y)$ coordinates in the image plane and CNN layer $t$, where a principal ray $(0,0,t)$ runs in the direction of information propagation through both the optical axis and the image center pixel located at $(x,y)=(0,0)$, about which the sharpest possible spatial focus is limited to a circle of confusion in the image plane. Our novel insight is to model the principal optical ray $(0,0,t)$ as geometrically equivalent to the medial vector in the positive orthant $I(x,y) \in R^{N+}$ of a $N$-channel activation space, e.g. along the greyscale (or luminance) vector $(t,t,t)$ in $RGB$ colour space. Information is thus concentrated into an energy potential $E(x,y,t)=\|I(x,y,t)\|^2$, which, particularly for bottleneck layers $t$ of generic CNNs, is highly concentrated and symmetric about the spatial origin $(0,0,t)$ and exhibits the well-known "Sombrero" potential of the boson particle. This symmetry is broken in classification, where bottleneck layers of generic pre-trained CNN models exhibit a consistent class-specific bias towards an angle $θ\in U(1)$ defined simultaneously in the image plane and in activation feature space. Initial observations validate our hypothesis from generic pre-trained CNN activation maps and a bare-bones memory-based classification scheme, with no training or tuning. Training from scratch using combined one-hot $+ U(1)$ loss improves classification for all tasks tested including ImageNet.

Louis-François Bouchard, Mohsen Ben Lazreg, Matthew Toews

This paper proposes a novel hue-like angular parameter to model the structure of deep convolutional neural network (CNN) activation space, referred to as the {\em activation hue}, for the purpose of regularizing models for more effective learning. The activation hue generalizes the notion of color hue angle in standard 3-channel RGB intensity space to $N$-channel activation space. A series of observations based on nearest neighbor indexing of activation vectors with pre-trained networks indicate that class-informative activations are concentrated about an angle $θ$ in both the $(x,y)$ image plane and in multi-channel activation space. A regularization term in the form of hue-like angular $θ$ labels is proposed to complement standard one-hot loss. Training from scratch using combined one-hot + activation hue loss improves classification performance modestly for a wide variety of classification tasks, including ImageNet.

L. Chauvin, M. Ben Lazreg, J. B. Carluer et al.

We propose a unified appearance model accounting for traditional shallow (i.e. 3D SIFT keypoints) and deep (i.e. CNN output layers) image feature representations, encoding respectively specific, localized neuroanatomical patterns and rich global information into a single indexing and classification framework. A novel Bayesian model combines shallow and deep features based on an assumption of conditional independence and validated by experiments indexing specific family members and general group categories in 3D MRI neuroimage data of 1010 subjects from the Human Connectome Project, including twins and non-twin siblings. A novel domain adaptation strategy is presented, transforming deep CNN vectors elements into binary class-informative descriptors. A GPU-based implementation of all processing is provided. State-of-the-art performance is achieved in large-scale neuroimage indexing, both in terms of computational complexity, accuracy in identifying family members and sex classification.