Dynamics in Deep Classifiers Trained with the Square Loss: Normalization, Low Rank, Neural Collapse, and Generalization Bounds.

We overview several properties-old and new-of training overparameterized deep networks under the square loss. We first consider a model of the dynamics of gradient flow under the square loss in deep homogeneous rectified linear unit networks. We study the convergence to a solution with the absolute minimum , which is the product of the Frobenius norms of each layer weight matrix, when normalization by Lagrange multipliers is used together with weight decay under different forms of gradient descent.

Theoretical issues in deep networks.

While deep learning is successful in a number of applications, it is not yet well understood theoretically. A theoretical characterization of deep learning should answer questions about their approximation power, the dynamics of optimization, and good out-of-sample performance, despite overparameterization and the absence of explicit regularization. We review our recent results toward this goal.

Complexity control by gradient descent in deep networks.

Overparametrized deep networks predict well, despite the lack of an explicit complexity control during training, such as an explicit regularization term. For exponential-type loss functions, we solve this puzzle by showing an effective regularization effect of gradient descent in terms of the normalized weights that are relevant for classification.

Scale and translation-invariance for novel objects in human vision.

Though the range of invariance in recognition of novel objects is a basic aspect of human vision, its characterization has remained surprisingly elusive. Here we report tolerance to scale and position changes in one-shot learning by measuring recognition accuracy of Korean letters presented in a flash to non-Korean subjects who had no previous experience with Korean letters. We found that humans have significant scale-invariance after only a single exposure to a novel object.

Invariant Recognition Shapes Neural Representations of Visual Input.

Recognizing the people, objects, and actions in the world around us is a crucial aspect of human perception that allows us to plan and act in our environment. Remarkably, our proficiency in recognizing semantic categories from visual input is unhindered by transformations that substantially alter their appearance (e.g.

Invariant recognition drives neural representations of action sequences.

Recognizing the actions of others from visual stimuli is a crucial aspect of human perception that allows individuals to respond to social cues. Humans are able to discriminate between similar actions despite transformations, like changes in viewpoint or actor, that substantially alter the visual appearance of a scene. This ability to generalize across complex transformations is a hallmark of human visual intelligence.

A fast, invariant representation for human action in the visual system.

Humans can effortlessly recognize others' actions in the presence of complex transformations, such as changes in viewpoint. Several studies have located the regions in the brain involved in invariant action recognition; however, the underlying neural computations remain poorly understood. We use magnetoencephalography decoding and a data set of well-controlled, naturalistic videos of five actions (run, walk, jump, eat, drink) performed by different actors at different viewpoints to study the computational steps used to recognize actions across complex transformations.

View-Tolerant Face Recognition and Hebbian Learning Imply Mirror-Symmetric Neural Tuning to Head Orientation.

The primate brain contains a hierarchy of visual areas, dubbed the ventral stream, which rapidly computes object representations that are both specific for object identity and robust against identity-preserving transformations, like depth rotations [1, 2]. Current computational models of object recognition, including recent deep-learning networks, generate these properties through a hierarchy of alternating selectivity-increasing filtering and tolerance-increasing pooling operations, similar to simple-complex cells operations [3-6]. Here, we prove that a class of hierarchical architectures and a broad set of biologically plausible learning rules generate approximate invariance to identity-preserving transformations at the top level of the processing hierarchy.

Neural Tuning Size in a Model of Primate Visual Processing Accounts for Three Key Markers of Holistic Face Processing.

Faces are an important and unique class of visual stimuli, and have been of interest to neuroscientists for many years. Faces are known to elicit certain characteristic behavioral markers, collectively labeled "holistic processing", while non-face objects are not processed holistically. However, little is known about the underlying neural mechanisms.

The Invariance Hypothesis Implies Domain-Specific Regions in Visual Cortex.

Is visual cortex made up of general-purpose information processing machinery, or does it consist of a collection of specialized modules? If prior knowledge, acquired from learning a set of objects is only transferable to new objects that share properties with the old, then the recognition system's optimal organization must be one containing specialized modules for different object classes. Our analysis starts from a premise we call the invariance hypothesis: that the computational goal of the ventral stream is to compute an invariant-to-transformations and discriminative signature for recognition. The key condition enabling approximate transfer of invariance without sacrificing discriminability turns out to be that the learned and novel objects transform similarly.

The dynamics of invariant object recognition in the human visual system.

The human visual system can rapidly recognize objects despite transformations that alter their appearance. The precise timing of when the brain computes neural representations that are invariant to particular transformations, however, has not been mapped in humans. Here we employ magnetoencephalography decoding analysis to measure the dynamics of size- and position-invariant visual information development in the ventral visual stream.

Vision: are models of object recognition catching up with the brain?

Object recognition has been a central yet elusive goal of computational vision. For many years, computer performance seemed highly deficient and unable to emulate the basic capabilities of the human recognition system. Over the past decade or so, computer scientists and neuroscientists have developed algorithms and systems-and models of visual cortex-that have come much closer to human performance in visual identification and categorization.

The Levels of Understanding framework, revised.

I discuss the "levels of understanding" framework described in Marr's Vision and propose an updated version to capture the changes in computation and neuroscience over the last 30 years.

Learning and disrupting invariance in visual recognition with a temporal association rule.

Learning by temporal association rules such as Foldiak's trace rule is an attractive hypothesis that explains the development of invariance in visual recognition. Consistent with these rules, several recent experiments have shown that invariance can be broken at both the psychophysical and single cell levels. We show (1) that temporal association learning provides appropriate invariance in models of object recognition inspired by the visual cortex, (2) that we can replicate the "invariance disruption" experiments using these models with a temporal association learning rule to develop and maintain invariance, and (3) that despite dramatic single cell effects, a population of cells is very robust to these disruptions.

Object decoding with attention in inferior temporal cortex.

Recognizing objects in cluttered scenes requires attentional mechanisms to filter out distracting information. Previous studies have found several physiological correlates of attention in visual cortex, including larger responses for attended objects. However, it has been unclear whether these attention-related changes have a large impact on information about objects at the neural population level.

Automated home-cage behavioural phenotyping of mice.

Neurobehavioural analysis of mouse phenotypes requires the monitoring of mouse behaviour over long periods of time. In this study, we describe a trainable computer vision system enabling the automated analysis of complex mouse behaviours. We provide software and an extensive manually annotated video database used for training and testing the system.

Prefrontal cortex activity during flexible categorization.

Items are categorized differently depending on the behavioral context. For instance, a lion can be categorized as an African animal or a type of cat. We recorded lateral prefrontal cortex (PFC) neural activity while monkeys switched between categorizing the same image set along two different category schemes with orthogonal boundaries.

What and where: a Bayesian inference theory of attention.

In the theoretical framework of this paper, attention is part of the inference process that solves the visual recognition problem of what is where. The theory proposes a computational role for attention and leads to a model that predicts some of its main properties at the level of psychophysics and physiology. In our approach, the main goal of the visual system is to infer the identity and the position of objects in visual scenes: spatial attention emerges as a strategy to reduce the uncertainty in shape information while feature-based attention reduces the uncertainty in spatial information.

Dynamic population coding of category information in inferior temporal and prefrontal cortex.

Most electrophysiology studies analyze the activity of each neuron separately. While such studies have given much insight into properties of the visual system, they have also potentially overlooked important aspects of information coded in changing patterns of activity that are distributed over larger populations of neurons. In this work, we apply a population decoding method to better estimate what information is available in neuronal ensembles and how this information is coded in dynamic patterns of neural activity in data recorded from inferior temporal cortex (ITC) and prefrontal cortex (PFC) as macaque monkeys engaged in a delayed match-to-category task.

A canonical neural circuit for cortical nonlinear operations.

A few distinct cortical operations have been postulated over the past few years, suggested by experimental data on nonlinear neural response across different areas in the cortex. Among these, the energy model proposes the summation of quadrature pairs following a squaring nonlinearity in order to explain phase invariance of complex V1 cells. The divisive normalization model assumes a gain-controlling, divisive inhibition to explain sigmoid-like response profiles within a pool of neurons.

Trade-off between object selectivity and tolerance in monkey inferotemporal cortex.

Object recognition requires both selectivity among different objects and tolerance to vastly different retinal images of the same object, resulting from natural variation in (e.g.) position, size, illumination, and clutter.

A quantitative theory of immediate visual recognition.

Human and non-human primates excel at visual recognition tasks. The primate visual system exhibits a strong degree of selectivity while at the same time being robust to changes in the input image. We have developed a quantitative theory to account for the computations performed by the feedforward path in the ventral stream of the primate visual cortex.

A model of V4 shape selectivity and invariance.

Object recognition in primates is mediated by the ventral visual pathway and is classically described as a feedforward hierarchy of increasingly sophisticated representations. Neurons in macaque monkey area V4, an intermediate stage along the ventral pathway, have been shown to exhibit selectivity to complex boundary conformation and invariance to spatial translation. How could such a representation be derived from the signals in lower visual areas such as V1? We show that a quantitative model of hierarchical processing, which is part of a larger model of object recognition in the ventral pathway, provides a plausible mechanism for the translation-invariant shape representation observed in area V4.