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In this paper, we introduce a new post-training compression paradigm for Large Language Models (LLMs) to facilitate their wider adoption. We delve into LLM weight low-rank decomposition, and find that the challenges of this task stem from…

We consider the sample complexity of learning with adversarial robustness. Most prior theoretical results for this problem have considered a setting where different classes in the data are close together or overlapping. Motivated by some…

We study the problem of estimating multivariate log-concave probability density functions. We prove the first sample complexity upper bound for learning log-concave densities on $\mathbb{R}^d$, for all $d \geq 1$. Prior to our work, no…

External memory systems are pivotal for enabling Large Language Model (LLM) agents to maintain persistent knowledge and perform long-horizon decision-making. Existing paradigms typically follow a two-stage process: computationally expensive…

Two-timescale Stochastic Approximation (SA) algorithms are widely used in Reinforcement Learning (RL). Their iterates have two parts that are updated using distinct stepsizes. In this work, we develop a novel recipe for their finite sample…

Domain-specific intelligence demands specialized knowledge and sophisticated reasoning for problem-solving, posing significant challenges for large language models (LLMs) that struggle with knowledge hallucination and inadequate reasoning…

While 4-bit quantization has emerged as a memory-optimal choice for non-reasoning models and zero-shot tasks across scales, we show that this universal prescription fails for reasoning models, where the KV cache rather than model size can…

Linear TD($\lambda$) is one of the most fundamental reinforcement learning algorithms for policy evaluation. Previously, convergence rates are typically established under the assumption of linearly independent features, which does not hold…

Persistent AI memory is often reduced to a retrieval problem: store prior interactions as text, embed them, and ask the model to recover relevant context later. This design is useful for thematic recall, but it is mismatched to the kinds of…

Current LLM agents lack principled mechanisms for managing persistent memory across long interaction horizons. We present a biologically-grounded memory architecture comprising six cognitive mechanisms: (1) sleep-phase consolidation, (2)…

We are concerned with linear redundancy storage schemes regarding their ability to provide concurrent (local) recovery of multiple data objects. This paper initiates a study of such systems within the classical coding theory. We show how we…

Let X be a data matrix of rank \rho, whose rows represent n points in d-dimensional space. The linear support vector machine constructs a hyperplane separator that maximizes the 1-norm soft margin. We develop a new oblivious dimension…

We study the complexity of high-dimensional approximation in the $L_2$-norm when different classes of information are available; we compare the power of function evaluations with the power of arbitrary continuous linear measurements. Here,…

Auto-regressive decoding in Large Language Models (LLMs) is inherently memory-bound: every generation step requires loading the model weights and intermediate results from memory (e.g., High-Bandwidth Memory (HBM) for GPU servers), making…

Aligning large language models (LLMs) depends on high-quality datasets of human preference labels, which are costly to collect. Although active learning has been studied to improve sample efficiency relative to passive collection, many…

Simultaneous localization and mapping (SLAM) is a critical capability in autonomous navigation, but in order to scale SLAM to the setting of "lifelong" SLAM, particularly under memory or computation constraints, a robot must be able to…

Coded caching is a promising technique to smooth out network traffic by storing part of the library content at the users' local caches. The seminal work on coded caching for single file retrieval by Maddah-Ali and Niesen (MAN) showed the…

The success of Large Language Models (LLMs) has motivated a shift toward generative approaches to retrieval and ranking, aiming to supersede classical Dual Encoders (DEs) and Cross Encoders (CEs). A prominent paradigm is pointwise…

We study the problem of learning the topology of a directed Gaussian Graphical Model under the equal-variance assumption, where the graph has $n$ nodes and maximum in-degree $d$. Prior work has established that $O(d \log n)$ samples are…

We study finite sample expressivity, i.e., memorization power of ReLU networks. Recent results require $N$ hidden nodes to memorize/interpolate arbitrary $N$ data points. In contrast, by exploiting depth, we show that 3-layer ReLU networks…