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Vision-Language-Action driving models convert a pretrained Vision-Language Model into a driving policy, allowing them to use world knowledge and follow language guidances. However, existing VLA driving models still lack driving-oriented spatial intelligence: their policies are mainly grounded on perspective image tokens and language priors, while precise motion planning requires metric geometry, top-down scene structure, and attention to safety-critical perceptual cues. This limitation makes current models vulnerable to weak visual geometry modeling and perceptual coverage in expert demonstrations. In this paper, we present DriveStack-VLA, a framework built upon a large VLM backbone. To strengthen the spatial grounding of VLA driving, we develop dual visual modeling components. We inject a Bird-Eye-View representation into the Large Language Model decoder through a DeepStack-style connection, and propose Render-Teacher Alignment to align the perceptual focus of real images with that of rasterized images. Furthermore, to bridge the gap in multimodal trajectory selection, we introduce a head-based self-critique module that ranks sampled trajectories and conditionally refines the best one. DriveStack-VLA achieves 91.6 PDMS on NAVSIMv1, 91.0 EPDMS on NAVSIMv2 (with the human penalty filter enabled), and a driving score of 79.49 with a success rate of 56.36\% on the closed-loop Bench2Drive. More visualizations are available on our project page: https://anonymous.4open.science/w/drivestack-vla/.

Fabric moiré is a sampling-induced aliasing artifact caused by the interaction between fine textile patterns and camera sensor grids, producing structured interference that severely degrades image quality. Unlike screen-induced moiré, which stems from strictly periodic display lattices, fabric moiré is intrinsically more challenging due to the broadband and semi-periodic nature of textile weaves. The heavy spectral overlap between intrinsic texture and aliasing components renders fabric demoiréing substantially more ill-posed. Consequently, existing models trained on screen moiré datasets generalize poorly to these complex textile patterns. Despite its practical importance, fabric image demoiréing remains underexplored and lacks standardized benchmarks. We present the first comprehensive benchmark for fabric image demoiréing. To address the difficulty of acquiring pixel-aligned real-world pairs, we develop a physically motivated synthesis framework and construct a large-scale dataset comprising 16,050 paired multi-resolution fabric images with controllable aliasing severity. Furthermore, we customize a baseline model, which establishes promising performance on the proposed benchmark dataset with strong generalization ability. Our benchmark provides a standardized platform for advancing research in fabric image demoiréing.

Effective cross-modal feature alignment and interaction are central challenges in multispectral object detection. Although global cross-attention provides strong long-range modeling ability, its quadratic complexity with respect to feature size limits deployment on resource-constrained platforms. We therefore propose Progressive Pixel-Neighborhood Deformable Cross-Attention for multispectral feature fusion, termed PNAFusion. The proposed framework is motivated by two observations: weak misalignment between visible and thermal images is usually concentrated around local neighborhoods, and semantic correspondence across modalities often follows non-linear spatial mappings that fixed receptive fields cannot model well. To address these issues, PNAFusion incorporates local spatial priors into its architectural design to concentrate feature interaction and alignment on the most relevant neighborhoods. Specifically, a Pixel-Neighborhood Cross-Attention (PNCA) module is introduced to avoid redundant global feature matching and suppress background noise. Meanwhile, an Adaptive Deformable Alignment (ADA) module captures non-linear spatial correspondences through learned pixel-wise offsets. These components are further integrated through an iterative feedback mechanism to progressively refine cross-modal feature alignment. Experiments on FLIR, M3FD, and DroneVehicle show that PNAFusion achieves 84.2, 90.5, and 85.5 mAP@0.5, respectively, under the YOLOv5 detector, and further reaches 86.8 mAP@0.5 on FLIR and 90.8 mAP@0.5 on M3FD when transferred to Co-DETR. Efficiency analysis indicates that PNAFusion reduces allocated GPU memory by 33.0\% compared with ICAFusion and reduces theoretical FLOPs from 194.8 G to 156.4 G, although the deformable sampling and iterative refinement introduce additional latency. Our code will be available at https://github.com/DanielQiuTian/PNAFusion.

Modern spoken language understanding (SLU) systems are increasingly deployed in real-world settings, where specific functionalities may need to be removed due to policy or safety constraints. In SLU, a functionality corresponds to an intent and its associated slot-generation behavior. However, in autoregressive models, suppressing a target intent does not eliminate the conditional mapping that generates slots conditioned on that intent. When the intent prefix is externally supplied, the model can reconstruct the original intent-slot structure. We identify this structural failure as \textbf{\emph{capability persistence}}. We propose \textit{\underline{B}inding \underline{S}ubspace (BSU)}, a representation-level framework that isolates and attenuates intent-conditioned directions underlying this mapping. Across SLU benchmarks, BSU substantially reduces forced-prefix recoverability while preserving retained performance.

Most electronic health record (EHR) foundation models encode clinical events as discrete event tokens from a fixed vocabulary and therefore cannot directly represent events containing unseen concepts or new combinations of concepts and attributes such as numeric values. This limits transfer across institutions and even across deployment pipelines within the same institution. We introduce PORTER, a language-grounded structured EHR foundation model that decouples event representation from this fixed vocabulary. PORTER represents events through their descriptions using a frozen text encoder, integrates numeric values through a dedicated pathway, and learns clinical dynamics over patient timelines with an autoregressively pretrained temporal backbone. Across 74 clinical prediction tasks at a pediatric hospital, PORTER matched the mean AUROC of a fixed-vocabulary model with the same temporal backbone and pretraining objective. When the same patient timelines were rendered using event descriptions not seen during pretraining, PORTER transferred without retraining or vocabulary mapping, recovering 97.1% of the mean AUROC of a model trained directly on the target vocabulary. When transferred to MIMIC, PORTER outperformed the fixed-vocabulary model, which dropped 69% of events because their tokens were unseen. Mechanistic analyses showed cross-vocabulary transfer tracked preservation of patient-level representation geometry rather than the scale of the text encoder, and the numeric pathway improved sensitivity to magnitude without disrupting clinical concept identity. PORTER also achieved higher AUROC than a task-specific text serialization comparator, at 329-fold lower amortized compute. PORTER is a step toward vocabulary-independent EHR foundation models that reduce the need for vocabulary harmonization while preserving in-domain performance and enabling efficient cross-task reuse.

Automated diabetic retinopathy (DR) grading from colour fundus photographs can achieve strong predictive performance, but clinical interpretation requires more than an image-level label. It requires understanding how lesion evidence is distributed around retinal vessels and how this evidence relates to quantitative vascular biomarkers. We present a dual-edge spatial-Jacobian image graph for interpretable DR grading. Each fundus image is represented as a graph node with four aligned evidence streams: AutoMorph vessel information (\(X_1\)), DR-XAI-style lesion evidence maps (\(X_2\)), a 128-dimensional lesion-based contrastive image embedding (\(X_3\)), and AutoMorph morphometric biomarkers (\(X_4\)). The spatial edge branch (\(X_{12}\)) encodes vessel-lesion geometry, while the Jacobian branch (\(X_{34}\)) models embedding-biomarker sensitivity. Lightweight two-token attention fuses both edge families into a final image graph. On 2,910 matched non-augmented APTOS images, the full graph achieves 0.8076 accuracy, 0.8312 quadratic weighted kappa, 0.5915 macro-F1, and 0.9330 adjacent-grade accuracy; referable DR reaches 0.9055 accuracy and 0.9711 AUROC. The framework is positioned as an explainable representation-learning tool for lesion-biomarker hypothesis generation, rather than as a deployment-ready clinical classifier. The code is available at https://github.com/Inamullah-Colab/dual-edge-dr-graph-xai.

Stochastic quantum neural networks (SQNNs) encode neuronal activations as qubits, synaptic topology as entanglement, and neural noise through a Lindblad master equation. A recent conference study applied a ring-entangled SQNN to collaborative intrusion detection and reached three conclusions: ring entanglement is \emph{essential} for non-local anomaly detection; an adversarial-resilience bound holds but is \emph{conservative}; and the depolarising channel \emph{fails} to act as a dropout-style regulariser, behaving instead as output noise. It left open whether a per-gate stochastic deactivation (``true quantum dropout'') could regularise where the depolarising channel could not, and whether the loose robustness bound could be replaced by a predictive theory. This paper resolves both and extends the framework to real data and to neutral-atom hardware. We give an \(N\)-qubit formulation through the stochastic master equation and its vectorised Liouvillian, and prove a \emph{decoherence-contraction theorem}: a depolarising channel of strength \(γ\) over \(L\) entangling layers contracts every weight-\(w\) Pauli read-out by a factor \((1-4γ/3)^{wL}\) (for the weight-\(1\) read-out used here, \((1-4γ/3)^{L}\)); building on the general noise-as-defence result of Du et al., we make this quantitative and operational for intrusion detection. On the real NSL-KDD dataset under white-box FGSM and PGD attacks, a depolarising SQNN trained with the channel is, over seven seeds under strong \(\ell_\infty\)/\(\ell_2\) attacks, significantly more robust than the noiseless circuit (\(\ell_\infty\) PGD-\(20\), \(p=0.04\), large effect) and, critically, never suffers the catastrophic robustness collapse that the noiseless model and gradient-trained classical detectors (which fall from \(95\%\) to \(47\%\)) do, cutting robustness variance roughly twofold; we show this robustness arises from a noise-reshaped training boundary rather than from attack-time gradient contraction. For generalisation, we derive an adaptive-penalty formula showing that per-gate dropout implements a curvature-weighted \(L_2\) penalty \(\tfrac{p(1-p)}{2}\sumθ^2\partial^2_θL\) in weight space, maximised at \(p=1/2\), whereas depolarising noise implements an output-space penalty. A \(30\)-seed study confirms the formula's quantitative prediction: both mechanisms reduce the train-test gap by a small but statistically significant margin (\(\approx\!0.01\); \(p<10^{-4}\) and \(p=0.004\)), are statistically indistinguishable from each other, and the effect is concentrated where overfitting is largest; increasing the dropout rate past \(1/2\) does not help, as the formula predicts. The single-seed dichotomy of prior work does not survive replication. We close with a neutral-atom realisation and a feasibility-by-\(N\) analysis.

Efficient genomic k-mer indexing depends on approximate membership query (AMQ) structures that must deliver high throughput, low false-positive rates (FPR), and modest memory footprints. The Super Bloom filter (SBF) is attractive for this scenario because minimizer-guided sharding and the Findere scheme exploit the redundancy of overlapping k-mers. However, those same features cause high per-k-mer compute cost, severe register pressure, and irregular memory accesses, which hinder an effective GPU implementation. We present cuSBF, an open-source, header-only CUDA library that implements SBF for sequence-native workloads. cuSBF's design merges sectorized shards, cooperative shared-memory tiling, warp-level shard sharing, and segmented warp reductions, turning super-k-mer locality into scalable GPU parallelism. Across real genomic workloads on RTX PRO 6000 Blackwell and GH200 systems, cuSBF achieves the highest throughput among all evaluated sequence-capable baselines. On the RTX PRO 6000, it surpasses the cuCollections blocked Bloom filter baseline by up to 9.1x for insertion and 7.7x for query, while reaching up to 92x and 234x speedups over the multi-threaded CPU Super Bloom reference implementation. It also outperforms GPU-based dynamic AMQs (Cuckoo, Two-Choice, Quotient filters) by 1.5-3400x depending on workload characteristics. A parameter sweep identifies (s = 28, m = 16, H = 4) as Pareto-optimal for k = 31, yielding significantly lower FPR than cuCollections at matched memory budgets. Crucially, cuSBF's architecture-aware design sustains 85% streaming multiprocessor utilization even for out-of-cache filters - proving that sequence locality, not raw bandwidth, is the key to GPU-accelerated genomic indexing.

Commercial large language models bill, scale latency, and budget context per token. Yet tokenizers assign more subword tokens to the same meaning in some languages than in others, so speakers of languages with high token-fertility pay a structural penalty before a model is ever invoked. This penalty is documented for multilingual settings in general, but it has not been measured systematically for African languages at the level of enterprise deployment economics and cognitive context capacity. We measure it across 20 African languages spanning five language families and three scripts (Latin, Ge'ez/Ethiopic, N'Ko; 19 appear in the primary FLORES-200+ corpus, with Nigerian Pidgin measured via MAFAND-MT only), using parallel corpora so that the language effect is isolated from content. Across 11 frontier and open tokenizers on FLORES-200+, every African language carries a tokenization premium above English (median 1.88x on GPT-5 / o200k_base, up to 8.92x for N'Ko); the penalty is largest for Ethiopic and N'Ko scripts (reaching 7-9x) and is near-invariant across corpora (FLORES vs SIB-200 Pearson r = 0.9998). Translated into deployment terms, this results in up to 8.9x inference cost and an equivalent generation-latency multiplier (N'Ko vs English on GPT-5; 7.4x for Amharic), and as little as 11% of English's effective context window. The best currently available tokenizer for African languages, Gemma 4, reduces the mean premium from 3.31x (cl100k_base) to 2.38x, but no tokenizer eliminates the penalty. We release an open measurement tool (afri-fertility), a public leaderboard, a results dataset, and mitigation guidance for African builders. The penalty falls hardest on the languages whose speakers can least afford it, a digital divide encoded directly into the subword vocabulary.

Vision-language-action (VLA) models have made rapid progress in generalist robot manipulation by harnessing semantic knowledge from pretrained vision-language backbones, but their visual tokens remain grounded in 2D image coordinates rather than the calibrated geometry of the robot's cameras -- a mismatch especially pronounced in multi-camera setups, where views are coupled by known intrinsics and extrinsics yet processed as independent images. We propose G\(^3\)VLA, a camera-aware geometric module that injects calibrated structure into the visual-token stream of a pretrained VLA without altering its action space or imitation objective, combining intrinsic-conditioned ray embeddings, projective positional encoding (PRoPE), and bidirectional cross-view fusion. Geometric supervision is provided either from ground-truth point maps when available, or from confidence-gated \(π^3\)X teacher predictions, requiring no depth sensors or manual annotations. Instantiated on \(π_0\), G\(^3\)VLA yields consistent gains across the LIBERO suites, RoboCasa24, RoboTwin2.0, and real-robot settings, with the largest improvements on spatially and object-sensitive tasks. We further validate on \(π_{0.5}\) and GR00T 1.5, with results suggesting that geometric transfer is most effective when geometry-aware tokens have direct access to the action generation pathway. Our project page is at https://sites.google.com/view/g3vla

Simulator-in-the-loop optimization offers a promising inference-time mechanism for robot manipulation. It uses a physical simulator as a backend rollout engine to evaluate candidate trajectories in parallel and refine nominal actions online, a paradigm proven effective in rigid-body manipulation where state and contact are relatively tractable. We bring this paradigm to real-world cloth manipulation from a single RGB input through three pillars. (i) We design a scalable synthetic-data generation and inference-time rollout pipeline built on FLASH, a deformable-object simulator that provides a practical balance among physical fidelity, numerical stability, and rollout efficiency. (ii) We develop a real-to-sim module, trained purely on synthetic data, that maps a single RGB observation to simulation-compatible cloth state by fusing pretrained visual features with learnable canonical tokens. (iii) We perform online planning by coupling a sparse-mesh rollout backend with prior-guided MPPI, anchored at an offline-distilled policy trajectory, preserving manipulation-relevant deformation and contact while enabling sufficient parallel rollout batches. Real-robot experiments show higher success rates and stronger robustness than baseline methods.

Linear Quadratic (LQ) control problems are at the heart of linear control theory and Model Predictive Control (MPC). While performant, standard approaches to solving such problems are inherently serial, limiting real-time scalability despite the parallel computing power available on modern multi-core CPUs. Contributing to addressing this challenge and motivated by ``divide and conquer'' strategies, we present a parallel-in-time approach that solves computationally demanding conic optimal control problems through the use of the alternating direction method of multipliers (ADMM). In particular, we formulate the inner primal update of ADMM as an LQ problem and split the reformulated problem along the time horizon. This enables us to derive a variant of the Riccati recursion using dynamic programming to solve each subproblem in parallel. Numerical benchmarks on two real-world applications demonstrate as much as a 5x speedup compared to existing related approaches on multi-core CPU hardware.

Discrete diffusion language model (DLM) fine-tuning inherits inexpensive diagnostics from denoising-time confidence monitors, but their PEFT-training meaning is untested. We test top-1 argmax concentration as a collapse warning. Across 816 LoRA/PEFT configurations from three DLM families, the warning fires for every configuration while logs record 0/816 actual collapses at the 200 step horizon, giving zero precision. The cause is pre-equilibrium saturation: top-1 concentration is already high before optimization and quickly becomes insensitive to final training stability. We then evaluate max LoRA gradient norm, a parameter-side signal that samples gradient routing rather than token concentration. On a pooled held-out LLaDA-family split, a train-optimized threshold identifies top-decile final-loss configurations with precision 0.68 and F1=0.79, above the all-positive top-1 baseline even at the lower split-bootstrap confidence bound. Autoregressive controls and cross-family threshold failures bound the result to short-horizon DLM-LoRA inspection rather than a universal collapse detector. Workflow: drop top-1 as a PEFT alarm, log max-gradient early in training, and calibrate thresholds per DLM family before routing runs for inspection.

Despite the extensive discussions of human-centric AI (HCAI) in Industry 5.0, its effects on firms' idiosyncratic risks (IR) remains underexplored. This is an imperative issue for firms navigate financial risks during the current technological revolution, as IR reflects investor reactions to corporate heterogeneous AI strategies and implementations by isolating firm-level stock volatility from systematic factors. Integrating situated AI theory with social-technical systems theory, we conceptualise HCAI as a situated AI strategy that reduces AI-related ethical risks and fosters AI-Human synergies in firms' business operations, ultimately reducing IR by aligning with stakeholders' diverse expectations. Moreover, socio-technical factors, namely digitalisation, operational efficiency, executive shareholding, and CEOs with IT background, may moderate the HCAI-IR relationship. Using a multi-source panel dataset of Chinese listed firms from 2015 to 2023, we find that HCAI is associated with lower firm IR. Furthermore, digitalisation and executive shareholding strengthen this risk-reducing effect, whereas operational efficiency and CEOs with IT background surprisingly attenuate it. Our findings offer theoretical contributions and practical insights for both ethical AI governance and firm financial risk management in the AI era.

We introduce EgoSAT, the first comprehensive benchmark for egocentric video reasoning in streaming settings, designed to evaluate the capabilities of modern vision-language models (VLMs). The benchmark targets streaming interaction understanding, where video frames arrive sequentially and models must continuously interpret evolving visual context. EgoSAT unifies several previously distinct tasks within a single streaming framework. In this formulation, queries about completed events correspond to retrospective reasoning, queries about ongoing activities require online understanding, and queries about future actions involve prospective anticipation. This unified setting requires models to reason about the past, present, and future while operating under the constraint that only previously observed frames are available. EgoSAT contains 1,997 unique videos spanning 165 hours of egocentric footage and around 4,800 high-quality question-answer pairs, carefully designed to probe reasoning across varying temporal contexts. Using this benchmark, we evaluate a diverse set of both open-weight and closed-weight VLMs, providing a systematic assessment of their ability for streaming interaction understanding. By distinguishing answerability and conducting diagnostics on confidence of models, we find existing models not only struggle with prospective and retrospective modeling, but also exhibit severe mis-calibration: confidence often fails to track inherent answerability, leading to dangerous "confidently wrong" behaviors. Project page: https://leiyj23.github.io/EgoSAT/

Frontier AI training is increasingly shaped by access to dense, centrally controlled accelerator clusters. This creates a structural advantage for hyperscalers and large centralized laboratories, and makes open or independent AI efforts depend on scarce capital, privileged infrastructure, and data-center geography. We present Spheroid BlockTrain, a decentralized training protocol in which a model is partitioned into independently trainable blocks, each optimized on a local objective derived from the same global target and composed at inference into one model. On byte-level WikiText, BlockTrain reaches cross entropy 1.359 (perplexity 3.89), within about 0.04 CE of a same-setup end-to-end Transformer reference, while each active worker trains only one block and avoids full-model optimizer state. A shared six-worker block training run reaches CE 1.385 by averaging same-block updates into one assembled model. HTTP/TCP transport experiments move real serialized checkpoints and updates, including a public-IP three-host run that improves CE from 5.580 to 1.811 while moving 15.22 GB. For inference, the current BlockTrain path uses one block-stack traversal per full output and serves over direct TCP across three public-network GPU hosts up to a 75.80B-parameter logical fp16 shape, outperforming a matched plain-autoregressive TCP pipeline baseline because it emits a full sequence per WAN pipeline traversal rather than one token per traversal.

Progress in deep learning is, at scale, more a matter of systems engineering than of modelling: the behaviour of a model in training (its throughput, its memory footprint, and the numerical fidelity of the result) is determined less by the architecture itself than by how that architecture is expressed on the hardware. To achieve absolute control over this hardware expression while abstracting away systems complexity to make modelling seamless and eliminating the need for repetitive orchestration logic, BluTrain was architected from first principles as a robust, lightweight, and architecture-general training framework in standard C++ and the core CUDA programming model. Every layer is implemented natively: a typed tensor module with reverse-mode autograd, a linear-algebra library, a caching allocator, a multi-mode distributed-execution module, and an MLIR-based deep-learning compiler. In formal evaluations training a 124M-parameter GPT-2 baseline in FP32 on an 8-GPU 6000 Ada system, BluTrain outperforms industry-standard baselines in both throughput (sustaining an average of 407K tokens/s versus PyTorch's 395K tokens/s) and memory efficiency (achieving up to a 22% footprint reduction), while strictly preserving numerical fidelity and converging to a marginally lower final validation loss. With every layer explicitly open to native tuning, the performance ceiling is the framework's own to raise.

Stereo-based 3D object detection still faces two critical safety challenges: real-time performance and open-set generalization. Existing stereo 3D methods typically achieve twice the accuracy of monocular methods but suffer from significantly lower inference speeds, making them unsuitable for real-time applications. Meanwhile, recent advances in open-world detection have introduced open-set and open-vocabulary algorithms in monocular 2D and 3D settings, yet stereo-based open-set detection remains largely unexplored. To bridge this gap, we propose DDStereo, a novel Dual-Decoder Stereo Transformer for real-time open-set 3D object detection. DDStereo features two lightweight decoder branches: one for open-set foreground 2D detection and the other for 3D attribute regression. These decoders share object-level queries to achieve unified target-level alignment. To enhance inference efficiency, we designed a compact disparity feature extractor and a streamlined decoder architecture. Experiments on public stereo 3D benchmarks demonstrate that DDStereo achieves state-of-the-art accuracy under both closed-set and open-set protocols. Notably, our method surpasses existing stereo 3D detectors in inference speed and, for the first time, achieves real-time performance comparable to monocular approaches.

Omnidirectional stereo images provide full-surround perception but violate the geometric assumptions of classical disparity estimation: in spherical or fisheye views, epipolar correspondences follow curved great-circle paths, producing two-dimensional displacements that cannot be treated as single-axis disparity before geometric rectification. In this work, we adopt a standard spherical-to-equirectangular (ERP) projection as a preprocessing step, which straightens epipolar curves and restores a one-dimensional disparity structure - horizontal for left-right rigs and vertical for top-bottom rigs. Building on our previously introduced RAFT + Epipolar-Aligned Channel Selection (EACS) framework, originally developed for rectilinear and ERP stereo, we examine whether the same modular pipeline remains accurate when the input originates from spherical stereo imagery. After ERP projection, dense optical flow from RAFT is reduced to disparity by retaining only the baseline-aligned flow component. Experiments on synthetic fisheye stereo datasets show that this spherical-to-ERP-to-RAFT+EACS pipeline produces accurate, smooth, and structurally consistent disparity maps at real-time speed. These findings confirm that established ERP preprocessing can be effectively combined with our earlier RAFT+EACS method to enable practical, interpretable, and efficient disparity estimation from spherical stereo, providing a straightforward pathway for extending conventional stereo pipelines to 360 imaging.

Fourier Neural Operators (FNO) learn solution operators of partial differential equations by parameterizing global convolutions in the complex Fourier domain. For real-valued PDE solutions, the complex FFT carries representational redundancy through conjugate symmetry. We introduce the Hartley Neural Operator (HNO), the exact real-valued mirror of FNO: it replaces the FFT with the purely real Discrete Hartley Transform and learns a single real multiplier per retained spectral mode, with no complex arithmetic. Because the real Hartley spectrum is not halved by conjugate symmetry, HNO retains twice as many frequency corners as FNO but one real weight where FNO carries a complex pair, so the two operators are iso-parametric at equal width and differ only in spectral basis. Our central thesis is that the best basis is a property of the operator. Self-adjoint elliptic operators (Poisson, biharmonic) have real, symmetric Green's functions that the real Hartley multiplier diagonalizes exactly, and HNO is favored there. Time-dependent operators carry phase, from oscillation in the wave equation to transport in advection, Burgers, and Navier-Stokes, which a real diagonal multiplier cannot represent, so FNO is favored there, and increasingly so with the operator's phase content, leaving the phaseless heat equation as the borderline case. Training both operators identically and benchmarking across PDE classes, initial-condition families, and boundary conditions, we find an elliptic-versus-time-dependent split that is monotone in operator phase content and matches the Green's-function theory we develop. Rather than a universal winner, our findings give a predictive rule: match the spectral basis to the symmetry of the solution operator.