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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Oct 1, 2026cs.CV

Moore, Escher, Penrose: A Conformal Golden Braid

I don't think I have ever done anything as peculiar in my life. Among other things, it shows a young man looking with interest at a print on the wall of an exhibition that features himself. How can this be? Perhaps I am not far removed from Einstein's curved universe.'' So wrote M.C. Escher about his 1956 lithograph Print Gallery. Nearly half a century later, a mathematical analysis related its geometry to an untwisted source image through a conformal power map

z \mapsto z^α

,

α\in \mathbb{C}

. Building on this construction, we use a frozen text-to-image diffusion model to generate new self-referential scenes. Prompting alone does not enforce the recursion, while a post-hoc transformation can leave structures poorly connected. Applying the transformation during sampling is also insufficient: the denoiser may "repair" the intended distortion or drift out of the prescribed geometry. We construct a generalized inverse

T^\dagger

of the non-invertible image transformation

T

, adapted to its recursive constraint. In the idealized formulation, the Penrose identity

TT^\dagger T = T

makes

TT^\dagger

an idempotent projection onto geometrically admissible images. Yet denoising only the transformed image remains an out-of-distribution task, even with projection. We therefore braid denoising steps with

T

and

T^\dagger

: source-space steps develop the untwisted scene, while transformed-space steps refine its appearance and connections in the final geometry. We generate Print Gallery-like compositions and explore further transformations. Rather than distorting a finished image, we let the scene and its distortion develop together.

Sophia Feldman, Assaf Shocher

Technion - Israel Institute of Technology

Conformal Selection Projection

Oct 1, 2026cs.AI

FedLore: Communication and Memory Efficient Federated Learning via Shared Gradient Low-Rank Projection

Federated training of foundation models is constrained by client memory and communication costs. LoRA-based methods reduce these costs through low-rank adapters, but their fixed rank budget can limit adaptation. Gradient low-rank optimization offers greater flexibility, yet independently chosen client subspaces create a problem we term \emph{subspace fragmentation}: local projections interact with data heterogeneity to bias aggregated directions, while aggregation can increase update rank and communication cost. Thus, accurate local gradient compression need not preserve global descent. We propose \texttt{FedLore}, which shares a low-rank optimization basis within each round and refreshes it across rounds. The shared basis enables exact aggregation in low-rank coordinates and eliminates the identified projection bias. Subspace refresh allows the accumulated model update to exceed the per-round rank budget. We characterize the aggregation bias and establish an

O(T^{-1/2})

stationarity bound for the projected-SGD variant under a global-gradient coverage condition and standard smoothness and variance assumptions, with bounded gradient heterogeneity. Experiments on vision and language tasks, including federated pre-training, show that \texttt{FedLore} outperforms the evaluated low-rank adapter baselines and matches or exceeds full-parameter training, while reducing communication and optimizer-state memory.

Junkang Liu

Tianjin University

Federated Learning Fedavg Low-Rank Structure Subspace Fragmentation Projection

Sep 29, 2026cs.AI

Brain-SAD: A Brain-Inspired Safe Autonomous Driving Control Framework with Dynamic Fear-Oriented Constraint on Dual-Policy

Constrained Reinforcement Learning has recently gained increasing attention in the field of Safe Autonomous Driving, where the general mechanism is to maximize the expected reward while keeping the overall action risk bounded. In this way, the safety issues arising in AD can be mitigated through constrained actions. However, existing Constrained RL methods still lack dynamics on the imposed constraints. For instance, the action cost adopted by the existing Primal-Dual/soft-constrained methods is often defined as static state-to-cost mapping, and the safe-action projection in hard-constrained methods relies on the static projection with the fixed feasible region boundary estimated from offline demonstrations. The above drawback tightly couples the imposed constraints to the training scenarios, leaving the AD policy hard to handle different interaction scenarios, due to the improper state-level action-cost and the static projection boundary. Consequently, in this paper, we propose Brain-SAD, a brain-inspired safe autonomous driving control framework with dynamic fear-oriented constraints. By perceiving the current vehicle-interaction scene, Brain-SAD generates dynamic fear signal as fear reaction to online decide long-term policy for regular interaction or short-term policy for urgent-collision defense. In such two policy, the above fear-reaction will be constructed as the dynamic fear constraints, respectively reflecting the overall fear cost directly coupled with action-impact, and the dynamic fear boundary of the feasible region derived from different risky neighbors, both of which will in turn serve for the online policy optimization. Experimental results show that Brain-SAD outperforms existing methods, achieving higher success rate in shorter task-completion and collision-recovery time, and exhibits stronger reliability across continuous intersections of fluctuating complexity.

Huan Rong, Chao Yin, Anouar Imel +2

School of Artificial Intelligence, Nanjing University of Information Science & Technology, Jiangsu, Nanjing, 210-044, China · School of Information and Communication Engineering, University of Electronic Science and Technology of China, Sichuan, Chengdu, 611731, China · School of Software, Nanjing University of Information Science & Technology, 210044, Jiangsu, China +1

Safety Constraints Collision Avoidance Projection

Sep 29, 2026cs.LG

Scaling Influence Functions in LLMs through Eigenbasis-Corrected One-Bit Gradient Projection

Influence functions estimate how individual training examples affect the behavior of large language models (LLMs). Analyzing how training data influence different behaviors of an LLM involves repeated influence computation. Reusing stored training gradients reduces the computational cost, but storing full gradients is prohibitively expensive at LLM scale. We study how to compress these gradients while preserving influence estimates for future queries that are unknown at storage time. Through a worst-case analysis, we characterize the optimal fixed-dimensional linear representation and propose eigenbasis-corrected one-bit gradient projection (EOGP) to approximate it at scale. Specifically, EOGP uses EK-FAC to reduce gradient dimensionality, then applies PCA within the retained subspace to learn compression directions from the training gradients. We then apply one-bit quantization to the resulting coordinates, allowing more coordinates to be retained within a fixed storage budget. On GPT-2, EOGP predicts retraining outcomes more accurately than the evaluated compression baselines while using one-sixteenth of their per-example storage. On OLMo 2 SFT models from 1B to 32B parameters, EOGP remains competitive with the baselines allocated over 100 times as much storage per example.

Jaeseung Heo, J Rosser, Dongwoo Kim

POSTECH · University of Oxford

Influence Function Multi-Stage Training Projection

Sep 29, 2026cs.AI

Semantic Projection for Continual Self-Evolution of Language Agents

Language-model agents increasingly rely on persistent natural-language skills to adapt beyond their frozen model parameters. When a shared skill is repeatedly revised from a non-stationary, heterogeneous task stream, however, improvements for new tasks can overwrite procedures needed for earlier ones. In continual learning, Orthogonal Gradient Descent (OGD) addresses analogous interference by projecting a new-task gradient onto a subspace that locally preserves prior predictions. Natural-language skill revisions, however, have neither gradients nor a canonical vector space in which such a projection can be performed. We introduce \emph{Semantic-Scope Projected Evolution} (SSPE), which transfers the functional principle of gradient projection from parameter space to behavior space. SSPE treats an unconstrained skill revision as a proposed update, identifies acquired capabilities with which it may interfere, and uses the observed gains and regressions to construct a compatible revision rather than merely rejecting the update. This enables one shared skill to evolve across latent and recurring task contexts without exposing semantic domain identities to the evolution model. Across controlled synthetic streams and heterogeneous real-agent benchmarks, SSPE improves final cross-domain competence and mitigates forgetting relative to strong skill-evolution baselines. The evolved skill also retains the strongest average performance after transfer to a different executor model. These results establish semantic projection as a promising principle for stable and adaptive self evolution of language agents.

Ziyu Liu, Jun Chen, Lixu Wang

University of Pennsylvania · Hark · The Chinese University of Hong Kong, Shenzhen

Self-Evolution Multilingual Agents Natural Language Projection

Sep 27, 2026math.OC

Local LMO is Secretly a Projection Method!

The local linear minimization oracle (Ferris and Zavriev, 1996; arXiv:2605.08850), or Local LMO, solves constrained convex problems without having to compute a projection: it minimizes a linear model over the intersection of the feasible set with a ball around the current iterate. We show that, whenever the ball radius does not exceed the Polyak radius, the Local LMO step is the Euclidean projection of the current iterate onto the intersection of the feasible set with a half-space that separates the iterate from the solution set; this projection is nonetheless computable by a linear oracle alone. We demonstrate that Local LMO belongs to a broader family of projection methods which may be indexed by the depth of the localizing half-space. For objectives with

\vartheta

-Hölder continuous gradient, every method from this family whose half-space lies sufficiently deep drives the best of its first

K

iterates to optimality at the universal rate

\mathcal{O}(K^{-(1+\vartheta)/2})

, matching the non-accelerated universal gradient method of Nesterov (2015). Run at the Polyak radius, Local LMO attains the same rate when the constrained optima are also unconstrained (

\|\nabla f(x_\star)\| = 0

), and the rate

\mathcal{O}(K^{-1/(2-\vartheta)})

otherwise.

Peter Richtárik, Ammar Mahran

King Abdullah University of Science and Technology, Thuwal, Saudi Arabia

Convex Optimization Projection Gradient Descent

Sep 21, 2026cs.CV

Anatomy-Decomposed Chest Computed Tomography (CT) Projections as Scalable Supervision for Bone Suppression in Chest Radiographs

Bone overlap can obscure abnormalities in chest radiographs, while scarce paired training data limit supervised bone suppression. We address this challenge with a digitally reconstructed radiograph (DRR) framework that converts chest computed tomography (CT) into paired supervision for component suppression. A novel bone segmentation algorithm enables CT decomposition into bone, non-lung soft-tissue, and lung components, which are projected separately. Their weighted combination yields synthetic radiographs with pixel-registered component images that sum exactly to the full DRR. Models trained on these data suppress bone or lung components by predicting the target component and recovering the remainder by subtraction, transferring to real radiographs without real paired training data. As an extension, their outputs on real radiographs provide target domains for unpaired, component-wise DRR translation, reducing the appearance gap while retaining anatomical details. Across multiple public datasets, downstream detection experiments demonstrate the utility of bone suppression, with gains concentrated on abnormalities with substantial bone overlap. Compared with open-source DRR engines applied to the same CTs, our unmodified DRRs achieve comparable realism and preservation of label-relevant anatomy, while translated DRRs achieve the best Fréchet inception distance (FID), lung-field sharpness, and agreement with source-CT anatomy among the evaluated methods. Models and inference code: https://huggingface.co/qureaiorg/bone-suppression ; Translated projections: https://huggingface.co/datasets/qureaiorg/ct2xr-projections.

Mrunmay Angaitkar, Piyush Kumar, Aarjav Satia +4

Qure.ai, Mumbai, India

Digitally Reconstructed Radiographs Cone-Beam Computed Tomography Anatomy Projection

Sep 21, 2026cs.RO

SPARSER: Sparse Variable Projection by Exploiting Separable Structure in Robotic Perception

Robotic perception often requires solving large nonlinear least-squares (NLS) problems. While sparsity has been widely exploited to scale solvers, a complementary and underused structure is \emph{separability}: some variables, such as visual landmarks, appear linearly in the residuals and admit a closed-form solution once the remaining variables, such as poses, are fixed. Variable projection (VarPro) exploits this structure by analytically eliminating the linear variables, yielding a reduced problem with favorable computational properties. However, its use in robotic perception has been limited by gauge symmetries, such as invariance to global translations and rotations, which introduce challenges for standard VarPro methods. We present SPARSER (\textbf{S}parsity \textbf{P}reserving \textbf{A}nalytic \textbf{R}eduction for \textbf{S}eparable \textbf{R}obotic \textbf{P}erception), a VarPro framework for gauge-symmetric problems that jointly exploits separability and sparsity. Our method constructs a \emph{matrix-free Schur complement operator} for efficient evaluation of reduced costs, gradients, and Hessian-vector products, enabling integration with iterative NLS solvers. We characterize the applicable problem class, identify common cases admitting further analytical simplifications, and show that IRLS-based robust costs preserve most of the exploitable structure. Across synthetic and real SLAM, SNL, and SfM benchmarks, SPARSER is on average

5\times

--

7\times

faster than state-of-the-art baselines on CPU and GPU, with gains exceeding

40\times

on individual datasets. On outlier-corrupted multi-robot SLAM data, the robust variant is

2\times

--

16\times

faster than a state-of-the-art GNC solver. We release open-source C++ code and all datasets.

Nikolas R. Sanderson, Andrew Fishberg, Haoyu Han +5

Department of Naval Architecture and Marine Engineering, University of Michigan, Ann Arbor, MI, USA · Institute of Experiential Robotics, Northeastern University, Boston, MA, USA · Aerospace Controls Lab, Massachusetts Institute of Technology, Cambridge, MA, USA +1

Robotic Perception Simultaneous Localization And Mapping Solver Iterations Sparsity Projection Separability

Sep 17, 2026cs.CL

Summarization Bias: The Directional Collapse of Objective Projection into Told-Mode Labels in Large Language Models --- A Conceptual Framework and Registered Test Protocol

This paper introduces and operationalizes summarization bias: a proposed systematic tendency of large language models (LLMs) to represent narrative meaning as an abstract summary label rather than as the reconstructable inferential structure that produces it. Within the Bulut Doctrine, narrative effect is theorized along a told-shown axis: in told mode, emotional and informational content is declared explicitly and requires little reader reconstruction; in shown mode, that content is suppressed at the surface and must be reconstructed from physical cues and indirection (Objective Projection). Shown mode is the higher-load condition the doctrine is designed to measure. The claim is that LLMs fail along this axis in a specific direction. Summarization bias is hypothesized to operate in two regimes: (i) a generative regime, in which a model asked to render an emotion through Objective Projection defaults to declaring it instead; and (ii) an evaluative regime, in which a model judging narrative quality rewards told-mode explicitness and under-detects shown-mode suppression. The evaluative regime is the more consequential, since LLMs increasingly serve as judges and reward models, and a directional bias toward told mode would impose a selection pressure degrading prose toward flat declaration. This report does not claim the bias is validated. It defines the construct, situates it against LLM-as-judge biases, rereads a completed independent reliability study as directional evidence consistent with it, and pre-registers a two-regime test with decision rules under which the construct would be abandoned.

Levent Bulut

Independent Researcher

Large Language Model Bias Summarization Narratives Projection

Sep 16, 2026cs.LG

Directions That Don't Drift: Stiefel Manifold Routing for Transformer Attention

The query and key projections

\WQ,\WK

in attention are almost always trained by Euclidean optimizers with no geometric constraint. We constrain them to the Stiefel manifold and optimize with a Riemannian Adam carrying one scalar second moment per frame---the form of \citet{becigneul2019}, here extended to the compact, non-Hadamard

\St(d,r)

with a tangent projector, step-norm cap, and polar retraction. Four propositions prove steepest descent in the embedded metric, gradient-scale independence, well-conditioning, and exact

\mathrm{O}(d)

-equivariance. A fifth records that weight decay has \emph{identically zero} Riemannian gradient on

\St(d,r)

(

W{=}WI_r

lies in the normal space), so decay cannot act on the constrained frames. On a CIFAR-10 patch benchmark at

n{=}10\mathrm{k}

this rule gains

\mathbf{+6.79}

,pp over AdamW across 12 paired starts (

t{=}38.33

,

12/12

); earlier fixed-step Riemannian SGD gains

+1.97

,pp, of which

+1.69

,pp comes from frozen orthonormal initialization alone. The corrected Adam's lead grows with data:

+1.9

,pp at

n{=}1\mathrm{k}

to

+6.7

,pp at

n{=}50\mathrm{k}

. A 12-seed ablation credits all gain to the scale-free step (

+4.63

,pp,

12/12

), nothing to the projector or equivariance; a targeted

\varepsilon

-sweep causally confirms the mechanism (

-2.6

,pp at

\varepsilon{=}0.1

,

p{<}0.001

). Two five-seed grokking studies confirm the constrained arm does not grok better than the baseline (

p{=}0.019

, A2 wins): the weight-decay exemption has no grokking consequence. A single-seed pilot exploiting this localization achieves the first stable grokking under slingshot conditions---Stiefel + targeted circuit regularization keeps routing-frame isometry error

10^6\times

lower than the unconstrained ablation through every collapse.

Rubén Darío Guerrero

NeuroTechNet S.A.S., 1108831, Bogotá, Colombia

Riemannian Optimization Adam Transformer Architectures Projection Manifolds

Sep 14, 2026cs.CG

Multi-Stage NeRF for Efficient 3D Coronary Artery Reconstruction from Two Narrow-Angle Angiographic Projections

X-ray coronary angiography is the clinical gold standard for coronary artery disease during real-time cardiac interventions, but provides only 2D projections of inherently 3D vessels. Existing learning-based 2D-to-3D reconstruction methods typically require wide angular coverage or multiple views, assumptions that are rarely satisfied in routine practice where only two projections with narrow angular separation are available. To address these challenges, we propose NeCA++, a multi-stage self-supervised neural radiance field (NeRF) framework tailored to clinically realistic acquisition constraints. The framework decomposes reconstruction into two stages that progressively refine spatial support and representation capacity. In the first stage, a coarse 3D representation of the vasculature is reconstructed, restricting the subsequent optimisation to regions with a higher likelihood of vessel presence, termed an active region. Afterward reconstruction is restricted to this region while higher-resolution representations are progressively activated to recover fine vascular details. This multi-stage strategy focuses learning on anatomically plausible regions, mitigates gradient dilution under extreme sparsity, and stabilises global topology before recovering fine vascular branches. Furthermore, two vessel-specific regularisations are introduced: a ray-aligned constraint to reduce projection-induced ambiguity, and a bimodal density penalty to enable early vessel-background separation. Extensive experiments across three datasets (ImageCAS, ASOCA, and Synthetic RCA) and four angular configurations demonstrate consistent superiority over state-of-the-art baselines, particularly under clinically realistic narrow-angle settings, while achieving reconstruction within 58 seconds per case.

Deyu Meng, Mojtaba Lashgari, Yiying Wang +1

Institute of Biomedical Engineering, Department of Engineering Science, University of Oxford, Oxford, United Kingdom

Coronary Angiography Neural Radiance Fields Vessels Projection Integrated C++ Development

Sep 12, 2026cs.CL

Cross-Lingual Clinical Annotation Projection as Constrained Text Generation: A Six-Language Study

Background: To determine whether cross-lingual clinical annotation projection can be formulated as a text-preserving, document-level generative task that produces verifiable character-level annotations for multilingual clinical corpus construction, and to characterize its robustness and computational trade-offs relative to candidate-based projection pipelines. Methods: We developed a constrained LLM projection workflow that inserts entity tags directly into immutable target-language text, followed by deterministic validation and character-offset reconstruction. We evaluated it alongside supervised candidate-span projection and hybrid ML-LLM refinement for transferring Spanish Disease, Symptom, and Procedure annotations into six languages. Evaluation used MultiClinAI gold standard with strict span matching and character-overlap F1 Results: Direct LLM projection achieved the strongest and most consistent performance. GLM 5.2 obtained a mean Strict F1 of 0.9201 across 18 language-entity combinations, while locally deployable Gemma4:31B achieved 0.9133. The best LLM configuration improved Strict F1 over the previous state of the art in all 18 settings, by 0.0564-0.1512, yielding 55,416 grounded mentions with reconstructed offsets. Conclusions: Direct LLM-based projection enables high-quality multilingual clinical annotation transfer and provides a practical approach for extending clinical NLP resources to languages with fewer annotated datasets and language-specific tools. Combined with local inference and deterministic validation, it can substantially reduce expert time and cost for multilingual clinical corpus construction.

Álvaro Rey-Blanes, Francisco J. Moreno-Barea, Francisco J. Veredas

Department of Programming Languages and Computer Sciences, Universidad de Málaga, Málaga, Spain · Research Institute of Multilingual Language Technologies, Universidad de Málaga, Málaga, Spain · IBIMA Plataforma BIONAND, Instituto de Investigación Biomédica de Málaga, Málaga, Spain

Natural Language Processing Motion-Language Alignment Language Pairs Text Corpora Projection Text Analysis and Detection

Sep 7, 2026cs.AI

Reducing Hallucinated Transcripts in Whisper via Hallucination Space Projection

Whisper is a widely used foundation model for automatic speech recognition (ASR), but its generative decoder can produce fluent hallucinated transcripts for inputs containing little or no speech. We propose a training-free, inference-time method to reduce these hallucinations using low-rank projection of decoder activations. A compact hallucination-associated subspace is estimated from non-speech calibration data, and decoder hidden states are projected away from this subspace during inference. We evaluate two variants: always-on, which applies projection to all inputs, and gated, which applies it only when Whisper predicts that an input is likely non-speech. Across non-speech benchmarks, always-on projection reduces average hallucination rate (HR) from 31.31% to 2.44%, a 92.21% relative reduction, while gated projection reduces HR to 3.74%, an 88.05% relative reduction, with lower false rejection of genuine speech. On LibriSpeech, gated projection increases absolute word error rate (WER) by 0.33-4.39 percentage points and yields false-rejection rates (FRR) of 0.41--9.97% across model and split settings. These results show that low-rank activation projection can substantially suppress Whisper hallucinations without retraining, while providing a controllable trade-off between hallucination suppression and speech recognition performance.

Maryam Abbasihafshejani, Murtuza Jadliwala

The university of Texas at San Antonio

Automatic Speaker Verification Hallucination Mitigation Generative Hallucination Transcript Projection

Sep 2, 2026cs.CV

Aggregating Neighbor Embedding Projection and Rank-Based Manifold Learning for Image Retrieval

Content-based image retrieval (CBIR) has advanced significantly with deep learning, yet effectively ranking similar images remains challenging, particularly in high-dimensional feature spaces, where pairwise distances often fail to capture contextual relationships and the semantic gap between visual features and high-level concepts persists. Manifold learning and rank-based refinement methods have emerged as complementary strategies, respectively improving feature representations and exploiting contextual information embedded in ranked lists, such as neighborhood relationships among images. However, combining these projection-based and rank-based strategies to exploit their complementary properties remains a challenging research problem. To address this, we propose a framework that combines neighbor embedding projections with rank-based manifold learning through rank aggregation. Uniform Manifold Approximation and Projection (UMAP) generates alternative low-dimensional feature representations, and ranked lists obtained from UMAP projections and rank-based re-ranking methods are combined using the Borda Count aggregation strategy. Experiments were conducted on several public datasets using deep learning features extracted from ResNet152, Swin Transformer, and DINOv2 models. Results show that the proposed approach improves retrieval effectiveness in several scenarios, particularly when the baseline representation struggles to achieve high precision. The aggregation strategy also often improves the quality of top-ranked positions, leading to competitive Mean Average Precision (MAP) and Precision values across different datasets and feature extractors. These findings suggest that combining projection-based and rank-based manifold learning strategies through rank aggregation can provide complementary contextual information for image retrieval tasks.

Vinicius Atsushi Sato Kawai, Gustavo Rosseto Leticio, Lucas Pascotti Valem +1

Department of Statistics, Applied Mathematics, and Computing (DEMAC), São Paulo State University (UNESP), Av. 24 A, Rio Claro, SP, 13506-900, Brazil. · Institute of Mathematics and Computer Science (ICMC), University of São Paulo (USP), Av. Trabalhador São-carlense, 400 - Centro, São Carlos, SP, 13566-590, Brazil.

Composed Image Retrieval Projection

Sep 1, 2026cs.AI

Neuro-Symbolic Geometric Abstraction (NeuSOGA): From Observations to Symbolic Mathematical Representations

A fundamental challenge in artificial intelligence is the transformation of observations into explicit symbolic representations suitable for abstraction, interpretation, and reasoning. While modern AI systems achieve remarkable perceptual capabilities through large-scale statistical learning, the resulting knowledge is typically encoded within latent parameters that are difficult to inspect or manipulate analytically. Inspired by Neuro-Symbolic AI and theories of human abstraction, this paper investigates the formation of symbolic mathematical representations from geometric observations. We propose NeuSOGA (Neuro-Symbolic Geometric Abstraction), a framework that progressively transforms observations into topological abstractions, geometric abstractions, and ultimately symbolic mathematical representations. The architecture combines topology-guided structural discovery using Euclidean Distance Transforms, foundation-model perception using Segment Anything, adaptive multi-scale geometric abstraction, and symbolic synthesis through Implicit Area Splines. The resulting representation is an analytical implicit model supporting arbitrary-order smoothness, additive composition, and closed-form evaluation. Unlike neural latent encodings, the generated representation remains interpretable, editable, and mathematically explicit. Experiments on ModelNet40 point clouds, arbitrary-view projections, and segmented optical observations demonstrate that NeuSOGA transforms diverse observations into compact symbolic representations while preserving essential geometric and topological structure across sensing modalities and viewing directions. NeuSOGA provides an interpretable and explainable pathway from observation to symbol and establishes

Qingde Li, Qingqi Hong, Zihan Li +1

Computer Science, School of Digital and Physical Sciences, University of Hull, HU6 7RX, UK · The Institute of Artificial Intelligence, Xiamen University, Xiamen, China

Neuro-Symbolic Framework Symbol-Neural Representations Artificial Intelligence Systems Projection

Sep 1, 2026cs.CL

Behaviorally Effective LoRA Writes Are Sparse and Structured

Low-rank adaptation fixes the rank of the update, but it does not identify which parts of a trained write actually carry behavior. We study that question directly and show that behaviorally effective LoRA writes are sparse, structured, and far more concentrated than the raw low-rank parameterization suggests. We use Learned-Basis LoRA, a learned-basis continuation recipe, to expose that structure. The recipe warms up an unconstrained adapter, converts its learned write columns into a module-wise orthonormal basis, freezes that basis, and continues training inside the constrained parameterization. Across 14 exact switches from unconstrained to constrained form, held-out accuracy is unchanged at the conversion step and reconstructed write matrices differ by at most 0.25% relative Frobenius error. Same-state continuation then shows that the same trained checkpoint develops differently under different write subspaces, establishing write geometry as a causal state variable. A no-retraining projection test shows that useful write signal stays inside the learned write space and largely disappears from random or frozen-activation PCA controls. The concentration pattern is strong at both local and global scales. Across GSM8K, MathQA, and AQuA, per-module top-k continuation reaches its optimum at k in {2, 4} in all twelve seed-level cases we test. A stricter global ranking test shows that learned top-16 and top-32 subsets outperform matched random subsets, especially on GSM8K/Qwen and MathQA/Qwen. Single-direction ablations further reveal a sparse set of late q_proj, o_proj, and down_proj components with outsized behavioral impact.

Haruto Sato, Yuki Tanaka, Ren Nakamura +2

Independent Researchers

Behavioral Divergence Continuation Projection Private Signals

Sep 1, 2026cs.CV

Soft-Argmax for the Projective Plane via the Veronese Embedding

From horizon detection to fibre structures in X-ray imaging, many vision tasks recover lines via peak detection in Hough space

H=S^1\times\mathbb{R}

, the domain of orientation-offset pairs

(θ,ρ)

. Differentiable pipelines extract coordinates via \emph{soft-argmax}, a probability-weighted average that is only meaningful in a globally linear space. However,

(θ,ρ)

and

(θ+π,-ρ)

describe the same undirected line, so

H

double-covers the space of undirected lines

H/\mathbb{Z}_2

: a Möbius strip, obtained by identifying each pair under

\mathbb{Z}_2

action. Soft-argmax operates on the cover

H

, but since

H/\mathbb{Z}_2

admits no linear structure, it tears geometrically adjacent lines apart. Thus we need a

\mathbb{Z}_2

-invariant embedding of lines into a linear space, on which soft-argmax is well-defined. We achieve this by parametrising lines via unit-norm homogeneous vectors

\ell=(1+ρ^2)^{-1/2}(\cosθ,\sinθ,-ρ)^{\top}\in\mathbb{R}^3

and applying the Veronese map

v_2(\ell)=\ell\ell^{\top}

that satisfies

v_2(\ell)=v_2(-\ell)

. This descends continuously to an embedding of the quotient

H/\mathbb{Z}_2

into the linear space

\mathrm{Sym}^2(\mathbb{R}^3)

, where the antipodal ambiguity vanishes. Line extraction becomes a barycentre in

\mathrm{Sym}^2(\mathbb{R}^3)

, projected back via its leading eigenvector. We validate our \emph{Veronese soft-argmax} in a Hough transform-based network across all resolvable lines, confirming uniform and seam-free recovery. We further derive that the

L_2

-loss on isometrically weighted Veronese embeddings equals the squared chordal distance between lines in projective space, enabling a geometrically precise training objective.

Benjamin El-Zein, Dominik Eckert, Paul Zech +4

Siemens Healthineers AG, X-ray Products, Forchheim, Germany · Artificial Intelligence Lab, Otto-von-Guericke-University, Magdeburg, Germany

Projection Spherical Latent Space Homography Gumbel-Softmax Relaxation Horizon

Aug 25, 2026cs.LG

PRQ-KMeans: Projection Residual Quantization for Semantic ID Tokenization

Semantic identifiers (SIDs) represent entities as hierarchical token sequences for generative retrieval and recommendation. Residual-quantization tokenizers construct these sequences by selecting a codeword at each level and passing a residual to the next. We view this process as progressive commonality removal: each token captures a component shared within its group, while later tokens should model the remaining differences. This view reveals three limitations: a corpus-wide shared component can consume first-level capacity, hard assignment ignores graded similarities to nearby codewords, and full-codeword subtraction can leave variation along the selected-codeword direction in the next residual. We therefore develop our solution in the post-hoc setting, where residual construction is not constrained by input reconstruction. Specifically, we propose PRQ-KMeans, which removes the global-mean component, refines centroids with Top-k similarity-weighted updates, and replaces full-codeword subtraction with a projection residual that removes each representation's selected-centroid component. Experiments on a large-scale industrial search dataset and four public recommendation benchmarks show that PRQ-KMeans achieves the strongest overall performance among the evaluated tokenizers, including gains of up to 7.4% in HitRate and 11.8% in MRR on the industrial dataset.

Yunxiao Luo, Siyuan Wang, Ben Chen +2

1Kuaishou Technology

K-Means Projection

Aug 11, 2026cs.IR

Post-Calibration Reliability Reranking of Relevance Decisions via Label-wise Monotone Projection

Web search, product search, and question-answering retrieval systems often assign a relevance label and confidence score to each query-candidate pair. The relevance label describes how well a page, product, or passage matches the query, while the confidence often guides downstream use or fallback decisions. Post-hoc calibration is therefore needed because misaligned confidence can make systems over-trust wrong predictions or unnecessarily defer correct ones. However, calibration mainly aligns confidence with average correctness, and does not remove predicted-label-dependent reliability differences that remain within the same calibrated confidence level. We address this gap with Label-wise Monotone Reliability Projection (MRP), which learns label-wise monotone functions that map calibrated confidence to correctness reliability while preserving the original predicted labels and class probabilities. The resulting reliability score reranks fixed predictions according to residual risk. Across six information access relevance datasets and multiple post-hoc calibrators, MRP improves reliability reranking and average fallback utility while preserving full-coverage accuracy and ECE. Structural ablations show that the main gains come from label-wise residual reliability rather than from global confidence remapping. We further analyze when MRP reliability scores can be embedded back into top-label probability geometry, showing that this projection is useful as a compatibility analysis but is distinct from the main reliability-reranking objective. The implementation will be made publicly available.

Inwoo Tae, Yongjae Lee

UNIST Ulsan, Republic of Korea · LinqAlpha New York, NY, USA

Relevance Projection

Aug 10, 2026cs.CL

Off-Axis, On Purpose: Where a Transformer Computes Concepts and Why it Does So

A transformer's answer lives on one axis: the direction its unembedding reads. Its intermediate states largely do not, and that off-axis position is usually treated as an obstacle to interpretation. We show it is functional. A 12-layer model computes in two phases. Through the first, every sublayer writes into a subspace held near-orthogonal to the read-out, attention 75 to 96 degrees off it at every depth. Moving attention's values onto the read-out is 64 to 84 times more damaging than a matched random rotation, and the damage is entirely in cross-token mixing: the subspace insulates composition from the vocabulary. Beneath it the frame itself turns rigidly with depth. In the second phase the answer arrives on-axis, late, and by addition rather than by turning accumulated content onto the read-out. Pressing every layer onto the read-out instead, as training for early exit does, matches the baseline on perplexity, LAMBADA and BLiMP while cutting the concept-phase workspace from about twenty-five effective dimensions to fourteen, a change none of those benchmarks register. The geometry can also be imposed, though not by asking for it. Prescribing it through the loss is a lottery: six of eight seeds collapse, because a model told to null its read-out projection obeys most cheaply by discarding dimensions. Inserting one fixed rotation at the phase boundary lands it instead, at baseline quality. A sparse rotation the surrounding weights can absorb converges on all nine seeds, against five of nine for ordinary training. Which rotation is immaterial: twenty-five runs across thirteen distinct ones reach the same quality, and two baselines from different seeds hold their concepts in near-orthogonal frames while agreeing on their read-outs. That freedom is usable: a basis drawn at random and prescribed before training is adopted across the concept phase, with quality unchanged.

Mark Oskin

School of Computer Science and Engineering University of Washington

Transformer Architectures Projection

Aug 10, 2026cs.LG

Recurrent Neural Networks Beyond Time: Learning from Multiple Ordered Projections

Recurrent neural networks (RNNs) are widely used for sequence learning, yet their application is commonly associated with temporal data, although recurrent computation fundamentally operates on ordered sequences rather than on time itself. Building on this observation, we introduce the Ordered Structural Dependency Hypothesis (OSDH), which proposes that multiple admissible orderings of the same observations may reveal complementary structural dependencies inaccessible through a single sequential organization. To operationalize this hypothesis, we propose the Independent Structural Expert Principle (ISEP), whereby projection-specific sequence models are trained independently before their learned representations are integrated through a dedicated fusion model. As a concrete realization, we present Structural Evolution RNNs (SE-RNNs), which employ conventional RNNs as projection-specific structural experts while preserving the underlying recurrent computation unchanged. Proof-of-concept experiments on three synthetic datasets with substantially different levels of structural complexity demonstrate that the proposed architecture consistently benefits from multiple ordered projections when hidden structural dependencies are present, while remaining competitive on simpler datasets. Since OSDH is independent of the underlying sequence-processing model, the proposed framework naturally extends beyond recurrent networks and may be instantiated using alternative architectures. The results suggest a general computational perspective for exploiting complementary ordered representations across diverse structured learning problems.

Vagan Terziyan, Artur Terziian, Oleksandra Vitko

Faculty of Information Technology, University of Jyväskylä, FINLAND · Faculty of Informatics and Statistics, Prague University of Economics and Business, Czech Republic · Department of Artificial Intelligence, Kharkiv National University of Radio Electronics, Ukraine

Recurrent Neural Networks Sequence Modeling High-Order Correlations Sequential Neural Network Projection

Aug 9, 2026cs.CV

Damage Classification for 3D Point Cloud Data via 3D Data Analysis and Vision Foundation Model-based 2D Projections

Fine-grained damage classification of 3D point cloud data (PCD) remains a persistent challenge, constrained by high computational demands and limited labeled data. This study examines two methods: 3D PCD-based damage assessment (3PDA) algorithm and 2D projection damage assessment (2PDA) In our 3PDA analysis algorithm, TDA is used to derive compact representations of 3D PCD segmented by pointNet, which are then integrated with anomaly detection algorithms to quantify structural degradation. We show that TDA effectively compresses geometric structure from VFM-segmented components into discriminative feature vectors and that anomaly detection models can reliably distinguish components with varying damage severity using only 3D PCD inputs. In the 2D projection analysis algorithm, we leverage large VFMs for granular damage detection by projecting 3D PCD into 2D views. These projections allow VFM based models to achieve competitive classification performance while requiring only a fraction of the computational cost associated with full 3D data processing. Our results demonstrate that 2D VFM pipelines in 2PDA can perform strongly on fine-grained damage classification tasks, highlighting their viability as lightweight, resource-efficient alternatives to traditional 3PDA architectures. Comparative evaluation shows that the 3PDA attains higher accuracy but only for a narrow subset of object geometries and at substantially higher computational cost due to its reliance on TDA and the scarcity of high-fidelity 3D datasets. In contrast, the 2PDA algorithm yields slightly lower accuracy but offers an order of magnitude reduction in time complexity and generalizes across a far broader range of object categories.

Evan Perez, Kalelo Dukuray, Erika Ardiles-Cruz +1

Dept. of Computer Science, City College of New York, NY 10031, USA · Air Force Research Lab, Rome, NY 13441, USA

Point Clouds Interactive 3D Segmentation Post-Disaster Damage Assessment Structural Damage 3D Generation Projection+1

Aug 9, 2026cs.LG

Exact Rank-Space KL Projection for Shared-Marginal Low-Rank Factors: Application to Doubly Stochastic Clustering

We study exact Kullback--Leibler (KL) projection for low-rank factorizations whose two nonnegative factors have prescribed row marginals and a shared, learned column marginal. For arbitrary positive row marginals of equal total mass, the joint KL projection reduces exactly to a strictly convex gauge-fixed dual with only

r-1

effective variables; its Hessian is a sum of categorical covariance terms and admits

O((n+m)r)

matrix-free Hessian--vector products. The projection theorem is objective-independent. We then specialize this geometry to doubly stochastic (DS) graph learning through

W=U\operatorname{Diag}(g)^{-1}V^\top

, where row-simplex factors with a common column mass induce an exactly DS graph without materializing an

n\times n

optimization variable. Combined with observed-edge sparse fitting, a stochastic anchor-reduced manifold regularizer, and Bregman backtracking, the resulting mirror-descent method preserves exact feasibility at every accepted step. Under a nonvanishing latent-mass condition, it satisfies sufficient decrease and an

O(1/N)

mirror-stationarity bound, while strictly positive accumulation points are KKT stationary. Matched clustering experiments show competitive accuracy, feasibility residuals near numerical precision, and favorable anytime behavior without a dense learned graph.

Enliang Hu

Low-Rank Structure Factor Hessian Kullback-Leibler Divergence Projection

Aug 2, 2026cs.AI

Toward Fine-Grained Forgetting:Attribute Unlearning for Multimodal Large Language Models

Multimodal large language models (MLLMs) exhibit strong vision--language capabilities but may also memorize and disclose sensitive information. Machine unlearning seeks to remove designated knowledge without retraining from scratch while preserving general utility. Existing privacy-oriented benchmarks primarily adopt profile-level deletion, whereas practical requests are often finer grained: a model should forget a specified attribute while retaining non-sensitive information about the same identity. We therefore introduce attribute-level MLLM unlearning as a finer-grained task and construct a benchmark spanning long-text, numeric, and short-text targets, multiple forget ratios, and diverse question types. Our evaluation reveals that target and retained attributes share identity-specific and visual evidence, making selective forgetting susceptible to residual leakage or collateral degradation; accordingly, existing methods exhibit unstable forgetting--retention trade-offs in this setting. To address this challenge, we propose Causal Localization and Retain-Aware Projection (CLRP), a lightweight training-free framework. CLRP uses activation patching to identify the layer that causally mediates target-attribute disclosure, then applies a retain-aware projection that removes the target-attribute subspace while preserving same-identity evidence. Experiments across multiple widely used MLLMs with distinct architectures and parameter scales demonstrate the effectiveness of CLRP.

Junkai Lin, Junkai Chen, Siqi Hou +5

Institute of Automation, Chinese Academy of Sciences · The Chinese University of Hong Kong · The Australian National University +3

Large Language Model Unlearning Multimodal Large Language Models Catastrophic Forgetting Forgetting Data Leakage Projection

Aug 1, 2026cs.RO

OmniAI: A Surface-Adaptive Aerial Projection Interface for Human--Drone Interaction

Drones in human environments often lack spatially grounded in- terfaces for situated communication. We present OmniAI, an em- bodied aerial agent that supports surface-adaptive interaction by switching projection between an onboard screen and nearby en- vironmental surfaces. A servo-actuated MEMS laser projector renders text-and-image responses from a web-augmented LLM pipeline. Projection surfaces are detected online using RGB-D sensing and RANSAC plane fitting, without pre-mapped geometry. OmniAI provides functionally equivalent voice and gesture con- trol for both drone motion and projected content. By combining speech, mid-air gestures, adaptive projection, and aerial mobility, OmniAI demonstrates a mobile spatial AR interface for context- aware human-drone interaction.

Nikita Kuzmin, Yuhua Jin, Georgii Demianchuk +6

Intelligent Space Robotics Lab, Skolkovo Institute of Science and Technology, Moscow, Russian Federation · School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, Guangdong, China

Embodied Artificial Intelligence Omni Omnimem Projection Mobility

Jul 24, 2026cs.CL

Simple Language Normalization Wins: Cross-Lingual Speaker Verification for the TidyVoice 2026 Challenge

Cross-lingual mismatch remains a key source of overall degradation in modern speaker verification. The TidyVoice2026 Challenge targets this setting with text-independent verification, comprising 3,666 training and 808 development speakers in 40 languages and 2,200 evaluation speakers in 38 unseen languages, without language labels at test time. Starting from the official SimAM-ResNet34 baseline pretrained on VoxBlink2 and VoxCeleb2 and fine-tuned on TidyVoice, we revisit Nuisance Attribute Projection (NAP) as a simple language-normalization step in the embedding space. We estimate a compact language subspace from cross-language same-speaker differences and project embeddings onto its orthogonal complement before cosine scoring with Adaptive Symmetric score normalization. This reduces development EER from 2.97% with cosine and 2.70% with AS-Norm to 2.18% and yields a Codabench evaluation score of 8.40, showing that simple back-end language normalization can rival more complex systems.

Nina Hosseini-Kivanani

University of Luxembourg & Radio T´el´evisioun L¨etzebuerg (RTL), Luxembourg

Automatic Speaker Verification Cross-Lingual Consistency Projection

Jul 17, 2026cs.CL

EpiNarrate: Agentic Generation of Grounded Narratives from Epidemiological Scenario Projections

Generation of clear and accessible public health narratives is critical for communicating complex epidemiological projections to policymakers and the general public at large. Such narratives require more than simply reporting numbers: projections must be contextualized and quantitatively grounded across multiple dimensions. Further, projections are often derived from large ensemble datasets which combine intervention assumptions, geographic and demographic strata, outcomes, time horizons, and uncertainty quantiles. However, directly using large language models (LLMs) to summarize and contextualize such data often leads to inconsistencies, omissions, and fragile behavior. We introduce an agentic framework (EpiNarrate) for public health report generation that separates structured numerical reasoning from natural-language generation. The framework first extracts scenario axes and organizes them into a partial-order schema, enabling systematic traversal of the underlying multidimensional space. It then constructs an augmented dataset and derives valid quantitative statements through a comparison grammar that enforces semantic and arithmetic consistency. To balance coverage and non-redundancy, we introduce an interestingness-driven selection mechanism based on maximum-entropy principles. Experiments on the COVID-19 Scenario Modeling Hub demonstrate that our model produces narratives with improved factual grounding and broader coverage of salient epidemiological patterns, while preserving the style of expert-written reports.

Rituparna Datta, Srini Venkatramanan, Bryan L. Lewis +6

Department of Computer Science University of Virginia · Biocomplexity Institute University of Virginia · Department of Computer Science Virginia Tech +1

Epidemiological Models Medical Report Generation Narratives Projection

Jul 15, 2026cs.LG

HyperShadow: A Benchmark for Detecting 3D Projections of Higher-Dimensional Spatial Objects

Machine-learning datasets labelled "4D" universally denote three spatial dimensions plus time. We introduce HyperShadow, the first public benchmark in which the fourth, fifth, and sixth dimensions are spatial: the task is to decide whether a 3D point cloud is a native three-dimensional shape or the projection, the "shadow", of a rigid object living in R^N (N = 4-6). We show this task is fundamentally distinct from intrinsic-dimension estimation: a shadow is still at-most-3-dimensional data, and standard estimators (TwoNN, Levina-Bickel MLE) reach only 71-73% accuracy. Detection instead requires projection signatures, density folds, filled volumes with characteristic radial profiles, and topology changes, which a 190k-parameter point network recovers at 96.6% accuracy across four corruption tiers, generalizing at 79-91% to object families never seen in training. On a temporal track of rigidly rotating objects we introduce a zero-parameter rigidity witness: the residual of the optimal rigid 3D alignment (Kabsch) between consecutive frames, which must vanish for any rigid 3D motion but cannot vanish for the shadow of a rigid rotation in R^N. This single interpretable statistic separates the classes at AUROC 0.982. All data are generated reproducibly from seeds; the dataset, models, and code are released publicly. HyperShadow makes no claim about physical reality; it is a controlled instrument for studying which observable statistics can certify incompatibility with a purely three-dimensional explanation.

Akshay Sasi

Independent Researcher

Projection 4D Rigid Objects Objects

Jul 13, 2026cs.CL

Unified Gradient Projection: Language-Balanced Continual Learning for Multilingual Low-Resource ASR

Large-scale pretrained ASR models such as Whisper exhibit strong multilingual capabilities. However, fine-tuning on low-resource languages often causes catastrophic forgetting. Although continual learning mitigates this issue, existing methods struggle to regulate cross-task interference in multilingual settings, where dominant languages bias optimization. We propose Unified Gradient Projection (UGP), which constrains parameter updates using reference gradients from language-balanced replay in a unified projection space. By equalizing per-language contributions in the projection, UGP reduces dominant-language bias and improves cross-lingual stability. We further show that combining gradient-level projection with data-level replay yields complementary gains in stability and plasticity. Across diverse low-resource language groups and model scales, UGP enables effective adaptation while substantially mitigating forgetting. On Whisper-large-v3, it achieves near-zero average forgetting.

Ziang Ren, Guodong Lin, Yuchen Ai +2

Department of Electronic Engineering, Tsinghua University, China

Multilingual Automatic Speech Recognition Whisper-Large-V3 Cross-Lingual Consistency Continual Learning Projection

Jul 10, 2026cs.LG

Graph-Regularized Low-Rank Matrix Completion by Variable Projection

We address the low-rank matrix completion problem by incorporating graph regularization into the existing Riemannian Trust-Region Matrix Completion (RTRMC) framework. The latter uses the geometry of the low-rank constraint to remodel the problem as an unconstrained optimization problem on a single Grassmann manifold. Our approach, named Graph-Regularized RTRMC (GR-RTRMC), exploits the inherent relationships between rows and columns of the matrix. By using these relationships, we aim to improve the accuracy and robustness of matrix completion, particularly in scenarios where the underlying data exhibits strong correlations between rows or columns.

Benoît Loucheur, P. -A. Absil, Michel Journée

ICTEAM Institute, UCLouvain, 1348 Louvain-la-Neuve, Belgium. · Department of Climatology, Royal Meteorological Institute of Belgium, 1180 Uccle, Belgium.

Tensor Completion Low-Rank Structure Matrix Regularization Projection Completion

Jul 6, 2026cs.LG

PatchOptic for Shared-State LLM Workflows with Projected Views and Verified Structured Updates

Agentic workflows often operate over shared, structured state. Because LLM context windows are limited, each model invocation is typically shown only the state fragment needed for the current workflow step, a pattern commonly known as progressive disclosure. Modern systems construct such model-facing views using grep-like keyword search, retrieval-augmented generation (RAG), abstract-syntax-tree (AST) queries, and task-specific agent skills. These methods make the read side manageable, but they do not define when a locally proposed rewrite is valid after it is applied back to the full state. The missing piece is a contract between local updates and global validity. We introduce PatchOptic, an optic-inspired interface for shared-state LLM workflows. Optics are compositional bidirectional accessors that describe how views of structured data are read and updated. PatchOptic borrows this view/update intuition and realizes it through projected reads and verified structured patches. Each workflow step declares a projected read view, an authorized write region, and a patch-source region. Beyond runtime enforcement, the same declaration yields a path-level footprint that supports delegation, sub-workflow composition, and static certificates for reordering independent steps within the same phase. We evaluate this design with PatchBench, a benchmark with 46 cases across domains. The results show that projected reads reduce reported leakage and token cost while preserving accepted-output quality under the strong actor. Runtime verification blocks declared workflow-contract violations before commit, and patch-read enforcement rejects compromised patch artifacts that use hidden sources.

Zhaoyu Bai, Jiaqi Cai

Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot, Israel, 7610001 · Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA, 02139

Large Language Model Workflows Disclosures Projection

Jul 6, 2026cs.LG

Platonic Projection Structures: Operator-Induced Observability in Representation Learning

We characterize observability in representation learning through Platonic Projection Structures (PPS), an operator-theoretic framework for analyzing representation accessibility under partial observation. Rather than treating observable outputs as direct reflections of latent representations, PPS models observation through a self-adjoint positive semidefinite operator acting on a latent representation space. A system is represented as a triple

(H, Π, O)

, where

H

is a latent representation space,

Π\succeq 0

is an observation operator, and

O(v)=\langle v,Πv\rangle

defines an induced scalar observable. Observability is characterized by the quotient geometry

H/\ker(Π)

, representing equivalence classes of latent states indistinguishable under observation. We show that quantum measurement and representation inference under linear observation models share this operator-theoretic structure while differing in the algebraic properties of their observation operators; the correspondence is structural rather than physical. Representation transfer and knowledge distillation can likewise be interpreted as approximate preservation of observable geometry through

ΦΠ_T \approx Π_S Φ

. PPS also reveals a structural limitation of output-based interpretability: latent components in

\ker(Π)

are inaccessible from induced observables, imposing intrinsic constraints on attribution and explanation methods. Controlled empirical validations demonstrate kernel-invariant observability, projection-induced attribution gaps, and rank-controlled observable geometry in latent representation spaces. PPS thus provides an explicit characterization of observability through operator-induced quotient geometry and a unified perspective on representation accessibility, interpretability, and projection-mediated inference.

Kazuo Ishii, Bishnu Prasad Gautam, Jieling Wu +1

Department of Applied Information Engineering, Faculty of Engineering, Suwa University of Science, Chino 391-0292, Nagano, Japan · Department of Information Engineering, Kanazawa Gakuin University, Kanazawa 920-1392, Ishikawa, Japan

Partial Observability Representation Space Latent States Representation Learning Projection

Jul 4, 2026cs.HC

Scalable Semantic Steering of Embedding Projections

Low-dimensional projections support interactive visual analysis of high-dimensional data embeddings, but their structure often does not align with analyst-defined semantic relationships. Recent LLM-augmented semantic steering methods address this gap by externalizing analyst intent from user-defined groups of seed examples, but they propagate intent through per-item LLM reasoning, causing LLM calls and cost to grow linearly with collection size. We propose a scalable semantic steering method that shifts semantic computation from individual items to user-defined groups. A single LLM call generates structured profiles for all groups, which are embedded and combined with seed centroids to form hybrid semantic prototypes. The method then propagates intent without retraining, using embedding-space soft assignment, abstention, and alignment-scaled updates before reprojection. On a 5K-document LitCovid corpus, our method achieves global alignment comparable to per-item LLM steering while reducing LLM calls by over three orders of magnitude. An image case study shows that the same prototype-based mechanism extends to multimodal embeddings. These results suggest that group-level representations can make semantic steering more practical for larger embedding collections.

Wei Liu, Eric Krokos, Kirsten Whitley +2

Virginia Tech · Department of Defense · Tulane University

Semantic Relationships Learnable Prototypes Projection Text Corpora

Jul 1, 2026cs.CL

Recovering Input Text from Hidden States: Study of Gradient-Based Inversion of Decoder-Only Language Models

This work studies the hidden-state inversion problem: recovering the original input token sequence of a decoder-only language model from its last-layer hidden states. Rather than treating inversion as a one-shot reconstruction, we study it as a continuous embedding-space optimisation in which a soft proxy is driven towards the leaked target without any hard-token projection during the search, and a token is committed only once, at the end of the inner loop. This design choice has two consequences which are the main focus of this paper. First, keeping the optimisation entirely in continuous space exposes a rich set of internal signals: rank trajectories of the ground-truth token, per-position loss curves, and a discrete loss measured at commit time. Second, the discrete loss allows assessing the correctness of recovery via cumulative discrete loss. We further analyse which tokens break the reconstructions and find a sharp categorical asymmetry: space-prefixed, high-frequency function words in dense regions of the embedding matrix dominate the failures, while content-bearing tokens are recovered almost perfectly. On 10-token C4 prompts the exact-match rate rises from 66.9% to 97.5% (mean similarity 0.994) as the candidate window is widened, confirming that most errors are recoverable near-misses rather than genuine ambiguities. A comparison with the released SIPIT reference situates these findings: per-step hard projection is faster, but the continuous formulation is what makes the optimisation observable and its failures detectable. The results show that last-layer hidden states of GPT-2 are as sensitive as the original text.

Mikołaj Słowikowski, Maciej Witold Majewski

AGH University of Krakow, Faculty of Physics and Applied Computer Science, al. Mickiewicza 30, 30-059 Krakow, Poland

Hidden States Diffusion Inversion Behavioral Embeddings Projection

Jun 30, 2026cs.LG

SNAP-FM: Sparse Nonlinear Accelerated Projection for Physics-Constrained Generative Modeling

Generative models have emerged as scalable surrogates for physical simulation, yet they offer no guarantee that their outputs respect the conservation laws, boundary conditions, and nonlinear invariants that govern the underlying physics. Constrained sampling closes this gap, enforcing such constraints exactly at inference time without retraining, but at a computational cost: projection, correction and trajectory-optimization steps are repeated during sampling, with these steps becoming expensive for nonlinear constraints. Standard ML frameworks exacerbate this: their dense tensor algebra and limited sparse solver composability obscure the structure that physical constraints naturally induce, making efficient batched nonlinear optimization difficult to realize in practice. We address this bottleneck by exploiting the structure that sample-wise batching and local PDE couplings induce in the projection subproblems -- namely, block-sparse Jacobian and KKT systems -- exposing this structure using ExaModels.jl and solving the resulting sparse nonlinear programs with MadNLP.jl and GPU sparse factorization. Applied to Physics-Constrained Flow Matching (PCFM), on PDE benchmarks with linear, nonlinear, one-dimensional, and two-dimensional constraints, this approach accelerates nonlinear constraint projection while maintaining constraint satisfaction. These results show that sparse GPU nonlinear optimization is a practical foundation for constrained generative sampling in scientific machine learning.

Alaina Kolli, Theodoros Xenakis, Utkarsh Utkarsh +4

Massachusetts Institute of Technology, Cambridge, MA, USA · Norwegian University of Science and Technology, Trondheim, Norway

Inequality Constraints Solver Iterations Generative Models Conditional Flow Matching Physics Simulation Solvers+3

Jun 29, 2026cs.HC

Information Terra: A Narrative-Anchored Semantic-First Projection of Document Embeddings

We introduce Information Terra, a narrative-anchored semantic-first projection that places a document corpus on an Earth-like globe whose poles are two user-chosen endpoint documents and whose prime meridian is the great-circle geodesic between them on the embedding hypersphere -- so latitude encodes narrative progress and longitude thematic deviation. Land features are recovered from document density via kernel density estimation and labeled by theme. A narrative trail built from the underlying narrative coherence graph, and constrained to be monotone in geodesic progress, provides a readable storyline. The projection's axes are semantically grounded in the user's chosen narrative endpoints, and the globe metaphor affords rotation and antipodal reading. We demonstrate the method on a 540-article Cuban Protests corpus, showing a storyline from Obama's 2016 visit to the 2021 International Aid during the protests.

Brian Keith-Norambuena, Fausto German, Chris North

Universidad Cat´olica del Norte, Chile · Virginia Tech

Narratives Text Embeddings Semantic Geometry Projection Text Corpora Metaphors

Jun 22, 2026math.OC

Constrained Variable Projection for Structured Problems

Variable projection is a classical technique for separable nonlinear least-squares problems, in which variables that enter linearly are eliminated exactly, yielding a reduced nonlinear problem. By expressing this framework as a particular instance of a broader class of bilevel optimization problems, we develop a constrained variable-projection framework for data-science models, where the remaining variables are subject to convex constraints and the eliminated variables arise from a lower-level least-squares problem. In particular, by interpreting variable projection as a collapsed bilevel optimization problem, we derive exact reduced-gradient formulas compatible with automatic differentiation and propose a conditional-gradient algorithm for the resulting constrained reduced problem. We establish convergence guarantees under standard smoothness and compactness assumptions, and discuss extensions to structured lower-level variables. Numerical experiments on sparse autoencoding, dictionary learning, blind deconvolution, and few-shot learning suggest that the method can improve wall-clock efficiency and data efficiency relative to natural joint-optimization baselines.

Emanuele Zangrando, Sara Venturini, Francesco Rinaldi +1

Gran Sasso Science Institute, L’Aquila, Italy. · MOBS Lab, Northeastern University, Boston, USA. · University of Padova, Padova, Italy. +1

Bilevel Optimization Projection Least Squares

Jun 21, 2026cs.CV

MAPS: Multi-Anchor Projection Similarity for Joint Vision-Language Geo-Localization

Humans localize places by integrating perceptual cues from vision with semantic reasoning from language, forming a scene understanding that is both intuitive and structured. Although existing geo-localization models have made substantial progress in cross-view and cross-modal settings, they are largely built upon point-to-point alignment, which is insufficient for joint vision-language queries. In such queries, visual and textual cues do not simply act as independent references, but jointly define a semantic subspace for locating the target. In this paper, we formulate vision-language geo-localization (VLGL) with joint image-text queries as a multi-anchor geometric alignment problem and propose a unified framework for this setting. To realize this formulation, we propose Multi-Anchor Projection Similarity (MAPS), a new metric which constructs an anchor plane from visual and textual query features in a high-dimensional space and measures similarity by the projection length of the target feature onto this plane. Unlike cosine similarity which evaluates isolated pairwise relations, MAPS captures the geometric consistency between the target feature and the joint query subspace, providing a more discriminative ranking criterion during retrieval. To make the learned representation consistent with this geometry, we further introduce a MAPS-based contrastive loss that drives target features toward the corresponding anchor plane. The proposed framework, similarity metric, and training objective jointly yield state-of-the-art performance in VLGL.

Yutong Hu, Siyuan Tan, Shaocheng Yan +3

School of Remote Sensing and Information Engineering, Wuhan University, Wuhan 430079, China

Cross-View Geo-Localization Vision-Language Alignment Projection Similarity and Metrics Subspace

Jun 21, 2026cs.CV

Physically-guided Image Generation for Multi-Projection Mapping

Projection Mapping (PM) enables seamless superimposition of digital content onto real-world 3D objects, serving as a fundamental technique for immersive visualization, digital twins, and interactive art. Although text-to-image diffusion models have greatly facilitated customized content creation, directly integrating them into practical PM pipelines remains challenging due to the mismatch between idealized 2D generation and physical constraints. To bridge this gap, this paper formalizes two application-level generative paradigms: the cooperative paradigm (harmonizing generated semantics with physical attributes) and the adversarial paradigm (eliminating surface interference via radiometric compensation). Based on this, we propose ConPhyG, a unified controllable physically-guided generative multi-projection mapping framework that enables creators to interactively adjust physical constraints and flexibly switch generative paradigms. In cooperative mode, multi-dimensional physical priors (per-pixel gamut, depth, and edges) are injected into the diffusion process. In adversarial mode, the framework releases the generative potential and applies bounded numerical optimization for multi-projector radiometric compensation. It allows users to dynamically switch constraints to balance artistic freedom with physical feasibility. Furthermore, we extend ConPhyG to 360-degree multi-view consistent PM using a sequential generation strategy. Quantitative and qualitative evaluations on a real-world four-projector setup demonstrate that ConPhyG significantly outperforms state-of-the-art methods in geometric alignment, gamut utilization, and semantic fidelity.

Xingyun Liu, Yuqi Li, Jinhui Xiang +2

Ningbo University, Ningbo, 315211 P.R.China.

Projection Multimodal Diffusion Models Image Generation Adversarial Robustness

Jun 21, 2026cs.LG

Encoder-Decoder Manifold Alignment for Idempotent Generation

Recently, several learning paradigms have been introduced to enforce idempotency in generative models. The goal is to ensure that repeated application of a model leaves samples unchanged once they lie on the target data manifold. In practice, however, many of these approaches fail to achieve exact fixed points, leading to instability and drift under repeated application. In this work, we argue that a key reason for this failure is a geometric mismatch between the manifolds learned by the encoder and decoder. The encoder projects inputs onto one latent manifold, while the decoder implicitly learns to reconstruct data from a different manifold. This discrepancy prevents the model from learning truly idempotent mappings. To address this issue, we propose a new training framework that explicitly closes this gap by forcing the encoder and decoder to learn consistent representations of the same underlying data manifold. By aligning the geometry of these components, our method encourages stable projections. Empirically, we show that our approach achieves significantly lower idempotency error and consistently regenerates identical outputs under repeated application, compared to existing methods. We demonstrate the effectiveness of the proposed framework on both image generation and image editing tasks. Finally, we show that enforcing idempotency in this manner improves identity preservation and information stability, leading to more realistic and controllable generative editing models.

Dareen Alharthi, Abdul Waheed, Bhiksha Raj

Carnegie Mellon University

Generative Models Data Manifold Projection

Jun 15, 2026cs.LG

PhysGuard: Fisher-Guided Gradient Projection for Sim-to-Real Neural PDE Surrogates

Neural operator models trained on simulation data often lose accuracy when applied to experimental measurements due to the sim-to-real gap. Standard fine-tuning with limited real data can reduce this gap, but it may also damage the core physics-relevant representations learned during pretraining. Although knowledge-preserving adaptation has been widely investigated in vision or language tasks, it remains unclear whether these methods are suitable for neural operators whose architectures and protected knowledge are fundamentally different. Neural operators need to preserve core-scale physical structures rather than semantic or visual features. We propose PhysGuard, a physics-preserving framework for accurate sim-to-real adaptation of neural operators. Specifically, PhysGuard uses the empirical Fisher Information Matrix computed on simulation data to identify physics-critical parameter directions, then restricts fine-tuning updates to directions that do not interfere with them. A layer-wise Gram-matrix formulation makes this efficient for models with millions of parameters, while an adaptive threshold automatically determines the protected subspace size. A spectral probe experiment shows that the dominant Fisher directions are strongly associated with low-frequency output structures. Experiments on benchmark across four neural operator architectures and different physical systems show that PhysGuard performs strongly on most evaluation metrics compared to baselines. The benefits are most evident under severe domain shift, where it reduces low-frequency error by up to 32% compared to standard fine-tuning while maintaining adaptability. Our code is available at https://github.com/ZhouChaunge/PhysGuard.

Changjian Zhou, Junfeng Fang, Negin Yousefpour +3

Faculty of Engineering and IT, University of Melbourne · School of Computing, National University of Singapore · Artificial Intelligence Research Institute, IFLYTEK Co., Ltd.

Neural Operators Parametric Physics-Informed Neural Network Fisher Information Matrix Sim-To-Real Gap Projection

Jun 15, 2026cs.CV

Transformation-driven generation of comparable projection images from multimodal anatomical scenes

This work addresses the computational problem of generating reproducible projection-space observations from heterogeneous anatomical scenes whose components may undergo independent spatial transformations. We propose a transformation-driven framework for synthetic projection imaging from multimodal anatomical data and demonstrate it on mandibular-motion scenarios. In contrast to conventional Digitally Reconstructed Radiograph (DRR) approaches primarily designed for registration, projection realism, or rendering efficiency, the proposed formulation treats projection imaging as an observation process operating on an explicitly represented anatomical scene. Independently transformable volumetric and surface-based anatomical objects are embedded within a shared scene representation and propagated directly into projection space through explicit transformations. Projection geometry, acquisition modelling, material interpretation, and image presentation remain explicitly separated, enabling controlled exploration of methodological assumptions while preserving reproducibility and direct comparability between generated projections. Particular emphasis is placed on transformation-driven anatomical scenarios relevant to craniofacial analysis, including mandibular motion and therapeutic repositioning. Using a shared anatomical reference scene composed of CT/CBCT volumes, segmented structures, surface models, and auxiliary anatomical or therapeutic objects, the framework enables generation of directly comparable VirtualRTG projections from multiple anatomical configurations while preserving identical imaging assumptions. Rather than aiming at fully physically faithful radiographic simulation, the proposed approach provides a controllable and reproducible methodological environment for studying anatomy--projection relationships, motion observability, and transformation-aware imaging workflows.

Dariusz Pojda, Krzysztof Domino, Michał Tarnawski +1

Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, Bałtycka 5, 44-100, Gliwice, Poland

Digitally Reconstructed Radiographs Anatomy Projection Vision-Language Reprojection Consistency Occlusal Constraint

Jun 14, 2026cs.CV

Shear-Free Viewport Magnification for 360-Degree via Spherical Mobius Boosts

Viewport-adaptive 360-degree imaging seeks to allocate a fixed sampling budget to the region a viewer is likely to observe. Existing view-biased projections increase viewport resolution through non-conformal warps, which can introduce anisotropic stretching and shear. We formulate spherical Mobius boosts as exact conformal maps for fixed-budget viewport magnification. The continuous spherical warp has quasiconformal dilatation K = 1, reallocating samples toward a target direction while preserving local angles. On a SUN360 saliency audit with 72 panoramas and 216 paired viewport targets, C1 Mobius boosting improves viewport PSNR over optimized offset cubemap on all paired cases, with case-level median gain +3.26 dB, image-level median gain +3.23 dB, and panorama-level bootstrap 95% CI [+3.15, +3.33] dB. Pareto analysis shows that this is not a free global-quality improvement: C1 trades full-sphere WS-PSNR for shear-free viewport fidelity. Prediction-error and filtering studies identify the operating envelope: strong boosts are useful for accurately targeted viewports, while large target uncertainty calls for weaker boosts or fallback. These results position Mobius boosting as a geometric primitive for prediction-conditioned foveated 360-degree resampling rather than a universal encode-once layout.

Boyang Li, Hezhao Xu

Peking University

Omnidirectional Images Vision-Language Reprojection Consistency Distortion Projection

Jun 13, 2026cs.LG

Rethinking Structural Anomaly Detection: From Decision Boundaries to Projection Operators

Most existing anomaly detection methods rely on estimating a probability density or learning an enclosing decision boundary, implicitly assuming that normal data occupies a region of non-zero volume in the ambient space. In contrast, structural anomaly detection considers data that lies near a low-dimensional manifold, creating a mismatch between the inductive bias of existing methods and the structure of the data, often resulting in degraded performance. To address this mismatch, we introduce a geometric perspective. Specifically, we learn a projection operator onto the manifold of normal samples and define a sample as anomalous if it is altered by this projection. This formulation naturally integrates the inductive bias of manifold-supported data and reframes anomaly detection in terms of a projection residual, thereby resolving issues arising from modeling degenerate distributions. Notably, it provides a unifying interpretation of reconstruction-based methods by explaining their success and failure in terms of projection quality. In particular, it explains the strong generalization ability of projection-aligned models as a consequence of contraction behavior toward the manifold. Moreover, by decoupling anomaly detection from probabilistic modeling, it reduces the tendency to misclassify rare but normal samples, a widely recognized limitation of existing approaches. Empirically, we demonstrate that projection-aligned methods achieve strong performance, outperforming boundary-based methods while improving upon existing reconstruction-based approaches.

Alexander Bauer

Machine Learning Group, TU Berlin · BIFOLD, Berlin, Germany

Graph Anomaly Detection Projection Data Manifold Decision Boundaries Inductive Bias

Jun 11, 2026eess.AS

Generating Training Targets for Real-World Speech Enhancement via Close-to-Distant Microphone Projection

Training neural networks (NNs) for speech enhancement (SE) in distant speech-capturing scenarios requires paired distorted and clean reference speech signals. While such data are often generated through simulation, the mismatch between simulated and real recordings significantly limits SE accuracy. To address this issue, we propose Close-to-Distant microphone Projection (C2D projection), a method that generates paired data from real recordings captured by close and distant microphones. C2D projection estimates an optimal projection matrix that transforms close-microphone inputs into clean reference signals aligned with distant-microphone recordings, while simultaneously performing denoising. We show this projection can be effectively realized using a variant of the Parametric Multichannel Wiener Filter (PMWF). Experimental results demonstrate that an NN trained with C2D-projected data outperforms the state-of-the-art Guided Source Separation (GSS) on the challenging CHiME6 dinner party ASR task under oracle diarization, when using the enhanced output from GSS as an auxiliary input to the NN.

Tomohiro Nakatani, Rintaro Ikeshita, Naoyuki Kamo +2

NTT, Inc., Japan

Speech Enhancement Speech Separation Microphone Array Projection

Jun 10, 2026cs.CV

Spatially Coupled Phase-to-Depth Calibration for Fringe Projection Profilometry

In fringe projection profilometry (FPP), depth is commonly recovered by fitting a phase-to-depth relation independently at each camera pixel. Although such pixel-wise calibration achieves high local accuracy, neighboring pixels can acquire markedly different calibration functions even when they observe the same smooth surface, producing spatially inconsistent geometry and structured surface artifacts. We propose a spatially coupled phase-depth transformation in which all pixels share a single low-dimensional mapping-global phase scalars combined with affine spatial terms on the undistorted reference-camera grid-rather than independent per-pixel fits, optionally augmented by a bounded, spatially smooth correction field. We further introduce a native-grid pairing scheme that constructs phase-depth calibration pairs directly on the reference-camera grid: when depth supervision comes from a rectified active-stereo pipeline, planes are fitted in stereo 3D and sampled back onto the camera grid along native rays, so the phase maps are never rectified. On a dental target with high-resolution scanner ground truth, the proposed model attains point-to-surface RMSE comparable to an active-stereo reference (about 12μm aggregate) while substantially improving spatial coherence over pixel-wise polynomial and rational calibration, and reduces the runtime mapping to a few element-wise operations per pixel with negligible parameter storage.

Sehoon Tak, Jae-Sang Hyun

Department of Mechanical Engineering, Yonsei University, Seoul 03722, South Korea.

Projection Bird'S-Eye View

Jun 8, 2026cs.CL

Toward Signing Activity Projection in Sign Language Interaction

Social robots must interact robustly not only with users assumed by speech-centered systems but also with diverse users whose communication relies on different modalities, e.g., sign language. One important capability gap is predictive turn-taking with signing users. Although Voice Activity Projection (VAP) has been successfully used to model future voice activity in spoken interaction, it remains unclear whether the framework transfers to sign language interaction. This paper presents an initial transfer study of adapting a VAP architecture to dyadic sign language interaction. Using interaction recordings from the Public DGS Corpus, we derive binary signing activity streams from lexical sign annotations and formulate proxy tasks for turn-taking prediction. The model uses pose-derived hand, eye-region, and mouth-region features extracted for each signer. The results show that SHIFT/HOLD prediction is promising, especially with hand cues, while SHIFT-prediction remains difficult. These findings provide initial evidence for both the promise and the current limitations of transferring predictive turn-taking models from spoken interaction to sign language interaction. Predictive modeling of sign language interaction still requires sign-language-specific event definitions that go beyond speech-derived categories.

Takao Obi, Wang Yusong, Koji Inoue +1

Institute of Science Tokyo, Yokohama 230-0045, Japan · Kyoto University, Yoshida-honmachi, Sakyoku, Kyoto, Japan

Sign Language Translation Turn-Taking Nonverbal Cues Action Prediction Language Pairs Projection

Jun 7, 2026cs.LG

Hierarchical Projection for Adaptive Knowledge Transfer

Modern data-driven applications increasingly involve learning from multiple heterogeneous sources, where a target dataset is limited but related information is available across domains. Naively combining these sources can degrade performance when relevance varies or spurious signals are present, posing a fundamental challenge for trustworthy cross-domain learning. We propose Projection Transfer Learning (ProjectionTL), a unified framework that integrates hierarchical Bayesian modeling with adaptive projection for selective knowledge transfer. The key idea is to decouple transfer at two levels: first, we construct a source-guided hierarchical prior that aggregates information across sources using data-driven weights, capturing global alignment between each source and the target; second, we refine this borrowing through a posterior-projection step that operates at the feature level, selectively retaining coordinates that exhibit local agreement with the target signal. This two-stage design enables the method to simultaneously perform source selection and feature selection, thereby mitigating negative transfer while preserving interpretability. ProjectionTL provides a principled approach to integrating heterogeneous data across domains, bridging statistical modeling and modern machine learning paradigms for robust and interpretable transfer. Through simulations and real-world biomedical applications, we demonstrate improved accuracy, stability, and interpretability compared to existing methods. Our framework offers a scalable and generalizable strategy for trustworthy cross-domain learning in high-dimensional settings.

Samhita Pal, Tian Gu

Vanderbilt University Medical Center · Columbia University

Transfer Learning Domain Adaptation Cross-Task Knowledge Transfer Projection Biomedical

Jun 6, 2026stat.ML

Barycentric Projections of Optimal Transport Plans on Riemannian Manifolds

Optimal transport couplings are probabilistic objects, while many learning pipelines require deterministic maps. In Euclidean space, barycentric projection converts a coupling into a map by taking conditional expectations, but on a Riemannian manifold curvature and cut loci make this operation nontrivial. We develop a framework for barycentric projections of transport couplings on Riemannian manifolds. The intrinsic projection maps each source point to the conditional Fréchet mean of its destination law and is shown to be the best deterministic representative under squared geodesic loss. The corresponding minimum value is an integrated conditional Fréchet variance, which vanishes exactly for map-induced couplings and therefore defines a conditional-variance Monge defect. We also study a tangential log-exp projection, prove its Euclidean exactness, its compatibility with Brenier-McCann maps in the Monge case, and its interpretation as the first unit Riemannian gradient update for the intrinsic objective. For discrete couplings, both constructions decompose row-wise into weighted Fréchet mean and log-exp problems. Experiments on spherical data, synthetic SPD data, and real EEG covariance matrices support the proposed division of roles: the intrinsic projection is the variational representative, while the tangential projection is a useful local displacement surrogate.

Kisung You

Department of Mathematics Baruch College

Riemannian Manifolds Projection Fréchet Inception Distance Electroencephalography

Jun 3, 2026cs.RO

COP-Q: Safety-First Reinforcement Learning for Robot Control via Cholesky-Ordered Projection

Safe robot control requires maximizing return while satisfying safety constraints. In off-policy safe reinforcement learning, reward and safety Q-values are commonly learned by separate critic ensembles, with uncertainty handled independently for each objective. This objective-wise treatment neglects inter-objective correlation and can lead to overly conservative value estimates, thereby reducing sample efficiency. To address this issue, we propose Cholesky-Ordered Projection Q-learning (COP-Q), a safety-first method that incorporates inter-objective covariance into vector-valued Q-value estimation. COP-Q constructs a generalized confidence bound in the joint Q-value space and uses Cholesky factorization to encode objective priority in a sequential form. This preserves conservatism on safety while adaptively reducing excessive conservatism on the reward objective. The resulting estimate is used in both temporal-difference target computation and actor optimization. COP-Q incurs minimal computational overhead and is readily compatible with most existing deep Q-learning frameworks. Experiments on robot locomotion in Brax and safe navigation in Safety-Gymnasium, covering both hard- and soft-safety settings, demonstrate that COP-Q achieves strong safety performance together with competitive or improved sample efficiency relative to representative baselines.

Guopeng Li, Moritz A. Zanger, Matthijs T. J. Spaan +1

Department of Cognitive Robotics, Delft University of Technology · School of Transportation, Southeast University, China · Department of Intelligent Systems, Delft University of Technology, the Netherlands

Safety Constraints Q-Learning Robot Systems Covariance Projection

Jun 2, 2026cs.CV

SBP-Net: Learning Thin Structure Reconstruction with Sliding-Box Projections

Reconstructing thin 3D structures is challenging due to their sparsity, scale variation, and complex geometry. Such structures arise in a wide range of domains, including medical imaging of vascular systems and industrial pipe systems. While recent neural methods perform well on dense surfaces, they often fail to recover fine thin geometries. We propose a reconstruction approach based on local depth projections, which provide an efficient and informative 2D representation of thin structures. Specifically, we traverse the 3D model with a sliding box to generate local orthographic depth projections, which are processed by a neural network to reconstruct missing thin structures in 2D. The local reconstructions are subsequently fused back into the 3D model to produce a coherent and detailed shape. Experiments on pulmonary artery reconstruction from CT volumes and industrial pipeline recovery from synthetic and real scans demonstrate improved preservation of fine structural details over existing methods.

Ofir Gilad, Andrei Sharf

Faculty of Computer and Information Science, Ben Gurion University of the Negev Beer Sheva, Israel

3D Models Deterministic Reconstruction Cone-Beam Computed Tomography Projection

Jun 2, 2026cs.CV

Beyond Compression: Quantifying Spectral Accessibility in Vision Representations

Vision-language models map visual features into a shared embedding space through learned projection layers, yet it remains unclear how these transformations alter the structure of visual information. This study examines changes in representation through spatial-frequency accessibility, measured by the linear recoverability of band-limited Fourier energy from model representations. To isolate effects beyond dimensionality reduction, we introduce Residual Spectral Loss (RSL), which evaluates changes relative to a dimension-matched random projection baseline. To reduce confounding effects from optimization, the analysis uses pretrained models with all parameters frozen. The experimental results show consistent frequency-dependent changes in accessibility across CLIP and DINOv2 on ImageNet and MS-COCO datasets. Spectral accessibility follows a non-monotonic trajectory across depth, peaking at intermediate layers before decreasing toward the output representation. The final transformation differs across architectures: CLIP's learned projection is spectrally neutral, with changes explained by compression, whereas DINOv2's [CLS] pooling induces a structured loss across the spectrum. These findings identify intermediate layers and pooling mechanisms as primary drivers of spectral transformation in modern vision encoders.

Akayou A. Kitessa, Yijun Zhao

Fordham University New York City, NY

Vision Encoders Spectral Layer-Wise Projection Imagenet Data Compression Methods+1

Jun 2, 2026cs.LG

LiftQuant: Continuous Bit-Width LLM via Dimensional Lifting and Projection

Existing quantization methods are fundamentally limited by rigid, integer-based bit-widths (e.g., 2, 3-bit), resulting in a

deployment gap" where Large Language Models cannot be optimally fitted to specific memory budgets. To bridge this gap, we introduce LiftQuant, a novel framework that enables continuous bit-width control for true Pareto-optimal deployment. The core innovation is a

lift-then-project" mechanism which approximates low-dimensional weight vectors by projecting a simple 1-bit lattice from a higher-dimensional ``lifted" space. Crucially, the effective bit-width is determined simply by the ratio of the lifted dimension to the original dimension, which allows the bit-width to be tuned quasi-continuous as the dimension is a flexible structural parameter. This projection generates a structured yet non-uniform codebook, capturing the expressive power of Vector Quantization (VQ). While beneficial over VQ, LiftQuant's decoding path relies solely on linear transformations and 1-bit uniform quantizers, retaining hardware-friendly nature. This flexibility is transformative: LiftQuant enables a 70B LLM to be compressed to 2.4 bits to precisely fit a 24GB GPU, where its performance significantly surpasses state-of-the-art 2-bit models fitted on the same device. Our code and ckpt is available at https://github.com/Heliulu/LiftQuant.

Liulu He, XuanAng Liu, Juntao Liu +8

Nanjing University, China · China Mobile Research Institute, China · Xiaomi Corporation, China +2

Large Language Model Quantization Quantizer Projection Pareto Frontier

Jun 1, 2026cs.LG

Do Transformers Need Three Projections? Systematic Study of QKV Variants

Transformers have become the standard solution for various AI tasks, with the query, key, and value (QKV) attention formulation playing a central role. However, the individual contribution of these three projections and the impact of omitting some remain poorly understood. We systematically evaluate three projection sharing constraints: a) Q-K=V (shared key-value), b) Q=K-V (shared query-key), and c) Q=K=V (single projection). The last two variants produce symmetric attention maps; to address this, we also explore asymmetric attention via 2D positional encodings. Through experiments spanning synthetic tasks, vision (MNIST, CIFAR, TinyImageNet, anomaly), and language modeling (300M and 1.2B parameter models on 10B tokens), we discovered that our transformers perform on par or occasionally better than the QKV transformer. In language modeling, Q-K=V projection sharing achieves 50% KV cache reduction with only 3.1% perplexity degradation. Crucially, projection sharing is complementary to head sharing (GQA/MQA): combining Q-K=V with GQA-4 yields 87.5% cache reduction, while Q-K=V + MQA achieves 96.9%, enabling practical on-device inference. We show that Q-K=V preserves quality because keys and values can occupy similar representational spaces and attention operates in a low-rank regime, whereas Q=K-V breaks attention directionality. Our results systematically characterize projection sharing as an underexplored instance of weight tying in attention, with direct, quantifiable inference memory benefits, particularly valuable for edge deployment. The code is publicly available at https://github.com/Brainchip-Inc/Do-Transformers-Need-3-Projections

Ali Kayyam, Anusha Madan Gopal, M Anthony Lewis

BrainChip Inc., Laguna Hills, CA, USA.

Key-Value Cache Quantization Transformer Architectures Keys And Value Projection Low-Rank Structure Systematic Study

May 30, 2026cs.LG

Logit Distillation on Manifolds: Mapping by Learning

A simple way to improve the performance of almost any machine learning model is not to train a single but several models with diverse algorithms which will make slightly distinct kinds of predictions and errors on the same data, and thus improve the average predictions and robustness. However, making predictions using a whole ensemble of models is cumbersome and computationally too expensive to allow deployment to a large number of users, especially if the models are large neural nets. In response to this, we introduce a layer and point wise projection mapping, which maps student and teacher representations into an aligned high-dimensional embedding space during training process. The proposed approach combined with LoRA injection reduces the student model trainable parameters to less than 1% of the teacher model, while significantly improving word error rate (WER) compared to other distillation methods, as demonstrated in ablation studies. Unlike a mixture of experts, our method can be trained rapidly and in parallel.

Yiru Yang, Junling Wang, Nishant Kumar Singh +2

University of Zurich · ETH Zurich · Deutsche Bank Securities

Residual Distillation Teacher Projection Neural Network Manifolds

May 30, 2026cs.CV

CR-JEPA: Cross-Modal Joint-Embedding Predictive Learning for Remote Sensing Image Retrieval

Cross-modal remote sensing image retrieval aims to retrieve semantically related scenes across heterogeneous sensing modalities. This remains challenging because paired observations may differ substantially in imaging physics, spatial resolution, spectral configuration, and visual appearance. Moreover, a single retrieval projection trained with one objective may be insufficient to jointly support cross-modal semantic alignment and same-modal neighbourhood preservation. We propose CR-JEPA, a Cross-modal Retrieval Joint-Embedding Predictive Architecture for dual-modality remote sensing retrieval. The model uses modality-specific stems, a shared transformer trunk, and JEPA-style predictive objectives to estimate masked latent target features within and across modalities. Inspired by LeJEPA, we apply Sketched Isotropic Gaussian Regularization to raw retrieval projections to stabilize embeddings and mitigate collapse. CR-JEPA further employs a decoupled-head design with a unified retrieval head for same-modal retrieval and a cross-modal retrieval head for cross-modal search. We evaluate CR-JEPA on BEN-14K, CBRSIR_VS, and DSRSID. On BEN-14K, CR-JEPA improves S1 to S2 retrieval from 61.23% to 75.82% and S2 to S1 retrieval from 63.73% to 75.40% over X-JEPA, while also achieving competitive same-modal retrieval with fewer parameters.

Md Aminur Hossain, Ayush V. Patel, Nitant Dube +1

Space Applications Centre, Indian Space Research Organisation, Ahmedabad, India · Centre of Studies in Resources Engineering, Indian Institute of Technology Bombay, Mumbai, India

Remote Sensing Cross-Modal S-Jepa Projection

May 28, 2026cs.CL

Reasoning-preserved Efficient Distillation of Large Language Models via Activation-aware Initialization

Efficient Distillation (EDistill) compresses large language models (LLMs) by structured pruning parameters and tuning lightweight modules with high training efficiency. Although these EDistilled LLMs achieve state-of-the-art (SOTA) performance on general ability benchmarks relative to similarly sized LLMs, we identify a severe degradation in their multi-step reasoning ability, which we term reasoning collapse. We systematically analyze the geometric origins of reasoning collapse and show that the SOTA EDistill method based on width-reducing projection matrices suffers from eRank collapse, in which the effective rank (eRank) of hidden representations drops. We theoretically explain how singular values of randomly initialized projection matrices become unevenly distributed, leading to eRank collapse and thus token indistinguishability. To address this issue, we propose RED (Reasoning-preserved Efficient Distillation) for LLMs, which introduces activation-aware initialization to initialize projection matrices as channel-selection matrices, thus theoretically mitigating eRank collapse. Experiments on Llama and Qwen series demonstrate that RED substantially recovers reasoning while maintaining high training efficiency and SOTA general ability.

Junlin He, Yihong Tang, Tong Nie +5

The Hong Kong Polytechnic University, Hong Kong SAR, China · McGill University, Montreal, QC, Canada

Efficient Large Language Model Symbolic Distillation Residual Distillation Collapse Projection

May 27, 2026cs.CL

Chinese Word Boundary Recovery through Character Alignment Projection

Chinese word segmentation is especially fragile in non-standard text, where language learner errors and other character-level divergences disrupt the word boundaries assumed by downstream annotation and evaluation. This paper formulates Chinese word boundary recovery as an alignment-based projection task. Given a noisy source sentence and a cleaner target counterpart, we first align the two strings at the character level and then project target-side word boundaries back onto the source. Beyond the recovery method itself, we introduce two evaluation resources: a manually checked learner Chinese benchmark based on MuCGEC and a controlled synthetic benchmark derived from the Chinese Penn Treebank. Experiments show that direct segmentation remains vulnerable to compound fragmentation in learner input, whereas the proposed two step projection method corrects many over-segmentation errors by using the corrected target to recover source-side word spans. The results show that word boundary recovery is distinct from ordinary segmentation and that alignment projection provides a principled mechanism for stabilizing Chinese annotation and evaluation under noisy input.

Lusha Wang, Yuchen Li, Su Yuan +1

The University of British Columbia, Vancouver, Canada · Korea Advanced Institute of Science & Technology, Daejeon, South Korea

Document Segmentation Character Error Rate Delineation Projection

May 26, 2026cs.DC

Accelerating Birkhoff Projection for Manifold-Constrained Hyper-Connections

Manifold-constrained hyper-connections (mHCs) have recently been proposed as a principled extension of hyper-connections, where the residual mixing matrices are constrained to be doubly stochastic via projection onto the Birkhoff polytope. In practical mHC implementations, this constraint is enforced by Sinkhorn-Knopp iterations, and the backward pass relies on unrolling the iterative solver. This design introduces substantial computation and memory overhead, and may also yield inaccurate projections when the algorithm converges slowly on challenging inputs, undermining the intended norm-control and stability guarantees of mHCs. In this work, we focus on the practically important 4x4 Birkhoff projection setting and develop an end-to-end acceleration framework. By leveraging the dual formulation, we reduce the problem to a three-dimensional unconstrained convex problem and solve it with Newton's method, achieving fast convergence and high accuracy. For the backward pass, we replace the unrolled differentiation with implicit differentiation, yielding exact gradients without storing intermediate states. To exploit massive parallelism, we design a warp-level CUDA kernel that uses only register-level primitives, avoiding global and shared memory I/O. Extensive experiments against representative open-source baselines demonstrate that the proposed solver yields substantially more reliable doubly stochastic projections -- especially when the input magnitude is large -- and achieves significant end-to-end speedups (including the backward pass), reaching over 20x acceleration at large batch sizes while maintaining orders of magnitude smaller marginal errors.

Chenrui Wang, Yixuan Qiu

RenminSchoolUniversityof Statisticsof China · School of Statistics and Data Science & Institute of Big Data Research · Shanghai University of Finance and Economics

Solver Iterations Projection Matrix Multiplication Convergence Cuda

May 25, 2026cs.CV

Concept Unlearning via Cross-Attention Activation Projection for Diffusion Models

Existing closed-form methods for concept unlearning in text-to-image diffusion models typically derive editing directions from fixed text embeddings, which may not fully capture how concepts are expressed across latent states, timesteps, and layers. To capture this variation, we investigate cross-attention activations collected during denoising. In controlled probing experiments using the same anchor prompts, activation-derived bases achieve approximately five times the recall of text-derived bases on held-out prompts expressing the target concepts. Based on this finding, we propose Cross-Attention Subspace Erasure (CASE), a closed-form method that constructs layer-specific forget and retain subspaces from cross-attention activations. These subspaces define a retain-constrained linear operator incorporated directly into cross-attention weights, requiring no gradient-based fine-tuning or additional inference-time computation. Across ten concepts spanning four categories, CASE achieves the highest harmonic-mean score among evaluated baselines in all four categories, balancing suppression, retention, adversarial robustness, and generation quality. Further experiments demonstrate robustness to recovery attacks and a favorable suppression-retention trade-off when jointly unlearning up to 100 artistic styles. The benefits of activation-derived editing also extend to larger diffusion models, including SDXL and FLUX.

Saemi Moon, Suhyeon Jun, Seoyeon Lee +1

CSE, POSTECH · GSAI, POSTECH

Text-To-Image Diffusion Models Diffusion Models Unlearning Method Cross-Attention Adversarial Prompts Projection