相关论文: Small Spans in Scaled Dimension
In this work, we study two types of constraints on two-dimensional binary arrays. In particular, given $p,\epsilon>0$, we study (i) The $p$-bounded constraint: a binary vector of size $m$ is said to be $p$-bounded if its weight is at most…
We introduce a concept of efficiency for which we can prove that it applies to all paddable languages, but still does not conflict with potential worst case intractability. Note that the family of paddable languages apparently includes all…
In this work, the relativistic phenomena of Lorentz contraction and time dilation are derived using a modified distance formula appropriate for discrete space. This new distance formula is different than Pythagoras's theorem but converges…
This paper introduces "Semantic Scaling," a novel method for ideal point estimation from text. I leverage large language models to classify documents based on their expressed stances and extract survey-like data. I then use item response…
We give a polynomial time algorithm to decode multivariate polynomial codes of degree $d$ up to half their minimum distance, when the evaluation points are an arbitrary product set $S^m$, for every $d < |S|$. Previously known algorithms can…
Owing to their reasoning capabilities, large language models (LLMs) have been evaluated on planning tasks described in natural language. However, LLMs have largely been tested on planning domains without constraints. In order to deploy them…
Large language models improve with scale, yet feedback-based alignment still exhibits systematic deviations from intended behavior. Motivated by bounded rationality in economics and cognitive science, we view judgment as resource-limited…
Recent work has demonstrated the remarkable potential of Large Language Models (LLMs) in test-time scaling. By making models think before answering, they are able to achieve much higher accuracy with extra inference computation. However, in…
The Schwartz-Zippel Lemma states that if a low-degree multivariate polynomial with coefficients in a field is not zero everywhere in the field, then it has few roots on every finite subcube of the field. This fundamental fact about…
Pretrained Language Models (LMs) have been shown to possess significant linguistic, common sense, and factual knowledge. One form of knowledge that has not been studied yet in this context is information about the scalar magnitudes of…
In this paper we investigate the problem of building a static data structure that represents a string s using space close to its compressed size, and allows fast access to individual characters of s. This type of structures was investigated…
We show tight lower bounds for the entire trade-off between space and query time for the Approximate Near Neighbor search problem. Our lower bounds hold in a restricted model of computation, which captures all hashing-based approaches. In…
Roughly half of numerical investigations of the Anderson transition are based on consideration of an associated quasi-1D system and postulation of one-parameter scaling for the minimal Lyapunov exponent. If this algorithm is taken…
As language models scale, the amount of data they require grows -- yet many target data sources, such as low-resource languages or specialized domains, are inherently limited in size. A common strategy is to mix this scarce but valuable…
Large Language Models (LLMs) are distinguished by their architecture, which dictates their parameter size and performance capabilities. Social scientists have increasingly adopted LLMs for text classification tasks, which are difficult to…
In this paper, we prove super-polynomial lower bounds for the model of \emph{sum of ordered set-multilinear algebraic branching programs}, each with a possibly different ordering ($\sum \mathsf{smABP}$). Specifically, we give an explicit…
Scaling the amount of compute used to train language models has dramatically improved their capabilities. However, when it comes to inference, we often limit models to making only one attempt at a problem. Here, we explore inference compute…
Small language models (SLMs) enable low-cost, private, on-device inference, but they often fail on problems that require specialized domain knowledge or multi-step reasoning. Existing approaches for improving reasoning either rely on scale…
A temporal (constraint) language is a relational structure with a first-order definition in the rational numbers with the order. We study here the complexity of the Quantified Constraint Satisfaction Problem (QCSP) for temporal constraint…
It has been shown that the conditional probability distributions obtained by performing measurements on an uncharacterized physical system can be used to infer its underlying dimension in a device-independent way both in the classical and…