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We present an automated verification of the well-known modal logic cube in Isabelle/HOL, in which we prove the inclusion relations between the cube's logics using automated reasoning tools. Prior work addresses this problem but without…
Modular integer arithmetic occurs in many algorithms for computer algebra, cryptography, and error correcting codes. Although recent microprocessors typically offer a wide range of highly optimized arithmetic functions, modular integer…
Formal verification techniques based on computer algebra have proven highly effective for circuit verification. The circuit, given as an and-inverter graph, is encoded as a set of polynomials that automatically generates a Gr\"obner basis…
Many approaches for verifying input-output properties of neural networks have been proposed recently. However, existing algorithms do not scale well to large networks. Recent work in the field of model compression studied binarized neural…
Verification is one of the central tasks in circuit and system design. While simulation and emulation are widely used, complete correctness can only be ensured based on formal proof techniques. But these approaches often have very high run…
Temporal Logic Model Checking is a verification method in which we describe a system, the model, and then we verify whether some properties, expressed in a temporal logic formula, hold in the system. It has many industrial applications. In…
We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…
Code review is one of the key processes in the software development lifecycle and is essential to maintain code quality. However, manual code review is subjective and time consuming. Given its rule-based nature, code review is well suited…
Mathematical reasoning has long been a key benchmark for evaluating large language models. Although substantial progress has been made on math word problems, the need for reasoning over tabular data in real-world applications has been…
We suggest a programming realization of an algorithm for verifying a given set of algebraic relations in the form of a supercommutator multiplication table for the Verma module, which is constructed according to a generalized Cartan…
This paper proposes the use of "multicalibration" to yield interpretable and reliable confidence scores for outputs generated by large language models (LLMs). Multicalibration asks for calibration not just marginally, but simultaneously…
Large Language Models (LLMs) have recently achieved remarkable progress in mathematical reasoning. To enable such capabilities, many existing works distill strong reasoning models into long chains of thought or design algorithms to…
Recently, with the chain of thought (CoT) prompting, large language models (LLMs), e.g., GPT-3, have shown strong reasoning ability in several natural language processing tasks such as arithmetic, commonsense, and logical reasoning.…
Multimodal Large Language Models demonstrate strong performance on multimodal benchmarks, yet often exhibit poor robustness when exposed to spurious modality interference, such as irrelevant text in vision understanding, or irrelevant…
Side-channel attacks, which are capable of breaking secrecy via side-channel information, pose a growing threat to the implementation of cryptographic algorithms. Masking is an effective countermeasure against side-channel attacks by…
Applying Gr\"obner basis theory to concrete problems in Lean 4 remains difficult since the current formalization of multivariate polynomials is based on a non-computable representation and is therefore not suitable for efficient symbolic…
We present a new technique for verifying nonlinear and hybrid models with inputs. We observe that once an input signal is fixed, the sensitivity analysis of the model can be computed much more precisely. Based on this result, we propose a…
Analog neural networks are gaining attention due to their efficiency in terms of power consumption and processing speed. However, since analog neural networks are implemented as physical circuits, they are highly sensitive to manufacturing…
Multiple polylogarithms appear in analytic calculations of higher order corrections in quantum field theory. In this article we study the numerical evaluation of multiple polylogarithms. We provide algorithms, which allow the evaluation for…
Based on an idea in Hironaka's proof of resolution of singularities, we present an algorithmic smoothness test for algebraic varieties. The test is inherently parallel and does not involve the calculation of codimension-sized minors of the…