Papers

On-policy distillation (OPD) trains a student on prefixes sampled from its own policy while matching a stronger teacher. This addresses the prefix mismatch of offline distillation, but early student rollouts can still be poor, placing teacher supervision on weak or low-quality prefixes. We propose Trust-Region behavior Blending (TRB), a warmup method that replaces the early rollout policy with the closest-to-teacher behavior policy inside a student-centered KL trust region, while keeping the per-prefix reverse-KL OPD loss unchanged. The KL budget is annealed to zero, so training returns to pure student rollouts after warmup. Across two math-reasoning distillation settings, TRB attains the strongest average among the compared methods.

Interactive video world models generate video chunk by chunk in response to user-controlled camera movements, enabling applications such as real-time game simulation, virtual scene navigation, and embodied AI training. However, scaling to long interactive trajectories is prohibitively expensive due to growing context memory, quadratic attention complexity, and repeated denoising steps. We present Light Interaction, a training-free inference acceleration framework for interactive video world models. Our key insight is that interaction naturally enables trajectory-dependent adaptive computation: retrieved spatial memory can be discarded during novel exploration, temporal context can be adjusted according to local latent dynamics, and early-step model outputs can be reused when the camera revisits familiar regions. Based on this insight, Light Interaction combines adaptive context management, denoising cache acceleration, and hardware-software co-designed 3D block sparse attention with fused Triton kernels. Evaluated on HY-WorldPlay and Matrix-Game-3.0, Light Interaction achieves up to 2.59x speedup without model retraining while maintaining competitive visual quality.

Causal discovery aims to recover directed causal relations from observational and interventional data, providing a basis for mechanistic understanding and reliable decision-making. Causal discovery foundation models (CDFMs) seek to amortize this problem by mapping a dataset directly to a causal graph in a single forward pass, avoiding per-dataset testing, search, or optimization. However, existing CDFMs remain limited, often failing to consistently match strong classical methods, and we find that a key bottleneck is how causal pretraining tasks are constructed. Based on this observation, we propose TabCausal, a data-driven CDFM trained with broad causal pretraining over diverse graph priors, structural mechanisms, noise models, dimensions, sample sizes, and intervention regimes. A dynamic task construction strategy composes these causal environments into varied discovery tasks, enabling more transferable structural learning from observational and mixed-interventional data. On large-scale synthetic benchmarks, TabCausal achieves better macro-averaged performance than a diverse set of causal discovery baselines. To further bridge abstract synthetic generators and realistic causal reasoning scenarios, we introduce a protocol-guided and LLM-audited semantic causal environment benchmark, where domain-grounded SCMs generate interpretable observational and interventional datasets for out-of-distribution analysis. Across both synthetic and semantic environments, TabCausal demonstrates robust structure recovery, especially under interventional evidence, highlighting broad causal pretraining as a key ingredient for transferable amortized causal discovery.

Out-of-distribution (OOD) detection for time-series data remains comparatively underexplored compared to vision and language, with a limited principled understanding of how supervised time-series representations can be leveraged for reliable detection under distributional shifts. This work formulates time-series OOD detection as representation learning with hyperspherical embeddings, where class-conditional structure is induced by a von Mises-Fisher (vMF) likelihood-based objective on the unit sphere. The learned representation combines time- and frequency-domain views of the input signal via domain-specific encoders, integrating them into a joint embedding space for OOD detection. Detection uses distance-based scores over the learned embeddings, including k-nearest neighbors (k-NN) and Mahalanobis scores. We evaluate the approach at scale on the complete UCR and UEA time-series archives under a cross-dataset protocol. Empirical results show consistent improvements under both k-NN and Mahalanobis scoring over strong contrastive learning and post-hoc baselines in the same setting. Code is available at https://github.com/tiiuae/hypertf-time-series-ood.

This paper studies how efficiently deep ReLU neural networks can approximate and learn smooth functions. When the error is measured in $L^p([0,1]^d)$ norm and the approximator is a network with width $W$ and depth $L$, recent works have proven the supper approximation rate $\mathcal{O}((WL)^{-2s/d})$ for Besov space $\mathcal{B}^s_{q,r}([0,1]^d)$ under the Sobolev embedding condition $s/d>1/q-1/p$. In order to overcome the curse of dimensionality in this rate, we extent this result to anisotropic and mixed smooth function classes. We establish the approximation rate $\mathcal{O}((WL)^{-2\tilde{s}})$ for anisotropic Besov space $\mathcal{B}^{\boldsymbol{s}}_{q,r}([0,1]^d)$ with anisotropic smoothness $\boldsymbol{s}=(s_1,\dots,s_d)$ under the embedding condition $\tilde{s} > 1/q-1/p$, where the mean smoothness $\tilde{s} = (\sum_{i=1}^d s_i^{-1})^{-1}$. For mixed smooth Besov space $\mathcal{MB}^s_{q,r}([0,1]^d)$ with mixed smoothness $s>1/q-1/p$, we show that the approximation rate $\mathcal{O}((WL)^{-2s})$ holds up to logarithmic factors. Using these results, we also derive approximation bounds for the composition of anisotropic Besov functions. As an application, it is shown that deep ReLU neural networks can achieve minimax optimal rates up to logarithmic factors for a wide range of smooth function classes.

In-context localization (ICL) seeks to localize a target object specified by a small set of support examples in a query image, operating on the fly without training or parameter updates. Despite rapid advances in vision-language models (VLMs), achieving category-agnostic and visually grounded ICL remains an open problem, even though it is essential for applications such as image editing, personalized visual search, and retrieval. Existing methods are fragile and rely on explicit category supervision, which not only limits applicability in realistic settings with unnamed or instance-specific objects but also introduces category bias that steers predictions toward semantic priors rather than visual evidence. We introduce a two-stage training framework that explicitly optimizes in-context attention between support bounding boxes and query images without category supervision. We further refine localization via reinforcement learning using Group Relative Policy Optimization (GRPO) to directly minimize localization error. This formulation enforces visual correspondence over semantic priors, yielding robust instance-level localization. Empirically, a 7B-parameter model trained with our objectives outperforms models up to 72B parameters, demonstrating that context-aware localization objectives can surpass scaling alone. Comprehensive ablations validate the contribution of each component.

Multi-scale modeling has emerged as an effective design principle for time-series forecasting by capturing temporal dynamics at multiple resolutions. As no principled foundation has been established in the literature, we unify existing scaling methods into a scaling operator family, revealing a fundamental limitation of existing approaches: reliance on fixed and discrete scaling. To address this limitation, we propose SiGMA (Single Generalized Multi-scale Architecture), which enables distance-aware scaling via the learnable discrete Gaussian (LDG) kernel grounded in scale-space theory. We evaluate SiGMA comprehensively on long- and short-term forecasting benchmarks against state-of-the-art multi-scale baselines. SiGMA outperforms all competitors on both tasks, especially achieving the best performance in 13 out of 16 long-term evaluation settings. Beyond accuracy, SiGMA significantly improves training speed by up to 5.3 times and reduces memory consumption by up to 3.8 times over the strongest competitors. Code is available at https://github.com/cheonwoolee/SiGMA.

Nonlinear conservation laws are at the heart of many of the most important dynamical systems in science and engineering. In practical applications, such systems are often subject to various sources of uncertainty, e.g. due to sparse or noisy measurements. Inferring physical quantities and fields of interest then becomes an ill-posed problem which both classical numerical methods and modern deep learning-based methods struggle to treat appropriately. Recent work has framed classical numerical methods as Bayesian inference under Gaussian process priors, resulting in a physics-aware treatment of uncertainties. Following this line of work, we develop a novel numerically conservative method for uncertainty-aware simulations of nonlinear conservation laws. We use recent sparse approximation techniques to scale up to large-scale forward and inverse problems. For forward simulation, we inherit the accuracy of classical solvers while providing structured uncertainty quantification. On inverse problems, we recover posteriors over nonparametric source fields in seconds – outperforming neural baselines that take minutes to produce a less accurate point estimate.

Can a language model improve from plain text sampled from itself, with no prompts, no teacher, no verifier, and no reward model? Yes, but only when the synthetic corpus is compatible with the student, a relational property of the source-student pair rather than an intrinsic property of the data. We call this the latent capability resurfacing hypothesis: weak self-training can amplify capabilities already present in the pretrained model, but only under this compatibility condition. We study this in the minimal setting of prompt-free unconditional self-training, where base language models are fine-tuned on text generated from the BOS token alone, with no task specification or external supervision. We report three findings. First, synthetic utility is relational rather than intrinsic: self-generated data is the most effective source, same-lineage transfer outperforms stronger but differently trained sources, and cross-family transfer is substantially weaker. Second, common intrinsic proxies fail: neither benchmark-level semantic similarity nor average per-token likelihood under the student predicts which corpora help. Third, this regime produces a surprising byproduct. In controlled Pythia experiments, capability and verbatim memorization decouple: benchmark utility is preserved or improved while held-out exact-match extraction drops by over 95 percent, with no forget set, privacy objective, or targeted unlearning. Together, these results suggest that prompt-free self-training works by amplifying what the student already knows, not by importing structure from the data. They also reveal a regime in which capability and verbatim memorization can be separated without any explicit unlearning objective.

Deep reinforcement learning (RL) has driven rapid progress in physically-based motion generation, yet synthesizing robust motion policies in dense fluid environments (e.g. swimming) remains unsolved. Unlike land motion, where environmental impact is sparse and can be coarsely modeled (e.g. gravity, normal reaction), swimming requires continuous, full-body coordination under pressure and flow forces across the entire body surface; fully-coupled rigid-fluid simulation is far too slow for the millions of interactions RL requires. We propose SWIM, an RL framework for physically-based human swimming learned from a single reference motion. Its core is a compact, low-dimensional environment representation: a dual-branch graph-convolutional VQ-VAE that tokenizes per-link body-water forces and torques, informative enough for control yet robust to the rapidly changing force exchanges that would otherwise destabilize training. We pair this with a GPU-based Lagrangian solver with rigid-fluid coupling that yields 10-15x faster training. Across hundreds of training runs and several hundred zero-shot conditions, SWIM generalizes to unseen goals and trajectories, fluids with varying density, external flows and perturbations, altered body morphologies, and all four competitive swimming styles. Against imitation-learning baselines (MimicKit-DeepMimic, MimicKit-AMP, ADD) and alternative force models (a PINN world model, MuJoCo's inertial fluid model, and an underwater-robotics simulator), SWIM achieves better stability, goal satisfaction, and physical realism: a 63.9% success rate on held-out generalization versus 36.8% for the strongest baseline.

In robotics, dangers and adversity modes are often embodiment-specific and relative to each agent. A frontier of autonomous mobile robotics is to enable agents to operate effectively in the wild in unseen unstructured environments. A significant challenge in unseen unstructured environments is that it may not be possible to predict all the dangers to the specific robot. Although recent work has used large foundation vision-language models (VLMs) to preemptively predict an exhaustive list of common-sense dangers, it remains difficult to capture possible interaction and embodiment-dependent adversities. We propose a continual learning framework for a mobile embodied agent to learn online from disturbances and attribute anomalous behaviours to causes through semantics, enabling better prediction and planning of the world in the future. Our framework, "Don't Fool Me Twice", first observes disturbances and describes their effects on the robot; this description is augmented with visual context to query a VLM to predict possible causes; the local disturbance is characterized using kernel regression, which allows for efficient, few-shot modeling of transient anomalies. We leverage semantic voxel-centric modeling to estimate epistemic uncertainty, enabling richer downstream recovery by treating interaction-driven disturbances as learnable spatial behaviors. We present four hypotheses and validate them in simulation and on hardware across embodiments and adversity modes.

World models used for planning learn to predict how a scene evolves, yet they rarely hold a global view of how far a task has progressed. We argue that such a view should be part of the representation, and that it can be compact: describing a scene takes many dimensions, but where the scene stands on its way to the goal can be summarised by only a few. We propose SD-JEPA, a joint-embedding predictive world model whose latent is split into a small progression subspace and a large content subspace. A temporal triplet loss keeps consecutive frames of a trajectory close in the progression coordinates and separates different trajectories, while a distributional regulariser keeps the content coordinates from collapsing. On four control benchmarks, the model plans as well as the same architecture without the split. In return, its latent becomes easier to read. A few percent of its dimensions are enough to predict progress within an episode, and the angle they form follows the task, moves backward when the agent backtracks and changes fastest around events such as grasps and releases. Surprise also becomes anchored in the trajectory: when the scene changes mid-episode, the angle spikes and then relocalizes on a new part of the progression, anchoring surprise in the agent's own map of the task.

In this work we introduce a novel approach to domain incremental learning, adapting models over time to evolving, non-stationary data. In contrast to other works, we do not attempt to avoid catastrophic forgetting, but rather allow it and exploit it. Our model combines a main task head with a self-supervised masked autoencoder (MAE) head. We then learn domain-specific LoRA adapters during incremental training. Each adapter specializes to its domain, naturally inducing forgetting on other domains in both heads. At inference, we perform online test-time training on the self-supervised MAE head to identify which LoRAs best matches the current input, so the model can `remember' the domain again. Our scheme is especially well-suited to real-world streaming data, such as video, where consecutive samples are highly correlated and domain shifts are gradual. We demonstrate our method on domain-incremental action recognition and semantic segmentation tasks.

Riemannian diffusion models generalize score-based generative modeling to manifold-supported data via stochastic diffusion equations on the manifold. However, training requires sampling from and differentiating the manifold heat kernel, which is rarely available in closed form beyond a few highly symmetric manifolds. We propose a general approach that approximates the heat kernel by directly solving the manifold heat equation with a physics-informed neural network (PINN). Given an explicit manifold specification, we choose a coordinate system, derive the corresponding heat (Fokker–Planck) equation and a short-time asymptotic approximation, and then train a PINN to learn the log heat kernel. The resulting surrogate enables both forward noising (heat-kernel sampling) and conditional-score evaluation for denoising score matching. We demonstrate the method on diverse manifolds including $S^2$, $SO(3)$, $\mathrm{SPD}(n)$, and permutation-quotiented point clouds.

Bidding in the European Frequency Containment Reserve (FCR) market is challenging for flexibility providers because competing offers are hidden and bidders observe only partial feedback form the market, such as, clearing price and awarded quantity. For a participant active in a single country, we show that the multi-country FCR clearing problem can be recast as a repeated multi-unit uniform-price auction against an endogenous vector of opposing bids. This reformulation yields an online learning problem and allows us to adapt a Best-of-Both-Worlds combinatorial semi-bandit algorithm implementable from this standard market feedback. The resulting bidder achieves logarithmic pseudo-regret in stochastic environments and $\mathcal{O}(\sqrt{T})$ regret in adversarial ones. Synthetic experiments confirm the expected scaling, and backtests on historical European FCR data show competitive performance in practice: the method performs especially well on stable products, while EXP3-type baselines can be safer under stronger non-stationarity. Overall, the results show that learning-based bidding in FCR markets is theoretically grounded and practically useful when the learning rule matches product-level market stability.

Free energy estimation is a fundamental yet challenging problem, from physics to statistics. Classical approaches rely on thermodynamic transformations, ranging from direct estimation, quasistatic integration, to finite-time averaging. Recent work [He and Du et al., 2025] learns neural transports to significantly accelerate the efficiency in the finite-time regime. In this paper, we generalize this framework to arbitrary state spaces. Building on this view, we develop a generalized neural transport learning approach for efficient estimation. Experiments validate the effectiveness and efficiency of the proposed method beyond continuous settings, extending to discrete and multimodal spaces as well as autoregressive settings. Beyond free energy estimation, we establish algebraic identities and reveal a group-theoretic structure linking infinitesimal time reversal and generalized Doob's $h$-transforms, showing that their compositions form a generalized dihedral group.

We present a novel method for learning interpretable representations of progressive time series, that is, data capturing irreversible state transitions such as degradation or task completion. Our approach uses a self-supervised contrastive objective to learn a low-dimensional latent space whose geometry is itself the interpretation: each observation becomes a point on a manifold anchored between two fixed orthogonal prototype vectors, and a trajectory becomes a path across that manifold. From this structure we read a latent compass, the polar coordinates ({\theta}, r) of the latent vector, in which {\theta} tracks the progression of the underlying state (e.g., from healthy to failed) and r identifies the active mode (e.g., the operating condition), without any proxy labels. We evaluate the approach against the state of the art on diverse domains, including industrial degradation, robotic tasks, and neural activity, validating three key capabilities: (1) end-state prediction, (2) multi-step forecasting, and (3) interpretable phase separation. Our method matches or improves over black-box counterparts on all of these while providing transparency about the underlying mechanisms. A simple linear regressor on top of the latent compass coordinates is competitive with deep architectures, direct quantitative evidence that the underlying state is encoded in a geometrically accessible form.

Dense self-attention is the compute and quality bottleneck of long-video diffusion inference: cost grows quadratically with the sequence length, and beyond the training horizon the model converges to near-static output, that is, "frozen" repetitive video. State of the art approaches are either too costly, e.g., they require retraining, or fail to satisfy both performance and quality objectives in a scalable manner. To this end, we introduce Long Video Sparse Attention (LVSA), a training-free model-agnostic block-sparse attention for video diffusion transformers that combines a structured window pattern with rotating global anchors, thus removing the fixed-grid bias which causes long-range temporal artifacts. LVSA, combined with a FlashInfer kernel, reduces compute up to 3.17x on Wan 2.1 1.3B at a 6x horizon, 2.98x on Wan 2.1 14B at a 6x horizon, and 3.33x on HunyuanVideo 1.5 at a 1.5x horizon, compared to dense attention. Beyond reducing compute, LVSA enables HunyuanVideo 1.5 generation at a 2x horizon, which is otherwise out-of-memory on a single GPU. Moreover, LVSA provides speedups up to 2.41x compared to RIFLEx and 3.27x compared to UltraViCo on Wan 2.1 1.3B. To demonstrate applicability across diverse platforms, we apply LVSA on NPUs and achieve speedups up to 2.71x on Wan 2.2 A14B and 3.24x on Wan 2.1 1.3B compared to dense attention. To evaluate quality in a fair way, we introduce VQeval, a tool properly scoring loopy video failures, which instead are rewarded in state of the art evaluators like VBench-Long. LVSA is quality-neutral for generation at training horizon length and quality-positive at extended lengths.

Bayesian optimization (BO) is effective for expensive black-box optimization, but its performance often degrades on multimodal or high-dimensional problems. A promising remedy is to run multiple local search processes, such as trust region–based BO, and allocate evaluations to those with high potential. However, current best values do not always reflect the final performance of each process. We propose a trajectory-aware best-arm identification (BAI) framework that uses optimization history to guide this allocation. The proposed method extrapolates improvement trajectories, estimates final performance, and progressively eliminates low-potential candidates. For trust region–based BO, we theoretically show that the proposed BAI-guided allocation accelerates convergence to the global optimum under mild assumptions. Experiments on synthetic and real-world benchmarks demonstrate that our method improves BO on multimodal problems. We also show that the same mechanism can enhance other local or population-based optimizers, suggesting its potential as a general extension strategy for multimodal black-box optimization.

Combinatorial and optimization problems are fundamental to many industrial AI applications. Solving large-scale real-world instances of such problems typically requires careful problem formalization, specialized solvers, and expert-designed heuristics. Thus, experts need to specify not only what solutions are, but also how they are derived. By introducing the tool CHECKMATE, we show that algorithm generation via code evolution represents a paradigm shift by eliminating the need to formulate the how. CHECKMATE solely relies on the what. Specifically, a formal specification ensures solutions' correctness and enables systematic performance evaluation of the generated programs, while a natural language description guides the evolutionary process. The effectiveness of our method is demonstrated on selected problems from two industrial domains: configuration and scheduling. In all cases, the evolved algorithms consistently outperform state-of-the-art solvers. This underscores the potential of formal methods in guiding code evolution for automatically solving complex real-world problems.

Reinforcement learning has shown promising results for optimizing the control of industrial energy systems, yet most existing studies remain limited to the application in simulation environments. We investigate the challenges of deploying reinforcement learning in a real-world industrial energy system, considering a thermal heating network as a use case. We formulate the task as a Markov Decision Process and systematically analyze the associated challenges along the structure of the formal description, including partial observability, action space design, reward design, and the simulation-to-reality gap. The challenges are grounded in an existing real-world deployment, where reinforcement learning achieves operational stability but shows a significant performance gap compared to simulation.

Deep networks on the symmetric positive-definite (SPD) manifold promise expressive representations by encoding data geometry as an inductive bias, but stacking BiMap layers with the standard ReEig nonlinearity often adds no capacity: on real, preconditioned EEG data, ReEig rarely activates, so the stack behaves as a single layer at any depth. In the worst case, when domains share no discriminative directions, we prove a single filter has a capacity ceiling, so it cannot fully align every domain at once. To overcome that, we propose SCAP (Stiefel Cross-Attention Pool), a layer implementing a family of Stiefel filters by combining a pool of $K$ experts into a sample-specific bilinear map via cross-attention. We show that it matches a per-domain filter bank to first order with fewer experts than domains when domain-optimal filters span few directions near a shared tangent-space basepoint; in the worst case, its alignment empirically stays nearly flat as domains grow, escaping the fixed-filter ceiling. Naively trained, however, this routing can collapse to a fixed filter; we diagnose why and adapt three mechanisms to mitigate it. SCAP significantly improves balanced accuracy over fixed-filter SPDNet on all five cross-domain EEG motor-imagery datasets, and matches or exceeds three domain-adaptive baselines on four out of five.

Developing effective representations for register transfer level (RTL) designs is crucial for accelerating the hardware design workflow. Existing approaches, however, typically rely on a single data modality, either the RTL code or its associated graph-based representation, limiting the expressiveness and generalization ability of the learned representations. For RTL, the control data flow graph (CDFG) offers a comprehensive structural representation that preserves complete information, while the code modality explicitly encodes semantic and functional information. We argue that integrating these complementary modalities is essential for a thorough understanding of RTL designs. To this end, we propose UniRTL, a multimodal pretraining framework that learns unified RTL representations by jointly leveraging code and CDFG. UniRTL achieves fine-grained alignment between code and graph through mutual masked modeling and employs a hierarchical training strategy that incorporates a pretrained graph-aware tokenizer and staged alignment of text (i.e., functional summary) and code prior to graph integration. We evaluate UniRTL on two downstream tasks, performance prediction and code retrieval, under multiple settings. Experimental results show that UniRTL consistently outperforms prior methods, establishing it as a more robust and powerful foundation for advancing hardware design automation.

Online advertising platforms rely on machine learning models to predict click-through rates (pCTR) and conversion rates (pCVR) for auction mechanisms. We introduce a novel framework to study the interaction between recommender system model quality, auction format, and autobidder behavior. We formalize when model improvements – defined via a refinement relation inspired by filtrations in probability theory – lead to improvements in platform-level Evaluation Criteria Metrics (ECM) such as revenue, welfare, or liquid welfare. Our main contributions are: (1) a formal definition of model improvement based on cluster refinement, and (2) a systematic characterization of ECM monotonicity across different combinations of bidder types (tCPA, max-CPA), auction formats (first-price, second-price, VCG), and budget constraints. We show that first-price auctions with uniform bidding guarantee revenue monotonicity for tCPA bidders without budgets (via Jensen's inequality), while second-price auctions and budget constraints can break this property. We provide full numerical constructions for the non-monotonicity results. Our findings have practical implications for advertising platforms seeking to align model improvements with business outcomes.

Reinforcement learning with verifiable rewards and group-based policy optimization methods update a stochastic policy by sampling multiple completions per prompt and increasing the policy's probability on those with higher reward. These updates, unline the exploration mechanism in Thompson sampling and UCB, do not include explicit mechanisms that track epistemic uncertainty. This paper studies a stylized explanation for why such uncertainty-agnostic updates can nevertheless be effective. We analyze an annealed softmax policy that selects actions according to a softmax of empirical mean rewards in a many-armed Bayesian Bernoulli bandit. Under a linear upper-tail condition on the prior, which implies an abundance of near-optimal arms, we prove that annealed softmax greedy achieves Bayes regret $\tilde{O}(m + T/m)$, and in particular $\tilde{O}(\sqrt{T})$ when the number of arms scales as $m = \Theta(\sqrt{T})$. This is the near-optimal Bayes regret rate in this regime, attained also by empirical-mean greedy. Under the upper-tail condition, many arms keep empirical means near the optimum throughout learning, so the probability that softmax places away from the empirical best falls mostly on other near-optimal arms. By contrast, with a small number of arms, the same kind of softmax policy can suffer linear regret (Cesa-Bianchi et al., 2017). The result also provides a structural analogy to RLVR, where a base policy with a non-negligible probability of producing a correct completion plays the role of the tail condition. Simulations support the theory and motivate prior-anchored variants of greedy and annealed softmax that score arms by the Beta posterior mean and skip the forced initialization; with an arm-specific prior, accurate or noisy, these variants outperform baselines, including Thompson Sampling, when the number of arms is large.

Solving high-frequency partial differential equations (PDEs) with neural networks is notoriously difficult due to the spectral bias of conventional architectures. We propose the Multi-Scale Separable Fourier Neural Network (MS-SFNN), a framework designed to overcome this limitation by explicitly encoding multi-scale Fourier features within a separable representation. The network factorizes the solution into $d$ single-coordinate subnetworks with fixed, randomly initialized weights; these subnetworks are combined via element-wise products to form a rich set of basis functions. This separable construction scales linearly with the problem dimension, thus inherently alleviating the curse of dimensionality. Crucially, each subnetwork is equipped with trainable scaling factors coupled with cosine activations, providing an adaptive mechanism for multi-scale frequency selection that endows the model with strong spectral approximation capability. The PDE solution is expressed as a linear combination of these learned basis functions, and the combination coefficients are determined by solving a large-scale least-squares system. To resolve the memory bottleneck in high-frequency or three-dimensional settings, we replace automatic differentiation (AD) with analytical derivatives of the basis functions and use a memory-efficient batched QR decomposition for solving the least-squares systems efficiently. Extensive numerical experiments demonstrate that MS-SFNN achieves superior accuracy and substantially outperforms state-of-the-art methods, including Physics-Informed Neural Network (PINN) and the Separated-Variable Spectral Neural Network (SV-SNN).

This work addresses the problem of autonomous resource management in heterogeneous satellite cluster conducting Earth Observation (EO) missions including optical and Synthetic Aperture Radar (SAR) satellites. In autonomous operation mode, satellites are equipped with intelligent capabilities enabling real-time decision-making based on the latest conditions, while requiring minimal interaction with ground operators. Traditional scheduling approaches typically rely on mathematical models to represent satellite mission and resource management. Then, this problem is solved by using optimization algorithms. However, such solutions become less effective when the underlying models are not available, over complex, and inaccurate due to dynamic changes and uncertainties inherent in the space mission environment. A promising alternative is to reformulate the problem as a sequential decision-making process and apply model-free reinforcement learning techniques to enable adaptive and real-time resource management. To this end, we propose a novel transformer-based architecture tailored for heterogeneous satellite cluster autonomous EO Mission with relational observations-actions tokenization and differential attention mechanism. Our experimental results demonstrate significant performance improvements compared to the available baselines. Moreover, the proposed architecture exhibits strong adaptability and transferability with respect to varying numbers of satellite clusters.

Predictive coding (PC) is a local-learning alternative to backpropagation (BP), training deep networks via local energy-minimization dynamics rather than a global backward pass. We introduce Augmented Lagrangian Predictive Coding (PC-ALM), which maintains PC's inference budget but aligns each weight update toward BP by accumulating per-layer constraint errors into a layer-local Lagrange multiplier. In linear PC networks, PC-ALM converges to an equilibrium with exact BP gradients distributed across the network via only layer-local updates. We analyze PC-ALM in nonlinear PC networks up to depth 128 and show that it matches BP performance across all width-depth regimes, notably in deep narrow networks where PC underperforms. PC-ALM introduces recurrent dynamics in each layer's activations. Compared to PC's heat flow on a scalar energy, PC-ALM dynamics are driven by dual ascent on the augmented Lagrangian. We observe "ballistic" credit propagation across very deep networks, with credit signals evenly distributed across layers, compared to PC's slow, diffusive credit propagation. Beyond the algorithm itself, the augmented Lagrangian framework offers a generalization of PC, and may yield insights into how distributed systems could compute and propagate BP-like credit signals through purely local dynamics.

Current alignment paradigms for generative artificial intelligence rely predominantly on monolithic benchmarking frameworks that reduce the plurality of human judgment to aggregated statistical baselines, thereby obscuring cultural, demographic, and contextual variability in evaluation. We introduce a state-space constrained emulation framework for AI evaluation that replaces singular assessment functions with a structured manifold of synthetic cognitive profiles representing diverse human perspectives. We show that modern generative architectures can instantiate and maintain these evaluative personas with high consistency, enabling a form of pluralistic, perspective-dependent benchmarking that more closely reflects real-world consensus variability. However, we further analyze the stability of these simulated evaluators under sequential inference and stochastic prompt perturbations, revealing systematic degradation in persona coherence that manifests as state-space drift and semantic inconsistency. These findings suggest that static alignment constraints are insufficient for sustaining robust evaluative behavior over time. Instead, we argue for the necessity of embedding dynamic, viability-driven regulatory mechanisms within generative systems to preserve coherent cognitive emulation. By framing persona-based evaluation as a structured dynamical system over latent representation manifolds, this study provides a foundation for more adaptive, human-aligned, and context-sensitive approaches to AI evaluation.

Graph condensation (GC) is pivotal for enabling Graph Neural Networks (GNNs) deployment in resource-constrained scenarios by compressing large-scale graphs into compact synthetic counterparts. Existing GC methods commonly suffer from computational inefficiency due to coupled optimization as well as encountering poor generalization across GNN architectures. To address these challenges, this study proposes an Efficient and Scalable Graph Condensation with Structure-Preserving (SP-ESGC), which possesses a decoupled design that separates node condensation from graph structure generation. Specifically, it first employs heat kernel feature propagation to generate node representation via spectral graph theory-inspired diffusion. Further, a novel hybrid clustering strategy is designed to extracts discriminative intra-class centroids from the node representation. Finally, a pre-trained edge predictor infers transferable structural patterns from the original graph, ensuring accurate synthetic graph generation. Extensive experiments on real-world graph datasets demonstrate that the proposed SP-ESGC implementes a precise GC with significantly high computational efficiency. Moreover, SP-ESGC also generalizes well across diverse GNN architectures.