Search Results for author: Tomaso Poggio

Found 52 papers, 10 papers with code

Distribution of Classification Margins: Are All Data Equal?

no code implementations21 Jul 2021 Andrzej Banburski, Fernanda De La Torre, Nishka Pant, Ishana Shastri, Tomaso Poggio

Recent theoretical results show that gradient descent on deep neural networks under exponential loss functions locally maximizes classification margin, which is equivalent to minimizing the norm of the weight matrices under margin constraints.


The Effects of Image Distribution and Task on Adversarial Robustness

no code implementations21 Feb 2021 Owen Kunhardt, Arturo Deza, Tomaso Poggio

In this paper, we propose an adaptation to the area under the curve (AUC) metric to measure the adversarial robustness of a model over a particular $\epsilon$-interval $[\epsilon_0, \epsilon_1]$ (interval of adversarial perturbation strengths) that facilitates unbiased comparisons across models when they have different initial $\epsilon_0$ performance.

Object Recognition

Explicit regularization and implicit bias in deep network classifiers trained with the square loss

no code implementations31 Dec 2020 Tomaso Poggio, Qianli Liao

Deep ReLU networks trained with the square loss have been observed to perform well in classification tasks.

CUDA-Optimized real-time rendering of a Foveated Visual System

1 code implementation15 Dec 2020 Elian Malkin, Arturo Deza, Tomaso Poggio

The spatially-varying field of the human visual system has recently received a resurgence of interest with the development of virtual reality (VR) and neural networks.

Foveation Virtual Reality

Biologically Inspired Mechanisms for Adversarial Robustness

1 code implementation NeurIPS 2020 Manish V. Reddy, Andrzej Banburski, Nishka Pant, Tomaso Poggio

A convolutional neural network strongly robust to adversarial perturbations at reasonable computational and performance cost has not yet been demonstrated.

For interpolating kernel machines, minimizing the norm of the ERM solution minimizes stability

no code implementations28 Jun 2020 Akshay Rangamani, Lorenzo Rosasco, Tomaso Poggio

We study the average $\mbox{CV}_{loo}$ stability of kernel ridge-less regression and derive corresponding risk bounds.

Hierarchically Compositional Tasks and Deep Convolutional Networks

no code implementations24 Jun 2020 Arturo Deza, Qianli Liao, Andrzej Banburski, Tomaso Poggio

For object recognition we find, as expected, that scrambling does not affect the performance of shallow or deep fully connected networks contrary to the out-performance of convolutional networks.

Hierarchical structure Object Recognition

Double descent in the condition number

no code implementations12 Dec 2019 Tomaso Poggio, Gil Kur, Andrzej Banburski

In solving a system of $n$ linear equations in $d$ variables $Ax=b$, the condition number of the $n, d$ matrix $A$ measures how much errors in the data $b$ affect the solution $x$.

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization

no code implementations25 Aug 2019 Tomaso Poggio, Andrzej Banburski, Qianli Liao

In approximation theory both shallow and deep networks have been shown to approximate any continuous functions on a bounded domain at the expense of an exponential number of parameters (exponential in the dimensionality of the function).

Theory III: Dynamics and Generalization in Deep Networks

no code implementations12 Mar 2019 Andrzej Banburski, Qianli Liao, Brando Miranda, Lorenzo Rosasco, Fernanda De La Torre, Jack Hidary, Tomaso Poggio

In particular, gradient descent induces a dynamics of the normalized weights which converge for $t \to \infty$ to an equilibrium which corresponds to a minimum norm (or maximum margin) solution.

Biologically-plausible learning algorithms can scale to large datasets

2 code implementations ICLR 2019 Will Xiao, Honglin Chen, Qianli Liao, Tomaso Poggio

These results complement the study by Bartunov et al. (2018), and establish a new benchmark for future biologically plausible learning algorithms on more difficult datasets and more complex architectures.

Biologically-plausible Training

A Surprising Linear Relationship Predicts Test Performance in Deep Networks

2 code implementations25 Jul 2018 Qianli Liao, Brando Miranda, Andrzej Banburski, Jack Hidary, Tomaso Poggio

Given two networks with the same training loss on a dataset, when would they have drastically different test losses and errors?

General Classification Generalization Bounds

Theory IIIb: Generalization in Deep Networks

no code implementations29 Jun 2018 Tomaso Poggio, Qianli Liao, Brando Miranda, Andrzej Banburski, Xavier Boix, Jack Hidary

Here we prove a similar result for nonlinear multilayer DNNs near zero minima of the empirical loss.

Approximate inference with Wasserstein gradient flows

no code implementations12 Jun 2018 Charlie Frogner, Tomaso Poggio

We present a novel approximate inference method for diffusion processes, based on the Wasserstein gradient flow formulation of the diffusion.

An analysis of training and generalization errors in shallow and deep networks

no code implementations17 Feb 2018 Hrushikesh Mhaskar, Tomaso Poggio

We argue that the minimal expected value of the square loss is inappropriate to measure the generalization error in approximation of compositional functions in order to take full advantage of the compositional structure.

Theory of Deep Learning IIb: Optimization Properties of SGD

no code implementations7 Jan 2018 Chiyuan Zhang, Qianli Liao, Alexander Rakhlin, Brando Miranda, Noah Golowich, Tomaso Poggio

In Theory IIb we characterize with a mix of theory and experiments the optimization of deep convolutional networks by Stochastic Gradient Descent.

Theory of Deep Learning III: explaining the non-overfitting puzzle

no code implementations30 Dec 2017 Tomaso Poggio, Kenji Kawaguchi, Qianli Liao, Brando Miranda, Lorenzo Rosasco, Xavier Boix, Jack Hidary, Hrushikesh Mhaskar

In this note, we show that the dynamics associated to gradient descent minimization of nonlinear networks is topologically equivalent, near the asymptotically stable minima of the empirical error, to linear gradient system in a quadratic potential with a degenerate (for square loss) or almost degenerate (for logistic or crossentropy loss) Hessian.

General Classification

Fisher-Rao Metric, Geometry, and Complexity of Neural Networks

1 code implementation5 Nov 2017 Tengyuan Liang, Tomaso Poggio, Alexander Rakhlin, James Stokes

We study the relationship between geometry and capacity measures for deep neural networks from an invariance viewpoint.

Pruning Convolutional Neural Networks for Image Instance Retrieval

no code implementations18 Jul 2017 Gaurav Manek, Jie Lin, Vijay Chandrasekhar, Ling-Yu Duan, Sateesh Giduthuri, Xiao-Li Li, Tomaso Poggio

In this work, we focus on the problem of image instance retrieval with deep descriptors extracted from pruned Convolutional Neural Networks (CNN).

Image Instance Retrieval

Do Deep Neural Networks Suffer from Crowding?

2 code implementations NeurIPS 2017 Anna Volokitin, Gemma Roig, Tomaso Poggio

Also, for all tested networks, when trained on targets in isolation, we find that recognition accuracy of the networks decreases the closer the flankers are to the target and the more flankers there are.

Object Recognition

Theory II: Landscape of the Empirical Risk in Deep Learning

no code implementations28 Mar 2017 Qianli Liao, Tomaso Poggio

Previous theoretical work on deep learning and neural network optimization tend to focus on avoiding saddle points and local minima.

Compression of Deep Neural Networks for Image Instance Retrieval

no code implementations18 Jan 2017 Vijay Chandrasekhar, Jie Lin, Qianli Liao, Olivier Morère, Antoine Veillard, Ling-Yu Duan, Tomaso Poggio

One major drawback of CNN-based {\it global descriptors} is that uncompressed deep neural network models require hundreds of megabytes of storage making them inconvenient to deploy in mobile applications or in custom hardware.

Image Instance Retrieval Model Compression +1

Why and When Can Deep -- but Not Shallow -- Networks Avoid the Curse of Dimensionality: a Review

no code implementations2 Nov 2016 Tomaso Poggio, Hrushikesh Mhaskar, Lorenzo Rosasco, Brando Miranda, Qianli Liao

The paper characterizes classes of functions for which deep learning can be exponentially better than shallow learning.

Streaming Normalization: Towards Simpler and More Biologically-plausible Normalizations for Online and Recurrent Learning

no code implementations19 Oct 2016 Qianli Liao, Kenji Kawaguchi, Tomaso Poggio

We systematically explored a spectrum of normalization algorithms related to Batch Normalization (BN) and propose a generalized formulation that simultaneously solves two major limitations of BN: (1) online learning and (2) recurrent learning.

Deep vs. shallow networks : An approximation theory perspective

no code implementations10 Aug 2016 Hrushikesh Mhaskar, Tomaso Poggio

The paper announces new results for a non-smooth activation function - the ReLU function - used in present-day neural networks, as well as for the Gaussian networks.

View-tolerant face recognition and Hebbian learning imply mirror-symmetric neural tuning to head orientation

no code implementations5 Jun 2016 Joel Z. Leibo, Qianli Liao, Winrich Freiwald, Fabio Anselmi, Tomaso Poggio

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 relatively robust against identity-preserving transformations like depth-rotations.

Face Recognition Object Recognition

Bridging the Gaps Between Residual Learning, Recurrent Neural Networks and Visual Cortex

1 code implementation13 Apr 2016 Qianli Liao, Tomaso Poggio

We discuss relations between Residual Networks (ResNet), Recurrent Neural Networks (RNNs) and the primate visual cortex.

Nested Invariance Pooling and RBM Hashing for Image Instance Retrieval

no code implementations15 Mar 2016 Olivier Morère, Jie Lin, Antoine Veillard, Vijay Chandrasekhar, Tomaso Poggio

The first one is Nested Invariance Pooling (NIP), a method inspired from i-theory, a mathematical theory for computing group invariant transformations with feed-forward neural networks.

Image Instance Retrieval Translation

Learning Functions: When Is Deep Better Than Shallow

no code implementations3 Mar 2016 Hrushikesh Mhaskar, Qianli Liao, Tomaso Poggio

While the universal approximation property holds both for hierarchical and shallow networks, we prove that deep (hierarchical) networks can approximate the class of compositional functions with the same accuracy as shallow networks but with exponentially lower number of training parameters as well as VC-dimension.

Group Invariant Deep Representations for Image Instance Retrieval

no code implementations9 Jan 2016 Olivier Morère, Antoine Veillard, Jie Lin, Julie Petta, Vijay Chandrasekhar, Tomaso Poggio

Based on a thorough empirical evaluation using several publicly available datasets, we show that our method is able to significantly and consistently improve retrieval results every time a new type of invariance is incorporated.

Dimensionality Reduction Image Classification +2

Foveation-based Mechanisms Alleviate Adversarial Examples

no code implementations19 Nov 2015 Yan Luo, Xavier Boix, Gemma Roig, Tomaso Poggio, Qi Zhao

To see this, first, we report results in ImageNet that lead to a revision of the hypothesis that adversarial perturbations are a consequence of CNNs acting as a linear classifier: CNNs act locally linearly to changes in the image regions with objects recognized by the CNN, and in other regions the CNN may act non-linearly.

Foveation Translation

How Important is Weight Symmetry in Backpropagation?

2 code implementations17 Oct 2015 Qianli Liao, Joel Z. Leibo, Tomaso Poggio

Gradient backpropagation (BP) requires symmetric feedforward and feedback connections -- the same weights must be used for forward and backward passes.

 Ranked #1 on Handwritten Digit Recognition on MNIST (PERCENTAGE ERROR metric)

Handwritten Digit Recognition Image Classification

Holographic Embeddings of Knowledge Graphs

3 code implementations16 Oct 2015 Maximilian Nickel, Lorenzo Rosasco, Tomaso Poggio

Learning embeddings of entities and relations is an efficient and versatile method to perform machine learning on relational data such as knowledge graphs.

Knowledge Graphs Link Prediction +1

Deep Convolutional Networks are Hierarchical Kernel Machines

no code implementations5 Aug 2015 Fabio Anselmi, Lorenzo Rosasco, Cheston Tan, Tomaso Poggio

In i-theory a typical layer of a hierarchical architecture consists of HW modules pooling the dot products of the inputs to the layer with the transformations of a few templates under a group.

Learning with Group Invariant Features: A Kernel Perspective

no code implementations NeurIPS 2015 Youssef Mroueh, Stephen Voinea, Tomaso Poggio

Our analysis bridges invariant feature learning with kernel methods, as we show that this feature map defines an expected Haar integration kernel that is invariant to the specified group action.

Convex Learning of Multiple Tasks and their Structure

1 code implementation13 Apr 2015 Carlo Ciliberto, Youssef Mroueh, Tomaso Poggio, Lorenzo Rosasco

In this context a fundamental question is how to incorporate the tasks structure in the learning problem. We tackle this question by studying a general computational framework that allows to encode a-priori knowledge of the tasks structure in the form of a convex penalty; in this setting a variety of previously proposed methods can be recovered as special cases, including linear and non-linear approaches.

Multi-Task Learning

On Invariance and Selectivity in Representation Learning

no code implementations19 Mar 2015 Fabio Anselmi, Lorenzo Rosasco, Tomaso Poggio

We discuss data representation which can be learned automatically from data, are invariant to transformations, and at the same time selective, in the sense that two points have the same representation only if they are one the transformation of the other.

Representation Learning

Unsupervised learning of clutter-resistant visual representations from natural videos

no code implementations12 Sep 2014 Qianli Liao, Joel Z. Leibo, Tomaso Poggio

Populations of neurons in inferotemporal cortex (IT) maintain an explicit code for object identity that also tolerates transformations of object appearance e. g., position, scale, viewing angle [1, 2, 3].

Face Recognition

Learning An Invariant Speech Representation

no code implementations16 Jun 2014 Georgios Evangelopoulos, Stephen Voinea, Chiyuan Zhang, Lorenzo Rosasco, Tomaso Poggio

Recognition of speech, and in particular the ability to generalize and learn from small sets of labelled examples like humans do, depends on an appropriate representation of the acoustic input.

General Classification Vowel Classification

Neural tuning size is a key factor underlying holistic face processing

no code implementations15 Jun 2014 Cheston Tan, Tomaso Poggio

The main aim of this work is to further the fundamental understanding of what causes the visual processing of faces to be different from that of objects.

Face Recognition

Computational role of eccentricity dependent cortical magnification

no code implementations6 Jun 2014 Tomaso Poggio, Jim Mutch, Leyla Isik

From the slope of the inverse of the magnification factor, M-theory predicts a cortical "fovea" in V1 in the order of $40$ by $40$ basic units at each receptive field size -- corresponding to a foveola of size around $26$ minutes of arc at the highest resolution, $\approx 6$ degrees at the lowest resolution.


A Deep Representation for Invariance And Music Classification

no code implementations1 Apr 2014 Chiyuan Zhang, Georgios Evangelopoulos, Stephen Voinea, Lorenzo Rosasco, Tomaso Poggio

We present the main theoretical and computational aspects of a framework for unsupervised learning of invariant audio representations, empirically evaluated on music genre classification.

Classification General Classification +3

Neural representation of action sequences: how far can a simple snippet-matching model take us?

no code implementations NeurIPS 2013 Cheston Tan, Jedediah M. Singer, Thomas Serre, David Sheinberg, Tomaso Poggio

The macaque Superior Temporal Sulcus (STS) is a brain area that receives and integrates inputs from both the ventral and dorsal visual processing streams (thought to specialize in form and motion processing respectively).

Learning invariant representations and applications to face verification

no code implementations NeurIPS 2013 Qianli Liao, Joel Z. Leibo, Tomaso Poggio

Next, we apply the model to non-affine transformations: as expected, it performs well on face verification tasks requiring invariance to the relatively smooth transformations of 3D rotation-in-depth and changes in illumination direction.

Face Verification Object Recognition

Unsupervised Learning of Invariant Representations in Hierarchical Architectures

no code implementations17 Nov 2013 Fabio Anselmi, Joel Z. Leibo, Lorenzo Rosasco, Jim Mutch, Andrea Tacchetti, Tomaso Poggio

It also suggests that the main computational goal of the ventral stream of visual cortex is to provide a hierarchical representation of new objects/images which is invariant to transformations, stable, and discriminative for recognition---and that this representation may be continuously learned in an unsupervised way during development and visual experience.

Object Recognition Speech Recognition

Can a biologically-plausible hierarchy effectively replace face detection, alignment, and recognition pipelines?

no code implementations16 Nov 2013 Qianli Liao, Joel Z. Leibo, Youssef Mroueh, Tomaso Poggio

The standard approach to unconstrained face recognition in natural photographs is via a detection, alignment, recognition pipeline.

Face Detection Face Recognition

On Learnability, Complexity and Stability

no code implementations24 Mar 2013 Silvia Villa, Lorenzo Rosasco, Tomaso Poggio

We consider the fundamental question of learnability of a hypotheses class in the supervised learning setting and in the general learning setting introduced by Vladimir Vapnik.

Multiclass Learning with Simplex Coding

no code implementations NeurIPS 2012 Youssef Mroueh, Tomaso Poggio, Lorenzo Rosasco, Jean-Jeacques Slotine

In this paper we dicuss a novel framework for multiclass learning, defined by a suitable coding/decoding strategy, namely the simplex coding, that allows to generalize to multiple classes a relaxation approach commonly used in binary classification.

General Classification

Why The Brain Separates Face Recognition From Object Recognition

no code implementations NeurIPS 2011 Joel Z. Leibo, Jim Mutch, Tomaso Poggio

Many studies have uncovered evidence that visual cortex contains specialized regions involved in processing faces but not other object classes.

Face Identification Face Recognition +1

On Invariance in Hierarchical Models

no code implementations NeurIPS 2009 Jake Bouvrie, Lorenzo Rosasco, Tomaso Poggio

A goal of central importance in the study of hierarchical models for object recognition -- and indeed the visual cortex -- is that of understanding quantitatively the trade-off between invariance and selectivity, and how invariance and discrimination properties contribute towards providing an improved representation useful for learning from data.

Object Recognition

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