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 $k \approx 0.05$), 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 $1.47\times$ on a single TPUv5e device.

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 $\kappa$-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 \citep{gradu2020non} and \citep{sun2023optimal}. Finally, we show that the more general problem of BCO with (non-affine) memory is harder. We derive a $\tilde{\Omega}(T^{2/3})$ regret lower bound, even under the assumption of smooth and quadratic losses.

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.

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 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.

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.

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.

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.

Machine learned models are increasingly entering wider ranges of domains in our lives, driving a constantly increasing number of important systems. Large scale systems can be trained in highly parallel and distributed training environments, with a large amount of randomness in training the models. While some systems may tolerate such randomness leading to models that differ from one another every time a model retrains, for many applications, reproducible models are required, where slight changes in training do not lead to drastic differences in the model learned. Beyond practical deployments of machine learned models, the reproducibility crisis in the machine learning academic world has also been well-documented: see [Pineau et al., 2021] and the references therein for an excellent discussion of the reasons for irreproducibility (insufficient exploration of hyperparameters and experimental setups, lack of sufficient documentation, inaccessible code, and different computational hardware) and for mitigation recommendations. However, recent papers [Chen et al., 2020, D'Amour et al., 2020, Dusenberry et al., 2020, Snapp and Shamir, 2021, Summers and Dinneen, 2021, Yu et al., 2021] have also demonstrated that even when models Part of this work was done when Kwangjun Ahn and Ziwei Ji were interns at Google Research.

We consider the setting of vector valued non-linear dynamical systems $X_{t+1} = \phi(A^* X_t) + \eta_t$, where $\eta_t$ is unbiased noise and $\phi : \mathbb{R} \to \mathbb{R}$ is a known link function that satisfies certain {\em expansivity property}. The goal is to learn $A^*$ from a single trajectory $X_1,\cdots,X_T$ of {\em dependent or correlated} samples. While the problem is well-studied in the linear case, where $\phi$ is identity, with optimal error rates even for non-mixing systems, existing results in the non-linear case hold only for mixing systems. In this work, we improve existing results for learning nonlinear systems in a number of ways: a) we provide the first offline algorithm that can learn non-linear dynamical systems without the mixing assumption, b) we significantly improve upon the sample complexity of existing results for mixing systems, c) in the much harder one-pass, streaming setting we study a SGD with Reverse Experience Replay ($\mathsf{SGD-RER}$) method, and demonstrate that for mixing systems, it achieves the same sample complexity as our offline algorithm, d) we justify the expansivity assumption by showing that for the popular ReLU link function -- a non-expansive but easy to learn link function with i.i.d. samples -- any method would require exponentially many samples (with respect to dimension of $X_t$) from the dynamical system. We validate our results via. simulations and demonstrate that a naive application of SGD can be highly sub-optimal. Indeed, our work demonstrates that for correlated data, specialized methods designed for the dependency structure in data can significantly outperform standard SGD based methods.