Hessian-Informed Flow Matching

Modeling complex systems that evolve toward equilibrium distributions is important in various physical applications, including molecular dynamics and robotic control. These systems often follow the stochastic gradient descent of an underlying energy function, converging to stationary distributions around energy minima. The local covariance of these distributions is shaped by the energy landscape's curvature, often resulting in anisotropic characteristics. While flow-based generative models have gained traction in generating samples from equilibrium distributions in such applications, they predominately employ isotropic conditional probability paths, limiting their ability to capture such covariance structures. In this paper, we introduce Hessian-Informed Flow Matching (HI-FM), a novel approach that integrates the Hessian of an energy function into conditional flows within the flow matching framework. This integration allows HI-FM to account for local curvature and anisotropic covariance structures. Our approach leverages the linearization theorem from dynamical systems and incorporates additional considerations such as time transformations and equivariance. Empirical evaluations on the MNIST and Lennard-Jones particles datasets demonstrate that HI-FM improves the likelihood of test samples.

Medical Image Segmentation with SAM-generated Annotations

The field of medical image segmentation is hindered by the scarcity of large, publicly available annotated datasets. Not all datasets are made public for privacy reasons, and creating annotations for a large dataset is time-consuming and expensive, as it requires specialized expertise to accurately identify regions of interest (ROIs) within the images. To address these challenges, we evaluate the performance of the Segment Anything Model (SAM) as an annotation tool for medical data by using it to produce so-called "pseudo labels" on the Medical Segmentation Decathlon (MSD) computed tomography (CT) tasks. The pseudo labels are then used in place of ground truth labels to train a UNet model in a weakly-supervised manner. We experiment with different prompt types on SAM and find that the bounding box prompt is a simple yet effective method for generating pseudo labels. This method allows us to develop a weakly-supervised model that performs comparably to a fully supervised model.

Inverse Problems with Diffusion Models: A MAP Estimation Perspective

Inverse problems have many applications in science and engineering. In Computer vision, several image restoration tasks such as inpainting, deblurring, and super-resolution can be formally modeled as inverse problems. Recently, methods have been developed for solving inverse problems that only leverage a pre-trained unconditional diffusion model and do not require additional task-specific training. In such methods, however, the inherent intractability of determining the conditional score function during the reverse diffusion process poses a real challenge, leaving the methods to settle with an approximation instead, which affects their performance in practice. Here, we propose a MAP estimation framework to model the reverse conditional generation process of a continuous time diffusion model as an optimization process of the underlying MAP objective, whose gradient term is tractable. In theory, the proposed framework can be applied to solve general inverse problems using gradient-based optimization methods. However, given the highly non-convex nature of the loss objective, finding a perfect gradient-based optimization algorithm can be quite challenging, nevertheless, our framework offers several potential research directions. We use our proposed formulation and develop empirically effective algorithms for solving noiseless and noisy image inpainting tasks. We validate our proposed algorithms with extensive experiments across diverse mask settings.

Revisiting Score Function Estimators for $k$-Subset Sampling

Are score function estimators an underestimated approach to learning with $k$-subset sampling? Sampling $k$-subsets is a fundamental operation in many machine learning tasks that is not amenable to differentiable parametrization, impeding gradient-based optimization. Prior work has focused on relaxed sampling or pathwise gradient estimators. Inspired by the success of score function estimators in variational inference and reinforcement learning, we revisit them within the context of $k$-subset sampling. Specifically, we demonstrate how to efficiently compute the $k$-subset distribution's score function using a discrete Fourier transform, and reduce the estimator's variance with control variates. The resulting estimator provides both exact samples and unbiased gradient estimates while also applying to non-differentiable downstream models, unlike existing methods. Experiments in feature selection show results competitive with current methods, despite weaker assumptions.

Continuous Urban Change Detection from Satellite Image Time Series with Temporal Feature Refinement and Multi-Task Integration

Urbanization advances at unprecedented rates, resulting in negative effects on the environment and human well-being. Remote sensing has the potential to mitigate these effects by supporting sustainable development strategies with accurate information on urban growth. Deep learning-based methods have achieved promising urban change detection results from optical satellite image pairs using convolutional neural networks (ConvNets), transformers, and a multi-task learning setup. However, transformers have not been leveraged for urban change detection with multi-temporal data, i.e., >2 images, and multi-task learning methods lack integration approaches that combine change and segmentation outputs. To fill this research gap, we propose a continuous urban change detection method that identifies changes in each consecutive image pair of a satellite image time series. Specifically, we propose a temporal feature refinement (TFR) module that utilizes self-attention to improve ConvNet-based multi-temporal building representations. Furthermore, we propose a multi-task integration (MTI) module that utilizes Markov networks to find an optimal building map time series based on segmentation and dense change outputs. The proposed method effectively identifies urban changes based on high-resolution satellite image time series acquired by the PlanetScope constellation (F1 score 0.551) and Gaofen-2 (F1 score 0.440). Moreover, our experiments on two challenging datasets demonstrate the effectiveness of the proposed method compared to bi-temporal and multi-temporal urban change detection and segmentation methods.

Opportunities for machine learning in scientific discovery

Technological advancements have substantially increased computational power and data availability, enabling the application of powerful machine-learning (ML) techniques across various fields. However, our ability to leverage ML methods for scientific discovery, {\it i.e.} to obtain fundamental and formalized knowledge about natural processes, is still in its infancy. In this review, we explore how the scientific community can increasingly leverage ML techniques to achieve scientific discoveries. We observe that the applicability and opportunity of ML depends strongly on the nature of the problem domain, and whether we have full ({\it e.g.}, turbulence), partial ({\it e.g.}, computational biochemistry), or no ({\it e.g.}, neuroscience) {\it a-priori} knowledge about the governing equations and physical properties of the system. Although challenges remain, principled use of ML is opening up new avenues for fundamental scientific discoveries. Throughout these diverse fields, there is a theme that ML is enabling researchers to embrace complexity in observational data that was previously intractable to classic analysis and numerical investigations.

Indirectly Parameterized Concrete Autoencoders

Feature selection is a crucial task in settings where data is high-dimensional or acquiring the full set of features is costly. Recent developments in neural network-based embedded feature selection show promising results across a wide range of applications. Concrete Autoencoders (CAEs), considered state-of-the-art in embedded feature selection, may struggle to achieve stable joint optimization, hurting their training time and generalization. In this work, we identify that this instability is correlated with the CAE learning duplicate selections. To remedy this, we propose a simple and effective improvement: Indirectly Parameterized CAEs (IP-CAEs). IP-CAEs learn an embedding and a mapping from it to the Gumbel-Softmax distributions' parameters. Despite being simple to implement, IP-CAE exhibits significant and consistent improvements over CAE in both generalization and training time across several datasets for reconstruction and classification. Unlike CAE, IP-CAE effectively leverages non-linear relationships and does not require retraining the jointly optimized decoder. Furthermore, our approach is, in principle, generalizable to Gumbel-Softmax distributions beyond feature selection.

Stable Autonomous Flow Matching

In contexts where data samples represent a physically stable state, it is often assumed that the data points represent the local minima of an energy landscape. In control theory, it is well-known that energy can serve as an effective Lyapunov function. Despite this, connections between control theory and generative models in the literature are sparse, even though there are several machine learning applications with physically stable data points. In this paper, we focus on such data and a recent class of deep generative models called flow matching. We apply tools of stochastic stability for time-independent systems to flow matching models. In doing so, we characterize the space of flow matching models that are amenable to this treatment, as well as draw connections to other control theory principles. We demonstrate our theoretical results on two examples.

To Adapt or Not to Adapt? Real-Time Adaptation for Semantic Segmentation

The goal of Online Domain Adaptation for semantic segmentation is to handle unforeseeable domain changes that occur during deployment, like sudden weather events. However, the high computational costs associated with brute-force adaptation make this paradigm unfeasible for real-world applications. In this paper we propose HAMLET, a Hardware-Aware Modular Least Expensive Training framework for real-time domain adaptation. Our approach includes a hardware-aware back-propagation orchestration agent (HAMT) and a dedicated domain-shift detector that enables active control over when and how the model is adapted (LT). Thanks to these advancements, our approach is capable of performing semantic segmentation while simultaneously adapting at more than 29FPS on a single consumer-grade GPU. Our framework's encouraging accuracy and speed trade-off is demonstrated on OnDA and SHIFT benchmarks through experimental results.

Logistic-Normal Likelihoods for Heteroscedastic Label Noise in Classification

A natural way of estimating heteroscedastic label noise in regression is to model the observed (potentially noisy) target as a sample from a normal distribution, whose parameters can be learned by minimizing the negative log-likelihood. This loss has desirable loss attenuation properties, as it can reduce the contribution of high-error examples. Intuitively, this behavior can improve robustness against label noise by reducing overfitting. We propose an extension of this simple and probabilistic approach to classification that has the same desirable loss attenuation properties. We evaluate the effectiveness of the method by measuring its robustness against label noise in classification. We perform enlightening experiments exploring the inner workings of the method, including sensitivity to hyperparameters, ablation studies, and more.