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Applications · Health

Deli Yu, Shengzhi Wang, Kai WU, Xiaozhong Ji, Bo Cui, Jieqiong Cao, Huichao Wang, Boyuan Jiang, Xu Wang, Qian Xu 等

Body-surface health conditions, spanning diverse clinical departments, represent some of the most frequent diagnostic scenarios and a primary target for medical multimodal large language models (MLLMs). Yet existing medical benchmarks are either built from publicly available sources with limited expert curation or focus narrowly on disease classification, failing to reflect the stepwise recognition and reasoning processes physicians follow in real practice. To address this gap, we introduce MedLesionVQA, the first benchmark explicitly designed to evaluate MLLMs on the visual diagnostic workflow for body-surface conditions in large scale. All questions are derived from authentic clinical visual diagnosis scenarios and verified by medical experts with over 20 years of experience, while the data are drawn from 10k+ real patient visits, ensuring authenticity, clinical reality and diversity. MedLesionVQA consists of 12K in-house images (never publicly leaked) and 19K expert-verified question–answer pairs, with fine-grained annotations of 94 lesion types, 110 body regions, and 96 diseases. We evaluate 20+ state-of-the-art MLLMs against human physicians: the best model reaches 56.2% accuracy, far below primary physicians (61.4%) and senior specialists (73.2%). These results expose the persistent gap between MLLMs and clinical expertise, underscoring the need for the multimodal benchmarks to drive trustworthy medical AI. The dataset can be found in https://github.com/bytedance/MedLesionVQA.

Applications · Language, Speech and Dialog

Martijn Bartelds, Ananjan Nandi, Moussa Koulako Bala Doumbouya, Dan Jurafsky, Tatsunori Hashimoto, Karen Livescu

Modern deep learning models often achieve high overall performance, but consistently fail on specific subgroups. Group distributionally robust optimization (group DRO) addresses this problem by minimizing the worst-group loss, but it fails when group losses misrepresent performance differences between groups. This is common in domains like speech, where the widely used connectionist temporal classification (CTC) loss not only scales with input length but also varies with linguistic and acoustic properties, leading to spurious differences between group losses. We present CTC-DRO, which addresses the shortcomings of the group DRO objective by smoothing the group weight update to prevent overemphasis on consistently high-loss groups, while using input length-matched batching to mitigate CTC's scaling issues. We evaluate CTC-DRO on the task of multilingual automatic speech recognition (ASR) across five language sets from the diverse ML-SUPERB 2.0 benchmark. CTC-DRO consistently outperforms group DRO and CTC-based baseline models, reducing the worst-language error by up to 47.1% and the average error by up to 32.9%. CTC-DRO can be applied to ASR with minimal computational costs, and, while motivated by multilingual ASR, offers the potential for reducing group disparities in other domains with similar challenges.

Applications · Time Series

Ruirui Wang, Yanke Li, Manuel Günther, Diego Paez-Granados

Healthcare data, such as Intensive Care Unit (ICU) records, comprise heterogeneous multivariate time series sampled at irregular intervals with pervasive missingness. However, clinical applications demand predictive models that are both accurate and interpretable. We present our Graph Attention-based Relational Learning for Intensive Care (GARLIC) model, a novel neural network architecture that imputes missing data through a learnable exponential-decay encoder, captures inter-sensor dependencies via time-lagged summary graphs, and fuses global patterns with cross-dimensional sequential attention. All attention weights and graph edges are learned end-to-end to serve as built-in observation-, signal-, and edge-level explanations. To reconcile auxiliary reconstruction and primary classification objectives, we developed an alternating decoupled optimization scheme that stabilizes training. On three ICU benchmarks (PhysioNet 2012 \& 2019, MIMIC-III), GARLIC sets the new state of the art in outcome prediction, significantly improving AUROC and AUPRC over best-performing baselines at comparable computational cost. Ablation studies confirm the contribution of each module, and feature-removal trials validate the fidelity of importance attribution through a monotonic performance drop (full > top 50\% > random 50\% > bottom 50\%). Real-time case studies demonstrate actionable risk warnings with transparent explanations, marking a significant advance toward accurate, explainable deep learning for irregularly sampled ICU time series data. Moreover, we demonstrated GARLIC's superiority in data imputation and classification on various time-series datasets beyond the ICU domain, showing its generalizability and applicability to broader tasks.

Computer Vision · Classification and Understanding

Alexander Baumann, Leonardo Ayala, Silvia Seidlitz, Jan Sellner, Alexander Studier-Fischer, Berkin Özdemir, Lena Maier-Hein, Slobodan Ilic

Spectral imaging offers promising applications across diverse domains, including medicine and urban scene understanding, and is already established as a critical modality in remote sensing. However, variability in channel dimensionality and captured wavelengths among spectral cameras impede the development of AI-driven methodologies, leading to camera-specific models with limited generalizability and inadequate cross-camera applicability. To address this bottleneck, we introduce CARL, a model for Camera-Agnostic Representation Learning across RGB, multispectral, and hyperspectral imaging modalities. To enable the conversion of a spectral image with any channel dimensionality to a camera-agnostic representation, we introduce a novel spectral encoder, featuring a self-attention-cross-attention mechanism, to distill salient spectral information into learned spectral representations. Spatio-spectral pre-training is achieved with a novel feature-based self-supervision strategy tailored to CARL. Large-scale experiments across the domains of medical imaging, autonomous driving, and satellite imaging demonstrate our model's unique robustness to spectral heterogeneity, outperforming on datasets with simulated and real-world cross-camera spectral variations. The scalability and versatility of the proposed approach position our model as a backbone for future spectral foundation models. Code and model weights are publicly available at https://github.com/IMSY-DKFZ/CARL.

Theory · Interpretability and Visualization

Joshua Melander, Zaki Alaoui, Shenghua Liu, Surya Ganguli, Stephen Baccus

Understanding how neural networks transform inputs into outputs is crucial for interpreting and manipulating their behavior. Most existing approaches analyze internal representations by identifying hidden-layer activation patterns correlated with human-interpretable concepts. Here we take a direct approach to examine how hidden neurons act to drive network outputs. We introduce CODEC ($\textbf{Co}$ntribution $\textbf{Dec}$omposition), a method that uses sparse autoencoders to decompose network behavior into sparse motifs of hidden-neuron contributions, revealing causal processes that cannot be determined by analyzing activations alone. Applying CODEC to benchmark image-classification networks, we find that contributions grow in sparsity and dimensionality across layers and, unexpectedly, that they progressively decorrelate positive and negative effects on network outputs. We further show that decomposing contributions into sparse modes enables greater control and interpretation of intermediate layers, supporting both causal manipulations of network output and human-interpretable visualizations of distinct image components that combine to drive that output. Finally, by analyzing state-of-the-art models of neural activity in the vertebrate retina, we demonstrate that CODEC uncovers combinatorial actions of model interneurons and identifies the sources of dynamic receptive fields. Overall, CODEC provides a rich and interpretable framework for understanding how nonlinear computations evolve across hierarchical layers, establishing contribution modes as an informative unit of analysis for mechanistic insights into artificial neural networks.

Applications · Health

Xinyao Wu, Zhe Xu, Raymond Kai-yu Tong

Class-incremental learning (CIL) in medical image-guided diagnosis requires models to preserve knowledge of historical disease classes while adapting to emerging categories. Pre-trained models (PTMs) with well-generalized features provide a strong foundation, yet most PTM-based CIL strategies, such as prompt tuning, task-specific adapters and model mixtures, rely on increasingly complex designs. While effective in general-domain benchmarks, these methods falter in medical imaging, where low intra-class variability and high inter-domain shifts (from scanners, protocols and institutions) make CIL particularly prone to representation collapse and domain misalignment. Under such conditions, we find that lightweight representation calibration strategies, often dismissed in general-domain CIL for their modest gains, can be remarkably effective for adapting PTMs in medical settings. To this end, we introduce Random Anchors with Low-rank Decorrelated Learning (RA-LDL), a minimalist representation-based framework that combines (a) PTM-based feature extraction with optional ViT-Adapter tuning, (b) feature calibration via frozen Random Anchor projection and a single-session-trained Low-Rank Projection (LRP), and (c) analytical closed-form decorrelated learning. The entire pipeline requires only one training session and minimal task-specific tuning, making it appealing for efficient deployment. Despite its simplicity, RA-LDL achieves consistent and substantial improvements across both general-domain and medical-specific PTMs, and outperforms recent state-of-the-art methods on four diverse medical imaging datasets. These results highlight that minimalist representation recalibration, rather than complex architectural modifications, can unlock the underexplored potential of PTMs in medical CIL. We hope this work establishes a practical and extensible foundation for future research in class-incremental image-guided diagnosis. Code will be made publicly available.

Deep Learning · Everything Else

Adnan El Assadi, Isaac Chung, Roman Solomatin, Niklas Muennighoff, Kenneth Enevoldsen

Comparing human and model performance offers a valuable perspective for understanding the strengths and limitations of embedding models, highlighting where they succeed and where they fail to capture meaning and nuance. However, such comparisons are rarely made, as human performance on embedding tasks is difficult to measure. To fill this gap, we introduce HUME: Human Evaluation Framework for Text Embeddings. While frameworks like MTEB provide broad model evaluation, they lack reliable estimates of human performance, limiting the interpretability of model scores. We measure human performance across 16 MTEB datasets spanning reranking, classification, clustering, and semantic textual similarity across linguistically diverse high- and low-resource languages. Humans achieve an average performance of 77.6% compared to 80.1% for the best embedding model, though with substantial variation: models reach high performance on some datasets while struggling on notably low-resource languages. Our human annotations also reveal multiple dataset issues. We additionally benchmark nine LLMs as annotators on reranking, classification, and STS tasks, finding that they fall short of human performance (76.1% vs. 81.2%) despite offering scalability advantages. We provide human performance baselines, insights into task difficulty patterns, and an extensible evaluation framework that enables a more meaningful interpretation of results and informs the development of both models and benchmarks. Our code, dataset, and leaderboard are publicly available at https://github.com/embeddings-benchmark/mteb.

General Machine Learning · Representation Learning

Dominik Sturm, Hiba Bensalem, Ivo Sbalzarini

We introduce spatially informed variational autoencoders (SI-VAE) as self-supervised deep-learning models that use stochastic point processes to predict spatial organization patterns from images. Existing approaches to learning visual representations based on variational autoencoders (VAE) struggle to capture spatial correlations between objects or events, focusing instead on pixel intensities. We address this limitation by incorporating a point-process likelihood, derived from the Papangelou conditional intensity, as a self-supervision target. This results in a hybrid model that learns statistically interpretable representations of spatial localization patterns and enables zero-shot conditional simulation directly from images. Experiments with synthetic images show that SI-VAE improve the classification accuracy of attractive, repulsive, and uncorrelated point patterns from 48% (VAE) to over 80% in the worst case and 90% in the best case, while generalizing to unseen data. We apply SI-VAE to a real-world microscopy data set, demonstrating its use for studying the spatial organization of proteins in human cells and for using the representations in downstream statistical analysis.

Applications · Time Series

Nan Huang, Haishuai Wang, Zihuai He, Marinka Zitnik, Xiang Zhang

Medical time series (MedTS) classification suffers from poor generalizability in real-world deployment due to inter- and intra-dataset heterogeneity, such as varying numbers of channels, signal lengths, task definitions, and patient characteristics. % implicit patient characteristics, variable channel configurations, time series lengths, and diagnostic tasks. To address this, we propose FORMED, a novel framework for repurposing a backbone foundation model, pre-trained on generic time series, to enable highly generalizable MedTS classification on unseen datasets. FORMED combines the backbone with a novel classifier comprising two components: (1) task-specific channel embeddings and label queries, dynamically sized to match any number of channels and target classes, and (2) a shared decoding attention layer, jointly trained across datasets to capture medical domain knowledge through task-agnostic feature-query interactions. After repurposing, FORMED achieves seamless adaptation to unseen MedTS datasets through lightweight label query training (0.1\% of parameters), eliminating the need for full fine-tuning or architectural redesign. We evaluate FORMED on 5 diverse MedTS datasets, benchmarking against 11 Task-Specific Models (TSM) and 4 Task-Specific Adaptation (TSA) methods. Our results demonstrate FORMED's dominant performance, achieving up to 35\% absolute improvement in F1-score (on ADFTD dataset) over specialized baselines. By decoupling domain-invariant representation learning from task-specific adaptation, FORMED establishes a scalable and resource-efficient paradigm for foundation model repurposing in healthcare. This approach prioritizes clinical adaptability over rigid task-centric design, offering a practical pathway for real-world implementation.

Computer Vision · Classification and Understanding

Wenhao Li, Xianjing Meng, Qiangchang Wang, Zhongyi Han, Zhibin Wu, Yilong Yin

Few-shot learning (FSL) aims to generalize to novel categories with only a few samples. Recent approaches incorporate large language models (LLMs) to enrich visual representations with semantic embeddings derived from class names. However, they overlook progressive and adaptive alignment between vision and language from low-level to high-level semantics, resulting in limited semantic gains. To address these challenges, we propose Dual-level Vision–Language Alignment with Reinforcement Learning gating (DVLA-RL), which consists of Dual-level Semantic Construction (DSC) and RL-gated Attention (RLA). Specifically, DSC conditions LLMs on both class names and support samples to generate discriminative attributes, progressively selects the most relevant ones, and then synthesizes them into coherent class descriptions. This process provides complementary low-level attributes and high-level descriptions, enabling both fine-grained grounding and holistic class understanding. To dynamically integrate dual-level semantics along with the visual network layers, RLA formulates cross-modal fusion as a sequential decision process. A lightweight policy trained with episodic REINFORCE adaptively adjusts the contributions of self-attention and cross-attention to integrate textual and visual tokens. As a result, shallow layers refine local attributes and deep layers emphasize global semantics, enabling more precise cross-modal alignment. This achieves class-specific discrimination and generalized representations with merely a few support samples. DVLA-RL achieves new state-of-the-art performance across nine benchmarks in three diverse FSL scenarios.

General Machine Learning · Representation Learning

Yue Wu, Jialin Zhao, Carlo Vittorio Cannistraci

With the advent of the neural network era, traditional machine learning methods have increasingly been overshadowed. Nevertheless, continuing research on the role of geometry for learning in data science is crucial to envision and understand new principles behind the design of efficient machine learning. Linear classifiers are favored in certain tasks due to their reduced susceptibility to overfitting and their ability to provide interpretable decision boundaries. However, achieving both scalability and high predictive performance in linear classification remains a persistent challenge. Here, we propose a theoretical framework named geometric discriminant analysis (GDA). GDA includes the family of linear classifiers that can be expressed as a function of a centroid discriminant basis (CDB0) - the connection line between two centroids - adjusted by geometric corrections under different constraints. We demonstrate that linear discriminant analysis (LDA) is a subcase of the GDA theoretical framework, and we show its convergence to CDB0 under certain conditions. Then, based on the GDA framework, we propose an efficient linear classifier named centroid discriminant analysis (CDA) which is defined as a special case of GDA under a 2D plane geometric constraint. CDA training is initialized starting from CDB0 and involves the iterative calculation of new adjusted centroid discriminant lines whose optimal rotations on the associated 2D planes are searched via Bayesian optimization. CDA has good scalability (quadratic time complexity) which is lower than LDA and support vector machine (SVM) (cubic complexity). Results on 27 real datasets across classification tasks of standard images, medical images and chemical properties, offer empirical evidence that CDA outperforms other linear methods such as LDA, SVM and logistic regression (LR) in terms of scalability, performance and stability. Furthermore, we show that linear CDA can be generalized to nonlinear CDA via kernel method, demonstrating improvements on the linear version with tests on three challenging datasets of images and chemical data. GDA's general validity as a new theoretical framework may inspire the design of new classifiers under the definition of different geometric constraints, paving the way towards a deeper understanding of the role of geometry in learning from data.

Deep Learning · Graph Neural Networks

Michael Ito, Danai Koutra, Jenna Wiens

While message-passing NNs (MPNNs) are naturally invariant on graphs, they are fundamentally limited in expressive power, oversmooth, and oversquash. Canonicalization offers a powerful alternative by mapping each graph to a unique, invariant representation on which expressive non-invariant encoders can operate. However, existing approaches rely on a single canonical sequence that distorts graph distances and restricts expressivity. To address these limitations, we introduce Canonical Tree Cover Neural Networks (CTNNs), which represent the graph with a canonical spanning tree cover. Each tree is then processed with an expressive tree encoder. Theoretically, tree covers better preserve graph distances in comparison to sequences, and on sparse graphs, the cover recovers all edges with a logarithmic number of trees in the graph size, making CTNNs strictly more expressive than sequence-based canonicalization approaches. Empirically, CTNNs consistently outperform invariant GNNs and sequence-based canonical GNNs across sparse molecular and protein graph classification benchmarks. Overall, CTNNs advance graph learning by providing an efficient, invariant, and expressive representation learning framework on sparse graphs via tree cover-based canonicalization.

Deep Learning · Everything Else

Donato Crisostomi, Alessandro Zirilli, Antonio Andrea Gargiulo, Maria Sofia Bucarelli, Simone Scardapane, Fabrizio Silvestri, Iacopo Masi, Emanuele Rodolà

Model merging has recently emerged as a lightweight alternative to ensembling, combining multiple fine-tuned models into a single set of parameters with no additional training overhead. Yet, existing merging methods fall short of matching the full accuracy of separately fine-tuned endpoints. We present MASS (MoErging through Adaptive Subspace Selection), a new approach that closes this gap by unifying multiple fine-tuned models while retaining near state-of-the-art performance across tasks. Building on the low-rank decomposition of per-task updates, MASS stores only the most salient singular components for each task and merges them into a shared model. At inference time, a non-parametric, data-free router identifies which subspace (or combination thereof) best explains an input's intermediate features and activates the corresponding task-specific block. This procedure is fully training-free and introduces only a two-pass inference overhead plus a ~2 storage factor compared to a single pretrained model, irrespective of the number of tasks. We evaluate MASS on CLIP-based image classification using ViT-B-16, ViT-B-32 and ViT-L-14 for benchmarks of 8, 14 and 20 tasks respectively, establishing a new state-of-the-art. Most notably, MASS recovers up to ~98% of the average accuracy of individual fine-tuned models, making it a practical alternative to ensembling at a fraction of the storage cost.

General Machine Learning · Representation Learning

Ismail Khalfaoui Hassani, Stefan Kesselheim

Which functions can be used as activations in deep neural networks? This article explores families of functions based on orthonormal bases, including the Hermite polynomial basis and the Fourier trigonometric basis, as well as a basis resulting from the tropicalization of a polynomial basis. Our study shows that, through a simple variance-preserving initialization and without additional clamping mechanisms, these activations can successfully be used to train deep models, such as GPT-2 for next-token prediction on OpenWebText and ConvNeXt for image classification on ImageNet. Our work addresses the issue of exploding and vanishing activations and gradients, particularly prevalent with polynomial activations, and opens the door for improving the efficiency of large-scale learning tasks. Furthermore, our approach provides insight into the structure of neural networks, revealing that networks with polynomial activations can be interpreted as multivariate polynomial mappings. Finally, using Hermite interpolation, we show that our activations can closely approximate classical ones in pre-trained models by matching both the function and its derivative, making them especially useful for fine-tuning tasks. These activations are available in the torchortho library.

Social Aspects · Trustworthy Machine Learning

Senrong Xu, Yanke Zhou, Yuhao Tan, Zenan Li, Yuan Yao, Taolue Chen, Feng Xu, Xiaoxing Ma

Conformal prediction methods provide statistically rigorous marginal coverage guarantees for machine learning models, but such guarantees fail to account for algorithmic biases, thereby undermining fairness and trust. This paper introduces a fair conformal inference framework for classification tasks. The proposed method constructs prediction sets that guarantee conditional coverage on adaptively identified subgroups, which can be implicitly defined through nonlinear feature combinations. By balancing effectiveness and efficiency in producing compact, informative prediction sets and ensuring adaptive equalized coverage across unfairly treated subgroups, our approach paves a practical pathway toward trustworthy machine learning. Extensive experiments on both synthetic and real-world datasets demonstrate the effectiveness of the framework.

Deep Learning · Attention Mechanisms

Feijiang Han, Xiaodong Yu, Jianheng Tang, Delip Rao, Weihua Du, Lyle Ungar

Token-level attention tuning -- a class of training-free methods including Post-hoc Attention Steering (PASTA) and Attention Calibration (ACT) -- has emerged as a promising approach for improving frozen LLMs via interpretable interventions. However, these methods rely on auxiliary heuristics to identify important task-specific tokens, which can introduce bias and limit applicability when token importance is ambiguous or when optimized kernels make attention maps inaccessible. We propose a simpler alternative: intervening only on the initial token (e.g., in LLaMA). We theoretically show that adding lightweight biases to this token’s attention logits systematically shifts and reshapes downstream attention patterns -- an effect amplified by its natural role as an attention sink. Empirically, we find that this tuning can improve LLM performance and better elicit pretrained knowledge, with stronger effects in early layers and distinct scaling preferences across attention heads. Building on these findings, we introduce ZeroTuning, a training-free method that improves LLM performance by applying head-specific attention adjustments to the initial token, requiring no parameter updates. We present two variants: a supervised mode that calibrates on validation examples, and an unsupervised mode that directly minimizes output entropy. ZeroTuning requires no KV-cache or decoding changes and is kernel-agnostic (works with SDPA and FlashAttention). It requires only four lines of modification to standard \texttt{LlamaAttention} code, achieves gains across 15 datasets, and outperforms prior, more complex methods. For example, on Llama-3.1-8B, it yields relative improvements of 19.9% on classification, 4.5% on question answering, and 2.1% on dialogue. ZeroTuning also works out of the box with quantized inference and maintains its improvements as context length increases. Our work provides a lightweight tool for inference-time improvement, advancing both optimization and interpretability. Our code and runnable demo are available at https://anonymous.4open.science/r/ZeroTuning.

General Machine Learning · Representation Learning

Yi-Ge Zhang, Jingyi Cui, Qiran Li, Yisen Wang

Unsupervised contrastive learning has shown significant performance improvements in recent years, often approaching or even rivaling supervised learning in various tasks. However, its learning mechanism is fundamentally different from supervised learning. Previous works have shown that difficult examples (well-recognized in supervised learning as examples around the decision boundary), which are essential in supervised learning, contribute minimally in unsupervised settings. In this paper, perhaps surprisingly, we find that the direct removal of difficult examples, although reduces the sample size, can boost the downstream classification performance of contrastive learning. To uncover the reasons behind this, we develop a theoretical framework modeling the similarity between different pairs of samples. Guided by this framework, we conduct a thorough theoretical analysis revealing that the presence of difficult examples negatively affects the generalization of contrastive learning. Furthermore, we demonstrate that the removal of these examples, and techniques such as margin tuning and temperature scaling can enhance its generalization bounds, thereby improving performance. Empirically, we propose a simple and efficient mechanism for selecting difficult examples and validate the effectiveness of the aforementioned methods, which substantiates the reliability of our proposed theoretical framework.

Applications · Language, Speech and Dialog

Anindya Sundar Das, Kangjie Chen, Monowar Bhuyan

Pre-trained language models have achieved remarkable success across a wide range of natural language processing (NLP) tasks, particularly when fine-tuned on large, domain-relevant datasets. However, they remain vulnerable to backdoor attacks, where adversaries embed malicious behaviors using trigger patterns in the training data. These triggers remain dormant during normal usage, but, when activated, can cause targeted misclassifications. In this work, we investigate the internal behavior of backdoored pre-trained encoder-based language models, focusing on the consistent shift in attention and gradient attribution when processing poisoned inputs; where the trigger token dominates both attention and gradient signals, overriding the surrounding context. We propose an inference-time defense that constructs anomaly scores by combining token-level attention and gradient information. Extensive experiments on text classification tasks across diverse backdoor attack scenarios demonstrate that our method significantly reduces attack success rates compared to existing baselines. Furthermore, we provide an interpretability-driven analysis of the scoring mechanism, shedding light on trigger localization and the robustness of the proposed defense.

Shurong Wang, Yuqi Pan, Zhuoyang Shen, Meng Zhang, Hongwei Wang, Guoqi Li

Associative memory models are content-addressable memory systems fundamental to biological intelligence and are notable for their high interpretability. However, existing models evaluate the quality of retrieval based on proximity, which cannot guarantee that the retrieved pattern has the strongest association with the query, failing correctness. We reframe this problem by proposing that a query is a generative variant of a stored memory pattern, and define a variant distribution to model this subtle context-dependent generative process. Consequently, correct retrieval should return the memory pattern with the maximum a posteriori probability of being the query's origin. This perspective reveals that an ideal similarity measure should approximate the likelihood of each stored pattern generating the query in accordance with variant distribution, which is impossible for fixed and pre-defined similarities used by existing associative memories. To this end, we develop adaptive similarity, a novel mechanism that learns to approximate this insightful but unknown likelihood from samples drawn from context, aiming for correct retrieval. We theoretically prove that our proposed adaptive similarity achieves optimal correct retrieval under three canonical and widely applicable types of variants: noisy, masked, and biased. We integrate this mechanism into a novel adaptive Hopfield network (`A-Hop`), and empirical results show that it achieves state-of-the-art performance across diverse tasks, including memory retrieval, tabular classification, image classification, and multiple instance learning. Our code is publicly available at https://github.com/shurongwang/Adaptive-Hopfield-Network.

Dung Viet Nguyen, Anh Thi, Minh Hoang Nguyen, Luc Nguyen, Shiqi Jiang, Ethan Fetaya, Duy Linh Tran, Gal Chechik, Tan Nguyen

Existing expert merging strategies for Sparse Mixture of Experts (SMoE) typically rely on input-dependent or input-independent averaging of expert parameters, but often lack a principled weighting mechanism. In this work, we reinterpret expert merging through the lens of game theory, revealing cooperative and competitive dynamics among experts. Based on this perspective, we introduce Nash Merging of Experts (NAMEx), a novel framework that incorporates Nash Bargaining into the merging process, enabling more balanced and efficient collaboration among experts. Additionally, we incorporate complex momentum into NAMEx to accelerate expert propagation with theoretical guarantees for convergence. Extensive experiments across language modeling, text classification, image classification, and zero-shot robustness under data corruption show that NAMEx consistently outperforms competing methods while integrating seamlessly with popular MoE architectures. Finally, we demonstrate NAMEx’s scalability by applying it to large-scale systems, including Qwen1.5-MoE (14B) and DeepSeek-MoE (16B), where it proves effective in both zero-shot and fine-tuning settings.