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Attention is a powerful and ubiquitous mechanism for allowing neural models to focus on particular salient pieces of information by taking their weighted average when making predictions. In particular, multi-headed attention is a driving…

We study the hardness of approximation of clause minimum and literal minimum representations of pure Horn functions in $n$ Boolean variables. We show that unless P=NP, it is not possible to approximate in polynomial time the minimum number…

Memory and forgetting constitute two sides of the same coin, and although the first has been rigorously investigated, the latter is often overlooked. A number of experiments under the realm of psychology and experimental neuroscience have…

We consider the problem of how to verify the security of probabilistic oblivious algorithms formally and systematically. Unfortunately, prior program logics fail to support a number of complexities that feature in the semantics and…

A growing body of research in continual learning focuses on the catastrophic forgetting problem. While many attempts have been made to alleviate this problem, the majority of the methods assume a single model in the continual learning…

For a large class of polynomials, the standard method of polynomial evaluation, Horner's method, can be very inaccurate. The alternative method given here is on average 100 to 1000 times more accurate than Horner's Method. The number of…

In games with imperfect recall, players may forget the sequence of decisions they made in the past. When players also forget whether they have already encountered their current decision point, they are said to be absent-minded. Solving…

A definite Horn theory is a set of n-dimensional Boolean vectors whose characteristic function is expressible as a definite Horn formula, that is, as conjunction of definite Horn clauses. The class of definite Horn theories is known to be…

This paper aims to improve the performance of large language models by addressing the variable computational demands in inference steps, where some tokens require more computational resources than others. We present HARP, a simple…

In this paper, we show that the derivability problem for the primal propositional logic remains solvable in polynomial time upon adding a certain form of the principle of equivalent form substitution; and that, upon adding another form of…

How can we help a forgetful learner learn multiple concepts within a limited time frame? While there have been extensive studies in designing optimal schedules for teaching a single concept given a learner's memory model, existing…

We consider approximating data structures with collections of the items that they contain. For examples, lists, binary trees, tuples, etc, can be approximated by sets or multisets of the items within them. Such approximations can be used to…

We address lower bounds on the time complexity of algorithms solving the propositional satisfiability problem. Namely, we consider two DPLL-type algorithms, enhanced with the unit clause and pure literal heuristics. Exponential lower bounds…

Decision-making AI agents are often faced with two important challenges: the depth of the planning horizon, and the branching factor due to having many choices. Hierarchical reinforcement learning methods aim to solve the first problem, by…

Constraint Logic Programming (CLP) and Hereditary Harrop formulas (HH) are two well known ways to enhance the expressivity of Horn clauses. In this paper, we present a novel combination of these two approaches. We show how to enrich the…

Long-horizon conversational agents require persistent memory for coherent reasoning, yet uncontrolled accumulation causes temporal decay and false memory propagation. Benchmarks such as LOCOMO and LOCCO report performance degradation from…

We consider the problems of finding the lexicographically minimal (or maximal) satisfying assignment of propositional formulae for different restricted formula classes. It turns out that for each class from our framework, the above problem…

Large Language Models (LLMs) are often evaluated against ideals of perfect Bayesian inference, yet growing evidence suggests that their in-context reasoning exhibits systematic forgetting of past information. Rather than viewing this…

We investigate the ability of language models to perform compositional reasoning tasks where the overall solution depends on correctly composing the answers to sub-problems. We measure how often models can correctly answer all sub-problems…

In this article, we tackle the math word problem, namely, automatically answering a mathematical problem according to its textual description. Although recent methods have demonstrated their promising results, most of these methods are…