Related papers: Modular Reasoning about Error Bounds for Concurren…
Logarithmic Number Systems (LNS) hold considerable promise in helping reduce the number of bits needed to represent a high dynamic range of real-numbers with finite precision, and also efficiently support multiplication and division.…
This paper presents a novel method to identify and insert redundant logic into a combinational circuit to improve its fault tolerance without having to replicate the entire circuit as is the case with conventional redundancy techniques. In…
Large language models (LLMs) have demonstrated impressive performance across various language tasks. However, existing LLM reasoning strategies mainly rely on the LLM itself with fast or slow mode (like o1 thinking) and thus struggle to…
Starting with Hoare Logic over 50 years ago, numerous program logics have been devised to reason about the diverse programs encountered in the real world. This includes reasoning about computational effects, particularly those effects that…
Multi-core machines are ubiquitous. However, most inductive logic programming (ILP) approaches use only a single core, which severely limits their scalability. To address this limitation, we introduce parallel techniques based on…
Large language models (LLMs) can improve their accuracy on various tasks through iteratively refining and revising their output based on feedback. We observe that these revisions can introduce errors, in which case it is better to roll back…
Recent advancements in large language models (LLMs) underscore the need for stronger reasoning capabilities to solve complex problems effectively. While Chain-of-Thought (CoT) reasoning has been a step forward, it remains insufficient for…
Most implementations of sampling algorithms for continuous distributions use floating-point numbers, which introduce round-off errors and approximations. These errors can be difficult to analyze, and can cause security issues when used in…
For performance and verification in machine learning, new methods have recently been proposed that optimise learning systems to satisfy formally expressed logical properties. Among these methods, differentiable logics (DLs) are used to…
A concatenated coding scheme over binary memoryless symmetric (BMS) channels using a polarization transformation followed by outer sub-codes is analyzed. Achievable error exponents and upper bounds on the error rate are derived. The first…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
Artificial Intelligence has gained a lot of traction in the recent years, with machine learning notably starting to see more applications across a varied range of fields. One specific machine learning application that is of interest to us…
Logical reasoning about program data often requires dealing with heap structures as well as scalar data types. Recent advances in Satisfiability Modular Theory (SMT) already offer efficient procedures for dealing with scalars, yet they lack…
Large Language Models excel at code generation yet struggle with complex programming tasks that demand sophisticated reasoning. To bridge this gap, traditional process supervision relies on learned reward models requiring costly training…
The generation of comprehensible explanations is an essential feature of modern artificial intelligence systems. In this work, we consider probabilistic logic programming, an extension of logic programming which can be useful to model…
Separation logic is often praised for its ability to closely mimic the locality of state updates when reasoning about them at the level of assertions. The prover only needs to concern themselves with the footprint of the computation at…
Robot sequential decision-making in the real world is a challenge because it requires the robots to simultaneously reason about the current world state and dynamics, while planning actions to accomplish complex tasks. On the one hand,…
First-order probabilistic models combine representational power of first-order logic with graphical models. There is an ongoing effort to design lifted inference algorithms for first-order probabilistic models. We analyze lifted inference…
In this survey, we present in a unified way the categorical and syntactical settings of coherent differentiation introduced recently, which shows that the basic ideas of differential linear logic and of the differential lambda-calculus are…
Recent approaches to verifying programs in separation logics for concurrency have used state transition systems (STSs) to specify the atomic operations of programs. A key challenge in the setting has been to compose such STSs into larger…