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Harsh Mehta

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11 papers

2 author rows

NeurIPS Conference 2024 Conference Paper

The Road Less Scheduled

Aaron Defazio
Xingyu Yang
Harsh Mehta
Konstantin Mishchenko
Ahmed Khaled
Ashok Cutkosky

Existing learning rate schedules that do not require specification of the optimization stopping step $T$ are greatly out-performed by learning rate schedules that depend on $T$. We propose an approach that avoids the need for this stopping time by eschewing the use of schedules entirely, while exhibiting state-of-the-art performance compared to schedules across a wide family of problems ranging from convex problems to large-scale deep learning problems. Our Schedule-Free approach introduces no additional hyper-parameters over standard optimizers with momentum. Our method is a direct consequence of a new theory we develop that unifies scheduling and iterate averaging. An open source implementation of our method is available at https: //github. com/facebookresearch/schedule_free. Schedule-Free AdamW is the core algorithm behind our winning entry to the MLCommons 2024 AlgoPerf Algorithmic Efficiency Challenge Self-Tuning track.

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TMLR Journal 2023 Journal Article

Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models

Aarohi Srivastava
Abhinav Rastogi
Abhishek Rao
Abu Awal Md Shoeb
Abubakar Abid
Adam Fisch
Adam R. Brown
Adam Santoro

Language models demonstrate both quantitative improvement and new qualitative capabilities with increasing scale. Despite their potentially transformative impact, these new capabilities are as yet poorly characterized. In order to inform future research, prepare for disruptive new model capabilities, and ameliorate socially harmful effects, it is vital that we understand the present and near-future capabilities and limitations of language models. To address this challenge, we introduce the Beyond the Imitation Game benchmark (BIG- bench). BIG-bench currently consists of 204 tasks, contributed by 450 authors across 132 institutions. Task topics are diverse, drawing problems from linguistics, childhood develop- ment, math, common-sense reasoning, biology, physics, social bias, software development, and beyond. BIG-bench focuses on tasks that are believed to be beyond the capabilities of current language models. We evaluate the behavior of OpenAI's GPT models, Google- internal dense transformer architectures, and Switch-style sparse transformers on BIG-bench, across model sizes spanning millions to hundreds of billions of parameters. In addition, a team of human expert raters performed all tasks in order to provide a strong baseline. Findings include: model performance and calibration both improve with scale, but are poor in absolute terms (and when compared with rater performance); performance is remarkably similar across model classes, though with benefits from sparsity; tasks that improve gradually and predictably commonly involve a large knowledge or memorization component, whereas tasks that exhibit "breakthrough" behavior at a critical scale often involve multiple steps or components, or brittle metrics; social bias typically increases with scale in settings with ambiguous context, but this can be improved with prompting.

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TMLR Journal 2023 Journal Article

Differentially Private Image Classification from Features

Harsh Mehta
Walid Krichene
Abhradeep Guha Thakurta
Alexey Kurakin
Ashok Cutkosky

In deep learning, leveraging transfer learning has recently been shown to be an effective strategy for training large high performance models with Differential Privacy (DP). Moreover, somewhat surprisingly, recent works have found that privately training just the last layer of a pre-trained model provides the best utility with DP. While past studies largely rely on using first-order differentially private training algorithms like DP-SGD for training large models, in the specific case of privately learning from features, we observe that computational burden is often low enough to allow for more sophisticated optimization schemes, including second-order methods. To that end, we systematically explore the effect of design parameters such as loss function and optimization algorithm. We find that, while commonly used logistic regression performs better than linear regression in the non-private setting, the situation is reversed in the private setting. We find that least-squares linear regression is much more effective than logistic regression from both privacy and computational standpoint, especially at stricter epsilon values ($\epsilon < 1$). On the optimization side, we also explore using Newton's method, and find that second-order information is quite helpful even with privacy, although the benefit significantly diminishes with stricter privacy guarantees. While both methods use second-order information, least squares is more effective at lower epsilon values while Newton's method is more effective at larger epsilon values. To combine the benefits of both methods, we propose a novel optimization algorithm called DP-FC, which leverages feature covariance instead of the Hessian of the logistic regression loss and performs well across all $\epsilon$ values we tried. With this, we obtain new SOTA results on ImageNet-1k, CIFAR-100 and CIFAR-10 across all values of $\epsilon$ typically considered. Most remarkably, on ImageNet-1K, we obtain top-1 accuracy of 88\% under DP guarantee of (8, $8 * 10^{-7}$) and 84.3\% under (0.1, $8 * 10^{-7}$).

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ICLR Conference 2023 Conference Paper

Long Range Language Modeling via Gated State Spaces

Harsh Mehta
Ankit Gupta 0001
Ashok Cutkosky
Behnam Neyshabur

State space models have shown to be effective at modeling long range dependencies, specially on sequence classification tasks. In this work we focus on autoregressive sequence modeling over English books, Github source code and ArXiv mathematics articles. Based on recent developments around the effectiveness of gated activation functions, we propose a new layer named \textit{Gated State Space} (GSS) and show that it trains significantly faster than the diagonal version of S4 (i.e. DSS) on TPUs, is fairly competitive with several well-tuned Transformer-based baselines and exhibits zero-shot generalization to longer inputs while being straightforward to implement. Finally, we show that leveraging self-attention to model local dependencies improves the performance of GSS even further.

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NeurIPS Conference 2023 Conference Paper

Mechanic: A Learning Rate Tuner

Ashok Cutkosky
Aaron Defazio
Harsh Mehta

We introduce a technique for tuning the learning rate scale factor of any base optimization algorithm and schedule automatically, which we call Mechanic. Our method provides a practical realization of recent theoretical reductions for accomplishing a similar goal in online convex optimization. We rigorously evaluate Mechanic on a range of large scale deep learning tasks with varying batch sizes, schedules, and base optimization algorithms. These experiments demonstrate that depending on the problem, Mechanic either comes very close to, matches or even improves upon manual tuning of learning rates.

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ICML Conference 2023 Conference Paper

Optimal Stochastic Non-smooth Non-convex Optimization through Online-to-Non-convex Conversion

Ashok Cutkosky
Harsh Mehta
Francesco Orabona

We present new algorithms for optimizing non-smooth, non-convex stochastic objectives based on a novel analysis technique. This improves the current best-known complexity for finding a $(\delta, \epsilon)$-stationary point from $O(\epsilon^{-4}\delta^{-1})$ stochastic gradient queries to $O(\epsilon^{-3}\delta^{-1})$, which we also show to be optimal. Our primary technique is a reduction from non-smooth non-convex optimization to online learning, after which our results follow from standard regret bounds in online learning. For deterministic and second-order smooth objectives, applying more advanced optimistic online learning techniques enables a new complexity of $O(\epsilon^{-1. 5}\delta^{-0. 5})$. Our improved non-smooth analysis also immediately recovers all optimal or best-known results for finding $\epsilon$ stationary points of smooth or second-order smooth objectives in both stochastic and deterministic settings.

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TMLR Journal 2023 Journal Article

Towards Large Scale Transfer Learning for Differentially Private Image Classification

Harsh Mehta
Abhradeep Guha Thakurta
Alexey Kurakin
Ashok Cutkosky

Differentially Private Stochastic Gradient Descent (DP-SGD) has emerged as a popular private training algorithm. Unfortunately, the computational cost of training large-scale models with DP-SGD is substantially higher than non-private training. This is further exacerbated by the fact that increasing the number of parameters leads to larger degradation in utility with DP. In this work, we zoom in on the ImageNet dataset and demonstrate that, similar to the non-private case, pre-training over-parameterized models on a large public dataset can lead to substantial gains when the models are finetuned privately. Moreover, by systematically comparing private and non-private models across a range of large batch sizes, we find that similar to the non-private setting, the choice of optimizer can further improve performance substantially with DP. By using the LAMB optimizer, we saw improvement of up to 20$\%$ points (absolute). We also show that finetuning just the last layer for a \emph{single step} in the full batch setting, combined with extremely small-scale (near-zero) initialization leads to both SOTA results of 81.7 $\%$ under a wide privacy budget range of $\epsilon \in [4, 10]$ and $\delta$ = $10^{-6}$ while minimizing the computational overhead substantially. Finally, we present additional results on CIFAR-10 and CIFAR-100, surpassing previous state of the art by leveraging transfer learning with our recommendations.

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NeurIPS Conference 2022 Conference Paper

Transformer Memory as a Differentiable Search Index

Yi Tay
Vinh Tran
Mostafa Dehghani
Jianmo Ni
Dara Bahri
Harsh Mehta
Zhen Qin
Kai Hui

In this paper, we demonstrate that information retrieval can be accomplished with a single Transformer, in which all information about the corpus is encoded in the parameters of the model. To this end, we introduce the Differentiable Search Index (DSI), a new paradigm that learns a text-to-text model that maps string queries directly to relevant docids; in other words, a DSI model answers queries directly using only its parameters, dramatically simplifying the whole retrieval process. We study variations in how documents and their identifiers are represented, variations in training procedures, and the interplay between models and corpus sizes. Experiments demonstrate that given appropriate design choices, DSI significantly outperforms strong baselines such as dual encoder models. Moreover, DSI demonstrates strong generalization capabilities, outperforming a BM25 baseline in a zero-shot setup.

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ICLR Conference 2021 Conference Paper

Extreme Memorization via Scale of Initialization

Harsh Mehta
Ashok Cutkosky
Behnam Neyshabur

We construct an experimental setup in which changing the scale of initialization strongly impacts the implicit regularization induced by SGD, interpolating from good generalization performance to completely memorizing the training set while making little progress on the test set. Moreover, we find that the extent and manner in which generalization ability is affected depends on the activation and loss function used, with sin activation being the most extreme. In the case of the homogeneous ReLU activation, we show that this behavior can be attributed to the loss function. Our empirical investigation reveals that increasing the scale of initialization correlates with misalignment of representations and gradients across examples in the same class. This insight allows us to device an alignment measure over gradients and representations which can capture this phenomenon. We demonstrate that our alignment measure correlates with generalization of deep models trained on image classification tasks.

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NeurIPS Conference 2021 Conference Paper

High-probability Bounds for Non-Convex Stochastic Optimization with Heavy Tails

Ashok Cutkosky
Harsh Mehta

We consider non-convex stochastic optimization using first-order algorithms for which the gradient estimates may have heavy tails. We show that a combination of gradient clipping, momentum, and normalized gradient descent yields convergence to critical points in high-probability with best-known rates for smooth losses when the gradients only have bounded $\mathfrak{p}$th moments for some $\mathfrak{p}\in(1, 2]$. We then consider the case of second-order smooth losses, which to our knowledge have not been studied in this setting, and again obtain high-probability bounds for any $\mathfrak{p}$. Moreover, our results hold for arbitrary smooth norms, in contrast to the typical SGD analysis which requires a Hilbert space norm. Further, we show that after a suitable "burn-in" period, the objective value will monotonically decrease for every iteration until a critical point is identified, which provides intuition behind the popular practice of learning rate "warm-up'' and also yields a last-iterate guarantee.

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ICML Conference 2020 Conference Paper

Momentum Improves Normalized SGD

Ashok Cutkosky
Harsh Mehta

We provide an improved analysis of normalized SGD showing that adding momentum provably removes the need for large batch sizes on non-convex objectives. Then, we consider the case of objectives with bounded second derivative and show that in this case a small tweak to the momentum formula allows normalized SGD with momentum to find an $\epsilon$-critical point in $O(1/\epsilon^{3. 5})$ iterations, matching the best-known rates without accruing any logarithmic factors or dependence on dimension. We provide an adaptive learning rate schedule that automatically improves convergence rates when the variance in the gradients is small. Finally, we show that our method is effective when employed on popular large scale tasks such as ResNet-50 and BERT pretraining, matching the performance of the disparate methods used to get state-of-the-art results on both tasks.

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