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We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
Typical evaluations of Large Language Models (LLMs) report a single metric per dataset, often representing the model's best-case performance under carefully selected settings. Unfortunately, this approach overlooks model robustness and…
Sequence theories are an extension of theories of strings with an infinite alphabet of letters, together with a corresponding alphabet theory (e.g. linear integer arithmetic). Sequences are natural abstractions of extendable arrays, which…
Large language models have recently demonstrated advanced capabilities in solving IMO and Putnam problems; yet their role in research mathematics has remained fairly limited. The key difficulty is verification: suggested proofs may look…
We present Sequence Salience, a visual tool for interactive prompt debugging with input salience methods. Sequence Salience builds on widely used salience methods for text classification and single-token prediction, and extends this to a…
We present an extension to the robust phase estimation protocol, which can identify incorrect results that would otherwise lie outside the expected statistical range. Robust phase estimation is increasingly a method of choice for…
Provably correct software is one of the key challenges in our softwaredriven society. While formal verification establishes the correctness of a given program, the result of program synthesis is a program which is correct by construction.…
This work elaborates on a High performance computing (HPC) architecture based on Simple Linux Utility for Resource Management (SLURM) [1] for deploying heterogeneous Large Language Models (LLMs) into a scalable inference engine. Dynamic…
Understanding how data moves, transforms, and persists, known as data flow, is fundamental to reasoning in procedural tasks. Despite their fluency in natural and programming languages, large language models (LLMs), although increasingly…
Termination analysis of C programs is a challenging task. On the one hand, the analysis needs to be precise enough to draw meaningful conclusions. On the other hand, relevant programs in practice are large and require substantial…
On one hand, termination analysis of logic programs is now a fairly established research topic within the logic programming community. On the other hand, non-termination analysis seems to remain a much less attractive subject. If we divide…
Information-flow control mechanisms are difficult both to design and to prove correct. To reduce the time wasted on doomed proof attempts due to broken definitions, we advocate modern random testing techniques for finding counterexamples…
The dominant way of judging Large Language Models (LLMs) has been to ask how well they can recall explicit facts from very long inputs. While today's best models achieve near perfect recall, this masks a harder skill: performing multi-step…
We provide a necessary condition that a quantum measurement can be implemented by the class of protocols known as Local Operations and Classical Communication, or LOCC, including when an error is allowed but must vanish in the limit of an…
Cryptographic research takes software timing side channels seriously. Approaches to mitigate them include constant-time coding and techniques to enforce such practices. However, recent attacks like Meltdown [42], Spectre [37], and…
The increasing scale of near-term quantum hardware motivates the need for efficient noise characterization methods, since qubit and gate level techniques cannot capture crosstalk and correlated noise in many qubit systems. While scalable…
Bitcoin is the first fully-decentralized permissionless blockchain protocol to achieve a high level of security, but at the expense of poor throughput and latency. Scaling the performance of Bitcoin has a been a major recent direction of…
A new technique is presented to prove non-termination of term rewriting. The basic idea is to find a non-empty regular language of terms that is closed under rewriting and does not contain normal forms. It is automated by representing the…
Incorrectness Separation Logic (ISL) is a proof system that is tailored specifically to resolve problems of under-approximation in programs that manipulate heaps, and it primarily focuses on bug detection. This approach is different from…
The multi-dithering method has been well verified in phase locking of polarization coherent combination experiment. However, it is hard to apply to low repetition frequency pulsed lasers, since there exists an overlap frequency domain…