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Karl Gemayel

Publications and source records attributed to Karl Gemayel.

2 recordsLinked to original sources

Tiny Moves: Game-based Hypothesis Refinement

Most machine learning approaches to scientific discovery frame hypotheses as end-to-end predictions, obscuring the incremental structure of scientific reasoning. We propose The Hypothesis Game, a symbolic formalism for hypothesis refinement in which LLM agents operate on a shared hypothesis state using a fixed grammar of reasoning moves. The framework is motivated by the observation that scientific progress often proceeds through small, localized revisions, grounded in domain context, rather than extensive rewrites. We instantiate a minimal game with LLM agents and evaluate it on pathway-level mechanistic refinement tasks. In the primary setting of corruption recovery, where hypotheses contain controlled errors, the game-based approach consistently removes more errors and achieves higher precision than strong prompting baselines, while preserving valid structure through incremental edits. In a secondary reconstruction setting from partial cues, it performs comparably to the strongest baseline, indicating that explicit move-based refinement remains competitive even when ground-truth recovery is difficult. These findings support game-based reasoning as a principled route to more controllable, interpretable, and transferable hypothesis refinement systems for scientific discovery.

cs.MA

Efficient sparse polynomial factoring using the Funnel heap

This work is a comprehensive extension of Abu-Salem et al. (2015) that investigates the prowess of the Funnel Heap for implementing sums of products in the polytope method for factoring polynomials, when the polynomials are in sparse distributed representation. We exploit that the work and cache complexity of an Insert operation using Funnel Heap can be refined to de- pend on the rank of the inserted monomial product, where rank corresponds to its lifetime in Funnel Heap. By optimising on the pattern by which insertions and extractions occur during the Hensel lifting phase of the polytope method, we are able to obtain an adaptive Funnel Heap that minimises all of the work, cache, and space complexity of this phase. Additionally, we conduct a detailed empirical study confirming the superiority of Funnel Heap over the generic Binary Heap once swaps to external memory begin to take place. We demonstrate that Funnel Heap is a more efficient merger than the cache oblivious k-merger, which fails to achieve its optimal (and amortised) cache complexity when used for performing sums of products. This provides an empirical proof of concept that the overlapping approach for perform- ing sums of products using one global Funnel Heap is more suited than the serialised approach, even when the latter uses the best merging structures available.

cs.SC