Projection

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12 papers in the last four weeks, up 100% on the four weeks before. 0.1% of all new papers.

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Latest papers 89

May 24, 2026cs.LG

Directional Alignment Mitigates Reward Hacking in Reinforcement Learning for Language Models

Reward hacking arises when a model improves a proxy reward by exploiting shortcuts rather than solving the intended task. We study this failure mode through the geometry of reinforcement learning updates in language models and argue that hacking emerges when optimization drifts away from a stable low-dimensional learning trajectory. We analyze this drift through dominant singular directions of parameter updates and show that reward-hacking runs exhibit substantially larger directional change than clean runs. Motivated by this observation, we introduce trusted-direction projection, which constrains gradients to remain within a clean reference subspace. Across reward-hacking experiments on mathematical reasoning, the proposed approach delays shortcut exploitation and better preserves task performance.

Wenlong Deng, Jiaji Huang, Kaan Ozkara +4

University of British Columbia · Vector Institute · Amazon

Reward Gradients Exploitation Projection

May 24, 2026math.OC

Lifted Schrödinger Bridges for Gaussian Mixture Endpoints: Projection Gaps and Path-Space Obstructions

We study stochastic density control between Gaussian-mixture endpoint distributions under Brownian prior dynamics. Since the direct Schrödinger bridge between Gaussian mixtures is generally not available in closed form, we introduce a lifted path-space construction in which each trajectory is augmented with a source--target component label. Consequently, the problem decomposes into Gaussian component-to-component Schrödinger bridges with explicit marginal, drift, and cost formulas, while the mixture-level assignment reduces to a finite-dimensional entropic coupling problem with a Sinkhorn scaling form. We then analyze the projection obtained by discarding or forgetting the label. By construction, the projected law satisfies the original Gaussian-mixture endpoint constraints, but its relative entropy generally differs from the lifted relative entropy by a nonnegative conditional label-information gap. This gap reveals a path-space obstruction: the lifted optimizer cannot, in general, be identified with the direct unlabeled Schrödinger bridge after projection. We also derive the posterior-averaged Markov drift associated with the projected marginal flow, prove a kinetic-energy upper bound, and identify a common path-potential condition under which the projection gap vanishes. Several numerical illustrations showing density and shape control are recorded for a self-contained exposition.

Siddhartha Ganguly, George Rapakoulias, Panagiotis Tsiotras

S. Ganguly, G. Rapakoulias, and P. Tsiotras are with Daniel Guggenheim School of Aerospace, Georgia Institute of Technology, ½ Atlanta, USA.

Schrödinger Bridges Gaussian Mixture Models Projection Scale Gap

May 20, 2026cs.CV

Soft Tuy-Completeness for Robust Projection Selection in Cone-Beam CT

This work introduces a continuous soft near-orthogonality score and a resolution-aware saturated coverage objective for projection selection in region-of-interest focused cone-beam CT, grounded in Tuy's completeness theory. Replacing the binary hit-or-miss model of classical Tuy completeness with a graded, differentiable formulation preserves a direct link to achievable feature sizes while enabling both efficient approximate and exact optimisation. We establish that the underlying discrete decision problems are NP-complete via polynomial-time reductions from Set Cover, motivating a submodular greedy algorithm with proven

(1-1/\mathrm{e})

approximation guarantees and a mixed-integer linear program (MILP) that provides certified optimality bounds. The MILP serves as a quality certificate for the greedy solution rather than a competing optimiser. The primary empirical finding confirms this relationship: across a systematic benchmark spanning six target regions, multiple projection budgets, and four controlled occlusion conditions, the pooled median greedy-to-MILP objective ratio was 0.998, with a substantial fraction of cases certified globally optimal. A binary formulation is included as a diagnostic baseline; it strengthens hard directional completeness but is weaker on the continuous coverage scale. We additionally introduce Effective Spatial Resolution (ESR), a physically interpretable trajectory-level diagnostic that maps directional sampling gaps to achievable feature sizes. ESR correlates reliably with matched reconstruction quality across projection budgets and occlusion levels, providing a practical bridge between the selection stage and the image domain without requiring reconstruction.

Linda-Sophie Schneider, Andreas Maier

Pattern Recognition Lab, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany

Cone-Beam Computed Tomography Projection Adaptive Thresholding Completion

May 18, 2026stat.ML

On Stability and Decomposition of Sample Quantiles under Heavy-Tailed Distributions

We study sample quantiles of distributions indexed by estimated parameters, with a on Value-at-Risk related to linear projections of financial returns that whose underlying probability law is heavy-tailed. In this setting, the projection direction and the empirical quantile threshold are estimated from the data, so the standard Bahadur representation under a fixed distribution does not separate the distinct sources of instability. A canonical starting point is Bahadur's representation, which expresses the sample quantile through the empirical distribution function plus a remainder term \cite{bahadur1966}. Empirical-process theory provides a usable scaffolding through the mechanics of half-spaces, symmetric differences, and Glivenko--Cantelli uniform convergence. They yield stability bounds, but absorb changes in projection direction and changes in quantile threshold into a single symmetric-difference measure. Interestingly, a global uniform-convergence requirement is imposed on what is intrinsically a local quantile-stability problem. This paper introduces a Q-Q orthogonality formulation for separating projection-direction and quantile-threshold effects. The object of interest is the difference between the empirical quantile computed using the estimated projection direction and the population quantile computed at the reference projection direction. We decompose this difference into three terms,

\hat q_α(\hat w)-q_α(w_0)=D_1+D_2+D_3

. Here,

D_1

measures the population quantile movement induced by perturbing the projection direction,

D_2

measures the empirical quantile fluctuation with the projection direction held fixed, and

D_3

is the Bahadur-type remainder.

Choudur Lakshminarayan

School of Business, Stevens Institute of Technology

Quantile Regression Long-Tailed Distribution Conditional-Value-At-Risk Fluctuation-Dissipation Theorem Distributions Projection+1

May 15, 2026cs.CV

On RGB-TIR Stereo Calibration under Extreme Resolution Asymmetry

Accurate geometric calibration of RGB-thermal infrared (TIR) stereo camera systems is essential for multimodal building envelope analysis, yet remains challenging when low-cost thermal sensors with very low spatial resolution are employed. This paper presents a practical stereo calibration framework for an RGB camera (2028 x 1520 px) paired with a TIR camera operating at only 80 x 62 px - a pixel-count ratio of approximately 1:625. An active OLED screen dynamically switches modality-specific patterns (checkerboard for TIR, ChArUco for RGB) on a single physical surface, providing controlled and repeatable thermal contrast. A dedicated corner detection algorithm combining perspective rectification, Hessian saddle-point analysis, and Mean Shift localisation achieves reliable checkerboard detection at 80 x 62 px without per-frame parameter tuning. A baseline-constrained bundle adjustment enforces physically consistent rig geometry under the planar-calibration-object degeneracy, yielding a stereo baseline of 32.7 mm (nominal 30 mm) with an overall reprojection error of 0.382 px. The system is validated on a thermally active building mock-up using constant-depth and per-pixel depth estimation, demonstrating consistent TIR-to-RGB projection suitable for building energy performance assessment.

Michał Król, Michał Salamonowicz, Władysław Skarbek +1

Independent Researcher, Poland · Warsaw University of Technology, Poland · Polish Japanese Academy of Information Technology, Poland

Camera Intrinsics Projection

May 14, 2026cs.LG

A Novel Schur-Decomposition-Based Weight Projection Method for Stable State-Space Neural-Network Architectures

Building black-box models for dynamical systems from data is a challenging problem in machine learning, especially when asymptotic stability guarantees are required. In this paper, we introduce a novel stability-ensuring and backpropagation-compatible projection scheme based on the Schur decomposition for the state matrix of linear discrete-time state-space layers, as well as an alternative pre-factorized formulation of the methodology. The proposed methods dynamically project the quasi-triangular factor of the state matrix's real Schur decomposition onto its nearest stable peer, ensuring stable dynamics with minimal overparameterization. Experiments on synthetic linear systems demonstrate that the method achieves accuracy and convergence rates comparable to those of state-of-the-art stable-system identification techniques, despite a marginal increase in computational complexity. Furthermore, the lower weight count facilitates convergence during training without sacrificing accuracy in stacked neural-network architectures with static nonlinearities targeting real-world datasets. These results suggest that the Schur-based projection provides a numerically robust framework for identifying complex dynamics on par with the State of the Art while satisfying strict asymptotic-stability requirements.

Sergio Vanegas, Lasse Lensu, Fredy Ruiz

Computational Engineering LUT University Lappeenranta, Finland · DEIB Politecnico di Milano Milan, Italy

System Identification State Space Models Deep Learning Architectures Projection

May 12, 2026math.OC

Efficient and provably convergent end-to-end training of deep neural networks with linear constraints

Training a deep neural network with the outputs of selected layers satisfying linear constraints is required in many contemporary data-driven applications. While this can be achieved by incorporating projection layers into the neural network, its end-to-end training remains challenging due to the lack of rigorous theory and efficient algorithms for backpropagation. A key difficulty in developing the theory and efficient algorithms for backpropagation arose from the nonsmoothness of the solution mapping of the projection layer. To address this bottleneck, we introduce an efficiently computable HS-Jacobian to the projection layer. Importantly, we prove that the HS-Jacobian is a conservative mapping for the projection operator onto the polyhedral set, enabling its seamless integration into the nonsmooth automatic differentiation framework for backpropagation. Therefore, many efficient algorithms, such as Adam, can be applied for end-to-end training of deep neural networks with linear constraints. Particularly, we establish convergence guarantees of the HS-Jacobian based Adam algorithm for training linearly constrained deep neural networks. Extensive experiment results on several important applications, including finance, computer vision, and network architecture design, demonstrate the superior performance of our method compared to other existing popular methods.

Zonglin Yang, Zhexuan Gu, Yancheng Yuan

Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong

Backpropagation Inequality Constraints Jacobian Adam Projection

May 12, 2026cs.LG

Metric-Gradient Projection for Stable Multi-Agent Policy Learning

General-sum multi-agent learning is often governed by a stacked update field in which each agent's policy update changes the optimization landscape faced by the others. This coupling can entangle an integrable component of collective improvement with cyclic interaction dynamics, leading to slow or unstable multi-agent learning. Existing approaches, such as regularization, credit assignment, and consensus methods, stabilize MARL through local or algorithmic modifications; HPML complements them by projecting the joint update field onto a metric-gradient component. We introduce \textbf{HPML} (\textbf{H}odge-\textbf{P}rojected \textbf{M}ulti-agent \textbf{L}earning), which views the joint update field of a multi-agent system as an element of an

L^2

space of vector fields and computes a Hodge-type projection onto the closest metric-gradient potential flow. HPML follows the projected component as the update direction, yielding the closest metric-gradient field under the chosen metric and sampling measure. The projection is defined variationally, characterized by a Poisson-type equation, and implemented through graph-based and amortized neural realizations that recover projected directions from samples. We show that the projected dynamics admit a Lyapunov potential and yield equilibrium-gap bounds with an explicit additive non-potentiality term. Controlled experiments validate the geometric mechanism, and CTDE benchmarks show improved stability and normalized return when HPML is used as a plug-in projection layer in MARL pipelines.

Zuyuan Zhang, Sizhe Tang, Mahdi Imani +1

The George Washington University · Northeastern University

Multi-Agent Reinforcement Learning Wasserstein Gradient Flows Joint Search Projection

May 10, 2026cs.CL

Towards Compact Sign Language Translation: Frame Rate and Model Size Trade-offs

Sign Language Translation (SLT) converts sign language videos into spoken-language text, bridging communication between Deaf and hearing communities. Current gloss-free approaches rely on large encoder-decoder models, limiting deployment. We propose a compact 77M-parameter pipeline that couples MMPose skeletal pose extraction with a single linear projection into T5-small. By varying the input frame rate, we expose a practical efficiency trade-off: at 12 fps the model halves its sequence length, achieving a 75% reduction in encoder quadratic self-attention computational complexity while incurring only a modest BLEU-4 drop (9.53 vs. 10.06 at 24 fps on How2Sign). Our system is roughly 3x smaller than prior T5-base systems, demonstrating that a lightweight architecture can remain competitive without hierarchical encoders or large-scale models.

Kuanwei Chen, Mengfeng Tsai

Computer Science and Information Engineering, National Central University, Zhongli, Taiwan

Gloss-Free Sign Language Translation Sign Language Translation Speech Translation Small Large Language Models Decoder Layers Frame Rate+3

May 10, 2026stat.ML

Optimal Regret for Single Index Bandits

We study the

\textit{single-index bandit}

problem, where rewards depend on an unknown one-dimensional projection of high-dimensional contexts through an unknown reward function. This model extends linear and generalized linear bandits to a nonparametric setting, and is particularly relevant when the reward function is not known in advance. While optimal regret guarantees are known for monotone reward functions, the general non-monotone case remains poorly understood, with the best known bound being

\tilde{\mathcal{O}}(T^{3/4})

(under standard boundedness and Lipschitz assumptions on the reward function [Kang et al., 2025]). We close this gap by establishing the optimal regret for general single-index bandits. We propose a simple two-phase algorithm, namely, Zoomed Single Index Bandit with Upper Confidence Bound (

\texttt{ZoomSIB-UCB}

), that first estimates the projection direction via a normalized Stein estimator, and then reduces the problem to a one-dimensional bandit using discretization and finally use UCB. This approach achieves a regret of

\tilde{\mathcal{O}}(T^{2/3})

, and improves significantly upon prior work without any additional assumptions. We also prove a matching minimax lower bound of

\tildeΩ(T^{2/3})

, showing that the upper bound is essentially tight. Our upper and lower bounds together provide a sharp characterization of the regret in single-index bandits. Moreover, the empirical results further demonstrate the effectiveness and robustness of our approach.

Devdan Dey, Sujoy Bhore, Avishek Ghosh

Department of Computer Science and Engineering, Indian Institute of Technology Bombay.

Stochastic Multi-Armed Bandits Optimal Regret Regret Projection

May 10, 2026cs.LG

Adversary-Robust Learning from Fully Asynchronous Directional Derivative Estimates

We propose FAR-SIGN (Fully Asynchronous Robust optimization via SIGNed directional projections) for adversary-resilient learning in parameter-server--worker systems. FAR-SIGN achieves robustness through sign-based updates along carefully designed directions and mitigates the resulting bias via a two-timescale mechanism. It admits both first-order and zeroth-order implementations and enables fully asynchronous execution without requiring a private reference dataset at the server. We establish almost-sure convergence of FAR-SIGN to the set of stationary points for smooth, nonconvex objectives. Moreover, we prove the near-optimal rate of

O(n^{-1/4+ε})

in the first-order setting and the standard

O(n^{-1/6+ε})

in the zeroth-order setting, where

n

is the iteration count and

ε>0

can be chosen arbitrarily small. Experiments on MNIST show that FAR-SIGN outperforms robust aggregation-based methods in both accuracy and wall-clock time.

Anik Kumar Paul, Nibedita Roy, Nagesh Talagani +3

Computer Science and Automation, Indian Institute of Science, Bengaluru · Edwardson School of Industrial Engineering, Purdue University · Department of Computer Science, IMT Atlantique

Learning-Augmented Algorithms Zeroth-Order Projection

May 7, 2026cs.LG

A Flow Matching Algorithm for Many-Shot Adaptation to Unseen Distributions

While generative modeling has achieved remarkable success on tasks like natural language-conditioned image generation, enabling model adaptation from example data points remains a relatively underexplored and challenging problem. To this end, we propose Function Projection for Flow Matching (FP-FM), an algorithm that directly conditions generation on samples from the target distribution. FP-FM learns basis functions to span the velocity fields corresponding to a set of training distributions, and adapts to new distributions by computing a simple least-squares projection onto this basis. This enables efficient generation of samples from diverse target distributions without additional training at inference time. We further introduce multiple variants of FP-FM that provide a trade-off in expressivity and compute by enriching the coefficient calculation, e.g., by making the coefficients dependent on time. FP-FM achieves greatly improved precision and recall relative to baselines across synthetic and image-based datasets, with especially strong gains on unseen distributions.

Tyler Ingebrand, Ruihan Zhao, Kushagra Gupta +3

University of Texas at Austin

Generative Flow Networks Generative Models Parameter-Efficient Adaptation Velocity Field Projection

May 7, 2026cs.LG

Listwise Policy Optimization: Group-based RLVR as Target-Projection on the LLM Response Simplex

Reinforcement learning with verifiable rewards (RLVR) has become a standard approach for large language models (LLMs) post-training to incentivize reasoning capacity. Among existing recipes, group-based policy gradient is prevalent, which samples a group of responses per prompt and updates the policy via group-relative advantage signals. This work reveals that these optimization strategies share a common geometric structure: each implicitly defines a target distribution on the response simplex and projects toward it via first-order approximation. Building on this insight, we propose Listwise Policy Optimization (LPO) to explicitly conduct the target-projection, which demystifies the implicit target by restricting the proximal RL objective to the response simplex, and then projects the policy via exact divergence minimization. This framework provides (i) monotonic improvement on the listwise objective with bounded, zero-sum, and self-correcting projection gradients, and (ii) flexibility in divergence selection with distinct structural properties through the decoupled projection step. On diverse reasoning tasks and LLM backbones, LPO consistently improves training performance over typical policy gradient baselines under matched targets, while intrinsically preserving optimization stability and response diversity.

Yun Qu, Qi Wang, Yixiu Mao +11

Department of Automation, Tsinghua University · 2LLM Department, Tencent

Reinforcement Learning With Verifiable Reward Proximal Policy Optimization Responses Projection

May 3, 2026cs.HC

LLM-Augmented Semantic Steering of Text Embedding Projection Spaces

Low-dimensional projections of text embeddings support visual analysis of document collections, but their spatial organization may not reflect the relationships an analyst intends to examine. Existing semantic interaction approaches encode semantic intent indirectly through geometric constraints or model updates, limiting interpretability and flexibility. We introduce LLM-augmented semantic steering, which enables analysts to express semantic intent by grouping a small set of example documents within the projection. A large language model externalizes this intent as natural-language representations and selectively extends it to related documents; the resulting semantic information is then incorporated into document representations via text augmentation or embedding-level blending, without retraining the underlying models. A case study illustrates how the same corpus can be reorganized from different semantic perspectives, while simulation-based evaluation shows that semantic steering improves global and local alignment with target semantic structures using only minimal interaction. Embedding-level blending further enables continuous and controllable steering of projection layouts. These results position projection spaces as intent-dependent semantic workspaces that can be reshaped through explicit, interpretable, language-mediated interaction.

Wei Liu, Eric Krokos, Kirsten Whitley +2

Virginia Tech Blacksburg, Virginia, USA · Department of Defense Washington, DC, USA · Tulane University New Orleans, Louisiana, USA

Text Embeddings Projection Text Analysis and Detection Layouts

May 2, 2026cs.CV

SplAttN: Bridging 2D and 3D with Gaussian Soft Splatting and Attention for Point Cloud Completion

Although multi-modal learning has advanced point cloud completion, the theoretical mechanisms remain unclear. Recent works attribute success to the connection between modalities, yet we identify that standard hard projection severs this connection: projecting a sparse point cloud onto the image plane yields an extremely sparse support, which hinders visual prior propagation, a failure mode we term Cross-Modal Entropy Collapse. To address this practical limitation, we propose SplAttN, which replaces hard projection with Differentiable Gaussian Splatting to produce a dense, continuous image-plane representation. By reformulating projection as continuous density estimation, SplAttN avoids collapsed sparse support, facilitates gradient flow, and improves cross-modal connection learnability. Extensive experiments show that SplAttN achieves state-of-the-art performance on PCN and ShapeNet-55/34. Crucially, we utilize the real-world KITTI benchmark as a stress test for multi-modal reliance. Counter-factual evaluation reveals that while baselines degenerate into unimodal template retrievers insensitive to visual removal, SplAttN maintains a robust dependency on visual cues, validating that our method establishes an effective cross-modal connection. Code is available at https://github.com/zay002/SplAttN.

Zhaoyang Li, Zhichao You, Tianrui Li

School of Computing and Artificial Intelligence, Southwest Jiaotong University, Chengdu, China

Point Clouds Gaussian Splatting Cross-Modal Projection Bridging Language

Apr 24, 2026cs.CV

CheXmix: Unified Generative Pretraining for Vision Language Models in Medical Imaging

Recent medical multimodal foundation models are built as multimodal LLMs (MLLMs) by connecting a CLIP-pretrained vision encoder to an LLM using LLaVA-style finetuning. This two-stage, decoupled approach introduces a projection layer that can distort visual features. This is especially concerning in medical imaging where subtle cues are essential for accurate diagnoses. In contrast, early-fusion generative approaches such as Chameleon eliminate the projection bottleneck by processing image and text tokens within a single unified sequence, enabling joint representation learning that leverages the inductive priors of language models. We present CheXmix, a unified early-fusion generative model trained on a large corpus of chest X-rays paired with radiology reports. We expand on Chameleon's autoregressive framework by introducing a two-stage multimodal generative pretraining strategy that combines the representational strengths of masked autoencoders with MLLMs. The resulting models are highly flexible, supporting both discriminative and generative tasks at both coarse and fine-grained scales. Our approach outperforms well-established generative models across all masking ratios by 6.0% and surpasses CheXagent by 8.6% on AUROC at high image masking ratios on the CheXpert classification task. We further inpaint images over 51.0% better than text-only generative models and outperform CheXagent by 45% on the GREEN metric for radiology report generation. These results demonstrate that CheXmix captures fine-grained information across a broad spectrum of chest X-ray tasks. Our code is at: https://github.com/StanfordMIMI/CheXmix.

Ashwin Kumar, Robbie Holland, Corey Barrett +8

Stanford AIMI, Stanford University · Oracle Health AI · Department of Radiology, Stanford University

Chest X-Ray Medical Vision-Language Models Radiology Report Generation Multimodal Pretraining Medical Imaging Single-Cell Foundation Models+4

Apr 24, 2026cs.CV

Contrastive Semantic Projection: Faithful Neuron Labeling with Contrastive Examples

Neuron labeling assigns textual descriptions to internal units of deep networks. Existing approaches typically rely on highly activating examples, often yielding broad or misleading labels by focusing on dominant but incidental visual factors. Prior work such as FALCON introduced contrastive examples -- inputs that are semantically similar to activating examples but elicit low activations -- to sharpen explanations, but it primarily addresses subspace-level interpretability rather than scalable neuron-level labeling. We revisit contrastive explanations for neuron-level labeling in two stages: (1) candidate label generation with vision language models (VLMs) and (2) label assignment with CLIP-like encoders. First, we show that providing contrastive image sets to VLMs yields candidate labels that are more specific and more faithful. Second, we introduce Contrastive Semantic Projection (CSP), an extension of SemanticLens that incorporates contrastive examples directly into its CLIP-based scoring and selection pipeline. Across extensive experiments and a case study on melanoma detection, contrastive labeling improves both faithfulness and semantic granularity over state-of-the-art baselines. Our results demonstrate that contrastive examples are a simple yet powerful and currently underutilized component of neuron labeling and analysis pipelines.

Oussama Bouanani, Jim Berend, Wojciech Samek +2

Fraunhofer Heinrich Hertz Institute, Berlin, Germany · Technische Universität Berlin, Berlin, Germany · BIFOLD – Berlin Institute for the Foundations of Learning and Data, Berlin, Germany +1

Contrastive Learning Neurons Interpretability Projection Encoders

Apr 23, 2026cs.CV

Local Neighborhood Instability in Parametric Projections: Quantitative and Visual Analysis

Parametric projections let analysts embed new points in real time, but input variations from measurement noise or data drift can produce unpredictable shifts in the 2D layout. Whether and where a projection is locally stable remains largely unexamined. In this paper, we present a stability evaluation framework that probes parametric projections with Gaussian perturbations around selected anchor points and assesses how neighborhoods deform in the 2D embedding. Our approach combines quantitative measures of mean displacement, bias, and nearest-anchor assignment error with per-anchor visualizations of displacement vectors, local PCA ellipsoids, and Voronoi misassignment for detailed inspection. We demonstrate the framework's effectiveness on UMAP- and t-SNE-based neural projectors of varying network sizes and study the effect of Jacobian regularization as a gradient-based robustness strategy. We apply our framework to the MNIST and Fashion-MNIST datasets. The results show that our framework identifies unstable projection regions invisible to reconstruction error or neighborhood-preservation metrics.

Frederik L. Dennig, Daniel A. Keim

University of Konstanz, Germany

Projection Projection Heads Visualization Quantifying

Apr 22, 2026cs.SD

ONOTE: Benchmarking Omnimodal Notation Processing for Expert-level Music Intelligence

Omnimodal Notation Processing (ONP) represents a unique frontier for omnimodal AI due to the rigorous, multi-dimensional alignment required across auditory, visual, and symbolic domains. Current research remains fragmented, focusing on isolated transcription tasks that fail to bridge the gap between superficial pattern recognition and the underlying musical logic. This landscape is further complicated by severe notation biases toward Western staff and the inherent unreliability of "LLM-as-a-judge" metrics, which often mask structural reasoning failures with systemic hallucinations. To establish a more rigorous standard, we introduce ONOTE, a multi-format benchmark that utilizes a deterministic pipeline--grounded in canonical pitch projection--to eliminate subjective scoring biases across diverse notation systems. Our evaluation of leading omnimodal models exposes a fundamental disconnect between perceptual accuracy and music-theoretic comprehension, providing a necessary framework for diagnosing reasoning vulnerabilities in complex, rule-constrained domains.

Menghe Ma, Siqing Wei, Yuecheng Xing +5

Beijing University of Posts and Telecommunications Beijing, China · China Conservatory of Music Beijing, China · Nanyang Technological University Singapore, Singapore

Music Structure Analysis Notes Intelligence Projection

Apr 16, 2026cs.CL

Schema-Key Wording as an Instruction Channel in Structured Generation under Constrained Decoding

Constrained decoding is widely used to make large language models produce structured outputs that satisfy schemas such as JSON. Existing work mainly treats schemas as structural constraints, overlooking that schema-key tokens also enter the autoregressive context and may guide generation. To the best of our knowledge, we present the first systematic study of schema keys as an implicit instruction channel under constrained decoding. We formulate structured generation as a multi-channel instruction problem, where task signals can be placed in prompts, schema keys, or both. We further provide a projection-aware analysis that gives a sufficient condition under which an unconstrained expected-score advantage of an instructional key is preserved after grammar projection. Experiments on GSM8K and Math500 across seven language models show that changing only schema-key wording can substantially affect accuracy, with both positive and negative effects across models. Prompt-level and schema-level instructions also interact non-additively. The evidence is substantially stronger on GSM8K than on Math500. Our findings show that schema design is not merely output formatting, but part of instruction specification in structured generation.

Yifan Le

Independent Researcher

Constrained Decoding Data Generation Instruction Decoding Projection

Feb 13, 2026cs.LG

High-Resolution Climate Projections Using Diffusion-Based Downscaling of a Lightweight Climate Emulator

The proliferation of data-driven models in weather and climate sciences has marked a significant paradigm shift, with advanced models demonstrating exceptional skill in medium-range forecasting. However, these models are often limited by long-term instabilities, climatological drift, and substantial computational costs during training and inference, restricting their broader application for climate studies. Addressing these limitations, Guan et al. (2024) introduced LUCIE, a lightweight, physically consistent climate emulator utilizing a Spherical Fourier Neural Operator (SFNO) architecture. This model is able to reproduce accurate long-term statistics including climatological mean and seasonal variability. However, LUCIE's native resolution (~300 km) is inadequate for detailed regional impact assessments. To overcome this limitation, we introduce a deep learning-based downscaling framework, leveraging probabilistic diffusion-based generative models with conditional and posterior sampling frameworks. These models downscale coarse LUCIE outputs to 25 km resolution. They are trained on approximately 14,000 ERA5 timesteps spanning 2000-2009 and evaluated on LUCIE predictions from 2010 to 2020. Model performance is assessed through diverse metrics, including latitude-averaged RMSE, power spectrum, probability density functions and First Empirical Orthogonal Function of the zonal wind. We observe that the proposed approach is able to preserve the coarse-grained dynamics from LUCIE while generating fine-scaled climatological statistics at ~28km resolution.

Haiwen Guan, Dibyajyoti Chakraborty, Moein Darman +3

1Information Sciences and Technology, The Pennsylvania State University, University Park, Pennsylvania · Department of Applied Mathematics, University of California, Santa Cruz, California · 3Allen Institute for Artificial Intelligence (AI2), Seattle, Washington +1

Dynamical Downscaling Wind Lightweight Fourier Neural Operators Projection

Sep 18, 2025cs.RO

BEV-ODOM2: Enhanced BEV-based Monocular Visual Odometry with PV-BEV Fusion and Dense Flow Supervision for Ground Robots

Scale-consistent ego-motion estimation is fundamental for autonomous ground robots. Bird's-Eye-View (BEV) representation naturally addresses the scale drift problem of monocular visual odometry (MVO) by providing a metric-scaled planar workspace, enabling the simplification of 6-DoF ego-motion to a more robust 3-DoF model. However, existing BEV-based methods suffer from two key limitations: sparse supervision signals from pose-only training, and information loss during perspective-to-BEV projection. We present BEV-ODOM2, an enhanced framework in the BEV-ODOM line that addresses both limitations without supervision modalities beyond the pose ground truth. Our approach introduces (1) pose-derived dense rigid BEV flow supervision, which reparameterizes the 3-DoF pose ground truth into a pixel-level training signal, and (2) Perspective View (PV)-BEV fusion, which computes correlation volumes before projection to retain additional motion cues and help alleviate projection ambiguity. An enhanced rotation sampling strategy further balances diverse motion patterns during training. We evaluate on four datasets with varied spatial scales: KITTI, Oxford, NCLT, and our newly collected ZJH-VO benchmark. BEV-ODOM2 reduces the RTE of BEV-ODOM by 39% on average across the four datasets. It further enables closed-loop navigation on a physical robot with centimeter-level cross-track error. Real-time inference on an NVIDIA Jetson AGX Orin confirms edge deployment feasibility. The code and the ZJH-VO dataset are publicly released to facilitate future research.

Yufei Wei, Chenxiao Hu, Wangtao Lu +5

Visual Inertial Odometry Bird'S-Eye View Odometry Monocular Projection Enhancement

Sep 10, 2025eess.IV

Deep Unrolling of Sparsity-Induced RDO for 3D Point Cloud Attribute Coding

Given encoded 3D point cloud geometry available at the decoder, we study the problem of lossy attribute compression in a multi-resolution B-spline projection framework. A target continuous 3D attribute function is first projected onto a sequence of nested subspaces

\mathcal{F}^{(p)}_{l_0} \subseteq \cdots \subseteq \mathcal{F}^{(p)}_{L}

, where

\mathcal{F}^{(p)}_{l}

is a family of functions spanned by a B-spline basis function of order

p

at a chosen scale and its integer shifts. The projected low-pass coefficients

F_l^*

are computed by variable-complexity unrolling of a rate-distortion (RD) optimization algorithm into a feed-forward network, where the rate term is the sparsity-promoting

\ell_1

-norm. Thus, the projection operation is end-to-end differentiable. For a chosen coarse-to-fine predictor, the coefficients are then adjusted to account for the prediction from a lower-resolution to a higher-resolution, which is also optimized in a data-driven manner.

Tam Thuc Do, Philip A. Chou, Gene Cheung

department of EECS, York University, 4700 Keele Street, Toronto, M3J 1P3, Canada

Point Clouds Deep Unfolding Networks Sparsity Splines Projection Sparse-View+2

Aug 16, 2025cs.LG

DE-VAE: Revealing Uncertainty in Parametric and Inverse Projections with Variational Autoencoders using Differential Entropy

Recently, autoencoders (AEs) have gained interest for creating parametric and invertible projections of multidimensional data. Parametric projections make it possible to embed new, unseen samples without recalculating the entire projection, while invertible projections allow the synthesis of new data instances. However, existing methods perform poorly when dealing with out-of-distribution samples in either the data or embedding space. Thus, we propose DE-VAE, an uncertainty-aware variational AE using differential entropy (DE) to improve the learned parametric and invertible projections. Given a fixed projection, we train DE-VAE to learn a mapping into 2D space and an inverse mapping back to the original space. We conduct quantitative and qualitative evaluations on four well-known datasets, using UMAP and t-SNE as baseline projection methods. Our findings show that DE-VAE can create parametric and inverse projections with comparable accuracy to other current AE-based approaches while enabling the analysis of embedding uncertainty.

Frederik L. Dennig, Daniel A. Keim

University of Konstanz

Conditional Variational Autoencoder Star-Vae Autoencoder Architectures Projection Uncertainty Entropy+1

May 10, 2025stat.ML

Out-of-Sample Embedding with Proximity Data: Projection versus Restricted Reconstruction

The problem of using proximity (similarity or dissimilarity) data for the purpose of "adding a point to a vector diagram" was first studied by J.C. Gower in 1968. Since then, a number of methods -- mostly kernel methods -- have been proposed for solving what has come to be called the problem of out-of-sample embedding. We survey the various kernel methods that we have encountered and show that each can be derived from one or the other of two competing strategies: projection or restricted reconstruction. Projection can be analogized to a well-known formula for adding a point to a principal component analysis. Restricted reconstruction poses a different challenge: how to best approximate redoing the entire multivariate analysis while holding fixed the vector diagram that was previously obtained. This strategy results in a nonlinear optimization problem that can be simplified to a unidimensional search. Various circumstances may warrant either projection or restricted reconstruction.

Michael W. Trosset, Kaiyi Tan, Minh Tang +1

Department of Statistics, Indiana University. · Department of Statistics, North Carolina State University. · Department of Applied Mathematics & Statistics, Johns Hopkins University.

Principal Component Analysis Projection Kernel Method Proximity Operations Motion Reconstruction Branch Diagrams

Jun 10, 2022cs.LG

Anisotropic View Distance Metric for High-Dimensional Data: Theory, Geometry, and Fast Computation

K-Means clustering algorithm is one of the most commonly used clustering algorithms because of its simplicity and efficiency. K-Means clustering algorithm based on Euclidean distance only pays attention to the linear distance between Euclidean distance is an efficient and interpretable similarity measurement, but its effectiveness may deteriorate in sample spaces with anisotropic structures, redundant features, or complex feature interactions. In this paper, we propose a novel distance metric called View distance. Inspired by orthographic projection, the proposed metric projects the sample space onto

n(n-1)/2

two-dimensional planes and defines the final distance as the sum of the Euclidean distances across the projected planes. Theoretical derivations verify that the View distance strictly satisfies the metric axioms and norm constraints. Beyond that, the View distance achieves feature coupling through projection and not only enables constant features to indirectly participate in distance calculation, but also suppresses interference from redundant features while exhibiting anisotropic geometric properties. Furthermore, to address the high computational complexity and poor scalability of full-projection View distance, we propose a two-dimensional projection plane selection strategy based on iterative Maximum Weight Matching, which reduces the computational complexity of distance calculation from

\mathcal{O}(n^2)

to

\mathcal{O}(k)

. Extensive experiments on 12 diverse datasets demonstrate that View distance and the deterministic selection strategy provide competitive or superior performance compared with Euclidean distance and other

L_{p}

metrics while maintaining strong interpretability and computational efficiency. The View distance provides a new perspective and option for similarity measurements.

Yiqun Zhang, Hou-biao Li

School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China

K-Means Distance High-Dimensional Spherical Latent Space Maximum Mean Discrepancy Anisotropic+1

Jun 21, 2021cs.CV

EPMF: Efficient Perception-aware Multi-sensor Fusion for 3D Semantic Segmentation

We study multi-sensor fusion for 3D semantic segmentation that is important to scene understanding for many applications, such as autonomous driving and robotics. Existing fusion-based methods, however, may not achieve promising performance due to the vast difference between the two modalities. In this work, we investigate a collaborative fusion scheme called perception-aware multi-sensor fusion (PMF) to effectively exploit perceptual information from two modalities, namely, appearance information from RGB images and spatio-depth information from point clouds. To this end, we project point clouds to the camera coordinate using perspective projection, and process both inputs from LiDAR and cameras in 2D space while preventing the information loss of RGB images. Then, we propose a two-stream network to extract features from the two modalities, separately. The extracted features are fused by effective residual-based fusion modules. Moreover, we introduce additional perception-aware losses to measure the perceptual difference between the two modalities. Last, we propose an improved version of PMF, i.e., EPMF, which is more efficient and effective by optimizing data pre-processing and network architecture under perspective projection. Specifically, we propose cross-modal alignment and cropping to obtain tight inputs and reduce unnecessary computational costs. We then explore more efficient contextual modules under perspective projection and fuse the LiDAR features into the camera stream to boost the performance of the two-stream network. Extensive experiments on benchmark data sets show the superiority of our method. For example, on nuScenes test set, our EPMF outperforms the state-of-the-art method, i.e., RangeFormer, by 0.9% in mIoU. Our source code is available at https://github.com/ICEORY/PMF.

Mingkui Tan, Zhuangwei Zhuang, Sitao Chen +4

School of Software Engineering, South China University of Technology · Pazhou Laboratory, Guangzhou, China · School of Electronic and Information Engineering, South China University of Technology +2

Multi-Sensor Fusion 3D Perception Lidar Projection

Date pendingcs.CV

Differentiable Jitter Correction using Deep Learning-based Image Quality Metric for Phase-Contrast Micro-CT

This paper proposes a fully differentiable jitter correction method for X-ray phase-contrast micro computed tomography using a deep learning-based image quality metric that estimates and compensates per-projection rigid jitter directly from the acquired projection data, without a pre-scan motion-free reference. The approach builds on a gradient-based auto-focus strategy adapted to parallel-beam geometry. A set of candidate objective functions is benchmarked in a controlled study, and the sensitivity of the visual information fidelity (VIF) metric to the jitter artifact is verified with the target phase-contrast data. To operate without a clean reference, a compact 3D convolutional neural network is trained to predict the VIF score from a single corrupted volume. A spatially selective total variation penalty applied exclusively to the image background is introduced to penalize spurious high-frequency structures that otherwise emerge during optimization. Experiments on biological specimens acquired at different synchrotron beamlines are conducted. Evaluation uses jitter motion applied to simulated and experimentally acquired projection data. The result confirms that the integrated pipeline reliably recovers fine structural detail lost due to jitter, with generalization demonstrated across morphologically distinct samples.

Junan Chen, Yiting Jia, Joscha Maier +6

ImFusion GmbH, Ridlerstr. 57, 80339 Munich, Germany. · Research Group Biomedical Imaging Physics, Department of Physics, TUM School of Natural Sciences and Munich Institute of Biomedical Engineering, Technical University of Munich, James-Franck-Str. 1, 85748 Garching, Germany. · Centre for X-Ray and Nano Science CXNS, Deutsches Elektronen-Synchrotron (DESY), Notkestr. 85, 22067 Hamburg, Germany. +1

Cone-Beam Computed Tomography Image Registration Image Quality Assessment Projection

Date pendingcs.LG

Denoising as Projection: Constrained Optimization with Gradient-Guided Diffusion

Diffusion models are increasingly used not only for sampling from learned data distributions, but also for generating samples that optimize task-specific objectives. A common approach is to guide the reverse diffusion process using gradients of an external objective. However, when the data distribution is supported on a structured feasible set, such as a manifold or a constraint set, gradient guidance can move samples away from the learned data geometry. In this paper, we study a simple projected-gradient-guided diffusion update based on the observation that the Stein denoising operator can act as an approximate projection onto the data geometry. The proposed update incorporates the objective gradient inside the denoising step, yielding an inference-time method that uses only a pretrained denoiser and gradient evaluations. We analyze this update as an inexact projected-gradient method for constrained optimization over learned feasible geometries. Our theory covers three settings: linear manifolds, compact convex feasible sets, and compact Riemannian submanifolds. In all these settings, we prove descent and finite-time convergence guarantees. Numerical experiments support the theoretical interpretation and illustrate how the proposed update balances objective descent with preservation of the learned geometry.

Runyu Zhang, Jiawei Zhang, Gioele Zardini +2

MIT · University of Wisconsin–Madison

Wasserstein Gradient Flows Diffusion Models Iterative Denoising Methods Constrained Optimization Projection