NeurIPS 2026 Papers

Conference on Neural Information Processing Systems

Decision breakdown

6,437papers

Counted from the official paper list; may differ slightly from the number the conference announced.

  • Oral
    991.5%
  • Spotlight
    2403.7%
  • Poster
    6,09894.7%

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Topic: Image Generation · 453 papers · Reset filters

SpatialFlow-GRPO: Where Spatial Credit Drives Image Editing

Yankai Yang, Yancheng Long, Wei Chen, Xingyu Lu, Hongyang Wei, Bin Wen, Fan Yang, Tingting Gao, Han Li, Shuo Yang

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Recent online reinforcement learning has substantially improved image editing quality. However, existing Flow-GRPO-style methods usually rely on a single whole-image reward, which makes fine-grained editing optimization difficult. We observe that a key obstacle in image editing is this spatial uniformity assumption: a whole-image reward cannot distinguish how different spatial regions contribute to image quality. To address this issue, we propose **SpatialFlow-GRPO**, a training framework that makes spatial reward feedback more fine-grained. The framework converts region-aware rewards into semantic-region-level optimization signals and aligns region advantages with the corresponding latent positions during policy updates. We also train a region-aware reward model, **SFReward**, construct **SFReward-14K** with region-annotated editing samples, and introduce **MultiEditBench** to evaluate multi-region editing ability. On OmniGen2 and FLUX.2-klein-4B, SpatialFlow-GRPO outperforms Flow-GRPO on GEdit-Bench, ImgEdit-Bench, and MultiEditBench. The results show that SpatialFlow-GRPO can turn local feedback into more accurate update signals and improve editing quality.

Poster
Sparse Internal Control of Language Models

Xizhe Zhang

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Language models are increasingly used in text generation, decision support, and automated interaction, where their behavior must be controlled in a localized, reversible, and selective way. Existing methods either update shared parameters or constrain generation through external interfaces, leaving open whether frozen models contain compact internal control. We introduce sparse internal control, a framework for steering target behavior by applying inference-time interventions to a small set of internal model nodes. The framework formulates control through local target controllability, where candidate site–direction pairs are characterized by their behavioral effects under target, preservation, and energy constraints. This yields two complementary selectors: Driver-OMP, which selects nodes that sparsely reconstruct a desired behavioral displacement, and Coverage-Driver, which favors nodes whose effects cover prompts stably. We further propose a six-axis control-evaluation protocol measuring reachability, signed reversal, dose response, feedback controllability, off-target preservation, and held-out reuse. Across IOI, MMLU MCQA, and sentiment steering on models from GPT-2 small to Qwen3-4B, sparse driver sets act as executable actuators: they steer target behavior, respond monotonically to dose, support closed-loop control, and preserve unrelated next-token behavior. On refusal steering, the same protocol exposes a boundary case that passes all evaluated axes except strict reachability. Held-out reuse separates prompt-specific controls requiring refitted strengths from population-level controls that transfer as frozen interventions. These results show that model control can move beyond output-side steering: mechanistic internal variables can be selected, certified, and reused as localized control handles for frozen language models.

Poster
Source-Causal Control of Historical Context in Longitudinal Radiology Report Generation

Dmitry Lvov, Ilya Pershin

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Longitudinal radiology report generation increasingly conditions on prior images and reports. This history is clinically valuable, but it creates a source-validity failure mode: a generator can carry prior-only findings into the current report. Weintroduce source-causal robustness, a stress-test and control framework that holds the current chest X-ray fixed while intervening on historical context. On a full eligible MIMIC-CXR longitudinal study (18,716 pairs; 93,580 generations across five source conditions), historical context consistently trades fewer missed findings for more unsupported positives. Matched wrong-history, the key negative control, increases proxy-defined false positives by +0.366 per report while reducing false negatives by −0.129; random wrong-history yields an even larger false positive stress signal (+0.465 FP/report). We propose the Source-Causal Finding Router (SCFR), a source-validity controller trained with within-evaluation subject exclusion. Across three held-out evaluations, SCFR repairs matched wrong-history false-positive inflation by −0.343, −0.550, and −0.457 per report, passes Holm corrected primary testing at the bootstrap resolution floor (Holm-adjusted p ≤ 0.0012), and satisfies fixed current-only parity margins. Cross-generator stress panels with RadInfer and Libra, together with ReXPref-Prior, RadGraph2, Chest ImaGenome, ablations, and case review, support the mechanism. These results establish a protocol-defined state-of-the-art source-causal robustness/control result for longitudinal radiology report generation under matched wrong-history stress tests.

Poster
SocialDirector: Training-Free Social Interaction Control for Multi-Person Video Generation

Liangyang Ouyang, Ruicong Liu, Caixin Kang, Yifei Huang, Yoichi Sato

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Video generation has advanced rapidly, producing photorealistic videos from text or image prompts. Meanwhile, film production and social robotics increasingly demand multi-person videos with rich social interactions, including conversations, gestures, and coordinated actions. However, existing models offer no explicit control over interactions, such as who performs which action, when it occurs, and toward whom it is directed. This often results in wrong person performing unintended actions (actor-action mismatch), disordered social dynamics, and wrong action targets. To address these challenges, we present SocialDirector, a training-free interaction controller that enhances the generation model by modulating cross-attention maps. SocialDirector contains two modules: Social Actor Masking and Directional Reweighting. Social Actor Masking constrains each person's visual tokens to attend only to their own textual descriptions via a spatiotemporal mask, avoiding actor-action mismatch and disordered social dynamics. Directional Reweighting amplifies attention to directional words (e.g., "leftward", "right"), leading each action towards its intended target. To evaluate generated social interactions, we annotate existing datasets with interaction descriptions and build a fully automated evaluation pipeline powered by open-source VLMs. Experiments on different video generation models show that SocialDirector significantly improves interaction fidelity and approaches the upper bound set by real videos.

Poster
SliceWorld: A Predictive and Controllable World-State Model for CT Report Generation

Yuanhe Tian, Yan Song

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CT report generation (CTRG) requires models to summarize three-dimensional anatomical context and pathological findings from hundreds of axial slices. Existing methods typically learn a direct image-to-text mapping, providing limited mechanisms for modeling how CT evidence evolves across slices or how reports respond to controlled changes in latent lesion-related factors. We propose SliceWorld, a CT-specific world-state framework that treats an axial CT scan as an ordered sequence along the z-axis. SliceWorld encodes prefix CT evidence into factor-aware latent states containing anatomy, lesion, and uncertainty components, and projects these states into world tokens used for multi-step future-slice feature prediction, lesion-factor intervention, and LLM-based report generation. The model is first pretrained on CT slice sequences with predictive, factor-aware, and counterfactual objectives, and is then fine-tuned on paired CT-report data. Experiments on M3D-Cap and CT-RATE show that SliceWorld improves natural language generation metrics and clinically oriented automatic evaluation. Further analyses demonstrate multi-horizon future-slice prediction, measurable factor alignment, reduced-slice robustness, and selective lesion-sensitive report modulation.

Poster
SkillCIR: Intent-Guided Skill Composition for Training-Free Composed Image Retrieval

Yuanmin Tang, Lin Li, Yang Du, Yuan Gao, Massimiliano Mancini, Jun Song, Gaopeng Gou, Gang Xiong, Meikang Qiu, Cheng Yu, Bo Zheng

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Composed Image Retrieval (CIR) retrieves a target image given a reference image and a textual edit. Existing training-free methods prompt a frozen multimodal large language model (MLLM) to infer the user's edit intent and rewrite the composed query into a single retrieval artifact, such as a target caption, an edited image, or a modality-fused embedding. These methods can reason about the edit, but they have limited means to execute that reasoning during retrieval. A key remaining bottleneck for training-free CIR appears to be not only intent understanding, but intent execution. To address this challenge, we propose SkillCIR, a training-free framework that tackles the intent execution gap by routing the inferred constraints to specialized retrieval skills. Specifically, the same frozen MLLM that infers the intent also emits a structured plan of active constraints; each constraint activates a typed skill that scores gallery candidates along one evidence channel, and the per-skill scores are composed in score space with explicit signs and re-checked by a local verification step. Across three benchmarks and three CLIP backbones, SkillCIR improves the primary recall/mAP metrics by 2.8 to 7.9 points at the latency of typical training-free CIR pipelines and around 23x faster than the latest training-free state of the art. These gains hold with a fixed skill pool and no model-parameter updates, suggesting that improving the means to execute the inferred edit is a useful complement to stronger reasoning about it.

Poster
Single Shot HDR Recovery via a Video Diffusion Prior

Chinmay Talegaonkar, Jinshi He, Nicholas Antipa

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Recent generative methods for single-shot high dynamic range (HDR) image reconstruction show promising results, but often struggle with preserving fidelity to the input image: they hallucinate content, require separate models to handle highlights and shadows, or sacrifice interpretability by directly predicting the final HDR image. We address these limitations by re-casting single-shot HDR reconstruction as conditional video generation and fusing the generated frames into an HDR image. We fine-tune a video diffusion model to generate an exposure bracket, conditioned on a low dynamic range (LDR) input. We fuse this image bracket using per-pixel weights predicted by a light-weight UNet. This formulation is simple, interpretable, and effective. Rather than directly hallucinating an HDR image, it explicitly reconstructs the intermediate exposure stack and fuses it into the final output. Our method eliminates the need for separate models across exposure regimes and produces HDR reconstructions with high input fidelity. On quantitative benchmarks, we outperform state-of-the-art generative baselines with comparable model capacity on several reconstruction metrics. Human evaluators further prefer our results in 72% of pairwise comparisons against existing methods. Finally, we show that this input-conditioned sequence generation and fusion framework extends beyond HDR to other image reconstruction tasks, such as all-in-focus image recovery from a single defocus-blurred input.

Poster
Simplified Reversible Residual Networks

Erland Brandser Olsson, Zhirong Yang

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The de facto standard way of training neural networks requires storing activations at each layer to memory, in order to compute gradients in backpropagation. As progress has often been made by stacking larger and more layers, memory consumption has now become a major bottleneck for making frontier models available to everyone. In this work, we take advantage of the Residual Network (ResNet) layer formulation that is now used in many state-of-the-art neural network architectures to recompute the activations at each layer on-the-fly during backpropagation instead of storing them in memory. We propose a modification to Reversible Residual Network (RevNet) that overcomes its limitation of requiring to replace the ResNet layer network function with two new network functions, by setting either one to an identity function. This modification is simple yet has a significant advantage because now there is no need to change the original ResNet architecture. Our method can work as a drop-in replacement for layers with residual connections such as in ordinary ResNets or Transformers with practically no loss in performance while offering significant reductions in memory consumption. With this simple modification, we are able to maintain the same computational cost and ease of use as activation checkpointing, which requires no architectural changes, while leveraging a reversible procedure such that we only need to store the activations from the last layer. The method is called Simplified RevNet, and compared to previous work in reversible architectures, we here propose a simpler and more streamlined approach that comes in two variants based on which of $F$ or $G$ in RevNet becomes an identity function. Empirically, we demonstrate performance at practically the same level as the non-reversible counterparts on ImageNet image classification with ResNets and on OpenWebText language modeling with Transformers.

Poster
SimWorld Studio: Automatic Environment Generation with Evolving Coding Agent for Embodied Agent Learning

Haoqiang Kang, Xiaokang Ye, Yuhan Liu, Siddhant Hitesh Mantri, Lingjun Mao, James Fleming, Drishti Regmi, Lianhui Qin

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LLM/VLM-based digital agents have advanced rapidly thanks to scalable sandboxes for coding, web navigation, and computer use, which provide rich interactive training grounds. In contrast, embodied agents still lack abundant, diverse, and automatically generated 3D environments for interactive learning. Existing embodied simulators rely on manually crafted scenes or procedural templates, while recent LLM-based 3D generation systems mainly produce static scenes rather than deployable environments with verifiable tasks and standard learning interfaces. We introduce SimWorld Studio, an open-source platform built on Unreal Engine 5 for generating evolving embodied learning environments. At its core is SimCoder, a tool/skill-augmented coding agent that writes and executes engine-level code to construct physically grounded 3D worlds from language/image instructions. SimCoder self-evolves by using verifier feedback (e.g., compilation errors, physics checks, VLM critiques) to revise environments and autonomously add reusable tools and skills to its library. Generated worlds are exported as Gym-style environments for embodied agent learning. SimWorld Studio further enables co-evolution between environment generation and embodied learning: agent performance feedback guides SimCoder to generate adaptive curricula near the learner’s capability frontier, so that environments become increasingly challenging as the embodied agent improves. Three case studies on embodied navigation show that self-evolution improves generation reliability, generated environments substantially improve embodied agent performance that generalizes to unseen benchmarks, and co-evolution yields an 18-point success-rate gain over fixed-environment learning and a 40-point gain over an untrained agent.

Poster
SemISP: Semantic-Consistent Diffusion for Cross-Camera RAW-to-sRGB Generation

ZHE PANG, Haina Qin, Ziyu Feng, Zewen Chen, Juan Wang, Bing Li, Weiming Hu

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Cross-camera RAW-to-sRGB mapping seeks to convert smartphone RAW captures into DSLR-quality sRGB images, yet the large domain gap between linear RAW and nonlinear sRGB spaces makes this task highly challenging. Existing methods mainly condition on pixel-level supervision and local RAW cues, where content preservation and domain translation remain entangled in low-level measurements. We propose SemISP, a semantic-guided diffusion framework that uses scene semantics as a domain-invariant anchor for cross-domain generation. Specifically, we adopt a frozen DINOv3 as the sRGB semantic backbone and develop a Domain Alignment Adapter to extract sRGB-consistent semantic representations from RAW inputs through parameter-efficient adaptation. Because semantic priors and RAW signals operate at fundamentally different information levels, and the diffusion denoising process follows a coarse-to-fine trajectory, we further design a Time-aware Dual-stream Adaptive Modulation (TDAM) module that separately encodes both condition streams and uses the diffusion timestep to dynamically balance their contributions---emphasizing semantic anchoring at early stages and fine-grained RAW details at later ones. Experiments on two established cross-camera benchmarks show consistent improvements over prior methods in both fidelity and perceptual quality.

Poster
SemGeo-Gen: Unsupervised Generation of Approximate Cross-Instance Semantic-Geometric Correspondences

Roy Amoyal, Shira Ifergane, Oren Freifeld

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We introduce SemGeo-Gen, an unsupervised method for generating approximate cross-instance semantic-geometric supervision from weakly aligned 3D object collections. Our goal is not to recover exact point-level correspondences, which are often ambiguous across different instances and would require expensive, impractical manual supervision at scale. Instead, we automatically produce approximate correspondences that are semantically meaningful, geometrically consistent, and diverse enough to train modern correspondence models. Given only coarse category-level rotation alignment, SemGeo-Gen lifts multi-view DINOv2 features to 3D, aligns object instances using continuous piecewise-affine registration, and prunes candidate matches using semantic consistency. The resulting 3D correspondences can be projected into rendered views, yielding scalable 3D-3D, 3D-2D, and 2D-2D supervision without manual annotation. We validate the generated correspondences against sparse human annotations from KeypointNet, obtaining 93% PCK@0.10 and 97% PCK@0.15. More importantly, we show that using the generated correspondences for synthetic pretraining improves recent state-of-the-art semantic correspondence models on SPair-71k after fine-tuning on real data, with gains of up to 5 PCK@0.10 points. Together, these results indicate that approximate semantic-geometric supervision generated from 3D assets can improve real-image correspondence learning and serve as a scalable alternative to costly manual annotation. Code and generated data will be released upon acceptance.

Poster
Self-Cleaning Diffusion Models

Adrian Rodriguez-Munoz*, Adam Klivans, Antonio Torralba, Constantinos Daskalakis, Giannis Daras

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We present Self-Cleaning Diffusion Models, a principled and effective framework for training diffusion models from heterogeneous data. In many domains, high-quality data is scarce or expensive to collect, while low-quality and out-of-distribution (OOD) data is abundant. Leveraging these ubiquitous samples is critical for scaling generative models. Still, principled techniques remain elusive, leaving practitioners to rely on simple heuristics such as high-quality finetuning or explicit quality conditioning. Self-Cleaning Diffusion Models bridges this gap by decoupling data correction from prior learning. We first train a transport map between the abundant OOD and the limited in-distribution samples. We then train an unconditional generative prior on a mixture of the few in-distribution samples and *noisy* versions of the transported points. Crucially, this noise injection prevents learning errors in the transport map from propagating to the generative prior. Theoretically, we demonstrate that transporting OOD samples towards the empirical proxy reduces the distance to the underlying distribution under mild assumptions. Empirically, we achieve state-of-the-art results across a diverse range of settings, from mitigating synthetic corruptions to increasing diversity and transcending dataset quality.

Poster
Selective Disk Bispectrum: A Complete and Rotation Invariant Image Descriptor

Adele Lantow, Nina Miolane

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Rotation invariance is a fundamental requirement across many computer vision tasks. Historically, this inductive bias has been encoded through hand-crafted rotation-invariant representations. These are compact, interpretable, and fast to compute, but they come at the cost of descriptive power. More recently, architectures achieve inductive bias through learned representations. These are highly descriptive and achieve strong empirical performance, at the cost of efficiency and interpretability. In this work, we propose an alternative at the intersection of both paradigms. We introduce the selective disk bispectrum (SDB), a complex-valued rotation-invariant vector that preserves all information about the image except its orientation. Our key theoretical contributions are the selective disk bispectrum, its inversion, its (reduced) spatial and computational complexities (compared to the full disk bispectrum), and its expectation and variance under noise. Furthermore, we propose a numerical SDB approximation and provide theoretical guarantees for its accuracy and rotation invariance. Empirically, we validate SDB's invariance and robustness to noise classification tasks. We test our reconstruction algorithm on multi-reference alignment of rotated images.

Poster
Seg3DParts: Segmentation-Grounded Controllable Part-Level 3D Generation

Jiantao Lin, Meixi Chen, Yingjie Xu, Chenbo FU, Leyi Wu, Hao Chen, Yinchuan Li, Yingcong Chen

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Part-level 3D assets are essential for editing, reassembly, and interaction, yet recovering such structure from a single image remains challenging due to occlusion, ambiguous boundaries, and the need for coherent multi-part reasoning. Existing approaches struggle to achieve both controllable part-level generation and coherent multi-part structure, as part identity and spatial allocation are typically inferred implicitly. We present Seg3DParts, a segmentation-grounded framework for controllable part-level 3D generation from a single image. By treating segmentation as an explicit grounding signal, our method defines part identity during generation, enabling each component to be anchored to a corresponding image region. To ensure coherent assemblies, we introduce structured cross-part interaction that allows components to exchange global context throughout the generative process. As a result, Seg3DParts directly generates well-aligned part meshes in a shared canonical space without post-hoc alignment, supporting flexible and controllable decomposition. We further introduce PartObjectNet, a large-scale dataset with over 200K objects and 1M annotated parts. Experiments demonstrate that Seg3DParts achieves superior geometry quality, cross-part coherence, and part-level controllability over existing methods.

Poster
Seeing the World through Any Eyes

Yang Fu, Jianqin Wang, Xiangtai Li, Henghui Ding

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Egocentric video generation aims to synthesize first-person visual experiences, enabling applications in filmmaking, virtual reality, and embodied AI. Generating egocentric videos from exocentric observations is particularly challenging, as it requires reasoning across large viewpoint changes, limited visual overlap, and substantially different camera motions. To address these modeling challenges, we propose **EgoEye**, a framework that generates egocentric videos from a single exocentric input video. EgoEye integrates reward-guided egocentric context reasoning for inferring unseen first-person content, multi-stage motion alignment for enforcing cross-view temporal consistency, and egocentric pretraining for improving first-person realism. To support training and evaluation under diverse and distortion-free exo-ego settings, we further introduce **EgoScape**, a large-scale dataset comprising 19.5K time-aligned exo-ego video pairs and 24.2K in-the-wild egocentric videos. EgoScape provides paired cross-view supervision while enriching the first-person visual priors needed for realistic egocentric synthesis. Extensive experiments demonstrate that the proposed EgoEye generates realistic and temporally consistent egocentric videos across diverse scenarios.

Poster
Seeing the Unseen: Unified Visible–Invisible Motion for Physically Consistent Video Generation

Mingyang Bao, Fangda Ye, Xihao Chen, Bobo Li, Xiangtai Li, Shengqiong Wu

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Recent advances in video generation have achieved impressive visual quality, yet they often fail to produce physically consistent dynamics due to the lack of explicit modeling of underlying physical processes. Existing approaches either rely on simulators with strong assumptions or use coarse semantic guidance, and further struggle to effectively inject physical priors into generation models. In this work, we propose Seeing the Unseen, a unified framework for physics-grounded video generation. Our approach decomposes the problem into two stages: learning physical dynamics and injecting them into video synthesis. First, we introduce a lightweight Particle-based Graph Dynamics Simulator (PGDS) that learns generalizable physical interactions from data and predicts plausible 3D motion trajectories. Second, we propose a Visible–Invisible Motion Field (VIMF) that captures both motion observable in the input frame and motion that emerges over time due to object dynamics. This representation enables more complete and structured motion guidance compared to conventional physical signals. By integrating these trajectories into a diffusion-based generator, our method produces videos that are both visually coherent and physically consistent. Extensive experiments demonstrate improved motion accuracy, interaction consistency, and reduced physical artifacts compared to strong baselines.

Poster
Search-Augmented Masked Diffusion Models for Constrained Generation

Huu Binh Ta, Michael Cardei, Alvaro Velasquez, Ferdinando Fioretto

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Discrete diffusion models generate sequences by iteratively denoising samples corrupted by categorical noise, offering an appealing alternative to autoregressive decoding for structured and symbolic generation. However, standard training targets a likelihood-based objective that primarily matches the data distribution and provides no native mechanism for enforcing hard constraints or optimizing non-differentiable properties at inference time. This work addresses this limitation and introduces Search-Augmented Masked Diffusion (SearchDiff), a training-free neurosymbolic inference framework that integrates informed search directly into the reverse denoising process. At each denoising step, the model predictions define a proposal set that is optimized under a user-specified property satisfaction, yielding a modified reverse transition that steers sampling toward probable and feasible solutions. Experiments in biological design and symbolic reasoning illustrate that SearchDiff substantially improves constraint satisfaction and property adherence, while consistently outperforming discrete diffusion and autoregressive baselines.

Poster
ScrapeGraphAI-100k: Dataset for Schema-Constrained LLM Generation

William Brach, Francesco Zuppichini, Lorenzo Padoan, Marco Vinciguerra

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Producing output that conforms to a specified JSON schema underlies tool use, structured extraction, and knowledge base construction in modern large language models. Despite this centrality, public datasets for the task remain small, synthetic, or text-only, and rarely pair real page content with the prompts and schemas used in practice. We introduce ScrapeGraphAI-100k, 93{,}695 schema-constrained extraction events collected via opt-in ScrapeGraphAI telemetry in Q2--Q3 2025, deduplicated and balanced by schema from 9M raw events. The corpus spans 18{,}000+ unique schemas across 15 named languages plus a long-tail Other category, with English and Traditional Chinese covering 88\% of detected content, each instance pairs Markdown-converted page content with a prompt, schema, LLM response, and per-example jsonschema-rs structural conformance labels (semantic correctness is out of scope, and raw HTML is deferred beyond v1.0). We characterize structural diversity across the corpus and identify sharp failure thresholds as schema complexity grows. As a case study, a 1.7B student fine-tuned on this data closely tracks the output distribution of its GPT-5-nano teacher, though it still trails a 30B-A3B reference (3.3B active parameters) on schema compliance. We offer this distillation result as preliminary evidence that grounding schema-constrained generation in real practitioner workloads at scale enables training and benchmarking that prior synthetic or text-only corpora could not support.

Poster
Scalable Fair Learning via Cramér-von Mises Regularization

Albert Gimó Contreras, Mariia Vladimirova, Olga Petrova, Reda CHHAIBI, Patrick Loiseau

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A standard way to enforce group fairness in machine learning models is to add a fairness regularizer to the training loss. Existing dependence-based regularizers, however, are often computationally expensive, with per-batch costs that are typically quadratic or higher in the batch size $B$. We propose a novel group-fairness regularizer based on the Cramér-von-Mises (CvM) sensitivity index, which penalizes statistical dependence between model predictions and a sensitive attribute during training. Our method combines a rank-based CvM estimator with differentiable soft ranking, yielding a bounded training penalty with $\Oc(B \log B)$ per-batch complexity. This is the first sub-quadratic in-processing fairness method that targets genuine joint-distribution dependence. We further establish theoretical connections between the CvM regularizer and standard fairness metrics such as demographic parity and equality of opportunity. Experiments on tabular and image datasets show competitive fairness-utility trade-offs while substantially lowering training overhead compared to existing dependence-based regularizers.

Poster
Same Function, Different Mechanism: Implementation-Local Geometry Beyond Accuracy

Miroslav Lžičař

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Two finite-domain implementations, including neural-network parameterizations restricted to an evaluation domain, can agree on every input while implementing the computation through different mechanisms, such as independent lookup storage or a shared reusable rule. We formalize this distinction as a statement about the local Kullback-Leibler geometry of an implementation chart: a mechanism-specified local family of perturbations around a fixed predictive distribution. For finite input-output distributions with full support, we prove a logit-Fisher pullback theorem: the Hessian rank of a chart equals the dimension of its tangent image in the quotient logit space, so the quadratic active contribution to the local learning coefficient is half this rank under the analytic/dead-kernel conditions stated below. We prove that this rank is invariant under local reparameterizations, dead parameters, and redundant duplications, but changes when the allowed perturbation class changes; hence it is a first-order chart-germ invariant, not a function-only invariant. For mechanisms specified by exact finite-group sharing, we give a closed-form orbit-count formula for the active dimension. Lookup and shared cyclic modular addition are then immediate corollaries: both implement the same softened conditional distribution, yet their active ranks are $p^2(p-1)$ and $p-1$, respectively. The results clarify when Bayesian/Singular-Learning-Theory complexity can distinguish extensionally equivalent algorithms and when chart dependence is a real modeling choice rather than a defect.

Poster