We prove an exponential separation in sample complexity between Euclidean and hyperbolic representations for learning on hierarchical data under standard Lipschitz regularization. For depth-$R$ hierarchies with branching factor $m$, we first establish a geometric obstruction for Euclidean space: any bounded-radius embedding forces volumetric collapse, mapping exponentially many tree-distant points to nearby locations. This necessitates Lipschitz constants scaling as $exp(Ω(R))$ to realize even simple hierarchical targets, yielding exponential sample complexity under capacity control. We then show this obstruction vanishes […]

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Geometric deep learning by starting with the XOR affair I’ve just spent two days at an AI school (ANAIS ) in Kathmandu listening to lectures on geometric deep learning from bright folks from Oxford, TU Wien, and top institutions. Geometric deep learning from Michael Bronstein  (who also coined the term; needs no introduction really). The program is super organised, covering symmetry groups, graph neural networks and fundamental principles underlying modern AI before it eventually catches up to modern trends. […]

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Accurate modeling of robot dynamics is essential for model-based control, yet remains challenging under distributional shifts and real-time constraints. In this work, we formulate system identification as an in-context meta-learning problem and compare deterministic and generative sequence models for forward dynamics prediction. We take a Transformer-based meta-model, as a strong deterministic baseline, and introduce to this setting two complementary diffusion-based approaches: (i) inpainting diffusion (Diffuser), which learns the joint input-observation distribution, and (ii) conditioned diffusion models (CNN and […]

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arXiv:2602.12458v1 Announce Type: new Abstract: A central challenge in multi-agent reinforcement learning is enabling agents to adapt to previously unseen teammates in a zero-shot fashion. Prior work in zero-shot coordination often follows a two-stage process, first generating a diverse training pool of partner agents, and then training a best-response agent to collaborate effectively with the entire training pool. While many previous works have achieved strong performance by devising better ways to diversify the partner agent pool, there has […]

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Rare events are central to the evolution of complex many-body systems, characterized as key transitional configurations on the free energy surface (FES). Conventional methods require adequate sampling of rare event transitions to obtain the FES, which is computationally very demanding. Here we introduce the variational free energy surface (VaFES), a dataset-free framework that directly models FESs using tractable-density generative models. Rare events can then be immediately identified from the FES with their configurations generated directly via one-shot sampling […]

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arXiv:2603.24730v1 Announce Type: new Abstract: The classic duck-rabbit illusion reveals that when visual evidence is ambiguous, the human brain must decide what it sees. But where exactly do human observers draw the line between ”duck” and ”rabbit”, and do machine classifiers draw it in the same place? We use semantically ambiguous images as interpretability probes to expose how vision models represent the boundaries between concepts. We present a psychophysically-informed framework that interpolates between concepts in the CLIP embedding […]

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Can general-purpose AI architectures go beyond prediction to discover the physical laws governing the universe? True intelligence relies on "world models" — causal abstractions that allow an agent to not only predict future states but understand the underlying governing dynamics. While previous "AI Physicist" approaches have successfully recovered such laws, they typically rely on strong, domain-specific priors that effectively "bake in" the physics. Conversely, Vafa et al. recently showed that generic Transformers fail to acquire these world models, […]

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arXiv:2302.01701v3 Announce Type: replace Abstract: Deep learning methods achieve remarkable predictive performance in modeling complex, large-scale data. However, assessing the quality of derived models has become increasingly challenging, as more classical statistical assumptions may no longer apply. These difficulties are particularly pronounced for spatio-temporal data, which exhibit dependencies across both space and time and are often characterized by nonlinear dynamics, time variance, and missing observations, hence calling for new accuracy assessment methodologies. This paper introduces a residual correlation […]

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Recent work shows that flow matching can be effective for scalar Q-value function estimation in reinforcement learning (RL), but it remains unclear why or how this approach differs from standard critics. Contrary to conventional belief, we show that their success is not explained by distributional RL, as explicitly modeling return distributions can reduce performance. Instead, we argue that the use of integration for reading out values and dense velocity supervision at each step of this integration process for […]

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