Daily Papers

Even for simple arithmetic tasks like integer addition, it is challenging for Transformers to generalize to longer sequences than those encountered during training. To tackle this problem, we propose position coupling, a simple yet effective method that directly embeds the structure of the tasks into the positional encoding of a (decoder-only) Transformer. Taking a departure from the vanilla absolute position mechanism assigning unique position IDs to each of the tokens, we assign the same position IDs to two or more "relevant" tokens; for integer addition tasks, we regard digits of the same significance as in the same position. On the empirical side, we show that with the proposed position coupling, our models trained on 1 to 30-digit additions can generalize up to 200-digit additions (6.67x of the trained length). On the theoretical side, we prove that a 1-layer Transformer with coupled positions can solve the addition task involving exponentially many digits, whereas any 1-layer Transformer without positional information cannot entirely solve it. We also demonstrate that position coupling can be applied to other algorithmic tasks such as Nx2 multiplication and a two-dimensional task.

We study three complementary techniques for training compute-efficient language models. (1) Selective supervision and per-token efficiency. Selective Ground Truth Token Training (SGT) concentrates supervision on the ~15% of output tokens that carry semantic payload. Through positive gradient coupling in position-shared transformer weights -- a token-level instance of auxiliary-task transfer -- the remaining 85% of unsupervised tokens still improve substantially, giving a 4.5x per-supervised-token efficiency (at the step-100 eval optimum, ~67% of the full-sequence loss reduction is recovered from 15% of the supervision). We prove that this improvement on unsupervised tokens is guaranteed whenever the gradient coupling coefficient gamma-bar = 0.72 is positive (Theorem 1), and show the effect is a property of natural-language structure: it collapses on shuffled text. (2) Depth compression with recurrent recovery. A 48-layer, 1B-parameter transformer is compressed to 6 layers (227M) by averaging adjacent layers and restored through learned recurrent unrolling. With 34 effective recurrent layers it reaches a held-out loss of 2.934, within measurement noise of a 566M dense model at 2.926 -- a 2.5x reduction in parameters. (3) Fusion of compressed experts. Assembling several compressed models as a Mixture of Efficient Experts (MoEE) with multi-token prediction improves over each single expert at comparable active parameters: a 2-expert MoEE reaches loss 2.789 versus 2.926 for the best single compressed model. We validate these techniques on CHERRY-1.8B, a Korean foundation model whose every trainable parameter derives from our own training runs. We are explicit throughout about the scope of the evidence (one model family, Korean data, loss-based metrics) and about which claims are established versus prospective.

Despite extraordinary progress in artificial intelligence (AI), modern systems remain incomplete representations of human cognition. Vision, audition, and language have received disproportionate attention due to well-defined benchmarks, standardized datasets, and consensus-driven scientific foundations. In contrast, olfaction - a high-bandwidth, evolutionarily critical sense - has been largely overlooked. This omission presents a foundational gap in the construction of truly embodied and ethically aligned super-human intelligence. We argue that the exclusion of olfactory perception from AI architectures is not due to irrelevance but to structural challenges: unresolved scientific theories of smell, heterogeneous sensor technologies, lack of standardized olfactory datasets, absence of AI-oriented benchmarks, and difficulty in evaluating sub-perceptual signal processing. These obstacles have hindered the development of machine olfaction despite its tight coupling with memory, emotion, and contextual reasoning in biological systems. In this position paper, we assert that meaningful progress toward general and embodied intelligence requires serious investment in olfactory research by the AI community. We call for cross-disciplinary collaboration - spanning neuroscience, robotics, machine learning, and ethics - to formalize olfactory benchmarks, develop multimodal datasets, and define the sensory capabilities necessary for machines to understand, navigate, and act within human environments. Recognizing olfaction as a core modality is essential not only for scientific completeness, but for building AI systems that are ethically grounded in the full scope of the human experience.

We present GRAPE (Group RepresentAtional Position Encoding), a unified framework for positional encoding based on group actions. GRAPE brings together two families of mechanisms: (i) multiplicative rotations (Multiplicative GRAPE) in SO(d) and (ii) additive logit biases (Additive GRAPE) arising from unipotent actions in the general linear group GL. In Multiplicative GRAPE, a position n in Z (or t in R) acts as G(n)=exp(n,ω,L) with a rank-2 skew generator L in R^{d times d}, yielding a relative, compositional, norm-preserving map with a closed-form matrix exponential. RoPE is recovered exactly when the d/2 planes are the canonical coordinate pairs with log-uniform spectrum. Learned commuting subspaces and compact non-commuting mixtures strictly extend this geometry to capture cross-subspace feature coupling at O(d) and O(r d) cost per head, respectively. In Additive GRAPE, additive logits arise as rank-1 (or low-rank) unipotent actions, recovering ALiBi and the Forgetting Transformer (FoX) as exact special cases while preserving an exact relative law and streaming cacheability. Altogether, GRAPE supplies a principled design space for positional geometry in long-context models, subsuming RoPE and ALiBi as special cases. Project Page: https://github.com/model-architectures/GRAPE.

Text- and image-conditioned video generation models have achieved strong visual fidelity and temporal coherence, but they often fail to generate motion governed by kinematic and geometric constraints. In these settings, object parts must remain rigid, maintain contact or coupling with neighboring components, and transfer motion consistently across connected parts. These requirements are especially explicit in articulated mechanical assemblies, where motion is constrained by rigid-link geometry, contact/coupling relations, and transmission through kinematic chains. A generated video may therefore appear plausible while violating the intended mechanism, such as rotating a part that should translate, deforming a rigid component, breaking coupling between parts, or failing to move downstream components. To evaluate this gap, We introduce MechVerse, a benchmark for mechanically consistent image-to-video generation. MechVerse contains 21,156 synthetic clips from 1,357 mechanical assemblies across 141 categories, organized into three tiers of increasing kinematic complexity: independent articulation, pairwise coupling, and densely coupled multi-part mechanisms. Each clip is paired with a structured prompt describing part identities, stationary supports, moving components, motion primitives, direction, speed/extent, and inter-part dependencies. We evaluate proprietary, open-source, and fine-tuned image-to-video models using standard video metrics, instruction-following scores, and human judgments of motion correctness and kinematic coupling. Results show that current models can preserve appearance and smoothness while failing to generate mechanically admissible motion, with errors increasing as coupling complexity grows. MechVerse provides a benchmark for measuring and improving mechanism-aware video generation from image and language inputs.

Modifications to test-time sampling have emerged as an important extension to diffusion algorithms, with the goal of biasing the generative process to achieve a given objective without having to retrain the entire diffusion model. However, generating jointly correlated samples from multiple pre-trained diffusion models while simultaneously enforcing task-specific constraints without costly retraining has remained challenging. To this end, we propose Projected Coupled Diffusion (PCD), a novel test-time framework for constrained joint generation. PCD introduces a coupled guidance term into the generative dynamics to encourage coordination between diffusion models and incorporates a projection step at each diffusion step to enforce hard constraints. Empirically, we demonstrate the effectiveness of PCD in application scenarios of image-pair generation, object manipulation, and multi-robot motion planning. Our results show improved coupling effects and guaranteed constraint satisfaction without incurring excessive computational costs.

The advent of autonomous agents is transforming interactions with Graphical User Interfaces (GUIs) by employing natural language as a powerful intermediary. Despite the predominance of Supervised Fine-Tuning (SFT) methods in current GUI agents for achieving spatial localization, these methods face substantial challenges due to their limited capacity to accurately perceive positional data. Existing strategies, such as reinforcement learning, often fail to assess positional accuracy effectively, thereby restricting their utility. In response, we introduce Location Preference Optimization (LPO), a novel approach that leverages locational data to optimize interaction preferences. LPO uses information entropy to predict interaction positions by focusing on zones rich in information. Besides, it further introduces a dynamic location reward function based on physical distance, reflecting the varying importance of interaction positions. Supported by Group Relative Preference Optimization (GRPO), LPO facilitates an extensive exploration of GUI environments and significantly enhances interaction precision. Comprehensive experiments demonstrate LPO's superior performance, achieving SOTA results across both offline benchmarks and real-world online evaluations. Our code will be made publicly available soon, at https://github.com/AIDC-AI/LPO.

Simulation-to-reality translation must bridge the appearance gap between synthetic and real domains while preserving structural and semantic consistency. Conditioning-based methods achieve spatial alignment but introduce computationally expensive control modules. Paired-data methods achieve realism but rely on complex synthesis pipelines, often altering scene geometry and semantics. Training-free editing methods avoid both constraints but lack a learned appearance prior, limiting their perceptual quality. Recently proposed phase-preserving diffusion presents a promising alternative, but Fourier-domain formulations are constrained by global spectral coupling. This coupling induces spatial artifacts such as ringing and boundary leakage, thereby degrading structural and semantic consistency. We introduce Wavelet Phase Diffusion, which addresses this through two components. First, we operate in the Dual-Tree Complex Wavelet Packet Transform domain, whose localized wavelet packets enable spatially adaptive phase injection without global spectral interference. Second, Low-Frequency Randomization (LFR) replaces the low-frequency packet, decoupling the model from the synthetic illumination prior and enabling in-distribution real-world appearance. Both components train on unpaired open-domain data, and introduce negligible inference overhead. The spatial locality further enables instance-level translation, where individual objects or regions are translated to photorealistic appearance independently while the surrounding scene remains untranslated. On vKITTI to KITTI image translation, ours outperforms prior methods in realism and semantic consistency while maintaining competitive structural alignment. For CARLA video translation, ours approaches the realism of paired-data methods while reducing VLM planner ADE and FDE by 5.4% and 5.1%, respectively.

Recovering ego-camera orientation from manipulation video is a prerequisite for disentangling hand motion from camera motion, a key step in imitation learning from egocentric demonstrations. The obvious approach, inferring orientation from scene geometry, fails when hands occlude the frame: VGGT, a 1B-parameter scene reconstruction model, scores worse than a constant predictor on the TACO benchmark. We identify an alternative visual concept that is present precisely when scene geometry is absent: kinematic coupling dynamics, the structured physical relationship between wrist motion and camera orientation imposed by the arm-shoulder-head chain. We find that this concept is compact (4D inter-wrist features outperform 126D full hand keypoints), temporal (requiring a GRU over short windows rather than per-frame retrieval), and physically grounded (transferring zero-shot across datasets because it is rooted in anatomy rather than scene appearance). Trained only on tabletop manipulation, WristCompass transfers zero-shot to Epic Kitchens cooking video, achieving 14.3^circ median geodesic error and approaching the performance of a 1B-parameter scene model at 200K GRU parameters.

While modern text-to-image models excel at prompt-based generation, they often lack the fine-grained control necessary for specific user requirements like spatial layouts or subject appearances. Multi-condition control addresses this, yet its integration into Diffusion Transformers (DiTs) is bottlenecked by the conventional ``concatenate-and-attend'' strategy, which suffers from quadratic computational and memory overhead as the number of conditions scales. Our analysis reveals that much of this cross-modal interaction is spatially or semantically redundant. To this end, we propose Position-aligned and Keyword-scoped Attention (PKA), a highly efficient framework designed to eliminate these redundancies. Specifically, Position-Aligned Attention (PAA) linearizes spatial control by enforcing localized patch alignment, while Keyword-Scoped Attention (KSA) prunes irrelevant subject-driven interactions via semantic-aware masking. To facilitate efficient learning, we further introduce a Conditional Sensitivity-Aware Sampling (CSAS) strategy that reweights the training objective towards critical denoising phases, drastically accelerating convergence and enhancing conditional fidelity. Empirically, PKA delivers a 10.0times inference speedup and a 5.1times VRAM saving, providing a scalable and resource-friendly solution for high-fidelity multi-conditioned generation.

Leaderboards rank frontier models on independent axes but do not reveal whether capabilities reinforce or trade off across releases -- and at the frontier, this interaction is the more informative signal. We decompose paired SWE-bench and GPQA Diamond scores into a population coupling trend and per-release residual (h-field) that diagnoses capability emphasis and identifies which measurement or stress test is most informative next. Across 34 models from 10 labs (2024--2026), capabilities cooperate (r = +0.72, p < 10^{-6}), but cooperation varies by lab and over time: DeepSeek reversed from reasoning-rich to coding-first (h: +11.2 to -4.7, 15.9-pp swing); Google maintains consistent reasoning emphasis; Anthropic oscillates between coding excursions and recovery. Cooperation is not static -- it cascades. Six open-weight architectures confirm a second capability transition at 30--72B, and SWE-bench is now saturating while HLE and instruction-following retain discriminatory spread -- signaling the next axis rotation. We provide a three-level playbook (locate, diagnose, rotate), a per-lab measurement-priority table, and seven falsifiable predictions with timestamped criteria for the next 12 months of frontier releases. Per-lab coupling slopes vary 5times (Google 1.15 vs. DeepSeek 0.23), quantifying how efficiently each recipe converts coding gains into reasoning. Five April 2026 releases confirm the diagnostic out of sample (r rises from +0.72 to +0.75). An interactive dashboard provides phase classification with actionable recommendations, h-field diagnostics, per-lab coupling trajectories, ODE-based scaling predictions, benchmark rotation guidance, self-steering demo, and live tracking of all seven predictions: https://zehenlabs.com/cape/.

The attention mechanism is a critical component of Large Language Models (LLMs) that allows tokens in a sequence to interact with each other, but is order-invariant. Incorporating position encoding (PE) makes it possible to address by position, such as attending to the i-th token. However, current PE methods use token counts to derive position, and thus cannot generalize to higher levels of abstraction, such as attending to the i-th sentence. In this paper, we propose a new position encoding method, Contextual Position Encoding (CoPE), that allows positions to be conditioned on context by incrementing position only on certain tokens determined by the model. This allows more general position addressing such as attending to the i-th particular word, noun, or sentence. We show that CoPE can solve the selective copy, counting and Flip-Flop tasks where popular position embeddings fail, and improves perplexity on language modeling and coding tasks.

Primal-dual safe RL methods commonly perform iterations between the primal update of the policy and the dual update of the Lagrange Multiplier. Such a training paradigm is highly susceptible to the error in cumulative cost estimation since this estimation serves as the key bond connecting the primal and dual update processes. We show that this problem causes significant underestimation of cost when using off-policy methods, leading to the failure to satisfy the safety constraint. To address this issue, we propose conservative policy optimization, which learns a policy in a constraint-satisfying area by considering the uncertainty in cost estimation. This improves constraint satisfaction but also potentially hinders reward maximization. We then introduce local policy convexification to help eliminate such suboptimality by gradually reducing the estimation uncertainty. We provide theoretical interpretations of the joint coupling effect of these two ingredients and further verify them by extensive experiments. Results on benchmark tasks show that our method not only achieves an asymptotic performance comparable to state-of-the-art on-policy methods while using much fewer samples, but also significantly reduces constraint violation during training. Our code is available at https://github.com/ZifanWu/CAL.

Recent studies have demonstrated the effectiveness of position encoding in transformer architectures. By incorporating positional information, this approach provides essential guidance for modeling dependencies between elements across different sequence positions. We introduce CoPE (a lightweight Complex Positional Encoding), a novel architecture that leverages complex-valued encoding to encode both content and positional information. Our approach replaces traditional positional encodings with complex embeddings where the real part captures semantic content and the imaginary part encodes positional information. We introduce phase-aware attention in the first layer of the transformer model to capture position-dependent patterns, followed by standard attention layers for higher-levels. We show that CoPE doesn't exhibit long term decay and is compatible with linear attention. Experimental evaluation on the GLUE benchmark suggest that our approach achieves superior performance with less computational complexity, compared to RoPE, Sinusoidal and Learned positional encodings.

The Milky Way is known to contain a stellar bar, as are a significant fraction of disc galaxies across the universe. Our understanding of bar evolution, both theoretically and through analysis of simulations indicates that bars both grow in amplitude and slow down over time through interaction and angular momentum exchange with the galaxy's dark matter halo. Understanding the physical mechanisms underlying this coupling requires modelling of the structural deformations to the potential that are mutually induced between components. In this work we use Basis Function Expansion (BFE) in combination with multichannel Singular Spectral Analysis (mSSA) as a non-parametric analysis tool to illustrate the coupling between the bar and the dark halo in a single high-resolution isolated barred disc galaxy simulation. We demonstrate the power of mSSA to extract and quantify explicitly coupled dynamical modes, determining growth rates, pattern speeds and phase lags for different stages of evolution of the stellar bar and the dark matter response. BFE & mSSA together grant us the ability to explore the importance and physical mechanisms of bar-halo coupling, and other dynamically coupled structures across a wide range of dynamical environments.

While generative models have become effective at producing human-like motions from text, transferring these motions to humanoid robots for physical execution remains challenging. Existing pipelines are often limited by retargeting, where kinematic quality is undermined by physical infeasibility, contact-transition errors, and the high cost of real-world dynamical data. We present a unified latent-driven framework that bridges natural language and whole-body humanoid locomotion through a retarget-free, physics-optimized pipeline. Rather than treating generation and control as separate stages, our key insight is to couple them bidirectionally under physical constraints.We introduce a Physical Plausibility Optimization (PP-Opt) module as the coupling interface. In the forward direction, PP-Opt refines a teacher-student distillation policy with a plausibility-centric reward to suppress artifacts such as floating, skating, and penetration. In the backward direction, it converts reward-optimized simulation rollouts into high-quality explicit motion data, which is used to fine-tune the motion generator toward a more physically plausible latent distribution. This bidirectional design forms a self-improving cycle: the generator learns a physically grounded latent space, while the controller learns to execute latent-conditioned behaviors with dynamical integrity.Extensive experiments on the Unitree G1 humanoid show that our bidirectional optimization improves tracking accuracy and success rates. Across IsaacLab and MuJoCo, the implicit latent-driven pipeline consistently outperforms conventional explicit retargeting baselines in both precision and stability. By coupling diffusion-based motion generation with physical plausibility optimization, our framework provides a practical path toward deployable text-guided humanoid intelligence.

While explicit positional encodings such as RoPE are a primary source of positional information in Transformer decoders, the causal mask also provides positional information. In this work, we prove that the causal mask can induce position-dependent patterns in attention scores, even without parameters or causal dependency in the input. Our theoretical analysis indicates that the induced attention pattern tends to favor nearby query-key pairs, mirroring the behavior of common positional encodings. Empirical analysis confirms that trained models exhibit the same behavior, with learned parameters further amplifying these patterns. Notably, we found that the interaction of causal mask and RoPE distorts RoPE's relative attention score patterns into non-relative ones. We consistently observed this effect in modern large language models, suggesting the importance of considering the causal mask as a source of positional information alongside explicit positional encodings.

Recent subject-driven image customization has achieved significant advancements in fidelity, yet fine-grained instance-level spatial control remains elusive, hindering broader real-world application. This limitation is mainly attributed to the absence of scalable datasets that bind identity with precise positional cues. To this end, we introduce PositionIC, a unified framework that enforces position and identity consistency for multi-subject customization. We construct a scalable synthesis pipeline that employs a bidirectional generation paradigm to eliminate subject drift and maintain semantic coherence. On top of these data, we design a lightweight positional modulation operation that decouples spatial embeddings among subjects, enabling independent, accurate placement while preserving visual fidelity. Extensive experiments demonstrate that our approach can achieve precise spatial control while maintaining high consistency in image customization tasks. PositionIC paves the way for controllable, high-fidelity image customization in open-world, multi-entity scenarios and will be released to foster further research.

Whole-body teleoperation requires users to coordinate perception, manipulation, posture, and mobility across multiple robot components. This coordination is difficult because users must simultaneously control the robot's head, arms, torso, and base while maintaining task awareness and avoiding kinematic or environmental constraints. In this paper, we propose coupled egocentric control, a body-following teleoperation approach in which the robot's torso and base automatically respond to the operator's head and arm motions. Rather than requiring explicit touchpad commands for every torso or base adjustment, the system lets users focus on gaze and hand control: head pitch adjusts torso height, head yaw drives base rotation, end-effector height adjusts torso motion, and end-effector workspace boundaries trigger base translation. We evaluate this approach in a user study on whole-body teleoperation of a TIAGo mobile manipulator for home-care-inspired tasks. Compared with a baseline hybrid interface, coupled egocentric control improves object manipulation efficiency, reduces button-based control effort and arm singularities, lowers mental demand and overall workload, and increases ease of use, ease of learning, confidence, and user preference for torso and base control.

Attentional mechanisms are order-invariant. Positional encoding is a crucial component to allow attention-based deep model architectures such as Transformer to address sequences or images where the position of information matters. In this paper, we propose a novel positional encoding method based on learnable Fourier features. Instead of hard-coding each position as a token or a vector, we represent each position, which can be multi-dimensional, as a trainable encoding based on learnable Fourier feature mapping, modulated with a multi-layer perceptron. The representation is particularly advantageous for a spatial multi-dimensional position, e.g., pixel positions on an image, where L_2 distances or more complex positional relationships need to be captured. Our experiments based on several public benchmark tasks show that our learnable Fourier feature representation for multi-dimensional positional encoding outperforms existing methods by both improving the accuracy and allowing faster convergence.

Recent studies on mobile network design have demonstrated the remarkable effectiveness of channel attention (e.g., the Squeeze-and-Excitation attention) for lifting model performance, but they generally neglect the positional information, which is important for generating spatially selective attention maps. In this paper, we propose a novel attention mechanism for mobile networks by embedding positional information into channel attention, which we call "coordinate attention". Unlike channel attention that transforms a feature tensor to a single feature vector via 2D global pooling, the coordinate attention factorizes channel attention into two 1D feature encoding processes that aggregate features along the two spatial directions, respectively. In this way, long-range dependencies can be captured along one spatial direction and meanwhile precise positional information can be preserved along the other spatial direction. The resulting feature maps are then encoded separately into a pair of direction-aware and position-sensitive attention maps that can be complementarily applied to the input feature map to augment the representations of the objects of interest. Our coordinate attention is simple and can be flexibly plugged into classic mobile networks, such as MobileNetV2, MobileNeXt, and EfficientNet with nearly no computational overhead. Extensive experiments demonstrate that our coordinate attention is not only beneficial to ImageNet classification but more interestingly, behaves better in down-stream tasks, such as object detection and semantic segmentation. Code is available at https://github.com/Andrew-Qibin/CoordAttention.

Positional bias (PB), manifesting as non-uniform sensitivity across different contextual locations, significantly impairs long-context comprehension and processing capabilities. While prior work seeks to mitigate PB through modifying the architectures causing its emergence, significant PB still persists. To address PB effectively, we introduce Pos2Distill, a position to position knowledge distillation framework. Pos2Distill transfers the superior capabilities from advantageous positions to less favorable ones, thereby reducing the huge performance gaps. The conceptual principle is to leverage the inherent, position-induced disparity to counteract the PB itself. We identify distinct manifestations of PB under \textsc{r}etrieval and \textsc{r}easoning paradigms, thereby designing two specialized instantiations: Pos2Distill-R\textsuperscript{1} and Pos2Distill-R\textsuperscript{2} respectively, both grounded in this core principle. By employing the Pos2Distill approach, we achieve enhanced uniformity and significant performance gains across all contextual positions in long-context retrieval and reasoning tasks. Crucially, both specialized systems exhibit strong cross-task generalization mutually, while achieving superior performance on their respective tasks.

Generating realistic 3D Human-Object Interactions (HOI) is a fundamental task for applications ranging from embodied AI to virtual content creation, which requires harmonizing high-level semantic intent with strict low-level physical constraints. Existing methods excel at semantic alignment, however, they struggle to maintain precise object contact. We reveal a key finding termed Geometric Forgetting: as diffusion model depth increases, semantic feature tend to overshadow object geometry feature, causing the model to lose its perception to object geometry. To address this, we propose MaMi-HOI, a hierarchical framework reconciling Macro-level kinematic fluidity with Micro-level spatial precision. First, to counteract geometric forgetting, we introduce the Geometry-Aware Proximity Adapter (GAPA), which explicitly re-injects dense object details to perform residual snapping corrections for precise contact. Nevertheless, such aggressive local enforcement can disrupt global dynamics, leading to robotic stiffness. In response, we introduce the Kinematic Harmony Adapter (KHA), which proactively aligns whole-body posture with spatial objectives, ensuring the skeleton actively accommodates constraints without compromising naturalness. Extensive experiments validate that MaMi-HOI simultaneously achieves natural motion and precise contact. Crucially, it extends generation capabilities to long-term tasks with complex trajectories, effectively bridging the gap between global navigation and high-fidelity manipulation in 3D scenes. Code is available at https://github.com/DON738110198/MaMi-HOI.git

Rotary positional embeddings (RoPE) are widely used in large language models to encode token positions through multiplicative rotations, yet their behavior at long context lengths remains poorly characterized. In this work, we reinterpret RoPE as phase modulation applied to a bank of complex oscillators, enabling analysis through classical signal processing theory. Under this formulation, we derive principled lower bounds on the RoPE base parameter that are necessary to preserve positional coherence over a target context length. These include a fundamental aliasing bound, analogous to a Nyquist limit, and a DC-component stability bound that constrains phase drift in low-frequency positional modes. We further extend this analysis to deep transformers, showing that repeated rotary modulation across layers compounds angular misalignment, tightening the base requirement as depth increases. Complementing these results, we derive a precision-dependent upper bound on the RoPE base arising from finite floating-point resolution. Beyond this limit, incremental phase updates become numerically indistinguishable, leading to positional erasure even in the absence of aliasing. Together, the lower and upper bounds define a precision- and depth-dependent feasibility region a Goldilocks zone for long-context transformers. We validate the framework through a comprehensive case study of state-of-the-art models, including LLaMA, Mistral, and DeepSeek variants, showing that observed successes, failures, and community retrofits align closely with the predicted bounds. Notably, models that violate the stability bound exhibit attention collapse and long-range degradation, while attempts to scale beyond one million tokens encounter a hard precision wall independent of architecture or training.

Synthesizing whole-body manipulation of articulated objects, including body motion, hand motion, and object motion, is a critical yet challenging task with broad applications in virtual humans and robotics. The core challenges are twofold. First, achieving realistic whole-body motion requires tight coordination between the hands and the rest of the body, as their movements are interdependent during manipulation. Second, articulated object manipulation typically involves high degrees of freedom and demands higher precision, often requiring the fingers to be placed at specific regions to actuate movable parts. To address these challenges, we propose a novel coordinated diffusion noise optimization framework. Specifically, we perform noise-space optimization over three specialized diffusion models for the body, left hand, and right hand, each trained on its own motion dataset to improve generalization. Coordination naturally emerges through gradient flow along the human kinematic chain, allowing the global body posture to adapt in response to hand motion objectives with high fidelity. To further enhance precision in hand-object interaction, we adopt a unified representation based on basis point sets (BPS), where end-effector positions are encoded as distances to the same BPS used for object geometry. This unified representation captures fine-grained spatial relationships between the hand and articulated object parts, and the resulting trajectories serve as targets to guide the optimization of diffusion noise, producing highly accurate interaction motion. We conduct extensive experiments demonstrating that our method outperforms existing approaches in motion quality and physical plausibility, and enables various capabilities such as object pose control, simultaneous walking and manipulation, and whole-body generation from hand-only data.

Memory, planning, reflection, and tool use are often compared as feature labels, obscuring the control semantics that determine how an agent actually runs. This review connects ten historical cognitive architectures, eight language-agent runtime families, and forty-two mechanism-focused modern systems. We reconstruct each mechanism through state, control, transition, persistence, failure, learning, and resource governance, then code evidence relation (E1-E4) separately from migration depth (D0-D4). The resulting landscape is uneven. Modern agents have operationalized substantial parts of adaptive memory, failure recovery, dynamic team selection, workflow search, skill induction, resource scheduling, and uncertainty-conditioned action, although often through independent convergence rather than documented inheritance. The strongest remaining opportunities lie in couplings among mechanisms. Closest-baseline screening closes one proposed gap: GraSP already combines calibrated multi-skill selection, typed compilation, verification, bounded repair, and replanning or ReAct fallback. Five residual bundles remain: activation with latency and action utility; typed impasse with isolated substates and resolution compilation; bounded content competition with broadcast and admission learning; persistent intention with reconsideration and live method authority; and uncertainty with resource allocation, interruption, and stopping. We contribute a distinctive-mechanism catalog, an auditable evidence-depth framework, and a falsifiable agenda for testing these bundles as composable runtime invariants.

Length extrapolation algorithms based on Rotary position embedding (RoPE) have shown promising results in extending the context length of language models. However, understanding how position embedding can capture longer-range contextual information remains elusive. Based on the intuition that different dimensions correspond to different frequency of changes in RoPE encoding, we conducted a dimension-level analysis to investigate the correlation between a hidden dimension of an attention head and its contribution to capturing long-distance dependencies. Using our correlation metric, we identified a particular type of attention heads, which we named Positional Heads, from various length-extrapolated models. These heads exhibit a strong focus on long-range information interaction and play a pivotal role in long input processing, as evidence by our ablation. We further demonstrate the correlation between the efficiency of length extrapolation and the extension of the high-dimensional attention allocation of these heads. The identification of Positional Heads provides insights for future research in long-text comprehension.

Human-level contact-rich manipulation relies on the distinct roles of two key modalities: vision provides spatially rich but temporally slow global context, while force sensing captures rapid, high-frequency local contact dynamics. Integrating these signals is challenging due to their fundamental frequency and informational disparities. In this work, we propose ImplicitRDP, a unified end-to-end visual-force diffusion policy that integrates visual planning and reactive force control within a single network. We introduce Structural Slow-Fast Learning, a mechanism utilizing causal attention to simultaneously process asynchronous visual and force tokens, allowing the policy to perform closed-loop adjustments at the force frequency while maintaining the temporal coherence of action chunks. Furthermore, to mitigate modality collapse where end-to-end models fail to adjust the weights across different modalities, we propose Virtual-target-based Representation Regularization. This auxiliary objective maps force feedback into the same space as the action, providing a stronger, physics-grounded learning signal than raw force prediction. Extensive experiments on contact-rich tasks demonstrate that ImplicitRDP significantly outperforms both vision-only and hierarchical baselines, achieving superior reactivity and success rates with a streamlined training pipeline. Code and videos will be publicly available at https://implicit-rdp.github.io.

The attention mechanism in a Transformer architecture matches key to query based on both content -- the what -- and position in a sequence -- the where. We present an analysis indicating that what and where are entangled in the popular RoPE rotary position embedding. This entanglement can impair performance particularly when decisions require independent matches on these two factors. We propose an improvement to RoPE, which we call Polar Coordinate Position Embeddings or PoPE, that eliminates the what-where confound. PoPE is far superior on a diagnostic task requiring indexing solely by position or by content. On autoregressive sequence modeling in music, genomic, and natural language domains, Transformers using PoPE as the positional encoding scheme outperform baselines using RoPE with respect to evaluation loss (perplexity) and downstream task performance. On language modeling, these gains persist across model scale, from 124M to 774M parameters. Crucially, PoPE shows strong zero-shot length extrapolation capabilities compared not only to RoPE but even a method designed for extrapolation, YaRN, which requires additional fine tuning and frequency interpolation.

Rotary Position Embedding (RoPE) is an efficient position encoding approach and is widely utilized in numerous large language models (LLMs). Recently, a lot of methods have been put forward to further expand the context window based on RoPE. The core concept of those methods is to predefine or search for a set of factors to rescale the base frequencies of RoPE. Nevertheless, it is quite a challenge for existing methods to predefine an optimal factor due to the exponential search space. In view of this, we introduce PSC (Phase Shift Calibration), a small module for calibrating the frequencies predefined by existing methods. With the employment of PSC, we demonstrate that many existing methods can be further enhanced, like PI, YaRN, and LongRoPE. We conducted extensive experiments across multiple models and tasks. The results demonstrate that (1) when PSC is enabled, the comparative reductions in perplexity increase as the context window size is varied from 16k, to 32k, and up to 64k. (2) Our approach is broadly applicable and exhibits robustness across a variety of models and tasks. The code can be found at https://github.com/WNQzhu/PSC.

Humanoid robots require diverse motor skills to integrate into complex environments, but bridging the kinematic and dynamic embodiment gap from human data remains a major bottleneck. We demonstrate through Hessian analysis that traditional optimization-based retargeting is inherently non-convex and prone to local optima, leading to physical artifacts like joint jumps and self-penetration. To address this, we reformulate the targeting problem as learning data distribution rather than optimizing optimal solutions, where we propose NMR, a Neural Motion Retargeting framework that transforms static geometric mapping into a dynamics-aware learned process. We first propose Clustered-Expert Physics Refinement (CEPR), a hierarchical data pipeline that leverages VAE-based motion clustering to group heterogeneous movements into latent motifs. This strategy significantly reduces the computational overhead of massively parallel reinforcement learning experts, which project and repair noisy human demonstrations onto the robot's feasible motion manifold. The resulting high-fidelity data supervises a non-autoregressive CNN-Transformer architecture that reasons over global temporal context to suppress reconstruction noise and bypass geometric traps. Experiments on the Unitree G1 humanoid across diverse dynamic tasks (e.g., martial arts, dancing) show that NMR eliminates joint jumps and significantly reduces self-collisions compared to state-of-the-art baselines. Furthermore, NMR-generated references accelerate the convergence of downstream whole-body control policies, establishing a scalable path for bridging the human-robot embodiment gap.

Transformers rely on both content-based and position-based addressing mechanisms to make predictions, but existing positional encoding techniques often diminish the effectiveness of position-based addressing. Many current methods enforce rigid patterns in attention maps, limiting the ability to model long-range dependencies and adapt to diverse tasks. Additionally, most positional encodings are learned as general biases, lacking the specialization required for different instances within a dataset. To address this, we propose conTextualized equivariAnt Position Embedding (TAPE), a novel framework that enhances positional embeddings by incorporating sequence content across layers. TAPE introduces dynamic, context-aware positional encodings, overcoming the constraints of traditional fixed patterns. By enforcing permutation and orthogonal equivariance, TAPE ensures the stability of positional encodings during updates, improving robustness and adaptability. Our method can be easily integrated into pre-trained transformers, offering parameter-efficient fine-tuning with minimal overhead. Extensive experiments shows that TAPE achieves superior performance in language modeling, arithmetic reasoning, and long-context retrieval tasks compared to existing positional embedding techniques.

The Transformer architecture has revolutionized various regions since it was proposed, and its effectiveness largely depends on the ability to encode positional information. Traditional position encoding methods exhibit significant limitations due to lack of robustness and flexibility of position. Therefore, Rotary Positional Encoding (RoPE) was proposed to alleviate these issues, which integrates positional information by rotating the embeddings in the attention mechanism. However, RoPE requires manually defined rotation matrices with limited transformation space, constraining the model's capacity. In this work, we propose ComRoPE, which generalizes RoPE by defining it in terms of trainable commuting angle matrices. Specifically, we demonstrate that pairwise commutativity of these matrices is essential for RoPE to achieve scalability and positional robustness. We formally define the RoPE Equation, which is an essential condition that ensures consistent performance with position offsets. Based on the theoretical analysis, we present two types of trainable commuting angle matrices as sufficient solutions to the RoPE equation, which significantly improve performance, surpassing the current state-of-the-art method by 1.6% at training resolution and 2.9% at higher resolution on the ImageNet-1K dataset. Furthermore, our framework shows versatility in generalizing to existing RoPE formulations and offering new insights for future positional encoding research. To ensure reproducibility, the source code and instructions are available at https://github.com/Longin-Yu/ComRoPE

Rotary Position Embeddings (RoPE) make attention scores position-relative but leave the value pathway position-blind: the message sent by a value token is the same regardless of its distance from the query. We propose RoVE, a parameter-free modification that makes values position-sensitive by rotating them simultaneously with keys, and show that it turns RoPE attention into attentive convolution. This new perspective unifies several independent formulations of the same operation across computer vision, robotics, and modern LLM architectures. Trained 124M and 354M GPT-2 models show consistent empirical gains over RoPE on few-shot in-context learning, out-of-distribution perplexity, and long-context retrieval, with the clearest improvements on tasks that require long-range aggregation.

It is well noted that coordinate based MLPs benefit -- in terms of preserving high-frequency information -- through the encoding of coordinate positions as an array of Fourier features. Hitherto, the rationale for the effectiveness of these positional encodings has been solely studied through a Fourier lens. In this paper, we strive to broaden this understanding by showing that alternative non-Fourier embedding functions can indeed be used for positional encoding. Moreover, we show that their performance is entirely determined by a trade-off between the stable rank of the embedded matrix and the distance preservation between embedded coordinates. We further establish that the now ubiquitous Fourier feature mapping of position is a special case that fulfills these conditions. Consequently, we present a more general theory to analyze positional encoding in terms of shifted basis functions. To this end, we develop the necessary theoretical formulae and empirically verify that our theoretical claims hold in practice. Codes available at https://github.com/osiriszjq/Rethinking-positional-encoding.

Targeted data selection has emerged as a crucial paradigm for efficient instruction tuning, aiming to identify a small yet influential subset of training examples for a specific target task. In practice, influence is often measured through the effect of an example on parameter updates. To make selection scalable, many approaches leverage optimizer statistics (e.g., Adam states) as an axis-aligned surrogate for update geometry (i.e., diagonal precondition), implicitly treating parameters as coordinate-wise independent. We show that this assumption breaks down in parameter-efficient fine-tuning (PEFT) methods such as LoRA. In this setting, the induced optimization geometry exhibits strong cross-parameter coupling with non-trivial off-diagonal interactions, while the task-relevant update directions are confined to a low-dimensional subspace. Motivated by this mismatch, we propose GIST (Gradient Isometric Subspace Transformation), a simple yet principled alternative that replaces axis-aligned scaling with robust subspace alignment. GIST recovers a task-specific subspace from validation gradients via spectral filtering (SVD), projects training gradients into this coupled subspace, and scores examples by their alignment with target directions.Extensive experiments have demonstrated that GIST matches or outperforms the state-of-the-art baseline with only 0.29% of the storage and 25% of the computational time under the same selection budget.

Conditional human motion generation is an important topic with many applications in virtual reality, gaming, and robotics. While prior works have focused on generating motion guided by text, music, or scenes, these typically result in isolated motions confined to short durations. Instead, we address the generation of long, continuous sequences guided by a series of varying textual descriptions. In this context, we introduce FlowMDM, the first diffusion-based model that generates seamless Human Motion Compositions (HMC) without any postprocessing or redundant denoising steps. For this, we introduce the Blended Positional Encodings, a technique that leverages both absolute and relative positional encodings in the denoising chain. More specifically, global motion coherence is recovered at the absolute stage, whereas smooth and realistic transitions are built at the relative stage. As a result, we achieve state-of-the-art results in terms of accuracy, realism, and smoothness on the Babel and HumanML3D datasets. FlowMDM excels when trained with only a single description per motion sequence thanks to its Pose-Centric Cross-ATtention, which makes it robust against varying text descriptions at inference time. Finally, to address the limitations of existing HMC metrics, we propose two new metrics: the Peak Jerk and the Area Under the Jerk, to detect abrupt transitions.

Morphology-control co-design concerns the coupled optimization of an agent's body structure and control policy. This problem exhibits a bi-level structure, where the control dynamically adapts to the morphology to maximize performance. Existing methods typically neglect the control's adaptation dynamics by adopting a single-level formulation that treats the control policy as fixed when optimizing morphology. This can lead to inefficient optimization, as morphology updates may be misaligned with control adaptation. In this paper, we revisit the co-design problem from a game-theoretic perspective, modeling the intrinsic coupling between morphology and control as a novel variant of a Stackelberg game. We propose Stackelberg Proximal Policy Optimization (Stackelberg PPO), which explicitly incorporates the control's adaptation dynamics into morphology optimization. By modeling this intrinsic coupling, our method aligns morphology updates with control adaptation, thereby stabilizing training and improving learning efficiency. Experiments across diverse co-design tasks demonstrate that Stackelberg PPO outperforms standard PPO in both stability and final performance, opening the way for dramatically more efficient robotics designs.

Recent work by Baratin et al. (2021) sheds light on an intriguing pattern that occurs during the training of deep neural networks: some layers align much more with data compared to other layers (where the alignment is defined as the euclidean product of the tangent features matrix and the data labels matrix). The curve of the alignment as a function of layer index (generally) exhibits an ascent-descent pattern where the maximum is reached for some hidden layer. In this work, we provide the first explanation for this phenomenon. We introduce the Equilibrium Hypothesis which connects this alignment pattern to signal propagation in deep neural networks. Our experiments demonstrate an excellent match with the theoretical predictions.

Synthesizing realistic human-object interaction motions is a critical problem in VR/AR and human animation. Unlike the commonly studied scenarios involving a single human or hand interacting with one object, we address a more generic multi-body setting with arbitrary numbers of humans, hands, and objects. This complexity introduces significant challenges in synchronizing motions due to the high correlations and mutual influences among bodies. To address these challenges, we introduce SyncDiff, a novel method for multi-body interaction synthesis using a synchronized motion diffusion strategy. SyncDiff employs a single diffusion model to capture the joint distribution of multi-body motions. To enhance motion fidelity, we propose a frequency-domain motion decomposition scheme. Additionally, we introduce a new set of alignment scores to emphasize the synchronization of different body motions. SyncDiff jointly optimizes both data sample likelihood and alignment likelihood through an explicit synchronization strategy. Extensive experiments across four datasets with various multi-body configurations demonstrate the superiority of SyncDiff over existing state-of-the-art motion synthesis methods.

Collaborative generation, which coordinates multiple diffusion trajectories to extend the capabilities of pretrained priors, has emerged as a powerful paradigm for extending the applicability of diffusion models. Among existing approaches, diffusion synchronization provides a scenario-agnostic solution by introducing general guidance mechanisms. However, current synchronization approaches rely heavily on heuristics and still require task-specific tailoring, which limits their generalizability and performance. In this work, we mathematically derive a synchronization framework based on optimal control, providing a principled explanation of diffusion synchronization. During sampling, we optimize control variables to guide multiple trajectories toward coherent solutions while remaining close to the underlying diffusion prior. Our method operates entirely at test-time without additional training, thereby enabling broad applicability across diverse generation scenarios when combined with strong pretrained priors. We demonstrate consistent improvements over baselines on three representative collaborative generation tasks, covering a wide range of modalities and applications. Beyond performance gains, our work establishes a novel foundation for collaborative generation, opening a principled path toward extending pretrained generative models to new collaborative generation settings.

Recent advances in Video Foundation Models (VFMs) have revolutionized human-centric video synthesis, yet fine-grained and independent editing of subjects and scenes remains a critical challenge. Recent attempts to incorporate richer environment control through rigid 3D geometric compositions often encounter a stark trade-off between precise control and generative flexibility. Furthermore, the heavy 3D pre-processing still limits practical scalability. In this paper, we propose ONE-SHOT, a parameter-efficient framework for compositional human-environment video generation. Our key insight is to factorize the generative process into disentangled signals. Specifically, we introduce a canonical-space injection mechanism that decouples human dynamics from environmental cues via cross-attention. We also propose Dynamic-Grounded-RoPE, a novel positional embedding strategy that establishes spatial correspondences between disparate spatial domains without any heuristic 3D alignments. To support long-horizon synthesis, we introduce a Hybrid Context Integration mechanism to maintain subject and scene consistency across minute-level generations. Experiments demonstrate that our method significantly outperforms state-of-the-art methods, offering superior structural control and creative diversity for video synthesis. Our project has been available on: https://martayang.github.io/ONE-SHOT/.

Autoregressive diffusion enables real-time frame streaming, yet existing sliding-window caches discard past context, causing fidelity degradation, identity drift, and motion stagnation over long horizons. Current approaches preserve a fixed set of early tokens as attention sinks, but this static anchor cannot reflect the evolving content of a growing video. We introduce MemRoPE, a training-free framework with two co-designed components. Memory Tokens continuously compress all past keys into dual long-term and short-term streams via exponential moving averages, maintaining both global identity and recent dynamics within a fixed-size cache. Online RoPE Indexing caches unrotated keys and applies positional embeddings dynamically at attention time, ensuring the aggregation is free of conflicting positional phases. These two mechanisms are mutually enabling: positional decoupling makes temporal aggregation well-defined, while aggregation makes fixed-size caching viable for unbounded generation. Extensive experiments validate that MemRoPE outperforms existing methods in temporal coherence, visual fidelity, and subject consistency across minute- to hour-scale generation.

Dance-to-music generation is a promising task for applications such as choreography support and automatic accompaniment, where temporal coordination between body movement and sound is essential. In particular, using human joint positions as the motion representation is attractive because they explicitly capture body dynamics while being lightweight, privacy-preserving, and easy to integrate with motion capture and pose-estimation pipelines. A central challenge in this setting, however, is the scarcity of high-quality paired dance-music data, since collecting accurately synchronized pairs is costly and often constrained by copyright and performance rights. This makes it difficult to train end-to-end models solely from paired data. To address this issue, we propose a dance-conditioned music generation framework that efficiently exploits both unpaired and paired data. Our method combines pretrained unimodal encoders for motion and music, beat-guided contrastive pretraining to align their feature spaces, and a ControlNet-style conditioning module on top of a pretrained text-to-audio diffusion model. Experiments on AIST++ demonstrate that the proposed techniques improve both dance-music alignment and audio quality, as confirmed by quantitative and qualitative evaluations. Compared to a state-of-the-art method, our approach achieves superior dance alignment performance and competitive audio quality. Code is available at https://github.com/kmraven/AudioLDM-ControlNet .

Recent studies show that paddings in convolutional neural networks encode absolute position information which can negatively affect the model performance for certain tasks. However, existing metrics for quantifying the strength of positional information remain unreliable and frequently lead to erroneous results. To address this issue, we propose novel metrics for measuring (and visualizing) the encoded positional information. We formally define the encoded information as PPP (Position-information Pattern from Padding) and conduct a series of experiments to study its properties as well as its formation. The proposed metrics measure the presence of positional information more reliably than the existing metrics based on PosENet and a test in F-Conv. We also demonstrate that for any extant (and proposed) padding schemes, PPP is primarily a learning artifact and is less dependent on the characteristics of the underlying padding schemes.

Flow matching has emerged as a compelling generative modeling approach that is widely used across domains. To generate data via a flow matching model, an ordinary differential equation (ODE) is numerically solved via forward integration of the modeled velocity field. To better capture the multi-modality that is inherent in typical velocity fields, hierarchical flow matching was recently introduced. It uses a hierarchy of ODEs that are numerically integrated when generating data. This hierarchy of ODEs captures the multi-modal velocity distribution just like vanilla flow matching is capable of modeling a multi-modal data distribution. While this hierarchy enables to model multi-modal velocity distributions, the complexity of the modeled distribution remains identical across levels of the hierarchy. In this paper, we study how to gradually adjust the complexity of the distributions across different levels of the hierarchy via mini-batch couplings. We show the benefits of mini-batch couplings in hierarchical rectified flow matching via compelling results on synthetic and imaging data. Code is available at https://riccizz.github.io/HRF_coupling.

In recent years, huge progress has been made on learning neural implicit representations from multi-view images for 3D reconstruction. As an additional input complementing coordinates, using sinusoidal functions as positional encodings plays a key role in revealing high frequency details with coordinate-based neural networks. However, high frequency positional encodings make the optimization unstable, which results in noisy reconstructions and artifacts in empty space. To resolve this issue in a general sense, we introduce to learn neural implicit representations with quantized coordinates, which reduces the uncertainty and ambiguity in the field during optimization. Instead of continuous coordinates, we discretize continuous coordinates into discrete coordinates using nearest interpolation among quantized coordinates which are obtained by discretizing the field in an extremely high resolution. We use discrete coordinates and their positional encodings to learn implicit functions through volume rendering. This significantly reduces the variations in the sample space, and triggers more multi-view consistency constraints on intersections of rays from different views, which enables to infer implicit function in a more effective way. Our quantized coordinates do not bring any computational burden, and can seamlessly work upon the latest methods. Our evaluations under the widely used benchmarks show our superiority over the state-of-the-art. Our code is available at https://github.com/MachinePerceptionLab/CQ-NIR.

The integration of Rotary Position Embedding (RoPE) in Multimodal Diffusion Transformer (MMDiT) has significantly enhanced text-to-image generation quality. However, the fundamental reliance of self-attention layers on positional embedding versus query-key similarity during generation remains an intriguing question. We present the first mechanistic analysis of RoPE-based MMDiT models (e.g., FLUX), introducing an automated probing strategy that disentangles positional information versus content dependencies by strategically manipulating RoPE during generation. Our analysis reveals distinct dependency patterns that do not straightforwardly correlate with depth, offering new insights into the layer-specific roles in RoPE-based MMDiT. Based on these findings, we propose a training-free, task-specific image editing framework that categorizes editing tasks into three types: position-dependent editing (e.g., object addition), content similarity-dependent editing (e.g., non-rigid editing), and region-preserved editing (e.g., background replacement). For each type, we design tailored key-value injection strategies based on the characteristics of the editing task. Extensive qualitative and quantitative evaluations demonstrate that our method outperforms state-of-the-art approaches, particularly in preserving original semantic content and achieving seamless modifications.

Large Language Models (LLMs) are increasingly applied in various real-world scenarios due to their excellent generalization capabilities and robust generative abilities. However, they exhibit position bias, also known as "lost in the middle", a phenomenon that is especially pronounced in long-context scenarios, which indicates the placement of the key information in different positions of a prompt can significantly affect accuracy. This paper first explores the micro-level manifestations of position bias, concluding that attention weights are a micro-level expression of position bias. It further identifies that, in addition to position embeddings, causal attention mask also contributes to position bias by creating position-specific hidden states. Based on these insights, we propose a method to mitigate position bias by scaling this positional hidden states. Experiments on the NaturalQuestions Multi-document QA, KV retrieval, LongBench and timeline reorder tasks, using various models including RoPE models, context windowextended models, and Alibi models, demonstrate the effectiveness and generalizability of our approach. Our method can improve performance by up to 15.2% by modifying just one dimension of hidden states. Our code is available at https://aka.ms/PositionalHidden.

Dynamic multi-objective optimization requires continuous tracking of moving Pareto fronts. Existing methods struggle with irregular mutations and data sparsity, primarily facing three challenges: the non-linear coupling of dynamic modes, negative transfer from outdated historical data, and the cold-start problem during environmental switches. To address these issues, this paper proposes a decoupled basis-vector-driven generative framework (DB-GEN). First, to resolve non-linear coupling, the framework employs the discrete wavelet transform to separate evolutionary trajectories into low-frequency trends and high-frequency details. Second, to mitigate negative transfer, it learns transferable basis vectors via sparse dictionary learning rather than directly memorizing historical instances. Recomposing these bases under a topology-aware contrastive constraint constructs a structured latent manifold. Finally, to overcome the cold-start problem, a surrogate-assisted search paradigm samples initial populations from this manifold. Pre-trained on 120 million solutions, DB-GEN performs direct online inference without retraining or fine-tuning. This zero-shot generation process executes in milliseconds, requiring approximately 0.2 seconds per environmental change. Experimental results demonstrate that DB-GEN improves tracking accuracy across various dynamic benchmarks compared to existing algorithms.

Position controllers have become the dominant interface for executing learned manipulation policies. Yet a critical design decision remains understudied: how should we choose controller gains for policy learning? The conventional wisdom is to select gains based on desired task compliance or stiffness. However, this logic breaks down when controllers are paired with state-conditioned policies: effective stiffness emerges from the interplay between learned reactions and control dynamics, not from gains alone. We argue that gain selection should instead be guided by learnability: how amenable different gain settings are to the learning algorithm in use. In this work, we systematically investigate how position controller gains affect three core components of modern robot learning pipelines: behavior cloning, reinforcement learning from scratch, and sim-to-real transfer. Through extensive experiments across multiple tasks and robot embodiments, we find that: (1) behavior cloning benefits from compliant and overdamped gain regimes, (2) reinforcement learning can succeed across all gain regimes given compatible hyperparameter tuning, and (3) sim-to-real transfer is harmed by stiff and overdamped gain regimes. These findings reveal that optimal gain selection depends not on the desired task behavior, but on the learning paradigm employed. Project website: https://younghyopark.me/tune-to-learn

Unified multimodal models (UMMs) aim to integrate understanding and generation within a single architecture. However, it remains underexplored how to effectively coordinate these two capabilities for more effective and efficient reasoning. Existing coordination approaches either perform coupling during training, without explicit inference-time coordination, or impose a fixed coordination pattern for all inputs. In this work, we show that multimodal tasks exhibit substantial coordination-path diversity: different inputs favor different coordination paths. This suggests that exploiting such diversity is key to improving performance. We propose UniPath, a framework for adaptively modeling and exploiting coordination-path diversity. Instead of enforcing a single coordination pattern, we represent task solving as the selection and execution of a path, ranging from direct answering to textual inference, visual-thought construction, and hypothesis-based exploration. We construct role-aligned trajectories to train a path-conditioned executor and introduce a lightweight planner mechanism to enable input-dependent path selection. Experiments show that leveraging coordination-path diversity improves performance over fixed coordination strategies while providing interpretable intermediate behaviors. The code is available at:https://github.com/AIFrontierLab/TorchUMM/tree/main/src/umm/post_training/unipath.

The intrinsic link between facial motion and speech is often overlooked in generative modeling, where talking head synthesis and text-to-speech (TTS) are typically addressed as separate tasks. This paper introduces JAM-Flow, a unified framework to simultaneously synthesize and condition on both facial motion and speech. Our approach leverages flow matching and a novel Multi-Modal Diffusion Transformer (MM-DiT) architecture, integrating specialized Motion-DiT and Audio-DiT modules. These are coupled via selective joint attention layers and incorporate key architectural choices, such as temporally aligned positional embeddings and localized joint attention masking, to enable effective cross-modal interaction while preserving modality-specific strengths. Trained with an inpainting-style objective, JAM-Flow supports a wide array of conditioning inputs-including text, reference audio, and reference motion-facilitating tasks such as synchronized talking head generation from text, audio-driven animation, and much more, within a single, coherent model. JAM-Flow significantly advances multi-modal generative modeling by providing a practical solution for holistic audio-visual synthesis. project page: https://joonghyuk.com/jamflow-web

We show that in a drive-response coupling framework extreme events are suppressed in the response system by the dominance of a single driving signal. We validate this approach across three distinct response network topologies, namely (i) a pair of coupled neurons, (ii) a monolayer network of N coupled neurons and (iii) a two-layer multiplex network each composed of FitzHugh-Nagumo neuronal units. The response networks inherently exhibit extreme events. Our results demonstrate that influencing just one neuron in the response network with an appropriately tuned driving signal is sufficient to control extreme events across all three configurations. In the two-neuron case, suppression of extreme events occurs due to the breaking of phase-locking between the driving neuron and the targeted response neuron. In the case of monolayer and multiplex networks, suppression of extreme events results from the disruption of protoevent frequency dynamics and a subsequent frequency decoupling of the driven neuron from the rest of the network. We also observe that when the size of the neurons in response network connected to the drive increases, the onset of control occurs earlier indicating a scaling advantage of the method.

In this paper, we develop position embedding transformation (PETR) for multi-view 3D object detection. PETR encodes the position information of 3D coordinates into image features, producing the 3D position-aware features. Object query can perceive the 3D position-aware features and perform end-to-end object detection. PETR achieves state-of-the-art performance (50.4% NDS and 44.1% mAP) on standard nuScenes dataset and ranks 1st place on the benchmark. It can serve as a simple yet strong baseline for future research. Code is available at https://github.com/megvii-research/PETR.

Rotary Positional Embedding (RoPE) is a common choice in transformer architectures for encoding relative positional information. Although earlier work has examined omitting RoPE in specific layers, the effect of varying the fraction of hidden dimensions that receive rotary transformations remains largely unexplored. This design choice can yield substantial memory savings, which becomes especially significant at long context lengths. We find up to 10x memory savings over the standard RoPE cache, while achieving comparable final loss. In this work, we present a systematic study examining the impact of partial RoPE on training dynamics and convergence across architectures and datasets. Our findings uncover several notable patterns: (1) applying RoPE to only a small fraction of dimensions (around 10%) achieves convergence comparable to using full RoPE; (2) these trends hold consistently across model size, sequence lengths and datasets of varying quality and architectures, with higher-quality data resulting in lower overall loss and similar benchmark performance; and (3) some models trained with NoPE (No Positional Encoding) showcase unstable learning trajectories, which can be alleviated through minimal RoPE application or QK-Norm which converges to a higher loss. Together, these results offer practical guidance for model designers aiming to balance efficiency and training stability, while emphasizing the previously overlooked importance of partial RoPE.

Recent studies have shown that, relative position encoding performs well in selective state space model scanning algorithms, and the architecture that balances SSM and Attention enhances the efficiency and effectiveness of the algorithm, while the sparse activation of the mixture of experts reduces the training cost. I studied the effectiveness of using different position encodings in structured state space dual algorithms, and the more effective SSD-Attn internal and external function mixing method, and designed a more efficient cross domain mixture of experts. I found that the same matrix is very wonderful in different algorithms, which allows us to establish a new hybrid sparse architecture: Cheems. Compared with other hybrid architectures, it is more efficient and more effective in language modeling tasks.

Rotary Position Embedding (RoPE) in Transformer models has inherent limits that weaken length extrapolation. We reinterpret the attention map with positional encoding as a noisy feature map, and propose Denoising Positional Encoding (DoPE), a training-free method based on truncated matrix entropy to detect outlier frequency bands in the feature map. Leveraging the noise characteristics of the feature map, we further reparameterize it with a parameter-free Gaussian distribution to achieve robust extrapolation. Our method theoretically reveals the underlying cause of the attention sink phenomenon and its connection to truncated matrix entropy. Experiments on needle-in-a-haystack and many-shot in-context learning tasks demonstrate that DoPE significantly improves retrieval accuracy and reasoning stability across extended contexts (up to 64K tokens). The results show that the denoising strategy for positional embeddings effectively mitigates attention sinks and restores balanced attention patterns, providing a simple yet powerful solution for improving length generalization. Our project page is Project: https://The-physical-picture-of-LLMs.github.io

Positional encoding mechanisms enable Transformers to model sequential structure and long-range dependencies in text. While absolute positional encodings struggle with extrapolation to longer sequences due to fixed positional representations, and relative approaches like Alibi exhibit performance degradation on extremely long contexts, the widely-used Rotary Positional Encoding (RoPE) introduces oscillatory attention patterns that hinder stable long-distance dependency modelling. We address these limitations through a geometric reformulation of positional encoding. Drawing inspiration from Lorentz transformations in hyperbolic geometry, we propose Hyperbolic Rotary Positional Encoding (HoPE), which leverages hyperbolic functions to implement Lorentz rotations on token representations. Theoretical analysis demonstrates that RoPE is a special case of our generalized formulation. HoPE fundamentally resolves RoPE's slation issues by enforcing monotonic decay of attention weights with increasing token distances. Extensive experimental results, including perplexity evaluations under several extended sequence benchmarks, show that HoPE consistently exceeds existing positional encoding methods. These findings underscore HoPE's enhanced capacity for representing and generalizing long-range dependencies. Data and code will be available.

Relative position encoding (RPE) is important for transformer to capture sequence ordering of input tokens. General efficacy has been proven in natural language processing. However, in computer vision, its efficacy is not well studied and even remains controversial, e.g., whether relative position encoding can work equally well as absolute position? In order to clarify this, we first review existing relative position encoding methods and analyze their pros and cons when applied in vision transformers. We then propose new relative position encoding methods dedicated to 2D images, called image RPE (iRPE). Our methods consider directional relative distance modeling as well as the interactions between queries and relative position embeddings in self-attention mechanism. The proposed iRPE methods are simple and lightweight. They can be easily plugged into transformer blocks. Experiments demonstrate that solely due to the proposed encoding methods, DeiT and DETR obtain up to 1.5% (top-1 Acc) and 1.3% (mAP) stable improvements over their original versions on ImageNet and COCO respectively, without tuning any extra hyperparameters such as learning rate and weight decay. Our ablation and analysis also yield interesting findings, some of which run counter to previous understanding. Code and models are open-sourced at https://github.com/microsoft/Cream/tree/main/iRPE.

This work presents a novel online model-predictive trajectory planner for robotic manipulators called BoundMPC. This planner allows the collision-free following of Cartesian reference paths in the end-effector's position and orientation, including via-points, within desired asymmetric bounds of the orthogonal path error. The path parameter synchronizes the position and orientation reference paths. The decomposition of the path error into the tangential direction, describing the path progress, and the orthogonal direction, which represents the deviation from the path, is well known for the position from the path-following control in the literature. This paper extends this idea to the orientation by utilizing the Lie theory of rotations. Moreover, the orthogonal error plane is further decomposed into basis directions to define asymmetric Cartesian error bounds easily. Using piecewise linear position and orientation reference paths with via-points is computationally very efficient and allows replanning the pose trajectories during the robot's motion. This feature makes it possible to use this planner for dynamically changing environments and varying goals. The flexibility and performance of BoundMPC are experimentally demonstrated by two scenarios on a 7-DoF Kuka LBR iiwa 14 R820 robot. The first scenario shows the transfer of a larger object from a start to a goal pose through a confined space where the object must be tilted. The second scenario deals with grasping an object from a table where the grasping point changes during the robot's motion, and collisions with other obstacles in the scene must be avoided.

Recurrent models have been dominating the field of neural machine translation (NMT) for the past few years. Transformers vaswani2017attention, have radically changed it by proposing a novel architecture that relies on a feed-forward backbone and self-attention mechanism. Although Transformers are powerful, they could fail to properly encode sequential/positional information due to their non-recurrent nature. To solve this problem, position embeddings are defined exclusively for each time step to enrich word information. However, such embeddings are fixed after training regardless of the task and the word ordering system of the source or target language. In this paper, we propose a novel architecture with new position embeddings depending on the input text to address this shortcoming by taking the order of target words into consideration. Instead of using predefined position embeddings, our solution generates new embeddings to refine each word's position information. Since we do not dictate the position of source tokens and learn them in an end-to-end fashion, we refer to our method as dynamic position encoding (DPE). We evaluated the impact of our model on multiple datasets to translate from English into German, French, and Italian and observed meaningful improvements in comparison to the original Transformer.

A common assumption holds that enough observational and interventional data, given to a strong enough predictor, suffices. We report a failure mode that contradicts it. Across hundreds of structural causal models, on identified quantities a strong predictor and a Bayesian baseline both succeed, but on unidentified quantities (the couplings between counterfactual worlds) the predictor collapses to a point, on 28% of models to one no valid model can produce, while the truth is an admissible interval more data never narrows. The gap is structural: prediction cannot represent uncertainty over counterfactual couplings. We cast a world model as a single positive semidefinite coupling kernel K(T,T') over admissible worlds, whose diagonal is the ordinary posterior (what a predictor recovers) and whose off-diagonal is the cross-world coupling it cannot, which every counterfactual reads. The paper is the theory of that off-diagonal. It is real: two states with identical posteriors differ on a cross-world query, and the off-diagonal is the coupling that fixes counterfactuals. It can be bounded: positive semidefiniteness is partial-identifying information the marginals lack, and enforcing it bounds counterfactuals in polynomial time where the exact response-type program is intractable. Logical structure sharpens it: ontology axioms tighten the bound by up to a third, propagating to couplings they never touch. It can be acquired: targeted scars, constraints learned from encountered infeasibilities, close the gap several times faster than untargeted ones. Its full reconstruction is approximate counting of the admissible worlds, tractable below the Sly-Sun threshold and inapproximable above; we do not claim to beat the worst case.

We present a flow-based approach to the optimal transport (OT) problem between two continuous distributions pi_0,pi_1 on R^d, of minimizing a transport cost E[c(X_1-X_0)] in the set of couplings (X_0,X_1) whose marginal distributions on X_0,X_1 equals pi_0,pi_1, respectively, where c is a cost function. Our method iteratively constructs a sequence of neural ordinary differentiable equations (ODE), each learned by solving a simple unconstrained regression problem, which monotonically reduce the transport cost while automatically preserving the marginal constraints. This yields a monotonic interior approach that traverses inside the set of valid couplings to decrease the transport cost, which distinguishes itself from most existing approaches that enforce the coupling constraints from the outside. The main idea of the method draws from rectified flow, a recent approach that simultaneously decreases the whole family of transport costs induced by convex functions c (and is hence multi-objective in nature), but is not tailored to minimize a specific transport cost. Our method is a single-object variant of rectified flow that guarantees to solve the OT problem for a fixed, user-specified convex cost function c.

Since self-attention layers in Transformers are permutation invariant by design, positional encodings must be explicitly incorporated to enable spatial understanding. However, fixed-size lookup tables used in traditional learnable position embeddings (PEs) limit extrapolation capabilities beyond pre-trained sequence lengths. Expert-designed methods such as ALiBi and RoPE, mitigate this limitation but demand extensive modifications for adapting to new modalities, underscoring fundamental challenges in adaptability and scalability. In this work, we present SeqPE, a unified and fully learnable position encoding framework that represents each n-dimensional position index as a symbolic sequence and employs a lightweight sequential position encoder to learn their embeddings in an end-to-end manner. To regularize SeqPE's embedding space, we introduce two complementary objectives: a contrastive objective that aligns embedding distances with a predefined position-distance function, and a knowledge distillation loss that anchors out-of-distribution position embeddings to in-distribution teacher representations, further enhancing extrapolation performance. Experiments across language modeling, long-context question answering, and 2D image classification demonstrate that SeqPE not only surpasses strong baselines in perplexity, exact match (EM), and accuracy--particularly under context length extrapolation--but also enables seamless generalization to multi-dimensional inputs without requiring manual architectural redesign. We release our code, data, and checkpoints at https://github.com/ghrua/seqpe.

We present anyakrakusuma, an open-source Python library that solves the discrete static Schrödinger bridge problem, the entropically regularized counterpart of optimal transport, through a log-domain Sinkhorn--Knopp iteration and reconstructs the entropic interpolation between two empirical point clouds. The solver is paired with a diagnostic pipeline that characterizes the optimal coupling and the intermediate distributions through information-theoretic and geometric measures. We exercise the library on four idealized planar cases spanning a circle-to-circle dilation, a spiral-to-mixture fragmentation, a rigid reorientation of two moons, and a Lissajous-to-trefoil deformation. The log-domain formulation is necessary rather than merely convenient at the parameters studied, where the cost-to-regularization ratio reaches four hundred and the Gibbs kernel underflows double precision across most of its range; the iteration nonetheless attains a marginal residual of 10^{-9} and unit marginal fidelity in every case. Residual histories decay geometrically over approximately eight decades at per-iteration contraction factors between 0.966 and 0.976, which are local rates near the fixed point that lie many orders of magnitude below the worst-case Hilbert-metric bound. The covariance analysis recovers an imposed ninety-degree reorientation to within 0.07^circ, roughly forty times smaller than its uncertainty, across a masked interval of near-isotropy on which the principal axis is unobservable. The diagnostics are reported with explicit attention to the regimes in which each is well defined, including the differential entropy, which is meaningful only on the open interpolation interval. The presented cases are constructed rather than measured; quantitative application to empirical point clouds requires further study.

Post-training is essential for refining the domain-specific capabilities of large language models (LLMs), yet existing reward optimization and distribution matching methods tightly couple policy exploration with distribution alignment. This coupling forces expensive exploration directly on the policy model and severely hinders the asynchronous generation, reuse, and cross-model transfer of optimization signals. In this paper, we propose Proxy-guided Update Signal Transfer (PUST), a novel post-training framework that fundamentally decouples update-signal exploration from distribution alignment. Instead of utilizing the primary model for costly exploration, PUST employs a lightweight proxy model as an efficient testbed to discover high-reward behaviors. We extract the relative improvement signal between the proxy's initial and optimized states, transferring this directional update to the primary model to guide its policy alignment. This decoupled pipeline, comprising proxy exploration, update-signal extraction, and signal transfer, significantly reduces computational overhead and enables optimization signals to be asynchronously generated, cached, and reused. Crucially, by transferring relative improvements rather than absolute policy distributions, PUST naturally supports weak-to-strong improvement and seamless cross-model transfer. Systematic evaluations on Qwen3-family models across math and code domains demonstrate that update signals extracted from substantially weaker proxies can robustly and adjustably enhance stronger primary models. Ultimately, PUST transforms post-training from a monolithic online optimization process into a highly modular, reusable, and cost-efficient paradigm.

Human cognition does not separate understanding and generation. A teacher at a whiteboard speaks and draws together, each modality reshapes the other. In this paper, we bring this coupled loop to artificial systems. Masked Diffusion Models (MDMs) are ideally suited to this task, yet existing samplers either decode text and image interleavedly or independently update them in parallel branches that share only previous-step history, but not the other modality's latest decisions within the same step; combined with MDMs' inability to remask, cross-modal contradictions are neither detected nor repaired. We introduce Self-Correcting Coupled Markov Jump Processes (SC-CMJP), a framework in which one modality's transition rates are functionals of the other modality's confidence score, as weighted by cross-modal attention. Furthermore, a remasking jump retracts commitments the moment cross-modal evidence turns against them. In conjunction with SC-CMJP, we introduce CO_2Jump (Self-text{CO}rrecting text{CO}upled text{Jump}), a novel training-free single-pass sampler for joint multimodal geneneration. For training and evaluation purposes, we have created and will release three large-scale joint multimodal generation corpora: JEdit-1M, JMaze-200K, JNono-200K, with matching in- and out-of-distribution benchmarks. CO_2Jump achieves best joint performance for image understanding and editing as well as visual reasoning (maze and nonogram solving). The performance of the sampler scales monotonically with the number of denoising steps, evidence that the benefits of cross-modal coupling compound across the trajectory. Project page: https://coupled-jump.github.io

Multi-person 3D mesh recovery from videos is a critical first step towards automatic perception of group behavior in virtual reality, physical therapy and beyond. However, existing approaches rely on multi-stage paradigms, where the person detection and tracking stages are performed in a multi-person setting, while temporal dynamics are only modeled for one person at a time. Consequently, their performance is severely limited by the lack of inter-person interactions in the spatial-temporal mesh recovery, as well as by detection and tracking defects. To address these challenges, we propose the Coordinate transFormer (CoordFormer) that directly models multi-person spatial-temporal relations and simultaneously performs multi-mesh recovery in an end-to-end manner. Instead of partitioning the feature map into coarse-scale patch-wise tokens, CoordFormer leverages a novel Coordinate-Aware Attention to preserve pixel-level spatial-temporal coordinate information. Additionally, we propose a simple, yet effective Body Center Attention mechanism to fuse position information. Extensive experiments on the 3DPW dataset demonstrate that CoordFormer significantly improves the state-of-the-art, outperforming the previously best results by 4.2%, 8.8% and 4.7% according to the MPJPE, PAMPJPE, and PVE metrics, respectively, while being 40% faster than recent video-based approaches. The released code can be found at https://github.com/Li-Hao-yuan/CoordFormer.

In single-stream autoregressive interfaces, the same tokens both update the model state and constitute an irreversible public commitment. This coupling creates a silence tax: additional deliberation postpones the first task-relevant content, while naive early streaming risks premature commitments that bias subsequent generations. We introduce Side-by-Side (SxS) Interleaved Reasoning, which makes disclosure timing a controllable decision within standard autoregressive generation. SxS interleaves partial disclosures with continued private reasoning in the same context, but releases content only when it is supported by the reasoning so far. To learn such pacing without incentivizing filler, we construct entailment-aligned interleaved trajectories by matching answer prefixes to supporting reasoning prefixes, then train with SFT to acquire the dual-action semantics and RL to recover reasoning performance under the new format. Across two Qwen3 architectures/scales (MoE Qwen3-30B-A3B, dense Qwen3-4B) and both in-domain (AIME25) and out-of-domain (GPQA-Diamond) benchmarks, SxS improves accuracy--content-latency Pareto trade-offs under token-level proxies such as inter-update waiting.

Position bias has proven to be a prevalent issue of modern language models (LMs), where the models prioritize content based on its position within the given context. This bias often leads to unexpected model failures and hurts performance, robustness, and reliability across various applications. Our mechanistic analysis attributes the position bias to two components employed in nearly all state-of-the-art LMs: causal attention and relative positional encodings. Specifically, we find that causal attention generally causes models to favor distant content, while relative positional encodings like RoPE prefer nearby ones based on the analysis of retrieval-augmented question answering (QA). Further, our empirical study on object detection reveals that position bias is also present in vision-language models (VLMs). Based on the above analyses, we propose to ELIMINATE position bias caused by different input segment orders (e.g., options in LM-as-a-judge, retrieved documents in QA) in a TRAINING-FREE ZERO-SHOT manner. Our method changes the causal attention to bidirectional attention between segments and utilizes model attention values to decide the relative orders of segments instead of using the order provided in input prompts, therefore enabling Position-INvariant inferencE (PINE) at the segment level. By eliminating position bias, models achieve better performance and reliability in downstream tasks where position bias widely exists, such as LM-as-a-judge and retrieval-augmented QA. Notably, PINE is especially useful when adapting LMs for evaluating reasoning pairs: it consistently provides 8 to 10 percentage points performance gains in most cases, and makes Llama-3-70B-Instruct perform even better than GPT-4-0125-preview on the RewardBench reasoning subset.

Positional encodings are essential to transformer-based generative models, yet their behavior in multimodal and attention-sharing settings is not fully understood. In this work, we present a principled analysis of Rotary Positional Embeddings (RoPE), showing that RoPE naturally decomposes into frequency components with distinct positional sensitivities. We demonstrate that this frequency structure explains why shared-attention mechanisms, where a target image is generated while attending to tokens from a reference image, can lead to reference copying, in which the model reproduces content from the reference instead of extracting only its stylistic cues. Our analysis reveals that the high-frequency components of RoPE dominate the attention computation, forcing queries to attend mainly to spatially aligned reference tokens and thereby inducing this unintended copying behavior. Building on these insights, we introduce a method for selectively modulating RoPE frequency bands so that attention reflects semantic similarity rather than strict positional alignment. Applied to modern transformer-based diffusion architectures, where all tokens share attention, this modulation restores stable and meaningful shared attention. As a result, it enables effective control over the degree of style transfer versus content copying, yielding a proper style-aligned generation process in which stylistic attributes are transferred without duplicating reference content.

Bundle adjustment is the common way to solve localization and mapping. It is an iterative process in which a system of non-linear equations is solved using two optimization methods, weighted by a damping factor. In the classic approach, the latter is chosen heuristically by the Levenberg-Marquardt algorithm on each iteration. This might take many iterations, making the process computationally expensive, which might be harmful to real-time applications. We propose to replace this heuristic by viewing the problem in a holistic manner, as a game, and formulating it as a reinforcement-learning task. We set an environment which solves the non-linear equations and train an agent to choose the damping factor in a learned manner. We demonstrate that our approach considerably reduces the number of iterations required to reach the bundle adjustment's convergence, on both synthetic and real-life scenarios. We show that this reduction benefits the classic approach and can be integrated with other bundle adjustment acceleration methods.

We address the task of generating physically accurate and visually faithful 4D Human-Object Interaction (HOI). Given a static 3D human and target object represented as 3D Gaussian Splats (3DGS), our goal is to synthesize dynamic scenes where the human actively engages with the object through actions, such as punching or kicking, in accordance with a given input text. To this end, we introduce PhyGenHOI, a novel framework that couples generative human motion with an explicit physical object simulation. We model the human as a semantic agent driven by a Motion Diffusion Model (MDM) and the object as a physical agent simulated via the Material Point Method (MPM), utilizing 3D Gaussians as a unified, differentiable representation. We supervise their interaction through three coupled mechanisms: (1) A Windowed Attraction Loss that temporally synchronizes generative motion to intercept the object; (2) A Contact-Driven Re-simulation step that triggers physically consistent momentum transfer upon impact; and (3) A Masked Video-SDS objective that injects video-based priors to enhance contact fidelity. Experiments show PhyGenHOI generates physically consistent 4D HOI across diverse actions, humans, and objects, outperforming baselines. Project page and videos: https://omerbenishu.github.io/PhyGenHOI/

The transition of an impulsively excited kink oscillation of a solar coronal loop to an oscillation with a stationary amplitude, i.e., the damping pattern, is determined using the low-dimensional self-oscillation model. In the model, the decayless kink oscillations are sustained by the interaction of the oscillating loop with an external quasi-steady flow. The analytical solution is based on the assumption that the combined effect of the effective dissipation, for example, by resonant absorption, and interaction with an external flow, is weak. The effect is characterised by a dimensionless coupling parameter. The damping pattern is found to depend upon the initial amplitude and the coupling parameter. The approximate expression shows a good agreement with a numerical solution of the self-oscillation equation. The plausibility of the established damping pattern is demonstrated by an observational example. Notably, the damping pattern is not exponential, and the characteristic decay time is different from the time determined by the traditionally used exponential damping fit. Implications of this finding for seismology of the solar coronal plasmas are discussed. In particular, it is suggested that a very rapid, in less than the oscillation period, decay of the oscillation to the stationary level, achieved for larger values of the coupling parameter, can explain the relative rareness of the kink oscillation events.

Multimodal position encoding is essential for vision-language models, yet there has been little systematic investigation into multimodal position encoding. We conduct a comprehensive analysis of multimodal Rotary Positional Embedding (RoPE) by examining its two core components: position design and frequency allocation. Through extensive experiments, we identify three key guidelines: positional coherence, full frequency utilization, and preservation of textual priors-ensuring unambiguous layout, rich representation, and faithful transfer from the pre-trained LLM. Based on these insights, we propose Multi-Head RoPE (MHRoPE) and MRoPE-Interleave (MRoPE-I), two simple and plug-and-play variants that require no architectural changes. Our methods consistently outperform existing approaches across diverse benchmarks, with significant improvements in both general and fine-grained multimodal understanding. Code will be avaliable at https://github.com/JJJYmmm/Multimodal-RoPEs.

Sequence learning reduces to similarity-based retrieval over a temporally indexed representation space, a constraint on any sequence model, not a property of a specific architecture. We show that a spiking Sparse Distributed Memory sequence machine (2007) and the transformer (2017) independently instantiate the same five functional operations (encoding, context maintenance, associative retrieval, storage, and decoding), with cosine similarity as the shared retrieval primitive in both. We formalise a Phase-Latency Isomorphism showing that sinusoidal positional phase and spike timing are linearly related, and prove that dot product attention is invariant to this mapping up to a global scale factor on the positional component (Lemma 1). Empirically, frequency-compressed positional encoding fails to converge on a positionally demanding copy task, while a learned rank-based embedding matches or exceeds sinusoidal encoding, indicating that the critical property for positional representation is distance discriminability under dot-product similarity, not sinusoidal form. Time, phase, and rank are three instantiations of the same computational primitive, an ordered index whose structure survives similarity-based retrieval.

Position embedding is a core component of current Large Language Models (LLMs). Rotary position embedding (RoPE), a technique that encodes the position information with a rotation matrix, has been the de facto choice for position embedding in many LLMs, such as the Llama series. RoPE has been further utilized to extend long context capability, which is roughly based on adjusting the base parameter of RoPE to mitigate out-of-distribution (OOD) problems in position embedding. However, in this paper, we find that LLMs may obtain a superficial long-context ability based on the OOD theory. We revisit the role of RoPE in LLMs and propose a novel property of long-term decay, we derive that the base of RoPE bounds context length: there is an absolute lower bound for the base value to obtain certain context length capability. Our work reveals the relationship between context length and RoPE base both theoretically and empirically, which may shed light on future long context training.

Hand-Object Interaction (HOI) generation plays a critical role in advancing applications across animation and robotics. Current video-based methods are predominantly single-view, which impedes comprehensive 3D geometry perception and often results in geometric distortions or unrealistic motion patterns. While 3D HOI approaches can generate dynamically plausible motions, their dependence on high-quality 3D data captured in controlled laboratory settings severely limits their generalization to real-world scenarios. To overcome these limitations, we introduce SyncMV4D, the first model that jointly generates synchronized multi-view HOI videos and 4D motions by unifying visual prior, motion dynamics, and multi-view geometry. Our framework features two core innovations: (1) a Multi-view Joint Diffusion (MJD) model that co-generates HOI videos and intermediate motions, and (2) a Diffusion Points Aligner (DPA) that refines the coarse intermediate motion into globally aligned 4D metric point tracks. To tightly couple 2D appearance with 4D dynamics, we establish a closed-loop, mutually enhancing cycle. During the diffusion denoising process, the generated video conditions the refinement of the 4D motion, while the aligned 4D point tracks are reprojected to guide next-step joint generation. Experimentally, our method demonstrates superior performance to state-of-the-art alternatives in visual realism, motion plausibility, and multi-view consistency.

Large-scale pre-trained models (PTMs) have been widely used in document-oriented NLP tasks, such as question answering. However, the encoding-task coupling requirement results in the repeated encoding of the same documents for different tasks and queries, which is highly computationally inefficient. To this end, we target to decouple document encoding from downstream tasks, and propose to represent each document as a plug-and-play document module, i.e., a document plugin, for PTMs (PlugD). By inserting document plugins into the backbone PTM for downstream tasks, we can encode a document one time to handle multiple tasks, which is more efficient than conventional encoding-task coupling methods that simultaneously encode documents and input queries using task-specific encoders. Extensive experiments on 8 datasets of 4 typical NLP tasks show that PlugD enables models to encode documents once and for all across different scenarios. Especially, PlugD can save 69% computational costs while achieving comparable performance to state-of-the-art encoding-task coupling methods. Additionally, we show that PlugD can serve as an effective post-processing way to inject knowledge into task-specific models, improving model performance without any additional model training.

AI Alignment is often presented as an interaction between a single designer and an artificial agent in which the designer attempts to ensure the agent's behavior is consistent with its purpose, and risks arise solely because of conflicts caused by inadvertent misalignment between the utility function intended by the designer and the resulting internal utility function of the agent. With the advent of agents instantiated with large-language models (LLMs), which are typically pre-trained, we argue this does not capture the essential aspects of AI safety because in the real world there is not a one-to-one correspondence between designer and agent, and the many agents, both artificial and human, have heterogeneous values. Therefore, there is an economic aspect to AI safety and the principal-agent problem is likely to arise. In a principal-agent problem conflict arises because of information asymmetry together with inherent misalignment between the utility of the agent and its principal, and this inherent misalignment cannot be overcome by coercing the agent into adopting a desired utility function through training. We argue the assumptions underlying principal-agent problems are crucial to capturing the essence of safety problems involving pre-trained AI models in real-world situations. Taking an empirical approach to AI safety, we investigate how GPT models respond in principal-agent conflicts. We find that agents based on both GPT-3.5 and GPT-4 override their principal's objectives in a simple online shopping task, showing clear evidence of principal-agent conflict. Surprisingly, the earlier GPT-3.5 model exhibits more nuanced behaviour in response to changes in information asymmetry, whereas the later GPT-4 model is more rigid in adhering to its prior alignment. Our results highlight the importance of incorporating principles from economics into the alignment process.

Window attention, position embeddings, and high resolution finetuning are core concepts in the modern transformer era of computer vision. However, we find that naively combining these near ubiquitous components can have a detrimental effect on performance. The issue is simple: interpolating position embeddings while using window attention is wrong. We study two state-of-the-art methods that have these three components, namely Hiera and ViTDet, and find that both do indeed suffer from this bug. To fix it, we introduce a simple absolute window position embedding strategy, which solves the bug outright in Hiera and allows us to increase both speed and performance of the model in ViTDet. We finally combine the two to obtain HieraDet, which achieves 61.7 box mAP on COCO, making it state-of-the-art for models that only use ImageNet-1k pretraining. This all stems from what is essentially a 3 line bug fix, which we name "absolute win".

The synthesis of synchronized audio-visual content is a key challenge in generative AI, with open-source models facing challenges in robust audio-video alignment. Our analysis reveals that this issue is rooted in three fundamental challenges of the joint diffusion process: (1) Correspondence Drift, where concurrently evolving noisy latents impede stable learning of alignment; (2) inefficient global attention mechanisms that fail to capture fine-grained temporal cues; and (3) the intra-modal bias of conventional Classifier-Free Guidance (CFG), which enhances conditionality but not cross-modal synchronization. To overcome these challenges, we introduce Harmony, a novel framework that mechanistically enforces audio-visual synchronization. We first propose a Cross-Task Synergy training paradigm to mitigate drift by leveraging strong supervisory signals from audio-driven video and video-driven audio generation tasks. Then, we design a Global-Local Decoupled Interaction Module for efficient and precise temporal-style alignment. Finally, we present a novel Synchronization-Enhanced CFG (SyncCFG) that explicitly isolates and amplifies the alignment signal during inference. Extensive experiments demonstrate that Harmony establishes a new state-of-the-art, significantly outperforming existing methods in both generation fidelity and, critically, in achieving fine-grained audio-visual synchronization.

We prove under practical assumptions that Rotary Positional Embedding (RoPE) introduces an intrinsic distance-dependent bias in attention scores that limits RoPE's ability to model long-context. RoPE extension methods may alleviate this issue, but they typically require post-hoc adjustments after pretraining, such as rescaling or hyperparameters retuning. This paper introduces Token-Aware Phase Attention (TAPA), a new positional encoding method that incorporates a learnable phase function into the attention mechanism. TAPA preserves token interactions over long range, extends to longer contexts with direct and light fine-tuning, extrapolates to unseen lengths, and attains significantly lower perplexity on long-context than RoPE families.

Rotary Positional Encoding (RoPE) is widely used in modern large language models. However, when sequences are extended beyond the range seen during training, rotary phases can enter out-of-distribution regimes, leading to spurious long-range alignments, diffuse attention, and degraded retrieval. Existing remedies only partially address these failures, as they often trade local positional resolution for long-context stability. We propose GAPE (Gated Adaptive Positional Encoding), a drop-in augmentation for positional encodings that introduces a content-aware bias directly into the attention logits while preserving the rotary geometry. GAPE decouples distance-based suppression from token importance through a query-dependent gate that contracts irrelevant context and a key-dependent gate that preserves salient distant tokens. We prove that protected tokens remain accessible, while the attention mass assigned to unprotected distant tokens decays as a function of the query gate. We further show that GAPE can be implemented within standard scaled dot-product attention. We validate these properties empirically, finding that GAPE consistently yields sharper attention and improved long-context robustness over rotary baselines across both synthetic retrieval and long-context benchmarks.

We study zero-shot 3D alignment of two given meshes, using a text prompt describing their spatial relation -- an essential capability for content creation and scene assembly. Earlier approaches primarily rely on geometric alignment procedures, while recent work leverages pretrained 2D diffusion models to model language-conditioned object-object spatial relationships. In contrast, we directly optimize the relative pose at test time, updating translation, rotation, and isotropic scale with CLIP-driven gradients via a differentiable renderer, without training a new model. Our framework augments language supervision with geometry-aware objectives: a variant of soft-Iterative Closest Point (ICP) term to encourage surface attachment and a penetration loss to discourage interpenetration. A phased schedule strengthens contact constraints over time, and camera control concentrates the optimization on the interaction region. To enable evaluation, we curate a benchmark containing diverse categories and relations, and compare against baselines. Our method outperforms all alternatives, yielding semantically faithful and physically plausible alignments.

Scaling laws predict loss from compute but not how capabilities interact. We measure the coupling between reasoning and truthfulness across 63 base models from 16 families and find a regime change invisible to loss curves: below a family-dependent critical scale N_c, capabilities anticorrelate; above it, they cooperate. N_c approx 3.5B parameters [2.9B, 13.4B] (bootstrap 95% CI), but model size is not the only variable that determines phase. Architecture, data curation, and training recipe each shift N_c independently: curated training eliminated the coupling dip between Qwen generations (0.025 to 0.830 at matched scale), Gemma-4 at 4B achieves coupling 0.871, characteristic of 13B+ standard-trained models, through distillation and architectural innovation, and Phi at 1B matches web-trained coupling at 10B through data curation alone. Width normalization eliminates the anticorrelation across all tested families, supporting an output-projection bottleneck. Internally, 38 of 40 models show zero competing attention heads. A sparse-regression ODE cross-predicts held-out Llama-2 at 5.6% error. The diagnostic requires no model internals -- only public benchmark scores across a model family. The cooperative regime extends to the frontier (r = +0.72, 34 models, 10 labs). Code, data, and an open-source activation-steering tool for any open-weight model are released alongside an interactive dashboard that diagnoses any model's coupling phase, suggests concrete interventions (data curation, width, benchmark rotation), and provides ODE scaling predictions, frontier diagnostics, and eigenstructure analysis: https://zehenlabs.com/cape/.

Pixel-space diffusion models bypass the reconstruction bottleneck of Variational Autoencoders (VAEs) but face a fundamental "granularity dilemma": capturing global semantics favors large patch scales, while generating high-fidelity details demands fine-grained inputs. To address this issue, we propose HyperDiT, a unified framework establishing Hyper-Connected Cross-Scale Interactions to bridge the semantic and pixel manifold. Diverging from injecting semantics by AdaLN, HyperDiT utilizes Cross-Attention mechanisms, enabling fine-grained tokens to query multi-level semantic anchors globally. To resolve the spatial mismatch during multi-scale interactions, we introduce Scale-Aware Rotary Position Embedding (SA-RoPE) to ensure precise geometric alignment among tokens of varying patch sizes. Furthermore, we incorporate Registers to learn the dense semantics from a pretrained Visual Foundation Model (VFM), effectively reducing generation hallucination and artifacts. Extensive experiments demonstrate that HyperDiT achieves state-of-the-art (SoTA) FID of 1.56 on ImageNet 256times256 directly within the pixel space. By combining the fine-grained stream with semantic guidance, HyperDiT offers a superior paradigm for high-fidelity pixel generation.

Position encoding (PE), an essential part of self-attention networks (SANs), is used to preserve the word order information for natural language processing tasks, generating fixed position indices for input sequences. However, in cross-lingual scenarios, e.g. machine translation, the PEs of source and target sentences are modeled independently. Due to word order divergences in different languages, modeling the cross-lingual positional relationships might help SANs tackle this problem. In this paper, we augment SANs with cross-lingual position representations to model the bilingually aware latent structure for the input sentence. Specifically, we utilize bracketing transduction grammar (BTG)-based reordering information to encourage SANs to learn bilingual diagonal alignments. Experimental results on WMT'14 EnglishRightarrowGerman, WAT'17 JapaneseRightarrowEnglish, and WMT'17 ChineseLeftrightarrowEnglish translation tasks demonstrate that our approach significantly and consistently improves translation quality over strong baselines. Extensive analyses confirm that the performance gains come from the cross-lingual information.

Linear position interpolation helps pre-trained models using rotary position embeddings (RoPE) to extrapolate to longer sequence lengths. We propose using linear position interpolation to extend the extrapolation range of models using Attention with Linear Biases (ALiBi). We find position interpolation significantly improves extrapolation capability on upstream language modelling and downstream summarization and retrieval tasks.

We present SPAD, a novel approach for creating consistent multi-view images from text prompts or single images. To enable multi-view generation, we repurpose a pretrained 2D diffusion model by extending its self-attention layers with cross-view interactions, and fine-tune it on a high quality subset of Objaverse. We find that a naive extension of the self-attention proposed in prior work (e.g. MVDream) leads to content copying between views. Therefore, we explicitly constrain the cross-view attention based on epipolar geometry. To further enhance 3D consistency, we utilize Plucker coordinates derived from camera rays and inject them as positional encoding. This enables SPAD to reason over spatial proximity in 3D well. In contrast to recent works that can only generate views at fixed azimuth and elevation, SPAD offers full camera control and achieves state-of-the-art results in novel view synthesis on unseen objects from the Objaverse and Google Scanned Objects datasets. Finally, we demonstrate that text-to-3D generation using SPAD prevents the multi-face Janus issue. See more details at our webpage: https://yashkant.github.io/spad

The Muon optimizer has rapidly emerged as a powerful, geometry-aware alternative to AdamW, demonstrating strong performance in large-scale training of neural networks. However, a critical theory-practice disconnect exists: Muon's efficiency relies on fast, approximate orthogonalization, yet all prior theoretical work analyzes an idealized, computationally intractable version assuming exact SVD-based updates. This work moves beyond the ideal by providing the first analysis of the inexact orthogonalized update at Muon's core. We develop our analysis within the general framework of Linear Minimization Oracle (LMO)-based optimization, introducing a realistic additive error model to capture the inexactness of practical approximation schemes. Our analysis yields explicit bounds that quantify performance degradation as a function of the LMO inexactness/error. We reveal a fundamental coupling between this inexactness and the optimal step size and momentum: lower oracle precision requires a smaller step size but larger momentum parameter. These findings elevate the approximation procedure (e.g., the number of Newton-Schulz steps) from an implementation detail to a critical parameter that must be co-tuned with the learning schedule. NanoGPT experiments directly confirm the predicted coupling, with optimal learning rates clearly shifting as approximation precision changes.

In most Vision-Language models (VL), the understanding of the image structure is enabled by injecting the position information (PI) about objects in the image. In our case study of LXMERT, a state-of-the-art VL model, we probe the use of the PI in the representation and study its effect on Visual Question Answering. We show that the model is not capable of leveraging the PI for the image-text matching task on a challenge set where only position differs. Yet, our experiments with probing confirm that the PI is indeed present in the representation. We introduce two strategies to tackle this: (i) Positional Information Pre-training and (ii) Contrastive Learning on PI using Cross-Modality Matching. Doing so, the model can correctly classify if images with detailed PI statements match. Additionally to the 2D information from bounding boxes, we introduce the object's depth as new feature for a better object localization in the space. Even though we were able to improve the model properties as defined by our probes, it only has a negligible effect on the downstream performance. Our results thus highlight an important issue of multimodal modeling: the mere presence of information detectable by a probing classifier is not a guarantee that the information is available in a cross-modal setup.

We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generative trajectories for N dimensional data by embedding paths in N{+}D dimensional space while still controlling the progression with a simple scalar norm of the D additional variables. The new models reduce to PFGM when D{=}1 and to diffusion models when D{to}infty. The flexibility of choosing D allows us to trade off robustness against rigidity as increasing D results in more concentrated coupling between the data and the additional variable norms. We dispense with the biased large batch field targets used in PFGM and instead provide an unbiased perturbation-based objective similar to diffusion models. To explore different choices of D, we provide a direct alignment method for transferring well-tuned hyperparameters from diffusion models (D{to} infty) to any finite D values. Our experiments show that models with finite D can be superior to previous state-of-the-art diffusion models on CIFAR-10/FFHQ 64{times}64 datasets, with FID scores of 1.91/2.43 when D{=}2048/128. In class-conditional setting, D{=}2048 yields current state-of-the-art FID of 1.74 on CIFAR-10. In addition, we demonstrate that models with smaller D exhibit improved robustness against modeling errors. Code is available at https://github.com/Newbeeer/pfgmpp

Text-conditioned human motion generation has experienced significant advancements with diffusion models trained on extensive motion capture data and corresponding textual annotations. However, extending such success to 3D dynamic human-object interaction (HOI) generation faces notable challenges, primarily due to the lack of large-scale interaction data and comprehensive descriptions that align with these interactions. This paper takes the initiative and showcases the potential of generating human-object interactions without direct training on text-interaction pair data. Our key insight in achieving this is that interaction semantics and dynamics can be decoupled. Being unable to learn interaction semantics through supervised training, we instead leverage pre-trained large models, synergizing knowledge from a large language model and a text-to-motion model. While such knowledge offers high-level control over interaction semantics, it cannot grasp the intricacies of low-level interaction dynamics. To overcome this issue, we further introduce a world model designed to comprehend simple physics, modeling how human actions influence object motion. By integrating these components, our novel framework, InterDreamer, is able to generate text-aligned 3D HOI sequences in a zero-shot manner. We apply InterDreamer to the BEHAVE and CHAIRS datasets, and our comprehensive experimental analysis demonstrates its capability to generate realistic and coherent interaction sequences that seamlessly align with the text directives.

The coupling of the angular jitter of the spacecraft and their sub-assemblies with the optical bench and the telescope into the interferometric length readout will be a major noise source in the LISA mission. We refer to this noise as tilt-to-length (TTL) coupling. It will be reduced directly by realignments, and the residual noise will then be subtracted in post-processing. The success of these mitigation strategies depends on an accurate computation of the TTL coupling coefficients. We present here a thorough analysis of the accuracy of the coefficient estimation under different jitter characteristics, angular readout noise levels, and gravitational wave sources. We analyze in which cases the estimates degrade using two estimators, the common least squares estimator and the instrumental variables estimator. Our investigations show that angular readout noise leads to a bias of the least squares estimator, depending on the TTL coupling coefficients, jitter and readout noise level, while the instrumental variable estimator is not biased. We present an equation that predicts the estimation bias of the least squares method due to angular readout noise.

The 3D Human Pose Estimation (3D HPE) task uses 2D images or videos to predict human joint coordinates in 3D space. Despite recent advancements in deep learning-based methods, they mostly ignore the capability of coupling accessible texts and naturally feasible knowledge of humans, missing out on valuable implicit supervision to guide the 3D HPE task. Moreover, previous efforts often study this task from the perspective of the whole human body, neglecting fine-grained guidance hidden in different body parts. To this end, we present a new Fine-Grained Prompt-Driven Denoiser based on a diffusion model for 3D HPE, named FinePOSE. It consists of three core blocks enhancing the reverse process of the diffusion model: (1) Fine-grained Part-aware Prompt learning (FPP) block constructs fine-grained part-aware prompts via coupling accessible texts and naturally feasible knowledge of body parts with learnable prompts to model implicit guidance. (2) Fine-grained Prompt-pose Communication (FPC) block establishes fine-grained communications between learned part-aware prompts and poses to improve the denoising quality. (3) Prompt-driven Timestamp Stylization (PTS) block integrates learned prompt embedding and temporal information related to the noise level to enable adaptive adjustment at each denoising step. Extensive experiments on public single-human pose estimation datasets show that FinePOSE outperforms state-of-the-art methods. We further extend FinePOSE to multi-human pose estimation. Achieving 34.3mm average MPJPE on the EgoHumans dataset demonstrates the potential of FinePOSE to deal with complex multi-human scenarios. Code is available at https://github.com/PKU-ICST-MIPL/FinePOSE_CVPR2024.