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

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.

Latent Matters: Learning Deep State-Space Models

Deep state-space models (DSSMs) enable temporal predictions by learning the underlying dynamics of observed sequence data. They are often trained by maximising the evidence lower bound. However, as we show, this does not ensure the model actually learns the underlying dynamics. We therefore propose a constrained optimisation framework as a general approach for training DSSMs. Building upon this, we introduce the extended Kalman VAE (EKVAE), which combines amortised variational inference with classic Bayesian filtering/smoothing to model dynamics more accurately than RNN-based DSSMs. Our results show that the constrained optimisation framework significantly improves system identification and prediction accuracy on the example of established state-of-the-art DSSMs. The EKVAE outperforms previous models w.r.t. prediction accuracy, achieves remarkable results in identifying dynamical systems, and can furthermore successfully learn state-space representations where static and dynamic features are disentangled.

Closing the gap on tabular data with Fourier and Implicit Categorical Features

While Deep Learning has demonstrated impressive results in applications on various data types, it continues to lag behind tree-based methods when applied to tabular data, often referred to as the last "unconquered castle" for neural networks. We hypothesize that a significant advantage of tree-based methods lies in their intrinsic capability to model and exploit non-linear interactions induced by features with categorical characteristics. In contrast, neural-based methods exhibit biases toward uniform numerical processing of features and smooth solutions, making it challenging for them to effectively leverage such patterns. We address this performance gap by using statistical-based feature processing techniques to identify features that are strongly correlated with the target once discretized. We further mitigate the bias of deep models for overly-smooth solutions, a bias that does not align with the inherent properties of the data, using Learned Fourier. We show that our proposed feature preprocessing significantly boosts the performance of deep learning models and enables them to achieve a performance that closely matches or surpasses XGBoost on a comprehensive tabular data benchmark.

RepSPD: Enhancing SPD Manifold Representation in EEGs via Dynamic Graphs

Decoding brain activity from electroencephalography (EEG) is crucial for neuroscience and clinical applications. Among recent advances in deep learning for EEG, geometric learning stands out as its theoretical underpinnings on symmetric positive definite (SPD) allows revealing structural connectivity analysis in a physics-grounded manner. However, current SPD-based methods focus predominantly on statistical aggregation of EEGs, with frequency-specific synchronization and local topological structures of brain regions neglected. Given this, we propose RepSPD, a novel geometric deep learning (GDL)-based model. RepSPD implements a cross-attention mechanism on the Riemannian manifold to modulate the geometric attributes of SPD with graph-derived functional connectivity features. On top of this, we introduce a global bidirectional alignment strategy to reshape tangent-space embeddings, mitigating geometric distortions caused by curvature and thereby enhancing geometric consistency. Extensive experiments demonstrate that our proposed framework significantly outperforms existing EEG representation methods, exhibiting superior robustness and generalization capabilities.

FlexMS is a flexible framework for benchmarking deep learning-based mass spectrum prediction tools in metabolomics

The identification and property prediction of chemical molecules is of central importance in the advancement of drug discovery and material science, where the tandem mass spectrometry technology gives valuable fragmentation cues in the form of mass-to-charge ratio peaks. However, the lack of experimental spectra hinders the attachment of each molecular identification, and thus urges the establishment of prediction approaches for computational models. Deep learning models appear promising for predicting molecular structure spectra, but overall assessment remains challenging as a result of the heterogeneity in methods and the lack of well-defined benchmarks. To address this, our contribution is the creation of benchmark framework FlexMS for constructing and evaluating diverse model architectures in mass spectrum prediction. With its easy-to-use flexibility, FlexMS supports the dynamic construction of numerous distinct combinations of model architectures, while assessing their performance on preprocessed public datasets using different metrics. In this paper, we provide insights into factors influencing performance, including the structural diversity of datasets, hyperparameters like learning rate and data sparsity, pretraining effects, metadata ablation settings and cross-domain transfer learning analysis. This provides practical guidance in choosing suitable models. Moreover, retrieval benchmarks simulate practical identification scenarios and score potential matches based on predicted spectra.

MEDNA-DFM: A Dual-View FiLM-MoE Model for Explainable DNA Methylation Prediction

Accurate computational identification of DNA methylation is essential for understanding epigenetic regulation. Although deep learning excels in this binary classification task, its "black-box" nature impedes biological insight. We address this by introducing a high-performance model MEDNA-DFM, alongside mechanism-inspired signal purification algorithms. Our investigation demonstrates that MEDNA-DFM effectively captures conserved methylation patterns, achieving robust distinction across diverse species. Validation on external independent datasets confirms that the model's generalization is driven by conserved intrinsic motifs (e.g., GC content) rather than phylogenetic proximity. Furthermore, applying our developed algorithms extracted motifs with significantly higher reliability than prior studies. Finally, empirical evidence from a Drosophila 6mA case study prompted us to propose a "sequence-structure synergy" hypothesis, suggesting that the GAGG core motif and an upstream A-tract element function cooperatively. We further validated this hypothesis via in silico mutagenesis, confirming that the ablation of either or both elements significantly degrades the model's recognition capabilities. This work provides a powerful tool for methylation prediction and demonstrates how explainable deep learning can drive both methodological innovation and the generation of biological hypotheses.

Bound to Disagree: Generalization Bounds via Certifiable Surrogates

Generalization bounds for deep learning models are typically vacuous, not computable or restricted to specific model classes. In this paper, we tackle these issues by providing new disagreement-based certificates for the gap between the true risk of any two predictors. We then bound the true risk of the predictor of interest via a surrogate model that enjoys tight generalization guarantees, and evaluating our disagreement bound on an unlabeled dataset. We empirically demonstrate the tightness of the obtained certificates and showcase the versatility of the approach by training surrogate models leveraging three different frameworks: sample compression, model compression and PAC-Bayes theory. Importantly, such guarantees are achieved without modifying the target model, nor adapting the training procedure to the generalization framework.

Through BrokenEyes: How Eye Disorders Impact Face Detection?

Vision disorders significantly impact millions of lives, altering how visual information is processed and perceived. In this work, a computational framework was developed using the BrokenEyes system to simulate five common eye disorders: Age-related macular degeneration, cataract, glaucoma, refractive errors, and diabetic retinopathy and analyze their effects on neural-like feature representations in deep learning models. Leveraging a combination of human and non-human datasets, models trained under normal and disorder-specific conditions revealed critical disruptions in feature maps, particularly for cataract and glaucoma, which align with known neural processing challenges in these conditions. Evaluation metrics such as activation energy and cosine similarity quantified the severity of these distortions, providing insights into the interplay between degraded visual inputs and learned representations.

No Labels, No Look-Ahead: Unsupervised Online Video Stabilization with Classical Priors

We propose a new unsupervised framework for online video stabilization. Unlike methods based on deep learning that require paired stable and unstable datasets, our approach instantiates the classical stabilization pipeline with three stages and incorporates a multithreaded buffering mechanism. This design addresses three longstanding challenges in end-to-end learning: limited data, poor controllability, and inefficiency on hardware with constrained resources. Existing benchmarks focus mainly on handheld videos with a forward view in visible light, which restricts the applicability of stabilization to domains such as UAV nighttime remote sensing. To fill this gap, we introduce a new multimodal UAV aerial video dataset (UAV-Test). Experiments show that our method consistently outperforms state-of-the-art online stabilizers in both quantitative metrics and visual quality, while achieving performance comparable to offline methods.

KMLP: A Scalable Hybrid Architecture for Web-Scale Tabular Data Modeling

Predictive modeling on web-scale tabular data with billions of instances and hundreds of heterogeneous numerical features faces significant scalability challenges. These features exhibit anisotropy, heavy-tailed distributions, and non-stationarity, creating bottlenecks for models like Gradient Boosting Decision Trees and requiring laborious manual feature engineering. We introduce KMLP, a hybrid deep architecture integrating a shallow Kolmogorov-Arnold Network (KAN) front-end with a Gated Multilayer Perceptron (gMLP) backbone. The KAN front-end uses learnable activation functions to automatically model complex non-linear transformations for each feature, while the gMLP backbone captures high-order interactions. Experiments on public benchmarks and an industrial dataset with billions of samples show KMLP achieves state-of-the-art performance, with advantages over baselines like GBDTs increasing at larger scales, validating KMLP as a scalable deep learning paradigm for large-scale web tabular data.