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Beyond Trajectory-Level Attribution: Graph-Based Credit Assignment for Agentic Reinforcement Learning
Xin Cheng, Shuo He, Lang Feng, Haiyang Xu, Ming Yan, Lei Feng, Bo An
Group-based reinforcement learning (RL) methods have achieved remarkable success in improving the performance of large language models (LLMs) and have been rapidly extended to agentic tasks. However, their credit assignment relies heavily on coarse-grained trajectory-level attribution according to final outcomes, making it difficult to capture the contribution of individual steps, such as valuable steps obscured within failed trajectories. To uncover latent information and enable more faithful step-level credit assignment, we propose Graph-based Group Policy Optimization (GraphGPO), which first aggregates all rollout trajectories into a unified state-transition graph and then estimates the distance from each state to the task goal using the global information encoded in the graph. Finally, GraphGPO assigns credit to each edge by estimating a graph-based advantage, based on how much the transition reduces the distance to the task goal. In this way, GraphGPO significantly improves training efficiency and achieves state-of-the-art performance across a range of challenging benchmarks.
DAVE: Distribution-Aware Attribution via ViT Gradient Decomposition
Adam Wróbel, Siddhartha Gairola, Jacek Tabor, Bernt Schiele, Bartosz Michał Zieliński, Dawid Damian Rymarczyk
Vision Transformers (ViTs) have become a dominant architecture in computer vision, yet producing stable and high-resolution attribution maps remains challenging. Architectural components such as patch embeddings and attention routing often introduce structured artifacts in pixel-level explanations, leading many existing methods to rely on coarse patch-level attributions. We introduce DAVE (Distribution-Aware Attribution via ViT Gradient Decomposition), a mathematically grounded attribution method for ViTs based on a structured decomposition of the input gradient. By exploiting architectural properties of ViTs, DAVE isolates locally equivariant and stable components of the effective input-output mapping while suppressing architecture-induced artifacts and instability. Consequently, DAVE produces robust, precise, and class-consistent attribution maps that highlight model-relevant visual features. Experimental results show that across supervised, self-supervised, and inherently interpretable ViTs, DAVE outperforms prior methods on localization, faithfulness, and user studies.
QPoint: End-to-End Lightweight Point Cloud Processing via Robust Quaternion Feature Learning
Zhiming Zhou, Yong He, Chaoxu Mu, Qiaoyun Wu, Ajmal Saeed Mian
The inherent sparsity, lack of structure, and rotation sensitivity of point clouds often lead to high computational and parameter cost in robust feature learning. To address these problems, we present QPoint, a lightweight framework that leverages robust quaternion feature learning. QPoint incorporates a Quaternion-Enhanced local perception module that uses learnable rotations to stabilize local features against geometric transformations, and a Quaternion global attention mechanism that employs quaternion similarity to capture global geometric context with inherent rotation invariance. Extensive experiments show that QPoint achieves top performance across multiple tasks. It achieves excellent 95.0%, 93.9%, and 92.1% on the challenging ScanObjectNN variants (OBJ_BG, OBJ_ONLY, PB_T50_RS), 94.7% overall accuracy on ModelNet40, and 87.0% instance mIoU on ShapeNetParts. Furthermore, QPoint exhibits superior generalization in few-shot learning scenarios. Crucially, it accomplishes this with extremely minimal parameter and computational requirements, establishing a strong and efficient baseline for point cloud processing. Our source code is in the supplementary material and will be released to the public.
Explaining Concept Shift with Interpretable Feature Attribution
Ruiqi Lyu, Alistair Turcan, Bryan Wilder
Concept shift occurs when the distribution of labels conditioned on the features changes between domains, which can make even a well-tuned ML model miscalibrated on a new domain. Identifying these shifted features provides unique insight into how feature-label relationships differ between domains, considering the difference may be across a scientifically relevant dimension, such as time, disease status, population, etc. In this paper, we propose SGShift, a method for attributing performance degradation under concept shift in tabular data to a sparse set of shifted features. We frame concept shift as a feature selection task to learn the features that can explain performance differences between models in the source and target domain. This framework enables SGShift to adapt powerful statistical tools such as generalized additive models, knockoffs, and absorption towards identifying these shifted features. We conduct extensive experiments in synthetic and real data across various ML models and find SGShift can identify shifted features much more accurately than baseline methods, requires few samples in the shifted domain, and is robust to complex cases of concept shift.
Dichotomy of Feature Learning and Unlearning: Fast-Slow Analysis on Neural Networks with Stochastic Gradient Descent
Shota Imai, Sota Nishiyama, Masaaki Imaizumi
The dynamics of gradient-based training in neural networks often exhibit nontrivial structures; hence, understanding them remains a central challenge in theoretical machine learning. In particular, the concept of feature unlearning, in which a neural network progressively loses previously learned features over long training, has gained attention. In this study, we consider the infinite-width limit of a two-layer neural network trained with a large-batch stochastic gradient, then derive differential equations with different time scales, revealing the mechanism and conditions for feature unlearning to occur. Specifically, we utilize the fast-slow dynamics: while an alignment of first-layer weights develops rapidly, the second-layer weights develop slowly. The direction of the flow on a critical manifold, determined by the slow dynamics, decides whether feature unlearning occurs. We give numerical validation of the result and derive theoretical grounding and scaling laws for the feature unlearning. Our results yield the following insights: (i) the strength of the primary nonlinear term in the data induces the feature unlearning, and (ii) an initial scale of the second-layer weights mitigates the feature unlearning. Our result should be understood as a population loss of alignment rather than finite-sample overfitting. Technically, our analysis utilizes Tensor Programs and singular perturbation theory.
Feature Collapse Under Corruption: An Entropy Perspective on Robust Neural Networks
Vishesh Kumar, Akshay Agarwal
Even after decades of advances in neural network training, the inherent robustness challenge remains open. While the sensitivity to adversarial perturbations is understandable given their intentional learning, the most surprising fact is the vulnerability to natural corruptions. Surprisingly, not only is the cause of this inherent vulnerability unknown, but the concern extends beyond traditional CNNs; it also applies to current models, including transformers and large foundation models. For the first time, through this work, we observe that natural corruptions often collapse the network's internal feature space into a high-entropy state, causing predictions to rely on a small subset of fragile features. Inspired by this, we propose a simple yet effective entropy-guided fine-tuning framework, Dem-HEC, that strengthens corruption robustness while maintaining clean accuracy. Our method generates high-entropy samples within a bounded perturbation region and repairs the model using both clean and high-entropy samples. We further combine this objective with distilling knowledge from a teacher snapshot to maintain stable predictions. The proposed Dem-HEC is effective across datasets ranging from small to large-resolution, from pure CNNs to transformers, and to large foundation models, including DinoV3. The proposed approach outperforms the state-of-the-art (SOTA) models not only in improving robustness but also in retaining or boosting clean accuracy.
Activation with Intrinsic-Extrinsic Consensus
Tian Qiu, Zunlei Feng, Yang Gao, Bingde Hu, Yi Gao, Mingli Song
Artificial Neural Networks (ANNs) are powerful tools for complex decision-making tasks. While existing activation mechanisms often promote sparsity through thresholding, they lack explicit awareness of feature channel relevance, causing networks to continuously suffer from interference by noisy channels. Such irrelevant activation signals can propagate through the network and adversely affect the final decision. Inspired by observations that channel relevance can be reflected in both intrinsic activity levels and extrinsic decision weights, and that there is strong consensus between these two aspects, we propose AIEC (Activation with Intrinsic-Extrinsic Consensus), a novel activation mechanism that has the ability to identify and suppress irrelevant feature channels during training. With a basic threshold activation, AIEC integrates an intrinsic Activation-Counting Unit that tracks channel activation statistics, an extrinsic Decision-Making Unit that learns channel decision weights, and a Consensus Gatekeeping Unit that suppresses irrelevant channels based on the agreement between intrinsic and extrinsic channel relevance assessments. Extensive experiments demonstrate that AIEC can effectively suppress irrelevant channels and encourage sparser representations. Furthermore, AIEC is compatible with a wide range of mainstream ANN architectures and achieves superior performance compared to existing activation mechanisms across multiple tasks and domains. Code is available at https://github.com/horrible-dong/AIEC.
$\texttt{ShaplEIG}$: Bayesian Experimental Design for Shapley Value Estimation
David Rundel, Fabian Fumagalli, Maximilian Muschalik, Bernd Bischl, Matthias Feurer
Shapley values are a principled attribution measure widely used in interpretable machine learning, but their exact computation scales exponentially with the number of players, motivating a wide range of approximation methods based on value function evaluations of sampled coalitions. This raises the question of whether approximation accuracy can be improved by *adaptively* selecting coalitions for evaluation based on previous evaluations. This is particularly relevant in settings where the value function is *costly* and the number of evaluations is severely limited, such as retraining-based feature importance, data valuation, and hyperparameter importance. For this purpose, we propose $\texttt{ShaplEIG}$, a Bayesian experimental design approach that approximates the expensive value function using a Gaussian process surrogate and adaptively selects coalitions based on their expected information gain about the Shapley values. By the linearity of the Shapley values in the value function, we show that the expected information gain is available in *closed form*. Furthermore, we propose an *efficient* computation scheme that reduces the complexity from exponential to polynomial in the number of players via elementary symmetric polynomials. In extensive experiments across diverse costly applications, our method consistently improves sample efficiency in the low-budget regime over state-of-the-art baselines.
Priority-Aware Shapley Value
Kiljae Lee, Ziqi Liu, Weijing Tang, Yuan Zhang
Shapley values are widely used for model-agnostic data valuation and feature attribution, yet they implicitly assume contributors are interchangeable. This can be problematic when contributors are dependent (e.g., reused/augmented data or causal feature orderings) or when contributions should be adjusted by factors such as trust or risk. We propose Priority-Aware Shapley Value (PASV), which incorporates both hard precedence constraints and soft, contributor-specific priority weights. PASV is applicable to general precedence structures, recovers precedence-only and weight-only Shapley variants as special cases, and is uniquely characterized by natural axioms. We develop an efficient adjacent-swap Metropolis–Hastings sampler for scalable Monte Carlo estimation and analyze limiting regimes induced by extreme priority weights. Experiments on data valuation (MNIST/CIFAR10) and feature attribution (Census Income) demonstrate more structure-faithful allocations and a practical sensitivity analysis via our proposed ``priority sweeping".
Aggregate Models, Not Explanations: Improving Feature Importance Estimation
Joseph Paillard, Angel David REYERO LOBO, Denis-Alexander Engemann, Bertrand Thirion
Feature-importance methods show promise for transforming machine learning (ML) models from predictive engines into tools for scientific discovery. However, expressive models can be unstable due to data sampling and algorithmic stochasticity, leading to inaccurate variable importance estimates, undermining their utility in critical biomedical applications. While ensembling offers a remedy, the choice between explaining a single ensemble model or aggregating individual model explanations is non-trivial due to the non-linearity of importance measures, and remains largely understudied. Our theoretical analysis, developed under assumptions accommodating complex state-of-the-art ML models, reveals that this choice is governed by a trade-off involving the model's excess risk. In contrast to prior literature, we show that ensembling at the model level provides more accurate variable-importance estimates, particularly for expressive models, by reducing this leading error term. We validate these findings on classical benchmarks and a large-scale proteomic study from the UK Biobank.
Decomposing Query-Key Feature Interactions Using Contrastive Covariances
Andrew Lee, Yonatan Belinkov, Fernanda Viégas, Martin Wattenberg
Despite the central role of attention heads in Transformers, we lack tools to understand why a model attends to a particular token. To address this, we study the query-key (QK) space -- the bilinear joint embedding space between queries and keys. We present a contrastive covariance method to decompose the QK space into low-rank, human-interpretable components. It is when features in keys and queries align in these low-rank subspaces that high attention scores are produced. We first study our method both analytically and empirically in a simplified setting. We then apply our method to large language models to identify human-interpretable QK subspaces for categorical semantic features and binding features. Finally, we demonstrate how attention scores can be attributed to our identified features.
Towards the Explainability of Temporal Graph Networks via Memory Backtracking and Topological Attribution
Yazheng Liu, Xi Zhang, Sihong Xie, Hui Xiong
Temporal graphs are ubiquitous in real-world applications and Temporal Graph Networks (TGNs) have achieved superior predictive accuracy. Understanding which historical events drive model predictions can enhance trustworthiness of TGNs. Existing explanation methods overlook the memory module, the core component that records and updates node histories, leaving the influence of past events unexplored. To address this, we attribute TGNs predictions through the topology attribution tree and memory backtracking tree. The topology attribution tree captures the influence of neighbors and their memory vectors, then the memory backtracking tree quantifies how historical events shape node memory vectors. We apply the LRP in TGNs, ensuring that the total contribution of events equals the model’s logits. Finally, top-k selection may be unfaithful due to the nonlinear mapping from logits to probabilities, we design optimization objectives to identify the important events. Experiments on nine temporal graph datasets, spanning node property prediction, link prediction tasks and graph classification tasks, show that our method provides faithful explanations and outperforms state-of-the-art baselines. The code is available at https://github.com/yazhengliu/MemExplainer.
Diversity-Aware Recursive Feature Multiple Kernel Learning
Nan Cao, Xu Zhao, Teng Zhang
\textit{\underline{M}ultiple \underline{k}ernel \underline{l}earning}~(MKL) combines several base kernels in the spirit of ensemble learning, yet existing methods rarely model kernel diversity---a known cornerstone of ensembles---and most traditional kernels weight all features uniformly, ignoring feature-level discriminability. We address both gaps with DARFMMKL: a data-driven kernel family (Recursive Feature Machine kernels) that learns feature importance directly from data, paired with a kernel selection method that jointly optimizes diversity and quality. The resulting NP-hard binary quadratic program is reformulated via Glover linearization and continuous relaxation into a linear program, and accelerated by Nystr\"om sketching, yielding a selector whose cost is decoupled from the sample size. We provide a covering-number generalization bound that explicitly relates kernel diversity to estimation error. Experiments on 12 benchmark datasets show that DARFMMKL consistently outperforms 9 state-of-the-art MKL methods.
From Parameters to Feature Space: Task Arithmetic for Backdoor Mitigation in Model Merging
Zhenqian Zhu, Yamin Hu, Yiya Diao, Weixiang Li, Haodong LI, Wenjian Luo
Model merging (MM) has gained significant attention as a cost-effective approach to integrate multiple task-specific models into a unified model. However, recent work reveals that MM is highly susceptible to backdoor attacks. Existing defenses based on task arithmetic often fail to eliminate backdoors without substantially degrading clean-task performance, owing to their reliance on direct parameter-space editing. To address this gap, we propose Linear Feature Path Minimization (LFPM), a backdoor mitigation framework for model merging, which introduces an anti-backdoor task vector into the backdoored merged model. Unlike prior approaches, LFPM formulates the backdoor robustness of the merged model from a unified feature-space perspective under the Cross-Task Linearity (CTL) framework, which leverages the approximate linearity of features across tasks. This perspective guides the optimization of the anti-backdoor task to suppress backdoors while preserving clean-task performance. Furthermore, we introduce an effective optimization mechanism based on gradient accumulation and loss path-integral, ensuring robust backdoor suppression along the interpolation path. Extensive experiments demonstrate that LFPM consistently exhibits strong robustness against backdoor attacks in both full fine-tuning and Parameter-Efficient Fine-Tuning (PEFT) settings.
Nonparametric Data Attribution for Diffusion Models
Yutian Zhao, Chao Du, Xiaosen Zheng, Tianyu Pang, Min Lin
Data attribution for generative models seeks to quantify the influence of individual training examples on model outputs. Existing methods for diffusion models typically require access to model gradients or retraining, limiting their applicability in proprietary or large-scale settings. We propose a *nonparametric* attribution method that operates directly on data, measuring influence via patch-level similarity between generated and training images. Our approach is grounded in the analytical form of the optimal score function, extends naturally to multiscale representations, and remains computationally efficient through convolution-based acceleration. In addition to producing spatially interpretable attributions, our framework uncovers patch-level correspondences between training data and generated outputs. Experiments show that NDA substantially outperforms existing nonparametric baselines and achieves the best attribution performance among the evaluated methods that do not use target-model parameters or gradients.
A unified theory of feature learning in RNNs and DNNs
Jan Philipp Bauer, Kirsten Fischer, Moritz Helias, Agostina Palmigiano
Recurrent and deep neural networks (RNNs/DNNs) are cornerstone architectures in machine learning. Remarkably, RNNs differ from DNNs only by weight sharing, as can be shown through unrolling in time. How does this structural similarity fit with the distinct functional properties these networks exhibit? To address this question, we here develop a unified mean-field theory for RNNs and DNNs in terms of representational kernels, describing fully trained networks in the feature learning ($\mu$P) regime. This theory casts training as Bayesian inference over sequences and patterns, directly revealing the functional implications induced by the RNNs' weight sharing. In DNN-typical tasks, we identify a phase transition when the learning signal overcomes the noise due to randomness in the weights: below this threshold, RNNs and DNNs behave identically; above it, only RNNs develop correlated representations across timesteps. For sequential tasks, the RNNs' weight sharing furthermore induces an inductive bias that aids generalization by interpolating unobserved time steps. Overall, our theory offers a way to connect architectural structure to functional biases.
SSA: Sparse Sparse Attention by Aligning Full and Sparse Attention Outputs in Feature Space
Zhenyi Shen, Junru Lu, Lin Gui, Jiazheng Li, Yulan He, Di Yin, Xing Sun
Sparse attention reduces the quadratic complexity of full self-attention but faces two challenges: (1) an attention gap, where applying sparse attention to full-attention-trained models causes performance degradation due to train-inference distribution mismatch, and (2) a capability gap, where models trained purely with sparse attention lack complete gradient flow, preventing them from matching full-attention performance. We propose SSA (Sparse Sparse Attention), a training framework that integrates both sparse and full attention with bidirectional attention-output alignment. We prove that the approximation error scales linearly with the attention mass dropped under sparse attention, and show that SSA's alignment objective substantially reduces this quantity compared to baselines. Experiments demonstrate that SSA achieves state-of-the-art performance under both inference modes, adapts smoothly to varying sparsity budgets, and demonstrates superior long-context capabilities. Code is available at https://github.com/zhenyi4/ssa.
On the Accuracy of Newton Step and Influence Function Data Attributions
Ittai Rubinstein, Samuel B. Hopkins
Data attribution estimates how a trained model would change if a subset of training points were removed, and is a central primitive for tasks such as interpretability, data valuation, and machine unlearning. Despite its widespread use, our theoretical understanding of key data attribution methods -- Influence Functions (IF) and a single Newton Step (NS) -- remains limited: existing guarantees heavily rely on *global* strong convexity and yield bounds with pessimistic dependence on the parameter dimension $d$ and the number of removed samples $k$. We give a new analysis of IF and NS for convex ERM that replaces global assumptions with *local* conditions: it suffices that the loss is strongly convex and sufficiently smooth only in a neighborhood of the first Newton step. As a concrete validation, we analyze logistic regression with Gaussian features and show that our bounds capture the correct scaling up to polylogarithmic factors, yielding matching upper and lower bounds and explaining observed regimes in which NS is markedly more accurate than IF, thereby resolving open questions raised by (Koh et al., 2019).
On the Relationship Between Activation Outliers and Feature Death in Sparse Autoencoders
Elana Simon, Etowah Adams, James Zou
Sparse autoencoders (SAEs) decompose neural network activations into interpretable features, but many learned features never activate, a problem called feature death that wastes dictionary capacity and can reintroduce superposition. Death rates vary dramatically between models: near-zero on GPT-2, over 70\% on AlphaFold3 with identical configurations. We find that dimension-level activation outliers (dimensions whose mean magnitude is large relative to per-token variation) cause this by shifting pre-activations at initialization based on each feature's alignment with the activation mean. Features anti-aligned with the mean receive permanently negative pre-activations and never fire. We formalize outlier severity as $\gamma = \|\boldsymbol{\mu}\|/\|\boldsymbol{\sigma}\|$; it predicts initial death rates (Spearman $\rho = 0.89$ for dead-by-TopK, $0.82$ for dead-by-ReLU) across 454 model-layer combinations spanning language, vision, protein, and genomic models. Dead features can revive during training, but recovery requires the SAE bias to learn the activation mean, a process that is prohibitively slow at high $\gamma$. Mean-centering (subtracting the activation mean) sidesteps this and eliminates outlier-induced death across all tested models, confirming the mechanism and providing a principled basis for when and why this preprocessing step is necessary.
GOTabPFN: From Feature Ordering to Compact Tokenization for Tabular Foundation Models on High-Dimensional Data
Al Zadid Sultan Bin Habib, Md Younus Ahamed, Prashnna Kumar Gyawali, Gianfranco Doretto, Donald Adjeroh
We investigate how to make small tabular foundation models effective for High-Dimensional, Low-Sample Size (HDLSS) tabular prediction without retraining large backbones. We introduce Graph-guided Ordering with Local Refinement (GO-LR), show its equivalence to weighted Minimum Linear Arrangement, and interpret the practical solver as a TSP-path-style surrogate. We propose GOTabPFN,which builds on GO-LR, and a Neuro-Inspired Subunit Compression (NSC) unit to pool locally adjacent ordered features into meta-features, yielding a compact representation that makes TabPFN-style prediction practical in HDLSS regimes. Across tabular benchmarks, GOTabPFN improves stability and accuracy under tight token budgets.