Agniva Chowdhury

Sahil Joshi, Agniva Chowdhury, Wyatt Bellinger et al.

Exploiting sparsity during long-context inference is central to scaling large language models, as attention dominates the cost of autoregressive decoding. Sparse attention reduces this cost by restricting computation to a subset of tokens, but its effectiveness depends critically on efficient scoring and selection of relevant tokens at inference time. We revisit Locality-Sensitive Hashing (LSH) as a sparsification primitive and introduce SOCKET, a SOft Collision Kernel EsTimator that replaces hard bucket matches with probabilistic, similarity-aware aggregation. Our key insight is that hard LSH produces discrete collision signals and is therefore poorly suited for ranking. In contrast, soft LSH aggregates graded collision evidence across hash tables, preserving the stability of relative ordering among the true top-$k$ tokens. This transformation elevates LSH from a candidate-generation heuristic to a principled and mathematically grounded scoring kernel for sparse attention. Leveraging this property, SOCKET enables efficient token selection without ad-hoc voting mechanism, and matches or surpasses established sparse attention baselines across multiple long-context benchmarks using diverse set of models. With a custom CUDA kernel for scoring keys and a Flash Decode Triton backend for sparse attention, SOCKET achieves up to 1.5$\times$ higher throughput than FlashAttention, making it an effective tool for long-context inference. Code is open-sourced at https://github.com/amarka8/SOCKET.

Sahil Joshi, Prithvi Dixit, Agniva Chowdhury et al.

Sparsity has long been a central theme in LLM efficiency, but its role in context processing remains unresolved. As LLM workloads shift toward longer contexts and agentic interactions, the compute and memory bottlenecks of attention become increasingly critical, raising the question of whether these constraints are fundamental. Our position is that these constraints are artificial and unnecessary, and that the future of LLM inference lies in extreme but principled sparsity along the context dimension. This position is supported by several strands of empirical and theoretical evidence. First, we find the insistence on dense attention unreasonable, since in a long context a query effectively projects O(N) attention information into a hidden space of dimension d << N, making the process inherently lossy. Second, we perform an extensive study of sparsity in LLMs spanning 20 models across five model families, varying context lengths, and different sparsity levels. We empirically demonstrate a strong trend: current LLMs, despite not being trained for context sparsity, are remarkably robust to inference-time decode sparsity across tasks of varying complexity, including retrieval, multi-hop QA, mathematical reasoning, and agentic coding. Importantly, we also show that current hardware is already sufficient to realize substantial gains from this sparsity. For example, our sparse decode kernels accelerate large-context processing by up to 10x over FlashInfer at 50x sparsity levels on hardware such as the H100. Overall, these results position extreme context sparsity not as a heuristic, but as a principled foundation for LLM inference, training, and architecture design: one that is both feasible and beneficial, and a compelling direction for future systems.

Frank Liu, Agniva Chowdhury

In various scientific and engineering applications, there is typically an approximate model of the underlying complex system, even though it contains both aleatoric and epistemic uncertainties. In this paper, we present a principled method to incorporate these approximate models as physics priors in modeling, to prevent overfitting and enhancing the generalization capabilities of the trained models. Utilizing the structural risk minimization (SRM) inductive principle pioneered by Vapnik, this approach structures the physics priors into generalized regularizers. The experimental results demonstrate that our method achieves up to two orders of magnitude of improvement in testing accuracy.

Agniva Chowdhury, Pradeep Ramuhalli

In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we present a simple, randomized sampling-based algorithm for logistic regression problem that guarantees high-quality approximations to both the estimated probabilities and the overall discrepancy of the model. Our analysis builds upon two simple structural conditions that boil down to randomized matrix multiplication, a fundamental and well-understood primitive of randomized numerical linear algebra. We analyze the properties of estimated probabilities of logistic regression when leverage scores are used to sample observations, and prove that accurate approximations can be achieved with a sample whose size is much smaller than the total number of observations. To further validate our theoretical findings, we conduct comprehensive empirical evaluations. Overall, our work sheds light on the potential of using randomized sampling approaches to efficiently approximate the estimated probabilities in logistic regression, offering a practical and computationally efficient solution for large-scale datasets.

Sahil Joshi, Agniva Chowdhury, Amar Kanakamedala et al.

Softmax Attention has a quadratic time complexity, which becomes prohibitive to run at long contexts, even with highly optimized GPU kernels. For example, FlashAttention (an exact, GPU-optimized implementation of Softmax Attention) cannot complete a single forward-backward pass of a multi-head attention layer once the context exceeds ~4 million tokens on an NVIDIA GH200 (96 GB). We introduce RACE Attention, a kernel-inspired alternative to Softmax Attention that is linear in sequence length and embedding dimension. RACE Attention replaces the exponential kernel with a sharpened angular (cosine) similarity, and approximates attention outputs via randomized projections and soft Locality-Sensitive Hashing (LSH). Across language modeling, masked language modeling, and text classification, RACE Attention matches the accuracy of strong baselines while reducing runtime and memory. In a controlled scale test, it processes up to 12 million tokens during a single forward-backward pass on an NVIDIA GH200 GPU and 75 million tokens on an Intel Xeon Gold 5220R CPU, well beyond the practical limits of the current state-of-the-art attention implementations. RACE Attention thus offers a practical, theoretically grounded mechanism for outrageously long context windows on today's hardware. We hope that it gets adopted in practice.

Agniva Chowdhury, Petros Drineas, David P. Woodruff et al.

Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have been proposed, which are termed Sparse Principal Component Analysis (SPCA). In this paper, we present thresholding as a provably accurate, polynomial time, approximation algorithm for the SPCA problem, without imposing any restrictive assumptions on the input covariance matrix. Our first thresholding algorithm using the Singular Value Decomposition is conceptually simple; is faster than current state-of-the-art; and performs well in practice. On the negative side, our (novel) theoretical bounds do not accurately predict the strong practical performance of this approach. The second algorithm solves a well-known semidefinite programming relaxation and then uses a novel, two step, deterministic thresholding scheme to compute a sparse principal vector. It works very well in practice and, remarkably, this solid practical performance is accurately predicted by our theoretical bounds, which bridge the theory-practice gap better than current state-of-the-art.

Agniva Chowdhury, Jiasen Yang, Petros Drineas

Fisher discriminant analysis (FDA) is a widely used method for classification and dimensionality reduction. When the number of predictor variables greatly exceeds the number of observations, one of the alternatives for conventional FDA is regularized Fisher discriminant analysis (RFDA). In this paper, we present a simple, iterative, sketching-based algorithm for RFDA that comes with provable accuracy guarantees when compared to the conventional approach. Our analysis builds upon two simple structural results that boil down to randomized matrix multiplication, a fundamental and well-understood primitive of randomized linear algebra. We analyze the behavior of RFDA when the ridge leverage and the standard leverage scores are used to select predictor variables and we prove that accurate approximations can be achieved by a sample whose size depends on the effective degrees of freedom of the RFDA problem. Our results yield significant improvements over existing approaches and our empirical evaluations support our theoretical analyses.

Agniva Chowdhury, Jiasen Yang, Petros Drineas

Projection-cost preservation is a low-rank approximation guarantee which ensures that the cost of any rank-$k$ projection can be preserved using a smaller sketch of the original data matrix. We present a general structural result outlining four sufficient conditions to achieve projection-cost preservation. These conditions can be satisfied using tools from the Randomized Linear Algebra literature.