Sparse Variable Projection in Robotic Perception: Exploiting Separable Structure for Efficient Nonlinear Optimization

Robotic perception often requires solving large nonlinear least-squares (NLS) problems. While sparsity has been well-exploited to scale solvers, a complementary and underexploited structure is \emph{separability} -- where some variables (e.g., visual landmarks) appear linearly in the residuals and, for any estimate of the remaining variables (e.g., poses), have a closed-form solution. Variable projection (VarPro) methods are a family of techniques that exploit this structure by analytically eliminating the linear variables and presenting a reduced problem in the remaining variables that has favorable properties. However, VarPro has seen limited use in robotic perception; a major challenge arises from gauge symmetries (e.g., cost invariance to global shifts and rotations), which are common in perception and induce specific computational challenges in standard VarPro approaches. We present a VarPro scheme designed for problems with gauge symmetries that jointly exploits separability and sparsity. Our method can be applied as a one-time preprocessing step to construct a \emph{matrix-free Schur complement operator}. This operator allows efficient evaluation of costs, gradients, and Hessian-vector products of the reduced problem and readily integrates with standard iterative NLS solvers. We provide precise conditions under which our method applies, and describe extensions when these conditions are only partially met. Across synthetic and real benchmarks in SLAM, SNL, and SfM, our approach achieves up to \textbf{2$\times$--35$\times$ faster runtimes} than state-of-the-art methods while maintaining accuracy. We release an open-source C++ implementation and all datasets from our experiments.

Socrates-Mol: Self-Oriented Cognitive Reasoning through Autonomous Trial-and-Error with Empirical-Bayesian Screening for Molecules

Molecular property prediction is fundamental to chemical engineering applications such as solvent screening. We present Socrates-Mol, a framework that transforms language models into empirical Bayesian reasoners through context engineering, addressing cold start problems without model fine-tuning. The system implements a reflective-prediction cycle where initial outputs serve as priors, retrieved molecular cases provide evidence, and refined predictions form posteriors, extracting reusable chemical rules from sparse data. We introduce ranking tasks aligned with industrial screening priorities and employ cross-model self-consistency across five language models to reduce variance. Experiments on amine solvent LogP prediction reveal task-dependent patterns: regression achieves 72% MAE reduction and 112% R-squared improvement through self-consistency, while ranking tasks show limited gains due to systematic multi-model biases. The framework reduces deployment costs by over 70% compared to full fine-tuning, providing a scalable solution for molecular property prediction while elucidating the task-adaptive nature of self-consistency mechanisms.

Compose by Focus: Scene Graph-based Atomic Skills

A key requirement for generalist robots is compositional generalization - the ability to combine atomic skills to solve complex, long-horizon tasks. While prior work has primarily focused on synthesizing a planner that sequences pre-learned skills, robust execution of the individual skills themselves remains challenging, as visuomotor policies often fail under distribution shifts induced by scene composition. To address this, we introduce a scene graph-based representation that focuses on task-relevant objects and relations, thereby mitigating sensitivity to irrelevant variation. Building on this idea, we develop a scene-graph skill learning framework that integrates graph neural networks with diffusion-based imitation learning, and further combine "focused" scene-graph skills with a vision-language model (VLM) based task planner. Experiments in both simulation and real-world manipulation tasks demonstrate substantially higher success rates than state-of-the-art baselines, highlighting improved robustness and compositional generalization in long-horizon tasks.

Leveraging Correlation Across Test Platforms for Variance-Reduced Metric Estimation

Learning-based robotic systems demand rigorous validation to assure reliable performance, but extensive real-world testing is often prohibitively expensive, and if conducted may still yield insufficient data for high-confidence guarantees. In this work, we introduce a general estimation framework that leverages paired data across test platforms, e.g., paired simulation and real-world observations, to achieve better estimates of real-world metrics via the method of control variates. By incorporating cheap and abundant auxiliary measurements (for example, simulator outputs) as control variates for costly real-world samples, our method provably reduces the variance of Monte Carlo estimates and thus requires significantly fewer real-world samples to attain a specified confidence bound on the mean performance. We provide theoretical analysis characterizing the variance and sample-efficiency improvement, and demonstrate empirically in autonomous driving and quadruped robotics settings that our approach achieves high-probability bounds with markedly improved sample efficiency. Our technique can lower the real-world testing burden for validating the performance of the stack, thereby enabling more efficient and cost-effective experimental evaluation of robotic systems.

OmniGenBench: A Modular Platform for Reproducible Genomic Foundation Models Benchmarking

The code of nature, embedded in DNA and RNA genomes since the origin of life, holds immense potential to impact both humans and ecosystems through genome modeling. Genomic Foundation Models (GFMs) have emerged as a transformative approach to decoding the genome. As GFMs scale up and reshape the landscape of AI-driven genomics, the field faces an urgent need for rigorous and reproducible evaluation. We present OmniGenBench, a modular benchmarking platform designed to unify the data, model, benchmarking, and interpretability layers across GFMs. OmniGenBench enables standardized, one-command evaluation of any GFM across five benchmark suites, with seamless integration of over 31 open-source models. Through automated pipelines and community-extensible features, the platform addresses critical reproducibility challenges, including data transparency, model interoperability, benchmark fragmentation, and black-box interpretability. OmniGenBench aims to serve as foundational infrastructure for reproducible genomic AI research, accelerating trustworthy discovery and collaborative innovation in the era of genome-scale modeling.

FedGraM: Defending Against Untargeted Attacks in Federated Learning via Embedding Gram Matrix

Federated Learning (FL) enables geographically distributed clients to collaboratively train machine learning models by sharing only their local models, ensuring data privacy. However, FL is vulnerable to untargeted attacks that aim to degrade the global model's performance on the underlying data distribution. Existing defense mechanisms attempt to improve FL's resilience against such attacks, but their effectiveness is limited in practical FL environments due to data heterogeneity. On the contrary, we aim to detect and remove the attacks to mitigate their impact. Generalization contribution plays a crucial role in distinguishing untargeted attacks. Our observations indicate that, with limited data, the divergence between embeddings representing different classes provides a better measure of generalization than direct accuracy. In light of this, we propose a novel robust aggregation method, FedGraM, designed to defend against untargeted attacks in FL. The server maintains an auxiliary dataset containing one sample per class to support aggregation. This dataset is fed to the local models to extract embeddings. Then, the server calculates the norm of the Gram Matrix of the embeddings for each local model. The norm serves as an indicator of each model's inter-class separation capability in the embedding space. FedGraM identifies and removes potentially malicious models by filtering out those with the largest norms, then averages the remaining local models to form the global model. We conduct extensive experiments to evaluate the performance of FedGraM. Our empirical results show that with limited data samples used to construct the auxiliary dataset, FedGraM achieves exceptional performance, outperforming state-of-the-art defense methods.

Image-Editing Specialists: An RLAIF Approach for Diffusion Models

We present a novel approach to training specialized instruction-based image-editing diffusion models, addressing key challenges in structural preservation with input images and semantic alignment with user prompts. We introduce an online reinforcement learning framework that aligns the diffusion model with human preferences without relying on extensive human annotations or curating a large dataset. Our method significantly improves the realism and alignment with instructions in two ways. First, the proposed models achieve precise and structurally coherent modifications in complex scenes while maintaining high fidelity in instruction-irrelevant areas. Second, they capture fine nuances in the desired edit by leveraging a visual prompt, enabling detailed control over visual edits without lengthy textual prompts. This approach simplifies users' efforts to achieve highly specific edits, requiring only 5 reference images depicting a certain concept for training. Experimental results demonstrate that our models can perform intricate edits in complex scenes, after just 10 training steps. Finally, we showcase the versatility of our method by applying it to robotics, where enhancing the visual realism of simulated environments through targeted sim-to-real image edits improves their utility as proxies for real-world settings.

Online Aggregation of Trajectory Predictors

Trajectory prediction, the task of forecasting future agent behavior from past data, is central to safe and efficient autonomous driving. A diverse set of methods (e.g., rule-based or learned with different architectures and datasets) have been proposed, yet it is often the case that the performance of these methods is sensitive to the deployment environment (e.g., how well the design rules model the environment, or how accurately the test data match the training data). Building upon the principled theory of online convex optimization but also going beyond convexity and stationarity, we present a lightweight and model-agnostic method to aggregate different trajectory predictors online. We propose treating each individual trajectory predictor as an "expert" and maintaining a probability vector to mix the outputs of different experts. Then, the key technical approach lies in leveraging online data -the true agent behavior to be revealed at the next timestep- to form a convex-or-nonconvex, stationary-or-dynamic loss function whose gradient steers the probability vector towards choosing the best mixture of experts. We instantiate this method to aggregate trajectory predictors trained on different cities in the NUSCENES dataset and show that it performs just as well, if not better than, any singular model, even when deployed on the out-of-distribution LYFT dataset.

Building Rome with Convex Optimization

Global bundle adjustment is made easy by depth prediction and convex optimization. We (i) propose a scaled bundle adjustment (SBA) formulation that lifts 2D keypoint measurements to 3D with learned depth, (ii) design an empirically tight convex semidfinite program (SDP) relaxation that solves SBA to certfiable global optimality, (iii) solve the SDP relaxations at extreme scale with Burer-Monteiro factorization and a CUDA-based trust-region Riemannian optimizer (dubbed XM), (iv) build a structure from motion (SfM) pipeline with XM as the optimization engine and show that XM-SfM dominates or compares favorably with existing SfM pipelines in terms of reconstruction quality while being faster, more scalable, and initialization-free.

Global Contact-Rich Planning with Sparsity-Rich Semidefinite Relaxations

We show that contact-rich motion planning is also sparsity-rich when viewed as polynomial optimization (POP). We can exploit not only the correlative and term sparsity patterns that are general to all POPs, but also specialized sparsity patterns from the robot kinematic structure and the separability of contact modes. Such sparsity enables the design of high-order but sparse semidefinite programming (SDPs) relaxations--building upon Lasserre's moment and sums of squares hierarchy--that (i) can be solved in seconds by off-the-shelf SDP solvers, and (ii) compute near globally optimal solutions to the nonconvex contact-rich planning problems with small certified suboptimality. Through extensive experiments both in simulation (Push Bot, Push Box, Push Box with Obstacles, and Planar Hand) and real world (Push T), we demonstrate the power of using convex SDP relaxations to generate global contact-rich motion plans. As a contribution of independent interest, we release the Sparse Polynomial Optimization Toolbox (SPOT)--implemented in C++ with interfaces to both Python and Matlab--that automates sparsity exploitation for robotics and beyond.