How abundant are good interpolators?

The talk presents a rigorous theoretical analysis of the generalization properties of interpolators in high-dimensional linear classification. The speaker clearly defines the problem, introduces the relevant models, and states a main theorem (large deviation principle) that provides a complete characterization of the proportion of interpolators with a given generalization error. The mathematical framework is sound, relying on established tools from high-dimensional probability and statistical physics. The assumptions are clearly stated, and the asymptotic regime (n,d → ∞ with n/d → α) is standard in the field. The results are novel and contribute to the understanding of the interpolation regime, a topic of significant recent interest. The speaker also discusses the interpolation threshold, connecting to prior work, and highlights the contrast between convex and non-convex regimes. The presentation is well-structured, with clear motivation and intuitive explanations of the geometric picture. However, the talk is highly technical and may be inaccessible to non-specialists. The speaker does not provide full proofs, but sketches the main ideas. The results are limited to specific data distributions (logistic and Gaussian mixture), and the extension to more general settings is not discussed. The claim that typical interpolators are ‘bad’ is based on the comparison with ERM, but the practical implications are not explored. Overall, the talk is of high scientific quality, with clear contributions to the theory of interpolation in machine learning. The title accurately reflects the content, and the presentation is coherent. The only minor weakness is the lack of discussion of practical implications or connections to other work beyond the cited references.

The title accurately reflects the central question: the abundance (proportion) of interpolators with good generalization performance.

8/10

The talk presents rigorous mathematical results (large deviation principles) with clear assumptions and proofs sketched. The speaker is a recognized researcher at Cornell, and the work is joint with a student. The presentation is technical and precise, with no obvious overclaims. However, the results are asymptotic and rely on idealized models, and the talk does not provide full proofs or external validation within the video.

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

• 00:00Introduction and motivation: performance of interpolators in overparameterized models.
• 03:00Definition of interpolators and the set S of classifiers with zero training loss.
• 07:00Simplification to linear classification and the geometric view of interpolators as intersection of half-spheres.
• 11:00Introduction of data-generating models: pure noise, logistic, and Gaussian mixture.
• 15:00Discussion of interpolation threshold and capacity results for positive margin.
• 19:00Challenges with negative margin: non-convexity and disconnected solution set.
• 23:00Asymptotic regime and known bounds on interpolation threshold for negative margin.
• 27:00Main theorem: large deviation principle for the proportion of interpolators with given overlap.
• 31:00Consequences: typical interpolator has overlap x* and is 'bad' compared to ERM.
• 35:00Open problems: sampling typical interpolators and algorithmic access.

• Simons Institute talk page — Official page for the talk, providing abstract and context.

• Simons Institute talk page — The abstract aligns with the content of the talk.