arXiv:2606.02248v1 Announce Type: new
Abstract: Large language models solve complex problems by generating lengthy chains of explicit reasoning tokens. While effective, this makes reasoning expensive, length-sensitive, and constrained to (discrete) natural language. While latent reasoning offers a continuous alternative, determining useful structures for intermediate latent states is an open challenge. In this paper, we formulate latent reasoning as a geometric path-approximation problem within the model's pretrained token-embedding space. We introduce Geometric Latent Reasoning (GLR), which uses a lightweight transition head to predict iterative direction updates in embedding space. Using textual chain-of-thought traces as anchors, GLR learns to approximate discrete reasoning trajectories while permitting continuous deviations from exact token embeddings. Evaluations on mathematical reasoning benchmarks using Qwen3 models reveal an emergent phenomenon: geometric latent reasoning induces substantially shorter generations without an explicit length objective. By replacing early explicit reasoning with continuous latent steps, models often reach correct answers using substantially fewer total generation steps. These findings suggest that continuous trajectories act as compact intermediate reasoning states, exposing a new tradeoff between latent computation budget, output length, and accuracy.
Science Journals
arXiv:2603.02238v2 Announce Type: replace
Abstract: Length generalization is a key property of a learning algorithm that enables it to make correct predictions on inputs of any length, given finite training data. To provide such a guarantee, one needs to be able to compute a length generalization bound, beyond which the model is guaranteed to generalize. This paper concerns the open problem of the computability of such generalization bounds for C-RASP, a class of languages which is closely linked to transformers. A positive partial result was recently shown by Chen et al. for C-RASP with only one layer and, under some restrictions, also with two layers. We provide complete answers to the above open problem. Our main result is the non-existence of computable length generalization bounds for C-RASP (already with two layers) and hence for transformers. To complement this, we provide a computable bound for the positive fragment of C-RASP, which we show equivalent to fixed-precision transformers. For both positive C-RASP and fixed-precision transformers, we show that the length complexity is exponential, and prove optimality of the bounds.
arXiv:2605.31545v1 Announce Type: new
Abstract: As Large Language Models (LLMs) evolve from general-purpose assistants to user-centric agents, personalization has become central to aligning model behavior with individual preferences, making the evaluation of personalized alignment a critical bottleneck. Existing evaluation methods-ranging from automatic metrics to LLM-as-a-judge approaches-fail to capture subjective, user-specific preferences embedded in long-term interaction histories. We identify three essential principles for reliable and effective personalized evaluation: Representativeness, User-Consistency, and Discriminativeness. To address these principles, we introduce Personalized Evaluation as Learning, a paradigm that formulates personalized evaluation as a learning problem rather than a static judgment. Under this paradigm, we propose PARL (Preference-Aware Rubric Learning for Personalized Evaluation), a framework that learns to induce preference-aware evaluation rubrics directly from raw user histories and performs a self-validation mechanism to ensure consistency with the user's preferences. PARL integrates rubric induction with a discriminative reinforcement learning objective that contrasts user-authored responses against competitive personalized model outputs, enabling the learned rubrics to capture precise, user-specific decision boundaries. Experiments on real-world personalized text generation tasks show that PARL consistently induces high-fidelity rubrics that reliably identify user-aligned responses and generalize across users and tasks, while capturing stable stylistic preferences and fine-grained evaluative patterns. To ensure reproducibility, our code is available at https://github.com/SnowCharmQ/PARL.
arXiv:2605.31560v1 Announce Type: new
Abstract: Repurposing natural gas pipelines for hydrogen transport requires understanding how external defects, like dents and gouges, affect structural integrity under H$_2$ exposure. To address this, we combine experiments with a new hydrogen embrittlement model aimed at large plastic straining scenarios, which integrates: (i) multi-trap hydrogen transport, (ii) finite-strain plasticity, and (iii) a hydrogen- and triaxiality-dependent damage law. Each constituent of the model is validated with experiments on X65 pipeline steel: (i) hydrogen permeation, (ii) full-scale pipe-indentation, and (iii) mechanical testing at different hydrogen and triaxiality levels. The validated model is used to study \textit{passive} (indent before H$_2$ exposure) and \textit{active} (indent with H$_2$) dents and gouges. Results reveal that hydrogen does not significantly increase the damage severity of those defects, unless hydrogen egress is completely precluded at the outer surface of a pipeline that is being pressurised internally and contains a pre-existing \textit{passive} dent with a gouge.
arXiv:2605.31575v1 Announce Type: new
Abstract: Scalable information retrieval testing needs corpora that are large enough to stress index construction, ranking latency, query routing, and evaluation tooling, yet human-judged test collections remain expensive and may be unavailable when documents are private or still under design. This paper introduces SPECTRA, a reproducible framework for generating synthetic text corpora and retrieval test collections through a separation of latent topical structure, surface text realization, metadata controls, query intent generation, and deterministic relevance oracles. The framework is intended as a diagnostic complement to Cranfield-style and TREC-style evaluation, not as a replacement for human assessment. A single-process Python prototype generated corpora up to 60,000 documents and 9.61 million tokens while preserving controllable long-tail vocabulary growth and producing graded relevance labels for 96 queries. In the local simulation study, generation remained close to linear at roughly 12K to 14K documents per second, estimated Zipf slopes stayed near 0.86 in absolute value, and increasing cross-topic distractor text reduced BM25 nDCG@10 from 1.00 at 2% distractors to 0.43 at 36% distractors. These results show that lightweight synthetic corpora can expose retrieval-system scaling and failure modes before costly collection construction begins.
arXiv:2605.30509v1 Announce Type: cross
Abstract: We present improved bounds for estimating discrete probability distributions under the $\ell_\infty$ norm. These include minimax bounds in expectation and high-probability tail bounds. We resolve some of the open questions posed in Kontorovich and Painsky (JMLR, 2025) -- including a fully empirical version of the tightest risk bound they presented and identifying the form of the worst-case extremal distribution. Encouraging empirical results are reported as well.
arXiv:2605.30735v1 Announce Type: cross
Abstract: In tensor dynamics for liquid crystals derived from molecular models, a common problem is closure approximation. For rod-like molecules, the Bingham closure has proved to outperform other methods because it inherits the gradient flow structure of the molecular model, but is difficult to achieve efficient computations maintaining the gradient flow structure. We propose a closure approximation by the quasi-entropy that has been successfully applied to the free energy, based on which we construct the tensor gradient flow. The quasi-entropy closure has the same symmetry properties as the Bingham closure. The resulting tensor gradient flow is able to constrain the eigenvalues of the tensor within the physical range, guaranteeing the positive definiteness of the dissipation operator given by the higher-order tensors. The quasi-entropy closure is easy to implement since it can be reduced to minimizing an elementary function of three variables. As a result, we construct a numerical scheme preserving the eigenvalue constraints and energy dissipation, with the closure approximation decoupled from solving the scheme. Numerical simulations are carried out for the interface between the isotropic and the uniaxial nematic phase, as well as the defect evolutions, where the higher-order tensors indeed make a difference.
arXiv:2605.31268v1 Announce Type: new
Abstract: We present Mellum 2, an open-weight 12B-parameter Mixture-of-Experts (MoE) language model with 2.5B active parameters per token. Mellum 2 is a general-purpose language model specialized in software engineering, spanning code generation and editing, debugging, multi-step reasoning, tool use and function calling, agentic coding, and conversational programming assistance, and it is the successor to the completion-focused 4B dense Mellum model. The architecture builds on the Mixture-of-Experts (64 experts, 8 active) and combines Grouped-Query Attention with 4 KV heads, Sliding Window Attention on three of every four layers, and a single Multi-Token Prediction head that doubles as both an auxiliary pre-training objective and a built-in draft model for speculative decoding; each choice was validated by ablation with inference efficiency on commodity GPUs as a design constraint. Pre-training spans approximately 10.6 trillion tokens through a three-phase curriculum that progressively shifts the mixture from diverse web data toward curated code and mathematical content, optimized with Muon under FP8 hybrid precision and a Warmup-Hold-Decay schedule with linear decay to zero. The pre-trained base is extended to a 128K context window via a layer-selective YaRN and then post-trained in two stages (supervised fine-tuning followed by RLVR), yielding two released variants: an Instruct model that answers directly and a Thinking model that emits an explicit reasoning trace before its final answer. Across code generation, math and reasoning, tool use, knowledge, and safety benchmarks, Mellum 2 is competitive with open-weight baselines in the 4B-14B range while running at the per-token compute of a 2.5B dense model. We release the base, instruct, and thinking checkpoints, together with this report on the architecture decisions, data pipeline, and training recipe behind them, under the Apache 2.0 license.
arXiv:2605.31257v1 Announce Type: new
Abstract: Fraud detection in payment networks relies on labels generated through heterogeneous and imperfect observation processes, yet existing approaches treat fraud as a homogeneous binary variable. We show that this assumption is structurally incorrect and leads to provable inefficiency. We introduce an observation-mechanism taxonomy that partitions fraud into five classes, each defined by a distinct censorship and labeling pipeline. We prove that estimating fraud rates separately by class and aggregating strictly dominates pooled estimation, with the efficiency gap characterized as a Jensen penalty arising from heterogeneous observation rates. For each class, we derive the binding theoretical constraint on detection, including endogenous label corruption, structural non-observability, and feature non-informativeness. These results establish that fraud detection is fundamentally a collection of distinct estimation problems, each governed by its own observation structure and detection limit.
arXiv:2605.31253v1 Announce Type: new
Abstract: With strong evidence in the literature showing that fairness and truthfulness are incompatible, there is a recent line of work focusing on the fairness properties of equilibria of simple fair division mechanisms, especially Round-Robin. We consider the Envy Cycle Elimination (E-C-E) procedure of Lipton et al. [23], one of the most versatile tools in fair division. While this simple and intuitive algorithm achieves allocations that are envy-free up to one item (EF1) for any number of agents and general monotone valuation functions, surprisingly little is known about its behavior when agents act strategically. We demonstrate how the presence of incentives, although highly natural and relevant for the majority of applications, completely removes the intuitive clarity in the algorithm's execution, even for a few agents and very simple valuation functions. Additionally, while in the standard algorithmic setting there is great flexibility in how the details of E-C-E are implemented, here additional specifications are needed before the procedure is clearly defined, the choice of which has a potentially huge impact on the agents' behavior. Despite these obstacles, for various natural versions of E-C-E, we give the first results on the existence of Pure Nash Equilibria of the resulting mechanisms, and show there exist versions where fairness guarantees are approximately preserved for agents who play best responses.
arXiv:2605.31273v1 Announce Type: new
Abstract: While self-supervised Contrastive Reinforcement Learning (CRL) has shown remarkable depth-scaling capabilities, successfully using networks over 64 layers, scaled CRL still struggles with long-horizon goal-conditioned planning due to the uniformity-tolerance dilemma inherent in contrastive losses. We introduce Survival Reinforcement Learning (SRL), an online classification-based alternative that extends the survival value learning framework by maximizing the agent's dwell time at target goals. SRL bypasses the structural constraints of CRL and mitigates the "bang-bang" control solutions inherent to survival frameworks, which often induce undesirable behavior in complex dynamical systems. Evaluated across diverse robotic benchmarks, scaled SRL matches state-of-the-art CRL on manipulation tasks and outperforms it by 2x to 8x on stable, long-horizon locomotion tasks. Our results provide strong additional evidence that classification-based methods may serve as a key primitive in the broader effort to scale reinforcement learning.
arXiv:2605.31306v1 Announce Type: cross
Abstract: We introduce the notion of worst-case posterior and worst-case likelihood sensitivity. These measure, respectively, the sensitivity of the expected cost to worst-case perturbations of the posterior distribution and worst-case perturbations of the likelihood of a Bayesian model. Each defines a quantitative measure of robustness. A decision maker concerned about the sensitivity of the out-of-sample expected cost to deviations from her assumptions will want a decision for which both sensitivities are small. We derive posterior and likelihood sensitivities for uncertainty sets defined in terms of deviation measures. Posterior sensitivity vanishes when the posterior variance shrinks to zero, which occurs when parameter uncertainty is eliminated from learning. Parameter learning does not eliminate likelihood sensitivity. A distributionally robust formulation of a Bayesian optimization problem makes a near-Pareto-optimal tradeoff between performance (expected cost) and robustness (posterior and likelihood sensitivity).
arXiv:2605.31345v1 Announce Type: cross
Abstract: Compositional data must be analysed through log-ratios: scale invariance, the defining axiom of the field, leaves no alternative. The centred log-ratio divides by the geometric mean of every part, so a single contaminated component shifts every centred-log-ratio coordinate at once, displacing the log-ratio vector by a fixed amount that no choice of coordinates can reduce. We develop a theory of cellwise contamination on the simplex around this observation. A scale-invariant contamination model built from multiplicative perturbation combines with a propagation theorem showing that corruption of a single raw part induces a rank-one shift of the log-ratio vector, with direction determined by the contrast matrix. The resulting perturbation pattern is not equivalent to any independent cellwise contamination model in log-ratio coordinates -- so standard Euclidean cellwise methods applied to log-ratios are ill-posed under the simplex contamination mechanism. For estimators whose Euclidean cellwise breakdown is witnessed by a column-concentrated configuration -- a class including MCD, $S$-, $\tau$-, and coordinate-wise $M$-estimators of location and scatter -- the cellwise breakdown value on the simplex is reduced by the factor $(D-1)/D$ relative to its Euclidean counterpart, a reduction that is tight and arises purely from the normalisation mismatch between $nD$ raw cells and $n(D-1)$ ilr cells. The cellwise influence function for the variation matrix carries a diagnostic fingerprint: contamination of a single part inflates exactly one row and column, identifying the responsible component. These results form the theoretical foundation for cellwise-robust methods on the simplex; a companion paper develops a cellwise-robust PCA estimator that exploits the propagation geometry and demonstrates it on simulated and geochemical data.
arXiv:2511.04393v2 Announce Type: replace
Abstract: Large language models (LLMs) are increasingly deployed as "agents" for decision-making (DM) in interactive and dynamic environments. Yet, since they were not originally designed for DM, recent studies show that LLMs can struggle even in basic online DM problems, failing to achieve low regret or an effective exploration-exploitation tradeoff. To address this, we introduce Iterative Regret-Minimization Fine-Tuning (Iterative RMFT), a post-training procedure that repeatedly distills low-regret decision trajectories back into the base model. At each iteration, the model rolls out multiple decision trajectories, selects the k-lowest regret ones, and fine-tunes itself on them. Unlike prior methods that (a) distill action sequences from known DM algorithms or (b) rely on manually crafted chain-of-thought templates, our approach leverages the regret metric to elicit the model's own DM ability and reasoning rationales. This reliance on model-generated reasoning avoids rigid output engineering and provides more flexible, natural-language training signals. Empirical results show that Iterative RMFT improves LLMs' DM performance across diverse models - from Transformers with numerical input/output, to open-weight LLMs, and advanced closed-weight models like GPT-4o mini. Its flexibility in output and reasoning formats enables generalization across tasks with varying horizons, action spaces, reward processes, and natural-language contexts. Finally, we provide theoretical insight showing that a single-layer Transformer under this paradigm can act as a no-regret learner in a simplified setting. Overall, Iterative RMFT offers a principled and general post-training framework for enhancing LLMs' decision-making capabilities.
arXiv:2605.30578v1 Announce Type: new
Abstract: Adversarial patches are physical patterns attached to real objects to mislead AI vision systems. Their real-world risk is not determined by a single successful prediction, but by whether they remain effective after deployment under changing viewpoints, distances, and scene conditions. We refer to this property as scene robustness, the effectiveness of a deployed patch across conditions in a real environment. Yet existing evaluations do not measure scene robustness well: real image benchmarks are realistic but fixed, while simulators are controllable but not grounded in a specific real scene.
We present AdvScene, a scene-grounded framework for measuring the scene robustness of adversarial patches in reconstructed real environments. AdvScene reframes evaluation as operational measurement: given a fixed deployed patch, it characterizes the patch's operational envelope - where and when the attack succeeds - as a function of viewpoint, distance, and scene context. A key challenge is that the attack is typically defined only in a single anchor view, while evaluation requires a representation that remains faithful under viewpoint changes. We formalize this as a constrained lifting problem and introduce Adversarial Patch-to-Scene Embedding (APSE), which resolves cross-view ambiguity while preserving attack-critical appearance and enforcing locality, target-surface attachment, and cross-view consistency. We validate AdvScene using real-world physical data and conduct a comprehensive evaluation of existing adversarial patches. Our results show that AdvScene reveals substantial scene-dependent variation in attack effectiveness that is not captured by existing image-centric or simulator-based evaluations.
arXiv:2605.30359v1 Announce Type: new
Abstract: Generating high-performance GPU kernels remains challenging due to the need for both correctness and hardware-aware optimization. While large language models (LLMs) show promise in code generation, they often fail to produce kernels that are both correct and efficient.
We propose Kernel Foundry, a diagnosis-driven evolutionary framework for automatic GPU kernel optimization. Our method combines expert-guided, retrieval-augmented initialization with a multi-island evolutionary search, where candidate kernels are iteratively refined using structured diagnostic feedback. A centralized experience library accumulates reusable optimization knowledge to guide subsequent evolution, while explicit mechanisms prevent cheating behaviors that bypass kernel-level computation.
Experiments on KernelBench show that our method consistently improves both correctness and performance over strong baselines, achieving up to 100% correctness on Level~2.
arXiv:2409.14583v4 Announce Type: replace
Abstract: LLM bias evaluation is critical as large language models (LLMs) increasingly influence high-stakes decisions. This paper provides a comprehensive assessment of gender, racial, and age disparities in leading LLMs, revealing that debiasing efforts often create new fairness trade-offs. Recent advancements in LLMs have been notable, yet widespread enterprise adoption remains limited due to various constraints. This paper examines bias in LLMs - a crucial issue affecting their usability, reliability, and fairness. Our study evaluates gender bias in occupational scenarios and gender, age, and racial bias in crime scenarios across four leading LLMs released in 2024: Gemini 1.5 Pro, Llama 3 70B, Claude 3 Opus, and GPT-4o. Findings reveal that LLMs often depict female characters more frequently than male ones in various occupations, showing a 37% deviation from US BLS data. In crime scenarios, deviations from US FBI data are 54% for gender, 28% for race, and 17% for age. Critically, we observe that efforts to reduce gender and racial bias often lead to outcomes that may over-index one sub-class, potentially exacerbating disparities - a "debiasing paradox" that highlights the limitations of current bias mitigation techniques and underscores the need for more effective approaches.
arXiv:2507.06161v2 Announce Type: replace
Abstract: Smoothing a signal based on local neighborhoods is a core operation in machine learning and geometry processing. On well-structured domains such as vector spaces and manifolds, the Laplace operator derived from differential geometry offers a principled approach to smoothing via heat diffusion, with strong theoretical guarantees. However, constructing such Laplacians requires a carefully defined domain structure, which is not always available. Most practitioners thus rely on simple convolution kernels and message-passing layers, which are biased against the boundaries of the domain. We bridge this gap by introducing a broad class of smoothing operators, derived from general similarity or adjacency matrices, and demonstrate that they can be normalized into diffusion-like operators that inherit desirable properties from Laplacians. Our approach relies on a symmetric variant of the Sinkhorn algorithm, which rescales positive smoothing operators to match the structural behavior of heat diffusion. This construction enables Laplacian-like smoothing and processing of irregular data such as point clouds, sparse voxel grids or mixture of Gaussians. We show that the resulting operators not only approximate heat diffusion but also retain spectral information from the Laplacian itself, with applications to shape analysis and matching.
arXiv:2410.15475v2 Announce Type: replace
Abstract: Multimodal learning aims to preserve as much task-related information as possible from different inputs. However, current fusion designs often distort the feedback loop to feature extractors. Aggressively merging modalities entangles their representations, making the feature extractors fragile to incomplete inputs. Meanwhile, attempting to separate features via auxiliary losses frequently introduces optimization conflicts that distract from the primary task. We propose the Self-Consistent Field Autoencoder (SCFAE) to provide a better path for task gradients. Our method follows the self-consistent field principle to balance task learning with feature organization, thereby minimizing mutual information. We use small autoencoders for each modality to keep information intact. The task loss acts as a driving force to select predictive features. The reconstruction loss acts as a constraint to separate these features into independent subspaces. These dual objectives operate through complementary feature subspaces, thereby mitigating optimization interference. We evaluate SCFAE on audio-visual-text, audio-visual, and image-video benchmarks. Results show that SCFAE handles missing data and unequal input sizes more robustly via a simple structure. Gradient analysis confirms that SCFAE avoids conflicts and maintains stable training dynamics.
arXiv:2411.06844v2 Announce Type: replace
Abstract: The numerical method of dynamical low-rank approximation (DLRA) has recently been applied to various kinetic equations showing a significant reduction of the computational effort. In this paper, we apply this concept to the linear Boltzmann-Bhatnagar-Gross-Krook (Boltzmann-BGK) equation which due its high dimensionality is challenging to solve. Inspired by the special structure of the non-linear Boltzmann-BGK problem, we consider a multiplicative splitting of the distribution function. We propose a rank-adaptive DLRA scheme making use of the basis update & Galerkin integrator and combine it with an additional basis augmentation to ensure numerical stability, for which an analytical proof is given and a classical hyperbolic Courant-Friedrichs-Lewy (CFL) condition is derived. This allows for a further acceleration of computational times and a better understanding of the underlying problem in finding a suitable discretization of the system. Numerical results of a series of different test examples confirm the accuracy and efficiency of the proposed method compared to the numerical solution of the full system.
arXiv:2412.02926v3 Announce Type: replace
Abstract: In this third part of a multi-paper series, we present quantitative image reconstruction results from aerial measurements of eight different surrogate distributed gamma-ray sources on flat terrain. We show that our quantitative imaging methods can accurately reconstruct the expected shapes, and, after appropriate calibration, the absolute activity of the distributed sources. We conduct several studies of imaging performance versus various measurement and reconstruction parameters, including detector altitude and raster pass spacing, data and modeling fidelity, and regularization type and strength. The imaging quality performance is quantified using various quantitative image quality metrics. Our results confirm the utility of point source arrays as surrogates for truly distributed radiological sources, and advance the quantitative capabilities of Scene Data Fusion gamma-ray imaging methods.
arXiv:2502.04554v2 Announce Type: replace
Abstract: Data selection has emerged as a crucial downstream application of data valuation, yet the theoretical foundations for using data values in selection remain underexplored. We reformulate data selection as a sequential decision-making problem where the optimal selection sequence arises from dynamic programming, and data values can be understood as encodings of this optimal sequence. This framework unifies and reinterprets existing methods like Data Shapley through the lens of approximate dynamic programming, revealing them as myopic linear approximations to the sequential problem. We further analyze how selection optimality degrades with utility curvature under submodularity, explaining when and why these approximations fail. To bridge theory and practice, we propose an efficient bipartite graph-based surrogate that preserves submodular structure while enabling scalable greedy selection with provable guarantees. Experiments on classical ML benchmarks and large-scale LLM fine-tuning data selection demonstrate substantial improvements over existing methods. Code is publicly available at https://github.com/frankhlchi/SeqDataVal
arXiv:2503.05846v3 Announce Type: replace
Abstract: Large Language Models (LLMs) have achieved impressive progress across a wide range of tasks, yet their heavy reliance on English-centric training data leads to significant performance degradation in non-English languages. While existing multilingual prompting methods emphasize reformulating queries into English or enhancing reasoning capabilities, they often fail to incorporate the language- and culture-specific grounding that is essential for some queries. To address this limitation, we propose EMCEE (Extracting synthetic Multilingual Context and merging), a simple yet effective framework that enhances the multilingual capabilities of LLMs by explicitly extracting and utilizing query-relevant knowledge from the LLM itself. In particular, EMCEE first extracts synthetic context to uncover latent, language-specific knowledge encoded within the LLM, and then dynamically merges this contextual insight with reasoning-oriented outputs through a judgment-based selection mechanism. Extensive experiments on four multilingual benchmarks covering diverse languages and tasks demonstrate that EMCEE consistently outperforms prior approaches, achieving an average relative improvement of 16.4% overall and 31.7% in low-resource languages.
arXiv:2508.11911v2 Announce Type: replace
Abstract: We introduce a novel data-driven symplectic induced-order modeling (ROM) framework for high-dimensional Hamiltonian systems that unifies latent-space discovery and dynamics learning within a single, end-to-end neural architecture. The encoder-decoder is built from Henon neural networks (HenonNets) and may be augmented with linear SGS-reflector layers. This yields an exact symplectic map between full and latent phase spaces. Latent dynamics are advanced by a symplectic flow map implemented as a HenonNet. This unified neural architecture ensures exact preservation of the underlying symplectic structure at the reduced-order level, significantly enhancing the fidelity and long-term stability of the resulting ROM. We validate our method through comprehensive numerical experiments on canonical Hamiltonian systems. The results demonstrate the method's capability for accurate trajectory reconstruction, robust predictive performance beyond the training horizon, and accurate Hamiltonian preservation. These promising outcomes underscore the effectiveness and potential applicability of our symplectic ROM framework for complex dynamical systems across a broad range of scientific and engineering disciplines.
arXiv:2509.19111v2 Announce Type: replace
Abstract: Synchronous reference frame phase-locked loop (SRF-PLL) techniques are widely used for interfacing and control applications in the power systems and energy conversion at large. Since a PLL system synchronizes its output with an exogenous harmonic signal, often 3-phases voltage or current, the locking of the frequency and phase angle depends on the performance of the feedback loop with at least two integrator terms, and on the distortions of the measured input quantities. For the conventional SRF-PLL with a proportional-integral (PI) control in feedback, we are providing a robust design which maximizes the phase margin and uses the normalization scheme for yielding the loop insensitive to the input amplitude variations. The main improvement in the transient behavior and also in tracking of frequency ramps is achieved by using the robust feed-forward frequency estimator, which is model-free and suitable for the noisy and time-varying harmonic signals. The proposed feed-forward-feedback SRF-PLL scheme is experimentally evaluated on the 3-phases harmonic currents from a standard PMSM drive with the varying angular speeds and loads. Both, the tracked angular frequency and locked phase angle are assessed as performance indicators of the proposed SRF-PLL with feedforwarding.