Solving Olympiad-level mathematical problems represents a significant advancement in machine intelligence and automated reasoning. Current machine learning methods, however, struggle to solve Olympiad-level problems beyond Euclidean plane geometry due to a lack of large-scale, high-quality datasets. The challenge is even greater in algebraic systems, which involve infinite reasoning spaces within finite conditions. To address these issues, we propose AIPS, an Algebraic Inequality Proving System capable of autonomously generating complex inequality theorems and effectively solving Olympiad-level inequality problems without requiring human demonstrations. During proof search in a mixed reasoning manner, a value curriculum learning strategy on generated datasets is implemented to improve proving performance, demonstrating strong mathematical intuitions. On a test set of 20 International Mathematical Olympiad-level inequality problems, AIPS successfully solved 10, outperforming state-of-the-art methods. Furthermore, AIPS automatically generated a vast array of non-trivial theorems without human intervention, some of which have been evaluated by professional contestants and deemed to reach the level of the International Mathematical Olympiad. Notably, one theorem was selected as a competition problem in a major city's 2024 Mathematical Olympiad. All the materials are available at sites.google.com/view/aips2.

Modern machine learning models are becoming increasingly expensive to train for real-world image and text classification tasks, where massive web-scale data is collected in a streaming fashion. To reduce the training cost, online batch selection techniques have been developed to choose the most informative datapoints. However, many existing techniques are not robust to class imbalance and distributional shifts, and can suffer from poor worst-class generalization performance. This work introduces REDUCR, a robust and efficient data downsampling method that uses class priority reweighting. REDUCR reduces the training data while preserving worst-class generalization performance. REDUCR assigns priority weights to datapoints in a class-aware manner using an online learning algorithm. We demonstrate the data efficiency and robust performance of REDUCR on vision and text classification tasks. On web-scraped datasets with imbalanced class distributions, REDUCR significantly improves worst-class test accuracy (and average accuracy), surpassing state-of-the-art methods by around 15%.

Data-driven generative models have emerged as promising approaches towards achieving efficient mechanical inverse design. However, due to prohibitively high cost in time and money, there is still lack of open-source and large-scale benchmarks in this field. It is mainly the case for airfoil inverse design, which requires to generate and edit diverse geometric-qualified and aerodynamic-qualified airfoils following the multimodal instructions, i.e., dragging points and physical parameters. This paper presents the open-source endeavors in airfoil inverse design, AFBench, including a large-scale dataset with 200 thousand airfoils and high-quality aerodynamic and geometric labels, two novel and practical airfoil inverse design tasks, i.e., conditional generation on multimodal physical parameters, controllable editing, and comprehensive metrics to evaluate various existing airfoil inverse design methods. Our aim is to establish AFBench as an ecosystem for training and evaluating airfoil inverse design methods, with a specific focus on data-driven controllable inverse design models by multimodal instructions capable of bridging the gap between ideas and execution, the academic research and industrial applications. We have provided baseline models, comprehensive experimental observations, and analysis to accelerate future research.

In many real-world decision problems there is partially observed, hidden or latent information that remains fixed throughout an interaction. Such decision problems can be modeled as Latent Markov Decision Processes (LMDPs), where a latent variable is selected at the beginning of an interaction and is not disclosed to the agent. In the last decade, there has been significant progress in solving LMDPs under different structural assumptions. However, for general LMDPs, even in the tabular case, no algorithm is known to provably match the existing lower bound [41]. We introduce the first sample-efficient algorithm for LMDPs without any additional distributional assumptions. Our result builds off a new perspective on the role of offpolicy evaluation guarantees and coverage coefficients in LMDPs, a perspective, that has been overlooked in the context of exploration in partially observed environments. Specifically, we establish a novel off-policy evaluation lemma and introduce a new coverage coefficient for LMDPs. Then, we show how these can be used to derive near-optimal guarantees of an optimistic exploration algorithm. These results, we believe, can be valuable for a wide range of interactive learning problems beyond LMDPs, and especially, for partially observed environments.

In real-world machine learning applications, data subsets correspond to especially critical outcomes: vulnerable cyclist detections are safety-critical in an autonomous driving task, and "question" sentences might be important to a dialogue agent's language understanding for product purposes. While machine learning models can achieve high quality performance on coarse-grained metrics like F1-score and overall accuracy, they may underperform on critical subsets--we define these as slices, the key abstraction in our approach. To address slice-level performance, practitioners often train separate "expert" models on slice subsets or use multi-task hard parameter sharing. We propose Slice-based Learning, a new programming model in which the slicing function (SF), a programming interface, specifies critical data subsets for which the model should commit additional capacity. Any model can leverage SFs to learn slice expert representations, which are combined with an attention mechanism to make slice-aware predictions. We show that our approach maintains a parameter-efficient representation while improving over baselines by up to 19.0 F1 on slices and 4.6 F1 overall on datasets spanning language understanding (e.g.

We show for the first time that it is possible to reconcile in online learning in zero-sum games two seemingly contradictory objectives: vanishing time-average regret and non-vanishing step sizes. This phenomenon, that we coin "fast and furious" learning in games, sets a new benchmark about what is possible both in max-min optimization as well as in multi-agent systems. Our analysis does not depend on introducing a carefully tailored dynamic. Instead we focus on the most well studied online dynamic, gradient descent. Similarly, we focus on the simplest textbook class of games, two-agent two-strategy zero-sum games, such as Matching Pennies. Even for this simplest of benchmarks the best known bound for total regret, prior to our work, was the trivial one of O(T), which is immediately applicable even to a non-learning agent. Based on a tight understanding of the geometry of the non-equilibrating trajectories in the dual space we prove a regret bound of Θ( T) matching the well known optimal bound for adaptive step sizes in the online setting. This guarantee holds for all fixed step-sizes without having to know the time horizon in advance and adapt the fixed step-size accordingly.As a corollary, we establish that even with fixed learning rates the time-average of mixed strategies, utilities converge to their exact Nash equilibrium values. We also provide experimental evidence suggesting the stronger regret bound holds for all zero-sum games.

Multiple clustering aims to discover various latent structures of data from different aspects. Deep multiple clustering methods have achieved remarkable performance by exploiting complex patterns and relationships in data. However, existing works struggle to flexibly adapt to diverse user-specific needs in data grouping, which may require manual understanding of each clustering. To address these limitations, we introduce Multi-Sub, a novel end-to-end multiple clustering approach that incorporates a multi-modal subspace proxy learning framework in this work. Utilizing the synergistic capabilities of CLIP and GPT-4, Multi-Sub aligns textual prompts expressing user preferences with their corresponding visual representations. This is achieved by automatically generating proxy words from large language models that act as subspace bases, thus allowing for the customized representation of data in terms specific to the user's interests. Our method consistently outperforms existing baselines across a broad set of datasets in visual multiple clustering tasks.

This work presents a novel approach to neural architecture search (NAS) that aims to increase carbon efficiency for the model design process. The proposed framework CE-NAS addresses the key challenge of high carbon cost associated with NAS by exploring the carbon emission variations of energy and energy differences of different NAS algorithms. At the high level, CE-NAS leverages a reinforcement-learning agent to dynamically adjust GPU resources based on carbon intensity, predicted by a time-series transformer, to balance energy-efficient sampling and energy-intensive evaluation tasks. Furthermore, CE-NAS leverages a recently proposed multi-objective optimizer to effectively reduce the NAS search space. We demonstrate the efficacy of CE-NAS in lowering carbon emissions while achieving SOTA results for both NAS benchmarks and open-domain NAS tasks. For example, on the HW-NasBench, CE-NAS reduces carbon emissions by up to 7.22X while maintaining a search efficiency comparable to vanilla NAS. For opendomain NAS tasks, CE-NAS achieves SOTA results with 97.35% top-1 accuracy on CIFAR-10 with only 1.68M parameters and a carbon consumption of 38.53 lbs of CO

This supplementary material is organized as follows: In Section A, we discuss additional priors that were not presented in the main paper, but which are in principle compatible with our framework, and we provide more details about potential games. In Section B, we provide implementation details that are useful to reproduce the results of our paper (note that the code is also provided). In Section C, we present additional quantitative results and additional results regarding inference speed of our models that were not included in the main paper for space limitation reasons. Finally, in Section D, we present additional qualitative results (which require zooming on a computer screen). A.1 Additional Priors Our framework makes it possible to handle models of the form: In the main paper, several regularization functions have been considered, including the total variation, variance reduction, or non-local group regularization penalties.

We thank the reviewers for their constructive comments. We provide our answers below. Presentation: if the paper is accepted, we will improve our presentation, notably by better explaining "the big picture" R1: "The authors consider both gradient l1 an l2 type regularization, as well as "standard" l1 and l2 methods [..]". "PSNR values by themselves don't really provide an overly compelling justification". Finally, we also plan to include SSIM scores.