Papers

Intrinsic explainability remains a challenging problem, particularly in contexts where multilayer perceptrons (MLPs) require dynamic re-training within an optimization environment. This paper investigates how MLPs and their training dynamics can be represented and studied in non-Euclidean spaces; our representation features the Poincaré model of hyperbolic geometry. We aim to capture the geometric evolution of their weighted topology and self-organization over time. Instead of restricting the analysis to single checkpoints—as per established measure-based explainability methods—we construct temporal parameter graphs, i.e., snapshots over time $T$ steps of the optimization/training process for MLPs. This reflects the view that neural networks encode information not only in their weights but also in the trajectory traced during training. Drawing on the idea that many complex networks admit embeddings in hidden metric spaces where distances correspond to connection likelihood, we present a geometric and temporal graph-based metalearning framework for obtaining dynamic hyperbolic representations of the underlying neural parameter graphs. Our model embeds temporal parameter graphs in the Poincaré model ball, and learns from them while maintaining equivariance to within-snapshot neuron permutations and invariance to permutations of past snapshots. In doing so, the approach preserves functional equivalence over time and recovers the latent evolving geometry of the network. Experiments on regression and classification tasks with trained MLPs show strong meta-network performance, accompanied by hyperbolic temporal representations. This reveals how the network structure emerges over time under specific training environments, thus providing insights into the network's self-organization.

Thermonuclear flame fronts in Type Ia supernovae develop hydrodynamic instabilities that generate turbulent mesoscale flow and substantial local thermodynamic variability. Recent work by \citet{Brooker+25} demonstrated systematic shortening of fuel ignition times near Rayleigh–Taylor unstable deflagration fronts, but the physical origin remained unclear. We investigate the thermodynamic evolution of fuel near the flame front using multidimensional simulations and Lagrangian tracer-particle analysis, focusing on flame-driven expansion and ignition-time variability in partially degenerate carbon–oxygen plasma. Tracer trajectories show that the most strongly preconditioned fuel parcels near the flame front, which form a minority of the fuel layer, undergo approximately pressure-constrained expansion with modest density reductions and temperature increases of $\approx 2\times10^{8}$~K to $\approx7\times10^{8}$~K ($\approx13$ to $63$ per cent above the unperturbed fuel temperature) between the low- and high-density models. Despite moderate thermodynamic perturbations, the strong temperature sensitivity of carbon ignition produces substantial shortening of ignition times. The results indicate a two-step mechanism: flame thermal expansion perturbs the fuel away from hydrostatic equilibrium, while restoration of pressure balance by weak acoustic waves redistributes internal energy from degenerate to thermal components. This raises the fuel temperature and produces localized thermodynamic preconditioning. These results suggest that unsteady thermonuclear flames can shorten ignition times ahead of the flame, influencing fuel over distances larger than the laminar flame thickness. Whether this preconditioning leads to secondary ignition or contributes to deflagration-to-detonation transition remains untested here, as nuclear burning is disabled in the analyzed fuel.

The problem of segregation measurement is to quantitatively describe the interaction of a population's attributes (such as race, ethnicity, education level, or income) with a separating distinction (such as organizational rank, school district, or spatial location). This primarily expository article gives an opinionated tour of one mathematical approach to measuring segregation. We begin with some basic intuitions about diversity and unify these through the framework of convex functions on the probability simplex. Formalizing segregation as a local-to-global comparison of diversity measures, resulting in the general class of Jensen informations as segregation measurements. We describe and computationally illustrate three ways to incorporate spatial structure into segregation measurements: spatial smoothing, aggregation, and local Jensen information. We close with several suggestions for future work.

Iterative fine-tuning on synthetic data causes model collapse: output diversity narrows as rare patterns are progressively lost, a signature most visible as phrase-level repetition. Existing mitigations either require model log-probabilities, an external oracle, or continued access to real human data. Here we develop a new approach grounded in mathematical information theory: the non-parametric Kontoyiannis entropy rate estimator $h_k$, computed entirely from raw text via match-length statistics, with no model of any kind. We show that this is in fact a superior training-data filter on text-diversity metrics in a fully-synthetic, single-lineage fine-tuning setting. In a six-generation QLoRA collapse experiment on Llama-3.1-8B, logprob-based filtering (the most established model-access-requiring baseline) provides no significant text-diversity benefit on any metric ($p > 0.23$), whereas $h_k$-filtering yields $+42\%$ unique trigrams, $+30\%$ vocabulary, and $-19\%$ repetition (all $p < 0.001$). We validate $h_k$ as a cross-domain entropy proxy ($\beta = 0.924$, $R^2 = 0.746$) and collapse detector ($\rho = +0.454$, $p < 0.0001$) across 4~domains, 2~temperatures, 2~generator–scorer model pairs, and 1{,}520 generated documents. Our results demonstrate that information theoretic approaches to collapse mitigation are efficient, and suggest new approaches for maintaining multi-agent diversity.

In general, measurement error constrains the performance of information engines. However, this may not hold universally. In this work, we propose a class of two-reservoirs information engines (TRIEs) with a two-level system and demonstrate that the monotonic relationships between the work output, the efficiency, as well as the work fluctuations of the TRIEs and measurement error are determined by the demon's control parameters. Utilizing this, we establish the conditions that allow the TRIEs to generate useful work under any level of measurement error, and identify the regimes in which these performance parameters can be optimized simultaneously by the measurement error. Furthermore, we demonstrate that when the demon's energy cost is supplied solely by the cold reservoir, the efficiency that accounts for this cost can surpass the standard Carnot bound without violating the second law. Finally, we design a dual Otto cycles TRIE and provide an experimental scheme for its implementation based on a trapped $^{40}\mathrm{Ca}^+$ ion. Significantly, our results can be applied to the multi-level system information engines.

In nuclear and particle physics experiments, event selection is often a multidimensional classification problem which involves several correlated observables. The widely used sWeight technique provides a statistically rigorous means of separating signal and background using discriminating variables, but its conventional formulation is generally applied to a single discriminating variable or a simultaneous multidimensional fit. In this paper we present a novel extension of the widely used sWeight technique, in which an arbitrary number of discriminating variables can be used to construct a multidimensional sequential framework. This method allows the extraction of signal distributions in controlled variables in a rigorous way. Particular attention is given to the treatment of signal and background correlations, as well as the propagation of statistical uncertainties through successive weighting stages. The method yields high-purity signal samples even in the presence of large and correlated backgrounds. As a benchmark application, the validity of this technique is demonstrated on kaon identification in a dataset collected with the CLAS12 detector at the Thomas Jefferson National Laboratory for cascade baryon searches. The final workflow is shown to be robust and consistent across different run periods and beam/detector conditions, demonstrating minimal systematical uncertainties associated with the method. Statistical uncertainties are proved to be evaluable using a bootstrap-based procedure. The method provides a general framework for multidimensional event weighting and is intended for application in complex analyses requiring robust signal selection in the presence of complex correlated backgrounds.

Full detector simulation and reconstruction of collider events are projected to become major bottlenecks at the High-Luminosity Large Hadron Collider, motivating the development of fast, ML-based surrogates. At the same time, LLMs have driven fast progress in generative discrete modeling: autoregressive transformers trained on tokenized data now represent the state of the art across a range of generative tasks. We extend the discrete modeling paradigm by introducing a particle-level generative model trained on residual-quantized full-event data. We demonstrate the ability of this model family to perform conditional generation from detector-stable particles; we study its scaling behavior across a range of dataset and model sizes, characterize the effects of repeated data exposure and demonstrate that token-level loss systematically predicts downstream physical fidelity. These results provide an empirical framework for scalable collider full-event generation based on residual-quantized representations.

We present B-GRASP (Bayesian GRAph inference with SPDE priors), a Bayesian framework for inferring uncertain edge weights in stochastic dynamical systems on graphs from noisy observations of nodal states. The unknown edge weights parameterize the graph differential operator and therefore directly govern the evolution of the graph process. Motivated by connections between differential operators in PDEs and SPDEs and their graph counterparts, we construct stochastic graph models incorporating diffusion, reaction dynamics, and stochastic forcing. The resulting hierarchical formulation jointly represents uncertainty in the graph structure and stochastic forcing. Latent graph variables determine positive edge weights and the corresponding graph Laplacian, while latent Brownian variables represent the stochastic forcing. Conditional on these variables, the graph dynamics define a deterministic forward map from which the likelihood and posterior distribution are constructed. We characterize the posterior using maximum a posteriori estimation and the No-U-Turn Sampler, enabling both point estimation and uncertainty quantification. We demonstrate the framework on a one-dimensional inverse heat-conduction problem, stationary and nonstationary graph reaction-diffusion systems with nonlinear dynamics, and state-level COVID-19 data in the United States. The numerical results show that posterior uncertainty provides information not captured by point estimates, particularly for weakly identifiable or highly conductive edges, and enables uncertainty in both graph connectivity and stochastic forcing to be quantified within a Bayesian framework.

Global Dust Storms (GDSs) dominate the Martian climate, yet the mechanisms of dust lifting, transport, and deposition remain poorly constrained because in situ observations are limited: landers are stationary, and their Radioisotope Thermoelectric Generators (RTGs) contaminate local measurements. Our solution is a swarm of lightweight, wind-propelled spherical rovers – Dust Rovers (DRs) – that follow natural wind patterns to collect high-spatial-resolution in situ dust data during storms. Here, we quantify the dispersion and communication connectivity of this robotic architecture. Using 625 wind states calculated using the Mars Climate Database (MCD) for the MY34 storm at the Curiosity site, we build a bivariate-normal model of the near-surface wind velocity and characterise its diurnal structure. Rover trajectories and swarm dispersion are propagated with three integrators: the Euler and fourth-order Runge-Kutta schemes for the deterministic dynamics, and a stochastic Ornstein-Uhlenbeck formulation that simulates turbulent gust forcing. Dispersion is controlled by the unmeasured gust correlation time: with a static rolling threshold enforced, the white-gust case (tau_g = Delta t = 1 s) provides a two-rover separation below 1 m over an hour (0.44 km over a sol), whereas correlation times of 10-60 s yield 6-25 m over an hour (1.4-3.3 km over a sol). We demonstrate that a 20-rover swarm needs only a 1.6-4.1 km per-rover range to remain connected over a sol, and stays connected across the plausible envelope – for gust amplitudes up to twice the nominal value with tau_g <= 60 s, and at the nominal amplitude up to tau_g ~ 150 s.

We investigate the accuracy and computational efficiency of posterior approximations for gravitational-wave (GW) parameter estimation based on Fisher Matrix and its higher-order extension, the Derivative Approximation for LIkelihoods (DALI), in the context of tests of General Relativity using parameterized deviations in the inspiral waveforms (the TIGER formalism). We adopt the IMRPhenomD waveform and compare the exact posterior sampling to the following approximations in increasing order of complexity: the traditional Fisher Matrix, the Fisher sampling (singlet-DALI), the doublet-DALI and the triplet-DALI. We find that both singlet and doublet-DALI are significantly faster than the exact posterior by factors between 20 and 1000, depending on the inspiral SNRs – larger gains correspond to larger SNRs. These gains are considerably larger for more complete waveforms, such as IMRPhenomHM. To evaluate the accuracy of the approximations, we use Jensen-Shannon divergence. We conclude that both singlet and doublet-DALI systematically improves over the standard Fisher Matrix approximation, while triplet-DALI shows large variability, limiting its practical advantage. We also introduce a code with a new implementation of Fisher and DALI analysis (Symbolic DALI, SymDALI) which computes derivatives symbolically via Wolfram Language.

Two-sample tests are widely applicable in inference and generative modelling, yet users frequently fall back on heuristics and visual inspection due to lack of an accessible test that operates in multiple dimensions. I present Permutation Test using the Energy Distance (PTED), a Python implementation of a powerful two-sample test described in Székely and Rizzo [2004]. The test statistic is the energy distance, a metric on probability distributions that admits a natural sample estimator built from pairwise distances. A permutation test is run on energy distances to produce an exact two-sample test. Because the statistic depends on the data only through pairwise distances, the test applies in high dimensions, on learned feature representations, at large or small or imbalanced sample sizes, and to any data type on which a distance can be defined. An approximation to the formula allows PTED to scale linearly with both number of dimensions and samples while retaining most discriminative power. I highlight a number of instructive sensitivity tests on PTED alongside other multi-dimensional two-sample tests for comparison. PTED is the only method that is sensitive to all tests, though conventional Maximum Mean Discrepancy is identical for all but an over-fitting test.

Recent progress in network renormalization has identified various ways to transform network representations consistently across resolution levels. In particular, the renormalization flow describing how random graph models transform under node aggregation has identified a fixed point corresponding to an aggregation-invariant model that preserves the form of the connection probability across arbitrary scales. While this probabilistic multiscale approach has successfully been used to model real-world networks, construct latent-space node embeddings, and reconstruct finer-grained versions of aggregate network data in a principled resolution-invariant way, it has so far been restricted to binary graphs. Here we reformulate multiscale network renormalization for weighted random graphs. Via a generating-function approach, we identify a weighted multiscale model whose full probability law, encoding both link creation and weight assignment, has an invariant compound-Poisson form under arbitrary node aggregation. The renormalization rules that transform parameters across aggregation levels allow the ensemble to be calibrated at one level and applied at another, enabling consistent modeling and reconstruction of weighted networks across arbitrary scales.

Network reconstruction from partial information is usually performed at the same resolution level at which constraints are observable. This becomes problematic when only coarse-grained information is available, while the relevant process occurs at a finer scale. Here we employ the multiscale model of weighted networks introduced in a companion paper and turn it into a probabilistic framework for reconstructing weighted networks across arbitrary aggregation levels. The model is built to preserve its functional form under coarse-graining, so that global parameters calibrated on an observable aggregate layer can be transferred to finer layers without refitting. We test the method on two empirical systems with different aggregation mechanisms. In the International Trade Network, countries are aggregated into geographic macro-regions and the observed coarse-grained layer is used to infer the underlying country-level network. In the Dutch production network, sectoral flows are reconstructed across the hierarchical industrial classification, using coarser sectoral layers to infer finer ones. In both geographical and sectoral settings, we benchmark our genuinely multiscale reconstruction method against a state-of-the-art weighted reconstruction model calibrated directly at the target resolution, and therefore using additional information available at the same (finer) scale at which performance is evaluated. Remarkably, despite this informational disadvantage, our method recovers the fine-scale binary structure with high accuracy, improving precision, specificity, accuracy and maximum degree-error diagnostics, while remaining nearly equivalent in sensitivity.

A droplet breaks up in tens of microseconds, and a recording captures perhaps a dozen frames. The states in between cannot be recovered without repeating the experiment, and simulating them is too costly to sweep an operating envelope. Yet they are present in the corpus as a whole: a campaign spanning a device's actuation range produces morphologies resembling those any single recording missed. Exploiting that requires a representation that is low-dimensional, invertible, and faithful to shape rather than to sampling. Proper orthogonal decomposition supplies the first two but measures distance in sampled coordinates; manifold learning supplies the third but no map back to a shape; elastic shape analysis supplies a shape metric but no reduced coordinates. SHROM composes all three. Interfaces are represented by their square-root velocity functions, a neighbour graph is built over that shape space, and an autoencoder is trained to reconstruct while penalising latents in which graph neighbours are not latent neighbours. The demonstration uses 301,539 inkjet droplet contours and four filmed break-up sequences. The graph term does not improve reconstruction. It determines whether position in the latent carries meaning: clustering the latent of an otherwise identical model recovers the shape-space partition at chance level (ARI = 0.063 +/- 0.059), and at 0.781 +/- 0.049 with the term active. Waveform parameters predict the full contour at R^2 = 0.878 +/- 0.026. Negative results are reported in the same terms. The graph metric proved immaterial across five choices, and interpolation error saturates at the reconstruction limit, so a plain autoencoder leads that task. The main limitation is interpolation across a topology change: no component of the regularised latent holds both a single-component and a post-break-up shape, whereas an unregularised autoencoder mixes them freely.

Information-flow theory quantifies directional coupling through the rate of change of a target's Shannon entropy, a bulk functional insensitive to the tail of the distribution. We ask instead how a source variable contributes to the probability that the target exceeds a threshold. For source-additive drift the source's share of the marginal probability current is exact, and it separates into a mean-forcing part and a conditional-excess part that vanishes under independence. An identity links the two descriptions: the Liang information flow is the density-weighted mean of the derivative of the specific source current, whereas the exceedance current is its level at the threshold. This explains why entropy-based coupling collapses in saturated regimes where the source contributes most to the extreme; the Rényi information flow, a higher-order expansion and a Fisher-normalised response fail for the same reason. The flux decomposition, although exact, does not attribute: its terms are gross transports that nearly cancel. The quantity that does attribute is an adjoint response built from the backward generator which, read as a relative change, is uniformly accurate across two decades of event probability. We map the operating envelope of the estimator under omitted drivers, hidden slow memory, state-dependent coupling and multiplicative noise. Under correct specification the attribution carries a reproducible shortfall of ten to twenty-five per cent; the misspecifications we test bias it upward by up to ninety per cent. Applied to the 2003 European and 2010 Russian heatwaves in reanalysis, the attributed contribution of soil moisture is strongly threshold dependent, rising from the per cent level at moderate thresholds to a factor of two at the rarest, so a contribution quoted without its threshold is underspecified.

The future Electron-Ion Collider (EIC) will offer new opportunities to search for physics beyond the Standard Model. We study resonant anomaly detection using machine learning and the full particle content of an event. We consider a new neutral gauge boson and a heavy neutral lepton as illustrative signals with different electron-jet topologies. Weakly supervised learning uses this event information to enhance the sensitivity of an invariant-mass search without identifying individual signal events during training. Comparisons with high-level observables show that the electron kinematics account for an important part of the separation, while correlations among the particles provide further sensitivity. We also construct a conditional full-event generator by adapting a model pretrained on LHC jets to produce EIC background events. A scan over signal fractions demonstrates substantial signal enhancement using the learned background reference, providing a proof of concept for this approach at the EIC. Finally, we consider a fully unsupervised graph autoencoder that provides modest signal enhancement but retains sensitivity at signal fractions too small for effective weak supervision. Our results motivate full-event anomaly detection as part of the EIC physics program and identify directions for developing methods suited to its distinct kinematics.

Our recent research on Langevin dynamics with self-harmonic drift and classical spins has revealed a strong connection to “Stochastic Localization," a concept attracting attention in the fields of mathematical geometry and data science. Roughly speaking, the former can be viewed as a version of the latter in which the $n$-dimensional Euclidean space - the domain of the probability distribution function appearing in the latter - is “compactified” to the surface of an $n$-dimensional sphere. By comparing the two frameworks, we argue that this compactification is a consequence of requiring the drift to be autonomous. The relationship between the two approaches may expand the scope of Stochastic Localization.

The cryosphere regulates global cycles of water, energy, and carbon, affecting societies and ecosystems. By assimilating observations into models, we can infer the past trajectory of state variables, generating a cryospheric reanalysis. Existing cryospheric reanalyses typically treat each water year independently, with no pooling of information across years. With sparse and noisy observations, such 'climate-assumed' reanalyses perform poorly, reverting to an assumed yet uncalibrated background climatology. Conversely, Bayesian calibration with static parameters completely pools information across water years, inferring climatological parameters without capturing inter-annual variability. Here, we propose a new hierarchical Bayesian approach using partial pooling, which we coin 'climate-informed' cryospheric reanalysis. It jointly infers state trajectories, annual parameters, and local climatological hyperparameters using a nested hybrid particle smoothing workflow. We test the approach through three experiments by assimilating in situ snow water equivalent, satellite-based fractional snow-covered area, and glacier-wide mass balance data into a temperature index model at eight study areas, from the Swiss Alps to the High Arctic. Hierarchical reanalysis with partial pooling outperforms annually independent cryospheric reanalysis (no pooling) and static parameter calibration (complete pooling) for all experiments during calibration and for all but one during validation. Overall, it yields a 51% improvement in continuous ranked probability score relative to the prior, markedly exceeding that of annual reanalysis (38%) and static calibration (19%). Compared to a particle Markov chain Monte Carlo benchmark, our workflow reduces computational cost by several orders of magnitude through recycling and expectation maximization, with comparable or improved skill.

We develop two hybrid techniques that approach the performance of neural simulation-based inference (NSBI) analyses while substantially reducing the computational cost of inference and preserving some or all of the reliability guarantees of parametric methods. The first approach is broadly applicable, while the second is tailored to a class of particle physics analyses that admit a semi-parametric NSBI formulation. With only a modest compromise in raw sensitivity, these methods represent an important step toward computationally efficient NSBI in offline analyses and also open the door to the exploration of trigger-level applications in the future. Based on our comparison studies, we recommend the use of our first approach, Latent Categories, for robust and efficient inference.

This article describes a behavioural dataset from a collective-risk dilemma public experiment carried out in Barcelona, Spain, within the citizen science xAire air quality project. Participants played a ten-round game in groups of six, each deciding every round how many monetary units to contribute from a private endowment toward a shared target; groups that fell short forfeited all remaining capital. Three endowment treatments held the group total fixed: an equal condition and two unequal conditions in which low-endowment participants formed either the minority or the majority of the group. Data were collected at two public outdoor venues using a tablet-based interface under lab-in-the-field protocols. Participants were recruited on-site from a demographically heterogeneous pool of individuals passing through the venues, mostly local residents. The dataset comprises 462 participants across 77 six-player games, 4\,620 contribution decisions in total. Each participant record links the full ten-round contribution trajectory to initial endowment, wealth treatment, venue, district of residence and its measured nitrogen-dioxide concentration, and socio-demographic and attitudinal survey items covering gender, age, education, economic and working status, air-quality perception, fairness norms, environmental-justice beliefs, residential mobility, and community participation. The release provides raw and cleaned participant tables, a variable codebook, the survey instrument, the district-pollution linkage, and the preprocessing code.

Dimensionless descriptions of complex physical systems can sometimes be reduced further when multiple input groups combine into a single composite scaling coordinate. Identifying such structure from noisy response evaluations is difficult because apparent departures may reflect either genuine response structure or evaluation noise. Here we develop equal-response probing with replicate calibration to assess whether two dimensionless inputs support a one-group representation under prescribed directional and collapse tolerances. Equal-response geometry provides a candidate coordinate without direct numerical differentiation, while a second stage evaluates the accuracy of the resulting one-dimensional collapse. Replicate evaluations estimate the noise contribution to both stages, enabling reducible, not-red and unresolved outcomes. We evaluate the framework across eight model-based benchmark regimes spanning rough-pipe flow, cell-monolayer wound closure, microfluidic droplet generation and column buckling. Six regimes satisfy both criteria and two fail both, while known reduced coordinates are recovered in exact-reduction benchmarks. Controlled synthetic tests assess false-alarm behaviour, sensitivity to structural departures and noise calibration. These results show how replicate-calibrated equal-response probing distinguishes regime-specific scaling structure from variation attributable to evaluation noise while retaining an unresolved outcome when evaluation noise precludes a definitive verdict at the prescribed tolerances.

We formulate scattering experiments in terms of parameterized finite measures on outcome spaces and develop the associated information geometry defined by the Fisher metric. The decomposition of a scattering measure into total mass and normalized shape separates Fisher information into contributions from changes in overall scattering strength and redistribution among outcomes. Measurement processes are represented by probability or sub-probability kernels acting on the scattering measure. Such kernels contract Fisher information, placing a broad class of experimental operations within a common information-theoretic framework. This formulation connects scattering experiments to the theory of optimal experimental design through the Fisher geometry of scattering measures. The same finite-measure structure arises naturally in quantum measurements with incomplete detection, clarifying its place in the hierarchy from quantum measurement to classical outcome statistics.

The information-theoretic construct of synergy refers to the statistical structure that is contained in three or more variables, but not in any subset of them. Here we leverage recent advances in multivariate information theory to show that synergy is far more prevalent in complex systems than previously thought. In particular, we show that many-body systems tend to become strongly dominated by synergy as the number of subcomponents grows. At the same time, our results also reveal that commonly used tools for statistical modelling severely underestimate synergistic structures. These findings imply that synergy constitutes a prevalent, yet often invisible, informational component of complex systems. With a certain poetic licence, we interpret these results as suggesting that synergy is the dark matter of statistics - interdependencies that we know exist, but standard instruments fail to detect.

We propose a training recipe that treats charged-particle trajectory parameter regression on high-energy physics detector data as a sequence-modeling task. Kalman filters and linearized least-squares fits have been the classical standard approach for this task: they are optimal estimators for sparsely sampled linear-Gaussian data and are commonly used for trajectory parameter regression (fitting). The classical fitting techniques implemented for this domain reach a final precision of one part in $10^5$ through detailed modeling of detector geometry, material, detection effects and precise numerical integration of the equations of motion through the detector's inhomogeneous magnetic field. With this study, we demonstrate that using a bidirectional gated linear recurrent encoder, one is able to reproduce the full precision of classical track fitting techniques. Using a custom kernel, we also achieve significantly higher throughput during GPU inference, compared to classical fitting software running on similarly priced multi-core CPU servers representing typically employed hardware. Such a speedup would lead to considerable cost savings for the pattern recognition at the Large Hadron Collider. To our knowledge, this is the first end-to-end learned track fit to reach the full precision and, at the same time, offer the opportunity to reduce the computing costs.

We study how well gravitational-wave phase deviations can be identified using a neural network with classification and regression heads. The classification head distinguishes general relativity (GR) from six parametrized post-Einsteinian phase families with exponents $b\in\{-7,-5,-3,-1,+1,+2\}$; the regression head predicts the logarithm of the coupling magnitude, $\log_{10}|\beta|$. The network input is a response function quantifying the sensitivity of waveform mismatch to waveform deformations. We use stationary Gaussian noise with the Advanced LIGO design spectrum for 262 sources and a measured Hanford spectrum from the third observing run (O3) for 132 sources, and also test injections into recorded Hanford strain. On the two Gaussian datasets, the network identifies the exponent of deviations clearly above the noise with accuracies of $0.427$ and $0.329$. To interpret these results, we compare the network with an approximate classifier built from predicted waveform residuals for the six phase families and same sources. The two classifiers often confuse the same families. Examining residuals left by different phase corrections, we link these errors to similarities between the underlying deviations. On selected recorded Hanford strain, networks trained on simulated or recorded noise achieve overall classification accuracies close to those on simulated Hanford noise. Of thirteen neural-network variants tested on the Advanced LIGO design dataset, the recurrent network has the highest mean classification accuracy for loud deviations, although all variants remain below the approximate classifier. The network nearly matches that classifier's accuracy, indicating that identification is limited by similarities between neighboring phase families rather than by the network, for known intrinsic source parameters.

Reconstruction and simulation at a collider experiment are long chains of specialised algorithms, each tuned to a single step. We explore how one model can serve many of those steps at once, while still producing the intermediate objects (tracks, calorimeter cells, clusters, particles and jets) that make the chain interpretable. To do so, we represent every object in a jet in a single shared token vocabulary and train one model to map any subset of these modalities to any other. A task is then only a choice of which modalities to provide and which to request: particle flow, detector simulation and charged energy subtraction are all directions through the same set of weights. We train over all modality combinations, with a decoder emitting tokens either autoregressively or in parallel. With tokenisation, both architectures train stably with little tuning. In evaluations, both models produce realistic reconstruction and simulation objects, with the autoregressive model particularly faithful to output from Geant4. The autoregressive model also outperforms a state-of-the-art particle flow algorithm on many typical jet reconstruction metrics.

Detector simulation and event reconstruction will be computationally expensive for future $e^+e^-$ collider programs and are currently critical bottlenecks for accurate feasibility studies. To address this challenge, we build a Parnassus model for the CLD detector concept. Parnassus is a framework for automatically tuning a surrogate model, in our case, a conditional flow matching neural network, to emulate a full detector simulation and reconstruction. We train on $e^+e^-\to Z\to q\bar q$ events at $\sqrt{s}=91.2$ GeV processed through a Geant4 simulation of the CLD detector concept and the Pandora particle-flow reconstruction and reproduce single-particle kinematics, particle-IDs, and impact-parameter distributions. We also examine jet- and event-level features, inclusively and split by flavor, and find excellent fidelity, significantly better than the parameterized program Delphes. Furthermore, we train a transformer-based flavor tagger on the reconstructed particle-flow constituents and show that the surrogate preserves the $b/c/s/q$ discrimination of the full CLD reconstruction. The Parnassus CLD model achieves a generation cost of about 1.2 ms (40 ms) per event on a single GPU (CPU), over three (two) orders of magnitude faster than full simulation and reconstruction. Our model is publicly available for feasibility and design studies.

Validating whether the underlying physics of a model has been retained after a full phase-space reweighting poses a unique challenge. Often, validation relies on comparing histograms of 1D observables; however, this can mask correlations and biases in the complete prediction. We present a novel, unbinned approach to comparing the performance of such reweighting schemes based on the "Cross-Section-Mover's Distance", an application of Optimal Transport that quantifies the work required to transform one theoretical prediction into another and enables an interpretation of results in terms of metric spaces. We demonstrate its utility when benchmarking various reweighting schemes that mitigate the effects of negative weights in a Monte Carlo simulation. This approach can be broadly applied in other scenarios where biases in full phase-space reweighting schemes should be studied in an unbinned way.

As the accuracy of experimental results in high energy physics (HEP) increases, so does the demand for precision Monte Carlo (MC) simulation. Higher-accuracy event generation at next-to-leading order (NLO) and beyond brings with it negatively weighted events. These negatively weighted events reduce the statistical power of samples, increasing the number of events that need to be produced and straining already limited computational resources. We present a post-hoc reweighting scheme that employs cell-based resampling using an IRC-safe metric to define the cell radii. An optimal metric embeds kinematically similar events within the same cells, minimizing bias when reweighted. This motivates our exploration of a Optimal Transport (OT) based distance metrics. We compare the performance of the reweighting algorithm with different choices of metric, and explicitly demonstrate the performance on simulated Z+jets events produced at NLO accuracy.

High-dimensional, unbinned neural simulation-based inference often relies on neural ratio estimation, which uses expressive supervised models to estimate density ratios, but a learned ratio by itself provides neither an explicit normalized density nor a generative model. Flow-based surrogate models instead enable tractable density evaluation and efficient sampling, but residual density-estimation errors can limit precision for complex implicit distributions. We propose hybrid neural density estimation, which uses a flow to define a parameter-independent reference distribution, and classifiers to estimate target-to-reference density ratios. Multiplying a learned ratio by the reference density gives an evaluable target density surrogate. The ratio also provides importance weights for integration and resampling. We show how this representation defines an exact Asimov dataset, whose maximum likelihood fit returns the generating parameters. We also show how the tractable reference supplies renewable samples for pseudo-experiments and how it enables methods to reduce the Monte Carlo variance of expected test statistic calculations. We demonstrate the construction in a toy statistical model motivated by high-energy physics measurements, but for which the exact densities are known analytically.