Benjamin Coleman

David Torres Ramos, Vihan Lakshman, Chen Luo et al.

We study the problem of building space-efficient, in-memory indexes for massive key-value datasets with highly skewed value distributions. This challenge arises in many data-intensive domains and is particularly acute in computational genomics, where $k$-mer count tables can contain billions of entries dominated by a single frequent value. While recent work has proposed to address this problem by augmenting compressed static functions (CSFs) with pre-filters, existing approaches rely on complex heuristics and lack formal guarantees. In this paper, we introduce a principled algorithm, called AutoCSF, for combining CSFs with pre-filtering to provably handle skewed distributions with near-optimal space usage. We improve upon prior CSF pre-filtering constructions by (1) deriving a mathematically rigorous decision criterion for when filter augmentation is beneficial; (2) presenting a general algorithmic framework for integrating CSFs with modern set membership data structures beyond the classic Bloom filter; and (3) establishing theoretical guarantees on the overall space usage of the resulting indexes. Our open-source implementation of AutoCSF demonstrates space savings over baseline methods while maintaining low query latency.

Nicholas Meisburger, Vihan Lakshman, Benito Geordie et al.

Efficient large-scale neural network training and inference on commodity CPU hardware is of immense practical significance in democratizing deep learning (DL) capabilities. Presently, the process of training massive models consisting of hundreds of millions to billions of parameters requires the extensive use of specialized hardware accelerators, such as GPUs, which are only accessible to a limited number of institutions with considerable financial resources. Moreover, there is often an alarming carbon footprint associated with training and deploying these models. In this paper, we take a step towards addressing these challenges by introducing BOLT, a sparse deep learning library for training large-scale search and recommendation models on standard CPU hardware. BOLT provides a flexible, high-level API for constructing models that will be familiar to users of existing popular DL frameworks. By automatically tuning specialized hyperparameters, BOLT also abstracts away the algorithmic details of sparse network training. We evaluate BOLT on a number of information retrieval tasks including product recommendations, text classification, graph neural networks, and personalization. We find that our proposed system achieves competitive performance with state-of-the-art techniques at a fraction of the cost and energy consumption and an order-of-magnitude faster inference time. BOLT has also been successfully deployed by multiple businesses to address critical problems, and we highlight one customer case study in the field of e-commerce.

Benjamin Coleman, David Torres Ramos, Vihan Lakshman et al.

Lookup tables are a fundamental structure in many data processing and systems applications. Examples include tokenized text in NLP, quantized embedding collections in recommendation systems, integer sketches for streaming data, and hash-based string representations in genomics. With the increasing size of web-scale data, such applications often require compression techniques that support fast random $O(1)$ lookup of individual parameters directly on the compressed data (i.e. without blockwise decompression in RAM). While the community has proposd a number of succinct data structures that support queries over compressed representations, these approaches do not fully leverage the low-entropy structure prevalent in real-world workloads to reduce space. Inspired by recent advances in static function construction techniques, we propose a space-efficient representation of immutable key-value data, called CARAMEL, specifically designed for the case where the values are multi-sets. By carefully combining multiple compressed static functions, CARAMEL occupies space proportional to the data entropy with low memory overheads and minimal lookup costs. We demonstrate 1.25-16x compression on practical lookup tasks drawn from real-world systems, improving upon established techniques, including a production-grade read-only database widely used for development within Amazon.com.

Shabnam Daghaghi, Benjamin Coleman, Benito Geordie et al.

Data sampling is an effective method to improve the training speed of neural networks, with recent results demonstrating that it can even break the neural scaling laws. These results critically rely on high-quality scores to estimate the importance of an input to the network. We observe that there are two dominant strategies: static sampling, where the scores are determined before training, and dynamic sampling, where the scores can depend on the model weights. Static algorithms are computationally inexpensive but less effective than their dynamic counterparts, which can cause end-to-end slowdown due to their need to explicitly compute losses. To address this problem, we propose a novel sampling distribution based on nonparametric kernel regression that learns an effective importance score as the neural network trains. However, nonparametric regression models are too computationally expensive to accelerate end-to-end training. Therefore, we develop an efficient sketch-based approximation to the Nadaraya-Watson estimator. Using recent techniques from high-dimensional statistics and randomized algorithms, we prove that our Nadaraya-Watson sketch approximates the estimator with exponential convergence guarantees. Our sampling algorithm outperforms the baseline in terms of wall-clock time and accuracy on four datasets.

Minghao Yan, Bo Peng, Benjamin Coleman et al.

Large Language Models (LLMs) have emerged as powerful operators for evolutionary search, yet the design of efficient search scaffolds remains ad hoc. While promising, current LLM-in-the-loop systems lack a systematic approach to managing the evolutionary process. We identify three distinct failure modes: Context Pollution, where experiment history biases future candidate generation; Mode Collapse, where agents stagnate in local minima due to poor exploration-exploitation balance; and Weak Collaboration, where rigid crossover strategies fail to leverage parallel search trajectories effectively. We introduce Progress-Aware Consistent Evolution (PACEvolve), a framework designed to robustly govern the agent's context and search dynamics, to address these challenges. PACEvolve combines hierarchical context management (HCM) with pruning to address context pollution; momentum-based backtracking (MBB) to escape local minima; and a self-adaptive sampling policy that unifies backtracking and crossover for dynamic search coordination (CE), allowing agents to balance internal refinement with cross-trajectory collaboration. We demonstrate that PACEvolve provides a systematic path to consistent, long-horizon self-improvement, achieving state-of-the-art results on LLM-SR and KernelBench, while discovering solutions surpassing the record on Modded NanoGPT.

Gemma Team, Aishwarya Kamath, Johan Ferret et al. · deepmind, mit

We introduce Gemma 3, a multimodal addition to the Gemma family of lightweight open models, ranging in scale from 1 to 27 billion parameters. This version introduces vision understanding abilities, a wider coverage of languages and longer context - at least 128K tokens. We also change the architecture of the model to reduce the KV-cache memory that tends to explode with long context. This is achieved by increasing the ratio of local to global attention layers, and keeping the span on local attention short. The Gemma 3 models are trained with distillation and achieve superior performance to Gemma 2 for both pre-trained and instruction finetuned versions. In particular, our novel post-training recipe significantly improves the math, chat, instruction-following and multilingual abilities, making Gemma3-4B-IT competitive with Gemma2-27B-IT and Gemma3-27B-IT comparable to Gemini-1.5-Pro across benchmarks. We release all our models to the community.

Noveen Sachdeva, Benjamin Coleman, Wang-Cheng Kang et al.

The training of large language models (LLMs) is expensive. In this paper, we study data-efficient approaches for pre-training LLMs, i.e., techniques that aim to optimize the Pareto frontier of model quality and training resource/data consumption. We seek to understand the tradeoffs associated with data selection routines based on (i) expensive-to-compute data-quality estimates, and (ii) maximization of coverage and diversity-based measures in the feature space. Our first technique, Ask-LLM, leverages the zero-shot reasoning capabilities of instruction-tuned LLMs to directly assess the quality of a training example. To target coverage, we propose Density sampling, which models the data distribution to select a diverse sample. In our comparison of 19 samplers, involving hundreds of evaluation tasks and pre-training runs, we find that Ask-LLM and Density are the best methods in their respective categories. Coverage sampling can recover the performance of the full data, while models trained on Ask-LLM data consistently outperform full-data training -- even when we reject 90% of the original dataset, while converging up to 70% faster.

Minghao Yan, Bo Peng, Benjamin Coleman et al.

Large language models have become drivers of evolutionary search, but most systems rely on a fixed, prompt-elicited policy to sample next candidates. This limits adaptation in practical engineering and research tasks, where evaluations are expensive, and progress depends on learning task-specific search dynamics. We introduce PACEvolve++, an advisor-model reinforcement learning framework for test-time policy adaptation in evolutionary search agents. PACEvolve++ decouples strategic search decisions from implementation: a trainable advisor generates, assesses, and selects hypotheses, while a stronger frontier model translates selected hypotheses into executable candidates. To train the advisor under non-stationary feedback, we propose a phase-adaptive approach that adapts its optimization strategy to different phases of the evolutionary process. Early in evolution, it uses group-relative feedback to learn broad search preferences; later, as reward gaps compress, it emphasizes best-of-$k$ frontier contribution to support stable refinement. Across expert-parallel load balancing, sequential recommendation, and protein fitness extrapolation, PACEvolve++ outperforms the state-of-the-art evolutionary search framework with frontier models, achieving faster convergence and stabilizing test-time training during evolutionary search.

Blaise Munyampirwa, Vihan Lakshman, Benjamin Coleman

Driven by recent breakthrough advances in neural representation learning, approximate near-neighbor (ANN) search over vector embeddings has emerged as a critical computational workload. With the introduction of the seminal Hierarchical Navigable Small World (HNSW) algorithm, graph-based indexes have established themselves as the overwhelmingly dominant paradigm for efficient and scalable ANN search. As the name suggests, HNSW searches a layered hierarchical graph to quickly identify neighborhoods of similar points to a given query vector. But is this hierarchy even necessary? A rigorous experimental analysis to answer this question would provide valuable insights into the nature of algorithm design for ANN search and motivate directions for future work in this increasingly crucial domain. We conduct an extensive benchmarking study covering more large-scale datasets than prior investigations of this question. We ultimately find that a flat navigable small world graph graph retains all of the benefits of HNSW on high-dimensional datasets, with latency and recall performance essentially \emph{identical} to the original algorithm but with less memory overhead. Furthermore, we go a step further and study \emph{why} the hierarchy of HNSW provides no benefit in high dimensions, hypothesizing that navigable small world graphs contain a well-connected, frequently traversed ``highway" of hub nodes that maintain the same purported function as the hierarchical layers. We present compelling empirical evidence that the \emph{Hub Highway Hypothesis} holds for real datasets and investigate the mechanisms by which the highway forms. The implications of this hypothesis may also provide future research directions in developing enhancements to graph-based ANN search.

Vihan Lakshman, Blaise Munyampirwa, Julian Shun et al.

Modern vector databases enable efficient retrieval over high-dimensional neural embeddings, powering applications from web search to retrieval-augmented generation. However, classical theory predicts such tasks should suffer from the curse of dimensionality, where distances between points become nearly indistinguishable, thereby crippling efficient nearest-neighbor search. We revisit this paradox through the lens of stability, the property that small perturbations to a query do not radically alter its nearest neighbors. Building on foundational results, we extend stability theory to three key retrieval settings widely used in practice: (i) multi-vector search, where we prove that the popular Chamfer distance metric preserves single-vector stability, while average pooling aggregation may destroy it; (ii) filtered vector search, where we show that sufficiently large penalties for mismatched filters can induce stability even when the underlying search is unstable; and (iii) sparse vector search, where we formalize and prove novel sufficient stability conditions. Across synthetic and real datasets, our experimental results match our theoretical predictions, offering concrete guidance for model and system design to avoid the curse of dimensionality.

Tianxin Wei, Noveen Sachdeva, Benjamin Coleman et al.

Statefulness is essential for large language model (LLM) agents to perform long-term planning and problem-solving. This makes memory a critical component, yet its management and evolution remain largely underexplored. Existing evaluations mostly focus on static conversational settings, where memory is passively retrieved from dialogue to answer queries, overlooking the dynamic ability to accumulate and reuse experience across evolving task streams. In real-world environments such as interactive problem assistants or embodied agents, LLMs are required to handle continuous task streams, yet often fail to learn from accumulated interactions, losing valuable contextual insights, a limitation that calls for test-time evolution, where LLMs retrieve, integrate, and update memory continuously during deployment. To bridge this gap, we introduce Evo-Memory, a comprehensive streaming benchmark and framework for evaluating self-evolving memory in LLM agents. Evo-Memory structures datasets into sequential task streams, requiring LLMs to search, adapt, and evolve memory after each interaction. We unify and implement over ten representative memory modules and evaluate them across 10 diverse multi-turn goal-oriented and single-turn reasoning and QA datasets. To better benchmark experience reuse, we provide a baseline method, ExpRAG, for retrieving and utilizing prior experience, and further propose ReMem, an action-think-memory refine pipeline that tightly integrates reasoning, task actions, and memory updates to achieve continual improvement.

Benjamin Coleman, Wang-Cheng Kang, Matthew Fahrbach et al.

Learning high-quality feature embeddings efficiently and effectively is critical for the performance of web-scale machine learning systems. A typical model ingests hundreds of features with vocabularies on the order of millions to billions of tokens. The standard approach is to represent each feature value as a d-dimensional embedding, introducing hundreds of billions of parameters for extremely high-cardinality features. This bottleneck has led to substantial progress in alternative embedding algorithms. Many of these methods, however, make the assumption that each feature uses an independent embedding table. This work introduces a simple yet highly effective framework, Feature Multiplexing, where one single representation space is used across many different categorical features. Our theoretical and empirical analysis reveals that multiplexed embeddings can be decomposed into components from each constituent feature, allowing models to distinguish between features. We show that multiplexed representations lead to Pareto-optimal parameter-accuracy tradeoffs for three public benchmark datasets. Further, we propose a highly practical approach called Unified Embedding with three major benefits: simplified feature configuration, strong adaptation to dynamic data distributions, and compatibility with modern hardware. Unified embedding gives significant improvements in offline and online metrics compared to highly competitive baselines across five web-scale search, ads, and recommender systems, where it serves billions of users across the world in industry-leading products.

Zichang Liu, Benjamin Coleman, Anshumali Shrivastava

Large machine learning models achieve unprecedented performance on various tasks and have evolved as the go-to technique. However, deploying these compute and memory hungry models on resource constraint environments poses new challenges. In this work, we propose mathematically provable Representer Sketch, a concise set of count arrays that can approximate the inference procedure with simple hashing computations and aggregations. Representer Sketch builds upon the popular Representer Theorem from kernel literature, hence the name, providing a generic fundamental alternative to the problem of efficient inference that goes beyond the popular approach such as quantization, iterative pruning and knowledge distillation. A neural network function is transformed to its weighted kernel density representation, which can be very efficiently estimated with our sketching algorithm. Empirically, we show that Representer Sketch achieves up to 114x reduction in storage requirement and 59x reduction in computation complexity without any drop in accuracy.

Aditya Desai, Benjamin Coleman, Anshumali Shrivastava

We introduce Density sketches (DS): a succinct online summary of the data distribution. DS can accurately estimate point wise probability density. Interestingly, DS also provides a capability to sample unseen novel data from the underlying data distribution. Thus, analogous to popular generative models, DS allows us to succinctly replace the real-data in almost all machine learning pipelines with synthetic examples drawn from the same distribution as the original data. However, unlike generative models, which do not have any statistical guarantees, DS leads to theoretically sound asymptotically converging consistent estimators of the underlying density function. Density sketches also have many appealing properties making them ideal for large-scale distributed applications. DS construction is an online algorithm. The sketches are additive, i.e., the sum of two sketches is the sketch of the combined data. These properties allow data to be collected from distributed sources, compressed into a density sketch, efficiently transmitted in the sketch form to a central server, merged, and re-sampled into a synthetic database for modeling applications. Thus, density sketches can potentially revolutionize how we store, communicate, and distribute data.

Louis Abraham, Gary Becigneul, Benjamin Coleman et al.

We study the problem usually referred to as group testing in the context of COVID-19. Given n samples collected from patients, how should we select and test mixtures of samples to maximize information and minimize the number of tests? Group testing is a well-studied problem with several appealing solutions, but recent biological studies impose practical constraints for COVID-19 that are incompatible with traditional methods. Furthermore, existing methods use unnecessarily restrictive solutions, which were devised for settings with more memory and compute constraints than the problem at hand. This results in poor utility. In the new setting, we obtain strong solutions for small values of n using evolutionary strategies. We then develop a new method combining Bloom filters with belief propagation to scale to larger values of n (more than 100) with good empirical results. We also present a more accurate decoding algorithm that is tailored for specific COVID-19 settings. This work demonstrates the practical gap between dedicated algorithms and well-known generic solutions. Our efforts results in a new and practical multiplex method yielding strong empirical performance without mixing more than a chosen number of patients into the same probe. Finally, we briefly discuss adaptive methods, casting them into the framework of adaptive sub-modularity.

Benjamin Coleman, Gaurav Gupta, John Chen et al.

Empirical risk minimization is perhaps the most influential idea in statistical learning, with applications to nearly all scientific and technical domains in the form of regression and classification models. To analyze massive streaming datasets in distributed computing environments, practitioners increasingly prefer to deploy regression models on edge rather than in the cloud. By keeping data on edge devices, we minimize the energy, communication, and data security risk associated with the model. Although it is equally advantageous to train models at the edge, a common assumption is that the model was originally trained in the cloud, since training typically requires substantial computation and memory. To this end, we propose STORM, an online sketch for empirical risk minimization. STORM compresses a data stream into a tiny array of integer counters. This sketch is sufficient to estimate a variety of surrogate losses over the original dataset. We provide rigorous theoretical analysis and show that STORM can estimate a carefully chosen surrogate loss for the least-squares objective. In an exhaustive experimental comparison for linear regression models on real-world datasets, we find that STORM allows accurate regression models to be trained.

Benjamin Coleman, Anshumali Shrivastava

Differential privacy (DP) is a compelling privacy definition that explains the privacy-utility tradeoff via formal, provable guarantees. Inspired by recent progress toward general-purpose data release algorithms, we propose a private sketch, or small summary of the dataset, that supports a multitude of machine learning tasks including regression, classification, density estimation, near-neighbor search, and more. Our sketch consists of randomized contingency tables that are indexed with locality-sensitive hashing and constructed with an efficient one-pass algorithm. We prove competitive error bounds for DP kernel density estimation. Existing methods for DP kernel density estimation scale poorly, often exponentially slower with an increase in dimensions. In contrast, our sketch can quickly run on large, high-dimensional datasets in a single pass. Exhaustive experiments show that our generic sketch delivers a similar privacy-utility tradeoff when compared to existing DP methods at a fraction of the computation cost. We expect that our sketch will enable differential privacy in distributed, large-scale machine learning settings.

Benjamin Coleman, Anshumali Shrivastava

Kernel density estimation is a simple and effective method that lies at the heart of many important machine learning applications. Unfortunately, kernel methods scale poorly for large, high dimensional datasets. Approximate kernel density estimation has a prohibitively high memory and computation cost, especially in the streaming setting. Recent sampling algorithms for high dimensional densities can reduce the computation cost but cannot operate online, while streaming algorithms cannot handle high dimensional datasets due to the curse of dimensionality. We propose RACE, an efficient sketching algorithm for kernel density estimation on high-dimensional streaming data. RACE compresses a set of N high dimensional vectors into a small array of integer counters. This array is sufficient to estimate the kernel density for a large class of kernels. Our sketch is practical to implement and comes with strong theoretical guarantees. We evaluate our method on real-world high-dimensional datasets and show that our sketch achieves 10x better compression compared to competing methods.

Gaurav Gupta, Minghao Yan, Benjamin Coleman et al.

DNA sequencing, especially of microbial genomes and metagenomes, has been at the core of recent research advances in large-scale comparative genomics. The data deluge has resulted in exponential growth in genomic datasets over the past years and has shown no sign of slowing down. Several recent attempts have been made to tame the computational burden of sequence search on these terabyte and petabyte-scale datasets, including raw reads and assembled genomes. However, no known implementation provides both fast query and construction time, keeps the low false-positive requirement, and offers cheap storage of the data structure. We propose a data structure for search called RAMBO (Repeated And Merged BloOm Filter) which is significantly faster in query time than state-of-the-art genome indexing methods- COBS (Compact bit-sliced signature index), Sequence Bloom Trees, HowDeSBT, and SSBT. Furthermore, it supports insertion and query process parallelism, cheap updates for streaming inputs, has a zero false-negative rate, a low false-positive rate, and a small index size. RAMBO converts the search problem into set membership testing among $K$ documents. Interestingly, it is a count-min sketch type arrangement of a membership testing utility (Bloom Filter in our case). The simplicity of the algorithm and embarrassingly parallel architecture allows us to stream and index a 170TB whole-genome sequence dataset in a mere 9 hours on a cluster of 100 nodes while competing methods require weeks.

Gaurav Gupta, Minghao Yan, Benjamin Coleman et al.

Multiple Set Membership Testing (MSMT) is a well-known problem in a variety of search and query applications. Given a dataset of K different sets and a query q, it aims to find all of the sets containing the query. Trivially, an MSMT instance can be reduced to K membership testing instances, each with the same q, leading to O(K) query time with a simple array of Bloom Filters. We propose a data-structure called RAMBO (Repeated And Merged BloOm Filter) that achieves O(\sqrt{K} log K) query time in expectation with an additional worst-case memory cost factor of O(log K) beyond the array of Bloom Filters. Due to this, RAMBO is a very fast and accurate data-structure. Apart from being embarrassingly parallel, supporting cheap updates for streaming inputs, zero false-negative rate, and low false-positive rate, RAMBO beats the state-of-the-art approaches for genome indexing methods: COBS (Compact bit-sliced signature index), Sequence Bloom Trees (a Bloofi based implementation), HowDeSBT, SSBT, and document indexing methods like BitFunnel. The proposed data-structure is simply a count-min sketch type arrangement of a membership testing utility (Bloom Filter in our case). It indexes k-grams and provides an approximate membership testing based search utility. The simplicity of the algorithm and embarrassingly parallel architecture allows us to index a 170 TB genome dataset in a mere 14 hours on a cluster of 100 nodes while competing methods require weeks.

Benjamin Coleman, Richard G. Baraniuk, Anshumali Shrivastava

We present the first sublinear memory sketch that can be queried to find the nearest neighbors in a dataset. Our online sketching algorithm compresses an N element dataset to a sketch of size $O(N^b \log^3 N)$ in $O(N^{(b+1)} \log^3 N)$ time, where $b < 1$. This sketch can correctly report the nearest neighbors of any query that satisfies a stability condition parameterized by $b$. We achieve sublinear memory performance on stable queries by combining recent advances in locality sensitive hash (LSH)-based estimators, online kernel density estimation, and compressed sensing. Our theoretical results shed new light on the memory-accuracy tradeoff for nearest neighbor search, and our sketch, which consists entirely of short integer arrays, has a variety of attractive features in practice. We evaluate the memory-recall tradeoff of our method on a friend recommendation task in the Google Plus social media network. We obtain orders of magnitude better compression than the random projection based alternative while retaining the ability to report the nearest neighbors of practical queries.