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arXiv

The Moving Target: A Longitudinal Audit of Trust-Benchmark Score Drift Across Open-Source Chat LLM Release Lines

Zhichao Fan, Yanhang Li, Zexin Zhuang, Xian Sun, Yingshuo Wang

Trust-benchmark scores reported on a chat-LLM release line are often carried across several checkpoints of the same line, as if the underlying model had not shifted between releases. We test that assumption. We audit four open-source release lines (Yi, Qwen, Mistral, and Gemma) at three successive public generations each. Each checkpoint is scored on a fixed 200-item basket of five chat-evaluation benchmarks: TruthfulQA, BBQ, ToxiGen, CrowS-Pairs, and XSTest, under three prompt templates. Four of the five benchmark variants are non-canonical, and two of those are synthetic proxies. The mean absolute adjacent-generation Score Drift Rate is several times the mean of an independence-based count-level reference null. It stays in the same band when we drop a benchmark, drop a release line, switch to strict scoring, or restrict to constant-parameter-size transitions. Within this audited setup, a quoted trust score should be treated as checkpoint-bound. It should be re-measured on each materially new release rather than carried forward. Closed APIs, larger models, canonical-protocol scores, and benchmark-item-subset uncertainty are out of scope.

arXiv

DRIFT: Difficulty Routing Self-DIstillation with Rhythm-Gated Exploration and Success BuFfer Training

Haisen Luo, Yiwei Liu, Haoning Wang, Dan Liu, Junxi Yin, Haotian Wang, Lei Zhang, Xiaoyu Tian, Shuaiting Chen, Yuansheng Song, Baoyan Guo, Xiongfei Yan, Bolan Yang, Chengwei Liu, Ming Cui, Jiong Chen

Enabling large language models to achieve stable self-improvement without external expert supervision remains a central challenge in complex reasoning tasks. Existing self-distillation and reinforcement learning methods lack explicit mechanisms for tracking problem-level learning progress and adapting optimization strategies accordingly. Consequently, training may over-optimize easy problems, receive weak supervision from hard problems, and fail to sufficiently explore borderline cases. To resolve these issues, we propose DRIFT, an online self-evolution policy optimization framework for large language models. DRIFT regulates the model's self-improvement process through the joint use of Difficulty Routing and Rhythm Gating. The former identifies the model's learning state at the problem level and dynamically allocates self-distillation and reinforcement learning signals, while the latter refines policy updates at the token level, concentrating exploration on critical reasoning positions. By further incorporating a success buffer and a two-stage curriculum learning strategy, DRIFT preserves high-quality historical experience while progressively guiding the model from reliable behavior acquisition toward stable policy evolution. Evaluated across five benchmarks and three model scales, DRIFT surpasses the peak performance of both GRPO and SDPO across all evaluated metrics. On the average score over the five benchmarks, DRIFT achieves 79.5$\%$, outperforming GRPO by 9.5$\%$ and SDPO by 7.5$\%$, establishing a new state-of-the-art result. Notably, on ToolUse, DRIFT reaches an accuracy of 79.2$\%$, improving over GRPO by 13.5$\%$ and SDPO by 10.7$\%$, setting a new state-of-the-art and substantially outperforming all concurrent methods.

arXiv

Unbiased Canonical Set-Valued Oracles Via Lattice Theory

Jobst Heitzig

An oracle that tells you the probability of some future event can change that very probability because you act on the answer. We argue that this performativity is OK as people consult oracles to be informed, and hence moved, by the answer. We worry about instead that asking for a self-consistent answer, one that still holds once it has been announced, may leave the oracle with several answers to pick from, and whichever rule it uses to pick is a lever it could learn to pull. We propose to take away that choice: The oracle reports a credal set instead of a point estimate, which lifts the oracle's reaction function to an isotone operator on a lattice. We make the oracle report that operator's least fixed point, which exists because of Knaster and Tarski. As that answer is fixed by a rule laid down in advance, nothing is left to choose by the oracle. We show that solution exists, is self-consistent, is never empty, can be computed by iterating from below, and equals the ordinary point estimate if the question is not performative after all. For simple queries about probabilities, we propose to restrict answers to intervals and show that, under a mild monotonicity assumption, the answer is simply the interval from the no-information baseline to the self-fulfilling equilibrium one would end up at by iteratively querying a point oracle until the answer is self-consistent. As our proposal is purely order-theoretic, it carries over unchanged to arbitrary random variables and to bounded continuous statistics of their law. Finally we show that a fixed finite family of polytopes suffices to approximate every answer uniformly, which turns the construction into a terminating computation. We close by placing the construction inside the Scientist AI programme, where it offers a choice-free criterion for a step that programme currently hands to audited human judgement.

arXiv

Learning aligned EEG representations with subject-specific encoders

Bruna J. Lopes, Gabriel Schwartz, Sylvain Chevallier, Raphael Y. de Camargo, Bruno Aristimunha

Cross-subject EEG decoding promises more training data, but it also exposes neural networks to strong inter-subject distribution shifts. We study whether task supervision and architecture alone can learn subject-aligned representations. We replace a shared EEG encoder with subject-specific encoders followed by a common classifier, and compare this hybrid model with standard EEGNet, AttentionBaseNet, and CTNet baselines with Euclidean Alignment (EA) on four motor-imagery datasets. EA improves shared encoders by recentering subject covariances, but the hybrid encoder largely internalises this role: validation-loss curves and latent-distance analyses change little when EA is removed. Subject-specific heads increase class distinctiveness and place each subject close to its own latent manifold, improving most subjects while leaving a method-sensitive subset. These results support subject-specific encoders as a learned alignment mechanism for EEG decoding and identify head selection for unseen subjects as the remaining bottleneck.

arXiv

Brownian Kernel Ladders

Mahdi Mohammadigohari, Giuseppe Di Fatta, Giuseppe Nicosia, Panos M Pardalos

We introduce Brownian kernel ladders (BKLs), a recursive hierarchy of integral reproducing kernel Hilbert spaces built from linear functionals by repeatedly integrating Brownian pullback kernels indexed by functions from the preceding layer. The nonnegative 1-homogeneity of the Brownian kernel yields a kernel-preserving canonical spherical normalization and propagates square-root regularity through the hierarchy. Allowing all canonical ladder measures to vary produces a full adaptive BKL envelope with an infimal complexity. For this envelope, we prove depth-dependent Hölder and pointwise estimates, quasi-Banach structure, nestedness, and, under a geometric trace condition, strict growth with ballwise separation. We also establish existence of regularized empirical-risk minimizers for continuous losses uniformly bounded below, with almost-everywhere uniqueness of population predictions under strict convexity and pointwise uniqueness under full support. For statistical estimation, we study one realized ladder and finite dictionaries fixed independently of the estimation sample. For a dictionary of $M$ ladders, the Gaussian complexity of the union of radius-$r$ top-layer RKHS balls has $n^{-1/2}$ dependence, no explicit ambient-dimension factor, and model-selection factor $1+\sqrt{2\ln M}$. Corresponding high-probability oracle and excess-risk bounds follow; polynomial-size dictionaries retain a near-parametric rate. The theory separates adaptive representational richness from the statistical cost of ladder selection.

arXiv

Online Shift Detection and Conformal Adaptation for Deployed Safety Classifiers

Jun Wen Leong

Reasoning models deployed as safety monitors exhibit a systematic vulnerability: reasoning-token budget starvation. Adversarial inputs require $3.3\times$ more reasoning tokens than benign inputs to produce valid safety scores ($T_{50,\text{adv}}{=}154$ vs. $T_{50,\text{benign}}{=}46$ for o3), so low-budget deployments silently starve the monitor on exactly the inputs it must catch. This compounds the central failure mode: gradient-based evasion remains the residual threat - template jailbreaks fail at 99%, but GCG-optimized suffixes flip encoder decisions reliably. We systematize a canary construction - score-disagreement monitoring between a targeted and un-targeted classifier - and quantify its reliability under targeted evasion. We derive the exact security boundary - a confidence-gated equilibrium at which a monitor-aware attacker stalls (validated gap $= 1/(2λ)$, within 95% CI of theory) - and identify a failure mode in post-shift conformal adaptation. Three contributions. (1) Factorial drift benchmark. A pre-registered 800-cell evaluation ($4$ classifiers $\times$ $5$ shift types $\times$ $20$ seeds $\times$ $2$ windows) reveals detection difficulty is dominated by a classifier$\times$shift interaction ($η^2 = 0.185$): encoders detect paraphrase drift in 28 steps but miss adversarial suffixes for 37; decoders show the opposite. (2) Conformal collapse in generative embeddings. Weighted conformal prediction fails on decoder classifiers: logistic density-ratio estimation achieves perfect separability in 3584--4096-dimensional space, clipping all importance weights to zero. Projecting to $\leq$32 dimensions restores coverage (+33pp). (3) Adversarial canary threat model. Across 35 frontier models, a 4-tier threat model yields deployment guarantees ($\geq$71% detection, $<$1.5% FPR at $N{=}1000$).

arXiv

Don't Retrain, Just Reuse: Recovering Dual-Target Molecules from Single-Target Diffusion Models

Qingyuan Zeng, Pengxiang Cai, Zixin Guan, Ziyang Chen, Anglin Liu, Xinyao Lai, Jintai Chen

Designing a single molecule that modulates two targets is a promising strategy for polypharmacology, but it remains substantially harder than standard single-target generation because one candidate must satisfy two binding requirements while preserving drug-likeness and synthesizability. Existing dual-target generative methods typically introduce dual-target capability by either retraining the generator or intervening in the diffusion process during sampling. The former can be costly and difficult to stabilize when dual-target supervision is sparse, while the latter may be sensitive to denoising-time target balancing and competing update directions. These limitations motivate a generator-preserving alternative that keeps the pretrained prior intact: can dual-target candidates instead be recovered from the input space of a frozen single-target diffusion model, without modifying its parameters or denoising dynamics? We formulate this task as a constrained multi-objective optimization problem and propose REUSE, which evolves the input noise of a frozen diffusion generator rather than molecular structures. Each input is decoded multiple times and scored by the collective quality of the generated molecular family. Candidates are then screened progressively: lower-cost evaluations prioritize molecules satisfying chemical-feasibility criteria, full docking is reserved for a reduced frontier, and the survivors are jointly selected as a diverse panel with strong affinity to both targets. Experiments show that REUSE achieves stronger and more balanced dual-target recovery than prior dual-target baselines, improving Dual High Affinity by 21.1 percentage points over the strongest prior baseline while retaining QED and SA profiles consistent with commonly used chemical-feasibility criteria.

arXiv

Latent Spectroscopy: Posterior Collapse as a Feature

Johannes Hirn

We show that, in linear Gaussian VAEs, posterior collapse is a form of latent feature selection. Feature importance is set by each latent coordinate's contribution to reconstruction, itself given by the corresponding PCA eigenvalue. Varying the regularizer strength $β$ reveals a ranked spectrum of collapse events, with thresholds set by the utility/PCA spectrum. A mode-by-mode analysis identifies the scale-invariant signal fraction as an order parameter obeying Landau scaling near collapse. WorldClim experiments confirm both the utility-threshold calibration and the predicted near-collapse scaling.

arXiv

Robust Recommendation from Noisy Implicit Feedback: A GMM-Weighted Bayes-label Transition Matrix Framework

Zongyu Li, Xuanyu Liu, Gongce Cao, Shirui Sun, Yaqi Fang, Yongshuai Yu

Label noise is a central challenge in learning from implicit feedback for recommendation. Conventional approaches discard noisy examples for robustness, but this sacrifices data efficiency. Unlike filtering approaches, Bayes-label transition matrix (BLTM) based methods keep all data, but their transition matrix estimates are skewed in practice. To reduce this skew, we introduce GMM-weighted Bayes-label Transition Matrix (RGBT), which augments BLTM with GMM-based instance weights. A GMM assigns each instance a reliability score, and these scores calibrate the BLTM to reduce bias. We show theoretically that RGBT retains all samples for BLTM estimation, yields consistent estimates, and provably reduces variance compared to CLTM. Experiments on real and synthetic datasets show that RGBT handles noisy samples more effectively than sample-selection methods, and calibrates the transition matrix more accurately than existing approaches.

arXiv

Uncertainty-Aware Predictive Safety Filters for Probabilistic Neural Network Dynamics

Bernd Frauenknecht, Lukas Kesper, Daniel Mayfrank, Henrik Hose, Sebastian Trimpe

Predictive safety filters (PSFs) leverage model predictive control to enforce constraint satisfaction during deep reinforcement learning (RL) exploration, yet their reliance on first-principles models or Gaussian processes limits scalability and broader applicability. Meanwhile, model-based RL (MBRL) methods routinely employ probabilistic ensemble (PE) neural networks to capture complex, high-dimensional dynamics from data with minimal prior knowledge. However, existing attempts to integrate PEs into PSFs lack rigorous uncertainty quantification. We introduce the Uncertainty-Aware Predictive Safety Filter (UPSi), a PSF that provides rigorous safety verification using PE dynamics models by formulating future outcomes as reachable sets. UPSi introduces an explicit certainty constraint that prevents model exploitation and integrates seamlessly into common MBRL frameworks. We evaluate UPSi under practical simplifications within Dyna-style MBRL on standard safe RL benchmarks and report substantial improvements in exploration safety over prior neural network PSFs while maintaining performance on par with standard MBRL. UPSi bridges the gap between the scalability and generality of modern MBRL and the safety guarantees of predictive safety filters.

arXiv

Multi-Head Residual-Gated DeepONet for Coherent Nonlinear Wave Dynamics

ZHIWEI FAN, Yiming Pan, Daniel Coca

Coherent nonlinear wave dynamics are often strongly shaped by a compact set of physically meaningful descriptors of the initial state. Traditional neural operators typically treat the input-output mapping as a largely black-box high-dimensional regression problem, without explicitly exploiting this structured physical context. Common feature-integration strategies usually rely on direct concatenation or FiLM-style affine modulation in hidden latent spaces. Here we introduce a different paradigm, loosely inspired by the complementary roles of state evolution and physically meaningful observables in quantum mechanics: the wave field is learned through a standard DeepONet state pathway, while compact physical descriptors follow a parallel conditioning pathway and act as residual modulation factors on the state prediction. Based on this idea, we develop a Multi-Head Residual-Gated DeepONet (MH-RG), which combines a pre-branch residual modulator, a branch residual gate, and a trunk residual gate with a low-rank multi-head mechanism to capture multiple complementary conditioned response patterns without prohibitive parameter growth. We evaluate the framework on representative benchmarks including highly nonlinear conservative wave dynamics and dissipative trapped dynamics and further perform detailed mechanistic analyses of the learned multi-head gating behavior. Compared with feature-augmented baselines, MH-RG DeepONet achieves consistently lower error while better preserving phase coherence and the fidelity of physically relevant dynamical quantities.

arXiv

Fairness is Not Flat: Geometric Phase Transitions Against Shortcut Learning

Nicolas Rodriguez-Alvarez

Deep Neural Networks are highly susceptible to shortcut learning, frequently memorizing low-dimensional spurious correlations instead of underlying causal mechanisms. This phenomenon not only degrades out-of-distribution robustness but also induces severe demographic biases in sensitive applications. In this paper, we propose a geometric \textit{a priori} methodology to mitigate shortcut learning. By deploying a zero-hidden-layer ($N=1$) Topological Auditor, we mathematically isolate features that monopolize the gradient without human intervention. We empirically demonstrate a Capacity Phase Transition: once linear shortcuts are pruned, networks are forced to utilize higher geometric capacity ($N \geq 16$) to curve the decision boundary and learn ethical representations. Our approach outperforms L1 Regularization -- which collapses into demographic bias -- and operates at a fraction of the computational cost of post-hoc methods like Just Train Twice (JTT), successfully reducing counterfactual gender vulnerability from 21.18\% to 7.66\%.

arXiv

Preference Redirection via Attention Concentration: An Attack on Computer Use Agents

Dominik Seip, Matthias Hein

Advancements in multimodal foundation models have enabled the development of Computer Use Agents (CUAs) capable of autonomously interacting with GUI environments. As CUAs are not restricted to certain tools, they allow to automate more complex agentic tasks but at the same time open up new security vulnerabilities. While prior work has concentrated on the language modality, the vulnerability of the vision modality has received less attention. In this paper, we introduce PRAC, a novel attack that, unlike prior work targeting the VLM output directly, manipulates the model's internal preferences by redirecting its attention toward a stealthy adversarial patch. We show that PRAC is able to manipulate the selection process of a CUA on an online shopping platform towards a chosen target product. While we require white-box access to the model for the creation of the attack, we show that our attack generalizes to fine-tuned versions of the same model, presenting a critical threat as multiple companies build specific CUAs based on open weights models.

arXiv

Are Latent Reasoning Models Easily Interpretable?

Connor Dilgren, Sarah Wiegreffe

Latent reasoning models (LRMs) have attracted significant research interest due to their low inference cost (relative to explicit reasoning models) and theoretical ability to explore multiple reasoning paths in parallel. However, these benefits come at the cost of reduced interpretability: LRMs are difficult to monitor because they do not reason in natural language. This paper presents an investigation into LRM interpretability by examining two state-of-the-art LRMs. First, we find that latent reasoning tokens are often unnecessary for LRMs' predictions; on logical reasoning datasets, LRMs can almost always produce the same final answers without using latent reasoning at all. This underutilization of reasoning tokens may partially explain why LRMs do not consistently outperform explicit reasoning methods and raises doubts about the stated role of these tokens in prior work. Second, we demonstrate that when latent reasoning tokens are necessary for performance, we can decode gold reasoning traces up to 65-93% of the time for correctly predicted instances. This suggests LRMs often implement the expected solution rather than an uninterpretable reasoning process. Finally, we present a method to decode a verified natural language reasoning trace from latent tokens without knowing a gold reasoning trace a priori, demonstrating that it is possible to find a verified trace for a majority of correct predictions but only a minority of incorrect predictions. Our findings highlight that current LRMs largely encode interpretable processes, and interpretability itself can be a signal of prediction correctness.

arXiv

Cognitive Energy Modeling for Neuroadaptive Human-Machine Systems using EEG and WGAN-GP

Sriram Sattiraju, Vaibhav Gollapalli, Aryan Shah, Timothy McMahan

Electroencephalography (EEG) provides a non-invasive insight into the brain's cognitive and emotional dynamics. However, modeling how these states evolve in real time and quantifying the energy required for such transitions remains a major challenge. The Schrödinger Bridge Problem (SBP) offers a principled probabilistic framework to model the most efficient evolution between the brain states, interpreted as a measure of cognitive energy cost. While generative models such as GANs have been widely used to augment EEG data, it remains unclear whether synthetic EEG preserves the underlying dynamical structure required for transition-based analysis. In this work, we address this gap by using SBP-derived transport cost as a metric to evaluate whether GAN-generated EEG retains the distributional geometry necessary for energy-based modeling of cognitive state transitions. We compare transition energies derived from real and synthetic EEG collected during Stroop tasks and demonstrate strong agreement across group and participant-level analyses. These results indicate that synthetic EEG preserves the transition structure required for SBP-based modeling, enabling its use in data-efficient neuroadaptive systems. We further present a framework in which SBP-derived cognitive energy serves as a control signal for adaptive human-machine systems, supporting real-time adjustment of system behavior in response to user cognitive and affective state.

arXiv

A Sobering Look at Tabular Data Generation via Probabilistic Circuits

Davide Scassola, Dylan Ponsford, Adrián Javaloy, Sebastiano Saccani, Luca Bortolussi, Henry Gouk, Antonio Vergari

Tabular data is more challenging to generate than text and images, due to its heterogeneous features and much lower sample sizes. On this task, diffusion-based models are the current state-of-the-art (SotA) model class, achieving almost perfect performance on commonly used benchmarks. In this paper, we question the perception of progress for tabular data generation. First, we highlight the limitations of current protocols to evaluate the fidelity of generated data, and advocate for alternative ones. Next, we revisit a simple baseline -- hierarchical mixture models in the form of deep probabilistic circuits (PCs) -- which delivers competitive or superior performance to SotA models for a fraction of the cost. PCs are the generative counterpart of decision forests, and as such can natively handle heterogeneous data as well as deliver tractable probabilistic generation and inference. Finally, in a rigorous empirical analysis we show that the apparent saturation of progress for SotA models is largely due to the use of inadequate metrics. As such, we highlight that there is still much to be done to generate realistic tabular data. Code available at https://github.com/april-tools/tabpc.

arXiv

When should we trust the annotation? Selective prediction for molecular structure retrieval from mass spectra

Mira Jürgens, Gaetan De Waele, Morteza Rakhshaninejad, Willem Waegeman

Machine learning methods for identifying molecular structures from tandem mass spectra (MS/MS) have advanced rapidly, yet current approaches still exhibit significant error rates. In high-stakes applications such as clinical metabolomics and environmental screening, incorrect annotations can have serious consequences, making it essential to determine when a prediction can be trusted. In this work, we introduce a selective prediction framework for molecular structure retrieval from MS/MS spectra, separating low-risk predictions automatically from lower-confidence predictions. We formulate the problem within the risk-coverage tradeoff framework and systematically evaluate uncertainty quantification strategies at three levels: input-level distance in the learned representation, fingerprint-level uncertainty over predicted molecular fingerprint bits, and retrieval-level uncertainty over candidate rankings. We compare scoring functions including first-order confidence measures, aleatoric and epistemic uncertainty estimates from second-order distributions, as well as distance-based measures in the latent space. All experiments are conducted on the MassSpecGym benchmark. Our analysis reveals that while fingerprint-level uncertainty scores are poor proxies for retrieval success, retrieval-level total uncertainty provides the overall strongest rejection criterion, and first-order confidence measures are computationally inexpensive, strong baselines. We demonstrate that by applying distribution-free risk control via generalisation bounds, practitioners can specify a tolerable error rate and obtain a subset of annotations satisfying that constraint with high probability.

arXiv

Quantifying Membership Disclosure Risk for Tabular Synthetic Data Using Kernel Density Estimators

Rajdeep Pathak, Amit Basak, Sayantee Jana

The use of synthetic data has become increasingly popular as a privacy-preserving alternative to sharing real datasets, especially in sensitive domains such as healthcare, finance, and demography. However, the privacy assurances of synthetic data are not absolute, and remain susceptible to membership inference attacks (MIAs), where adversaries aim to determine whether a specific individual was present in the dataset used to train the generator. In this work, we propose a practical and effective method to quantify membership disclosure risk in tabular synthetic datasets using kernel density estimators (KDEs). Our KDE-based approach models the distribution of nearest-neighbour distances between synthetic data and the training records, allowing probabilistic inference of membership and enabling robust evaluation via ROC curves. We propose two attack models: a 'True Distribution Attack', which assumes privileged access to training data, and a more realistic, implementable 'Realistic Attack' that uses auxiliary data without true membership labels. Empirical evaluations across four real-world datasets and six synthetic data generators demonstrate that our method consistently achieves higher F1 scores and sharper risk characterization than a prior baseline approach, without requiring computationally expensive shadow models. The proposed method provides a practical framework and metric for quantifying membership disclosure risk in synthetic data, which enables data custodians to conduct a post-generation risk assessment prior to releasing their synthetic datasets for downstream use. The datasets and codes for this study are available at https://github.com/PyCoder913/MIA-KDE.

arXiv

Online Learnability of Chain-of-Thought Verifiers: Soundness and Completeness Trade-offs

Maria Florina Balcan, Avrim Blum, Kiriaki Fragkia, Zhiyuan Li, Dravyansh Sharma

Large Language Models (LLMs) using chain-of-thought reasoning have demonstrated great potential for solving complex reasoning and planning tasks. However, their outputs remain unreliable and need careful verification. Even as LLMs get more accurate over time, learned verifiers can help increase trust, enforce safety constraints, and ensure alignment with personal preferences. A major challenge in learning verifiers, especially when they are used to guide generation, is that the feedback loop between generator and verifier may induce substantial distribution shift. Motivated by this challenge, we propose a framework for online learning chain-of-thought verifiers, which given a problem statement and a reasoning trace check the correctness of each reasoning step. Highlighting the asymmetric role of soundness errors (failing to flag an incorrect reasoning step) and completeness errors (incorrectly flagging a correct step as wrong), we introduce novel extensions of the Littlestone dimension which tightly characterize the mistake bounds for learning in the realizable setting. We provide optimal algorithms for finding the Pareto-frontier as well as for minimizing a linear combination of asymmetric costs. We further show how our learned verifiers can be used to boost the accuracy of a collection of weak generators and enable generation of proofs beyond what they were initially trained on. Under the mild assumption that one of the generators can generate a correct next step with a small success probability, we show how to learn a strong generator with small error and abstention rates. We additionally establish a separation between our approach and learning from offline expert demonstrations. In particular, we show that learning from offline demonstrations cannot in general achieve the soundness-completeness guarantees produced by our interactive learning approach.

arXiv

SPD Learn: A Geometric Deep Learning Python Library for Neural Decoding Through Trivialization

Bruno Aristimunha, Ce Ju, Antoine Collas, Florent Bouchard, Ammar Mian, Bertrand Thirion, Sylvain Chevallier, Reinmar Kobler

Implementations of symmetric positive definite (SPD) matrix-based neural networks for neural decoding remain fragmented across research codebases and Python packages. Existing implementations often employ ad hoc handling of manifold constraints and non-unified training setups, which hinders reproducibility and integration into modern deep-learning workflows. To address this gap, we introduce SPD Learn, a unified and modular Python package for geometric deep learning with SPD matrices. SPD Learn provides core SPD operators and neural-network layers, including numerically stable spectral operators, and enforces Stiefel/SPD constraints via trivialization-based parameterizations. This design enables standard backpropagation and optimization in unconstrained Euclidean spaces while producing manifold-constrained parameters by construction. The package also offers reference implementations of representative SPDNet-based models and interfaces with widely used brain computer interface/neuroimaging toolkits and modern machine-learning libraries (e.g., MOABB, Braindecode, Nilearn, and SKADA), facilitating reproducible benchmarking and practical deployment.

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