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Sep 2

The Gauss-Markov Adjunction: Categorical Semantics of Residuals in Supervised Learning

Enhancing the intelligibility and interpretability of machine learning is a crucial task in responding to the demand for Explicability as an AI principle, and in promoting the better social implementation of AI. The aim of our research is to contribute to this improvement by reformulating machine learning models through the lens of category theory, thereby developing a semantic framework for structuring and understanding AI systems. Our categorical modeling in this paper clarifies and formalizes the structural interplay between residuals and parameters in supervised learning. The present paper focuses on the multiple linear regression model, which represents the most basic form of supervised learning. By defining two concrete categories corresponding to parameters and data, along with an adjoint pair of functors between them, we introduce our categorical formulation of supervised learning. We show that the essential structure of this framework is captured by what we call the Gauss-Markov Adjunction. Within this setting, the dual flow of information can be explicitly described as a correspondence between variations in parameters and residuals. The ordinary least squares estimator for the parameters and the minimum residual are related via the preservation of limits by the right adjoint functor. Furthermore, we position this formulation as an instance of extended denotational semantics for supervised learning, and propose applying a semantic perspective developed in theoretical computer science as a formal foundation for Explicability in AI.

Enhancing Image Rescaling using Dual Latent Variables in Invertible Neural Network

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.

Gaussian-Flow: 4D Reconstruction with Dynamic 3D Gaussian Particle

We introduce Gaussian-Flow, a novel point-based approach for fast dynamic scene reconstruction and real-time rendering from both multi-view and monocular videos. In contrast to the prevalent NeRF-based approaches hampered by slow training and rendering speeds, our approach harnesses recent advancements in point-based 3D Gaussian Splatting (3DGS). Specifically, a novel Dual-Domain Deformation Model (DDDM) is proposed to explicitly model attribute deformations of each Gaussian point, where the time-dependent residual of each attribute is captured by a polynomial fitting in the time domain, and a Fourier series fitting in the frequency domain. The proposed DDDM is capable of modeling complex scene deformations across long video footage, eliminating the need for training separate 3DGS for each frame or introducing an additional implicit neural field to model 3D dynamics. Moreover, the explicit deformation modeling for discretized Gaussian points ensures ultra-fast training and rendering of a 4D scene, which is comparable to the original 3DGS designed for static 3D reconstruction. Our proposed approach showcases a substantial efficiency improvement, achieving a 5times faster training speed compared to the per-frame 3DGS modeling. In addition, quantitative results demonstrate that the proposed Gaussian-Flow significantly outperforms previous leading methods in novel view rendering quality. Project page: https://nju-3dv.github.io/projects/Gaussian-Flow

EarthCrafter: Scalable 3D Earth Generation via Dual-Sparse Latent Diffusion

Despite the remarkable developments achieved by recent 3D generation works, scaling these methods to geographic extents, such as modeling thousands of square kilometers of Earth's surface, remains an open challenge. We address this through a dual innovation in data infrastructure and model architecture. First, we introduce Aerial-Earth3D, the largest 3D aerial dataset to date, consisting of 50k curated scenes (each measuring 600m x 600m) captured across the U.S. mainland, comprising 45M multi-view Google Earth frames. Each scene provides pose-annotated multi-view images, depth maps, normals, semantic segmentation, and camera poses, with explicit quality control to ensure terrain diversity. Building on this foundation, we propose EarthCrafter, a tailored framework for large-scale 3D Earth generation via sparse-decoupled latent diffusion. Our architecture separates structural and textural generation: 1) Dual sparse 3D-VAEs compress high-resolution geometric voxels and textural 2D Gaussian Splats (2DGS) into compact latent spaces, largely alleviating the costly computation suffering from vast geographic scales while preserving critical information. 2) We propose condition-aware flow matching models trained on mixed inputs (semantics, images, or neither) to flexibly model latent geometry and texture features independently. Extensive experiments demonstrate that EarthCrafter performs substantially better in extremely large-scale generation. The framework further supports versatile applications, from semantic-guided urban layout generation to unconditional terrain synthesis, while maintaining geographic plausibility through our rich data priors from Aerial-Earth3D. Our project page is available at https://whiteinblue.github.io/earthcrafter/

Towards a Generalizable Bimanual Foundation Policy via Flow-based Video Prediction

Learning a generalizable bimanual manipulation policy is extremely challenging for embodied agents due to the large action space and the need for coordinated arm movements. Existing approaches rely on Vision-Language-Action (VLA) models to acquire bimanual policies. However, transferring knowledge from single-arm datasets or pre-trained VLA models often fails to generalize effectively, primarily due to the scarcity of bimanual data and the fundamental differences between single-arm and bimanual manipulation. In this paper, we propose a novel bimanual foundation policy by fine-tuning the leading text-to-video models to predict robot trajectories and training a lightweight diffusion policy for action generation. Given the lack of embodied knowledge in text-to-video models, we introduce a two-stage paradigm that fine-tunes independent text-to-flow and flow-to-video models derived from a pre-trained text-to-video model. Specifically, optical flow serves as an intermediate variable, providing a concise representation of subtle movements between images. The text-to-flow model predicts optical flow to concretize the intent of language instructions, and the flow-to-video model leverages this flow for fine-grained video prediction. Our method mitigates the ambiguity of language in single-stage text-to-video prediction and significantly reduces the robot-data requirement by avoiding direct use of low-level actions. In experiments, we collect high-quality manipulation data for real dual-arm robot, and the results of simulation and real-world experiments demonstrate the effectiveness of our method.

StableVC: Style Controllable Zero-Shot Voice Conversion with Conditional Flow Matching

Zero-shot voice conversion (VC) aims to transfer the timbre from the source speaker to an arbitrary unseen speaker while preserving the original linguistic content. Despite recent advancements in zero-shot VC using language model-based or diffusion-based approaches, several challenges remain: 1) current approaches primarily focus on adapting timbre from unseen speakers and are unable to transfer style and timbre to different unseen speakers independently; 2) these approaches often suffer from slower inference speeds due to the autoregressive modeling methods or the need for numerous sampling steps; 3) the quality and similarity of the converted samples are still not fully satisfactory. To address these challenges, we propose a style controllable zero-shot VC approach named StableVC, which aims to transfer timbre and style from source speech to different unseen target speakers. Specifically, we decompose speech into linguistic content, timbre, and style, and then employ a conditional flow matching module to reconstruct the high-quality mel-spectrogram based on these decomposed features. To effectively capture timbre and style in a zero-shot manner, we introduce a novel dual attention mechanism with an adaptive gate, rather than using conventional feature concatenation. With this non-autoregressive design, StableVC can efficiently capture the intricate timbre and style from different unseen speakers and generate high-quality speech significantly faster than real-time. Experiments demonstrate that our proposed StableVC outperforms state-of-the-art baseline systems in zero-shot VC and achieves flexible control over timbre and style from different unseen speakers. Moreover, StableVC offers approximately 25x and 1.65x faster sampling compared to autoregressive and diffusion-based baselines.

IDOL: Unified Dual-Modal Latent Diffusion for Human-Centric Joint Video-Depth Generation

Significant advances have been made in human-centric video generation, yet the joint video-depth generation problem remains underexplored. Most existing monocular depth estimation methods may not generalize well to synthesized images or videos, and multi-view-based methods have difficulty controlling the human appearance and motion. In this work, we present IDOL (unIfied Dual-mOdal Latent diffusion) for high-quality human-centric joint video-depth generation. Our IDOL consists of two novel designs. First, to enable dual-modal generation and maximize the information exchange between video and depth generation, we propose a unified dual-modal U-Net, a parameter-sharing framework for joint video and depth denoising, wherein a modality label guides the denoising target, and cross-modal attention enables the mutual information flow. Second, to ensure a precise video-depth spatial alignment, we propose a motion consistency loss that enforces consistency between the video and depth feature motion fields, leading to harmonized outputs. Additionally, a cross-attention map consistency loss is applied to align the cross-attention map of the video denoising with that of the depth denoising, further facilitating spatial alignment. Extensive experiments on the TikTok and NTU120 datasets show our superior performance, significantly surpassing existing methods in terms of video FVD and depth accuracy.

Accelerated Bayesian Inference for Pulsar Timing Arrays: Normalizing Flows for Rapid Model Comparison Across Stochastic Gravitational-Wave Background Sources

The recent detection of nanohertz stochastic gravitational-wave backgrounds (SGWBs) by pulsar timing arrays (PTAs) promises unique insights into astrophysical and cosmological origins. However, traditional Markov Chain Monte Carlo (MCMC) approaches become prohibitively expensive for large datasets. We employ a normalizing flow (NF)-based machine learning framework to accelerate Bayesian inference in PTA analyses. For the first time, we perform Bayesian model comparison across SGWB source models in the framework of machine learning by training NF architectures on the PTA dataset (NANOGrav 15-year) and enabling direct evidence estimation via learned harmonic mean estimators. Our examples include 10 conventional SGWB source models such as supermassive black hole binaries, power-law spectrum, cosmic strings, domain walls, scalar-induced GWs, first-order phase transitions, and dual scenario/inflationary gravitational wave. Our approach jointly infers 20 red noise parameters and 2 SGWB parameters per model in sim 20\,hours (including training), compared to sim 10\,days with MCMC. Critically, the NF method preserves rigorous model selection accuracy, with small Hellinger distances (lesssim 0.3) relative to MCMC posteriors, and reproduces MCMC-based Bayes factors across all tested scenarios. This scalable technique for SGWB source comparison will be essential for future PTA expansions and next-generation arrays such as the SKA, offering orders-of-magnitude efficiency gains without sacrificing physical interpretability.

Beyond One-to-One: Rethinking the Referring Image Segmentation

Referring image segmentation aims to segment the target object referred by a natural language expression. However, previous methods rely on the strong assumption that one sentence must describe one target in the image, which is often not the case in real-world applications. As a result, such methods fail when the expressions refer to either no objects or multiple objects. In this paper, we address this issue from two perspectives. First, we propose a Dual Multi-Modal Interaction (DMMI) Network, which contains two decoder branches and enables information flow in two directions. In the text-to-image decoder, text embedding is utilized to query the visual feature and localize the corresponding target. Meanwhile, the image-to-text decoder is implemented to reconstruct the erased entity-phrase conditioned on the visual feature. In this way, visual features are encouraged to contain the critical semantic information about target entity, which supports the accurate segmentation in the text-to-image decoder in turn. Secondly, we collect a new challenging but realistic dataset called Ref-ZOM, which includes image-text pairs under different settings. Extensive experiments demonstrate our method achieves state-of-the-art performance on different datasets, and the Ref-ZOM-trained model performs well on various types of text inputs. Codes and datasets are available at https://github.com/toggle1995/RIS-DMMI.