Normalizing flow is a class of deep generative models for efficient sampling and likelihood estimation, which achieves attractive performance, particularly in high dimensions. The flow is often implemented using a sequence of invertible residual blocks. Existing works adopt special network architectures and regularization of flow trajectories. In this paper, we develop a neural ODE flow network called JKOiFlow, inspired by the Jordan-Kinderleherer-Otto (JKO) scheme, which unfolds the discrete-time dynamic of the Wasserstein gradient flow. The proposed method stacks residual blocks one after another, allowing efficient block-wise training of the residual blocks, avoiding sampling SDE trajectories and score matching or variational learning, thus reducing the memory load and difficulty in end-to-end training. We also develop adaptive time reparameterization of the flow network with a progressive refinement of the induced trajectory in probability space to improve the model accuracy further. Experiments with synthetic and real data show that the proposed JKO-iFlow network achieves competitive performance compared with existing flow and diffusion models at a significantly reduced computational and memory cost.

In this work, we conduct a systematic study of stochastic saddle point problems (SSP) and stochastic variational inequalities (SVI) under the constraint of (ϵ, δ)- differential privacy (DP) in both Euclidean and non-Euclidean setups.

Districting is a complex combinatorial problem that consists in partitioning a geographical area into small districts. In logistics, it is a major strategic decision determining operating costs for several years. Solving districting problems using traditional methods is intractable even for small geographical areas and existing heuristics often provide sub-optimal results. We present a structured learning approach to find high-quality solutions to real-world districting problems in a few minutes. It is based on integrating a combinatorial optimization layer, the capacitated minimum spanning tree problem, into a graph neural network architecture. To train this pipeline in a decision-aware fashion, we show how to construct target solutions embedded in a suitable space and learn from target solutions. Experiments show that our approach outperforms existing methods as it can significantly reduce costs on real-world cities.

Figure 1: The Slice-100K dataset consists of STL files and their G-code counterparts. Each pair here consists of STL (left) and its slices (right) for G-code. Slice-100K will provide a foundational platform that enables broader research at the intersection of manufacturing and artificial intelligence, particularly with the recent advances in multimodal large language models (LLMs). Furthermore, openly-available data is essential for the democratization of knowledge in the scientific community. We believe Slice-100K will benefit the economy and will be a net positive contribution. However, we do foresee some potential negative societal impacts.

G-code (Geometric code) or RS-274 is the most widely used computer numerical control (CNC) and 3D printing programming language. G-code provides machine instructions for the movement of the 3D printer, especially for the nozzle, stage, and extrusion of material for extrusion-based additive manufacturing. Currently, there does not exist a large repository of curated CAD models along with their corresponding G-code files for additive manufacturing. To address this issue, we present Slice-100K, a first-of-its-kind dataset of over 100,000 G-code files, along with their tessellated CAD model, LVIS (Large Vocabulary Instance Segmentation) categories, geometric properties, and renderings. We build our dataset from triangulated meshes derived from Objaverse-XL and Thingi10K datasets. We demonstrate the utility of this dataset by finetuning GPT-2 on a subset of the dataset for G-code translation from a legacy G-code format (Sailfish) to a more modern, widely used format (Marlin). Our dataset can be found here. Slice-100K will be the first step in developing a multimodal foundation model for digital manufacturing.

As disambiguating examples become more scarce, uncertainty sampling increasingly upsamples them relative to their prevalence in the unlabeled training set.

Machine learning (ML) algorithms can often differ in performance across domains. Understanding why their performance differs is crucial for determining what types of interventions (e.g., algorithmic or operational) are most effective at closing the performance gaps. Aggregate decompositions express the total performance gap as the gap due to a shift in the feature distribution p(X) plus the gap due to a shift in the outcome's conditional distribution p(Y |X). While this coarse explanation is helpful for guiding root cause analyses, it provides limited details and can only suggest coarse fixes involving all variables in an ML system. Detailed decompositions quantify the importance of each variable to each term in the aggregate decomposition, which can provide a deeper understanding and suggest more targeted interventions. Although parametric methods exist for conducting a full hierarchical decomposition of an algorithm's performance gap at the aggregate and detailed levels, current nonparametric methods only cover parts of the hierarchy; many also require knowledge of the entire causal graph. We introduce a nonparametric hierarchical framework for explaining why the performance of an ML algorithm differs across domains, without requiring causal knowledge. Furthermore, we derive debiased, computationally-efficient estimators and statistical inference procedures to construct confidence intervals for the explanations.

We propose a Regularized Adaptive Momentum Dual Averaging (RAMDA) algorithm for training structured neural networks. Similar to existing regularized adaptive methods, the subproblem for computing the update direction of RAMDA involves a nonsmooth regularizer and a diagonal preconditioner, and therefore does not possess a closed-form solution in general. We thus also carefully devise an implementable inexactness condition that retains convergence guarantees similar to the exact versions, and propose a companion efficient solver for the subproblems of both RAMDA and existing methods to make them practically feasible. We leverage the theory of manifold identification in variational analysis to show that, even in the presence of such inexactness, the iterates of RAMDA attain the ideal structure induced by the regularizer at the stationary point of asymptotic convergence. This structure is locally optimal near the point of convergence, so RAMDA is guaranteed to obtain the best structure possible among all methods converging to the same point, making it the first regularized adaptive method outputting models that possess outstanding predictive performance while being (locally) optimally structured. Extensive numerical experiments in large-scale modern computer vision, language modeling, and speech tasks show that the proposed RAMDA is efficient and consistently outperforms state of the art for training structured neural network.