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Sashank Reddi

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9 papers

1 author row

NeurIPS Conference 2023 Conference Paper

What is the Inductive Bias of Flatness Regularization? A Study of Deep Matrix Factorization Models

Khashayar Gatmiry
Zhiyuan Li
Tengyu Ma
Sashank Reddi
Stefanie Jegelka
Ching-Yao Chuang

Recent works on over-parameterized neural networks have shown that the stochasticity in optimizers has the implicit regularization effect of minimizing the sharpness of the loss function (in particular, the trace of its Hessian) over the family zero-loss solutions. More explicit forms of flatness regularization also empirically improve the generalization performance. However, it remains unclear why and when flatness regularization leads to better generalization. This work takes the first step towards understanding the inductive bias of the minimum trace of the Hessian solutions in an important setting: learning deep linear networks from linear measurements, also known as \emph{deep matrix factorization}. We show that with the standard Restricted Isometry Property (RIP) on the measurements, minimizing the trace of Hessian is approximately equivalent to minimizing the Schatten 1-norm of the corresponding end-to-end matrix parameters (i. e. , the product of all layer matrices), which in turn leads to better generalization.

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NeurIPS Conference 2021 Conference Paper

Breaking the centralized barrier for cross-device federated learning

Sai Praneeth Karimireddy
Martin Jaggi
Satyen Kale
Mehryar Mohri
Sashank Reddi
Sebastian U. Stich
Ananda Theertha Suresh

Federated learning (FL) is a challenging setting for optimization due to the heterogeneity of the data across different clients which gives rise to the client drift phenomenon. In fact, obtaining an algorithm for FL which is uniformly better than simple centralized training has been a major open problem thus far. In this work, we propose a general algorithmic framework, Mime, which i) mitigates client drift and ii) adapts arbitrary centralized optimization algorithms such as momentum and Adam to the cross-device federated learning setting. Mime uses a combination of control-variates and server-level statistics (e. g. momentum) at every client-update step to ensure that each local update mimics that of the centralized method run on iid data. We prove a reduction result showing that Mime can translate the convergence of a generic algorithm in the centralized setting into convergence in the federated setting. Further, we show that when combined with momentum based variance reduction, Mime is provably faster than any centralized method--the first such result. We also perform a thorough experimental exploration of Mime's performance on real world datasets.

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NeurIPS Conference 2021 Conference Paper

Efficient Training of Retrieval Models using Negative Cache

Erik Lindgren
Sashank Reddi
Ruiqi Guo
Sanjiv Kumar

Factorized models, such as two tower neural network models, are widely used for scoring (query, document) pairs in information retrieval tasks. These models are typically trained by optimizing the model parameters to score relevant positive" pairs higher than the irrelevant negative" ones. While a large set of negatives typically improves the model performance, limited computation and memory budgets place constraints on the number of negatives used during training. In this paper, we develop a novel negative sampling technique for accelerating training with softmax cross-entropy loss. By using cached (possibly stale) item embeddings, our technique enables training with a large pool of negatives with reduced memory and computation. We also develop a streaming variant of our algorithm geared towards very large datasets. Furthermore, we establish a theoretical basis for our approach by showing that updating a very small fraction of the cache at each iteration can still ensure fast convergence. Finally, we experimentally validate our approach and show that it is efficient and compares favorably with more complex, state-of-the-art approaches.

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NeurIPS Conference 2020 Conference Paper

O(n) Connections are Expressive Enough: Universal Approximability of Sparse Transformers

Chulhee Yun
Yin-Wen Chang
Srinadh Bhojanapalli
Ankit Singh Rawat
Sashank Reddi
Sanjiv Kumar

Recently, Transformer networks have redefined the state of the art in many NLP tasks. However, these models suffer from quadratic computational cost in the input sequence length $n$ to compute pairwise attention in each layer. This has prompted recent research into sparse Transformers that sparsify the connections in the attention layers. While empirically promising for long sequences, fundamental questions remain unanswered: Can sparse Transformers approximate any arbitrary sequence-to-sequence function, similar to their dense counterparts? How does the sparsity pattern and the sparsity level affect their performance? In this paper, we address these questions and provide a unifying framework that captures existing sparse attention models. We propose sufficient conditions under which we prove that a sparse attention model can universally approximate any sequence-to-sequence function. Surprisingly, our results show that sparse Transformers with only $O(n)$ connections per attention layer can approximate the same function class as the dense model with $n^2$ connections. Lastly, we present experiments comparing different patterns/levels of sparsity on standard NLP tasks.

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NeurIPS Conference 2020 Conference Paper

Why are Adaptive Methods Good for Attention Models?

Jingzhao Zhang
Sai Praneeth Karimireddy
Andreas Veit
Seungyeon Kim
Sashank Reddi
Sanjiv Kumar
Suvrit Sra

While stochastic gradient descent (SGD) is still the de facto algorithm in deep learning, adaptive methods like Clipped SGD/Adam have been observed to outperform SGD across important tasks, such as attention models. The settings under which SGD performs poorly in comparison to adaptive methods are not well understood yet. In this paper, we provide empirical and theoretical evidence that a heavy-tailed distribution of the noise in stochastic gradients is one cause of SGD's poor performance. We provide the first tight upper and lower convergence bounds for adaptive gradient methods under heavy-tailed noise. Further, we demonstrate how gradient clipping plays a key role in addressing heavy-tailed gradient noise. Subsequently, we show how clipping can be applied in practice by developing an adaptive coordinate-wise clipping algorithm (ACClip) and demonstrate its superior performance on BERT pretraining and finetuning tasks.

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NeurIPS Conference 2019 Conference Paper

Breaking the Glass Ceiling for Embedding-Based Classifiers for Large Output Spaces

Chuan Guo
Ali Mousavi
Xiang Wu
Daniel Holtmann-Rice
Satyen Kale
Sashank Reddi
Sanjiv Kumar

In extreme classification settings, embedding-based neural network models are currently not competitive with sparse linear and tree-based methods in terms of accuracy. Most prior works attribute this poor performance to the low-dimensional bottleneck in embedding-based methods. In this paper, we demonstrate that theoretically there is no limitation to using low-dimensional embedding-based methods, and provide experimental evidence that overfitting is the root cause of the poor performance of embedding-based methods. These findings motivate us to investigate novel data augmentation and regularization techniques to mitigate overfitting. To this end, we propose GLaS, a new regularizer for embedding-based neural network approaches. It is a natural generalization from the graph Laplacian and spread-out regularizers, and empirically it addresses the drawback of each regularizer alone when applied to the extreme classification setup. With the proposed techniques, we attain or improve upon the state-of-the-art on most widely tested public extreme classification datasets with hundreds of thousands of labels.

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NeurIPS Conference 2019 Conference Paper

Multilabel reductions: what is my loss optimising?

Aditya Menon
Ankit Singh Rawat
Sashank Reddi
Sanjiv Kumar

Multilabel classification is a challenging problem arising in applications ranging from information retrieval to image tagging. A popular approach to this problem is to employ a reduction to a suitable series of binary or multiclass problems (e. g. , computing a softmax based cross-entropy over the relevant labels). While such methods have seen empirical success, less is understood about how well they approximate two fundamental performance measures: precision@$k$ and recall@$k$. In this paper, we study five commonly used reductions, including the one-versus-all reduction, a reduction to multiclass classification, and normalised versions of the same, wherein the contribution of each instance is normalised by the number of relevant labels. Our main result is a formal justification of each reduction: we explicate their underlying risks, and show they are each consistent with respect to either precision or recall. Further, we show that in general no reduction can be optimal for both measures. We empirically validate our results, demonstrating scenarios where normalised reductions yield recall gains over unnormalised counterparts.

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NeurIPS Conference 2018 Conference Paper

Adaptive Methods for Nonconvex Optimization

Manzil Zaheer
Sashank Reddi
Devendra Sachan
Satyen Kale
Sanjiv Kumar

Adaptive gradient methods that rely on scaling gradients down by the square root of exponential moving averages of past squared gradients, such RMSProp, Adam, Adadelta have found wide application in optimizing the nonconvex problems that arise in deep learning. However, it has been recently demonstrated that such methods can fail to converge even in simple convex optimization settings. In this work, we provide a new analysis of such methods applied to nonconvex stochastic optimization problems, characterizing the effect of increasing minibatch size. Our analysis shows that under this scenario such methods do converge to stationarity up to the statistical limit of variance in the stochastic gradients (scaled by a constant factor). In particular, our result implies that increasing minibatch sizes enables convergence, thus providing a way to circumvent the non-convergence issues. Furthermore, we provide a new adaptive optimization algorithm, Yogi, which controls the increase in effective learning rate, leading to even better performance with similar theoretical guarantees on convergence. Extensive experiments show that Yogi with very little hyperparameter tuning outperforms methods such as Adam in several challenging machine learning tasks.

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AAAI Conference 2015 Conference Paper

Doubly Robust Covariate Shift Correction

Sashank Reddi
Barnabas Poczos
Alex Smola

Covariate shift correction allows one to perform supervised learning even when the distribution of the covariates on the training set does not match that on the test set. This is achieved by re-weighting observations. Such a strategy removes bias, potentially at the expense of greatly increased variance. We propose a simple strategy for removing bias while retaining small variance. It uses a biased, low variance estimate as a prior and corrects the final estimate relative to the prior. We prove that this yields an efficient estimator and demonstrate good experimental performance.

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