Gradient_Descent
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Distributed Optimization with Streaming Data: A Temporal Weighting Perspective
2026-08-10 13:02:58Muhammad Faraz Ul Abrar, Nicol\`o Michelusi, Erik G. LarssonAbstract
Optimization theory is a widely used tool for intelligent decision-making. While classical optimization deals with fixed, time-invariant objective functions, many modern applications operate in dynamic environments where data arrive sequentially, and the learning objective evolves over time, often under decentralized data and communication constraints. Motivated by these trends, we study decentralized optimization from streaming data through a structured time-varying formulation in which the global objective is a temporally weighted average of losses observed across the network. We analyze multi-iteration decentralized first-order methods, including decentralized gradient descent. For strongly convex and smooth losses, we develop guarantees for the Euclidean-norm \emph{tracking error} through a contraction-mapping viewpoint. The resulting bounds decompose the tracking error into a fixed-point tracking component and a bias term induced by decentralization and data heterogeneity. We specialize our analysis to uniform and exponentially discounted weights, as well as their finite-memory \emph{windowed} counterparts. The bounds explicitly characterize the roles of the temporal weighting rule, per-step iteration budget, step size, and network connectivity. Uniform weighting yields a vanishing fixed-point tracking contribution of order $\mathcal O(1/t)$, whereas discounted and windowed strategies generally induce non-vanishing tracking floors governed by the discount factor and effective memory, respectively. In all cases, decentralization induces an additional non-zero bias floor under a constant step size. Numerical experiments illustrate the predicted trends.
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URL
https://arxiv.org/abs/2608.09565
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OGG-FR: Orthogonal Gradient Gaming and Frequency Rectification for Unmanned Aerial Vehicle Infrared Image Super-Resolution
2026-08-10 05:55:05Yongsong Huang, Qingzhong Wang, Xiaofeng Liu, Tomo Miyazaki, Yaohou Fan, Shinichiro OmachiAbstract
Unmanned aerial vehicle (UAV) infrared image super-resolution aims to recover weak thermal structures for deployment on resource-constrained platforms; lightweight models are therefore preferred, but multi-loss training can be unstable. A common strategy combines pixel-domain and frequency-domain objectives; however, low contrast, limited high-frequency content, and sensor-specific noise often make their gradients weakly aligned or conflicting. To address this optimization ambiguity, we propose Orthogonal Gradient Gaming and Frequency Rectification (OGG-FR), a plug-and-play optimization framework that decomposes the frequency gradient into a redundant parallel component and an orthogonal innovation component relative to the pixel gradient. In the conflict regime, OGG-FR computes a safe base gradient using the Multiple Gradient Descent Algorithm (MGDA) and adds a variance-rectified orthogonal innovation; in the compatible regime, it discards redundant parallel information and injects the orthogonal innovation according to a confidence score estimated from the high-frequency residual. Experimental results on the UAV thermal benchmark show broad gains under BI and BD degradations at $\times 4$ and $\times 8$ scales, while gradient analyses support the effectiveness of the proposed conflict-aware update rule.
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URL
https://arxiv.org/abs/2608.09150
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SkillProx: Self-Evolving Agent Skills via Proximal Textual Gradient Descent
2026-08-07 17:40:33Mingxuan Zheng, Yujin Zhou, Chuxue Cao, Boqin Yin, Yuyao Zhang, Jiapeng Sun, Shuaishuai Gong, Sirui Han, Yike GuoAbstract
LLM agents increasingly adapt to recurring tasks by accumulating procedural knowledge in skills. These skills are lightweight, reusable textual artifacts that are loaded into the agent's context without weight updates. Recent methods refine skills through iterative task execution, failure diagnosis, and trajectory-guided text-space updates. However, existing frameworks lack explicit diagnosis--outcome feedback and treat deletion as a generic edit operation rather than a dedicated mechanism for consolidating accumulated knowledge. We introduce SkillProx, a proximal-gradient-inspired forward--backward framework that couples closed-loop diagnostic evolution with utility-aware proximal refinement. Motivated by a composite objective balancing task loss and skill complexity, the forward stage re-executes diagnosis-driven edits on the same task batch, rolls back regressions, and feeds measured outcomes into subsequent diagnoses. The backward stage decomposes the resulting skill into auditable knowledge units, estimates their contributions using a frozen leave-one-out utility audit, and applies validation-gated consolidation, demotion, or removal. Experiments on in-distribution and out-of-distribution benchmarks across multiple backbone LLMs show that SkillProx improves average accuracy by 3.0 percentage points over the strongest gradient-based baseline. Component ablations demonstrate the complementary effects of closed-loop diagnosis and proximal refinement.
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URL
https://arxiv.org/abs/2608.07449
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Adaptive Hybrid Particle Swarm Optimization with Gradient Descent
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Gradient injection helps Particle Swarm Optimization (PSO) only when the swarm has identified a basin with smooth local structure, not universally. We propose Adaptive Hybrid PSO (AHPSO), which uses a sigmoid function on swarm diversity to automatically modulate gradient influence: near-zero during exploration, near-maximum during exploitation, with no manual phase-switching. Under budget-normalized comparison (PSO given equivalent total function evaluations), PSO wins 52.5% of 40 configurations versus AHPSO's 20% (p = 7.0e-5, Friedman). AHPSO retains advantage specifically on problems with smooth local basins (F8, F24-F27) where directed descent outperforms undirected sampling even at equal cost. Under iteration-matched comparison across 29 functions (42 configurations, 14,700 runs), AHPSO-Adadelta ranks first of 9 methods including CMA-ES (p = 9.75e-4). The contribution is a principled characterization of when gradient injection provides value in swarm-based search, not a claim of universal superiority.
Abstract (translated)
URL
https://arxiv.org/abs/2608.11258
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Hidden Gauge Controls Feature Specialization in ReLU Networks
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Training changes a network's predictions while allocating task-relevant structure across its internal units. In an overparameterized ReLU network, several neurons can begin with exactly the same functional role, yet one may acquire a teacher feature while the others become redundant. We call the identity of that neuron feature ownership and ask whether it can be controlled by a parameter choice invisible to the initial predictor. In a tractable Gaussian teacher--student model, we fix the complete initial function and vary only a positive-homogeneous scaling gauge. Opposite gauges produce distinct feature trajectories and a sharp $\Theta(D^2)$ separation in specialization time that no global change of clock can explain. Among any fixed number of initially duplicate students, assigning the favorable gauge to one neuron deterministically selects it as the owner and drives the remaining functional contribution to zero. An exact reaction--transport decomposition attributes the effect to different mobilities for changing a feature's coefficient and direction. We prove global selection and functional pruning, extend finite-time selection to visible perturbations and small-step full-batch gradient descent, and verify the predicted loss, alignment, pruning, and dissipation trajectories in population and finite-sample training. The initial predictor therefore determines neither when the feature is learned nor which neuron learns it.
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URL
https://arxiv.org/abs/2608.06766
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DoctorAgents: an agentic framework to iteratively refine AutoML pipeline for small clinical temporal data
2026-08-05 19:52:55Ruilin Wang, Bo-Hong Wang, Elizabeth Kourbatski, Jun Bai, Hegang Chen, Ziyang Song, Gilles Boire, Marie Hudson, Yue LiAbstract
Clinical machine learning (ML) has the potential to support high-stakes medical decision-making, but reliable deployment is often constrained by scarce, heterogeneous, and temporal complexity. Developing effective ML pipelines for such data remains time-consuming and error-prone, while existing automated machine learning (AutoML) systems only partially address this challenge because they largely rely on brute-force search over predefined spaces and lack explicit reasoning and memory. We therefore reformulate AutoML for small clinical data from exhaustive search to reasoning-driven refinement. We propose DoctorAgents, an agentic AI framework that autonomously constructs and optimizes end-to-end ML pipelines through specialized large language model (LLM) agents for generation, validation, and refinement. DoctorAgents backpropagates natural-language feedback through textual gradient descent to perform targeted updates without exhaustive search. Experiments across diverse clinical tasks show that DoctorAgents consistently outperforms established AutoML baselines while producing more interpretable task-specific representations.
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URL
https://arxiv.org/abs/2608.05375
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SVI-DAG: A Structured Variational Inference Approach to Bayesian Causal Discovery
2026-08-05 14:56:14Shrenik ZinageAbstract
Bayesian causal discovery seeks to determine the posterior distribution of causal theories, which are interpreted as directed acyclic graphs (DAGs) that explain the observed data. The resulting posterior allows systematic reasoning regarding epistemic uncertainty within these theories. Nonetheless, finding such graphs is difficult due to identifiability problems and limited observational data. Furthermore, precisely approximating posterior over graphs is challenging given vast range of potential DAGs. Recent Bayesian approaches have addressed some of these challenges, yet they remain limited as they fail to encode dependencies between edges, and lack principled ways to incorporate domain knowledge as inductive biases during the search process. To overcome these limitations, we propose SVI-DAG, a structured variational inference approach to Bayesian causal discovery using observational data and prior beliefs that uses normalizing flows to model dependencies between edges, supporting expressive and multimodal posterior learning over DAGs. To mitigate mode seeking behaviour in evidence lower bound optimization and promote mode coverage, we use stein variational gradient descent to update the node potentials using a kernel in acyclicity space. We evaluate SVI-DAG against 5 state-of-the-art Bayesian DAG learning methods and demonstrate superior performance in uncertainty quantification while remaining competitive in terms of structural accuracy.
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URL
https://arxiv.org/abs/2608.04930
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MESH: Memory-Efficient Sinkhorn Optimization for Mixture-of-Experts Training
2026-08-05 03:23:31Masato FujitakeAbstract
Memory-efficient matrix optimizers such as Sinkhorn gradient descent remove most AdamW optimizer state for dense Transformer matrices, but direct application to Mixture-of-Experts (MoE) training is unreliable. We study this failure in a controlled 110M-parameter nanowhale DeepSeek-style MoE pretraining setting. A SAGE/Sinkhorn hybrid reduces optimizer state from 0.883GB to 0.331GB but degrades evaluation loss to 3.8265, far above the AdamW baselines observed in the same setup (3.58--3.64 across the seeds we study). We show that routed MoE expert matrices are the dominant failure point: their gradients are conditional, temporally varying, and poorly served by stateless Sinkhorn normalization. We propose MESH, a hidden-momentum Sinkhorn update for MoE experts. MESH restores a temporal first-moment signal through the gradient-buffer lifecycle, without storing the expert first moment as optimizer state. MESH is an optional block-preconditioned variant that adds a coarse neuron/block inverse-RMS multiplier. Across ablations, temporal smoothing before matrix normalization is the primary causal ingredient; block/neuron preconditioning can improve the memory-quality frontier, but is not established as universally necessary. In two additional seeds, MESH and MESH-B reduce optimizer-state memory by 62.5\% and peak PyTorch CUDA allocation by about 12.6\% relative to AdamW, with a modest evaluation-loss gap. Full-state diagnostic variants recover AdamW-like performance in ablations, supporting the conclusion that MoE experts need temporal smoothing, but not necessarily full coordinate-wise AdamW state.
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URL
https://arxiv.org/abs/2608.04407
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SRAP: SVD-Refined Adversarial Perturbations for Imperceptible Face-Swap Defense
2026-08-04 09:48:46Sungwon Cho, Kwanghyun Ko, Myungjoo KangAbstract
Deepfake technologies pose increasing threats to facial privacy and identity security, motivating proactive defenses that protect facial images before misuse. Although adversarial perturbations generated by projected gradient descent (PGD) can disrupt the identity representations used by face-swapping models, their visual quality is degraded by two characteristics: perturbations are distributed broadly over the image, including identity-insensitive regions, and they contain visually salient high-frequency components. We analyze these spatial and spectral inefficiencies through identity-sensitivity estimation and the singular-value decomposition (SVD) of PGD perturbations. Our analysis shows that later singular components contain a disproportionate amount of high-frequency energy, while the leading components preserve most of the perturbation energy and defense utility. Based on these observations, we propose SRAP, which combines per-channel truncated SVD refinement with an identity-importance mask at every optimization step. The SVD refinement suppresses high-rank, high-frequency residuals, while the mask restricts perturbations to locations that strongly influence identity representations. Experiments on CelebA-HQ and VGGFace2-HQ demonstrate that SRAP substantially improves protected-image fidelity across all reported metrics while maintaining competitive identity-disruption performance, yielding a favorable trade-off between face-swap defense and visual imperceptibility.
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URL
https://arxiv.org/abs/2608.03395
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NanoMorph-3D: An End-to-End Physics-Driven Unrolling Framework for Nanomaterial Reconstruction
2026-08-04 07:30:48Beiyuan Zhang, Hesong Li, Ziqi Wu, Ruiwen Shao, Ying FuAbstract
Precise 3D characterization of nanomaterials is essential for unlocking structure-property relationships. However, standard electron tomography is fundamentally limited by the missing wedge problem. Consequently, conventional algorithms suffer from severe geometric distortions, a challenge further complicated by pervasive noise interference. Current learning-based methods either rely on physics-blind post-processing or employ end-to-end architectures constrained by local receptive fields, failing to capture complex 3D topologies. We propose NanoMorph-3D, a unified end-to-end framework grounded in a comprehensive Nanomorphological Taxonomy. Powered by a large-scale synthetic dataset explicitly modeling non-linear electron attenuation, we design a Physics-Driven Unrolled Network mapping proximal gradient descent into a learnable architecture. To capture complex internal topologies, we formulate a hierarchical attention mechanism with Physics-Normalization for long-range 3D dependencies and scale invariance. Crucially, our Dual-Domain strategy leverages Sinusoidal Attention to explicitly model physical projection trajectories, enforcing strict sinogram consistency to mitigate missing wedge artifacts. Finally, an unsupervised dual-stream mechanism bridges the simulation-to-reality gap. Experiments demonstrate NanoMorph-3D reconstructs diverse topologies with superior fidelity and speed.
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URL
https://arxiv.org/abs/2608.03257
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From Digital to Physical Reservoir Computing: Co-Optimizing Soft Robotic Reservoirs via Dynamics Matching
2026-08-01 07:21:23Nicola Visentin, Maximilian St\"olzle, Mariano Ram\'irez Montero, Francesco Braghin, Daniela Rus, Cosimo Della SantinaAbstract
Soft robotic substrates are promising for Physical Reservoir Computing (PRC) because their compliant nonlinear dynamics can provide temporal memory, high-dimensional state transformations, and efficient inference. However, physical reservoirs are often adopted as-is rather than pretrained or co-optimized, potentially limiting soft robotic PRC performance relative to digital reservoirs. We investigate whether a physical reservoir can instead be pretrained against high-performing digital reference dynamics. Our formulation jointly optimizes physical parameters, a diffeomorphic physical-reference state map, and feedforward-feedback control using a differentiable physical model and an acceleration-level equation-error objective that avoids temporal integration. As a proof of concept, we instantiate the formulation with simulated soft robots, a Random Oscillators Network (RON) reference, and parallel multi-start gradient descent. We evaluate the optimized reservoirs on classification (sMNIST and ADIAC) and forecasting (Mackey-Glass and Lorenz96) tasks across four reservoir dimensions. Compared with unoptimized soft robot reservoirs, the optimized reservoirs achieve a mean relative improvement of 33.7% across all tasks and datasets, while remaining close to the digital reference. These results demonstrate the feasibility of dynamics-level co-optimization for the simulated soft robotic reservoirs considered here.
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URL
https://arxiv.org/abs/2608.00484
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Shared Symbolic Backbones for Physically Consistent Multi-Output Symbolic Regression
2026-07-29 06:47:36Manuel RodriguezAbstract
Symbolic regression provides analytical expressions, but it is usually applied one output at a time. This is limiting in process systems, where state variables are often coupled through shared physical parameters. Independent symbolic regression can give accurate individual equations that are difficult to interpret as one model. We present a neuro-evolutionary symbolic regression method for coupled multi-output systems. The method searches for a shared symbolic backbone: a set of latent symbolic units that is discovered once and reused by several outputs through sparse additive or multiplicative read-outs. The discrete model structure is evolved by mutation and crossover, whereas the continuous parameters are tuned by gradient descent and inherited by the offspring. The method is assessed on a set of benchmarks with known ground truth and on a hydrothermal liquefaction yield case. The results show that coupling is not a general route to lower prediction error. Its main contribution is the enforcement and diagnosis of cross-output consistency when a physically shared factor is embedded in a latent expression and is weakly identifiable from the data. This occurs for Langmuir-Hinshelwood and site-coverage denominators, for which independent PySR does not close the consistency gap or recover the same shared form. Conversely, when each output is already identifiable, as in the Van de Vusse benchmark, independent symbolic regression matches or improves the coupled model. The proposed framework, rather than a general purpose predictor, is a structured shared-mechanism extractor. Its value is highest when the target structure is sparse, shared, weakly identifiable or constrained by closure.
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URL
https://arxiv.org/abs/2607.26528
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Quotient Dynamics, Effective Curvature, and Implicit Bias in Positive Quadratic Networks
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Positive quadratic networks admit the low-rank representation f_U(x)=x^top UU^top x, where Uinmathbb{R}^{dtimes r} is identifiable only up to right orthogonal multiplication, representing a rank-r PSD matrix Q=UU^top. We study how this quotient structure governs training dynamics, curvature, recovery, and interpolation bias. On the full-column-rank stratum, we identify mathbb{R}^{dtimes r}_*/O(r) with the rank-r PSD manifold. For smooth objectives L(U)=ell(UU^top), the Euclidean factor gradient is horizontal. Thus, factor gradient flow projects exactly to quotient Riemannian gradient flow, while finite-step gradient descent induces an exact congruence recursion for the predictor. For quadratic regression, we derive the effective Hessian at interpolators as the empirical measurement Gram form restricted to the tangent space relative to the quotient metric. Under Gaussian rank-one measurements, we compute population curvature, prove uniform deviation bounds for the empirical normal operator, construct a spectral initializer, and establish local exponential convergence for gradient flow and linear convergence for small-step descent. Recovery guarantees are explicit but conservative due to reliance on full-space second-moment control. In underdetermined commuting regimes, factor gradient flow becomes an exact entropy mirror flow in joint spectral coordinates. Strictly positive initializations converge to Bregman projections onto the interpolation set. With isotropic initialization q(0)=varepsilon^2mathbf{1}, predictors approach the minimum-trace solution set as varepsilondownarrow0, resolving nonuniqueness via weighted entropy within the invariant joint spectral algebra. Finite-step descent selects interpolants differing from continuous-time Bregman projections by O(eta). Numerical experiments verify these quotient identities, curvature predictions, recovery behaviors, and selection laws.
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URL
https://arxiv.org/abs/2607.25624
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Extracting Voice Styles from Frozen TTS Models via Gradient-Based Inverse Optimization
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Some text-to-speech systems ship a synthesis model and preset style vectors but not the reference encoder that turns audio into such a vector. The model still accepts a style vector; a user with a voice of their own cannot produce one. We solve for that input directly, inverting the released pipeline by gradient descent: every weight stays frozen and only the style vector is optimized, against time-pooled WavLM statistics of one recording. Because the objective discards the time axis, the synthesized text may differ from the recording, so no transcript and no alignment are needed. On 154 speakers from two corpora, ECAPA-TDNN similarity rises from 0.132 to 0.413 and ResNet from 0.099 to 0.401, improving for every speaker; a verifier at its equal-error point accepts 53% of the recovered voices as the target, against 1% for the presets they start from.
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URL
https://arxiv.org/abs/2607.25351
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Scale Weight Decay and Train Better
2026-07-26 17:55:40Anuj ApteAbstract
The discovery of scaling laws has motivated training neural networks on ever increasing quantities of data. This is typically done with a constant decoupled weight decay which causes the network weights to shrink steadily over the course of training. Taking inspiration from the Robbins--Monro conditions, we propose to scale weight decay by the fraction of the peak learning rate $\eta/\eta_{\max}$. We prove that this scaled weight decay preserves the asymptotic stationarity guarantees of the corresponding unregularized methods for both stochastic gradient descent and the non-Euclidean spectral optimizer Muon, thereby avoiding the additional asymptotic bias introduced by constant decoupled weight decay. This retains the stability benefits of weight decay without changing the asymptotic optimization target. Using a steady-state analysis, we explain why under standard weight decay the weight norm shrinks steadily as training proceeds, whereas under scaled weight decay it settles to a roughly constant value. When applied to the training of mixture-of-experts models, Muon with scaled weight decay (Muon-SW) consistently outpaces Muon with identical hyperparameters, reaching the same validation loss $\mathbf{30\%}$ faster at our largest scale across models from $72 - 930$ million parameters trained at $\sim 600$ tokens per active parameter. If this trend continues to hold, the method promises to substantially accelerate the pre-training of frontier models while requiring only a few lines of code to implement.
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URL
https://arxiv.org/abs/2607.23777
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Exact Network Surgery: Functional Invariance and Gradient Plasticity in Reactive Computational Graphs
2026-07-18 00:48:24Abdallah Khemais (ISITCOM, University of Sousse)Abstract
Function-preserving network growth techniques such as Net2Net and progressive stacking expand a model's capacity without destroying its learned function, but existing formulations either tolerate numerical perturbations or require a full rebuild of the training program. We formalize Exact Network Surgery: the in-place insertion of a residual block into a live computational graph such that (i) the network function is preserved -- bit-exactly under explicit floating-point hypotheses -- and (ii) inserted parameters remain trainable immediately after insertion. We prove an identity-morphism theorem for gated residual blocks, a structural-locality theorem showing that a reactive invalidation engine recomputes exactly the downstream cone of the insertion point, leaving every other node's value and optimizer state untouched, and an escape-from-initialization proposition showing that the Gradient Shadowing gate alpha, initialized at zero over a randomly initialized branch, receives a generically non-zero gradient at insertion time. We identify a degenerate configuration -- zero-initialized output projections combined with a zero gate -- that is an exact saddle point gradient descent cannot escape. Every claim is validated on the reference implementation in NeuroDSL, a reactive graph engine in Julia: grafting is bit-exact on every logit tested (0 mismatches out of 1600); the gate escapes zero at the first optimizer step and unlocks branch gradients at the second, exactly as predicted; the degenerate configuration exhibits gradients identically zero for the entire 600-step run; surgery cost tracks downstream cone size with r = 0.9992 while graft-plus-invalidation bookkeeping is constant (about 0.75 ms) across insertion depths; and training resumes bit-identically across a real process restart. A flagged preliminary appendix reports first single-seed observations on post-insertion gate dynamics.
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URL
https://arxiv.org/abs/2607.16568
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In-context learning of closed form solution to simple linear regression task using transformer with linear self-attention
2026-07-17 10:28:27Katsuyuki HagiwaraAbstract
In-context learning is a remarkable property of transformers and has recently received a lot of interest. In many studies of in-context learning, it has been shown that transformers are capable of implementing solver for linear and non-linear regression problems, in which the most of them implement gradient descent algorithm. However, it is still unclear whether those implementations have actually been acquired through training. In this paper, we construct a transformer with linear self-attention, which in-context learns the least squares estimate in a simple regression task. The point here is that the closed form (analytical) solution is approximately obtained by using layer normalization rather than an approximate solution based on gradient descent algorithm. Then, we show an experimental example, in which our implementation is mainly used in the transformer trained with l1 regularization when the target output is the least squares estimate.
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URL
https://arxiv.org/abs/2607.15819
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RoboTTT: Context Scaling for Robot Policies
2026-07-16 17:59:06Yunfan Jiang, Yevgen Chebotar, Ruijie Zheng, Fengyuan Hu, Yunhao Ge, Jimmy Wu, Tianyuan Dai, Scott Reed, Li Fei-Fei, Yuke Zhu, Linxi "Jim" FanAbstract
Recent robot foundation models operate with single-step or short-history visuomotor context. We introduce Test-Time-Training Robot Policies (RoboTTT), a robot model and training recipe that scale visuomotor context to 8K timesteps, three orders of magnitude beyond state-of-the-art policies, without growing inference latency. At this context length, we unlock new robot capabilities: one-shot in-context imitation from human video demonstrations, on-the-fly policy improvement, robustness to perturbations, and stronger performance on multi-stage, long-horizon tasks. We also observe, for the first time, steady gains in closed-loop performance as pretraining context length scales. At its core, RoboTTT integrates Test-Time Training into robot foundation models such as Vision-Language-Action policies, yielding a sequence model whose recurrent state consists of fast weights, parameters updated by gradient descent during both training and inference, compressing histories into weight space and retrieving contextual information for long-context conditioning. To scale training context length, the recipe combines sequence action forcing with truncated backpropagation through time. On challenging real-robot manipulation tasks, RoboTTT improves overall performance by 87% over the single-step context baseline and fully completes a five-minute, ten-stage assembly task, which no baseline ever does. RoboTTT trained with 8K-timestep context outperforms the same model pretrained with 1K timesteps by 62%, suggesting context length as a new scaling axis for robot foundation models. Videos are available at this https URL
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URL
https://arxiv.org/abs/2607.15275
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Efficient Tuning Before Low-Bit Post-Training Quantization for Stochastic Gradient Descent-optimized Models
2026-07-13 10:24:36Peng Xia, Junbiao Pang, Muhammad Ayub SabirAbstract
Post-training quantization (PTQ) compresses deep neural networks for deployment under limited memory and computational budgets. However, low-bit (i.e., 2-bit or 4-bit) PTQ often suffers from substantial performance degradation. Most existing PTQ methods operate on an unconstrained full-precision (FP) model and primarily address quantization errors through post-hoc reconstruction. We argue that low-bit PTQ accuracy is limited not only by post-quantization error minimization, but also by the quantization-error tolerance of a FP model itself. In this paper, we propose Efficient Tuning Before Quantization (ETBQ), a pre-conditioning tuning stage for Stochastic Gradient Descent (SGD)-optimized models before PTQ. During tuning, the FP model is optimized under perturbations sampled from the error distributions of weight and activation quantization, guiding the model toward a loss-landscape region that is less sensitive to the subsequent PTQ. Unlike QAT, ETBQ does not train a fake-quantized deployment model, which is computationally and memory intensive. Instead, ETBQ outputs a FP model that can be used by any PTQ backend. Experiments on CIFAR-100, Tiny-ImageNet, ImageNet, and Cityscapes provide consistent evidence that ETBQ improves low-bit PTQ across diverse tasks. Under W2A4 settings, e.g., ETBQ improves over naive PTQ by 2.14\% top-1 accuracy on Tiny-ImageNet and by 5.80\% mIoU on Cityscapes. Code is available at this https URL.
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URL
https://arxiv.org/abs/2607.11359
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Quantum Compressed Sensing CT Reconstruction Algorithm Based on Penalized Weighted Least Squares and Guided Total Variation
2026-07-12 04:48:08Yuwen Zhang, Yujie Liu, Ao Wang, Yikuang Yuluo, Shuangyang Zhong, Haijun Yu, Yixing HuangAbstract
Objective. Existing quadratic unconstrained binary optimization (QUBO)-based sparse-view computed tomography (CT) reconstruction neglects photon-counting statistics and anatomical heterogeneity. We address both limitations within the QUBO this http URL. We propose a quantum compressed-sensing CT method combining penalized weighted least squares (PWLS) and guided total variation (GTV). PWLS weights projection residuals by photon-count reliability, whereas GTV uses gradients from a prior image reconstructed by the simultaneous algebraic reconstruction technique (SART) to preserve edges and suppress noise in homogeneous regions. After binary encoding, both terms form a unified QUBO model. Experiments used four 40 times 40 CT images under a 10-view fan-beam geometry with Poisson noise. Comparisons included conventional reconstruction methods, QUBO variants, gradient descent, simulated annealing, and a D-Wave hybrid quantum-classical this http URL results. PWLS-GTV achieved the best reconstruction quality across all cases. In the representative chest case, it reached a peak signal-to-noise ratio (PSNR) of 36.64 dB, compared with 22.48 dB for SART, the best conventional baseline. GTV consistently outperformed conventional total variation. Simulated annealing and the D-Wave hybrid solver produced similar reconstructions, whereas gradient descent was ineffective. Repeated hybrid-solver runs showed stable this http URL. The framework incorporates photon-statistical weighting and structure-guided regularization into QUBO-based CT reconstruction without changing its quadratic form, providing a proof of concept for quantum-assisted sparse-view CT reconstruction.
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URL
https://arxiv.org/abs/2607.10566
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