Related papers: Repetitive Reduction Patterns in Lambda Calculus w…
A non-deterministic call-by-need lambda-calculus \calc with case, constructors, letrec and a (non-deterministic) erratic choice, based on rewriting rules is investigated. A standard reduction is defined as a variant of left-most outermost…
The lambda calculus since more than half a century is a model and foundation of functional programming languages. However, lambda expressions can be evaluated with different reduction strategies and thus, there is no fixed cost model nor…
Optimizing deep learning models is generally performed in two steps: (i) high-level graph optimizations such as kernel fusion and (ii) low level kernel optimizations such as those found in vendor libraries. This approach often leaves…
Slow running or straggler tasks can significantly reduce computation speed in distributed computation. Recently, coding-theory-inspired approaches have been applied to mitigate the effect of straggling, through embedding redundancy in…
Computational efficiency has remained a critical consideration in scaling high-capacity language models, with inference latency and resource consumption presenting significant constraints on real-time applications. The study has introduced…
Optimizing Neural networks is a difficult task which is still not well understood. On the other hand, fixed representation methods such as kernels and random features have provable optimization guarantees but inferior performance due to…
We address a problem connected to the unfolding semantics of functional programming languages: give a useful characterization of those infinite lambda-terms that are lambda_{letrec}-expressible in the sense that they arise as infinite…
This paper explores the semantics of a combinatory fragment of reFLect, the lambda-calculus underlying a functional language used by Intel Corporation for hardware design and verification. ReFLect is similar to ML, but has a primitive data…
To support the understanding of declarative probabilistic programming languages, we introduce a lambda-calculus with a fair binary probabilistic choice that chooses between its arguments with equal probability. The reduction strategy of the…
Reduction-based interpreters are traditionally defined in terms of a one-step reduction function which systematically decomposes a term into a potential redex and context, contracts the redex, and recomposes it to construct the new term to…
Many automatic theorem-provers rely on rewriting. Using theorems as rewrite rules helps to simplify the subgoals that arise during a proof. LCF is an interactive theorem-prover intended for reasoning about computation. Its implementation of…
LLMs are increasingly used as general-purpose reasoners, but long inputs remain bottlenecked by a fixed context window. Recursive Language Models (RLMs) address this by externalising the prompt and recursively solving subproblems. Yet…
Large-scale autoregressive models pretrained on next-token prediction and finetuned with reinforcement learning (RL) have achieved unprecedented success on many problem domains. During RL, these models explore by generating new outputs, one…
Recently, small models with latent recursion have obtained promising results on complex reasoning tasks. These results are typically explained by the theory that such recursion increases a networks depth, allowing it to compactly emulate…
LLMs demonstrate strong performance on code benchmarks, yet consistent reasoning across forward and backward execution remains elusive. We present RoundTripCodeEval (RTCE), a benchmark of four code execution reasoning tasks that evaluates…
The compactness lemma in programming language theory states that any recursive function can be simulated by a finite unrolling of the function. One important use case it has is in the logical relations proof technique for proving properties…
We prove that orthogonal constructor term rewrite systems and lambda-calculus with weak (i.e., no reduction is allowed under the scope of a lambda-abstraction) call-by-value reduction can simulate each other with a linear overhead. In…
From a multi-model compression perspective, model merging enables memory-efficient serving of multiple models fine-tuned from the same base, but suffers from degraded performance due to interference among their task-specific parameter…
Reed-Muller (RM) codes are one of the oldest families of codes. Recently, a recursive projection aggregation (RPA) decoder has been proposed, which achieves a performance that is close to the maximum likelihood decoder for short-length RM…
As a supplement to my talk at the workshop, this extended abstract motivates and summarizes my work with co-authors on problems in two separate areas: first, in the lambda-calculus with letrec, a universal model of computation, and second,…