arXiv:2602.00841v4 Announce Type: replace Abstract: Visual Place Recognition (VPR) demands representations robust to drastic environmental and viewpoint shifts. Existing aggregation paradigms either depend on extensive supervised training or rely on first-order pooling, often struggling to preserve structural correlations under extreme shifts or incurring high adaptation costs. In this work, we propose Riemannian Invariant Aggregation (RIA), a unified geometric framework that explicitly models second-order scene structure on the Symmetric Positive Definite (SPD) manifold. By treating perturbations as tractable congruence transformations, RIA leverages geometry-aware Riemannian mappings to project covariance descriptors into a linearized Euclidean space, effectively preserving invariant structural components while suppressing noise. Extensive evaluations demonstrate that RIA achieves zero-shot performance comparable to supervised methods, and establishes state-of-the-art accuracy with simple fine-tuning, particularly in unstructured environments. The source code will be released.
Science Journals
arXiv:2605.15298v1 Announce Type: new Abstract: Vision-language-action models have advanced rapidly, but robot trajectories alone provide limited coverage for learning broad physical understanding. PhysBrain 1.0 studies a complementary route: converting large-scale human egocentric video into structured physical commonsense supervision before robot adaptation. Our data engine extracts scene elements, spatial dynamics, action execution, and depth-aware relations, then turns them into question-answer supervision for training PhysBrain VLMs. The resulting physical priors are further transferred to VLA policies through a capability-preserving and language-sensitive adaptation design. Across multimodal QA benchmarks and embodied control benchmarks, including ERQA, PhysBench, SimplerEnv-WidowX, LIBERO, and RoboCasa, PhysBrain 1.0 achieves SOTA results and shows especially strong out-of-domain performance on SimplerEnv. These results suggest that scaling physical commonsense from human interaction video can provide an effective bridge from multimodal understanding to robot action.
arXiv:2605.15295v1 Announce Type: new Abstract: Machine learning (ML) algorithms are increasingly deployed in high-stakes decision-making domains such as loan approvals, hiring, and recidivism predictions. While existing fairness metrics (e.g., statistical parity, equal opportunity) effectively quantify outcome-oriented disparities, they offer limited insight into the procedure or explanation behind biased decisions. To address this gap, we propose Group-level Explanation Stability Disparity (GESD), a \textit{procedural-oriented} fairness metric that measures disparities in the stability, robustness, and sensitivity of model explanations across different subgroups in a protected category. %GESD is explainer-agnostic, model-agnostic, and extends the scope of fairness analyses to the level of explainability. We further integrate GESD into a multi-objective optimization framework that jointly optimizes for utility, outcome-based fairness, and explanation-based fairness called FEU (Fairness--Explainability--Utility). Empirical results on multiple benchmark datasets show that GESD effectively captures group-wise discrepancies in explanation quality, and that FEU improves both utility and fairness over state-of-the-art methods. By bridging outcome-based and explanation-based fairness, GESD offers a comprehensive tool for diagnosing and mitigating bias in predictive modeling. Our code and datasets are available on GitHub {\hyperlink{https://github.com/horlahsunbo/GESD}{https://github.com/horlahsunbo/GESD}}
arXiv:2605.15294v1 Announce Type: new Abstract: A DFA separates two disjoint languages $L_1$ and $L_2$ if it accepts every word in $L_1$ and rejects every word in $L_2$. Algorithms for active learning of small separating DFAs have many applications, e.g., for learning network invariants, learning contextual assumptions in compositional verification, learning state machines from large amounts of log data, and learning bug pattern descriptions. We propose a simple active learning algorithm, inspired by $L^{\#}$, that learns a minimal separating DFA for disjoint languages $L_1$ and $L_2$ if one exists. Experiments show that our algorithm significantly outperforms existing active learning algorithms on both randomly generated and industrial benchmarks.
arXiv:2605.15290v1 Announce Type: new Abstract: Hyperparameter transfer across model architectures dramatically reduces the amount of compute necessary for tuning large language models (LLMs). The maximal update parameterization ({\mu}P) ensures transfer through principled mathematical analysis but can be challenging to derive for new model architectures. Building on the spectral feature-learning view of Yang et al. (2023a), we make two advances. First, we promote spectral norm conditions on the weights from a heuristic to the definition of feature learning, and as a consequence arrive at the Complete-P depth and weight-decay scalings without recourse to lazy-learning. Second, we consider a modified spectral norm that preserves the valid scaling law of network weights when weight matrices are not full rank. This enables (to our knowledge, the first) derivation of {\mu}P scalings for grouped-query attention (GQA). We demonstrate the efficacy of our theoretical derivations by showing learning rate transfer across the GQA repetition hyperparameter as well as experiments regarding transfer over weight decay.
arXiv:2601.23068v2 Announce Type: replace Abstract: Computing the importance of features in supervised classification tasks is critical for model interpretability. Shapley values are a widely used approach for explaining model predictions, but require direct access to the underlying model, an assumption frequently violated in real-world deployments. We investigate whether meaningful feature attributions can be obtained in a zero-shot setting, using only the input data distribution and no evaluations of the target model. Because multiple models can produce identical predictions yet yield different Shapley decompositions, the mapping from data to attributions is not uniquely identifiable. We therefore target attributions that are "true to the data" rather than "true to the model", learning a posterior mean attribution under a meta-training prior. To this end, we introduce ExplainerPFN, a tabular foundation model built on TabPFN, pretrained on synthetic structural causal datasets supervised with exact or near-exact Shapley values, that predicts feature attributions for unseen tabular datasets without model access, gradients, or example explanations. Our contributions are fourfold: (1) we show that few-shot surrogate explainers achieve high SHAP fidelity with as few as two reference observations; (2) we propose ExplainerPFN, the first zero-shot method for estimating Shapley-value-style feature attributions without access to the underlying model or reference explanations, providing a principled attribution where no existing explainer can be applied; (3) we release an open-source implementation including the full training pipeline and synthetic data generator; and (4) through extensive experiments on real and synthetic datasets, we show that ExplainerPFN achieves performance competitive with few-shot surrogate explainers that rely on 2-10 SHAP examples.
arXiv:2601.21798v2 Announce Type: replace Abstract: Large Language Models(LLMs) have revolutionized text generation and multimodal perception,but their capabilities in 3D content generation remain underexplored. Existing methods compromise by producing either low-resolution meshes or coarse structural proxies, failing to capture finegrained geometry natively. In this paper, we propose CG-MLLM, a novel Multi-modal Large Language Model (MLLM) capable of 3D captioning and high-resolution 3D generation in a single framework. Leveraging the Mixture-ofTransformer architecture, CG-MLLM decouples disparate modeling needs, where the Token-level Autoregressive (TokenAR) Transformer handles token-level content, and the Block-level Autoregressive (BlockAR) Transformer handles blocklevel content. By integrating a pre-trained visionlanguage backbone with a specialized 3D VAE latent space, CG-MLLM facilitates long-context interactions between standard tokens and spatial blocks within a single integrated architecture. Experimental results show that CG-MLLM significantly outperforms existing MLLMs in generating high-fidelity 3D objects, effectively bringing high-resolution 3D content creation into the mainstream LLM paradigm. Beyond generation, we further observe that learning to produce 3D content transfers back to perception, strengthening the model's image-based 3D understanding.
arXiv:2605.15288v1 Announce Type: new Abstract: The Electron-Ion Collider (EIC) is a next-generation particle accelerator facility designed to probe the fundamental structure of matter such as the origins of nucleon mass, spin, and the dynamic behavior of quarks and gluons within nucleon and nucleus. As the electromagnetic calorimeter in the barrel region, the Barrel Imaging Calorimeter (BIC) is tasked with precise energy measurements of electrons and photons as well as efficient separation of these particles from background pions. The BIC integrates Pb/SciFi sampling layers and AstroPix silicon pixel sensors for three-dimensional shower imaging. The Korean group has actively contributed through silicon chip testing, module assembly, prototype development, beam test, readout system design, and detailed simulations. This presentation highlights the recent progress and plans for the R\&D of the Barrel Imaging Calorimeter in Korea.
arXiv:2605.15285v1 Announce Type: new Abstract: Derivative-Informed Operator Learning (DIOL), i.e. learning a (nonlinear) operator and its derivatives, is an open research frontier at the foundations of the influential field of Operator Learning (OL). In particular, Universal Approximation Theorems (UATs) of nonlinear operators and their derivatives are foundational open questions and delicate problems in nonlinear functional analysis. In this manuscript, we prove the first UATs of non-linear $k$-times differentiable operators between Banach spaces and their derivatives, uniformly on compact sets and in weighted Sobolev norms for general finite input measures, via OL architectures. Our results are the first complete generalizations of the corresponding influential classical results in [Hornik, 1991] to infinite-dimensional settings and OL. We discuss several open areas where DIOL and our UATs find applications: high-order accuracy in OL, fast constrained optimization in Banach spaces (e.g. optimal control of PDEs, inverse problems) and numerical methods for infinite-dimensional PDEs (e.g. HJB PDEs on Banach spaces from optimal control of PDEs, SPDEs, path-dependent systems, partially observed systems, mean-field control). We parameterize nonlinear operators via Encoder-Decoder Architectures, renowned classes in OL due to their generality, including classical architectures, such as DeepONets, Deep-H-ONets, PCA-Nets. Our results are based on four key features that allow us to prove UATs in full generality: (i) Approximation Properties of Banach spaces. (ii) $k$-times continuous differentiability in the sense of Bastiani (weaker than $k$-times continuous Fr\'echet differentiability). (iii) Natural compact-open topologies for UA; indeed, we show that UA in standard compact-open topologies induced by operator norms is violated even for Fr\'echet derivatives. (iv) Construction of novel weighted Sobolev spaces for the UA.
arXiv:2601.21702v3 Announce Type: replace Abstract: We consider Representation Misdirection (RM), a class of large language model (LLM) unlearning methods that achieve forgetting by redirecting the forget-representations, that is, latent representations of forget-samples, toward a target vector. Despite being important, the roles of the target vector used in RM, however, remain underexplored. Here, we approach and revisit RM through the lens of the Linear Representation Hypothesis. Specifically, if one can identify a one-dimensional representation corresponding to a high-level concept, the Linear Representation Hypothesis enables linear operations on this concept vector within the forget-representation space. Under this view, we hypothesize that, beyond forgetting, machine unlearning via RM elicits controllable emergent side behaviors and stronger side capabilities corresponding to the high-level concept. Our hypothesis is empirically validated across a wide range of tasks, including behavioral control (e.g., controlling unlearned models' truthfulness, sentiment, refusal, and language) and capability enhancement (e.g., improving unlearned models' in-context learning (ICL) capability). Our findings reveal that this phenomenon could be either a hidden risk if misused or a mechanism that can be harnessed for developing unlearned models that require stronger capabilities and controllable behaviors.
arXiv:2605.09869v2 Announce Type: replace Abstract: Zero-shot object navigation has advanced rapidly with open-vocabulary detectors, image--text models, and language-guided exploration. However, even after current methods detect a plausible target hypothesis, the agent may still oscillate between exploration and pursuit, or abandon the object near success. We identify this failure mode as an action consistency gap: semantic evidence is repeatedly reinterpreted at each step without persistent commitment across the episode. We introduce ConsistNav, a training-free zero-shot ObjectNav framework built around a semantic executive composed of three coordinated modules: Finite-State Executive Controller stages target pursuit through guarded semantic phases; Persistent Candidate Memory accumulates cross-frame target evidence into stable object hypotheses; and Stability-Aware Action Control suppresses rotational stagnation, ineffective pursuit, and unverified stopping. This design changes neither the detector nor the low-level planner; instead, it controls when semantic evidence should influence navigation and when it should be suppressed or revisited. We conduct extensive experiments on HM3D and MP3D, where ConsistNav achieves state-of-the-art results among compared zero-shot ObjectNav methods and improves SR by 11.4% and SPL by 7.9% over the controlled baseline on MP3D. Ablation studies and real-world deployment experiments further demonstrate the effectiveness and robustness of the proposed executive mechanism.
arXiv:2601.20761v2 Announce Type: replace Abstract: In this letter, we address the problem of developing quantum state tomography (QST) methods that remain valid at any time during a sequence of measurements. Specifically, the aim is to provide a rigorous quantification of the uncertainty associated with the current state estimate as data are acquired incrementally. To this end, the proposed framework augments existing QST techniques by associating current point estimates of the state with confidence sets that are guaranteed to contain the true quantum state with a user-defined probability. The methodology is grounded in recent statistical advances in anytime-valid confidence sequences. Numerical results confirm the theoretical coverage properties of the proposed anytime-valid QST.
arXiv:2601.20477v4 Announce Type: replace Abstract: We study the training dynamics of neural classifiers through the lens of binary hypothesis testing. We re-formalize classification as a collection of binary tests between class-conditional distributions induced by learned representations and show empirically that, along training trajectories, well-generalizing networks progressively approach Neyman-Pearson optimal decision rules, as measured by monotonic growth in the KL divergence retained by learned representations. We provide sufficient conditions for exact optimality, discuss its implications for training regularization, and define an informational plane, (so-called Evidence-Error plane) where convergence can be assessed methodically across network architecture.
arXiv:2605.15647v1 Announce Type: new Abstract: Edge machine learning presents a unique set of constraints not encountered in cloud-scale model deployment: strict memory budgets, limited compute, and non-negotiable accuracy thresholds must all be satisfied simultaneously. Existing compression and optimization techniques can trade one resource for another, but rarely improve both accuracy and model size at the same time. This paper presents the application of Perforated Backpropagation to keyword spotting on the Edge Impulse platform, an experiment that won the Best Model award at the Edge Impulse 2025 Hackathon in December 2025. By adding artificial Dendrite Nodes to a standard convolutional neural network trained on the Edge Impulse keyword spotting tutorial pipeline, we demonstrate that dendritic models outperform traditional architectures at every level of parameter count and at every accuracy threshold tested across 800 hyperparameter trials. The best dendritic model achieved a test accuracy of 0.933 with only 1,500 parameters, versus the baseline accuracy of 0.921 requiring approximately 4,000 parameters. These results suggest that Perforated Backpropagation is a powerful addition to the edge AI engineer's toolkit, offering simultaneous gains in both model quality and deployment efficiency.
arXiv:2601.19923v2 Announce Type: replace Abstract: As Large Language Models (LLMs) evolve into the core of Web-based autonomous agents and complex Web Information Systems, their ability to faithfully translate natural language into rigorous structured formats has become paramount, as this capability is critical for Web API invocation and data exchange. However, evaluating this structural fidelity in Web-native payloads remains a challenge: traditional text metrics fail to capture topological consistency in semi-structured Web data, while manual evaluation is prohibitively costly. To address this, we propose Structure-BiEval, a novel self-supervised framework for quantitative, annotation-free assessment tailored for Web data engineering. By leveraging deterministic Intermediate Representations, our framework effectively decouples structure from content, utilizing Content Semantic Accuracy and Normalized Tree Edit Distance as precise metrics. We empirically benchmark 15 state-of-the-art LLMs across dual Web structural topologies, namely Hierarchical Data (Web backend payloads) and Tabular Data (Web frontend presentation). The results reveal substantial variability in structural performance, including cases where mid-sized models unexpectedly outperform larger counterparts in Web data formatting. Furthermore, our findings show that deep recursive nesting poses a consistent challenge for Web agents across varying parameter scales.
arXiv:2605.15648v1 Announce Type: new Abstract: Differentially Private Stochastic Gradient Descent (DP-SGD) is widely used to protect training data in machine learning. Its privacy guarantee is commonly analyzed through a security game in which an adversary infers whether a target record is included in the training dataset from the mechanism output. The resulting privacy leakage is characterized by a privacy curve, which reports the false negative rate as a function of the false positive rate. We identify a mismatch between this formal analysis and common DP-SGD implementations. Existing analyses often model DP-SGD and its variants as the Subsampled Gaussian Mechanism (SGM), where Gaussian noise is added to the sum of clipped gradients computed from a Poisson-sampled batch. In practice, however, many implementations apply an additional normalization step: the noisy gradient sum is divided either by the expected batch size or by the sampled batch size. These mechanisms are therefore better formalized as the Expected-Averaged SGM (EASGM) or the Batch-Averaged SGM (ASGM), respectively. We re-analyze the privacy guarantees of DP-SGD under the EASGM and ASGM formulations. Our theoretical results show that these guarantees can be weaker than the standard SGM-based guarantee, implying that the true privacy leakage may exceed the reported guarantee in some regimes. We further audit four state-of-the-art DP-SGD implementations, including Meta's Opacus library, and observe empirical leakage beyond the SGM-based guarantees. Finally, we audit Opacus versions v0.9.0 to v1.5.4 and derive a corrected privacy guarantee for the latest implementation.
arXiv:2605.15284v1 Announce Type: new Abstract: We introduce Tadpole, a novel foundation model for three-dimensional partial differential equations (PDEs) that addresses key challenges in transferability, scalability to high dimensionality, and multi-functionality. Tadpole is pre-trained as an autoencoder on synthetic 3D PDE data generated by an efficient online data-generation framework. This enables large-scale, diverse training without storage or I/O overhead, demonstrated by scaling to an equivalent of hundreds of terabytes of training data. By autoencoding single-channel spatial crops, Tadpole learns rich and transferable representations across heterogeneous physical systems with varying numbers of state variables and spatial resolutions. Although pre-trained solely as an autoencoder, Tadpole can be efficiently applied for multiple downstream tasks beyond reconstruction, including dynamics learning and generative modeling. For dynamics learning, we propose a novel parameter-efficient fine-tuning strategy that integrates low-rank adaptation, latent-space transformations, and reintroduced skip connections, achieving accurate temporal modeling with a minimal number of trainable parameters. Tadpole demonstrates strong fine-tuning performance across various downstream tasks, highlighting its versatility and effectiveness as a foundation model for 3D PDE learning. Source code and pre-trained weights of Tadpole are available at https://github.com/tum-pbs/tadpole
arXiv:2604.17824v2 Announce Type: replace-cross Abstract: Continuous quantum phase transitions are characterized by an order parameter and correlation functions that are often challenging to access experimentally or in direct numerical simulations. The energy of an added impurity can on the other hand be probed by established polaron spectroscopy, or numerically with Monte Carlo methods. We provide evidence from ground-state quantum Monte Carlo calculations that the energy of a mobile impurity interacting weakly with a surrounding lattice Bose gas provides access to the critical behavior of the Mott insulator-superfluid phase transition. Finite-size scaling of the energy reveals that its value is scale invariant at the critical point of the quantum phase transition, and we extract a scaling exponent that is currently unexplained by theory. For a small lattice we further observe a flattening of the impurity-boson density-density correlations at the critical point, which hints at a divergence of a corresponding length scale in the thermodynamic limit. Our results suggest that impurity spectroscopy represents a useful way to probe the critical properties of quantum phase transitions in general.
arXiv:2605.15108v2 Announce Type: replace-cross Abstract: Off-policy evaluation (OPE) estimates the value of a target treatment policy (e.g., a recommender system) using data collected by a different logging policy. It enables high-stakes experimentation without live deployment, yet in practice accuracy depends heavily on the logging policy used to collect data for computing the estimate. We study how to design logging policies that minimize OPE error for given target policies. We characterize a fundamental reward-coverage tradeoff: concentrating probability mass on high-reward actions reduces variance but risks missing signal on actions the target policy may take. We propose a unifying framework for logging policy design and derive optimal policies in canonical informational regimes where the target policy and reward distribution are (i) known, (ii) unknown, and (iii) partially known through priors or noisy estimates at logging time. Our results provide actionable guidance for firms choosing among multiple candidate recommendation systems. We demonstrate the importance of treatment selection when gathering data for OPE, and describe theoretically optimal approaches when this is a firm's primary objective. We also distill practical design principles for selecting logging policies when operational constraints prevent implementing the theoretical optimum.
arXiv:2601.18349v2 Announce Type: replace Abstract: The Orbit Problem asks whether the orbit of a point under a matrix reaches a given target set. When the target is a single point, the problem was shown to be decidable in polynomial time by Kannan and Lipton. This decidability result was later extended by Chonev et al. to targets of dimension 3 (in arbitrary ambient dimension), but decidability remains open for subspaces of dimension 4. At the other extreme, the special case of the Orbit Problem in which the target set is a hyperplane of codimension 1 is equivalent to the Skolem Problem for linear recurrence sequences, whose decidability has been open for many decades. In this paper, we show that the Orbit Problem is decidable if the target subspace has dimension logarithmic in the dimension of the orbit. Over rationals, we moreover obtain a complexity bound NP^RP in this case. On the other hand, we show that the version of the Orbit Problem where the dimension of the target subspace is linear in the dimension of the orbit is as hard as the Skolem Problem.
arXiv:2605.15282v1 Announce Type: new Abstract: Literary translation requires balancing target-language fluency with faithfulness to the source. Recent large language models (LLMs) often produce fluent translations, but it remains unclear whether fluency corresponds to semantic preservation in literary text. We examine this relationship using 130,486 translated paragraphs from 106 novels in 16 source languages, including human, Google Translate, and TranslateGemma translations. Fluency is measured as original-likeness with a translationese classifier trained on paragraph part-of-speech n-grams, and faithfulness with the automatic translation evaluation metric COMET-KIWI. We control for paragraph length and find a consistent negative correlation between fluency and faithfulness. The pattern appears for both human and Google Translate, but is weaker and often non-significant for TranslateGemma. These results show that segment length matters for automatic evaluation and suggest a tradeoff between fluency and faithfulness in literary translation.
arXiv:2601.17198v3 Announce Type: replace Abstract: This paper proposes sufficient, yet more general conditions for applying FastTwoSum as an error-free transformation (EFT) under all faithful rounding modes. Additionally, it also identifies guarantees tailored to round-to-odd for establishing FastTwoSum as an EFT. This paper also describes a floating-point splitting tailored for round-to-odd that is an EFT where the distribution of bits is configurable (i.e., ExtractScalar for round-to-odd). Our sufficient conditions are more general than those previously known in the literature (i.e., it applies to a wider operand domain).
arXiv:2605.15281v1 Announce Type: new Abstract: Modern web test suites rot. A UI refactor breaks locators, a timing change causes race conditions, and within weeks developers abandon the suite entirely. This paper presents an AI-driven autonomous testing framework that addresses these failure modes through five integrated strategies - navigation reliability, context-aware selector generation, post-generation validation, smart wait injection, and failure learning - implemented over a containerised worker architecture that decouples orchestration from long-running browser execution. Evaluated across four production applications and 176 scenarios, the framework improves script generation success from 55% to 93%, achieves an 8x reduction in navigation failures, eliminates 80% of timing-related race conditions, and reduces test creation time by 75% compared to manual Selenium authoring. The framework extends naturally to security validation: testers describe attack scenarios in plain English - "try accessing another user's invoice" - which the agent converts to OWASP Top 10-aligned browser probes, detecting 85% of authentication bypass vulnerabilities and 95% of input validation flaws with false positive rates below 12%. Natural-language-driven security testing of this kind represents, to our knowledge, a novel contribution to the field.
arXiv:2605.15279v1 Announce Type: new Abstract: Piezoelectric resonators (PRs) have been seen as a competitive alternative to magnetic components. In PR-based converters, the motional current (in the LC series branch of the equivalent circuit) is vital for control proposes but cannot be measured directly. The difficulties to detect the zero-crossing points or to measure the amplitude of the motional current has been one of the most dominating obstacles that complicates the control strategies and limits the frequency range of the PR-based converters. This work discusses a ring-dot shaped piezoelectric transformer (PT) based motional current sensing method that provides current information with low-delay, low-loss and intrinsic isolation. It is physically proven that the proposed method is robust with various non-ideal factors of the piezoceramic and circuit implementation. Based on this, an event-driven control strategy is introduced, consisting of only a finite state machine, a PI loop, a low-speed ADC and several comparators. Experiments on a step-down PR-based converter verify that the proposed approach realize ZVS for all transitions within a switching cycle with reduced hardware and software resources, enhances stability and is capable of self-startup.
arXiv:2601.15637v2 Announce Type: replace Abstract: Elastoinertial turbulence (EIT) is a self-sustaining chaotic state resulting from the interplay between inertia and elasticity in the flow of dilute polymeric solutions, and its emergence is believed to limit the achievable drag reduction in turbulence flow using polymer additives. In the present study, we introduce a viscoelastic variant of spectral proper orthogonal decomposition (VESPOD) that decomposes velocity and polymeric stress fields of EIT together into well-defined orthogonal oscillating modes such that the decomposition is optimal in the terms of the total mechanical energy of the flow. Using this technique, we investigate the dominant coherently evolving structures underlying the dynamics of EIT in axisymmetric pipe flow. By analyzing distinct peaks in the leading eigenvalue of the VESPOD eigenvalue spectrum, we find that the dynamics of EIT in pipe flow is dominated by three distinct families of traveling waves, where the higher wavenumber structures of each family are simple harmonics of their respective fundamental waves. The radial velocity fields of the traveling waves are characterized by the formation of large-scale structures spanning the pipe radial direction. However, the polymeric stress fields corresponding to them are characterized by the formation of thin inclined sheets of high stress fluctuations at the critical layers of the respective waves, i.e.~ the locations where the wave speed of the VESPOD mode matches the mean streamwise velocity. Additionally, these sheets exhibit nested structures, where the polymeric sheets of faster waves are confined by those of the immediately slower waves.