OmniGenome: Aligning RNA Sequences with Secondary Structures in Genomic Foundation Models

The structures of RNA sequences play a vital role in various cellular processes, while existing genomic foundation models (FMs) have struggled with precise sequence-structure alignment, due to the complexity of exponential combinations of nucleotide bases. In this study, we introduce OmniGenome, a foundation model that addresses this critical challenge of sequence-structure alignment in RNA FMs. OmniGenome bridges the sequences with secondary structures using structure-contextualized modeling, enabling hard in-silico genomic tasks that existing FMs cannot handle, e.g., RNA design tasks. The results on two comprehensive genomic benchmarks show that OmniGenome achieves state-of-the-art performance on complex RNA subtasks. For example, OmniGenome solved 74% of complex puzzles, compared to SpliceBERT which solved only 3% of the puzzles. Besides, OmniGenome solves most of the puzzles within $1$ hour, while the existing methods usually allocate $24$ hours for each puzzle. Overall, OmniGenome establishes wide genomic application cases and offers profound insights into biological mechanisms from the perspective of sequence-structure alignment.

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. 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.

Adapting Conformal Prediction to Distribution Shifts Without Labels

Conformal prediction (CP) enables machine learning models to output prediction sets with guaranteed coverage rate, assuming exchangeable data. Unfortunately, the exchangeability assumption is frequently violated due to distribution shifts in practice, and the challenge is often compounded by the lack of ground truth labels at test time. Focusing on classification in this paper, our goal is to improve the quality of CP-generated prediction sets using only unlabeled data from the test domain. This is achieved by two new methods called ECP and EACP, that adjust the score function in CP according to the base model's uncertainty on the unlabeled test data. 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 supervised algorithms.

Pick up the PACE: 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 PACE, which requires no tuning or prior knowledge about the distribution shifts. Extensive experiments on Procgen, Atari, and Gym Control environments show that PACE works surprisingly well$\unicode{x2013}$mitigating loss of plasticity and rapidly adapting to challenging distribution shifts$\unicode{x2013}$despite the underlying optimization problem being nonconvex and nonstationary.

CLOSURE: Fast Quantification of Pose Uncertainty Sets

We investigate uncertainty quantification of 6D pose estimation from keypoint measurements. Assuming unknown-but-bounded measurement noises, a pose uncertainty set (PURSE) is a subset of SE(3) that contains all possible 6D poses compatible with the measurements. Despite being simple to formulate and its ability to embed uncertainty, the PURSE is difficult to manipulate and interpret due to the many abstract nonconvex polynomial constraints. An appealing simplification of PURSE is to find its minimum enclosing geodesic ball (MEGB), i.e., a point pose estimation with minimum worst-case error bound. We contribute (i) a dynamical system perspective, and (ii) a fast algorithm to inner approximate the MEGB. Particularly, we show the PURSE corresponds to the feasible set of a constrained dynamical system, and this perspective allows us to design an algorithm to densely sample the boundary of the PURSE through strategic random walks. We then use the miniball algorithm to compute the MEGB of PURSE samples, leading to an inner approximation. Our algorithm is named CLOSURE (enClosing baLl frOm purSe boUndaRy samplEs) and it enables computing a certificate of approximation tightness by calculating the relative size ratio between the inner approximation and the outer approximation. Running on a single RTX 3090 GPU, CLOSURE achieves the relative ratio of 92.8% on the LM-O object pose estimation dataset and 91.4% on the 3DMatch point cloud registration dataset with the average runtime less than 0.2 second. Obtaining comparable worst-case error bound but 398x and 833x faster than the outer approximation GRCC, CLOSURE enables uncertainty quantification of 6D pose estimation to be implemented in real-time robot perception applications.

Q-SLAM: Quadric Representations for Monocular SLAM

Monocular SLAM has long grappled with the challenge of accurately modeling 3D geometries. Recent advances in Neural Radiance Fields (NeRF)-based monocular SLAM have shown promise, yet these methods typically focus on novel view synthesis rather than precise 3D geometry modeling. This focus results in a significant disconnect between NeRF applications, i.e., novel-view synthesis and the requirements of SLAM. We identify that the gap results from the volumetric representations used in NeRF, which are often dense and noisy. In this study, we propose a novel approach that reimagines volumetric representations through the lens of quadric forms. We posit that most scene components can be effectively represented as quadric planes. Leveraging this assumption, we reshape the volumetric representations with million of cubes by several quadric planes, which leads to more accurate and efficient modeling of 3D scenes in SLAM contexts. Our method involves two key steps: First, we use the quadric assumption to enhance coarse depth estimations obtained from tracking modules, e.g., Droid-SLAM. This step alone significantly improves depth estimation accuracy. Second, in the subsequent mapping phase, we diverge from previous NeRF-based SLAM methods that distribute sampling points across the entire volume space. Instead, we concentrate sampling points around quadric planes and aggregate them using a novel quadric-decomposed Transformer. Additionally, we introduce an end-to-end joint optimization strategy that synchronizes pose estimation with 3D reconstruction.

Discounted Adaptive Online Prediction

Online learning is not always about memorizing everything. Since the future can be statistically very different from the past, a critical challenge is to gracefully forget the history while new data comes in. To formalize this intuition, we revisit the classical notion of discounted regret using recently developed techniques in adaptive online learning. Our main result is a new algorithm that adapts to the complexity of both the loss sequence and the comparator, improving the widespread non-adaptive algorithm - gradient descent with a constant learning rate. In particular, our theoretical guarantee does not require any structural assumption beyond convexity, and the algorithm is provably robust to suboptimal hyperparameter tuning. We further demonstrate such benefits through online conformal prediction, a downstream online learning task with set-membership decisions.

PAC-Bayes Generalization Certificates for Learned Inductive Conformal Prediction

Inductive Conformal Prediction (ICP) provides a practical and effective approach for equipping deep learning models with uncertainty estimates in the form of set-valued predictions which are guaranteed to contain the ground truth with high probability. Despite the appeal of this coverage guarantee, these sets may not be efficient: the size and contents of the prediction sets are not directly controlled, and instead depend on the underlying model and choice of score function. To remedy this, recent work has proposed learning model and score function parameters using data to directly optimize the efficiency of the ICP prediction sets. While appealing, the generalization theory for such an approach is lacking: direct optimization of empirical efficiency may yield prediction sets that are either no longer efficient on test data, or no longer obtain the required coverage on test data. In this work, we use PAC-Bayes theory to obtain generalization bounds on both the coverage and the efficiency of set-valued predictors which can be directly optimized to maximize efficiency while satisfying a desired test coverage. In contrast to prior work, our framework allows us to utilize the entire calibration dataset to learn the parameters of the model and score function, instead of requiring a separate hold-out set for obtaining test-time coverage guarantees. We leverage these theoretical results to provide a practical algorithm for using calibration data to simultaneously fine-tune the parameters of a model and score function while guaranteeing test-time coverage and efficiency of the resulting prediction sets. We evaluate the approach on regression and classification tasks, and outperform baselines calibrated using a Hoeffding bound-based PAC guarantee on ICP, especially in the low-data regime.

Uncertainty Quantification of Set-Membership Estimation in Control and Perception: Revisiting the Minimum Enclosing Ellipsoid

Set-membership estimation (SME) outputs a set estimator that guarantees to cover the groundtruth. Such sets are, however, defined by (many) abstract (and potentially nonconvex) constraints and therefore difficult to manipulate. We present tractable algorithms to compute simple and tight overapproximations of SME in the form of minimum enclosing ellipsoids (MEE). We first introduce the hierarchy of enclosing ellipsoids proposed by Nie and Demmel (2005), based on sums-ofsquares relaxations, that asymptotically converge to the MEE of a basic semialgebraic set. This framework, however, struggles in modern control and perception problems due to computational challenges. We contribute three computational enhancements to make this framework practical, namely constraints pruning, generalized relaxed Chebyshev center, and handling non-Euclidean geometry. We showcase numerical examples on system identification and object pose estimation.

InstOptima: Evolutionary Multi-objective Instruction Optimization via Large Language Model-based Instruction Operators

Instruction-based language modeling has received significant attention in pretrained language models. However, the efficiency of instruction engineering remains low and hinders the development of instruction studies. Recent studies have focused on automating instruction generation, but they primarily aim to improve performance without considering other crucial objectives that impact instruction quality, such as instruction length and perplexity. Therefore, we propose a novel approach (i.e., InstOptima) that treats instruction generation as an evolutionary multi-objective optimization problem. In contrast to text edition-based methods, our approach utilizes a large language model (LLM) to simulate instruction operators, including mutation and crossover. Furthermore, we introduce an objective-guided mechanism for these operators, allowing the LLM to comprehend the objectives and enhance the quality of the generated instructions. Experimental results demonstrate improved fine-tuning performance and the generation of a diverse set of high-quality instructions.