arXiv subjects

Antonio Vergari

Publications and source records attributed to Antonio Vergari.

At least 19 recordsLinked to original sources

arXiv2026

A Sobering Look at Tabular Data Generation via Probabilistic Circuits

Tabular data is more challenging to generate than text and images, due to its heterogeneous features and much lower sample sizes. On this task, diffusion-based models are the current state-of-the-art (SotA) model class, achieving almost perfect performance on commonly used benchmarks. In this paper, we question the perception of progress for tabular data generation. First, we highlight the limitations of current protocols to evaluate the fidelity of generated data, and advocate for alternative ones. Next, we revisit a simple baseline -- hierarchical mixture models in the form of deep probabilistic circuits (PCs) -- which delivers competitive or superior performance to SotA models for a fraction of the cost. PCs are the generative counterpart of decision forests, and as such can natively handle heterogeneous data as well as deliver tractable probabilistic generation and inference. Finally, in a rigorous empirical analysis we show that the apparent saturation of progress for SotA models is largely due to the use of inadequate metrics. As such, we highlight that there is still much to be done to generate realistic tabular data. Code available at https://github.com/april-tools/tabpc.

cs.LG↗

arXiv2026

Symbol Grounding in Neuro-Symbolic AI: A Gentle Introduction to Reasoning Shortcuts

Neuro-symbolic (NeSy) AI aims to develop deep neural networks whose predictions comply with prior knowledge encoding, e.g. safety or structural constraints. As such, it represents one of the most promising avenues for reliable and trustworthy AI. The core idea behind NeSy AI is to combine neural and symbolic steps: neural networks are typically responsible for mapping low-level inputs into high-level symbolic concepts, while symbolic reasoning infers predictions compatible with the extracted concepts and the prior knowledge. Despite their promise, it was recently shown that - whenever the concepts are not supervised directly - NeSy models can be affected by Reasoning Shortcuts (RSs). That is, they can achieve high label accuracy by grounding the concepts incorrectly. RSs can compromise the interpretability of the model's explanations, performance in out-of-distribution scenarios, and therefore reliability. At the same time, RSs are difficult to detect and prevent unless concept supervision is available, which is typically not the case. However, the literature on RSs is scattered, making it difficult for researchers and practitioners to understand and tackle this challenging problem. This overview addresses this issue by providing a gentle introduction to RSs, discussing their causes and consequences in intuitive terms. It also reviews and elucidates existing theoretical characterizations of this phenomenon. Finally, it details methods for dealing with RSs, including mitigation and awareness strategies, and maps their benefits and limitations. By reformulating advanced material in a digestible form, this overview aims to provide a unifying perspective on RSs to lower the bar to entry for tackling them. Ultimately, we hope this overview contributes to the development of reliable NeSy and trustworthy AI models.

cs.AI↗

arXiv2026

The RAIL Principles for Neurosymbolic AI: Reasoning, Assurances, Interfacing and Learning

Neurosymbolic AI systems that integrate machine learning and symbolic reasoning are rapidly gaining attention. They complement the data-intensive statistical approaches of neural networks and language models with symbolic reasoning algorithms to function in high-stakes domains or in low-data regimes that characterize many real-world applications. We argue that the neurosymbolic combination of machine learning and formal reasoning is not a niche approach within AI, but rather includes many already successful techniques that are of crucial importance to the development of reliable, efficient and, ultimately, trustworthy systems. This perspective prompts a re-examination of the design of current AI systems. We show that many leading AI systems, including some that are not traditionally considered as neurosymbolic, can be analysed from the perspective of four principles of neurosymbolic AI design: Reasoning, Assurances, Interfacing and Learning (RAIL). Applying the RAIL framework offers a unified view of seemingly disparate AI systems, ranging from physics-aware machine learning to neuro-guided search (such as Google DeepMind's Alpha-* suite), causal learning and tool-augmented Large Language Models. Importantly, the RAIL principles will enable engineers to make better-informed and more principled decisions about the design and deployment of production-level AI systems. In this article, we introduce the RAIL principles, examine how they can be applied across major areas of AI, and illustrate how they may guide practitioners to integrate neurosymbolic methods into next-generation AI technologies.

cs.AI↗

arXiv2026

An Embarrassingly Simple Way to Optimize Orthogonal Matrices at Scale

Orthogonality constraints are ubiquitous in robust and probabilistic machine learning. Unfortunately, current optimizers are computationally expensive and do not scale to problems with hundreds or thousands of constraints. One notable exception is the Landing algorithm (Ablin et al., 2024) which, however comes at the expense of temporarily relaxing orthogonality. In this work, we revisit and improve on the ideas behind Landing, enabling the inclusion of modern adaptive optimizers while ensuring that orthogonal constraints are effectively met. Remarkably, these improvements come at little to no cost, and reduce the number of required hyperparemeters. Our algorithm POGO is fast and GPU-friendly, consisting of only 5 matrix products, and in practice maintains orthogonality at all times. On several challenging benchmarks, POGO greatly outperforms recent optimizers and shows it can optimize problems with thousands of orthogonal matrices in minutes while alternatives would take hours. As such, POGO sets a milestone to finally exploit orthogonality constraints in ML at scale. A PyTorch implementation of POGO is publicly available at https://github.com/adrianjav/pogo.

cs.LG↗

arXiv2026

Can VLMs Reason Robustly? A Neuro-Symbolic Investigation

Vision-Language Models (VLMs) have been applied to a wide range of reasoning tasks, yet it remains unclear whether they can reason robustly under distribution shifts. In this paper, we study covariate shifts in which the perceptual input distribution changes while the underlying prediction rules do not. To investigate this question, we consider visual deductive reasoning tasks, where a model is required to answer a query given an image and logical rules defined over the object concepts in the image. Empirically, we find that VLMs fine-tuned through gradient-based end-to-end training can achieve high in-distribution accuracy but fail to generalize under such shifts, suggesting that fine-tuning does not reliably induce the underlying reasoning function. This motivates a neuro-symbolic perspective that decouples perception from reasoning. However, we further observe that recent neuro-symbolic approaches that rely on black-box components for reasoning can still exhibit inconsistent robustness across tasks. To address this issue, we propose VLC, a neuro-symbolic method that combines VLM-based concept recognition with circuit-based symbolic reasoning. In particular, task rules are compiled into a symbolic program, specifically a circuit, which executes the rules exactly over the object concepts recognized by the VLM. Experiments on three simple visual deductive reasoning tasks with distinct rule sets show that VLC consistently achieves higher task accuracy on out-of-distribution data than other reasoning paradigms. Code is available at https://github.com/uiuctml/VLC.

cs.LG↗

arXiv2026

Neural network surrogates with uncertainty quantification for inverse problems in partial differential equations

Inverse problems for differential equations arise throughout science and engineering, where one seeks to infer unknown model parameters from noisy or incomplete observations. Traditional numerical methods for these problems are often computationally expensive, particularly in Bayesian settings where evaluating the likelihood becomes costly for complex forward models and high-dimensional parameter spaces. To address this challenge, we introduce DeepGaLA, a neural-network surrogate for differential equation solvers that provides uncertainty-aware predictions, reducing overconfident inference when training data are limited. To evaluate the fidelity of the surrogate-induced posterior approximations in practice, we show that a short run of delayed-acceptance Markov chain Monte Carlo can serve as an effective diagnostic. Across a range of numerical experiments, DeepGaLA delivers forward-model approximations with accuracy comparable to established Gaussian-process surrogates, while better maintaining efficiency as parameter dimension grows. Moreover, it can incorporate differential-equation constraints, including in nonlinear settings. Overall, these results indicate that uncertainty-quantified neural surrogates can enable scalable and reliable Bayesian inference for inverse problems in complex systems.

cs.LG↗

arXiv2026

Half a Link can Be Enough to Predict a Whole Link: Understanding Generalization in Knowledge Graph Foundation Models

Knowledge graph (KG) foundation models (KGFMs) are zero-shot generalizers: trained once, they can predict links on unseen graphs without retraining. However, understanding when and how they can robustly generalize across KGs is still an open question. In this paper, we shed some light on their generalization mechanisms highlighting how their performance on unseen KGs is not uniform when it comes to partially seen links, which we call half-links. In fact, we show that to predict a test triple $(h,r,t)$ it might suffice in practice to have observed the half-link $(h,r)$ or $(r,t)$ in the inference graph. This yields a taxonomy of four scenarios when combinations of these half-links are observed or not. In a rigorous stratified analysis over these scenarios, we reveal that SoTA KGFMs use seen half links for predictions, while unseen half-links pose different challenges. As such, our finer-grained taxonomy can be a diagnostic protocol for robust KGFM generalization and highlights where novel KGFMs can improve.

cs.LG↗

arXiv2026

Even More Guarantees for Variational Inference in the Presence of Symmetries

When approximating an intractable density via variational inference (VI) the variational family is typically chosen as a simple parametric family that very likely does not contain the target. This raises the question: Under which conditions can we recover characteristics of the target despite misspecification? In this work, we extend previous theoretical results on robust VI with location-scale families under target symmetries in two substantial ways: (1) We open them up to a wider range of divergences by providing sufficient conditions for exact recovery of the target mean and correlation matrix when using the forward Kullback-Leibler divergence and $α$-divergences. (2) By doing so, we find that we can drop the restrictive assumption of a log-concave target made in previous work, allowing us to give guarantees for a wider range of targets, including multi-modal ones. In our experiments, we show how our guarantees can serve as guidelines for the choice of the variational family and $α$-value and we illustrate on a diverse set of examples how and why optimization can fail in the absence of our sufficient conditions.

cs.LG↗

arXiv2026

Fast and Expressive Multi-Byte Prediction with Probabilistic Circuits

Multi-token prediction (MTP) is a prominent strategy to significantly speed up generation in large language models (LLMs), especially in byte-level LLMs, which are tokeniser-free but prohibitively slow. However, many existing MTP methods either assume independence between future tokens, sacrificing expressiveness, or generate tokens one at a time within the window, increasing latency. In this work, we investigate the trade-off between expressiveness and latency in MTP within the framework of probabilistic circuits (PCs). Our framework, MTPC, allows one to explore different ways to encode the joint distributions over future tokens by selecting circuit architectures, generalising classical models such as (hierarchical) mixture models, hidden Markov models, and tensor networks. We show the efficacy of MTPC by retrofitting existing byte-level LLMs, such as EvaByte, and byte-fied subword models, such as Llama3.2 3B. Our experiments show that, when combined with speculative decoding, MTPC substantially speeds up generation compared to MTP with independence assumptions, while guaranteeing to retain the performance of the original verifier LLM. We also rigorously study the optimal trade-off between expressiveness and latency when exploring the possible parameterisations of MTPC, such as PC architectures and partial layer sharing between the verifier and draft LLMs.

cs.LG↗

arXiv2026

Tractable Hierarchical Control of Autoregressive Language Models

Constraining the generation of autoregressive large language models (LLMs) is an important component of integrating language models into formal systems. In the generation of code and data for tasks like program synthesis, ensuring that language models produce syntactically valid output is a prerequisite for processing such output. These languages (such as SQL or JSON) are often designed as $LR(k)$ context-free grammars. By distilling the LLM to a tractable probabilistic model, its autoregressive generation can be steered and masked to incorporate the probability of satisfying logical constraints, ensuring high quality output that is guaranteed to be valid. This paper demonstrates that the satisfaction of any $LR(k)$ grammar of finite duration can be calculated in polynomial time, an improvement over the exponential time of applying previous methods to such grammars. This result enables efficient constraint and steering of LLM generation towards output that better satisfies formal syntactic constraints.

cs.AI↗

arXiv2026

How to Square Tensor Networks and Circuits Without Squaring Them

Squared tensor networks (TNs) and their extension as computational graphs--squared circuits--have been used as expressive distribution estimators, yet supporting closed-form marginalization. However, the squaring operation introduces additional complexity when computing the partition function or marginalizing variables, which hinders their applicability in ML. To solve this issue, canonical forms of TNs are parameterized via unitary matrices to simplify the computation of marginals. However, these canonical forms do not apply to circuits, as they can represent factorizations that do not directly map to a known TN. Inspired by the ideas of orthogonality in canonical forms and determinism in circuits enabling tractable maximization, we show how to parameterize squared circuits to overcome their marginalization overhead. Our parameterizations unlock efficient marginalization even in factorizations different from TNs, but encoded as circuits, whose structure would otherwise make marginalization computationally hard. Finally, our experiments on distribution estimation show how our proposed conditions in squared circuits come with no expressiveness loss, while enabling more efficient learning.

cs.LG↗

arXiv2026

Can LLMs Compress (and Decompress)? Evaluating Code Understanding and Execution via Invertibility

LLMs demonstrate strong performance on code benchmarks, yet consistent reasoning across forward and backward execution remains elusive. We present RoundTripCodeEval (RTCE), a benchmark of four code execution reasoning tasks that evaluates round-trip consistency through execution-free, exact-match assessment of bijection fidelity across four lossless compression algorithms. We evaluate state-of-the-art Code-LLMs under zero-shot prompting, supervised fine-tuning on execution traces, and iterative self-reflection. All approaches yield only modest improvements and none closes the gap, revealing that current LLMs lack the internal coherence required for reliable bidirectional code reasoning. RTCE surfaces findings invisible to existing benchmarks: models frequently pass individual forward and backward tasks yet fail the combined round-trip, exposing mutually inconsistent internal representations; SFT and self-reflection saturate after one revision round, indicating they cannot repair fundamental algorithmic misunderstandings; and failures persist even on simple bijections such as RLE, suggesting that algorithmic complexity is not the sole root cause.\footnote{Code and dataset are available at https://github.com/Nickil21/round-trip-code-compression.

cs.LG↗

arXiv2026

How to Approximate Inference with Subtractive Mixture Models

Classical mixture models (MMs) are widely used tractable proposals for approximate inference settings such as variational inference (VI) and importance sampling (IS). Recently, mixture models with negative coefficients, called subtractive mixture models (SMMs), have been proposed as a potentially more expressive alternative. However, how to effectively use SMMs for VI and IS is still an open question as they do not provide latent variable semantics and therefore cannot use sampling schemes for classical MMs. In this work, we study how to circumvent this issue by designing several expectation estimators for IS and learning schemes for VI with SMMs, and we empirically evaluate them for distribution approximation. Finally, we discuss the additional challenges in estimation stability and learning efficiency that they carry and propose ways to overcome them. Code is available at: https://github.com/april-tools/delta-vi.

cs.LG↗

arXiv2026

MIXAR: Scaling Autoregressive Pixel-based Language Models to Multiple Languages and Scripts

Pixel-based language models are gaining momentum as alternatives to traditional token-based approaches, promising to circumvent tokenization challenges. However, the inherent perceptual diversity across languages poses a significant hurdle for multilingual generalization in pixel space. This paper introduces MIXAR, the first generative pixel-based language model trained on eight different languages utilizing a range of different scripts. We empirically evaluate MIXAR against previous pixel-based models as well as comparable tokenizer-based models, demonstrating substantial performance improvement on discriminative and generative multilingual tasks. Additionally, we show how MIXAR is robust to languages never seen during the training. These results are further strengthened when scaling the model to 0.5B parameters which not only improves its capabilities in generative tasks like LAMBADA but also its robustness when challenged with input perturbations such as orthographic attacks.

cs.CL↗

arXiv2026

The Theory and Practice of MAP Inference over Non-Convex Constraints

In many safety-critical settings, probabilistic ML systems have to make predictions subject to algebraic constraints, e.g., predicting the most likely trajectory that does not cross obstacles. These real-world constraints are rarely convex, nor the densities considered are (log-)concave. This makes computing this constrained maximum a posteriori (MAP) prediction efficiently and reliably extremely challenging. In this paper, we first investigate under which conditions we can perform constrained MAP inference over continuous variables exactly and efficiently and devise a scalable message-passing algorithm for this tractable fragment. Then, we devise a general constrained MAP strategy that interleaves partitioning the domain into convex feasible regions with numerical constrained optimization. We evaluate both methods on synthetic and real-world benchmarks, showing our approaches outperform constraint-agnostic baselines, and scale to complex densities intractable for SoTA exact solvers.

cs.LG↗

arXiv2026

To Neuro-Symbolic Classification and Beyond by Compiling Description Logic Ontologies to Probabilistic Circuits

Background: Neuro-symbolic methods enhance the reliability of neural network classifiers through logical constraints, but they lack native support for ontologies. Objectives: We aim to develop a neuro-symbolic method that reliably outputs predictions consistent with a Description Logic ontology that formalizes domain-specific knowledge. Methods: We encode a Description Logic ontology as a circuit, a feed-forward differentiable computational graph that supports tractable execution of queries and transformations. We show that the circuit can be used to (i) generate synthetic datasets that capture the semantics of the ontology; (ii) efficiently perform deductive reasoning on a GPU; (iii) implement neuro-symbolic models whose predictions are approximately or provably consistent with the knowledge defined in the ontology. Results We show that the synthetic dataset generated using the circuit qualitatively captures the semantics of the ontology while being challenging for Machine Learning classifiers, including neural networks. Moreover, we show that compiling the ontology into a circuit is a promising approach for scalable deductive reasoning, with runtimes up to three orders of magnitude faster than available reasoners. Finally, we show that our neuro-symbolic classifiers reliably produce consistent predictions when compared to neural network baselines, maintaining competitive performances or even outperforming them. Conclusions By compiling Description Logic ontologies into circuits, we obtain a tighter integration between the Deep Learning and Knowledge Representation fields. We show that a single circuit representation can be used to tackle different challenging tasks closely related to real-world applications.

cs.AI↗

arXiv2025

COPA: Comparing the incomparable in multi-objective model evaluation

In machine learning (ML), we often need to choose one among hundreds of trained ML models at hand, based on various objectives such as accuracy, robustness, fairness or scalability. However, it is often unclear how to compare, aggregate and, ultimately, trade-off these objectives, making it a time-consuming task that requires expert knowledge, as objectives may be measured in different units and scales. In this work, we investigate how objectives can be automatically normalized and aggregated to systematically help the user navigate their Pareto front. To this end, we make incomparable objectives comparable using their cumulative functions, approximated by their relative rankings. As a result, our proposed approach, COPA, can aggregate them while matching user-specific preferences, allowing practitioners to meaningfully navigate and search for models in the Pareto front. We demonstrate the potential impact of COPA in both model selection and benchmarking tasks across diverse ML areas such as fair ML, domain generalization, AutoML and foundation models, where classical ways to normalize and aggregate objectives fall short.

cs.LG↗

arXiv2025

Can LLMs subtract numbers?

We present a systematic study of subtraction in large language models (LLMs). While prior benchmarks emphasize addition and multiplication, subtraction has received comparatively little attention despite being structurally distinct as a non-commutative operation. We evaluate eight pretrained LLMs spanning four families on addition and subtraction problems. Our experiments reveal that subtraction accuracy lags behind addition by a wide margin. We find that the errors for ($a-b$) are concentrated in cases where ($a<b$). In such cases, LLMs frequently produce the correct magnitude but omit the negative sign. Probing analyses show that LLMs internally encode whether results should be negative, yet this information is often not reflected in generated outputs. We further test well-known techniques such as few-shot learning and instruction-tuning to see if they can improve the LLMs' performance. Our results suggest that while few-shot prompting yields modest gains, the instruction-tuned models achieve near-perfect accuracies in generating the negative sign. Together, these findings provide a clearer characterization of the limitations and recoverability of LLMs' arithmetic capabilities in subtraction.

cs.LG↗