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Gabriele Beltramo

Publications and source records attributed to Gabriele Beltramo.

3 recordsLinked to original sources

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

Persistent Homology in $\ell_{\infty}$ Metric

Proximity complexes and filtrations are central constructions in topological data analysis. Built using distance functions, or more generally metrics, they are often used to infer connectivity information from point clouds. Here we investigate proximity complexes and filtrations built over the Chebyshev metric, also known as the maximum metric or $\ell_{\infty}$ metric, rather than the classical Euclidean metric. Somewhat surprisingly, the $\ell_{\infty}$ case has not been investigated thoroughly. In this paper, we examine a number of classical complexes under this metric, including the Čech, Vietoris-Rips, and Alpha complexes. We define two new families of flag complexes, which we call the Alpha flag and Minibox complexes, and prove their equivalence to Čech complexes in homological degrees zero and one. Moreover, we provide algorithms for finding Minibox edges of two, three, and higher-dimensional points. Finally, we present computational experiments on random points, which shows that Minibox filtrations can often be used to speed up persistent homology computations in homological degrees zero and one by reducing the number of simplices in the filtration.

cs.CG

Euler Characteristic Surfaces

We study the use of the Euler characteristic for multiparameter topological data analysis. Euler characteristic is a classical, well-understood topological invariant that has appeared in numerous applications, including in the context of random fields. The goal of this paper is to present the extension of using the Euler characteristic in higher-dimensional parameter spaces. While topological data analysis of higher-dimensional parameter spaces using stronger invariants such as homology continues to be the subject of intense research, Euler characteristic is more manageable theoretically and computationally, and this analysis can be seen as an important intermediary step in multi-parameter topological data analysis. We show the usefulness of the techniques using artificially generated examples, and a real-world application of detecting diabetic retinopathy in retinal images.

math.AT