arXiv:2607.18077v1 Announce Type: new
Abstract: What gives the Bellman equation its form? We show that the recursive properties of optimal value functions follow from three conditions: that the dynamics decomposes through sufficient statistics, that the return decomposes recursively, and that the aggregation of uncertainty is compatible with both. When all three conditions hold on a common state, the Bellman equation arises from their mutual consistency; when one fails, tractability can often be recovered by augmenting the state or by deforming return or dynamics. The same conditions are shown to give rise to three dualities: one between probability and return, one between return and aggregation, and one between aggregation and probability. Our framework reveals these dualities as arising from a single construction, unifying methods developed separately across reinforcement learning, control, and decision theory.
Science Journals
arXiv:2607.18100v1 Announce Type: new
Abstract: Extended reasoning has become standard for frontier Large Language Models (LLMs), yet the trajectories these models produce remain largely uncontrollable. Existing methods for shaping how a model reasons are prompt based approaches and operate at the input level, offering no fine-grained control over the reasoning process itself. Related work analyzes and discovers latent transition dynamics in the reasoning traces from Large Language Models. Building on this, we statistically characterize these states, and show that failure trajectories get stuck in self-loops, exhausting the token budget without progress toward the final answer. To intervene on these failures, We propose SOPHIA: Steering Of reasoning Processes via Hidden-state Intervention and Activations. We treat each reasoning trace as a sequence of latent states rather than an unstructured texts, and investigate whether inference time interventions can provide fine-grained control over the self-looping reasoning process. We classify every prefix to a latent state, record step level transitions, and use them to construct a bank of steering vectors indexed by state pairs. At inference time, a controller infers the current state and, given a target state, retrieves the corresponding vector and can also detect self-loops online from the transition structure to prevent the model from sinking into a reasoning black hole. Through extensive experiments, our method reliably intervenes on self-loop failures, with steering vectors that generalize to different state pairs. End task accuracy and token efficiency indicate that fine-grained controllability results in better reasoning quality.
arXiv:2607.18012v1 Announce Type: new
Abstract: We introduce a physics-informed neural network (PINN) approach for designing phase profiles in flat optics that reshape an incident beam into a prescribed target intensity distribution. The method solves Monge--Amp\`ere beam-shaping equations associated with energy-conserving ray mappings generated by a phase-only optical element. We treat both finite-distance and far-field targets using a generalized-Snell-law formulation. The learned phase profiles are validated by scalar diffraction simulations and compared with conventional phase-retrieval methods such as Gerchberg--Saxton. To our knowledge, this is the first time a PINN has been used for beam shaping problems in flat optics.
arXiv:2607.17841v1 Announce Type: new
Abstract: Modern DBMSs expose multiple configurable components (e.g., knobs, query hints, and indexes) that jointly determine query performance. Multi-component tuning is challenging due to the large combinatorial search space and the difficulty of learning effective tuning policies under limited feedback. Existing approaches still rely on blind search over the configuration space and interaction-heavy policy learning, leading to high tuning overhead and limited performance gains. Recent advances in large language models (LLMs) enable knowledge-driven tuning, but existing LLM-based methods fail to effectively exploit online feedback and historical observations, often converging prematurely to suboptimal configurations.
In this paper, we present EvoTune, a memory-aware evolution framework for multi-component DBMS tuning. EvoTune first localizes a query-specific high-impact subspace via collaborative diagnosis, which combines lightweight pattern learning with LLM-based reasoning. It further introduces a utility-aware retrieval policy that selects informative observations based on their resulting long-term performance improvement, instead of similarity-based retrieval. To support continual improvement, EvoTune organizes tuning feedback into a hierarchical memory and incrementally refines both subspace localization and tuning policies without requiring LLM fine-tuning. Extensive experiments show that EvoTune consistently outperforms state-of-the-art baselines, achieving up to 44.5% performance improvement under the same tuning budget and reaching the best competing baseline's final performance up to 3.9X faster.
arXiv:2411.10921v2 Announce Type: replace
Abstract: Accurate forecasts of distributed solar generation are necessary to maintain grid stability amid the increased uptake of distributed solar photovoltaic (PV) systems. However, the high variability of solar generation over short time intervals (seconds to minutes) caused by cloud movement makes this forecasting task difficult. To address this, using cloud images, which capture the second-to-second changes in cloud cover affecting solar generation, has shown promise. Recently, deep neural networks with attention that focus on important regions of an image have been applied with success in many computer vision applications. However, whether such methods provide meaningful benefits for cloud movement forecasting, and how such improvements propagate through to downstream solar generation forecasting accuracy, remains under-explored. In this study, we conduct a large-scale empirical investigation of the impact of attention-based cloud forecasting on solar generation forecasting, addressing a gap that has been overlooked in the literature. To this end, we develop a pipeline that incorporates an attention-enhanced convolutional long short-term memory network and an existing self-attention-based video prediction method to forecast cloud movement using satellite imagery. The effectiveness of the resulting cloud forecasts is evaluated through their downstream impact on solar forecasting across 50 PV sites in Australia. We further provide insights into the cloud conditions under which attention-based cloud forecasting methods yield the most significant improvements in downstream solar forecasting accuracy. We find that for clouds at high altitudes, the cloud predictions obtained using attention-based methods result in solar forecast skill score improvements of 5.86% or more compared to non-attention-based methods.
arXiv:2512.05292v3 Announce Type: replace
Abstract: In commercial robotic systems, it is common to encounter a closed inner-loop torque controller that is not user-modifiable. However, the outer-loop controller, which sends kinematic commands such as position or velocity for the inner-loop controller to track, is typically exposed to users. In this work, we focus on the development of an easily integrated add-on at the outer-loop layer by combining disturbance rejection control and robust control barrier function for high-performance tracking and safe control of the whole dynamic system of an industrial manipulator. This is particularly beneficial when 1) the inner-loop controller is imperfect, unmodifiable, and uncertain; and 2) the dynamic model exhibits significant uncertainty. Stability analysis, formal safety guarantee proof, and hardware experiments with a PUMA robotic manipulator are presented. Our solution demonstrates superior performance in terms of simplicity of implementation, robustness, tracking precision, and safety compared to the state of the art. A demonstration video is available at https://youtu.be/e0palGVU_50.
arXiv:2607.17857v1 Announce Type: new
Abstract: Deep learning models excel in visual recognition but suffer severe performance drops when training labels are corrupted by noise. Under label noise prior work cannot learn accurate similarities and thus misguide the learning process. In this paper, we uncover a complementary and novel phenomenon, Dissimilarity Invariance, whereby semantic dissimilarity between unrelated samples remains stable despite label noise. Leveraging this insight, we propose NegScale, a plug-and-play framework that shifts focus from fragile similarity to robust dissimilarity. NegScale integrates: (1) Structured Negative Orthogonality Penalty (SNOP), enforcing subspace orthogonality for unrelated samples; and (2) Dissimilarity-Calibrated Similarity Adjustment (DCSA), suppressing spurious similarity using dissimilarity anchors. We also give theoretical analysis that proves Dissimilarity Invariance and the effectiveness of NegScale. Empirical results demonstrate that NegScale consistently outperforms state-of-the-art baselines, establishing new benchmarks on CIFAR with synthetic noise and real-world datasets.
arXiv:2607.16269v1 Announce Type: cross
Abstract: Integrated sensing and communications (ISAC) is moving from proof-of-concept demonstrations to system-level deployment in sixth-generation (6G) networks. Because sensing and communication share hardware, spectrum, and waveform resources, ISAC design now involves many tightly coupled choices, including waveform selection, sensing algorithm setup, resource scheduling, and deployment planning. This design space is already too large to manage well through manual tuning or isolated optimizers. This article introduces the \textit{Agent Compiler}, a large language model (LLM)-enabled compilation layer that translates high-level engineering intent into complete and executable ISAC system configurations. The Agent Compiler works in four stages: intent parsing, task decomposition, policy graph synthesis, and infrastructure mapping. It produces a verifiable intermediate representation called the ISAC Policy Graph (IPG). A runtime engine then deploys the compiled configuration and supports closed-loop adaptation at three levels: fast parameter updates, partial recompilation of affected subgraphs, and full workflow recompilation. The core design principle is strict time-scale separation: the LLM handles slow-loop strategic decisions, while proven algorithms retain real-time control in the fast loop. A UAV-assisted disaster rescue example illustrates the full compilation process. We also discuss open issues, including compilation latency, output reliability, constraint verification, and pipeline security, to guide future research.
arXiv:2607.18121v1 Announce Type: new
Abstract: We revisit the classical Krasnosel'skii-Mann fixed point iteration for contractions and nonexpansive maps in general normed spaces. This iteration is ubiquitous across a wide range of areas, including convex optimization, monotone inclusions, Markov decision processes, under-relaxed methods for nonlinear PDEs, and more. Drawing on a remarkable connection with a Markov chain on $\mathbb{Z}^2$, and using counting arguments from enumerative combinatorics of lattice paths, we derive explicit estimates for the distance between iterates, as well as non-asymptotic error bounds for the fixed point residuals. As the contraction parameter approaches one, these bounds smoothly recover the known estimates for nonexpansive maps. Building upon these estimates, we further derive error bounds for inexact Krasnosel'skii-Mann iterations.
arXiv:2607.17884v1 Announce Type: new
Abstract: Vision Language Models (VLMs) achieve strong reasoning with Chain-of-Thought (CoT) prompting but incur high sequential-generation cost, error accumulation, and limited self-correction. Diffusion Multimodal Large Language Models (dMLLMs) unmask tokens in an order-agnostic process, improving efficiency and enabling iterative refinement, yet their reasoning and how to enhance it remain underexplored. We propose a training-free method, Spatio-Temporal Token Veto (ST-Veto), which leverages the ability to observe all token positions at each diffusion step. Rather than relying only on current-step confidence, ST-Veto vetoes temporally unstable tokens via second-order Taylor prediction of confidence dynamics and filters weakly grounded tokens using image-attention mass, swapping them with safer candidates. Across multiple dMLLMs and multimodal reasoning benchmarks, ST-Veto consistently outperforms standard decoding policies and prior VLM reasoning methods, improving accuracy by up to 9% with no additional training or generation cost. Analyses show that ST-Veto steers generation toward higher-confidence, better-grounded paths.
arXiv:2507.07247v2 Announce Type: replace
Abstract: As large language models (LLMs) and visual language models (VLMs) grow in scale and application, attention mechanisms have become a central computational bottleneck due to their high memory and time complexity. While many efficient attention variants have been proposed, there remains a lack of rigorous evaluation on their actual energy usage and hardware resource demands during training. In this work, we benchmark eight attention mechanisms in training GPT-2 architecture, measuring key metrics including training time, GPU memory usage, FLOPS, CPU usage, and power consumption. Our results reveal that attention mechanisms with optimized kernel implementations, including Flash Attention, Locality-Sensitive Hashing (LSH) Attention, and Multi-Head Latent Attention (MLA), achieve the best energy efficiency. We further show that lower GPU power alone does not guarantee reduced energy use, as training time plays an equally important role. Our study highlights the importance of energy-aware benchmarking in attention design and provides a practical insight for selecting resource-efficient mechanisms. All our codes are available at GitHub.
arXiv:2607.18049v1 Announce Type: new
Abstract: We consider the problem of verifying a message passing program in which the number of processes is a parameter NP and each process knows its unique ID. Processes communicate using send and receive commands which specify a single destination or source. To verify the program, the user provides functions specifying the number of messages sent from process i to process j, the level of each communication event in the happens-before hierarchy, and a fact that holds for the k-th message sent from i to j. These are used to transform the program to a parameterized sequential program which can be verified using any techniques appropriate for such programs. We realize this approach in an extension to Frama-C/Wp to verify C/MPI programs.
arXiv:2607.17899v1 Announce Type: new
Abstract: Data-parallel workloads in deep learning and scientific computing continue to drive demand for higher processor throughput, energy efficiency, and scalability. The RISC-V Vector Extension (RVV) supports scalable execution through a vector-length-agnostic programming model. However, many tightly coupled implementations still rely on the scalar core to supply vector instructions one at a time, making execution susceptible to vector-instruction supply gaps, scalar-side progression delays, and conservative dependence handling in short-vector, loop-tail, and control/memory-interleaved phases. This paper presents SEAM-V, a hybrid-decoupled vector execution architecture for RVV. SEAM-V forms a continuous stream of execute packets (EPs) through task-level decoupling, local instruction supply, and VLIW-style packing. After an EP is serialized into individual requests, its EP identity and request-bound prefetch context remain visible to the dynamic vector backend, enabling same-EP candidate-hazard suppression and request-bound prefetching. The hybrid-dispatch path can also provide limited cross-EP vector overlap when the required safety conditions are satisfied. Cross-EP dependences, dependences not exempted by the EP contract, resource conflicts, and memory ordering remain dynamically managed by the backend. Cycle-accurate RTL evaluation shows that, compared with an Ara-based tightly coupled RVV implementation (TC), SEAM-V achieves a geometric-mean speedup of 1.34x across 17 representative kernels. The one-dimensional variable-AVL, BLAS and matrix, and fixed-size application groups achieve speedups of 1.50x, 1.25x, and 1.27x, respectively. At AVL=32, the geometric-mean speedup across six one-dimensional vector kernels approaches 3x.
arXiv:2607.16276v1 Announce Type: cross
Abstract: Quantum-repeater networks require adaptive control policies that balance entanglement generation rate, end-to-end fidelity, purification overhead, and memory-induced latency. This tradeoff becomes more complex when the classical control plane is degraded by cyber anomalies or denial-of-service traffic. We develop a CUDA-Q/SeQUeNCe co-simulation workflow for studying adaptive entanglement purification in heterogeneous linear repeater chains. CUDA-Q noisy quantum kernels are used to estimate primitive entanglement purification and swapping behavior, while SeQUeNCe provides an event-layer model for stochastic link generation, waiting-time-dependent memory decay, purification failure, and end-to-end swapping. Under stationary conditions, we compare no purification, local threshold purification, mean-field predictive purification, fixed purification, and a resource-penalized risk-aware predictive policy. In an 8-node chain, the resource-penalized risk-aware controller increases above-target delivery probability relative to fixed purification while reducing latency and purification overhead. We then couple the quantum-network controller to anomaly scores derived from the CSE-CIC-IDS2018 benign-to-SSDP intrusion-detection trace. During the attack period, the attack-unaware controller maintains high raw delivery, but its above-target entanglement delivery falls to 0.098+/-0.007; the IDS-aware resource-adaptive controller switches to more purification-heavy masks and increases above-target delivery to 0.344+/-0.011, closely matching the oracle-aware value of approximately 0.335. These results demonstrate that cyber-state awareness can improve useful quantum-network outcomes by trading raw throughput for fidelity-qualified entanglement delivery.
arXiv:2607.18147v1 Announce Type: new
Abstract: Large language models (LLMs) and agentic AI systems have evolved from natural language tasks to using external tools to plan, retrieve, and act in technical domains. In smart grids, recent work applies agentic schemes to forecasting, optimization, and control, wrapping trusted solvers behind language interfaces and orchestrating multi-step workflows. The literature lacks a unified approach to designing and evaluating such systems. LLMs can produce numerically plausible yet physically infeasible outputs, evaluation protocols vary across tasks, and the boundary between what the model should and should not compute is implicit. This paper presents a solver-grounded design principle: a numerical result is reported only when it originates from a trusted tool and passes explicit verification. We review the building blocks of LLM and agentic AI systems for power systems: prompting strategies and agentic architectures. We instantiate the principle in four case studies: wind power forecasting, EV charging scheduling, power flow analysis, and contingency diagnosis, each comparing an LLM-only baseline against its solver-grounded counterpart on identical data and metrics. EVAgent reproduces the CVXPY optimum while reducing LLM-only unmet energy by 7.5-9.5x, and GridDebugAgent repairs 17/39 contingency cases while reducing total violations by 52.3%. We propose a four-group evaluation framework spanning task utility, solver-grounded correctness, faithfulness and safe failure, and cost and latency. A consistent division of labor emerges: the agentic system reliably orchestrates, retrieves, and explains, while trusted tools compute and a verification gate decides what is reported.
arXiv:2507.20804v3 Announce Type: replace
Abstract: Large Language Models (LLMs) suffer from hallucinations due to their static parametric knowledge. Retrieval-Augmented Generation (RAG) and GraphRAG mitigate this issue by incorporating external knowledge and structured reasoning over knowledge graphs (KGs). However, existing approaches remain largely text-centric, as constructing fine-grained multimodal knowledge graphs (MMKGs) with explicit cross-modal semantics remains challenging. In this paper, we propose MMGraphRAG, a framework for building interpretable MMKGs that unify textual and visual knowledge. Our approach represents visual content as structured scene graphs and integrates them with textual KGs through a novel cross-modal entity linking method, SpecLink, which leverages spectral clustering to jointly model semantic similarity and graph structure. This design preserves explicit entities, relations, and reasoning paths across modalities, enabling structure-aware retrieval and generation. To support evaluation, we introduce the CMEL dataset, a benchmark for fine-grained cross-modal entity alignment. Experimental results on CMEL demonstrate improved entity linking accuracy, while evaluations on DocBench and MMLongBench show that MMGraphRAG achieves superior performance and stronger robustness, particularly in complex multimodal reasoning scenarios.
arXiv:2501.15303v4 Announce Type: replace
Abstract: We study the guarded negation fragment of transitive closure logic (GNTC). We show that the satisfiability problem for GNTC is 2ExpTime-complete, by establishing the following reductions: (i) a polynomial-time reduction from the satisfiability problem for GNTC to the satisfiability problem for the unary negation fragment UNTC of GNTC, and (ii) a direct exponential-time reduction from the satisfiability problem for UNTC to the non-emptiness problem for 2-way alternating parity tree automata. Furthermore, we show that the model checking problem for GNTC is $\mathsf{P}^{\mathsf{NP}[\mathcal{O}(\log^2 n)]}$-complete in combined complexity. Our result implies $\mathsf{P}^{\mathsf{NP}[\mathcal{O}(\log^2 n)]}$-completeness for both UNTC and $\mathrm{UNFO}^{\mathrm{reg}}$, which were left open in previous works.
arXiv:2607.17796v1 Announce Type: new
Abstract: Ptychography allows ordinary cameras to perform both quantitative phase and intensity imaging. However, the requirement for relative object to probe motion and high measurement count significantly limits imaging speed and application scope. In this work, we introduce optically modulated aperture ptychography, using a silicon photomodulator as a rapidly reconfigurable aperture, deployable across the microwave, millimeter wave and terahertz bands. We demonstrate experimentally at ~ 0.1 THz real-time ptychographic image capture, without moving parts. Furthermore, a reconfigurable aperture facilitates diverse and spatially multiplexed probes. We use a multiplexed known-probe reconstruction strategy that improves signal-to-noise ratio and increases the information content per measurement, enabling the capture of fluid dynamics at 16 fps. Our optical modulation approach enables high-throughput ptychographic imaging of dynamic samples, for applications such as non-destructive evaluation and in-vivo biomedical imaging.
arXiv:2607.18006v1 Announce Type: new
Abstract: Large language models achieve strong reasoning performance, but often at prohibitive training cost - a challenge that is especially acute for compact models ($\leq 4 \, \mathrm{B}$ parameters) trained under limited budgets. We introduce MADA-RL, a post-training framework that specializes compact models into generator and critic roles and trains them with a debate-aware learning signal, fine-tuning only a small subset of parameters via LoRA adapters. Our central contribution is a counterfactual critic advantage: a dynamic, role-conditioned baseline that redefines the critic's advantage as its reward minus the generator ensemble's per-instance accuracy. This explicitly optimizes critics to improve over generator consensus rather than to merely reproduce a correct answer, yielding more targeted credit assignment than static mean-reward normalization. At deployment, the specialized agents are composed in a lightweight multi-round protocol. Across five mathematical reasoning benchmarks, MADA-RL raises the accuracy of the DeepSeek-R1-Distill-Qwen-1.5B model from $39.9 \, \%$ to $41.9 \, \%$ ($+2.0$ points, $p < 0.001$) using $16$ times fewer trainable parameters than fully fine-tuned baselines, placing it on the accuracy-trainable-parameter Pareto front. It approaches, but does not surpass, the strongest baselines (DeepScaleR, STILL-3), which are trained on substantially larger datasets; we analyse this gap and the associated inference-time cost directly. A controlled study isolates the source of MADA-RL's gains: the counterfactual advantage produces the highest critic improvement rate of any model evaluated, indicating that trained critics learn to correct generator errors rather than to imitate them.
arXiv:2607.17679v1 Announce Type: cross
Abstract: This is an invited commentary on the Psychometrika focus article "Fairness Issues and Evaluation in Psychometrics and AI/ML: What Can We Learn from Each Field?" by Ying Cheng (2026, doi:10.1017/psy.2026.10110). Cheng offers a systematic comparison between long-standing test fairness and modern algorithmic fairness. Her mapping of the entire testing workflow onto the AI/ML fairness paradigm, rather than only the final selection stage, is a crucial contribution to interdisciplinary fairness research. This commentary extends her discussion by examining two conceptual issues: the distinction between equality and equity, and the role of causality in fairness research. Together, the focus article and this commentary point to directions for future fairness research across the psychometrics and AI/ML communities.
arXiv:2607.17694v1 Announce Type: new
Abstract: Urban transportation systems generate heterogeneous data, yet these data do not automatically become actionable management intelligence. This chapter adopts a behavior-centered perspective on artificial intelligence (AI), treating mobility records and passenger-generated text as behavioral evidence rather than behavioral truth. It examines four directions: bus arrival prediction for service reliability, taxi mobility pattern discovery for demand analysis and planning, abnormal behavior detection for accountable regulatory support, and passenger-perceived risk mining for service improvement. These directions are integrated through a closed-loop framework linking data input, behavior representation, AI inference, decision support, public value, and governance feedback. The chapter identifies data quality, privacy, fairness, interpretability, uncertainty, transferability, and human accountability as essential conditions for deployment. It thereby establishes a unified pathway from behavioral evidence to operational, planning, regulatory, and passenger-service decisions.
arXiv:2607.18072v1 Announce Type: new
Abstract: Generative models trained on a source domain often produce samples that are poorly aligned with shifted target domains, limiting their effectiveness for target-domain data augmentation. Although target-specific adaptation can reduce this mismatch, it typically requires additional optimization and domain-specific parameters. We propose a Similarity-based Generative Network (SGN), a reusable framework that is trained once on labeled source data and applied to new target domains without parameter updates. SGN learns a latent space structured by label-induced pairwise similarities while preserving reconstructive information through an encoder-decoder architecture. At generation time, a small labeled representative set from the target domain is encoded and combined in the learned latent space, allowing the generated samples to inherit target-specific characteristics while maintaining class consistency. We further analyze the realizability and dimensionality requirements of the proposed similarity structure. Experiments on image and tabular datasets demonstrate the effectiveness of SGN for target-guided data augmentation under source-to-target distribution shifts.
arXiv:2512.05610v2 Announce Type: replace
Abstract: Laser scanning has proven to be an invaluable tool in assessing the decomposition of forest environments. Mobile laser scanning (MLS) has shown to be highly promising for extremely accurate, tree level inventory. In this study, we present NormalView, a projection-based deep learning method for classifying tree species from point cloud data. NormalView embeds local geometric information into two-dimensional projections, in the form of normal vector estimates, and uses the projections as inputs to an image classification network, YOLOv11. In addition, we inspected the effect of multispectral radiometric intensity information on classification performance. We trained and tested our model on high-density MLS data (7 species, ~5000 pts/m2), as well as high-density airborne laser scanning (ALS) data (9 species, >1000 pts/m2). On the MLS data, NormalView achieves an overall accuracy (macro-average accuracy) of 95.5 % (94.8 %), and 91.8 % (79.1 %) on the ALS data. We found that having intensity information from multiple scanners provides benefits in tree species classification, and the best model on the multispectral ALS dataset was a model using intensity information from all three channels of the multispectral ALS. This study demonstrates that projection-based methods, when enhanced with geometric information and coupled with state-of-the-art image classification backbones, can achieve exceptional results. Crucially, these methods rely only on geometric information, and thus are compatible with most sensors. Additionally, we publically release the MLS dataset used in the study, containing 1915 samples.
arXiv:2607.17822v1 Announce Type: new
Abstract: While Root Mean Square Normalization has become the de facto standard for accelerating modern sequence models, its reliance on the quadratic accumulation of independent scalars ($\sum x^2$) inherently triggers outlier-induced numerical instability, gradient starvation, and anisotropic phase distortion. We introduce Mean Root Square Normalization (MRSNorm). By structurally pairing channels into 2D phasors, MRSNorm mathematically inverts the traditional scaling paradigm: it computes the localized $L_2$ magnitudes (Root Square) before aggregating them via a global $L_1$ average (Mean).
This operational inversion strictly constrains activations to a phasor manifold, preserving conformal invariance. By sharing a single affine weight across phasor components, MRSNorm halves the total number of learnable parameters, proving that unconstrained spatial scaling in standard norms is a harmful redundancy. We analytically demonstrate that this geometric constraint yields a built-in, trigonometric gradient clipper governed by the Pythagorean identity, unconditionally equalizing the local gradient norm to ensure Gradient Homogeneity.
Empirical evaluations on a ResNet with CIFAR-100 show that despite halved parameters, MRSNorm provides critical structural stability under rigorous stress tests. Under extreme hyperparameter settings where standard normalizations suffer from gradient divergence, MRSNorm successfully prevents numerical explosion and secures stable optimization trajectories. Our findings propose a fundamental paradigm shift toward phasor-based deep representation learning. The implementation of MRSNorm is available at Appendix C.
arXiv:2607.16592v1 Announce Type: cross
Abstract: We develop a quantum model for the rotational dynamics of a freely floating levitated ferromagnetic gyroscope (LFG), emphasizing the interplay between intrinsic spin $\boldsymbol{S}$, mechanical angular momentum $\boldsymbol{L}$, and magnetic torque. The conserved total angular momentum projection along the $z$-directed magnetic field $\boldsymbol{B}$, $J_z=S_z+L_z$, is quantized, leading in the small-libration-amplitude limit to discrete precessional states $|m\rangle$ (eigenstates of $J_z$ with eigenvalues $J_z = m\hbar$) and librational harmonic oscillator states $|n\rangle$ ($n=0,1,2,\ldots$). The discreteness of the energies and dynamical variables is governed by the quantum precession scale $\Omega_Q=\hbar/I$, where $I$ is the moment of inertia of the LFG. We find that the phenomenon of LFG precession persists into high-field regimes where the magnitude of the rotational angular momentum associated with precession exceeds the total intrinsic spin. We analyze the complementary quantum limits of localized semiclassical LFG orientation wave packets and exact $J_z$-eigenstates $|m\rangle$, clarifying the relation between classical precession signals and the underlying quantized spin-rotor dynamics. We further show that radio-frequency fields can drive $\Delta m = \pm 1$ and $\Delta n = \pm 1$ transitions, enabling ladder spectroscopy, tilt-angle control, and sideband-like coupling between precession and libration. The coupled dynamics also exhibit branch-point magnetic resonances where precession and librational motion become strongly coupled. These results establish a framework for using LFGs not only as ultrasensitive torque and magnetic-field sensors, but also as controllable mesoscopic quantum systems. The techniques developed here may be applied to searches for exotic, beyond-the-standard model spin-dependent interactions, ultralight dark matter, and spin-gravity couplings.