The discovery of the *lazy neuron phenomenon* (Li et al., 2022), where fewer than 10% of the feedforward networks (FFN) parameters in trained Transformers are activated per token, has spurred significant interests in *activation sparsity* for enhancing large model efficiency. While notable progress has been made in translating such sparsity to wall-time benefits across CPUs, GPUs, and TPUs, modern Transformers have moved away from the ReLU activation function crucial to this phenomenon. Existing efforts on re-introducing activation sparsity, e.g., by reverting to ReLU or applying top-k masking, often degrade model quality, increase parameter count, or complicate training. Sparse attention, the application of sparse activation to the attention mechanism, often face similar challenges. This paper introduces the Spark Transformer, a novel architecture that achieves high activation sparsity in both FFN and the attention mechanism while maintaining model quality, parameter count, and standard training procedures. Our method realizes sparsity via top-$k$ masking for explicit control over sparsity level. Crucially, we introduce *statistical top-k*, a hardware-accelerator-friendly, linear-time approximate algorithm that avoids costly sorting and mitigates significant training slowdown from standard top-k operators. Furthermore, Spark Transformer reallocates existing FFN parameters and attention key embeddings to form a low-cost predictor for identifying activated entries. This design not only mitigates quality loss from enforced sparsity, but also enhances wall-time benefit. Pretrained with the Gemma-2 recipe, Spark Transformer demonstrates competitive performance on standard benchmarks while exhibiting significant sparsity: only 8\% of FFN neurons are activated, and each token attends to a maximum of 256 tokens. This translates to a 2.5x reduction in FLOPs, leading to decoding wall-time speedups of up to 1.79x on CPU and 1.40xon GPU.

Large Language Models (LLMs) have been shown to be able to learn different tasks without explicit finetuning when given many input-output examples / demonstrations through In-Context Learning (ICL). Increasing the number of examples, called “shots”, improves downstream task performance but incurs higher memory and computational costs. In this work, we study an approach to improve the memory and computational efficiency of ICL inference by compressing the many-shot prompts. Given many shots comprising t tokens, our goal is to generate a m soft-token summary, where m < t. We first show that existing prompt compression methods are ineffective for many-shot compression, and simply using fewer shots as a baseline is surprisingly strong. To achieve effective compression, we find that: (a) a stronger compressor model with more trainable parameters is necessary, and (b) compressing many-shot representations at each transformer layer enables more fine-grained compression by providing each layer with its own compressed representation. Based on these insights, we propose MemCom, a layer-wise compression method. We systematically evaluate various compressor models and training approaches across different model sizes (2B and 7B), architectures (Gemma and Mistral), many-shot sequence lengths (3k-6k tokens), and compression ratios (3x to 8x). MemCom outperforms strong baselines across all compression ratios on multiple classification tasks with large label sets. Notably, while baseline performance degrades sharply at higher compression ratios, often by over 20-30

We consider the Top-K selection problem, which aims to identify the largest K elements in an array. Top-K selection arises in many machine learning algorithms and often becomes a bottleneck on accelerators, which are optimized for dense matrix multiplications. To address this problem, Chern et al. (2022) proposed a fast two-stage approximate Top-K algorithm that: (i) partitions the input array into equal-sized chunks and selects the top-1 element from each partition; and (ii) sorts the resulting smaller subset and returns the top K elements. In this paper, we generalize the first stage so that each partition selects the top K' elements (for 1 ≤ K' ≤ K). Our contributions include: (i) an expression for the expected recall of this generalized algorithm under random partitioning, and a demonstration that choosing K' > 1 with fewer partitions in the first stage more effectively reduces the input size to the second stage while maintaining the same expected recall as the original algorithm; (ii) a bound on the expected recall of the original algorithm as a function of the algorithm parameters that is provably tighter by a factor of 2 than the bound reported by Chern et al. (2022); and (iii) an implementation of our algorithm on Cloud TPUv5e that achieves approximately an order of magnitude speedup over the original algorithm without sacrificing recall.

This paper considers the problem of Hierarchical Multi-Label Classification (HMC), where (i) several labels can be present for each example, and (ii) labels are related via a domain-specific hierarchy tree. Guided by the intuition that all mistakes are not equal, we present Comprehensive Hierarchy Aware Multi-label Predictions (CHAMP), a framework that penalizes a misprediction depending on its severity as per the hierarchy tree. While there have been works that apply such an idea to single-label classification, to the best of our knowledge, there are limited such works for multilabel classification focusing on the severity of mistakes. The key reason is that there is no clear way of quantifying the severity of a misprediction a priori in the multilabel setting. In this work, we propose a simple but effective metric to quantify the severity of a mistake in HMC, naturally leading to CHAMP. Extensive experiments on six public HMC datasets across modalities (image, audio, and text) demonstrate that incorporating hierarchical information leads to substantial gains as CHAMP improves both AUPRC (2.6% median percentage improvement) and hierarchical metrics (2.85% median percentage improvement), over stand-alone hierarchical or multilabel classification methods. Compared to standard multilabel baselines, CHAMP provides improved AUPRC in both robustness (8.87% mean percentage improvement ) and less data regimes. Further, our method provides a framework to enhance existing multilabel classification algorithms with better mistakes (18.1% mean percentage increment).

The autoregressive nature of conventional large language models (LLMs) inherently limits inference speed, as tokens are generated sequentially. While speculative and parallel decoding techniques attempt to mitigate this, they face limitations: either relying on less accurate smaller models for generation or failing to fully leverage the base LLM's representations. We introduce a novel architecture, Tandem transformers, to address these issues. This architecture uniquely combines (1) a small autoregressive model and (2) a large model operating in block mode (processing multiple tokens simultaneously). The small model's predictive accuracy is substantially enhanced by granting it attention to the large model's richer representations. On the PaLM2 pretraining dataset, a tandem of PaLM2-Bison and PaLM2-Gecko demonstrates a 3.3% improvement in next-token prediction accuracy over a standalone PaLM2-Gecko, offering a 1.16x speedup compared to a PaLM2-Otter model with comparable downstream performance. We further incorporate the tandem model within the speculative decoding (SPEED) framework where the large model validates tokens from the small model. This ensures that the Tandem of PaLM2-Bison and PaLM2-Gecko achieves substantial speedup (around 1.14x faster than using vanilla PaLM2-Gecko in SPEED) while maintaining identical downstream task accuracy.

We present consistent algorithms for multiclass learning with complex performance metrics and constraints, where the objective and constraints are defined by arbitrary functions of the confusion matrix. This setting includes many common performance metrics such as the multiclass G-mean and micro F1-measure, and constraints such as those on the classifier's precision and recall and more recent measures of fairness discrepancy. We give a general framework for designing consistent algorithms for such complex design goals by viewing the learning problem as an optimization problem over the set of feasible confusion matrices. We provide multiple instantiations of our framework under different assumptions on the performance metrics and constraints, and in each case show rates of convergence to the optimal (feasible) classifier (and thus asymptotic consistency). Experiments on a variety of multiclass classification tasks and fairness-constrained problems show that our algorithms compare favorably to the state-of-the-art baselines.

Bandit convex optimization (BCO) is a general framework for online decision making under uncertainty. While tight regret bounds for general convex losses have been established, existing algorithms achieving these bounds have prohibitive computational costs for high dimensional data. In this paper, we propose a simple and practical BCO algorithm inspired by the online Newton step algorithm. We show that our algorithm achieves optimal (in terms of horizon) regret bounds for a large class of convex functions that we call κ-convex. This class contains a wide range of practically relevant loss functions including linear, quadratic, and generalized linear models. In addition to optimal regret, this method is the most efficient known algorithm for several well-studied applications including bandit logistic regression. Furthermore, we investigate the adaptation of our second-order bandit algorithm to online convex optimization with memory. We show that for loss functions with a certain affine structure, the extended algorithm attains optimal regret. This leads to an algorithm with optimal regret for bandit LQR/LQG problems under a fully adversarial noise model, thereby resolving an open question posed in and . Finally, we show that the more general problem of BCO with (non-affine) memory is harder. We derive a Ω̃(T^2/3) regret lower bound, even under the assumption of smooth and quadratic losses.

Deep learning succeeds by doing hierarchical feature learning, yet tuning hyper-parameters (HP) such as initialization scales, learning rates etc., only give indirect control over this behavior. In this paper, we introduce a key notion to predict and control feature learning: the angle $\theta_\ell$ between the feature updates and the backward pass (at layer index $\ell$). We show that the magnitude of feature updates after one GD step, at any training time, can be expressed via a simple and general *feature speed formula* in terms of this angle $\theta_\ell$, the loss decay, and the magnitude of the backward pass. This angle $\theta_\ell$ is controlled by the conditioning of the layer-to-layer Jacobians and at random initialization, it is determined by the spectrum of a certain kernel, which coincides with the Neural Tangent Kernel when $\ell=\text{depth}$. Given $\theta_\ell$, the feature speed formula provides us with rules to adjust HPs (scales and learning rates) so as to satisfy certain dynamical properties, such as feature learning and loss decay. We investigate the implications of our approach for ReLU MLPs and ResNets in the large width-then-depth limit. Relying on prior work, we show that in ReLU MLPs with iid initialization, the angle degenerates with depth as $\cos(\theta_\ell)=\Theta(1/\sqrt{\ell})$. In contrast, ResNets with branch scale $O(1/\sqrt{\text{depth}})$ maintain a non-degenerate angle $\cos(\theta_\ell)=\Theta(1)$. We use these insights to recover key properties of known HP scalings (such as $\mu$P), and also introduce a new HP scaling for large depth ReLU MLPs with favorable theoretical properties.

Autoregressive decoding with generative Large Language Models (LLMs) on accelerators (GPUs/TPUs) is often memory-bound where most of the time is spent on transferring model parameters from high bandwidth memory (HBM) to cache. On the other hand, recent works show that LLMs can maintain quality with significant sparsity/redundancy in the feedforward (FFN) layers by appropriately training the model to operate on a top-k fraction of rows/columns (where k ≈ 0.05), there by suggesting a way to reduce the transfer of model parameters, and hence latency. However, exploiting this sparsity for improving latency is hindered by the fact that identifying top rows/columns is data-dependent and is usually performed using full matrix operations, severely limiting potential gains. To address these issues, we introduce HiRE (High Recall Approximate Top-k Estimation). HiRE comprises of two novel components: (i) a compression scheme to cheaply predict top-k rows/columns with high recall, followed by full computation restricted to the predicted subset, and (ii) DA-TOP-k: an efficient multi-device approximate top-k operator. We demonstrate that on a one billion parameter model, HiRE applied to both the softmax as well as feedforward layers, achieves almost matching pretraining and downstream accuracy, and speeds up inference latency by 1.47× on a single TPUv5e device.

Recent works have demonstrated that neural networks exhibit extreme simplicity bias(SB). That is, they learn only the simplest features to solve a task at hand, even in the presence of other, more robust but more complex features. Due to the lack of a general and rigorous definition of features, these works showcase SB on semi-synthetic datasets such as Color-MNIST, MNIST-CIFAR where defining features is relatively easier. In this work, we rigorously define as well as thoroughly establish SB for one hidden layer neural networks. More concretely, (i) we define SB as the network essentially being a function of a low dimensional projection of the inputs (ii) theoretically, we show that when the data is linearly separable, the network primarily depends on only the linearly separable (1-dimensional) subspace even in the presence of an arbitrarily large number of other, more complex features which could have led to a significantly more robust classifier, (iii) empirically, we show that models trained on real datasets such as Imagenette and Waterbirds-Landbirds indeed depend on a low dimensional projection of the inputs, thereby demonstrating SB on these datasets, iv) finally, we present a natural ensemble approach that encourages diversity in models by training successive models on features not used by earlier models, and demonstrate that it yields models that are significantly more robust to Gaussian noise.

Deep learning succeeds by doing hierarchical feature learning, yet tuning Hyper-Parameters (HP) such as initialization scales, learning rates etc., only give indirect control over this behavior. In this paper, we propose the alignment between the feature updates and the backward pass as a key notion to predict, measure and control feature learning. On the one hand, we show that when alignment holds, the magnitude of feature updates after one SGD step is related to the magnitude of the forward and backward passes by a simple and general formula. This leads to techniques to automatically adjust HPs (initialization scales and learning rates) at initialization and throughout training to attain a desired feature learning behavior. On the other hand, we show that, at random initialization, this alignment is determined by the spectrum of a certain kernel, and that well-conditioned layer-to-layer Jacobians (aka dynamical isometry) implies alignment. Finally, we investigate ReLU MLPs and ResNets in the large width-then-depth limit. Combining hints from random matrix theory and numerical experiments, we show that (i) in MLP with iid initializations, alignment degenerates with depth, making it impossible to start training, and that (ii) in ResNets, the branch scale $1/\sqrt{\text{depth}}$ is the only one maintaining non-trivial alignment at infinite depth.

We consider the task of self-supervised representation learning (SSL) for tabular data: tabular-SSL. Typical contrastive learning based SSL methods require instance-wise data augmentations which are difficult to design for unstructured tabular data. Existing tabular-SSL methods design such augmentations in a relatively ad-hoc fashion and can fail to capture the underlying data manifold. Instead of augmentations based approaches for tabular-SSL, we propose a new reconstruction based method, called Masked Encoding for Tabular Data (MET), that does not require augmentations. MET is based on the popular MAE approach for vision-SSL [He et al., 2021] and uses two key ideas: (i) since each coordinate in a tabular dataset has a distinct meaning, we need to use separate representations for all coordinates, and (ii) using an adversarial reconstruction loss in addition to the standard one. Empirical results on five diverse tabular datasets show that MET achieves a new state of the art (SOTA) on all of these datasets and improves up to 9% over current SOTA methods. We shed more light on the working of MET via experiments on carefully designed simple datasets.

This paper introduces a simple efficient learning algorithms for general sequential decision making. The algorithm combines Optimism for exploration with Maximum Likelihood Estimation for model estimation, which is thus named OMLE. We prove that OMLE learns the near-optimal policies of an enormously rich class of sequential decision making problems in a polynomial number of samples. This rich class includes not only a majority of known tractable model-based Reinforcement Learning (RL) problems (such as tabular MDPs, factored MDPs, low witness rank problems, tabular weakly-revealing/observable POMDPs and multi-step decodable POMDPs), but also many new challenging RL problems especially in the partially observable setting that were not previously known to be tractable. Notably, the new problems addressed by this paper include (1) observable POMDPs with continuous observation and function approximation, where we achieve the first sample complexity that is completely independent of the size of observation space; (2) well-conditioned low-rank sequential decision making problems (also known as Predictive State Representations (PSRs)), which include and generalize all known tractable POMDP examples under a more intrinsic representation; (3) general sequential decision making problems under SAIL condition, which unifies our existing understandings of model-based RL in both fully observable and partially observable settings. SAIL condition is identified by this paper, which can be viewed as a natural generalization of Bellman/witness rank to address partial observability. This paper also presents a reward-free variant of OMLE algorithm, which learns approximate dynamic models that enable the computation of near-optimal policies for all reward functions simultaneously.

We consider the problem of heteroscedastic linear regression, where, given $n$ samples $(\mathbf{x}_i, y_i)$ from $y_i = \langle \mathbf{w}^{*}, \mathbf{x}_i \rangle + \epsilon_i \cdot \langle \mathbf{f}^{*}, \mathbf{x}_i \rangle$ with $\mathbf{x}_i \sim N(0,\mathbf{I})$, $\epsilon_i \sim N(0,1)$, we aim to estimate $\mathbf{w}^{*}$. Beyond classical applications of such models in statistics, econometrics, time series analysis etc., it is also particularly relevant in machine learning when data is collected from multiple sources of varying but apriori unknown quality. Our work shows that we can estimate $\mathbf{w}^{*}$ in squared norm up to an error of $\tilde{O}\left(\|\mathbf{f}^{*}\|^2 \cdot \left(\frac{1}{n} + \left(\frac{d}{n}\right)^2\right)\right)$ and prove a matching lower bound (upto log factors). This represents a substantial improvement upon the previous best known upper bound of $\tilde{O}\left(\|\mathbf{f}^{*}\|^2\cdot \frac{d}{n}\right)$. Our algorithm is an alternating minimization procedure with two key subroutines 1. An adaptation of the classical weighted least squares heuristic to estimate $\mathbf{w}^{*}$, for which we provide the first non-asymptotic guarantee. 2. A nonconvex pseudogradient descent procedure for estimating $\mathbf{f}^{*}$ inspired by phase retrieval. As corollaries, we obtain fast non-asymptotic rates for two important problems, linear regression with multiplicative noise and phase retrieval with multiplicative noise, both of which are of independent interest. Beyond this, the proof of our lower bound, which involves a novel adaptation of LeCam's method for handling infinite mutual information quantities (thereby preventing a direct application of standard techniques like Fano's method), could also be of broader interest for establishing lower bounds for other heteroscedastic or heavy-tailed statistical problems.

Deep Neural Networks are known to be brittle to even minor distribution shifts compared to the training distribution. While one line of work has demonstrated that \emph{Simplicity Bias} (SB) of DNNs -- bias towards learning only the simplest features -- is a key reason for this brittleness, another recent line of work has surprisingly found that diverse/ complex features are indeed learned by the backbone, and their brittleness is due to the linear classification head relying primarily on the simplest features. To bridge the gap between these two lines of work, we first hypothesize and verify that while SB may not altogether preclude learning complex features, it amplifies simpler features over complex ones. Namely, simple features are replicated several times in the learned representations while complex features might not be replicated. This phenomenon, we term \emph{Feature Replication Hypothesis}, coupled with the \emph{Implicit Bias} of SGD to converge to maximum margin solutions in the feature space, leads the models to rely mostly on the simple features for classification. To mitigate this bias, we propose \emph{Feature Reconstruction Regularizer (FRR)} to ensure that the learned features can be reconstructed back from the logits. The use of \emph{FRR} in linear layer training (\emph{FRR-L}) encourages the use of more diverse features for classification. We further propose to finetune the full network by freezing the weights of the linear layer trained using \emph{FRR-L}, to refine the learned features, making them more suitable for classification. Using this simple solution, we demonstrate up to 15\% gains in OOD accuracy on the recently introduced semi-synthetic datasets with extreme distribution shifts. Moreover, we demonstrate noteworthy gains over existing SOTA methods on the standard OOD benchmark DomainBed as well.

In this work, we consider the problem of collaborative multi-user reinforcement learning. In this setting there are multiple users with the same state-action space and transition probabilities but with different rewards. Under the assumption that the reward matrix of the $N$ users has a low-rank structure -- a standard and practically successful assumption in the offline collaborative filtering setting -- the question is can we design algorithms with significantly lower sample complexity compared to the ones that learn the MDP individually for each user. Our main contribution is an algorithm which explores rewards collaboratively with $N$ user-specific MDPs and can learn rewards efficiently in two key settings: tabular MDPs and linear MDPs. When $N$ is large and the rank is constant, the sample complexity per MDP depends logarithmically over the size of the state-space, which represents an exponential reduction (in the state-space size) when compared to the standard ``non-collaborative'' algorithms.

Q-learning is a popular Reinforcement Learning (RL) algorithm which is widely used in practice with function approximation (Mnih et al., 2015). In contrast, existing theoretical results are pessimistic about Q-learning. For example, (Baird, 1995) shows that Q-learning does not converge even with linear function approximation for linear MDPs. Furthermore, even for tabular MDPs with synchronous updates, Q-learning was shown to have sub-optimal sample complexity (Li et al., 2021;Azar et al., 2013). The goal of this work is to bridge the gap between practical success of Q-learning and the relatively pessimistic theoretical results. The starting point of our work is the observation that in practice, Q-learning is used with two important modifications: (i) training with two networks, called online network and target network simultaneously (online target learning, or OTL) , and (ii) experience replay (ER) (Mnih et al., 2015). While they have been observed to play a significant role in the practical success of Q-learning, a thorough theoretical understanding of how these two modifications improve the convergence behavior of Q-learning has been missing in literature. By carefully combining Q-learning with OTL and reverse experience replay (RER) (a form of experience replay), we present novel methods Q-Rex and Q-RexDaRe (Q-Rex + data reuse). We show that Q-Rex efficiently finds the optimal policy for linear MDPs (or more generally for MDPs with zero inherent Bellman error with linear approximation (ZIBEL)) and provide non-asymptotic bounds on sample complexity -- the first such result for a Q-learning method for this class of MDPs under standard assumptions. Furthermore, we demonstrate that Q-RexDaRe in fact achieves near optimal sample complexity in the tabular setting, improving upon the existing results for vanilla Q-learning.

We initiate a formal study of reproducibility in optimization. We define a quantitative measure of reproducibility of optimization procedures in the face of noisy or error-prone operations such as inexact or stochastic gradient computations or inexact initialization. We then analyze several convex optimization settings of interest such as smooth, non-smooth, and strongly-convex objective functions and establish tight bounds on the limits of reproducibility in each setting. Our analysis reveals a fundamental trade-off between computation and reproducibility: more computation is necessary (and sufficient) for better reproducibility.

We consider the problem of OOD generalization, where the goal is to train a model that performs well on test distributions that are different from the training distribution. Deep learning models are known to be fragile to such shifts and can suffer large accuracy drops even for slightly different test distributions. We propose a new method - DAFT - based on the intuition that adversarially robust combination of a large number of rich features should provide OOD robustness. Our method carefully distills the knowledge from a powerful teacher that learns several discriminative features using standard training while combining them using adversarial training. The standard adversarial training procedure is modified to produce teachers which can guide the student better. We evaluate DAFT on standard benchmarks in the DomainBed framework, and demonstrate that DAFT achieves significant improvements over the current state-of-the-art OOD generalization methods. DAFT consistently out-performs well-tuned ERM and distillation baselines by up to 6%, with more pronounced gains for smaller networks.

This paper considers minimax optimization $\min_x \max_y f(x, y)$ in the challenging setting where $f$ can be both nonconvex in $x$ and nonconcave in $y$. Though such optimization problems arise in many machine learning paradigms including training generative adversarial networks (GANs) and adversarially robust models, many fundamental issues remain in theory, such as the absence of efficiently computable optimality notions, and cyclic or diverging behavior of existing algorithms. Our framework sprouts from the practical consideration that under a computational budget, the max-player can not fully maximize $f(x,\cdot)$ since nonconcave maximization is NP-hard in general. So, we propose a new algorithm for the min-player to play against smooth algorithms deployed by the adversary (i.e., the max-player) instead of against full maximization. Our algorithm is guaranteed to make monotonic progress (thus having no limit cycles), and to find an appropriate"stationary point"in a polynomial number of iterations. Our framework covers practical settings where the smooth algorithms deployed by the adversary are multi-step stochastic gradient ascent, and its accelerated version. We further provide complementing experiments that confirm our theoretical findings and demonstrate the effectiveness of the proposed approach in practice.