Reflection Layers

We study vector-valued binary affine refinement operators with finitely supported matrix masks and compactly supported continuous piecewise linear input and forcing data. We prove that every finite refinement iterate admits an exact ReLU realization of fixed width and depth linear in the number of iterations. No separation of the forcing profile from the binary cell seams is required. The main mechanism is universal reflection doubling. Pairing each residual profile with its reflection replaces the two binary transition matrices by one fixed block matrix together with a fixed swap involution. The cell-seam identity makes the two branch candidates agree at the tent fold, while their swap-odd component is bounded linearly by the distance to the fold. This permits exact branch selection by a fixed continuous piecewise linear cone switch, without multiplication by a variable selector. The resulting primal recursion requires the residual orbit in reverse order. We obtain exact backward replay from the residual memory controller developed previously for affine refinement, interpreted here through the reflection quotient of circle doubling. The construction propagates the full vectorized profiles rather than decomposing the input and forcing into reference atoms. We also treat stage-dependent forcing from a fixed finite-dimensional family and show that genuine reflection equivariance reduces the doubled cascade to a single parity sector.

We propose an all-reflective two-mirror projection system for extreme ultraviolet (EUV) lithography operating at exposure wavelengths of $13.5$~nm (Mo/Si) and $11.2$~nm (Ru/Be), delivering a fourfold ($4\times$) demagnification of the periodic mask pattern at a numerical aperture approaching unity ($\mathrm{NA}_{\max} \approx 0.993$). In contrast to conventional EUV projection objectives that incorporate 6--10 aspheric mirrors with an overall optical throughput of less than $15\%$, the proposed design redirects each accepted discrete spatial diffraction order scattered by the mask onto the wafer via a dedicated pair of planar mirror facets. The number of reflections is strictly fixed at two for all accepted orders, retaining $50$--$60\%$ of the power leaving the mask in each accepted order. We derive a spatial geometry providing rigorous optical path length equalization across all diffraction orders, thereby removing order-dependent propagation phase shifts. Individually optimized 30-bilayer Bragg multilayer coatings are designed for each facet using the transfer matrix method combined with global evolutionary optimization algorithms. The architecture is generalized to a three-dimensional vector formulation with a two-dimensionally periodic mask. Utilizing inverse lithography technology, Fourier parameterization, and a differentiable electromagnetic modal waveguide solver, we solve the synthesis problem for binary absorber masks (La absorber on a Ru/Be/Sr multilayer mirror). We demonstrate simulated aerial images of sub-10-nm features on the wafer (isolated peaks with a full width at half maximum (FWHM) of approximately $5.4$~nm and line pairs with a critical dimension of $6$~nm) and find that the two peaks remain resolved for the tested wafer defocus values from $0$ to $5$~nm along the $z$-axis.

Mirrors are common in real-world images, yet producing geometrically consistent reflections with generative models remains challenging. Unlike most objects, mirror appearance depends on scene geometry and viewpoint, making it hard to synthesize using learned appearance priors alone. We address this in the mirror inpainting setting, where the scene is fixed and only the mirror region is generated. Our key insight is that much mirror content is geometrically constrained by the visible scene and need not be hallucinated. We estimate scene geometry and project visible content into the mirror to recover reflection regions determined by geometry. A generative model then completes the mirror region via a two-mask diffusion strategy balancing geometric constraints with the model's learned priors, reducing projection artifacts and improving reflection consistency. The method is training-free and applicable to complex real-world scenes. We evaluate on MirrorBench-V2 (synthetic) and real images. Using standard and geometry-aware metrics, we show that explicitly using scene geometry improves consistency.

Videos captured through glass often contain reflections that degrade visual quality and interfere with downstream vision tasks. Although single-image reflection removal has been extensively studied, video reflection removal remains largely underexplored due to the lack of paired video data, temporally coherent removal models, and dedicated evaluation benchmarks. We present a closed-loop framework that unifies physics-grounded reflection simulation, diffusion-based video dereflection, and benchmark evaluation. Our S2R-Synthesis pipeline generates paired reflected and reflection-free videos by performing physics-grounded augmentation in the structure space and rendering realistic reflected videos with a trained video diffusion renderer; the augmentation models key glass-related effects including roughness-induced blur, thickness-induced ghosting, and reflectance variation. Based on the synthesized data, we introduce S2R-Removal, the first diffusion-based video reflection removal model, which adapts a pretrained video diffusion prior through reflection-aware latent adaptation and one-step pixel-geometric refinement, recovering the clean transmission in a single denoising step. We further build S2R-Bench, the first benchmark for video reflection removal, supporting both full-reference evaluation and real-world human perceptual assessment. Experiments on S2R-Bench and multiple public image benchmarks demonstrate state-of-the-art performance and faster inference than even non-diffusion baselines, and validate the effectiveness of S2R-Synthesis. Project page: https://codingwzp.github.io/VideoDereflection_S2R.

Recent advances in video diffusion models (VDMs) have enabled high-fidelity video synthesis. However, generating mirror reflections remains challenging because the content within a mirror must remain consistent with the surrounding scene. Existing VDMs are not specifically designed to model scene-to-mirror relationships, which can lead to reflections with incorrect content or inconsistent spatial arrangements. We observe that mirror reflection generation involves two complementary challenges: determining what scene content should be reflected and how the reflected content should be spatially arranged within the mirror region. Motivated by this observation, we propose MirrorWorld, a reflection-aware video inpainting framework that models scene-to-mirror relationships during generation. Specifically, we introduce Semantic Relation Distillation (SRD), which transfers relational information from a frozen visual foundation model to encourage semantic associations between visible scene content and mirror regions. We further propose Geometric Transformation Alignment (GTA), which learns a transformation that guides the spatial arrangement of reflected content. The two components play complementary roles, with SRD modeling what should be reflected and GTA modeling how it should be arranged. To facilitate research on this problem, we construct a benchmark for video mirror reflection generation by repurposing four existing video mirror datasets into a unified reflection reconstruction task. Experimental results show that MirrorWorld achieves improved reflection reconstruction quality over representative image-based reflection generation methods and strong video inpainting baselines.

Despite remarkable progress in reflection removal, current methods primarily exploit static image priors from a single frame and still suffer from severe residual artifacts due to the inherent ambiguity between the reflection and transmission layers. In this paper, we propose leveraging event signals to break this ambiguity. By employing event cameras to capture micro-dynamics, we reveal the differential motion between these two layers. We thereby present a novel event-driven reflection removal network, EvReflection, that utilizes these dynamic cues for layer separation. Specifically, we design a Micro-Dynamics Decoupler to disentangle layer-specific motions from event streams as priors, which then guide a Parallax-Attention Rectifier to cleanly remove artifacts from the RGB image. Furthermore, to address data scarcity, we develop a parallax-aware simulation pipeline and construct the EVR$^2$ benchmark dataset, the first real-world dataset for this task. Extensive experiments demonstrate that EvReflection achieves state-of-the-art performance on both synthetic and real-world benchmarks, surpassing the best competing method by more than 1.6 dB and 1.2 dB in PSNR, respectively. The code, dataset, and pre-trained models are available at https://github.com/JiaxiaoWang/EvReflection.

We study score learning for reflected diffusion on bounded domains. Reflection keeps trajectories feasible but does not ensure that the learned score satisfies the boundary behavior implied by the forward process. With implicit score matching, integration by parts leaves a boundary term, and we show that it depends on one scalar at each boundary point: the diffusion- weighted normal component of the score, or conormal trace. The no-flux condition fixes this value while leaving the re- maining boundary components unrestricted; under anisotropic diffusion it generally differs from the ordinary normal score component. On hyperrectangles, our parametrization enforces the required trace without additional trainable parameters or a stochastic boundary estimator and, under regularity assump- tions, can represent the true score, whereas fixing an incorrect value creates an error that more data cannot remove. We ex- tend the construction to simplices and polygonal domains and identify reflection masking: hard reflection can keep samples feasible even when the learned trace is wrong, so post-reflection metrics may hide the error. Experiments show the clearest separation with less frequent reflection, anisotropic diffusion, and mass near intersections of constraints; under full reflection, final sample placement improves inconsistently, illustrating how hard repair can mask boundary-score errors and decouple score accuracy from downstream generation quality.

Reflection, the ability to revisit and revise prior reasoning, is central to how humans improve their answers. Large language models (LLMs) are increasingly prompted to "reflect," yet whether this resembles human revision remains unclear. We introduce the Human-LLM Reflection Framework (HRF), a controlled two-pass protocol comparing human and LLM revision under identical conditions across self-, peer-, and cross-agent settings. Using an information-theoretic analysis based on per-iteration cross-entropy reduction, we find two failure modes of LLM reflection. On objective tasks with finite answer spaces, reflection yields near-zero information gain (Delta I approx 0), behaving as neutral re-generation indistinguishable from re-sampling. On subjective tasks, it yields significant negative gain (Delta I < 0), moving predictions away from the target. Human revision, by contrast, yields positive gain in both settings. Cross-agent experiments localize the failure to the revision step, not input quality: LLMs degrade even high-quality human responses. Diagnostic analyses (revision conditioned on first-pass correctness, and oracle-guided revision against a random-reshuffle baseline) show that which sub-step dominates varies by task and by model rather than reducing to a single mechanism: self-error detection is present on objective multiple-choice tasks but weak on subjective ones, and recovery under an oracle error signal exceeds the baseline for some models and falls below it for others. The unifying account is structural: without external information, self-conditioned revision cannot reduce uncertainty about the target, so LLM reflection is better understood as conditioned re-generation than as genuine error-driven revision.

Generative AI tools for creative work tend to be designed around the goal of removing friction, on the assumption that smoother iteration and faster output translate into more value for the designer. We argue, however, that this framing leaves out something important about how design ideation works, namely reflection-in-action. The act of accepting, rejecting and reworking candidate ideas is both a path to a final outcome and the process through which designers develop the rationale that allows them to think with their ideas and to communicate them to others. This becomes particularly important in group ideation, where ideas need to be expressed and explained to others to allow the group to extend, reject or combine them further. We suggest that AI in design ideation might be more usefully thought of as a friction agent for reflection rather than as a smoothing agent for output. This reframing opens up a different role for AI in design ideation, one that supports designers in building and carrying rationale rather than substituting for it.

Reflections from shiny objects and glass facades naturally extend the field of view of a camera, capturing the surrounding environment without the need to pan the camera or acquire a full panorama. We propose PanoLess, a Gaussian-splat-based framework that reconstructs the surrounding environment as a distant illumination map from images captured on only one side of a reflective surface. PanoLess leverages surface-aligned 2D Gaussian splats with deferred shading to recover accurate per-pixel normals and reflection cues, which are fused into a neural cubemap representation of the environment. In addition, PanoLess produces a visibility map that explicitly denotes which regions of the environment are supported by the partial reflective observations. Unlike existing inverse-rendering and reflection-aware Gaussian-splatting approaches, which typically require full 360-degree coverage and struggle under incomplete views, PanoLess enables consistent, physically grounded illumination estimation from partial-view input. We show that PanoLess achieves high-fidelity and geometrically consistent environment reconstruction, outperforming reflection-aware baselines on a new custom synthetic benchmark and publicly available datasets, and demonstrating generalization to real-world reflective captures.

Mirror Theory proposes that an intelligent system should be studied not only by what it represents, but by what coherent continuations it can sustain under repeated reflection. We make this claim operational through \emph{viable path entropy} (VPE), a finite-budget measure of verified continuation capacity. Given a mirror state, a rollout protocol, a verifier, and a mode map, VPE decomposes bounded capability into two parts: the probability of reaching a viable continuation and the diversity of verified continuation modes reached among successful rollouts. This paper restores the full theoretical scaffold behind the measure: intuition as local underdetermining constraint, taste as invariant-selecting pressure, reflection as taste-guided resolution of underdetermination, and geometry as the learned structure that makes future reflection stable. We then instantiate the theory in language-model reasoning experiments on GSM8K. Across Qwen2.5-Instruct models, 32 sampled rollouts per problem, and two reflection horizons, increasing the token budget from 96 to 160 substantially expands verified reachability, reduces zero-reachability, increases verified-mode entropy, and improves smoothed VPE. At 160 tokens, Qwen2.5-1.5B realizes the strongest mirror horizon among the tested models, even though Qwen2.5-3B has more parameters. This shows that mirror horizon is not parameter count, but accessible verified continuation capacity under a bounded reflection protocol. The result supports Mirror Theory as a measure-level account: capability is the structure of viable continuations made reachable, not merely one-shot accuracy or pass@k.

Measuring the extent to which emergent languages encode the visual content of their inputs is an open problem. We refer to this property as visual reflection: the extent to which emergent messages preserve information about their source images that can be recovered without appeal to the speaker-listener pair that produced them. Existing metrics measure it only indirectly, through proxies such as human-defined concept inventories, natural-language captions, structural distance correlations, or Referential Game accuracy, each of which can either miss visual content the message encodes or credit content it does not. We propose EmCom-Diffusion, an evaluation framework that measures visual reflection directly: it reconstructs each input image from its emergent message and compares the reconstruction with the original image itself, rather than with human-defined targets. Concretely, it finetunes a pretrained text-to-image diffusion model on (image, emergent-message) pairs and scores visual reflection as the perceptual similarity between the reconstructed and original images, operating generatively rather than discriminatively. Instantiating it on MS-COCO with a Referential Game, we validate the metric against random and fixed-token baselines under three pretrained visual encoders, and compare it against four existing metrics (CBM, supervised translation, TopSim, and R@1). EmCom-Diffusion captures visual content the other metrics miss.

Synthesizing physically accurate mirror reflections remains a fundamental challenge for modern text-to-image diffusion models, which are increasingly critical for generating synthetic training data for embodied AI and robotic perception. These models typically struggle with strict geometric constraints, leading to hallucinations that degrade the utility of the synthetic data. To address this, we introduce a novel, end-to-end physics-aware generation framework namely PhysMirror that natively enforces projective geometry through explicit 3D spatial priors. Our method automatically lifts prompted objects into 3D meshes and constructs a lightweight, mathematically exact mirror scene within a simulated environment. By rendering this explicit 3D scene, we extract precise 2D conditioning elements, such as depth maps and segmentation maps, that serve as robust guiding signals for downstream diffusion models, guiding them to generate images with physically correct mirror reflections. Moreover, we introduce Mirror Consistency Score (MCS), reference-free, fully automated metric that quantifies physical correctness using dense feature matching and vanishing point convergence. Experimental results on our newly constructed MirrOB dataset demonstrate that our approach outperforms state-of-the-art baselines in reflection accuracy and physical realism, while maintaining strong text-to-image semantic alignment, providing a reliable pipeline for embodied AI data generation. The source code is released at https://duyphuc0701.github.io/PhysMirror.

Mirror Illusion Art is a novel reflection-conditioned 3D illusion where one object yields two target appearances (front and mirror). The task is formulated as inverse design from two target 2D images (front and mirror) to a printable 3D object with geometry and texture. Prior topology-driven and shadow-based approaches demand substantial manual effort, optimize shape only, and often yield non-smooth or incomplete geometry. To address these challenges, we propose AutoMIA, an automated Mirror Illusion Art design pipeline that jointly optimizes shape and color. To stabilize optimization and suppress artifacts, four mechanisms are introduced: (1) projection-alignment component (PAC) selection to reduce surface noise, (2) position-weighted adaptive (PWA) suppression for background noise, (3) internal voxel preservation (IVP) to prevent internal fractures, and (4) shape-color decoupled (SCD) optimization that balance shape and color optimization. AutoMIA generate diverse smooth Mirror Illusion artworks successfully both in the digital and physical world, with only around 76s design time and 2.6 GB memory on average using a single RTX 3090, advancing inverse graphics and computational design. Our code is available at https://github.com/zxp555/AutoMIA.

Multi-round reflection lets agents built on large language models recover from failures within a single task, but each task remains an isolated episode: lessons learned across many reflection rounds on one task are discarded before the next begins. We study this gap on a code-generation task: from a scientific paper section, the agent writes Python in the open-source Manim library to render a mathematical animation. We present ManimAgent, a self-evolving multimodal agent that carries reflection experience across tasks through a dual-channel Episodic Memory Bank grown entirely from its own task stream, with no weight updates and no human seeds. After each animation converges, a vision-language model scores the rendered keyframes; the resulting signals populate a positive channel M+ that stores success rationales as soft Reference Examples, and a negative channel M- that stores validated failure patterns as hard Known Pitfalls. On a fixed-probe evaluation against no-memory, matched-budget retrieval-augmented generation, and shuffled-memory baselines, blind human Pass@1 rises and reflection rounds fall as memory size grows. We will release the code, frozen memory snapshots, and the task stream.

Large Vision Language Models (LVLMs) have achieved remarkable success on vision-language tasks, yet fine-grained perception over high-resolution images and long-context videos remains challenging. As the number of visual tokens increases, the visual attention sink phenomenon becomes increasingly severe, causing irrelevant tokens to absorb a disproportionate amount of attention mass. Recent approaches attempt to mitigate this issue by explicitly predicting bounding boxes or temporal spans and re-encoding the cropped visual regions. Such methods depend on unreliable numeric localization in the discrete token space and incur significant computational overhead due to additional forward passes. In this work, we propose VisReflect, a simple yet effective framework that improves fine-grained perception in long visual contexts through latent visual reflection. Instead of decoding intermediate predictions into discrete tokens, the model generates continuous visual reflection that represents question-relevant visual features in the latent space. These reflections selectively emphasize salient regions or frames, guiding attention towards relevant visual tokens within a single forward pass. We conduct comprehensive evaluations on challenging high-resolution image benchmarks, including BLINK, V*, and HRBench-4K/8K, as well as video understanding benchmarks such as MVBench, VideoMME, and MLVU. Our method consistently improves over strong baselines, achieving gains of 4.1% on image benchmarks and 1.8% on video benchmarks. Compared with zooming-based methods, our model achieves comparable performance while reducing inference time by roughly 44% on video understanding.

Existing digitization of buildings with reflective glass facades suffers from geometric reconstruction distortion, unrealistic view-dependent texture rendering, and difficulties in object-based semantic enhancement. Therefore, we propose RefGlass-GS, a fusion framework that enables end-to-end UAV-based photorealistic, semantic, and interactive digitization of reflective glass facades. The contributions include: (1) proposing an individual glass panel segmentation method based on maximum a posteriori estimation with structural regularities, robust to severe reflection and background interference; (2) formulating a UAV viewpoint planning optimization function that maximizes the coverage of view-dependent appearance for sufficient data capture; (3) developing an optimized Gaussian Splatting framework with a Reflection MLP, a novel deferred shading function, and two enhanced regularization terms for effective modeling of high-frequency near-field reflections; (4) introducing a standardized data organization paradigm for structuring GS-based representations into object-based models, facilitating interactive facility management on digital twin platforms. Experiments on real-world reflective glass facade scenes validate the effectiveness and superiority of the proposed method. Specifically, the glass panel segmentation achieves an improvement of 0.1927 in mIoU over SOTA methods, and only our method enables instance-level panel extraction. The UAV view planning improves novel view synthesis for reflective facades by 13.15 dB in PSNR compared to commercially used nap-of-the-object planning methods. The RefGlass-GS modeling outperforms SOTA Gaussian Splatting approaches for reflective scenes with an average improvement of 5.08 dB in PSNR.

Single-image reflection separation is highly challenging under extreme conditions like glare or weak reflections. Existing methods often struggle to recover both layers in glare or weak-reflection scenarios because of insufficient information. This paper presents a diffusion model explicitly fine-tuned for this task, leveraging generative diffusion priors for robust separation. Our method simultaneously generates transmission and reflection layers through a unified diffusion model, incorporating a novel cross-layer self-attention mechanism for better feature disentanglement. We further introduce a disjoint sampling strategy to iteratively reduce interference between the layers during diffusion and a latent optimization step with a learned composition function for improved results in complex real-world scenarios. Extensive experiments demonstrate that our approach surpasses state-of-the-art methods on multiple real-world benchmarks. Project page: https://brian90709.github.io/diff-reflection-separation/

Single-image reflection separation is fundamentally challenged by the entanglement of transmission and reflection layers under complex image formation processes. Existing approaches largely rely on simplified assumptions or independent modeling, limiting their ability to handle real-world scenarios. In this work, we revisit the problem from a unified perspective and identify a key issue of existing approaches, i.e., the widely adopted linear composition model in the sRGB domain fails to capture the nonlinear coupling introduced by real-world image signal processing pipelines. To address this, we introduce a learnable nonlinear superposition model that more faithfully characterizes layer interactions and improves decomposition fidelity. Building upon this formulation, we propose a generalized dual-stream interactive framework that explicitly models bidirectional dependencies between transmission and reflection through feature exchange. This framework unifies activation-, gating-, and attention-based interaction mechanisms, and is compatible with both CNN and Transformer backbones. Extensive experiments on diverse real-world benchmarks demonstrate that the proposed approach achieves superior performance with strong generalization capability. More importantly, our study reveals that reflection separation is not about undoing a linear mixture, but about learning nonlinear formation and interaction}, offering new insights into the design of principled image decomposition models. Code and models are publicly available at https://mingcv.github.io/DIRS-Page.

Large Language Models (LLMs) often produce explicit reflective traces during complex reasoning, accompanied by anthropomorphic markers such as wait, hmm, and alternatively. Although these markers are commonly used as visible indicators of reflection, their mechanisms remain unclear, which leaves the risk of overthinking associated with redundant and repetitive reflection markers. In this work, we revisit anthropomorphic reflection markers, examining their necessity for reasoning and role in the reflection. We suppress these markers through prompt-level and token-level interventions, and analyze their effects on task performance across four benchmarks and two model scales. Our results show that anthropomorphic markers are not uniformly necessary for reasoning performance: suppressing them can preserve or improve performance in several settings, especially under larger sampling budgets. Meanwhile, marker suppression does not necessarily remove reflection behavior, as models can still perform marker-free verification. These suggest that anthropomorphic markers tend to be surface cues rather than reliable proxies for reflection itself, and motivate future research on reasoning mechanisms beyond explicit marker patterns.

Reinforcement learning has long struggled with poor sample efficiency. One promising approach to mitigate this problem is leveraging group-invariant Markov Decision Processes ($G$-invariant MDPs). Existing works in this direction have primarily focused on image-based RL and rotational symmetry such as $\mathrm{SO(2)}$, leaving state-based RL and reflection symmetry largely underexplored. In this work, we focus on state-based continuous control tasks and exploit reflection symmetry by introducing Reflex, a paradigm that seamlessly integrates with both on-policy and off-policy RL algorithms. We formalize two types of reflection-axial reflection and bilateral reflection, and characterize their corresponding transformations. Building on a theoretical analysis of symmetry-preserving optimal value functions and policies, Reflex integrates reflection symmetry into policy learning through principled symmetry regularization mechanisms. We integrate Reflex with PPO and SAC, and evaluate it on a suite of OpenAI Gym and DeepMind Control benchmarks, demonstrating superior performance over standard baselines while improving sample efficiency. Our code is available at https://github.com/TonyStark042/Reflex.

Designing mechanical linkages involves combinatorial topology selection and continuous parameter fitting. We show that language models can systematically improve linkage designs through symbolic representations. Language model agents explore discrete topologies while numerical optimisers fit continuous parameters. A symbolic lifting operator translates simulator trajectories into qualitative descriptors, motion labels, temporal predicates, and structural diagnostics that models interpret across iterative design cycles. Across six engineering-relevant motion targets and three open-source models (Llama 3.3 70B, Qwen3 4B, Qwen3 MoE 30B-A3B), the modular architecture reduces geometric error by up to 68% and improves structural validity by up to 134% over monolithic baselines. Critically, 78.6% of iterative refinement trajectories show measurable improvement, with the system correctly diagnosing overconstraint (56.3%) and underconstraint (35.6%) failure modes and proposing grounded corrections. Models across all three families acquire interpretable mechanical reasoning strategies without fine-tuning, demonstrating that principled symbolic abstraction bridges generative AI and the numerical precision required for engineering design.