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Social Aspects · Accountability, Transparency, and Interpretability

Sihui Wei, Gavin McCracken, Gabriela Moisescu-Pareja, Harley Wiltzer, Doina Precup, Irina Rish, Jonathan Love

We find multilayer perceptrons and transformers both universally learn an instantiation of the same divide-and-conquer algorithm that requires only a logarithmic number of neural representations to solve dihedral multiplication. Clustering neurons based on similar activation behaviour reveals remarkably clear structure: each neural representation corresponds to a Cayley graph. To our knowledge, this is the first work that fully characterizes and describes all neural representations that are learnable on a dataset, while prior work on group multiplications studied neuron-level behavior, or preliminarily investigated cluster behavior. Thus, we can understand the algorithm networks universally learn at three levels of abstraction: 1) Neurons activate on coset or approximate coset structure of the dihedral group. 2) Groups of neurons together form neural representations that act to divide the dataset into different subproblems, being Cayley graphs, where the equivalence class of the answer is computed. 3) The global algorithm then linearly combines each neural representation (subproblem) together at the logits. This work provides a deep case study and provides the community with a very well understood toy model for interpretability, as well as makes steps toward proving the conjecture that DNNs will divide and conquer all group multiplication tasks.

Deep Learning · Attention Mechanisms

Yordan Yordanov, Matteo Forasassi, Bayar Menzat, Tommaso Salvatori, Ruizhi Wang, Markus Kaltenberger, Amine M'Charrak, Chang Qi, Thomas Lukasiewicz

While state-of-the-art language models (LMs) surpass the vast majority of humans in certain domains, their reasoning remains largely opaque, reducing trust and risking deception and hallucination. In this work, we introduce the Prototype Transformer (ProtoT)—an autoregressive LM architecture that replaces the quadratic-cost self-attention in the transformer with a linear-cost module based on prototypes (parameter vectors). In ProtoT, the prototypes create communication channels aggregating contextual information at different time scales. We show that this leads to the prototypes automatically capturing nameable concepts (e.g. “woman”) during training, and it provides the potential to interpret the model’s reasoning and do targeted edits of its behavior. Compared to baselines, ProtoT scales well with model and data size, shows robustness to input perturbations, and performs well on text generation and downstream tasks (GLUE). Reaching close to the performance of state-of-the-art architectures, ProtoT paves the way to creating well-performing autoregressive LMs interpretable by design.

Social Aspects · Accountability, Transparency, and Interpretability

Gouki Minegishi, Jingyuan Feng, Hiroki Furuta, Takeshi Kojima, Yusuke Iwasawa, Yutaka Matsuo

Analogy is a central faculty of human intelligence, enabling abstract patterns discovered in one domain to be applied to another. However, the mechanisms underlying analogical reasoning in Transformers remain poorly understood. In this work, inspired by the notion of functors in category theory, we formalize analogical reasoning as the inference of correspondences between entities across categories. Based on this formulation, we introduce synthetic tasks that evaluate the emergence of analogical reasoning under controlled settings. We find that the emergence of analogical reasoning is highly sensitive to data characteristics, optimization choices, and model scale. Through mechanistic analysis, we show that analogical reasoning in Transformers decomposes into two key components: (1) geometric alignment of relational structure in the embedding space, and (2) the application of a functor within the Transformer. These mechanisms enable models to transfer relational structure from one category to another, realizing analogy. Finally, we quantify these effects and find that the same trends are observed in pretrained LLMs. In doing so, we move analogy from an abstract cognitive notion to a concrete, mechanistically grounded phenomenon in modern neural networks.

Deep Learning · Graph Neural Networks

Celia Rubio-Madrigal, Rebekka Burkholz

Graph neural networks (GNNs) are widely believed to excel at node representation learning through trainable neighborhood aggregations. We challenge this view by introducing Fixed Aggregation Features (FAFs), a training-free approach that transforms graph learning tasks into tabular problems. This simple shift enables the use of well-established tabular methods, offering strong interpretability and the flexibility to deploy diverse classifiers. Across 14 benchmarks, well-tuned multilayer perceptrons trained on FAFs rival or outperform state-of-the-art GNNs and graph transformers on 12 tasks—often using only mean aggregation. The only exceptions are the Roman Empire and Minesweeper datasets, which typically require unusually deep GNNs. To explain the theoretical possibility of non-trainable aggregations, we connect our findings to Kolmogorov–Arnold representations and discuss when mean aggregation can be sufficient. In conclusion, our results call for (i) richer benchmarks benefiting from learning diverse neighborhood aggregations, (ii) strong tabular baselines as standard, and (iii) employing and advancing tabular models for graph data to gain new insights into related tasks.

Social Aspects · Accountability, Transparency, and Interpretability

Andrea Marzo, Alessio Ragno, Roberto Capobianco

Reinforcement learning (RL) has achieved remarkable success across complex decision-making tasks, especially with the advent of deep neural networks. However, the resulting models are often opaque, making their deployment in safety-critical domains challenging. Explainable AI aims to address this issue, but most specific efforts for deep RL remain limited either to post-hoc explanation methods or to imitation learning and distillation procedures. These latter approaches rely on pre-trained black-box agents and are typically restricted to environments with discrete action spaces, limiting their scalability and interpretability. In this paper, we introduce ProtoSAC, a novel deep RL architecture that integrates a prototype-based actor into the Soft Actor-Critic (SAC) algorithm, enabling intrinsic interpretability in continuous action spaces. Our method learns a set of prototypes that represent interpretable state clusters, each associated with a Gaussian action distribution. Actions are generated as a similarity-weighted mixture over these prototypes, providing transparent decision-making without sacrificing performance. We evaluate ProtoSAC on continuous action-space environments and show that it matches the performance of the original SAC while offering enhanced interpretability.

Yanguang Chen, Wenzhi Gao, Wanyu Zhang, Dongdong Ge, Huikang Liu, Yinyu Ye

This paper introduces Probabilistic Multi-Variable Branching (PMVB), a simple and effective technique for accelerating mixed-integer optimization using data-driven machine learning models. At its core, PMVB employs a multi-variable branching procedure that partitions the feasible region via data-driven hyperplanes and requires only two lines of code to implement. Moreover, PMVB is model-agnostic and compatible with a wide range of machine learning models. Leveraging tools from statistical learning theory, we develop interpretable hyperparameter selection strategies and propose several extensions to further enhance performance. We evaluate PMVB by integrating it into state-of-the-art MIP solvers and conducting experiments on both classical benchmark datasets and real-world instances. The results demonstrate the effectiveness of PMVB in improving MIP-solving efficiency.

Theory · Reinforcement Learning and Planning

Tommaso Giorgi, Pierriccardo Olivieri, Keyue Jiang, Laura Toni, Matteo Papini

Learning state representations in Markov Decision Processes (MDPs) has proven crucial for addressing the curse of dimensionality in large-scale reinforcement learning (RL) problems. A widely recognized approach exploits structural priors on the MDP by constructing state representations as linear combinations of the state-graph Laplacian eigenvectors. When there is no prior knowledge of the graph, or the state space is too large, the spectral features can be estimated in a model-free fashion. In this work, we prove an upper bound on the approximation error of linear value function approximation based on learned spectral features. We show how this error scales with the algebraic connectivity of the state-graph, making it interpretable in terms of the MDP topology. We also bound the error arising from the estimation of the spectral features themselves, providing an all-round view of the representation learning pipeline. Additionally, we provide a new expression of the Laplacian operator in the RL setting that clarifies some subtle ambiguities in the literature. Our results apply to general (non-uniform) policies without making any assumptions on the symmetry of the induced transition kernel. We validate our theoretical findings with numerical simulations on gridworld environments.

Applications · Chemistry, Physics, and Earth Sciences

Francisco Giral, Álvaro Sevillano, Ignacio Perez, Ricardo Vinuesa, Soledad Le Clainche

Urban wind flow reconstruction is essential for assessing air quality, heat dispersion, and pedestrian comfort, yet remains challenging when only sparse sensor data are available. We propose GenDA, a generative data assimilation framework that reconstructs high-resolution wind fields on unstructured meshes from limited observations. The model employs a multiscale graph-based diffusion architecture trained on computational fluid dynamics (CFD) simulations and interprets classifier-free guidance as a learned posterior reconstruction mechanism: the unconditional branch learns a geometry-aware flow prior, while the sensor-conditioned branch injects observational constraints during sampling. This formulation enables obstacle-aware reconstruction and generalization across unseen geometries, wind directions, and mesh resolutions without retraining. We consider both sparse fixed sensors and trajectory-based observations using the same reconstruction procedure. When evaluated against supervised graph neural network (GNN) baselines and classical reduced-order data assimilation methods, GenDA reduces the relative root-mean-square error (RRMSE) by 25-57% and increases the structural similarity index (SSIM) by 23-33% across the tested meshes. Experiments are conducted on Reynolds-averaged Navier-Stokes (RANS) simulations of a real urban neighborhood in Bristol, United Kingdom, at a characteristic Reynolds number of $\mathrm{Re}\approx2\times10^{7}$, featuring complex building geometry and irregular terrain. The proposed framework provides a scalable path toward generative, geometry-aware data assimilation for environmental monitoring in complex domains.

Social Aspects · Accountability, Transparency, and Interpretability

Nils Philipp Walter, Jilles Vreeken, Jonas Fischer

Attribution methods reveal which input features a neural network uses for a prediction, adding transparency to their decisions. A common problem is that these attributions seem unspecific, highlighting both important and irrelevant features. We revisit the common attribution pipeline and observe that using logits as attribution target is a main cause of this phenomenon. We show that the solution is in plain sight: considering distributions of attributions over multiple classes using existing attribution methods yields specific and fine-grained attributions. On common benchmarks, including the grid-pointing game and randomization-based sanity checks, this improves the ability of 18 attribution methods across 7 architectures up to $2\times$, agnostic to model architecture.

Social Aspects · Accountability, Transparency, and Interpretability

Xiaoou Liu, Tiejin Chen, Dengjia Zhang, Yaqing Wang, Lu Cheng, Hua Wei

Large Language Models have achieved strong performance on reasoning tasks with objective answers by generating step-by-step solutions, but diagnosing where a multi-step reasoning trace might fail remains difficult. Confidence estimation offers a natural diagnostic signal, yet existing methods are restricted to final answers or require internal model access. We introduce Stepwise Confidence Attribution (SCA), a framework for closed-source LLMs that assigns step-level confidence based only on generated reasoning traces. SCA applies the Information Bottleneck principle: steps aligning with consensus structures across correct solutions receive high confidence, while deviations are flagged as potentially erroneous. We propose two complementary methods: (1) NIBS, a non-parametric IB approach measuring consistency without graph structures, and (2) GIBS, a graph-based IB model that learns subgraphs through a differentiable mask to capture logical variability. Extensive experiments on mathematical reasoning and multi-hop question answering show that SCA reliably identifies low-confidence steps strongly correlated with reasoning errors. Moreover, using step-level confidence to guide self-correction improves the correction success rate by up to 13.5\% over answer-level feedback.

Social Aspects · Accountability, Transparency, and Interpretability

Tiejin Chen, Longchao Da, Xiaoou Liu, Hua Wei

Uncertainty Quantification (UQ) is widely regarded as the primary safeguard for deploying Large Language Models (LLMs) in high-stakes domains. However, \textbf{we argue that the field suffers from a category error: prevailing UQ methods are just unsupervised clustering algorithms.} We demonstrate that most current approaches inherently quantify the internal consistency of the model's generations rather than their external correctness. Consequently, current methods are fundamentally blind to factual reality and fail to detect ``confident hallucinations,'' where models exhibit high confidence in stable but incorrect answers. Therefore, the current UQ methods may create a deceptive sense of safety when deploying the models with uncertainty. In detail, we identify three critical pathologies resulting from this dependence on internal state: a hyperparameter sensitivity crisis that renders deployment unsafe, an internal evaluation cycle that conflates stability with truth, and a fundamental lack of ground truth that forces reliance on unstable proxy metrics to evaluate uncertainty. To resolve this impasse, we advocate for a paradigm shift to UQ and outline a roadmap for the research community to adopt better evaluation metrics and settings, implement mechanism changes for native uncertainty, and anchor verification in objective truth, ensuring that model confidence serves as a reliable proxy for reality.

Social Aspects · Accountability, Transparency, and Interpretability

Peng Cui, Jiahao Zhang, Lijie Hu

While Contrastive Learning (CL) has revolutionized self-supervised representation learning, its latent representations remain highly entangled and opaque, limiting their interpretability in safety-critical applications. We identify that a fundamental cause of this entanglement is the reliance on deterministic similarity measures, which treat all feature dimensions equally. In compositional scenes, this creates an Optimization Conflict: common background features, such as, "blue sky", are encouraged to align in positive pairs but simultaneously repelled in negative pairs, causing gradient oscillations that hinder precise semantic disentanglement. To address this, we propose **BayesNCL** (Bayesian Gated Non-Negative Contrastive Learning). Unlike standard approaches, BayesNCL introduces a probabilistic gating mechanism that dynamically filters out task-irrelevant, high-frequency common features while selectively retaining discriminative semantics. By formalizing feature selection as a variational inference problem with a sparse Bernoulli prior, our method effectively resolves the optimization conflict. Empirical experimental results on benchmark datasets demonstrate that BayesNCL achieves a remarkable 142.1\% improvement in semantic consistency compared to state-of-the-art baselines, yielding highly interpretable representations without compromising downstream task performance.

Deep Learning · Graph Neural Networks

Ali Azizpour, Madeline Navarro, Santiago Segarra

We propose an adaptive node feature selection approach for graph neural networks (GNNs) that identifies and removes unnecessary features during training. The ability to measure how features contribute to model output is key for interpreting decisions and reducing dimensionality by eliminating unhelpful variables. However, graph-structured data introduces complex dependencies that may be unsuited to classical feature importance metrics. Inspired by this, we present a data-, model-, and task-agnostic method that determines relevant features during training based on changes in validation performance upon permuting feature values. We theoretically motivate our approach by characterizing how the relationships between node data and graph structure influences GNN performance. Empirically, we show that (i) our highly general approach rivals the performance of tailored feature selection approaches that exploit prior assumptions; (ii) we return meaningful feature importance scores well before the GNN is fully trained; and (iii) our scores demonstrably extract relevant properties that inform feature importance for various graph learning settings.

Applications · Chemistry, Physics, and Earth Sciences

Aleksander Krasowski, Jonas Naujoks, Moritz Weckbecker, Galip Yolcu, Thomas Wiegand, Sebastian Lapuschkin, Wojciech Samek, René P. Klausen

Physics-informed neural networks (PINNs) have emerged as a powerful deep learning approach for solving partial differential equations (PDEs) in the physical sciences, yet their behavior remains largely opaque and is typically understood through failure mode analyses rather than explicit interpretability. To address this issue, we introduce PINNfluence, a training data attribution framework for interpreting PINNs based on influence functions. By extending influence functions to composite physics-informed training objectives, we enable fine-grained attribution between predictions, loss components, and training data points. Through benchmark experiments across various PDEs, we demonstrate that influence patterns provide granular diagnostics that distinguish different PINN failure modes. PINNfluence thus opens a new avenue for understanding and improving the reliability of PINNs through the lens of their data.

Applications · Health / Medicine

Yang Song, Yixuan Zhang, Lingfa Meng, Tongyuan Hu, Haizhou Shi, Hao Wang, Samir Bhatt, Hengguan Huang

Reliable microbiome-based diagnosis is critical for precision medicine at scale in inflammatory diseases, yet current post-training pipelines in LLMs often overlook the interaction structure that governs microbial ecosystems. In inflammatory bowel disease (IBD), disease signals arise not only from species-level abundance shifts but also from latent microbe–microbe cross-talk. We propose iLoRA, a parameter-efficient Bayesian LoRA framework that infers latent interaction graphs from microbiome inputs and integrates them into adaptation, enabling joint clinical prediction and interaction discovery. Unlike correlation-based post hoc analysis, iLoRA models microbial interactions as latent variables learned end-to-end, yielding uncertainty-aware estimates of cross-talk. We evaluate iLoRA on (i) interactive question answering with human-annotated interaction graphs to quantify structural recovery and (ii) gut microbiome cohorts for IBD diagnosis. Across both domains, iLoRA consistently improves accuracy over strong LoRA baselines while producing interpretable interaction graphs consistent with annotated relations and conventional microbiome association networks.

Social Aspects · Fairness

Qifen Yang, Yuhui Deng, Jiande Huang, Peng Zhou, Xiwen Lu, Lin Cui

With the widespread application of data-driven classifiers in high-risk domains, group fairness has increasingly become a key research focus. However, most existing methods rely on model constraints or data reweighting, which often suffer from limited interpretability and may distort the original data distribution. Granular-ball computing (GBC), as a structured and highly interpretable learning framework, provides a natural foundation for incorporating group fairness into the data partitioning process. Building on this insight, we first propose a $\textbf{Fair}$ $\textbf{G}$ranular-$\textbf{B}$all $\textbf{G}$eneration framework (FairGBG), which employs the fair clustering algorithm to ensure a balanced proportion of sensitive groups within each granular-ball (GB) during its construction, aiming to enhance within-ball group fairness. Theoretical analysis shows that FairGBG preserves high purity within each GB while satisfying group fairness. Furthermore, we introduce a $\textbf{Fair} \textbf{G}$ranular-$\textbf{B}$all-based $\textbf{F}$air data $\textbf{C}$lassification method (FairGBFC), which enhances classification fairness by leveraging group fairness within GBs. Experimental results on multiple benchmark datasets demonstrate that, compared to existing methods, FairGBFC significantly improves classification fairness while maintaining competitive accuracy. Notably, FairGBFC exhibits superior classification performance compared to standard GB-based methods across all benchmark datasets. Furthermore, compared with state-of-the-art fairness-aware baselines, it achieves a superior trade-off between accuracy and fairness, effectively mitigating bias while preserving high utility.

Social Aspects · Accountability, Transparency, and Interpretability

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".

Applications · Time Series

Hua Wang, Xianhao Jiao, Fan Zhang

Deep forecasting models often suffer from attenuated periodic perception and entangled trend–noise representations as network depth increases. Moreover, the widely adopted channel-independent paradigm, while improving training stability, disrupts intrinsic dynamic coordination among variables, hindering the modeling of cross-variable consistency in multivariate time series. To address these issues, we propose PESD-TSF, a physics-inspired structured decomposition framework for long-term time series forecasting that jointly emphasizes interpretability and predictive accuracy. PESD-TSF introduces three key designs. First, a Multiplicative Periodic Gating mechanism incorporates continuous-time priors to dynamically modulate signal amplitudes, preserving periodic structures across deep layers. Second, a multi-scale structured encoder integrates detrended attention with hierarchical sampling to explicitly decouple long-term trends from high-frequency variations while retaining fine-grained temporal semantics. Third, to recover disrupted inter-variable dependencies, we propose Cross-Scale Collaborative Attention (CSCA) together with an RLC regularization scheme, which reconstructs global inter-variable topology in deep feature spaces and enforces physically consistent collaboration through orthogonality and consistency constraints. Extensive experiments on benchmark datasets from multiple domains demonstrate that PESD-TSF consistently achieves state-of-the-art performance, with particularly strong gains on multivariate forecasting tasks involving complex inter-variable coupling, highlighting its superior structural modeling capability and generalization.

Applications · Chemistry, Physics, and Earth Sciences

In Huh, Changwook Jeong, Muhammad Alam

Data-driven dynamical system models often fail to recover the long-term structure of the underlying system, as their behavior is weakly constrained off the data manifold. Conjugacy-based approaches address this limitation by learning a diffeomorphism that pushes forward a source vector field to match observed dynamics, inheriting qualitative topology from the source. However, such methods typically presuppose that the chosen source system is topologically compatible with the target data. When this assumption is violated, the conjugacy problem becomes ill-posed, and arbitrary corrections can be traded off against diffeomorphic variation, leading to non-identifiability. We propose a framework that relaxes this assumed prior by jointly learning the diffeomorphic conjugacy together with controlled adjustments to the source dynamics via low-dimensional context modulation. Inspired by versal unfolding theory, we enforce the modulation space to be orthogonal to the worst-case orbit-tangent directions, obtained by adversarially searching over a class of parameterized diffeomorphisms. This promotes an identifiable decomposition of dynamical variation into diffeomorphic and intrinsic, topology-changing components, enabling interpretable corrections that recover the canonical structure such as normal forms and symmetries.

Deep Learning · Generative Models and Autoencoders

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 entirely 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 and naturally extends to multiscale representations, while remaining computationally efficient through convolution-based acceleration. In addition to producing spatially interpretable attributions, our framework uncovers patterns that reflect intrinsic relationships between training data and outputs, independent of any specific model. Experiments demonstrate that our method achieves strong attribution performance, closely matching gradient-based approaches and substantially outperforming existing nonparametric baselines.