#01Oct 29, 2026
eess.SY
Adaptive Scenario Generation for KL-DRO Around a Learned Density Model
Aron Brenner, Saurabh Amin
Distributionally robust optimization (DRO) hedges data-driven two-stage stochastic programs against error in the distribution estimated from a finite record, and standard ambiguity sets differ in how they treat realizations absent from that record. A divergence ball around the empirical distribution contains only reweightings of the record, whereas a transport ball also contains distributions supported off the record, including on realizations the data-generating process cannot produce, against which the decision is then hedged as well. We instead propose a Kullback-Leibler (KL) ball centered at a density model fitted to the record, the learned nominal, which lets the adversary up-weight costly unobserved realizations in proportion to the probability the model assigns them. Solving the resulting problem poses a second difficulty, because it can accommodate only a few scenarios, and an independent sample of that size is likely to omit the rare realizations on which the worst case concentrates. We therefore build the scenario set adaptively, alternating between solving the finite problem and drawing new realizations from the learned nominal, steered toward the worst case at the current decision, with importance weights that correct the draws back to the model. On a multi-item newsvendor problem and a capacity expansion problem on realistic grid data, centering the ball at the learned nominal rather than at the record lowers cost under distribution shift, at comparable in-distribution cost, when the record is scarce and the model class captures structure that lets it extrapolate beyond the record. The advantage fades as the record grows or as the shift departs from the structure the model has learned.
#02Oct 29, 2026
cs.AI
FARMS: A Verifiable Foundation for Automated Computational Science
Di Wu, Ling Liang, Haizhao Yang
Automated computational science could accelerate discovery by selecting, adapting and developing numerical methods. This prospect requires mathematical knowledge that AI systems can interpret and reuse with explicit guarantees. Here we present FARMS, a faithful and efficient foundation that transforms computational mathematics into AI-ready computing knowledge. FARMS connects formal statements to source context, algorithmic meaning and quantitative guarantees through source preparation, reusable representations and semantic review. Across 171 targets in randomized numerical linear algebra and numerical partial differential equations, 157 were accepted by the pipeline, with mean estimated costs of US \$0.85-2.29 per target across sources. Lean-checked implications from explicit source premises connect selected statements to computational skills, illustrated by a heat-flow solve and wave-response compression. FARMS therefore supports an affordable, reusable knowledge foundation for trustworthy automated computational science.
#03Oct 29, 2026
cs.LG
Training Foundation Models with a Single Algorithm
Yuda Song, Alvin Zhang, Fahim Tajwar and 7 more
Foundation models are typically trained in stages: pretraining, midtraining, supervised fine-tuning (SFT), and reinforcement learning (RL), with changes in both data and learning algorithms. We show that this algorithmic separation is not fundamental. By deriving suitable RL objectives as maximum-likelihood fitting to model-generated target distributions, we place all of these stages under a single likelihood-based training algorithm, unified training. This perspective turns the foundation-model training lifecycle into a problem of choosing which data to train on, in what proportions, and when, with conventional staged training as a special case. We instantiate this framework in a unified training system that mixes static data and RL generations within a single trainer. Across controlled and real-world experiments, unified training improves the accuracy-compute tradeoff and task coverage while preserving broader capabilities, and provides a stronger starting point for continual learning. This work lays the groundwork for a unified science of foundation-model training, connecting mathematical principles, training infrastructure, and the development of model capabilities.
#04Oct 29, 2026
cs.AI
Efficient Scalable Oversight via Rewinding
Ziyi Guan, Yael Tauman Kalai, Ron Rothblum and 1 more
Scalable oversight asks how a weak verifier can check the outputs of computations performed by more powerful AI systems. One proposed approach uses relativizing interactive proofs, in which a weak verifier checks the output of a complex oracle-aided computation by interacting with one or more powerful provers. A prominent example is debate, which is highly efficient but assumes that one of two powerful AI models, or provers, is truthful. For certain classes of oracle-aided computations, this assumption can be removed, but at substantially greater computational cost. In this work, we introduce \emph{rewindable interactive proofs} (RIPs), a new model of relativizing interactive proofs for scalable oversight. In an RIP, the verifier may rewind the prover to an earlier state of the interaction and continue from there. This is possible when the prover is an AI model, since the verifier can save a snapshot of the model's state and later restore it. We construct a relativizing RIP for computations whose outputs are robust to changing a small fraction of oracle answers. Our construction is more efficient than prior relativizing proofs that do not assume a truthful prover, and it uses no cryptography. In our construction the honest prover runs in time linear in that of the original computation, and the verifier, after a one-time preprocessing step, runs in time nearly linear in the input length (which can be much smaller than the computation itself). We implement our protocol, report a preliminary MNIST experiment, and show that an RIP can be faster than a state-of-the-art deployed proof system. RIPs may be of independent interest. Rewinding is possible whenever the verifier controls the prover's machine, for example when the prover runs on trusted hardware or in a virtual machine whose state can be checkpointed.
#05Oct 29, 2026
cs.LG
Propose-Filter-Release: Scaling Noise to Typical Sensitivity via Private Filtering
Moshe Shenfeld, Eliad Tsfadia, Katrina Ligett
An estimator can be accurate and stable on typical data, yet sensitive to a few possible records. Differentially private mechanisms commonly scale their noise to the worst-case influence of a single record, which lets these records dictate the noise even when the remaining data would allow far less. Removing them first would restore the smaller scale, but the removal must itself be private. We introduce \emph{propose-filter-release} (PFR), which, by privately filtering its input, turns a mechanism that protects the addition or removal of a typical record, one that fits the remaining data, into one that is differentially private in the standard sense, on every input. Using our novel filtering step, PFR requires only a concave friendliness score, which measures how well a record fits a dataset, and a release mechanism that is friendly-DP, that is, private when the changed record fits the remaining data. For every such score and release mechanism, it guarantees differential privacy under public conditions on the number of records, so it is a general privacy primitive, comparable to propose-test-release, and FriendlyCore can be viewed as one of its implementations. We illustrate the generality of PFR by instantiating it for scalar statistics, principal subspace estimation, the KL divergence of user histograms, the effective resistances of a graph, and treatment-rule selection.