Sampling with First Order Information

Sampling with First Order Information

by Sasha Rakhlin

Formal & Physical Sciences AI — Models & Research UYQArtificial intelligence (AI)UYQMMachine learning
🎙 Sasha Rakhlin 👥 4K 📅 May 3, 2026 ⏱ 36 min 👁 34 📄 original study 🧭 2026-08-13
Available in: English (current) Français

Keywords

samplingfirst-orderdiffusionlog-concaveBernoulli factory

Summary

Sasha Rakhlin presents a novel framework for sampling from distributions proportional to exp(-f(x)) using only first-order (gradient) information, achieving polylogarithmic convergence rates in the target accuracy. The key idea is a ‘first-order rejection sampling’ (FORCE) method that uses a Poissonization trick to unbiasedly estimate the exponential of an expectation, enabling rejection sampling without evaluating f. This is applied to Gaussian tilts, log-concave sampling, and diffusion models. For log-concave sampling, the method achieves a K^2 sqrt(d) log(1/delta) gradient complexity, and extends to stochastic gradients with a separation from optimization. For diffusion models, the method yields a polylog(1/delta) complexity, with the intrinsic dimension appearing in the step size. The talk highlights a separation between sampling and optimization, where sampling is more forgiving with stochastic gradients, but tail conditions are crucial. Open questions include practical implementation and connections to other high-accuracy samplers.

139 words

Critical Evaluation

Value of the Information & Strength of the Argument

The talk presents a significant theoretical contribution: a unified framework for high-accuracy sampling using only first-order information, achieving polylogarithmic rates. The argumentation is rigorous, with clear problem formulations, algorithmic constructions, and theoretical guarantees. The speaker motivates the work by contrasting with optimization and existing sampling methods, and provides intuition for the key techniques. The results are novel and address open questions in the field. The presentation is dense but well-structured, with a clear logical flow from the core idea to applications.

Scientific Rigor, Source Quality, Title Accuracy

The talk is based on original research by the speaker and collaborators, with references to prior work (e.g., Peter Bartlett’s lower bound, Lee et al. 2021, Zigzag sampler). The speaker acknowledges concurrent work. The title accurately reflects the content. The presentation is a conference talk, so it lacks full proofs, but the claims are plausible and supported by the presented derivations. No external sources are provided in the description, so the analysis relies on the talk’s content.

173 words

Title / Content Match

The title accurately reflects the content, which focuses on sampling algorithms using first-order (gradient) information.

Quality & Reliability

8/10

Presentation of original research by a leading researcher, with clear mathematical derivations and references to prior work. However, the talk is a conference presentation without peer review or detailed proofs, and some claims are presented without full context.

Key Moments

Markers derived by PSI from the transcript: the creator did not define chapters.

Cited Sources

  • Lower bound for sampling (Peter Bartlett, 2022) — Mentioned as a lower bound for sampling requiring 1/delta^2 queries.
  • Proximal sampler (Lee et al., 2021) — Technique used for log-concave sampling.
  • Zigzag sampler (Luing Wang) — Mentioned as an exception achieving polylog rates but with warm start assumption.

Concurring Sources

  • MALA (Metropolis-adjusted Langevin algorithm) — Mentioned as a method achieving polylog rates but requiring zeroth-order information.

Contribution & Novelties

The talk introduces a novel framework (FORCE) for high-accuracy sampling using only first-order information, achieving polylogarithmic convergence rates. This is a significant departure from existing methods that require zeroth-order information or have polynomial rates. The framework is applied to log-concave sampling and diffusion models, with results that separate sampling from optimization. The use of a Bernoulli factory to unbiasedly estimate the exponential of an expectation is a key innovation.

Pour aller plus loin :

  • Bernoulli factory — Concept underlying the Poissonization trick.
  • Langevin dynamics — Standard sampling method using gradients.
  • Diffusion models — Generative models where the method is applied.

100 words

Radar Profile

The radar profile shows high scores in technical level and information quality, with slightly lower scores in quantity and reliability. This reflects a dense, original research talk with strong theoretical content but limited breadth and no external verification.

Reliability 8/10