Prior Knowledge

Multi-agent reinforcement learning (MARL) is crucial for AI systems that operate collaboratively in distributed and adversarial settings, particularly in multi-domain operations (MDO). A central challenge in cooperative MARL is determining how agents should coordinate: existing approaches must either hand-specify graph topology, rely on proximity-based heuristics, or learn structure entirely from environment interaction; all of which are brittle, semantically uninformed, or data-intensive. We investigate whether large language models (LLMs) can generate useful coordination graph priors for MARL by using minimal natural language descriptions of agent observations to infer latent coordination patterns. These priors are integrated into MARL algorithms via graph convolutional layers within a graph neural network (GNN)-based pipeline, and evaluated on four cooperative scenarios from the Multi-Agent Particle Environment (MPE) benchmark against baselines spanning the full spectrum of coordination modeling, from independent learners to state-of-the-art graph-based methods. We further ablate across five compact open-source LLMs to assess the sensitivity of prior quality to model choice. Our results provide the first quantitative evidence that LLM-derived graph priors can enhance coordination and adaptability in dynamic multi-agent environments, and demonstrate that models as small as 1.5B parameters are sufficient for effective prior generation.

Object level hallucination remains a central reliability challenge for vision language models (VLMs), particularly in binary object existence verification. Existing benchmarks emphasize aggregate accuracy but rarely disentangle whether errors stem from perceptual limitations or from the influence of contextual textual priors, leaving underlying failure mechanisms ambiguous. We introduce DO-Bench, a controlled diagnostic benchmark that isolates these sources through structured multimodal interventions. Rather than evaluating models in unconstrained settings, DO-Bench probes two complementary dimensions: the Prior Override dimension progressively strengthens contextual textual priors while holding visual evidence constant to assess resistance to prior pressure, and the Perception-Limited dimension incrementally enhances visual evidence from full-scene context to localized object crops to measure perceptual grounding strength. This paired design enables attribution of errors to prior suppression, perceptual insufficiency, or their interaction. We further define two diagnostic metrics, PriorRobust and PerceptionAbility, to quantify these behaviors consistently. Evaluations across diverse open- and closed-source VLMs reveal systematic differences in prior sensitivity and perceptual reliability, demonstrating that object hallucination reflects heterogeneous, mechanism dependent failure patterns beyond aggregate accuracy.

As forgery types continue to emerge consistently, Incremental Face Forgery Detection (IFFD) has become a crucial paradigm. However, existing methods typically rely on data replay or coarse binary supervision, which fails to explicitly constrain the feature space, leading to severe feature drift and catastrophic forgetting. To address this, we propose AIFIND, Artifact-Aware Interpreting Fine-Grained Alignment for Incremental Face Forgery Detection, which leverages semantic anchors to stabilize incremental learning. We design the Artifact-Driven Semantic Prior Generator to instantiate invariant semantic anchors, establishing a fixed coordinate system from low-level artifact cues. These anchors are injected into the image encoder via Artifact-Probe Attention, which explicitly constrains volatile visual features to align with stable semantic anchors. Adaptive Decision Harmonizer harmonizes the classifiers by preserving angular relationships of semantic anchors, maintaining geometric consistency across tasks. Extensive experiments on multiple incremental protocols validate the superiority of AIFIND.

Video object insertion is a critical task for dynamically inserting new objects into existing environments. Previous video generation methods focus primarily on synthesizing entire scenes while struggling with ensuring consistent object appearance, spatial alignment, and temporal coherence when inserting objects into existing videos. In this paper, we propose a novel solution for Video Object Insertion, which integrates multi-view object priors to address the common challenges of appearance inconsistency and occlusion handling in dynamic environments. By lifting 2D reference images into multi-view representations and leveraging a dual-path view-consistent conditioning mechanism, our framework ensures stable identity guidance and robust integration across diverse viewpoints. A quality-aware weighting mechanism is also employed to adaptively handle noisy or imperfect inputs. Additionally, we introduce an Integration-Aware Consistency Module that guarantees spatial realism, effectively resolving occlusion and boundary artifacts while maintaining temporal continuity across frames. Experimental results show that our solution significantly improves the quality of video object insertion, providing stable and realistic integration.

Attention sinks are defined as tokens that attract disproportionate attention. While these have been studied in single modality transformers, their cross-modal impact in Large Vision-Language Models (LVLM) remains largely unexplored: are they redundant artifacts or essential global priors? This paper first categorizes visual sinks into two distinct categories: ViT-emerged sinks (V-sinks), which propagate from the vision encoder, and LLM-emerged sinks (L-sinks), which arise within deep LLM layers. Based on the new definition, our analysis reveals a fundamental performance trade-off: while sinks effectively encode global scene-level priors, their dominance can suppress the fine-grained visual evidence required for local perception. Furthermore, we identify specific functional layers where modulating these sinks most significantly impacts downstream performance. To leverage these insights, we propose Layer-wise Sink Gating (LSG), a lightweight, plug-and-play module that dynamically scales the attention contributions of V-sink and the rest visual tokens. LSG is trained via standard next-token prediction, requiring no task-specific supervision while keeping the LVLM backbone frozen. In most layers, LSG yields improvements on representative multimodal benchmarks, effectively balancing global reasoning and precise local evidence.

Neural radiance fields (NeRFs) have emerged as a prominent pre-training paradigm for vision-centric autonomous driving, which enhances 3D geometry and appearance understanding in a fully self-supervised manner. To apply NeRF-based pretraining to 3D perception models, recent approaches have simply applied NeRFs to volumetric features obtained from view transformation. However, coupling NeRFs with view transformation inherits conflicting priors; view transformation imposes discrete and rigid representations, whereas radiance fields assume continuous and adaptive functions. When these opposing assumptions are forced into a single pipeline, the misalignment surfaces as blurry and ambiguous 3D representations that ultimately limit 3D scene understanding. Moreover, the NeRF network for pre-training is discarded during downstream tasks, resulting in inefficient utilization of enhanced 3D representations through NeRF. In this paper, we propose a novel NeRF-Resembled Point-based 3D detector that can learn continuous 3D representation and thus avoid the misaligned priors from view transformation. NeRP3D preserves the pre-trained NeRF network regardless of the tasks, inheriting the principle of continuous 3D representation learning and leading to greater potentials for both scene reconstruction and detection tasks. Experiments on nuScenes dataset demonstrate that our proposed approach significantly improves previous state-of-the-art methods, outperforming not only pretext scene reconstruction tasks but also downstream detection tasks.

Multimodal multiple-choice question answering (MCQA) provides a standardized and objectively measurable setting for evaluating vision-language models (VLMs). However, because the MCQA format incorporates the candidate choices into the input context, it introduces several unintended biases. Previous work has primarily focused on structural biases, such as preferences for certain choices. Instead, we argue that the choices act as textual priors, causing models to favor linguistically plausible options regardless of the visual content. We hypothesize and empirically verify that a model genuinely relies on visual evidence only when its multimodal distribution significantly diverges from its text-only distribution. Based on this observation we propose BUZZY,a training-free decoding method that corrects multimodal predictions by subtracting the text-only distribution. Experiments with five VLMs on five multimodal MCQA benchmarks demonstrate that BUZZY achieves the highest average accuracy among state-of-the-art methods while reducing inference latency by over 28% compared to prior contrastive decoding approaches. Overall, these results suggest that amplifying the visual signal by penalizing text-only preferences is key to efficient and robust multimodal MCQA reasoning.

Face images captured in real-world low light suffer multiple degradations-low illumination, blur, noise, and low visibility, etc. Existing cascaded solutions often suffer from severe error accumulation, while generic joint models lack explicit facial priors and struggle to resolve clear face structures. In this paper, we propose PASDiff, a Physics-Aware Semantic Diffusion with a training-free manner. To achieve a plausible illumination and color distribution, we leverage inverse intensity weighting and Retinex theory to introduce photometric constraints, thereby reliably recovering visibility and natural chromaticity. To faithfully reconstruct facial details, our Style-Agnostic Structural Injection (SASI) extracts structures from an off-the-shelf facial prior while filtering out its intrinsic photometric biases, seamlessly harmonizing identity features with physical constraints. Furthermore, we construct WildDark-Face, a real-world benchmark of 700 low-light facial images with complex degradations. Extensive experiments demonstrate that PASDiff significantly outperforms existing methods, achieving a superior balance among natural illumination, color recovery, and identity consistency. Code and dataset will be available at https://github.com/IVIPLab/PASDiff.

Recent depth foundation models trained on perspective imagery achieve strong performance, yet generalize poorly to 360$^\circ$ images due to the substantial geometric discrepancy between perspective and panoramic domains. Moreover, fully fine-tuning these models typically requires large amounts of panoramic data. To address this issue, we propose RePer-360, a distortion-aware self-modulation framework for monocular panoramic depth estimation that adapts depth foundation models while preserving powerful pretrained perspective priors. Specifically, we design a lightweight geometry-aligned guidance module to derive a modulation signal from two complementary projections (i.e., ERP and CP) and use it to guide the model toward the panoramic domain without overwriting its pretrained perspective knowledge. We further introduce a Self-Conditioned AdaLN-Zero mechanism that produces pixel-wise scaling factors to reduce the feature distribution gap between the perspective and panoramic domains. In addition, a cubemap-domain consistency loss further improves training stability and cross-projection alignment. By shifting the focus from complementary-projection fusion to panoramic domain adaptation under preserved pretrained perspective priors, RePer-360 surpasses standard fine-tuning methods while using only 1% of the training data. Under the same in-domain training setting, it further achieves an approximately 20% improvement in RMSE. The code is available at https://github.com/munimo/RePer360.

Accurate longitudinal analysis of brain MRI is often hindered by evolving lesions, which bias automated neuroimaging pipelines. While deep generative models have shown promise in inpainting these lesions, most existing methods operate cross-sectionally or lack 3D anatomical continuity. We present a novel pseudo-3D longitudinal inpainting framework based on Denoising Diffusion Probabilistic Models (DDPM). Our approach utilizes multi-channel conditioning to incorporate longitudinal context from distinct visits (t_1, t_2) and extends Region-Aware Diffusion (RAD) to the medical domain, focusing the generative process on pathological regions without altering surrounding healthy tissue. We evaluated our model against state-of-the-art baselines on longitudinal brain MRI from 93 patients. Our model significantly outperforms the leading baseline (FastSurfer-LIT) in terms of perceptual fidelity, reducing the Learned Perceptual Image Patch Similarity (LPIPS) distance from 0.07 to 0.03 while effectively eliminating inter-slice discontinuities. Furthermore, our model demonstrates high longitudinal stability with a Temporal Fidelity Index of 1.024, closely approaching the ideal value of 1.0 and substantially narrowing the gap compared to LIT's TFI of 1.22. Notably, the RAD mechanism provides a substantial gain in efficiency; our framework achieves an average processing time of 2.53 min per volume, representing approximately 10x speedup over the 24.30 min required by LIT. By leveraging longitudinal priors and region-specific denoising, our framework provides a highly reliable and efficient preprocessing step for the study of progressive neurodegenerative diseases. A derivative dataset consisting of 93 pre-processed scans used for testing will be available upon request after acceptance. Code will be released upon acceptance.

Leveraging the priors of 2D diffusion models for 3D editing has emerged as a promising paradigm. However, multi-view consistency remains challenging in edited results, and the extreme scarcity of paired 3D-consistent editing data makes supervised fine-tuning (SFT) impractical, despite its effectiveness for editing tasks. In this paper, we observe that, while generating multi-view consistent 3D content is highly challenging, verifying 3D consistency is tractable, naturally positioning reinforcement learning (RL) as a feasible solution. Motivated by this, we propose RL3DEdit, a single-pass framework driven by RL optimization with novel rewards derived from the 3D foundation model, VGGT. Specifically, we leverage VGGT's robust priors learned from massive real-world data, feed the edited images into it, and utilize the output confidence maps and pose estimation errors as reward signals, effectively anchoring the 2D editing priors onto a 3D-consistent manifold via RL. Extensive experiments demonstrate that RL3DEdit achieves stable multi-view consistency and outperforms state-of-the-art methods in editing quality with high efficiency. To promote the development of 3D editing, we will release the code and model.

Medical diagnosis requires the effective synthesis of visual manifestations and clinical metadata. However, existing methods often treat metadata as isolated tags, failing to exploit the rich semantic knowledge embedded in clinical descriptions. We propose PRIMA (Pre-training with Risk-integrated Image-Metadata Alignment), a framework that integrates domain-specific knowledge into multi-modal representation learning. We first curate an expert corpus of risk--disease correlations via Retrieval-Augmented Generation (RAG) to refine Clinical ModernBERT, embedding diagnostic priors into the text encoder. To bridge the modality gap, we introduce a dual-encoder pre-training strategy utilizing DINOv3 and our refined Clinical ModernBERT, optimized by a suite of four complementary loss functions. These losses are designed to capture multi-granular semantic alignment and handle the ambiguity of clinical correlations through soft labels. Finally, we leverage Qwen3 to fuse these aligned features for precise disease classification. Extensive experiments demonstrate that PRIMA effectively harmonizes pixel-level features with abstract clinical expertise, consistently outperforming other state-of-the-art methods. Notably, our framework achieves strong performance without requiring massive data collection or exhaustive computational resources. Our code will is available at https://github.com/yqwang01/PRIMA.

We theoretically justify the recent empirical finding of [Teh et al., 2025] that a transformer pretrained on synthetically generated data achieves strong performance on empirical Bayes (EB) problems. We take an indirect approach to this question: rather than analyzing the model architecture or training dynamics, we ask why a pretrained Bayes estimator, trained under a prespecified training distribution, can adapt to arbitrary test distributions. Focusing on Poisson EB problems, we identify the existence of universal priors such that training under these priors yields a near-optimal regret bound of $\widetilde{O}(\frac{1}{n})$ uniformly over all test distributions. Our analysis leverages the classical phenomenon of posterior contraction in Bayesian statistics, showing that the pretrained transformer adapts to unknown test distributions precisely through posterior contraction. This perspective also explains the phenomenon of length generalization, in which the test sequence length exceeds the training length, as the model performs Bayesian inference using a generalized posterior.

Video-Language Models (VidLMs) achieve strong benchmark scores, yet these scores often hide whether models use the video at all. We show that VidLM failures follow two pathways: some visual signals are never reliably encoded, while others are encoded but overridden by model priors. We introduce REVEAL, a diagnostic stress-test benchmark for quantifying when and why VidLMs under-use visual evidence. REVEAL contains five controlled probes: camera-motion sensitivity, cross-frame integration, video sycophancy, language-only shortcuts, and temporal expectation bias. Together, they test whether models encode basic video signals, combine evidence across frames, and preserve visual evidence against user assertions, language cues, and learned event expectations. Across 12 VidLMs we find systematic failures along both pathways, with most models falling below chance on the binary and six-way probes that humans solve at 78--100% accuracy. Under assertive prompts, a model's output distribution becomes nearly invariant to whether it is shown a real video or random noise, making visual evidence effectively causally inert. We further carry out mechanistic probes to identify where these failures arise in the model pipeline and why visual evidence is lost. REVEAL provides a scalable, human-verified framework for moving beyond aggregate scores toward structured, reproducible evaluation of multimodal reliability.

Large language models (LLMs) exhibit strong general-purpose reasoning capabilities, yet they frequently hallucinate when used as world models (WMs), where strict compliance with deterministic transition rules--particularly in corner cases--is essential. In contrast, Symbolic WMs provide logical consistency but lack semantic expressivity. To bridge this gap, we propose Neuro-Symbolic Synergy (NeSyS), a framework that integrates the probabilistic semantic priors of LLMs with executable symbolic rules to achieve both expressivity and robustness. NeSyS alternates training between the two models using trajectories inadequately explained by the other. Unlike rule-based prompting, the symbolic WM contributes candidate-level scores through log-linear reranking, without requiring the LLM to interpret rule text. Rule-guided sampling prioritizes transitions that are weakly covered by symbolic rules, using 35--60% of the training pairs while outperforming full-data supervised fine-tuning in five of six settings. Experiments on ScienceWorld, WebShop, and PlanCraft demonstrate consistent gains in WM prediction accuracy and data efficiency; one-step lookahead on open-ended WebShop also improves agent reward. Our models, rules, and code are available at https://github.com/tianyi-lab/NeSyS.

Map-based LiDAR pose tracking is essential for long-term autonomous operation, where onboard map priors need be compact for scalable storage and fast retrieval, while online observations are often partial, repetitive, and heavily occluded. We propose Graph-Loc, a graph-based localization framework that tracks the platform pose against compact structural map priors represented as a lightweight point-line graph. Such priors can be constructed from heterogeneous sources commonly available in practice, including polygon outlines vectorized from occupancy/grid maps and CAD/model/floor-plan layouts. For each incoming LiDAR scan, Graph-Loc extracts sparse point and line primitives to form an observation graph, retrieves a pose-conditioned visible subgraph via LiDAR ray simulation, and performs scan-to-map association through unbalanced optimal transport with a local graph-context regularizer. The unbalanced formulation relaxes mass conservation, improving robustness to missing, spurious, and fragmented structures under occlusion. To enhance stability in low-observability segments, we estimate information anisotropy from the refinement normal matrix and defer updates along weakly constrained directions until sufficient constraints reappear. Experiments on public benchmarks, controlled stress tests, and real-world deployments demonstrate accurate and stable tracking with KB-level priors from heterogeneous map sources, including under geometrically degenerate and sustained occlusion and in the presence of gradual scene changes.

Current audio foundation models typically rely on rigid, task-specific supervision, addressing isolated factors of audio rather than the whole. In contrast, human intelligence processes audio holistically, seamlessly bridging physical signals with abstract cognitive concepts to execute complex tasks. Grounded in this philosophy, we introduce Bagpiper, an 8B audio foundation model that interprets physical audio via rich captions, i.e., comprehensive natural language descriptions that encapsulate the critical cognitive concepts inherent in the signal (e.g., transcription, audio events). By pre-training on a massive corpus of 600B tokens, the model establishes a robust bidirectional mapping between raw audio and this high-level conceptual space. During fine-tuning, Bagpiper adopts a caption-then-process workflow, simulating an intermediate cognitive reasoning step to solve diverse tasks without task-specific priors. Experimentally, Bagpiper outperforms Qwen-2.5-Omni on MMAU and AIRBench for audio understanding and surpasses CosyVoice3 and TangoFlux in generation quality, capable of synthesizing arbitrary compositions of speech, music, and sound effects. To the best of our knowledge, Bagpiper is among the first works that achieve unified understanding generation for general audio. Model, data, and code are available at Bagpiper Home Page.

Reliable models should not only predict correctly, but also justify decisions with acceptable evidence. Yet conventional supervised learning typically provides only class-level labels, allowing models to achieve high accuracy through shortcut correlations rather than the intended evidence. Human priors can help constrain such behavior, but aligning models to these priors remains challenging because learned representations often diverge from human perception. To address this challenge, we propose an attribution-based human prior alignment method. We encode human priors as input regions that the model is expected to rely on (e.g., bounding boxes), and leverage a highly faithful subset-selection-based attribution approach to expose the model's decision evidence during training. When the attribution region deviates substantially from the prior regions, we penalize reliance on off-prior evidence, encouraging the model to shift its attribution toward the intended regions. This is achieved through a training objective that imposes attribution constraints induced by the human prior. We validate our method on both image classification and click decision tasks in MLLM-based GUI agent models. Across conventional classification and autoregressive generation settings, human prior alignment consistently improves task accuracy while also enhancing the model's decision reasonability.

Time series forecasting has witnessed significant progress with deep learning. While prevailing approaches enhance forecasting performance by modifying architectures or introducing novel enhancement strategies, they often fail to dynamically disentangle and leverage the complex, intertwined temporal patterns inherent in time series, thus resulting in the learning of static, averaged representations that lack context-aware capabilities. To address this, we propose the Dual-Prototype Adaptive Disentanglement framework (DPAD), a model-agnostic auxiliary method that equips forecasting models with the ability of pattern disentanglement and context-aware adaptation. Specifically, we construct a Dynamic Dual-Prototype bank (DDP), comprising a common pattern bank with strong temporal priors to capture prevailing trend or seasonal patterns, and a rare pattern bank dynamically memorizing critical yet infrequent events, and then an Dual-Path Context-aware routing (DPC) mechanism is proposed to enhance outputs with selectively retrieved context-specific pattern representations from the DDP. Additionally, we introduce a Disentanglement-Guided Loss (DGLoss) to ensure that each prototype bank specializes in its designated role while maintaining comprehensive coverage. Comprehensive experiments demonstrate that DPAD consistently improves forecasting performance and reliability of state-of-the-art models across diverse real-world benchmarks.

Single-photon avalanche diodes (SPADs) record light as a discrete stream of individual detections. The signal is stochastic. Its statistical structure depends on the sensor's operation mode: binary detection in fixed bins, timestamped detection in fixed bins, or free-running timestamped detection. We derive the likelihood score function for each of these three passive modes. From this single object, stem both fundamental limits of recovery (Cramer-Rao bounds) and practical recovery algorithms based on diffusion posterior sampling. The paper further generalizes fundamental limits to Bayesian Cramer-Rao lower bounds. This generalization makes use of a learned approximation of the score function of signal priors. In prior art, analyses and diffusion-based reconstruction for SPAD data have treated individual modes in isolation. Our unified treatment shows a qualitative high-flux gap between modes: binary counts saturate exponentially, while timestamped modes degrade only linearly. We further extend diffusion posterior sampling, previously restricted to binary SPAD data, to a full timestamped case using the suitable score function. We demonstrate experimentally that matching the score to the operation mode is beneficial for high-fidelity reconstruction. By tying the recovery bounds and diffusion to the score function, this work aims to establish a common foundation for both asking what is recoverable in single-photon sensing, and building methods that approach the bound.

We prove that Thompson sampling exhibits $\tilde{O}(σd \sqrt{T} + d r \sqrt{\mathrm{Tr}(Σ_0)})$ Bayesian regret in the linear-Gaussian bandit with a $\mathcal{N}(μ_0, Σ_0)$ prior distribution on the coefficients, where $d$ is the dimension, $T$ is the time horizon, $r$ is the maximum $\ell_2$ norm of the actions, and $σ^2$ is the noise variance. In contrast to existing regret bounds, this shows that to within logarithmic factors, the prior-dependent burn-in'' term $d r \sqrt{\mathrm{Tr}(Σ_0)}$ decouples additively from the minimax (long run) regret $σd \sqrt{T}$. Previous regret bounds exhibit a multiplicative dependence on these terms. We establish these results via a new elliptical potential'' lemma, and also provide a lower bound indicating that the burn-in term is unavoidable.

Vision-language-action (VLA) models provide strong action priors for robotic manipulation, but their reactive behavior can fail under distribution shift and long-horizon task structure. Recent VLA-guided planning methods improve execution by using pretrained policies to guide tree search, yet node selection still depends heavily on policy priors and visit-count exploration. Consequently, when the policy favors poor actions, the planner lacks a learned value signal to correct this bias. Prior work has shown that VLA representations encode rollout success and failure information, suggesting that they may also support value estimation during planning. We introduce Value-Guided Vision-Language-Action Planning and Search (V-VLAPS), which augments VLA-guided planning with a lightweight value head trained on offline VLA rollouts to predict Monte Carlo returns. These predictions guide Monte Carlo Tree Search in simulation toward higher-value branches. Across five LIBERO suites, V-VLAPS matches value-free planning baseline at the default search budget in aggregate, and analysis shows that many hard failures are root-level timeouts where predicted values are weakly separated. With a larger search budget, V-VLAPS improves over the baseline in all task suites with +6 percentage points on LIBERO-Object and +4 percentage points on LIBERO-10. Our results suggest that VLA representations can support not only failure prediction, but also value-guided planning when search reaches branches where value-based ranking matters.

Recent advances in Gaussian Splatting-based inverse rendering extend Gaussian primitives with shading parameters and physically grounded light transport, enabling high-quality material recovery from dense multi-view captures. However, the accuracy of these methods degrades under sparse-view settings, where limited observations lead to severe ambiguity between geometry, reflectance, and lighting. We introduce GAINS (Gaussian-based Inverse rendering from Sparse multi-view captures), a two-stage inverse rendering framework that leverages foundation models as priors to stabilize geometry and material estimation. The core technical contribution of this paper is an inverse rendering framework that unifies foundation model priors with physically-based representations in an optimization scheme. GAINS first refines geometry using monocular depth, normal, and diffusion priors, and then employs segmentation, intrinsic image decomposition (IID), and diffusion priors to regularize material recovery. Extensive experiments on synthetic and real-world datasets show that GAINS significantly improves material parameter accuracy, relighting quality, and novel-view synthesis compared to state-of-the-art Gaussian-based inverse rendering methods. While GAINS outperforms and remains competitive across a wide range of objects captured with 4 to 32 cameras, the improvement is particularly pronounced under sparse-view settings, where ambiguity is high and learning-based priors become especially beneficial. Project page: https://patrickbail.github.io/gains/

Generating complete 3D objects under partial occlusions (i.e., amodal scenarios) is a practically important yet challenging problem, as large portions of object geometry are unobserved in real-world scenarios. Existing approaches either operate directly in 3D, which ensures geometric consistency but often lacks generative expressiveness, or rely on 2D amodal completion, which provides strong appearance priors but does not guarantee reliable 3D structure. This raises a key question: how can we achieve both generative plausibility and geometric coherence in amodal 3D modeling? To answer this question, we introduce GENA3D (GENarative Amodal 3D), a framework that integrates learned 2D generative priors with explicit 3D geometric reasoning within a conditional 3D generation paradigm. The 2D priors enable the model to plausibly infer diverse occluded content, while the 3D representation enforces multi-view consistency and spatial validity. Our design incorporates a novel View-Wise Cross-Attention for multi-view alignment and a Stereo-Conditioned Cross-Attention to anchor generative predictions in 3D relationships. By combining generative imagination with structural constraints, GENA3D generates complete and coherent 3D objects from limited observations without sacrificing geometric fidelity. Experiments demonstrate that our method outperforms existing approaches in both synthetic and real-world amodal scenarios, highlighting the effectiveness of bridging 2D priors and 3D coherence in generating plausible and geometrically consistent 3D structures in complex environments.

Monocular 3D human pose estimation remains a fundamentally ill-posed inverse problem due to the inherent depth ambiguity in 2D-to-3D lifting. While contemporary video-based methods leverage temporal context to enhance spatial reasoning, they operate under a critical paradigm limitation: processing each sequence in isolation, thereby failing to exploit the strong structural regularities and repetitive motion patterns that pervade human movement across sequences. This work introduces the Pattern Reuse Graph Convolutional Network (PRGCN), a novel framework that formalizes pose estimation as a problem of pattern retrieval and adaptation. At its core, PRGCN features a graph memory bank that learns and stores a compact set of pose prototypes, encoded as relational graphs, which are dynamically retrieved via an attention mechanism to provide structured priors. These priors are adaptively fused with hard-coded anatomical constraints through a memory-driven graph convolution, ensuring geometrical plausibility. To underpin this retrieval process with robust spatiotemporal features, we design a dual-stream hybrid architecture that synergistically combines the linear-complexity, local temporal modeling of Mamba-based state-space models with the global relational capacity of self-attention. Extensive evaluations on Human3.6M and MPI-INF-3DHP benchmarks demonstrate that PRGCN establishes a new state-of-the-art, achieving an MPJPE of 37.1mm and 13.4mm, respectively, while exhibiting enhanced cross-domain generalization capability. Our work posits that the long-overlooked mechanism of cross-sequence pattern reuse is pivotal to advancing the field, shifting the paradigm from per-sequence optimization towards cumulative knowledge learning.

Tabular prediction has long been dominated by gradient-boosted decision trees and specialized deep tabular models, while large language models (LLMs) remain difficult to make competitive despite their cross-task adaptability and transparent reasoning traces. We address this gap by incorporating tabular structural priors into LLM post-training. Specifically, we propose Permutation Relative Policy Optimization (PRPO), which operationalizes column-permutation invariance through label-preserving column permutations and two-level advantage estimation. This design converts sparse outcome rewards into denser and more stable optimization signals. Extensive experiments on 139 OpenML datasets show that our 8B model reaches a genuinely competitive regime against strong specialized tabular baselines. It achieves strong fully supervised performance, dominates zero-shot settings, and performs on par with 32-shot strong baselines. Moreover, it substantially outperforms much larger general-purpose and reasoning LLMs, including up to a 53.17% improvement over DeepSeek-R1 (685B). These results show that structural-prior RL post-training is an effective route for making LLMs competitive in tabular prediction.

We study program-learning methods that are efficient in both samples and computation. Classical learning theory suggests that when the target admits a short program description, for example a short piece of ``Python code'', it can be learned from few examples by ERM over the program class. However, this approach relies on enumerating candidate programs, which is typically exponential in the description length; gradient-based training avoids this explicit search but, for some families of short programs, can require exponentially many samples to succeed. We propose \textsc{LLM-PV}, a propose-and-verify recipe that enables ERM-style selection over a discrete program class without exhaustive enumeration: a pretrained LLM induces a proposal distribution over candidate programs, each proposal is executed and scored on a held-out validation set, and the best program is selected, with no gradient updates or validation feedback used to adapt the sampling distribution. Across algorithmic tasks including parity variants, pattern matching, and primality testing, \textsc{LLM-PV} often recovers the exact underlying rule from a small labeled set and generalizes far beyond the training sequence lengths, while SGD-trained transformers, fine-tuning, in-context learning, and classical ML baselines can fit the training data yet fail to generalize reliably. Together, these results suggest that pretrained LLM priors can serve as effective search biases for ERM, narrowing the gap between statistical and computational efficiency.

In this work, we establish the sufficient conditions under which nonlinear Canonical Correlation Analysis (CCA) recovers ground-truth latent factors up to an affine transformation. By transporting the analysis from the observation space to the source space, we extend classical statistical results on orthogonal polynomial expansions of bivariate distributions to representation learning, proving affine identifiability under specific distributional priors. We formally demonstrate that whitening is strictly necessary to ensure the boundedness and well-conditioning of the learned mappings. Furthermore, we bridge the gap between theory and practice by proving that ridge-regularized empirical CCA converges to its population counterpart in the finite-sample regime. Finally, our findings provide a rigorous theoretical foundation explaining the empirical success of recent correlation-based non-contrastive learning methods. Experiments on synthetic and rendered image datasets, alongside systematic ablations, validate the predicted recovery behavior and illustrate the failure modes that arise when the assumptions are violated.

We seek to recover an unknown signal from nonlinear amplitude-only measurements, a challenging inverse problem. Strong theoretical guarantees have been established for idealized random measurements, defining the sampling ratio required for signal recovery. However, these results neglect signal priors, which can fundamentally shift these limits, potentially enabling reconstruction with far fewer measurements and simpler models. We evaluate a variety of image priors in the context of severe undersampling with physically-grounded random measurement models. Our results show that these priors enable accurate recovery well below the weak recovery limit, the theoretical threshold required for recovery better than a random guess.

Maximum A Posteriori (MAP) estimation is a cornerstone framework for blind inverse problems, where an image and a forward operator are jointly estimated as the maximizers of a posterior distribution. In applications such as blind deblurring, this principle is used to recover sharp images from degraded observations. In this paper, we analyze the recovery guarantees of MAP-based methods by adopting a \emph{Morse--Bott framework}. We model the image potential as a Morse--Bott function, where natural images are modeled as residing locally on a critical submanifold. This means that while the potential is locally flat along the natural'' directions of the image manifold, it is strictly convex in the directions normal to it. We demonstrate that this Morse--Bott hypothesis aligns with the structural properties of state-of-the-art learned priors, a finding we validate through an experimental analysis of the potential landscape and its Hessian spectrum. Our theoretical results show that, in a neighborhood of the ground-truth image and operator, the posterior admits local minimizers that are stable both with respect to initialization (gradient descents converge to the same minimizer) and to small perturbations of the data (solutions vary smoothly with the observations). This local stability potentially provides a theoretical justification for the empirical success of well designed gradient-based optimization in these settings. However, we also demonstrate that this local stability is a \textbf{local} property: the blurry trap'', well-known for sparse priors in blind deconvolution, persists even with state-of-the-art learned priors. Our findings demonstrate that the failure of MAP in blind deconvolution is not a limitation of prior quality, but an intrinsic characteristic of the landscape. We conclude that successful recovery depends on strategic initialization around favorable local minima.

3D affordance grounding aims to understand how diverse objects can be manipulated, making it a cornerstone of embodied interaction. However, prior works struggle to generalize to out-of-distribution, open-world scenarios, leaving a critical gap between limited dataset performance and real-world application needs. Inspired by the saying: \textit{\textbf{``What I can not create, I do not understand''}}, we find generative models can generate semantically valid HOI images, which indicates inherent encoding of affordance concepts. Building on this insight, we propose DAG, the first innovative diffusion-based 3D affordance grounding framework that extracts general affordance knowledge from text-to-image diffusion models for 3D affordance prediction. Specifically, we extract the affordance priors from a diffusion model to encode HOI priors, and design an affordance block with a multi-source affordance decoder for dense 3D affordance prediction. Extensive experiments show that DAG consistently outperforms state-of-the-art methods and exhibits strong open-world generalization, even in the challenging one-shot setting. The code of our method is released on \textcolor{blue}{\textit{https://github.com/hq-King/DAG}}.

In many real-world applications of regression, conditional probability estimation, and uncertainty quantification, exploiting symmetries rooted in physics or geometry can dramatically improve generalization and sample efficiency. While geometric deep learning has made empirical advances by incorporating symmetry and geometry priors, less attention has been given to statistical learning guarantees. In this paper, we introduce an equivariant representation learning framework that simultaneously addresses regression, conditional probability estimation, and uncertainty quantification while providing first-of-its-kind non-asymptotic statistical learning guarantees. Grounded in operator and group representation theory, our framework approximates the spectral decomposition of the conditional expectation operator, building representations that are both equivariant and disentangled along independent symmetry quotient groups. Empirical evaluations on synthetic datasets and real-world robotics applications confirm the potential of our approach, matching or outperforming existing equivariant baselines in regression while providing well-calibrated uncertainty estimates.

In this work, we evaluate the potential of Large Language Models (LLMs) in building Bayesian Networks (BNs) by approximating domain expert priors. LLMs have demonstrated potential as factual knowledge bases; however, their capability to generate probabilistic knowledge about real-world events remains understudied. We explore utilizing the probabilistic knowledge inherent in LLMs to derive probability estimates for statements regarding events and their relationships within a BN. Using LLMs in this context allows for the parameterization of BNs, enabling probabilistic modeling within specific domains. Our experiments on eighty publicly available Bayesian Networks, from healthcare to finance, demonstrate that querying LLMs about the conditional probabilities of events provides meaningful results when compared to baselines, including random and uniform distributions, as well as approaches based on next-token generation probabilities. We explore how these LLM-derived distributions can serve as expert priors to refine distributions extracted from data, especially when data is scarce. Overall, this work introduces a promising strategy for automatically constructing Bayesian Networks by combining probabilistic knowledge extracted from LLMs with real-world data. Additionally, we establish the first comprehensive baseline for assessing LLM performance in extracting probabilistic knowledge.

The advances in Vision-Language models (VLMs) offer exciting opportunities for robotic applications involving image geo-localization - the problem of identifying the geo-coordinates of a place based on visual data only. In robotics, such capabilities are particularly relevant to the global re-localization stage of the kidnapped robot problem, where a robot must recover its pose without prior knowledge of its location. Recent work has focused on using a VLM as embedding extractor for geo-localization. However, the most sophisticated VLMs may only be available as black boxes that are accessible through an API, and come with a number of limitations: there is no access to training data, model features and gradients; retraining is not possible; and the number of predictions may be limited by the API. The potential of state-of-the-art VLMs as a stand-alone, zero-shot geo-localization systems at planet scale using a single text-based prompt is largely unexplored. To bridge this gap, this paper undertakes the first systematic study, to the best of our knowledge, to investigate state-of-the-art generative VLMs as stand-alone, zero-shot geo-localization systems in a black-box setting with realistic constraints. We consider three main scenarios for this thorough investigation: a) fixed text-based prompt; b) semantically-equivalent text-based prompts; and c) semantically-equivalent query images. Beyond standard accuracy, we introduce model consistency as a metric to account for the auto-regressive and probabilistic nature of generative VLMs. Our findings reveal that while VLMs demonstrate strong coarse-level localization and navigation priors, fine-grained localization degrades significantly under realistic variations, highlighting reliability challenges for deploying generative VLMs in robust, open-world robotic navigation systems.

In this paper, we propose MoDGS, a new pipeline to render novel views of dy namic scenes from a casually captured monocular video. Previous monocular dynamic NeRF or Gaussian Splatting methods strongly rely on the rapid move ment of input cameras to construct multiview consistency but struggle to recon struct dynamic scenes on casually captured input videos whose cameras are either static or move slowly. To address this challenging task, MoDGS adopts recent single-view depth estimation methods to guide the learning of the dynamic scene. Then, a novel 3D-aware initialization method is proposed to learn a reasonable deformation field and a new robust depth loss is proposed to guide the learning of dynamic scene geometry. Comprehensive experiments demonstrate that MoDGS is able to render high-quality novel view images of dynamic scenes from just a casually captured monocular video, which outperforms state-of-the-art meth ods by a significant margin. The code is publicly available now.

A key challenge of real-world image super-resolution (SR) is to recover the missing details in low-resolution (LR) images with complex unknown degradations (e.g., downsampling, noise and compression). Most previous works restore such missing details in the image space. To cope with the high diversity of natural images, they either rely on the unstable GANs that are difficult to train and prone to artifacts, or resort to explicit references from high-resolution (HR) images that are usually unavailable. In this work, we propose Feature Matching SR (FeMaSR), which restores realistic HR images in a much more compact feature space. Unlike image-space methods, our FeMaSR restores HR images by matching distorted LR image features to their distortion-free HR counterparts in our pretrained HR priors, and decoding the matched features to obtain realistic HR images. Specifically, our HR priors contain a discrete feature codebook and its associated decoder, which are pretrained on HR images with a Vector Quantized Generative Adversarial Network (VQGAN). Notably, we incorporate a novel semantic regularization in VQGAN to improve the quality of reconstructed images. For the feature matching, we first extract LR features with an LR encoder consisting of several Swin Transformer blocks and then follow a simple nearest neighbour strategy to match them with the pretrained codebook. In particular, we equip the LR encoder with residual shortcut connections to the decoder, which is critical to the optimization of feature matching loss and also helps to complement the possible feature matching errors. Experimental results show that our approach produces more realistic HR images than previous methods. Codes are released at https://github.com/chaofengc/FeMaSR.

Inverse problems are important mathematical problems that seek to recover model parameters from noisy data. Since inverse problems are often ill-posed, they require regularization or incorporation of prior information about the underlying model or unknown variables. Proximal operators, ubiquitous in nonsmooth optimization, are central to this because they encode priors and yield efficient iterative algorithms. They have also recently become key to modern machine learning methods, e.g., plug-and-play methods with learned denoisers and deep neural architectures for learning priors of proximal operators. The latter was developed partly due to recent work characterizing proximal operators of nonconvex priors as subdifferentials of convex potentials. In this work, we propose to leverage connections between proximal operators and Hamilton--Jacobi partial differential equations (HJ PDEs) to develop deep learning architectures for learning the prior. In contrast to other existing methods, we learn the prior directly without recourse to inverting the prior after training. We present numerical results in dimensions up to $64$, where the recovered prior is evaluated in a single forward pass.

Post-training quantization (PTQ) is a practical way to reduce the memory footprint of large language models, but low-bit quantization is sensitive to mismatches between the quantization codebook and the empirical weight/activation distributions. We revisit Benford-like leading-digit statistics as a lightweight diagnostic of scale-broad behavior in transformer tensors. Across several model families, we observe a consistent functional dichotomy: transformational nn.Linear weights tend to be Benford-like, whereas LayerNorm parameters systematically deviate. Motivated by this observation, we propose BenQ, a data-free PTQ codebook that uses a simple log-spaced grid as a proxy for scale-broad distributions and applies it selectively to transformational layers while keeping stability-critical parameters in higher precision. In 4-bit group-wise PTQ, BenQ consistently improves over uniform RTN and trades wins with NF4 across architectures and tasks, while remaining substantially simpler than optimization-based methods. We additionally report dynamic activation quantization as an exploratory stress test: the results show that log-spaced grids can reduce RTN failures in some families, but also reveal that outlier handling remains essential for reliable low-bit activation PTQ. Code is available at https://github.com/ufopcsilab/benford-quant.

External text can override conflicting image evidence in multimodal large language models, a failure we call multimodal contextual sycophancy. We introduce a 998-case diagnostic that independently varies visual evidence, commonsense priors, and external text, and probe when this failure arises by moving the information boundary around a context-blind visual witness. On abnormal images paired with Gemini-generated false text, GPT-5.1 scores 7.9% under joint conditioning, 49.7% when the context-blind witness report is scored directly, 63.7% under a matched two-call witness-arbiter pipeline that exposes the witness to the text, and 84.2% under System-2 Visual Arbitration (S2VA), which withholds the text from the witness. Across six models, S2VA improves over the direct witness report by 19.7 to 44.1 points, with all paired 95% confidence intervals excluding zero. The best information boundary is not uniform: textual context scaffolds some models, and a GPT-4o-regenerated subset changes the relative ordering of joint conditioning, Witness-Only, and S2VA. Contextual sycophancy is therefore sensitive to when text is introduced, as well as to the model and context source.