FP method and the minorization-maximization theory to verify the convergence.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. Online Learning with Costly Features and Labels Summary: The paper discusses a version of sequential prediction where there is a cost associated to obtaining features and labels. First, the case where labels are given but features are bought. Here the regret bound is of the form sqrt{2^d T}. The time dependence is as desired, and a lower bound shows that the exponential dependence in the dimension of the features space cannot be reduced in general.

Large Language Models (LLMs) for formal theorem proving have shown significant promise, yet they often lack generalizability and are fragile to even minor transformations of problem statements. To address this limitation, we introduce a novel data augmentation pipeline designed to enhance model robustness from two perspectives: symmetry and difficulty. From the symmetry perspective, we propose two complementary methods: EvolAST, an Abstract Syntax Tree (AST) based approach that targets syntactic symmetry to generate semantically equivalent problem variants, and EvolDomain, which leverages LLMs to address semantic symmetry by translating theorems across mathematical domains. From the difficulty perspective, we propose EvolDifficulty, which uses carefully designed evolutionary instructions to guide LLMs in generating new theorems with a wider range of difficulty. We then use the evolved data to train EvolProver, a 7B-parameter non-reasoning theorem prover. EvolProver establishes a new state-of-the-art (SOTA) on FormalMATH-Lite with a 53.8% pass@32 rate, surpassing all models of comparable size, including reasoning-based models. It also sets new SOTA records for non-reasoning models on MiniF2F-Test (69.8% pass@32), Ineq-Comp-Seed (52.2% pass@32), and Ineq-Comp-Transformed (34.0% pass@32). Ablation studies further confirm our data augmentation pipeline's effectiveness across multiple benchmarks.

We thank all the reviewers for their insightful comments! Regarding Theorem 1, yes, global indices are only needed in ordered cases. We will try to improve the title. This also indicates that our model learns a more compact latent space. We will add this possible explanation in the revised version.

The authors deal with a new problem that extends existing problems in a natural way, and present new solutions that extend existing solutions in a natural way; thus in some ways the paper is not very original, but it must be noted that the problem #opt has some surprising properties that make the whole endeavor quite interesting. As for the contribution, it is a valuable piece with new algorithms that have good performance. I really take issue with the emphasis on semirings; I cannot see how this helps the whole effort. Are semirings bringing new insights here? Or are they just more general so that the algorithm applies to other problems?

Cascades are a common type of machine learning systems in which a large, remote model can be queried if a local model is not able to accurately label a user's data by itself. Serving stacks for large language models (LLMs) increasingly use cascades due to their ability to preserve task performance while dramatically reducing inference costs. However, applying cascade systems in situations where the local model has access to sensitive data constitutes a significant privacy risk for users since such data could be forwarded to the remote model. In this work, we show the feasibility of applying cascade systems in such setups by equipping the local model with privacy-preserving techniques that reduce the risk of leaking private information when querying the remote model. To quantify information leakage in such setups, we introduce two privacy measures. We then propose a system that leverages the recently introduced social learning paradigm in which LLMs collaboratively learn from each other by exchanging natural language. Using this paradigm, we demonstrate on several datasets that our methods minimize the privacy loss while at the same time improving task performance compared to a non-cascade baseline.

LLMs have become the go-to choice for code generation tasks, with an exponential increase in the training, development, and usage of LLMs specifically for code generation. To evaluate the ability of LLMs on code, both academic and industry practitioners rely on popular handcrafted benchmarks. However, prior benchmarks contain only a very limited set of problems, both in quantity and variety. Further, due to popularity and age, many benchmarks are prone to data leakage where example solutions can be readily found on the web and thus potentially in training data. Such limitations inevitably lead us to inquire: Is the leaderboard performance on existing benchmarks reliable and comprehensive enough to measure the program synthesis ability of LLMs? To address this, we introduce EvoEval -- a program synthesis benchmark suite created by evolving existing benchmarks into different targeted domains for a comprehensive evaluation of LLM coding abilities. Our study on 51 LLMs shows that compared to the high performance obtained on standard benchmarks like HumanEval, there is a significant drop in performance (on average 39.4%) when using EvoEval. Additionally, the decrease in performance can range from 19.6% to 47.7%, leading to drastic ranking changes amongst LLMs and showing potential overfitting of existing benchmarks. Furthermore, we showcase various insights, including the brittleness of instruction-following models when encountering rewording or subtle changes as well as the importance of learning problem composition and decomposition. EvoEval not only provides comprehensive benchmarks, but can be used to further evolve arbitrary problems to keep up with advances and the ever-changing landscape of LLMs for code. We have open-sourced our benchmarks, tools, and complete LLM generations at https://github.com/evo-eval/evoeval

Building on our recent research on neural heuristic quantization systems, results on learning quantized motions and resilience to channel dropouts are reported. We propose a general emulation problem consistent with the neuromimetic paradigm. This optimal quantization problem can be solved by model predictive control (MPC), but because the optimization step involves integer programming, the approach suffers from combinatorial complexity when the number of input channels becomes large. Even if we collect data points to train a neural network simultaneously, collection of training data and the training itself are still time-consuming. Therefore, we propose a general Deep Q Network (DQN) algorithm that can not only learn the trajectory but also exhibit the advantages of resilience to channel dropout. Furthermore, to transfer the model to other emulation problems, a mapping-based transfer learning approach can be used directly on the current model to obtain the optimal direction for the new emulation problems.

If you've seen photos of a teapot shaped like an avocado or read a well-written article that veers off on slightly weird tangents, you may have been exposed to a new trend in artificial intelligence (AI). Machine learning systems called DALL-E, GPT and PaLM are making a splash with their incredible ability to generate creative work. These systems are known as "foundation models" and are not all hype and party tricks. So how does this new approach to AI work? And will it be the end of human creativity and the start of a deep-fake nightmare?