arXiv subjects

Sourav Chakraborty

Publications and source records attributed to Sourav Chakraborty.

At least 37 records · Page 2Linked to original sources

arXiv2025

Assessing the Quality of Binomial Samplers: A Statistical Distance Framework

Randomized algorithms depend on accurate sampling from probability distributions, as their correctness and performance hinge on the quality of the generated samples. However, even for common distributions like Binomial, exact sampling is computationally challenging, leading standard library implementations to rely on heuristics. These heuristics, while efficient, suffer from approximation and system representation errors, causing deviations from the ideal distribution. Although seemingly minor, such deviations can accumulate in downstream applications requiring large-scale sampling, potentially undermining algorithmic guarantees. In this work, we propose statistical distance as a robust metric for analyzing the quality of Binomial samplers, quantifying deviations from the ideal distribution. We derive rigorous bounds on the statistical distance for standard implementations and demonstrate the practical utility of our framework by enhancing APSEst, a DNF model counter, with improved reliability and error guarantees. To support practical adoption, we propose an interface extension that allows users to control and monitor statistical distance via explicit input/output parameters. Our findings emphasize the critical need for thorough and systematic error analysis in sampler design. As the first work to focus exclusively on Binomial samplers, our approach lays the groundwork for extending rigorous analysis to other common distributions, opening avenues for more robust and reliable randomized algorithms.

stat.CO↗

arXiv2025

Characterizing and Optimizing LLM Inference Workloads on CPU-GPU Coupled Architectures

Large language model (LLM)-based inference workloads increasingly dominate data center costs and resource utilization. Therefore, understanding the inference workload characteristics on evolving CPU-GPU coupled architectures is crucial for optimization. This paper presents an in-depth analysis of LLM inference behavior on loosely-coupled (PCIe A100/H100) and closely-coupled (GH200) systems. We analyze performance dynamics using fine-grained operator-to-kernel trace analysis, facilitated by our novel profiler SKIP and metrics like Total Kernel Launch and Queuing Time (TKLQT). Results show that closely-coupled (CC) GH200 significantly outperforms loosely-coupled (LC) systems at large batch sizes, achieving 1.9x-2.7x faster prefill latency for Llama 3.2-1B. However, our analysis also reveals that GH200 remains CPU-bound up to 4x larger batch sizes than LC systems. In this extended CPU-bound region, we identify the performance characteristics of the Grace CPU as a key factor contributing to higher inference latency at low batch sizes on GH200. We demonstrate that TKLQT accurately identifies this CPU/GPU-bound transition point. Based on this analysis, we further show that kernel fusion offers significant potential to mitigate GH200's low-batch latency bottleneck by reducing kernel launch overhead. This detailed kernel-level characterization provides critical insights for optimizing diverse CPU-GPU coupling strategies. This work is an initial effort, and we plan to explore other major AI/DL workloads that demand different degrees of CPU-GPU heterogeneous architectures.

cs.DC↗

arXiv2025

Certificate Games and Consequences for the Classical Adversary Bound

We introduce and study Certificate Game complexity, a measure of complexity based on the probability of winning a game where two players are given inputs with different function values and are asked to output some index $i$ such that $x_i\neq y_i$, in a zero-communication setting. We study four versions of certificate games, namely private coin, public coin, shared entanglement and non-signaling games. The public-coin variant of certificate games gives a new characterization of the classical adversary bound, a lower bound on randomized query complexity which was introduced as a classical version of the quantum (non-negative) quantum adversary bound. We show that complexity in the public coin model (therefore also the classical adversary) is bounded above by certificate complexity, as well as by expectational certificate complexity and sabotage complexity. On the other hand, it is bounded below by fractional and randomized certificate complexity. The quantum measure reveals an interesting and surprising difference between classical and quantum query models: the quantum certificate game complexity can be quadratically larger than quantum query complexity. We use non-signaling, a notion from quantum information, to give a lower bound of $n$ on the quantum certificate game complexity of the OR function, whose quantum query complexity is $Θ(\sqrt{n})$, then go on to show that this ``non-signaling bottleneck'' applies to all functions with high sensitivity, block sensitivity, fractional block sensitivity, as well as classical adversary. This implies the collapse of all models of certificate games, except private randomness, to the classical adversary bound. We consider the single-bit version of certificate games, where the inputs of the two players are restricted to having Hamming distance 1, and give a new characterization of sensitivity and spectral sensitivity.

cs.CC↗

arXiv2025

Approximate Degree Composition for Recursive Functions

Determining the approximate degree composition for Boolean functions remains a significant unsolved problem in Boolean function complexity. In recent decades, researchers have concentrated on proving that approximate degree composes for special types of inner and outer functions. An important and extensively studied class of functions are the recursive functions, i.e.~functions obtained by composing a base function with itself a number of times. Let $h^d$ denote the standard $d$-fold composition of the base function $h$. The main result of this work is to show that the approximate degree composes if either of the following conditions holds: (I) The outer function $f:\{0,1\}^n\to \{0,1\}$ is a recursive function of the form $h^d$, with $h$ being any base function and $d= Ω(\log\log n)$. (II) The inner function is a recursive function of the form $h^d$, with $h$ being any constant arity base function (other than AND and OR) and $d= Ω(\log\log n)$, where $n$ is the arity of the outer function. In terms of proof techniques, we first observe that the lower bound for composition can be obtained by introducing majority in between the inner and the outer functions. We then show that majority can be \emph{efficiently eliminated} if the inner or outer function is a recursive function.

cs.CC↗

arXiv2024

Testing vs Estimation for Index-Invariant Properties in the Huge Object Model

The Huge Object model of property testing [Goldreich and Ron, TheoretiCS 23] concerns properties of distributions supported on $\{0,1\}^n$, where $n$ is so large that even reading a single sampled string is unrealistic. Instead, query access is provided to the samples, and the efficiency of the algorithm is measured by the total number of queries that were made to them. Index-invariant properties under this model were defined in [Chakraborty et al., COLT 23], as a compromise between enduring the full intricacies of string testing when considering unconstrained properties, and giving up completely on the string structure when considering label-invariant properties. Index-invariant properties are those that are invariant through a consistent reordering of the bits of the involved strings. Here we provide an adaptation of Szemerédi's regularity method for this setting, and in particular show that if an index-invariant property admits an $ε$-test with a number of queries depending only on the proximity parameter $ε$, then it also admits a distance estimation algorithm whose number of queries depends only on the approximation parameter.

cs.DS↗

arXiv2024

Testing Credibility of Public and Private Surveys through the Lens of Regression

Testing whether a sample survey is a credible representation of the population is an important question to ensure the validity of any downstream research. While this problem, in general, does not have an efficient solution, one might take a task-based approach and aim to understand whether a certain data analysis tool, like linear regression, would yield similar answers both on the population and the sample survey. In this paper, we design an algorithm to test the credibility of a sample survey in terms of linear regression. In other words, we design an algorithm that can certify if a sample survey is good enough to guarantee the correctness of data analysis done using linear regression tools. Nowadays, one is naturally concerned about data privacy in surveys. Thus, we further test the credibility of surveys published in a differentially private manner. Specifically, we focus on Local Differential Privacy (LDP), which is a standard technique to ensure privacy in surveys where the survey participants might not trust the aggregator. We extend our algorithm to work even when the data analysis has been done using surveys with LDP. In the process, we also propose an algorithm that learns with high probability the guarantees a linear regression model on a survey published with LDP. Our algorithm also serves as a mechanism to learn linear regression models from data corrupted with noise coming from any subexponential distribution. We prove that it achieves the optimal estimation error bound for $\ell_1$ linear regression, which might be of broader interest. We prove the theoretical correctness of our algorithms while trying to reduce the sample complexity for both public and private surveys. We also numerically demonstrate the performance of our algorithms on real and synthetic datasets.

cs.LG↗

arXiv2024

Emergent scalar-chirality \& colossal transverse-magnetoresponse in strongly correlated nodal-line half-metal

Understanding the interplay of strong correlation and temperature in nodal-line semimetals can offer novel ways to control spin currents. Here we consider the 3d-5d double-perovskite Ba$_{2}$CoWO$_{6}$, which features mirror-symmetry-protected nodal-lines, strong Co-site interactions, and spin-orbit coupling (SOC) at W sites. Our first principles and exact diagonalization results reveal a half-metallic ground state with high-spin Co and topologically non-trivial bands. We demonstrate that SOC gaps out nodal points, causes band-inversion and generates anomalous Hall response. A semi-classical Monte Carlo finite-temperature simulation of five-orbital Hubbard model uncovers an emergent Co-spin scalar chirality and colossal positive transverse-magnetoresponse. We predict the temperature and magnetic field scales for the tunability of scalar-chirality and magnetoresponse.

cond-mat.str-el↗

arXiv2024

Engineering an Efficient Approximate DNF-Counter

Model counting is a fundamental problem in many practical applications, including query evaluation in probabilistic databases and failure-probability estimation of networks. In this work, we focus on a variant of this problem where the underlying formula is expressed in the Disjunctive Normal Form (DNF), also known as #DNF. This problem has been shown to be #P-complete, making it often intractable to solve exactly. Much research has therefore focused on obtaining approximate solutions, particularly in the form of $(\varepsilon, δ)$ approximations. The primary contribution of this paper is a new approach, called pepin, an approximate #DNF counter that significantly outperforms prior state-of-the-art approaches. Our work is based on the recent breakthrough in the context of the union of sets in the streaming model. We demonstrate the effectiveness of our approach through extensive experiments and show that it provides an affirmative answer to the challenge of efficiently computing #DNF.

cs.DS↗

arXiv2024

Layer Resolved Magnetotransport Properties in Antiferromagnetic/Paramagnetic Superlattices

We investigate the layer resolved magnetotransport properties of the antiferromagnetic/paramagnetic superlattices based on one band half-filled Hubbard model in three dimensions. In our set up the correlated layers (with on-site repulsion strength $U \ne$ 0) are intercalated between the uncorrelated (U = 0) layers. Our calculations based on the semi-classical Monte-Carlo technique show that the magnetic moments are induced in the uncorrelated layers at low temperatures due to kinetic hopping of the carriers across the interface. The average induced magnetic moment in the uncorrelated layer varies nonmonotonically with the $U$ values of the correlated layer. Interestingly, the induced magnetic moments are antiferromagnetically arranged in uncorrelated layers and mediates the antiferromagnetic ordering between correlated layers. As a result the whole SL system turns out to be antiferromagnetic insulating at low temperatures. For $U \sim$ bandwidth the local moments in the correlated planes increases as a function of the distance from the interface. Expectedly our in-plane resistivity calculations show that the metal insulator transition temperature of the central plane is larger than the edge planes in the correlated layers. On the other hand, although the induced moments in uncorrelated planes decreases considerably as move from edge planes to center planes the metal insulator transition temperature remains more or less same for all planes. The induced moments in uncorrelated layers gradually dissipates with increasing the thickness of uncorrelated layer and as a result the long range antiferromagnetic ordering vanishes in the superlattices similar to the experiments.

cond-mat.str-el↗

arXiv2024

A faster FPRAS for #NFA

Given a non-deterministic finite automaton (NFA) A with m states, and a natural number n (presented in unary), the #NFA problem asks to determine the size of the set L(A_n) of words of length n accepted by A. While the corresponding decision problem of checking the emptiness of L(A_n) is solvable in polynomial time, the #NFA problem is known to be #P-hard. Recently, the long-standing open question -- whether there is an FPRAS (fully polynomial time randomized approximation scheme) for #NFA -- was resolved in \cite{ACJR19}. The FPRAS due to \cite{ACJR19} relies on the interreducibility of counting and sampling, and computes, for each pair of state q and natural number i <= n, a set of O(\frac{m^7 n^7}{epsilon^7}) many uniformly chosen samples from the set of words of length i that have a run ending at q (εis the error tolerance parameter of the FPRAS). This informative measure -- the number of samples maintained per state and length -- also affects the overall time complexity with a quadratic dependence. Given the prohibitively high time complexity, in terms of each of the input parameters, of the FPRAS due to \cite{ACJR19}, and considering the widespread application of approximate counting (and sampling) in various tasks in Computer Science, a natural question arises: Is there a faster FPRAS for #NFA that can pave the way for the practical implementation of approximate #NFA tools? In this work, we demonstrate that significant improvements in time complexity are achievable. Specifically, we have reduced the number of samples required for each state to be independent of m, with significantly less dependence on $n$ and $ε$, maintaining only \widetilde{O}(\frac{n^4}{epsilon^2}) samples per state.

cs.DS↗

arXiv2024

Incentivized Exploration of Non-Stationary Stochastic Bandits

We study incentivized exploration for the multi-armed bandit (MAB) problem with non-stationary reward distributions, where players receive compensation for exploring arms other than the greedy choice and may provide biased feedback on the reward. We consider two different non-stationary environments: abruptly-changing and continuously-changing, and propose respective incentivized exploration algorithms. We show that the proposed algorithms achieve sublinear regret and compensation over time, thus effectively incentivizing exploration despite the nonstationarity and the biased or drifted feedback.

cs.LG↗

arXiv2024

Equivalence Testing: The Power of Bounded Adaptivity

Equivalence testing, a fundamental problem in the field of distribution testing, seeks to infer if two unknown distributions on $[n]$ are the same or far apart in the total variation distance. Conditional sampling has emerged as a powerful query model and has been investigated by theoreticians and practitioners alike, leading to the design of optimal algorithms albeit in a sequential setting (also referred to as adaptive tester). Given the profound impact of parallel computing over the past decades, there has been a strong desire to design algorithms that enable high parallelization. Despite significant algorithmic advancements over the last decade, parallelizable techniques (also termed non-adaptive testers) have $\tilde{O}(\log^{12}n)$ query complexity, a prohibitively large complexity to be of practical usage. Therefore, the primary challenge is whether it is possible to design algorithms that enable high parallelization while achieving efficient query complexity. Our work provides an affirmative answer to the aforementioned challenge: we present a highly parallelizable tester with a query complexity of $\tilde{O}(\log n)$, achieved through a single round of adaptivity, marking a significant stride towards harmonizing parallelizability and efficiency in equivalence testing.

cs.DS↗

arXiv2023

Testing Self-Reducible Samplers

Samplers are the backbone of the implementations of any randomised algorithm. Unfortunately, obtaining an efficient algorithm to test the correctness of samplers is very hard to find. Recently, in a series of works, testers like $\mathsf{Barbarik}$, $\mathsf{Teq}$, $\mathsf{Flash}$ for testing of some particular kinds of samplers, like CNF-samplers and Horn-samplers, were obtained. But their techniques have a significant limitation because one can not expect to use their methods to test for other samplers, such as perfect matching samplers or samplers for sampling linear extensions in posets. In this paper, we present a new testing algorithm that works for such samplers and can estimate the distance of a new sampler from a known sampler (say, uniform sampler). Testing the identity of distributions is the heart of testing the correctness of samplers. This paper's main technical contribution is developing a new distance estimation algorithm for distributions over high-dimensional cubes using the recently proposed sub-cube conditioning sampling model. Given subcube conditioning access to an unknown distribution $P$, and a known distribution $Q$ defined over $\{0,1\}^n$, our algorithm $\mathsf{CubeProbeEst}$ estimates the variation distance between $P$ and $Q$ within additive error $ζ$ using $O\left({n^2}/{ζ^4}\right)$ subcube conditional samples from $P$. Following the testing-via-learning paradigm, we also get a tester which distinguishes between the cases when $P$ and $Q$ are $\varepsilon$-close or $η$-far in variation distance with probability at least $0.99$ using $O({n^2}/{(η-\varepsilon)^4})$ subcube conditional samples. The estimation algorithm in the sub-cube conditioning sampling model helps us to design the first tester for self-reducible samplers.

cs.DS↗

arXiv2023

Tight Lower Bound on Equivalence Testing in Conditional Sampling Model

We study the equivalence testing problem where the goal is to determine if the given two unknown distributions on $[n]$ are equal or $ε$-far in the total variation distance in the conditional sampling model (CFGM, SICOMP16; CRS, SICOMP15) wherein a tester can get a sample from the distribution conditioned on any subset. Equivalence testing is a central problem in distribution testing, and there has been a plethora of work on this topic in various sampling models. Despite significant efforts over the years, there remains a gap in the current best-known upper bound of $\tilde{O}(\log \log n)$ [FJOPS, COLT 2015] and lower bound of $Ω(\sqrt{\log \log n})$[ACK, RANDOM 2015, Theory of Computing 2018]. Closing this gap has been repeatedly posed as an open problem (listed as problems 66 and 87 at sublinear.info). In this paper, we completely resolve the query complexity of this problem by showing a lower bound of $\tildeΩ(\log \log n)$. For that purpose, we develop a novel and generic proof technique that enables us to break the $\sqrt{\log \log n}$ barrier, not only for the equivalence testing problem but also for other distribution testing problems, such as uniblock property.

cs.DS↗

arXiv2023

On the Composition of Randomized Query Complexity and Approximate Degree

For any Boolean functions $f$ and $g$, the question whether $R(f\circ g) = \tildeΘ(R(f)R(g))$, is known as the composition question for the randomized query complexity. Similarly, the composition question for the approximate degree asks whether $\widetilde{deg}(f\circ g) = \tildeΘ(\widetilde{deg}(f)\cdot\widetilde{deg}(g))$. These questions are two of the most important and well-studied problems, and yet we are far from answering them satisfactorily. It is known that the measures compose if one assumes various properties of the outer function $f$ (or inner function $g$). This paper extends the class of outer functions for which $\text{R}$ and $\widetilde{\text{deg}}$ compose. A recent landmark result (Ben-David and Blais, 2020) showed that $R(f \circ g) = Ω(noisyR(f)\cdot R(g))$. This implies that composition holds whenever $noisyR(f) = \TildeΘ(R(f))$. We show two results: (1)When $R(f) = Θ(n)$, then $noisyR(f) = Θ(R(f))$. (2) If $\text{R}$ composes with respect to an outer function, then $\text{noisyR}$ also composes with respect to the same outer function. On the other hand, no result of the type $\widetilde{deg}(f \circ g) = Ω(M(f) \cdot \widetilde{deg}(g))$ (for some non-trivial complexity measure $M(\cdot)$) was known to the best of our knowledge. We prove that $\widetilde{deg}(f\circ g) = \widetildeΩ(\sqrt{bs(f)} \cdot \widetilde{deg}(g)),$ where $bs(f)$ is the block sensitivity of $f$. This implies that $\widetilde{\text{deg}}$ composes when $\widetilde{\text{deg}}(f)$ is asymptotically equal to $\sqrt{\text{bs}(f)}$. It is already known that both $\text{R}$ and $\widetilde{\text{deg}}$ compose when the outer function is symmetric. We also extend these results to weaker notions of symmetry with respect to the outer function.

cs.CC↗

arXiv2023

Approximate Model Counting: Is SAT Oracle More Powerful than NP Oracle?

Given a Boolean formula $ϕ$ over $n$ variables, the problem of model counting is to compute the number of solutions of $ϕ$. Model counting is a fundamental problem in computer science with wide-ranging applications. Owing to the \#P-hardness of the problems, Stockmeyer initiated the study of the complexity of approximate counting. Stockmeyer showed that $\log n$ calls to an NP oracle are necessary and sufficient to achieve $(\varepsilon,δ)$ guarantees. The hashing-based framework proposed by Stockmeyer has been very influential in designing practical counters over the past decade, wherein the SAT solver substitutes the NP oracle calls in practice. It is well known that an NP oracle does not fully capture the behavior of SAT solvers, as SAT solvers are also designed to provide satisfying assignments when a formula is satisfiable, without additional overhead. Accordingly, the notion of SAT oracle has been proposed to capture the behavior of SAT solver wherein given a Boolean formula, an SAT oracle returns a satisfying assignment if the formula is satisfiable or returns unsatisfiable otherwise. Since the practical state-of-the-art approximate counting techniques use SAT solvers, a natural question is whether an SAT oracle is more powerful than an NP oracle in the context of approximate model counting. The primary contribution of this work is to study the relative power of the NP oracle and SAT oracle in the context of approximate model counting. The previous techniques proposed in the context of an NP oracle are weak to provide strong bounds in the context of SAT oracle since, in contrast to an NP oracle that provides only one bit of information, a SAT oracle can provide $n$ bits of information. We therefore develop a new methodology to achieve the main result: a SAT oracle is no more powerful than an NP oracle in the context of approximate model counting.

cs.CC↗

arXiv2023

On simple expectations and observations of intelligent agents: A complexity study

Public observation logic (POL) reasons about agent expectations and agent observations in various real world situations. The expectations of agents take shape based on certain protocols about the world around and they remove those possible scenarios where their expectations and observations do not match. This in turn influences the epistemic reasoning of these agents. In this work, we study the computational complexity of the satisfaction problems of various fragments of POL. In the process, we also highlight the inevitable link that these fragments have with the well-studied Public announcement logic.

cs.LO↗

arXiv2023

Distinct Elements in Streams: An Algorithm for the (Text) Book

Given a data stream $\mathcal{A} = \langle a_1, a_2, \ldots, a_m \rangle$ of $m$ elements where each $a_i \in [n]$, the Distinct Elements problem is to estimate the number of distinct elements in $\mathcal{A}$.Distinct Elements has been a subject of theoretical and empirical investigations over the past four decades resulting in space optimal algorithms for it.All the current state-of-the-art algorithms are, however, beyond the reach of an undergraduate textbook owing to their reliance on the usage of notions such as pairwise independence and universal hash functions. We present a simple, intuitive, sampling-based space-efficient algorithm whose description and the proof are accessible to undergraduates with the knowledge of basic probability theory.

cs.DS↗