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The Gap-Hamming-Distance problem arose in the context of proving space lower bounds for a number of key problems in the data stream model. In this problem, Alice and Bob have to decide whether the Hamming distance between their $n$-bit…
We study an extension of the standard two-party communication model in which Alice and Bob hold probability distributions $p$ and $q$ over domains $X$ and $Y$, respectively. Their goal is to estimate \[ \mathbb{E}_{x \sim p,\, y \sim…
Recent advancements in large audio-language models (LALMs) have shown impressive capabilities in understanding and reasoning about audio and speech information. However, these models still face challenges, including hallucinating…
We study associative memory based on temporal coding in which successful retrieval is realized as an entrainment in a network of simple phase oscillators with distributed natural frequencies under the influence of white noise. The memory…
Meshless methods approximate operators in a specific node as a weighted sum of values in its neighbours. Higher order approximations of derivatives provide more accurate solutions with better convergence characteristics, but they come at…
We consider a two-user secure computation problem in which Alice and Bob communicate interactively in order to compute some deterministic functions of the inputs. The privacy requirement is that each user should not learn any additional…
Language models draw on two knowledge sources: facts baked into weights (parametric memory, PM) and information in context (working memory, WM). We study two mechanistically distinct failure modes--conflict, when PM and WM disagree and…
Discrete Diffusion Language Models progressed rapidly as an alternative to autoregressive (AR) models, motivated by their parallel generation abilities. However, for tractability, discrete diffusion models sample from a factorized…
A system of communicating finite state machines is synchronizable if its send trace semantics, i.e.the set of sequences of sendings it can perform, is the same when its communications are FIFO asynchronous and when they are just rendez-vous…
We study the problem of randomized Leader Election in synchronous distributed networks with indistinguishable nodes. We consider algorithms that work on networks of arbitrary topology in two settings, depending on whether the size of the…
Motivated by the recent interest in approximate message passing (AMP) for matrix-valued linear observations with superposition of \emph{multiple statistically asymmetric signal sources}, we introduce a multi-source AMP framework in which…
Continual learning systems operating in fixed-dimensional spaces face a fundamental geometric barrier: the flat manifold problem. When experience is represented as a linear trajectory in Euclidean space, the geodesic distance between…
Fog and edge computing require adaptive control schemes that can handle partial observability, severe latency requirements, and dynamically changing workloads. Recent research on Agentic AI (AAI) increasingly integrates reasoning systems…
Studying distributed computing through the lens of algebraic topology has been the source of many significant breakthroughs during the last two decades, especially in the design of lower bounds or impossibility results for deterministic…
Function calling, also known as tool use, is a core capability of modern LLM agents but is typically constrained by synchronous execution semantics. Under these semantics, LLM decoding is blocked until each function call completes,…
We consider two social consensus models, the AB-model and the Naming Game restricted to two conventions, which describe a population of interacting agents that can be in either of two equivalent states (A or B) or in a third mixed (AB)…
We present the \emph{discrete beeping} communication model, which assumes nodes have minimal knowledge about their environment and severely limited communication capabilities. Specifically, nodes have no information regarding the local or…
In this paper, we study fault-tolerant distributed consensus in wireless systems. In more detail, we produce two new randomized algorithms that solve this problem in the abstract MAC layer model, which captures the basic interface and…
Approximate Message Passing (AMP) algorithms provide a valuable tool for studying mean-field approximations and dynamics in a variety of applications. Although these algorithms are often first derived for matrices having independent…
All communication networks comprise of transmission systems and switching systems, even though they are usually treated as two separate issues. Communication channels are generally disturbed by noise from various sources. In circuit…