From Judgments to Issues: Structured Extraction of Legal Reasoning with Citation-Hallucination Control

We present an automated pipeline that decomposes Italian tax-court judgments into individual legal issues and extracts, for each issue, a structured XML representation grounded in the IRAC framework and the legal syllogism. The pipeline targets a corpus of approximately $330{,}000$ first- and second-instance decisions of the Italian tax courts and is built around a capable yet cost-efficient general-purpose model (DeepSeek V3), a choice driven by the need to process several hundred thousand documents at a sustainable cost. To address the well-documented unreliability of large language models on legal citations, we couple the extraction step with an automatic hallucination-detection filter that compares the references produced by the model with those identified in the judgment text by a dedicated parser (Linkoln), normalised to standard identifiers (URN-NIR, ECLI, CELEX). We validate the pipeline on $50$ judgments annotated by two PhDs in tax law, computing inter-annotator agreement and LLM-vs-expert agreement on both issue extraction and legal citations, together with a stand-alone evaluation of the hallucination filter. To the best of our knowledge, this is the first issue-level, expert-validated structured extraction pipeline with hallucination control for Italian tax-court decisions, and it provides a concrete starting point for downstream applications such as issue-level retrieval, citation-network analysis, and the construction of large-scale datasets of legal reasoning.

PCA recovery thresholds in low-rank matrix inference with sparse noise

We study the high-dimensional inference of a rank-one signal corrupted by sparse noise. The noise is modelled as the adjacency matrix of a weighted undirected graph with finite average connectivity in the large size limit. Using the replica method from statistical physics, we analytically compute the typical value of the top eigenvalue, the top eigenvector component density, and the overlap between the signal vector and the top eigenvector. The solution is given in terms of recursive distributional equations for auxiliary probability density functions which can be efficiently solved using a population dynamics algorithm. Specialising the noise matrix to Poissonian and Random Regular degree distributions, the critical signal strength is analytically identified at which a transition happens for the recovery of the signal via the top eigenvector, thus generalising the celebrated BBP transition to the sparse noise case. In the large-connectivity limit, known results for dense noise are recovered. Analytical results are in agreement with numerical diagonalisation of large matrices.

Classification of Superstatistical Features in High Dimensions

We characterise the learning of a mixture of two clouds of data points with generic centroids via empirical risk minimisation in the high dimensional regime, under the assumptions of generic convex loss and convex regularisation. Each cloud of data points is obtained by sampling from a possibly uncountable superposition of Gaussian distributions, whose variance has a generic probability density $\varrho$. Our analysis covers therefore a large family of data distributions, including the case of power-law-tailed distributions with no covariance. We study the generalisation performance of the obtained estimator, we analyse the role of regularisation, and the dependence of the separability transition on the distribution scale parameters.