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Tabular foundation models (TFMs) are increasingly popular because they deliver strong predictions on new datasets through in-context learning, without task-specific training or extensive tuning. Yet released TFMs differ simultaneously in their pretraining priors, architectures, and objectives, obscuring their respectiv...
This work observes an interesting phenomenon: the relationship between the change of generation outputs and the scale of initial noise perturbation is highly linear through the diffusion ODE sampling, and proposes a novel C ontrollable and C onstrained S ampling ( CCS) method, along with a new controller algorithm for...
Sampling latency compounds in diffusion workflows, where users generate and discard many candidates before keeping one. Surprisingly, the poor outputs of standard few-step samplers do not reflect a lack of reconstruction capacity: by optimizing only the initial noise, frozen 3-4-step samplers can closely reproduce thei...
Let $(X_1,\ldots,X_n)$ be independent nonnegative random variables with $\mathbb{E} X_i\le1$, and write $S=\sum_iX_i$. For $\delta>0$, we prove that \[ \mathbb{P}\left(S<\mathbb{E} S+\delta\right)\ge b_{n,\delta}, \] where $b_{n,\delta}=\delta(n/(n+\delta))^n$ for $0<\delta<1$ and $b_{n,\delta}=(1-1/(n+\delta))^n$ for...
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