arXiv subjects

Sidak Pal Singh

Publications and source records attributed to Sidak Pal Singh.

24 records · Page 2Linked to original sources

arXiv2022

Signal Propagation in Transformers: Theoretical Perspectives and the Role of Rank Collapse

Transformers have achieved remarkable success in several domains, ranging from natural language processing to computer vision. Nevertheless, it has been recently shown that stacking self-attention layers - the distinctive architectural component of Transformers - can result in rank collapse of the tokens' representations at initialization. The question of if and how rank collapse affects training is still largely unanswered, and its investigation is necessary for a more comprehensive understanding of this architecture. In this work, we shed new light on the causes and the effects of this phenomenon. First, we show that rank collapse of the tokens' representations hinders training by causing the gradients of the queries and keys to vanish at initialization. Furthermore, we provide a thorough description of the origin of rank collapse and discuss how to prevent it via an appropriate depth-dependent scaling of the residual branches. Finally, our analysis unveils that specific architectural hyperparameters affect the gradients of queries and values differently, leading to disproportionate gradient norms. This suggests an explanation for the widespread use of adaptive methods for Transformers' optimization.

cs.LG↗

arXiv2022

Phenomenology of Double Descent in Finite-Width Neural Networks

`Double descent' delineates the generalization behaviour of models depending on the regime they belong to: under- or over-parameterized. The current theoretical understanding behind the occurrence of this phenomenon is primarily based on linear and kernel regression models -- with informal parallels to neural networks via the Neural Tangent Kernel. Therefore such analyses do not adequately capture the mechanisms behind double descent in finite-width neural networks, as well as, disregard crucial components -- such as the choice of the loss function. We address these shortcomings by leveraging influence functions in order to derive suitable expressions of the population loss and its lower bound, while imposing minimal assumptions on the form of the parametric model. Our derived bounds bear an intimate connection with the spectrum of the Hessian at the optimum, and importantly, exhibit a double descent behaviour at the interpolation threshold. Building on our analysis, we further investigate how the loss function affects double descent -- and thus uncover interesting properties of neural networks and their Hessian spectra near the interpolation threshold.

stat.ML↗

arXiv2021

Analytic Insights into Structure and Rank of Neural Network Hessian Maps

The Hessian of a neural network captures parameter interactions through second-order derivatives of the loss. It is a fundamental object of study, closely tied to various problems in deep learning, including model design, optimization, and generalization. Most prior work has been empirical, typically focusing on low-rank approximations and heuristics that are blind to the network structure. In contrast, we develop theoretical tools to analyze the range of the Hessian map, providing us with a precise understanding of its rank deficiency as well as the structural reasons behind it. This yields exact formulas and tight upper bounds for the Hessian rank of deep linear networks, allowing for an elegant interpretation in terms of rank deficiency. Moreover, we demonstrate that our bounds remain faithful as an estimate of the numerical Hessian rank, for a larger class of models such as rectified and hyperbolic tangent networks. Further, we also investigate the implications of model architecture (e.g.~width, depth, bias) on the rank deficiency. Overall, our work provides novel insights into the source and extent of redundancy in overparameterized networks.

cs.LG↗

arXiv2020

WoodFisher: Efficient Second-Order Approximation for Neural Network Compression

Second-order information, in the form of Hessian- or Inverse-Hessian-vector products, is a fundamental tool for solving optimization problems. Recently, there has been significant interest in utilizing this information in the context of deep neural networks; however, relatively little is known about the quality of existing approximations in this context. Our work examines this question, identifies issues with existing approaches, and proposes a method called WoodFisher to compute a faithful and efficient estimate of the inverse Hessian. Our main application is to neural network compression, where we build on the classic Optimal Brain Damage/Surgeon framework. We demonstrate that WoodFisher significantly outperforms popular state-of-the-art methods for one-shot pruning. Further, even when iterative, gradual pruning is considered, our method results in a gain in test accuracy over the state-of-the-art approaches, for pruning popular neural networks (like ResNet-50, MobileNetV1) trained on standard image classification datasets such as ImageNet ILSVRC. We examine how our method can be extended to take into account first-order information, as well as illustrate its ability to automatically set layer-wise pruning thresholds and perform compression in the limited-data regime. The code is available at the following link, https://github.com/IST-DASLab/WoodFisher.

cs.LG↗

arXiv2020

Context Mover's Distance & Barycenters: Optimal Transport of Contexts for Building Representations

We present a framework for building unsupervised representations of entities and their compositions, where each entity is viewed as a probability distribution rather than a vector embedding. In particular, this distribution is supported over the contexts which co-occur with the entity and are embedded in a suitable low-dimensional space. This enables us to consider representation learning from the perspective of Optimal Transport and take advantage of its tools such as Wasserstein distance and barycenters. We elaborate how the method can be applied for obtaining unsupervised representations of text and illustrate the performance (quantitatively as well as qualitatively) on tasks such as measuring sentence similarity, word entailment and similarity, where we empirically observe significant gains (e.g., 4.1% relative improvement over Sent2vec, GenSen). The key benefits of the proposed approach include: (a) capturing uncertainty and polysemy via modeling the entities as distributions, (b) utilizing the underlying geometry of the particular task (with the ground cost), (c) simultaneously providing interpretability with the notion of optimal transport between contexts and (d) easy applicability on top of existing point embedding methods. The code, as well as prebuilt histograms, are available under https://github.com/context-mover/.

cs.CL↗

arXiv2019

GLOSS: Generative Latent Optimization of Sentence Representations

We propose a method to learn unsupervised sentence representations in a non-compositional manner based on Generative Latent Optimization. Our approach does not impose any assumptions on how words are to be combined into a sentence representation. We discuss a simple Bag of Words model as well as a variant that models word positions. Both are trained to reconstruct the sentence based on a latent code and our model can be used to generate text. Experiments show large improvements over the related Paragraph Vectors. Compared to uSIF, we achieve a relative improvement of 5% when trained on the same data and our method performs competitively to Sent2vec while trained on 30 times less data.

cs.CL↗