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新论文 · v1arXiv:2611.07410

Spectral symmetry fingerprints in equivariant representations

Jiacheng Cen, Anyi Li, Ning Lin, Zihe Wang, Ji-Rong Wen, Wenbing Huang

原文摘要

Symmetry governs the organization of physical structures, while symmetry breaking reveals their transformations. In geometric deep learning, symmetry imposes rank constraints on equivariant representations, limiting the expressive capacity of equivariant graph neural networks (GNNs). Here we show that these constraints can instead be exploited: the singular-value spectra of equivariant representations provide a unified fingerprint of structural symmetry. We introduce spectral symmetry fingerprints (SymFP), which enable discrete point-group identification through rank-template matching and continuous symmetry analysis by quantifying spectral energy beyond target rank constraints. SymFP is orientation invariant and architecture agnostic, enabling a parameter-free GNN implementation. Its spectra can be reused across multiple target groups, and the resulting leakage scores satisfy subgroup monotonicity. Across synthetic structures, molecules, coordination complexes and large biological assemblies, SymFP accurately identifies point groups, tracks controlled symmetry breaking and reveals local and degree-resolved symmetry changes that can be obscured by global geometric measures. These results establish the spectral structure of equivariant representations as a general framework for characterizing symmetry across physical systems.

cs.LG · cond-mat.mtrl-sci · math-ph · physics.chem-ph

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2602.05943

Orthogonal Model Merging

Sihan Yang, Kexuan Shi, Weiyang Liu

原文摘要

Merging finetuned Large Language Models (LLMs) has become increasingly important for integrating diverse capabilities into a single unified model. However, prevailing model merging methods rely on linear arithmetic in Euclidean space, which often destroys the intrinsic geometric properties of pretrained weights, such as hyperspherical energy. To address this, we propose Orthogonal Model Merging (OrthoMerge), a method that performs merging operations on the Riemannian manifold formed by the orthogonal group to preserve the geometric structure of the model's weights. By mapping task-specific orthogonal matrices learned by Orthogonal Finetuning (OFT) to the Lie algebra, OrthoMerge enables a principled yet efficient integration that takes into account both the direction and intensity of adaptations. In addition to directly leveraging orthogonal matrices obtained by OFT, we further extend this approach to general models finetuned with non-OFT methods (i.e., low-rank finetuning, full finetuning) via an Orthogonal-Residual Decoupling strategy. This technique extracts the orthogonal components of expert models by solving the orthogonal Procrustes problem, which are then merged on the manifold of the orthogonal group, while the remaining linear residuals are processed through standard additive merging. Extensive empirical results demonstrate the effectiveness of OrthoMerge in mitigating catastrophic forgetting and maintaining model performance across diverse tasks.

cs.LG

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.39418

LinQuant: Functional Invariances for Low-Precision Linear Recurrences

Neehal Tumma, Philipp Nazari, Rohan Cherukuri, Daniela Rus, T. Konstantin Rusch

原文摘要

Linear recurrences are emerging as practical alternatives to softmax attention in large language models, appearing in both standalone and hybrid architectures. However, despite their rapid emergence, low-precision inference remains much less developed for these models than for softmax attention. During prefill, chunkwise-parallel algorithms cast much of the recurrence as dense matrix multiplications, suggesting a natural path to low-precision execution. Simply quantizing these operations in their native form, however, can be fragile. In this work, we identify functional invariances that preserve the full-precision computation while making the operands more amenable to quantization. Building on this observation, we introduce LinQuant, a framework for low-precision recurrent prefill based on seven such invariances, including rotations, diagonal rescalings, and alternative placements of recurrent decay and write factors. We derive when these transformations remain valid across common recurrence families spanning linear, gated, and delta-rule updates, and show that they provide complementary degrees of freedom for improving low-precision accuracy. Finally, we translate this framework to production by augmenting SSDi8, an existing low-precision prefill pipeline for Mamba-2, with the applicable invariances. LinQuant improves perplexity at matched latency on Mamba-2 1.3B, 2.7B, and 8B and Nemotron-H 8B, demonstrating the practical utility of invariance-based quantization for recurrent models.

cs.LG

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2604.13622

Self-Organizing Maps with Optimized Latent Positions

Seiki Ubukata, Akira Notsu, Katsuhiro Honda

原文摘要

Self-Organizing Maps (SOM) are a classical method for unsupervised learning, vector quantization, and topographic mapping of high-dimensional data. However, existing SOM formulations often involve a trade-off between computational efficiency and a clearly defined optimization objective. Objective-based variants such as Soft Topographic Vector Quantization (STVQ) provide a principled formulation, but their neighborhood-coupled computations become expensive as the number of latent nodes increases. In this paper, we propose Self-Organizing Maps with Optimized Latent Positions (SOM-OLP), an objective-based topographic mapping method that introduces a continuous latent position for each data point. Starting from the neighborhood distortion of STVQ, we construct a separable surrogate local cost based on its local quadratic structure and formulate an entropy-regularized objective based on it. This yields a simple block coordinate descent scheme with closed-form updates for assignment probabilities, latent positions, and reference vectors, while guaranteeing monotonic non-increase of the objective and retaining linear per-iteration complexity in the numbers of data points and latent nodes. Experiments on a synthetic saddle manifold, scalability studies on the Digits and MNIST datasets, and 16 benchmark datasets show that SOM-OLP achieves competitive neighborhood preservation and quantization performance, favorable scalability for large numbers of latent nodes and large datasets, and the best average rank among the compared methods on the benchmark datasets.

cs.LG

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2610.05961

Strategic Multi-Agent Learning for Interpretable Action Valuation of All Players in Football

Kenjiro Ide, Taiga Someya, Kohei Kawaguchi, Keisuke Fujii

原文摘要

Valuing player actions in football, a complex multi-agent system, requires accounting for strategic interactions among 22 players, including off-ball movements and defensive positioning. Existing reinforcement-learning-based valuation methods commonly incorporate other players through the observed state while retaining independent-agent value formulations. To our knowledge, we introduce the first Markov perfect equilibrium (MPE)-inspired framework for valuing the actions of all 22 players using real football tracking and event data, formulating each possession as a finite-horizon multi-agent dynamic game. To improve interpretability, the framework uses Expandable Decision-Making States (EDMS) and decomposes each Q-value into a successor-feature basis and a linear reward-weight vector. The value basis is estimated through a two-stage procedure combining linear temporal-difference initialization with nonlinear iterative refinement from observed state-action transitions. Using tracking and event data from 95 J1 League matches, we compare the proposed formulation with an independent reinforcement learning baseline under both Position and Velocity States (PVS) and EDMS representations. With EDMS held fixed, the independent baseline assigns the highest value to forward movement in 99.21% of evaluated off-ball states, whereas the most frequent direction under the proposed formulation accounts for 17.63%. Qualitative analyses illustrate context-dependent off-ball valuations and highlight limitations of the current state representation for defensive positioning. Overall, the framework provides an MPE-inspired approach to interpretable action valuation in football, enabling analysis under alternative tactical reward weights.

cs.LG

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2609.36472

DisCoMBO: Steering Expert-in-the-Loop Black-Box Optimization via Distributional Conformance

Jonas Seng, Bennet Wittelsbach, Kristian Kersting

原文摘要

Sequential Model-Based Optimization (SMBO) traditionally relies on Bayesian or ensembling surrogates for uncertainty quantification. While historically treated as fully data-driven, SMBO increasingly integrates external domain expertise to accelerate discovery. To overcome the opaque guidance and diminished integration fidelity of standard acquisition re-weighting, Probabilistic Circuits (PCs) have emerged as a generative surrogate alternative, enabling direct knowledge injection via conditional sampling. However, these generative routines lack the formal exploration-exploitation semantics required for rigorous optimization. We introduce the Distributional Conformance Score (DisCo), a novel metric that unifies the flexibility and efficiency of PCs with a formal uncertainty framework. DisCo provides a bounded, $[0, 1]$-normalized measure of model "surprise" that (1) recovers properties comparable to kernel-based uncertainty known from, e.g., Gaussian Processes, while maintaining linear-time inference, and (2) enables accurate assessment of conformance of external knowledge w.r.t. model evidence. We then present DisCoMBO, a framework leveraging these properties for robust, knowledge-aware optimization. We prove that DisCoMBO is a zero-regret algorithm and demonstrate its effectiveness across diverse benchmarks from AutoML, material optimization, and wind park optimization.

cs.LG

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arXiv ↗PDF ↗