The very challenging task of learning solution operators of PDEs on arbitrary domains accurately and efficiently is of vital importance to engineering and industrial simulations. Despite the existence of many operator learning algorithms to approximate such PDEs, we find that accurate models are not necessarily computationally efficient and vice versa. We address this issue by proposing a geometry aware operator transformer (GAOT) for learning PDEs on arbitrary domains. GAOT combines novel multiscale attentional graph neural operator encoders and decoders, together with geometry embeddings and (vision) transformer processors to accurately map information about the domain and the inputs into a robust approximation of the PDE solution. Multiple innovations in the implementation of GAOT also ensure computational efficiency and scalability. We demonstrate this significant gain in both accuracy and efficiency of GAOT over several baselines on a large number of learning tasks from a diverse set of PDEs, including achieving state of the art performance on a large scale three-dimensional industrial CFD dataset.
We address the optimization problem of simultaneously minimizing multiple objective functionals over a family of probability distributions. This type of Multi-Objective Distributional Optimization commonly arises in machine learning and statistics, with applications in areas such as multiple target sampling, multi-task learning, and multi-objective generative modeling. To solve this problem, we propose an iterative particle-based algorithm, which we call Muliple Wasserstein Gradient Descent (MWGraD), which constructs a flow of intermediate empirical distributions, each being represented by a set of particles, which gradually minimize the multiple objective functionals simultaneously. Specifically, MWGraD consists of two key steps at each iteration. First, it estimates the Wasserstein gradient for each objective functional based on the current particles. Then, it aggregates these gradients into a single Wasserstein gradient using dynamically adjusted weights and updates the particles accordingly. In addition, we provide theoretical analysis and present experimental results on both synthetic and real-world datasets, demonstrating the effectiveness of MWGraD.
The ever-growing size of neural networks poses serious challenges on resource-constrained devices, such as embedded sensors. Compression algorithms that reduce their size can mitigate these problems, provided that model performance stays close to the original. We propose a novel post-training compression framework that combines rate-aware quantization with entropy coding by (1) extending the well-known layer-wise loss by a quadratic rate estimation, and (2) providing locally exact solutions to this modified objective following the Optimal Brain Surgeon (OBS) method. Our method allows for very fast decoding and is compatible with arbitrary quantization grids. We verify our results empirically by testing on various computer-vision networks, achieving a 20-40\% decrease in bit rate at the same performance as the popular compression algorithm NNCodec. Our code is available at https://github.com/Conzel/cerwu.
Quantization and fine-tuning are crucial for deploying large language models (LLMs) on resource-constrained edge devices. However, fine-tuning quantized models presents significant challenges, primarily stemming from: First, the mismatch in data types between the low-precision quantized weights (e.g., 4-bit) and the high-precision adaptation weights (e.g., 16-bit). This mismatch limits the computational efficiency advantage offered by quantized weights during inference. Second, potential accuracy degradation when merging these high-precision adaptation weights into the low-precision quantized weights, as the adaptation weights often necessitate approximation or truncation. Third, as far as we know, no existing methods support the lossless merging of adaptation while adjusting all quantized weights. To address these challenges, we introduce lossless ternary adaptation for quantization-aware fine-tuning (LoTA-QAF). This is a novel fine-tuning method specifically designed for quantized LLMs, enabling the lossless merging of ternary adaptation weights into quantized weights and the adjustment of all quantized weights. LoTA-QAF operates through a combination of: i) A custom-designed ternary adaptation (TA) that aligns ternary weights with the quantization grid and uses these ternary weights to adjust quantized weights. ii) A TA-based mechanism that enables the lossless merging of adaptation weights. iii) Ternary signed gradient descent (t-SignSGD) for updating the TA weights. We apply LoTA-QAF to Llama-3.1/3.3 and Qwen-2.5 model families and validate its effectiveness on several downstream tasks. On the MMLU benchmark, our method effectively recovers performance for quantized models, surpassing 16-bit LoRA by up to 5.14\%. For task-specific fine-tuning, 16-bit LoRA achieves superior results, but LoTA-QAF still outperforms other methods.
Transformers have achieved state-of-the-art performance across various tasks, but suffer from a notable quadratic complexity in sequence length due to the attention mechanism. In this work, we propose MonarchAttention -- a novel approach to sub-quadratic attention approximation via Monarch matrices, an expressive class of structured matrices. Based on the variational form of softmax, we describe an efficient optimization-based algorithm to compute an approximate projection of softmax attention onto the class of Monarch matrices with $\Theta(N\sqrt{N} d)$ computational complexity and $\Theta(Nd)$ memory/IO complexity. Unlike previous approaches, MonarchAttention is both (1) transferable, yielding minimal performance loss with no additional training, even when replacing every attention layer of the transformer, and (2) hardware-efficient, utilizing the highest-throughput tensor core units on modern GPUs. With optimized kernels, MonarchAttention achieves substantial speed-ups in wall-time over FlashAttention-2: $1.4\times$ for shorter sequences $(N=256)$, $4.5\times$ for medium-length sequences $(N=4K)$, and $8.2\times$ for longer sequences $(N=16K)$. We demonstrate the quality of MonarchAttention on diverse tasks and architectures in vision and language problems, showing that it flexibly and accurately approximates softmax attention in a variety of contexts. Our code is available at https://github.com/cjyaras/monarch-attention.
Nowadays, real-world data, including graph-structure data, often arrives in a streaming manner, which means that learning systems need to continuously acquire new knowledge without forgetting previously learned information. Although substantial existing works attempt to address catastrophic forgetting in graph machine learning, they are all based on training from scratch with streaming data. With the rise of pretrained models, an increasing number of studies have leveraged their strong generalization ability for continual learning. Therefore, in this work, we attempt to answer whether large language models (LLMs) can mitigate catastrophic forgetting in Graph Continual Learning (GCL). We first point out that current experimental setups for GCL have significant flaws, as the evaluation stage may lead to task ID leakage. Then, we evaluate the performance of LLMs in more realistic scenarios and find that even minor modifications can lead to outstanding results. Finally, based on extensive experiments, we propose a simple-yet-effective method, Simple Graph Continual Learning (SimGCL), that surpasses the previous state-of-the-art GNN-based baseline by around 20% under the rehearsal-free constraint. To facilitate reproducibility, we have developed an easy-to-use benchmark LLM4GCL for training and evaluating existing GCL methods. The code is available at: https://github.com/ZhixunLEE/LLM4GCL.
We introduce an encoder-only approach to learn the evolution operators of large-scale non-linear dynamical systems, such as those describing complex natural phenomena. Evolution operators are particularly well-suited for analyzing systems that exhibit complex spatio-temporal patterns and have become a key analytical tool across various scientific communities. As terabyte-scale weather datasets and simulation tools capable of running millions of molecular dynamics steps per day are becoming commodities, our approach provides an effective tool to make sense of them from a data-driven perspective. The core of it lies in a remarkable connection between self-supervised representation learning methods and the recently established learning theory of evolution operators. To show the usefulness of the proposed method, we test it across multiple scientific domains: explaining the folding dynamics of small proteins, the binding process of drug-like molecules in host sites, and autonomously finding patterns in climate data. Code and data to reproduce the experiments are made available open source.
Inspired by the power of large language models (LLMs), our research adapts them to quantum federated learning (QFL) to boost efficiency and performance. We propose a federated fine-tuning method that distills an LLM within QFL, allowing each client to locally adapt the model to its own data while preserving privacy and reducing unnecessary global updates. The fine-tuned LLM also acts as a reinforcement agent, optimizing QFL by adjusting optimizer steps, cutting down communication rounds, and intelligently selecting clients. Experiments show significant efficiency gains. We pioneer a synergy between LLM and QFL, offering: i) practical efficiency: Reduced communication costs and faster convergence. ii) theoretical rigor: Provable guarantees for adaptive federated optimization. iii) scalability: PEFT methods (LoRA, QLoRA) enable deployment on resource-constrained quantum devices. Code implementation is available here 1.
Low-Rank Adaptation (LoRA) is widely adopted for downstream fine-tuning of foundation models due to its efficiency and zero additional inference cost. Many real-world applications require foundation models to specialize in multiple tasks simultaneously, motivating the need for efficient multi-task adaptation. While recent approaches integrate LoRA with mixture-of-experts (MoE) to address this, the use of routers prevents parameter mergeability, which increases inference overhead and hinders unified multi-task adaptation, thereby limiting deployment practicality. In this work, we propose ThanoRA, a Task Heterogeneity-Aware Multi-Task Low-Rank Adaptation framework that enables multi-task adaptation while preserving the inference efficiency of LoRA. ThanoRA jointly models task heterogeneity and mitigates subspace interference throughout training. Specifically, motivated by inherent differences in complexity and heterogeneity across tasks, ThanoRA constructs task-specific LoRA subspaces at initialization, enabling fine-grained knowledge injection aligned with task heterogeneity. Furthermore, to prevent task interference and subspace collapse during multi-task training, ThanoRA introduces a subspace-preserving regularization that maintains the independence of task-specific representations. With the synergy of both components, ThanoRA enables efficient and unified multi-task adaptation. Extensive experiments across multimodal and text-only benchmarks under varying multi-task mixtures demonstrate that ThanoRA consistently achieves robust and superior performance over strong baselines without introducing additional inference overhead. Our code is publicly available at: https://github.com/LiangJian24/ThanoRA.
The Area Under the ROC Curve (AUC) is a key metric for classification, especially under class imbalance, with growing research focus on optimizing AUC over accuracy in applications like medical image analysis and deepfake detection. This leads to fairness in AUC optimization becoming crucial as biases can impact protected groups. While various fairness mitigation techniques exist, fairness considerations in AUC optimization remain in their early stages, with most research focusing on improving AUC fairness under the assumption of clean protected groups. However, these studies often overlook the impact of noisy protected groups, leading to fairness violations in practice. To address this, we propose the first robust AUC fairness approach under noisy protected groups with fairness theoretical guarantees using distributionally robust optimization. Extensive experiments on tabular and image datasets show that our method outperforms state-of-the-art approaches in preserving AUC fairness. The code is in https://github.com/Purdue-M2/AUC_Fairness_with_Noisy_Groups.
Deep learning models perform poorly when domain shifts exist between training and test data. Test-time adaptation (TTA) is a paradigm to mitigate this issue by adapting pre-trained models using only unlabeled test samples. However, existing TTA methods can fail under severe domain shifts, while recent active TTA approaches requiring full-class labels are impractical due to high labeling costs. To address this issue, we introduce a new setting of TTA with binary feedback. This setting uses a few binary feedback inputs from annotators to indicate whether model predictions are correct, thereby significantly reducing the labeling burden of annotators. Under the setting, we propose BiTTA, a novel dual-path optimization framework that leverages reinforcement learning to balance binary feedback-guided adaptation on uncertain samples with agreement-based self-adaptation on confident predictions. Experiments show BiTTA achieves 13.3%p accuracy improvements over state-of-the-art baselines, demonstrating its effectiveness in handling severe distribution shifts with minimal labeling effort. The source code is available at https://github.com/taeckyung/BiTTA.
Training data attribution (TDA) methods aim to measure how training data impacts a model's predictions. While gradient-based attribution methods, such as influence functions, offer theoretical grounding, their computational costs make them impractical for large-scale applications. Representation-based approaches are far more scalable, but typically rely on heuristic embeddings that are not optimized for attribution, limiting their fidelity. To address these challenges, we propose AirRep, a scalable, representation-based approach that closes this gap by learning task-specific and model-aligned representations optimized explicitly for TDA. AirRep introduces two key innovations: a trainable encoder tuned for attribution quality, and an attention-based pooling mechanism that enables accurate estimation of group-wise influence. We train AirRep using a ranking objective over automatically constructed training subsets labeled by their empirical effect on target predictions. Experiments on instruction-tuned LLMs demonstrate that AirRep achieves performance on par with state-of-the-art gradient-based approaches while being nearly two orders of magnitude more efficient at inference time. Further analysis highlights its robustness and generalization across tasks and models. Our code is available at https://github.com/sunnweiwei/AirRep.
Graphs are a widely used paradigm for representing non-Euclidean data, with applications ranging from social network analysis to biomolecular prediction. Conventional graph learning approaches typically rely on fixed structural assumptions or fully observed data, limiting their effectiveness in more complex, noisy, or evolving settings. Consequently, real-world graph data often violates the assumptions of traditional graph learning methods, in particular, it leads to four fundamental challenges: (1) Incompleteness, real-world graphs have missing nodes, edges, or attributes; (2) Imbalance, the distribution of the labels of nodes or edges and their structures for real-world graphs are highly skewed; (3) Cross-domain Heterogeneity, graphs from different domains exhibit incompatible feature spaces or structural patterns; and (4) Dynamic Instability, graphs evolve over time in unpredictable ways. Recent advances in Large Language Models (LLMs) offer the potential to tackle these challenges by leveraging rich semantic reasoning and external knowledge. This survey provides a comprehensive review of how LLMs can be integrated with graph learning to address the aforementioned challenges. For each challenge, we review both traditional solutions and modern LLM-driven approaches, highlighting how LLMs contribute unique advantages. Finally, we discuss open research questions and promising future directions in this emerging interdisciplinary field. To support further exploration, we have curated a repository of recent advances on graph learning challenges: https://github.com/limengran98/Awesome-Literature-Graph-Learning-Challenges.
Time-series forecasting plays a critical role in many real-world applications. Although increasingly powerful models have been developed and achieved superior results on benchmark datasets, through a fine-grained sample-level inspection, we find that (i) no single model consistently outperforms others across different test samples, but instead (ii) each model excels in specific cases. These findings prompt us to explore how to adaptively leverage the distinct strengths of various forecasting models for different samples. We introduce TimeFuse, a framework for collective time-series forecasting with sample-level adaptive fusion of heterogeneous models. TimeFuse utilizes meta-features to characterize input time series and trains a learnable fusor to predict optimal model fusion weights for any given input. The fusor can leverage samples from diverse datasets for joint training, allowing it to adapt to a wide variety of temporal patterns and thus generalize to new inputs, even from unseen datasets. Extensive experiments demonstrate the effectiveness of TimeFuse in various long-/short-term forecasting tasks, achieving near-universal improvement over the state-of-the-art individual models. Code is available at https://github.com/ZhiningLiu1998/TimeFuse.
We study the problem of selecting a subset from a large action space shared by a family of bandits, with the goal of achieving performance nearly matching that of using the full action space. We assume that similar actions tend to have related payoffs, modeled by a Gaussian process. To exploit this structure, we propose a simple epsilon-net algorithm to select a representative subset. We provide theoretical guarantees for its performance and compare it empirically to Thompson Sampling and Upper Confidence Bound.
This study presents a novel approach for decomposing urban water demand patterns using Skewed Gaussian Distributions (SGD) to derive behavioral insights and support operational planning. Hourly demand profiles contain critical information for both long-term infrastructure design and daily operations, influencing network pressures, water quality, energy consumption, and overall reliability. By breaking down each daily demand curve into a baseline component and distinct peak components, the proposed SGD method characterizes each peak with interpretable parameters, including peak amplitude, timing (mean), spread (duration), and skewness (asymmetry), thereby reconstructing the observed pattern and uncovering latent usage dynamics. This detailed peak-level decomposition enables both operational applications, e.g. anomaly and leakage detection, real-time demand management, and strategic analyses, e.g. identifying behavioral shifts, seasonal influences, or policy impacts on consumption patterns. Unlike traditional symmetric Gaussian or purely statistical time-series models, SGDs explicitly capture asymmetric peak shapes such as sharp morning surges followed by gradual declines, improving the fidelity of synthetic pattern generation and enhancing the detection of irregular consumption behavior. The method is demonstrated on several real-world datasets, showing that SGD outperforms symmetric Gaussian models in reconstruction accuracy, reducing root-mean-square error by over 50% on average, while maintaining physical interpretability. The SGD framework can also be used to construct synthetic demand scenarios by designing daily peak profiles with chosen characteristics. All implementation code is publicly available at: https://github.com/Relkayam/water-demand-decomposition-sgd
There is a large ongoing scientific effort in mechanistic interpretability to map embeddings and internal representations of AI systems into human-understandable concepts. A key element of this effort is the linear representation hypothesis, which posits that neural representations are sparse linear combinations of `almost-orthogonal' direction vectors, reflecting the presence or absence of different features. This model underpins the use of sparse autoencoders to recover features from representations. Moving towards a fuller model of features, in which neural representations could encode not just the presence but also a potentially continuous and multidimensional value for a feature, has been a subject of intense recent discourse. We describe why and how a feature might be represented as a manifold, demonstrating in particular that cosine similarity in representation space may encode the intrinsic geometry of a feature through shortest, on-manifold paths, potentially answering the question of how distance in representation space and relatedness in concept space could be connected. The critical assumptions and predictions of the theory are validated on text embeddings and token activations of large language models.
In this paper, we propose a robust and reinforcement-learning-enhanced network intrusion detection system (NIDS) designed for class-imbalanced and few-shot attack scenarios in Industrial Internet of Things (IIoT) environments. Our model integrates a TabTransformer for effective tabular feature representation with Proximal Policy Optimization (PPO) to optimize classification decisions via policy learning. Evaluated on the TON\textunderscore IoT benchmark, our method achieves a macro F1-score of 97.73\% and accuracy of 98.85\%. Remarkably, even on extremely rare classes like man-in-the-middle (MITM), our model achieves an F1-score of 88.79\%, showcasing strong robustness and few-shot detection capabilities. Extensive ablation experiments confirm the complementary roles of TabTransformer and PPO in mitigating class imbalance and improving generalization. These results highlight the potential of combining transformer-based tabular learning with reinforcement learning for real-world NIDS applications.
In Transformer architectures, tokens\textemdash discrete units derived from raw data\textemdash are formed by segmenting inputs into fixed-length chunks. Each token is then mapped to an embedding, enabling parallel attention computations while preserving the input's essential information. Due to the quadratic computational complexity of transformer self-attention mechanisms, token reduction has primarily been used as an efficiency strategy. This is especially true in single vision and language domains, where it helps balance computational costs, memory usage, and inference latency. Despite these advances, this paper argues that token reduction should transcend its traditional efficiency-oriented role in the era of large generative models. Instead, we position it as a fundamental principle in generative modeling, critically influencing both model architecture and broader applications. Specifically, we contend that across vision, language, and multimodal systems, token reduction can: (i) facilitate deeper multimodal integration and alignment, (ii) mitigate "overthinking" and hallucinations, (iii) maintain coherence over long inputs, and (iv) enhance training stability, etc. We reframe token reduction as more than an efficiency measure. By doing so, we outline promising future directions, including algorithm design, reinforcement learning-guided token reduction, token optimization for in-context learning, and broader ML and scientific domains. We highlight its potential to drive new model architectures and learning strategies that improve robustness, increase interpretability, and better align with the objectives of generative modeling.
Arabic poetry is one of the richest and most culturally rooted forms of expression in the Arabic language, known for its layered meanings, stylistic diversity, and deep historical continuity. Although large language models (LLMs) have demonstrated strong performance across languages and tasks, their ability to understand Arabic poetry remains largely unexplored. In this work, we introduce \emph{Fann or Flop}, the first benchmark designed to assess the comprehension of Arabic poetry by LLMs in 12 historical eras, covering 14 core poetic genres and a variety of metrical forms, from classical structures to contemporary free verse. The benchmark comprises a curated corpus of poems with explanations that assess semantic understanding, metaphor interpretation, prosodic awareness, and cultural context. We argue that poetic comprehension offers a strong indicator for testing how good the LLM understands classical Arabic through Arabic poetry. Unlike surface-level tasks, this domain demands deeper interpretive reasoning and cultural sensitivity. Our evaluation of state-of-the-art LLMs shows that most models struggle with poetic understanding despite strong results on standard Arabic benchmarks. We release "Fann or Flop" along with the evaluation suite as an open-source resource to enable rigorous evaluation and advancement for Arabic language models. Code is available at: https://github.com/mbzuai-oryx/FannOrFlop.