#01Jul 21, 2026
cs.CV
ERank in Latent Space as an Image-Complexity and Richness Measure
Maksim Smirnov, Grigory Kononov, Anastasiia Linich and 2 more
We propose the effective rank (ERank) of the channel covariance of an image's deep feature map as a per-sample, label-free measure of visual richness, computed from a single forward pass through a frozen pretrained encoder. ERank counts how many decorrelated channel directions an image activates, and we characterize its properties, including its behavior under noise. Empirically, ERank orders images from plain to visually rich, correlates with codec bitrate, sharpness, and edge density, and correlates with human complexity annotations on IC9600 with $r = 0.72$. As a data-selection criterion, removing low-ERank samples improves super-resolution and removing high-ERank samples improves OCR, in both pretraining and finetuning, while selection does not help classification, segmentation, or denoising. ERank is thus a cheap richness signal, useful exactly when task difficulty is governed by input richness.
#02Jul 21, 2026
cs.CV
No Training, Better Flights: Test-Time Scaled VLMs for UAV Navigation
Feinan Cheng, Dongliang Xu, Wenli Nong and 4 more
Test-time scaling offers a promising method to improve the inference performance of Vision-Language Models (VLMs) without additional training. Existing approaches to vision-language navigation (VLN) for Unmanned Aerial Vehicle (UAV) typically relies on a single inference pass, which can falter in complex environments by producing suboptimal or unsafe trajectories. In this paper, we explore a simple and effective approach to apply test-time scaling to VLN for UAV. We enhance navigation reasoning through an iterative refinement process that requires no extra model training, guiding the model to re-evaluate its initial navigation plan for better accuracy and safety. Our method first prompts the model to generate multiple parallel candidates and then performs a self-correction step, achieving deeper and more robust planning without changing the underlying model. To further strengthen decision-making, we design a multi-criteria scoring function to evaluate the refined candidates based on safety, goal alignment, and forward-progress. This simple yet powerful combination enables a frozen UAV navigation VLMs to self-correct and generate more accurate and reliable flight plans, achieving SOTA performance in this task.
#03Jul 21, 2026
cs.LG
Riemannian Deep Learning:Modules, Networks, and Geometries
Chen Ziheng
Deep neural networks on manifold-valued representations have attracted growing interest, but many basic components remain tied to specific manifolds, rely on Euclidean approximations, or require costly and numerically fragile geometric operations. This thesis develops a unified framework for Riemannian deep learning from three complementary perspectives: reusable neural modules, manifold-specific network architectures, and the design of underlying geometries. It generalizes batch normalization from Euclidean spaces and individual manifolds to broad classes of Lie groups and gyrogroups, and extends multinomial logistic regression from Euclidean space to SPD manifolds and then to general Riemannian manifolds. It further develops neural networks for several important geometric representations, including an unconstrained model of hyperbolic space, Busemann-based hyperbolic learning, and full-rank correlation matrices. Finally, it introduces adaptive and computationally efficient Riemannian metrics on SPD manifolds, including learnable Log-Euclidean geometries and fast, stable Cholesky-based geometries. The proposed methods are supported by theoretical analysis and validated through numerical experiments and applications in vision, signal processing, graph learning, and genomics.
#04Jul 21, 2026
math.NA
1-Lipschitz Neural Networks on Hadamard Manifolds
Davide Murari, Marta Ghirardelli, Ben Adcock and 3 more
Controlling the Lipschitz constant of a neural network is a standard way to promote robustness and stability. Most existing constraining strategies are designed for Euclidean spaces. In this work, we construct and analyze a class of 1-Lipschitz neural networks on Hadamard manifolds. Our layers are of gradient-descent type, $1$-Lipschitz, and quasi-$α$-firmly nonexpansive. The core building blocks of the proposed architecture are Busemann functions, and we exploit the properties of Busemann gradient flows to design $1$-Lipschitz geometry-preserving layers. We provide explicit constructions and examples for hyperbolic manifolds and the manifold of symmetric positive definite (SPD) matrices. We test the proposed architecture in two numerical experiments: robust classification on the Poincaré disk and masked-Wishart covariance reconstruction. On the Poincaré disk, the proposed networks yield robust classifiers under hyperbolic perturbations. On the SPD manifold, we train SPD-valued denoisers and adopt them as a Plug-and-Play prior for a masked-Wishart covariance reconstruction problem. We show improved results from the nonexpansive denoiser over static, data-only, and Log-Euclidean denoising baselines, and empirically test its convergence properties.
#05Jul 21, 2026
cs.CV
ExpertVerse: A General-Purpose Benchmark for Expert-Level Reasoning in Knowledge-Intensive Visual Synthesis
Yuan Wang, Yongchao Du, Mengting Chen and 3 more
Recent advances in multimodal generative models have enabled instruction-based image generation to move beyond semantic manipulation to knowledge-driven visual reasoning. However, these methods focus on explicit commonsense reasoning, shallow causal understanding, and direct knowledge recall, failing at knowledge-intensive generation. We develop \textbf{ExpertVerse}, a capability-centric benchmark to evaluate generative models via knowledge-intensive lens. ExpertVerse stratifies reasoning generation across an orthogonal taxonomy of \textit{9 cognitive capabilities} and \textit{8 expert disciplines}, yielding \textit{58 sub-disciplines}. We curate 1,611 expert-annotated instances covering single-image editing, multi-image composition, and text-to-image generation. We further develop an automated workflow to produce \textbf{ExpertVerse-100K}, a large-scale dataset with reasoning traces and knowledge-anchored rationale annotations. Based on this, we train \textbf{KnowThinker} with RL fine-tuning, a VLM reasoning engine with world knowledge that jointly generates thinking processes and refined instructions. Towards the cross-modal credit misalignment and multi-objective gradient conflicts in multi-reward optimization, we propose a tailored Bootstrapped Pareto Policy Optimization (BPPO), which synergizes Bootstrapping Reward Rectification (BRR) and Conflict-Aware Pareto Advantage Fusion (CPAF). Extensive results of both open-source and proprietary models exposes critical reasoning deficits, highlighting imperative for knowledge-intensive benchmarks towards next-generation visual generation.