Daily Papers

Low-Rank Adaptation (LoRA) reparameterizes a weight update as a product of two low-rank factors, but the Jacobian J_{G} of the generator mapping the factors to the weight matrix is rank-deficient, so the factor-space preconditioner J_{G}^* {F}_t J_{G} induced by any {W}-space preconditioner {F}_t is singular, and consequently the standard chain rule cannot be uniquely inverted to map a preconditioned {W}-space direction back to a factor-space update. We cast existing LoRA optimizers in a unified framework parameterized by two choices: (i) which invertible surrogate for J_{G}^* {F}_t J_{G} to use, and (ii) which {F}_t on {W} to use. Existing methods occupy four families along these axes: factor-space adaptive updates, block-diagonal surrogates for J_{G}^* J_{G}, Frobenius-residual pseudoinverse methods, and Riemannian manifold constraint. Within this design space, a gradient-statistics-aware {F}_t paired with a closed-form factor-space solve at {O}((m+n)r) memory remains underexplored. We propose AdaPreLoRA, which fills this gap by adopting the Adafactor diagonal Kronecker preconditioner {H}_t on {W} and selecting from the resulting factor-space solution family the element minimizing an {H}_t-weighted imbalance between the two factor contributions; by construction, the resulting factor update is the closest LoRA approximation to the preconditioned {W}-space direction under the {H}_t-weighted norm. Across GPT-2 (E2E), Mistral-7B and Qwen2-7B (GLUE, ARC, GSM8K), and diffusion-model personalization, AdaPreLoRA is competitive with or improves over a representative set of LoRA optimizers while keeping peak GPU memory at the LoRA optimizer level.

Likelihood approximations for images are not trivial to compute and can be useful in many applications. We examine the use of Contrastive Language-Image Pre-training (CLIP) to assess the likelihood of images and captions. We introduce Whitened CLIP, a novel transformation of the CLIP latent space via an invertible linear operation. This transformation ensures that each feature in the embedding space has zero mean, unit standard deviation, and no correlation with all other features, resulting in an identity covariance matrix. We show that the whitened embeddings statistics can be well approximated as a standard normal distribution, thus, the log-likelihood is estimated simply by the square Euclidean norm in the whitened embedding space. The whitening procedure is completely training-free and performed using a pre-computed whitening matrix, hence, is very fast. We present several preliminary experiments demonstrating the properties and applicability of these likelihood scores to images and captions.

In Federated Learning (FL) and many other distributed training frameworks, collaborators can hold their private data locally and only share the network weights trained with the local data after multiple iterations. Gradient inversion is a family of privacy attacks that recovers data from its generated gradients. Seemingly, FL can provide a degree of protection against gradient inversion attacks on weight updates, since the gradient of a single step is concealed by the accumulation of gradients over multiple local iterations. In this work, we propose a principled way to extend gradient inversion attacks to weight updates in FL, thereby better exposing weaknesses in the presumed privacy protection inherent in FL. In particular, we propose a surrogate model method based on the characteristic of two-dimensional gradient flow and low-rank property of local updates. Our method largely boosts the ability of gradient inversion attacks on weight updates containing many iterations and achieves state-of-the-art (SOTA) performance. Additionally, our method runs up to 100times faster than the SOTA baseline in the common FL scenario. Our work re-evaluates and highlights the privacy risk of sharing network weights. Our code is available at https://github.com/JunyiZhu-AI/surrogate_model_extension.

Recent years have seen a surge in deep learning approaches to accelerate numerical solvers, which provide faithful but computationally intensive simulations of the physical world. These deep surrogates are generally trained in a supervised manner from limited amounts of data slowly generated by the same solver they intend to accelerate. We propose an open-source framework that enables the online training of these models from a large ensemble run of simulations. It leverages multiple levels of parallelism to generate rich datasets. The framework avoids I/O bottlenecks and storage issues by directly streaming the generated data. A training reservoir mitigates the inherent bias of streaming while maximizing GPU throughput. Experiment on training a fully connected network as a surrogate for the heat equation shows the proposed approach enables training on 8TB of data in 2 hours with an accuracy improved by 47% and a batch throughput multiplied by 13 compared to a traditional offline procedure.

In computer-aided engineering design, the goal of a designer is to find an optimal design on a given requirement using the numerical simulator in loop with an optimization method. In this design optimization process, a good design optimization process is one that can reduce the time from inception to design. In this work, we take a class of design problem, that is computationally cheap to evaluate but has high dimensional design space. In such cases, traditional surrogate-based optimization does not offer any benefits. In this work, we propose an alternative way to use ML model to surrogate the design process that formulates the search problem as an inverse problem and can save time by finding the optimal design or at least a good initial seed design for optimization. By using this trained surrogate model with the traditional optimization method, we can get the best of both worlds. We call this as Surrogate Assisted Optimization (SAO)- a hybrid approach by mixing ML surrogate with the traditional optimization method. Empirical evaluations of propeller design problems show that a better efficient design can be found in fewer evaluations using SAO.

Designing urban spaces that provide pedestrian wind comfort and safety requires time-resolved Computational Fluid Dynamics (CFD) simulations, but their current computational cost makes extensive design exploration impractical. We introduce WinDiNet (Wind Diffusion Network), a pretrained video diffusion model that is repurposed as a fast, differentiable surrogate for this task. Starting from LTX-Video, a 2B-parameter latent video transformer, we fine-tune on 10,000 2D incompressible CFD simulations over procedurally generated building layouts. A systematic study of training regimes, conditioning mechanisms, and VAE adaptation strategies, including a physics-informed decoder loss, identifies a configuration that outperforms purpose-built neural PDE solvers. The resulting model generates full 112-frame rollouts in under a second. As the surrogate is end-to-end differentiable, it doubles as a physics simulator for gradient-based inverse optimization: given an urban footprint layout, we optimize building positions directly through backpropagation to improve wind safety as well as pedestrian wind comfort. Experiments on single- and multi-inlet layouts show that the optimizer discovers effective layouts even under challenging multi-objective configurations, with all improvements confirmed by ground-truth CFD simulations.

An established way to improve the transferability of black-box evasion attacks is to craft the adversarial examples on an ensemble-based surrogate to increase diversity. We argue that transferability is fundamentally related to uncertainty. Based on a state-of-the-art Bayesian Deep Learning technique, we propose a new method to efficiently build a surrogate by sampling approximately from the posterior distribution of neural network weights, which represents the belief about the value of each parameter. Our extensive experiments on ImageNet, CIFAR-10 and MNIST show that our approach improves the success rates of four state-of-the-art attacks significantly (up to 83.2 percentage points), in both intra-architecture and inter-architecture transferability. On ImageNet, our approach can reach 94% of success rate while reducing training computations from 11.6 to 2.4 exaflops, compared to an ensemble of independently trained DNNs. Our vanilla surrogate achieves 87.5% of the time higher transferability than three test-time techniques designed for this purpose. Our work demonstrates that the way to train a surrogate has been overlooked, although it is an important element of transfer-based attacks. We are, therefore, the first to review the effectiveness of several training methods in increasing transferability. We provide new directions to better understand the transferability phenomenon and offer a simple but strong baseline for future work.

Numerical simulations in climate, chemistry, or astrophysics are computationally too expensive for uncertainty quantification or parameter-exploration at high-resolution. Reduced-order or surrogate models are multiple orders of magnitude faster, but traditional surrogates are inflexible or inaccurate and pure machine learning (ML)-based surrogates too data-hungry. We propose a hybrid, flexible surrogate model that exploits known physics for simulating large-scale dynamics and limits learning to the hard-to-model term, which is called parametrization or closure and captures the effect of fine- onto large-scale dynamics. Leveraging neural operators, we are the first to learn grid-independent, non-local, and flexible parametrizations. Our multiscale neural operator is motivated by a rich literature in multiscale modeling, has quasilinear runtime complexity, is more accurate or flexible than state-of-the-art parametrizations and demonstrated on the chaotic equation multiscale Lorenz96.

This paper studies the black-box optimization task which aims to find the maxima of a black-box function using a static set of its observed input-output pairs. This is often achieved via learning and optimizing a surrogate function with that offline data. Alternatively, it can also be framed as an inverse modeling task that maps a desired performance to potential input candidates that achieve it. Both approaches are constrained by the limited amount of offline data. To mitigate this limitation, we introduce a new perspective that casts offline optimization as a distributional translation task. This is formulated as learning a probabilistic bridge transforming an implicit distribution of low-value inputs (i.e., offline data) into another distribution of high-value inputs (i.e., solution candidates). Such probabilistic bridge can be learned using low- and high-value inputs sampled from synthetic functions that resemble the target function. These synthetic functions are constructed as the mean posterior of multiple Gaussian processes fitted with different parameterizations on the offline data, alleviating the data bottleneck. The proposed approach is evaluated on an extensive benchmark comprising most recent methods, demonstrating significant improvement and establishing a new state-of-the-art performance. Our code is publicly available at https://github.com/cuong-dm/ROOT.

Neural networks are a commonly used approach to replace physical models with computationally cheap surrogates. Parametric uncertainty quantification can be included in training, assuming that an accurate prior distribution of the model parameters is available. Here we study the common opposite situation, where direct screening or random sampling of model parameters leads to exhaustive training times and evaluations at unphysical parameter values. Our solution is to decouple uncertainty quantification from network architecture. Instead of sampling network weights, we introduce the model-parameter distribution as an input to network training via Markov chain Monte Carlo (MCMC). In this way, the surrogate achieves the same uncertainty quantification as the underlying physical model, but with substantially reduced computation time. The approach is fully agnostic with respect to the neural network choice. In our examples, we present a quantile emulator for prediction and a novel autoencoder-based ODE network emulator that can flexibly estimate different trajectory paths corresponding to different ODE model parameters. Moreover, we present a mathematical analysis that provides a transparent way to relate potential performance loss to measurable distribution mismatch.

We introduced a novel method to solve Bayesian inverse problems governed by PDE equations with a hybrid two-level MCMC where we took advantage of the AI surrogate model speed and the accuracy of numerical models. We show theoretically the potential to solve Bayesian inverse problems accurately with only a small number of numerical samples when the AI surrogate model error is small. Several numerical experiment results are included which demonstrates the advantage of the hybrid method.

Neural surrogates for partial differential equations (PDEs) have become popular due to their potential to quickly simulate physics. With a few exceptions, neural surrogates generally treat the forward evolution of time-dependent PDEs as a black box by directly predicting the next state. While this is a natural and easy framework for applying neural surrogates, it can be an over-simplified and rigid framework for predicting physics. In this work, we propose an alternative framework in which neural solvers predict the temporal derivative and an ODE integrator forwards the solution in time, which has little overhead and is broadly applicable across model architectures and PDEs. We find that by simply changing the training target and introducing numerical integration during inference, neural surrogates can gain accuracy and stability. Predicting temporal derivatives also allows models to not be constrained to a specific temporal discretization, allowing for flexible time-stepping during inference or training on higher-resolution PDE data. Lastly, we investigate why this new framework can be beneficial and in what situations does it work well.

Offline optimization has recently emerged as an increasingly popular approach to mitigate the prohibitively expensive cost of online experimentation. The key idea is to learn a surrogate of the black-box function that underlines the target experiment using a static (offline) dataset of its previous input-output queries. Such an approach is, however, fraught with an out-of-distribution issue where the learned surrogate becomes inaccurate outside the offline data regimes. To mitigate this, existing offline optimizers have proposed numerous conditioning techniques to prevent the learned surrogate from being too erratic. Nonetheless, such conditioning strategies are often specific to particular surrogate or search models, which might not generalize to a different model choice. This motivates us to develop a model-agnostic approach instead, which incorporates a notion of model sharpness into the training loss of the surrogate as a regularizer. Our approach is supported by a new theoretical analysis demonstrating that reducing surrogate sharpness on the offline dataset provably reduces its generalized sharpness on unseen data. Our analysis extends existing theories from bounding generalized prediction loss (on unseen data) with loss sharpness to bounding the worst-case generalized surrogate sharpness with its empirical estimate on training data, providing a new perspective on sharpness regularization. Our extensive experimentation on a diverse range of optimization tasks also shows that reducing surrogate sharpness often leads to significant improvement, marking (up to) a noticeable 9.6% performance boost. Our code is publicly available at https://github.com/cuong-dm/IGNITE

Bayesian optimization is a highly efficient approach to optimizing objective functions which are expensive to query. These objectives are typically represented by Gaussian process (GP) surrogate models which are easy to optimize and support exact inference. While standard GP surrogates have been well-established in Bayesian optimization, Bayesian neural networks (BNNs) have recently become practical function approximators, with many benefits over standard GPs such as the ability to naturally handle non-stationarity and learn representations for high-dimensional data. In this paper, we study BNNs as alternatives to standard GP surrogates for optimization. We consider a variety of approximate inference procedures for finite-width BNNs, including high-quality Hamiltonian Monte Carlo, low-cost stochastic MCMC, and heuristics such as deep ensembles. We also consider infinite-width BNNs and partially stochastic models such as deep kernel learning. We evaluate this collection of surrogate models on diverse problems with varying dimensionality, number of objectives, non-stationarity, and discrete and continuous inputs. We find: (i) the ranking of methods is highly problem dependent, suggesting the need for tailored inductive biases; (ii) HMC is the most successful approximate inference procedure for fully stochastic BNNs; (iii) full stochasticity may be unnecessary as deep kernel learning is relatively competitive; (iv) infinite-width BNNs are particularly promising, especially in high dimensions.

We, team AImsterdam, summarize our submission to the fastMRI challenge (Zbontar et al., 2018). Our approach builds on recent advances in invertible learning to infer models as presented in Putzky and Welling (2019). Both, our single-coil and our multi-coil model share the same basic architecture.

Offline optimization is an important task in numerous material engineering domains where online experimentation to collect data is too expensive and needs to be replaced by an in silico maximization of a surrogate of the black-box function. Although such a surrogate can be learned from offline data, its prediction might not be reliable outside the offline data regime, which happens when the surrogate has narrow prediction margin and is (therefore) sensitive to small perturbations of its parameterization. This raises the following questions: (1) how to regulate the sensitivity of a surrogate model; and (2) whether conditioning an offline optimizer with such less sensitive surrogate will lead to better optimization performance. To address these questions, we develop an optimizable sensitivity measurement for the surrogate model, which then inspires a sensitivity-informed regularizer that is applicable to a wide range of offline optimizers. This development is both orthogonal and synergistic to prior research on offline optimization, which is demonstrated in our extensive experiment benchmark.

Despite unconditional feature inversion being the foundation of many image synthesis applications, training an inverter demands a high computational budget, large decoding capacity and imposing conditions such as autoregressive priors. To address these limitations, we propose the use of adversarially robust representations as a perceptual primitive for feature inversion. We train an adversarially robust encoder to extract disentangled and perceptually-aligned image representations, making them easily invertible. By training a simple generator with the mirror architecture of the encoder, we achieve superior reconstruction quality and generalization over standard models. Based on this, we propose an adversarially robust autoencoder and demonstrate its improved performance on style transfer, image denoising and anomaly detection tasks. Compared to recent ImageNet feature inversion methods, our model attains improved performance with significantly less complexity.

Clinical trials or studies oftentimes require long-term and/or costly follow-up of participants to evaluate a novel treatment/drug/vaccine. There has been increasing interest in the past few decades in using short-term surrogate outcomes as a replacement of the primary outcome i.e., in using the surrogate outcome, which can potentially be observed sooner, to make inference about the treatment effect on the long-term primary outcome. Very few of the available statistical methods to evaluate a surrogate are applicable to settings where both the surrogate and the primary outcome are time-to-event outcomes subject to censoring. Methods that can handle this setting tend to require parametric assumptions or be limited to assessing only the restricted mean survival time. In this paper, we propose a non-parametric approach to evaluate a censored surrogate outcome, such as time to progression, when the primary outcome is also a censored time-to-event outcome, such as time to death, and the treatment effect of interest is the difference in overall survival. Specifically, we define the proportion of the treatment effect on the primary outcome that is explained (PTE) by the censored surrogate outcome in this context, and estimate this proportion by defining and deriving an optimal transformation of the surrogate information. Our approach provides the added advantage of relaxed assumptions to guarantee that the true PTE is within (0,1), along with being model-free. Finite sample performance of our estimators are illustrated via extensive simulation studies and a real data application examining progression-free survival as a surrogate for overall survival for patients with metastatic colorectal cancer.

Neural networks excel as function approximators, but their complexity often obscures the types of functions they learn, making it difficult to explain their behavior. To address this, the linearity score lambda(f) is introduced, a simple and interpretable diagnostic that quantifies how well a regression network's output can be mimicked by a linear model. Defined as the R^2 value between the network's predictions and those of a trained linear surrogate, lambda(f) measures linear decodability: the extent to which the network's behavior aligns with a structurally simple model. This framework is evaluated on both synthetic and real-world datasets, using dataset-specific networks and surrogates. High lambda(f) scores reliably indicate alignment with the network's outputs; however, they do not guarantee accuracy with respect to the ground truth. These results highlight the risk of using surrogate fidelity as a proxy for model understanding, especially in high-stakes regression tasks.

Gravitational-wave approximants are essential for gravitational-wave astronomy, allowing the coverage binary black hole parameter space for inference or match filtering without costly numerical relativity (NR) simulations, but generally trading some accuracy for computational efficiency. To reduce this trade-off, NR surrogate models can be constructed using interpolation within NR waveform space. We present a 2-stage training approach for neural network-based NR surrogate models. Initially trained on approximant-generated waveforms and then fine-tuned with NR data, these dual-stage artificial neural surrogate (DANSur) models offer rapid and competitively accurate waveform generation, generating millions in under 20ms on a GPU while keeping mean mismatches with NR around 10^{-4}. Implemented in the bilby framework, we show they can be used for parameter estimation tasks.

We present extensive empirical evidence showing that current Bayesian simulation-based inference algorithms can produce computationally unfaithful posterior approximations. Our results show that all benchmarked algorithms -- (Sequential) Neural Posterior Estimation, (Sequential) Neural Ratio Estimation, Sequential Neural Likelihood and variants of Approximate Bayesian Computation -- can yield overconfident posterior approximations, which makes them unreliable for scientific use cases and falsificationist inquiry. Failing to address this issue may reduce the range of applicability of simulation-based inference. For this reason, we argue that research efforts should be made towards theoretical and methodological developments of conservative approximate inference algorithms and present research directions towards this objective. In this regard, we show empirical evidence that ensembling posterior surrogates provides more reliable approximations and mitigates the issue.

Normalizing flows are an essential alternative to GANs for generative modelling, which can be optimized directly on the maximum likelihood of the dataset. They also allow computation of the exact latent vector corresponding to an image since they are composed of invertible transformations. However, the requirement of invertibility of the transformation prevents standard and expressive neural network models such as CNNs from being directly used. Emergent convolutions were proposed to construct an invertible 3times3 CNN layer using a pair of masked CNN layers, making them inefficient. We study conditions such that 3times3 CNNs are invertible, allowing them to construct expressive normalizing flows. We derive necessary and sufficient conditions on a padded CNN for it to be invertible. Our conditions for invertibility are simple, can easily be maintained during the training process. Since we require only a single CNN layer for every effective invertible CNN layer, our approach is more efficient than emerging convolutions. We also proposed a coupling method, Quad-coupling. We benchmark our approach and show similar performance results to emergent convolutions while improving the model's efficiency.

We consider minimizing functions for which it is expensive to compute the (possibly stochastic) gradient. Such functions are prevalent in reinforcement learning, imitation learning and adversarial training. Our target optimization framework uses the (expensive) gradient computation to construct surrogate functions in a target space (e.g. the logits output by a linear model for classification) that can be minimized efficiently. This allows for multiple parameter updates to the model, amortizing the cost of gradient computation. In the full-batch setting, we prove that our surrogate is a global upper-bound on the loss, and can be (locally) minimized using a black-box optimization algorithm. We prove that the resulting majorization-minimization algorithm ensures convergence to a stationary point of the loss. Next, we instantiate our framework in the stochastic setting and propose the SSO algorithm, which can be viewed as projected stochastic gradient descent in the target space. This connection enables us to prove theoretical guarantees for SSO when minimizing convex functions. Our framework allows the use of standard stochastic optimization algorithms to construct surrogates which can be minimized by any deterministic optimization method. To evaluate our framework, we consider a suite of supervised learning and imitation learning problems. Our experiments indicate the benefits of target optimization and the effectiveness of SSO.

To plan and optimize energy storage demands that account for Li-ion battery aging dynamics, techniques need to be developed to diagnose battery internal states accurately and rapidly. This study seeks to reduce the computational resources needed to determine a battery's internal states by replacing physics-based Li-ion battery models -- such as the single-particle model (SPM) and the pseudo-2D (P2D) model -- with a physics-informed neural network (PINN) surrogate. The surrogate model makes high-throughput techniques, such as Bayesian calibration, tractable to determine battery internal parameters from voltage responses. This manuscript is the first of a two-part series that introduces PINN surrogates of Li-ion battery models for parameter inference (i.e., state-of-health diagnostics). In this first part, a method is presented for constructing a PINN surrogate of the SPM. A multi-fidelity hierarchical training, where several neural nets are trained with multiple physics-loss fidelities is shown to significantly improve the surrogate accuracy when only training on the governing equation residuals. The implementation is made available in a companion repository (https://github.com/NREL/pinnstripes). The techniques used to develop a PINN surrogate of the SPM are extended in Part II for the PINN surrogate for the P2D battery model, and explore the Bayesian calibration capabilities of both surrogates.

The existence of a plethora of language models makes the problem of selecting the best one for a custom task challenging. Most state-of-the-art methods leverage transformer-based models (e.g., BERT) or their variants. Training such models and exploring their hyperparameter space, however, is computationally expensive. Prior work proposes several neural architecture search (NAS) methods that employ performance predictors (e.g., surrogate models) to address this issue; however, analysis has been limited to homogeneous models that use fixed dimensionality throughout the network. This leads to sub-optimal architectures. To address this limitation, we propose a suite of heterogeneous and flexible models, namely FlexiBERT, that have varied encoder layers with a diverse set of possible operations and different hidden dimensions. For better-posed surrogate modeling in this expanded design space, we propose a new graph-similarity-based embedding scheme. We also propose a novel NAS policy, called BOSHNAS, that leverages this new scheme, Bayesian modeling, and second-order optimization, to quickly train and use a neural surrogate model to converge to the optimal architecture. A comprehensive set of experiments shows that the proposed policy, when applied to the FlexiBERT design space, pushes the performance frontier upwards compared to traditional models. FlexiBERT-Mini, one of our proposed models, has 3% fewer parameters than BERT-Mini and achieves 8.9% higher GLUE score. A FlexiBERT model with equivalent performance as the best homogeneous model achieves 2.6x smaller size. FlexiBERT-Large, another proposed model, achieves state-of-the-art results, outperforming the baseline models by at least 5.7% on the GLUE benchmark.

We propose a new uncertainty estimator for gradient-free optimisation of black-box simulators using deep generative surrogate models. Optimisation of these simulators is especially challenging for stochastic simulators and higher dimensions. To address these issues, we utilise a deep generative surrogate approach to model the black box response for the entire parameter space. We then leverage this knowledge to estimate the proposed uncertainty based on the Wasserstein distance - the Wasserstein uncertainty. This approach is employed in a posterior agnostic gradient-free optimisation algorithm that minimises regret over the entire parameter space. A series of tests were conducted to demonstrate that our method is more robust to the shape of both the black box function and the stochastic response of the black box than state-of-the-art methods, such as efficient global optimisation with a deep Gaussian process surrogate.

Bayesian optimisation is a popular, surrogate model-based approach for optimising expensive black-box functions. Given a surrogate model, the next location to expensively evaluate is chosen via maximisation of a cheap-to-query acquisition function. We present an epsilon-greedy procedure for Bayesian optimisation in batch settings in which the black-box function can be evaluated multiple times in parallel. Our epsilon-shotgun algorithm leverages the model's prediction, uncertainty, and the approximated rate of change of the landscape to determine the spread of batch solutions to be distributed around a putative location. The initial target location is selected either in an exploitative fashion on the mean prediction, or -- with probability epsilon -- from elsewhere in the design space. This results in locations that are more densely sampled in regions where the function is changing rapidly and in locations predicted to be good (i.e close to predicted optima), with more scattered samples in regions where the function is flatter and/or of poorer quality. We empirically evaluate the epsilon-shotgun methods on a range of synthetic functions and two real-world problems, finding that they perform at least as well as state-of-the-art batch methods and in many cases exceed their performance.

Invertible neural networks (INNs) are neural network architectures with invertibility by design. Thanks to their invertibility and the tractability of Jacobian, INNs have various machine learning applications such as probabilistic modeling, generative modeling, and representation learning. However, their attractive properties often come at the cost of restricting the layer designs, which poses a question on their representation power: can we use these models to approximate sufficiently diverse functions? To answer this question, we have developed a general theoretical framework to investigate the representation power of INNs, building on a structure theorem of differential geometry. The framework simplifies the approximation problem of diffeomorphisms, which enables us to show the universal approximation properties of INNs. We apply the framework to two representative classes of INNs, namely Coupling-Flow-based INNs (CF-INNs) and Neural Ordinary Differential Equations (NODEs), and elucidate their high representation power despite the restrictions on their architectures.

In a model inversion (MI) attack, an adversary abuses access to a machine learning (ML) model to infer and reconstruct private training data. Remarkable progress has been made in the white-box and black-box setups, where the adversary has access to the complete model or the model's soft output respectively. However, there is very limited study in the most challenging but practically important setup: Label-only MI attacks, where the adversary only has access to the model's predicted label (hard label) without confidence scores nor any other model information. In this work, we propose LOKT, a novel approach for label-only MI attacks. Our idea is based on transfer of knowledge from the opaque target model to surrogate models. Subsequently, using these surrogate models, our approach can harness advanced white-box attacks. We propose knowledge transfer based on generative modelling, and introduce a new model, Target model-assisted ACGAN (T-ACGAN), for effective knowledge transfer. Our method casts the challenging label-only MI into the more tractable white-box setup. We provide analysis to support that surrogate models based on our approach serve as effective proxies for the target model for MI. Our experiments show that our method significantly outperforms existing SOTA Label-only MI attack by more than 15% across all MI benchmarks. Furthermore, our method compares favorably in terms of query budget. Our study highlights rising privacy threats for ML models even when minimal information (i.e., hard labels) is exposed. Our study highlights rising privacy threats for ML models even when minimal information (i.e., hard labels) is exposed. Our code, demo, models and reconstructed data are available at our project page: https://ngoc-nguyen-0.github.io/lokt/

Invertible convolutions have been an essential element for building expressive normalizing flow-based generative models since their introduction in Glow. Several attempts have been made to design invertible k times k convolutions that are efficient in training and sampling passes. Though these attempts have improved the expressivity and sampling efficiency, they severely lagged behind Glow which used only 1 times 1 convolutions in terms of sampling time. Also, many of the approaches mask a large number of parameters of the underlying convolution, resulting in lower expressivity on a fixed run-time budget. We propose a k times k convolutional layer and Deep Normalizing Flow architecture which i.) has a fast parallel inversion algorithm with running time O(n k^2) (n is height and width of the input image and k is kernel size), ii.) masks the minimal amount of learnable parameters in a layer. iii.) gives better forward pass and sampling times comparable to other k times k convolution-based models on real-world benchmarks. We provide an implementation of the proposed parallel algorithm for sampling using our invertible convolutions on GPUs. Benchmarks on CIFAR-10, ImageNet, and CelebA datasets show comparable performance to previous works regarding bits per dimension while significantly improving the sampling time.

Building local surrogates to accelerate stationary point searches on potential energy surfaces spans decades of effort. Done correctly, surrogates can reduce the number of expensive electronic structure evaluations by roughly an order of magnitude while preserving the accuracy of the underlying theory, with the gain depending on oracle cost, search distance, and the availability of analytical forces. We present a unified Bayesian optimization view of minimization, single-point saddle searches, and double-ended path searches: all three share one six-step surrogate loop and differ only in the inner optimization target and the acquisition criterion. The framework uses Gaussian process regression with derivative observations, inverse-distance kernels, and active learning, and we develop optional extensions for production use, including farthest-point sampling with the Earth Mover's Distance, MAP regularization, an adaptive trust radius, and random Fourier features for scaling. Accompanying pedagogical Rust code demonstrates that all three applications use the same Bayesian optimization loop, bridging the gap between theoretical formulation and practical execution.

Inverse design refers to the problem of optimizing the input of an objective function in order to enact a target outcome. For many real-world engineering problems, the objective function takes the form of a simulator that predicts how the system state will evolve over time, and the design challenge is to optimize the initial conditions that lead to a target outcome. Recent developments in learned simulation have shown that graph neural networks (GNNs) can be used for accurate, efficient, differentiable estimation of simulator dynamics, and support high-quality design optimization with gradient- or sampling-based optimization procedures. However, optimizing designs from scratch requires many expensive model queries, and these procedures exhibit basic failures on either non-convex or high-dimensional problems.In this work, we show how denoising diffusion models (DDMs) can be used to solve inverse design problems efficiently and propose a particle sampling algorithm for further improving their efficiency. We perform experiments on a number of fluid dynamics design challenges, and find that our approach substantially reduces the number of calls to the simulator compared to standard techniques.

Normalizing Flows (NFs) have been established as a principled framework for generative modeling. Standard NFs consist of a forward process and a reverse process: the forward process maps data to noise, while the reverse process generates samples by inverting it. Typical NF forward transformations are constrained by explicit invertibility, ensuring that the reverse process can serve as their exact analytic inverse. Recent developments in TARFlow and its variants have revitalized NF methods by combining Transformers and autoregressive flows, but have also exposed causal decoding as a major bottleneck. In this work, we introduce Bidirectional Normalizing Flow (BiFlow), a framework that removes the need for an exact analytic inverse. BiFlow learns a reverse model that approximates the underlying noise-to-data inverse mapping, enabling more flexible loss functions and architectures. Experiments on ImageNet demonstrate that BiFlow, compared to its causal decoding counterpart, improves generation quality while accelerating sampling by up to two orders of magnitude. BiFlow yields state-of-the-art results among NF-based methods and competitive performance among single-evaluation ("1-NFE") methods. Following recent encouraging progress on NFs, we hope our work will draw further attention to this classical paradigm.

We consider the inverse problem of reconstructing the spatial layout of a place, a home floorplan for example, from a user`s movements inside that layout. Direct inversion is ill-posed since many floorplans can explain the same movement trajectories. We adopt a diffusion-based posterior sampler to generate layouts consistent with the measurements. While active research is in progress on generative inverse solvers, we find that the forward operator in our problem poses new challenges. The path-planning process inside a floorplan is a non-invertible, non-differentiable function, and causes instability while optimizing using the likelihood score. We break-away from existing approaches and reformulate the likelihood score in a smoother embedding space. The embedding space is trained with a contrastive loss which brings compatible floorplans and trajectories close to each other, while pushing mismatched pairs far apart. We show that a surrogate form of the likelihood score in this embedding space is a valid approximation of the true likelihood score, making it possible to steer the denoising process towards the posterior. Across extensive experiments, our model CoGuide produces more consistent floorplans from trajectories, and is more robust than differentiable-planner baselines and guided-diffusion methods.

Resided at the intersection of multi-fidelity optimization (MFO) and Bayesian optimization (BO), MF BO has found a niche in solving expensive engineering design optimization problems, thanks to its advantages in incorporating physical and mathematical understandings of the problems, saving resources, addressing exploitation-exploration trade-off, considering uncertainty, and processing parallel computing. The increasing number of works dedicated to MF BO suggests the need for a comprehensive review of this advanced optimization technique. In this paper, we survey recent developments of two essential ingredients of MF BO: Gaussian process (GP) based MF surrogates and acquisition functions. We first categorize the existing MF modeling methods and MFO strategies to locate MF BO in a large family of surrogate-based optimization and MFO algorithms. We then exploit the common properties shared between the methods from each ingredient of MF BO to describe important GP-based MF surrogate models and review various acquisition functions. By doing so, we expect to provide a structured understanding of MF BO. Finally, we attempt to reveal important aspects that require further research for applications of MF BO in solving intricate yet important design optimization problems, including constrained optimization, high-dimensional optimization, optimization under uncertainty, and multi-objective optimization.

With the increasing computational costs associated with deep learning, automated hyperparameter optimization methods, strongly relying on black-box Bayesian optimization (BO), face limitations. Freeze-thaw BO offers a promising grey-box alternative, strategically allocating scarce resources incrementally to different configurations. However, the frequent surrogate model updates inherent to this approach pose challenges for existing methods, requiring retraining or fine-tuning their neural network surrogates online, introducing overhead, instability, and hyper-hyperparameters. In this work, we propose FT-PFN, a novel surrogate for Freeze-thaw style BO. FT-PFN is a prior-data fitted network (PFN) that leverages the transformers' in-context learning ability to efficiently and reliably do Bayesian learning curve extrapolation in a single forward pass. Our empirical analysis across three benchmark suites shows that the predictions made by FT-PFN are more accurate and 10-100 times faster than those of the deep Gaussian process and deep ensemble surrogates used in previous work. Furthermore, we show that, when combined with our novel acquisition mechanism (MFPI-random), the resulting in-context freeze-thaw BO method (ifBO), yields new state-of-the-art performance in the same three families of deep learning HPO benchmarks considered in prior work.

Neural architecture search (NAS) faces a challenge in balancing the exploration of expressive, broad search spaces that enable architectural innovation with the need for efficient evaluation of architectures to effectively search such spaces. We investigate surrogate model training for improving search in highly expressive NAS search spaces based on context-free grammars. We show that i) surrogate models trained either using zero-cost-proxy metrics and neural graph features (GRAF) or by fine-tuning an off-the-shelf LM have high predictive power for the performance of architectures both within and across datasets, ii) these surrogates can be used to filter out bad architectures when searching on novel datasets, thereby significantly speeding up search and achieving better final performances, and iii) the surrogates can be further used directly as the search objective for huge speed-ups.

We propose constrained causal Bayesian optimization (cCBO), an approach for finding interventions in a known causal graph that optimize a target variable under some constraints. cCBO first reduces the search space by exploiting the graph structure and, if available, an observational dataset; and then solves the restricted optimization problem by modelling target and constraint quantities using Gaussian processes and by sequentially selecting interventions via a constrained expected improvement acquisition function. We propose different surrogate models that enable to integrate observational and interventional data while capturing correlation among effects with increasing levels of sophistication. We evaluate cCBO on artificial and real-world causal graphs showing successful trade off between fast convergence and percentage of feasible interventions.

Scientific Machine Learning (SciML) is concerned with the development of learned emulators of physical systems governed by partial differential equations (PDE). In application domains such as weather forecasting, molecular dynamics, and inverse design, ML-based surrogate models are increasingly used to augment or replace inefficient and often non-differentiable numerical simulation algorithms. While a number of ML-based methods for approximating the solutions of PDEs have been proposed in recent years, they typically do not adapt to the parameters of the PDEs, making it difficult to generalize to PDE parameters not seen during training. We propose a Channel Attention mechanism guided by PDE Parameter Embeddings (CAPE) component for neural surrogate models and a simple yet effective curriculum learning strategy. The CAPE module can be combined with neural PDE solvers allowing them to adapt to unseen PDE parameters. The curriculum learning strategy provides a seamless transition between teacher-forcing and fully auto-regressive training. We compare CAPE in conjunction with the curriculum learning strategy using a popular PDE benchmark and obtain consistent and significant improvements over the baseline models. The experiments also show several advantages of CAPE, such as its increased ability to generalize to unseen PDE parameters without large increases inference time and parameter count.

The spatiotemporal resolution of Partial Differential Equations (PDEs) plays important roles in the mathematical description of the world's physical phenomena. In general, scientists and engineers solve PDEs numerically by the use of computationally demanding solvers. Recently, deep learning algorithms have emerged as a viable alternative for obtaining fast solutions for PDEs. Models are usually trained on synthetic data generated by solvers, stored on disk and read back for training. This paper advocates that relying on a traditional static dataset to train these models does not allow the full benefit of the solver to be used as a data generator. It proposes an open source online training framework for deep surrogate models. The framework implements several levels of parallelism focused on simultaneously generating numerical simulations and training deep neural networks. This approach suppresses the I/O and storage bottleneck associated with disk-loaded datasets, and opens the way to training on significantly larger datasets. Experiments compare the offline and online training of four surrogate models, including state-of-the-art architectures. Results indicate that exposing deep surrogate models to more dataset diversity, up to hundreds of GB, can increase model generalization capabilities. Fully connected neural networks, Fourier Neural Operator (FNO), and Message Passing PDE Solver prediction accuracy is improved by 68%, 16% and 7%, respectively.

Inverse graphics -- the task of inverting an image into physical variables that, when rendered, enable reproduction of the observed scene -- is a fundamental challenge in computer vision and graphics. Disentangling an image into its constituent elements, such as the shape, color, and material properties of the objects of the 3D scene that produced it, requires a comprehensive understanding of the environment. This requirement limits the ability of existing carefully engineered approaches to generalize across domains. Inspired by the zero-shot ability of large language models (LLMs) to generalize to novel contexts, we investigate the possibility of leveraging the broad world knowledge encoded in such models in solving inverse-graphics problems. To this end, we propose the Inverse-Graphics Large Language Model (IG-LLM), an inverse-graphics framework centered around an LLM, that autoregressively decodes a visual embedding into a structured, compositional 3D-scene representation. We incorporate a frozen pre-trained visual encoder and a continuous numeric head to enable end-to-end training. Through our investigation, we demonstrate the potential of LLMs to facilitate inverse graphics through next-token prediction, without the use of image-space supervision. Our analysis opens up new possibilities for precise spatial reasoning about images that exploit the visual knowledge of LLMs. We will release our code and data to ensure the reproducibility of our investigation and to facilitate future research at https://ig-llm.is.tue.mpg.de/

Surrogate models are necessary to optimize meaningful quantities in physical dynamics as their recursive numerical resolutions are often prohibitively expensive. It is mainly the case for fluid dynamics and the resolution of Navier-Stokes equations. However, despite the fast-growing field of data-driven models for physical systems, reference datasets representing real-world phenomena are lacking. In this work, we develop AirfRANS, a dataset for studying the two-dimensional incompressible steady-state Reynolds-Averaged Navier-Stokes equations over airfoils at a subsonic regime and for different angles of attacks. We also introduce metrics on the stress forces at the surface of geometries and visualization of boundary layers to assess the capabilities of models to accurately predict the meaningful information of the problem. Finally, we propose deep learning baselines on four machine learning tasks to study AirfRANS under different constraints for generalization considerations: big and scarce data regime, Reynolds number, and angle of attack extrapolation.

As Contrastive Language-Image Pre-training (CLIP) models are increasingly adopted for diverse downstream tasks and integrated into large vision-language models (VLMs), their susceptibility to adversarial perturbations has emerged as a critical concern. In this work, we introduce X-Transfer, a novel attack method that exposes a universal adversarial vulnerability in CLIP. X-Transfer generates a Universal Adversarial Perturbation (UAP) capable of deceiving various CLIP encoders and downstream VLMs across different samples, tasks, and domains. We refer to this property as super transferability--a single perturbation achieving cross-data, cross-domain, cross-model, and cross-task adversarial transferability simultaneously. This is achieved through surrogate scaling, a key innovation of our approach. Unlike existing methods that rely on fixed surrogate models, which are computationally intensive to scale, X-Transfer employs an efficient surrogate scaling strategy that dynamically selects a small subset of suitable surrogates from a large search space. Extensive evaluations demonstrate that X-Transfer significantly outperforms previous state-of-the-art UAP methods, establishing a new benchmark for adversarial transferability across CLIP models. The code is publicly available in our https://github.com/HanxunH/XTransferBench{GitHub repository}.

Inverse of an invertible convolution is an important operation that comes up in Normalizing Flows, Image Deblurring, etc. The naive algorithm for backpropagation of this operation using Gaussian elimination has running time O(n^3) where n is the number of pixels in the image. We give a fast parallel backpropagation algorithm with running time O(n) for a square image and provide a GPU implementation of the same. Inverse Convolutions are usually used in Normalizing Flows in the sampling pass, making them slow. We propose to use Inverse Convolutions in the forward (image to latent vector) pass of the Normalizing flow. Since the sampling pass is the inverse of the forward pass, it will use convolutions only, resulting in efficient sampling times. We use our parallel backpropagation algorithm for optimizing the inverse convolution layer resulting in fast training times also. We implement this approach in various Normalizing Flow backbones, resulting in our Inverse-Flow models. We benchmark Inverse-Flow on standard datasets and show significantly improved sampling times with similar bits per dimension compared to previous models.

Deep generative models based on neural differential equations have quickly become the state-of-the-art for numerous generation tasks across many different applications. These models rely on ODE/SDE solvers which integrate from a prior distribution to the data distribution. In many applications it is highly desirable to then integrate in the other direction. The standard solvers, however, accumulate discretization errors which don't align with the forward trajectory, thereby prohibiting an exact inversion. In applications where the precision of the generative model is paramount this inaccuracy in inversion is often unacceptable. Current approaches to solving the inversion of these models results in significant downstream issues with poor stability and low-order of convergence; moreover, they are strictly limited to the ODE domain. In this work, we propose a new family of reversible exponential (stochastic) Runge-Kutta solvers which we refer to as Rex developed by an application of Lawson methods to convert any explicit (stochastic) Runge-Kutta scheme into a reversible one. In addition to a rigorous theoretical analysis of the proposed solvers, we also empirically demonstrate the utility of Rex on improving the sampling of Boltzmann distributions with flow models, and improving image generation and editing capabilities with diffusion models.

Fast, geometry-generalizing surrogates for unsteady flow remain challenging. We present a time-dependent, geometry-aware Deep Operator Network that predicts velocity fields for moderate-Re flows around parametric and non-parametric shapes. The model encodes geometry via a signed distance field (SDF) trunk and flow history via a CNN branch, trained on 841 high-fidelity simulations. On held-out shapes, it attains sim 5% relative L2 single-step error and up to 1000X speedups over CFD. We provide physics-centric rollout diagnostics, including phase error at probes and divergence norms, to quantify long-horizon fidelity. These reveal accurate near-term transients but error accumulation in fine-scale wakes, most pronounced for sharp-cornered geometries. We analyze failure modes and outline practical mitigations. Code, splits, and scripts are openly released at: https://github.com/baskargroup/TimeDependent-DeepONet to support reproducibility and benchmarking.

We study the problem of classification with a reject option for a fixed predictor, applicable in natural language processing. We introduce a new problem formulation for this scenario, and an algorithm minimizing a new surrogate loss function. We provide a complete theoretical analysis of the surrogate loss function with a strong H-consistency guarantee. For evaluation, we choose the decontextualization task, and provide a manually-labelled dataset of 2mathord,000 examples. Our algorithm significantly outperforms the baselines considered, with a sim!!25% improvement in coverage when halving the error rate, which is only sim!! 3 % away from the theoretical limit.

State-of-the-art neural network training methods depend on the gradient of the network function. Therefore, they cannot be applied to networks whose activation functions do not have useful derivatives, such as binary and discrete-time spiking neural networks. To overcome this problem, the activation function's derivative is commonly substituted with a surrogate derivative, giving rise to surrogate gradient learning (SGL). This method works well in practice but lacks theoretical foundation. The neural tangent kernel (NTK) has proven successful in the analysis of gradient descent. Here, we provide a generalization of the NTK, which we call the surrogate gradient NTK, that enables the analysis of SGL. First, we study a naive extension of the NTK to activation functions with jumps, demonstrating that gradient descent for such activation functions is also ill-posed in the infinite-width limit. To address this problem, we generalize the NTK to gradient descent with surrogate derivatives, i.e., SGL. We carefully define this generalization and expand the existing key theorems on the NTK with mathematical rigor. Further, we illustrate our findings with numerical experiments. Finally, we numerically compare SGL in networks with sign activation function and finite width to kernel regression with the surrogate gradient NTK; the results confirm that the surrogate gradient NTK provides a good characterization of SGL.

Data-driven surrogate models improve the efficiency of simulating continuous dynamical systems, yet their autoregressive rollouts are often limited by instability and spectral blow-up. While global regularization techniques can enforce contractive dynamics, they uniformly damp high-frequency features, introducing a contraction-dissipation dilemma. Furthermore, long-horizon trajectory optimization methods that explicitly correct drift are bottlenecked by memory constraints. In this work, we propose Jacobian-Adaptive Weighting for Stability (JAWS), a probabilistic regularization strategy designed to mitigate these limitations. By framing operator learning as Maximum A Posteriori (MAP) estimation with spatially heteroscedastic uncertainty, JAWS dynamically modulates the regularization strength based on local physical complexity. This allows the model to enforce contraction in smooth regions to suppress noise, while relaxing constraints near singular features to preserve gradients, effectively realizing a behavior similar to numerical shock-capturing schemes. Experiments demonstrate that this spatially-adaptive prior serves as an effective spectral pre-conditioner, which reduces the base operator's burden of handling high-frequency instabilities. This reduction enables memory-efficient, short-horizon trajectory optimization to match or exceed the long-term accuracy of long-horizon baselines. Evaluated on the 1D viscous Burgers' equation, our hybrid approach improves long-term stability, shock fidelity, and out-of-distribution generalization while reducing training computational costs.

Generative AI models have made significant progress in automating the creation of 3D shapes, which has the potential to transform car design. In engineering design and optimization, evaluating engineering metrics is crucial. To make generative models performance-aware and enable them to create high-performing designs, surrogate modeling of these metrics is necessary. However, the currently used representations of three-dimensional (3D) shapes either require extensive computational resources to learn or suffer from significant information loss, which impairs their effectiveness in surrogate modeling. To address this issue, we propose a new two-dimensional (2D) representation of 3D shapes. We develop a surrogate drag model based on this representation to verify its effectiveness in predicting 3D car drag. We construct a diverse dataset of 9,070 high-quality 3D car meshes labeled by drag coefficients computed from computational fluid dynamics (CFD) simulations to train our model. Our experiments demonstrate that our model can accurately and efficiently evaluate drag coefficients with an R^2 value above 0.84 for various car categories. Moreover, the proposed representation method can be generalized to many other product categories beyond cars. Our model is implemented using deep neural networks, making it compatible with recent AI image generation tools (such as Stable Diffusion) and a significant step towards the automatic generation of drag-optimized car designs. We have made the dataset and code publicly available at https://decode.mit.edu/projects/dragprediction/.

Recent text-guided diffusion models provide powerful image generation capabilities. Currently, a massive effort is given to enable the modification of these images using text only as means to offer intuitive and versatile editing. To edit a real image using these state-of-the-art tools, one must first invert the image with a meaningful text prompt into the pretrained model's domain. In this paper, we introduce an accurate inversion technique and thus facilitate an intuitive text-based modification of the image. Our proposed inversion consists of two novel key components: (i) Pivotal inversion for diffusion models. While current methods aim at mapping random noise samples to a single input image, we use a single pivotal noise vector for each timestamp and optimize around it. We demonstrate that a direct inversion is inadequate on its own, but does provide a good anchor for our optimization. (ii) NULL-text optimization, where we only modify the unconditional textual embedding that is used for classifier-free guidance, rather than the input text embedding. This allows for keeping both the model weights and the conditional embedding intact and hence enables applying prompt-based editing while avoiding the cumbersome tuning of the model's weights. Our Null-text inversion, based on the publicly available Stable Diffusion model, is extensively evaluated on a variety of images and prompt editing, showing high-fidelity editing of real images.

Sampling from the posterior distribution poses a major computational challenge in solving inverse problems using latent diffusion models. Common methods rely on Tweedie's first-order moments, which are known to induce a quality-limiting bias. Existing second-order approximations are impractical due to prohibitive computational costs, making standard reverse diffusion processes intractable for posterior sampling. This paper introduces Second-order Tweedie sampler from Surrogate Loss (STSL), a novel sampler that offers efficiency comparable to first-order Tweedie with a tractable reverse process using second-order approximation. Our theoretical results reveal that the second-order approximation is lower bounded by our surrogate loss that only requires O(1) compute using the trace of the Hessian, and by the lower bound we derive a new drift term to make the reverse process tractable. Our method surpasses SoTA solvers PSLD and P2L, achieving 4X and 8X reduction in neural function evaluations, respectively, while notably enhancing sampling quality on FFHQ, ImageNet, and COCO benchmarks. In addition, we show STSL extends to text-guided image editing and addresses residual distortions present from corrupted images in leading text-guided image editing methods. To our best knowledge, this is the first work to offer an efficient second-order approximation in solving inverse problems using latent diffusion and editing real-world images with corruptions.

Advancements in high-computing devices increase the necessity for improved and new understanding and development of smart manufacturing factories. Discrete-event models with simulators have been shown to be critical to architect, designing, building, and operating the manufacturing of semiconductor chips. The diffusion, implantation, and lithography machines have intricate processes due to their feedforward and feedback connectivity. The dataset collected from simulations of the factory models holds the promise of generating valuable machine-learning models. As surrogate data-based models, their executions are highly efficient compared to the physics-based counterpart models. For the development of surrogate models, it is beneficial to have publicly available benchmark simulation models that are grounded in factory models that have concise structures and accurate behaviors. Hence, in this research, a dataset is devised and constructed based on a benchmark model of an Intel semiconductor fabrication factory. The model is formalized using the Parallel Discrete-Event System Specification and executed using the DEVS-Suite simulator. The time series dataset is constructed using discrete-event time trajectories. This dataset is further analyzed and used to develop baseline univariate and multivariate machine learning models. The dataset can also be utilized in the machine learning community for behavioral analysis based on formalized and scalable component-based discrete-event models and simulations.

Normalizing flow models have been used successfully for generative image super-resolution (SR) by approximating complex distribution of natural images to simple tractable distribution in latent space through Invertible Neural Networks (INN). These models can generate multiple realistic SR images from one low-resolution (LR) input using randomly sampled points in the latent space, simulating the ill-posed nature of image upscaling where multiple high-resolution (HR) images correspond to the same LR. Lately, the invertible process in INN has also been used successfully by bidirectional image rescaling models like IRN and HCFlow for joint optimization of downscaling and inverse upscaling, resulting in significant improvements in upscaled image quality. While they are optimized for image downscaling too, the ill-posed nature of image downscaling, where one HR image could be downsized to multiple LR images depending on different interpolation kernels and resampling methods, is not considered. A new downscaling latent variable, in addition to the original one representing uncertainties in image upscaling, is introduced to model variations in the image downscaling process. This dual latent variable enhancement is applicable to different image rescaling models and it is shown in extensive experiments that it can improve image upscaling accuracy consistently without sacrificing image quality in downscaled LR images. It is also shown to be effective in enhancing other INN-based models for image restoration applications like image hiding.

Bayesian optimization is an approach to optimizing objective functions that take a long time (minutes or hours) to evaluate. It is best-suited for optimization over continuous domains of less than 20 dimensions, and tolerates stochastic noise in function evaluations. It builds a surrogate for the objective and quantifies the uncertainty in that surrogate using a Bayesian machine learning technique, Gaussian process regression, and then uses an acquisition function defined from this surrogate to decide where to sample. In this tutorial, we describe how Bayesian optimization works, including Gaussian process regression and three common acquisition functions: expected improvement, entropy search, and knowledge gradient. We then discuss more advanced techniques, including running multiple function evaluations in parallel, multi-fidelity and multi-information source optimization, expensive-to-evaluate constraints, random environmental conditions, multi-task Bayesian optimization, and the inclusion of derivative information. We conclude with a discussion of Bayesian optimization software and future research directions in the field. Within our tutorial material we provide a generalization of expected improvement to noisy evaluations, beyond the noise-free setting where it is more commonly applied. This generalization is justified by a formal decision-theoretic argument, standing in contrast to previous ad hoc modifications.

Solving the inverse problem is the key step in evaluating the capacity of a physical model to describe real phenomena. In medical image computing, it aligns with the classical theme of image-based model personalization. Traditionally, a solution to the problem is obtained by performing either sampling or variational inference based methods. Both approaches aim to identify a set of free physical model parameters that results in a simulation best matching an empirical observation. When applied to brain tumor modeling, one of the instances of image-based model personalization in medical image computing, the overarching drawback of the methods is the time complexity for finding such a set. In a clinical setting with limited time between imaging and diagnosis or even intervention, this time complexity may prove critical. As the history of quantitative science is the history of compression, we align in this paper with the historical tendency and propose a method compressing complex traditional strategies for solving an inverse problem into a simple database query task. We evaluated different ways of performing the database query task assessing the trade-off between accuracy and execution time. On the exemplary task of brain tumor growth modeling, we prove that the proposed method achieves one order speed-up compared to existing approaches for solving the inverse problem. The resulting compute time offers critical means for relying on more complex and, hence, realistic models, for integrating image preprocessing and inverse modeling even deeper, or for implementing the current model into a clinical workflow.

We propose transferability from Large Geometric Vicinity (LGV), a new technique to increase the transferability of black-box adversarial attacks. LGV starts from a pretrained surrogate model and collects multiple weight sets from a few additional training epochs with a constant and high learning rate. LGV exploits two geometric properties that we relate to transferability. First, models that belong to a wider weight optimum are better surrogates. Second, we identify a subspace able to generate an effective surrogate ensemble among this wider optimum. Through extensive experiments, we show that LGV alone outperforms all (combinations of) four established test-time transformations by 1.8 to 59.9 percentage points. Our findings shed new light on the importance of the geometry of the weight space to explain the transferability of adversarial examples.

Every call to an LLM classification endpoint produces a labeled input-output pair already retained in production logs. These pairs constitute a free, growing training set: a lightweight surrogate trained on them can absorb a significant portion of future traffic at near-zero marginal inference cost. The open questions are when the surrogate is reliable enough to deploy, what it handles versus defers, and how that boundary evolves as data accumulates. We introduce TRACER (Trace-based Adaptive Cost-Efficient Routing), an open-source system that trains ML surrogates on an LLM's own production traces and governs deployment through a parity gate: the surrogate is activated only when its agreement with the LLM exceeds a user-specified threshold α. To make the routing boundary transparent, TRACER generates interpretability artifacts describing which input regions the surrogate handles, where it plateaus, and why it defers. On a 77-class intent benchmark with a Sonnet 4.6 teacher, TRACER achieves 83-100% surrogate coverage depending on the quality target α; on a 150-class benchmark, the surrogate fully replaces the teacher. On a natural language inference task, the parity gate correctly refuses deployment because the embedding representation cannot support reliable separation. The system is available as open-source software.

Perturbative availability poisons (PAPs) add small changes to images to prevent their use for model training. Current research adopts the belief that practical and effective approaches to countering PAPs do not exist. In this paper, we argue that it is time to abandon this belief. We present extensive experiments showing that 12 state-of-the-art PAP methods are vulnerable to Image Shortcut Squeezing (ISS), which is based on simple compression. For example, on average, ISS restores the CIFAR-10 model accuracy to 81.73%, surpassing the previous best preprocessing-based countermeasures by 37.97% absolute. ISS also (slightly) outperforms adversarial training and has higher generalizability to unseen perturbation norms and also higher efficiency. Our investigation reveals that the property of PAP perturbations depends on the type of surrogate model used for poison generation, and it explains why a specific ISS compression yields the best performance for a specific type of PAP perturbation. We further test stronger, adaptive poisoning, and show it falls short of being an ideal defense against ISS. Overall, our results demonstrate the importance of considering various (simple) countermeasures to ensure the meaningfulness of analysis carried out during the development of PAP methods.

Many state-of-the-art hyperparameter optimization (HPO) algorithms rely on model-based optimizers that learn surrogate models of the target function to guide the search. Gaussian processes are the de facto surrogate model due to their ability to capture uncertainty but they make strong assumptions about the observation noise, which might not be warranted in practice. In this work, we propose to leverage conformalized quantile regression which makes minimal assumptions about the observation noise and, as a result, models the target function in a more realistic and robust fashion which translates to quicker HPO convergence on empirical benchmarks. To apply our method in a multi-fidelity setting, we propose a simple, yet effective, technique that aggregates observed results across different resource levels and outperforms conventional methods across many empirical tasks.

Traditional scientific discovery relies on an iterative hypothesise-experiment-refine cycle that has driven progress for centuries, but its intuitive, ad-hoc implementation often wastes resources, yields inefficient designs, and misses critical insights. This tutorial presents Bayesian Optimisation (BO), a principled probability-driven framework that formalises and automates this core scientific cycle. BO uses surrogate models (e.g., Gaussian processes) to model empirical observations as evolving hypotheses, and acquisition functions to guide experiment selection, balancing exploitation of known knowledge and exploration of uncharted domains to eliminate guesswork and manual trial-and-error. We first frame scientific discovery as an optimisation problem, then unpack BO's core components, end-to-end workflows, and real-world efficacy via case studies in catalysis, materials science, organic synthesis, and molecule discovery. We also cover critical technical extensions for scientific applications, including batched experimentation, heteroscedasticity, contextual optimisation, and human-in-the-loop integration. Tailored for a broad audience, this tutorial bridges AI advances in BO with practical natural science applications, offering tiered content to empower cross-disciplinary researchers to design more efficient experiments and accelerate principled scientific discovery.

The Muon optimizer has received considerable attention for its strong performance in training large language models, yet the design principle behind its matrix-gradient orthogonalization remains largely elusive. In this paper, we introduce a surrogate model that not only sheds new light on the design of Muon, but more importantly leads to a new optimizer. In the same spirit as the derivation of Newton's method, the surrogate approximates the loss as a quadratic function of the perturbation to a weight matrix W using only three matrices: the gradient G, an output-space curvature matrix H, and the data matrix Z that stacks the layer inputs. By minimizing this surrogate in one step and adopting a certain isotropic assumption on the weights, we obtain the closed-form update rule (up to momentum and weight decay) W leftarrow W - ηcdot msgn(G(ZZ^top)^{-1}), where η is the learning rate and msgn(X)=UV^top if X=USV^top is a compact singular value decomposition. This new optimization method, which we refer to as Newton-Muon, shows that standard Muon can be interpreted as an implicit Newton-type method that neglects the right preconditioning induced by the input second moment. Empirically, on a reproduction of the earliest publicly released Modded-NanoGPT speedrun configuration using Muon for GPT-2 pretraining, Newton-Muon reaches the target validation loss in 6\% fewer iteration steps and reduces wall-clock training time by about 4\%.

Optimization problems with nonlinear cost functions and combinatorial constraints appear in many real-world applications but remain challenging to solve efficiently compared to their linear counterparts. To bridge this gap, we propose SurCo that learns linear text{Sur}rogate costs which can be used in existing text{Co}mbinatorial solvers to output good solutions to the original nonlinear combinatorial optimization problem. The surrogate costs are learned end-to-end with nonlinear loss by differentiating through the linear surrogate solver, combining the flexibility of gradient-based methods with the structure of linear combinatorial optimization. We propose three SurCo variants: SurCo-zero for individual nonlinear problems, SurCo-prior for problem distributions, and SurCo-hybrid to combine both distribution and problem-specific information. We give theoretical intuition motivating SurCo, and evaluate it empirically. Experiments show that SurCo finds better solutions faster than state-of-the-art and domain expert approaches in real-world optimization problems such as embedding table sharding, inverse photonic design, and nonlinear route planning.

It is widely believed that the success of deep convolutional networks is based on progressively discarding uninformative variability about the input with respect to the problem at hand. This is supported empirically by the difficulty of recovering images from their hidden representations, in most commonly used network architectures. In this paper we show via a one-to-one mapping that this loss of information is not a necessary condition to learn representations that generalize well on complicated problems, such as ImageNet. Via a cascade of homeomorphic layers, we build the i-RevNet, a network that can be fully inverted up to the final projection onto the classes, i.e. no information is discarded. Building an invertible architecture is difficult, for one, because the local inversion is ill-conditioned, we overcome this by providing an explicit inverse. An analysis of i-RevNets learned representations suggests an alternative explanation for the success of deep networks by a progressive contraction and linear separation with depth. To shed light on the nature of the model learned by the i-RevNet we reconstruct linear interpolations between natural image representations.

In computational social science (CSS), researchers analyze documents to explain social and political phenomena. In most scenarios, CSS researchers first obtain labels for documents and then explain labels using interpretable regression analyses in the second step. One increasingly common way to annotate documents cheaply at scale is through large language models (LLMs). However, like other scalable ways of producing annotations, such surrogate labels are often imperfect and biased. We present a new algorithm for using imperfect annotation surrogates for downstream statistical analyses while guaranteeing statistical properties -- like asymptotic unbiasedness and proper uncertainty quantification -- which are fundamental to CSS research. We show that direct use of surrogate labels in downstream statistical analyses leads to substantial bias and invalid confidence intervals, even with high surrogate accuracy of 80-90%. To address this, we build on debiased machine learning to propose the design-based supervised learning (DSL) estimator. DSL employs a doubly-robust procedure to combine surrogate labels with a smaller number of high-quality, gold-standard labels. Our approach guarantees valid inference for downstream statistical analyses, even when surrogates are arbitrarily biased and without requiring stringent assumptions, by controlling the probability of sampling documents for gold-standard labeling. Both our theoretical analysis and experimental results show that DSL provides valid statistical inference while achieving root mean squared errors comparable to existing alternatives that focus only on prediction without inferential guarantees.

Policy-based reinforcement learning algorithms are widely used in various fields. Among them, mainstream policy optimization algorithms such as TRPO and PPO introduce importance sampling into policy iteration, which allows the reuse of historical data. However, this can also lead to a high variance of the surrogate objective and indirectly affects the stability and convergence of the algorithm. In this paper, we first derived an upper bound of the surrogate objective variance, which can grow quadratically with the increase of the surrogate objective. Next, we proposed the dropout technique to avoid the excessive increase of the surrogate objective variance caused by importance sampling. Then, we introduced a general reinforcement learning framework applicable to mainstream policy optimization methods, and applied the dropout technique to the PPO algorithm to obtain the D-PPO variant. Finally, we conduct comparative experiments between D-PPO and PPO algorithms in the Atari 2600 environment, and the results show that D-PPO achieved significant performance improvements compared to PPO, and effectively limited the excessive increase of the surrogate objective variance during training.

Invertible neural networks based on coupling flows (CF-INNs) have various machine learning applications such as image synthesis and representation learning. However, their desirable characteristics such as analytic invertibility come at the cost of restricting the functional forms. This poses a question on their representation power: are CF-INNs universal approximators for invertible functions? Without a universality, there could be a well-behaved invertible transformation that the CF-INN can never approximate, hence it would render the model class unreliable. We answer this question by showing a convenient criterion: a CF-INN is universal if its layers contain affine coupling and invertible linear functions as special cases. As its corollary, we can affirmatively resolve a previously unsolved problem: whether normalizing flow models based on affine coupling can be universal distributional approximators. In the course of proving the universality, we prove a general theorem to show the equivalence of the universality for certain diffeomorphism classes, a theoretical insight that is of interest by itself.

This paper introduces a novel surrogate modeling framework for aerodynamic applications based on Neural Fields. The proposed approach, MARIO (Modulated Aerodynamic Resolution Invariant Operator), addresses non parametric geometric variability through an efficient shape encoding mechanism and exploits the discretization-invariant nature of Neural Fields. It enables training on significantly downsampled meshes, while maintaining consistent accuracy during full-resolution inference. These properties allow for efficient modeling of diverse flow conditions, while reducing computational cost and memory requirements compared to traditional CFD solvers and existing surrogate methods. The framework is validated on two complementary datasets that reflect industrial constraints. First, the AirfRANS dataset consists in a two-dimensional airfoil benchmark with non-parametric shape variations. Performance evaluation of MARIO on this case demonstrates an order of magnitude improvement in prediction accuracy over existing methods across velocity, pressure, and turbulent viscosity fields, while accurately capturing boundary layer phenomena and aerodynamic coefficients. Second, the NASA Common Research Model features three-dimensional pressure distributions on a full aircraft surface mesh, with parametric control surface deflections. This configuration confirms MARIO's accuracy and scalability. Benchmarking against state-of-the-art methods demonstrates that Neural Field surrogates can provide rapid and accurate aerodynamic predictions under the computational and data limitations characteristic of industrial applications.

We address the challenges of precise image inversion and disentangled image editing in the context of few-step diffusion models. We introduce an encoder based iterative inversion technique. The inversion network is conditioned on the input image and the reconstructed image from the previous step, allowing for correction of the next reconstruction towards the input image. We demonstrate that disentangled controls can be easily achieved in the few-step diffusion model by conditioning on an (automatically generated) detailed text prompt. To manipulate the inverted image, we freeze the noise maps and modify one attribute in the text prompt (either manually or via instruction based editing driven by an LLM), resulting in the generation of a new image similar to the input image with only one attribute changed. It can further control the editing strength and accept instructive text prompt. Our approach facilitates realistic text-guided image edits in real-time, requiring only 8 number of functional evaluations (NFEs) in inversion (one-time cost) and 4 NFEs per edit. Our method is not only fast, but also significantly outperforms state-of-the-art multi-step diffusion editing techniques.

We present a generative framework for inverse design of five-layer transmissive Huygens' metasurfaces (HMSs), addressing a longstanding challenge in achieving full-phase, high-efficiency unit cell designs with minimal full-wave simulations. The key to achieving this is our reliance on the field-based semianalytical (SA) scheme developed in Part I of this paper, which allows rapid and highly effective synthesis of such multilayer composites, however with limited accuracy. To overcome the prohibitive data demands of traditional pipelines, we employ Mamba, a selective state space model well suited for long-range sequence modeling as the backbone of our learning framework. A bidirectional Mamba (Bi-Mamba) forward surrogate is first trained on SA-generated data and subsequently fine-tuned with full-wave CST samples. An ablation over a 1080-sample CST pool shows that as few as 270 full-wave calibration samples suffice to reach near-CST-level agreement at a fraction of the simulation cost. An autoregressive Mamba inverse generator is subsequently trained on surrogate-augmented data, treating unit-cell synthesis as a sequential generation task. The resulting one-to-many generative model produces diverse unit cell geometries conditioned on target scattering responses. It achieves CST-validated designs with field transmission magnitude 0.9 across the full 0-2π phase range at 20 GHz. Moreover, a CST-calibrated surrogate trained to accurately predict frequency responses (18-22 GHz) enables functional post-selection of inverse generated designs. Together, the hybrid SA-generative methodology in this two-part compilation establishes a scalable and data-efficient solution for multilayer HMS synthesis, with natural extensions toward broadband, oblique-incidence, and higher-dimensional electromagnetic inverse-design problems.

Multimodal contrastive learning models like CLIP have demonstrated remarkable vision-language alignment capabilities, yet their vulnerability to backdoor attacks poses critical security risks. Attackers can implant latent triggers that persist through downstream tasks, enabling malicious control of model behavior upon trigger presentation. Despite great success in recent defense mechanisms, they remain impractical due to strong assumptions about attacker knowledge or excessive clean data requirements. In this paper, we introduce InverTune, the first backdoor defense framework for multimodal models under minimal attacker assumptions, requiring neither prior knowledge of attack targets nor access to the poisoned dataset. Unlike existing defense methods that rely on the same dataset used in the poisoning stage, InverTune effectively identifies and removes backdoor artifacts through three key components, achieving robust protection against backdoor attacks. Specifically, InverTune first exposes attack signatures through adversarial simulation, probabilistically identifying the target label by analyzing model response patterns. Building on this, we develop a gradient inversion technique to reconstruct latent triggers through activation pattern analysis. Finally, a clustering-guided fine-tuning strategy is employed to erase the backdoor function with only a small amount of arbitrary clean data, while preserving the original model capabilities. Experimental results show that InverTune reduces the average attack success rate (ASR) by 97.87% against the state-of-the-art (SOTA) attacks while limiting clean accuracy (CA) degradation to just 3.07%. This work establishes a new paradigm for securing multimodal systems, advancing security in foundation model deployment without compromising performance.

Normalising Flows are non-parametric statistical models characterised by their dual capabilities of density estimation and generation. This duality requires an inherently invertible architecture. However, the requirement of invertibility imposes constraints on their expressiveness, necessitating a large number of parameters and innovative architectural designs to achieve good results. Whilst flow-based models predominantly rely on neural-network-based transformations for expressive designs, alternative transformation methods have received limited attention. In this work, we present Ferumal flow, a novel kernelised normalising flow paradigm that integrates kernels into the framework. Our results demonstrate that a kernelised flow can yield competitive or superior results compared to neural network-based flows whilst maintaining parameter efficiency. Kernelised flows excel especially in the low-data regime, enabling flexible non-parametric density estimation in applications with sparse data availability.

Embedding inversion, i.e., reconstructing text given its embedding and black-box access to the embedding encoder, is a fundamental problem in both NLP and security. From the NLP perspective, it helps determine how much semantic information about the input is retained in the embedding. From the security perspective, it measures how much information is leaked by vector databases and embedding-based retrieval systems. State-of-the-art methods for embedding inversion, such as vec2text, have high accuracy but require (a) training a separate model for each embedding, and (b) a large number of queries to the corresponding encoder. We design, implement, and evaluate ZSInvert, a zero-shot inversion method based on the recently proposed adversarial decoding technique. ZSInvert is fast, query-efficient, and can be used for any text embedding without training an embedding-specific inversion model. We measure the effectiveness of ZSInvert on several embeddings and demonstrate that it recovers key semantic information about the corresponding texts.

A digital twin is a virtual replica of a real-world physical phenomena that uses mathematical modeling to characterize and simulate its defining features. By constructing digital twins for disease processes, we can perform in-silico simulations that mimic patients' health conditions and counterfactual outcomes under hypothetical interventions in a virtual setting. This eliminates the need for invasive procedures or uncertain treatment decisions. In this paper, we propose a method to identify digital twin model parameters using only noninvasive patient health data. We approach the digital twin modeling as a composite inverse problem, and observe that its structure resembles pretraining and finetuning in self-supervised learning (SSL). Leveraging this, we introduce a physics-informed SSL algorithm that initially pretrains a neural network on the pretext task of solving the physical model equations. Subsequently, the model is trained to reconstruct low-dimensional health measurements from noninvasive modalities while being constrained by the physical equations learned in pretraining. We apply our method to identify digital twins of cardiac hemodynamics using noninvasive echocardiogram videos, and demonstrate its utility in unsupervised disease detection and in-silico clinical trials.

Multiscale problems are ubiquitous in physics. Numerical simulations of such problems by solving partial differential equations (PDEs) at high resolution are computationally too expensive for many-query scenarios, e.g., uncertainty quantification, remeshing applications, topology optimization, and so forth. This limitation has motivated the application of data-driven surrogate models, where the microscale computations are substituted with a surrogate, usually acting as a black-box mapping between macroscale quantities. These models offer significant speedups but struggle with incorporating microscale physical constraints, such as the balance of linear momentum and constitutive models. In this contribution, we propose Equilibrium Neural Operator (EquiNO) as a complementary physics-informed PDE surrogate for predicting microscale physics and compare it with variational physics-informed neural and operator networks. Our framework, applicable to the so-called multiscale FE^{,2}, computations, introduces the FE-OL approach by integrating the finite element (FE) method with operator learning (OL). We apply the proposed FE-OL approach to quasi-static problems of solid mechanics. The results demonstrate that FE-OL can yield accurate solutions even when confronted with a restricted dataset during model development. Our results show that EquiNO achieves speedup factors exceeding 8000-fold compared to traditional methods and offers an optimal balance between data-driven and physics-based strategies.

Existing techniques for model inversion typically rely on hard-to-tune regularizers, such as total variation or feature regularization, which must be individually calibrated for each network in order to produce adequate images. In this work, we introduce Plug-In Inversion, which relies on a simple set of augmentations and does not require excessive hyper-parameter tuning. Under our proposed augmentation-based scheme, the same set of augmentation hyper-parameters can be used for inverting a wide range of image classification models, regardless of input dimensions or the architecture. We illustrate the practicality of our approach by inverting Vision Transformers (ViTs) and Multi-Layer Perceptrons (MLPs) trained on the ImageNet dataset, tasks which to the best of our knowledge have not been successfully accomplished by any previous works.

Bayesian parameter inference is useful to improve Li-ion battery diagnostics and can help formulate battery aging models. However, it is computationally intensive and cannot be easily repeated for multiple cycles, multiple operating conditions, or multiple replicate cells. To reduce the computational cost of Bayesian calibration, numerical solvers for physics-based models can be replaced with faster surrogates. A physics-informed neural network (PINN) is developed as a surrogate for the pseudo-2D (P2D) battery model calibration. For the P2D surrogate, additional training regularization was needed as compared to the PINN single-particle model (SPM) developed in Part I. Both the PINN SPM and P2D surrogate models are exercised for parameter inference and compared to data obtained from a direct numerical solution of the governing equations. A parameter inference study highlights the ability to use these PINNs to calibrate scaling parameters for the cathode Li diffusion and the anode exchange current density. By realizing computational speed-ups of 2250x for the P2D model, as compared to using standard integrating methods, the PINN surrogates enable rapid state-of-health diagnostics. In the low-data availability scenario, the testing error was estimated to 2mV for the SPM surrogate and 10mV for the P2D surrogate which could be mitigated with additional data.

We propose iterative inversion -- an algorithm for learning an inverse function without input-output pairs, but only with samples from the desired output distribution and access to the forward function. The key challenge is a distribution shift between the desired outputs and the outputs of an initial random guess, and we prove that iterative inversion can steer the learning correctly, under rather strict conditions on the function. We apply iterative inversion to learn control. Our input is a set of demonstrations of desired behavior, given as video embeddings of trajectories (without actions), and our method iteratively learns to imitate trajectories generated by the current policy, perturbed by random exploration noise. Our approach does not require rewards, and only employs supervised learning, which can be easily scaled to use state-of-the-art trajectory embedding techniques and policy representations. Indeed, with a VQ-VAE embedding, and a transformer-based policy, we demonstrate non-trivial continuous control on several tasks. Further, we report an improved performance on imitating diverse behaviors compared to reward based methods.

Large language models perform near-Bayesian inference yet violate permutation invariance on exchangeable data. We resolve this by showing transformers minimize expected conditional description length (cross-entropy) over orderings, E_pi[ell(Y mid Gamma_pi(X))], which admits a Kolmogorov-complexity interpretation up to additive constants, rather than the permutation-invariant description length ell(Y mid X). This makes them Bayesian in expectation, not in realization. We derive (i) a Quantified Martingale Violation bound showing order-induced deviations scale as O(log n) with constants; (ii) the Expectation-level Decompression Law linking information budgets to reliability for Bernoulli predicates; and (iii) deployable planners (B2T/RoH/ISR) for answer/abstain decisions. Empirically, permutation dispersion follows a+bln n (Qwen2-7B b approx 0.377, Llama-3.1-8B b approx 0.147); permutation mixtures improve ground-truth likelihood/accuracy; and randomized dose-response shows hallucinations drop by sim 0.13 per additional nat. A pre-specified audit with a fixed ISR=1.0 achieves near-0\% hallucinations via calibrated refusal at 24\% abstention. The framework turns hallucinations into predictable compression failures and enables principled information budgeting.

Modern power systems require fast and accurate dynamic simulations for stability assessment, digital twins, and real-time control, but classical ODE solvers are often too slow for large-scale or online applications. We propose a neural-operator framework for surrogate modeling of power system components, using Deep Operator Networks (DeepONets) to learn mappings from system states and time-varying inputs to full trajectories without step-by-step integration. To enhance generalization and data efficiency, we introduce Physics-Informed DeepONets (PI-DeepONets), which embed the residuals of governing equations into the training loss. Our results show that DeepONets, and especially PI-DeepONets, achieve accurate predictions under diverse scenarios, providing over 30 times speedup compared to high-order ODE solvers. Benchmarking against Physics-Informed Neural Networks (PINNs) highlights superior stability and scalability. Our results demonstrate neural operators as a promising path toward real-time, physics-aware simulation of power system dynamics.

When solving inverse problems, it is increasingly popular to use pre-trained diffusion models as plug-and-play priors. This framework can accommodate different forward models without re-training while preserving the generative capability of diffusion models. Despite their success in many imaging inverse problems, most existing methods rely on privileged information such as derivative, pseudo-inverse, or full knowledge about the forward model. This reliance poses a substantial limitation that restricts their use in a wide range of problems where such information is unavailable, such as in many scientific applications. To address this issue, we propose Ensemble Kalman Diffusion Guidance (EnKG) for diffusion models, a derivative-free approach that can solve inverse problems by only accessing forward model evaluations and a pre-trained diffusion model prior. We study the empirical effectiveness of our method across various inverse problems, including scientific settings such as inferring fluid flows and astronomical objects, which are highly non-linear inverse problems that often only permit black-box access to the forward model.

Recent advancements in text-guided diffusion models have unlocked powerful image manipulation capabilities. However, applying these methods to real images necessitates the inversion of the images into the domain of the pretrained diffusion model. Achieving faithful inversion remains a challenge, particularly for more recent models trained to generate images with a small number of denoising steps. In this work, we introduce an inversion method with a high quality-to-operation ratio, enhancing reconstruction accuracy without increasing the number of operations. Building on reversing the diffusion sampling process, our method employs an iterative renoising mechanism at each inversion sampling step. This mechanism refines the approximation of a predicted point along the forward diffusion trajectory, by iteratively applying the pretrained diffusion model, and averaging these predictions. We evaluate the performance of our ReNoise technique using various sampling algorithms and models, including recent accelerated diffusion models. Through comprehensive evaluations and comparisons, we show its effectiveness in terms of both accuracy and speed. Furthermore, we confirm that our method preserves editability by demonstrating text-driven image editing on real images.

We introduce a gradient-free framework for Bayesian Optimal Experimental Design (BOED) in sequential settings, aimed at complex systems where gradient information is unavailable. Our method combines Ensemble Kalman Inversion (EKI) for design optimization with the Affine-Invariant Langevin Dynamics (ALDI) sampler for efficient posterior sampling-both of which are derivative-free and ensemble-based. To address the computational challenges posed by nested expectations in BOED, we propose variational Gaussian and parametrized Laplace approximations that provide tractable upper and lower bounds on the Expected Information Gain (EIG). These approximations enable scalable utility estimation in high-dimensional spaces and PDE-constrained inverse problems. We demonstrate the performance of our framework through numerical experiments ranging from linear Gaussian models to PDE-based inference tasks, highlighting the method's robustness, accuracy, and efficiency in information-driven experimental design.

We propose using Normalizing Flows as a trainable kernel within the molecular dynamics update of Hamiltonian Monte Carlo (HMC). By learning (invertible) transformations that simplify our dynamics, we can outperform traditional methods at generating independent configurations. We show that, using a carefully constructed network architecture, our approach can be easily scaled to large lattice volumes with minimal retraining effort. The source code for our implementation is publicly available online at https://github.com/nftqcd/fthmc.

To balance quality and cost, various domain areas of science and engineering run simulations at multiple levels of sophistication. Multi-fidelity active learning aims to learn a direct mapping from input parameters to simulation outputs at the highest fidelity by actively acquiring data from multiple fidelity levels. However, existing approaches based on Gaussian processes are hardly scalable to high-dimensional data. Deep learning-based methods often impose a hierarchical structure in hidden representations, which only supports passing information from low-fidelity to high-fidelity. These approaches can lead to the undesirable propagation of errors from low-fidelity representations to high-fidelity ones. We propose a novel framework called Disentangled Multi-fidelity Deep Bayesian Active Learning (D-MFDAL), which learns the surrogate models conditioned on the distribution of functions at multiple fidelities. On benchmark tasks of learning deep surrogates of partial differential equations including heat equation, Poisson's equation and fluid simulations, our approach significantly outperforms state-of-the-art in prediction accuracy and sample efficiency.

Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies to compute forces and higher-order derivatives. Furthermore, such densities are often defined on non-trivial topologies. A recent example are Boltzmann Generators for generating 3D-structures of peptides and small proteins. These generative models leverage the space of internal coordinates (dihedrals, angles, and bonds), which is a product of hypertori and compact intervals. In this work, we introduce a class of smooth mixture transformations working on both compact intervals and hypertori. Mixture transformations employ root-finding methods to invert them in practice, which has so far prevented bi-directional flow training. To this end, we show that parameter gradients and forces of such inverses can be computed from forward evaluations via the inverse function theorem. We demonstrate two advantages of such smooth flows: they allow training by force matching to simulation data and can be used as potentials in molecular dynamics simulations.

Given a sample of size N, it is often useful to select a subsample of smaller size n<N to be used for statistical estimation or learning. Such a data selection step is useful to reduce the requirements of data labeling and the computational complexity of learning. We assume to be given N unlabeled samples {{boldsymbol x}_i}_{ile N}, and to be given access to a `surrogate model' that can predict labels y_i better than random guessing. Our goal is to select a subset of the samples, to be denoted by {{boldsymbol x}_i}_{iin G}, of size |G|=n<N. We then acquire labels for this set and we use them to train a model via regularized empirical risk minimization. By using a mixture of numerical experiments on real and synthetic data, and mathematical derivations under low- and high- dimensional asymptotics, we show that: (i)~Data selection can be very effective, in particular beating training on the full sample in some cases; (ii)~Certain popular choices in data selection methods (e.g. unbiased reweighted subsampling, or influence function-based subsampling) can be substantially suboptimal.

Aligning denoising generative models with human preferences or verifiable rewards remains a key challenge. While policy-gradient online reinforcement learning (RL) offers a principled post-training framework, its direct application is hindered by the intractable likelihoods of these models. Prior work therefore either optimizes an induced Markov decision process (MDP) over sampling trajectories, which is stable but inefficient, or uses likelihood surrogates based on the diffusion evidence lower bound (ELBO), which have so far underperformed on visual generation. Our key insight is that the ELBO-based approach can, in fact, be made both stable and efficient. By reducing surrogate variance and controlling gradient steps, we show that this approach can beat MDP-based methods. To this end, we introduce Variational GRPO (V-GRPO), a method that integrates ELBO-based surrogates with the Group Relative Policy Optimization (GRPO) algorithm, alongside a set of simple yet essential techniques. Our method is easy to implement, aligns with pretraining objectives, and avoids the limitations of MDP-based methods. V-GRPO achieves state-of-the-art performance in text-to-image synthesis, while delivering a 2times speedup over MixGRPO and a 3times speedup over DiffusionNFT.

Large Language Models (LLMs) achieve strong performance on diverse tasks but often exhibit cognitive inertia, struggling to follow instructions that conflict with the standardized patterns learned during supervised fine-tuning (SFT). To evaluate this limitation, we propose Inverse IFEval, a benchmark that measures models Counter-intuitive Abilitytheir capacity to override training-induced biases and comply with adversarial instructions. Inverse IFEval introduces eight types of such challenges, including Question Correction, Intentional Textual Flaws, Code without Comments, and Counterfactual Answering. Using a human-in-the-loop pipeline, we construct a dataset of 1012 high-quality Chinese and English questions across 23 domains, evaluated under an optimized LLM-as-a-Judge framework. Experiments on existing leading LLMs demonstrate the necessity of our proposed Inverse IFEval benchmark. Our findings emphasize that future alignment efforts should not only pursue fluency and factual correctness but also account for adaptability under unconventional contexts. We hope that Inverse IFEval serves as both a diagnostic tool and a foundation for developing methods that mitigate cognitive inertia, reduce overfitting to narrow patterns, and ultimately enhance the instruction-following reliability of LLMs in diverse and unpredictable real-world scenarios.

Dynamic multi-objective optimization requires continuous tracking of moving Pareto fronts. Existing methods struggle with irregular mutations and data sparsity, primarily facing three challenges: the non-linear coupling of dynamic modes, negative transfer from outdated historical data, and the cold-start problem during environmental switches. To address these issues, this paper proposes a decoupled basis-vector-driven generative framework (DB-GEN). First, to resolve non-linear coupling, the framework employs the discrete wavelet transform to separate evolutionary trajectories into low-frequency trends and high-frequency details. Second, to mitigate negative transfer, it learns transferable basis vectors via sparse dictionary learning rather than directly memorizing historical instances. Recomposing these bases under a topology-aware contrastive constraint constructs a structured latent manifold. Finally, to overcome the cold-start problem, a surrogate-assisted search paradigm samples initial populations from this manifold. Pre-trained on 120 million solutions, DB-GEN performs direct online inference without retraining or fine-tuning. This zero-shot generation process executes in milliseconds, requiring approximately 0.2 seconds per environmental change. Experimental results demonstrate that DB-GEN improves tracking accuracy across various dynamic benchmarks compared to existing algorithms.

Diffusion probabilistic models (DPMs) and their extensions have emerged as competitive generative models yet confront challenges of efficient sampling. We propose a new bilateral denoising diffusion model (BDDM) that parameterizes both the forward and reverse processes with a schedule network and a score network, which can train with a novel bilateral modeling objective. We show that the new surrogate objective can achieve a lower bound of the log marginal likelihood tighter than a conventional surrogate. We also find that BDDM allows inheriting pre-trained score network parameters from any DPMs and consequently enables speedy and stable learning of the schedule network and optimization of a noise schedule for sampling. Our experiments demonstrate that BDDMs can generate high-fidelity audio samples with as few as three sampling steps. Moreover, compared to other state-of-the-art diffusion-based neural vocoders, BDDMs produce comparable or higher quality samples indistinguishable from human speech, notably with only seven sampling steps (143x faster than WaveGrad and 28.6x faster than DiffWave). We release our code at https://github.com/tencent-ailab/bddm.

Recent works show that reducing the number of layers in a convolutional neural network can enhance efficiency while maintaining the performance of the network. Existing depth compression methods remove redundant non-linear activation functions and merge the consecutive convolution layers into a single layer. However, these methods suffer from a critical drawback; the kernel size of the merged layers becomes larger, significantly undermining the latency reduction gained from reducing the depth of the network. We show that this problem can be addressed by jointly pruning convolution layers and activation functions. To this end, we propose LayerMerge, a novel depth compression method that selects which activation layers and convolution layers to remove, to achieve a desired inference speed-up while minimizing performance loss. Since the corresponding selection problem involves an exponential search space, we formulate a novel surrogate optimization problem and efficiently solve it via dynamic programming. Empirical results demonstrate that our method consistently outperforms existing depth compression and layer pruning methods on various network architectures, both on image classification and generation tasks. We release the code at https://github.com/snu-mllab/LayerMerge.

The aim of this study is to develop surrogate models for quick, accurate prediction of thrust forces generated through flapping fin propulsion for given operating conditions and fin geometries. Different network architectures and configurations are explored to model the training data separately for the lead fin and rear fin of a tandem fin setup. We progressively improve the data representation of the input parameter space for model predictions. The models are tested on three unseen fin geometries and the predictions validated with computational fluid dynamics (CFD) data. Finally, the orders of magnitude gains in computational performance of these surrogate models, compared to experimental and CFD runs, vs their tradeoff with accuracy is discussed within the context of this tandem fin configuration.

Recent diffusion-based models achieve photorealism in image inpainting but require many sampling steps, limiting practical use. Few-step text-to-image models offer faster generation, but naively applying them to inpainting yields poor harmonization and artifacts between the background and inpainted region. We trace this cause to random Gaussian noise initialization, which under low function evaluations causes semantic misalignment and reduced fidelity. To overcome this, we propose InverFill, a one-step inversion method tailored for inpainting that injects semantic information from the input masked image into the initial noise, enabling high-fidelity few-step inpainting. Instead of training inpainting models, InverFill leverages few-step text-to-image models in a blended sampling pipeline with semantically aligned noise as input, significantly improving vanilla blended sampling and even matching specialized inpainting models at low NFEs. Moreover, InverFill does not require real-image supervision and only adds minimal inference overhead. Extensive experiments show that InverFill consistently boosts baseline few-step models, improving image quality and text coherence without costly retraining or heavy iterative optimization.

Surgical simulation offers a promising addition to conventional surgical training. However, available simulation tools lack photorealism and rely on hardcoded behaviour. Denoising Diffusion Models are a promising alternative for high-fidelity image synthesis, but existing state-of-the-art conditioning methods fall short in providing precise control or interactivity over the generated scenes. We introduce SurGrID, a Scene Graph to Image Diffusion Model, allowing for controllable surgical scene synthesis by leveraging Scene Graphs. These graphs encode a surgical scene's components' spatial and semantic information, which are then translated into an intermediate representation using our novel pre-training step that explicitly captures local and global information. Our proposed method improves the fidelity of generated images and their coherence with the graph input over the state-of-the-art. Further, we demonstrate the simulation's realism and controllability in a user assessment study involving clinical experts. Scene Graphs can be effectively used for precise and interactive conditioning of Denoising Diffusion Models for simulating surgical scenes, enabling high fidelity and interactive control over the generated content.

Recent advances in neural surrogate modeling offer the potential for transformative innovations in applications such as automotive aerodynamics. Yet, industrial-scale problems often involve volumetric meshes with cell counts reaching the 100 millions, presenting major scalability challenges. Complex geometries further complicate modeling through intricate surface-volume interactions, while quantities such as vorticity are highly nonlinear and must satisfy strict divergence-free constraints. To address these requirements, we introduce AB-UPT as a novel modeling scheme for building neural surrogates for CFD simulations. AB-UPT is designed to: (i) decouple geometry encoding and prediction tasks via multi-branch operators; (ii) enable scalability to high-resolution outputs via neural simulation in a low-dimensional latent space, coupled with anchored neural field decoders to predict high-fidelity outputs; (iii) enforce physics consistency by a novel divergence-free formulation. We show that AB-UPT yields state-of-the-art predictive accuracy of surface and volume fields on automotive CFD simulations ranging from 33 thousand up to 150 million mesh cells. Furthermore, our anchored neural field architecture enables the enforcement of hard physical constraints on the physics predictions without degradation in performance, exemplified by modeling divergence-free vorticity fields. Notably, the proposed models can be trained on a single GPU in less than a day and predict industry-standard surface and volume fields within seconds. Additionally, we show that the flexible design of our method enables neural simulation from a CAD geometry alone, omitting the need for costly CFD meshing procedures.

Flow-based generative models parameterize probability distributions through an invertible transformation and can be trained by maximum likelihood. Invertible residual networks provide a flexible family of transformations where only Lipschitz conditions rather than strict architectural constraints are needed for enforcing invertibility. However, prior work trained invertible residual networks for density estimation by relying on biased log-density estimates whose bias increased with the network's expressiveness. We give a tractable unbiased estimate of the log density using a "Russian roulette" estimator, and reduce the memory required during training by using an alternative infinite series for the gradient. Furthermore, we improve invertible residual blocks by proposing the use of activation functions that avoid derivative saturation and generalizing the Lipschitz condition to induced mixed norms. The resulting approach, called Residual Flows, achieves state-of-the-art performance on density estimation amongst flow-based models, and outperforms networks that use coupling blocks at joint generative and discriminative modeling.

Medical video generation has transformative potential for enhancing surgical understanding and pathology insights through precise and controllable visual representations. However, current models face limitations in controllability and authenticity. To bridge this gap, we propose SurgSora, a motion-controllable surgical video generation framework that uses a single input frame and user-controllable motion cues. SurgSora consists of three key modules: the Dual Semantic Injector (DSI), which extracts object-relevant RGB and depth features from the input frame and integrates them with segmentation cues to capture detailed spatial features of complex anatomical structures; the Decoupled Flow Mapper (DFM), which fuses optical flow with semantic-RGB-D features at multiple scales to enhance temporal understanding and object spatial dynamics; and the Trajectory Controller (TC), which allows users to specify motion directions and estimates sparse optical flow, guiding the video generation process. The fused features are used as conditions for a frozen Stable Diffusion model to produce realistic, temporally coherent surgical videos. Extensive evaluations demonstrate that SurgSora outperforms state-of-the-art methods in controllability and authenticity, showing its potential to advance surgical video generation for medical education, training, and research.

The work focuses on gathering high-fidelity and low-fidelity numerical simulations data using Nektar++ (Solver based on Applied Mathematics) and XFOIL respectively. The utilization of the higher polynomial distribution in calculating the Coefficient of lift and drag has demonstrated superior accuracy and precision. Further, Co-kriging Data fusion and Adaptive sampling technique has been used to obtain the precise data predictions for the lift and drag within the confined domain without conducting the costly simulations on HPC clusters. This creates a methodology to quantifying uncertainty in computational fluid dynamics by minimizing the required number of samples. To minimize the reliability on high-fidelity numerical simulations in Uncertainty Quantification, a multi-fidelity strategy has been adopted. The effectiveness of the multi-fidelity deep neural network model has been validated through the approximation of benchmark functions across 1-, 32-, and 100-dimensional, encompassing both linear and nonlinear correlations. The surrogate modelling results showed that multi-fidelity deep neural network model has shown excellent approximation capabilities for the test functions and multi-fidelity deep neural network method has outperformed Co-kriging in effectiveness. In addition to that, multi-fidelity deep neural network model is utilized for the simulation of aleatory uncertainty propagation in 1-, 32-, and 100 dimensional function test, considering both uniform and Gaussian distributions for input uncertainties. The results have shown that multi-fidelity deep neural network model has efficiently predicted the probability density distributions of quantities of interest as well as the statistical moments with precision and accuracy. The Co-Kriging model has exhibited limitations when addressing 32-Dimension problems due to the limitation of memory capacity for storage and manipulation.

Alignment in large language models (LLMs) is used to enforce guidelines such as safety. Yet, alignment fails in the face of jailbreak attacks that modify inputs to induce unsafe outputs. In this paper, we present and evaluate a method to assess the robustness of LLM alignment. We observe that alignment embeds a safety classifier in the target model that is responsible for deciding between refusal and compliance. We seek to extract an approximation of this classifier, called a surrogate classifier, from the LLM. We develop an algorithm for identifying candidate classifiers from subsets of the LLM model. We evaluate the degree to which the candidate classifiers approximate the model's embedded classifier in benign (F1 score) and adversarial (using surrogates in a white-box attack) settings. Our evaluation shows that the best candidates achieve accurate agreement (an F1 score above 80%) using as little as 20% of the model architecture. Further, we find attacks mounted on the surrogate models can be transferred with high accuracy. For example, a surrogate using only 50% of the Llama 2 model achieved an attack success rate (ASR) of 70%, a substantial improvement over attacking the LLM directly, where we only observed a 22% ASR. These results show that extracting surrogate classifiers is a viable (and highly effective) means for modeling (and therein addressing) the vulnerability of aligned models to jailbreaking attacks.

This paper studies model-inversion attacks, in which the access to a model is abused to infer information about the training data. Since its first introduction, such attacks have raised serious concerns given that training data usually contain privacy-sensitive information. Thus far, successful model-inversion attacks have only been demonstrated on simple models, such as linear regression and logistic regression. Previous attempts to invert neural networks, even the ones with simple architectures, have failed to produce convincing results. We present a novel attack method, termed the generative model-inversion attack, which can invert deep neural networks with high success rates. Rather than reconstructing private training data from scratch, we leverage partial public information, which can be very generic, to learn a distributional prior via generative adversarial networks (GANs) and use it to guide the inversion process. Moreover, we theoretically prove that a model's predictive power and its vulnerability to inversion attacks are indeed two sides of the same coin---highly predictive models are able to establish a strong correlation between features and labels, which coincides exactly with what an adversary exploits to mount the attacks. Our extensive experiments demonstrate that the proposed attack improves identification accuracy over the existing work by about 75\% for reconstructing face images from a state-of-the-art face recognition classifier. We also show that differential privacy, in its canonical form, is of little avail to defend against our attacks.

We propose an extension of Thompson sampling to optimization problems over function spaces where the objective is a known functional of an unknown operator's output. We assume that queries to the operator (such as running a high-fidelity simulator or physical experiment) are costly, while functional evaluations on the operator's output are inexpensive. Our algorithm employs a sample-then-optimize approach using neural operator surrogates. This strategy avoids explicit uncertainty quantification by treating trained neural operators as approximate samples from a Gaussian process (GP) posterior. We derive regret bounds and theoretical results connecting neural operators with GPs in infinite-dimensional settings. Experiments benchmark our method against other Bayesian optimization baselines on functional optimization tasks involving partial differential equations of physical systems, demonstrating better sample efficiency and significant performance gains.

Inverse protein folding -- the task of predicting a protein sequence from its backbone atom coordinates -- has surfaced as an important problem in the "top down", de novo design of proteins. Contemporary approaches have cast this problem as a conditional generative modelling problem, where a large generative model over protein sequences is conditioned on the backbone. While these generative models very rapidly produce promising sequences, independent draws from generative models may fail to produce sequences that reliably fold to the correct backbone. Furthermore, it is challenging to adapt pure generative approaches to other settings, e.g., when constraints exist. In this paper, we cast the problem of improving generated inverse folds as an optimization problem that we solve using recent advances in "deep" or "latent space" Bayesian optimization. Our approach consistently produces protein sequences with greatly reduced structural error to the target backbone structure as measured by TM score and RMSD while using fewer computational resources. Additionally, we demonstrate other advantages of an optimization-based approach to the problem, such as the ability to handle constraints.

Image enhancement finds wide-ranging applications in real-world scenarios due to complex environments and the inherent limitations of imaging devices. Recent diffusion-based methods yield promising outcomes but necessitate prolonged and computationally intensive iterative sampling. In response, we propose InstaRevive, a straightforward yet powerful image enhancement framework that employs score-based diffusion distillation to harness potent generative capability and minimize the sampling steps. To fully exploit the potential of the pre-trained diffusion model, we devise a practical and effective diffusion distillation pipeline using dynamic control to address inaccuracies in updating direction during score matching. Our control strategy enables a dynamic diffusing scope, facilitating precise learning of denoising trajectories within the diffusion model and ensuring accurate distribution matching gradients during training. Additionally, to enrich guidance for the generative power, we incorporate textual prompts via image captioning as auxiliary conditions, fostering further exploration of the diffusion model. Extensive experiments substantiate the efficacy of our framework across a diverse array of challenging tasks and datasets, unveiling the compelling efficacy and efficiency of InstaRevive in delivering high-quality and visually appealing results. Code is available at https://github.com/EternalEvan/InstaRevive.

Recent advancements in large language models (LLMs) have been driven by their emergent reasoning capabilities, particularly through long chain-of-thought (CoT) prompting, which enables thorough exploration and deliberation. Despite these advances, long-CoT LLMs often exhibit suboptimal reasoning behaviors, such as overthinking and excessively protracted reasoning chains, which can impair performance. In this paper, we analyze reasoning processes through an optimization lens, framing CoT as a gradient descent procedure where each reasoning step constitutes an update toward problem resolution. Building on this perspective, we introduce RePro (Rectifying Process-level Reward), a novel approach to refine LLM reasoning during post-training. RePro defines a surrogate objective function to assess the optimization process underlying CoT, utilizing a dual scoring mechanism to quantify its intensity and stability. These scores are aggregated into a composite process-level reward, seamlessly integrated into reinforcement learning with verifiable rewards (RLVR) pipelines to optimize LLMs. Extensive experiments across multiple reinforcement learning algorithms and diverse LLMs, evaluated on benchmarks spanning mathematics, science, and coding, demonstrate that RePro consistently enhances reasoning performance and mitigates suboptimal reasoning behaviors.

This work introduces the Efficient Transformed Gaussian Process (ETGP), a new way of creating C stochastic processes characterized by: 1) the C processes are non-stationary, 2) the C processes are dependent by construction without needing a mixing matrix, 3) training and making predictions is very efficient since the number of Gaussian Processes (GP) operations (e.g. inverting the inducing point's covariance matrix) do not depend on the number of processes. This makes the ETGP particularly suited for multi-class problems with a very large number of classes, which are the problems studied in this work. ETGPs exploit the recently proposed Transformed Gaussian Process (TGP), a stochastic process specified by transforming a Gaussian Process using an invertible transformation. However, unlike TGPs, ETGPs are constructed by transforming a single sample from a GP using C invertible transformations. We derive an efficient sparse variational inference algorithm for the proposed model and demonstrate its utility in 5 classification tasks which include low/medium/large datasets and a different number of classes, ranging from just a few to hundreds. Our results show that ETGPs, in general, outperform state-of-the-art methods for multi-class classification based on GPs, and have a lower computational cost (around one order of magnitude smaller).

Traditional experimental and numerical approaches for fluid dynamics problems often suffer from high computational cost, mesh sensitivity, and limited capability in capturing complex physical behaviors. Moreover, conventional physics-informed neural networks (PINNs) frequently struggle in chaotic and highly unsteady flow regimes. In this work, we propose PhysicsFormer, a fast and efficient transformer-based physics-informed framework that incorporates multi-head encoder-decoder cross-attention. Unlike multilayer perceptron-based PINNs, PhysicsFormer operates on sequential representations constructed from spatio-temporal data, enabling effective learning of long-range temporal dependencies and improved propagation of initial condition information. A data-embedding strategy is employed to convert spatio-temporal points into pseudo-sequences, while a dynamics-weighted loss function replaces the standard PINNs formulation. Owing to its parallel learning structure, PhysicsFormer demonstrates superior computational efficiency compared to existing transformer-based approaches. The framework is validated on Burgers' equation and flow reconstruction governed by the Navier-Stokes equations, achieving mean squared errors on the order of 10^{-6}. In addition, an inverse problem involving parameter identification in the two-dimensional incompressible Navier-Stokes equations is investigated. For clean data, PhysicsFormer achieves zero identification error for both λ_1 and λ_2; under 1% Gaussian noise, the errors are 0.07% for λ_1 and 0% for λ_2. These results demonstrate that PhysicsFormer provides a reliable and computationally efficient surrogate modeling framework for time-dependent fluid flow problems.

We release Super Apriel, a 15B-parameter supernet in which every decoder layer provides four trained mixer choices -- Full Attention (FA), Sliding Window Attention (SWA), Kimi Delta Attention (KDA), and Gated DeltaNet (GDN). A placement selects one mixer per layer; placements can be switched between requests at serving time without reloading weights, enabling multiple speed presets from a single checkpoint. The shared checkpoint also enables speculative decoding without a separate draft model. The all-FA preset matches the Apriel 1.6 teacher on all reported benchmarks; recommended hybrid presets span 2.9times to 10.7times decode throughput at 96% to 77% quality retention, with throughput advantages that compound at longer context lengths. With four mixer types across 48 layers, the configuration space is vast. A surrogate that predicts placement quality from the per-layer mixer assignment makes the speed-quality landscape tractable and identifies the best tradeoffs at each speed level. We investigate whether the best configurations at each speed level can be identified early in training or only after convergence. Rankings stabilize quickly at 0.5B scale, but the most efficient configurations exhibit higher instability at 15B, cautioning against extrapolation from smaller models. Super Apriel is trained by stochastic distillation from a frozen Apriel 1.6 teacher, followed by supervised fine-tuning. We release the supernet weights, Fast-LLM training code, vLLM serving code, and a placement optimization toolkit.

Idempotence is the stability of image codec to re-compression. At the first glance, it is unrelated to perceptual image compression. However, we find that theoretically: 1) Conditional generative model-based perceptual codec satisfies idempotence; 2) Unconditional generative model with idempotence constraint is equivalent to conditional generative codec. Based on this newfound equivalence, we propose a new paradigm of perceptual image codec by inverting unconditional generative model with idempotence constraints. Our codec is theoretically equivalent to conditional generative codec, and it does not require training new models. Instead, it only requires a pre-trained mean-square-error codec and unconditional generative model. Empirically, we show that our proposed approach outperforms state-of-the-art methods such as HiFiC and ILLM, in terms of Fr\'echet Inception Distance (FID). The source code is provided in https://github.com/tongdaxu/Idempotence-and-Perceptual-Image-Compression.

Time-dependent partial differential equations (PDEs) are ubiquitous in science and engineering. Recently, mostly due to the high computational cost of traditional solution techniques, deep neural network based surrogates have gained increased interest. The practical utility of such neural PDE solvers relies on their ability to provide accurate, stable predictions over long time horizons, which is a notoriously hard problem. In this work, we present a large-scale analysis of common temporal rollout strategies, identifying the neglect of non-dominant spatial frequency information, often associated with high frequencies in PDE solutions, as the primary pitfall limiting stable, accurate rollout performance. Based on these insights, we draw inspiration from recent advances in diffusion models to introduce PDE-Refiner; a novel model class that enables more accurate modeling of all frequency components via a multistep refinement process. We validate PDE-Refiner on challenging benchmarks of complex fluid dynamics, demonstrating stable and accurate rollouts that consistently outperform state-of-the-art models, including neural, numerical, and hybrid neural-numerical architectures. We further demonstrate that PDE-Refiner greatly enhances data efficiency, since the denoising objective implicitly induces a novel form of spectral data augmentation. Finally, PDE-Refiner's connection to diffusion models enables an accurate and efficient assessment of the model's predictive uncertainty, allowing us to estimate when the surrogate becomes inaccurate.

We address the challenge of sound propagation simulations in 3D virtual rooms with moving sources, which have applications in virtual/augmented reality, game audio, and spatial computing. Solutions to the wave equation can describe wave phenomena such as diffraction and interference. However, simulating them using conventional numerical discretization methods with hundreds of source and receiver positions is intractable, making stimulating a sound field with moving sources impractical. To overcome this limitation, we propose using deep operator networks to approximate linear wave-equation operators. This enables the rapid prediction of sound propagation in realistic 3D acoustic scenes with moving sources, achieving millisecond-scale computations. By learning a compact surrogate model, we avoid the offline calculation and storage of impulse responses for all relevant source/listener pairs. Our experiments, including various complex scene geometries, show good agreement with reference solutions, with root mean squared errors ranging from 0.02 Pa to 0.10 Pa. Notably, our method signifies a paradigm shift as no prior machine learning approach has achieved precise predictions of complete wave fields within realistic domains. We anticipate that our findings will drive further exploration of deep neural operator methods, advancing research in immersive user experiences within virtual environments.

While deep neural networks (NN) significantly advance image compressed sensing (CS) by improving reconstruction quality, the necessity of training current CS NNs from scratch constrains their effectiveness and hampers rapid deployment. Although recent methods utilize pre-trained diffusion models for image reconstruction, they struggle with slow inference and restricted adaptability to CS. To tackle these challenges, this paper proposes Invertible Diffusion Models (IDM), a novel efficient, end-to-end diffusion-based CS method. IDM repurposes a large-scale diffusion sampling process as a reconstruction model, and fine-tunes it end-to-end to recover original images directly from CS measurements, moving beyond the traditional paradigm of one-step noise estimation learning. To enable such memory-intensive end-to-end fine-tuning, we propose a novel two-level invertible design to transform both (1) multi-step sampling process and (2) noise estimation U-Net in each step into invertible networks. As a result, most intermediate features are cleared during training to reduce up to 93.8% GPU memory. In addition, we develop a set of lightweight modules to inject measurements into noise estimator to further facilitate reconstruction. Experiments demonstrate that IDM outperforms existing state-of-the-art CS networks by up to 2.64dB in PSNR. Compared to the recent diffusion-based approach DDNM, our IDM achieves up to 10.09dB PSNR gain and 14.54 times faster inference. Code is available at https://github.com/Guaishou74851/IDM.

Digital cameras transform sensor RAW readings into RGB images by means of their Image Signal Processor (ISP). Computational photography tasks such as image denoising and colour constancy are commonly performed in the RAW domain, in part due to the inherent hardware design, but also due to the appealing simplicity of noise statistics that result from the direct sensor readings. Despite this, the availability of RAW images is limited in comparison with the abundance and diversity of available RGB data. Recent approaches have attempted to bridge this gap by estimating the RGB to RAW mapping: handcrafted model-based methods that are interpretable and controllable usually require manual parameter fine-tuning, while end-to-end learnable neural networks require large amounts of training data, at times with complex training procedures, and generally lack interpretability and parametric control. Towards addressing these existing limitations, we present a novel hybrid model-based and data-driven ISP that builds on canonical ISP operations and is both learnable and interpretable. Our proposed invertible model, capable of bidirectional mapping between RAW and RGB domains, employs end-to-end learning of rich parameter representations, i.e. dictionaries, that are free from direct parametric supervision and additionally enable simple and plausible data augmentation. We evidence the value of our data generation process by extensive experiments under both RAW image reconstruction and RAW image denoising tasks, obtaining state-of-the-art performance in both. Additionally, we show that our ISP can learn meaningful mappings from few data samples, and that denoising models trained with our dictionary-based data augmentation are competitive despite having only few or zero ground-truth labels.

In mechanical structures like airplanes, cars and houses, noise is generated and transmitted through vibrations. To take measures to reduce this noise, vibrations need to be simulated with expensive numerical computations. Deep learning surrogate models present a promising alternative to classical numerical simulations as they can be evaluated magnitudes faster, while trading-off accuracy. To quantify such trade-offs systematically and foster the development of methods, we present a benchmark on the task of predicting the vibration of harmonically excited plates. The benchmark features a total of 12,000 plate geometries with varying forms of beadings, material, boundary conditions, load position and sizes with associated numerical solutions. To address the benchmark task, we propose a new network architecture, named Frequency-Query Operator, which predicts vibration patterns of plate geometries given a specific excitation frequency. Applying principles from operator learning and implicit models for shape encoding, our approach effectively addresses the prediction of highly variable frequency response functions occurring in dynamic systems. To quantify the prediction quality, we introduce a set of evaluation metrics and evaluate the method on our vibrating-plates benchmark. Our method outperforms DeepONets, Fourier Neural Operators and more traditional neural network architectures and can be used for design optimization. Code, dataset and visualizations: https://github.com/ecker-lab/Learning_Vibrating_Plates

A promising class of generative models maps points from a simple distribution to a complex distribution through an invertible neural network. Likelihood-based training of these models requires restricting their architectures to allow cheap computation of Jacobian determinants. Alternatively, the Jacobian trace can be used if the transformation is specified by an ordinary differential equation. In this paper, we use Hutchinson's trace estimator to give a scalable unbiased estimate of the log-density. The result is a continuous-time invertible generative model with unbiased density estimation and one-pass sampling, while allowing unrestricted neural network architectures. We demonstrate our approach on high-dimensional density estimation, image generation, and variational inference, achieving the state-of-the-art among exact likelihood methods with efficient sampling.

Text-to-image diffusion models offer powerful image editing capabilities. To edit real images, many methods rely on the inversion of the image into Gaussian noise. A common approach to invert an image is to gradually add noise to the image, where the noise is determined by reversing the sampling equation. This process has an inherent tradeoff between reconstruction and editability, limiting the editing of challenging images such as highly-detailed ones. Recognizing the reliance of text-to-image models inversion on a text condition, this work explores the importance of the condition choice. We show that a condition that precisely aligns with the input image significantly improves the inversion quality. Based on our findings, we introduce Tight Inversion, an inversion method that utilizes the most possible precise condition -- the input image itself. This tight condition narrows the distribution of the model's output and enhances both reconstruction and editability. We demonstrate the effectiveness of our approach when combined with existing inversion methods through extensive experiments, evaluating the reconstruction accuracy as well as the integration with various editing methods.

Generative diffusion models are increasingly used for medical imaging data augmentation, but text prompting cannot produce causal training data. Re-prompting rerolls the entire generation trajectory, altering anatomy, texture, and background. Inversion-based editing methods introduce reconstruction error that causes structural drift. We propose MedSteer, a training-free activation-steering framework for endoscopic synthesis. MedSteer identifies a pathology vector for each contrastive prompt pair in the cross-attention layers of a diffusion transformer. At inference time, it steers image activations along this vector, generating counterfactual pairs from scratch where the only difference is the steered concept. All other structure is preserved by construction. We evaluate MedSteer across three experiments on Kvasir v3 and HyperKvasir. On counterfactual generation across three clinical concept pairs, MedSteer achieves flip rates of 0.800, 0.925, and 0.950, outperforming the best inversion-based baseline in both concept flip rate and structural preservation. On dye disentanglement, MedSteer achieves 75% dye removal against 20% (PnP) and 10% (h-Edit). On downstream polyp detection, augmenting with MedSteer counterfactual pairs achieves ViT AUC of 0.9755 versus 0.9083 for quantity-matched re-prompting, confirming that counterfactual structure drives the gain. Code is at link https://github.com/phamtrongthang123/medsteer

We investigate an experiential learning paradigm for acquiring an internal model of intuitive physics. Our model is evaluated on a real-world robotic manipulation task that requires displacing objects to target locations by poking. The robot gathered over 400 hours of experience by executing more than 100K pokes on different objects. We propose a novel approach based on deep neural networks for modeling the dynamics of robot's interactions directly from images, by jointly estimating forward and inverse models of dynamics. The inverse model objective provides supervision to construct informative visual features, which the forward model can then predict and in turn regularize the feature space for the inverse model. The interplay between these two objectives creates useful, accurate models that can then be used for multi-step decision making. This formulation has the additional benefit that it is possible to learn forward models in an abstract feature space and thus alleviate the need of predicting pixels. Our experiments show that this joint modeling approach outperforms alternative methods.

The fidelity of Generative Adversarial Networks (GAN) inversion is impeded by Out-Of-Domain (OOD) areas (e.g., background, accessories) in the image. Detecting the OOD areas beyond the generation ability of the pre-trained model and blending these regions with the input image can enhance fidelity. The "invertibility mask" figures out these OOD areas, and existing methods predict the mask with the reconstruction error. However, the estimated mask is usually inaccurate due to the influence of the reconstruction error in the In-Domain (ID) area. In this paper, we propose a novel framework that enhances the fidelity of human face inversion by designing a new module to decompose the input images to ID and OOD partitions with invertibility masks. Unlike previous works, our invertibility detector is simultaneously learned with a spatial alignment module. We iteratively align the generated features to the input geometry and reduce the reconstruction error in the ID regions. Thus, the OOD areas are more distinguishable and can be precisely predicted. Then, we improve the fidelity of our results by blending the OOD areas from the input image with the ID GAN inversion results. Our method produces photo-realistic results for real-world human face image inversion and manipulation. Extensive experiments demonstrate our method's superiority over existing methods in the quality of GAN inversion and attribute manipulation.

Classifier-free guidance (CFG) is a fundamental tool in modern diffusion models for text-guided generation. Although effective, CFG has notable drawbacks. For instance, DDIM with CFG lacks invertibility, complicating image editing; furthermore, high guidance scales, essential for high-quality outputs, frequently result in issues like mode collapse. Contrary to the widespread belief that these are inherent limitations of diffusion models, this paper reveals that the problems actually stem from the off-manifold phenomenon associated with CFG, rather than the diffusion models themselves. More specifically, inspired by the recent advancements of diffusion model-based inverse problem solvers (DIS), we reformulate text-guidance as an inverse problem with a text-conditioned score matching loss, and develop CFG++, a novel approach that tackles the off-manifold challenges inherent in traditional CFG. CFG++ features a surprisingly simple fix to CFG, yet it offers significant improvements, including better sample quality for text-to-image generation, invertibility, smaller guidance scales, reduced mode collapse, etc. Furthermore, CFG++ enables seamless interpolation between unconditional and conditional sampling at lower guidance scales, consistently outperforming traditional CFG at all scales. Experimental results confirm that our method significantly enhances performance in text-to-image generation, DDIM inversion, editing, and solving inverse problems, suggesting a wide-ranging impact and potential applications in various fields that utilize text guidance. Project Page: https://cfgpp-diffusion.github.io/.