Transformer-based scientific foundation models are increasingly deployed in high-stakes settings, but current architectures give deterministic outputs and provide limited support for calibrated predictive uncertainty. We propose Stochastic Attention, a lightweight inference-time modification that randomizes attention by replacing softmax weights with normalized multinomial samples controlled by a single concentration parameter, and produces predictive ensembles without retraining. To set this parameter, we introduce a calibration objective that matches the stochastic attention output with the target, yielding an efficient univariate post-hoc tuning problem. We evaluate this mechanism on two scientific foundation models for weather and timeseries forecasting along with an additional regression task. Across benchmarks against uncertainty-aware baselines, we find that Stochastic Attention achieves the strongest native calibration and the sharpest prediction intervals at comparable coverage, while requiring only minutes of post-hoc tuning versus days of retraining for competitive baselines.

In this paper, we establish an upper bound on the return gap between the oracle expert policy and an optimal decision tree policy. This enables us to recast the DT extraction problem into a novel non-euclidean clustering problem over the local observation and action values space of each agent, with action values as cluster labels and the upper bound on the return gap as clustering loss.

Recent studies show that adversarial attacks disproportionately impact the patterns within the phase of the sample's frequency spectrum--typically containing

Learning reliably safe autonomous control is one of the core problems in trustworthy autonomy.

Transformers with linear attention (i.e., linear transfor mers) and state-space models have recently been suggested as a viable linear-time alt ernative to transformers with softmax attention. However, these models still underp erform transformers especially on tasks that require in-context retrieval. Whil e more expressive variants of linear transformers which replace the additive upda te in linear transformers with the delta rule [DeltaNet; 101 ] have been found to be more effective at associative recall, existing algorithms for training such mode ls do not parallelize over sequence length and are thus inefficient to train on modern ha rdware. This work describes a hardware-efficient algorithm for training line ar transformers with the delta rule, which exploits a memory-efficient representati on for computing products of Householder matrices [ 11 ]. This algorithm allows us to scale up DeltaNet to standard language modeling settings. We train a 1.3B mode l for 100B tokens and find that it outperforms recent linear-time baselines su ch as Mamba [ 31 ] and GLA [ 124 ] in terms of perplexity and zero-shot performance on downst ream tasks. We also experiment with two hybrid models which combine Delt aNet layers with (1) sliding-window attention layers every other layer or (2) two global attention layers, and find that these hybrids outperform strong transf ormer baselines.

Beyond estimating parameters of interest from data, one of the key goals of statistical inference is to properly quantify uncertainty in these estimates.

The Benjamini-Hochberg (BH) procedure is widely used to control the false detection rate (FDR) in multiple testing.