Gradient_Descent
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Spectral Dynamics in Deep Networks: Feature Learning, Outlier Escape, and Learning Rate Transfer
2026-05-08 15:28:01Clarissa Lauditi, Cengiz Pehlevan, Blake BordelonAbstract
We study the evolution of hidden-weight spectra in wide neural networks trained by (stochastic) gradient descent. We develop a two-level dynamical mean-field theory (DMFT) that jointly tracks bulk and outlier spectral dynamics for spiked ensembles whose spike directions remain statistically dependent on the random bulk. We apply this framework to two settings: (1) infinite-width nonlinear networks in mean-field/$\mu$P scaling and (2) deep linear networks in the proportional high-dimensional limit, where width, input dimension, and sample size diverge with fixed ratios. Our theory predicts how outliers evolve with training time, width, output scale, and initialization variance. In deep linear networks, $\mu$P yields width-consistent outlier dynamics and hyperparameter transfer, including width-stable growth of the leading NTK mode toward the edge of stability (EoS). In contrast, NTK parameterization exhibits strongly width-dependent outlier dynamics, despite converging to a stable large-width limit. We show that this bulk+outlier picture is descriptive of simple tasks with small output channels, but that tasks involving large numbers of outputs (ImageNet classification or GPT language modeling) are better described by a restructuring of the spectral bulk. We develop a toy model with extensive output channels that recapitulates this phenomenon and show that edge of the spectrum still converges for sufficiently wide networks.
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URL
https://arxiv.org/abs/2605.07870
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Approximation-Free Differentiable Oblique Decision Trees
2026-05-08 15:04:04Subrat Prasad Panda, Blaise Genest, Arvind EaswaranAbstract
Decision Trees (DTs) are widely used in safety-critical domains such as medical diagnosis, valued for their interpretability and effectiveness on tabular data. However, training accurate oblique DTs is challenging due to complex optimization landscapes and overfitting risks, particularly in regression. Recent advances have introduced differentiable formulations that enable gradient-based training and joint optimization of decision boundaries and leaf regressors. Yet, existing approaches typically rely on approximations, either through probabilistic softening of boundaries (soft DTs) or quantized gradients such as the Straight-Through Estimator (STE). To overcome these limitations, we propose DTSemNet, a novel, semantically equivalent, and invertible representation of hard oblique DTs as neural networks. DTSemNet enables end-to-end training with standard gradient descent, eliminating the need for approximations in both classification and regression. While classification aligns naturally with this formulation, regression remains challenging due to the joint optimization of internal nodes and leaf regressors. To address this, we analyze the limitations of STE and introduce an annealed Top-k method that provides accurate gradient signals without approximation. Extensive experiments on classification and regression benchmarks show that DTSemNet-trained oblique DTs outperform state-of-the-art differentiable DTs. Furthermore, we demonstrate that DTSemNet can serve as programmatic DT policies in reinforcement learning environments, thereby broadening their applicability.
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URL
https://arxiv.org/abs/2605.07837
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Decentralized Time-Varying Optimization for Streaming Data via Temporal Weighting
2026-05-07 21:40:42Muhammad Faraz Ul Abrar, Nicol\`o Michelusi, Erik G. LarssonAbstract
Classical optimization theory largely focuses on fixed objective functions, whereas many modern learning systems operate in dynamic environments where data arrive sequentially and decisions must be updated continuously. In this work, we study optimization with streaming data over a distributed network of agents. We adopt a structured, weight-based formulation that explicitly captures the streaming-data origin of the time-varying objective: at each time step, every agent receives a new sample, and the network seeks to track the minimizer of a temporally weighted objective formed from all samples observed across the network so far. We focus on decentralized gradient descent (DGD) with a limited communication/computation budget, where at each time step, only a limited number of DGD iterations can be performed before the objective changes again. For strongly convex and smooth losses, we analyze the tracking error with respect to the time-varying minimizer through a fixed-point theory lens. Our analysis reveals that the tracking error decomposes into a fixed-point tracking term and a bias term induced by data heterogeneity across agents. We specialize the analysis to two natural weighting strategies: uniform weights, which treat all samples equally, and exponentially discounted weights, which geometrically decay the influence of older data. Under uniform weighting, DGD tracks the fixed-point at a rate $\mathcal{O}(1/t)$, whereas discounted weighting yields a non-vanishing fixed-point tracking floor controlled by the discount factor. In both cases, decentralization induces an additional non-zero bias floor under a constant step size. We validate our theoretical findings through numerical simulations.
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URL
https://arxiv.org/abs/2605.06971
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A Rod Flow Model for Adam at the Edge of Stability
Abstract
Cohen et al. (arXiv:2207.14484) observed that adaptive gradient methods such as Adam operate at the edge of stability. While there has been significant work on continuous-time modeling of gradient descent at the edge of stability, extending these models to momentum methods remains underdeveloped. In the gradient descent setting, Regis et al. (arXiv:2602.01480) introduced rod flow, which models consecutive iterates as an extended one-dimensional object -- a "rod." Here we extend rod flow to Adam by working in the joint phase space of parameters and first moment $(w, m)$ and treating the second moment $\nu$ as a smooth auxiliary variable. We also develop rod flows for heavy ball momentum, Nesterov momentum, and scalar and per-component versions of RMSProp, Adam, and NAdam. For all eight optimizers, we empirically evaluate rod flow on representative machine learning architectures, where it tracks the discrete iterates through the edge-of-stability regime significantly more accurately than the corresponding stable flow.
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URL
https://arxiv.org/abs/2605.06821
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The Weight Gram Matrix Captures Sequential Feature Linearization in Deep Networks
2026-05-07 13:35:11Taehun Cha, Daniel Beaglehole, Adityanarayanan Radhakrishnan, Donghun LeeAbstract
Understanding how deep neural networks learn representations remains a central challenge in machine learning theory. In this work, we propose a feature-centric framework for analyzing neural network training by relating weight updates to feature evolution. We introduce a simple identity, the Feature Learning Equation, which identifies the weight Gram matrix as the key object capturing feature dynamics. This enables us to interpret gradient descent as implicitly inducing a hypothetical evolution of features, whose covariance structure - termed the Virtual Covariance - characterizes how representations evolve during training. Building on this perspective, we introduce Target Linearity, a measure quantifying the linear alignment between features and targets. By analyzing the training and layer-wise dynamics, we show that deep networks learn to sequentially transform representations toward target-linear structure. This linearization perspective provides a unified interpretation of several empirical phenomena, including Neural Collapse and linear interpolation in generative models.
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URL
https://arxiv.org/abs/2605.06258
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Deciphering Shortcut Learning from an Evolutionary Game Theory Perspective
2026-05-05 10:46:41Xiayang Li, Kuo Gai, Shihua ZhangAbstract
Shortcut learning causes deep learning models to rely on non-essential features within the data. However, its formation in deep neural network training still lacks theoretical understanding. In this paper, we provide a formal definition of core and shortcut features and employ evolutionary game theory to analyze the origins of shortcut bias by modeling data samples as players and their corresponding neural tangent features as strategies, assuming the existence of core and shortcut subnetworks. We find that gradient descent (GD) and stochastic gradient descent (SGD) lead to two distinct stochastically stable states, each corresponding to a different strategy. The former primarily optimizes the shortcut subnetwork, while the latter primarily optimizes the core subnetwork. We investigate the influence of these strategies on shortcut bias through a continuous stochastic differential equation, and reveal the impact of data noise and optimization noise on the formation of shortcut bias. In brief, our work employs evolutionary game theory to characterize the dynamics of shortcut bias formation and provides a theoretical view on its mitigation.
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URL
https://arxiv.org/abs/2605.02658
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Real-Time Evaluation of Autonomous Systems under Adversarial Attacks
2026-05-05 08:30:18Adithya Mohan, Xujun Xie, Venkatesh Thirugnana Sambandham, Torsten Sch\"onAbstract
Most evaluations of autonomous driving policies under adversarial conditions are conducted in simulation, due to cost efficiency and the absence of physical risk. However, purely virtual testing fails to capture structural inconsistencies, supervision constraints, and state-representation effects that arise in real-world data and fundamentally shape policy robustness. This work presents an offline trajectory-learning and adversarial robustness evaluation framework grounded in real-world intersection driving data. Within a controlled data contract, we train and compare three trajectory-learning paradigms: Multi-Layer Perceptron (MLP)-based Behavior Cloning (BC), Transformer-based object-tokenized BC, and inverse reinforcement learning (IRL) formulated within a Generative Adversarial Imitation Learning (GAIL) framework. Models are evaluated using Average Displacement Error (ADE) and Final Displacement Error (FDE). Inference-time robustness is assessed by subjecting trained policies to gradient-based adversarial perturbations across multiple intersection scenarios, yielding a structured robustness evaluation matrix. Results show that state-structure design and architectural inductive biases critically influence adversarial stability, leading to markedly different robustness profiles despite comparable nominal prediction accuracy (ADE < 0.08). Inference-time Projected Gradient Descent (PGD) attacks induce final displacement errors of up to approximately 8 meters. The proposed framework establishes a scalable benchmark for studying offline trajectory learning and adversarial robustness in real-world autonomous driving settings.
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URL
https://arxiv.org/abs/2605.03491
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Natural Gradient Bayesian Filtering: Geometry-Aware Filter for Dynamical Systems
2026-05-04 07:59:02Chang Liu, Wenhan Cao, Zeju Sun, Tianyi Zhang, Jiayu Yuan, Yi Zeng, Ting Yuan, Yao Lyu, Wei Wu, Stephen Shing-Toung Yau, Shengbo Eben LiAbstract
Bayesian filtering is a cornerstone of state estimation in complex systems such as aerospace systems, yet exact solutions are available only for linear Gaussian models. In practice,nonlinear systems are handled through tractable approximations,with Gaussian filters such as the extended and unscented Kalman filters being among the most widely used methods. This tutorial revisits Gaussian filtering from an information-geometric perspective, viewing the prediction and measurement update steps as inference procedures over state distributions. Within this framework, we introduce a geometry-aware Gaussian filtering approach that leverages natural gradient descent on the statistical manifold of Gaussian distributions. The resulting Natural Gradient Gaussian Approximation (NANO) filter iteratively refines the posterior mean and covariance while respecting the intrinsic geometry of the Gaussian family and preserving the positive definiteness of the covariance matrix. We further highlight fundamental connections to the classical Kalman filtering, showing that a single natural-gradient step exactly recovers the Kalman measurement update in the linear-Gaussian case. The practical implications of the proposed framework are illustrated through case studies in representative nonlinear estimation problems,including satellite attitude estimation, simultaneous localization and mapping, and state estimation for robotic systems including quadruped and humanoid robots.
Abstract (translated)
URL
https://arxiv.org/abs/2605.02306
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Attractor FCM
Abstract
In this paper an attractor FCM is created, tested, and analyzed. This FCM is neither a hebbian based nor agentic, nor a hybrid; it rather is a gradient descent based, physics constrained, Jacobian version of an FCM. Moreover, this model has several quirks; it uses residual memory, back propagation through time, and a fixed point anchor that is recursively implemented to update its weights. The residuals update the recursive part without losing the system memory. The model's anchor enables it to converge in a fixed point for which back propagation through time unrolls it and ensures that the error minimization is for an accurate gradient. Furthermore, a new learning algorithm is utilized. The Newton's method finds the system's fixed point attractor and then gradient descend is adaptively changing the landscape; an adaptive term is used to directly manipulate the weights through the attractor dynamics. As the adaptive term changes, the descent through the landscape is constantly adjusting according to sigmoid saturation, and that prevents premature convergence to a local minimum. Lastly, the updates are filtered by causal mask that informs the network about the physics, respecting the initial expert based opinions, for which model reduces the error to the target in an efficient way.
Abstract (translated)
URL
https://arxiv.org/abs/2604.27947
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Safe Bilevel Delegation : A Formal Framework for Runtime Delegation Safety in Multi-Agent Systems
2026-04-30 03:15:05Yuan SunAbstract
As large language model (LLM) agents are deployed in high-stakes environments, the question of how safely to delegate subtasks to specialized sub-agents becomes critical. Existing work addresses multi-agent architecture selection at design time or provides broad empirical guidelines, but neither provides a runtime mechanism that dynamically adjusts the safety-efficiency trade-off as task context changes during execution. We propose Safe Bilevel Delegation (SBD), a formal framework for runtime delegation safety in hierarchical multi-agent systems. SBD formulates task delegation as a bilevel optimization problem: an outer meta-weight network phi learns context-dependent safety-efficiency weights lambda(s) in [0,1]; an inner loop optimizes the delegation policy pi subject to a probabilistic safety constraint P(safe) >= 1-delta. The continuous delegation degree alpha in [0, 1] controls how much decision authority is transferred to each sub-agent, interpolating smoothly between full human override (alpha=0) and fully autonomous execution (alpha=1). We establish three theoretical results: (1) Safety Monotonicity--higher outer safety weight produces a weakly safer inner policy; (2) Inner Policy Convergence--projected gradient descent on the inner problem converges linearly under standard smoothness assumptions; (3) an Accountability Propagation bound that distributes responsibility across multi-hop delegation chains with a provable per-agent ceiling. We instantiate SBD in three high-stakes domains--medical AI (MIMIC-III), financial risk control (S and P 500), and educational agent supervision (ASSISTments)--specifying datasets, safety constraint sets, baselines, and evaluation protocols. This manuscript presents the formal framework and theoretical results in full; empirical validation following the protocols described herein is planned and will be reported in a forthcoming revision.
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URL
https://arxiv.org/abs/2604.27358
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Test-Time Safety Alignment
2026-04-28 23:21:10Baturay Saglam, Dionysis KalogeriasAbstract
Recent work has shown that a model's input word embeddings can serve as effective control variables for steering its behavior toward outputs that satisfy desired properties. However, this has only been demonstrated for pretrained text-completion models on the relatively simple objective of reducing surface-level profanity in short continuations. A natural and practically important question is how well input embeddings can control aligned models, which produce an imbalanced bimodal refuse-or-comply output distribution rather than the smooth distribution characteristic of open-ended generation. We explore this in the context of safety, showing that input word embeddings can be optimized in a sub-lexical manner to minimize the semantic harmfulness of aligned model responses. Our approach uses zeroth-order gradient estimation of a black-box text-moderation API with respect to the input embeddings, and then applies gradient descent on these embeddings to minimize the harmfulness of the generated text. Experiments show that the proposed method can neutralize every safety-flagged response on standard safety benchmarks.
Abstract (translated)
URL
https://arxiv.org/abs/2604.26167
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Scalable Hyperparameter-Divergent Ensemble Training with Automatic Learning Rate Exploration for Large Models
2026-04-27 17:17:28Hailing Cheng, Tao Huang, Chen Zhu, Antonio AlonsoAbstract
Training large neural networks with data-parallel stochastic gradient descent allocates N GPU replicas to compute effectively identical updates -- a practice that leaves the rich space of learning rate configurations entirely unexplored during training. We propose Hyperparameter-Divergent Ensemble Training (HDET), a method that repurposes these replicas for simultaneous learning rate exploration at negligible communication overhead. HDET operates in alternating phases: a fan-out stage in which replicas train independently under a structured, symmetric spread of learning rates, and a converge stage in which parameters are averaged across all replicas via AllReduce every T steps. Building on this ensemble substrate, we further propose an automatic learning rate (auto-LR) controller that treats the relative training loss across replicas as a performance signal, updating the shared base schedule toward higher-performing configurations via a momentum-based gradient-free meta-update. The combined method produces a self-adapting learning rate schedule that improves both optimization quality and generalization without additional hyperparameter sweeps or training budget. Crucially, the framework generalizes beyond learning rate: any scalar hyperparameter that does not alter model architecture -- such as dropout rate, attention scale temperature, or weight-decay coefficient -- can be explored across replicas using the same fan-out/converge protocol, with inter-replica loss differences serving as zero-order hypergradients that guide the search direction. HDET is implemented as a drop-in replacement for PyTorch's OneCycleLR scheduler, requiring no changes to model architecture, optimizer, or data pipeline.
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URL
https://arxiv.org/abs/2604.24708
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Cortex-Inspired Continual Learning: Unsupervised Instantiation and Recovery of Functional Task Networks
2026-04-27 16:06:28Kevin McKee, Thomas Hazy, Yicong Zheng, Zacharie Bugaud, Thomas MiconiAbstract
Block-sequential continual learning demands that a single model both protect prior solutions from catastrophic forgetting and efficiently infer at inference time which prior solution matches the current input without task labels. We present Functional Task Networks (FTN), a parameter-isolation method inspired by structural and dynamical motifs found in the mammalian neocortex. Similar to mixture-of-experts, this method uses a high dimensional, self-organizing binary mask over a large population of small but deep networks, inspired by dendritic models of pyramidal neurons. The mask is produced by a three-stage procedure: (1) gradient descent on a continuous mask identifies task-relevant neurons, (2) a smoothing kernel biases the result toward spatial contiguity, (3) and k-winner-take-all binarizes the resulting group at a fixed capacity budget. Like mixture-of-experts, each neuron is an independent deep network, so disjoint masks give exactly disjoint gradient updates, providing structural guarantees against catastrophic forgetting. This three-stage procedure recovers the sub-network of a previously-trained task in a single gradient step, providing unsupervised task segmentation at inference time. We test it on three continual-learning benchmarks: (1) a synthetic multi-task classification/regression generator, (2) MNIST with shuffled class labels (pure concept shift), and (3) Permuted MNIST (domain shift). On all three, FTN with fine grained smoothing (FTN-Slow) results in nearly zero forgetting. FTN with a large kernel and only 2 iterations of smoothing (FTN-Fast) trades off some retention for increased speed. We show that the spatial organization mechanism reduces the effective mask search from the combinatorial top-k subset problem in O(C(H,K)) to the complexity of a near-linear scan in O(H) over compact cortical neighborhoods, which is parallelized by the gradient-based update.
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URL
https://arxiv.org/abs/2604.24637
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On the explainability of max-plus neural networks
2026-04-27 12:32:31Ikhlas Enaieh (S2A, LTCI), Olivier Fercoq (S2A, LTCI), Garc\'ia \'Angel (DATSI, UPM)Abstract
We investigate the explanability properties of the recently proposed linear-min-max neural networks. At initialization, they can be interpreted as k-medoids with the infinity norm as a distance. Then, they are trained using subgradient descent to better fit the data. The model has been shown to be a universal approximator. Yet, we can trace the decision process because a single most activated neuron is responsible for the value of the output. Using this property, we designed a pixel fragility measure that determines whether changes to a single pixel may be responsible to a change in the classification output. Experiments on the PneumoniaMnist dataset show that this explanation for the output of the neural network compares favorably to SHAP and Integrated Gradient.
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URL
https://arxiv.org/abs/2605.00889
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Thoughts-as-Planning: Latent World Models for Chain-of-Thoughts Optimization via Reinforcement Planning
2026-04-27 08:18:12Dong Liu, Yanxuan Yu, Ying Nian WuAbstract
The success of large language models (LLMs) across diverse NLP tasks has elevated the importance of reasoning chain optimization as a critical step in aligning model behavior with task objectives. Existing reasoning chain tuning methods often rely on black-box heuristics or gradient-free search, which lack interpretability, generalization, and sample efficiency. In this work, we introduce \textbf{Thoughts-as-Planning}, a novel framework that formalizes reasoning chain optimization as a sequential decision-making process over a latent semantic space. We model the LLM as a partially observable environment and learn a latent world model that simulates the effect of reasoning chain edits on downstream outputs. A proximity-preserving embedding space is constructed to encode reasoning chain-response dynamics, enabling planning via gradient descent or reinforcement learning. Our method supports multi-scale abstraction, allowing reasoning chain edits at token, segment, and instruction levels to be integrated into a unified planner. Through extensive experiments on language understanding and generation tasks, we demonstrate that Thoughts-as-Planning outperforms state-of-the-art reasoning chain tuning baselines in efficiency, robustness, and generalization, while offering interpretability through its structured planning trajectory. Our code is available at this https URL.
Abstract (translated)
URL
https://arxiv.org/abs/2605.28842
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Why Architecture Choice Matters in Symbolic Regression
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Symbolic regression discovers mathematical formulas from data. Some methods fix a tree of operators, assign learnable weights, and train by gradient descent. The tree's structure, which determines what operators and variables appear at each position, is chosen once and applied to every target. This paper tests whether that choice affects which targets are actually recovered. Three structures are compared, all sharing the same operator and target language but differing in how variables enter the tree; one is strictly more expressive. Across over 12,700 training runs, one structure recovers a target at 100% while another scores 0%, and the ranking reverses on a different target. Expressiveness guarantees that a solution exists in the search space, but not that gradient descent finds it: the most expressive structure fails on targets that a restricted alternative solves reliably. Switching the operator changes which targets succeed; reversing its gradient profile collapses recovery entirely. Balanced (non-chain) tree shapes are never recovered. These findings show that the optimization landscape, not expressiveness alone, determines what gradient-based symbolic regression recovers.
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URL
https://arxiv.org/abs/2604.23256
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Separable Expert Architecture: Toward Privacy-Preserving LLM Personalization via Composable Adapters and Deletable User Proxies
2026-04-23 11:51:31Chris Schneider, Philipp Schoenegger, Ben BariachAbstract
Current model training approaches incorporate user information directly into shared weights, making individual data removal computationally infeasible without retraining. This paper presents a three-layer architecture that decouples personal data from shared weights by combining a static base model, composable domain-expert LoRA adapters that shape behavior without imparting user data, and per-user proxy artefacts whose deletion constitutes deterministic unlearning. Evaluation on Phi-3.5-mini and Llama-3.1-8B confirms per-user differentiation in which personal data influences outputs while remaining isolated, verified by a return to baseline after proxy removal (KL divergence of approximately 0.21 nats, 82-89% verification pass rate) and near-zero cross-user contamination. Because user-specific information never enters shared weights, the architecture mitigates model inversion, membership inference, and training-data extraction against shared model components by construction. The approach converts machine unlearning from an intractable weight-editing problem into a deterministic deletion operation that preserves personalization alongside privacy-enhancing guarantees and is compatible with differentially private stochastic gradient descent (DP-SGD) for privacy-preserving shared model improvement.
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URL
https://arxiv.org/abs/2604.21571
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SGD at the Edge of Stability: The Stochastic Sharpness Gap
2026-04-22 19:02:52Fangshuo Liao, Afroditi Kolomvaki, Anastasios KyrillidisAbstract
When training neural networks with full-batch gradient descent (GD) and step size $\eta$, the largest eigenvalue of the Hessian -- the sharpness $S(\boldsymbol{\theta})$ -- rises to $2/\eta$ and hovers there, a phenomenon termed the Edge of Stability (EoS). \citet{damian2023selfstab} showed that this behavior is explained by a self-stabilization mechanism driven by third-order structure of the loss, and that GD implicitly follows projected gradient descent (PGD) on the constraint $ S(\boldsymbol{\theta})\leq 2/\eta$. For mini-batch stochastic gradient descent (SGD), the sharpness stabilizes below $2/\eta$, with the gap widening as the batch size decreases; yet no theoretical explanation exists for this suppression. We introduce stochastic self-stabilization, extending the self-stabilization framework to SGD. Our key insight is that gradient noise injects variance into the oscillatory dynamics along the top Hessian eigenvector, strengthening the cubic sharpness-reducing force and shifting the equilibrium below $2/\eta$. Following the approach of \citet{damian2023selfstab}, we define stochastic predicted dynamics relative to a moving projected gradient descent trajectory and prove a stochastic coupling theorem that bounds the deviation of SGD from these predictions. We derive a closed-form equilibrium sharpness gap: $\Delta S = \eta \beta \sigma_{\boldsymbol{u}}^{2}/(4\alpha)$, where $\alpha$ is the progressive sharpening rate, $\beta$ is the self-stabilization strength, and $\sigma_{ \boldsymbol{u}}^{2}$ is the gradient noise variance projected onto the top eigenvector. This formula predicts that smaller batch sizes yield flatter solutions and recovers GD when the batch equals the full dataset.
Abstract (translated)
URL
https://arxiv.org/abs/2604.21016
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Maximum Likelihood Reconstruction for Multi-Look Digital Holography with Markov-Modeled Speckle Correlation
2026-04-22 03:36:52Xi Chen, Arian Maleki, Shirin JalaliAbstract
Multi-look acquisition is a widely used strategy for reducing speckle noise in coherent imaging systems such as digital holography. By acquiring multiple measurements, speckle can be suppressed through averaging or joint reconstruction, typically under the assumption that speckle realizations across looks are statistically independent. In practice, however, hardware constraints limit measurement diversity, leading to inter-look correlation that degrades the performance of conventional methods. In this work, we study the reconstruction of speckle-free reflectivity from complex-valued multi-look measurements in the presence of correlated speckle. We model the inter-look dependence using a first-order Markov process and derive the corresponding likelihood under a first-order Markov approximation, resulting in a constrained maximum likelihood estimation problem. To solve this problem, we develop an efficient projected gradient descent framework that combines gradient-based updates with implicit regularization via deep image priors, and leverages Monte Carlo approximation and matrix-free operators for scalable computation. Simulation results demonstrate that the proposed approach remains robust under strong inter-look correlation, achieving performance close to the ideal independent-look scenario and consistently outperforming methods that ignore such dependencies. These results highlight the importance of explicitly modeling inter-look correlation and provide a practical framework for multi-look holographic reconstruction under realistic acquisition conditions. Our code is available at: this https URL.
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URL
https://arxiv.org/abs/2604.20154
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On the Stability and Generalization of First-order Bilevel Minimax Optimization
2026-04-22 02:27:24Xuelin Zhang, Peipei YuanAbstract
Bilevel optimization and bilevel minimax optimization have recently emerged as unifying frameworks for a range of machine-learning tasks, including hyperparameter optimization and reinforcement learning. The existing literature focuses on empirical efficiency and convergence guarantees, leaving a critical theoretical gap in understanding how well these algorithms generalize. To bridge this gap, we provide the first systematic generalization analysis for first-order gradient-based bilevel minimax solvers with lower-level minimax problems. Specifically, by leveraging algorithmic stability arguments, we derive fine-grained generalization bounds for three representative algorithms, including single-timescale stochastic gradient descent-ascent, and two variants of two-timescale stochastic gradient descent-ascent. Our results reveal a precise trade-off among algorithmic stability, generalization gaps, and practical settings. Furthermore, extensive empirical evaluations corroborate our theoretical insights on realistic optimization tasks with bilevel minimax structures.
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URL
https://arxiv.org/abs/2604.20115
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