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 visual deductive reasoning tasks with distinct rule sets show that VLC consistently achieves strong performance under covariate shifts, highlighting its ability to support robust reasoning.

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.

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.

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.

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.

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

LLMs demonstrate strong performance on code benchmarks, yet round-trip code execution reveals limitations in their ability to maintain consistent reasoning across forward and backward execution. We present RoundTripCodeEval (RTCE), a comprehensive benchmark consisting of four distinct code execution reasoning tasks designed to rigorously test round-trip consistency. RTCE provides an execution-free, exact-match evaluation of bijection fidelity, assessing whether models preserve a consistent one-to-one mapping between encoding and decoding operations across various algorithms and directions. We systematically evaluate state-of-the-art Code-LLMs using zero-shot prompting, supervised fine-tuning on execution traces, and self-reflection mechanisms. Each yields modest improvements, but none closes the gap, indicating that current LLMs struggle with true round-trip consistency, which demonstrates that they lack the internal coherence required for trustworthy code reasoning. RTCE surfaces several new and previously unmeasured insights that are not captured by existing I/O-prediction, execution-reasoning, or round-trip natural-language benchmarks. We will release the code and the dataset upon acceptance.

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.

Fast and Expressive Multi-Token Prediction with Probabilistic Circuits

Multi-token prediction (MTP) is a prominent strategy to significantly speed up generation in large language models (LLMs), including byte-level LLMs, which are tokeniser-free but prohibitively slow. However, existing MTP methods often sacrifice expressiveness by assuming independence between future tokens. In this work, we investigate the trade-off between expressiveness and latency in MTP within the framework of probabilistic circuits (PCs). Our framework, named MTPC, allows one to explore different ways to encode the joint distributions over future tokens by selecting different 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. Our experiments show that, when combined with speculative decoding, MTPC significantly 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.

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.

Neurosymbolic Reasoning Shortcuts under the Independence Assumption

The ubiquitous independence assumption among symbolic concepts in neurosymbolic (NeSy) predictors is a convenient simplification: NeSy predictors use it to speed up probabilistic reasoning. Recent works like van Krieken et al. (2024) and Marconato et al. (2024) argued that the independence assumption can hinder learning of NeSy predictors and, more crucially, prevent them from correctly modelling uncertainty. There is, however, scepticism in the NeSy community around the scenarios in which the independence assumption actually limits NeSy systems (Faronius and Dos Martires, 2025). In this work, we settle this question by formally showing that assuming independence among symbolic concepts entails that a model can never represent uncertainty over certain concept combinations. Thus, the model fails to be aware of reasoning shortcuts, i.e., the pathological behaviour of NeSy predictors that predict correct downstream tasks but for the wrong reasons.