Relative Position

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5 papers in the last four weeks, against 2 the four weeks before. 0.1% of all new papers.

Jul 6Week of Sep 21

Latest papers 17

Oct 1, 2026cs.LG

Relative Transitions, Not Absolute Destinations: A Transfer-and-Ground Framework for Target-Trajectory-Free Human Mobility Generation

Individual mobility trajectories support urban analysis and location-based services, yet most trajectory generators require observations from their deployment city. This assumption excludes precisely the cities where trajectories are unavailable even though points of interest (POIs) and their attributes can be obtained from public maps. We study target-trajectory-free generation: learning from POIs and trajectories in source cities while utilizing only POI coordinates and categories in a target city, with no target trajectory or trajectory-derived statistic available for training, model selection, or generation. Existing trajectory generators typically predict absolute destinations, entangling reusable movement behavior with city-specific POI identities and spatial layouts. Our core insight is to replace this city-bound output with context-conditioned relative transitions. We propose Nomad, a transfer-and-ground framework that separates learning how people move from determining where those movements are realized. Specifically, a history-conditioned flow-matching model learns from source trajectories a transition prior over semantic displacement between POI contexts, geographic displacement, and elapsed time; at inference, a behavior graph and an exploration--return walk ground sampled transitions onto the target POI map. This factorization enables a direct test of representation level transferability without assuming invariance of the full mobility distribution. Extensive experiments across ten cities and 14 transfers show that Nomad outperforms adaptation baselines in trajectory fidelity and downstream utility, lowering the average error over the best baseline of each metric by about 15% in distributional fidelity and about 3% in downstream utility.

Yidi Wang, Yunhe Zhang, Bangchao Deng +2

SKL-IOTSC, Department of CIS, University of Macau Macau SAR, China

Mobility Cities Absolute Pose Relative Position

Sep 28, 2026cs.CL

Who Is Left of Whom? Tracing Spatial Evidence and Role Binding in Relative-Position Reasoning

High instance-level accuracy can mask inconsistencies in spatial reasoning when objects exchange positions or their roles are reversed in the query. The internal representations supporting relative-position reasoning remain poorly understood. We investigate two complementary components of this process: tracking object locations in the input and representing their query roles. Across three VLMs with visual or textual inputs and their language-model backbones, activation patching reveals a staged progression from early-layer source representations through intermediate-layer query-object representations to late-layer answer states. Targeted interventions further establish causal links along this progression: manipulating source-side representations shifts location information at query-object mentions and ultimately alters relation predictions. Beyond object-location information, we also identify a stable query-side direction associated with the roles of the two objects in the comparison. Steering along directions estimated on synthetic scenes generalizes to natural-image benchmarks, improving accuracy and both forms of paired consistency in most settings without retraining. Our findings reveal complementary components of relational reasoning across visual and textual settings and show how targeted interventions can improve the consistency of models' behavior.

Yingjin Song, Denis Paperno, Albert Gatt

Utrecht University Utrecht, The Netherlands

Spatial Reasoning Relative Position Role

Sep 23, 2026cs.LG

Relative Discharge Stage (RDS) Classification: A Practical Indicator of Battery Discharge Progress

Accurate remaining discharge time (RDT) prediction is challenging in real-world battery applications because future load profiles are unknown and highly dynamic. To address the uncertainty of continuous RDT regression, this paper introduces Relative Discharge Stage (RDS), a battery-management indicator that represents the remaining discharge condition using five interpretable classes: Normal, Good, Moderate, Low, and Recharge Required. Unlike state of charge (SOC), which reflects the current charge level, RDS characterizes the remaining discharge process without requiring future-current information during inference. A physics-informed RDS classification framework is proposed, combining SOC estimation with lightweight temporal learning. The SOC-estimation component includes second-order ECM state and terminal-voltage prediction, hysteresis and OCV temperature correction, core-temperature estimation, and AEKF state correction, supported by OCV evaluation, online STC-ECM parameter adaptation, and pretrained neural residual-voltage correction. The measured current, terminal voltage, surface temperature, and estimated SOC are arranged into a sliding observation window and processed by a lightweight temporal convolutional network. Experiments on two public lithium-ion battery datasets demonstrate robust RDS classification, with accuracy exceeding 80% under varying load and thermal conditions.

Khoa Tran, Tri Le, Hung-Cuong Trinh +1

Data Science Laboratory, Faculty of Information Technology, Ton Duc Thang University, Ho Chi Minh City, 70000, Vietnam · AIWARE Limited Company, 17 Huynh Man Dat Street, Hoa Cuong Ward, Hai Chau District, Da Nang, 550000, Vietnam · Natural Language Processing and Knowledge Discovery Research Group, Faculty of Information Technology, Ton Duc Thang University, Ho Chi Minh City, 70000, Vietnam +2

Lithium-Ion Batteries Prognostics Relative Position

Sep 22, 2026cs.RO

Relative Contact Velocity-Controlled Hand-Object Mechanism for Dexterous Tool Manipulation

This work investigates how to enable general multi-finger robotic hands to perform the complete tool manipulation process, which entails picking up a tool, loading it into a suitable pose, and then wielding it. Inspired by human tool manipulation and mechanical design principles, we model the hand and the tool as a unified hand-object mechanism (HOM) composed of sub-assemblies. Specifically, we define a HOM as consisting of the hand, the object, and the generalized contact frames, allowing the HOM's motions to be expressed with the same set of Cartesian-space relative contact velocities, irrespective of the hand's kinematics and geometry. Then, we define a HOM's sub-assemblies as relative contact velocity and contact force constraints between fingers. Building on these definitions, we developed a lightweight and physically interpretable motion planning and contact estimation framework using least squares and a complementary filter. We evaluated our framework in simulation by teleoperating five different robotic hands. The results show that our framework enabled all five hands to execute the complete tool manipulation process, achieving dexterous behaviors even from identical, simple reference trajectories. Furthermore, the results showcase our framework's adaptability to different hands, tools, and tasks, enabled by its kinematic and geometric foundation.

Sunyu Wang, Jean Oh, Nancy S. Pollard

The authors are with the Robotics Institute at Carnegie Mellon University, Pittsburgh, USA.

Robotic Hands Dexterous Manipulation Hand Mechanical Systems Relative Position

Sep 21, 2026math.OC

Transformer-Informed Trajectory Optimization for Relative Motion in Cislunar Orbits

Autonomous spacecraft guidance and control requires a fast solution to non-convex trajectory optimization, which can be accelerated by providing a near-optimal initial guess to an optimization protocol, i.e., warm-starting. A robust warm starting method is especially useful for rendezvous, proximity operations, and docking (RPOD) in cislunar space, where the underlying dynamics become severely nonlinear and chaotic compared to those in Earth orbit, especially at perilune. This paper extends the Autonomous Rendezvous Transformer (ART), a transformer-based warm-start trajectory generation method, to cislunar RPOD scenarios for the first time. To accurately and reliably solve the nonconvex optimal control problems (OCPs) posed by these scenarios, a new and enhanced version of ART, ART-TWIN (Two-Way INference), is introduced. Inspired by forward-backward shooting methods used in other trajectory design applications, ART-TWIN autoregressively generates two arcs, one from the initial state and one from the desired terminal state, that are patched together at the midpoint of the timeseries. When evaluated on a set of simulated rendezvous scenarios that are initialized at perilune, ART-TWIN is demonstrated to substantially accelerate convergence and increase feasibility guarantees when used as a warm-start to sequential convex programming (SCP), compared to convex relaxations and the original ART. These results illustrate the necessity of ART-TWIN's dual-arc generation to enable the viability of and gain benefits from using transformer-based warm-start methods in the most challenging areas of the cislunar dynamical regime.

Walter J. Manuel, Yuji Takubo, Simone D'Amico

Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305

Intent-Aligned Autonomous Spacecraft Guidance Robust Trajectory Relative Position Motion

Sep 8, 2026cs.RO

DCLP++: Learning to Navigate with Footprint Clearance and Relative Motion

We present DCLP++, a local navigation frameworkthat uses footprint clearance as the geometric basis for studying relative motion features in dynamic environments. Each valid LiDAR return is mapped to its shortest Euclidean distance from the filled robot footprint before reciprocal encoding, replacing distance from the sensor with distance to the occupied body. Radial measurementsor simulated planar relative velocities provide short-horizon features without static-dynamic labels in the policy input. A preliminary study uses a rectangular robot with a speed limit of 1 m/s among 20 moving obstacles. On 100 fixed validation tasks, two selected training seeds yield mean success rates of 42% with sensor rangeand 70% with footprint clearance after 200,000 environment steps.Motion variants show mixed additional gains. These results supportthe clearance-based observation in the evaluated setting; reliable motion benefits and transfer across robots require further evaluation.

Shanze Wang, Wei Zhang

College of Information Science and Technology, Eastern Institute of Technology, Ningbo, China · Department of Aeronautical and Aviation Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

Dynamic Environments Footprint Relative Position Motion Integrated C++ Development

Sep 3, 2026cs.CV

Principia: Relational Physics Tests for Video Models

Evaluating physical reasoning in video models is difficult because absolute motion measurements depend on frame rate, object scale, and camera calibration, all of which are often ambiguous or unavailable in generated video. We propose a different approach. When two objects in the same scene obey the same physical law, their motions must satisfy predictable relationships, and these relationships hold independent of calibration. We introduce Principia, a benchmark that evaluates Newtonian physics through relational consistency between paired objects. Principia spans eight phenomena - gravity, restitution, friction, rotational inertia, projectile motion, momentum, pendulum, and mass-spring oscillation - across translational, rotational, collisional, and oscillatory dynamics, using real-world scenes recorded under controlled protocols. We also introduce a calibration-independent consistency score that quantifies physical violation directly in image space. Across thousands of generations from six state-of-the-art video generators, no model exceeds 0.42 on Principia despite all scoring around 0.8 on VBench. Vision-language models are evaluated on their ability to detect relational physics violations, with the best model achieving only 67% accuracy and most performing near chance level.

Varun Varma Thozhiyoor, Shivam Tripathi, Venkatesh Babu Radhakrishnan +1

Indian Institute of Science · Johns Hopkins University

Generative Video Models Physics-Aware Models Physical Plausibility Explanation Consistency Score Relative Position Principles+1

Aug 12, 2026cs.DC

Ready Cohorts: Bounding GPU Opportunity and Avoiding Host Round Trips in LLM-Agent Control

LLM-agent services repeatedly execute small deterministic transitions between model and tool calls: route an outcome, update state, and emit the next effect. We ask when this control path exposes enough concurrent work for GPU execution, and what changes when a GPU-computed route decision remains on device. We formalize the ready-cohort boundary using fixed-partition share F, exact offline share P*, local upper bound U, and online achieved share A. Under zero service time, unlimited capacity, and equal relative launch deadlines, a specialized dynamic program computes P* exactly. In a stationary Poisson replay of one pinned 851-session public trace panel, the primary condition at 100,000 target active sessions, K=256, and a 50 ms launch deadline gives F=30.19%, P*=43.00%, and U=45.85%. Exact packing recovers 81.83% of the opportunity lost at fixed window boundaries. The outcome-derived route key is a conditioning proxy, not proof of executable identity. A separate mechanism study keeps a GPU-computed binary decision on device instead of returning four bytes to the host and redispatching. Across four named GPU placements, the device-resident path is faster in all 36 configurations; within-placement row-median ratios range from 1.19x to 2.39x. Across both admissible mechanisms, all 14,557,440 tested batched invocations match a separately implemented host oracle. A fixed nested device graph that removes no host decision is slower in all 60 configurations across five placements. Together, the studies establish two measurable gates for GPU agent control: deadline-feasible cohort supply and observation placement. A joined finite online runtime is required to measure A, CPU displacement, and service-level benefit.

Josef Liyanjun Chen

Independent Researcher

Cpu-Gpu Hybrid Designs Cohort Path Relative Position

Aug 9, 2026cs.CL

Position Encoding in Transformers: From Absolute and Relative Methods to Rotary Position Embeddings and Long-Context Scaling

Self-attention models content-dependent interactions between tokens but does not by itself encode token order. Position encoding addresses this limitation by introducing absolute coordinates, relative distances, or position-dependent rotations into Transformer representations and attention scores. This technical survey develops a unified account of sinusoidal and learned absolute position embeddings, Shaw-style relative position representations, Transformer-XL, T5 relative position bias, ALiBi, and Rotary Position Embeddings (RoPE). We derive how RoPE converts absolute position indices into relative phase differences in Query-Key inner products and compare these methods in terms of where position is injected, computational cost, compatibility with KV caching, and length extrapolation. We then examine long-context extensions, including Position Interpolation, RoPE scaling laws, NTK-aware scaling, Dynamic NTK, NTK-by-parts, YaRN, LongRoPE, and LongRoPE2, with emphasis on frequency allocation, attention rescaling, training length, and target context length. We also summarize implementation considerations, evaluation protocols, and position-encoding choices in representative large language models. A central conclusion is that the ability to compute positional features beyond the training length does not imply reliable long-context generalization; context extension must be evaluated through short-context retention, position-wise perplexity, retrieval, reasoning, and long-context code tasks.

Jiguo Li

Rotary Position Embedding Positional Encoding Transformer Architectures Relative Position Position

Jul 29, 2026cs.LG

Journey Operators for Structured Multi-Axis Composition

Many kinds of data have structure along one or more axes: words in a sentence, pixels in an image, nodes in a tree, frames in audio, or cells in a 3D volume. Along one axis, order matters: "the dog bit the man" is different from "the man bit the dog." Across independent axes, however, neither composition nor movement should depend on the order of axes: in an image, composing right then down should give the same result as composing down then right, and moving right then down should describe the same relative position as moving down then right. We develop a framework for modeling this kind of multi-axis structure. Each data item carries its content together with a small transformation for each axis. A path connecting two positions defines a journey; the journey operator is the product of per-axis transformations along that path, governing both how data composes along the path and how relative position is described. When the transformations are fixed, our framework recovers Rotary Position Embedding (RoPE) and its multi-dimensional variants. When they depend on the data, the model gains a content-adaptive positional inductive bias. We show exactly when these paths are well-defined: both composition and movement across axes are path-independent precisely when the axis transformations commute. We also prove that, under the stated toral-frame symmetry, cocycle, bilinearity, and norm-preservation assumptions, the resulting pairwise scoring rule must take the form of block-wise rotations, explaining why RoPE-like methods arise naturally. Finally, we use this theory to design JoFormer, a model for value aggregation, and relate it to attention and state-space models (SSMs). Initial experiments across vision, language, and length generalization suggest that these inductive biases can have observable consequences in practice.

Mahesh Godavarti

A Carrot, Inc

Rotary Position Embedding Relative Position Inductive Bias Journey

Jul 21, 2026cs.LG

Relative Positions Generalize, Absolute Positions Memorize: An Implicit-Bias Account of Length Generalization in Attention

Transformers with relative positional encodings often extrapolate to sequences longer than those seen during training, whereas transformers with learned absolute encodings typically do not. This is a robust empirical regularity, and the explanations offered for it so far are chiefly about expressivity, that is, about whether a length-generalizing solution exists. We give an optimization explanation. On a minimal fixed-offset retrieval task that isolates positional selection, the gap is governed by the implicit bias of the trained attention head: among the many solutions that fit short sequences, which one gradient descent actually selects. We prove that rotary encodings make the attention logit a function of relative offset alone, an exact equivariance, so whatever selection rule is learned at training lengths is reproduced verbatim at every longer length. Learned absolute encodings instead leave out-of-range positions unconstrained, and the trained head pins to a fixed absolute position inside the training range. We characterize the learned rotary rule as a low-rank ``carrier'' kernel aligned with the target offset, and we derive the resulting graceful accuracy decay as an attention-dilution law; both predictions are confirmed across seeds and offsets. A linear-attention control shows the mechanism is specific to softmax: without normalization, training selects a min-norm interpolant that does not extrapolate. The phenomenon, the equivariance, and the carrier all transfer to a multi-layer, multi-head transformer trained on a full-sequence length-generalization task. The account connects the implicit bias of attention, implicit bias for extrapolation in recurrent models, and the learning side of the RASP-L conjecture.

Subham Singh, Ashutosh Mishra, Subha Raut

Department of Mathematics and Statistics, Mississippi State University · Independent Researcher

Positional Encoding Relative Position Sequence Modeling Absolute Pose Position Bias Extrapolation

Jul 8, 2026cs.AI

Measuring Intelligence Beyond Human Scale

How can we measure intelligence beyond human capability? Human-authored benchmarks saturate, and above human capability, examiners may not know which tasks are both hard and verifiable. We argue that this difficulty is inherent to absolute-scale evaluation and propose a new paradigm based on relative measurement in which models generate public challenges that separate other systems. Aggregating these outcomes yields an adversarial psychometric rating system that can scale with the systems being measured. We describe practical protocols that reduce incentives for private-information attacks, support judge-free adjudication, and naturally scale with agent capabilities. We instantiate the framework across verifiable and open-ended, non-verifiable domains, illustrating how model-generated evaluation can continue to measure systems beyond the human frontier.

Jerry Han, Rafael Moschopoulos, Ella Colby +5

Princeton Superalignment

General Intelligence Psychometric Properties Intelligence Relative Position

Jun 28, 2026cs.RO

Empowering a Single-Frequency GNSS Receiver to Achieve High-Precision Positioning with Relative Observations

Global Navigation Satellite System (GNSS) navigation is widely used to provide absolute, outdoor positioning in field robotics. Advances in Real-Time Kinematic (RTK) technology can achieve centimeter-level accuracy, facilitating autonomous navigation tasks. However, the cost and extra infrastructure used for RTK still hinder the application and more cost-effective solutions are desired. In this letter, we present a novel tightly-coupled state estimation framework that achieves high-precision localization by using low-cost, mass-market single-frequency GNSS receivers with any relative motion sensors (e.g., wheel encoder, camera, LiDAR). We propose a sliding-window factor graph that integrates generic relative motion with global epoch-to-anchor constraints derived from continuous carrier phase tracking. To eliminate the reliance on physical base stations, we introduce a virtual anchor mechanism: upon the initial observation of a satellite, its state is locked as a virtual reference to establish global epoch-to-anchor constraints. By substituting multi-frequency hardware redundancy with single-frequency multi-modal kinematic priors and a robust cycle-slip recovery technique, our approach ensures carrier-phase integrity on cheap receivers. Extensive real-world experiments on heterogeneous low-cost sensor suites validate that our method improves the accuracy of a single-frequency receiver from several meters to decimeter-level precision across diverse environments, providing an accurate, cost-effective and reliable alternative for autonomous navigation.

Xingpeng Wang, Ziwen Qu, Juncheng Chen +8

State Key Laboratory of Industrial Control Technology, Institute of Cyber Systems and Control, Zhejiang University, Hangzhou, China · Huzhou Institute of Zhejiang University, Huzhou, China

Global Navigation Satellite System Relative Position Kinematic Priors

Jun 9, 2026cs.CV

Leveraging Metric Depth for Relative Depth Prediction

We present our solution to the 2025 SoccerNet Monocular Depth Estimation Competition Challenge. Predicting the relative depth in football scenarios is challenging, especially with only thousands of training samples available. To address this issue, our method leverages the powerful zero-shot capabilities of models pretrained on large-scale datasets to learn metric depth for effective relative depth prediction, achieving a score of

2.68 \times 10^{-3}

on the challenge set.

Xiaoyang Bi, Shuaikun Liu, Zhaohong Liu +5

Beijing Key Laboratory of Intelligent Telecommunications Software and Multimedia · Beijing University of Posts and Telecommunications

Monocular Depth Estimation Dense Prediction Relative Position Scores

May 26, 2026cs.CV

$R^3$ : 3D Reconstruction via Relative Regression

Recent feed-forward geometry foundation models have demonstrated impressive generalization by recovering depth and poses in a single forward pass. However, these models are typically constrained by a global coordinate frame assumption. This dependency becomes a significant bottleneck for long-context and streaming reconstruction, as it forces the network to maintain an arbitrary temporal origin and handle translation magnitudes that grow unbounded over time. Our solution, which we call

R^3

, employs relative regression. We employ a lightweight MLP to predict confidence-weighted relative constraints. These confidences serve as a unified anchor: weighting losses during training and guiding pose aggregation during inference.

R^3

supports both full-context offline reconstruction and causal, bounded-memory streaming. Our evaluation in both offline and streaming settings validates the effectiveness of our relative mechanism. Project page: https://kevinxu02.github.io/r3-site

Congrong Xu, Huachen Gao, Xingyu Chen +3

University of Michigan · Westlake University · NVIDIA

Feed-Forward 3D Reconstruction 3D Reconstruction Relative Position

May 5, 2026cs.LG

Jordan-RoPE: Non-Semisimple Relative Positional Encoding via Complex Jordan Blocks

Relative positional encodings determine which functions of query-key lag can enter the primitive attention logit. RoPE supplies a rotary phase, while ALiBi supplies an additive distance bias. Motivated by group-theoretic views of linear translation-invariant positional encodings, we study a non-semisimple case in which a complex rotary eigenvalue and a nilpotent response live in the same defective Jordan block. The resulting relative operator generates oscillatory-polynomial features such as

e^{-γd}\cos(ωd)

,

e^{-γd}\sin(ωd)

,

d e^{-γd}\cos(ωd)

, and

d e^{-γd}\sin(ωd)

, for causal lag

d=i-j\geq 0

. Thus the construction realizes a distance-modulated phase basis

d e^{iωd}

, rather than merely adding a separate distance channel to RoPE. We formulate Exact Jordan-RoPE as a non-semisimple one-parameter representation, give its real block form, and specify the contragredient query action required by non-orthogonal positional maps. We also distinguish this exact representation from stabilized variants whose bounded shear improves numerical behavior but breaks the exact group law. Kernel-level diagnostics and a Jordan-friendly synthetic language-model task show that the coupled Jordan basis is useful when the target contains distance-modulated phase interactions. On a small WikiText-103 byte language model, a scaled-exact variant improves over RoPE and direct-sum baselines within the Jordan family, while RoPE+ALiBi remains strongest overall. The evidence is structural rather than a broad performance claim.

Yaobo Zhang

School of Physics, Ningxia University Yinchuan, 750021, China

Positional Encoding Relative Position Dynamic Rope Manipulation Linear Attention Oscillatory Dynamics

Apr 20, 2026cs.CV

URoPE: Universal Relative Position Embedding across Geometric Spaces

Relative position embedding has become a standard mechanism for encoding positional information in Transformers. However, existing formulations are typically limited to a fixed geometric space, namely 1D sequences or regular 2D/3D grids, which restricts their applicability to many computer vision tasks that require geometric reasoning across camera views or between 2D and 3D spaces. To address this limitation, we propose URoPE, a universal extension of Rotary Position Embedding (RoPE) to cross-view or cross-dimensional geometric spaces. For each key/value image patch, URoPE samples 3D points along the corresponding camera ray at predefined depth anchors and projects them into the query image plane. Standard 2D RoPE can then be applied using the projected pixel coordinates. URoPE is a parameter-free and intrinsics-aware relative position embedding that is invariant to the choice of global coordinate systems, while remaining fully compatible with existing RoPE-optimized attention kernels. We evaluate URoPE as a plug-in positional encoding for transformer architectures across a diverse set of tasks, including novel view synthesis, 3D object detection, object tracking, and depth estimation, covering 2D-2D, 2D-3D, and temporal scenarios. Experiments show that URoPE consistently improves the performance of transformer-based models across all tasks, demonstrating its effectiveness and generality for geometric reasoning. Our code is available on our project website: https://urope-pe.github.io/.

Yichen Xie, Depu Meng, Chensheng Peng +4

Applied Intuition · University of California, Berkeley

Visual Geometry Grounded Transformer Rotary Position Embedding Relative Position Transformer Architectures 3D Object Detection