Efficient and Guaranteed-Safe Non-Convex Trajectory Optimization with Constrained Diffusion Model

Trajectory optimization in robotics poses a challenging non-convex problem due to complex dynamics and environmental settings. Traditional numerical optimization methods are time-consuming in finding feasible solutions, whereas data-driven approaches lack safety guarantees for the output trajectories. In this paper, we introduce a general and fully parallelizable framework that combines diffusion models and numerical solvers for non-convex trajectory optimization, ensuring both computational efficiency and constraint satisfaction. A novel constrained diffusion model is proposed with an additional constraint violation loss for training. It aims to approximate the distribution of locally optimal solutions while minimizing constraint violations during sampling. The samples are then used as initial guesses for a numerical solver to refine and derive final solutions with formal verification of feasibility and optimality. Experimental evaluations on three tasks over different robotics domains verify the improved constraint satisfaction and computational efficiency with 4$\times$ to 22$\times$ acceleration using our proposed method, which generalizes across trajectory optimization problems and scales well with problem complexity.

DMLR: Data-centric Machine Learning Research -- Past, Present and Future

Drawing from discussions at the inaugural DMLR workshop at ICML 2023 and meetings prior, in this report we outline the relevance of community engagement and infrastructure development for the creation of next-generation public datasets that will advance machine learning science. We chart a path forward as a collective effort to sustain the creation and maintenance of these datasets and methods towards positive scientific, societal and business impact.

Cousins Of The Vendi Score: A Family Of Similarity-Based Diversity Metrics For Science And Machine Learning

Measuring diversity accurately is important for many scientific fields, including machine learning (ML), ecology, and chemistry. The Vendi Score was introduced as a generic similarity-based diversity metric that extends the Hill number of order q=1 by leveraging ideas from quantum statistical mechanics. Contrary to many diversity metrics in ecology, the Vendi Score accounts for similarity and does not require knowledge of the prevalence of the categories in the collection to be evaluated for diversity. However, the Vendi Score treats each item in a given collection with a level of sensitivity proportional to the item's prevalence. This is undesirable in settings where there is a significant imbalance in item prevalence. In this paper, we extend the other Hill numbers using similarity to provide flexibility in allocating sensitivity to rare or common items. This leads to a family of diversity metrics -- Vendi scores with different levels of sensitivity -- that can be used in a variety of applications. We study the properties of the scores in a synthetic controlled setting where the ground truth diversity is known. We then test their utility in improving molecular simulations via Vendi Sampling. Finally, we use the Vendi scores to better understand the behavior of image generative models in terms of memorization, duplication, diversity, and sample quality.

LLM-Prop: Predicting Physical And Electronic Properties Of Crystalline Solids From Their Text Descriptions

The prediction of crystal properties plays a crucial role in the crystal design process. Current methods for predicting crystal properties focus on modeling crystal structures using graph neural networks (GNNs). Although GNNs are powerful, accurately modeling the complex interactions between atoms and molecules within a crystal remains a challenge. Surprisingly, predicting crystal properties from crystal text descriptions is understudied, despite the rich information and expressiveness that text data offer. One of the main reasons is the lack of publicly available data for this task. In this paper, we develop and make public a benchmark dataset (called TextEdge) that contains text descriptions of crystal structures with their properties. We then propose LLM-Prop, a method that leverages the general-purpose learning capabilities of large language models (LLMs) to predict the physical and electronic properties of crystals from their text descriptions. LLM-Prop outperforms the current state-of-the-art GNN-based crystal property predictor by about 4% in predicting band gap, 3% in classifying whether the band gap is direct or indirect, and 66% in predicting unit cell volume. LLM-Prop also outperforms a finetuned MatBERT, a domain-specific pre-trained BERT model, despite having 3 times fewer parameters. Our empirical results may highlight the current inability of GNNs to capture information pertaining to space group symmetry and Wyckoff sites for accurate crystal property prediction.

The Vendi Score: A Diversity Evaluation Metric for Machine Learning

Diversity is an important criterion for many areas of machine learning (ML), including generative modeling and dataset curation. Yet little work has gone into understanding, formalizing, and measuring diversity in ML. In this paper, we address the diversity evaluation problem by proposing the Vendi Score, which connects and extends ideas from ecology and quantum statistical mechanics to ML. The Vendi Score is defined as the exponential of the Shannon entropy of the eigenvalues of a similarity matrix. This matrix is induced by a user-defined similarity function applied to the sample to be evaluated for diversity. In taking a similarity function as input, the Vendi Score enables its user to specify any desired form of diversity. Importantly, unlike many existing metrics in ML, the Vendi Score doesn't require a reference dataset or distribution over samples or labels, it is therefore general and applicable to any generative model, decoding algorithm, and dataset from any domain where similarity can be defined. We showcased the Vendi Score on molecular generative modeling, a domain where diversity plays an important role in enabling the discovery of novel molecules. We found that the Vendi Score addresses shortcomings of the current diversity metric of choice in that domain. We also applied the Vendi Score to generative models of images and decoding algorithms of text and found it confirms known results about diversity in those domains. Furthermore, we used the Vendi Score to measure mode collapse, a known limitation of generative adversarial networks (GANs). In particular, the Vendi Score revealed that even GANs that capture all the modes of a labeled dataset can be less diverse than the original dataset. Finally, the interpretability of the Vendi Score allowed us to diagnose several benchmark ML datasets for diversity, opening the door for diversity-informed data augmentation.

Markov Chain Score Ascent: A Unifying Framework of Variational Inference with Markovian Gradients

Minimizing the inclusive Kullback-Leibler (KL) divergence with stochastic gradient descent (SGD) is challenging since its gradient is defined as an integral over the posterior. Recently, multiple methods have been proposed to run SGD with biased gradient estimates obtained from a Markov chain. This paper provides the first non-asymptotic convergence analysis of these methods by establishing their mixing rate and gradient variance. To do this, we demonstrate that these methods-which we collectively refer to as Markov chain score ascent (MCSA) methods-can be cast as special cases of the Markov chain gradient descent framework. Furthermore, by leveraging this new understanding, we develop a novel MCSA scheme, parallel MCSA (pMCSA), that achieves a tighter bound on the gradient variance. We demonstrate that this improved theoretical result translates to superior empirical performance.