In this manuscript we introduce a novel Decision Flow (DF) framework for sampling from a target distribution while incorporating additional guidance from a prior sampler. DF can be viewed as an AI driven algorithmic reincarnation of the Markov Decision Process (MDP) approach in Stochastic Optimal Control. It extends the continuous space, continuous time path Integral Diffusion sampling technique to discrete time and space, while also generalizing the Generative Flow Network framework. In its most basic form, an explicit, Neural Network (NN) free formulation, DF leverages the linear solvability of the the underlying MDP to adjust the transition probabilities of the prior sampler. The resulting Markov Process is expressed as a convolution of the reverse time Green's function of the prior sampling with the target distribution. We illustrate the DF framework through an example of sampling from the Ising model, discuss potential NN based extensions, and outline how DF can enhance guided sampling across various applications.
Inspired by Well-initialized Lottery Ticket Hypothesis (WLTH), which provides suboptimal fine-tuning solutions, we propose a novel fully fine-tuned continual learning (CL) method referred to as Soft-TransFormers (Soft-TF). Soft-TF sequentially learns and selects an optimal soft-network or subnetwork for each task. During sequential training in CL, Soft-TF jointly optimizes the weights of sparse layers to obtain task-adaptive soft (real-valued) networks or subnetworks (binary masks), while keeping the well-pre-trained layer parameters frozen. In inference, the identified task-adaptive network of Soft-TF masks the parameters of the pre-trained network, mapping to an optimal solution for each task and minimizing Catastrophic Forgetting (CF) - the soft-masking preserves the knowledge of the pre-trained network. Extensive experiments on Vision Transformer (ViT) and CLIP demonstrate the effectiveness of Soft-TF, achieving state-of-the-art performance across various CL scenarios, including Class-Incremental Learning (CIL) and Task-Incremental Learning (TIL), supported by convergence theory.
Synthetic Aperture Radar (SAR) imagery provides robust environmental and temporal coverage (e.g., during clouds, seasons, day-night cycles), yet its noise and unique structural patterns pose interpretation challenges, especially for non-experts. SAR-to-EO (Electro-Optical) image translation (SET) has emerged to make SAR images more perceptually interpretable. However, traditional approaches trained from scratch on limited SAR-EO datasets are prone to overfitting. To address these challenges, we introduce Confidence Diffusion for SAR-to-EO Translation, called C-DiffSET, a framework leveraging pretrained Latent Diffusion Model (LDM) extensively trained on natural images, thus enabling effective adaptation to the EO domain. Remarkably, we find that the pretrained VAE encoder aligns SAR and EO images in the same latent space, even with varying noise levels in SAR inputs. To further improve pixel-wise fidelity for SET, we propose a confidence-guided diffusion (C-Diff) loss that mitigates artifacts from temporal discrepancies, such as appearing or disappearing objects, thereby enhancing structural accuracy. C-DiffSET achieves state-of-the-art (SOTA) results on multiple datasets, significantly outperforming the very recent image-to-image translation methods and SET methods with large margins.
Amortized inference is the task of training a parametric model, such as a neural network, to approximate a distribution with a given unnormalized density where exact sampling is intractable. When sampling is implemented as a sequential decision-making process, reinforcement learning (RL) methods, such as generative flow networks, can be used to train the sampling policy. Off-policy RL training facilitates the discovery of diverse, high-reward candidates, but existing methods still face challenges in efficient exploration. We propose to use an adaptive training distribution (the \teacher) to guide the training of the primary amortized sampler (the \student). The \teacher, an auxiliary behavior model, is trained to sample high-loss regions of the \student and can generalize across unexplored modes, thereby enhancing mode coverage by providing an efficient training curriculum. We validate the effectiveness of this approach in a synthetic environment designed to present an exploration challenge, two diffusion-based sampling tasks, and four biochemical discovery tasks demonstrating its ability to improve sample efficiency and mode coverage. Source code is available at https://github.com/alstn12088/adaptive-teacher.
We consider streaming principal component analysis when the stochastic data-generating model is subject to perturbations. While existing models assume a fixed covariance, we adopt a robust perspective where the covariance matrix belongs to a temporal uncertainty set. Under this setting, we provide fundamental limits on convergence of any algorithm recovering principal components. We analyze the convergence of the noisy power method and Oja's algorithm, both studied for the stationary data generating model, and argue that the noisy power method is rate-optimal in our setting. Finally, we demonstrate the validity of our analysis through numerical experiments on synthetic and real-world dataset.