#01Nov 5, 2026
math.OC
A Theoretical Analysis of a Bilevel Optimization Formulation for Combined Local-Global Optical Flow Models
El Mostafa Kalmoun
This paper analyzes a bilevel formulation for learning the regularization parameter of combined local-global (CLG) optical flow models. The lower-level problem computes the flow from a Lucas--Kanade data term and a quadratic or total variation (TV) regularizer, and the upper-level problem selects the parameter that minimizes the squared distance to a ground-truth flow. The setting is finite-dimensional, and a full-rank assumption makes the lower-level solution unique. For the quadratic model we derive sufficient conditions for the existence of an optimal parameter, for every optimal parameter to be positive, and for strict local optimality. For TV regularization an optimal parameter always exists, because the lower-level solution vanishes for large parameters, and we give a sufficient condition for positivity that accounts for the coupling of the two flow components through the local structure tensors. Synthetic examples illustrate the conditions, including cases in which they fail.
#02Nov 5, 2026
cs.LG
FewStepRL: Fine-tuning Few-step Diffusion Models with Reinforcement Learning
Haitao Lin, Minsi Ren, Yang Li and 4 more
Reinforcement learning (RL) has become a standard post-training method for diffusion models, but most RL objectives roll out the current policy at every iteration, and with a many-step sampler these rollouts typically dominate the cost of training. Few-step models cut this cost, yet they model an average velocity over an interval, whereas existing RL objectives are built for an instantaneous velocity with a many-step sampler. We adapt RL objectives to few-step models systematically in three phases, namely a transformation, a decomposition and an adaptation. The transformation to $x$-space expresses each objective we consider through a common policy prediction, at the clean end by default and at an explicitly marked level for transition or flow-map objectives, so that objectives stated over densities, velocities or rewards become comparable. The decomposition writes the gradient of each of these objectives as the sum of a self-regression toward a reference and a reward augmentation, so that a method reduces, at the gradient level, to a choice of anchors and weights. The adaptation computes each anchor from a few-step model at the end of its transport or along its tangent, with the instantaneous velocity recovered from the network itself or from an auxiliary network. This yields few-step versions of FlowGRPO, AWM, DiffusionNFT, DiffusionOPSD and ReFL in one modular codebase. In our experiments, reward-gradient-based methods are the most effective when the reward is differentiable and its gradient is affordable; otherwise DiffusionNFT-style methods generally reach high rewards in relatively few iterations despite a sometimes higher per-iteration cost. Extra inference steps show no systematic aggregate benefit in our experiments, although selected outputs visibly improve with two to four times as many sampling steps as in training.
#03Nov 5, 2026
cs.CV
Where and Why is Grounded Reasoning Useful?
David Yan, Le Xue, Forrest Huang and 4 more
Grounded reasoning, where a model outputs text coordinates of relevant locations in chain-of-thought reasoning, is a common strategy for solving complex visual reasoning problems. However, the benefits and limitations of grounded reasoning are understudied. We study where and why grounded reasoning is most useful. To do so, we introduce a chain-of-thought analysis method to measure how much a model uses its outputted grounding in its thinking trace and perform a detailed ablation study of a grounded reasoning training recipe. We find that grounded reasoning improves counting but shows no significant gain over baselines without coordinate grounding across a wide range of spatial reasoning and perception benchmarks. Using several synthetic tasks, we show that grounded reasoning is most useful when a task requires undescribable references, which are visual concepts that are difficult to describe in language. However, we observe that many existing visual reasoning benchmarks are solvable with only describable text references. To close this gap, we introduce BrickVision, a new benchmark that requires undescribable visual references to solve.
#04Nov 5, 2026
cs.CV
ManimCode: Learning Visual Self-Correction for Educational Animation
Zhengyang Liang, Lizi Liao
Manim supports precise, programmatic video generation, but a successfully rendered educational animation can still have visual defects, missing explanations, or incorrect content. Rendering does not directly identify the code changes needed to correct these visual failures, so feedback-driven revision is needed. Existing agentic frameworks use iterative rendering and revision but typically rely on large models, often proprietary. Existing Manim datasets primarily contain final programs and often lack quality verification and the trajectories of feedback and revisions needed to learn this refinement process. We introduce ManimData and ManimCode, a data and training framework for feedback-driven educational animation generation. We construct ManimData through a render-guided pipeline that iteratively generates, executes, reviews, and revises Manim programs with retrieved API documentation. Its 24,034 render-verified, quality-filtered records preserve intermediate programs, execution errors, visual critiques, and corrective revisions. We use role-conditioned supervised fine-tuning on these trajectories to train ManimCode, a single 4B model, to write, review, and revise animation programs. To improve correction of errors that differ from those in the collected trajectories, we then train the Reviser with reinforcement learning on self-generated states, using rendering outcomes and reference-free quality feedback. ManimCode achieves 96.6% and 97.0% render success on ManimData-test and ManimBench, compared with 52.6% and 82.0% for the untrained 4B model under the same inference setup, while also improving video quality scores from 2.48 to 2.94 and from 3.00 to 3.44. Integrating ManimCode into two long-form educational video generation systems increases completed videos from 19/117 to 107/117 and from 53/239 to 239/239, alongside improvements in educational effectiveness and visual quality.
#05Nov 5, 2026
cs.CV
Hierarchical Incremental Beta Splatting for Online Reconstruction
Linus Franke
Online 3D Gaussian Splatting reconstructs a scene during capture: each keyframe spawns primitives once and refines them for only a few dozen iterations, leaving little chance to fix poor initialization or missing detail. Gaussians are also inherently soft, needing many overlaps for solid surfaces. We present Hierarchical Incremental Beta Splatting (HIBS), which brings beta kernels to incremental reconstruction. Their shape parameter interpolates between a soft, Gaussian-like profile and a flat-topped, near-opaque surfel, acting as a confidence dial for geometry. Our confidence-aware spawning uses geometric observability and multi-view depth agreement to initialize both opacity and shape, producing solid primitives where geometry is verifiable and soft, correctable primitives where it is not. As online densification, error-driven relocation recycles stale primitives into photometric-error hotspots. Bounded beta kernel support enables exact tile culling and faster rasterization, and a closed-form, shape-preserving merging formulation provides a level-of-detail (LOD) hierarchy for fast optimization and real-time rendering. On Mip-NeRF 360 in the on-the-fly protocol, HIBS improves PSNR by up to 0.8 dB while reducing optimization time by up to 40%. Project page: https://linus-franke.com/hibs/