Large language models have demonstrated impressive performance on challenging mathematical reasoning tasks, which has triggered the discussion of whether the performance is achieved by true reasoning capability or memorization. To investigate this question, prior work has constructed mathematical benchmarks when questions undergo simple perturbations -- modifications that still preserve the underlying reasoning patterns of the solutions. However, no work has explored hard perturbations, which fundamentally change the nature of the problem so that the original solution steps do not apply. To bridge the gap, we construct MATH-P-Simple and MATH-P-Hard via simple perturbation and hard perturbation, respectively. Each consists of 279 perturbed math problems derived from level-5 (hardest) problems in the MATH dataset (Hendrycksmath et. al., 2021). We observe significant performance drops on MATH-P-Hard across various models, including o1-mini (-16.49%) and gemini-2.0-flash-thinking (-12.9%). We also raise concerns about a novel form of memorization where models blindly apply learned problem-solving skills without assessing their applicability to modified contexts. This issue is amplified when using original problems for in-context learning. We call for research efforts to address this challenge, which is critical for developing more robust and reliable reasoning models.

Ensembling outputs from diverse sources is a straightforward yet effective approach to boost performance. Mixture-of-Agents (MoA) is one such popular ensemble method that aggregates outputs from multiple different Large Language Models (LLMs). This paper raises the question in the context of language models: is mixing different LLMs truly beneficial? We propose Self-MoA -- an ensemble method that aggregates outputs from only the single top-performing LLM. Our extensive experiments reveal that, surprisingly, Self-MoA outperforms standard MoA that mixes different LLMs in a large number of scenarios: Self-MoA achieves $6.6\%$ improvement over MoA on the AlpacaEval 2.0 benchmark, and an average of $3.8\%$ improvement across various benchmarks, including MMLU, CRUX, and MATH. Applying Self-MoA to one of the top-ranking models in AlpacaEval 2.0 directly achieves the new state-of-the-art performance on the leaderboard. To understand the effectiveness of Self-MoA, we systematically investigate the trade-off between diversity and quality of outputs under various MoA settings. We confirm that the MoA performance is rather sensitive to the quality, and mixing different LLMs often lowers the average quality of the models. To complement the study, we identify the scenarios where mixing different LLMs could be helpful. This paper further introduces a sequential version of Self-MoA, that is capable of aggregating a large number of LLM outputs on-the-fly over multiple rounds, and is as effective as aggregating all outputs at once.

Recent advances in reinforcement learning (RL) heavily rely on a variety of well-designed benchmarks, which provide environmental platforms and consistent criteria to evaluate existing and novel algorithms. Specifically, in multi-agent RL (MARL), a plethora of benchmarks based on cooperative games have spurred the development of algorithms that improve the scalability of cooperative multi-agent systems. However, for the competitive setting, a lightweight and open-sourced benchmark with challenging gaming dynamics and visual inputs has not yet been established. In this work, we present FightLadder, a real-time fighting game platform, to empower competitive MARL research. Along with the platform, we provide implementations of state-of-the-art MARL algorithms for competitive games, as well as a set of evaluation metrics to characterize the performance and exploitability of agents. We demonstrate the feasibility of this platform by training a general agent that consistently defeats 12 built-in characters in single-player mode, and expose the difficulty of training a non-exploitable agent without human knowledge and demonstrations in two-player mode. FightLadder provides meticulously designed environments to address critical challenges in competitive MARL research, aiming to catalyze a new era of discovery and advancement in the field. Videos and code at https://sites.google.com/view/fightladder/home.

Multiplayer games, when the number of players exceeds two, present unique challenges that fundamentally distinguish them from the extensively studied two-player zero-sum games. These challenges arise from the non-uniqueness of equilibria and the risk of agents performing highly suboptimally when adopting equilibrium strategies. While a line of recent works developed learning systems successfully achieving human-level or even superhuman performance in popular multiplayer games such as Mahjong, Poker, and Diplomacy, two critical questions remain unaddressed: (1) What is the correct solution concept that AI agents should find? and (2) What is the general algorithmic framework that provably solves all games within this class? This paper takes the first step towards solving these unique challenges of multiplayer games by provably addressing both questions in multiplayer symmetric normal-form games. We also demonstrate that many meta-algorithms developed in prior practical systems for multiplayer games can fail to achieve even the basic goal of obtaining agent's equal share of the total reward.

Transformer has been considered the dominating neural architecture in NLP and CV, mostly under supervised settings. Recently, a similar surge of using Transformers has appeared in the domain of reinforcement learning (RL), but it is faced with unique design choices and challenges brought by the nature of RL. However, the evolution of Transformers in RL has not yet been well unraveled. In this paper, we seek to systematically review motivations and progress on using Transformers in RL, provide a taxonomy on existing works, discuss each sub-field, and summarize future prospects.

Offline reinforcement learning (RL) enables the agent to effectively learn from logged data, which significantly extends the applicability of RL algorithms in real-world scenarios where exploration can be expensive or unsafe. Previous works have shown that extracting primitive skills from the recurring and temporally extended structures in the logged data yields better learning. However, these methods suffer greatly when the primitives have limited representation ability to recover the original policy space, especially in offline settings. In this paper, we give a quantitative characterization of the performance of offline hierarchical learning and highlight the importance of learning lossless primitives. To this end, we propose to use a \emph{flow}-based structure as the representation for low-level policies. This allows us to represent the behaviors in the dataset faithfully while keeping the expression ability to recover the whole policy space. We show that such lossless primitives can drastically improve the performance of hierarchical policies. The experimental results and extensive ablation studies on the standard D4RL benchmark show that our method has a good representation ability for policies and achieves superior performance in most tasks.

Solving goal-conditioned tasks with sparse rewards using self-supervised learning is promising because of its simplicity and stability over current reinforcement learning (RL) algorithms. A recent work, called Goal-Conditioned Supervised Learning (GCSL), provides a new learning framework by iteratively relabeling and imitating self-generated experiences. In this paper, we revisit the theoretical property of GCSL -- optimizing a lower bound of the goal reaching objective, and extend GCSL as a novel offline goal-conditioned RL algorithm. The proposed method is named Weighted GCSL (WGCSL), in which we introduce an advanced compound weight consisting of three parts (1) discounted weight for goal relabeling, (2) goal-conditioned exponential advantage weight, and (3) best-advantage weight. Theoretically, WGCSL is proved to optimize an equivalent lower bound of the goal-conditioned RL objective and generates monotonically improved policies via an iterated scheme. The monotonic property holds for any behavior policies, and therefore WGCSL can be applied to both online and offline settings. To evaluate algorithms in the offline goal-conditioned RL setting, we provide a benchmark including a range of point and simulated robot domains. Experiments in the introduced benchmark demonstrate that WGCSL can consistently outperform GCSL and existing state-of-the-art offline methods in the fully offline goal-conditioned setting.

The first order derivative of a data density can be estimated efficiently by denoising score matching, and has become an important component in many applications, such as image generation and audio synthesis. Higher order derivatives provide additional local information about the data distribution and enable new applications. Although they can be estimated via automatic differentiation of a learned density model, this can amplify estimation errors and is expensive in high dimensional settings. To overcome these limitations, we propose a method to directly estimate high order derivatives (scores) of a data density from samples. We first show that denoising score matching can be interpreted as a particular case of Tweedie's formula. By leveraging Tweedie's formula on higher order moments, we generalize denoising score matching to estimate higher order derivatives. We demonstrate empirically that models trained with the proposed method can approximate second order derivatives more efficiently and accurately than via automatic differentiation. We show that our models can be used to quantify uncertainty in denoising and to improve the mixing speed of Langevin dynamics via Ozaki discretization for sampling synthetic data and natural images.

In offline reinforcement learning (offline RL), one of the main challenges is to deal with the distributional shift between the learning policy and the given dataset. To address this problem, recent offline RL methods attempt to introduce conservatism bias to encourage learning on high-confidence areas. Model-free approaches directly encode such bias into policy or value function learning using conservative regularizations or special network structures, but their constrained policy search limits the generalization beyond the offline dataset. Model-based approaches learn forward dynamics models with conservatism quantifications and then generate imaginary trajectories to extend the offline datasets. However, due to limited samples in offline dataset, conservatism quantifications often suffer from overgeneralization in out-of-support regions. The unreliable conservative measures will mislead forward model-based imaginations to undesired areas, leading to overaggressive behaviors. To encourage more conservatism, we propose a novel model-based offline RL framework, called Reverse Offline Model-based Imagination (ROMI). We learn a reverse dynamics model in conjunction with a novel reverse policy, which can generate rollouts leading to the target goal states within the offline dataset. These reverse imaginations provide informed data augmentation for the model-free policy learning and enable conservative generalization beyond the offline dataset. ROMI can effectively combine with off-the-shelf model-free algorithms to enable model-based generalization with proper conservatism. Empirical results show that our method can generate more conservative behaviors and achieve state-of-the-art performance on offline RL benchmark tasks.

Computing the expectation of some kernel function is ubiquitous in machine learning, from the classical theory of support vector machines, to exploiting kernel embeddings of distributions in applications ranging from probabilistic modeling, statistical inference, casual discovery, and deep learning. In all these scenarios, we tend to resort to Monte Carlo estimates as expectations of kernels are intractable in general. In this work, we characterize the conditions under which we can compute expected kernels exactly and efficiently, by leveraging recent advances in probabilistic circuit representations. We first construct a circuit representation for kernels and propose an approach to such tractable computation. We then demonstrate possible advancements for kernel embedding frameworks by exploiting tractable expected kernels to derive new algorithms for two challenging scenarios: 1) reasoning under missing data with kernel support vector regressors; 2) devising a collapsed black-box importance sampling scheme. Finally, we empirically evaluate both algorithms and show that they outperform standard baselines on a variety of datasets.