Diffusion-based generative models are extremely effective in generating high-quality images, with generated samples often surpassing the quality of those produced by other models under several metrics. One distinguishing feature of these models, however, is that they typically require long sampling chains to produce high-fidelity images. This presents a challenge not only from the lenses of sampling time, but also from the inherent difficulty in backpropagating through these chains in order to accomplish tasks such as model inversion, i.e. approximately finding latent states that generate known images. In this paper, we look at diffusion models through a different perspective, that of a (deep) equilibrium (DEQ) fixed point model. Specifically, we extend the recent denoising diffusion implicit model (DDIM; Song et al. 2020), and model the entire sampling chain as a joint, multivariate fixed point system. This setup provides an elegant unification of diffusion and equilibrium models, and shows benefits in 1) single image sampling, as it replaces the fully-serial typical sampling process with a parallel one; and 2) model inversion, where we can leverage fast gradients in the DEQ setting to much more quickly find the noise that generates a given image. The approach is also orthogonal and thus complementary to other methods used to reduce the sampling time, or improve model inversion. We demonstrate our method's strong performance across several datasets, including CIFAR10, CelebA, and LSUN Bedrooms and Churches.
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ACM/IEEE第23屆模型驅動工程語言和系統國際會議，是模型驅動軟件和系統工程的首要會議系列，由ACM-SIGSOFT和IEEE-TCSE支持組織。自1998年以來，模型涵蓋了建模的各個方面，從語言和方法到工具和應用程序。模特的參加者來自不同的背景，包括研究人員、學者、工程師和工業專業人士。MODELS 2019是一個論壇，參與者可以圍繞建模和模型驅動的軟件和系統交流前沿研究成果和創新實踐經驗。今年的版本將為建模社區提供進一步推進建模基礎的機會，并在網絡物理系統、嵌入式系統、社會技術系統、云計算、大數據、機器學習、安全、開源等新興領域提出建模的創新應用以及可持續性。
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Changing how pre-trained models behave -- e.g., improving their performance on a downstream task or mitigating biases learned during pre-training -- is a common practice when developing machine learning systems. In this work, we propose a new paradigm for steering the behavior of neural networks, centered around \textit{task vectors}. A task vector specifies a direction in the weight space of a pre-trained model, such that movement in that direction improves performance on the task. We build task vectors by subtracting the weights of a pre-trained model from the weights of the same model after fine-tuning on a task. We show that these task vectors can be modified and combined together through arithmetic operations such as negation and addition, and the behavior of the resulting model is steered accordingly. Negating a task vector decreases performance on the target task, with little change in model behavior on control tasks. Moreover, adding task vectors together can improve performance on multiple tasks at once. Finally, when tasks are linked by an analogy relationship of the form ``A is to B as C is to D", combining task vectors from three of the tasks can improve performance on the fourth, even when no data from the fourth task is used for training. Overall, our experiments with several models, modalities and tasks show that task arithmetic is a simple, efficient and effective way of editing models.
The optimal stopping problem is one of the core problems in financial markets, with broad applications such as pricing American and Bermudan options. The deep BSDE method [Han, Jentzen and E, PNAS, 115(34):8505-8510, 2018] has shown great power in solving high-dimensional forward-backward stochastic differential equations (FBSDEs), and inspired many applications. However, the method solves backward stochastic differential equations (BSDEs) in a forward manner, which can not be used for optimal stopping problems that in general require running BSDE backwardly. To overcome this difficulty, a recent paper [Wang, Chen, Sudjianto, Liu and Shen, arXiv:1807.06622, 2018] proposed the backward deep BSDE method to solve the optimal stopping problem. In this paper, we provide the rigorous theory for the backward deep BSDE method. Specifically, 1. We derive the a posteriori error estimation, i.e., the error of the numerical solution can be bounded by the training loss function; and; 2. We give an upper bound of the loss function, which can be sufficiently small subject to universal approximations. We give two numerical examples, which present consistent performance with the proved theory.
When one observes a sequence of variables $(x_1, y_1), \ldots, (x_n, y_n)$, Conformal Prediction (CP) is a methodology that allows to estimate a confidence set for $y_{n+1}$ given $x_{n+1}$ by merely assuming that the distribution of the data is exchangeable. CP sets have guaranteed coverage for any finite population size $n$. While appealing, the computation of such a set turns out to be infeasible in general, e.g. when the unknown variable $y_{n+1}$ is continuous. The bottleneck is that it is based on a procedure that readjusts a prediction model on data where we replace the unknown target by all its possible values in order to select the most probable one. This requires computing an infinite number of models, which often makes it intractable. In this paper, we combine CP techniques with classical algorithmic stability bounds to derive a prediction set computable with a single model fit. We demonstrate that our proposed confidence set does not lose any coverage guarantees while avoiding the need for data splitting as currently done in the literature. We provide some numerical experiments to illustrate the tightness of our estimation when the sample size is sufficiently large, on both synthetic and real datasets.
Probabilistic models based on continuous latent spaces, such as variational autoencoders, can be understood as uncountable mixture models where components depend continuously on the latent code. They have proven expressive tools for generative and probabilistic modelling, but are at odds with tractable probabilistic inference, that is, computing marginals and conditionals of the represented probability distribution. Meanwhile, tractable probabilistic models such as probabilistic circuits (PCs) can be understood as hierarchical discrete mixture models, which allows them to perform exact inference, but often they show subpar performance in comparison to continuous latent-space models. In this paper, we investigate a hybrid approach, namely continuous mixtures of tractable models with a small latent dimension. While these models are analytically intractable, they are well amenable to numerical integration schemes based on a finite set of integration points. With a large enough number of integration points the approximation becomes de-facto exact. Moreover, using a finite set of integration points, the approximation method can be compiled into a PC performing `exact inference in an approximate model'. In experiments, we show that this simple scheme proves remarkably effective, as PCs learned this way set new state-of-the-art for tractable models on many standard density estimation benchmarks.
Large language models have recently shown promising progress in mathematical reasoning when fine-tuned with human-generated sequences walking through a sequence of solution steps. However, the solution sequences are not formally structured and the resulting model-generated sequences may not reflect the kind of systematic reasoning we might expect an expert human to produce. In this paper, we study how to build stronger reasoning capability in language models using the idea of relational abstractions. We introduce new types of sequences that more explicitly provide an abstract characterization of the transitions through intermediate solution steps to the goal state. We find that models that are supplied with such sequences as prompts can solve tasks with a significantly higher accuracy, and models that are trained to produce such sequences solve problems better than those that are trained with previously used human-generated sequences and other baselines. Our work thus takes several steps toward elucidating and improving how language models perform on tasks requiring multi-step mathematical reasoning.
Sampling-based Model Predictive Control (MPC) is a flexible control framework that can reason about non-smooth dynamics and cost functions. Recently, significant work has focused on the use of machine learning to improve the performance of MPC, often through learning or fine-tuning the dynamics or cost function. In contrast, we focus on learning to optimize more effectively. In other words, to improve the update rule within MPC. We show that this can be particularly useful in sampling-based MPC, where we often wish to minimize the number of samples for computational reasons. Unfortunately, the cost of computational efficiency is a reduction in performance; fewer samples results in noisier updates. We show that we can contend with this noise by learning how to update the control distribution more effectively and make better use of the few samples that we have. Our learned controllers are trained via imitation learning to mimic an expert which has access to substantially more samples. We test the efficacy of our approach on multiple simulated robotics tasks in sample-constrained regimes and demonstrate that our approach can outperform a MPC controller with the same number of samples.
Structural topology optimization, which aims to find the optimal physical structure that maximizes mechanical performance, is vital in engineering design applications in aerospace, mechanical, and civil engineering. Generative adversarial networks (GANs) have recently emerged as a popular alternative to traditional iterative topology optimization methods. However, these models are often difficult to train, have limited generalizability, and due to their goal of mimicking optimal structures, neglect manufacturability and performance objectives like mechanical compliance. We propose TopoDiff - a conditional diffusion-model-based architecture to perform performance-aware and manufacturability-aware topology optimization that overcomes these issues. Our model introduces a surrogate model-based guidance strategy that actively favors structures with low compliance and good manufacturability. Our method significantly outperforms a state-of-art conditional GAN by reducing the average error on physical performance by a factor of eight and by producing eleven times fewer infeasible samples. By introducing diffusion models to topology optimization, we show that conditional diffusion models have the ability to outperform GANs in engineering design synthesis applications too. Our work also suggests a general framework for engineering optimization problems using diffusion models and external performance with constraint-aware guidance. We publicly share the data, code, and trained models here: //decode.mit.edu/projects/topodiff/.
Sampling-based methods have become a cornerstone of contemporary approaches to Model Predictive Control (MPC), as they make no restrictions on the differentiability of the dynamics or cost function and are straightforward to parallelize. However, their efficacy is highly dependent on the quality of the sampling distribution itself, which is often assumed to be simple, like a Gaussian. This restriction can result in samples which are far from optimal, leading to poor performance. Recent work has explored improving the performance of MPC by sampling in a learned latent space of controls. However, these methods ultimately perform all MPC parameter updates and warm-starting between time steps in the control space. This requires us to rely on a number of heuristics for generating samples and updating the distribution and may lead to sub-optimal performance. Instead, we propose to carry out all operations in the latent space, allowing us to take full advantage of the learned distribution. Specifically, we frame the learning problem as bi-level optimization and show how to train the controller with backpropagation-through-time. By using a normalizing flow parameterization of the distribution, we can leverage its tractable density to avoid requiring differentiability of the dynamics and cost function. Finally, we evaluate the proposed approach on simulated robotics tasks and demonstrate its ability to surpass the performance of prior methods and scale better with a reduced number of samples.
Graph machine learning has been extensively studied in both academic and industry. However, as the literature on graph learning booms with a vast number of emerging methods and techniques, it becomes increasingly difficult to manually design the optimal machine learning algorithm for different graph-related tasks. To tackle the challenge, automated graph machine learning, which aims at discovering the best hyper-parameter and neural architecture configuration for different graph tasks/data without manual design, is gaining an increasing number of attentions from the research community. In this paper, we extensively discuss automated graph machine approaches, covering hyper-parameter optimization (HPO) and neural architecture search (NAS) for graph machine learning. We briefly overview existing libraries designed for either graph machine learning or automated machine learning respectively, and further in depth introduce AutoGL, our dedicated and the world's first open-source library for automated graph machine learning. Last but not least, we share our insights on future research directions for automated graph machine learning. This paper is the first systematic and comprehensive discussion of approaches, libraries as well as directions for automated graph machine learning.
Training machine learning models in a meaningful order, from the easy samples to the hard ones, using curriculum learning can provide performance improvements over the standard training approach based on random data shuffling, without any additional computational costs. Curriculum learning strategies have been successfully employed in all areas of machine learning, in a wide range of tasks. However, the necessity of finding a way to rank the samples from easy to hard, as well as the right pacing function for introducing more difficult data can limit the usage of the curriculum approaches. In this survey, we show how these limits have been tackled in the literature, and we present different curriculum learning instantiations for various tasks in machine learning. We construct a multi-perspective taxonomy of curriculum learning approaches by hand, considering various classification criteria. We further build a hierarchical tree of curriculum learning methods using an agglomerative clustering algorithm, linking the discovered clusters with our taxonomy. At the end, we provide some interesting directions for future work.
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