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Running faster will only get you so far -- it is generally advisable to first understand where the roads lead, then get a car ... The renaissance of machine learning (ML) and deep learning (DL) over the last decade is accompanied by an…

Large Language Models (LLMs) that can continually improve beyond their training budgets are able to solve increasingly difficult problems by adapting at test time, a property we refer to as extrapolation. However, standard reinforcement…

Large language models have shown remarkable reasoning abilities and scaling laws suggest that large parameter count, especially along the depth axis, is the primary driver. In this work, we make a stronger claim -- many reasoning problems…

We study in-context learning (ICL) of linear regression in a deep linear self-attention model, characterizing how performance depends on various computational and statistical resources (width, depth, number of training steps, batch size and…

Large Language Models (LLMs) have attained human-level accuracy on medical question-answer (QA) benchmarks. However, their limitations in navigating open-ended clinical scenarios have recently been shown, raising concerns about the…

We study the catastrophic stationary self-focusing (collapse) of laser beam in nonlinear Kerr media. The width of a self-similar solutions near collapse distance $z=z_c$ obeys $(z_c-z)^{1/2}$ scaling law with the well-known leading order…

Generative LLM have achieved remarkable success in various industrial applications, owing to their promising In-Context Learning capabilities. However, the issue of long context in complex tasks poses a significant barrier to their wider…

We show how to combine the light-cone and matrix product algorithms to simulate quantum systems far from equilibrium for long times. For the case of the XXZ spin chain at $\Delta=0.5$, we simulate to a time of $\approx 22.5$. While part of…

Simulating large quantum circuits on hardware with limited qubit counts is often attempted through methods like circuit knitting, which typically incur sample costs that grow exponentially with the number of connections cut. In this work,…

Large reasoning models (LRMs) achieve impressive reasoning capabilities by generating lengthy chain-of-thoughts, but this "overthinking" incurs high latency and cost without commensurate accuracy gains. In this work, we introduce AALC, a…

We consider an \textit{Adaptive Random Convolutional Network Coding} (ARCNC) algorithm to address the issue of field size in random network coding for multicast, and study its memory and decoding delay performances through both analysis and…

In this work, we study the Lov\'asz local lemma (LLL) problem in the area of distributed quantum computing, which has been the focus of attention of recent advances in quantum computing [STOC'24, STOC'25, STOC'25]. We prove a lower bound of…

Large Language Models (LLMs) have garnered widespread attention due to their remarkable performance across various tasks. However, to mitigate the issue of hallucinations, LLMs often incorporate retrieval-augmented pipeline to provide them…

Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-understood how domain covering patterns (for example stripes and…

The inference of Large language models (LLMs) requires immense computation and memory resources. To curtail these costs, quantisation has merged as a promising solution, but existing LLM quantisation mainly focuses on 8-bit. In this work,…

Human cognition naturally engages with abstract and fluid concepts, whereas existing reasoning models often rely on generating discrete tokens, potentially constraining their expressive capabilities. Recent advancements aim to address this…

Chain-of-Thought (CoT) reasoning enhances large language models (LLMs) by enabling step-by-step problem-solving, yet its extension to Long-CoT introduces substantial computational overhead due to increased token length. Existing compression…

Recent work has shown that large pretrained Language Models (LMs) can not only perform remarkably well on a range of Natural Language Processing (NLP) tasks but also start improving on reasoning tasks such as arithmetic induction, symbolic…

Equipping large language models (LLMs) with latent-space memory has attracted increasing attention as they can extend the context window of existing language models. However, retaining information from the distant past remains a challenge.…

Recent advances in fine-tuning large language models (LLMs) with reinforcement learning (RL) have shown promising improvements in complex reasoning tasks, particularly when paired with chain-of-thought (CoT) prompting. However, these…