CBMM Memo Series
https://hdl.handle.net/1721.1/88531
2020-09-23T02:16:22ZImplicit dynamic regularization in deep networks
https://hdl.handle.net/1721.1/126653
Implicit dynamic regularization in deep networks
Poggio, Tomaso; Liao, Qianli
Square loss has been observed to perform well in classification tasks, at least as well as crossentropy. However, a theoretical justification is lacking. Here we develop a theoretical analysis for the square loss that also complements the existing asymptotic analysis for the exponential loss.
2020-08-17T00:00:00ZOn the Capability of Neural Networks to Generalize to Unseen Category-Pose Combinations
https://hdl.handle.net/1721.1/126262
On the Capability of Neural Networks to Generalize to Unseen Category-Pose Combinations
Madan, Spandan; Henry, Timothy; Dozier, Jamell; Ho, Helen; Bhandari, Nishchal; Sasaki, Tomotake; Durand, Fredo; Pfister, Hanspeter; Boix, Xavier
Recognizing an object’s category and pose lies at the heart of visual understanding. Recent works suggest that deep neural networks (DNNs) often fail to generalize to category-pose combinations not seen during training. However, it is unclear when and how such generalization may be possible. Does the number of combinations seen during training impact generalization? Is it better to learn category and pose in separate networks, or in a single shared network? Furthermore, what are the neural mechanisms that drive the network’s generalization? In this paper, we answer these questions by analyzing state-of-the-art DNNs trained to recognize both object category and pose (position, scale, and 3D viewpoint) with quantitative control over the number of category-pose combinations seen during training. We also investigate the emergence of two types of specialized neurons that can explain generalization to unseen combinations—neurons selective to category and invariant to pose, and vice versa. We perform experiments on MNIST extended with position or scale, the iLab dataset with vehicles at different viewpoints, and a challenging new dataset for car model recognition and viewpoint estimation that we introduce in this paper, the Biased-Cars dataset. Our results demonstrate that as the number of combinations seen during training increases, networks generalize better to unseen category-pose combinations, facilitated by an increase in the selectivity and invariance of individual neurons. We find that learning category and pose in separate networks compared to a shared one leads to an increase in such selectivity and invariance, as separate networks are not forced to preserve information about both category and pose. This enables separate networks to significantly outperform shared ones at predicting unseen category-pose combinations.
2020-07-17T00:00:00ZLoss landscape: SGD can have a better view than GD
https://hdl.handle.net/1721.1/126041
Loss landscape: SGD can have a better view than GD
Poggio, Tomaso; Cooper, Yaim
Consider a loss function L = ni=1 l2i with li = f(xi) − yi, where f(x) is a deep feedforward network with R layers, no bias terms and scalar output. Assume the network is overparametrized that is, d >> n, where d is the number of parameters and n is the number of data points. The networks are assumed to interpolate the training data (e.g. the minimum of L is zero). If GD converges, it will converge to a critical point of L, namely a solution of ni=1 li∇li = 0. There are two kinds of critical points - those for which each term of the above sum vanishes individually, and those for which the expression only vanishes when all the terms are summed. The main claim in this note is that while GD can converge to both types of critical points, SGD can only converge to the first kind, which include all global minima.
2020-07-01T00:00:00ZBiologically Inspired Mechanisms for Adversarial Robustness
https://hdl.handle.net/1721.1/125981
Biologically Inspired Mechanisms for Adversarial Robustness
Vuyyuru Reddy, Manish; Banburski, Andrzej; Plant, Nishka; Poggio, Tomaso
A convolutional neural network strongly robust to adversarial perturbations at reasonable computational and performance cost has not yet been demonstrated. The primate visual ventral stream seems to be robust to small perturbations in visual stimuli but the underlying mechanisms that give rise to this robust perception are not understood. In this work, we investigate the role of two biologically plausible mechanisms in adversarial robustness. We demonstrate that the non-uniform sampling performed by the primate retina and the presence of multiple receptive fields with a range of receptive field sizes at each eccentricity improve the robustness of neural networks to small adversarial perturbations. We verify that these two mechanisms do not suffer from gradient obfuscation and study their contribution to adversarial robustness through ablation studies.
2020-06-23T00:00:00Z