arXiv subjects

Taeyoung Kim

Publications and source records attributed to Taeyoung Kim.

At least 19 recordsLinked to original sources

arXiv2026

Why Rectified Power Unit Networks Fail and How to Improve It: An Effective Field Theory Perspective

The Rectified Power Unit (RePU) activation function, a differentiable generalization of the Rectified Linear Unit (ReLU), has shown promise in constructing neural networks due to its smoothness properties. However, deep RePU networks often suffer from critical issues such as vanishing or exploding values during training, rendering them unstable regardless of hyperparameter initialization. Leveraging the perspective of effective field theory, we identify the root causes of these failures and propose the Modified Rectified Power Unit (MRePU) activation function. MRePU addresses RePU's limitations while preserving its advantages, such as differentiability and universal approximation properties. Theoretical analysis demonstrates that MRePU satisfies the criticality conditions in the limit of a small kernel, and a finite-kernel analysis yields an initialization rule for deep MRePU networks. Experiments on polynomial regression, physics-informed neural networks (PINNs) and real-world vision tasks show that MRePU networks initialized by this rule remain trainable at depths at which RePU networks fail, while their accuracy relative to standard activations depends on the task.

cs.LG↗

arXiv2026

Human-to-Robot Transfer via Bridging Representation and Action Space in VLAs

Pretrained Vision-Language-Action (VLA) policies provide a strong starting point for deployment, but adapting them to a target robot and environment still requires costly embodiment-specific demonstrations. Human demonstrations are far easier to collect, yet directly leveraging them is challenging due to the substantial human-robot embodiment gap, particularly when the underlying VLA has been pretrained primarily on robot data. We introduce H2RB (Human-To-Robot Bridge), a human-robot co-training framework for adapting pretrained VLA policies from unpaired human and robot demonstrations. H2RB bridges the embodiment gap at both interfaces: geometry-anchored alignment grounds human and robot observations in a compatible representation, while a decoupled-decoder tokenizer shares action latents without forcing both domains through a single action mapping. This design allows human demonstrations to provide useful behavioral supervision while retaining the rich visual, semantic, and control priors of the pretrained VLA. Across real-world tasks, H2RB substantially improves object transfer performance from 8.0 to 51.8 and enables skill transfer to score 62.7, in settings where co-train baselines totally fail to transfer human-demonstrated skills. The benefit also persists under object-placement shifts, improving out-of-distribution transfer from 6.0 to 45.3. H2RB suggests a way for human demonstrations to serve as a scalable supervision source for adapting pretrained robotic policies, reducing the dependence on costly target-robot data collection.

cs.AI↗

arXiv2026

Adapting Video Models for Robot Control via Motion-guided Asymmetric Prediction

World Action Models (WAMs) leverage pretrained video generative models for robotic control by jointly predicting future visual observations and actions. The visual prediction objective plays a key role in adapting pretrained video representations to the target robot domain. Yet standard visual prediction inherited from video pretraining treats all visual regions uniformly, despite their differing relevance to robotic control. We therefore investigate the spatial allocation of visual supervision in WAMs and show that focusing supervision on dynamic regions can substantially improve policy performance. Building on this finding, we introduce Motion-Guided Asymmetric Prediction (MoGAP), which augments WAM training with motion-focused visual prediction. MoGAP allocates noise asymmetrically across regions, training the model to reconstruct more heavily corrupted dynamic regions using less corrupted static regions as context. MoGAP is trained alongside standard video-action prediction through a training-only auxiliary prediction path within the shared video diffusion backbone. It uses motion cues derived directly from training videos, requiring neither an external teacher nor additional modalities. Across robot manipulation benchmarks and WAM architectures, MoGAP consistently improves policy performance, increasing success rates on the GR-1 tabletop benchmark from 38.8% to 47.5% for Fast-WAM (Wan2.2-5B) and from 52.3% to 62.3% for Cosmos3-Nano.

cs.CV↗

arXiv2026

Implicit Neural Representations for Variational Problems on Graphons

We propose a neural exploratory framework for variational problems over graphons, i.e., symmetric measurable functions $[0,1]^2 \to [0,1]$, that arise as limits of dense graph sequences. Such problems are central to two parts of the mathematical literature: extremal graph theory, which studies graph parameter optimisation under given restrictions, often for those graphs with a large number of vertices, and the large deviation theory of dense random graphs, which characterises the structure of rare events through constrained graphon optimisation. We represent graphons by implicit neural networks and optimise graphon objectives by gradient descent. Our design combines three ingredients: a multi-scale sinusoidal residual architecture biased toward sharp, step-like graphons; an embedded solver that enforces a single empirical density constraint and is differentiated by implicit differentiation; and symmetry-aware Monte Carlo estimators. On generalised Turán problems that previously required substantial human effort, our framework rediscovers known optimal graphons without human intervention. Applied to open instances, it produces candidate optima, including a previously unreported family of extremal structures. Applied to the variational problems from the large deviation theory of Erdős--Rényi random graphs, the framework produces new candidate optimal graphons across both upper- and lower-tail regimes for multiple pattern graphs; for the case of the triangle graph and the upper-tail regime, these candidates improve upon the best-known reference construction of Lubetzky and Zhao. The structures found by our framework have also led to new theorems on the optimal graphons for both families of problems.

stat.ML↗

arXiv2026

PaceVLA: Adaptive Temporal Action Quantization in Vision-Language-Action Models

Fast and reliable manipulation is crucial for practical robot deployment. Although Vision-Language-Action (VLA) models have recently shown remarkable progress as generalist robot policies, their execution often remains temporally inefficient. A key source of this inefficiency is that policies learn fine-grained temporal patterns from teleoperated demonstrations, requiring many low-level action steps. Temporal action quantization offers a simple way to accelerate execution by aggregating consecutive low-level actions into temporally coarser actions. However, applying action quantization without considering when fine-grained control is required introduces a speed-accuracy trade-off: accelerated actions may efficiently reduce redundant steps in some phases, while discarding critical motion details in precision-sensitive interactions. To address this, we propose PaceVLA, a unified framework for adaptive temporal execution in VLAs that integrates two coupled components: (1) mode-specific action decoders built on a shared action expert, supporting multiple temporal granularities and prediction horizons, and (2) a quantizability-guided mode selection scheme which decides whether coarse execution is appropriate, and a context-conditioned router that selects an execution mode at each inference step. Experiments across three multi-task simulation benchmarks and six real-world tasks show that PaceVLA improves execution efficiency while maintaining task success rate across multiple embodiments, including long-horizon and dexterous manipulation.

cs.RO↗

arXiv2026

Goodman-type lower bounds for odd cycles I: The dense regime

Goodman proved a lower bound on triangle counts which, in graphon language, states that every graphon of edge density $p$ has triangle density at least $2p^2-p$. Bennett, Dudek, Lidický, and Pikhurko established the corresponding bound for $C_5$, determining its minimum density at every Turán density $p=1-1/k$ with an integer $k\ge3$. We extend this bound to every odd cycle in the dense regime: for every odd integer $m\ge3$ and every graphon $W$ with edge density $p\ge2/3$, $t(C_m, W) \ge p^m-p(1-p)^{m-1}.$ For $2/3\le p<1$, equality holds precisely for balanced complete $k$-partite graphons with an integer $k\ge3$, up to graphon equivalence, and we establish qualitative stability at these densities. In the same density range, we also strengthen Kim and Lee's density-sensitive commonality inequality for odd cycles by adding the nonnegative term $t(P_{m-1},1-W)-(1-p)^{m-1}$ to the lower bound, where $P_{m-1}$ is the path with $m-1$ edges. To prove the main results, we develop a spectral excursion expansion and use Dirichlet averaging to reduce the resulting polynomial inequalities in arbitrarily many spectral variables to a one-variable problem. We prove the one-variable inequality through a uniform inequality comparing odd and even moments of shifted Gamma random variables. We also formalise the odd-cycle lower-bound theorem in Lean 4.

math.CO↗

arXiv2026

Bipodal optimizers in the upper-tail variational problem for regular subgraph densities

Let $H$ be a fixed $d$-regular graph with $d\ge2$, and let $t(H,\cdot)$ denote its homomorphism density. We study the upper-tail event $t(H,G(n,p))\ge r^{|E(H)|}$ for fixed $0<p<r<1$ in a dense Erdős--Rényi random graph $G(n,p)$. Near the Lubetzky--Zhao replica-symmetric phase boundary and away from the exceptional target density $(d-1)/d$, we prove that the optimizer of the Chatterjee--Varadhan variational problem on the symmetry-breaking side is bipodal (two-block) and unique up to relabeling. Its block parameters depend analytically on $(p,r)$. To treat the exceptional boundary point, where the nonexceptional theory degenerates, we construct an analytic curve approaching that point from the symmetry-breaking side along which the unique optimizers are nonconstant rank-one bipodal graphons. In both settings, we derive asymptotic expansions of the edge-density deficit and the rate function that governs the exponential decay of the upper-tail probability. Moreover, the conditioned random graph converges in cut distance to the corresponding bipodal optimizer as $n\to\infty$. As $(p,r)$ approaches the phase boundary from the symmetry-breaking side, the optimizers converge to their constant limits through two distinct mechanisms. For each fixed nonexceptional target density, one block shrinks to zero measure, giving convergence in $L^1$ but not in $L^\infty$. Along the exceptional curve, both blocks remain macroscopic: their sizes tend to $1/2$ and all three block densities tend to $(d-1)/d$, yielding convergence in $L^\infty$.

math.PR↗

arXiv2026

Controllable Image Captioning with Prompt-Conditioned Scene Rewards

Large Vision-Language Models produce fluent image descriptions but offer limited semantic control: users cannot reliably specify whether captions should emphasize attributes, relations, or particular image regions. We present Fine-grained Captioning Control Using Scene Rewards (FoCUS), a controllable image captioning method that lets users steer captions toward specific semantic emphases through natural-language control prompts. The core idea is a prompt-conditioned control objective based on scene-graph-aligned component scores. Generated captions are parsed and aligned to scene-graph components such as objects, attributes, and relations. These components are differentially weighted, including negative weights, according to the requested emphasis. We optimize this objective with GRPO and further improve its reliability through a stricter object validity threshold and reasoning-based verification for attribute and relation scoring. To evaluate controllability, we introduce Semantic Control and Precision Evaluation (SCoPE), a benchmark with contrastive Include/Avoid constraints for measuring both target content coverage and out-of-scope suppression. Experiments on two VLM backbones show that FoCUS consistently improves controllability and fine-grained caption quality without degrading general caption performance.

cs.CV↗

arXiv2026

Loop Corrections in Random Feature Models: Training Error and Generalization Gap

We study fixed-design random feature ridge regression beyond the mean-kernel approximation. The expectation is taken over the frozen-feature ensemble, conditional on the training sample. Because the predictor is a nonlinear function of the empirical kernel, its mean training error, test error, and conditional generalization gap depend on centered kernel covariances as well as on mean kernel objects. We derive the covariance-level, or one-loop, corrections from a finite resolvent identity. This avoids an almost-sure Neumann-series assumption and yields an explicit remainder bound for the training error. The test correction additionally requires mixed train--test covariance tensors and therefore cannot, in general, be recovered from the train-restricted kernel law alone. Numerical experiments show that the covariance term removes the leading inverse-width discrepancy in a controlled regularization regime, while an ablation that discards the mixed train--test covariance fails for the test error even though the training correction is unchanged. They also identify a width--regularization boundary, measured by a resolvent-fluctuation diagnostic, beyond which the second-order truncation loses accuracy. All inverse-width statements are for fixed sample size, depth, design, and positive kernel-level regularization. The analysis concerns frozen features and does not model feature learning or neural-tangent-kernel evolution.

cs.LG↗

arXiv2026

A Robust In-Context Model for Conservation Laws: Injecting Context into Flux Neural Operators via Recurrent Vision Transformers

We propose an architecture that augments the Flux Neural Operator (Flux NO), which combines the classical finite volume method (FVM) with neural operators, with ViT-based context injection. Our model is formulated as a hypernetwork: it extracts solution dynamics over a finite temporal window, encodes them with a recurrent Vision Transformer, and generates the parameters of a context-conditioned neural operator. This enables the model to infer and solve conservation laws without explicit access to the governing equation or PDE coefficients. Experimentally, we show that the proposed method preserves the robustness, generalization ability, and long-time prediction advantages of Flux NO over standard neural operators, while delivering reliable numerical solutions across a broad range of conservative systems, including previously unseen fluxes. Our code is available at https://github.com/xx257xx/CONTEXT_FLUX_NO.

cs.LG↗

arXiv2026

Path Planning of Cleaning Robot with Reinforcement Learning

Recently, as the demand for cleaning robots has steadily increased, therefore household electricity consumption is also increasing. To solve this electricity consumption issue, the problem of efficient path planning for cleaning robot has become important and many studies have been conducted. However, most of them are about moving along a simple path segment, not about the whole path to clean all places. As the emerging deep learning technique, reinforcement learning (RL) has been adopted for cleaning robot. However, the models for RL operate only in a specific cleaning environment, not the various cleaning environment. The problem is that the models have to retrain whenever the cleaning environment changes. To solve this problem, the proximal policy optimization (PPO) algorithm is combined with an efficient path planning that operates in various cleaning environments, using transfer learning (TL), detection nearest cleaned tile, reward shaping, and making elite set methods. The proposed method is validated with an ablation study and comparison with conventional methods such as random and zigzag. The experimental results demonstrate that the proposed method achieves improved training performance and increased convergence speed over the original PPO. And it also demonstrates that this proposed method is better performance than conventional methods (random, zigzag).

cs.RO↗

arXiv2026

Grokking on the Weight-Decay Clock: A Rate Hierarchy from Softly Broken Symmetries

Delayed generalization, or grokking, remains poorly understood despite extensive empirical study. We identify an exactly solvable late-time relaxation mechanism for grokking in linear models trained with full-batch heavy-ball optimization and weight decay, together with a locally quadratic extension to nonlinear neural networks. Our analysis reveals a distinguished population-active component of the empirical null space, which we call the grokking subspace. Along this subspace, the training predictions remain unchanged, leaving weight decay as the sole restoring force and giving rise to a slow dissipative relaxation governed by an exact discrete-time and continuous-time law. We show that only this subspace contributes to the slow asymptotic decay of the population risk and derive explicit iteration-scale predictions for the grokking time, recovering the familiar $(1-β)/(ηλ)$ scaling in the weak-regularization regime. The theory further predicts distinct effects of optimizer choice, distinguishing coupled $L_2$ regularization from decoupled weight decay, and yields causal predictions for interventions that modify the grokking component. We verify all theoretical identities without fitted parameters in a synthetic model where every subspace and relaxation rate is computable in closed form. We further observe genuine delayed generalization in modular addition, where the measured delay follows the predicted scaling and the late-time relaxation agrees closely with the theoretical clock.

cs.AI↗

arXiv2026

Integrated Forward-Inverse Network for Lensless Image Reconstruction

Lensless imaging enables compact and versatile computational cameras by replacing bulky optics with thin coded elements. However, reconstruction from the resulting measurements is challenging: large-footprint point-spread functions (PSFs) produce highly multiplexed observations, making inversion severely ill-conditioned and sensitive to calibration errors and model mismatch. While deep learning approaches, including hybrid models that incorporate physics priors, have shown promise, explicitly maintaining data fidelity throughout the network hierarchy remains difficult. Here, we propose the Integrated Forward-Inverse Network (IFIN), a physics-guided architecture that interleaves differentiable forward projections with learnable inverse updates at every scale, enabling complementary cues to be exploited jointly in the measurement and image domains. This bidirectional coupling supports progressive, physics-consistent refinement and permits system-constrained PSF kernel adaptation under model uncertainty. On challenging lensless benchmarks, including a newly introduced dataset, IFIN achieves state-of-the-art reconstruction quality. We further observe competitive performance on Gaussian deblurring and simulated inline holography reconstruction, suggesting that the same interleaving principle can extend beyond lensless cameras.

cs.CV↗

arXiv2026

Contrastive Representation Regularization for Vision-Language-Action Models

Vision-Language-Action (VLA) models have shown strong capabilities in robot manipulation by leveraging rich representations from pre-trained Vision-Language Models (VLMs). However, their representations arguably remain suboptimal, lacking sensitivity to robotic signals such as control actions and proprioceptive information. To address the issue, we introduce Robot State-aware Contrastive Loss (RS-CL), a simple and effective representation regularization for VLA models, designed to bridge the gap between VLM representations and robotic signals. In particular, RS-CL aligns the representations more closely with the robot's proprioceptive states by using relative distances between the states as soft supervision. Complementing the original action prediction objective, RS-CL enhances control-relevant representation learning, while being lightweight and fully compatible with standard VLA training pipelines. Our empirical results demonstrate that RS-CL substantially improves the performance of state-of-the-art VLA models; it pushes the prior art to 69.7% achieving the state-of-the-art performance on the RoboCasa-Kitchen benchmark, and boosts success rates from 45.0% to 58.3% on challenging real-robot manipulation tasks.

cs.RO↗

arXiv2026

RLDX-1 Technical Report

While Vision-Language-Action models (VLAs) have shown remarkable progress toward human-like generalist robotic policies through the versatile intelligence (i.e. broad scene understanding and language-conditioned generalization) inherited from pre-trained Vision-Language Models, they still struggle with complex real-world tasks requiring broader functional capabilities (e.g. motion awareness, long-term memory, and physical sensing). To address this, we introduce RLDX-1, a general-purpose robotic policy for dexterous manipulation built on the Multi-Stream Action Transformer (MSAT), an architecture that unifies these capabilities by integrating heterogeneous modalities through modality-specific streams with cross-modal joint self-attention. RLDX-1 further combines this architecture with system-level design choices, including data synthesis for rare manipulation scenarios, learning procedures specialized for human-like manipulation, and inference optimizations for real-time deployment. Through empirical evaluation, we show that RLDX-1 consistently outperforms recent frontier VLAs (e.g. $π_{0.5}$ and GR00T N1.6) across both simulation benchmarks and real-world tasks that require broad functional capabilities beyond general versatility. In particular, RLDX-1 shows superiority in ALLEX humanoid tasks by achieving success rates of 86.8% while $π_{0.5}$ and GR00T N1.6 achieve around 40%, highlighting the ability of RLDX-1 to control a high-DoF humanoid robot under diverse functional demands. Together, these results position RLDX-1 as a promising step toward reliable VLAs for complex, contact-rich, and dynamic real-world dexterous manipulation.

cs.RO↗

arXiv2026

HAMLET: Switch your Vision-Language-Action Model into a History-Aware Policy

Inherently, robotic manipulation tasks are history-dependent: leveraging past context could be beneficial. However, most existing Vision-Language-Action models (VLAs) have been designed without considering this aspect, i.e., they rely solely on the current observation, ignoring preceding context. In this paper, we propose HAMLET, a scalable framework to adapt VLAs to attend to the historical context during action prediction. Specifically, we introduce moment tokens that compactly encode perceptual information at each timestep. Their representations are initialized with time-contrastive learning, allowing them to better capture temporally distinctive aspects. Next, we employ a lightweight memory module that integrates the moment tokens across past timesteps into memory features, which are then leveraged for action prediction. Through empirical evaluation, we show that HAMLET successfully transforms a state-of-the-art VLA into a history-aware policy, especially demonstrating significant improvements on long-horizon tasks that require historical context. In particular, on top of GR00T N1.5, HAMLET achieves an average success rate of 76.4% on history-dependent real-world tasks, surpassing the baseline performance by 47.2%. Furthermore, HAMLET pushes prior art performance from 64.1% to 66.4% on RoboCasa Kitchen (100-demo setup) and from 95.6% to 97.7% on LIBERO, highlighting its effectiveness even under generic robot-manipulation benchmarks.

cs.RO↗

arXiv2026

RoboAlign: Learning Test-Time Reasoning for Language-Action Alignment in Vision-Language-Action Models

Improving embodied reasoning in multimodal-large-language models (MLLMs) is essential for building vision-language-action models (VLAs) on top of them to readily translate multimodal understanding into low-level actions. Accordingly, recent work has explored enhancing embodied reasoning in MLLMs through supervision of vision-question-answering type. However, these approaches have been reported to result in unstable VLA performance, often yielding only marginal or even negative gains. In this paper, we propose a more systematic MLLM training framework RoboAlign that reliably improves VLA performance. Our key idea is to sample action tokens via zero-shot natural language reasoning and refines this reasoning using reinforcement learning (RL) to improve action accuracy. As a result, RoboAlign bridges the modality gap between language and low-level actions in MLLMs, and facilitate knowledge transfer from MLLM to VLA. To validate the effectiveness of RoboAlign, we train VLAs by adding a diffusion-based action head on top of an MLLM backbone and evaluate them on major robotics benchmarks. Remarkably, by performing RL-based alignment after SFT using less than 1\% of the data, RoboAlign achieves performance improvements of 17.5\%, 18.9\%, and 106.6\% over SFT baselines on LIBERO, CALVIN, and real-world environments, respectively.

cs.AI↗

arXiv2026

Analysis of Fourier Neural Operators via Effective Field Theory

Fourier Neural Operators (FNOs) have emerged as leading surrogates for solver operators for various functional problems, yet their stability, generalization and frequency behavior lack a principled explanation. We present a systematic effective field theory analysis of FNOs in an infinite-dimensional function space, deriving closed recursion relations for the layer kernel and four-point vertex and then examining three practically important settings-analytic activations, scale-invariant cases and architectures with residual connections. The theory shows that nonlinear activations inevitably couple frequency inputs to high frequency modes that are otherwise discarded by spectral truncation, and experiments confirm this frequency transfer. For wide networks, we derive explicit criticality conditions on the weight initialization ensemble that ensure small input perturbations maintain a uniform scale across depth, and we confirm experimentally that the theoretically predicted ratio of kernel perturbations matches the measurements. Taken together, our results quantify how nonlinearity enables neural operators to capture non-trivial features, supply criteria for hyperparameter selection via criticality analysis, and explain why scale-invariant activations and residual connections enhance feature learning in FNOs. Finally, we translate the criticality theory into a practical criterion-matched initialization (calibration) procedure; on a standard PDEBench Burgers benchmark, the calibrated FNO exhibits markedly more stable optimization, faster convergence, and improved test error relative to a vanilla FNO.

cs.LG↗