arXiv subjects

Manuj Mukherjee

Publications and source records attributed to Manuj Mukherjee.

At least 19 recordsLinked to original sources

arXiv2026

KGCQual: An Interpretable Framework for Evaluating the Knowledge Graph Construction Quality from Text

Knowledge Graphs (KGs) are increasingly constructed through automated extraction pipelines; however, such systems often introduce spurious or incomplete triples, which degrade downstream performance. Existing evaluation practices rely heavily on task-specific metrics or small-scale manual verification, offering limited insight into the structural and semantic fidelity of extracted graphs. We propose a novel, interpretable metric for intrinsic KG quality assessment that measures how closely an automatically extracted graph approximates an "ideal" graph capturing the key noun phrases, predicate relations, and basic linguistic phenomena such as negation expressed in the source text. Our framework integrates two complementary components: (1) an entity-level assessment that evaluates completeness, resolution quality, and connectivity, and (2) a relation-level assessment that judges predicate preservation and multiplicity using lexical similarity, dependency-parse alignment, and light-weight negation handling to ensure semantic faithfulness. We evaluate our metric across multiple state-of-the-art triple extraction systems and datasets, including WebNLG, TinyButMighty, and BenchIE, demonstrating that it reliably identifies omissions, redundancy, and structural deviations that existing metrics overlook. Our work offers a scalable, model-agnostic, and interpretable framework for comparing automated KG construction methods and provides a foundation for standardised evaluation. We further validate the metric through an ablation study isolating noun and verb components, and a downstream evaluation showing that KGCQual scores correlate significantly with link prediction performance on the same extracted KGs. The code repository is available at https://github.com/kracr/kg-quality-metric.

cs.AI↗

arXiv2026

Query-Limited Community Recovery in Stochastic Block Models

We study exact community recovery in the two-community stochastic block model on $n$ vertices under limited and noisy access to network data. The learner may query a noisy neighborhood oracle that reveals each true neighbor of a queried vertex independently with fixed probability and never returns non-neighbors, subject to a finite query budget. We consider both oracle-only access and a combined model where the learner also observes a single subsampled copy of the underlying graph. For oracle-only access, balanced uniform querying gives a sharp non-adaptive benchmark: when each vertex is queried the same integer number of times, the observations reduce to an SBM with attenuated edge probabilities and the Abbe-Bandeira-Hall exact-recovery threshold applies. We show that this benchmark is not adaptively optimal: a two-stage adaptive strategy succeeds with $n+o(n)$ queries in a regime where balanced uniform querying requires $m n$ queries for some $m>1$. With an additional subsampled graph, we prove a sublinear-query adaptivity gap: balanced data-independent uniform querying with a sublinear budget does not improve over the subsampled graph alone, whereas adaptive querying can target a small set of uncertain vertices and achieve exact recovery. Thus adaptive data acquisition can strictly improve the information-theoretic limits of exact recovery.

cs.IT↗

arXiv2026

Perfect Secret Key Generation for a class of Hypergraphical Sources

Nitinawarat and Narayan proposed a perfect secret key generation scheme for the so-called \emph{pairwise independent network (PIN) model} by exploiting the combinatorial properties of the underlying graph, namely the spanning tree packing rate. This work considers a generalization of the PIN model where the underlying graph is replaced with a hypergraph, and makes progress towards designing similar perfect secret key generation schemes by exploiting the combinatorial properties of the hypergraph. Our contributions are two-fold. We first provide a capacity achieving scheme for a complete $t$-uniform hypergraph on $m$ vertices by leveraging a packing of the complete $t$-uniform hypergraphs by what we refer to as star hypergraphs, and designing a scheme that gives $\binom{m-2}{t-2}$ bits of perfect secret key per star graph. Our second contribution is a 2-bit perfect secret key generation scheme for 3-uniform star hypergraphs whose projections are cycles. This scheme is then extended to a perfect secret key generation scheme for generic 3-uniform hypergraphs by exploiting star graph packing of 3-uniform hypergraphs and Hamiltonian packings of graphs. The scheme is then shown to be capacity achieving for certain classes of hypergraphs.

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arXiv2024

Generalization Bounds for Dependent Data using Online-to-Batch Conversion

In this work, we upper bound the generalization error of batch learning algorithms trained on samples drawn from a mixing stochastic process (i.e., a dependent data source) both in expectation and with high probability. Unlike previous results by Mohri et al. (2010) and Fu et al. (2023), our work does not require any stability assumptions on the batch learner, which allows us to derive upper bounds for any batch learning algorithm trained on dependent data. This is made possible due to our use of the Online-to-Batch ( OTB ) conversion framework, which allows us to shift the burden of stability from the batch learner to an artificially constructed online learner. We show that our bounds are equal to the bounds in the i.i.d. setting up to a term that depends on the decay rate of the underlying mixing stochastic process. Central to our analysis is a new notion of algorithmic stability for online learning algorithms based on Wasserstein distances of order one. Furthermore, we prove that the EWA algorithm, a textbook family of online learning algorithms, satisfies our new notion of stability. Following this, we instantiate our bounds using the EWA algorithm.

cs.LG↗

arXiv2024

Improved bounds on the interactive capacity via error pattern analysis

Any interactive protocol between a pair of parties can be reliably simulated in the presence of noise with a multiplicative overhead on the number of rounds (Schulman 1996). The reciprocal of the best (least) overhead is called the interactive capacity of the noisy channel. In this work, we present lower bounds on the interactive capacity of the binary erasure channel. Our lower bound improves the best known bound due to Ben-Yishai et al. 2021 by roughly a factor of 1.75. The improvement is due to a tighter analysis of the correctness of the simulation protocol using error pattern analysis. More precisely, instead of using the well-known technique of bounding the least number of erasures needed to make the simulation fail, we identify and bound the probability of specific erasure patterns causing simulation failure. We remark that error pattern analysis can be useful in solving other problems involving stochastic noise, such as bounding the interactive capacity of different channels.

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arXiv2023

Optimal storage codes on graphs with fixed locality

Storage codes on graphs are an instance of \emph{codes with locality}, which are used in distributed storage schemes to provide local repairability. Specifically, the nodes of the graph correspond to storage servers, and the neighbourhood of each server constitute the set of servers it can query to repair its stored data in the event of a failure. A storage code on a graph with $n$-vertices is a set of $n$-length codewords over $\field_q$ where the $i$th codeword symbol is stored in server $i$, and it can be recovered by querying the neighbours of server $i$ according to the underlying graph. In this work, we look at binary storage codes whose repair function is the parity check, and characterise the tradeoff between the locality of the code and its rate. Specifically, we show that the maximum rate of a code on $n$ vertices with locality $r$ is bounded between $1-1/n\lceil n/(r+1)\rceil$ and $1-1/n\lceil n/(r+1)\rceil$. The lower bound on the rate is derived by constructing an explicit family of graphs with locality $r$, while the upper bound is obtained via a lower bound on the binary-field rank of a class of symmetric binary matrices. Our upper bound on maximal rate of a storage code matches the upper bound on the larger class of codes with locality derived by Tamo and Barg. As a corollary to our result, we obtain the following asymptotic separation result: given a sequence $r(n), n\geq 1$, there exists a sequence of graphs on $n$-vertices with storage codes of rate $1-o(1)$ if and only if $r(n)=\omega(1)$.

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arXiv2021

Multiparty Interactive Coding over Networks of Intersecting Broadcast Links

We consider computations over networks with multiple broadcast channels that intersect at a single party. Each broadcast link suffers from random bit-flip noise that affects the receivers independently. We design interactive coding schemes that successfully perform any computation over these noisy networks and strive to reduce their communication overhead with respect to the original (noiseless) computation. A simple variant of a coding scheme by Rajagopalan and Schulman (STOC 1994) shows that any (noiseless) protocol of $R$ rounds can be reliably simulated in $O(R\log n)$ rounds over a network with $n=n_1n_2+1$ parties in which a single party is connected to $n_2$ noisy broadcast channels, each of which connects $n_1$ distinct parties. We design new coding schemes with improved overheads. Our approach divides the network into four regimes according to the relationship between $n_1$ and $n_2$. We employ a two-layer coding where the inner code protects each broadcast channel and is tailored to the specific conditions of the regime in consideration. The outer layer protects the computation in the network and is generally based on the scheme of Rajagopalan and Schulman, adapted to the case of broadcast channels. The overhead we obtain ranges from $O(\log\log n_2)$ to $O(\log n_2 \frac{\log\log n_1}{\log n_1})$ and beats the trivial $O(\log n)$ overhead in all four regimes.

cs.IT↗

arXiv2021

Reconfigurable Adaptive Channel Sensing

Channel sensing consists of probing the channel from time to time to check whether or not it is active - say, because of an incoming message. When communication is sparse with information being sent once in a long while, channel sensing becomes a significant source of energy consumption. How to reliably detect messages while minimizing the receiver energy consumption? This paper addresses this problem through a reconfigurable scheme, referred to as AdaSense, which exploits the dependency between the receiver noise figure (i.e., the receiver added noise) and the receiver power consumption; a higher power typically translates into less noisy channel observations. AdaSense begins in a low power low reliability mode and makes a first tentative decision based on a few channel observations. If a message is declared, it switches to a high power high reliability mode to confirm the decision, else it sleeps for the entire duration of the second phase. Compared to prominent detection schemes such as the BMAC protocol, AdaSense provides relative energy gains that grow unbounded in the small probability of false-alarm regime, as communication gets sparser. In the non-asymptotic regime energy gains are 30% to 75% for communication scenarios typically found in the context of wake-up receivers.

cs.IT↗

arXiv2021

Approximating Probability Distributions by ReLU Networks

How many neurons are needed to approximate a target probability distribution using a neural network with a given input distribution and approximation error? This paper examines this question for the case when the input distribution is uniform, and the target distribution belongs to the class of histogram distributions. We obtain a new upper bound on the number of required neurons, which is strictly better than previously existing upper bounds. The key ingredient in this improvement is an efficient construction of the neural nets representing piecewise linear functions. We also obtain a lower bound on the minimum number of neurons needed to approximate the histogram distributions.

cs.LG↗

arXiv2019

Multiterminal Secret Key Agreement with Nearly No Discussion

We consider the secret key agreement problem under the multiterminal source model proposed by Csiszár and Narayan. A single-letter characterization of the secrecy capacity is desired but remains unknown except in the extreme case with unlimited public discussion and without wiretapper's side information. Taking the problem to the opposite extreme by requiring the public discussion rate to be zero asymptotically, we obtain the desired characterization under surprisingly general setting with wiretapper's side information, silent users, trusted and untrusted helpers. An immediate consequence of the result is that the capacity with nearly no discussion is the same as the capacity with no discussion, resolving a previous conjecture in the affirmative. The idea of the proof is to characterize the capacity in the special case with neither wiretapper's side information nor untrusted helpers using a multivariate extension of Gács-Körner common information, and then extend the result to the general setting by a change of scenario that turns untrusted helpers into trusted helpers. We further show how to evaluate the capacity explicitly for finite linear sources and discuss how the current result can be extended to improve and unify existing bounds on the capacity for strictly positive discussion rates.

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arXiv2018

Upper Bounds via Lamination on the Constrained Secrecy Capacity of Hypergraphical Sources

Hypergraphical sources are a natural class of sources for secret key generation, within which different subsets of terminals sharing secrets are allowed to discuss publicly in order to agree upon a global secret key. While their secrecy capacity, i.e., the maximum rate of a secret key that can be agreed upon by the entire set of terminals, is well-understood, what remains open is the maximum rate of a secret key that can be generated when there is a restriction on the overall rate of public discussion allowed. In this work, we obtain a family of explicitly computable upper bounds on the number of bits of secret key that can be generated per bit of public discussion. These upper bounds are derived using a lamination technique based on the submodularity of the entropy function. In particular, a specific instance of these upper bounds, called the edge-partition bound, is shown to be tight for the pairwise independent network model, a special case of the hypergraphical source. The secret key generation scheme achieving this upper bound is the tree-packing protocol of Nitinawarat et al., thereby resolving in the affirmative the discussion rate optimality of the tree packing protocol.

cs.IT↗

arXiv2018

Multiterminal Secret Key Agreement at Asymptotically Zero Discussion Rate

In the multiterminal secret key agreement problem, a set of users want to discuss with each other until they share a common secret key independent of their discussion. We want to characterize the maximum secret key rate, called the secrecy capacity, asymptotically when the total discussion rate goes to zero. In the case of only two users, the capacity is equal to the Gács-Körner common information. However, when there are more than two users, the capacity is unknown. It is plausible that a multivariate extension of the Gács-Körner common information is the capacity, however, proving the converse is challenging. We resolved this for the hypergraphical sources and finite linear sources, and provide efficiently computable characterizations. We also give some ideas of extending the techniques to more general source models.

cs.IT↗

arXiv2018

On the Optimality of Secret Key Agreement via Omniscience

For the multiterminal secret key agreement problem under a private source model, it is known that the maximum key rate, i.e., the secrecy capacity, can be achieved through communication for omniscience, but the omniscience strategy can be strictly suboptimal in terms of minimizing the public discussion rate. While a single-letter characterization is not known for the minimum discussion rate needed for achieving the secrecy capacity, we derive single-letter lower and upper bounds that yield some simple conditions for omniscience to be discussion-rate optimal. These conditions turn out to be enough to deduce the optimality of omniscience for a large class of sources including the hypergraphical sources. Through conjectures and examples, we explore other source models to which our methods do not easily extend.

cs.IT↗

arXiv2017

Secret Key Agreement under Discussion Rate Constraints

For the multiterminal secret key agreement problem, new single-letter lower bounds are obtained on the public discussion rate required to achieve any given secret key rate below the secrecy capacity. The results apply to general source model without helpers or wiretapper's side information but can be strengthened for hypergraphical sources. In particular, for the pairwise independent network, the results give rise to a complete characterization of the maximum secret key rate achievable under a constraint on the total discussion rate.

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arXiv2016

Bounds on the Communication Rate Needed to Achieve SK Capacity in the Hypergraphical Source Model

In the multiterminal source model of Csisz$\text{á}$r and Narayan, the communication complexity, $R_{\text{SK}}$, for secret key (SK) generation is the minimum rate of communication required to achieve SK capacity. An obvious upper bound to $R_{\text{SK}}$ is given by $R_{\text{CO}}$, which is the minimum rate of communication required for \emph{omniscience}. In this paper we derive a better upper bound to $R_{\text{SK}}$ for the hypergraphical source model, which is a special instance of the multiterminal source model. The upper bound is based on the idea of fractional removal of hyperedges. It is further shown that this upper bound can be computed in polynomial time. We conjecture that our upper bound is tight. For the special case of a graphical source model, we also give an explicit lower bound on $R_{\text{SK}}$. This bound, however, is not tight, as demonstrated by a counterexample.

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arXiv2015

On the Public Communication Needed to Achieve SK Capacity in the Multiterminal Source Model

The focus of this paper is on the public communication required for generating a maximal-rate secret key (SK) within the multiterminal source model of Csisz{á}r and Narayan. Building on the prior work of Tyagi for the two-terminal scenario, we derive a lower bound on the communication complexity, $R_{\text{SK}}$, defined to be the minimum rate of public communication needed to generate a maximal-rate SK. It is well known that the minimum rate of communication for omniscience, denoted by $R_{\text{CO}}$, is an upper bound on $R_{\text{SK}}$. For the class of pairwise independent network (PIN) models defined on uniform hypergraphs, we show that a certain "Type $\mathcal{S}$" condition, which is verifiable in polynomial time, guarantees that our lower bound on $R_{\text{SK}}$ meets the $R_{\text{CO}}$ upper bound. Thus, PIN models satisfying our condition are $R_{\text{SK}}$-maximal, meaning that the upper bound $R_{\text{SK}} \le R_{\text{CO}}$ holds with equality. This allows us to explicitly evaluate $R_{\text{SK}}$ for such PIN models. We also give several examples of PIN models that satisfy our Type $\mathcal S$ condition. Finally, we prove that for an arbitrary multiterminal source model, a stricter version of our Type $\mathcal S$ condition implies that communication from \emph{all} terminals ("omnivocality") is needed for establishing a SK of maximum rate. For three-terminal source models, the converse is also true: omnivocality is needed for generating a maximal-rate SK only if the strict Type $\mathcal S$ condition is satisfied. Counterexamples exist that show that the converse is not true in general for source models with four or more terminals.

cs.IT↗

arXiv2015

The communication complexity of achieving SK capacity in a class of PIN models

The communication complexity of achieving secret key (SK) capacity in the multiterminal source model of Csisz$á$r and Narayan is the minimum rate of public communication required to generate a maximal-rate SK. It is well known that the minimum rate of communication for omniscience, denoted by $R_{\text{CO}}$, is an upper bound on the communication complexity, denoted by $R_{\text{SK}}$. A source model for which this upper bound is tight is called $R_{\text{SK}}$-maximal. In this paper, we establish a sufficient condition for $R_{\text{SK}}$-maximality within the class of pairwise independent network (PIN) models defined on hypergraphs. This allows us to compute $R_{\text{SK}}$ exactly within the class of PIN models satisfying this condition. On the other hand, we also provide a counterexample that shows that our condition does not in general guarantee $R_{\text{SK}}$-maximality for sources beyond PIN models.

cs.IT↗

arXiv2014

Achieving SK Capacity in the Source Model: When Must All Terminals Talk?

In this paper, we address the problem of characterizing the instances of the multiterminal source model of Csiszár and Narayan in which communication from all terminals is needed for establishing a secret key of maximum rate. We give an information-theoretic sufficient condition for identifying such instances. We believe that our sufficient condition is in fact an exact characterization, but we are only able to prove this in the case of the three-terminal source model. We also give a relatively simple criterion for determining whether or not our condition holds for a given multiterminal source model.

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