NTK-approximating MLP Fusion for Efficient Language Model Fine-tuning

Fine-tuning a pre-trained language model (PLM) emerges as the predominant strategy in many natural language processing applications. However, even fine-tuning the PLMs and doing inference are expensive, especially on edge devices with low computing power. Some general approaches (e.g. quantization and distillation) have been widely studied to reduce the compute/memory of PLM fine-tuning, while very few one-shot compression techniques are explored. In this paper, we investigate the neural tangent kernel (NTK)--which reveals the gradient descent dynamics of neural networks--of the multilayer perceptrons (MLP) modules in a PLM and propose to coin a lightweight PLM through NTK-approximating MLP fusion. To achieve this, we reconsider the MLP as a bundle of sub-MLPs, and cluster them into a given number of centroids, which can then be restored as a compressed MLP and surprisingly shown to well approximate the NTK of the original PLM. Extensive experiments of PLM fine-tuning on both natural language understanding (NLU) and generation (NLG) tasks are provided to verify the effectiveness of the proposed method MLP fusion. Our code is available at https://github.com/weitianxin/MLP_Fusion.

A Gromov--Wasserstein Geometric View of Spectrum-Preserving Graph Coarsening

Graph coarsening is a technique for solving large-scale graph problems by working on a smaller version of the original graph, and possibly interpolating the results back to the original graph. It has a long history in scientific computing and has recently gained popularity in machine learning, particularly in methods that preserve the graph spectrum. This work studies graph coarsening from a different perspective, developing a theory for preserving graph distances and proposing a method to achieve this. The geometric approach is useful when working with a collection of graphs, such as in graph classification and regression. In this study, we consider a graph as an element on a metric space equipped with the Gromov--Wasserstein (GW) distance, and bound the difference between the distance of two graphs and their coarsened versions. Minimizing this difference can be done using the popular weighted kernel $K$-means method, which improves existing spectrum-preserving methods with the proper choice of the kernel. The study includes a set of experiments to support the theory and method, including approximating the GW distance, preserving the graph spectrum, classifying graphs using spectral information, and performing regression using graph convolutional networks. Code is available at https://github.com/ychen-stat-ml/GW-Graph-Coarsening .

Error Analysis of Kernel/GP Methods for Nonlinear and Parametric PDEs

We introduce a priori Sobolev-space error estimates for the solution of nonlinear, and possibly parametric, PDEs using Gaussian process and kernel based methods. The primary assumptions are: (1) a continuous embedding of the reproducing kernel Hilbert space of the kernel into a Sobolev space of sufficient regularity; and (2) the stability of the differential operator and the solution map of the PDE between corresponding Sobolev spaces. The proof is articulated around Sobolev norm error estimates for kernel interpolants and relies on the minimizing norm property of the solution. The error estimates demonstrate dimension-benign convergence rates if the solution space of the PDE is smooth enough. We illustrate these points with applications to high-dimensional nonlinear elliptic PDEs and parametric PDEs. Although some recent machine learning methods have been presented as breaking the curse of dimensionality in solving high-dimensional PDEs, our analysis suggests a more nuanced picture: there is a trade-off between the regularity of the solution and the presence of the curse of dimensionality. Therefore, our results are in line with the understanding that the curse is absent when the solution is regular enough.

U-NEED: A Fine-grained Dataset for User Needs-Centric E-commerce Conversational Recommendation

Conversational recommender systems (CRSs) aim to understand the information needs and preferences expressed in a dialogue to recommend suitable items to the user. Most of the existing conversational recommendation datasets are synthesized or simulated with crowdsourcing, which has a large gap with real-world scenarios. To bridge the gap, previous work contributes a dataset E-ConvRec, based on pre-sales dialogues between users and customer service staff in E-commerce scenarios. However, E-ConvRec only supplies coarse-grained annotations and general tasks for making recommendations in pre-sales dialogues. Different from that, we use real user needs as a clue to explore the E-commerce conversational recommendation in complex pre-sales dialogues, namely user needs-centric E-commerce conversational recommendation (UNECR). In this paper, we construct a user needs-centric E-commerce conversational recommendation dataset (U-NEED) from real-world E-commerce scenarios. U-NEED consists of 3 types of resources: (i) 7,698 fine-grained annotated pre-sales dialogues in 5 top categories (ii) 333,879 user behaviors and (iii) 332,148 product knowledge tuples. To facilitate the research of UNECR, we propose 5 critical tasks: (i) pre-sales dialogue understanding (ii) user needs elicitation (iii) user needs-based recommendation (iv) pre-sales dialogue generation and (v) pre-sales dialogue evaluation. We establish baseline methods and evaluation metrics for each task. We report experimental results of 5 tasks on U-NEED. We also report results in 3 typical categories. Experimental results indicate that the challenges of UNECR in various categories are different.

Sparse Cholesky Factorization for Solving Nonlinear PDEs via Gaussian Processes

We study the computational scalability of a Gaussian process (GP) framework for solving general nonlinear partial differential equations (PDEs). This framework transforms solving PDEs to solving quadratic optimization problem with nonlinear constraints. Its complexity bottleneck lies in computing with dense kernel matrices obtained from pointwise evaluations of the covariance kernel of the GP and its partial derivatives at collocation points. We present a sparse Cholesky factorization algorithm for such kernel matrices based on the near-sparsity of the Cholesky factor under a new ordering of Diracs and derivative measurements. We rigorously identify the sparsity pattern and quantify the exponentially convergent accuracy of the corresponding Vecchia approximation of the GP, which is optimal in the Kullback-Leibler divergence. This enables us to compute $\epsilon$-approximate inverse Cholesky factors of the kernel matrices with complexity $O(N\log^d(N/\epsilon))$ in space and $O(N\log^{2d}(N/\epsilon))$ in time. With the sparse factors, gradient-based optimization methods become scalable. Furthermore, we can use the oftentimes more efficient Gauss-Newton method, for which we apply the conjugate gradient algorithm with the sparse factor of a reduced kernel matrix as a preconditioner to solve the linear system. We numerically illustrate our algorithm's near-linear space/time complexity for a broad class of nonlinear PDEs such as the nonlinear elliptic, Burgers, and Monge-Amp\`ere equations. In summary, we provide a fast, scalable, and accurate method for solving general PDEs with GPs.

Gradient Flows for Sampling: Mean-Field Models, Gaussian Approximations and Affine Invariance

Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimization problem over all probability measures, and an initial distribution can be evolved to the desired minimizer dynamically via gradient flows. Mean-field models, whose law is governed by the gradient flow in the space of probability measures, may also be identified; particle approximations of these mean-field models form the basis of algorithms. The gradient flow approach is also the basis of algorithms for variational inference, in which the optimization is performed over a parameterized family of probability distributions such as Gaussians, and the underlying gradient flow is restricted to the parameterized family. By choosing different energy functionals and metrics for the gradient flow, different algorithms with different convergence properties arise. In this paper, we concentrate on the Kullback-Leibler divergence after showing that, up to scaling, it has the unique property that the gradient flows resulting from this choice of energy do not depend on the normalization constant. For the metrics, we focus on variants of the Fisher-Rao, Wasserstein, and Stein metrics; we introduce the affine invariance property for gradient flows, and their corresponding mean-field models, determine whether a given metric leads to affine invariance, and modify it to make it affine invariant if it does not. We study the resulting gradient flows in both probability density space and Gaussian space. The flow in the Gaussian space may be understood as a Gaussian approximation of the flow. We demonstrate that the Gaussian approximation based on the metric and through moment closure coincide, establish connections between them, and study their long-time convergence properties showing the advantages of affine invariance.

A Flexible Multi-view Multi-modal Imaging System for Outdoor Scenes

Multi-view imaging systems enable uniform coverage of 3D space and reduce the impact of occlusion, which is beneficial for 3D object detection and tracking accuracy. However, existing imaging systems built with multi-view cameras or depth sensors are limited by the small applicable scene and complicated composition. In this paper, we propose a wireless multi-view multi-modal 3D imaging system generally applicable to large outdoor scenes, which consists of a master node and several slave nodes. Multiple spatially distributed slave nodes equipped with cameras and LiDARs are connected to form a wireless sensor network. While providing flexibility and scalability, the system applies automatic spatio-temporal calibration techniques to obtain accurate 3D multi-view multi-modal data. This system is the first imaging system that integrates mutli-view RGB cameras and LiDARs in large outdoor scenes among existing 3D imaging systems. We perform point clouds based 3D object detection and long-term tracking using the 3D imaging dataset collected by this system. The experimental results show that multi-view point clouds greatly improve 3D object detection and tracking accuracy regardless of complex and various outdoor environments.

Robust convex biclustering with a tuning-free method

Biclustering is widely used in different kinds of fields including gene information analysis, text mining, and recommendation system by effectively discovering the local correlation between samples and features. However, many biclustering algorithms will collapse when facing heavy-tailed data. In this paper, we propose a robust version of convex biclustering algorithm with Huber loss. Yet, the newly introduced robustification parameter brings an extra burden to selecting the optimal parameters. Therefore, we propose a tuning-free method for automatically selecting the optimal robustification parameter with high efficiency. The simulation study demonstrates the more fabulous performance of our proposed method than traditional biclustering methods when encountering heavy-tailed noise. A real-life biomedical application is also presented. The R package RcvxBiclustr is available at https://github.com/YifanChen3/RcvxBiclustr.