We present GaussPDE, a framework that injects physically structured partial differential equation (PDE) dynamics into pretrained 3D Gaussian scenes without mesh extraction, voxelization, or retraining. Our key observation is that PDE rendering requires not only accurate appearance, but also a reliable discrete computational domain. We therefore first introduce camera-aware regularization during 3DGS reconstruction to suppress camera-near floaters and oversized primitives that would create unstable graph topology. We then construct an active Gaussian graph using covariance-aware distances and opacity, appearance, and boundary-aware conductance, enabling mass-weighted graph Laplacian PDE evolution directly over Gaussian primitives. The evolving scalar PDE state is coupled back to rendering by modifying the direct-current spherical harmonic color coefficients while preserving geometry, opacity, and view-dependent rendering behavior. Experiments on real and synthetic scenes show that GaussPDE produces stable, controllable, and spatially coherent dynamic visualizations, with reduced cross-boundary leakage compared with baselines.
https://arxiv.org/abs/2609.27264
Prototype-based neural networks provide inherent interpretability through case-based reasoning, yet suffer from critical limitations: prototypes converge to redundant features, fail to capture diverse semantic parts, and lack quantitative interpretability assessment. We propose Diversity-Aware Prototype Learning (DAPL), which enforces prototype diversity through architectural constraints rather than explicit regularization. Our approach leverages multi-head self-attention with strict one-to-one attention-to-prototype mapping, ensuring each prototype specializes in distinct visual features. We further introduce foreground-aware training to focus prototypes on semantically meaningful regions and develop comprehensive evaluation metrics (Coverage and Diversity) for quantitative interpretability assessment. Experiments on CUB-200-2011 demonstrate substantial improvements: DAPL with foreground-aware training achieves 81.69\% accuracy with 0.596 Coverage and 0.427 Diversity, providing the best overall balance across all evaluated prototype-based methods. Code is available at this https URL.
https://arxiv.org/abs/2609.27194
Dissipativity is a fundamental system-theoretic property closely related to stability, passivity, and input--output stability, and is particularly important in robotics, where learned dynamics models are often embedded within feedback control loops. However, most existing approaches for learning dissipative dynamics are based on continuous-time formulations, which require ODE solvers during training or inference and can therefore be computationally expensive. Moreover, because practical implementations are inherently discrete-time, direct discretization of a continuous-time passive system does not necessarily preserve passivity, motivating the need for explicit discrete-time guarantees. This study proposes a method for learning incrementally dissipative dynamics from input--output time-series data using a deep multilayer perceptron formulated directly in discrete time. Through a constrained parameterization and a dedicated training procedure, the proposed model guarantees incremental dissipativity by construction rather than through regularization. Lyapunov-based analysis establishes the corresponding dissipativity and stability guarantees, while simulations on robotic dynamical systems demonstrate competitive prediction accuracy, computational efficiency, and consistent preservation of incremental dissipativity compared with baseline methods.
https://arxiv.org/abs/2609.27188
Stacking heterogeneous vision backbones (CNNs, ViTs, and hybrids) is the de facto recipe for accuracy, calibration, and robustness, yet two coupled pathologies limit its returns. Prediction-space multicollinearity ill-conditions the meta-learner's Gram matrix, inflating weight variance and producing brittle solutions on a thin manifold. Calibration collapse compounds constituent miscalibration through naive linear stacking, so adding more models can hurt expected calibration error (ECE). Existing remedies, ridge regularization, greedy selection, model soups, and SWAG address at most one of these issues, and none jointly target conditioning and calibration in heterogeneous prediction pools. We introduce CORE-STACK+, a preconditioning pipeline with four components: (i) a kernelized redundancy filter that removes non-linear inter-model dependencies invisible to Pearson correlation, using Centered Kernel Alignment (CKA) [23]; (ii) a $<15$K-parameter differentiable meta-feature gate that learns per-sample attention over ensemble statistics; (iii) a spectrum-adaptive Ridge penalty $lambda^{star}=lmax(Chat)/SNR(Chat)$ derived from a Marchenko-Pastur signal-noise decomposition, eliminating nested cross-validation; and (iv) a Laplace-approximate Bayesian blender replacing inverse-RMSE heuristics. We prove a PAC-Bayes excess-risk bound that, for the first time, jointly accounts for prediction-space redundancy and meta-learner capacity. Across six benchmarks, CORE-STACK+ delivers $+1.8\%$ top-1 on ImageNet-1K, $-4.2$ mCE on ImageNet-C, $+0.9$ mIoU on ADE20K, and $+1.3$ AP on COCO, while reducing retained models by 35-57% and inference FLOPs by up to $41%$. ECE improves $2.1\times$ over deep ensembles without post hoc temperature scaling.
https://arxiv.org/abs/2609.26905
Vector Quantization (VQ) is fundamental to discrete visual tokenizers that power modern autoregressive and masked image generation models. While recent shared-projection codebook methods have substantially advanced codebook utilization, training stability remains a critical and underexplored challenge. We argue that the root cause lies in the entanglement of the Encoder--Decoder and Codebook training: because neither module can reliably fulfill its own responsibility in isolation, the system can only function when the two subsystems happen to cooperate---a fragile condition that breaks down precisely when training is most stressed. We propose StableVQ, which revisits the proper learning objective of each module and resolves the problems that arise when each is trained to fulfill its own role independently. Concretely, (1) Dynamic STE corrects the instability in the Encoder's learning objective, enabling it to robustly optimize the reconstruction space under discrete regularization even when codebook utilization is low. (2) Region VQ Loss reconceives the Codebook's learning objective so that it can independently guarantee full tracking of the encoder output distribution, without relying on encoder oscillations to drive activation. (3) Decoupled Schedule recognizes that the distinct responsibilities of the Encoder--Decoder and the Codebook demand distinct optimization dynamics, and assigns each an independent learning rate schedule to ensure robust system-level behavior. Built on top of shared-projection codebooks, StableVQ is lightweight and introduces no learnable parameters. Experiments on ImageNet demonstrate consistent improvements in training stability, codebook utilization, and reconstruction quality across diverse codebook sizes and initialization settings.
https://arxiv.org/abs/2609.26774
The dimensional collapse of representations in self-supervised contrastive learning is an ever-present issue. One notable technique to prevent such a collapse of representations is using a multi-layered perceptron network called Projector. In several works, the projector has been found to heavily influence the quality of representations learned in a self-supervised contrastive pre-training task. However, the question still lingers. What role does the projector play? Assuming the projector mitigates dimensional collapse, what prevents the terminal layer of the base encoder from functioning as the projector in the absence of an explicit multi-layer perceptron (MLP) head? In this work, we intend to study what happens inside the projector by examining the rank dynamics of the same and the encoder through empirical study and analysis. Through mathematical analysis, we observe that the effect of rank reduction predominantly occurs in the last layer. Motivated by this insight, we propose a weight regularization strategy applied specifically to the last layer. We demonstrate that this targeted approach yields better performance than applying orthogonal weight regularization across the entire network (WeRank), both with and without a projector. Our method improves Top-1 accuracy by more than 1% on SimCLR on the ImageNet100 dataset and consistently outperforms baseline SimCLR variants on CIFAR datasets, supporting our interpretation of the projector's role.
https://arxiv.org/abs/2609.26334
An LLM agent's capability is largely magnified by its harness, namely the prompts, control flow, tooling, memory, and context management surrounding the frozen backbone model. Recent methods increasingly automate this process by iteratively proposing and selecting component-wise edits of an agent harness, practically establishing a form of recursive self-improvement (RSI) at the agent-system level. However, such recursive evolution may overfit by memorizing the training tasks, showing large in-distribution gains that shrink or even vanish on out-of-distribution benchmarks. We introduce Regularized Recursive Self-Improvement of Agent Harnesses (RRSI), which incorporates the principles of regularizations into harness self-improvement by constraining the evolution candidate proposal and selection. The proposer operates with a temporally annealed budget, limiting how many edits a candidate can bundle, and it encourages unexplored trajectories based on evolution history. The selector is equipped with a critic and a pruner: the critic screens benchmark-specific proposals, while the pruner, removes changes that are too small, too expensive, or no longer useful. Together these constraints favor reusable agent mechanisms over benchmark-specific ones or even noises. Across eight benchmarks spanning coding, agentic workspace and engineering design tasks, RRSI gains up to 14.1 points on the split it evolves against and up to 4.7 points on the five out-of-distribution benchmarks, while producing a harness that runs on 30% fewer policy tokens than the unregularized evolution. Code is available at this https URL and project page is this https URL.
https://arxiv.org/abs/2609.24972
As agents are deployed with increased autonomy, even extremely rare events along their stochastic output trajectories can occur and prove catastrophic. Safe deployment therefore does not depend on whether these events can occur, but on how often they might. We study the problem of estimating the probability of rare events that arise from stochastic variation in the agent's own actions. Estimating this type of risk requires searching over the combinatorially vast space of trajectories. Naive Monte Carlo is computationally prohibitive in this regime, and constructing effective importance sampling (IS) proposals requires coordinated changes to a context-dependent chain of conditional distributions. We develop a new IS method that perturbs the original model's weights to construct the proposal. The proposal is itself a differentiably parameterized language model, enabling gradient-based search over weight space. We formulate an objective that combines a differentiable surrogate for event amplification and an adaptive regularization scheme that dynamically balances amplification against estimator stability. We evaluate our approach on $\sim$120M and $\sim$2.6B models across three event families spanning 300+ rare events as rare as $10^{-9}$, with reference probabilities computed with $<10\%$ relative standard error. In our most verifiable settings, we observe that our IS estimator achieves over $800\times$ compute-weighted efficiency gains over naive Monte Carlo for events with probabilities lower than $10^{-7}$. Our implementation is available at this https URL.
https://arxiv.org/abs/2609.24969
Angular-margin speaker encoders are widely used in voice conversion, yet the geometry of their classifier prototypes remains poorly understood. We analyze ECAPA-TDNN classifier prototypes as points on the unit hypersphere and characterize their organization using rotation-invariant angular statistics together with global and local effective dimensionality measures. Our analysis shows that standard training can induce angular concentration and a substantial reduction in effective dimensionality. To address this, we investigate two geometric regularization strategies (hinged Riesz log-energy and effective-dimension maximization) applied to classifier prototypes to encourage more uniform hyperspherical coverage. The resulting prototype sets exhibit higher effective dimensionality and improved isotropy, with configuration-dependent effects on speaker-recognition performance. When the corresponding ECAPA-TDNN models are used as speaker encoders for Fast-VGAN, the regularized systems also exhibit improved robustness in zero-shot voice conversion, particularly for previously unseen speakers.
https://arxiv.org/abs/2609.24688
Hyperbolic vision-language models (VLMs) represent image and text features in a geometry naturally suited to hierarchy, but their adaptation to downstream tasks has largely relied on fixed prompts. Existing prompt learning methods, meanwhile, treat class labels as a flat set and do not exploit available taxonomic structure. We address this gap with a hierarchical prompt learning plug-in for frozen hyperbolic VLMs. Given a fixed offline parent-class hierarchy, it augments a class prompt learner with a separate parent prompt learner, parent-level supervision, hyperbolic entailment regularization, and parent-feedback logit fusion. We instantiate the method with CoOp, CoCoOp and MaPLe, yielding HyPLO, CoHyPLO and MaHyPLO. Across the standard 11-dataset benchmark, all variants improve base-to-new generalization and cross-dataset transfer, and remain comparable to their prompt learning baselines under domain shift. Six hierarchical metrics and embedding analyses show that the method produces more taxonomically consistent predictions and induces a hierarchy-consistent organization of parent, class, and image embeddings in hyperbolic space. Its gains are largest when novel classes must be placed within a fixed taxonomy, and smallest for fine-grained confusions among sibling classes or shifts affecting only the image distribution.
https://arxiv.org/abs/2609.24276
Atomic activity understanding aims to recognize and localize structured traffic behaviors that jointly encode motion patterns and their grounding in road topology. Unlike conventional action recognition, atomic activities are multi-agent, multi-label, and topology-aware: multiple activities co-occur while many agents remain inactive. We introduce Action-Slot, a structured action-centric representation learning framework. Slot attention is widely used for object-centric decomposition, but its permutation-invariant design and object-level inductive bias are misaligned with atomic activity semantics. We reformulate slot learning as structured activity decomposition through three designs: (1) category-aligned action slots that anchor slots to predefined activity categories, (2) parallel spatio-temporal slot updating for holistic video-level reasoning, and (3) background and negative-slot regularization that enforces competition between foreground activities and irrelevant regions. Together these establish an activity-centric inductive bias that disentangles concurrent and asynchronous activities directly from raw video. Beyond recognition, the learned representations encode transferable spatio-temporal grounding signals. We further propose an attention-difference-based pseudo mask selection framework that suppresses false positives by measuring attention changes before and after candidate region removal, enabling weakly supervised localization without dense annotations. To support systematic evaluation, we introduce TACO, a balanced synthetic dataset with full atomic activity coverage and pixel-level annotations. Experiments on OATS, TACO, and annotated nuScenes show superior recognition, strong sim-to-real transfer, and state-of-the-art weakly supervised localization.
https://arxiv.org/abs/2609.24127
Contrastive self-supervised learning has achieved strong performance by learning representations from multiple augmented views of the same image. However, most existing methods construct positive pairs using independently sampled stochastic augmentations, which may alter semantic content and ignore the intrinsic geometry of the data distribution. In this work, we propose OTCLR, an optimal transport-aware framework for contrastive learning representations that generates geometry-consistent positive samples. Instead of directly contrasting two randomly augmented views, we construct intermediate views between the original image and its augmented variants through entropic optimal-transport displacement interpolation. These transport-interpolated samples serve as positive views that better preserve image structure while explicitly modeling spatial distributional geometry. To further promote smooth representation learning, we evaluate auxiliary Sinkhorn regularization terms that encourage transport-interpolated views to remain consistent with their endpoint images. The proposed method can be incorporated into standard contrastive learning pipelines without modifying the encoder architecture. Experiments on multiple benchmark datasets show that our approach improves representation quality and transfer learning performance compared with conventional augmentation-based contrastive learning baselines.
https://arxiv.org/abs/2609.24125
Joint Embedding Predictive Architectures (JEPAs) are a promising paradigm for learning task-agnostic latent world models without visual reconstruction. However, standard JEPA training exhibits a strong inductive bias towards slow features, causing feature suppression and the collapse of latent representation. While inverse dynamics provides temporal anti-collapse, it relies on action labels and offers little incentive to embed general, unlabeled dynamics. We introduce Difference Image and Single image embedding Regularization (DISReg), a novel regularizer that builds on an inverse-dynamics-style module that predicts temporal difference image embeddings without any pixel reconstruction loss, encouraging balanced static and dynamic feature learning. DISReg consists of a static term that shapes the distribution of the image embedding and encourages slow features, and a dynamic term, which, unlike direct regularization on the embedding, imposes no constraint on the image embedding's shape or distribution and instead only incentivizes that dynamic features be present. By integrating this regularizer into a standard JEPA, we establish our new architecture, MotionJEPA. Latent probing demonstrates that MotionJEPA produces more complete representations than other methods, and our trajectory analysis shows it maintains geometrically simple latent embeddings with low curvature. We further show that MotionJEPA improves downstream planning success under static-background distractors across four environments.
https://arxiv.org/abs/2609.23881
Multimodal classifiers can converge to modality-dominant solutions in which one modality dominates the joint prediction, suppressing the learning of others. Existing balancing methods mainly adjust losses, gradients, or modality contributions, largely treating modality imbalance as an optimization problem while implicitly treating the weak modality as under-optimized but representationally intact. In this work, we find that this assumption does not always hold, as persistent modality dominance can induce a representation-level collapse of the weak modality, which we term \emph{manifold modality collapse} (MMC). MMC manifests as a coupled geometric degradation in which weak-modality representations collapse onto fewer directions within each class and become less separable across classes. Motivated by this observation, we propose \emph{GeoBalance}, a geometry-aware framework that monitors these two geometric properties and reconstructs the weak modality representation only when it exhibits signs of MMC. Once triggered, GeoBalance uses a fixed Simplex-ETF class scaffold and spectral regularization to restore class separation while preventing collapse onto a few feature directions. To preserve reconstruction during joint training, asymmetric gradient projection removes the joint-gradient component conflicting with reconstruction, leaving non-conflicting optimization unchanged. Extensive experiments across six multimodal benchmarks demonstrate great improvements over competitive balancing methods, validating its effectiveness.
https://arxiv.org/abs/2609.23533
Novel view synthesis from sparse observations is severely under-constrained. Although 3D Gaussian Splatting (3DGS) enables real-time rendering, it produces floaters, broken geometry, and washed-out backgrounds when trained with few views. We propose an alternating optimization framework that uses a pre-trained image diffusion model to generate geometrically consistent pseudo-views for additional 3DGS supervision. Generation is constrained by depth-conditioned ControlNet, IP-Adapter style transfer, LoRA scene adaptation, and img2img structural anchoring. We introduce Generative Active Pseudo-view Selection (GAPS) to balance reconstruction informativeness and generative reliability when choosing target views. Its annealing schedule shifts from conservative interpolation early in training to exploratory extrapolation later, gradually covering unobserved regions. A dual-criterion admission gate and uncertainty-weighted losses reject unreliable generations, while density-adaptive DropGaussian reduces overfitting in complex scenes. On LLFF with 3/6/9 views, our method improves average PSNR over vanilla 3DGS by 0.40/0.89/0.70 dB. On Mip-NeRF 360 with 12/24 views, the gains are 1.18/0.80 dB. SSIM improves and LPIPS decreases in every setting. Ablations show that active selection and density-adaptive regularization are both necessary; only the full method reduces LPIPS below the no-pseudo-view baseline on unbounded 360-degree scenes.
https://arxiv.org/abs/2609.23436
Data-driven Model Predictive Control (MPC) has lately been a core research subject in the field of control theory. The combination of an optimal control framework with deep learning paradigms opens up the possibility to accurately tracking control tasks without the need for complex analytical models. However, the system dynamics are often nuanced and the neural model lacks the potential to understand physical properties such as inertia and conservation of energy. In this work, we propose a novel energy-based regularization loss function which is applied to the training of a neural model that learns the residual dynamics of an omnidirectional aerial robot. Our energy-based regularization encourages the neural network to learn stabilizing control corrections. Without the regularization the network misses physical context. The learned residual dynamics are then integrated into the MPC framework. The positional mean absolute error (MAE) are shown to be improved in three real-world experiments by 23% compared to the analytical MPC. We also compare our method to a standard neural MPC implementation without regularization and primarily achieve an increased flight stability implicitly due to smoothening out the acceleration of the robot and thus up to 15% lower MAE. A complimentary video is available at: this https URL. We share our code under: this https URL.
https://arxiv.org/abs/2604.14678
While compressed-sensing regularizers enable interpretable reconstruction of 4D Flow CMR through transparent variational objectives, their hand-crafted nature is too restrictive under high acceleration. State-of-the-art learning-based approaches mitigate this, but typically encode regularization implicitly through unrolled network modules, which limits their interpretability. To address this limitation, we propose CLEAR, designed to combine the interpretability of compressed sensing with the flexibility of learned models. To the best of our knowledge, it is the first learned regularizer for a 4D reconstruction task. In the ultra-accelerated \(10\times\)--\(50\times\) regime of the CMRx4DFlow2026 challenge, CLEAR outperforms compressed sensing locally low-rank (LLR) and the popular variational network FlowVN, while using less than 10k parameters and preserving an interpretable regularization structure.
https://arxiv.org/abs/2609.22950
Clustering high-dimensional data is a fundamental task in unsupervised machine learning with applications to a variety of domains. In the centralized data scenario, this task is commonly solved using deep clustering methods that utilize deep neural network architectures to learn clustering-friendly latent space representations. In Federated Learning, where data is distributed between clients and is private, deep clustering methods are less explored. In particular, recently introduced federated deep clustering methods, despite showing very promising performance, still fall short in reliably providing good performance if data across clients are non-identically-independently distributed. In this work, we introduce a generalization of Deep Clustering Networks to the federated scenario, named FedDCN, that simultaneously optimizes a reconstruction loss and a clustering loss. To ensure robustness and latent space alignment in non-identically-independently distributed data scenarios, FedDCN generates synthetic data augmentations, and its learning objective includes a geometric regularization for latent space alignment. Through experimental evaluation, the effectiveness of the approach under IID and non-IID assumptions is demonstrated, and future research directions are identified.
https://arxiv.org/abs/2609.21829
Image registration is a vital preprocessing step in multimodal perception tasks, including image fusion, object detection, and semantic segmentation. In Advanced Driver- Assistance Systems (ADAS), spatial misalignment between visible (RGB) and infrared (IR) cameras -caused by non-coincident optical axes and field-of-view differences- introduces non-uniform parallax and visual ghosting. Classical keypoint-based methods are restricted to global homographies that fail under dynamic depth, while unconstrained dense flow algorithms lack structural regularization and suffer from temporal instability. In this paper, we propose XCalib, an unsupervised dense thermal-visible registration framework that bridges this gap. Rather than serving as an absolute metric calibration tool, XCalib leverages virtual pinhole camera parameterization strictly as a geometric constraint space. By optimizing effective relative pose and intrinsics alongside predicted monocular metric depth, XCalib restricts the search space of spatial displacements to physically valid projection geometries. Our key contributions are: (1) a novel registration paradigm that uses camera parameterization as an implicit regularizer for dense cross-modal warping; (2) Normalized Edges Correlation (NEC), a robust structural similarity metric tailored to cross- spectral alignment; and (3) extensive quantitative and qualitative evaluations across public ADAS datasets, demonstrating superior temporal stability and alignment accuracy over unconstrained dense flow baselines.
https://arxiv.org/abs/2609.21770
Large language models (LLMs) achieve strong performance but suffer from slow and costly inference. Existing acceleration methods often lead to noticeable performance degradation, while Mixture-of-Experts (MoE) models require extensive computational resources. In this paper, we propose L0-MoE, a lightweight MoE approach using L0-regularization to accelerate dense LLMs nearly without performance loss. Our method introduces a cluster confusion matrix for domain-aware dataset curation and applies dynamic batching for efficient training. Experiments show that L0-MoE achieves up to 2.5x speedup over dense models while maintaining competitive performance, outperforming existing LLM acceleration baselines.
https://arxiv.org/abs/2609.21672