相关论文: Haystack Hunting Hints and Locker Room Communicati…

Can autoregressive large language models (LLMs) learn consistent probability distributions when trained on sequences in different token orders? We prove formally that for any well-defined probability distribution, sequence perplexity is…

Space efficient algorithms play a central role in dealing with large amount of data. In such settings, one would like to analyse the large data using small amount of "working space". One of the key steps in many algorithms for analysing…

We analyze the general version of the classic guessing game Mastermind with $n$ positions and $k$ colors. Since the case $k \le n^{1-\varepsilon}$, $\varepsilon>0$ a constant, is well understood, we concentrate on larger numbers of colors.…

We show that randomization can lead to significant improvements for a few fundamental problems in distributed tracking. Our basis is the {\em count-tracking} problem, where there are $k$ players, each holding a counter $n_i$ that gets…

The Johnson-Lindenstrauss lemma is a fundamental result in probability with several applications in the design and analysis of algorithms in high dimensional geometry. Most known constructions of linear embeddings that satisfy the…

The problem of storing permutations in a distributed manner arises in several common scenarios, such as efficient updates of a large, encrypted, or compressed data set. This problem may be addressed in either a combinatorial or a coding…

This paper presents a mathematical method of playing the puzzle game Wordle. In Wordle, the player has six tries to guess a secret word. After each guess the player is told how their guess compares to the secret word. With the available…

While state-of-the-art LLMs have shown poor logical and basic mathematical reasoning, recent works try to improve their problem-solving abilities using prompting techniques. We propose giving "hints" to improve the language model's…

Assume we are given a set of items from a general metric space, but we neither have access to the representation of the data nor to the distances between data points. Instead, suppose that we can actively choose a triplet of items (A,B,C)…

It has been observed in recent years that transformers have problems with length generalization for certain types of reasoning and arithmetic tasks. In particular, the performance of a transformer model trained on tasks (say addition) up to…

We consider the basic problem of learning an unknown partition of $n$ elements into at most $k$ sets using simple queries that reveal information about a small subset of elements. Our starting point is the well-studied pairwise same-set…

Reinforcement learning has proven effective for enhancing multi-step reasoning in large language models (LLMs), yet its benefits have not fully translated to multilingual contexts. Existing methods struggle with a fundamental trade-off:…

We study the problem of testing identity against a given distribution with a focus on the high confidence regime. More precisely, given samples from an unknown distribution $p$ over $n$ elements, an explicitly given distribution $q$, and…

Large language models (LLMs) have quickly emerged as practical and versatile tools that provide new solutions for a wide range of domains. In this paper, we consider the application of LLMs on symmetric tasks where a query is asked on an…

Physically disentangling entangled objects from each other is a problem encountered in waste segregation or in any task that requires disassembly of structures. Often there are no object models, and, especially with cluttered irregularly…

Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such…

Using techniques from Poisson approximation, we prove explicit error bounds on the number of permutations that avoid any pattern. Most generally, we bound the total variation distance between the joint distribution of pattern occurrences…

We consider a (random permutation model) binary search tree with n nodes and give asymptotics on the loglog scale for the height H_n and saturation level h_n of the tree as n\to\infty, both almost surely and in probability. We then consider…

We consider the variable selection problem in linear regression. Suppose that we have a set of random variables $X_1,...,X_m,Y,\epsilon$ such that $Y=\sum_{k\in \pi}\alpha_kX_k+\epsilon$ with $\pi\subseteq \{1,...,m\}$ and $\alpha_k\in…

Recent advances have shown that optimizing prompts for Large Language Models (LLMs) can significantly improve task performance, yet many optimization techniques rely on heuristics or manual exploration. We present LatentPrompt, a…