We introduce a doubly hierarchical generative representation for strand-based 3D hairstyle geometry that progresses from coarse, low-pass filtered guide hair to densely populated hair strands rich in high-frequency details. We employ the Discrete Cosine Transform (DCT) to separate low-frequency structural curves from high-frequency curliness and noise, avoiding the Gibbs' oscillation issues associated with the standard Fourier transform in open curves. Unlike the guide hair sampled from the scalp UV map grids which may lose capturing details of the hairstyle in existing methods, our method samples optimal sparse guide strands by utilising $k$-medoids clustering centres from low-pass filtered dense strands, which more accurately retain the hairstyle's inherent characteristics. The proposed variational autoencoder-based generation network, with an architecture inspired by geometric deep learning and implicit neural representations, facilitates flexible, off-the-grid guide strand modelling and enables the completion of dense strands in any quantity and density, drawing on principles from implicit neural representations. Empirical evaluations confirm the capacity of the model to generate convincing guide hair and dense strands, complete with nuanced high-frequency details.

Our paper addresses the complex task of transferring a hairstyle from a reference image to an input photo for virtual hair try-on. This task is challenging due to the need to adapt to various photo poses, the sensitivity of hairstyles, and the lack of objective metrics. The current state of the art hairstyle transfer methods use an optimization process for different parts of the approach, making them inexcusably slow. At the same time, faster encoder-based models are of very low quality because they either operate in StyleGAN's W+ space or use other low-dimensional image generators. Additionally, both approaches have a problem with hairstyle transfer when the source pose is very different from the target pose, because they either don't consider the pose at all or deal with it inefficiently. In our paper, we present the HairFast model, which uniquely solves these problems and achieves high resolution, near real-time performance, and superior reconstruction compared to optimization problem-based methods. Our solution includes a new architecture operating in the FS latent space of StyleGAN, an enhanced inpainting approach, and improved encoders for better alignment, color transfer, and a new encoder for post-processing. The effectiveness of our approach is demonstrated on realism metrics after random hairstyle transfer and reconstruction when the original hairstyle is transferred. In the most difficult scenario of transferring both shape and color of a hairstyle from different images, our method performs in less than a second on the Nvidia V100.

We employ the Discrete Cosine Transform (DCT) to separate low-frequency structural curves from high-frequency curliness and noise, avoiding the Gibbs' oscillation issues associated with the standard Fourier transform in open curves.

This task is challenging due to the need to adapt to various photo poses, the sensitivity of hairstyles, and the lack of objective metrics. The current state of the art hairstyle transfer methods use an optimization process for different parts of the approach, making them inexcusably slow. At the same time, faster encoder-based models are of very low quality because they either operate in StyleGAN's W+ space or use other

StyleGAN to address this task.

This task is challenging due to the need to adapt to various photo poses, the sensitivity of hairstyles, and the lack of objective metrics. The current state of the art hairstyle transfer methods use an optimization process for different parts of the approach, making them inexcusably slow. At the same time, faster encoder-based models are of very low quality because they either operate in StyleGAN's W+ space or use other

StyleGAN to address this task.

Abstract-- Hair care is an essential daily activity, yet it remains inaccessible to individuals with limited mobility and challenging for autonomous robot systems due to the fine-grained physical structure and complex dynamics of hair . We introduce a novel dynamics learning paradigm that is suited for volumetric quantities such as hair, relying on an action-conditioned latent state editing mechanism, coupled with a compact 3D latent space of diverse hairstyles to improve generalizability. This latent space is pre-trained at scale using a novel hair physics simulator, enabling generalization across previously unseen hairstyles. Experiments in simulation demonstrate that DYMO-Hair's dynamics model outperforms baselines on capturing local deformation for diverse, unseen hairstyles. DYMO-Hair further outperforms baselines in closed-loop hair styling tasks on unseen hairstyles, with an average of 22% lower final geometric error and 42% higher success rate than the state-of-the-art system. Real-world experiments exhibit zero-shot transferability of our system to wigs, achieving consistent success on challenging unseen hairstyles where the state-of-the-art system fails. T ogether, these results introduce a foundation for model-based robot hair care, advancing toward more generalizable, flexible, and accessible robot hair styling in unconstrained physical environments. Hair is central to personal identity and self-esteem [1], [2], yet routine care is difficult for individuals with limited mobility due to reduced coordination, strength, and flexibility [3]. To improve accessibility and autonomy, robot hair care systems have been explored [4]-[7], but existing approaches rely on either handcrafted trajectories or rule-based controllers, restricting generalization across diverse hairstyles and goals. To address these limitations, we propose DYMO-Hair, a model-based robot hair care system. Our system is capable of generalizable and flexible visual goal-conditioned hair manipulation, across diverse hairstyles and objectives in unconstrained physical environments. Chengyang Zhao, Uksang Y oo, Jonathan Francis (by courtesy), Jeffrey Ichnowski, and Jean Oh are with Robotics Institute, Carnegie Mellon University, Pittsburgh, Pennsylvania, USA. Arkadeep Narayan Chaudhury is with Epic Games, Inc., Pittsburgh, Pennsylvania, USA. Giljoo Nam is with Meta Codec Avatars Lab, Pittsburgh, Pennsylvania, USA. Jonathan Francis is with Bosch Center for Artificial Intelligence, Pittsburgh, Pennsylvania, USA. Figure 1. We introduce DYMO-Hair, a unified, model-based robot hair care system.

Recent LLMs like DeepSeek-R1 have demonstrated state-of-the-art performance by integrating deep thinking and complex reasoning during generation. However, the internal mechanisms behind these reasoning processes remain unexplored. We observe reasoning LLMs consistently use vocabulary associated with human reasoning processes. We hypothesize these words correspond to specific reasoning moments within the models' internal mechanisms. To test this hypothesis, we employ Sparse Autoencoders (SAEs), a technique for sparse decomposition of neural network activations into human-interpretable features. We introduce ReasonScore, an automatic metric to identify active SAE features during these reasoning moments. We perform manual and automatic interpretation of the features detected by our metric, and find those with activation patterns matching uncertainty, exploratory thinking, and reflection. Through steering experiments, we demonstrate that amplifying these features increases performance on reasoning-intensive benchmarks (+2.2%) while producing longer reasoning traces (+20.5%). Using the model diffing technique, we provide evidence that these features are present only in models with reasoning capabilities. Our work provides the first step towards a mechanistic understanding of reasoning in LLMs. Code available at https://github.com/AIRI-Institute/SAE-Reasoning