Differentiable Programming

Real-world observations of deformable objects are often sparse or surface-level, while downstream tasks require hidden physical quantities such as internal deformation, stress fields, and interaction forces. Physics-based simulation can recover these quantities, but online real-to-sim adaptation remains challenging due to costly full-space optimization, limited feedback, and time-varying material properties. To address these challenges, we propose RealSimLoop, a differentiable framework for online real-to-sim adaptation using vision data as physical feedback. Our approach achieves quasi-real-time performance by executing differentiable simulation within a reduced-order neural subspace, drastically accelerating the optimization loop. We couple this efficient dynamics model with differentiable rendering, enabling direct gradient backpropagation that leverages high-fidelity pixel data to refine physical parameters such as material stiffness. Furthermore, by employing a sliding-window objective function, RealSimLoop enables robust online adaptation, allowing the system to track time-varying material properties and effectively bridge the real-to-sim gap arising from model reduction or unmodeled dynamics. Extensive experiments demonstrate that our method outperforms conventional offline methods, and we validate the framework's versatility in downstream applications, including external force prediction and 3D stress field reconstruction with novel view synthesis.

Laplacian-regularized minimization is fundamental in signal processing and machine learning, but is limited by the dense and ill-conditioned nature of the graph Laplacian pseudoinverse. While the Laplacian itself is sparse, its pseudoinverse is dense and often ill-conditioned, rendering direct computation impractical at scale. Moreover, pseudoinverse learning is more challenging than Laplacian learning. To address this challenge, this paper considers the setting where the graph Laplacian is given and proposes a Difference-of-Convex Regularizer (DCR) graph learning framework that approximates the spectral action of the Laplacian pseudoinverse without direct inversion via regularized Maximum Likelihood Estimation (MLE). By reformulating Laplacian-Regularized Nonnegative Least Squares (LR-NNLS) through a dual representation, DCR decouples pseudoinverse learning from instance-specific inference and enables efficient primal solution reconstruction via a differentiable dual-guided learning scheme. We establish theoretical guarantees on stability and the existence of a unique fixed point for DCR algorithm. Numerical experiments demonstrate improved performance over convex solvers and graph filtering baselines and robust performance across diverse graph topologies.

Visual token pruning reduces the computational cost of Vision-Language Models (VLMs) by removing redundant visual tokens. The key is to learn a score that measures whether a token is useful. Existing methods typically rely on Gumbel-Softmax to approximate discrete selection during training. Such selectors make the score depend on the behavior of a relaxed pruning operator, not directly on the consequence of information loss. In this paper, we propose DiffPrune, which gives token scores a direct meaning. During training, DiffPrune keeps all tokens and weakens each token's information according to its score. If weakening a token hurts the task, the scorer is pushed to protect it; if not, the token can receive a lower score. Because the loss is differentiated through this actual information-throttling path, the scorer avoids the unstable surrogate path of relaxed token selection. DiffPrune implements this idea with an Information Throttler, which injects variance-preserving noise into visual tokens, where high-score tokens remain close to their original representations, while low-score tokens carry less original information. At inference, the throttler is removed, and hard top-K pruning is applied using the learned scores. Across ten VLM benchmarks, DiffPrune retains 96.5% of full-model accuracy while accelerating LLM prefill by 2.85x, with only 0.69 ms inference overhead. Code will be publicly available.

Fortran has been the cornerstone of high-performance computing for decades and remains unmatched in many domains. Yet the language faces an expertise gap: a new generation of scientists is barely familiar with it, while many experienced Fortran developers are only now transitioning to modern ecosystems such as JAX. This gap often results in "Fython" - Python code written with a Fortran mindset - that fails to leverage modern frameworks. We present FGPT, a transpiler framework designed to bridge this gap. It provides a systematic pipeline that transpiles Fortran into GPU-adapted Fortran, auto-differentiable Fortran via Tapenade, or NumPy and JAX scripts. Its architecture comprises three stages: (i) a frontend that parses Fortran and extracts target procedures along with all their dependencies; (ii) a middle-end that lowers the code into an intermediate representation, then into GPU-adapted or auto-differentiable Fortran, or a NumPy class; and (iii) a backend that transforms NumPy scripts into JAX modules optimized for GPU acceleration and automatic differentiation. Large language models fail when applied to the scale of community scientific codes-often spanning hundreds of thousands of lines-where consistent transformations, strict numerical fidelity, and validation against production tests are non-negotiable. FGPT addresses these challenges by preserving program semantics throughout the entire translation. We verified the framework on representative climate modeling kernels and demonstrated that it produces correct, differentiable Python implementations without requiring manual intervention. By combining rigorous compiler techniques with modern accelerator support, FGPT offers a scalable, trustworthy path for modernizing legacy Fortran code.

Implicit Neural Representations (INRs) have become the standard for continuous 2D shape modeling, but they suffer from black-box uneditability, vulnerability to noise, and high parameter counts that severely hinder deployment on edge devices. We introduce Fluid-SDF, a highly compressed, differentiable Constructive Solid Geometry (CSG) framework that models shapes using explicit geometric primitives blended via a smooth minimum function. By replacing traditional multi-layer perceptrons (MLPs) with a parameterized primitive engine, Fluid-SDF reconstructs complex, non-convex topologies using strictly under 100 parameters, achieving comparable or superior intersection-over-union (mIoU) to standard neural baselines. Furthermore, we demonstrate that Fluid-SDF acts as a powerful geometric prior, inherently resisting high-frequency dataset noise where capacity-matched neural networks catastrophically overfit. Finally, unlike standard INRs, Fluid-SDF's explicit parameter space allows for direct, zero-shot user editing of local and global shape features without retraining. By bypassing expensive on-device gradient updates entirely, Fluid-SDF is uniquely suited for mobile AI, augmented reality, and resource-constrained embedded environments

Few-shot spheroid segmentation must adapt to new cell lines, microscopes, and illumination conditions from only a small set of annotated images. While foundation few-shot segmenters can be accurate, their large opaque backbones make it difficult to understand which visual cues drive success or failure. We study this question with HyperBank, a differentiable bank of classical image-processing operators combining Frangi vesselness, a Sauvola threshold pyramid, structure-tensor responses, gradient magnitude, and Laplacian-of-Gaussian filters. HyperBank is fitted on the annotated support images and evaluated on disjoint held-out images across three independently acquired spheroid datasets. We treat it not as a general replacement for foundation models, but as a compact, interpretable few-shot microscopy pipeline and an analytic-prior probe of which classical cues carry the few-shot signal. The results show that, adapted on the same few annotated support images, a compact bank of analytic priors is competitive with, and on small-cluster, contrast-driven data can outperform, much larger foundation models, while those models remain stronger on externally sourced, texture-dominated spheroids. Leave-one-family-out ablations indicate that the useful few-shot signal is distributed across operator families and strengthened by support-set-tuned morphology.

Achieving nanosecond-scale inference latency for deep neural networks (DNNs) has become a primary architectural concern for latency-critical applications. While Field-Programmable Gate Arrays (FPGAs) offer a promising substrate for low-latency inference, conventional FPGA accelerators remain arithmetic-centric, using LUTs primarily as building blocks for numerical operators and peripheral logic. In contrast, recent LUT-native neural networks treat LUTs as learnable neurons, revealing promising theoretical potential to exploit their intrinsic logic expressivity. However, existing methods are largely confined to algorithmic optimizations, failing to translate this theoretical potential into high-performance FPGA accelerators. Specifically, their differentiable formulations do not faithfully match FPGA LUT primitives, their physically-unaware topologies compromise routability and timing closure, and their lack of automated optimization flow hinders systematic design space exploration (DSE) and efficient hardware implementation. In this paper, we propose FPGN, an end-to-end physically-aware framework that closes the gap between LUT-native learning and latency-optimized FPGA implementation. FPGN addresses these challenges through (i) a hardware-aligned differentiable formulation for training FPGA-native LUT neurons, (ii) a structured LUT-native topology with a streaming hardware architecture to improve routing locality and timing closure, and (iii) a latency-driven compiler that leverages high-fidelity analytical Quality of Results models to automate DSE and hardware generation. Experiments show that FPGN achieves up to 205$\times$ latency reduction compared to representative FPGA-based BNN accelerators and up to 30$\times$ higher LUT efficiency than prior differentiable LUT-native networks, while maintaining competitive inference accuracy.

The increasing uncertainty from flexible demand and renewable generation has made distributionally robust optimization (DRO) an important tool for robust power system dispatch. DRO relies on forecast scenarios to construct ambiguity sets, but conventional scenario generation pipelines are often trained in an accuracy-oriented manner and may neglect spatial correlations among uncertainties. This mismatch can produce ambiguity sets that are statistically plausible but suboptimal for downstream operation. This work proposes a decision-focused generative framework for correlated scenario generation in DRO-based dispatch. Instead of training generative models solely to fit the historical uncertainty distribution, the proposed framework optimizes generated scenarios according to their induced downstream operational cost. The proposed framework is tailored to mainstream generative models, including variational autoencoders, generative adversarial networks, and diffusion models, while capturing the joint distribution of uncertainties across buses. To improve computational tractability, we further develop a differentiable scenario selector that selects decision-relevant scenarios from a generated pool and can be trained within the same decision-focused pipeline. Case studies demonstrate that the proposed framework effectively reduces 0.80%-2.02% operational cost across different generative models compared to accuracy-oriented methods.

AI systems increasingly propose executable scientific models whose value depends on both their symbolic structure and their fitted continuous parameters. This makes parameter calibration the bottleneck of program-and-parameter co-search: an outer loop can generate thousands of candidate programs, but each needs an inner gradient-based optimization before it can be assessed. Staging each candidate into its own differentiable graph makes individual models fast but sacrifices the program-as-data property that keeps search fluid; interpreter-based approaches preserve programs as runtime data but pay interpreter overhead that dominates the numerical work. We present the Native Differentiable Virtual Machine (NDVM), a runtime representation that differentiates executable programs without compiling each candidate into a separate graph. NDVM separates symbolic structure from differentiable numeric state: tags, symbols, environments, and control remain native runtime data, while numeric payloads live in dense batched buffers with exact reverse-mode gradients recorded along the realized execution trace, so one evaluator walk is amortized across large populations of parameter vectors. A locked cost model of a real differentiable self-hosted Scheme interpreter motivates the design. We realize NDVM as a native runtime with forward and gradient equivalence to the reference backend, about 60x per-lane batch amortization, near-linear multicore scaling, and two independent front ends. In fixed-budget co-search over LLM-proposed programs, NDVM reaches high-quality solutions about 24x sooner in wall-clock time, suggesting runtime differentiation as a practical systems foundation for scientific discovery workflows.

Extreme adaptive optics (AO) is necessary for high contrast astronomy at scales of the habitable zone of nearby systems. We seek to evaluate wavefront sensors that approach fundamental limits of wavefront sensing, enabling adaptive optics systems to run faster or on fainter targets. We present the phase-induced amplitude apodisation Zernike wavefront sensor (PIAA-ZWFS): an adaptation of the conventional Zernike wavefront sensor (ZWFS) that leverages lossless apodisation of the pupil to concentrate the starlight in the focal plane. We optimise and evaluate the sensor with a differentiable modelling framework, drawing on concepts from Bayesian experimental design to minimise the variance of a maximum likelihood estimator that uses the system in the high Strehl regime. Our architecture shows state-of-the-art performance in simulation for different apertures, bandwidths, photon fluxes and source sizes, closing the gap to the fundamental limit by a factor 10 (2.5) compared to the conventional ZWFS (optimised ZWFS) in a typical photon-limited case. For extended sources, we show that even an ideal point source sensor rapidly becomes sub-optimal, and our system outperforms it for stellar diameters larger than 0.8λ/D. We verify that these gains do not come at the cost of dynamic range with either linear or non-linear reconstructors. Finally, we present a proof that there must be a trade-off between the information gained about amplitude and phase errors for any wavefront sensor. The PIAA-ZWFS is a viable wavefront sensor operating near the fundamental sensitivity limits.

Visual prompt tuning has emerged as a parameter-efficient fine-tuning approach for adapting large-scale Vision Transformers (ViTs) to downstream tasks. As its learnable prompts are applied in input and feature spaces, prior to jointly going through attention in transformer layers, the most commonly used scheme for fusing image and prompt tokens is concatenation or addition. In this paper, we aim to study a fundamental yet essential problem in visual prompt tuning: whether a single fusion scheme tends to yield better results, and whether that would be beneficial to develop a hybrid fusion scheme. To this end, we formulate the task as a bi-level optimization problem, and solve it leveraging differentiable architecture search. In this context, the learnable prompts and their fusion schemes are jointly optimized. To enrich the search space in the architecture search, we propose two additional fusion schemes, namely, affine transformation and cross-attention, in addition to concatenation and addition. Extensive experiments on 34 datasets spanning VTAB-1k, FGVC, and HTA show consistent gains over prompt-tuning baselines. With a frozen ViT backbone, our method delivers a favorable accuracy--latency--parameter trade-off compared with VPT-Deep and recent variants. Our findings reveal that how prompts fuse with image tokens plays a significant role in visual prompt tuning, and a hybrid fusion fashion can more effectively leverage layer semantics of ViTs, contributing a novel perspective for visual prompt-tuning research.

Explanation requires ground truth: to verify an account of a system we must know its inner functioning-just what is missing where explainable AI (XAI) is most needed. Systems we can study fall into two camps. Simple, procedural one-decision trees, rule lists, sparse linear models-have a known but trivial mechanism, so explaining them tests nothing; genuinely complex ones-deep networks, real-world tasks-need XAI but have no ground-truth inner functioning, so an explanation can be plausible, confident, and wrong with no way to tell. We remove this dichotomy with a study object both genuinely complex and fully specified-inspectable by construction-and, so gradient methods apply, fully differentiable. We reimplement the Atari 2600 Video Computer System (VCS)-a real computer architecture, and the cradle of deep reinforcement learning-as two independent end-to-end differentiable emulators in Julia (jutari) and JAX (jaxtari), each validated bit-for-bit against xitari. Both reproduce xitari on all 64 supported Arcade Learning Environment (ALE) games: 64/64 byte-identical RAM and 64/64 pixel-identical screens. Treating the cartridge ROM as a weight tensor, RAM as a soft tape, and control flow as gates, we prove the differentiable (soft) execution equals the original (hard) one bit-for-bit in the forward pass at any finite temperature, while exposing surrogate gradients where the bit logic has none. The JAX port also opens a GPU path: batched differentiable rollouts reach millions of environment-steps/s on one commodity GPU. The system was built in roughly 137 active hours over 29 calendar days, much of it written autonomously by coding agents. This paper builds and validates the foundation, showing-theoretically and in a qualitative gradient study-that gradient-based XAI on it is feasible. Both ports' full code is available under the MIT license at https://github.com/akmaier/UnderstandingVCS.

Sparse Mixture-of-Experts (MoE) architectures enable scaling LLM parameters under a fixed inference budget by activating only a small subset of experts via top-$k$ routing. While this preserves causality and suits autoregressive language models, the discrete top-$k$ operator is not differentiable, forcing a fixed number of active experts per input and resulting in inefficient use of computation. We propose SoftMoE, which replaces discrete routing with a truncated soft top-$k$ LapSum relaxation, allowing gradient-based optimization of expert routing. We further parameterize the mean number of active experts per layer and impose a global budget constraint, enabling the model to learn how to allocate expert capacity across layers. SoftMoE remains fully compatible with autoregressive modeling and achieves performance comparable to or better than sparse MoE on language modeling and downstream tasks, while activating significantly fewer experts. Notably, the learned allocation is highly non-uniform, with later layers activating more experts. The source code is publicly available$^\dagger$.

Most existing approaches either fix the container in advance or optimize only a single container dimension through an outer search loop, leaving the remaining dimensions as a manual tuning problem. We present a differentiable packing framework that jointly optimizes all 6N object pose parameters and all three container side lengths inside a single gradient-based loop. The formulation combines six physics-inspired, differentiable loss terms computed directly on triangle meshes through axis-aligned bounding-box proxies. An adaptive squeezing mechanism periodically tightens the container whenever the overlap loss falls below a pair-count-scaled threshold, producing a large initial drop in container volume, followed by small refinements. All pairwise computations are written in tensor-broadcasting form, giving a 3.4 to 54 times speedup over a reference loop-based implementation. The pipeline is implemented in Python and PyTorch, with no physics engine, FFT library, or convex decomposition. On multiple object categories, the method produces containers that are 11 to 32 percent smaller than time-matched DBLF and simulated-annealing baselines at N =100, while running in under 4 minutes per instance on a single consumer GPU.

Neurosymbolic (NeSy) models integrate neural networks and symbolic reasoning for robust and interpretable AI. State-of-the-art NeSy models require that the symbolic component is expressed in a differentiable way, often complicating the use of approximate inference. We propose EM-NeSy which casts probabilistic NeSy learning as an instance of the Expectation-Maximization (EM) algorithm. In the expectation step, we compute the posterior over the neurally predicted symbols conditioned on the label via probabilistic inference. In the maximization step, we update the neural parameters based on this posterior using gradient descent only through the neural component. This formulation unlocks the full potential of the EM algorithm for NeSy learning. It allows NeSy to extend naturally to approximate reasoning without any additional modifications or differentiability requirements of the symbolic component. Furthermore, it recovers the standard end-to-end gradient-based NeSy setting under exact inference. Our experimental results demonstrate the scalability and computational efficiency of EM-NeSy.

Next-generation wireless networks, including satellite-to-Open RAN systems, demand agile and intelligent resource management capable of handling dynamic multi-user interference under stochastic quality of service constraints. This paper introduces DIFFRACT, a neuralized utility maximization framework that leverages differentiable programming to integrate deep learning with optimization in wireless networks. Central to our approach is the exploitation of the mathematical structure of standard interference functions, which are foundational in wireless power control. By developing a duality theory for these functions, we map iterative interference management algorithms into differentiable neural network architectures via algorithm unrolling. This enables distributed, end-to-end gradient-based learning at the network edge, supporting real-time adaptation to interference in both terrestrial and non-terrestrial environments. DIFFRACT allows for scalable and robust utility maximization by modeling complex channel dynamics and leveraging the expressiveness of differentiable models. Experimental results confirm the framework's theoretical soundness and practical effectiveness for next-generation wireless systems.

Differentiable programming offers transformative capabilities for scientific modeling, enabling gradient-based parameter estimation, sensitivity analysis, and data assimilation. Yet, migrating legacy codebases into differentiable frameworks remains a challenge. We present a five-phase LLM-based agentic pipeline that translates legacy Fortran into JAX: static dependency analysis determines module translation order from the full call graph; iterative compile-repair loops correct errors autonomously; and a Fortran reference oracle enforces numerical parity at the module level before integration and gradient verification. We instantiate and evaluate the pipeline on CLM-ml-v2, a 19,000-line Fortran land surface model, and analyze agent behavior across 73 module translation tasks. The resulting differentiable model computes the complete Jacobian in a single backward pass, recovers physical parameters in eight times fewer steps than gradient-free optimization, and achieves a 24 times wall-clock speedup over sequential Fortran at ensemble size N=2,048. Both the translated model and pipeline infrastructure are released as a reusable framework for differentiating other Earth system model components.

Advances in computational modeling, neuroimaging, and artificial intelligence are revolutionizing the modeling of neurological disorders for improved diagnostics, prognosis, and treatment planning. Mechanistic models provide valuable scientific insight into the disorders, but in practice they are often simplified with assumptions or computationally expensive and slow to solve. However, while purely data driven approaches provide speed and scalability, they require large, high quality data to train and generally suffer from interpretability and generalization issues. This perspective paper presents a structured overview of hybrid modeling strategies, which combine deep learning models with physics based solvers, and are categorized into parallel, series, and parallel-series architectures. Three main approaches that have been emphasized are residual modeling for missing or incomplete physics, Neural Ordinary Differential Equations (NODEs) for continuous time dynamics approximation, and solver in the loop that accelerates traditional solvers with neural approximations. These hybrid models integrate the governing differential equation based formulations and deep learning to characterize the evolution of neurological disorders, and promise advanced personalized neurological modeling. In addition, the study explores and proposes different hybrid configurations to improve diagnosis accuracy, predict disease progression, and inform treatment strategies across a range of neurological disorders. These capabilities outperform standalone mechanistic or purely data driven approaches, making hybrid modeling a powerful tool, especially in applications involving modeling the progression and treatment responses in neurological conditions such as brain tumors, Alzheimer's disease, and stroke.

Causal discovery with instantaneous effects in multivariate time series is challenging, as the instantaneous structure must be acyclic. Prior methods enforce this by either separating instantaneous and lagged estimation into multi-stage pipelines or imposing algebraic acyclicity constraints via complex augmented Lagrangian optimization, both of which incur high computational cost. In this work, we propose a different approach: we learn a differentiable permutation of variables using the Gumbel--Sinkhorn operator and triangularize the instantaneous coefficient matrix of a Structural Vector Autoregressive (SVAR) model in the learned order. This converts acyclicity from a hard constraint into a parameterization and keeps it valid throughout optimization. In doing so, our method enables unified, continuous optimization with gradient-based learning, leading to improved efficiency in time--series causal discovery. Across three real-world benchmarks, our method achieves the best overall performance compared with 12 baselines in both discovery accuracy and efficiency. On the large-scale benchmark, it further demonstrates strong scalability, achieving more than a 6x speedup over competing methods.

Differentiable simulation of soft bodies is a foundation for system identification, trajectory optimization, and Real2Sim transfer. Yet, existing methods such as the differentiable Projective Dynamics (DiffPD) struggle when faced with heterogeneous materials with extreme stiffness contrasts, hyperelasticity under large deformations, and contact-rich interactions, which are common scenarios in the real world. We present DiffPhD, a unified GPU-accelerated differentiable Projective Dynamics framework for heterogeneous materials that tackles these intertwined challenges simultaneously. Our key insight is a careful integration of: (i) stiffness-aware projective weights to embed heterogeneity into the global system; (ii) trust-region eigenvalue filtering lifted to the backward pass for stable hyperelastic gradients and a type-II Anderson Acceleration scheme with dual-gate convergence to stabilize forward iteration under large stiffness contrasts; and (iii) a unified GPU pipeline that reuses a single sparse factor across forward, backward, and contact computations, with stiffness-amplified Rayleigh damping folded into the same factor for heterogeneity-aware dissipation at zero recurring cost. DiffPhD achieves strict gradient accuracy while delivering up to an order-of-magnitude speedup over prior differentiable solvers on heterogeneous, hyperelastic, contact-rich benchmarks. Crucially, this speedup does not come at the cost of stability: DiffPhD remains convergent on stiffness contrasts up to 100x where prior PD solvers degrade. This unlocks end-to-end gradient-based optimization on regimes previously bottlenecked by either solver fragility or per-iteration cost -- shell--joint composite creatures, soft characters wielding stiff weapons, and soft-gripper robotic manipulation -- all handled within a single forward--backward pass.

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.

From neural ODEs to continuous-time machine learning, differentiable solvers allow physics, optimization, and simulation to become trainable components within deep learning systems. This has opened the path to a new generation of deep learning frameworks for scientific computing, with many promising applications still emerging. In this paper, we integrate a differentiable chemistry solver into a modified physics-informed neural network to solve parameterized reaction systems that are inherently stiff. The proposed framework introduces several key components required to overcome limitations of standard physics-informed neural networks. These include a differentiable chemistry solver, a network architecture for parameterized solutions, and residual weighting tailored to stiff reactions. We evaluate the framework on a set of differential equations related to hydrogen combustion, which include initial/boundary value problems, inverse parameter identification, and a parameterized partial differential equation. Our results highlight the ability of the proposed approach to extend physics-informed neural networks to stiff chemical systems that were previously inaccessible.

Reasoning photo retouching has gained significant traction, requiring models to analyze image defects, give reasoning processes, and execute precise retouching enhancements. However, existing approaches often rely on non-differentiable external software, creating optimization barriers and suffering from high parameter redundancy and limited generalization. To address these challenges, we propose VeraRetouch, a lightweight and fully differentiable framework for multi-task photo retouching. We employ a 0.5B Vision-Language Model (VLM) as the central intelligence to formulate retouching plans based on instructions and scene semantics. Furthermore, we develop a fully differentiable Retouch Renderer that replaces external tools, enabling direct end-to-end pixel-level training through decoupled control latents for lighting, global color, and specific color adjustments. To overcome data scarcity, we introduce AetherRetouch-1M+, the first million-scale dataset for professional retouching, constructed via a new inverse degradation workflow. Furthermore, we propose DAPO-AE, a reinforcement learning post-training strategy that enhances autonomous aesthetic cognition. Extensive experiments demonstrate that VeraRetouch achieves state-of-the-art performance across multiple benchmarks while maintaining a significantly smaller footprint, enabling mobile deployment. Our code and models are publicly available at https://github.com/OpenVeraTeam/VeraRetouch.

Systematic biases in General Circulation Model (GCM) outputs limit their direct applicability in regional planning, making bias correction a technically demanding but necessary step for both short-term and long-term impact assessment. Correcting precipitation is particularly challenging due to its non-Gaussian distribution, intermittent nature, and heavy-tailed extremes. However, traditional statistical bias-correction methods have limited ability to learn systematic patterns from large datasets or generalize to new locations. While machine learning (ML) provides greater flexibility, it can produce unpredictable and difficult-to-interpret results, limiting generalization across GCMs and locations. In this study, we propose a differentiable bias-adjustment framework called dCLIMBA, that learns a spatiotemporally adaptive parametric bias-adjustment procedure, rather than corrected precipitation directly, between historical CMIP6 model outputs and a gridded observation-based dataset, Livneh. Results demonstrate that the proposed method corrects the magnitude and distribution of extreme precipitation with particularly strong performance in the upper tail. The quantile distribution of precipitation was well reproduced across diverse U.S. cities, and spatial patterns were comparable to those from the widely used LOCA2 statistical downscaling product. In addition, the framework showed partial future trend preservation and promising attenuation of marginal biases in unseen regions. This work presents a modular and efficient bias-correction approach. The differentiable approach provides an easy-to-use option for connecting atmospheric-model outputs to on-the-ground impacts.

Generating intelligent robot behavior in contact-rich settings is a research problem where zeroth-order methods currently prevail. Developing methods that make use of first/second order information about rigid-body dynamics in the presence of contact holds great promise in terms of increasing the solution speed and computational efficiency. The main bottleneck in this research direction is the difficulty in obtaining gradients and Hessians that are actually useful for numerical optimization, due to pathologies in all three steps of a common simulation pipeline: i) collision detection, ii) contact dynamics, iii) time integration. This abstract proposes a method that aims to address the collision detection part of the puzzle, via a novel pipeline designed from scratch with smooth (i.e. twice) differentiability and massive vectorizability on GPUs as the main priorities. This is in contrast to standard collision detection routines that are instead optimized for runtime on CPUs and minimal memory footprint, but do employ logic and control flow that hinder differentiability and vectorization. The proposed pipeline consists of the following contributions: i) highly expressive and compute efficient SDF representations, ii) differentiable broad-phase and narrow-phase routines that use these representations to generate vertex-SDF and edge-SDF contacts, iii) a differentiable routine for convex decomposition based contact blending.

Capturing both geometry and rigid motion for structured dynamic objects, like multi-part assemblies or jointed mechanisms, remains a key challenge. Existing dynamic methods, such as deformable meshes or 3DGS, rely on unstructured representations and fail to jointly model suitable geometry and articulated motion. Primitive-based methods excel at structured static scenes, but their dynamic potential is still unexplored. We propose D-Prism, the first framework to achieve high-fidelity structured dynamic modeling by extending differentiable primitives to the dynamic domain. Specifically, we bind 3DGS to primitive surfaces, leveraging their respective strengths in appearance and geometry. We introduce a deformation network to control primitive motion, ensuring it accurately matches the object's movement. Furthermore, we design a novel adaptive control strategy to dynamically adjust primitive counts, better matching objects' true spatial footprint. Experiments confirm that our method excels at structured dynamic modeling, providing both structured geometry and precise motion tracking.

We motivate the use of differentiable probabilistic programming techniques in order to account for the large model-space inherent to astrophysical $γ$-ray analyses. Targeting the longstanding Galactic Center $γ$-ray Excess (GCE) puzzle, we construct differentiable forward model and likelihood that make liberal use of GPU acceleration and vectorization in order to simultaneously account for a continuum of possible spatial morphologies consistent with the GCE emission in a fully probabilistic manner. Our setup allows for efficient inference over the large model space using variational methods. Beyond application to $γ$-ray data, a goal of this work is to showcase how differentiable probabilistic programming can be used as a tool to enable flexible analyses of astrophysical datasets.

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.

Sorting and permutation learning are key concepts in optimization and machine learning, especially when organizing high-dimensional data into meaningful spatial layouts. The Gumbel-Sinkhorn method, while effective, requires N*N parameters to determine a full permutation matrix, making it computationally expensive for large datasets. Low-rank matrix factorization approximations reduce memory requirements to 2NM (with M << N), but they still struggle with very large problems. SoftSort, by providing a continuous relaxation of the argsort operator, allows differentiable 1D sorting, but it faces challenges with multidimensional data and complex permutations. In this paper, we present a novel method for learning permutations using only N parameters, which dramatically reduces storage costs. Our method extends SoftSort by iteratively shuffling the N indices of the elements and applying a few SoftSort optimization steps per iteration. This modification significantly improves sorting quality, especially for multidimensional data and complex optimization criteria, and outperforms pure SoftSort. Our method offers improved memory efficiency and scalability compared to existing approaches, while maintaining high-quality permutation learning. Its dramatically reduced memory requirements make it particularly well-suited for large-scale optimization tasks, such as "Self-Organizing Gaussians", where efficient and scalable permutation learning is critical.

This paper presents Adaptive Differentiable Model Predictive Contouring Control (AD-MPCC), a framework for autonomous racing that integrates differentiable MPCC with online parameter estimation to handle varying road-surface conditions. For online parameter estimation, we leverage a parameterized Pacejka Magic Formula together with a regularized moving-horizon estimation scheme with exponentially decaying weights to capture road interactions and update parameters in real time. Furthermore, we propose a differentiable MPCC (Diff-MPCC) framework that enables optimal adjustment of objective weights based on predefined long-horizon performance costs. To implement Diff-MPCC for online objective weight adaptation, we propose a Pacejka-informed machine learning model that is trained in a supervised manner using data generated by Diff-MPCC to tune the objective weights. Simulation results demonstrate that AD-MPCC reliably ensures safety and achieves faster lap times compared to baseline controllers in both single-surface and multiple-surface scenarios.