Large language models (LLMs) have become pivotal in recent research. However, during the inference process, LLMs still require substantial resources. In this paper, we propose CliqueParcel, a method designed to improve the efficiency of LLMs via prompt batching. Existing strategies to optimize inference efficiency often compromise on output quality, leading to a discounted output problem. This issue might result in reduced accuracy or outputs that are less detailed. CliqueParcel is our answer to this challenge. While ensuring accuracy and minimizing deviations from the original outputs (i.e., faithfulness), our method significantly improves efficiency during inference. To lay the groundwork, we first redefine efficiency measurements by excluding the reduction in running time due to shorter lengths. Then, we provide a comprehensive trade-off between efficiency and faithfulness to clarify the nature of the 'discounted output' problem. Within the CliqueParcel framework, we suggest multiple batching sub-methods and discuss the specific scenarios in which they can be applied. During evaluation, CliqueParcel is tested on eight widely recognized datasets, which can be classified into three types: reading comprehension, open-source question-answering, and reasoning. Our experiments explore the performance of CliqueParcel, including efficiency, faithfulness, and the trade-off between them. This work provides novel insights into inference efficiency and demonstrates promising performance.

The choice of batch sizes in stochastic gradient optimizers is critical for model training. However, the practice of varying batch sizes throughout the training process is less explored compared to other hyperparameters. We investigate adaptive batch size strategies derived from adaptive sampling methods, traditionally applied only in stochastic gradient descent. Given the significant interplay between learning rates and batch sizes, and considering the prevalence of adaptive gradient methods in deep learning, we emphasize the need for adaptive batch size strategies in these contexts. We introduce AdAdaGrad and its scalar variant AdAdaGradNorm, which incrementally increase batch sizes during training, while model updates are performed using AdaGrad and AdaGradNorm. We prove that AdaGradNorm converges with high probability at a rate of $\mathscr{O}(1/K)$ for finding a first-order stationary point of smooth nonconvex functions within $K$ iterations. AdaGrad also demonstrates similar convergence properties when integrated with a novel coordinate-wise variant of our adaptive batch size strategies. Our theoretical claims are supported by numerical experiments on various image classification tasks, highlighting the enhanced adaptability of progressive batching protocols in deep learning and the potential of such adaptive batch size strategies with adaptive gradient optimizers in large-scale model training.

We propose a novel method for {\em linear} dimensionality reduction of manifold modeled data. First, we show that with a small number M of {\em random projections} of sample points in \reals N belonging to an unknown K -dimensional Euclidean manifold, the intrinsic dimension (ID) of the sample set can be estimated to high accuracy. Second, we rigorously prove that using only this set of random projections, we can estimate the structure of the underlying manifold.

The stochastic approximation method is behind the solution to many important, actively-studied problems in machine learning. Despite its far-reaching application, there is almost no work on applying stochastic approximation to learning problems with constraints. The reason for this, we hypothesize, is that no robust, widely-applicable stochastic approximation method exists for handling such problems. We propose that interior-point methods are a natural solution. We establish the stability of a stochastic interior-point approximation method both analytically and empirically, and demonstrate its utility by deriving an on-line learning algorithm that also performs feature selection via L1 regularization.

"There are a lot of folks around the world, especially younger folks, contemplating whether to pursue a STEM degree or not. There might be self-doubt about whether their background becomes a barrier, or they might think tech is intimidating and whether they'll be able to do it. Even if one person who doesn't have enough resources or facing challenges, gathers the courage from examples like this, not just mine, it would bring a sense of achievement for me because I feel like there should be nothing that should stop a true learner." Pratibha serves on the AnitaB AI committee and has worked both in natural language processing and deep learning. She has founded a start-up in video analytics that was selected for the Target Accelerator program.

We present a new, massively parallel architecture for accelerating machine learning algorithms, based on arrays of variable-resolution arithmetic vector processing elements (VPE). Groups of VPEs operate in SIMD (single instruction multiple data) mode, and each group is connected to an independent memory bank. In this way memory bandwidth scales with the number of VPE, and the main data flows are local, keeping power dissipation low. With 256 VPEs, implemented on two FPGA (field programmable gate array) chips, we obtain a sustained speed of 19 GMACS (billion multiply-accumulate per sec.) for SVM training, and 86 GMACS for SVM classification. This performance is more than an order of magnitude higher than that of any FPGA implementation reported so far.

Regularized risk minimization often involves non-smooth optimization, either because of the loss function (e.g., hinge loss) or the regularizer (e.g., \ell_1 -regularizer). Gradient descent methods, though highly scalable and easy to implement, are known to converge slowly on these problems. In this paper, we develop novel accelerated gradient methods for stochastic optimization while still preserving their computational simplicity and scalability. The proposed algorithm, called SAGE (Stochastic Accelerated GradiEnt), exhibits fast convergence rates on stochastic optimization with both convex and strongly convex objectives. Experimental results show that SAGE is faster than recent (sub)gradient methods including FOLOS, SMIDAS and SCD.

Solving multi-agent reinforcement learning problems has proven difficult because of the lack of tractable algorithms. We provide the first approximation algorithm which solves stochastic games to within \epsilon relative error of the optimal game-theoretic solution, in time polynomial in 1/\epsilon . Our algorithm extends Murrays and Gordon's (2007) modified Bellman equation which determines the \emph{set} of all possible achievable utilities; this provides us a truly general framework for multi-agent learning. Further, we empirically validate our algorithm and find the computational cost to be orders of magnitude less than what the theory predicts.

A classic debate in cognitive science revolves around understanding how children learn complex linguistic rules, such as those governing restrictions on verb alternations, without negative evidence. Traditionally, formal learnability arguments have been used to claim that such learning is impossible without the aid of innate language-specific knowledge. However, recently, researchers have shown that statistical models are capable of learning complex rules from only positive evidence. These two kinds of learnability analyses differ in their assumptions about the role of the distribution from which linguistic input is generated. The former analyses assume that learners seek to identify grammatical sentences in a way that is robust to the distribution from which the sentences are generated, analogous to discriminative approaches in machine learning. The latter assume that learners are trying to estimate a generative model, with sentences being sampled from that model.

We propose a new nonparametric learning method based on multivariate dyadic regression trees (MDRTs). Unlike traditional dyadic decision trees (DDTs) or classification and regression trees (CARTs), MDRTs are constructed using penalized empirical risk minimization with a novel sparsity-inducing penalty. Theoretically, we show that MDRTs can simultaneously adapt to the unknown sparsity and smoothness of the true regression functions, and achieve the nearly optimal rates of convergence (in a minimax sense) for the class of (\alpha, C) -smooth functions. Empirically, MDRTs can simultaneously conduct function estimation and variable selection in high dimensions. To make MDRTs applicable for large-scale learning problems, we propose a greedy heuristics.