Differentiable Optimization

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6 papers in the last four weeks, against 2 the four weeks before. 0.1% of all new papers.

Jul 13Week of Sep 28

Latest papers 58

May 29, 2026cs.LG

Learning Multi-Agent Coordination via Sheaf-ADMM

We present a differentiable optimization framework for multi-agent coordination. An input is decomposed into overlapping local views, each processed by an agent that solves a convex subproblem parameterized by a neural encoder. Agents coordinate through the Alternating Direction Method of Multipliers (ADMM) with inter-agent constraints specified by a cellular sheaf. The sheaf specifies which aspects of neighboring solutions must agree, allowing for heterogeneous notions of global consensus. Backpropagating through the unrolled optimization jointly trains all components of the multi-agent system. We evaluate on maze pathfinding, image classification, and Sudoku, where agents with individually insufficient local views learn to coordinate to produce correct global outputs. On MNIST, the local-view decomposition yields improved robustness to distribution shifts relative to a standard CNN. On Sudoku, the optimization-derived structure yields markedly higher solve rates than parameter-matched MPNN baselines. Finally, the ADMM structure exposes distinct primal, consensus, and dual state variables, opening the coordination dynamics to direct analysis and intervention -- a property unavailable in standard message-passing architectures.

Jeffrey Seely, Bartłomiej Cupiał, Llion Jones

Sakana AI, Tokyo, Japan · University of Warsaw · AKCES NCBR

Multi-Agent System Optimization Multi-Agent Coordination Alternating Direction Method of Multipliers Multi-Agent Consensus Differentiable Optimization

May 28, 2026cs.LG

DisjunctiveNet: Neural Symbolic Learning via Differentiable Convexified Optimization Layers

Many learning tasks in science and engineering are characterized by sparse datasets, which limits the effectiveness of purely data-driven approaches. At the same time, these problems are often accompanied by rich domain knowledge derived from physical laws, operational requirements, and expert heuristics. Such knowledge is frequently expressed as rules involving logical propositions and linear inequalities. Existing neuro-symbolic methods typically enforce these rules approximately through soft penalties, assume input-independent rules when designing specialized architectures, or rely on non-differentiable post-processing at inference time to achieve hard constraint satisfaction. While recent advances in differentiable optimization layers enable end-to-end feasibility enforcement within neural networks, extending these approaches to logical or mixed-integer rules remains challenging due to inherent nonconvexity. In this work, we propose a unified end-to-end framework for enforcing hard, input-dependent mixed integer linear constraints within neural networks. Our approach represents rules as disjunctive constraints and applies hierarchical convex relaxations to obtain convex hull formulations. These relaxations yield tractable linear constraints that can be embedded as differentiable optimization layers while enabling exact rule satisfaction. We demonstrate the effectiveness of the proposed framework on real-world datasets, achieving perfect rule satisfaction and strong predictive performance.

Shraman Pal, Can Li

Davidson School of Chemical Engineering, Purdue University, West Lafayette, USA.

Differentiable Optimization Neurosymbolic Learning

May 20, 2026stat.ML

Semiparametric Efficient Bilevel Gradient Estimation

Functional bilevel methods estimate a lower-level function and plug it into a hypergradient, but this plug-in gradient can retain first-order bias when the lower-level problem is learned nonparametrically. To remove this bias, we develop a semiparametric debiasing theory for population bilevel gradients based on the efficient influence function. This perspective leads to a cross-fitted orthogonal hypergradient estimator for which we establish asymptotic normality together with uniform control over the outer parameter. Under quadratic losses, the estimator reduces to a simple doubly robust score based on conditional mean nuisances. On synthetic bilevel benchmarks with known ground truth, the method tracks the oracle efficient-gradient benchmark and improves over plug-in functional hypergradients and regularized kernel bilevel baselines.

Fares El Khoury, Houssam Zenati, Nathan Kallus +2

Université Grenoble Alpes, Inria, CNRS, Grenoble INP, LJK · Gatsby Computational Neuroscience Unit, University College London · Cornell University +1

Semiparametric Inference Bilevel Optimization Differentiable Optimization

May 19, 2026cs.CE

An End-to-End PyTorch Interface for Differentiable PDE Solvers: A RANS Model-Correction Study

This work presents an end-to-end strategy for solving inverse problems constrained by Partial Differential Equations within a fully differentiable Machine Learning framework. The proposed formulation provides a unified and user-friendly methodology applicable to a wide range of problems, from data assimilation to closure modeling. Our approach combines a baseline differentiable PDE solver, which predicts the state w from the nonlinear system

R(w) = 0

, with a generic additive, parametrized, and differentiable correction

f_φ(w)

, with trainable parameters

φ

. We show how to optimize phi within a fully differentiable Python workflow by reformulating the PDE as an implicit layer, enabling its integration into arbitrary objective functions, while leveraging PyTorch's automatic differentiation graph. The method is demonstrated on the Reynolds-Averaged Navier-Stokes equations for compressible flows, where the closure term, or a portion of it, is modeled using trainable parameters or a Neural Network. The first application considers the 2D NASA Wall-Mounted Hump test case, where a production-term parameter is optimized against time-averaged LES data. A second application is carried out on the VKI LS-59 turbine blade, where the Spalart-Allmaras eddy viscosity field is reconstructed through the optimization of a trainable spatial field. A dataset is generated starting from the VKI LS-59 turbine blade geometry using the differentiable BROADCAST solver with the Spalart-Allmaras turbulence model. The results highlight the flexibility of the framework, showing its applicability beyond turbulence modeling to a broader class of physics-informed PDE-constrained problems with data-driven components.

Luca Saverio, Michele Alessandro Bucci, Gianmarco Farro +2

MONHADE · Digital Sciences & Technologies Department, Safran Tech, Magny-Les-Hameaux, 78114, France. · DAAA, ONERA, Institut Polytechnique de Paris, Meudon, 92190, France. +1

PDE Solving Differentiable Optimization PDE Inverse Problems Computational Fluid Dynamics

May 16, 2026q-fin.PM

Financially Guided Deep Portfolio Optimization

Portfolio optimization in real-world financial markets is notoriously difficult due to non-stationarity, noisy data, and high transaction costs. Standard predict-then-optimize methods first forecast returns and then solve for weights, compounding prediction errors and often failing under regime shifts. We propose an end-to-end framework that directly optimizes differentiable surrogates of key financial metrics (Sharpe ratio, Omega ratio, Conditional Value-at-Risk, and risk parity), allowing neural networks to learn portfolio weights via backpropagation. Our expanding-window walk-forward procedure, applied to 50 S&P 500 stocks from 2007 to 2023, incorporates realistic bid-ask spread costs and rebalances quarterly. On the challenging out-of-sample test period (2022-2023), the best model, an AttentionLSTM with the Omega-CVaR-RiskParity loss, achieves an annualized Sharpe of 0.29 and a total compounded return of +7.86%, while the S&P 500 delivers -4.52% total compounded return and an annualized Sharpe of -0.02. This outperforms the S&P 500 by 12.38 percentage points, while keeping tail risk (CVaR) nearly unchanged. The framework outperforms the equal-weight portfolio, S&P 500, and traditional methods (MVP, HRP, NCO, ERC), demonstrating that embedding financial objectives directly into model training yields robust, economically meaningful outperformance even in adverse market conditions.

Rahul Fernandes, Travis Desell

Department of Software Engineering Rochester Institute of Technology Rochester, New York, USA

Quantitative Finance Portfolio Optimization Differentiable Optimization Financial Time Series

May 16, 2026cs.LG

Differentiable Optimization Layers for Guaranteed Fairness in Deep Learning

Differentiable optimization layers are traditionally integrated in predict-then-optimize frameworks where a neural model estimates parameters that subsequently serve as fixed inputs to downstream decision-making optimization problems. In this work, we introduce the concept of a "fairness layer": a differentiable optimization layer appended to a model's output layer that guarantees a chosen notion of output parity is satisfied when integrated into a neural network. Additionally, we introduce an online primal-dual inference algorithm that provides provable aggregate fairness guarantees for streaming predictions with arbitrarily small batch sizes, where traditional per-batch constraints become overly restrictive. Numerical experiments demonstrate the effectiveness of the fairness layer and associated algorithm, and theoretical analysis characterizes the layer's differentiability and stability properties during model training and backpropagation. Our code for these experiments is publicly available on GitHub (https://github.com/dtroxell19/FairDL-ICML-2026.git) and our public Python package documentation can be found online: https://dtroxell19.github.io/fairness_training/.

David Troxell, Noah Roemer, Guido Montúfar

Department of Statistics & Data Science, University of California, Los Angeles, USA · Department of Mathematics, University of California, Los Angeles, USA · Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany

Deep Learning Optimization Algorithmic Fairness Differentiable Optimization

May 13, 2026quant-ph

Neural QAOA $^{2}$ : Differentiable Joint Graph Partitioning and Parameter Initialization for Quantum Combinatorial Optimization

The quantum approximate optimization algorithm (QAOA) holds promise for combinatorial optimization but is constrained by limited qubits. While divide-and-conquer frameworks like QAOA

^{2}

address scalability by partitioning graphs into subgraphs, existing methods suffer from two fundamental limitations: i) misalignment between heuristic partitioning metrics and quantum optimization goals, and ii) topology-blind parameter initialization that leads to optimization cold starts. To bridge these gaps, we propose Neural QAOA

^{2}

, an end-to-end differentiable framework that jointly generates graph partitions and initial parameters. By integrating a generative evaluative network (GEN), our method utilizes a differentiable quantum evaluator as a high-fidelity performance surrogate to provide direct gradient guidance, enabling the joint generator to learn the intrinsic mapping from graph topology to high-quality partition and parameter configurations. Extensive experiments on 183 QUBO, Ising, and MaxCut instances (21 to 1000 variables) demonstrate that our gradient-driven approach broadly outperforms heuristic baselines, ranking first on 101 instances. It exhibits zero-shot generalization across out-of-distribution graph topologies and scales.

Zubin Zheng, Jiahao Wu, Shengcai Liu

Guangdong Provincial Key Labora- tory of Brain-Inspired Intelligent Computation, Department of CSE, SUSTech.

Quadratic Unconstrained Binary Optimization Differentiable Optimization Quantum Approximate Optimization Algorithm

May 12, 2026cs.CV

WildPose: A Unified Framework for Robust Pose Estimation in the Wild

Estimating camera pose in dynamic environments is a critical challenge, as most visual SLAM and SfM methods assume static scenes. While recent dynamic-aware methods exist, they are often not unified: semantic-based approaches are brittle, per-sequence optimization methods fail on short sequences, and other learned models may degrade on static-only scenes. We present WildPose, a unified monocular pose estimation framework that is robust in dynamic environments while maintaining state-of-the-art performance on static and low-ego-motion datasets. Our key insight is to connect two powerful paradigms in modern 3D vision: the rich perceptual frontend of feedforward models and the end-to-end optimization of differentiable bundle adjustment (BA). We achieve this with a 3D-aware update operator built on a frozen, pre-trained MASt3R feature backbone, together with a high-capacity motion mask detector that uses multi-level 3D-aware features from the same backbone. Extensive experiments show WildPose consistently outperforms prior methods across dynamic (Wild-SLAM, Bonn), static (TUM, 7-Scenes), and low-ego-motion (Sintel) benchmarks.

Jianhao Zheng, Liyuan Zhu, Zihan Zhu +1

1Stanford University · 2ETH Zürich

Camera Pose Estimation Visual SLAM Differentiable Optimization

May 12, 2026cs.CV

Vector Scaffolding: Inter-Scale Orchestration for Differentiable Image Vectorization

Differentiable vector graphics have enabled powerful gradient-based optimization of vector primitives directly from raster images. However, existing frameworks formulate this as a flat optimization problem, forcing hundreds to thousands of randomly initialized curves to blindly compete for pixel-level error reduction. This disordered optimization leads to topology collapse, where macroscopic structures are distorted by internal high-frequency noise, resulting in a redundant and uneditable "polygon soup" that limits practical editability. To address this limitation, we propose Vector Scaffolding, a novel hierarchical optimization framework that shifts from flat pixel-matching to structured topological construction tailored for vector graphics. By identifying a key cause of topology collapse as the mathematical imbalance between area and boundary gradients, we introduce Interior Gradient Aggregation to stabilize the learning dynamics of multi-scale curve mixtures. Upon this stabilized landscape, we employ Progressive Stratification and Rapid Inflation Scheduling to progressively densify vector primitives with extremely high learning rates (

\times 50

). Experiments demonstrate that our approach accelerates optimization by

2.5\times

while simultaneously improving PSNR by up to 1.4 dB over the previous state of the art.

Jaerin Lee, Kanggeon Lee, Kyoung Mu Lee

Dept. of ECE&ASRI, Seoul National University, Korea · IPAI, Seoul National University, Korea

Differentiable Rendering Differentiable Optimization

May 9, 2026math.OC

Select-then-differentiate: Solving Bilevel Optimization with Manifold Lower-level Solution Sets

We study optimistic bilevel optimization when the lower-level problem has a non-isolated manifold of minimizers. In this setting, the hyper-objective may be non-differentiable because the upper-level criterion must choose among multiple lower-level solutions. Under a local Polyak--Łojasiewicz (PŁ) condition, we show that differentiability does not require the lower-level solution set to be a singleton: uniqueness of the optimistic selection is sufficient. This yields an explicit pseudoinverse-based hyper-gradient formula extending the classical singleton-minimizer result. We further characterize the regularity of the hyper-objective: non-degeneracy of the selected minimizer along the solution manifold yields local smoothness, while failure of uniqueness can create many non-differentiable points and failure of non-degeneracy can destroy all positive Hölder regularity of the hyper-gradient. Motivated by this theory, we propose HG-MS, a select-then-differentiate method combining explicit optimistic selection with efficient pseudoinverse-based hyper-gradient computation. Despite the nonconvex nature of optimistic selection over the lower-level solution manifold, we show that HG-MS converges to a stationary point of the optimistic objective with complexity governed by the intrinsic dimension of the solution manifold rather than its ambient dimension. Empirically, we test a practical variant of HG-MS for matched-budget LLM source reweighting. This variant preserves the select-then-differentiate principle and obtains the best GSM8K/MATH scores across the tested backbones, along with competitive or best MT-Bench instruction-following results.

Saeed Masiha, Zebang Shen, Negar Kiyavash +1

EPFL School of Management of Technology, Station 5, 1015 Lausanne, Switzerland · ETH Department of Computer Science, Universitätstrasse 6, 8092 Zürich, Switzerland

Nonconvex Optimization Bilevel Optimization Differentiable Optimization

May 8, 2026cs.LG

Approximation-Free Differentiable Oblique Decision Trees

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.

Subrat Prasad Panda, Blaise Genest, Arvind Easwaran

College of Computing and Data Science Nanyang Technological University Singapore

Interpretable ML Tabular ML Differentiable Optimization

May 7, 2026cs.LG

SNAPO: Smooth Neural Adjoint Policy Optimization for Optimal Control via Differentiable Simulation

Many real-world problems require sequential decisions under uncertainty: when to inject or withdraw gas from storage, how to rebalance a pension portfolio each month, what temperature profile to run through a pharmaceutical reactor chain. Dynamic programming solves small instances exactly but scales exponentially in state dimensions. Black-box reinforcement learning handles high-dimensional states but trains slowly and produces no sensitivities. We introduce SNAPO (Smooth Neural Adjoint Policy Optimization), a framework that embeds a neural policy inside a known, differentiable simulator, replaces hard constraints with smooth approximations, and computes exact gradients of the objective with respect to all policy parameters and all inputs in a single adjoint pass. We demonstrate SNAPO on three domains: natural gas storage (training in under a minute, 365 forward curve sensitivities at no additional cost per sensitivity), pension fund asset-liability management (6.5x-200x sensitivity speedup over bump-and-revalue, scaling with the number of risk factors), and pharmaceutical manufacturing (cross-unit sensitivities through a 4-unit process chain, with 20 ICH Q8 regulatory sensitivities from 5 adjoint passes in 74.5 milliseconds). All sensitivities are produced by the same backward pass that trains the policy, at a cost proportional to one reverse pass regardless of how many sensitivities are computed.

Dmitri Goloubentsev, Natalija Karpichina

MatLogica, U.K.

Policy Optimization Differentiable Programming Differentiable Optimization Optimal Control

May 7, 2026eess.SP

CredibleDFGO: Differentiable Factor Graph Optimization with Credibility Supervision

Global navigation satellite system (GNSS) positioning is widely used for urban navigation, but the covariance reported by the GNSS solver is often unreliable in urban canyons. Existing differentiable factor graph optimization (DFGO) methods learn measurement weighting through the solver, but they still use position-only objectives. As a result, the position estimate may improve while the reported covariance remains too small, too large, or incorrectly oriented. We propose CredibleDFGO (CDFGO), a differentiable GNSS factor graph framework that makes covariance credibility an explicit training target. A Weighting Generation Network (WGN) predicts per-satellite reliability weights, and a differentiable Gauss-Newton solver maps these weights to a position estimate and a Hessian-derived posterior covariance. We use proper scoring rules to supervise the East-North predictive distribution end to end. We study negative log-likelihood (NLL), the energy score (ES), and their combination. Results on three UrbanNav test scenes show consistent gains in covariance credibility. Positioning accuracy also improves on the medium-urban and harsh-urban scenes; on the deep-urban scene, both the mean horizontal error and the 95th-percentile error improve. On the harsh-urban Mong Kok (MK) scene, CDFGO-Combined reduces the mean horizontal error from 13.77 m to 11.68 m, reduces NLL from 40.63 to 6.59, and reduces ES from 12.31 to 9.05 relative to DFGO (MAE). Case studies link the MK improvement to better axis-wise consistency, more credible local covariance ellipses, and satellite-level reweighting.

Liang Qian, Penggao Yan, Penghui Xu +1

Department of Aeronautical and Aviation Engineering The Hong Kong Polytechnic University, Hong Kong, China

Factor Graph Optimization Wireless Localization Differentiable Optimization Uncertainty Calibration

May 7, 2026cs.CV

InkDiffuser: High-Fidelity One-shot Chinese Calligraphy via Differentiable Morphological Optimization

Current Chinese calligraphy generation methods suffer from poor stroke rendering and unrealistic ink morphology, resulting in outputs with limited visual fidelity and artistic fluidity. To address this problem, we propose \textbf{InkDiffuser}, a diffusion-based generative framework for one-shot Chinese calligraphy synthesis. To guarantee high-fidelity rendering, we introduce two core contributions: a high-frequency enhancement mechanism and a Differentiable Ink Structure (DIS) loss that explicitly regularizes ink morphology. Inspired by the observation that high-frequency information in individual samples typically carries contour details, we enhance content extraction by explicitly fusing high-frequency representations for more accurate font structure. Furthermore, we propose a differentiable ink structure loss that integrates differentiable morphological operations into the diffusion process. By allowing the model to learn an explicit decomposition of ink-trace structures, DIS facilitates fine-grained refinement of stroke contours and delivers significantly improved visual realism in the generated calligraphy. Extensive experiments on various calligraphic styles and complex characters demonstrate that InkDiffuser can generate superior calligraphy fonts with realistic ink rendering effects from only a single reference glyph and outperform existing few-shot font generation approaches in structural consistency, detail fidelity, and visual authenticity. The code is available at the following address: https://github.com/JingVIPLab/InkDiffuser.

Kunchong Shi, Jing Zhang

Department of Computer Science and Engineering, East China University of Science and Technology, Shanghai, 200237 China

Image Generation Diffusion-Based Image Generation Differentiable Optimization

May 6, 2026cs.LG

Differentiable Parameter Optimization for DAEs with State-Dependent Events

Differential-algebraic equations (DAEs) with state-dependent events arise in systems whose continuous dynamics are constrained by algebraic equations and interrupted by mode changes, switching logic, impacts, or state reinitializations. Gradient-based parameter learning for such systems is challenging because algebraic variables are implicitly defined, event times depend on the parameters, and reset maps introduce discontinuities. This paper studies differentiable parameter optimization for semi-explicit DAEs with events. We formulate the learning problem as a constrained least-squares problem with DAE dynamics, algebraic constraints, guard equations, and reset maps. We then develop two complementary gradient-computation strategies. The first is an automatic-differentiation-through-simulation method that solves algebraic variables inside the vector field, differentiates the algebraic solve using the implicit function theorem, and handles events through segmented differentiable integration. The second is an explicit discrete-adjoint method that represents the forward simulation as an event-split residual system and computes gradients by solving for the Lagrange multipliers of smooth-segment and event residuals. The formulation clarifies that residual terms in the adjoint method are equality constraints, not heuristic penalties. We compare the two approaches in terms of gradient interpretation, event-time handling, implementation complexity, and local validity. Both methods provide gradients for the event path selected by the forward simulation and are valid under fixed event ordering and transversal guard crossings.

Ion Matei, Maksym Zhenirovskyy, Anthony Wong

Fujitsu Research of America

Dynamical Systems Automatic Differentiation Constrained Optimization Differentiable Physics Differentiable Optimization

May 6, 2026cs.LG

Graph Normalization: Fast Binarizing Dynamics for Differentiable MWIS

We introduce Graph Normalization (GN), a principled dynamical system on graphs that serves as a differentiable approximation engine for the NP-hard Maximum Weight Independent Set (MWIS) problem. MWIS encompasses many combinatorial challenges, including optimal assignment, scheduling, set packing, and MAP inference in discrete Markov Random Fields. Unlike Belief Propagation, we prove GN always converges to a binary indicator of a Maximum Independent Set. GN realizes a fast quasi-Newton descent through an exact Majorization-Minimization step, systematically improving the MWIS relaxed primal objective. We establish an equivalence between GN and the Replicator Dynamics of a nonlinear evolutionary game, where vertices compete for inclusion in an independent set. While a non-potential game, the GN game follows Fisher's Fundamental Theorem of Natural Selection, where the average fitness equals the MWIS primal objective and strictly increases. This connection leads to a weighted extension of the Motzkin-Straus theorem, showing MISes are in bijection with the local minima of a quadratic form over a tilted simplex. For the Assignment Problem, GN acts as a variant of the Sinkhorn algorithm that naturally converges to a hard assignment while generalizing to arbitrary constraint graphs. We demonstrate GN's performance as a fast binarization engine for the state-of-the-art Bregman-Sinkhorn relaxed MWIS solver. On real-world benchmarks with up to 1M edges, GN identifies solutions within 1% of the best known results in seconds on a CPU. GN opens new avenues for deep learning architectures requiring differentiable, "hard" decisions under constraints, with applications in structured sparse attention, dynamic network pruning, and Mixture-of-Experts. Beyond core AI, the GN framework enables end-to-end learning of constrained optimization in computer vision, computational biology, and resource allocation.

Laurent Guigues

Dynamical Systems Replicator Dynamics Combinatorial Optimization Nonconvex Optimization Differentiable Optimization

May 6, 2026cs.LG

Geometry-Aware Neural Optimizer for Shape Optimization and Inversion

Geometry is central to PDE-governed systems, motivating shape optimization and inversion. Classical pipelines conduct costly forward simulation with geometry processing, requiring substantial expert effort. Neural surrogates accelerate forward analysis but do not close the loop because gradients from objectives to geometry are often unavailable. Existing differentiable methods either rely on restrictive parameterizations or unstable latent optimization driven by scalar objectives, limiting interpretability and part-wise control. To address these challenges, we propose Geometry-Aware Neural Optimizer (\textbf{\textsc{GANO}}), an end-to-end differentiable framework that unifies geometry representation, field-level prediction, and automated optimization/inversion in a single latent-space loop. \textsc{GANO} encodes shapes with an auto-decoder and stabilizes latent updates via a denoising mechanism, and a geometry-informed surrogate provides a reliable gradient pathway for geometry updates. Moreover, \textsc{GANO} supports part-wise control through null-space projection and uses remeshing-free projection to accelerate geometry processing. We further prove that denoising induces an implicit Jacobian regularization that reduces decoder sensitivity, yielding controlled deformations. Experiments on three benchmarks spanning 2D Helmholtz, 2D airfoil, and 3D vehicles show state-of-the-art accuracy and stable, controllable updates, achieving up to +55.9% lift-to-drag improvement for airfoils and ~7% drag reduction for vehicles.

Guoze Sun, Tianya Miao, Haoyang Huang +4

Gaoling School of Artificial Intelligence, Renmin University of China

Neural Surrogate Modeling Geometric Representation Learning Constrained Optimization Differentiable Optimization

May 5, 2026eess.SY

Differentiable Optimization Layered Safety-Critical Control for Risk-Aware Navigation via Conformal Prediction

Risk-aware navigation in unknown environments is a fundamental challenge for autonomous vehicles operating in complex urban systems. To address this issue, this paper presents a differentiable optimization layered safety-critical control method based on conformal prediction. First, to handle uncertainties arising from sensor noise, the conformal prediction method is employed to generate risk-aware obstacle ellipsoids around an elliptical-shaped robot. Second, two nested differentiable optimization layers are introduced to build the control barrier functions for obstacle avoidance and feasibility guarantee, respectively. Then, a quadratic program based safety-critical control law is proposed to integrate the above control barrier function constraints as well as input constraints. In the end, the effectiveness of the proposed framework is demonstrated through numerical simulations.

Jinyang Dong, Shizhen Wu, Yongchun Fang

Institute of Robotics and Automatic Information Systems, College of Artificial Intelligence, Nankai University, Tianjin 300071, China · Academy for Advanced Interdisciplinary Studies, Nankai University, Tianjin 300071, China · Institute of Intelligence Technology and Robotic Systems, Shenzhen Research Institute of Nankai University, Shenzhen 518083, China

Safety-Critical Control Control Barrier Functions Safe Robot Navigation Robot Safety Differentiable Optimization

May 4, 2026cs.RO

Exact Higher-Order Derivatives for SE(3) via Analytical/AD Methods

Fast prototyping of new SE(3) estimation objectives remains awkward in practice. Modern Lie-group frameworks -- GTSAM, manif, Sophus, SymForce, Ceres -- target first-order workloads through different code-generation and automatic-differentiation strategies, each optimized for a particular seam between hand-derived geometry and generic differentiation. The remaining gap is a compact, AD-safe path from these first-order primitives to exact Hessians, observed-information matrices, and higher-order derivative tensors: the quantities needed for exact Newton steps, observed-information covariance estimates, and covariance correction. This paper presents a hybrid analytical/AD recipe for SE(3) negative log-likelihoods. The practitioner writes the NLL gradient once, generic over a scalar type, and places the analytical/AD seam at the point-action interface y = Tx. Closed-form Lie-group Jacobians are used up to this interface; AD is applied only beyond it. The same source is then instantiated with ordinary floating-point scalars for gradients, vector-seeded dual numbers for exact Hessians in a single forward-mode pass, and nested dual numbers for higher-order derivative tensors. On a representative 6-DoF, 5-landmark SE(3) NLL, the advocated seeded-Hessian path is approximately 5x faster than finite-differencing the AD gradient on this benchmark while matching a nested-AD oracle to machine precision. The implementation adds roughly 70 lines of analytical-Jacobian code over an AD-only baseline. We also identify and fix a removable singularity in the standard SO(3)/SE(3) scalar basis that would otherwise produce NaNs at the origin under seeded AD, and we audit which Lie-group derivative tensors require this stabilized basis. The result is a practical path from rapidly written SE(3) objectives to exact higher-order derivatives, with predictable runtime and no finite-difference tuning.

Frank O. Kuehnel

Sigma Point Labs, Denver, CO, USA

Automatic Differentiation Lie Group Methods Second-Order Optimization Differentiable Optimization

May 2, 2026cs.LG

Decision-Focused Learning via Tangent-Space Projection of Prediction Error

Decision-Focused Learning (DFL) trains predictors to improve downstream decision quality, but computing regret gradients typically requires differentiating through solvers or relying on surrogate losses, which can be computationally expensive or deviate from the true objective. We show that, under standard regularity with locally stable active constraints, the regret gradient admits a closed-form geometric characterization, equivalent to the prediction error projected onto the tangent space of active constraints, scaled by local curvature. This reveals that regret gradients can be obtained by filtering decision-irrelevant components from the MSE gradient, providing a simpler and more direct alternative to existing approaches. Based on this, we propose PEAR (Projected Error As Regret-gradient), which computes regret gradients via a reduced linear system over active constraints, avoiding differentiation through solver iterations or additional optimization solves. Experiments on LP benchmarks and a real-world QP task show that PEAR achieves the best decision quality among all baselines while being the most computationally efficient, with gains that persist under constraint shifts.

Junhyeong Lee, Sangjin Jin, Yongjae Lee

Department of Industrial Engineering, Ulsan National Institute of Science and Technology, Ulsan, South Korea.

Decision-Focused Learning Differentiable Optimization

May 1, 2026cs.CE

Differentiable Multiphysics Co-Optimization via Implicit Neural Representations: A Transient Hamburger-Cooking Benchmark

The co-optimization of geometry and physical parameters remains challenging in transient multiphysics systems involving moving boundaries, nonlinear material response, phase transitions, and competing objectives. Existing methods often optimize geometry and physical variables separately, rely on simplified steady-state physics, or require offline data generation and reduced design spaces. Here, we present an end-to-end differentiable co-optimization framework that couples an implicit neural representation of geometry with a JAX-compiled Eulerian multiphysics solver. Geometry is represented as a signed distance field using Fourier-feature-encoded spatial coordinates, while boundary conditions, initial conditions, process controls, and material parameters are optimized within the same differentiable loop. Continuous relaxations represent non-smooth physical transitions while preserving compatibility with reverse-mode automatic differentiation and backpropagation through time. We demonstrate the framework using a transient hamburger-cooking benchmark, selected as an interpretable multiphysics problem rather than a culinary optimization exercise. The benchmark combines conductive and convective heat transfer, latent energy effects, moisture and fat transport, shrinkage-induced geometry evolution, evolving contact boundary conditions, flipping-induced boundary-condition changes, and competing quality objectives. Results show that geometry-only optimization modifies shape to relieve thermal bottlenecks, while joint co-optimization distributes the design response across geometry, material state, process variables, and boundary conditions through gradients propagated over the full transient rollout.

Navid Zobeiry

Department of Materials Science and Engineering, University of Washington · William E. Boeing Department of Aeronautics & Astronautics, University of Washington, Seattle, WA 98195, USA

Differentiable Optimization Multi-Objective Optimization

Apr 30, 2026cs.LG

NLPOpt-Net: A Learning Method for Nonlinear Optimization with Feasibility Guarantees

Nonlinear Parametric Optimization Network (NLPOpt-Net) is an unsupervised learning architecture to solve constrained nonlinear programs (NLP). Given the structure of an NLP, it learns the parametric solution maps with guaranteed constraint satisfaction. The architecture consists of a backbone neural network (NN) followed by a multilayer (

k

-layered) projection. While the NN drives toward optimality through a loss function consisting of a modified Lagrangian augmented with a consistency loss, the projection ensures feasibility by projecting the NN predictions in the original constraint manifold. Instead of typical distance minimization, our projection exploits local quadratic approximations of the original NLP. Under certain conditions (such as convexity), the projection has a descent property, which improves the NN predictions further. NLPOpt-Net deploys an inversion-free, modified Chambolle-Pock algorithm to solve the constrained quadratic projections during the forward pass and uses the implicit function theorem for efficient backpropagation. The fixed structure of the projection further allows decoupling of the NN and the projection once the training is complete. NLPOpt-Net solves large-scale convex QP, QCQP, NLP, and nonconvex problems with near zero optimality gap and constraint violations reduced to machine precision. Additionally, it provides near accurate prediction of the active sets and corresponding dual variables, thereby enabling a scalable approach for multiparametric programming. Compiling the projection in C provides order of magnitude improvement in inference time compared to JAX. We provide the codes and NLPOpt-Net as a ready to use package that includes GPU support.

Bimol Nath Roy, Rahul Golder, MM Faruque Hasan

Texas A&M University

Neural Network Optimization Learning to Optimize Constrained Optimization Differentiable Optimization

Apr 21, 2026cs.RO

Differentiable Satellite Constellation Configuration via Relaxed Coverage and Revisit Objectives

Satellite constellation design requires optimizing orbital parameters across multiple satellites to maximize mission specific metrics. For many types of mission, it is desirable to maximize coverage and minimize revisit gaps over ground targets. Existing approaches to constellation design either restrict the design space to symmetric parametric families such as Walker constellations, or rely on metaheuristic methods that require significant compute and many iterations. Gradient-based optimization has been considered intractable due to the non-differentiability of coverage and revisit metrics, which involve binary visibility indicators and discrete max operations. We introduce four continuous relaxations: soft sigmoid visibility, noisy-OR multi-satellite aggregation, leaky integrator revisit gap tracking, and LogSumExp soft-maximum, which when composed with the

\partial

SGP4 differentiable orbit propagator, yield a fully differentiable pipeline from orbital elements to mission-level objectives. We show that this scheme can recover Walker-Delta geometry from irregular initializations, and discovers elliptical Molniya-like orbits with apogee dwell over extreme latitudes from only gradients. Compared to simulated annealing (SA), genetic algorithm (GA), and differential evolution (DE) baselines, our gradient-based method recovers Walker-equivalent geometry within

{\sim}750

evaluations, whereas the three black-box baselines plateau at with significantly worse revisit even with roughly four times the evaluation budget.

Shreeyam Kacker, Kerri Cahoy

Department of Aeronautics and Astronautics MIT

Differentiable Programming Differentiable Optimization

Mar 28, 2026cs.RO

MetaTune: Adjoint-based Meta-tuning via Robotic Differentiable Dynamics

Disturbance observer-based control has shown promise in robustifying robotic systems against uncertainties. However, tuning such systems remains challenging due to the strong coupling between controller gains and observer parameters. In this work, we propose MetaTune, a unified framework for joint auto-tuning of feedback controllers and disturbance observers through differentiable closed-loop meta-learning. MetaTune integrates a portable neural policy with physics-informed gradients derived from differentiable system dynamics, enabling adaptive gains across tasks and operating conditions. We develop an adjoint method that efficiently computes the meta-gradients with respect to adaptive gains backward in time to directly minimize the cost-to-go. Compared to existing forward methods, our approach reduces the computational complexity to be linear in the data horizon. On quadrotor control tasks, MetaTune achieves competitive or improved tracking performance while reducing gradient computation time by more than 50%. In PX4-Gazebo hardware-in-the-loop simulation, the learned policy transfers zero-shot and reduces tracking RMSE by about 15--20% in aggressive flight and up to 40% under strong disturbances.

Xiexin Peng, Bingheng Wang, Tao Zhang +2

School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China · Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117583, Singapore · Wuhan Zhenyou Technology Co., Ltd., Wuhan 430205, China

Robust Control Feedback Control Quadrotor Control Differentiable Optimization Adaptive Control

Feb 5, 2026cs.LG

Shiva-DiT: Residual-Based Differentiable Top- $k$ Selection for Efficient Diffusion Transformers

Diffusion Transformers (DiTs) are costly at high resolution because self-attention scales quadratically with token sequence length. Existing pruning methods do not jointly provide end-to-end learnability, low training overhead, and deterministic token counts for predictable token-dependent computation. We propose Shiva-DiT, based on Residual-Based Differentiable Top-k Selection. Its forward pass executes hard top-k selection, while a residual-aware straight-through estimator propagates gradients to both token scores and the budget k without evaluating a second backbone path. A Context-Aware Router and Adaptive Ratio Policy learn layer- and timestep-dependent retention schedules under a target average budget. Experiments on SD3-Medium, Flux.1-dev, and PixArt-Σ show consistent reductions in FLOPs and measured latency. On SD3-Medium, Shiva-DiT provides four fidelity-latency operating points and reaches a 1.54x wall-clock speedup with competitive fidelity.

Jiaji Zhang, Hailiang Zhao, Jiaju Wu +3

College of Computer Science and Technology, Zhejiang University · 3Nanyang Technological University

Diffusion Model Acceleration Diffusion Transformer Token Pruning Differentiable Optimization

Jan 23, 2026cs.MS

Learning to Optimize by Differentiable Programming

Solving massive-scale optimization problems requires scalable first-order methods with low per-iteration cost. This tutorial highlights a shift in optimization: using differentiable programming not only to execute algorithms but to learn how to design them. Modern frameworks such as PyTorch, TensorFlow, and JAX enable this paradigm through efficient automatic differentiation. Embedding first-order methods within these systems allows end-to-end training that improves convergence and solution quality. Guided by Fenchel-Rockafellar duality, the tutorial demonstrates how duality-informed iterative schemes such as the alternating direction method of multipliers, and the primal-dual hybrid gradient can be learned and adapted through representative case studies.

Liping Tao, Xindi Tong, Chee Wei Tan

Nanyang Technological University, Singapore · Nanyang Technological University, Singapore, Singapore

Primal-Dual Optimization Learning to Optimize Alternating Direction Method of Multipliers Differentiable Programming Constrained Optimization Differentiable Optimization

Jan 12, 2026physics.data-an

Learning to bin: differentiable and Bayesian optimization for multi-dimensional discriminants in high-energy physics

Categorizing events using discriminant observables is central to many high-energy physics analyses. Yet, bin boundaries are often chosen manually. A simple, popular choice in multi-classification tasks is to assign events according to the largest per-class score ("argmax") and to apply equidistant binning to the resulting one-dimensional discriminants. We propose a binning optimization for signal significance directly in multi-dimensional discriminants. We use a Gaussian Mixture Model (GMM) to define flexible regions in the score space, which can be interpreted either as bins or as analysis categories. While this GMM-based strategy is applicable in both one and multiple dimensions, we also study a direct bin-boundary optimization in one dimension as a simpler alternative for binary discriminants. On this binning model, we study two optimization strategies: a differentiable and a Bayesian optimization approach. We study two toy setups: a binary classification and a three-class problem with two signals and backgrounds. In the one-dimensional case, both approaches achieve similar gains in signal sensitivity compared to equidistant binning for a given number of bins, while in the multi-dimensional case the differentiable approach performs best. We show that the GMM-based optimization can outperform argmax classification even after optimized binning is applied to the one-dimensional projections. We further study the performance of our methods on the FAIR Universe

H\rightarrowττ

dataset, where the GMM-based optimization gives the highest signal significance. Both methods are released as lightweight Python plugins intended for straightforward integration into existing analyses.

Johannes Erdmann, Nitish Kumar Kasaraguppe, Florian Mausolf

RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany

High-Energy Physics Differentiable Optimization

Sep 2, 2025cs.LG

Differentiable Expectation-Maximisation and Applications to Gaussian Mixture Model Optimal Transport

The Expectation-Maximisation (EM) algorithm is a central tool in statistics and machine learning, widely used for latent-variable models such as Gaussian Mixture Models (GMMs). Despite its ubiquity, EM is typically treated as a non-differentiable black box, preventing its integration into modern learning pipelines where end-to-end gradient propagation is essential. In this work, we present and compare several differentiation strategies for EM, from full automatic differentiation to approximate methods, assessing their accuracy and computational efficiency. As a key application, we leverage this differentiable EM in the computation of the Mixture Wasserstein distance

\mathrm{MW}_2

between GMMs, allowing

\mathrm{MW}_2

to be used as a differentiable loss in imaging and machine learning tasks. To complement our practical use of

\mathrm{MW}_2

, we contribute a novel stability result which provides theoretical justification for the use of

\mathrm{MW}_2

with EM, and also introduce a novel unbalanced variant of

\mathrm{MW}_2

. Numerical experiments on barycentre computation, colour and style transfer, image generation, and texture synthesis illustrate the versatility of the proposed approach in different settings.

Samuel Boïté, Eloi Tanguy, Julie Delon +2

Université Paris Cité, CNRS, MAP5, F-75006 Paris, France · Centre Borelli, CNRS and ENS Paris-Saclay, F-91190 Gif-sur-Yvette, France · CMAP, CNRS, Ecole Polytechnique, Institut Polytechnique de Paris

Gaussian Mixture Models Expectation-Maximization Differentiable Optimization Optimal Transport Wasserstein Distance