Shashank Rajput

Tuan Dinh, Yuchen Zeng, Ruisu Zhang et al.

Fine-tuning pretrained language models (LMs) without making any architectural changes has become a norm for learning various language downstream tasks. However, for non-language downstream tasks, a common practice is to employ task-specific designs for input, output layers, and loss functions. For instance, it is possible to fine-tune an LM into an MNIST classifier by replacing the word embedding layer with an image patch embedding layer, the word token output layer with a 10-way output layer, and the word prediction loss with a 10-way classification loss, respectively. A natural question arises: Can LM fine-tuning solve non-language downstream tasks without changing the model architecture or loss function? To answer this, we propose Language-Interfaced Fine-Tuning (LIFT) and study its efficacy and limitations by conducting an extensive empirical study on a suite of non-language classification and regression tasks. LIFT does not make any changes to the model architecture or loss function, and it solely relies on the natural language interface, enabling "no-code machine learning with LMs." We find that LIFT performs comparably well across a wide range of low-dimensional classification and regression tasks, matching the performances of the best baselines in many cases, especially for the classification tasks. We also report experimental results on the fundamental properties of LIFT, including inductive bias, robustness, and sample complexity. We also analyze the effect of pretraining on LIFT and a few properties/techniques specific to LIFT, e.g., context-aware learning via appropriate prompting, calibrated predictions, data generation, and two-stage fine-tuning. Our code is available at https://github.com/UW-Madison-Lee-Lab/LanguageInterfacedFineTuning.

Angeliki Giannou, Shashank Rajput, Jy-yong Sohn et al.

We present a framework for using transformer networks as universal computers by programming them with specific weights and placing them in a loop. Our input sequence acts as a punchcard, consisting of instructions and memory for data read/writes. We demonstrate that a constant number of encoder layers can emulate basic computing blocks, including embedding edit operations, non-linear functions, function calls, program counters, and conditional branches. Using these building blocks, we emulate a small instruction-set computer. This allows us to map iterative algorithms to programs that can be executed by a looped, 13-layer transformer. We show how this transformer, instructed by its input, can emulate a basic calculator, a basic linear algebra library, and in-context learning algorithms that employ backpropagation. Our work highlights the versatility of the attention mechanism, and demonstrates that even shallow transformers can execute full-fledged, general-purpose programs.

Angeliki Giannou, Shashank Rajput, Dimitris Papailiopoulos

Feature normalization transforms such as Batch and Layer-Normalization have become indispensable ingredients of state-of-the-art deep neural networks. Recent studies on fine-tuning large pretrained models indicate that just tuning the parameters of these affine transforms can achieve high accuracy for downstream tasks. These findings open the questions about the expressive power of tuning the normalization layers of frozen networks. In this work, we take the first step towards this question and show that for random ReLU networks, fine-tuning only its normalization layers can reconstruct any target network that is $O(\sqrt{\text{width}})$ times smaller. We show that this holds even for randomly sparsified networks, under sufficient overparameterization, in agreement with prior empirical work.

Samuel Horvath, Stefanos Laskaridis, Shashank Rajput et al.

Deep Neural Networks (DNNs) have been a large driver for AI breakthroughs in recent years. However, these models have been getting increasingly large as they become more accurate and safe. This means that their training becomes increasingly costly and time-consuming and typically yields a single model to fit all targets. Various techniques have been proposed in the literature to mitigate this, including pruning, sparsification, or quantization of model weights and updates. While achieving high compression rates, they often incur significant computational overheads at training or lead to non-negligible accuracy penalty. Alternatively, factorization methods have been leveraged for low-rank compression of DNNs. Similarly, such techniques (e.g., SVD) frequently rely on heavy iterative decompositions of layers and are potentially sub-optimal for non-linear models, such as DNNs. We take a further step in designing efficient low-rank models and propose Maestro, a framework for trainable low-rank layers. Instead of iteratively applying a priori decompositions, the low-rank structure is baked into the training process through LoD, a low-rank ordered decomposition. Not only is this the first time importance ordering via sampling is applied on the decomposed DNN structure, but it also allows selecting ranks at a layer granularity. Our theoretical analysis demonstrates that in special cases LoD recovers the SVD decomposition and PCA. Applied to DNNs, Maestro enables the extraction of lower footprint models that preserve performance. Simultaneously, it enables the graceful trade-off between accuracy-latency for deployment to even more constrained devices without retraining.

Tuan Dinh, Jy-yong Sohn, Shashank Rajput et al.

Word translation without parallel corpora has become feasible, rivaling the performance of supervised methods. Recent findings have shown that the accuracy and robustness of unsupervised word translation (UWT) can be improved by making use of visual observations, which are universal representations across languages. In this work, we investigate the potential of using not only visual observations but also pretrained language-image models for enabling a more efficient and robust UWT. Specifically, we develop a novel UWT method dubbed Word Alignment using Language-Image Pretraining (WALIP), which leverages visual observations via the shared embedding space of images and texts provided by CLIP models (Radford et al., 2021). WALIP has a two-step procedure. First, we retrieve word pairs with high confidences of similarity, computed using our proposed image-based fingerprints, which define the initial pivot for the word alignment. Second, we apply our robust Procrustes algorithm to estimate the linear mapping between two embedding spaces, which iteratively corrects and refines the estimated alignment. Our extensive experiments show that WALIP improves upon the state-of-the-art performance of bilingual word alignment for a few language pairs across different word embeddings and displays great robustness to the dissimilarity of language pairs or training corpora for two word embeddings.

Shashank Rajput, Ying Sheng, Sean Owen et al.

The size of the key-value (KV) cache plays a critical role in determining both the maximum context length and the number of concurrent requests supported during inference in modern language models. The KV cache size grows proportionally with the number of attention heads and the tokens processed, leading to increased memory consumption and slower inference for long inputs. In this work, we explore the use of MixAttention, a model architecture modification closely related to a blog published by Character.AI. MixAttention combines sliding window attention, where only a small subset of recent tokens is stored in the KV cache, with KV cache sharing across layers. Our experiments demonstrate that MixAttention significantly reduces memory usage and improves inference speed without sacrificing model performance in both short and long-context tasks. We also explore various configurations of this architecture, identifying those that maintain quality across evaluation metrics while optimizing resource efficiency.

Shashank Rajput, Nikhil Mehta, Anima Singh et al.

Modern recommender systems perform large-scale retrieval by first embedding queries and item candidates in the same unified space, followed by approximate nearest neighbor search to select top candidates given a query embedding. In this paper, we propose a novel generative retrieval approach, where the retrieval model autoregressively decodes the identifiers of the target candidates. To that end, we create semantically meaningful tuple of codewords to serve as a Semantic ID for each item. Given Semantic IDs for items in a user session, a Transformer-based sequence-to-sequence model is trained to predict the Semantic ID of the next item that the user will interact with. To the best of our knowledge, this is the first Semantic ID-based generative model for recommendation tasks. We show that recommender systems trained with the proposed paradigm significantly outperform the current SOTA models on various datasets. In addition, we show that incorporating Semantic IDs into the sequence-to-sequence model enhances its ability to generalize, as evidenced by the improved retrieval performance observed for items with no prior interaction history.

Chulhee Yun, Shashank Rajput, Suvrit Sra

In distributed learning, local SGD (also known as federated averaging) and its simple baseline minibatch SGD are widely studied optimization methods. Most existing analyses of these methods assume independent and unbiased gradient estimates obtained via with-replacement sampling. In contrast, we study shuffling-based variants: minibatch and local Random Reshuffling, which draw stochastic gradients without replacement and are thus closer to practice. For smooth functions satisfying the Polyak-Łojasiewicz condition, we obtain convergence bounds (in the large epoch regime) which show that these shuffling-based variants converge faster than their with-replacement counterparts. Moreover, we prove matching lower bounds showing that our convergence analysis is tight. Finally, we propose an algorithmic modification called synchronized shuffling that leads to convergence rates faster than our lower bounds in near-homogeneous settings.

Kartik Sreenivasan, Shashank Rajput, Jy-yong Sohn et al.

A recent work by Ramanujan et al. (2020) provides significant empirical evidence that sufficiently overparameterized, random neural networks contain untrained subnetworks that achieve state-of-the-art accuracy on several predictive tasks. A follow-up line of theoretical work provides justification of these findings by proving that slightly overparameterized neural networks, with commonly used continuous-valued random initializations can indeed be pruned to approximate any target network. In this work, we show that the amplitude of those random weights does not even matter. We prove that any target network can be approximated up to arbitrary accuracy by simply pruning a random network of binary $\{\pm1\}$ weights that is only a polylogarithmic factor wider and deeper than the target network.

Shashank Rajput, Kartik Sreenivasan, Dimitris Papailiopoulos et al.

It is well known that modern deep neural networks are powerful enough to memorize datasets even when the labels have been randomized. Recently, Vershynin (2020) settled a long standing question by Baum (1988), proving that \emph{deep threshold} networks can memorize $n$ points in $d$ dimensions using $\widetilde{\mathcal{O}}(e^{1/δ^2}+\sqrt{n})$ neurons and $\widetilde{\mathcal{O}}(e^{1/δ^2}(d+\sqrt{n})+n)$ weights, where $δ$ is the minimum distance between the points. In this work, we improve the dependence on $δ$ from exponential to almost linear, proving that $\widetilde{\mathcal{O}}(\frac{1}δ+\sqrt{n})$ neurons and $\widetilde{\mathcal{O}}(\frac{d}δ+n)$ weights are sufficient. Our construction uses Gaussian random weights only in the first layer, while all the subsequent layers use binary or integer weights. We also prove new lower bounds by connecting memorization in neural networks to the purely geometric problem of separating $n$ points on a sphere using hyperplanes.

Shashank Rajput, Kangwook Lee, Dimitris Papailiopoulos

A recent line of ground-breaking results for permutation-based SGD has corroborated a widely observed phenomenon: random permutations offer faster convergence than with-replacement sampling. However, is random optimal? We show that this depends heavily on what functions we are optimizing, and the convergence gap between optimal and random permutations can vary from exponential to nonexistent. We first show that for 1-dimensional strongly convex functions, with smooth second derivatives, there exist permutations that offer exponentially faster convergence compared to random. However, for general strongly convex functions, random permutations are optimal. Finally, we show that for quadratic, strongly-convex functions, there are easy-to-construct permutations that lead to accelerated convergence compared to random. Our results suggest that a general convergence characterization of optimal permutations cannot capture the nuances of individual function classes, and can mistakenly indicate that one cannot do much better than random.

Hongyi Wang, Kartik Sreenivasan, Shashank Rajput et al.

Due to its decentralized nature, Federated Learning (FL) lends itself to adversarial attacks in the form of backdoors during training. The goal of a backdoor is to corrupt the performance of the trained model on specific sub-tasks (e.g., by classifying green cars as frogs). A range of FL backdoor attacks have been introduced in the literature, but also methods to defend against them, and it is currently an open question whether FL systems can be tailored to be robust against backdoors. In this work, we provide evidence to the contrary. We first establish that, in the general case, robustness to backdoors implies model robustness to adversarial examples, a major open problem in itself. Furthermore, detecting the presence of a backdoor in a FL model is unlikely assuming first order oracles or polynomial time. We couple our theoretical results with a new family of backdoor attacks, which we refer to as edge-case backdoors. An edge-case backdoor forces a model to misclassify on seemingly easy inputs that are however unlikely to be part of the training, or test data, i.e., they live on the tail of the input distribution. We explain how these edge-case backdoors can lead to unsavory failures and may have serious repercussions on fairness, and exhibit that with careful tuning at the side of the adversary, one can insert them across a range of machine learning tasks (e.g., image classification, OCR, text prediction, sentiment analysis).

Ankit Pensia, Shashank Rajput, Alliot Nagle et al.

The strong {\it lottery ticket hypothesis} (LTH) postulates that one can approximate any target neural network by only pruning the weights of a sufficiently over-parameterized random network. A recent work by Malach et al. \cite{MalachEtAl20} establishes the first theoretical analysis for the strong LTH: one can provably approximate a neural network of width $d$ and depth $l$, by pruning a random one that is a factor $O(d^4l^2)$ wider and twice as deep. This polynomial over-parameterization requirement is at odds with recent experimental research that achieves good approximation with networks that are a small factor wider than the target. In this work, we close the gap and offer an exponential improvement to the over-parameterization requirement for the existence of lottery tickets. We show that any target network of width $d$ and depth $l$ can be approximated by pruning a random network that is a factor $O(\log(dl))$ wider and twice as deep. Our analysis heavily relies on connecting pruning random ReLU networks to random instances of the \textsc{SubsetSum} problem. We then show that this logarithmic over-parameterization is essentially optimal for constant depth networks. Finally, we verify several of our theoretical insights with experiments.

Shashank Rajput, Anant Gupta, Dimitris Papailiopoulos

Stochastic gradient descent without replacement sampling is widely used in practice for model training. However, the vast majority of SGD analyses assumes data is sampled with replacement, and when the function minimized is strongly convex, an $\mathcal{O}\left(\frac{1}{T}\right)$ rate can be established when SGD is run for $T$ iterations. A recent line of breakthrough works on SGD without replacement (SGDo) established an $\mathcal{O}\left(\frac{n}{T^2}\right)$ convergence rate when the function minimized is strongly convex and is a sum of $n$ smooth functions, and an $\mathcal{O}\left(\frac{1}{T^2}+\frac{n^3}{T^3}\right)$ rate for sums of quadratics. On the other hand, the tightest known lower bound postulates an $Ω\left(\frac{1}{T^2}+\frac{n^2}{T^3}\right)$ rate, leaving open the possibility of better SGDo convergence rates in the general case. In this paper, we close this gap and show that SGD without replacement achieves a rate of $\mathcal{O}\left(\frac{1}{T^2}+\frac{n^2}{T^3}\right)$ when the sum of the functions is a quadratic, and offer a new lower bound of $Ω\left(\frac{n}{T^2}\right)$ for strongly convex functions that are sums of smooth functions.

Shashank Rajput, Hongyi Wang, Zachary Charles et al.

To improve the resilience of distributed training to worst-case, or Byzantine node failures, several recent approaches have replaced gradient averaging with robust aggregation methods. Such techniques can have high computational costs, often quadratic in the number of compute nodes, and only have limited robustness guarantees. Other methods have instead used redundancy to guarantee robustness, but can only tolerate limited number of Byzantine failures. In this work, we present DETOX, a Byzantine-resilient distributed training framework that combines algorithmic redundancy with robust aggregation. DETOX operates in two steps, a filtering step that uses limited redundancy to significantly reduce the effect of Byzantine nodes, and a hierarchical aggregation step that can be used in tandem with any state-of-the-art robust aggregation method. We show theoretically that this leads to a substantial increase in robustness, and has a per iteration runtime that can be nearly linear in the number of compute nodes. We provide extensive experiments over real distributed setups across a variety of large-scale machine learning tasks, showing that DETOX leads to orders of magnitude accuracy and speedup improvements over many state-of-the-art Byzantine-resilient approaches.

Zachary Charles, Shashank Rajput, Stephen Wright et al.

Adversarial training is a technique for training robust machine learning models. To encourage robustness, it iteratively computes adversarial examples for the model, and then re-trains on these examples via some update rule. This work analyzes the performance of adversarial training on linearly separable data, and provides bounds on the number of iterations required for large margin. We show that when the update rule is given by an arbitrary empirical risk minimizer, adversarial training may require exponentially many iterations to obtain large margin. However, if gradient or stochastic gradient update rules are used, only polynomially many iterations are required to find a large-margin separator. By contrast, without the use of adversarial examples, gradient methods may require exponentially many iterations to achieve large margin. Our results are derived by showing that adversarial training with gradient updates minimizes a robust version of the empirical risk at a $\mathcal{O}(\ln(t)^2/t)$ rate, despite non-smoothness. We corroborate our theory empirically.

Shashank Rajput, Zhili Feng, Zachary Charles et al.

Data augmentation (DA) is commonly used during model training, as it significantly improves test error and model robustness. DA artificially expands the training set by applying random noise, rotations, crops, or even adversarial perturbations to the input data. Although DA is widely used, its capacity to provably improve robustness is not fully understood. In this work, we analyze the robustness that DA begets by quantifying the margin that DA enforces on empirical risk minimizers. We first focus on linear separators, and then a class of nonlinear models whose labeling is constant within small convex hulls of data points. We present lower bounds on the number of augmented data points required for non-zero margin, and show that commonly used DA techniques may only introduce significant margin after adding exponentially many points to the data set.