arXiv subjects

Alberto Acedo

Publications and source records attributed to Alberto Acedo.

3 recordsLinked to original sources

arXiv2026

Omega-N: Interpretable Structural Node Descriptors and Their Applicability Domain

A composite structural index summarises a network in one number, and for a triangle-based index it is spectrally redundant: Tr(A^3) is the third moment of the adjacency spectrum. The non-redundant content sits one level down, in diag(A^3), which depends on eigenvectors and is not spectrally determined. A corollary in the theory paper predicted that the global scalar should tie sharpened spectral baselines rather than beat them, while the node-wise attribution should do better where the number of structural epicentres is unknown. We construct Omega-N by localizing each of the four factors. The direct localization is badly conditioned; two corrections from published practice fix it, a configuration-null excess per factor and a personalized-PageRank neighbourhood at several scales, giving ten interpretable features per node, with no attributes, training or embeddings. Against a recursive feature engine at five levels of recursion, Omega-N wins on three and ties on two of the six in-domain evaluations, the sixth a declared null where every arm returns chance, with ten features against its 28 to 252 before pruning. Two statistics from the graph and labels, not from performance, partition the eight benchmarks without error, and the two they exclude are the two on which it loses. The strongest application is drug-target prioritisation on protein interaction networks: +0.032 to +0.103 AUPRC over a six-feature centrality battery and +0.084 to +0.208 over the four-feature one, across three constructions, replicated on an independent AP-MS network and label source (degree-matched: +0.0723 on STRING, +0.0560 on BioPlex, p=0.00195). Adding Omega-N to centralities plus Node2Vec changes nothing. The claim is narrow and it is the point: ten named features, computed without training, match or beat hand-crafted centralities and a recursive engine, and do not touch learned representations.

cs.SI↗

arXiv2026

The Triadic Stress Index in Financial Markets

The Triadic Stress Index (TSI) takes a network index whose four factors were first observed in soil microbiome co-occurrence networks and applies it, without alteration, to the correlation network of financial assets. We test it on five markets spanning 2006-2026 (equities including banking crises and the AI sector, cryptocurrencies, commodities, foreign exchange and sovereign debt), against three independent definitions of a crisis episode, at a fixed alarm budget, out of sample, with block-bootstrap intervals and a Holm correction across the family of tests. The benchmarks are the Absorption Ratio, the industry standard used by MSCI and central banks; the effective rank and the Vendi score, the sharpest spectral measures available; Ollivier-Ricci curvature; and the global and local balance indices of signed correlation networks. Three comparisons favour the index. It carries a per-node decomposition, diag(A^3), naming which asset is carrying the concentration with no parameter to select, and scores 0.97-0.99 against 0.33-0.84 for the only published per-node alternative, whereas spectral attribution must first choose how many components to read and collapses under a standard but wrong choice. Its alarms are the cleanest of anything tested, 4.0% of them with no matching episode against 14.7% for the effective rank and roughly 59% for the Absorption Ratio. And it beats the Absorption Ratio on detection by 0.273 in F1 out of sample, p<0.0005. The remaining comparisons are ties. Against the effective rank and the Vendi score the index ties in every scheme and both samples, and the margin over the Absorption Ratio narrows under the strictest labelling. On real matrices the far simpler node degree reproduces the attribution. A lead-lag analysis puts the peak cross-correlation at zero lag: this is a coincident state index, not a forecast.

physics.soc-ph↗

arXiv2026

Omega-S: A Functional Resilience Index for LLM Fine-Tuning

Fine-tuning a large language model on new data degrades what it previously learned. We present Omega-S, a drop-in penalty computed from the weight matrix alone: it needs no previous-task data, no Fisher matrix and no stored copy of the old weights. It is three lines in an existing training loop and adds under 4% to the cost of a step. Retention. On Llama-3-8B with LoRA, fine-tuned from code to prose and measured by HumanEval over ten seeds, Omega-S retains more of the original capability than no regularisation on 9 of 10 seeds (0.173 -> 0.238 absolute pass@1; sign test one-sided p=0.011, Wilcoxon p=0.006), as a retention ratio, 62.9% -> 84.1%. It also beats tuned weight decay on 10 of 10 seeds (p=0.002) and tuned EWC on 8 of 10 (p=0.014), every arm re-measured in the same session. Mechanism, measured rather than asserted. Omega-S is topological by construction, its objective built from Tr(A^3), but we measured which of its four factors actually moves and three do not: their elasticity with respect to the weights is at or below 1e-4, against 9e-3 for the degree-variance term. As implemented, the composite reduces to a penalty on the variance of node degrees, which means row magnitude in square modules and directional alignment in non-square ones. We report this because a method whose name promises one thing and whose gradient does another should say so. We also enumerate the open design choices, including a contrast-preserving construction that does what it was designed to do and makes retention worse on all ten seeds. Repeating an identical configuration, same seed and same hardware, gives a standard deviation of 0.104 in retention ratio. We have not found this quantified for low-rank fine-tuning of language models, and it bounds every seed-paired comparison in this literature, ours included. Code, per-seed results and the full record of negative results are available.

cs.LG↗