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Recent progress in tabular foundation models suggests that training on synthetic tasks can substantially improve in-context learning capabilities, with overall performance largely depending on how well models can infer task-specific predictive relationships from the available context during inference. In this paper, we...
A condition called the cross-Hessian Rank Constraint (HRC), which serves as a primitive rank-based tool for nonlinear latent causal discovery, shows that a rank-based property arises from the cross-Hessian of the observed-data log-density in the nonlinear case, revealing information about the latent variables.
This work identifies a surprising yet consistent phenomenon that it is identified: despite using high-dimensional embeddings, VQVAEs tend to compress their representations into a much smaller subspace, typically only 4 to 10 dimensions, and proposes Divide-and-Conquer VQ, which partitions the latent space into multiple...
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