Folding

All-atom structure predictors model diverse molecular interactions, but using their learned structural priors for binder design remains challenging. Here we present TorchCraft, a unified binder-design framework that optimizes sequence logits through a frozen all-atom predictor. Implemented in TorchFold, TorchCraft combines confidence, contact, geometric, and sequence-prior objectives within a shared optimization procedure for minibinders, framework-conditioned VHHs, cyclic peptides, and ligand-binding proteins. Using pretrained AlphaFold 3 weights, TorchCraft generated representative minibinders and VHHs with experimentally measured binding across four targets in each format, without post hoc sequence redesign. Computational benchmarks further demonstrated the framework's applicability to cyclic peptides and ligand-conditioned pocket design. TorchCraft extends predictor inversion to multiple binder formats and molecular contexts, providing a common framework for reusing all-atom structural priors in design.

This paper presents a low-clearance hinge joint mechanism based on the 3D printing on sheet fabrication method. This approach simplifies the fabrication of hinge mechanisms and overcomes limitations of conventional origami manufacturing by eliminating the need for adhesives commonly used during assembly, making it suitable for robots at the tens-of-centimeters scale. The advantages and disadvantages of three types of hinge joint mechanisms are compared, and a hinge joint that can be designed with low clearance for various facet thicknesses is selected. Based on the selected hinge joint, the twisting angle and bending force are analyzed, leading to the implementation of a clearance of 0.1 mm. Torsional resistance is experimentally evaluated to measure the torque required for twisting caused by plastic deformation and clearance. The results show that the torque associated with plastic deformation is sufficient to constrain the undesired degrees of freedom of the hinge joint, while the torque required for twisting due to clearance is minimal. Based on the analyzed data, the proposed hinge joint mechanism is applied to a 3-degree-of-freedom delta robot manipulator, demonstrating precise motion with low clearance.

Protein inverse folding aims to recover amino acid sequences for a given 3D protein structure, underpinning broad applications such as enzyme engineering and drug discovery.Current methods often follow a serial pipeline, in which a structure encoder predicts a coarse sequence, which is then refined by protein language models (PLMs). However, because PLMs only perform post-hoc sequence edits, the refinement is bounded by the quality of upstream predictions.Thanks to recent multimodal protein language models (MPLMs), we could directly encode structure to generate sequences with pretrained structural knowledge, but we observe that they are not effective for inverse folding. Therefore, we introduce a symmetric dual-path architecture that both leverages PLMs for pretrained sequence evolution knowledge and MPLMs for pretrained structural knowledge to iteratively guide protein sequence generation.Through extensive experiments across standard protein inverse folding benchmarks, our method achieves state-of-the-art performance, surpassing prior approaches, and ablation studies validate the rationale of our symmetric design, revealing a promising direction for the community.

Conventional soft robot actuators excel in compliance, but their uncontrolled deformations compromise accuracy and hinder scaling to multi-degree-of-freedom (DoF) systems. We introduce a MONOlithic ORIGAMI-inspired soft folding actuator design (MONORIGAMI) that establishes a design strategy based on spatially programmed stiffness anisotropy to preserve material compliance along desired folding directions while selectively restricting deformation in unwanted directions. The actuator leverages stiffness tiers based on material thickness, patterned in an origami-inspired geometry with facets and creases, converting unconstrained soft deformation into accurate, repeatable, and composable folding motions without additional reinforcements. The design is fully 3D-printable through a single-material, single-print process that requires no assembly. Each actuator serves as a scalable motion primitive, and linking and orienting multiple actuators mechanically programs multi-DoF trajectories. Using the same fundamental module, we demonstrate three 3D-printed soft multi-DoF robotic systems spanning distinct application domains: (1) a compact 4-DoF wearable haptic device for high-fidelity cutaneous feedback in virtual reality (VR), (2) a 3-DoF joystick for kinesthetic feedback in teleoperation, and (3) a modular robotic gripper capable of underwater operation with geometry-encoded grasp trajectories. These systems demonstrate the module's capabilities for compact multi-axis integration, controlled physical interaction, and geometry-programmed operation across different environments. Together, these results show that MONORIGAMI provides a general, composable, accessible, reliable, and scalable platform for high-precision soft multi-DoF robotics, addressing long-standing limitations in both soft actuator design and fabrication.

We present FoldingAgent, an agentic framework for inferring explicit parametric folding programs directly from origami demonstration videos. Our framework leverages the reasoning power of a pre-trained Vision-Language Model (VLM) equipped with a suite of specialized tools that enable the agent to simulate geometric transitions, verify physical plausibility, retrieve and compare visual content, and evaluate its own predictions. To translate visual content into folding programs, we define a parametric space that consists of the paper's geometry and a set of parametric folding actions. Unlike models that predict static crease patterns, our agent operates sequentially and possesses the ability to re-plan its actions, effectively mitigating the compounding errors inherent in multi-step folding. Our approach takes a step toward closing the gap between human origami knowledge, which is primarily shared through unstructured visual demonstrations, and computational methods, which typically rely on structured, parametric representations such as a crease pattern or an executable parametric plan. We evaluate our approach on PurelandFold, a newly curated benchmark of diverse Pureland origami videos with ground-truth geometry and action labels. Our results demonstrate that by combining VLM reasoning with a set of specialized tools and physical simulation, we can successfully transform unstructured visual demonstrations into executable, physically plausible folding procedures.

The passive adaptability inherent in soft robotic hands affords them advantages in applications that require safe and compliant interaction. However, existing soft robotic hands often struggle to simultaneously achieve adequate output performance and easy manufacturing due to their complicated structures. In this paper, we introduce the asymmetric origami bending (AOB) pattern for generating bending motion and the asymmetric dual-chamber (ADC) design for obtaining multifunction capability. The AOB single (AOB-S) chamber and AOB dual-chamber (AOB-D) units are designed and constitute the finger and palm actuators of the proposed Origami-inspired SOft Robotic (OSOR) hand. The OSOR hand achieves bio-inspired fingers-palm motions and adequate output performance within a monolithic structure that significantly simplifies the manufacturing process. By defining the asymmetric ratio to characterize the geometric asymmetry of the unit, the analytical models of the AOB and ADC structures are proposed. The Finite Element Analysis tool for the design of AOB actuators is obtained by geometric analysis. The asymmetric origami design grants the integrated manufacturing of the OSOR hand through a Selective Laser Sintering printing process with a single thermoplastic polyurethane material. The model and simulations are validated by experimental results. Experiments show the finger and palm maximum bending motion range of 203° and 40°, respectively, with output forces of 6.3 N and 16 N. The OSOR hand is capable of pinching a piece of tissue, stably grasping water bottles with two fingers, palm-only grasping, and completing the power grasps in the taxonomy of manufacturing grasps. The compactness, performance, and easy manufacturing of the proposed hand benefit the development of the soft robotic hand with new possibilities.

Accurately modeling biomolecular interactions is a central bottleneck in biology and therapeutic discovery. Here, we introduce Open Drug Discovery Engine (OpenDDE), an open-source, all-atom biomolecular foundation model that uses co-folding as the entry point to a scalable AI-driven drug discovery engine. Rather than treating structure prediction as an isolated endpoint, OpenDDE is designed as a shared structural reasoning layer for modeling sequence-structure-function relationships across biomolecular complexes, enabling complex structure prediction today while providing a foundation for de novo design, affinity estimation, structure-conditioned optimization, and more. OpenDDE integrates advances in all-atom architecture, atomic latent reasoning, inference optimization, and large-scale data processing to achieve IsoDDE-level co-folding accuracy within a reproducible and openly accessible framework. We also identify two scaling-law directions for co-folding models, revealing practical routes for continued improvement through data, model, inference, and training scaling. By releasing training code, inference pipelines, checkpoints, and benchmarks, OpenDDE aims to democratize access to frontier biomolecular intelligence, accelerate global collaboration, and lay an open foundation for next-generation drug discovery systems that can move from predicting molecular structures toward designing, scoring, and optimizing therapeutic candidates for human health.

Most artificial life simulators either operate on abstract substrates disconnected from physical reality, or simulate physically grounded worlds that do not scale to the population sizes required for open-ended evolution. We present Microcosmos, a simulation engine in which artificial lifeforms are modeled as elastic filament chains inhabiting a two-dimensional viscous fluid world, designed from the ground up for modern GPU hardware and end-to-end differentiable simulation. We validate the engine through four experiments. Hand-designed locomotion strategies confirm that the fluid coupling respects known physical constraints. Gradient-based optimization of filament folding demonstrates both the full differentiability of the simulator and the expressivity of the filament encodings. Neuroevolution and quality-diversity search produce a wide range of swimming and chemotaxis behaviors automatically. Linear scaling with particle count confirms the engine supports large-scale simulation. Microcosmos is released as an open platform with the long-term goal of supporting large-scale open-ended evolutionary simulations, designed to be physically plausible and computationally scalable.

Objectives: To characterize residual false positives in prostate MRI detection, and to evaluate a lightweight post-hoc refinement head for case-level specificity. Materials and Methods: This retrospective study used PI-CAI (5-fold cross-validation) and Prostate158 (n=158; external). A context-aware evidence head and an 89,216-parameter refinement head were trained on a frozen detection backbone; the evidence head was also trained on four further backbones (bare nnU-Net, bare U-Net, bare Mamba, MIGF-Mamba). For each false-positive region, T2-weighted, apparent-diffusion-coefficient, and high-b-value contrast ratios versus peri-lesional rings were compared against ground-truth lesions and contralateral benign regions. Results: False positives were closer to true cancers than to benign tissue in evidence and raw T2-weighted and apparent-diffusion-coefficient contrast, reproducing 35/35 across five architectures (Cohen's d 1.10; FP/benign evidence ratio 2.38x) and 105/105 across modality-perturbation scenarios. On PI-CAI fold-0, refinement raised case-level specificity from 0.469 to 0.549 (+17.2%) at preserved sensitivity (0.943); 5-fold cross-validation showed fold-conditional behavior (9/15 observations positive; range -22% to +28%). On Prostate158, both models saturated (McNemar pooled p=0.69), while the false-positive contrast-matching finding replicated. Conclusion: Residual false positives are contrast-matched to cancer (sharing raw imaging features rather than histologically confirmed mimicry), reproducing across five architectures -- a data-level imaging property, not model-specific artifacts; post-hoc refinement adds practical specificity in-domain but is fold-conditional.

While generative AI has achieved remarkable success in solving problems with verifiable solutions, generating physical art that satisfies both strict geometric constraints and subjective visual aesthetics remains a challenge. This paper presents an approach to tackle these difficulties in the domain of computational origami, a mathematically rigid environment that grounds artistic design within the equations of flat foldability. We present COrigami, an end-to-end AI-driven pipeline that assists the design cycle by generating crease patterns from natural language. Our pipeline involves generating a semantic stick figure, computing a base packing, solving for a flat-foldable crease pattern, shaping the flat-folded crease pattern, and refining the generated model using reinforcement learning driven by an autonomous aesthetic evaluation loop. Our system acts as a highly effective collaborative assistant, generating structural starting points that human artists can further expand and shape. By integrating algorithmic optimisation with autonomous aesthetic critique, this work demonstrates how AI systems can satisfy multi-objective physical constraints to enable reliable, mathematically grounded co-creativity.

All-atom generative modeling of 3D biomolecular complexes has emerged as the dominant paradigm for predicting the structure of proteins and protein-ligand systems. Generating structures at the atomic level of fidelity, however, typically requires expensive iterative diffusion rollouts, making both conventional deployment and inference-time search techniques computationally costly. In this paper, we introduce the Denoiser Cofolding All-Atom Flowmap (DeCAF) framework for distilling state-of-the-art all-atom cofolding models into all-atom flow maps that produce high-quality samples in only a few inference steps. We build DeCAF on a denoiser-based formulation of flow maps with endpoint losses that naturally support SE(3) rigid alignment, which we show is critical for training accurate models. We further derive a simple change of variables that lets DeCAF operate in the σ-space noise schedule of EDM-style architectures, enabling direct distillation from pretrained cofolding diffusion models. Equipped with DeCAF's flowmap lookahead, we introduce a purpose-built inference-time framework that improves sampling through reward-guided search. Empirically, DeCAF-Boltz statistically improves over Boltz-1x in both accuracy (RMSD) and physical validity scores of protein-ligand poses at strict NFE budgets on the challenging Runs N' Poses, while also showing a more optimal Pareto frontier across all inference compute budgets on PoseBusters. Distilling the state-of-the-art Pearl cofolding model, DeCAF-Pearl outperforms diffusion-based cofolding models and matches its teacher on success rate while using 5x fewer NFEs. We release our code at https://github.com/genesistherapeutics/decaf.

Real-world household robots require Vision-Language-Action (VLA) foundation models that can acquire reusable manipulation skills across diverse objects, task conditions, and household environments. Deformable-object folding is a representative challenge, requiring robots to handle clothing items from random initial states across varying categories, geometries, materials, and scenes. However, existing VLA systems commonly train separate policies for different object categories, while naively mixed multi-task training often suffers from task interference and degraded performance. To move beyond category-specific folding policies, we introduce DeMaVLA, a VLA foundation model for generalizable Deformable Manipulation. DeMaVLA adopts a VLM backbone with an action expert and formulates continuous action generation using flow matching. To improve efficiency, the action expert is constructed by pruning every other transformer layer while preserving layer-wise alignment with the VLM backbone, reducing training and inference cost. DeMaVLA is first pre-trained on approximately 5,000 hours of selected real-world dual-arm demonstrations to acquire general manipulation priors. It is then post-trained on mixed folding data that aggregates self-collected demonstrations and corrective trajectories from real-robot failures across multiple folding tasks through a human-in-the-loop Data Aggregation~(DAgger) pipeline. Experiments show that DeMaVLA achieves competitive performance on RoboTwin 2.0 and strong real-world results on our household folding benchmark. These results highlight the value of scalable real-world data, efficient action generation, and corrective learning for general-purpose VLA policies in deformable-object manipulation.

Protein structure classification (PSC) uses supervised learning to predict a protein's CATH/SCOP(e) class from the protein's sequence or 3D structural feature(s). We already modeled 3D structures as (static) protein structure networks (PSNs), demonstrating the competitiveness of PSN-based features to sequence or direct (i.e. non-network) 3D structural features in the PSC task. More recently, we demonstrated the power of features extracted from dynamic PSNs over features extracted from static PSNs (and thus by transitivity over sequence and direct 3D structural features) in the same task. That dynamic PSN approach used traditional machine learning (ML), combining manual (pre-engineered) features with an off-the-shelf classifier. Here, we evaluate whether automatic deep learning (DL) from the dynamic PSNs yields improvements. Our evaluation on 72 datasets spanning ~44,000 CATH- or SCOPe-labeled dynamic PSNs reveals that in terms of PSC accuracy, traditional ML and DL are (close to) tied for a large majority of the datasets, while DL is on average 10+ times slower. We are the first to evaluate traditional ML vs. DL in the dynamic PSN-based PSC task.

Cephalopod pulsed-jet locomotion is not a single isolated expulsion event, but a coordinated cycle involving jet expulsion, passive gliding, and mantle refilling. Inspired by this cycle-resolved biological strategy, this paper presents a cephalopod-inspired pulsed-jet robot with a rigid-soft hybrid origami mantle that enables large, actively driven, and geometry-guided body deformation. The proposed mantle integrates rigid folding panels with a compliant silicone framework, allowing a 75% effective cavity-volume reduction during expulsion and reducing the projected cross-sectional drag area by approximately 75.7% in the contracted gliding configuration. Using this platform, we formulate a cycle-resolved framework to separately investigate how expelled volume, glide duration, and refill pathway influence whole-cycle locomotion performance. Experiments show that the robot reaches a peak speed of approximately 0.5 m/s (3.8 BL/s) and an average speed exceeding 0.2 m/s (1.5 BL/s) within the first jetting cycle. The results further demonstrate the roles of high expelled-volume-ratio contraction in speed generation, reduced-drag-area gliding under different glide durations, and mantle-aperture-inspired passive inlet valves in assisting refill. This work provides both a robotic implementation of actively deformable cephalopod-like jet propulsion and a unified experimental platform for studying expulsion-gliding-refilling dynamics in pulsed-jet locomotion.

We introduce an elastic-driven self-folding approach that fabricates robots directly from flat 3D-printed conductive PLA nets. Elastic bands routed through printed hooks store energy that folds the sheet into programmed 3D geometries, while the flat state allows accurate placement of electronics and magnets before deployment. The same substrate doubles as electrodes for capacitive touch and supports a reusable platform I/O palette with Hall sensors and eccentric rotating mass (ERM) motors for docking detection and vibration actuation. We also derive a closed-form folding model that balances hinge stiffness with elastic band moment to predict equilibrium fold angles; experiments validate the model and yield a design map linking hinge thickness, band size, and hook spacing to target angles. Using this workflow we realize multiple polyhedral modules and demonstrate three applications: a cube that highlights the potential of self-folding for scalable modular robot collectives, a deployable gripper, and a tendon-driven finger. The method is low cost, stimulus-free, and integrates actuation and sensing.

De novo functional protein design aims to generate protein sequences that realize specified biochemical functions without relying on evolutionary templates, enabling broad applications in biotechnology and medicine. Existing approaches adopt either direct function-to-sequence mapping or decoupled structure-sequence generation strategies but often fail to achieve functionality and foldability simultaneously. To address this, we propose CodeFP, a Co-generative protein language model for de novo Functional Protein design that simultaneously decodes sequence and structure tokens, thereby enabling superior simultaneous realization of functionality and foldability. CodeFP utilizes functional local structures to enrich functional semantic encodings, overcoming the suboptimal translation of flat encodings into structure tokens, while introducing auxiliary functional supervision to alleviate training ambiguity stemming from the one-to-many structure-to-token mapping. Extensive experiments show that CodeFP consistently achieves average improvements of 6.1% in functional consistency and 3.2% in foldability over the strongest baseline.

Origami-inspired robotic grippers have shown promising potential for object manipulation tasks due to their compact volume and mechanical flexibility. However, robust capture of objects with random shapes in dynamic working environments often comes at the cost of additional actuation channels and control complexity. Here, we introduce a tendon-driven origami tentacle gripper capable of universal object gripping by exploiting a synergy between local, deterministic deformation programming and global, stochastic entanglements. Each origami tentacle is made by cutting thin Mylar sheets; It features carefully placed holes for routing an actuation tendon, origami creases for controlling the deformation, and a tapered shape. By tailoring these design features, one can prescribe the shrinking, bending, and twisting deformation, eventually creating deterministic coiling with a simple tendon pull. Then, when multiple coiling tentacles are placed in proximity, stochastic entanglement emerges, allowing the tentacles to braid, knot, and grip objects with random shapes. We derived a simulation model by integrating origami mechanics with Cosserat rods to correlate origami design, tendon deformation, and their collective gripping performance. Then, we experimentally tested how these coiling and entangling origami tentacles can grasp objects under gravity and in water. A stow-and-release deployment mechanism was also tested to simulate in-orbit grasping. Overall, the entertaining origami tentacle gripper presents a new strategy for robust object grasping with simple design and actuation.

Designing proteins that satisfy natural language functional requirements is a central goal in protein engineering. A straightforward baseline is to fine-tune generic instruction-tuned LLMs as direct text-to-sequence generators, but this is data- and compute-hungry. With limited supervision, LLMs can produce coherent plans in text yet fail to reliably realize them as sequences. This plan-execute gap motivates ProtoCycle, an agentic framework for protein design that uses LLMs primarily to drive a multi-round, feedback-driven decision cycle. ProtoCycle couples an LLM planner with a lightweight tool environment designed to emulate the iterative workflow of human protein engineering and uses LLM-driven reflection on tool feedback to revise plans. Trained with supervised trajectories and online reinforcement learning, ProtoCycle achieves strong language alignment while maintaining competitive foldability, and ablations show that reflection substantially improves sequence quality.

Kirigami is an increasingly useful fabrication method to produce shape-programmable metamaterial structures. However, inverse design remains difficult because deployment is nonlinear, and feasible cut layouts must satisfy discrete compatibility rules, avoid overlap, and map one target shape to valid designs. We present RL-Kirigami, an inverse design framework that combines optimal-transport conditional flow matching (OT-CFM) with reinforcement learning to generate compatible ratio fields for compact reconfigurable parallelogram quad kirigami. A marching decoder enforces global geometric compatibility, and Group Relative Policy Optimization (GRPO) aligns the generator with nondifferentiable rewards for silhouette matching, feasibility, and ratio-field regularity. Across procedurally generated target shape instances, a single sample from the pretrained OT-CFM prior reached $94.2$ sIoU and outperformed solver baselines while reducing forward simulator evaluations from hundreds to 1. GRPO improved accuracy to $94.91$ sIoU and, with regularity included, reduced $\mathrm{TV}(\mathbf{x})$ from 0.95 to 0.81 while maintaining $94.83$ sIoU. Generated layouts were exported to DXF and laser-cut in $50~μ\mathrm{m}$ polymeric sheets to produce deployable prototypes in $8.0 \pm 1.0$ minutes per part. These results support a manufacturing-aware inverse design workflow for deployable kirigami metamaterials under hard geometric feasibility constraints.

How do protein structure prediction models fold proteins? We investigate this question through causal interventions on the folding trunks of ESMFold, OpenFold, and Boltz-1. Across all three models, we find a shared two-stage computational structure. In the first stage, early blocks initialize pairwise biochemical signals: features like charge propagate from sequence into pairwise representations through architecture-specific pathways. In the second stage, late blocks develop pairwise spatial features: distance and contact information accumulate in the pairwise representation. We verify these mechanisms causally by showing that steering charge and distance features induces predictable structural changes. Furthermore, these representations are functionally interchangeable: pairwise states can be linearly aligned and substituted across models. Together, these results suggest that folding trunks with different architectures, inputs, and training procedures converge on a shared representational organization for mapping sequence chemistry into spatial geometry.

Origami structures have been an active area of research due to their high volume-to-mass ratio, packability, and shape adaptability. Previously-developed actuated foldable structures have either embedded linear actuators into the structure, or have attached non-folding rotary motors to the exterior structure. Further, in prior work, actuators directly embedded in the structure of folding media all contributed to linear or folding motion, not to continuous rotary motion. On the macro-scale there has not yet been a folding continuous rotary actuator. This paper details the development and testing of the first macro-scale origami rotary motor that can be folded flat, and then unfurled to operate. Using corona discharge for torque production, the prototype motor achieved an expansion ratio of over 3.8:1, reached a top speed of 1720 rpm when driven at -30 kV, and exhibited a maximum motor torque over 0.25 mNm with an active component torque density of 0.11 Nm/kg.