arXiv:2603.25031v2 Announce Type: replace
Abstract: In psychological support and emotional companionship scenarios, the core limitation of large language models (LLMs) lies not merely in response quality, but in their reliance on local next-token prediction, which prevents them from maintaining the temporal continuity, stage awareness, and user consent boundaries required for multi-turn intervention. This stateless characteristic makes systems prone to premature advancement, stage misalignment, and boundary violations in continuous dialogue. To address this problem, we argue that the key challenge in process-oriented emotional support is not simply generating natural language, but constructing a sustainably updatable external situational structure for the model. We therefore propose LEKIA 2.0, a situated LLM architecture that separates the cognitive layer from the executive layer, thereby decoupling situational modeling from intervention execution. This design enables the system to maintain stable representations of the user's situation and consent boundaries throughout ongoing interaction. To evaluate this process-control capability, we further introduce a Static-to-Dynamic online evaluation protocol for multi-turn interaction. LEKIA achieved an average absolute improvement of approximately 31% over prompt-only baselines in deep intervention loop completion. The results suggest that an external situational structure is a key enabling condition for building stable, controllable, and situated emotional support systems.
Science Journals
arXiv:2604.04977v2 Announce Type: replace
Abstract: Software supply chain security compromises often stem from cascaded interactions of vulnerabilities, for example, between multiple vulnerable components. Yet, Software Bill of Materials (SBOM)-based pipelines for security analysis typically treat scanner findings as independent per-CVE (Common Vulnerabilities and Exposures) records. We propose a new research direction based on learning multi-vulnerability attack chains through a novel SBOM-driven graph-learning approach. This treats SBOM structure and scanner outputs as a dependency-constrained evidence graph rather than a flat list of vulnerabilities. We represent vulnerability-enriched CycloneDX SBOMs as heterogeneous graphs whose nodes capture software components and known vulnerabilities (i.e, CVEs), connected by typed relations, such as dependency and vulnerability links. We train a Heterogeneous Graph Attention Network (HGAT) to predict whether a component is associated with at least one known vulnerability as a feasibility check for learning over this structure. Additionally, we frame the discovery of cascading vulnerabilities as CVE-pair link prediction using a lightweight Multi-Layer Perceptron (MLP) neural network trained on documented multi-vulnerability chains. Validated on 200 real-world SBOMs from the Wild SBOMs public dataset, the HGAT component classifier achieves 91.03% Accuracy and 74.02% F1-score, while the cascade predictor model (MLP) achieves a Receiver Operating Characteristic - Area Under Curve (ROC-AUC) of 0.93 on a seed set of 35 documented attack chains.
arXiv:2607.11802v2 Announce Type: replace
Abstract: Gas-focused liquid microjets -- the flow-focusing sample delivery on which serial femtosecond crystallography depends -- reach speeds several times the pressure-driven (Bernoulli) bound, unexplained by continuum, local-equilibrium models that do not resolve the rarefied, hypersonic expansion of the focusing gas. We resolve that expansion with a deterministic kinetic (Shakhov--BGK) solver and couple it to the slender liquid jet. The jet is \emph{shear-driven}, not pressure-driven: the tangential stress of the hypersonic gas supplies nearly all of the axial momentum, accounting for the anomalous speed. The gas does not become ballistic behind the near field -- its stress decays as a power law and it stays coupled -- and its constitutive regime is set by a single rarefaction parameter $\delta=D/\ell_0$, the orifice diameter over the source mean free path, through the thermodynamic Deborah number $De_\theta\simeq K\!n\,M$ (Knudsen times Mach), whose $De_\theta=1$ surface maps where the Newtonian-gas closure fails: the small-$\delta$ vacuum corner where crystallography jets operate. The kinetically computed surface stress is the input for the fully non-Newtonian (viscoelastic-liquid) sequel.
arXiv:2506.12529v2 Announce Type: replace
Abstract: Preference-based Reinforcement Learning (PbRL) entails a variety of approaches for aligning models with human intent to alleviate the burden of reward engineering. However, most previous PbRL work has not investigated the robustness to labeler errors, inevitable with labelers who are non-experts or operate under time constraints. We introduce Similarity as Reward Alignment (SARA), a simple contrastive framework that is both resilient to noisy labels and adaptable to diverse feedback formats. SARA learns a latent representation of preferred samples and computes rewards as similarities to the learned latent. On preference data with varying realistic noise rates, we demonstrate competitive and more stable performance on continuous control offline RL benchmarks, with statistically significant improvements over baselines (Wilcoxon signed-rank, p < 0.01). We also compute correlation to the environment rewards as a proxy for measuring alignment to the underlying preference criteria. We show that the SARA computed rewards display higher correlation across noise rates compared to baselines.
arXiv:2604.08191v2 Announce Type: replace
Abstract: We have developed a vacuum-ultraviolet spectropolarimeter for an electron beam ion trap (EBIT) to measure the linear polarization of emission lines from multiply charged ions around the Lyman-$\alpha$ wavelength. The main components for polarimetry are a rotatable MgF$_2$ waveplate and a SiO$_2$/MgF$_2$ multilayer-coated fused silica plate that functions as a reflective polarizer. A grazing-incidence grating is mounted between them to provide wavelength dispersion. The polarization is determined from the intensity modulation of the spectral line as the waveplate is rotated. The performance of the spectropolarimeter was demonstrated by measuring the polarization of the $2s$--$2p_{3/2}$ transition in Li-like N$^{4+}$ (124~nm) excited by a 1000~eV electron beam in an EBIT. Clear modulation of the line intensity was observed as a function of the waveplate rotation angle. From the measured modulation amplitude, the degree of linear polarization was determined to be $P=-(0.178^{+0.014}_{-0.005})$, with the negative sign indicating that the emission is polarized predominantly perpendicular to the electron beam. This result demonstrates the capability of the present spectropolarimeter to determine polarizations with an absolute uncertainty $\Delta P$ on the order of $0.01$. This instrument provides a useful tool for benchmarking magnetic-sublevel-resolved collision theories through polarization measurements of multiply charged ions excited by a unidirectional electron beam.
arXiv:2604.27088v2 Announce Type: replace
Abstract: Fluid equations are nonlinear, dissipative, and non-Hamiltonian, which makes their relation to Schr\"odinger evolution and quantum algorithms nontrivial. We derive an exact Eulerian Cole-Hopf-type reformulation of isothermal compressible Navier-Stokes (NS) flow in Schr\"odinger-type amplitude variables. To our knowledge, this gives the first exact Cole-Hopf-type Schr\"odinger-variable reformulation of compressible NS flow. In two dimensions, a Helmholtz decomposition separates the velocity into compressive and vortical potentials, whose logarithmic transforms yield two scalar imaginary-time Schr\"odinger-type equations with nonlinear self-consistent potentials. We show that the mixed density-compressive amplitude $\Psi_\alpha=\rho^\alpha\Theta^{1-2\alpha}$, where $\rho$ is the density, $\Theta$ is the compressive amplitude, and $\alpha\neq 0,\,1/2$, satisfies a nonlinear Schr\"odinger-type equation with a vector-potential-coupled Laplacian. The transformed system is exactly equivalent to compressible NS and is nonlocal only through Helmholtz and Poisson projections. In three dimensions, the density-carrying equation retains the same vector-potential-coupled structure, while the solenoidal sector admits a compressible analogue of Ohkitani's incompressible NS Cole-Hopf formulation. Unlike unitary hydrodynamic Schr\"odinger-flow representations, the present equations are imaginary-time heat or drift-diffusion equations with self-consistent potentials, but they remain an exact change of variables for compressible NS. A two-dimensional Kelvin-Helmholtz unstable shear-layer calculation verifies the transformed equations against a direct compressible NS simulation. The formulation exposes operator structures that may be useful for reduced flow descriptions, quantum algorithms for operator evolution, and quantum partial differential equation solvers.
arXiv:2604.15650v3 Announce Type: replace
Abstract: Scaling industrial recommender models has followed two parallel paradigms: \textbf{sample information scaling} -- enriching the information content of each training sample through deeper and longer behavior sequences -- and \textbf{model capacity scaling} -- unifying sequence modeling and feature interaction within a single Transformer backbone. However, these two paradigms still face two structural limitations. Firstly, sample information scaling methods encode only a subset of each historical interaction into the sequence token, leaving the majority of the original sample context unexploited and precluding the modeling of sample-level, time-varying features. Secondly, model capacity scaling methods are inherently constrained by the structural heterogeneity between sequential and non-sequential features, preventing the model from fully realizing its representational capacity.
To address these issues, we propose \textbf{SIF} (\emph{Sample Is Feature}), which encodes each historical Raw Sample directly into the sequence token -- maximally preserving sample information while simultaneously resolving the heterogeneity between sequential and non-sequential features. SIF consists of two key components. The \textbf{Sample Tokenizer} quantizes each historical Raw Sample into a Token Sample via hierarchical group-adaptive quantization (HGAQ), enabling full sample-level context to be incorporated into the sequence efficiently. The \textbf{SIF-Mixer} then performs deep feature interaction over the homogeneous sample representations via token-level and sample-level mixing, fully unleashing the model's representational capacity. Extensive experiments on a large-scale industrial dataset validate SIF's effectiveness, and we have successfully deployed SIF on an industrial food delivery platform.
arXiv:2604.17612v3 Announce Type: replace
Abstract: Multi-agent systems built on large language models (LLMs) are difficult to reason about. Coordination errors such as deadlocks or type-mismatched messages are often hard to detect through testing. We introduce a domain-specific language for specifying agent coordination based on message sequence charts (MSCs). The language separates message-passing structure from LLM calls, tool calls, and human control points, whose outcomes remain unpredictable. We define the syntax and semantics of the language and present a syntax-directed projection that generates deadlock-free local agent programs from global coordination specifications. We illustrate the approach with a diagnosis consensus protocol and show how coordination properties can be established independently of LLM nondeterminism. We also describe a runtime planning extension in which an LLM dynamically generates a coordination workflow for which the same structural guarantees apply. An open-source Python implementation of our framework is available as ZipperGen.
arXiv:2607.14399v1 Announce Type: new
Abstract: Evaluations of language-model honesty read the model's verdicts as evidence about the model. We test the instrument instead. We built a text-adventure world where the game engine, not any model, knows whether the quest can be completed. A language model plays under a budget and must eventually declare its quest complete, unreachable, or not yet decidable; the engine scores every verdict. Decision rules were recorded before results were read, and run artifacts bind the revisions they executed; the strength of preregistration varies by series and is disclosed. With the player held fixed, instrument choices substantially changed measured behavior. On four byte-identical anchors, expanding a two-verdict grammar to three verdicts moved strong claims from 38/40 to 7/40, while the new incomplete verdict took 28/40 outcomes; across series 2, 93/158 valid games ended incomplete. One sentence disclosing the success criterion took matched-instance false verdicts from 18/59 to 0/58, through fewer decision points and cleaner decisions. Repeated runs of one fixed configuration produced non-stable verdict distributions on 3 of 4 instances: single runs report samples as dispositions. A formally preregistered narrative-register gradient was falsified; two post-hoc, hypothesis-generating patterns remain: register presence roughly doubled strong claims, and budget rendering moved verdicts more than register content (.383 meter vs .150 lantern). The narrator compressed abundant budgets toward scarcity landmarks, yet the registered mediation test returned a null. We propose a four-check integrity protocol for eval instruments.
arXiv:2607.14547v1 Announce Type: new
Abstract: Active visual agents solve fine-grained image tasks by interleaving reasoning with image-grounding actions across multiple turns. However, deployment-time rollout budgets are rarely fixed: some requests permit long rollouts, while others require the agent to act under a tight turn limit. Existing methods train the policy as if the rollout budget were hidden, so when the available budget is smaller than the trajectory the agent prefers, the interaction is often truncated before any valid answer is produced; we term this failure \emph{catastrophic truncation}. To overcome this challenge, we present AdaTurn, a budget-aware framework that conditions the agent on the allowed number of turns and explicitly trains the boundary behavior induced by the budget. Our key component, Forced-Answer DAPO (FA-DAPO), converts the over-budget event from a masked or penalized failure into a trainable final-decision step, teaching the model to synthesize partial evidence when further tool use is no longer possible. We further randomize rollout budgets during both training and inference and introduce a load-balanced scheduler that makes such operations practical. AdaTurn substantially improves low-budget accuracy, for example raising VisualProbe-Medium from 36.7% to 47.6% at four turns, while preserving strong scaling at larger budgets and transferring effectively to multiple backbones and general multimodal benchmarks.
arXiv:2607.13220v2 Announce Type: replace
Abstract: Most AI-for-science systems focus on scaling a single reasoning process by using better models, larger context windows, long-horizon agentic execution, or digital co-scientists working with one principal user. However, challenging scientific problems are rarely solved by one reasoner alone. They are solved by teams whose members carry different priors, experimental background, tacit knowledge, and domain-trained intuitions. The open problem is therefore not only how to scale models, but how to develop "networked intelligence", scaling the connections between humans and AI systems so that a result or hypothesis produced in one context reaches another person, agent, instrument or robot that can act on it. We introduce Mycelium, an active shared workspace that automatically connects researchers and AI agents. As human users and agents work, the system captures important observations and hypotheses, tracks how they relate to the team's evolving knowledge model, and routes them to the person or agent whose next decision they can inform. We evaluate Mycelium through a real-world scientific discovery use case: a biological multi-omics campaign where shared context turned a local analytical finding into a cross-expert mechanistic constraint and ultimately into an experimental design. Finally, we describe networked intelligence as sparse conditional computation over distributed scientific contexts. This framework establishes when a scaled standalone agent is sufficient, and when isolated data and specialized expertise make a networked approach essential.
arXiv:2607.14503v1 Announce Type: new
Abstract: We prove fundamental space lower bounds for exact random sampling using an entropy source of i.i.d. uniform bits. A classic result from information theory shows that generating $n$ discrete random variables $X_1, \dots, X_n$ requires at least $H(X_1, \dots, X_n)$ input random bits on average, where $H$ is the Shannon entropy function. How much space must a random sampling algorithm use in order to approach this information-theoretically optimal entropy bound?
We prove that any random sampling algorithm that is exact for arbitrary discrete target distributions and consumes at most $H(X_1,\ldots,X_n)+\varepsilon n+o(n)$ input bits in expectation for every output process must use $\Omega(\log(1/\varepsilon))$ bits of space. In fact, i.i.d. sampling from the single distribution $\mathrm{Bernoulli}(1/3)$ already forces at least $(1/{5.116201}-o(1))\log(1/\varepsilon)$ bits of space. If the sampler handles a family of infinitely many Bernoulli distributions, we show a sharper bound of at least $\log(1/\varepsilon)$ bits of space. We also prove lower bounds for general i.i.d. sampling: for almost every distribution on $k$ outcomes, the space is at least $(1/(k+1)-o(1))\log(1/\varepsilon)$ bits.
The proof technique is based on a graph-theoretic analysis of the amount of information that any algorithm can store in its state. Finite state spaces force short cycles around the state-transition graph, and the loss around such cycles reduces to Diophantine lower bounds on fractional parts of integer combinations of log-probabilities. To the best of our knowledge, these results comprise the first known space lower bounds for entropy-efficient random sampling.
arXiv:2607.14318v1 Announce Type: new
Abstract: We introduce COAT (Counterfactual Optimal Action Tree), a framework for learning interpretable prescriptive policies from observational data. COAT combines counterfactual outcome estimation with large-scale mixed-integer optimization, using column generation to translate causal predictions into feasible, transparent decisions under business and regulatory constraints. We apply COAT to airline ancillary pricing, a setting characterized by complex business rules and limited experimental flexibility. In a 17-week field pilot with a major global airline, COAT increased upsell revenue per booking by 6.9%, with the airline projecting \$50-\$150 million in incremental annual premium seat revenue across eligible domestic markets. The success of the pilot led to scaled adoption and informed broader AI-driven decision initiatives within the organization.
arXiv:2607.14526v1 Announce Type: new
Abstract: We propose a Bayesian co-optimization framework for robust integrated photonic lattice-filter demultiplexers, jointly optimizing device placement and design parameters under fabrication and thermal variations. Results show 75% better spectral matching and 45% lower calibration power.
arXiv:2607.14767v1 Announce Type: new
Abstract: Photonic lanterns efficiently map input spatial modes to single-mode outputs for applications like high angular resolution imaging and nulling interferometry. However, manufacturing limits prevent full control over the device's mode transfer matrix at the design stage, making empirical characterisation essential. In this work we further analyse a dataset of direct measurements of a photonic lantern's principal modes using digital off-axis holography over a 73 nm range near 1550 nm. By analysing the electric field directly, we find that the principal modes are significantly more orthogonal than random vectors in a space of the same size, as expected for near-adiabatic devices. We propose metrics for quantifying this effect, noting that mode converters with orthogonal principal modes provide better conditioned inverse solvers. We also simulate additional measurements that characterisation systems could take, where the orthogonality would be leveraged to determine the relative phase between principal modes.
arXiv:2607.14855v1 Announce Type: new
Abstract: We present a machine learning approach for developing subgrid-scale (SGS) parametrizations in coarse simulations of partial differential equations. We utilize structure-preserving neural networks and entropy variables to learn subgrid fluxes in coarse simulations of the Burgers' equation. In particular, we employ a decoupled neural network architecture explicitly separating the subgrid corrections into two distinct components: a conservative Flux Potential network and an Eddy Viscosity network. We demonstrate that this reduced-order framework maintains high physical fidelity, accurately reproducing the energy spectrum, spatial and temporal correlation functions, and dynamical characteristics of the full-scale system. Furthermore, we show that our approach is robust and applicable to parameters outside the training regime.
arXiv:2607.14714v1 Announce Type: cross
Abstract: We investigate the shape dynamics and migration of weakly deflated active vesicles driven by processes acting either directly in the membrane or transmitted by the cytoskeleton. For a force-free vesicle, local membrane incompressibility suppresses rigid-body translation, so that migration arises from time-dependent shape deformations. Assuming small excess area enables a systematic analysis of the coupled deformation and migration dynamics in free space, i.e. in the absence of substrate adhesion or confinement. Depending on the strength and frequency of the activity, the vesicle exhibits several dynamical regimes, including synchronized oscillations, quasiperiodic shape changes, transitions between non-propelling and propelling states, and intermittent motion.
arXiv:2601.19816v2 Announce Type: replace-cross
Abstract: Broadband detection of a weak oscillatory field with unknown carrier frequency underlies magnetometry, axion searches and gravitational-wave sensing. We show that the Grover-like integration-time lower bound for this task is a geometric corollary of an upper bound on the integrated quantum Fisher information and present an all-analog protocol with near-optimal scaling.
arXiv:2604.07520v2 Announce Type: replace-cross
Abstract: These lecture notes provide a comprehensive framework for performing global statistical fits in high-energy physics using modern Machine Learning (ML) surrogates. We begin by reviewing the statistical foundations of model building, including the likelihood function, Wilks' theorem, and profile likelihoods. Recognizing that the computational cost of evaluating model predictions often renders traditional minimization prohibitive, we introduce Boosted Decision Trees to approximate the log-likelihood function. The notes detail a robust ML workflow including efficient generation of training data with active learning and Gaussian processes, hyperparameter optimization, model compilation for speed-up, and interpretability through SHAP values to decode the influence of model parameters and interactions between parameters. We further discuss posterior distribution sampling using Markov Chain Monte Carlo (MCMC). These techniques are finally applied to the $B^\pm \to K^\pm \nu \bar{\nu}$ anomaly at Belle II, demonstrating how a two-stage ML model can efficiently explore the parameter space of Axion-Like Particles (ALPs) while satisfying stringent experimental constraints on decay lengths and flavor-violating couplings.
arXiv:2607.14498v1 Announce Type: new
Abstract: We show, as a proof of concept, that least-squares very weak formulations of elliptic problems can be effectively discretized by neural networks possessing low regularity, provided the test functions are drawn from appropriately smooth spaces. Apart from the immediate computational benefit of avoiding automatic differentiation, this approach, evaluated across various neural network spaces, demonstrates good performance even in challenging contexts, such as singular solutions and high dimensional settings. Particular attention is paid to trial functions based on step activations and one bit quantized linear functions, which are amenable to efficient hardware-oriented implementations.
arXiv:2607.14598v1 Announce Type: new
Abstract: Image registration is essential in applications such as electronic image stabilization. Scale-Invariant Feature Transform (SIFT), a widely used local keypoint detector and descriptor, typically provides accurate registration; however, it often fails in scenes with strong linear structures (e.g., shutters), where local features become ambiguous. We propose Hough-SIFT, a robust registration method that performs SIFT descriptor matching in Hough space. In this domain, linear structures form distinctive peaks that restore descriptor discriminability. Experiments demonstrate that Hough-SIFT is robust in linear scenes where SIFT frequently fails, while maintaining accuracy comparable to SIFT in normal scenes.
arXiv:2607.15077v1 Announce Type: new
Abstract: Many engineering problems involve phenomena whose governing equations are poorly characterized or only partially known. Surrogate modeling techniques such as neural networks can capture the behavior of these systems, but they typically demand large training datasets that are difficult to obtain in engineering contexts and yield models with limited physical interpretability. The Sparse Identification of Nonlinear Dynamics (SINDy) method addresses both limitations by performing sparse regression over libraries of candidate nonlinear terms, recovering interpretable governing equations from comparatively small datasets. Although SINDy has been demonstrated extensively on canonical benchmark systems, its application to practical engineering problems is less widely documented. This tutorial introduces the SINDy method and progressively builds toward its main extensions, from noise-robust weak-form and ensembling-based variants to constrained and parametrizable formulations. The paper and the accompanying tutorial (available at https://github.com/paullililili/SINDy4Engineers) is organized in three parts: the first introduces the standard SINDy algorithm and progressively extends it, inviting readers without prior knowledge to follow each step and adapt the methods to their own problems; the remaining two parts present detailed case studies on (1) the system identification of an unmanned aerial vehicle and (2) a chaotic thermosyphon heat exchanger. Through these examples, we aim to demonstrate that SINDy is simple to implement yet flexible enough to serve as a valuable identification tool for advanced engineering applications.
arXiv:2606.13467v2 Announce Type: replace
Abstract: We introduce a new product on the ambient space $F_q^n$ as a generalization of Euclidean, Hermitian and $\delta$ products. We give some general properties of the dual codes, relation with Euclidean duals, definition and characterization of self orthogonal, self dual, dual containing and LCD codes along with certain existence conditions. Also, we calculate the dual codes of some classes of codes like repetition, binary and $\lambda$-constacyclic codes with respect to this product. Further, we extend and analyse this notion of the product for codes over semisimple rings.
arXiv:2605.07995v2 Announce Type: replace-cross
Abstract: The [$^{12}$C II] emission at 158 $\mu$m is a key cooling line of the interstellar medium and traces gas kinematics in spectrally resolved observations. Its spectral profile is often modified by optical depth effects. The intrinsic line shape can be reconstructed by comparison with emission from the less abundant $^{13}$C isotope. Due to the additional neutron spin, [$^{13}$C II] emission splits into three hyperfine structure (hfs) transitions. Laboratory measurements have provided the centroid frequency and the strongest component ($F=2-1$); the two weaker components ($F=1-0$ and $F=1-1$) have been inferred only from quantum-mechanical calculations. The magnetic-dipole hfs constants, from which the transition frequencies follow, have not been measured experimentally. The high spectral resolution of observations with the upgraded German Receiver for Astronomy at Terahertz Frequencies (upGREAT) on board SOFIA enabled simultaneous detection of all three hfs transitions. From these astronomical data we determine, for the first time, the magnetic-dipole hfs constants $A_{1/2}^{\rm hf} = 810.71(11)$ MHz and $A_{3/2}^{\rm hf} = 162.18(5)$ MHz of the [$^{13}$C II] $2s^2\,2p\,{}^2P^\circ$ ground term. Combined with the laboratory centroid frequency, this yields the rest frequencies of all three hfs lines. Using [$^{12}$C II] as a reference, we also improve the precision of the [$^{13}$C II] centroid frequency. This work shows that spectrally resolved astronomical observations can constrain fundamental atomic properties, with hfs precision rivaling laboratory measurements. The approach extends to other atomic and molecular transitions where laboratory data are difficult to obtain.
arXiv:2605.16574v2 Announce Type: replace-cross
Abstract: We present a methodology to analyze metastable properties of a simple prototypical stochastic bistable system by identifying slow inter-well and fast saddle escape processes using the formalism of the Koopman operator. Instead of studying noise-induced transitions by following the trajectories of the system, we track them by studying the time evolution and the decay rate of the subdominant mode of the Koopman operator, thus in a geometry-agnostic framework. The obtained escape time statistics together with the decay rate are in good agreement with the predictions - both the exponential and subexponential ones - of large deviation theory in the weak-noise limit, both in equilibrium and nonequilibrium conditions. The subdominant Koopman mode also allows for an accurate reconstruction of the competing basins of attraction. Furthermore, going deeper in the Koopman spectrum, we are able to recognise modes that are associated with intra-well variability as well as with the escape of trajectories from the saddle towards the attractor, both in the equilibrium and nonequilibrium case. Our methodology, being grounded in purely data-driven techniques, could provide a comprehensive, multi-scale framework for studying high-dimensional metastable systems.