Andrew Tomkins

Zhenting Qi, Susanna Maria Baby, Stefanie Anna Baby et al.

Recent work suggests that large language models (LLMs) can improve through self-evolution (SE), using supervision signals generated by the model itself. In this work, we ask: under a strict closed-loop setup, where the self-evolution algorithm has access only to an unlabeled prompt set and a base model, how close can internally generated supervision come to oracle-supervised training? We analyze four representative strategies in a unified offline self-evolution framework: single-round verification, multi-turn revision with feedback, iterative training, and curriculum learning. Our primary experiments use Knights and Knaves (KK) logical reasoning tasks, which provide deterministic solutions, controlled difficulty levels, and a clean testbed for easy-to-hard generalization. We first show that self-evolution consistently improves over the base model, but plateaus after excessive training compute is invested, and eventually still leaves a non-trivial gap to oracle supervision. We find that multi-turn critic-revision with large models can reach strong self-evolution performance, with Gemma 12B nearly matching oracle-supervised training. Beyond Knights and Knaves, we also evaluate self-evolution on real-world reasoning benchmarks, where gains are also modest. Overall, our results characterize when closed-loop self-evolution can help and show how internally generated supervision remains insufficient under this minimal formulation.

Flavio Chierichetti, Mirko Giacchini, Ravi Kumar et al.

In this work we settle the complexity of three sketching problems. (i) We show that sketching vertex neighborhood sizes in graphs requires $Ω(n^2)$ bits, standing in sharp contrast to the $\tilde{O}(n)$ complexity of sketching edge cuts. (ii) We obtain tight lower and upper bounds of $\tildeΘ(n^2)$ for sketching coverage functions with additive and multiplicative errors. (iii) We prove an $Ω(n^2)$ lower bound for sketching Random Utility Models under the $\ell_\infty$-norm, improving upon the previous $Ω(n \log n)$ bound and matching a known upper bound to within logarithmic factors. These bounds are obtained through a connection with the problem of sketching the intersection profile of a distribution $D$ on $2^{[n]}$. Specifically, we seek a succinct data structure that, for any query set $S \subseteq [n]$, approximates the quantity $\Pr_{T \sim D}[T \cap S \neq \varnothing]$ to within a small constant additive error. One can obtain lower bounds for this latter problem directly from known results about the itemset frequency estimation problem in databases for which tight bounds are known. As an additional contribution, we also provide an alternative proof for the intersection profile sketching lower bound, in the setting in which the accuracy parameter is constant. This proof relies solely on elementary probability avoiding the heavier machinery used in previous proofs.