Automated agent workflows can enhance the problem-solving ability of large language models (LLMs), but common search strategies rely on stochastic exploration and often traverse implausible branches. This occurs because current pipelines sample candidate steps from generic prompts or learned policies with weak domain priors, yielding near-random walks over operators, units, and formats. To promote ordered exploration, this paper introduces SCULPT, a constraint-guided approach for Monte Carlo Tree Search (MCTS) that integrates domain-aware scoring into selection, expansion, simulation, and backpropagation. SCULPT scores and prunes actions using a combination of symbolic checks (dimensional consistency, type compatibility, magnitude sanity, depth control, and diversity) and structural pattern guidance, thereby steering the search toward plausible reasoning paths. Under matched LLM configurations, SCULPT yields stable improvements on multiple datasets; additional results with GPT-5.2 assess executor transferability and performance on frontier reasoning models. Overall, domain-aware constraints can improve accuracy while maintaining efficiency and reasoning stability.
Generalized Category Discovery (GCD) aims to classify instances from both known and novel categories within a large-scale unlabeled dataset, a critical yet challenging task for real-world, open-world applications. However, existing methods often rely on pseudo-labeling, or two-stage clustering, which lack a principled mechanism to explicitly disentangle essential, category-defining signals from instance-specific noise. In this paper, we address this fundamental limitation by re-framing GCD from an information-theoretic perspective, grounded in the Information Bottleneck (IB) principle. We introduce InfoSculpt, a novel framework that systematically sculpts the representation space by minimizing a dual Conditional Mutual Information (CMI) objective. InfoSculpt uniquely combines a Category-Level CMI on labeled data to learn compact and discriminative representations for known classes, and a complementary Instance-Level CMI on all data to distill invariant features by compressing augmentation-induced noise. These two objectives work synergistically at different scales to produce a disentangled and robust latent space where categorical information is preserved while noisy, instance-spec
Phase sensitive detection in spectral domain optical coherence tomography (SD-OCT) is a powerful method for functional imaging of biological events with high spatiotemporal resolution. The depth-dependent signal-to-noise ratio (SNR) is a limiting factor on the minimum detectable phase changes of phase in shot noise-limited SD-OCT systems. The SNR over a depth is constrained by the terminal optics, usually using a focusing lens to project light into the tissue and collect the backscattered light. In situ ultrasonically sculpted optical waveguides have been used to improve SNR roll-off over depth compared to conventional SD-OCT systems. In this paper, we extend this feature to demonstrate phase sensitive detection at depth using ultrasonically enhanced OCT (ue-OCT). Our experimental results show that ultrasonically sculpted optical waveguides are phase stable and follow near shot-noise limited behavior. We measured milk flow velocity changes to demonstrate a phase sensitivity of 5.25 mrad at 10 dB SNR and dynamic range of 0.8 mm/s to 14.7 cm/s using ue-OCT. Our results show flow detection with ue-OCT at extended depths (i.e., 3.5 mm) otherwise not possible with conventional SD-OCT sy
Recent advances in implicit neural representations have made them a popular choice for modeling 3D geometry, achieving impressive results in tasks such as shape representation, reconstruction, and learning priors. However, directly editing these representations poses challenges due to the complex relationship between model weights and surface regions they influence. Among such editing tools, sculpting, which allows users to interactively carve or extrude the surface, is a valuable editing operation to the graphics and modeling community. While traditional mesh-based tools like ZBrush facilitate fast and intuitive edits, a comparable toolkit for sculpting neural SDFs is currently lacking. We introduce a framework that enables interactive surface sculpting edits directly on neural implicit representations. Unlike previous works limited to spot edits, our approach allows users to perform stroke-based modifications on the fly, ensuring intuitive shape manipulation without switching representations. By employing tubular neighborhoods to sample strokes and custom brush profiles, we achieve smooth deformations along user-defined curves, providing precise control over the sculpting process
The sample of host stars with multiple transiting planets has illuminated the orbital architectures of exoplanetary systems. These architectures may be shaped mostly by formation conditions, be continually sculpted by ongoing dynamical processes, or both. As more studies place planet occurrence within a galactic context, evidence has emerged for variable planet multiplicity over time. In this manuscript, we investigate the use of transit multiplicity as a tool to constrain longer-timescale (>1 Gyr) dynamical sculpting. First, with a suite of injection-and-recovery tests, we quantify sensitivity to sculpting laws across different regimes. We employ a forward modeling framework in which we generate synthetic planetary systems, according to a prescribed sculpting speed and timescale, around the FGK dwarfs studied by the Kepler Mission. Some sculpting scenarios are hypothetically detectable in the Kepler sample, while others can be disfavored from Kepler transit statistics alone. Secondly, we apply our analysis to reverse-engineer the sculpting laws consistent with the true yield from Kepler. We confirm the present-day fraction of host stars containing dynamically cool "systems with
The Martian brain terrain (MBT), characterized by its unique brain-like morphology, is a potential geological archive for finding hints of paleoclimatic conditions during its formation period. The morphological similarity of MBT to self-organized patterned ground on Earth suggests a shared formation mechanism. However, the lack of quantitative descriptions and robust physical modeling of self-organized stone transport jointly limits the study of the thermal and aqueous conditions governing MBT's formation. Here we established a specialized quantitative system for extracting the morphological features of MBT, taking a typical region located in the northern Arabia Terra as an example, and then employed a numerical model to investigate its formation mechanisms. Our simulation results accurately replicate the observed morphology of MBT, matching its key geometric metrics with deviations <15%. Crucially, however, we find that the self-organized transport can solely produce relief <0.5 m, insufficient to explain the formation of MBT with average relief of 3.29 \pm 0.65 m. We attribute this discrepancy to sculpting driven by late-stage sublimation, constraining cumulative subsurface
Achieving atomic precision in top-down manufacturing remains a fundamental challenge nanofabrication technology. Here, the focused electron beam of a scanning transmission electron microscope is used to demonstrate atomically precise sculpting of hexagonal boron nitride (h-BN) bilayers, achieving nanoribbons as narrow as 6 Å with atomically smooth edges. The key to this precision lies in understanding how the underlying atomic structure, particularly in twisted bilayer systems, influences the milling process. High-angle annular dark-field imaging combined with multislice simulations reveals distinct intensity signatures that allow identification of different stacking arrangements within moiré patterns. Mathematical analysis of moiré lattices provides a predictive framework for determining optimal cutting directions, with cuts along armchair directions yielding superior edge quality compared to zigzag orientations. Surprisingly, a sequential milling approach, where a small electron beam subscan area is translated during the process, produces significantly better results than parallel milling of the entire target region. To understand these differences we implemented a stochastic mil
Professional 3D asset creation often requires diverse sculpting brushes to add surface details and geometric structures. Despite recent progress in 3D generation, producing reusable sculpting brushes compatible with artists' workflows remains an open and challenging problem. These sculpting brushes are typically represented as vector displacement maps (VDMs), which existing models cannot easily generate compared to natural images. This paper presents Text2VDM, a novel framework for text-to-VDM brush generation through the deformation of a dense planar mesh guided by score distillation sampling (SDS). The original SDS loss is designed for generating full objects and struggles with generating desirable sub-object structures from scratch in brush generation. We refer to this issue as semantic coupling, which we address by introducing weighted blending of prompt tokens to SDS, resulting in a more accurate target distribution and semantic guidance. Experiments demonstrate that Text2VDM can generate diverse, high-quality VDM brushes for sculpting surface details and geometric structures. Our generated brushes can be seamlessly integrated into mainstream modeling software, enabling variou
We present SCULPT (Supervised Clustering and Uncovering Latent Patterns with Training), a comprehensive software platform for analyzing tabulated high-dimensional multi-particle coincidence data from Cold Target Recoil Ion Momentum Spectroscopy (COLTRIMS) experiments. The software addresses critical challenges in modern momentum spectroscopy by integrating advanced machine learning techniques with physics-informed analysis in an interactive web-based environment. SCULPT implements Uniform Manifold Approximation and Projection (UMAP) for non-linear dimensionality reduction to reveal correlations in highly dimensional data. We also discuss potential extensions to deep autoencoders for feature learning, and genetic programming for automated discovery of physically meaningful observables. A novel adaptive confidence scoring system provides quantitative reliability assessments by evaluating user-selected clustering quality metrics with predefined weights that reflect each metric's robustness. The platform features configurable molecular profiles for different experimental systems, interactive visualization with selection tools, and comprehensive data filtering capabilities. Utilizing a
Prompt optimization is essential for effective utilization of large language models (LLMs) across diverse tasks. While existing optimization methods are effective in optimizing short prompts, they struggle with longer, more complex ones, often risking information loss and being sensitive to small perturbations. To address these challenges, we propose SCULPT (Systematic Tuning of Long Prompts), a framework that treats prompt optimization as a hierarchical tree refinement problem. SCULPT represents prompts as tree structures, enabling targeted modifications while preserving contextual integrity. It employs a Critic-Actor framework that generates reflections and applies actions to refine the prompt. Evaluations demonstrate SCULPT's effectiveness on long prompts, its robustness to adversarial perturbations, and its ability to generate high-performing prompts even without any initial human-written prompt. Compared to existing state of the art methods, SCULPT consistently improves LLM performance by preserving essential task information while applying structured refinements. Both qualitative and quantitative analyses show that SCULPT produces more stable and interpretable prompt modifica
Pretrained vision-language models (VLMs), such as CLIP, have shown remarkable potential in few-shot image classification and led to numerous effective transfer learning strategies. These methods leverage the pretrained knowledge of VLMs to enable effective domain adaptation while mitigating overfitting through parameter-efficient tuning or instance-based consistency constraints. However, such regularizations often neglect the geometric structure of data distribution, which may lead to distortion of the overall semantic representation. To overcome this limitation, we propose a novel fine-tuning method, Manifold-Preserving and Sculpting Tuning (MPS-Tuning). Regarding the data distribution in feature space as a semantic manifold, MPS-Tuning explicitly constrains the intrinsic geometry of this manifold while further sculpting it to enhance class separability. Specifically, MPS-Tuning preserves both macroscopic and microscopic topological structures of the original manifold by aligning Gram matrices of features before and after fine-tuning. Theoretically, this constraint is shown to approximate an upper bound of the Gromov-Wasserstein distance. Furthermore, features from the image and t
Learning disentangled representations, where distinct factors of variation are captured by independent latent variables, is a central goal in machine learning. The dominant approach has been the Variational Autoencoder (VAE) framework, which uses a Kullback-Leibler (KL) divergence penalty to encourage the latent space to match a factorized Gaussian prior. In this work, however, we provide direct evidence that this KL-based regularizer is an unreliable mechanism, consistently failing to enforce the target distribution on the aggregate posterior. We validate this and quantify the resulting entanglement using our novel, unsupervised Latent Predictability Score (LPS). To address this failure, we introduce the Programmable Prior Framework, a method built on the Maximum Mean Discrepancy (MMD). Our framework allows practitioners to explicitly sculpt the latent space, achieving state-of-the-art mutual independence on complex datasets like CIFAR-10 and Tiny ImageNet without the common reconstruction trade-off. Furthermore, we demonstrate how this programmability can be used to engineer sophisticated priors that improve alignment with semantically meaningful features. Ultimately, our work pr
Manipulating deformable objects remains a challenge within robotics due to the difficulties of state estimation, long-horizon planning, and predicting how the object will deform given an interaction. These challenges are the most pronounced with 3D deformable objects. We propose SculptDiff, a goal-conditioned diffusion-based imitation learning framework that works with point cloud state observations to directly learn clay sculpting policies for a variety of target shapes. To the best of our knowledge this is the first real-world method that successfully learns manipulation policies for 3D deformable objects. For sculpting videos and access to our dataset and hardware CAD models, see the project website: https://sites.google.com/andrew.cmu.edu/imitation-sculpting/home
Transformers empirically perform precise probabilistic reasoning in carefully constructed ``Bayesian wind tunnels'' and in large-scale language models, yet the mechanisms by which gradient-based learning creates the required internal geometry remain opaque. We provide a complete first-order analysis of how cross-entropy training reshapes attention scores and value vectors in a transformer attention head. Our core result is an \emph{advantage-based routing law} for attention scores, \[ \frac{\partial L}{\partial s_{ij}} = α_{ij}\bigl(b_{ij}-\mathbb{E}_{α_i}[b]\bigr), \qquad b_{ij} := u_i^\top v_j, \] coupled with a \emph{responsibility-weighted update} for values, \[ Δv_j = -η\sum_i α_{ij} u_i, \] where $u_i$ is the upstream gradient at position $i$ and $α_{ij}$ are attention weights. These equations induce a positive feedback loop in which routing and content specialize together: queries route more strongly to values that are above-average for their error signal, and those values are pulled toward the queries that use them. We show that this coupled specialization behaves like a two-timescale EM procedure: attention weights implement an E-step (soft responsibilities), while values
We present Image Sculpting, a new framework for editing 2D images by incorporating tools from 3D geometry and graphics. This approach differs markedly from existing methods, which are confined to 2D spaces and typically rely on textual instructions, leading to ambiguity and limited control. Image Sculpting converts 2D objects into 3D, enabling direct interaction with their 3D geometry. Post-editing, these objects are re-rendered into 2D, merging into the original image to produce high-fidelity results through a coarse-to-fine enhancement process. The framework supports precise, quantifiable, and physically-plausible editing options such as pose editing, rotation, translation, 3D composition, carving, and serial addition. It marks an initial step towards combining the creative freedom of generative models with the precision of graphics pipelines.
The ability to sculpt light in space, time, and polarization has revolutionized studies of light-matter interaction and enabled breakthroughs in optical communication, imaging, and ultrafast science. Among the many degrees of freedom of light, orbital angular momentum (OAM) further expands these capabilities by unlocking new regimes of control in information encoding, particle trapping and manipulation, and symmetry-driven selection rules. However, exploiting OAM to drive nonlinear, non-perturbative effects in solids remains challenging, especially in the mid-infrared (MIR) spectral regime-a key region for accessing these effects in ambient air, where spatial light modulators do not operate. Here, we circumvent this limitation by generating femtosecond, few-cycle MIR Bessel-Gauss vortex (BGV) and perfect optical vortices (POVs), using a robust, static spatial-shaping strategy. By utilizing these beams to drive nonlinear optical processes such as second-harmonic generation (SHG) and high-harmonic generation (HHG) in various solid-state materials, we show that the resulting harmonic beams faithfully inherit the structural characteristics of the drivers: the constant-intensity ring of
While recent works have achieved great success on image-to-3D object generation, high quality and fidelity 3D head generation from a single image remains a great challenge. Previous text-based methods for generating 3D heads were limited by text descriptions and image-based methods struggled to produce high-quality head geometry. To handle this challenging problem, we propose a novel framework, ID-Sculpt, to generate high-quality 3D heads while preserving their identities. Our work incorporates the identity information of the portrait image into three parts: 1) geometry initialization, 2) geometry sculpting, and 3) texture generation stages. Given a reference portrait image, we first align the identity features with text features to realize ID-aware guidance enhancement, which contains the control signals representing the face information. We then use the canny map, ID features of the portrait image, and a pre-trained text-to-normal/depth diffusion model to generate ID-aware geometry supervision, and 3D-GAN inversion is employed to generate ID-aware geometry initialization. Furthermore, with the ability to inject identity information into 3D head generation, we use ID-aware guidanc
Compact systems of multiple close-in super-Earths/sub-Neptunes ("compact multis") are a ubiquitous outcome of planet formation. It was recently discovered that the outer edges of compact multis are located at smaller orbital periods than expected from geometric and detection biases alone, suggesting some truncation or transition in the outer architectures. Here we test whether this "edge-of-the-multis" might be explained in any part by distant giant planets in the outer regions ($\gtrsim 1$ AU) of the systems. We investigate the dynamical stability of observed compact multis in the presence of hypothetical giant ($\gtrsim 0.5 \ M_{\mathrm{Jup}}$) perturbing planets. We identify what parameters would be required for hypothetical perturbing planets if they were responsible for dynamically sculpting the outer edges of compact multis. "Edge-sculpting" perturbers are generally in the range $P\sim100-500$ days for the average compact multi, with most between $P\sim200-300$ days. Given the relatively close separation, we explore the detectability of the hypothetical edge-sculpting perturbing planets, finding that they would be readily detectable in transit and radial velocity data. We com
Significant efforts have been devoted to manipulating topological states, which often manifest as localized modes at interfaces between distinct topological phases. In this work, we demonstrate a versatile approach to sculpting topological modes (TMs) into any desired shapes by incorporating various artificial gauge fields (AGFs), including scalar, vector, and imaginary gauge potentials, and leveraging the power of artificial neural networks (ANNs). These AGFs enable precise tuning of the dissipation of the TMs across that of bulk modes, facilitating a transition from localized to fully delocalized states. Moreover, ANNs allow precise engineering of these eigenmodes to achieve tailored profiles of topological states, which remain spectrally isolated within the bandgap and exhibit minimal loss compared to other modes. Our theoretical results are experimentally validated on silicon photonic platforms, demonstrating flexible manipulation of TM profiles. This approach enables the design of topological states with customized properties, offering significant potential for diverse applications in photonics and beyond.
Despite their growing popularity, swarms of robots remain limited by the operating time of each individual. We present algorithms which allow a human to sculpt a swarm of robots into a shape that persists in space perpetually, independent of onboard energy constraints such as batteries. Robots generate a path through a shape such that robots cycle in and out of the shape. Robots inside the shape react to human initiated changes and adapt the path through the shape accordingly. Robots outside the shape recharge and return to the shape so that the shape can persist indefinitely. The presented algorithms communicate shape changes throughout the swarm using message passing and robot motion. These algorithms enable the swarm to persist through any arbitrary changes to the shape. We describe these algorithms in detail and present their performance in simulation and on a swarm of mobile robots. The result is a swarm behavior more suitable for extended duration, dynamic shape-based tasks in applications such as agriculture and emergency response.