Fabio Arnez
Publications
The SIGReg Objective as Variational Free Energy: A Theoretical Active-Inference Account of JEPA World Models
Joint-Embedding Predictive Architectures (JEPAs) are the dominant design for latent world models, yet they are usually justified by empirical performance rather than a normative principle. We show that the choice of anti-collapse regulariser determines whether a JEPA's training objective, a prediction loss plus a weighted embedding regulariser, is a valid Active Inference (AIF) variational free energy. We organise four non-contrastive regularisers (VICReg, LogDet, PairDist, and SIGReg) into an entropy-estimator hierarchy indexed by a prior-miscalibration gap, and show that the gap's sign, whether the estimator bounds the latent entropy from above or below, decides whether the AIF surprise bound survives: VICReg and LogDet are unsafe upper bounds, PairDist a safe lower bound, and SIGReg eliminates the gap. We then prove a correspondence theorem: under the standard constant-noise encoder model and successful SIGReg enforcement (isotropic-Gaussian embeddings), the gap vanishes, the objective becomes an exact information bottleneck, the surprise bound is preserved, and the latent goal cost becomes an exact proxy for AIF pragmatic value, whereas VICReg leaves an irreducible second-order anisotropy term. We extend the correspondence to multi-step expected free energy, ensemble epistemic value, and a learned-policy regime, and we identify the one AIF term no current JEPA world model computes: the state-epistemic value, a future-state coverage signal. The predictions differ in kind, not degree, and are stated here as theoretical consequences left for empirical test in separate work; full proofs are in Appendix A, and the algebraic core of every result is machine-verified in Lean 4 (Appendix D).
Oracle-Guided Soft Shielding for Safe Move Prediction in Chess
In high stakes environments, agents relying purely on imitation learning or reinforcement learning often struggle to avoid safety-critical errors during exploration. Existing reinforcement learning approaches for environments such as chess require hundreds of thousands of episodes and substantial computational resources to converge. Imitation learning, on the other hand, is more sample efficient but is brittle under distributional shift and lacks mechanisms for proactive risk avoidance. In this work, we propose Oracle-Guided Soft Shielding (OGSS), a simple yet effective framework for safer decision-making, enabling safe exploration by learning a probabilistic safety model from oracle feedback in an imitation learning setting. Focusing on the domain of chess, we train a model to predict strong moves based on past games, and separately learn a blunder prediction model from Stockfish evaluations to estimate the tactical risk of each move. During inference, the agent first generates a set of candidate moves and then uses the blunder model to determine high-risk options, and uses a utility function combining the predicted move likelihood from the policy model and the blunder probability to select actions that strike a balance between performance and safety. This enables the agent to explore and play competitively while significantly reducing the chance of tactical mistakes. Across hundreds of games against a strong chess engine, we compare our approach with other methods in the literature, such as action pruning, SafeDAgger, and uncertainty-based sampling. Our results demonstrate that OGSS variants maintain a lower blunder rate even as the agent's exploration ratio is increased by several folds, highlighting its ability to support broader exploration without compromising tactical soundness.