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Add to EdgeContinuum Transformers Perform In-Context Learning by Operator Gradient Descent
May 23, 2025
Transformers robustly exhibit the ability to perform in-context learning, whereby their predictive accuracy on a task can increase not by parameter updates but merely with the placement of training samples in their context windows. Recent works have shown that transformers achieve this by implementing gradient descent in their forward passes. Such results, however, are restricted to standard transformer architectures, which handle finite-dimensional inputs. In the space of PDE surrogate modeling, a generalization of transformers to handle infinite-dimensional function inputs, known as "continuum transformers," has been proposed and similarly observed to exhibit in-context learning. Despite impressive empirical performance, such in-context learning has yet to be theoretically characterized. We herein demonstrate that continuum transformers perform in-context operator learning by performing gradient descent in an operator RKHS. We demonstrate this using novel proof strategies that leverage a generalized representer theorem for Hilbert spaces and gradient flows over the space of functionals of a Hilbert space. We additionally show the operator learned in context is the Bayes Optimal Predictor in the infinite depth limit of the transformer. We then provide empirical validations of this optimality result and demonstrate that the parameters under which such gradient descent is performed are recovered through the continuum transformer training.
Operator Learning for Schrödinger Equation: Unitarity, Error Bounds, and Time Generalization
May 23, 2025We consider the problem of learning the evolution operator for the time-dependent Schr\"{o}dinger equation, where the Hamiltonian may vary with time. Existing neural network-based surrogates often ignore fundamental properties of the Schr\"{o}dinger equation, such as linearity and unitarity, and lack theoretical guarantees on prediction error or time generalization. To address this, we introduce a linear estimator for the evolution operator that preserves a weak form of unitarity. We establish both upper and lower bounds on the prediction error that hold uniformly over all sufficiently smooth initial wave functions. Additionally, we derive time generalization bounds that quantify how the estimator extrapolates beyond the time points seen during training. Experiments across real-world Hamiltonians -- including hydrogen atoms, ion traps for qubit design, and optical lattices -- show that our estimator achieves relative errors $10^{-2}$ to $10^{-3}$ times smaller than state-of-the-art methods such as the Fourier Neural Operator and DeepONet.
Three Things to Know about Deep Metric Learning
Dec 17, 2024This paper addresses supervised deep metric learning for open-set image retrieval, focusing on three key aspects: the loss function, mixup regularization, and model initialization. In deep metric learning, optimizing the retrieval evaluation metric, recall@k, via gradient descent is desirable but challenging due to its non-differentiable nature. To overcome this, we propose a differentiable surrogate loss that is computed on large batches, nearly equivalent to the entire training set. This computationally intensive process is made feasible through an implementation that bypasses the GPU memory limitations. Additionally, we introduce an efficient mixup regularization technique that operates on pairwise scalar similarities, effectively increasing the batch size even further. The training process is further enhanced by initializing the vision encoder using foundational models, which are pre-trained on large-scale datasets. Through a systematic study of these components, we demonstrate that their synergy enables large models to nearly solve popular benchmarks.
Wound Tissue Segmentation in Diabetic Foot Ulcer Images Using Deep Learning: A Pilot Study
Jun 23, 2024Identifying individual tissues, so-called tissue segmentation, in diabetic foot ulcer (DFU) images is a challenging task and little work has been published, largely due to the limited availability of a clinical image dataset. To address this gap, we have created a DFUTissue dataset for the research community to evaluate wound tissue segmentation algorithms. The dataset contains 110 images with tissues labeled by wound experts and 600 unlabeled images. Additionally, we conducted a pilot study on segmenting wound characteristics including fibrin, granulation, and callus using deep learning. Due to the limited amount of annotated data, our framework consists of both supervised learning (SL) and semi-supervised learning (SSL) phases. In the SL phase, we propose a hybrid model featuring a Mix Transformer (MiT-b3) in the encoder and a CNN in the decoder, enhanced by the integration of a parallel spatial and channel squeeze-and-excitation (P-scSE) module known for its efficacy in improving boundary accuracy. The SSL phase employs a pseudo-labeling-based approach, iteratively identifying and incorporating valuable unlabeled images to enhance overall segmentation performance. Comparative evaluations with state-of-the-art methods are conducted for both SL and SSL phases. The SL achieves a Dice Similarity Coefficient (DSC) of 84.89%, which has been improved to 87.64% in the SSL phase. Furthermore, the results are benchmarked against two widely used SSL approaches: Generative Adversarial Networks and Cross-Consistency Training. Additionally, our hybrid model outperforms the state-of-the-art methods with a 92.99% DSC in performing binary segmentation of DFU wound areas when tested on the Chronic Wound dataset. Codes and data are available at https://github.com/uwm-bigdata/DFUTissueSegNet.
Conformalized Late Fusion Multi-View Learning
May 25, 2024
Uncertainty quantification for multi-view learning is motivated by the increasing use of multi-view data in scientific problems. A common variant of multi-view learning is late fusion: train separate predictors on individual views and combine them after single-view predictions are available. Existing methods for uncertainty quantification for late fusion often rely on undesirable distributional assumptions for validity. Conformal prediction is one approach that avoids such distributional assumptions. However, naively applying conformal prediction to late-stage fusion pipelines often produces overly conservative and uninformative prediction regions, limiting its downstream utility. We propose a novel methodology, Multi-View Conformal Prediction (MVCP), where conformal prediction is instead performed separately on the single-view predictors and only fused subsequently. Our framework extends the standard scalar formulation of a score function to a multivariate score that produces more efficient downstream prediction regions in both classification and regression settings. We then demonstrate that such improvements can be realized in methods built atop conformalized regressors, specifically in robust predict-then-optimize pipelines.
Conformal Contextual Robust Optimization
Oct 16, 2023Data-driven approaches to predict-then-optimize decision-making problems seek to mitigate the risk of uncertainty region misspecification in safety-critical settings. Current approaches, however, suffer from considering overly conservative uncertainty regions, often resulting in suboptimal decisionmaking. To this end, we propose Conformal-Predict-Then-Optimize (CPO), a framework for leveraging highly informative, nonconvex conformal prediction regions over high-dimensional spaces based on conditional generative models, which have the desired distribution-free coverage guarantees. Despite guaranteeing robustness, such black-box optimization procedures alone inspire little confidence owing to the lack of explanation of why a particular decision was found to be optimal. We, therefore, augment CPO to additionally provide semantically meaningful visual summaries of the uncertainty regions to give qualitative intuition for the optimal decision. We highlight the CPO framework by demonstrating results on a suite of simulation-based inference benchmark tasks and a vehicle routing task based on probabilistic weather prediction.
Integrated Image and Location Analysis for Wound Classification: A Deep Learning Approach
Aug 24, 2023The global burden of acute and chronic wounds presents a compelling case for enhancing wound classification methods, a vital step in diagnosing and determining optimal treatments. Recognizing this need, we introduce an innovative multi-modal network based on a deep convolutional neural network for categorizing wounds into four categories: diabetic, pressure, surgical, and venous ulcers. Our multi-modal network uses wound images and their corresponding body locations for more precise classification. A unique aspect of our methodology is incorporating a body map system that facilitates accurate wound location tagging, improving upon traditional wound image classification techniques. A distinctive feature of our approach is the integration of models such as VGG16, ResNet152, and EfficientNet within a novel architecture. This architecture includes elements like spatial and channel-wise Squeeze-and-Excitation modules, Axial Attention, and an Adaptive Gated Multi-Layer Perceptron, providing a robust foundation for classification. Our multi-modal network was trained and evaluated on two distinct datasets comprising relevant images and corresponding location information. Notably, our proposed network outperformed traditional methods, reaching an accuracy range of 74.79% to 100% for Region of Interest (ROI) without location classifications, 73.98% to 100% for ROI with location classifications, and 78.10% to 100% for whole image classifications. This marks a significant enhancement over previously reported performance metrics in the literature. Our results indicate the potential of our multi-modal network as an effective decision-support tool for wound image classification, paving the way for its application in various clinical contexts.
Diffusion Models for Probabilistic Deconvolution of Galaxy Images
Jul 20, 2023
Telescopes capture images with a particular point spread function (PSF). Inferring what an image would have looked like with a much sharper PSF, a problem known as PSF deconvolution, is ill-posed because PSF convolution is not an invertible transformation. Deep generative models are appealing for PSF deconvolution because they can infer a posterior distribution over candidate images that, if convolved with the PSF, could have generated the observation. However, classical deep generative models such as VAEs and GANs often provide inadequate sample diversity. As an alternative, we propose a classifier-free conditional diffusion model for PSF deconvolution of galaxy images. We demonstrate that this diffusion model captures a greater diversity of possible deconvolutions compared to a conditional VAE.
Variational Inference with Coverage Guarantees
May 23, 2023
Amortized variational inference produces a posterior approximator that can compute a posterior approximation given any new observation. Unfortunately, there are few guarantees about the quality of these approximate posteriors. We propose Conformalized Amortized Neural Variational Inference (CANVI), a procedure that is scalable, easily implemented, and provides guaranteed marginal coverage. Given a collection of candidate amortized posterior approximators, CANVI constructs conformalized predictors based on each candidate, compares the predictors using a metric known as predictive efficiency, and returns the most efficient predictor. CANVI ensures that the resulting predictor constructs regions that contain the truth with high probability (exactly how high is prespecified by the user). CANVI is agnostic to design decisions in formulating the candidate approximators and only requires access to samples from the forward model, permitting its use in likelihood-free settings. We prove lower bounds on the predictive efficiency of the regions produced by CANVI and explore how the quality of a posterior approximation relates to the predictive efficiency of prediction regions based on that approximation. Finally, we demonstrate the accurate calibration and high predictive efficiency of CANVI on a suite of simulation-based inference benchmark tasks and an important scientific task: analyzing galaxy emission spectra.
FUSegNet: A Deep Convolutional Neural Network for Foot Ulcer Segmentation
May 04, 2023This paper presents FUSegNet, a new model for foot ulcer segmentation in diabetes patients, which uses the pre-trained EfficientNet-b7 as a backbone to address the issue of limited training samples. A modified spatial and channel squeeze-and-excitation (scSE) module called parallel scSE or P-scSE is proposed that combines additive and max-out scSE. A new arrangement is introduced for the module by fusing it in the middle of each decoder stage. As the top decoder stage carries a limited number of feature maps, max-out scSE is bypassed there to form a shorted P-scSE. A set of augmentations, comprising geometric, morphological, and intensity-based augmentations, is applied before feeding the data into the network. The proposed model is first evaluated on a publicly available chronic wound dataset where it achieves a data-based dice score of 92.70%, which is the highest score among the reported approaches. The model outperforms other scSE-based UNet models in terms of Pratt's figure of merits (PFOM) scores in most categories, which evaluates the accuracy of edge localization. The model is then tested in the MICCAI 2021 FUSeg challenge, where a variation of FUSegNet called x-FUSegNet is submitted. The x-FUSegNet model, which takes the average of outputs obtained by FUSegNet using 5-fold cross-validation, achieves a dice score of 89.23%, placing it at the top of the FUSeg Challenge leaderboard. The source code for the model is available on https://github.com/mrinal054/FUSegNet.