Iterative Refinement

Mechanistic accounts of in-context learning (ICL) have identified iterative algorithms for linear regression and related linear prediction tasks, often using linear or ReLU attention variants. For nonlinear ICL, prior work has related softmax and kernelized attention to functional-gradient-type dynamics, but it remains unclear whether a standard transformer with softmax attention can implement a convergent solver with an end-to-end prediction-error guarantee. In this paper, we study in-context kernel ridge regression (KRR) with Gaussian kernels and show that a standard softmax-attention transformer can approximate the KRR predictor during its forward pass by implementing preconditioned Richardson iteration on the associated kernel linear system. Under bounded-data assumptions, we construct a single-head transformer with $O(\log(1/ε))$ blocks and MLP width $O(\sqrt{N/ε})$ that achieves $ε$-accurate prediction for prompts of length $N$. Our construction reveals a functional decomposition within the transformer architecture: softmax attention produces a row-normalized Gaussian-kernel operator needed for cross-token interactions, while ReLU MLP layers act locally to approximate the intra-token scalar arithmetic required by the update. Empirically, we train GPT-2-style transformers on Gaussian-process regression tasks to further test the preconditioned Richardson interpretation. Through linear probing, we compare the transformer's layer-wise predictions with the step-wise outputs of classical KRR solvers and find that its error profiles align most consistently with preconditioned Richardson iteration. Ablation studies further support this interpretation. Together, our theory and experiments identify preconditioned Richardson iteration as a concrete mechanism that softmax-attention transformers can realize for nonlinear in-context Gaussian-kernel regression.

The concurrent target assignment and pathfinding (TAPF) problem extends multi-agent pathfinding (MAPF) by asking planners to allocate distinct targets and collision-free paths to agents. Prior work on TAPF has relied exclusively on Conflict-Based Search (CBS), which tightly couples target assignment and pathfinding, resulting in compute-intensive, non-scalable solutions. In contrast, we propose an iterative refinement framework that decouples target assignment from pathfinding. Our framework builds on modern, fast, suboptimal MAPF solvers, such as LaCAM. Specifically, within a given time budget, it repeatedly solves MAPF for the current target assignment, identifies bottleneck agents via MAPF feedback, and refines the assignment. Empirical results show that feedback-driven reassignment loop is effective, enabling our framework to scale well beyond the reach of the state-of-the-art CBS-based solver while maintaining decent solution quality. This represents a solid step toward practical, large scale TAPF suitable for real-world setups.

We study scalar dyadic refinement operators on R^2 of the form (Vf)(x,y) = sum_{(j,k) in Z^2} c_{j,k} f(2x-j, 2y-k), where only finitely many mask coefficients c_{j,k} are nonzero. Under a fixed support-window hypothesis, we prove that for every compactly supported continuous piecewise linear seed g:R^2->R, the iterates V^n g admit exact ReLU realizations of fixed width and depth O(n). This gives a first genuinely two-dimensional extension of the exact realization theory for refinement cascades. Using the one-dimensional exact loop-controller framework, the proof transports the tensor-product residual dynamics exactly on the product of two polygonal loops and reduces the remaining seam ambiguity to a final readout and selector step. The matrix cascade is then handled by a fixed-depth recursive block, and general compactly supported continuous piecewise linear seeds are reduced to a finite decomposition together with exact clamped gluing on the support window. This identifies the tensor-product dyadic case as a natural first multivariate instance of the loop-controller method for refinement iterates.

We study homogeneous refinement operators $(Vγ)(t)=\sum_{j\in\mathbb Z}A_jγ(Mt-j)$, acting on compactly supported continuous piecewise linear curves $γ:\mathbb R\to\mathbb R^p$, where $M\ge2$ and only finitely many matrices $A_j\in\mathbb R^{p\times p}$ are nonzero. We prove that the iterates $V^nγ$ admit exact ReLU realizations of fixed width and depth $O(n)$. The main new ingredient is an exact loop controller for the residual dynamics. Instead of propagating scalar residual surrogates, the construction transports the residual orbit by a forward-exact state on a polygonal loop. Scalar factors and digit selectors are then recovered from this loop state by complementary CPwL readouts. The loop seam is not removed, but its remaining ambiguity is confined to the final readout/selector stage, where it is harmless because the scalar atom is supported away from the seam. This gives a homogeneous $M$-ary vector-valued extension of the scalar binary refinable-function construction with a more geometric controller architecture. We also record crude exponential bounds on the network weights and biases. Affine forcing terms are handled by expanding affine iterates into finite sums of homogeneous iterates, giving exact fixed-width realizations with depth $O(n^2)$, and anchored open curves reduce to compactly supported defects with affine anchor mismatch. We also describe homogeneous polygonal generators, including dragon-type examples and a self-intersecting Hilbert-type prototype in arbitrary dimension. The extended version includes stage-dependent forcing, finite-state stacking reductions, and further geometric constructions such as Koch-, Gosper-, Morton-, and connector-based Hilbert-type variants.

Unified multimodal models (UMMs) integrate visual understanding and generation within a single framework. For text-to-image (T2I) tasks, this unified capability allows UMMs to refine outputs after their initial generation, potentially extending the performance upper bound. Current UMM-based refinement methods primarily follow a refinement-via-editing (RvE) paradigm, where UMMs produce editing instructions to modify misaligned regions while preserving aligned content. However, editing instructions often describe prompt-image misalignment only coarsely, leading to incomplete refinement. Moreover, pixel-level preservation, though necessary for editing, unnecessarily restricts the effective modification space for refinement. To address these limitations, we propose Refinement via Regeneration (RvR), a novel framework that reformulates refinement as conditional image regeneration rather than editing. Instead of relying on editing instructions and enforcing strict content preservation, RvR regenerates images conditioned on the target prompt and the semantic tokens of the initial image, enabling more complete semantic alignment with a larger modification space. Extensive experiments demonstrate the effectiveness of RvR, improving Geneval from 0.78 to 0.91, DPGBench from 84.02 to 87.21, and UniGenBench++ from 61.53 to 77.41.

Accurate autoregressive prediction of 3D turbulent flows remains challenging for neural PDE solvers, as small errors in fine-scale structures can accumulate rapidly over rollout. In this paper, we propose FlowRefiner, a flow matching-based iterative refinement framework for 3D turbulent flow simulation. The method replaces stochastic denoising refinement with deterministic ODE-based correction, uses a unified velocity-field regression objective across all refinement stages, and introduces a decoupled sigma schedule that fixes the noise range independently of refinement depth. These design choices yield stable and effective refinement in the small-noise regime. Experiments on large-scale 3D turbulence with rich multi-scale structures show that FlowRefiner achieves state-of-the-art autoregressive prediction accuracy and strong physical consistency. Although developed for turbulent flow simulation, the proposed framework is broadly applicable to iterative refinement problems in scientific modeling.

Multi-source stationary computed tomography (CT) has recently attracted attention for its ability to achieve rapid image reconstruction, making it suitable for time-sensitive clinical and industrial applications. However, practical systems are often constrained by ultra-sparse-view sampling, which significantly degrades reconstruction quality. Traditional methods struggle under ultra-sparse-view settings, where interpolation becomes inaccurate and the resulting reconstructions are unsatisfactory. To address this challenge, this study proposes Diffusion-Refined Neural Attenuation Fields (Diff-NAF), an iterative framework tailored for multi-source stationary CT under ultra-sparse-view conditions. Diff-NAF combines a Neural Attenuation Field representation with a dual-branch conditional diffusion model. The process begins by training an initial NAF using ultra-sparse-view projections. New projections are then generated through an Angle-Prior Guided Projection Synthesis strategy that exploits inter view priors, and are subsequently refined by a Diffusion-driven Reuse Projection Refinement Module. The refined projections are incorporated as pseudo-labels into the training set for the next iteration. Through iterative refinement, Diff-NAF progressively enhances projection completeness and reconstruction fidelity under ultra-sparse-view conditions, ultimately yielding high-quality CT reconstructions. Experimental results on multiple simulated 3D CT volumes and real projection data demonstrate that Diff-NAF achieves the best performance under ultra-sparse-view conditions.

Camouflaged object detection is an emerging and challenging computer vision task that requires identifying and segmenting objects that blend seamlessly into their environments due to high similarity in color, texture, and size. This task is further complicated by low-light conditions, partial occlusion, small object size, intricate background patterns, and multiple objects. While many sophisticated methods have been proposed for this task, current methods still struggle to precisely detect camouflaged objects in complex scenarios, especially with small and multiple objects, indicating room for improvement. We propose a Multi-Scale Recursive Network that extracts multi-scale features using a Pyramid Vision Transformer backbone and combines them with specialized Attention-Based Scale Integration Units, thereby enabling selective feature merging. For more precise object detection, our decoder recursively refines features by incorporating Multi-Granularity Fusion Units. A novel recursive-feedback decoding strategy is developed to enhance the model's understanding of global context, thereby helping it overcome the challenges of this task. By jointly leveraging multi-scale learning and recursive feature optimization, our proposed method achieves performance gains, successfully detecting small and multiple camouflaged objects. Our model achieves state-of-the-art results on two benchmark datasets for camouflaged object detection and ranks second on the remaining two. Our code, model weights, and results are available at https://github.com/linaagh98/MSRNet.