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Hadrien Espic

Publications and source records attributed to Hadrien Espic.

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ARC-AGI-2 Technical Report

The Abstraction and Reasoning Corpus (ARC) is designed to assess generalization beyond pattern matching, requiring models to infer symbolic rules from very few examples. In this work, we present a transformer-based system that advances ARC performance by combining neural inference with structure-aware priors and online task adaptation. Our approach is built on four key ideas. First, we reformulate ARC reasoning as a sequence modeling problem using a compact task encoding with only 125 tokens, enabling efficient long-context processing with a modified LongT5 architecture. Second, we introduce a principled augmentation framework based on group symmetries, grid traversals, and automata perturbations, enforcing invariance to representation changes. Third, we apply test-time training (TTT) with lightweight LoRA adaptation, allowing the model to specialize to each unseen task by learning its transformation logic from demonstrations. Fourth, we design a symmetry-aware decoding and scoring pipeline that aggregates likelihoods across augmented task views, effectively performing ``multi-perspective reasoning'' over candidate solutions. We demonstrate that these components work synergistically: augmentations expand hypothesis space, TTT sharpens local reasoning, and symmetry-based scoring improves solution consistency. Our final system achieves a significant improvement over transformer baselines and surpasses prior neural ARC solvers, closing the gap toward human-level generalization.

cs.CL

Koszul duality for categories with a fixed object set

We define a notion of Koszul dual of a monoid object in a monoidal biclosed model category. Our construction generalizes the classic Yoneda algebra $Ext_A(k,k)$. We apply this general construction to define the Koszul dual of a category enriched over spectra or chain complexes. This example relies on the classical observation that enriched categories are monoid objects in a category of enriched graphs. We observe that the category of enriched graphs is biclosed, meaning that it comes with both left and right internal hom objects. Given a category $R$ (which plays the role of the ground field $k$ in classical algebra), and an augmented $R$-algebra $C$, we define the Koszul dual of $C$, denoted $K(C)$, as the $R$-algebra of derived endomorphisms of $R$ in the category of right $C$-modules. We establish the expected adjunctions between the categories of modules over $C$ and modules over $K(C)$. We investigate the question of when the map from $C$ to its double dual $K(K(C))$ is an equivalence. We also show that Koszul duality of operads can be understood as a special case of Koszul duality of categories. In this way we incorporate Koszul duality of operads in a wider context, and possibly clarify some aspects of it.

math.CT