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Kirankumar Shiragur

Publications and source records attributed to Kirankumar Shiragur.

At least 19 recordsLinked to original sources
arXiv2026

EigenLI: Spectral Approximations to Late Interaction

Late-interaction models such as ColBERT achieve strong effectiveness by representing each document with many token-level vectors, but this expressivity leads to large indexing cost, storage footprints and expensive MaxSim scoring. We show that late-interaction representations exhibit an intrinsic low-rank structure: document token embeddings concentrate in a low-dimensional subspace that preserves most of the retrieval signal. Leveraging this observation, we introduce EigenLI, a spectral approximation framework that compresses late-interaction representations via document-specific low-dimensional subspaces. Unlike clustering or pooling methods, EigenLI identifies the dominant eigendirections of each document and uses them to construct reduced interaction representations. Empirically, $k$-EigenLI with $k \le 32$ outperforms k-means and Ward clustering based pooling methods on ColBERTv2 and AnswerAI-ColBERT-small; GTE-ModernColBERT exhibits a different tradeoff at $k=32$, where clustering methods perform better. The same spectral construction also yields EigenLI-SV, an ANN-compatible single-vector representation derived from the second-order summary of the reduced structure. Across multiple datasets and all three text models, EigenLI-SV consistently outperforms comparable single-vector surrogates such as MUVERA.

cs.IR↗
arXiv2026

Retrieval Needs Multivectors: An Exponential Separation

Recent works have highlighted the expressive limitations of embedding based retrieval models through both theoretical analyses and challenging benchmarks such as LIMIT. While multi-vector embeddings consistently outperform single-vector embeddings, the precise representational gap between them remains poorly understood. In this work, following Jayaram's work, we provide the first explicit family of query and document sets, together with their relevance matrices, for which single-vector embeddings that rank all relevant documents above irrelevant ones require exponential size, whereas polynomial-size multi-vector embeddings suffice. Our result establishes an exponential separation between the expressive power of single-vector and multi-vector embeddings for the task of ranking of documents as opposed to approximating numerical scores as in the work of Jayaram. Motivated by our theoretical construction, we introduce ANDOR, a new retrieval benchmark that naturally instantiates these hard examples. We show that state-of-the-art single-vector embedding models perform poorly on ANDOR in the zero-shot setting and exhibit only marginal improvements after fine-tuning, highlighting the inherent difficulty of the benchmark compared to prior work. In contrast, multi-vector models consistently outperform their single-vector counterparts and improve substantially with fine-tuning, closely aligning with our theoretical predictions.

cs.IR↗
arXiv2026

Quantization Beyond Uniform Bit Allocation

Quantization is a fundamental technique to handle the growing sizes of embeddings generated by modern models. Existing quantization schemes are largely embedding agnostic and allocate bits uniformly across dimensions. However, recent models produce embeddings with significant geometric structure. In this work, we investigate whether a variable bit allocation scheme can improve quantization quality under a fixed memory budget. We propose a simple variable bit allocation framework that partitions an embedding into contiguous buckets and allocates storage non-uniformly across them. Using a greedy allocation strategy, we instantiate this framework for both Product Quantization (PQ) and Scalar Quantization (SQ). We perform a series of experiments on embeddings known to have the Matryoshka property (MRL), and consistently observe that non-uniform allocations outperform uniform baselines at identical storage budgets. The largest improvements occur in the low-bit regime, where uniform allocation is particularly inefficient for MRL embeddings. At the same compression rates, variable allocation improves recall by up to 8\% for PQ and up to 18\% for SQ. Our results suggest a new direction for structure-aware compression and indexing techniques for large-scale retrieval systems.

cs.IR↗
arXiv2026

On Strengths and Limitations of Single-Vector Embeddings

Recent work (Weller et al., 2025) introduced a naturalistic dataset called LIMIT and showed empirically that a wide range of popular single-vector embedding models suffer substantial drops in retrieval quality, raising concerns about the reliability of single-vector embeddings for retrieval. Although (Weller et al., 2025) proposed limited dimensionality as the main factor contributing to this, we show that dimensionality alone cannot explain the observed failures. We observe from results in (Alon et al., 2016) that $2k+1$-dimensional vector embeddings suffice for top-$k$ retrieval. This result points to other drivers of poor performance. Controlling for tokenization artifacts and linguistic similarity between attributes yields only modest gains. In contrast, we find that domain shift and misalignment between embedding similarities and the task's underlying notion of relevance are major contributors; finetuning mitigates these effects and can improve recall substantially. Even with finetuning, however, single-vector models remain markedly weaker than multi-vector representations, pointing to fundamental limitations. Moreover, finetuning single-vector models on LIMIT-like datasets leads to catastrophic forgetting (performance on MSMARCO drops by more than 40%), whereas forgetting for multi-vector models is minimal. To better understand the gap between performance of single-vector and multi-vector models, we study the drowning in documents paradox (Reimers \& Gurevych, 2021; Jacob et al., 2025): as the corpus grows, relevant documents are increasingly "drowned out" because embedding similarities behave, in part, like noisy statistical proxies for relevance. Through experiments and mathematical calculations on toy mathematical models, we illustrate why single-vector models are more susceptible to drowning effects compared to multi-vector models.

cs.IR↗
arXiv2026

Chow-Liu Ordering for Long-Context Reasoning in Chain-of-Agents

Sequential multi-agent reasoning frameworks such as Chain-of-Agents (CoA) handle long-context queries by decomposing inputs into chunks and processing them sequentially using LLM-based worker agents that read from and update a bounded shared memory. From a probabilistic perspective, CoA aims to approximate the conditional distribution corresponding to a model capable of jointly reasoning over the entire long context. CoA achieves this through a latent-state factorization in which only bounded summaries of previously processed evidence are passed between agents. The resulting bounded-memory approximation introduces a lossy information bottleneck, making the final evidence state inherently dependent on the order in which chunks are processed. In this work, we study the problem of chunk ordering for long-context reasoning. We use the well-known Chow-Liu trees to learn a dependency structure that prioritizes strongly related chunks. Empirically, we show that a breadth-first traversal of the resulting tree yields chunk orderings that reduce information loss across agents and consistently outperform both default document-chunk ordering and semantic score-based ordering in answer relevance and exact-match accuracy across three long-context benchmarks.

cs.CL↗
arXiv2026

Welfarist Formulations for Diverse Similarity Search

Nearest Neighbor Search (NNS) is a fundamental problem in data structures with wide-ranging applications, such as web search, recommendation systems, and, more recently, retrieval-augmented generations (RAG). In such recent applications, in addition to the relevance (similarity) of the returned neighbors, diversity among the neighbors is a central requirement. In this paper, we develop principled welfare-based formulations in NNS for realizing diversity across attributes. Our formulations are based on welfare functions -- from mathematical economics -- that satisfy central diversity (fairness) and relevance (economic efficiency) axioms. With a particular focus on Nash social welfare, we note that our welfare-based formulations provide objective functions that adaptively balance relevance and diversity in a query-dependent manner. Notably, such a balance was not present in the prior constraint-based approach, which forced a fixed level of diversity and optimized for relevance. In addition, our formulation provides a parametric way to control the trade-off between relevance and diversity, providing practitioners with flexibility to tailor search results to task-specific requirements. We develop efficient nearest neighbor algorithms with provable guarantees for the welfare-based objectives. Notably, our algorithm can be applied on top of any standard ANN method (i.e., use standard ANN method as a subroutine) to efficiently find neighbors that approximately maximize our welfare-based objectives. Experimental results demonstrate that our approach is practical and substantially improves diversity while maintaining high relevance of the retrieved neighbors.

cs.DS↗
arXiv2025

Incorporating Token Importance in Multi-Vector Retrieval

ColBERT introduced a late interaction mechanism that independently encodes queries and documents using BERT, and computes similarity via fine-grained interactions over token-level vector representations. This design enables expressive matching while allowing efficient computation of scores, as the multi-vector document representations could be pre-computed offline. ColBERT models distance using a Chamfer-style function: for each query token, it selects the closest document token and sums these distances across all query tokens. In our work, we explore enhancements to the Chamfer distance function by computing a weighted sum over query token contributions, where weights reflect the token importance. Empirically, we show that this simple extension, requiring only token-weight training while keeping the multi-vector representations fixed, further enhances the expressiveness of late interaction multi-vector mechanism. In particular, on the BEIR benchmark, our method achieves an average improvement of 1.28\% in Recall@10 in the zero-shot setting using IDF-based weights, and 3.66\% through few-shot fine-tuning.

cs.IR↗
arXiv2025

COSMIR: Chain Orchestrated Structured Memory for Iterative Reasoning over Long Context

Reasoning over very long inputs remains difficult for large language models (LLMs). Common workarounds either shrink the input via retrieval (risking missed evidence), enlarge the context window (straining selectivity), or stage multiple agents to read in pieces. In staged pipelines (e.g., Chain of Agents, CoA), free-form summaries passed between agents can discard crucial details and amplify early mistakes. We introduce COSMIR (Chain Orchestrated Structured Memory for Iterative Reasoning), a chain-style framework that replaces ad hoc messages with a structured memory. A Planner agent first turns a user query into concrete, checkable sub-questions. worker agents process chunks via a fixed micro-cycle: Extract, Infer, Refine, writing all updates to the shared memory. A Manager agent then Synthesizes the final answer directly from the memory. This preserves step-wise read-then-reason benefits while changing both the communication medium (structured memory) and the worker procedure (fixed micro-cycle), yielding higher faithfulness, better long-range aggregation, and auditability. On long-context QA from the HELMET suite, COSMIR reduces propagation-stage information loss and improves accuracy over a CoA baseline.

cs.AI↗
arXiv2025

Cost Efficient Fairness Audit Under Partial Feedback

We study the problem of auditing the fairness of a given classifier under partial feedback, where true labels are available only for positively classified individuals, (e.g., loan repayment outcomes are observed only for approved applicants). We introduce a novel cost model for acquiring additional labeled data, designed to more accurately reflect real-world costs such as credit assessment, loan processing, and potential defaults. Our goal is to find optimal fairness audit algorithms that are more cost-effective than random exploration and natural baselines. In our work, we consider two audit settings: a black-box model with no assumptions on the data distribution, and a mixture model, where features and true labels follow a mixture of exponential family distributions. In the black-box setting, we propose a near-optimal auditing algorithm under mild assumptions and show that a natural baseline can be strictly suboptimal. In the mixture model setting, we design a novel algorithm that achieves significantly lower audit cost than the black-box case. Our approach leverages prior work on learning from truncated samples and maximum-a-posteriori oracles, and extends known results on spherical Gaussian mixtures to handle exponential family mixtures, which may be of independent interest. Moreover, our algorithms apply to popular fairness metrics including demographic parity, equal opportunity, and equalized odds. Empirically, we demonstrate strong performance of our algorithms on real-world fair classification datasets like Adult Income and Law School, consistently outperforming natural baselines by around 50% in terms of audit cost.

cs.LG↗
arXiv2025

Graph-Based Algorithms for Diverse Similarity Search

Nearest neighbor search is a fundamental data structure problem with many applications in machine learning, computer vision, recommendation systems and other fields. Although the main objective of the data structure is to quickly report data points that are closest to a given query, it has long been noted (Carbonell and Goldstein, 1998) that without additional constraints the reported answers can be redundant and/or duplicative. This issue is typically addressed in two stages: in the first stage, the algorithm retrieves a (large) number $r$ of points closest to the query, while in the second stage, the $r$ points are post-processed and a small subset is selected to maximize the desired diversity objective. Although popular, this method suffers from a fundamental efficiency bottleneck, as the set of points retrieved in the first stage often needs to be much larger than the final output. In this paper we present provably efficient algorithms for approximate nearest neighbor search with diversity constraints that bypass this two stage process. Our algorithms are based on popular graph-based methods, which allows us to "piggy-back" on the existing efficient implementations. These are the first graph-based algorithms for nearest neighbor search with diversity constraints. For data sets with low intrinsic dimension, our data structures report a diverse set of $k$ points approximately closest to the query, in time that only depends on $k$ and $\log \Delta$, where $\Delta$ is the ratio of the diameter to the closest pair distance in the data set. This bound is qualitatively similar to the best known bounds for standard (non-diverse) graph-based algorithms. Our experiments show that the search time of our algorithms is substantially lower than that using the standard two-stage approach.

cs.DS↗
arXiv2024

Learning Mixtures of Unknown Causal Interventions

The ability to conduct interventions plays a pivotal role in learning causal relationships among variables, thus facilitating applications across diverse scientific disciplines such as genomics, economics, and machine learning. However, in many instances within these applications, the process of generating interventional data is subject to noise: rather than data being sampled directly from the intended interventional distribution, interventions often yield data sampled from a blend of both intended and unintended interventional distributions. We consider the fundamental challenge of disentangling mixed interventional and observational data within linear Structural Equation Models (SEMs) with Gaussian additive noise without the knowledge of the true causal graph. We demonstrate that conducting interventions, whether do or soft, yields distributions with sufficient diversity and properties conducive to efficiently recovering each component within the mixture. Furthermore, we establish that the sample complexity required to disentangle mixed data inversely correlates with the extent of change induced by an intervention in the equations governing the affected variable values. As a result, the causal graph can be identified up to its interventional Markov Equivalence Class, similar to scenarios where no noise influences the generation of interventional data. We further support our theoretical findings by conducting simulations wherein we perform causal discovery from such mixed data.

stat.ML↗
arXiv2024

Causal Discovery with Fewer Conditional Independence Tests

Many questions in science center around the fundamental problem of understanding causal relationships. However, most constraint-based causal discovery algorithms, including the well-celebrated PC algorithm, often incur an exponential number of conditional independence (CI) tests, posing limitations in various applications. Addressing this, our work focuses on characterizing what can be learned about the underlying causal graph with a reduced number of CI tests. We show that it is possible to a learn a coarser representation of the hidden causal graph with a polynomial number of tests. This coarser representation, named Causal Consistent Partition Graph (CCPG), comprises of a partition of the vertices and a directed graph defined over its components. CCPG satisfies consistency of orientations and additional constraints which favor finer partitions. Furthermore, it reduces to the underlying causal graph when the causal graph is identifiable. As a consequence, our results offer the first efficient algorithm for recovering the true causal graph with a polynomial number of tests, in special cases where the causal graph is fully identifiable through observational data and potentially additional interventions.

cs.LG↗
arXiv2024

Quantifying the Gain in Weak-to-Strong Generalization

Recent advances in large language models have shown capabilities that are extraordinary and near-superhuman. These models operate with such complexity that reliably evaluating and aligning them proves challenging for humans. This leads to the natural question: can guidance from weak models (like humans) adequately direct the capabilities of strong models? In a recent and somewhat surprising work, Burns et al. (2023) empirically demonstrated that when strong models (like GPT-4) are finetuned using labels generated by weak supervisors (like GPT-2), the strong models outperform their weaker counterparts -- a phenomenon they term weak-to-strong generalization. In this work, we present a theoretical framework for understanding weak-to-strong generalization. Specifically, we show that the improvement in performance achieved by strong models over their weaker counterparts is quantified by the misfit error incurred by the strong model on labels generated by the weaker model. Our theory reveals several curious algorithmic insights. For instance, we can predict the amount by which the strong model will improve over the weak model, and also choose among different weak models to train the strong model, based on its misfit error. We validate our theoretical findings through various empirical assessments.

cs.LG↗
arXiv2024

Membership Testing in Markov Equivalence Classes via Independence Query Oracles

Understanding causal relationships between variables is a fundamental problem with broad impact in numerous scientific fields. While extensive research has been dedicated to learning causal graphs from data, its complementary concept of testing causal relationships has remained largely unexplored. While learning involves the task of recovering the Markov equivalence class (MEC) of the underlying causal graph from observational data, the testing counterpart addresses the following critical question: Given a specific MEC and observational data from some causal graph, can we determine if the data-generating causal graph belongs to the given MEC? We explore constraint-based testing methods by establishing bounds on the required number of conditional independence tests. Our bounds are in terms of the size of the maximum undirected clique ($s$) of the given MEC. In the worst case, we show a lower bound of $\exp(\Omega(s))$ independence tests. We then give an algorithm that resolves the task with $\exp(O(s))$ tests, matching our lower bound. Compared to the learning problem, where algorithms often use a number of independence tests that is exponential in the maximum in-degree, this shows that testing is relatively easier. In particular, it requires exponentially less independence tests in graphs featuring high in-degrees and small clique sizes. Additionally, using the DAG associahedron, we provide a geometric interpretation of testing versus learning and discuss how our testing result can aid learning.

cs.LG↗
arXiv2024

Causal Discovery under Off-Target Interventions

Causal graph discovery is a significant problem with applications across various disciplines. However, with observational data alone, the underlying causal graph can only be recovered up to its Markov equivalence class, and further assumptions or interventions are necessary to narrow down the true graph. This work addresses the causal discovery problem under the setting of stochastic interventions with the natural goal of minimizing the number of interventions performed. We propose the following stochastic intervention model which subsumes existing adaptive noiseless interventions in the literature while capturing scenarios such as fat-hand interventions and CRISPR gene knockouts: any intervention attempt results in an actual intervention on a random subset of vertices, drawn from a distribution dependent on attempted action. Under this model, we study the two fundamental problems in causal discovery of verification and search and provide approximation algorithms with polylogarithmic competitive ratios and provide some preliminary experimental results.

cs.LG↗
arXiv2023

Testing with Non-identically Distributed Samples

We examine the extent to which sublinear-sample property testing and estimation apply to settings where samples are independently but not identically distributed. Specifically, we consider the following distributional property testing framework: Suppose there is a set of distributions over a discrete support of size $k$, $p_1, p_2,\ldots,p_T$, and we obtain $c$ independent draws from each distribution. Suppose the goal is to learn or test a property of the average distribution, $p_{avg}$. This setup models a number of important practical settings where the individual distributions correspond to heterogeneous entities -- either individuals, chronologically distinct time periods, spatially separated data sources, etc. From a learning standpoint, even with $c=1$ samples from each distribution, $\Theta(k/\varepsilon^2)$ samples are necessary and sufficient to learn $p_{avg}$ to within error $\varepsilon$ in $\ell_1$ distance. To test uniformity or identity -- distinguishing the case that $p_{avg}$ is equal to some reference distribution, versus has $\ell_1$ distance at least $\varepsilon$ from the reference distribution, we show that a linear number of samples in $k$ is necessary given $c=1$ samples from each distribution. In contrast, for $c \ge 2$, we recover the usual sublinear sample testing guarantees of the i.i.d.\ setting: we show that $O(\sqrt{k}/\varepsilon^2 + 1/\varepsilon^4)$ total samples are sufficient, matching the optimal sample complexity in the i.i.d.\ case in the regime where $\varepsilon \ge k^{-1/4}$. Additionally, we show that in the $c=2$ case, there is a constant $\rho > 0$ such that even in the linear regime with $\rho k$ samples, no tester that considers the multiset of samples (ignoring which samples were drawn from the same $p_i$) can perform uniformity testing. We also extend our techniques to the problem of testing "closeness" of two distributions.

cs.DS↗
arXiv2023

Meek Separators and Their Applications in Targeted Causal Discovery

Learning causal structures from interventional data is a fundamental problem with broad applications across various fields. While many previous works have focused on recovering the entire causal graph, in practice, there are scenarios where learning only part of the causal graph suffices. This is called $targeted$ causal discovery. In our work, we focus on two such well-motivated problems: subset search and causal matching. We aim to minimize the number of interventions in both cases. Towards this, we introduce the $Meek~separator$, which is a subset of vertices that, when intervened, decomposes the remaining unoriented edges into smaller connected components. We then present an efficient algorithm to find Meek separators that are of small sizes. Such a procedure is helpful in designing various divide-and-conquer-based approaches. In particular, we propose two randomized algorithms that achieve logarithmic approximation for subset search and causal matching, respectively. Our results provide the first known average-case provable guarantees for both problems. We believe that this opens up possibilities to design near-optimal methods for many other targeted causal structure learning problems arising from various applications.

cs.LG↗
arXiv2023

Structured Semidefinite Programming for Recovering Structured Preconditioners

We develop a general framework for finding approximately-optimal preconditioners for solving linear systems. Leveraging this framework we obtain improved runtimes for fundamental preconditioning and linear system solving problems including the following. We give an algorithm which, given positive definite $\mathbf{K} \in \mathbb{R}^{d \times d}$ with $\mathrm{nnz}(\mathbf{K})$ nonzero entries, computes an $\epsilon$-optimal diagonal preconditioner in time $\widetilde{O}(\mathrm{nnz}(\mathbf{K}) \cdot \mathrm{poly}(\kappa^\star,\epsilon^{-1}))$, where $\kappa^\star$ is the optimal condition number of the rescaled matrix. We give an algorithm which, given $\mathbf{M} \in \mathbb{R}^{d \times d}$ that is either the pseudoinverse of a graph Laplacian matrix or a constant spectral approximation of one, solves linear systems in $\mathbf{M}$ in $\widetilde{O}(d^2)$ time. Our diagonal preconditioning results improve state-of-the-art runtimes of $\Omega(d^{3.5})$ attained by general-purpose semidefinite programming, and our solvers improve state-of-the-art runtimes of $\Omega(d^{\omega})$ where $\omega > 2.3$ is the current matrix multiplication constant. We attain our results via new algorithms for a class of semidefinite programs (SDPs) we call matrix-dictionary approximation SDPs, which we leverage to solve an associated problem we call matrix-dictionary recovery.

cs.DS↗