arXiv subjects

Eleonora Giunchiglia

Publications and source records attributed to Eleonora Giunchiglia.

At least 19 recordsLinked to original sources

arXiv2026

Magenta: Closing the Loop Between Mathematical Reasoning and Lean Verification

Most of mathematical knowledge has been communicated through so-called informal use of mathematics and natural language. With large language models (LLMs) being highly adept in using natural language, they achieve strong performance, yet not perfect, in informal mathematical reasoning. Restraining LLMs to informal reasoning misses out on the opportunity to use the discrete verification abilities that machines offer through machine-checkable proofs. In this paper, we bridge the gap between informal and formal reasoning by integrating Lean signals into the informal reasoning process. We introduce Magenta, a training-free agentic pipeline that, given only a natural-language problem, produces an answer, expresses it as a Lean 4 statement, and constructs a machine-checked proof. A statement judge verifies whether the formalisation preserves the original problem, while an error-attribution judge routes failed attempts either to mathematical re-derivation or local Lean repair. Magenta achieves 100% accuracy across all evaluated olympiad benchmarks, including AIME 2025, AIME 2026, and HMMT February 2026. When paired with the open-weight K2-Horizon-7B reasoner, it solves all six IMO 2026 problems. Our analysis shows that statement adjudication is essential for preventing false certificates and that feedback-guided correction outperforms independent resampling on difficult problems.

cs.AI↗

arXiv2026

Stay Within Your Bounds: Distance-Guided Decoding for Guaranteed Context-Free Grammar Compliance

Grammar-constrained decoding helps large language models produce syntactically valid structured outputs, such as code, JSON, and SQL. For context-free grammars, many practical decoders enforce local prefix feasibility: each token must keep the current prefix extendable to some valid completion. Yet, under tokenizer-grammar mismatch and finite token budgets, feasible prefixes may still fail to reach acceptance. We propose a lookahead-guided decoding framework for context-free grammars based on pushdown automata. Offline, we compute bounded pushdown summaries with reachability labels and upper-bound distances to acceptance. Online, these estimates guide horizon-aware pruning and beam search. The resulting decoder is syntactically sound: every output is accepted by the target grammar. Experiments on JSON, SQL, and Linear Temporal Logic (LTL) show both consistent syntactic validity and improved completion quality over existing baselines.

cs.AI↗

arXiv2026

PiCSAR: Probabilistic Confidence Selection And Ranking for Reasoning Chains

Best-of-n sampling improves the accuracy of large language models (LLMs) and large reasoning models (LRMs) by generating multiple candidate solutions and selecting the one with the highest reward. The key challenge for reasoning tasks is designing a scoring function that can identify correct reasoning chains without access to ground-truth answers. We propose Probabilistic Confidence Selection And Ranking (PiCSAR): a simple, training-free method that scores each candidate generation using the joint log-likelihood of the reasoning and final answer. The joint log-likelihood of the reasoning and final answer naturally decomposes into reasoning confidence and answer confidence. PiCSAR achieves substantial gains across diverse benchmarks (+10.18 on MATH500, +9.81 on AIME2025), outperforming baselines with at least 2x fewer samples in 16 out of 20 comparisons. Our analysis reveals that correct reasoning chains exhibit significantly higher reasoning and answer confidence, justifying the effectiveness of PiCSAR.

cs.CL↗

arXiv2026

ROAD-Waymo: A Large-Scale Action Awareness Dataset for Autonomous Driving

Autonomous Vehicle (AV) perception systems require more than simply seeing, via e.g., object detection or scene segmentation. They need a holistic understanding of what is happening within the scene for safe interaction with other road users. Few datasets exist for the purpose of developing and training algorithms to comprehend the actions of other road users. This paper presents ROAD-Waymo, an extensive dataset for the development and benchmarking of techniques for agent, action, location and event detection in road scenes, provided as a layer upon the (US) Waymo Open dataset. Considerably larger and more challenging than any existing dataset (and encompassing multiple cities), it comes with 198k annotated video frames, 54k agent tubes, 3.9M bounding boxes and a total of 12.4M labels. The integrity of the dataset has been confirmed and enhanced via a novel annotation pipeline designed for automatically identifying violations of requirements specifically designed for this dataset. As ROAD-Waymo is compatible with the original (UK) ROAD dataset, it provides the opportunity to tackle domain adaptation between real-world road scenarios in different countries within a novel benchmark: ROAD++.

cs.CV↗

arXiv2026

Pythagoras-Prover: Advancing Efficient Formal Proving via Augmented Lean Formalisation

Modern Lean theorem provers achieve strong performance only with substantial training and inference compute, driven in part by scarce verified proof data and the long reasoning traces of formal proof search, making both supervised fine-tuning (SFT) and sampling expensive. We introduce Pythagoras-Prover, a compute-efficient open-source family of Lean theorem provers built for practical compute budgets. The family spans two generation paradigms: autoregressive models at 4B and 32B parameters, and a first proof-of-concept diffusion-based prover (4B) that iteratively refines Lean proofs at inference time. For training efficiency, we build a Lean-verified corpus stratified into easy, medium, and hard problems for curriculum SFT, so models acquire proof skills progressively from shorter, simpler proofs to longer, harder ones. During SFT, a dynamic proof-reasoning filtering scheme preserves informative proof traces while keeping each instance within an 8k-token context budget. We also introduce Augmented Lean Formalisation (ALF), which expands scarce verified corpora into variants of formal statements, populated via self-distillation for extra training signal without formally verifying every mutated instance. By perturbing known problems while preserving their formal character, ALF reduces reliance on any statement's surface form. Empirically, Pythagoras-Prover-4B surpasses DeepSeek-Prover-V2-671B at pass@32 on MiniF2F-Test (86.1% vs 82.4%) with ~167x fewer parameters, while Pythagoras-Prover-32B sets the open-source state of the art at 93.0% on MiniF2F-Test and solves 93 of 672 PutnamBench problems. We release MiniF2F-ALF, an ALF-mutated contamination-sensitive benchmark on which every evaluated model loses accuracy; here our 32B remains strongest and our 4B matches the prior state of the art, Goedel-Prover-V2-32B.

cs.AI↗

arXiv2026

Can I Have Your Order? Monte-Carlo Tree Search for Slot Filling Ordering in Diffusion Language Models

While plan-and-infill decoding in Masked Diffusion Models (MDMs) shows promise for mathematical and code reasoning, performance remains highly sensitive to slot infilling order, often yielding substantial output variance. We introduce McDiffuSE, a framework that formulates slot selection as decision making and optimises infilling orders through Monte Carlo Tree Search (MCTS). McDiffuSE uses look-ahead simulations to evaluate partial completions before commitment, systematically exploring the combinatorial space of generation orders. Experiments show an average improvement of 3.2% over autoregressive baselines and 8.0% over baseline plan-and-infill, with notable gains of 19.5% on MBPP and 4.9% on MATH500. Our analysis reveals that while McDiffuSE predominantly follows sequential ordering, incorporating non-sequential generation is essential for maximising performance. We observe that larger exploration constants, rather than increased simulations, are necessary to overcome model confidence biases and discover effective orderings. These findings establish MCTS-based planning as an effective approach for enhancing generation quality in MDMs.

cs.AI↗

arXiv2026

A Survey on Deep Learning Approaches for Tabular Data Generation: Utility, Alignment, Fidelity, Privacy, Diversity, and Beyond

Generative modelling has become the standard approach for synthesising tabular data. However, different use cases demand synthetic data to comply with different requirements to be useful in practice. In this survey, we review deep generative modelling approaches for tabular data from the perspective of five types of requirements: utility of the synthetic data, alignment of the synthetic data with domain-specific knowledge, statistical fidelity of the synthetic data distribution compared to the real data distribution, privacy-preserving capabilities, and sampling diversity. We group the approaches along two levels of granularity: (i) based on the requirements they address and (ii) according to the underlying model they utilise. Additionally, we summarise the appropriate evaluation methods for each requirement, the relationships among the requirements, and the specific characteristics of each model type. Finally, we discuss future directions for the field, along with opportunities to improve the current evaluation methods. Overall, this survey can be seen as a user guide to tabular data generation: helping readers navigate available models and evaluation methods to find those best suited to their needs.

cs.LG↗

arXiv2026

Right for the Right Reasons: Avoiding Reasoning Shortcuts via Prototypical Neurosymbolic AI

Neurosymbolic AI is growing in popularity thanks to its ability to combine neural perception and symbolic reasoning in end-to-end trainable models. However, recent findings reveal these are prone to shortcut reasoning, i.e., to learning unindented concepts--or neural predicates--which exploit spurious correlations to satisfy the symbolic constraints. In this paper, we address reasoning shortcuts at their root cause and we introduce Prototypical Neurosymbolic architectures. These models are able to satisfy the symbolic constraints (be right) because they have learnt the correct basic concepts (for the right reasons) and not because of spurious correlations, even in extremely low data regimes. Leveraging the theory of prototypical learning, we demonstrate that we can effectively avoid reasoning shortcuts by training the models to satisfy the background knowledge while taking into account the similarity of the input with respect to the handful of labelled datapoints. We extensively validate our approach on the recently proposed rsbench benchmark suite in a variety of settings and tasks with very scarce supervision: we show significant improvements in learning the right concepts both in synthetic tasks (MNIST-EvenOdd and Kand-Logic) and real-world, high-stake ones (BDD-OIA). Our findings pave the way to prototype grounding as an effective, annotation-efficient strategy for safe and reliable neurosymbolic learning.

cs.LG↗

arXiv2025

ABS: Enforcing Constraint Satisfaction On Generated Sequences Via Automata-Guided Beam Search

Sequence generation and prediction form a cornerstone of modern machine learning, with applications spanning natural language processing, program synthesis, and time-series forecasting. These tasks are typically modeled in an autoregressive fashion, where each token is generated conditional on the preceding ones, and beam search is commonly used to balance exploration and fluency during decoding. While deep learning models and Large Language Models (LLMs) excel at capturing statistical patterns in this setting, they remain ill-equipped to guarantee compliance with formal constraints. In this paper, we introduce ABS: a general and model-agnostic inference-time algorithm that guarantees compliance with any constraint that can be compiled into a Deterministic Finite Automaton (DFA), without requiring retraining. ABS leverages the DFA to guide a constrained variant of beam search: at each decoding step, transitions leading to violations are masked, while remaining paths are dynamically re-ranked according to both the model's probabilities and the automaton's acceptance structure. We formally prove that the resulting sequences are guaranteed to satisfy the given constraints, and we empirically demonstrate that ABS also improves output quality. We validate our approach on three distinct tasks: constrained image-stream classification, controlled text generation, and text infilling. In all settings, ABS achieves perfect constraint satisfaction, while outperforming or matching state-of-the-art baselines on standard quality metrics and efficiency.

cs.LG↗

arXiv2025

Beyond the convexity assumption: Realistic tabular data generation under quantifier-free real linear constraints

Synthetic tabular data generation has traditionally been a challenging problem due to the high complexity of the underlying distributions that characterise this type of data. Despite recent advances in deep generative models (DGMs), existing methods often fail to produce realistic datapoints that are well-aligned with available background knowledge. In this paper, we address this limitation by introducing Disjunctive Refinement Layer (DRL), a novel layer designed to enforce the alignment of generated data with the background knowledge specified in user-defined constraints. DRL is the first method able to automatically make deep learning models inherently compliant with constraints as expressive as quantifier-free linear formulas, which can define non-convex and even disconnected spaces. Our experimental analysis shows that DRL not only guarantees constraint satisfaction but also improves efficacy in downstream tasks. Notably, when applied to DGMs that frequently violate constraints, DRL eliminates violations entirely. Further, it improves performance metrics by up to 21.4% in F1-score and 20.9% in Area Under the ROC Curve, thus demonstrating its practical impact on data generation.

cs.LG↗

arXiv2024

Deep generative models as an adversarial attack strategy for tabular machine learning

Deep Generative Models (DGMs) have found application in computer vision for generating adversarial examples to test the robustness of machine learning (ML) systems. Extending these adversarial techniques to tabular ML presents unique challenges due to the distinct nature of tabular data and the necessity to preserve domain constraints in adversarial examples. In this paper, we adapt four popular tabular DGMs into adversarial DGMs (AdvDGMs) and evaluate their effectiveness in generating realistic adversarial examples that conform to domain constraints.

cs.LG↗

arXiv2024

ULLER: A Unified Language for Learning and Reasoning

The field of neuro-symbolic artificial intelligence (NeSy), which combines learning and reasoning, has recently experienced significant growth. There now are a wide variety of NeSy frameworks, each with its own specific language for expressing background knowledge and how to relate it to neural networks. This heterogeneity hinders accessibility for newcomers and makes comparing different NeSy frameworks challenging. We propose a unified language for NeSy, which we call ULLER, a Unified Language for LEarning and Reasoning. ULLER encompasses a wide variety of settings, while ensuring that knowledge described in it can be used in existing NeSy systems. ULLER has a neuro-symbolic first-order syntax for which we provide example semantics including classical, fuzzy, and probabilistic logics. We believe ULLER is a first step towards making NeSy research more accessible and comparable, paving the way for libraries that streamline training and evaluation across a multitude of semantics, knowledge bases, and NeSy systems.

cs.AI↗

arXiv2024

PiShield: A PyTorch Package for Learning with Requirements

Deep learning models have shown their strengths in various application domains, however, they often struggle to meet safety requirements for their outputs. In this paper, we introduce PiShield, the first package ever allowing for the integration of the requirements into the neural networks' topology. PiShield guarantees compliance with these requirements, regardless of input. Additionally, it allows for integrating requirements both at inference and/or training time, depending on the practitioners' needs. Given the widespread application of deep learning, there is a growing need for frameworks allowing for the integration of the requirements across various domains. Here, we explore three application scenarios: functional genomics, autonomous driving, and tabular data generation.

cs.LG↗

arXiv2024

Exploiting T-norms for Deep Learning in Autonomous Driving

Deep learning has been at the core of the autonomous driving field development, due to the neural networks' success in finding patterns in raw data and turning them into accurate predictions. Moreover, recent neuro-symbolic works have shown that incorporating the available background knowledge about the problem at hand in the loss function via t-norms can further improve the deep learning models' performance. However, t-norm-based losses may have very high memory requirements and, thus, they may be impossible to apply in complex application domains like autonomous driving. In this paper, we show how it is possible to define memory-efficient t-norm-based losses, allowing for exploiting t-norms for the task of event detection in autonomous driving. We conduct an extensive experimental analysis on the ROAD-R dataset and show (i) that our proposal can be implemented and run on GPUs with less than 25 GiB of available memory, while standard t-norm-based losses are estimated to require more than 100 GiB, far exceeding the amount of memory normally available, (ii) that t-norm-based losses improve performance, especially when limited labelled data are available, and (iii) that t-norm-based losses can further improve performance when exploited on both labelled and unlabelled data.

cs.LG↗

arXiv2024

How Realistic Is Your Synthetic Data? Constraining Deep Generative Models for Tabular Data

Deep Generative Models (DGMs) have been shown to be powerful tools for generating tabular data, as they have been increasingly able to capture the complex distributions that characterize them. However, to generate realistic synthetic data, it is often not enough to have a good approximation of their distribution, as it also requires compliance with constraints that encode essential background knowledge on the problem at hand. In this paper, we address this limitation and show how DGMs for tabular data can be transformed into Constrained Deep Generative Models (C-DGMs), whose generated samples are guaranteed to be compliant with the given constraints. This is achieved by automatically parsing the constraints and transforming them into a Constraint Layer (CL) seamlessly integrated with the DGM. Our extensive experimental analysis with various DGMs and tasks reveals that standard DGMs often violate constraints, some exceeding $95\%$ non-compliance, while their corresponding C-DGMs are never non-compliant. Then, we quantitatively demonstrate that, at training time, C-DGMs are able to exploit the background knowledge expressed by the constraints to outperform their standard counterparts with up to $6.5\%$ improvement in utility and detection. Further, we show how our CL does not necessarily need to be integrated at training time, as it can be also used as a guardrail at inference time, still producing some improvements in the overall performance of the models. Finally, we show that our CL does not hinder the sample generation time of the models.

cs.LG↗

arXiv2024

Machine Learning with Requirements: a Manifesto

In the recent years, machine learning has made great advancements that have been at the root of many breakthroughs in different application domains. However, it is still an open issue how make them applicable to high-stakes or safety-critical application domains, as they can often be brittle and unreliable. In this paper, we argue that requirements definition and satisfaction can go a long way to make machine learning models even more fitting to the real world, especially in critical domains. To this end, we present two problems in which (i) requirements arise naturally, (ii) machine learning models are or can be fruitfully deployed, and (iii) neglecting the requirements can have dramatic consequences. We show how the requirements specification can be fruitfully integrated into the standard machine learning development pipeline, proposing a novel pyramid development process in which requirements definition may impact all the subsequent phases in the pipeline, and viceversa.

cs.LG↗

arXiv2022

ROAD-R: The Autonomous Driving Dataset with Logical Requirements

Neural networks have proven to be very powerful at computer vision tasks. However, they often exhibit unexpected behaviours, violating known requirements expressing background knowledge. This calls for models (i) able to learn from the requirements, and (ii) guaranteed to be compliant with the requirements themselves. Unfortunately, the development of such models is hampered by the lack of datasets equipped with formally specified requirements. In this paper, we introduce the ROad event Awareness Dataset with logical Requirements (ROAD-R), the first publicly available dataset for autonomous driving with requirements expressed as logical constraints. Given ROAD-R, we show that current state-of-the-art models often violate its logical constraints, and that it is possible to exploit them to create models that (i) have a better performance, and (ii) are guaranteed to be compliant with the requirements themselves.

cs.LG↗

arXiv2022

Deep Learning with Logical Constraints

In recent years, there has been an increasing interest in exploiting logically specified background knowledge in order to obtain neural models (i) with a better performance, (ii) able to learn from less data, and/or (iii) guaranteed to be compliant with the background knowledge itself, e.g., for safety-critical applications. In this survey, we retrace such works and categorize them based on (i) the logical language that they use to express the background knowledge and (ii) the goals that they achieve.

cs.AI↗