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Angela Zhou, Christoph Kern, Michael Kim

Estimating heterogeneous treatment effects is important to tailor treatments to those individuals who would most likely benefit. However, conditional average treatment effect predictors may often be trained on one population but possibly deployed on different, possibly unknown populations. We use methodology for learning multi-accurate predictors to post-process CATE T-learners (differenced regressions) to become robust to unknown covariate shifts at the time of deployment. The method works in general for pseudo-outcome regression, such as the DR-learner. We show how this approach can combine (large) confounded observational and (smaller) randomized datasets by learning a confounded predictor from the observational dataset, and auditing for multi-accuracy on the randomized controlled trial. We show improvements in bias and mean squared error in simulations with increasingly larger covariate shift, and on a semi-synthetic case study of a parallel large observational study and smaller randomized controlled experiment. Overall, we establish a connection between methods developed for multi-distribution learning and achieve appealing desiderata (e.g. external validity) in causal inference and machine learning.

Applications · Everything Else

Shaonan Wu, Shuai Lu, Yeyun Gong, Nan Duan, Ping Wei

Formal proofs are challenging to write even for experienced experts. Recent progress in Neural Theorem Proving (NTP) shows promise in expediting this process. However, the formal corpora available on the Internet are limited compared to the general text, posing a significant data scarcity challenge for NTP. To address this issue, this work proposes Alchemy, a general framework for data synthesis that constructs formal theorems through symbolic mutation. Specifically, for each candidate theorem in Mathlib, we identify all invocable theorems that can be used to rewrite or apply to it. Subsequently, we mutate the candidate theorem by replacing the corresponding term in the statement with its equivalent form or antecedent. As a result, our method increases the number of theorems in Mathlib by an order of magnitude, from 110k to 6M. Furthermore, we perform continual pretraining and supervised finetuning on this augmented corpus for large language models. Experimental results demonstrate the effectiveness of our approach, achieving a 4.70% absolute performance improvement on Leandojo benchmark. Additionally, our approach achieves a 2.47% absolute performance gain on the out-of-distribution miniF2F benchmark based on the synthetic data. To provide further insights, we conduct a comprehensive analysis of synthetic data composition and the training paradigm, offering valuable guidance for developing a strong theorem prover.

Reinforcement Learning · Inverse

Bo Yue, Shufan Wang, Ashish Gaurav, Jian Li, Pascal Poupart, Guiliang Liu

In practical applications, the underlying constraint knowledge is often unknown and difficult to specify. To address this issue, recent advances in Inverse Constrained Reinforcement Learning (ICRL) have focused on inferring these constraints from expert demonstrations. However, the ICRL approach typically characterizes constraint learning as a tri-level optimization problem, which is inherently complex due to its interdependent variables and multiple layers of optimization.Considering these challenges, a critical question arises: *Can we implicitly embed constraint signals into reward functions and effectively solve this problem using a classic reward inference algorithm?* The resulting method, known as Inverse Reward Correction (IRC), merits investigation. In this work, we conduct a theoretical analysis comparing the sample complexities of both solvers. Our findings confirm that the IRC solver achieves lower sample complexity than its ICRL counterpart.Nevertheless, this reduction in complexity comes at the expense of generalizability. Specifically, in the target environment, the reward correction terms may fail to guarantee the safety of the resulting policy, whereas this issue can be effectively mitigated by transferring the constraints via the ICRL solver. Advancing our inquiry, we investigate conditions under which the ICRL solver ensures $\epsilon$-optimality when transferring to new environments. Empirical results across various environments validate our theoretical findings, underscoring the nuanced trade-offs between complexity reduction and generalizability in safety-critical applications.

Reinforcement Learning · Multi-agent

GUOJUN XIONG, Shufan Wang, Daniel Jiang, Jian Li

Federated reinforcement learning (FedRL) enables multiple agents to collaboratively learn a policy without needing to share the local trajectories collected during agent-environment interactions. However, in practice, the environments faced by different agents are often heterogeneous, but since existing FedRL algorithms learn a single policy across all agents, this may lead to poor performance. In this paper, we introduce a personalized FedRL framework (PFedRL) by taking advantage of possibly shared common structure among agents in heterogeneous environments. Specifically, we develop a class of PFedRL algorithms named PFedRL-Rep that learns (1) a shared feature representation collaboratively among all agents, and (2) an agent-specific weight vector personalized to its local environment. We analyze the convergence of PFedTD-Rep, a particular instance of the framework with temporal difference (TD) learning and linear representations. To the best of our knowledge, we are the first to prove a linear convergence speedup with respect to the number of agents in the PFedRL setting. To achieve this, we show that PFedTD-Rep is an example of federated two-timescale stochastic approximation with Markovian noise. Experimental results demonstrate that PFedTD-Rep, along with an extension to the control setting based on deep Q-networks (DQN), not only improve learning in heterogeneous settings, but also provide better generalization to new environments.

Deep Learning · Robustness

Zhichao Hou, MohamadAli Torkamani, Hamid Krim, Xiaorui Liu

This work tackles an intriguing and fundamental open challenge in representation learning: Given a well-trained deep learning model, can it be reprogrammed to enhance its robustness against adversarial or noisy input perturbations without altering its parameters?To explore this, we revisit the core feature transformation mechanism in representation learning and propose a novel non-linear robust pattern matching technique as a robust alternative. Furthermore, we introduce three model reprogramming paradigms to offer flexible control of robustness under different efficiency requirements. Comprehensive experiments and ablation studies across diverse learning models ranging from basic linear model and MLPs to shallow and modern deep ConvNets demonstrate the effectiveness of our approaches.This work not only opens a promising and orthogonal direction for improving adversarial defenses in deep learning beyond existing methods but also provides new insights into designing more resilient AI systems with robust statistics. Our implementation is available at https://github.com/chris-hzc/Robustness-Reprogramming.

Deep Learning · Large Language Models

Jiachen Jiang, Jinxin Zhou, Zhihui Zhu

Analyzing the similarity of internal representations within and across different models has been an important technique for understanding the behavior of deep neural networks. Most existing methods for analyzing the similarity between representations of high dimensions, such as those based on Centered Kernel Alignment (CKA), rely on statistical properties of the representations for a set of data points. In this paper, we focus on transformer models and study the similarity of representations between the hidden layers of individual transformers. In this context, we show that a simple sample-wise cosine similarity metric is capable of capturing the similarity and aligns with the complicated CKA. Our experimental results on common transformers reveal that representations across layers are positively correlated, with similarity increasing when layers get closer. We provide a theoretical justification for this phenomenon under the geodesic curve assumption for the learned transformer, a property that may approximately hold for residual networks. We then show that an increase in representation similarity implies an increase in predicted probability when directly applying the last-layer classifier to any hidden layer representation. This offers a justification for {\it saturation events}, where the model's top prediction remains unchanged across subsequent layers, indicating that the shallow layer has already learned the necessary knowledge. We then propose an aligned training method to improve the effectiveness of shallow layer by enhancing the similarity between internal representations, with trained models that enjoy the following properties: (1) more early saturation events, (2) layer-wise accuracies monotonically increase and reveal the minimal depth needed for the given task, (3) when served as multi-exit models, they achieve on-par performance with standard multi-exit architectures which consist of additional classifiers designed for early exiting in shallow layers. To our knowledge, our work is the first to show that one common classifier is sufficient for multi-exit models. We conduct experiments on both vision and NLP tasks to demonstrate the performance of the proposed aligned training.

Applications · Computer Vision

Amin Karimi Monsefi, Mengxi Zhou, Nastaran Monsefi, Ser-Nam Lim, Wei-Lun Chao, Rajiv Ramnath

We present a novel frequency-based Self-Supervised Learning (SSL) approach that significantly enhances its efficacy for pre-training. Prior work in this direction masks out pre-defined frequencies in the input image and employs a reconstruction loss to pre-train the model. While achieving promising results, such an implementation has two fundamental limitations as identified in our paper. First, using pre-defined frequencies overlooks the variability of image frequency responses. Second, pre-trained with frequency-filtered images, the resulting model needs relatively more data to adapt to naturally looking images during fine-tuning. To address these drawbacks, we propose FOurier transform compression with seLf-Knowledge distillation (FOLK), integrating two dedicated ideas. First, inspired by image compression, we adaptively select the masked-out frequencies based on image frequency responses, creating more suitable SSL tasks for pre-training. Second, we employ a two-branch framework empowered by knowledge distillation, enabling the model to take both the filtered and original images as input, largely reducing the burden of downstream tasks. Our experimental results demonstrate the effectiveness of FOLK in achieving competitive performance to many state-of-the-art SSL methods across various downstream tasks, including image classification, few-shot learning, and semantic segmentation.

Deep Learning · Robustness

jiachen lei, Julius Berner, Jiongxiao Wang, Zhongzhu Chen, Chaowei Xiao, Zhongjie Ba, Kui Ren, Jun Zhu, anima anandkumar

Robustness is essential for deep neural networks, especially in security-sensitive applications. To this end, randomized smoothing provides theoretical guarantees for certifying robustness against adversarial perturbations. Recently, diffusion models have been successfully employed for randomized smoothing to purify noise-perturbed samples before making predictions with a standard classifier. While these methods excel at small perturbation radii, they struggle with larger perturbations and incur a significant computational overhead during inference compared to classical methods. To address this, we reformulate the generative modeling task along the diffusion trajectories in pixel space as a discriminative task in the latent space. Specifically, we use instance discrimination to achieve consistent representations along the trajectories by aligning temporally adjacent points. After fine-tuning based on the learned representations, our model enables implicit denoising-then-classification via a single prediction, substantially reducing inference costs. We conduct extensive experiments on various datasets and achieve state-of-the-art performance with minimal computation budget during inference. For example, our method outperforms the certified accuracy of diffusion-based methods on ImageNet across all perturbation radii by 5.3\% on average, with up to 11.6\% at larger radii, while reducing inference costs by 85x on average.

Applications · Language, Speech and Dialog

Yaxi Lu, Shenzhi Yang, Cheng Qian, Guirong Chen, Qinyu Luo, Yesai Wu, Huadong Wang, Xin Cong, Zhong Zhang, Yankai Lin 等

Agents powered by large language models have shown remarkable abilities in solving complex tasks. However, most agent systems remain reactive, limiting their effectiveness in scenarios requiring foresight and autonomous decision-making. In this paper, we tackle the challenge of developing proactive agents capable of anticipating and initiating tasks without explicit human instructions. We propose a novel data-driven approach for this problem. Firstly, we collect real-world human activities to generate proactive task predictions. These predictions are then labeled by human annotators as either accepted or rejected. The labeled data is used to train a reward model that simulates human judgment and serves as an automatic evaluator of the proactiveness of LLM agents. Building on this, we develop a comprehensive data generation pipeline to create a diverse dataset, ProactiveBench, containing 6,790 events. Finally, we demonstrate that fine-tuning models with the proposed ProactiveBench can significantly elicit the proactiveness of LLM agents. Experimental results show that our fine-tuned model achieves an F1-Score of 66.47% in proactively offering assistance, outperforming all open-source and close-source models. These results highlight the potential of our method in creating more proactive and effective agent systems, paving the way for future advancements in human-agent collaboration.

Shengda Fan, Xin Cong, Yuepeng Fu, Zhong Zhang, Shuyan Zhang, Yuanwei Liu, Yesai Wu, Yankai Lin, Zhiyuan Liu, Maosong Sun

Recent advancements in large language models (LLMs) have driven a revolutionary paradigm shift in process automation from Robotic Process Automation to Agentic Process Automation by automating the workflow orchestration procedure based on LLMs. However, existing LLMs (even the advanced OpenAI GPT-4o) are confined to achieving satisfactory capability in workflow orchestration. To address this limitation, we present WorkflowLLM, a data-centric framework elaborately designed to enhance the capability of LLMs in workflow orchestration. It first constructs a large-scale fine-tuning dataset WorkflowBench with 106, 763 samples, covering 1, 503 APIs from 83 applications across 28 categories. Specifically, the construction process can be divided into three phases: (1) Data Collection: we collect real-world workflow data from Apple Shortcuts and RoutineHub, transcribing them into Python-style code. We further equip them with generated hierarchical thought via GPT-4o-mini. (2) Query Expansion: we prompt GPT-4o-mini to generate more task queries to enrich the diversity and complexity of workflows. (3) Workflow Generation: we leverage an annotator model trained on collected data to generate workflows for synthesized queries. Finally, we merge the synthetic samples that pass quality confirmation with the collected samples to obtain the WorkflowBench. Based on WorkflowBench, we fine-tune Llama-3.1-8B to obtain WorkflowLlama. Our experiments show that WorkflowLlama demonstrates a strong capacity to orchestrate complex workflows, while also achieving notable generalization performance on previously unseen APIs. Additionally, WorkflowBench exhibits robust zero-shot generalization capabilities on an out-of-distribution task planning dataset, T-Eval. Our data and code are available at https://github.com/OpenBMB/WorkflowLLM.

Deep Learning · Generative Models and Autoencoders

Shuangqi Li, Hieu Le, Jingyi Xu, Mathieu Salzmann

Text-to-image diffusion models have demonstrated remarkable capability in generating realistic images from arbitrary text prompts. However, they often produce inconsistent results for compositional prompts such as "two dogs" or "a penguin on the right of a bowl". Understanding these inconsistencies is crucial for reliable image generation. In this paper, we highlight the significant role of initial noise in these inconsistencies, where certain noise patterns are more reliable for compositional prompts than others. Our analyses reveal that different initial random seeds tend to guide the model to place objects in distinct image areas, potentially adhering to specific patterns of camera angles and image composition associated with the seed. To improve the model's compositional ability, we propose a method for mining these reliable cases, resulting in a curated training set of generated images without requiring any manual annotation. By fine-tuning text-to-image models on these generated images, we significantly enhance their compositional capabilities. For numerical composition, we observe relative increases of 29.3\% and 19.5\% for Stable Diffusion and PixArt-$\alpha$, respectively. Spatial composition sees even larger gains, with 60.7\% for Stable Diffusion and 21.1\% for PixArt-$\alpha$.

Deep Learning · Large Language Models

Guoxin Chen, Zhong Zhang, Xin Cong, Fangda Guo, Yesai Wu, Yankai Lin, Wenzheng Feng, Yasheng Wang

Tool learning enables large language models (LLMs) to interact with external tools and APIs, greatly expanding the application scope of LLMs. However, due to the dynamic nature of external environments, these tools and APIs may become outdated over time, preventing LLMs from correctly invoking tools. Existing research primarily focuses on static environments and overlooks this issue, limiting the adaptability of LLMs in real-world applications. In this paper, we propose ToolEVO, a novel framework designed to enhance the adaptive and reflective capabilities of LLMs against tool variability. By leveraging Monte Carlo Tree Search, ToolEVO facilitates active exploration and interaction of LLMs within dynamic environments, allowing for autonomous self-reflection and self-updating of tool usage based on environmental feedback. Additionally, we introduce ToolQA-D, a benchmark specifically designed to evaluate the impact of tool variability. Extensive experiments demonstrate the effectiveness and stability of our approach, highlighting the importance of adaptability to tool variability for effective tool learning.

Social Aspects · Accountability, Transparency and Interpretability

Shuhan Zhang, Wendi Ren, Shuang Li

In this study, we propose a novel rule-based interpretable choice model, {\bf Logic-Logit}, designed to effectively learn and explain human choices. Choice models have been widely applied across various domains—such as commercial demand forecasting, recommendation systems, and consumer behavior analysis—typically categorized as parametric, nonparametric, or deep network-based. While recent innovations have favored neural network approaches for their computational power, these flexible models often involve large parameter sets and lack interpretability, limiting their effectiveness in contexts where transparency is essential.Previous empirical evidence shows that individuals usually use {\it heuristic decision rules} to form their consideration sets, from which they then choose. These rules are often represented as {\it disjunctions of conjunctions} (i.e., OR-of-ANDs). These rules-driven, {\it consider-then-choose} decision processes enable people to quickly screen numerous alternatives while reducing cognitive and search costs. Motivated by this insight, our approach leverages logic rules to elucidate human choices, providing a fresh perspective on preference modeling. We introduce a unique combination of column generation techniques and the Frank-Wolfe algorithm to facilitate efficient rule extraction for preference modeling—a process recognized as NP-hard. Our empirical evaluation, conducted on both synthetic datasets and real-world data from commercial and healthcare domains, demonstrates that Logic-Logit significantly outperforms baseline models in terms of interpretability and accuracy.

Pei Wang, Yanan Wu, Zekun Wang, JIAHENG LIU, Xiaoshuai Song, Z.Y. Peng, ken deng, Chenchen Zhang, JiakaiWang, Junran Peng 等

Large Language Models (LLMs) have displayed massive improvements in reason- ing and decision-making skills and can hold natural conversations with users. Recently, many tool-use benchmark datasets have been proposed. However, existing datasets have the following limitations: (1). Insufficient evaluation scenarios (e.g., only cover limited tool-use scenes). (2). Extensive evaluation costs (e.g., GPT API costs). To address these limitations, in this work, we propose a multi-granularity tool-use benchmark for large language models called MTU-Bench. For the "multi-granularity" property, our MTU-Bench covers five tool usage scenes (i.e., single-turn and single-tool, single-turn and multiple-tool, multiple-turn and single-tool, multiple-turn and multiple-tool, and out-of-distribution tasks). Besides, all evaluation metrics of our MTU-Bench are based on the prediction results and the ground truth without using any GPT or human evaluation metrics. Moreover, our MTU-Bench is collected by transforming existing high-quality datasets to simulate real-world tool usage scenarios, and we also propose an instruction dataset called MTU-Instruct data to enhance the tool-use abilities of existing LLMs. Comprehensive experimental results demonstrate the effectiveness of our MTU-Bench.

Deep Learning · Large Language Models

Jiahui Gao, Renjie Pi, Jipeng Zhang, Jiacheng Ye, Wanjun Zhong, Yufei Wang, Lanqing HONG, Jianhua Han, Hang Xu, Zhenguo Li 等

Large language models (LLMs) have shown remarkable proficiency in human-level reasoning and generation capabilities, which encourages extensive research on their application in mathematical problem solving. However, current work has been largely focused on text-based mathematical problems, with limited investigation in problems involving multi-modal geometric information. Addressing this gap, we aim to enable LLMs to solve geometric problems by understanding image input. We first identify the limitations of current Multimodal Large Language Models (MLLMs) in this area: they struggle to accurately comprehend basic geometric elements and their relationships. To address these challenges, we leverage the inherent attribute of logical structure compactness in geometric figures, utilizing text-only Large Language Models (LLMs) to curate a comprehensive multimodal geometry dataset. This dataset, named Geo170k, contains more than 170K geometric image-caption and question-answer pairs. Utilizing the Geo170k dataset, we introduce G-LLaVA, a model that demonstrates exceptional performance in solving geometric problems. It significantly outperforms GPT4-V on the geometry task of MathVista benchmark with only 7B parameters.

Deep Learning · Generative Models and Autoencoders

Minjae Jeong, Yechan Hwang, Jaejin Lee, Sungyoon Jung, Won Hwa Kim

Text-to-motion generation has significant potential in a wide range of applications including animation, robotics, and AR/VR. While recent works on masked motion models are promising, the task remains challenging due to the inherent ambiguity in text and the complexity of human motion dynamics. To overcome the issues, we propose a novel text-to-motion generation framework that integrates two key components: Hard Token Mining (HTM) and a Hierarchical Generative Masked Motion Model (HGM³). Our HTM identifies and masks challenging regions in motion sequences and directs the model to focus on hard-to-learn components for efficacy. Concurrently, the hierarchical model uses a semantic graph to represent sentences at different granularity, allowing the model to learn contextually feasible motions. By leveraging a shared-weight masked motion model, it reconstructs the same sequence under different conditioning levels and facilitates comprehensive learning of complex motion patterns. During inference, the model progressively generates motions by incrementally building up coarse-to-fine details. Extensive experiments on benchmark datasets, including HumanML3D and KIT-ML, demonstrate that our method outperforms existing methods in both qualitative and quantitative measures for generating context-aware motions.

Deep Learning · Large Language Models

Shubham Toshniwal, Wei Du, Ivan Moshkov, Branislav Kisacanin, Alexan Ayrapetyan, Igor Gitman

Mathematical reasoning continues to be a critical challenge in large language model (LLM) development with significant interest. However, most of the cutting-edge progress in mathematical reasoning with LLMs has become closed-source due to lack of access to training data. This lack of data access limits researchers from understanding the impact of different choices for synthesizing and utilizing the data. With the goal of creating a high-quality finetuning (SFT) dataset for math reasoning, we conduct careful ablation experiments on data synthesis using the recently released Llama3.1 family of models. Our experiments show that: (a) solution format matters, with excessively verbose solutions proving detrimental to SFT performance, (b) data generated by a strong teacher outperforms on-policy data generated by a weak student model, (c) SFT is robust to low-quality solutions, allowing for imprecise data filtering, and (d) question diversity is crucial for achieving data scaling gains. Based on these insights, we create the OpenMathInstruct-2 dataset which consists of 14M question-solution pairs (≈ 600K unique questions), making it nearly eight times larger than the previous largest open-source math reasoning dataset. Finetuning the Llama-3.1-8B-Base using OpenMathInstruct-2 outperforms Llama3.1-8B-Instruct on MATH by an absolute 15.9% (51.9% → 67.8%). Finally, to accelerate the open-source efforts, we release the code, the finetuned models, and the OpenMathInstruct-2 dataset under a commercially permissive license.

Reinforcement Learning · Multi-agent

Jie Liu, Pan Zhou, Yingjun Du, Ah-Hwee Tan, Cees G Snoek, Jan-jakob Sonke, Efstratios Gavves

In this work, we address the cooperation problem among large language model (LLM) based embodied agents, where agents must cooperate to achieve a common goal. Previous methods often execute actions extemporaneously and incoherently, without long-term strategic and cooperative planning, leading to redundant steps, failures, and even serious repercussions in complex tasks like search-and-rescue missions where discussion and cooperative plan are crucial. To solve this issue, we propose Cooperative Plan Optimization (CaPo) to enhance the cooperation efficiency of LLM-based embodied agents. Inspired by human cooperation schemes, CaPo improves cooperation efficiency with two phases: 1) meta plan generation, and 2) progress-adaptive meta plan and execution. In the first phase, all agents analyze the task, discuss, and cooperatively create a meta-plan that decomposes the task into subtasks with detailed steps, ensuring a long-term strategic and coherent plan for efficient coordination. In the second phase, agents execute tasks according to the meta-plan and dynamically adjust it based on their latest progress (e.g., discovering a target object) through multi-turn discussions. This progress-based adaptation eliminates redundant actions, improving the overall cooperation efficiency of agents. Experimental results on the ThreeDworld Multi-Agent Transport and Communicative Watch-And-Help tasks demonstrate CaPo's much higher task completion rate and efficiency compared with state-of-the-arts. The code is released at https://github.com/jliu4ai/CaPo.

Deep Learning · Generative Models and Autoencoders

Yongxing Zhang, Donglin Yang, Renjie Liao

The group of permutations $S_n$, also known as the finite symmetric groups, are essential in fields such as combinatorics, physics, and chemistry. However, learning a probability distribution over $S_n$ poses significant challenges due to its intractable size and discrete nature. In this paper, we introduce *SymmetricDiffusers*, a novel discrete diffusion model that simplifies the task of learning a complicated distribution over $S_n$ by decomposing it into learning simpler transitions of the reverse diffusion using deep neural networks. We identify the riffle shuffle as an effective forward transition and provide empirical guidelines for selecting the diffusion length based on the theory of random walks on finite groups. Additionally, we propose a generalized Plackett-Luce (PL) distribution for the reverse transition, which is provably more expressive than the PL distribution. We further introduce a theoretically grounded "denoising schedule" to improve sampling and learning efficiency. Extensive experiments show that our model achieves state-of-the-art or comparable performance on solving tasks including sorting 4-digit MNIST images, jigsaw puzzles, and traveling salesman problems. Our code is released at <https://github.com/DSL-Lab/SymmetricDiffusers>.

Liang CHEN, Li Shen, Yang Deng, Xiaoyan Zhao, Bin Liang, Kam-Fai Wong

The in-context learning (ICL) capability of large language models (LLMs) enables them to perform challenging tasks using provided demonstrations. However, ICL is highly sensitive to the ordering of demonstrations, leading to instability in predictions. This paper shows that this vulnerability can be exploited to design a natural attack—difficult for model providers to detect—that achieves nearly 80% success rate on LLaMA-3 by simply permuting the demonstrations. Existing mitigation methods primarily rely on post-processing and fail to enhance the model's inherent robustness to input permutations, raising concerns about safety and reliability of LLMs. To address this issue, we propose Permutation-resilient learning (PEARL), a novel framework based on distributionally robust optimization (DRO), which optimizes model performance against the worst-case input permutation. Specifically, PEARL consists of a permutation-proposal network (P-Net) and the LLM. The P-Net generates the most challenging permutations by treating it as an optimal transport problem, which is solved using an entropy-constrained Sinkhorn algorithm. Through minimax optimization, the P-Net and the LLM iteratively optimize against each other, progressively improving the LLM's robustness. Experiments on synthetic pre-training and real-world instruction tuning tasks demonstrate that PEARL effectively mitigates permutation attacks and enhances performance. Notably, despite being trained on fewer shots and shorter contexts, PEARL achieves performance gains of up to 40% when scaled to many-shot and long-context scenarios, highlighting its efficiency and generalization capabilities.