Nondeterministic Polynomial-time Problem Challenge: An Ever-Scaling Reasoning Benchmark for LLMs

Reasoning is the fundamental capability of large language models (LLMs). Due to the rapid progress of LLMs, there are two main issues of current benchmarks: i) these benchmarks can be crushed in a short time (less than 1 year), and ii) these benchmarks may be easily hacked. To handle these issues, we propose the ever-scalingness for building the benchmarks which are uncrushable, unhackable, auto-verifiable and general. This paper presents Nondeterministic Polynomial-time Problem Challenge (NPPC), an ever-scaling reasoning benchmark for LLMs. Specifically, the NPPC has three main modules: i) npgym, which provides a unified interface of 25 well-known NP-complete problems and can generate any number of instances with any levels of complexities, ii) npsolver: which provides a unified interface to evaluate the problem instances with both online and offline models via APIs and local deployments, respectively, and iii) npeval: which provides the comprehensive and ready-to-use tools to analyze the performances of LLMs over different problems, the number of tokens, the aha moments, the reasoning errors and the solution errors. Extensive experiments over widely-used LLMs demonstrate: i) NPPC can successfully decrease the performances of advanced LLMs' performances to below 10%, demonstrating that NPPC is uncrushable, ii) DeepSeek-R1, Claude-3.7-Sonnet, and o1/o3-mini are the most powerful LLMs, where DeepSeek-R1 outperforms Claude-3.7-Sonnet and o1/o3-mini in most NP-complete problems considered, and iii) the numbers of tokens, aha moments in the advanced LLMs, e.g., Claude-3.7-Sonnet and DeepSeek-R1, are observed first to increase and then decrease when the problem instances become more and more difficult. We believe that NPPC is the first ever-scaling reasoning benchmark, serving as the uncrushable and unhackable testbed for LLMs toward artificial general intelligence (AGI).

Graph-defined Language Learning with LLMs

Recent efforts leverage Large Language Models (LLMs) for modeling text-attributed graph structures in node classification tasks. These approaches describe graph structures for LLMs to understand or aggregate LLM-generated textual attribute embeddings through graph structure. However, these approaches face two main limitations in modeling graph structures with LLMs. (i) Graph descriptions become verbose in describing high-order graph structure. (ii) Textual attributes alone do not contain adequate graph structure information. It is challenging to model graph structure concisely and adequately with LLMs. LLMs lack built-in mechanisms to model graph structures directly. They also struggle with complex long-range dependencies between high-order nodes and target nodes. Inspired by the observation that LLMs pre-trained on one language can achieve exceptional performance on another with minimal additional training, we propose \textbf{G}raph-\textbf{D}efined \textbf{L}anguage for \textbf{L}arge \textbf{L}anguage \textbf{M}odel (GDL4LLM). This novel framework enables LLMs to transfer their powerful language understanding capabilities to graph-structured data. GDL4LLM translates graphs into a graph language corpus instead of graph descriptions and pre-trains LLMs on this corpus to adequately understand graph structures. During fine-tuning, this corpus describes the structural information of target nodes concisely with only a few tokens. By treating graphs as a new language, GDL4LLM enables LLMs to model graph structures adequately and concisely for node classification tasks. Extensive experiments on three real-world datasets demonstrate that GDL4LLM outperforms description-based and textual attribute embeddings-based baselines by efficiently modeling different orders of graph structure with LLMs.

The Scaling Law for LoRA Base on Mutual Information Upper Bound

LoRA (Low-Rank Adaptation) is a widely used model fine-tuning method. In fine-tuning, the law among model performance, model parameters, and data complexity has been a focal issue in the field. Existing methods often leverage external metrics (such as cross-entropy or perplexity) to evaluate model performance. In the fine-tuning process for large models, two types of knowledge are typically involved: the frozen, general knowledge acquired by the model during pre-training and the new knowledge learned through the LoRA module from the current data. Generally, the less LoRA's learned knowledge relies on the large model, the more it captures the specific knowledge of new data, thereby enhancing its adaptability to new tasks. However, external metrics do not readily capture the dependency relationship between these two types of knowledge. Therefore, we designed an internal metric based on the Mutual Information Upper Bound (MIUB) theory to investigate the scaling law of large-model LoRA fine-tuning. In our experiments, we validated this approach on benchmark datasets, using the Llama3-8B and Phi3-3B models. The results show that the proposed MIUB metric aligns more accurately and stably with the scaling law of LoRA fine-tuning compared to cross-entropy and perplexity.

Evaluating World Models with LLM for Decision Making

World model emerges as a key module in decision making, where MuZero and Dreamer achieve remarkable successes in complex tasks. Recent work leverages Large Language Models (LLMs) as general world simulators to simulate the dynamics of the world due to their generalizability. LLMs also serve as the world model for deliberative reasoning in Reasoning via Planning (RAP) and Tree of Thought (ToT). However, the world models are either evaluated as a general world simulator, or as a functional module of the agent, i.e., predicting the transitions to assist the planning. In this work, we propose a comprehensive evaluation of the world models with LLMs from the decision making perspective. Specifically, we leverage the 31 diverse environments from (Wang et al., 2023;2024) and curate the rule-based policy of each environment for the diverse evaluation. Then, we design three main tasks, i.e., policy verification, action proposal, and policy planning, where the world models can be used for decision making solely. Finally, we conduct the comprehensive evaluation of the advanced LLMs, i.e., GPT-4o and GPT-4o-mini, on the environments for the three main tasks under various settings. The key observations include: i) GPT-4o significantly outperforms GPT-4o-mini on the three main tasks, especially for the tasks which require the domain knowledge, ii) the performance of the world model with LLM will be decreased for long-term decision-making tasks, and iii) the combination of different functionalities of the world model will brings additional unstabilities of the performance.

In-Context Exploiter for Extensive-Form Games

Nash equilibrium (NE) is a widely adopted solution concept in game theory due to its stability property. However, we observe that the NE strategy might not always yield the best results, especially against opponents who do not adhere to NE strategies. Based on this observation, we pose a new game-solving question: Can we learn a model that can exploit any, even NE, opponent to maximize their own utility? In this work, we make the first attempt to investigate this problem through in-context learning. Specifically, we introduce a novel method, In-Context Exploiter (ICE), to train a single model that can act as any player in the game and adaptively exploit opponents entirely by in-context learning. Our ICE algorithm involves generating diverse opponent strategies, collecting interactive history training data by a reinforcement learning algorithm, and training a transformer-based agent within a well-designed curriculum learning framework. Finally, comprehensive experimental results validate the effectiveness of our ICE algorithm, showcasing its in-context learning ability to exploit any unknown opponent, thereby positively answering our initial game-solving question.

Graph Anomaly Detection with Noisy Labels by Reinforcement Learning

Graph anomaly detection (GAD) has been widely applied in many areas, e.g., fraud detection in finance and robot accounts in social networks. Existing methods are dedicated to identifying the outlier nodes that deviate from normal ones. While they heavily rely on high-quality annotation, which is hard to obtain in real-world scenarios, this could lead to severely degraded performance based on noisy labels. Thus, we are motivated to cut the edges of suspicious nodes to alleviate the impact of noise. However, it remains difficult to precisely identify the nodes with noisy labels. Moreover, it is hard to quantitatively evaluate the regret of cutting the edges, which may have either positive or negative influences. To this end, we propose a novel framework REGAD, i.e., REinforced Graph Anomaly Detector. Specifically, we aim to maximize the performance improvement (AUC) of a base detector by cutting noisy edges approximated through the nodes with high-confidence labels. (i) We design a tailored action and search space to train a policy network to carefully prune edges step by step, where only a few suspicious edges are prioritized in each step. (ii) We design a policy-in-the-loop mechanism to iteratively optimize the policy based on the feedback from base detector. The overall performance is evaluated by the cumulative rewards. Extensive experiments are conducted on three datasets under different anomaly ratios. The results indicate the superior performance of our proposed REGAD.

Configurable Mirror Descent: Towards a Unification of Decision Making

Decision-making problems, categorized as single-agent, e.g., Atari, cooperative multi-agent, e.g., Hanabi, competitive multi-agent, e.g., Hold'em poker, and mixed cooperative and competitive, e.g., football, are ubiquitous in the real world. Various methods are proposed to address the specific decision-making problems. Despite the successes in specific categories, these methods typically evolve independently and cannot generalize to other categories. Therefore, a fundamental question for decision-making is: \emph{Can we develop \textbf{a single algorithm} to tackle \textbf{ALL} categories of decision-making problems?} There are several main challenges to address this question: i) different decision-making categories involve different numbers of agents and different relationships between agents, ii) different categories have different solution concepts and evaluation measures, and iii) there lacks a comprehensive benchmark covering all the categories. This work presents a preliminary attempt to address the question with three main contributions. i) We propose the generalized mirror descent (GMD), a generalization of MD variants, which considers multiple historical policies and works with a broader class of Bregman divergences. ii) We propose the configurable mirror descent (CMD) where a meta-controller is introduced to dynamically adjust the hyper-parameters in GMD conditional on the evaluation measures. iii) We construct the \textsc{GameBench} with 15 academic-friendly games across different decision-making categories. Extensive experiments demonstrate that CMD achieves empirically competitive or better outcomes compared to baselines while providing the capability of exploring diverse dimensions of decision making.

Self-adaptive PSRO: Towards an Automatic Population-based Game Solver

Policy-Space Response Oracles (PSRO) as a general algorithmic framework has achieved state-of-the-art performance in learning equilibrium policies of two-player zero-sum games. However, the hand-crafted hyperparameter value selection in most of the existing works requires extensive domain knowledge, forming the main barrier to applying PSRO to different games. In this work, we make the first attempt to investigate the possibility of self-adaptively determining the optimal hyperparameter values in the PSRO framework. Our contributions are three-fold: (1) Using several hyperparameters, we propose a parametric PSRO that unifies the gradient descent ascent (GDA) and different PSRO variants. (2) We propose the self-adaptive PSRO (SPSRO) by casting the hyperparameter value selection of the parametric PSRO as a hyperparameter optimization (HPO) problem where our objective is to learn an HPO policy that can self-adaptively determine the optimal hyperparameter values during the running of the parametric PSRO. (3) To overcome the poor performance of online HPO methods, we propose a novel offline HPO approach to optimize the HPO policy based on the Transformer architecture. Experiments on various two-player zero-sum games demonstrate the superiority of SPSRO over different baselines.

A Game-Theoretic Perspective of Generalization in Reinforcement Learning

Generalization in reinforcement learning (RL) is of importance for real deployment of RL algorithms. Various schemes are proposed to address the generalization issues, including transfer learning, multi-task learning and meta learning, as well as the robust and adversarial reinforcement learning. However, there is not a unified formulation of the various schemes, as well as the comprehensive comparisons of methods across different schemes. In this work, we propose a game-theoretic framework for the generalization in reinforcement learning, named GiRL, where an RL agent is trained against an adversary over a set of tasks, where the adversary can manipulate the distributions over tasks within a given threshold. With different configurations, GiRL can reduce the various schemes mentioned above. To solve GiRL, we adapt the widely-used method in game theory, policy space response oracle (PSRO) with the following three important modifications: i) we use model-agnostic meta learning (MAML) as the best-response oracle, ii) we propose a modified projected replicated dynamics, i.e., R-PRD, which ensures the computed meta-strategy of the adversary fall in the threshold, and iii) we also propose a protocol for the few-shot learning of the multiple strategies during testing. Extensive experiments on MuJoCo environments demonstrate that our proposed methods can outperform existing baselines, e.g., MAML.