Papers

Spiking neural networks (SNNs) offer an energy-efficient computing paradigm through sparse event-driven computation, showing great potential for efficient multimodal learning. However, applying SNNs to high-level multimodal tasks, such as image-text retrieval (ITR), remains challenging, since sparse spike representations make it difficult to capture semantic structures required for cross-modal alignment. Existing spiking ITR methods rely on local alignment and additional soft-label supervision during training, while lacking awareness of structural and multi-granularity relationships. To address these issues, we propose a Multi-head Spiking Graph Attention Network (MSGAT) for structural modeling and equip it with dynamic attention heads to capture complementary relational patterns and enable spike-driven graph reasoning and aggregation. However, within a two-branch multi-granularity fusion framework, the fine-grained spike representations generated by MSGAT are sparse and discrete, whereas the global representations are continuous, making conventional feature-level fusion susceptible to interference across heterogeneous representations. Therefore, we introduce Sim-Fuse, a similarity-space fusion alignment strategy integrating coarse- and fine-grained matching relations while avoiding direct fusion of heterogeneous representations. Experiments on Flickr30K and MSCOCO show our method outperforms ANN methods under matched settings and existing SNN retrieval baselines. Moreover, with only two time steps, our SNN achieves comparable or superior performance to its ANN counterpart while reducing theoretical module-level energy by 55%. The code is provided in the Supplementary Materials.

Database systems are predominantly developed in unsafe languages (e.g., C/C++) to meet performance requirements through low-level memory management, yet this reliance renders them prone to systemic memory-safety issues that compromise reliability, consistency, security, and durability. Through an extensive bug analysis of prominent database systems, we show that these memory-safety issues persist in production environments despite advancements in database testing tools. While emerging hardware-assisted extensions, such as Arm's Memory Tagging Extension (MTE) and CHERI, offer a promising mitigation path for memory safety, their practical applicability and performance overhead within the specialized constraints of database systems remain largely unexplored. In this paper, we evaluate hardware extensions through the lens of what we define as the database trilemma: the fundamental trade-off between safety, performance, and portability, to determine their viability for production-grade database systems. We provide the first side-by-side comparison of MTE and CHERI across a database workload suite. Our bottom-up study spans microarchitecture, the compiler/runtime/OS stack, core data structures (ART, B+Tree, hash table, skip list, linked list, and queue), and full database systems (Redis, LevelDB, SQLite, MySQL, DuckDB, and LadyBugDB) to characterize their performance, safety guarantees, and ease of adoption. We find that while hardware extensions can offer near-deterministic protection, they introduce non-uniform performance taxes: MTE provides high portability with modest overheads (~10%), while CHERI delivers superior safety guarantees with higher performance penalties (20-60%) and significant porting effort. Our study equips database systems architects with an actionable guide toward building the next generation of reliable, secure databases using hardware-assisted safety mechanisms.

Existing singing pitch correction approaches rely on target melodies or accompaniment tracks, which may be unavailable in practice. We formulate reference-free singing pitch correction as a music-constrained sequence editing task that determines whether and how each note should be corrected from the input performance alone. A pretrained symbolic music encoder with lightweight singing-domain adapters produces contextual representations of the singing MIDI. Based on these representations, two lightweight correction heads jointly model correction necessity and signed pitch modification through a factorized pitch-editing distribution. An input-dependent tonal prior derived from the estimated key distribution then reranks the candidate offsets, favoring tonally compatible corrections without target melodies or ground-truth key annotations. Experiments on real paired amateur and professional singing recordings show that the method improves note-level pitch accuracy from 73.25 to 83.43, outperforming a context-based baseline by 3.99 percentage points while balancing error correction and preservation of correctly performed notes.

Federated reinforcement learning (FRL) enables distributed agents to collaboratively train decision-making policies, but its decentralized training process also exposes global policy learning to Byzantine manipulation. Existing poisoning attacks primarily focus on how to construct malicious updates, while trajectory-level intervention timing remains largely implicit. In sequential decision making, however, where an intervention is applied can alter subsequent trajectories and learning signals. Through controlled experiments, we find that changing the selected trajectory states materially alters attack efficacy even when the malicious-update construction is fixed. We therefore identify when as a distinct attack dimension and introduce the Viability-constrained Behavioral Steering Attack (V-BSA), which uses local policy uncertainty to select sparse intervention states and applies envelope-constrained behavioral steering. Across discrete-action benchmarks, V-BSA achieves substantial degradation against robust aggregators and ensemble defenses with only a fraction of the interventions used by dense poisoning, while revealing task- and aggregation-dependent boundaries. Overall, our results highlight intervention timing as a distinct dimension of sequential robustness in FRL. The code is available at https://github.com/Yodeesy/V-BSA

AutoCFD5 Case 2 compares the participants' CFD results with wind tunnel measurements of surface pressure, velocity profiles and force coefficients. To place each run on a diagram of error against computational cost, these quantities must be combined into one number. This note defines that number, the joint error. Following the practice of interlaboratory proficiency testing (ISO 13528), every deviation from the experiment is expressed in units of the spread of the participants' results at that point, estimated robustly with the standard's Algorithm A. The point-wise spreads are pooled into one scale per component, so that every measurement point carries equal weight within its component. The joint error is a fixed weighted sum of five component errors. The scales are computed once from all AutoCFD5 submissions received by 5 October 2026 and then frozen, so that scores are reproducible and comparable across workshops.

We introduce multiple $s$ values and prove that every alternating multiple zeta value is a $\mathbb{Q}$-linear combination of multiple $s$ values $s(k_1, \dots, k_r)$ with $k_i \in \{1, 2\}$. We also study when certain multiple $s$ values can be expressed as $\mathbb{Q}$-linear combinations of multiple zeta values.

End-to-end speech parsing, a task recently proposed, consists in predicting both the transcription and the syntactic tree for a spoken utterance. Existing architectures for speech parsing often utilise intermediate neural networks. In this work, we examine the effectiveness of intermediate neural networks (NN) for parsing, and, specifically, what role do they play. We introduce a simpler end-to-end architecture for speech parsing, where we remove these intermediate NN units, reducing the parameters by 12%, while achieving comparable or better performance than prior method on both automatic speech recognition (ASR) and parsing. We demonstrate that intermediate NN units help reduce the representational gap when the pre-trained encoder is frozen. We do a comprehensive evaluation of speech parsing on French, and medium-low resource languages Slovenian and Naija. We further investigate the impact of the training data size and intermediate layers of the pretrained speech encoder on speech parsing.

Reinforcement learning with verifiable rewards (RLVR) and on-policy distillation (OPD) have become two main paradigms for post-training reasoning models. RLVR gives each response a single outcome label, leaving the steps inside it without separate credit. OPD provides token-level guidance at student-visited prefixes, but its pointwise signal does not directly reflect the pattern of teacher–student disagreement across the vocabulary. Dense, unbounded log-ratio supervision can amplify the teacher's influence, yet a strong solver is not necessarily a suitable guide when the student's solution paths depart from the teacher's. We propose Residual Advantage (\RA{}), which treats the teacher–student probability residual as a bounded one-step reward, subtracts the corresponding state value under the student policy to form a standard advantage, and centers the result within each response before adding it to the verifier advantage. The guidance term has zero mean within each response, so the verifier advantage remains the response's mean label and the teacher only redistributes credit among the steps within it. \CoRA{} further updates a teacher LoRA with verifier advantages on the same scored student batch and uses the updated teacher in the next iteration's residual, adapting guidance to the student's attempts. With Qwen3-1.7B-Base and Qwen3-4B-Base students and a Qwen3-8B teacher, \RA{} combined with GRPO or REINFORCE++ improves the underlying sequence-advantage algorithm in all 24 comparisons on three mathematical benchmarks, raising macro Avg@8 by 1.7–3.6 points and Pass@8 by 3.9–6.3 points. Both combinations surpass teacher-only OPD, and \CoRA{} adds a further 1.0–1.5 Avg@8 points.

The decomposition of the Ricci scalar in terms of bulk and boundary terms gives rise to an interesting gravitational field theory as proposed by Böhmer and Jensko (BJ). BJ went on to suggest functional forms of the bulk contributions in the Lagrangian. For the purposes of astrophysical modelling the boundary terms are non-dynamical and the entire theory is built from the bulk contribution only. The field equations for a stellar perfect fluid distribution are obtained against the background of a conformostatic metric. Since the linear form of the function of the bulk term is equivalent to Einstein we probe the next level of complexity namely the pure quadratic case. The field equations are substantially more complicated than Einstein's equations. The equation of pressure isotropy proves intractable even with simple choices of one of the geometric potential functions. Accordingly we analyse the case of the potentials varying inversely with the radius. Viable models do not arise in this case and so we postulate a proportional relationship between the potentials. It turns out that a physically reasonable shell of isotropic fluid may be constructed that satisfies elementary physical requirements. Finally we investigate the isothermal fluid where both density and pressure go as the inverse square law of the radius. This results in fluid behaviour that is comparable to that in the corresponding Einstein model.

The Bermond–Thomassen Conjecture asserts that every digraph with minimum out-degree at least $2k-1$ contains $k$ disjoint directed cycles; it remains open in general. We asymptotically resolve it: there exist an absolute constant $K$ and a function $g(k)=o(k)$, independent of $n$, such that every $n$-vertex finite simple loopless digraph with minimum out-degree at least $2k+g(k)$ contains $k$ disjoint directed cycles for all integers $k\ge K$ and $n\ge1$. In fact we obtain the explicit error term $g(k)=O(k^{3/4}\sqrt{\log k})$.

We study the matroid secretary problem with a nonnegative monotone submodular objective. Elements arrive in uniformly random order, and every acceptance decision is immediate and irrevocable. We give an $8.699$-competitive algorithm for arbitrary matroids. The algorithm first rejects a randomly sized initial segment of the arrival sequence as a learning set and runs submodular greedy on all elements in this set. Each later element receives a fixed weight equal to the marginal value it would have when inserted into the stored greedy sequence. On these fixed weights, the algorithm runs a linear-objective matroid secretary subroutine. The algorithm uses $O(nr)$ value queries and $O(n^2)$ independence queries, where $r$ is the matroid rank.

We study the calibration of interaction-driven ordinary differential equation (ODE) models for traffic and pedestrian dynamics by means of optimal control and stochastic gradient descent. The interaction forces are either prescribed by classical physics-inspired laws, whose parameters are identified from trajectory data, or represented by feed-forward neural networks whose weights act as control variables. For the neural-network-driven particle system we prove well-posedness of the state equation, Lipschitz-continuous dependence of the trajectories on the initial data and on the network parameters, existence of an optimal parameter set, and a first-order optimality system with an explicit backward adjoint equation. The resulting adjoint representation of the gradient is combined with a projected mini-batch ADADELTA scheme, so that each gradient evaluation requires one forward and one backward ODE solve, independently of the number of network parameters. Building on this framework we propose two new second-order models, one for vehicular traffic and one for crowds, that combine goal-seeking, learned interaction, repulsion-alignment or dissipation, and external control terms. Numerical experiments compare six models (a follow-the-leader model of Lighthill-Whitham-Richards type, a neural-network traffic model, the social force model, a neural-network pedestrian model, and the two new models) in terms of cost reduction and root-mean-square trajectory deviation. The neural-network pedestrian model achieves the lowest final cost, while the richer second-order models trade a higher calibration cost for individualised, behaviourally interpretable dynamics. We conclude by discussing limitations and directions for incorporating richer behavioural and environmental effects.

Fault injection is increasingly used to evaluate the reliability of tool-using LLM agents. However, there has been limited study of how fault-adoption results should be interpreted when the agent itself determines which authoritative observations become visible during execution. In this paper, we present a systematic study of this evidential validity problem in agent fault-injection evaluation. We develop a measurement protocol that specifies what observations can refute an injected assertion, determines whether they can become visible before the affected fact is first used, and records whether the evaluated execution actually realizes this condition. We construct SSCBench as an instantiation of the protocol and evaluate four fault operators and five agent configurations over 1,191 faulted executions in two $\tau$-bench environments. Our experiments show that an admitted fault case and agent configuration can realize substantially different evidential conditions across executions, and that aggregate adoption can remain well defined even when the population supporting a timely-counterevidence claim is sparse or absent. For example, among 44 adopted runs in which counterevidence eventually became visible, only 17 received it before first use, while 27 received it afterward. We also find that first-error timing and later stance revision need not coincide, and that automated trajectory analysis can recover adoption without reliably recovering the first faulty-reliance event needed for temporal diagnosis. We argue that the evidential condition realized by an execution and the population supporting a claim-specific interpretation are part of fault-injection evaluation itself and should be reported before adoption is interpreted as failure under pre-use counterevidence.

Large-scale Quantum Key Distribution (QKD) networks rely on trusted repeaters, making the security properties of the selected communication path an essential part of end-to-end assurance. At the same time, network operators may be unwilling to disclose their internal topology. We present a topology-certification mechanism that lets a provider prove in zero knowledge that policy-compliant routes between two endpoints exist, without disclosing the routes in an individual presentation. Our main idea is to certify nodes and edges independently using multi-message signatures, rather than signing the complete graph as one object. For a route chosen in advance, proof size and cryptographic proving and verification work depend on its positions and attributes, independently of the overall network size, whereas route discovery and certification have separate graph-dependent costs. The construction hides the actual route length up to a public bound and sketches extensions to node-disjoint routes and monotonic additions within a graph epoch. We give a formal security model and conditional proofs of unforgeability and graph hiding for a generic construction. For a BBS-based construction, presentation-size estimates remain below $300$\,KiB at $\ell=m=n=50$, and measured generation and verification times remain below $400$\,ms at $\ell=64$ and $m=n=8$.

In this paper, we prove the existence of stationary pulse solutions for a bulk-surface reaction-diffusion system modeling cell polarization in two-dimensional domains. Using a singular perturbation method, we construct pulse solutions whose centers lie near non-degenerate critical points of a geometry-dependent potential expressed in terms of the Neumann Green's function, as formally predicted in \cite{watanabe2026}. The main analytical difficulty arises from the half-Laplacian induced by the logarithmic singularity of the Green's function, resulting in algebraically rather than exponentially decaying inner solutions. Our analysis may also serve as a useful guide for applying singular perturbation methods to other bulk-surface type systems.

Federated learning (FL) typically adopts a server-client architecture, where the server aggregates clients' local models (i.e., the input) and returns the aggregated global model (i.e., the output) to clients. An untrusted server may return a tampered global model to compromise the output integrity. Some existing schemes focus on verifying the output integrity. However, these schemes mostly rely on clients pre-negotiating a set of identical auxiliary information among themselves and keeping it confidential from the server. This dependency creates a verification vulnerability: if the auxiliary information is leaked, the verification method may be circumvented. Additionally, in some privacy-sensitive scenarios (e.g., commercial federated learning), the global model may need to be kept confidential from an untrusted server. However, only a few works achieve the output privacy while addressing verification vulnerability, at the cost of prohibitive computation and communication overhead. To address these challenges simultaneously, we propose a novel provably privacy-preserving FL method called EIFL. Specifically, we adopt a two-stage aggregation and combine it with symmetric encryption to protect the output privacy. To address the verification vulnerability, we propose an efficient verification method based on vector inner product for output integrity, and a random vector generation method for clients to agree on auxiliary information. EIFL innovatively binds the auxiliary information to the output integrity, and eliminates the need to keep the auxiliary information confidential from the server. Moreover, EIFL is robust against client dropout during the verification phase through a simple resending operation. Evaluation results validate the advantages of EIFL over state-of-the-art schemes in terms of computation and communication overhead.

Large language models (LLMs) often default to Modern Standard Arabic (MSA) when generating Arabic, even when prompted with dialectal Arabic. A natural explanation is that their internal representations are dominated by MSA. We test this hypothesis by adapting the language-dominance framework of Shani and Basirat (2025) (https://doi.org/10.18653/v1/2025.blackboxnlp-1.7) to 26 Arabic varieties. Across layers and model families, we find no evidence that MSA acts as a dominant internal representation for Arabic dialects. Instead, dialect representations form a dense and highly overlapping space: normalized mutual information drops sharply compared to patterns reported for more distinct languages. Moreover, the strongest separability effects are not confined to intermediate layers, but can shift toward later layers depending on the architecture. These findings challenge a common interpretation of MSA-biased generation: output preference does not necessarily reveal internal representational dominance. Analyses of multilingual and dialectal LLMs should therefore distinguish generation bias from the geometry of internal representations.

We study preservation of spatial convexity for viscosity solutions of first order Hamilton-Jacobi evolution equations with Neumann-type boundary conditions in bounded convex domains. Under a monotonicity assumption on the Hamiltonian in the outward normal direction, every viscosity supersolution of the Neumann problem is also a state-constraint supersolution. This reduces the boundary difficulty to a state-constraint problem and enables us to prove convexity preservation via the convex-envelope argument established by Alvarez, Lasry and Lions (1997). We also obtain propagation estimates for semiconvexity and strong convexity under similar structural assumptions.

Despite recent advances in Vision-Language-Action models (VLAs) for robotic manipulation, their performance remains sensitive to changes in camera configuration. The problem becomes more evident in cross-setup deployment, as reproducing the exact camera pose used for training is nearly impossible. Unlike fixed external views, wrist views are more challenging because the camera moves with the robot, causing even small mounting variations to alter fine-grained geometric cues. To address this, we propose WARP-VLA, a camera-view robust VLA for diverse wrist camera configurations. WARP-VLA adopts a Mixture-of-Experts (MoE) architecture where individual experts learn view-specific feature transformations, and a router combines them based on implicit view information. This allows the policy to be deployed without requiring camera extrinsic parameters as additional input. Through experiments on the LIBERO benchmark, WARP-VLA improves the average success rate of pi-0.5 from 39.2% to 78.3% under wrist-view perturbations. The real-robot experiments further show that the feature-level adaptation learned in simulation successfully transfers to diverse deployment settings. To facilitate reproducibility and future research, we release our wrist viewpoint robustness benchmark and a plug-and-play implementation.

Source-to-microphone distance enables speaker-independent speech extraction without prior enrollment. We propose a monaural continuous-radius regional speech extraction method that directly models the cumulative speech target within a queried radius. To realize continuous region control, the query radius is encoded as a continuous scalar and injected into a time-frequency extraction network, allowing a single model to operate over arbitrary radii within the trained range. Exploiting the nested structure of target-speaker sets across query radii, we introduce cross-radius consistency learning to stabilize predictions for adjacent radii sharing the same nonempty target-speaker set. Experiments on measured RIRs show that continuous-radius conditioning improves selective extraction over discrete conditioning. The proposed method achieves 29.25~dB SI-SDR, 4.40~dB SI-SDRi, 62.01~dB attenuation, and 0.46% RCE, outperforming fixed-threshold and local-range baselines. It also remains effective with more speakers and additive noise.

Graph clustering is a fundamental task in data analysis, aiming at grouping nodes with similar characteristics in the graph into clusters. This problem has been widely explored using graph neural networks (GNNs) due to their ability to leverage node attributes and graph topology for effective cluster assignments. However, representations learned through GNNs typically struggle to capture global relationships between nodes via local message-passing mechanisms. Moreover, the redundancy and noise inherently present in graph data may easily result in node representations lacking compactness and robustness. To address these issues, we propose a conjoint framework CoCo, which captures compactness and consistency in the learned node representations for deep graph clustering. Technically, our CoCo leverages graph convolutional filters to learn robust node representations from both local and global views, and then encodes them into low-rank compact embeddings, thus effectively removing the redundancy and noise as well as uncovering the intrinsic underlying structure. To further enrich the node semantics, we develop a consistency learning strategy based on compact embeddings to facilitate knowledge transfer from the two perspectives. Our experimental results indicate that our CoCo outperforms state-of-the-art counterparts on various datasets.

Humanoid robots possess the structural capability to traverse complex terrains. However, achieving stable t raversal without relying on perceived information remains challenging, particularly in complex environments. This paper introduces DAMP, a reinforcement learning framework aimed at achieving robust and naturalistic humanoid locomotion over challenging terrains, with the assumption that no perceived information is available. The framework leverages recurrent neural networks to capture temporal dependencies and implicitly infer privileged and other task-relevant latent information. By aligning the learned representations with the task objective, the method enables robust and goal-consistent policy learning. This end-to-end framework achieves transfer learning from simulation to real-world environments, demonstrating the proposed method's robustness and generalization capabilities. The video of the real-world demonstration can be found at the following link: https://youtu.be/AkI7TZB2DDM.

Modern autonomous driving systems rely on bird's-eye-view (BEV) perception models that fuse camera and LiDAR inputs to detect objects in 3D space. These models are accurate, but they cannot be deployed through standard inference runtimes. The reason is an operator mismatch between dense convolutions (which runtimes handle well), sparse 3D convolutions (which runtimes cannot represent), and geometric scatter operations (which runtimes have no vocabulary for). Today, every sparse convolution library is CUDA-only and PyTorch-coupled, locking BEV deployment to a single vendor's hardware and a single execution framework. We present BEVPIPE, a framework for deploying multimodal BEV perception pipelines using portable GPU compute APIs and integrating them with production inference runtimes. BEVPIPE partitions the model into runtime-managed dense subgraphs and three external operator extensions (voxelizer, sparse encoder, BEV projector), connected through a shared GPU memory space. BEVPIPE achieves a 19.5x end-to-end speedup over conventional deployments while retaining 98.5% of reference mAP. We also showcase that BEVPIPE is portable across different GPU backends.

We present a systematic study of the effects of chlorine substitution on the magneto-optical properties of the van der Waals layered semiconductor CrSBr. Our study shows that even at substitution level of $x=56\%$ the $\mathrm{CrSBr_{1-x}Cl_{x}}$ material exhibits qualitatively the same clear magneto-optical coupling that was observed in pure CrSBr crystals. The values of the relevant parameters are shown to vary smoothly across different substitution levels, thus offering promising tunability for this family of 2D magnetic materials.

Large Language Models (LLMs) have shown strong reasoning capabilities when fine-tuned with reinforcement learning (RL), particularly through Group Relative Policy Optimization (GRPO). However, existing GRPO methods assume centralized access to training data, which may not hold in practice due to privacy or regulatory constraints. To this end, we propose Fed-GRPO, a federated GRPO training framework that addresses these privacy constraints by enabling collaborative reasoning training without sharing raw data, which leverages the reward statistics naturally produced during GRPO training as zero-cost signals to guide aggregation, local training, and communication. Fed-GRPO contains three reward-signal-driven mechanisms: (i) signal-weighted aggregation that weights clients by their reward standard deviation, prioritizing clients with stronger learning signals; (ii) global reward calibration that re-weights per-prompt objectives based on the local-global reward gap, steering each client toward its relative weaknesses; and (iii) adaptive sparse communication that allocates bandwidth based on the informativeness of each client's update. Extensive experiments on mathematical reasoning tasks demonstrate that Fed-GRPO achieves the best performance among all federated methods, clearly outperforms FedAvg and approaches centralized training performance, while losslessly reducing communication by $32\times$ and supporting up to $621\times$ compression under tight bandwidth budgets with only graceful accuracy degradation. Our code is available at https://github.com/HKU-HealthAI/Fed-GRPO.

Despite the adoption of large language models (LLMs) in recommendation systems, prevailing approaches mostly model single-type behaviors (e.g., views or purchases). Even when incorporating multiple behaviors, existing methods flatten heterogeneous actions into homogeneous token sequences, ignoring their distinct decision-making roles. This flattening fails to capture semantic hierarchies and contextual nuances in complex decision-making, such as trade-offs between price and quality. Consequently, performance degrades in critical “difficult-choice” scenarios involving highly similar items. To bridge this gap, we propose MARI (Memory-Augmented Recommendation with Interpretability), which grounds predictions in explicit, structured decision evidence. MARI maintains a Decision Memory Bank (DMB) that archives users' past rationales as Structured Decision Memories (SDMs): concise records of goals, constraints, and trade-offs. These SDMs are generated offline via Post-Hoc Decision Distillation from heterogeneous behaviors and user-generated content. By retrieving relevant SDMs to augment LLM reasoning, MARI achieves interpretability and scalability without the prohibitive cost of processing long raw sequences. Extensive experiments show MARI significantly outperforms state-of-the-art baselines on standard next-item prediction and a newly introduced Difficult Choice Prediction task, incurring low latency overhead by decoupling memory construction from online inference. Qualitative analyses reveal actionable, human-readable insights into user decision-making, marking a concrete step toward reasoning-aware recommendation systems.

Bound states in the continuum (BIC) metasurfaces are typically described by geometry-specific parameters, hindering cross-geometry comparison, while ultranarrow qBIC features are easily diluted in full-spectrum learning. Here, 2015 samples from seven dielectric metasurface families are mapped to a shared reciprocal-lattice grid, where two frozen low-order Fourier channels capture resonance shifts with mean within-branch $R^2$ values of 0.871-0.999. Field-level analysis of two representative branches further confirms that these shifts are consistent with the Maxwell-Fourier perturbation picture. A five-channel K-space backbone models the broadband spectrum, while a local complex K-space expert parameterizes the qBIC resonance through a differentiable Fano layer. The expert reduces resonance-position mean absolute error (MAE) from 3.2 to 0.95 nm and the resonance-depth error by 14-fold on a geometry-blocked test set. The same coordinate supports spectrum-to-structure reconstruction.

For the nonrelativistic three-body Coulomb Hamiltonian, near-threshold resonances of the deuterium–tritium muonic molecular ion ($dt\mu$) are supported by the long-range dipole coupling between degenerate atomic $2s$ and $2p$ states. We study the effect of atomic $2s$–$2p$ splitting on their positions and decay widths. Three-body complex-absorbing-potential calculations resolve additional members of the $L^\pi=0^+$ and $1^-$ series. Their geometric spacing agrees with that expected from the $1/R^2$ dipole attraction, where $R$ is the atom–nucleus separation. To assess the effect of splitting, we scan a prescribed $2s$–$2p$ interval using an effective potential in a spin-independent, nonrelativistic Hamiltonian. This models the atomic splitting without an explicit Lamb-shift calculation. Within this model, the studied resonances lie closer to the $d\mu(2s)+t$ threshold and have smaller Coulomb decay widths than in the degenerate case. At an effective interval of $0.2\eV$, the seventh $1^-$ member lies within $2\meV$ of this threshold with a full width of about $4\meV$, compared with $48$ and $15.6\meV$ at degeneracy. These values characterize the response within the tested numerical representations. Its width decreases, but its separation from the threshold decreases more strongly. The long-range analysis attributes these shifts and width reductions to modified dipole mixing. It further suggests that atomic $2s$–$2p$ splitting may truncate the infinite accumulation of resonances predicted for degenerate atomic $2s$ and $2p$ levels.

Video diffusion and flow models require many sequential evaluations, making generation computationally expensive. Few-step distillation reduces this cost but poses a capacity allocation problem: a student must match the teacher's iterative generation with far less sequential computation. Existing trajectory methods ask the student to reproduce teacher transitions that are highly curved at high noise, which can exceed its capacity and degrade fine detail. We introduce Parametric Trajectory Distillation (PTD), which lets the student parameterize teacher trajectory segments as polynomials and learn from teacher guidance along its own predicted path. PTD is designed to let the learned curvature adapt to the backbone's predictive capacity, preserving motion and diversity. The curvature head is used only in training; inference keeps the original backbone architecture. On Wan2.1-14B, four-step PTD sets a new state of the art for trajectory distillation, significantly improving dynamic quality and naturalness over PDD, the best-performing trajectory-only method on this model, under the same training setting. On the 33B audio-video MiniMax-H3, LoRA-trained PTD significantly improves diversity and naturalness over the state-of-the-art LightX2V Turbo. Blinded human votes give PTD 55.1% and 63.4% preference shares against PDD and LightX2V Turbo. Project page: https://alan-lanfeng.github.io/PTD/.

We develop a semisimple obstruction theory for finite-length abelian categories. To each object \(X\) we associate a canonical obstruction subobject \(\mathcal O(X)\), consisting of the part invisible to all morphisms into semisimple objects. The quotient \(X/\mathcal O(X)\) is semisimple and universal among such morphisms, yielding a canonical semisimplification reflector and characterizing semisimplicity by the vanishing of obstruction. Iterating the construction gives an obstruction filtration which, in finite-length module categories, recovers the classical radical filtration and Loewy theory. Obstruction is also heart-dependent: under Happel–Reiten–Smalø tilting, extension data can appear as new obstruction layers, leading to obstruction shadows and visible torsion. Thus classical radical theory arises as the fixed-heart module-theoretic instance of a categorical framework for semisimple reconstruction, persistence, and variation of heart.