Papers

Coded computing mitigates stragglers in distributed computation. While Lagrange coded computing (LCC) enables exact polynomial computation over finite fields, Berrut approximated coded computing (BACC) enables approximate computation of arbitrary, including non-polynomial, functions in the analog domain. In applications such as multi-task learning and inference, multiple functions must be evaluated over different subsets of a common dataset, making single-round computation desirable to reduce communication overhead. An existing LCC approach addresses this requirement but is restricted to polynomial functions over finite fields, leaving single-round multi-function computation in the analog domain an open problem. In this work, we develop a single-round construction for computing multiple arbitrary functions using BACC. We first extend the existing multi-function computation approach in LCC to the BACC setting and derive an approximation-error bound. Building on this, we propose a construction based on Berrut basis functions for computing multiple arbitrary functions and derive its approximation-error bound. We analyze the scaling of both bounds with the number of functions and the number of data points per function, and numerically compare the two constructions over a wide range of arbitrary functions. The results demonstrate that the proposed construction achieves lower relative errors than the existing approach in the tested settings.

Low dose Computed Tomography (CT) is the standard imaging modality for lung cancer screening. On CT scans, lung cancer typically manifests as pulmonary nodules, whose manual identification is time-consuming and prone to observer variability, image quality limitations, and suboptimal reading conditions. Moreover, subtle temporal changes are often difficult to quantify reliably in CT scans from the same patient across follow-up examinations. Deep learning-based approaches for the automatic detection and segmentation of lung nodules have demonstrated improved accuracy and efficiency. However, most existing approaches provide only coarse region-of-interest localisation, rely on prior lesion annotations or human supervision, or treat detection and segmentation as separate tasks. In this work, we present NoduleFlow, a framework for lung nodule detection, classification, and segmentation directly from series of CT volumes. Our proposal consists of four interconnected modules and operates in an automated manner at inference time, without requiring prior lesion annotations, manual initialisation, or region-of-interest pre-selection. We further investigate whether nodule localization benefits from the propagation of candidate regions across follow-up scans through inter-scan registration fields, as opposed to conventional independent per-scan analysis. The generalisability of the framework is systematically evaluated across four independent datasets. The results underscore the potential of automated pipelines for lung nodule analysis in screening and diagnostic settings.

Sentence representation learning is still an open challenge in Natural Language Processing. In this work, we propose a new self-supervised framework for learning sentence representations, using a special type of neural network called a recursive hypernetwork. Our proposed model composes the representation of a sentence from representations of words by applying a recursive composition through the parse tree. We maintain a separate syntactic and semantic representation, and the semantic composition is guided by the information from the syntactic representation. To train this model, we introduce a novel set of six self-supervised tasks. By analysing the performance on 7 probing tasks, we validate that the generated sentence representation encodes richer linguistic information than both averaging baselines and state-of-the-art alternatives. Furthermore, we assess the impact of the six proposed self-supervised training tasks through ablation studies. We also demonstrate that the representations generated by our model are stable for sentences of varying length and that the semantic composition operators adapt to different syntactic categories\footnote{Code available: https://github.com/vasudev2020/codi/tree/main}.

Basic probabilistic models form the basis of modern deep learning largely by defining the final activation layer of a network and allowing the networks outputs to be interpreted through a probabilistic lens. By increasing the complexity of these final activation layers to include features such as spatial regularisation, allow for these models to improve in performance without requiring significantly more data. The challenge however is to ensure that these more complex probabilistic graphical models adapt well to being used in tandem with deep learning, that is, ensuring they converge and have meaningful derivatives. The goal of this paper is to show two algorithms with provable convergence properties to allow this type of regularisation for image and signal classification models. Through both rigorous mathematical analysis and in silico experiments, we can show the differing performance between these solution types.

Feature caching has become a mainstream training-free strategy for accelerating video diffusion models by reusing intermediate outputs across denoising steps. However, existing adaptive methods rely on heuristic difference measures misaligned with actual generation quality, employ a single global threshold that ignores heterogeneous phase dynamics, and never validate their budget estimates against true approximation error, allowing systematic bias to propagate uncorrected. We propose AlignCache, a closed-loop caching framework that directly aligns scheduling decisions with their true influence on the final generated video through three tightly coupled components: (1) phase-adaptive budget routing that partitions the denoising trajectory into structurally distinct phases, each governed by an independent threshold and a staleness-aware guard; (2) closed-loop threshold calibration that exploits counterfactual error measurement at the classifier-free guided output level to adjust decision boundaries online via an EMA feedback loop; and (3) momentum-augmented draft synthesis combining direction-magnitude gated residual extrapolation with anchor-guided unconditional correction. By transforming scheduling from a static risk accumulator into a feedback-driven, self-correcting controller, AlignCache consistently achieves superior acceleration-quality trade-offs across state-of-the-art video generation models. Our code is available at https://github.com/jiangjyjy/AlignCache.

The search for materials exhibiting a large bulk photovoltaic effect has recently expanded to low-band-gap systems capable of operating in the infrared regime, with potential applications in optoelectronics. Among the microscopic mechanisms contributing to this phenomenon, the shift current is one of the dominant sources of photocurrent generation. Owing to its geometric origin, the shift current is not only determined by the optical transition probability but also by the real-space displacement associated with the optical excitation, making non-centrosymmetric materials with obstructed electronic wave functions particularly promising candidates. In this work, using a tight-binding model of a quantum spin Hall insulator on a triangular lattice, we investigate the nonlinear photocurrent across trivial, quantum spin Hall, and higher-order topological insulating phases. We show that obstructed topological phases exhibit a substantially enhanced shift-current response, despite the similar electronic band structure. We identify the origin of this enhancement in optical transitions between states belonging to distinct Wannier-center sectors, which allow for a large real-space displacement upon photoexcitation and, depending on the topological phase, control the sign of the shift current. Our results extend the search for controllable bulk photovoltaic effects to materials characterized by real-space electronic obstruction and identify indenene, a monolayer of In on SiC(0001), as a promising candidate for realizing this phenomenon.

Multi-agent discussion produces reasoning collaboratively, while deployment still relies on a smaller student that must answer alone. Full-graph distillation transfers such discussions by treating each correct solution as a separate training target, but what teachers provide need not match what the student learns. This mismatch appears in two ways: several correct solutions may amount to the same lesson in the student's representation (over-teaching), while some training questions remain missed after learning (under-learning). We quantify both with rates that are high on discussion graphs. To address them, we introduce FAR (Fold–Attempt–Revisit), a learner-centered distillation procedure that organizes supervision around the student's own state. Before training, FAR folds solutions within each discussion state into representative lessons. After training, the student's own attempts identify missed questions, while poorly represented clusters indicate where folding may have lost useful variation; FAR then writes targeted lessons from retained discussion contexts. Across two students and four reasoning tasks, FAR outperforms full-graph distillation with far fewer training targets and lower under-learning. Further analyses examine the behavior of FAR and the sources of its gains. Overall, the results show that organizing discussion supervision around the student can make distillation both more effective and more efficient.

This work presents a hybrid numerical approach for solving linear systems arising from the discretization of the two-dimensional parametric Helmholtz equation. A convolutional neural network based on the U-Net architecture is trained in an self-supervised manner (i.e., without explicitly generating reference solutions) to approximate the inverse of the discretized Helmholtz operator, using a loss function involving the residual norm of the linear system. The trained network is used as a nonlinear preconditioner within the flexible GMRES (FGMRES) algorithm. Numerical experiments show that while the neural network is not accurate enough to act as a standalone solver, it significantly improves the convergence of FGMRES when employed as a preconditioner. The neural preconditioner demonstrates robust performance and generalization capabilities with respect to variations in the velocity field and the domain size. Comparisons with algebraic preconditioners, based on LU factorizations of approximations of the original system matrices, indicate the superior efficiency of the neural approach under equivalent conditions. We believe that the proposed method is not tied to a specific neural architecture and can be extended to other parametric PDEs.

We develop a support theory for wide subcategories of essentially small Krull–Schmidt \(n\)-abelian categories. We construct spectra associated with families of wide subcategories and establish the corresponding support and radical theories. In particular, we characterize prime wide subcategories as the completely meet-irreducible elements of the lattice of wide subcategories and prove that every wide subcategory is recovered from the prime wide subcategories containing it. We further show that any classifying support datum is recovered, together with its object supports, from the canonical prime spectrum. Finally, we provide a \(2\)-abelian example admitting no classifying support datum.

Closed-form formulas are derived for the cumulative distribution function and odd-order absolute moments of the variance-gamma distribution. As a special case, closed-form expressions are deduced for the cumulative distribution function and odd-order absolute central moments of the product of two correlated zero-mean normal random variables.

We determine the Maslov-graded next-to-top term of knot Floer homology for fibered positive links. Its rank in Maslov grading (-1) is the number of nontrivial prime connected-sum factors plus the number of components minus one, and the remaining summand is supported in Maslov grading zero. For a knot, the dimension of this remaining summand is determined by its Alexander polynomial. The proof combines a preferred-crossing construction with reductions of generalized Seifert surfaces to planar pretzel surfaces and a graded skein induction. We also obtain bounds on the fixed points of monodromies for fibered positive knots.

We present PatTransBench, a 12,000-item Chinese-English/Japanese/Korean patent machine translation (PatMT) benchmark with a four-dimensional evaluation protocol. The benchmark comprises 6,000 short-text (sentence/claim) and 6,000 long-text (paragraph) pairs, evenly split across three language pairs and both translation directions, built via IPC-section-stratified sampling and dualthreshold quality gating from upstream patent-family parallel corpora. The evaluation protocol spans literal n-gram overlap (BLEU, ROUGE-L, chrF), cross-lingual semantic textual similarity (CLSTS), 38-probe-language consistency testing, and serving performance under concurrency. A case study on PatMT2-7B and its fp8/AWQ4/AutoRound-4bit variants reveals direction-dependent quantization effects masked by aggregate scores and non-monotonic language-failure patterns across quantization schemes that are invisible to single-metric evaluation. We plan to release the benchmark, protocol, and case-study results upon publication to support reproducible PatMT evaluation.

In a variety of multi-agent and physical environments, an element's update depends strongly on a few other elements and weakly on many, and both the identity and the number of the elements that matter change with the state of the system. Such graded sparse mechanisms are common, for instance, in flocks, crowds, learned particle simulators and the neighborhood aggregation of graph networks, yet they have received little systematic study as a class of functions with the grading given. In this paper we study the supervised learning of the mechanism when the grading is provided by the environment, as a weight on every element. First, we define the class by axioms, where each element's influence is capped by its weight, the dependence on the weights is regular, and no element is distinguished, and prove a representation theorem: the class is exactly the Lipschitz ball of a transport metric on weighted multisets, and the metric is forced by the axioms. Next, the geometry of the representation gives generalization bounds that depend on the data in two ways. One is via the sparsity profile of the data – the law of how many elements matter and by how much – which bounds the rate over all designs with that profile, with an exponent from the profile and no dependence on the number of elements. In a number of natural cases we also show matching lower bounds, up to constants in the exponent. The other is empirical: due to the representation result, classical empirical discrepancy bounds apply to the class as they stand, and the resulting bound is the transport distance between the two halves of the sample in the class's own metric, computed exactly by a matching, with an additional concentration term. Finally, we study a simulated Vicsek flock under four interaction rules at two noise levels, and show that the certificate is non-vacuous, a small fraction of the trivial value on every rule.

We present CosmoAgent, an agentic AI framework using large language models (LLMs) to search for dark-energy and modified-gravity models. We define a covariant grammar that allows LLM agents to explore the space of modified-gravity Lagrangians. An in-house computational pipeline derives the equations of motion, solves the background dynamics, and evaluates the likelihood using late-time expansion data, including the DES 5-year type Ia supernova sample and the DESI Data Release 2 BAO measurements. Theories are ranked by the Akaike Information Criterion (AIC) to balance simplicity and likelihood. We benchmarked 8 frontier LLMs from ChatGPT, Claude, Gemini, Kimi, DeepSeek, and Qwen, and all LLMs are able to find theories with a lower nominal AIC than flat $\Lambda$CDM, with a best improvement of $\Delta$AIC = -3.328. Seven recover quadratic quintessence. Exploratory searches also return induced-gravity and scalar-Gauss-Bonnet structures. The modest AIC improvements do not establish an observational preference for these models over flat $\Lambda$CDM. The code is publicly available at wsunamoutlook-prog/AI-Modified-Gravity.

The idea that learning is closely tied to compression has long served as both a powerful principle and, at times, an informal analogy across machine learning and learning theory. Here we focus on settings in which that intuition can be made mathematically precise, surveying formal connections among learning algorithms, data compression, and computational complexity theory, with an emphasis on recent progress and current frontiers. We describe how techniques from complexity theory can guide the design of both supervised and unsupervised learning algorithms with provable guarantees, and conversely, how learning algorithms can yield new insights and results in complexity theory. A central theme is the role of data compression as a bridge between learning and complexity, especially through an area called meta-complexity, which studies the computational difficulty of compression problems and time-bounded variants of Kolmogorov complexity.

Deployed models can fail silently as the world they describe evolves. Attribution drift has served as an early warning in tabular data; we ask whether, in graph streams, a model's own explanations can forewarn the loss of nominal conformal coverage. Doing so requires repairing the naive drift statistic twice. A vanishing edge loses mask mass regardless of whether the model relied on it, so we condition the importance on edge presence. Evolving graphs also break edge identity: a relabelling that changes nothing shifts the identity-based statistic by 0.69 on synthetic graphs and 0.83 on real ego-networks, whereas aggregating over structural roles brings both to 0.0 and stays well-defined when the support changes. We test six pre-registered regimes on thirty seeds each. A two-channel monitor, tracking conditional mask mass and its distribution over roles, precedes coverage collapse by 8 to 14.5 steps across four gradual regimes (node addition, removal, replacement, and edge thinning), all surviving Holm correction. A sudden knockout yields the expected zero lead, and a harmless change triggers no alarm. Leads track the length of the transitional phase (Spearman 0.79 over 150 runs). On real transaction ego-networks, the untuned mass channel forewarns staged drift by 27 steps and is the only channel, attributional or structural, that never alarms on a stationary stream. The main limitation is that the mass channel is blind to covariate drift, which breaks the guarantee in every run; the distributional channel detects it and also rescues the rewiring regime, so we report the two channels separately rather than as a union.

Reinforcement learning with verifiable rewards (RLVR) is reshaping how large language models (LLMs) acquire reasoning capabilities, yet the optimizers used remain largely inherited from teacher-forcing training. This raises a fundamental question: does RLVR induce a distinct optimization geometry that calls for a different optimizer? We investigate this question through the spectral structure of LLM gradients and find that gradient energy progressively concentrates into a shrinking effective subspace, which is characteristic of RLVR, as it is absent under supervised fine-tuning (SFT) and is largely removed when the verifiable reward is replaced by a random one. Moreover, the rank required to capture a fixed fraction of gradient energy steadily decreases over training, revealing that the effective dimensionality of useful updates itself evolves with training. These findings motivate a new optimization principle: rather than prescribing the update rank externally, an optimizer should adapt its rank to the evolving spectral structure of the gradient. We introduce Ares (Adaptive Rank-Effective Spectral Optimization), which estimates the effective update rank from the gradient's spectral energy distribution, tracks its evolution, and confines the gradient signal driving each update to the resulting low-rank subspace. Across LLMs of different scales, Ares improves accuracy over widely used optimizers and generalizes across RLVR algorithms and tasks. Results suggest that effective optimization may require optimizers to be designed around the geometry and dynamics of the training process. We release the code and data at https://github.com/RUCAIBox/Ares.

This work develops a geometric theory of aerodynamic promptness for multirotor platforms whose propeller directions depend on a smooth orientation-mechanism configuration. The actuator state consists of the actual signed propeller speeds and the mechanism configuration, and the nonlinear actuator map retains both the signed-quadratic propeller law and the configuration-dependent thrust directions. Constant direction maps represent fixed propellers, while shared dependence on mechanism coordinates represents mechanically coupled tilts. A Riemannian metric on the product actuator manifold compares propeller accelerations and orientation-mechanism rates through physically interpretable scales. Composing the actuator-map differential, the musical isomorphism induced by this metric, and the dual differential defines a task-rate authority map from wrench covectors to wrench-rate vectors. In fixed task coordinates, the square root of the determinant of its matrix defines aerodynamic promptness. Positive promptness is equivalent to local wrench-rate surjectivity, while the associated spectrum resolves directional authority and conditioning. The same construction yields the metric horizontal inverse, the orthogonal projector onto wrench-fiber directions, and task-preserving internal motions that regulate promptness without changing the instantaneous wrench. The construction is related intrinsically to dynamic feedback linearization and specialized to the independently tilting, radially arranged Holocopter and Voliro architectures, clarifying how their established allocation and rank constructions fit within the same actuator-manifold geometry.

Model-internal signals, such as neuron activations and gradients, have been used for instruction data selection, yet how neuron relevance should be characterized remains underexplored. In particular, should selection prioritize the magnitude of relevance or how broadly it is distributed across neurons? To investigate this question, we construct sample-level relevance profiles using AttnLRP-guided attribution and introduce two complementary criteria: Effective Relevance Support (ERS), which measures the effective support of positive relevance, and Positive Relevance Magnitude (PRM), which captures its average strength. Our analyses reveal that these characterizations produce distinct sample rankings and selection preferences despite sharing the same underlying relevance profiles. On Qwen2 models, PRM exhibits stronger associations with activation-based selection, whereas ERS produces substantially different rankings. These differences extend to task composition, within-task sample preferences, and semantic selection patterns, with varying degrees of agreement across backbones. Experiments across three language models and five downstream benchmarks demonstrate the practical value of relevance-guided selection, with ERS achieving the best overall average performance rank among the evaluated methods. Our findings highlight that how neuron relevance is distributed and characterized, rather than its magnitude alone, matters for instruction data selection.

We study the least periods and multiplier orders in two constructions of Mercat for continued fractions with bounded partial quotients. Our main explicit result concerns a family in $\Q(\sqrt{127})$ with partial quotients at most $4$. For every integer $j\geq1$, we prove that its primitive period has length $92j+2$ and its multiplier order has conductor $y_{4j}/4$, where $(4730624+419775\sqrt{127})^k=x_k+y_k\sqrt{127}$. The totally positive unit group of this order has index $4j$ in that of the maximal order. These exact formulas give divisor-sum lower bounds at fixed traces and a lower bound of order $(\log X)^2$ for the number of bounded continued fractions with discriminant at most $X$. We also prove a primitive-period refinement of Mercat's palindromic construction. Combining this refinement with Hensley's counting theorem gives, for every $m\geq2$ and $\eta>0$, at least $X^{\delta_m/2-\eta}$ quadratic fields, up to a positive constant, that admit infinitely many purely periodic continued fractions with partial quotients at most $m$. Here $\delta_m$ is the Hausdorff dimension of the corresponding continued fraction Cantor set.

Plant fibers are increasingly used as sustainable reinforcements in composites, but the intrinsic variability of their microstructure causes substantial scatter in transverse mechanical behavior, complicating composite design. Characterizing this behavior relies on finite element (FE) simulations requiring several minutes of high-performance computing per fiber, making high-throughput characterization across realistic fiber populations impractical. In this study, we propose a deep learning framework replacing this FE bottleneck with a fast pipeline. It includes two coupled recursive U-Nets predicting the step-by-step evolution of fiber deformation and internal stress fields under transverse compression, followed by a regression CNN estimating the transverse Young's modulus from the final stress field. Unlike prior approaches predicting stress fields for fixed configurations or idealized geometries, our framework recursively resolves the full temporal stress evolution for synthetic fibers derived from real hemp cross-sections, with or without a lumen. Trained on 1,000 synthetic fiber geometries with FE ground truth, it reproduces the stress field sequence with a Structural Similarity Index Measure (SSIM) of $0.9574 \pm 0.0074$ and a Root Mean Squared Error (RMSE) of $0.0345 \pm 0.0079$. It estimates transverse Young's modulus with an $R^2$ of $0.938 \pm 0.024$, a Mean Absolute Error (MAE) of $24.31 \pm 1.23$ MPa, and a Mean Absolute Percentage Error (MAPE) of $5.25 \pm 0.91\%$. Inference requires under one second per fiber versus five minutes per FE simulation, drastically reducing computational cost. This offers a fast, reliable tool for mechanical characterization of synthetic plant fibers, with promising applications in designing natural fiber-reinforced composites.

Twisting van der Waals bilayers creates a moir'e stacking field with periodically varying local interlayer registry, enabling spatially patterned polarization. However, a systematic understanding of how this registry-controlled polar topology evolves with twist angle, temperature, and mechanical strain is still lacking. Here, using first-principles-trained deep-potential molecular dynamics simulations, we show that spatially varying interlayer registry governs the polarization texture and can be directly tuned by twist and relative layer deformation. As the twist angle decreases, the moir'e polarization texture evolves from compact, nearly circular vortex-like patterns to extended triangular AB/BA domains. This crossover arises from enhanced lattice relaxation at small twist angles, which expands low-energy, oppositely polarized AB/BA regions and confines in-plane polarization mainly to domain boundaries. Despite this reconstruction, the local in-plane winding remains tied to interlayer registry and persists up to 1000 K, indicating robust topology against thermal fluctuations. We further show that the mechanical response is dictated by whether deformation changes the relative registry: homogeneous deformation of both layers produces only weak distortions, whereas layer-selective deformation strongly reconstructs the moiré polarization texture. A mismatch-matrix registry-mapping model is developed to capture this response, explaining deformation-induced changes in vortex radii at larger twist angles and triangular-domain geometry at smaller twist angles. These results identify interlayer registry as the central control parameter for forming and tuning moir'e polar topology in twisted bilayer h-BN.

Broad-lined H-rich superluminous supernovae (SLSNe II) tend to show signs of interaction, including a UV excess compared to a blackbody function. However, a quantitative analysis of the CSM configuration and the UV excess has so far not been performed for most of the literature sample. Additionally, SN 2023gpw showed signs of asymmetry in its peculiar blackbody and spectral evolution, raising the question of whether similar properties can be found in other SLSNe II. We aim to characterize the circumstellar environment of SLSNe II by searching for signs of asymmetry, quantifying the UV excess, and investigating any IR echoes produced by dust. Diversity among SLSNe II is also explored. We fit blackbody functions to the SEDs of SLSNe II to quantify the UV excess luminosity and its evolution. We use this to investigate mass-loss rates required to produce the excess through interaction. We also investigate the line profiles in SLSN II at late times and compare line velocities to the blackbody radius evolution. We examine public WISE IR images and place constraints on IR echoes. We find mass loss rates of $\sim10^{-4}$ to $\sim0.03\, \mathrm{M_\odot}$~yr$^{-1}$ when assuming all interaction luminosity emerges in the UV, i.e., conservative lower limits for the total mass loss rate. Radii calculated from line velocities in late-time spectra are mostly too large for a spherical interaction photosphere, only compatible with the blackbody radius evolution if the CSM is non-spherical with a low filling factor. This is in some cases supported by a mismatch between spectroscopic and blackbody expansion velocities. Considerable diversity is seen in the sample, probably as a result of different viewing angles and CSM masses. WISE images seem too shallow to observe IR echoes in SLSNe II beyond $z\sim0.1$, but in the nearest event, SN 2020jhm, a likely IR echo is detected, suggesting pre-existing dust.

We study the one-dimensional periodic nonlinear Schrödinger equation with a power-type nonlinear damping, both in the focusing and the defocusing regime. For a sufficiently small damping parameter and initial data close in relative $H^1$ norm to a nonzero spatially homogeneous state, we prove global existence and asymptotic convergence, after a constant phase adjustment, to an explicit homogeneous solution. The \(L^2\) and \(H^1\) norms follow the explicit adiabatic decay law, with the same leading coefficient as the homogeneous solution. We obtain explicit convergence rates, including a \(t^{-1/2}\) bound for the relative spatial perturbation. For every nonconstant initial datum in a small neighborhood of the homogeneous solution, the kinetic energy has a strictly positive leading coefficient and decays one power of time faster than the squared \(L^2\) norm.

The non-Hermitian skin effect is one of the most remarkable topological features of non-conservative physics. It causes a macroscopic accumulation of states at the boundaries of a confined system, opening new ways for controlling and directing waves in non-Hermitian settings. This effect has recently been observed in experiments with Bose-Einstein condensates of exciton polaritons and ultracold bosonic quantum gases. The underlying physics is captured by a mean-field Hamiltonian with a trapping potential and an imaginary gauge field. While prior work has examined the effect of the imaginary gauge field term on the condensate itself, its effect on the collective excitations on top of the condensate remained unexplored. Here, we develop a new theory for the Bogoliubov excitations in a non-Hermitian framework and systematically study their spectrum across different interaction regimes. By analysing the position expectation values, we find that while the repulsive interactions oppose the localisation of the condensate due to the skin effect, the excitations remain strongly affected by the imaginary gauge field. As a consequence, in the presence of harmonic confinement, we predict a strong shift in the dipole oscillation frequency, which can be observed in experiments. This is in contrast to Hermitian systems, where this frequency is fixed by the trap dimensions. Furthermore, we develop a consistent second-quantised field theory of the collective excitations in this non-Hermitian system. Strikingly, we find that a second-quantised treatment removes the shift of the dipole oscillation frequency entirely. This intriguing discrepancy between the two theoretical approaches to the treatment of elementary excitations in a non-Hermitian system can be resolved in experiments.

Market making under realistic order-flow dynamics is challenging due to the clustered, self-exciting nature of order arrivals, which are naturally modeled by non-Markovian Hawkes processes. We propose a model-free reinforcement learning (RL) framework for market making with general Hawkes order-flow dynamics. We first establish non-asymptotic performance bounds that quantify the loss incurred by approximating the infinite-dimensional Hawkes state using a finite collection of exponentially weighted features. Guided by this analysis, we introduce the Hawkes-Structured Network (HSN), a novel neural architecture that encodes historical order flow through a learnable mixture-of-exponentials filter. HSN is trained end-to-end using model-free RL, jointly optimizing the feature representation and quoting policy directly from reward feedback. Experiments on single- and multi-asset market-making problems with mixture-of-exponentials, power-law, and regime-switching kernels demonstrate that HSN outperforms general-purpose neural architectures, achieving higher trading rewards while implicitly recovering the underlying order-flow intensities.

Training LLM agents to interact with users over multiple turns is challenging because the learning signal depends not only on the agent, but also on the user simulator and environment, which jointly shape the agent's experience. Simulated users can be stochastic or inconsistent, while environments may contain unreliable tools, incomplete state coverage, and incorrect verifiers. Prior work mainly addresses the resulting instability through reward shaping or denser supervision, while treating these components as fixed. We instead introduce EAU, a meta-agent framework for environment–agent–user co-evolution. During training, EAU monitors trajectories, tool traces, rewards, and training statistics; diagnoses failures and uninformative interactions; and proposes targeted modifications to the user simulator, environment, reward design, and RL configuration. Validated changes are hot-swapped into the ongoing run, allowing the training setup to evolve together with the policy. These adaptations also persist across runs, so later training can build on previously discovered improvements rather than restarting from a fixed setup. We enable this process through an editable symbolic representation of user and environment dynamics, while the agent remains a neural LLM optimized with RL. Across three interactive-agent benchmarks and two backbone models, EAU consistently outperforms prior RL methods, improving the overall score over the strongest baseline by 14.7–15.0% and increasing successful task completion on ColBench by up to 36.7%, showing that co-evolving the training system with the policy can substantially improve multi-turn RL.

Safe robot navigation in unknown, dynamic environments requires more than geometric collision checking: a robot still far from an obstacle may be unable to avoid it because of its speed, orientation, or the obstacle's motion. Hamilton–Jacobi (HJ) reachability analysis captures this in a value function whose sign separates states that admit a safe continuation from those where collision is unavoidable, but computing it online for every newly observed environment is too expensive. This dissertation trains neural implicit representations offline on reachability solutions to give optimization-based controllers this information in real time. Since the value function never exceeds the constraint, it equals a directly computed constraint, such as a signed distance, minus a nonnegative dynamics correction. Learning only this correction keeps represented obstacles outside the predicted safe set despite approximation errors. The first two of five methods use the learned function as a terminal constraint in model predictive control, for static local environments and predicted obstacle motion. The next two use it as a barrier candidate in control barrier function safety filters, for static environments and, through pairwise barriers in relative coordinates, for a varying number of moving obstacles. Simulations and hardware experiments on ground and aerial robots show better collision avoidance than geometric and hand-designed baselines, especially for short horizons and moving obstacles. The fifth method replaces the grid-based offline solver, which limits the first four to low-dimensional models. For control-affine dynamics with polytopic inputs, the HJ Hamiltonian is maximized at a vertex, so a parallelizable tree search over vertex inputs can generate training labels. With a loss from the HJ variational inequality, these labels yield barrier candidates for systems with up to 13 states.

Oxygen-vacancy formation and diffusion play important roles in determining the electronic and atomic transport properties of SrTiO$_3$ (STO). Accurate analysis of such point defects requires sufficiently large-scale and long-time molecular dynamics (MD) simulations; however, direct investigations of oxygen-vacancy dynamics using ab initio MD (AIMD) based on density functional theory (DFT) are limited to relatively small systems and short time scales because of their high computational cost. In this study, we develop a neural network potential (NNP) for pristine and oxygen-deficient STO using a reference dataset generated from AIMD simulations. The trained NNP model accurately reproduces the DFT reference energies, atomic forces, and virials for both pristine STO and STO containing an oxygen vacancy. The NNP also reproduces the supercell-size dependence of the total energies and oxygen-vacancy formation energies, including the formation energy extrapolated to the dilute limit. Large-scale and long-time MD simulations using the NNP (NNP-MD) are then performed to investigate oxygen-vacancy diffusion. The resulting oxygen-vacancy diffusion coefficients show substantially better agreement with experimental data than those obtained from conventional classical MD simulations. An Arrhenius analysis yields an oxygen-vacancy migration enthalpy of 0.64 eV, in close agreement with the experimental value of 0.67 eV. These results demonstrate that NNPs trained on first-principles data provide an accurate and computationally efficient framework for investigating defect formation and long-time vacancy transport in perovskite oxides.

Neural networks (NNs) have been employed in various ways to accelerate the solution of multi-parametric optimization problems (OPs), which prominently arise in model predictive control (MPC). Early approaches focused on approximating the parametric solution (e.g., the optimal control law) directly by NNs. More recently, learning-based techniques have been used to emulate or enhance solver iterations. For the direct approximation of the parametric solution, it has been demonstrated that exploiting structural properties of the underlying OP facilitates the design of suitable NN architectures. In this paper, we show that structural analysis can also be leveraged to systematically integrate learning into classical optimization algorithms, thereby enhancing their performance. We formalize our concept for the case of multi-parametric quadratic programs (mpQPs), which frequently arise in linear-quadratic MPC, as a representative application. More precisely, we demonstrate that tailored NNs enable a parameter-dependent fine-tuning of the step sizes in a standard dual projected gradient scheme. The design of the NNs is guided by the observation that optimal step sizes, which permit obtaining the exact optimal solution in finitely many iterations, are piecewise constant functions over the parameter space (e.g., the state space in MPC). We establish key theoretical properties of the proposed approach and illustrate its effectiveness in a numerical case study.