arXiv subjects

Heng Yang

Publications and source records attributed to Heng Yang.

At least 55 records · Page 3Linked to original sources

arXiv2025

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 compares favorably with existing pipelines in terms of reconstruction quality while being significantly faster, more scalable, and initialization-free.

cs.RO↗

arXiv2025

Adapting Prediction Sets to Distribution Shifts Without Labels

Recently there has been a surge of interest to deploy confidence set predictions rather than point predictions in machine learning. Unfortunately, the effectiveness of such prediction sets is frequently impaired by distribution shifts in practice, and the challenge is often compounded by the lack of ground truth labels at test time. Focusing on a standard set-valued prediction framework called conformal prediction (CP), this paper studies how to improve its practical performance using only unlabeled data from the shifted test domain. This is achieved by two new methods called ECP and EACP, whose main idea is to adjust the score function in CP according to its base model's own uncertainty evaluation. Through extensive experiments on a number of large-scale datasets and neural network architectures, we show that our methods provide consistent improvement over existing baselines and nearly match the performance of fully supervised methods.

cs.LG↗

arXiv2025

The Benefit of Being Bayesian in Online Conformal Prediction

Based on the framework of Conformal Prediction (CP), we study the online construction of confidence sets given a black-box machine learning model. By converting the target confidence levels into quantile levels, the problem can be reduced to predicting the quantiles (in hindsight) of a sequentially revealed data sequence. Two very different approaches have been studied previously: (i) Assuming the data sequence is iid or exchangeable, one could maintain the empirical distribution of the observed data as an algorithmic belief, and directly predict its quantiles. (ii) Due to the fragility of statistical assumptions, a recent trend is to consider the non-distributional, adversarial setting and apply first-order online optimization algorithms to moving quantile losses. However, it requires the oracle knowledge of the target quantile level, and suffers from a previously overlooked monotonicity issue due to the associated loss linearization. This paper presents an adaptive CP algorithm that combines their strengths. Without any statistical assumption, it is able to answer multiple arbitrary confidence level queries with low regret, while also overcoming the monotonicity issue suffered by first-order optimization baselines. Furthermore, if the data sequence is actually iid, then the same algorithm is automatically equipped with the "correct" coverage probability guarantee. To achieve such strengths, our key technical innovation is to regularize the aforementioned algorithmic belief (the empirical distribution) by a Bayesian prior, which robustifies it by simulating a non-linearized Follow the Regularized Leader (FTRL) algorithm on the output. Such a belief update backbone is shared by prediction heads targeting different confidence levels, bringing practical benefits analogous to the recently proposed concept of U-calibration (Kleinberg et al., 2023).

stat.ML↗

arXiv2025

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.

cs.LG↗

arXiv2025

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.

q-bio.GN↗

arXiv2025

On the Surprising Robustness of Sequential Convex Optimization for Contact-Implicit Motion Planning

Contact-implicit motion planning-embedding contact sequencing as implicit complementarity constraints-holds the promise of leveraging continuous optimization to discover new contact patterns online. Nevertheless, the resulting optimization, being an instance of Mathematical Programming with Complementary Constraints, fails the classical constraint qualifications that are crucial for the convergence of popular numerical solvers. We present robust contact-implicit motion planning with sequential convex programming (CRISP), a solver that departs from the usual primal-dual algorithmic framework but instead only focuses on the primal problem. CRISP solves a convex quadratic program with an adaptive trust region radius at each iteration, and its convergence is evaluated by a merit function using weighted penalty. We (i) provide sufficient conditions on CRISP's convergence to first-order stationary points of the merit function; (ii) release a high-performance C++ implementation of CRISP with a generic nonlinear programming interface; and (iii) demonstrate CRISP's surprising robustness in solving contact-implicit planning with naive initialization. In fact, CRISP solves several contact-implicit problems with all-zero initialization.

math.OC↗

arXiv2025

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.

cs.RO↗

arXiv2025

Control-oriented Clustering of Visual Latent Representation

We initiate a study of the geometry of the visual representation space -- the information channel from the vision encoder to the action decoder -- in an image-based control pipeline learned from behavior cloning. Inspired by the phenomenon of neural collapse (NC) in image classification (arXiv:2008.08186), we empirically demonstrate the prevalent emergence of a similar law of clustering in the visual representation space. Specifically, in discrete image-based control (e.g., Lunar Lander), the visual representations cluster according to the natural discrete action labels; in continuous image-based control (e.g., Planar Pushing and Block Stacking), the clustering emerges according to "control-oriented" classes that are based on (a) the relative pose between the object and the target in the input or (b) the relative pose of the object induced by expert actions in the output. Each of the classes corresponds to one relative pose orthant (REPO). Beyond empirical observation, we show such a law of clustering can be leveraged as an algorithmic tool to improve test-time performance when training a policy with limited expert demonstrations. Particularly, we pretrain the vision encoder using NC as a regularization to encourage control-oriented clustering of the visual features. Surprisingly, such an NC-pretrained vision encoder, when finetuned end-to-end with the action decoder, boosts the test-time performance by 10% to 35%. Real-world vision-based planar pushing experiments confirmed the surprising advantage of control-oriented visual representation pretraining.

cs.LG↗

arXiv2025

Learning Multiple Initial Solutions to Optimization Problems

Sequentially solving similar optimization problems under strict runtime constraints is essential for many applications, such as robot control, autonomous driving, and portfolio management. The performance of local optimization methods in these settings is sensitive to the initial solution: poor initialization can lead to slow convergence or suboptimal solutions. To address this challenge, we propose learning to predict \emph{multiple} diverse initial solutions given parameters that define the problem instance. We introduce two strategies for utilizing multiple initial solutions: (i) a single-optimizer approach, where the most promising initial solution is chosen using a selection function, and (ii) a multiple-optimizers approach, where several optimizers, potentially run in parallel, are each initialized with a different solution, with the best solution chosen afterward. Notably, by including a default initialization among predicted ones, the cost of the final output is guaranteed to be equal or lower than with the default initialization. We validate our method on three optimal control benchmark tasks: cart-pole, reacher, and autonomous driving, using different optimizers: DDP, MPPI, and iLQR. We find significant and consistent improvement with our method across all evaluation settings and demonstrate that it efficiently scales with the number of initial solutions required. The code is available at MISO (https://github.com/EladSharony/miso).

cs.LG↗

arXiv2024

Bridging Sequence-Structure Alignment in RNA Foundation Models

The alignment between RNA sequences and structures in foundation models (FMs) has yet to be thoroughly investigated. Existing FMs have struggled to establish sequence-structure alignment, hindering the free flow of genomic information between RNA sequences and structures. In this study, we introduce OmniGenome, an RNA FM trained to align RNA sequences with respect to secondary structures based on structure-contextualised modelling. The alignment enables free and bidirectional mappings between sequences and structures by utilising the flexible RNA modelling paradigm that supports versatile input and output modalities, i.e., sequence and/or structure as input/output. We implement RNA design and zero-shot secondary structure prediction as case studies to evaluate the Seq2Str and Str2Seq mapping capacity of OmniGenome. Results on the EternaV2 benchmark show that OmniGenome solved 74% of puzzles, whereas existing FMs only solved up to 3% of the puzzles due to the oversight of sequence-structure alignment. We leverage four comprehensive in-silico genome modelling benchmarks to evaluate performance across a diverse set of genome downstream tasks, where the results show that OmniGenome achieves state-of-the-art performance on RNA and DNA benchmarks, even without any training on DNA genomes.

q-bio.GN↗

arXiv2024

LoRA3D: Low-Rank Self-Calibration of 3D Geometric Foundation Models

Emerging 3D geometric foundation models, such as DUSt3R, offer a promising approach for in-the-wild 3D vision tasks. However, due to the high-dimensional nature of the problem space and scarcity of high-quality 3D data, these pre-trained models still struggle to generalize to many challenging circumstances, such as limited view overlap or low lighting. To address this, we propose LoRA3D, an efficient self-calibration pipeline to $\textit{specialize}$ the pre-trained models to target scenes using their own multi-view predictions. Taking sparse RGB images as input, we leverage robust optimization techniques to refine multi-view predictions and align them into a global coordinate frame. In particular, we incorporate prediction confidence into the geometric optimization process, automatically re-weighting the confidence to better reflect point estimation accuracy. We use the calibrated confidence to generate high-quality pseudo labels for the calibrating views and use low-rank adaptation (LoRA) to fine-tune the models on the pseudo-labeled data. Our method does not require any external priors or manual labels. It completes the self-calibration process on a $\textbf{single standard GPU within just 5 minutes}$. Each low-rank adapter requires only $\textbf{18MB}$ of storage. We evaluated our method on $\textbf{more than 160 scenes}$ from the Replica, TUM and Waymo Open datasets, achieving up to $\textbf{88% performance improvement}$ on 3D reconstruction, multi-view pose estimation and novel-view rendering.

cs.CV↗

arXiv2024

PreF3R: Pose-Free Feed-Forward 3D Gaussian Splatting from Variable-length Image Sequence

We present PreF3R, Pose-Free Feed-forward 3D Reconstruction from an image sequence of variable length. Unlike previous approaches, PreF3R removes the need for camera calibration and reconstructs the 3D Gaussian field within a canonical coordinate frame directly from a sequence of unposed images, enabling efficient novel-view rendering. We leverage DUSt3R's ability for pair-wise 3D structure reconstruction, and extend it to sequential multi-view input via a spatial memory network, eliminating the need for optimization-based global alignment. Additionally, PreF3R incorporates a dense Gaussian parameter prediction head, which enables subsequent novel-view synthesis with differentiable rasterization. This allows supervising our model with the combination of photometric loss and pointmap regression loss, enhancing both photorealism and structural accuracy. Given a sequence of ordered images, PreF3R incrementally reconstructs the 3D Gaussian field at 20 FPS, therefore enabling real-time novel-view rendering. Empirical experiments demonstrate that PreF3R is an effective solution for the challenging task of pose-free feed-forward novel-view synthesis, while also exhibiting robust generalization to unseen scenes.

cs.CV↗

arXiv2024

Q-SLAM: Quadric Representations for Monocular SLAM

In this paper, we reimagine volumetric representations through the lens of quadrics. We posit that rigid scene components can be effectively decomposed into quadric surfaces. Leveraging this assumption, we reshape the volumetric representations with million of cubes by several quadric planes, which results in more accurate and efficient modeling of 3D scenes in SLAM contexts. First, we use the quadric assumption to rectify noisy depth estimations from RGB inputs. This step significantly improves depth estimation accuracy, and allows us to efficiently sample ray points around quadric planes instead of the entire volume space in previous NeRF-SLAM systems. Second, we introduce a novel quadric-decomposed transformer to aggregate information across quadrics. The quadric semantics are not only explicitly used for depth correction and scene decomposition, but also serve as an implicit supervision signal for the mapping network. Through rigorous experimental evaluation, our method exhibits superior performance over other approaches relying on estimated depth, and achieves comparable accuracy to methods utilizing ground truth depth on both synthetic and real-world datasets.

cs.CV↗

arXiv2024

Necessary and sufficient conditions for boundedness of commutators of fractional integral operators on slice spaces

Let $0<t<\infty$, $0<α<n$, $1<p<r<\infty$ and $1<q<s<\infty$. In this paper, we prove that $b\in B M O\left(\mathbb{R}^{n}\right)$ if and only if the commutator $[b, T_{Ω,α}]$ generated by the fractional integral operator with the rough kernel $T_{Ω,α}$ and the locally integrable function $b$ is bounded from the slice space $(E_{p}^{q})_{t}(\mathbb{R}^{n})$ to $(E_{r}^{s})_{t}(\mathbb{R}^{n})$. Meanwhile, we also show that $b\in Lip_β(\mathbb{R}^{n}) $($0<β<1)$ if and only if the commutator $\left[b, T_{Ω,α}\right]$ is bounded from $(E_{p}^{q})_{t}(\mathbb{R}^{n})$ to $(E_{r}^{s})_{t}(\mathbb{R}^{n})$.

math.FA↗

arXiv2024

Fast TRAC: A Parameter-Free Optimizer for Lifelong Reinforcement Learning

A key challenge in lifelong reinforcement learning (RL) is the loss of plasticity, where previous learning progress hinders an agent's adaptation to new tasks. While regularization and resetting can help, they require precise hyperparameter selection at the outset and environment-dependent adjustments. Building on the principled theory of online convex optimization, we present a parameter-free optimizer for lifelong RL, called TRAC, which requires no tuning or prior knowledge about the distribution shifts. Extensive experiments on Procgen, Atari, and Gym Control environments show that TRAC works surprisingly well-mitigating loss of plasticity and rapidly adapting to challenging distribution shifts-despite the underlying optimization problem being nonconvex and nonstationary.

cs.LG↗

arXiv2024

Cocoon: Robust Multi-Modal Perception with Uncertainty-Aware Sensor Fusion

An important paradigm in 3D object detection is the use of multiple modalities to enhance accuracy in both normal and challenging conditions, particularly for long-tail scenarios. To address this, recent studies have explored two directions of adaptive approaches: MoE-based adaptive fusion, which struggles with uncertainties arising from distinct object configurations, and late fusion for output-level adaptive fusion, which relies on separate detection pipelines and limits comprehensive understanding. In this work, we introduce Cocoon, an object- and feature-level uncertainty-aware fusion framework. The key innovation lies in uncertainty quantification for heterogeneous representations, enabling fair comparison across modalities through the introduction of a feature aligner and a learnable surrogate ground truth, termed feature impression. We also define a training objective to ensure that their relationship provides a valid metric for uncertainty quantification. Cocoon consistently outperforms existing static and adaptive methods in both normal and challenging conditions, including those with natural and artificial corruptions. Furthermore, we show the validity and efficacy of our uncertainty metric across diverse datasets.

cs.CV↗

arXiv2024

OmniGenBench: Automating Large-scale in-silico Benchmarking for Genomic Foundation Models

The advancements in artificial intelligence in recent years, such as Large Language Models (LLMs), have fueled expectations for breakthroughs in genomic foundation models (GFMs). The code of nature, hidden in diverse genomes since the very beginning of life's evolution, holds immense potential for impacting humans and ecosystems through genome modeling. Recent breakthroughs in GFMs, such as Evo, have attracted significant investment and attention to genomic modeling, as they address long-standing challenges and transform in-silico genomic studies into automated, reliable, and efficient paradigms. In the context of this flourishing era of consecutive technological revolutions in genomics, GFM studies face two major challenges: the lack of GFM benchmarking tools and the absence of open-source software for diverse genomics. These challenges hinder the rapid evolution of GFMs and their wide application in tasks such as understanding and synthesizing genomes, problems that have persisted for decades. To address these challenges, we introduce GFMBench, a framework dedicated to GFM-oriented benchmarking. GFMBench standardizes benchmark suites and automates benchmarking for a wide range of open-source GFMs. It integrates millions of genomic sequences across hundreds of genomic tasks from four large-scale benchmarks, democratizing GFMs for a wide range of in-silico genomic applications. Additionally, GFMBench is released as open-source software, offering user-friendly interfaces and diverse tutorials, applicable for AutoBench and complex tasks like RNA design and structure prediction. To facilitate further advancements in genome modeling, we have launched a public leaderboard showcasing the benchmark performance derived from AutoBench. GFMBench represents a step toward standardizing GFM benchmarking and democratizing GFM applications.

q-bio.GN↗

arXiv2024

Fast and Certifiable Trajectory Optimization

We propose semidefinite trajectory optimization (STROM), a framework that computes fast and certifiably optimal solutions for nonconvex trajectory optimization problems defined by polynomial objectives and constraints. STROM employs sparse second-order Lasserre's hierarchy to generate semidefinite program (SDP) relaxations of trajectory optimization. Different from existing tools (e.g., YALMIP and SOSTOOLS in Matlab), STROM generates chain-like multiple-block SDPs with only positive semidefinite (PSD) variables. Moreover, STROM does so two orders of magnitude faster. Underpinning STROM is cuADMM, the first ADMM-based SDP solver implemented in CUDA and runs in GPUs (with C/C++ extension). cuADMM builds upon the symmetric Gauss-Seidel ADMM algorithm and leverages GPU parallelization to speedup solving sparse linear systems and projecting onto PSD cones. In five trajectory optimization problems (inverted pendulum, cart-pole, vehicle landing, flying robot, and car back-in), cuADMM computes optimal trajectories (with certified suboptimality below 1%) in minutes (when other solvers take hours or run out of memory) and seconds (when others take minutes). Further, when warmstarted by data-driven initialization in the inverted pendulum problem, cuADMM delivers real-time performance: providing certifiably optimal trajectories in 0.66 seconds despite the SDP has 49,500 variables and 47,351 constraints.

math.OC↗