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Federica Cecchetto

Publications and source records attributed to Federica Cecchetto.

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

Bridging the Gap Between Tree and Connectivity Augmentation: Unified and Stronger Approaches

We consider the Connectivity Augmentation Problem (CAP), a classical problem in the area of Survivable Network Design. It is about increasing the edge-connectivity of a graph by one unit in the cheapest possible way. More precisely, given a $k$-edge-connected graph $G=(V,E)$ and a set of extra edges, the task is to find a minimum cardinality subset of extra edges whose addition to $G$ makes the graph $(k+1)$-edge-connected. If $k$ is odd, the problem is known to reduce to the Tree Augmentation Problem (TAP) -- i.e., $G$ is a spanning tree -- for which significant progress has been achieved recently, leading to approximation factors below $1.5$ (the currently best factor is $1.458$). However, advances on TAP did not carry over to CAP so far. Indeed, only very recently, Byrka, Grandoni, and Ameli (STOC 2020) managed to obtain the first approximation factor below $2$ for CAP by presenting a $1.91$-approximation algorithm based on a method that is disjoint from recent advances for TAP. We first bridge the gap between TAP and CAP, by presenting techniques that allow for leveraging insights and methods from TAP to approach CAP. We then introduce a new way to get approximation factors below $1.5$, based on a new analysis technique. Through these ingredients, we obtain a $1.393$-approximation algorithm for CAP, and therefore also TAP. This leads to the currently best approximation result for both problems in a unified way, by significantly improving on the above-mentioned $1.91$-approximation for CAP and also the previously best approximation factor of $1.458$ for TAP by Grandoni, Kalaitzis, and Zenklusen (STOC 2018). Additionally, a feature we inherit from recent TAP advances is that our approach can deal with the weighted setting when the ratio between the largest to smallest cost on extra links is bounded, in which case we obtain approximation factors below $1.5$.

cs.DS

Better-Than-$\frac{4}{3}$-Approximations for Leaf-to-Leaf Tree and Connectivity Augmentation

The Connectivity Augmentation Problem (CAP) together with a well-known special case thereof known as the Tree Augmentation Problem (TAP) are among the most basic Network Design problems. There has been a surge of interest recently to find approximation algorithms with guarantees below $2$ for both TAP and CAP, culminating in the currently best approximation factor for both problems of $1.393$ through quite sophisticated techniques. We present a new and arguably simple matching-based method for the well-known special case of leaf-to-leaf instances. Combining our work with prior techniques, we readily obtain a $(\frac{4}{3}+ε)$-approximation for Leaf-to-Leaf CAP by returning the better of our solution and one of an existing method. Prior to our work, a $\frac{4}{3}$-guarantee was only known for Leaf-to-Leaf TAP instances on trees of height $2$. Moreover, when combining our technique with a recently introduced stack analysis approach, which is part of the above-mentioned $1.393$-approximation, we can further improve the approximation factor to $1.29$, obtaining for the first time a factor below $\frac{4}{3}$ for a nontrivial class of TAP/CAP instances.

cs.DS