arXiv subjects

Ricky T. Q. Chen

Publications and source records attributed to Ricky T. Q. Chen.

At least 55 records · Page 3Linked to original sources

arXiv2023

Flow Matching for Generative Modeling

We introduce a new paradigm for generative modeling built on Continuous Normalizing Flows (CNFs), allowing us to train CNFs at unprecedented scale. Specifically, we present the notion of Flow Matching (FM), a simulation-free approach for training CNFs based on regressing vector fields of fixed conditional probability paths. Flow Matching is compatible with a general family of Gaussian probability paths for transforming between noise and data samples -- which subsumes existing diffusion paths as specific instances. Interestingly, we find that employing FM with diffusion paths results in a more robust and stable alternative for training diffusion models. Furthermore, Flow Matching opens the door to training CNFs with other, non-diffusion probability paths. An instance of particular interest is using Optimal Transport (OT) displacement interpolation to define the conditional probability paths. These paths are more efficient than diffusion paths, provide faster training and sampling, and result in better generalization. Training CNFs using Flow Matching on ImageNet leads to consistently better performance than alternative diffusion-based methods in terms of both likelihood and sample quality, and allows fast and reliable sample generation using off-the-shelf numerical ODE solvers.

cs.LG↗

arXiv2023

Unifying Generative Models with GFlowNets and Beyond

There are many frameworks for deep generative modeling, each often presented with their own specific training algorithms and inference methods. Here, we demonstrate the connections between existing deep generative models and the recently introduced GFlowNet framework, a probabilistic inference machine which treats sampling as a decision-making process. This analysis sheds light on their overlapping traits and provides a unifying viewpoint through the lens of learning with Markovian trajectories. Our framework provides a means for unifying training and inference algorithms, and provides a route to shine a unifying light over many generative models. Beyond this, we provide a practical and experimentally verified recipe for improving generative modeling with insights from the GFlowNet perspective.

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arXiv2023

Theseus: A Library for Differentiable Nonlinear Optimization

We present Theseus, an efficient application-agnostic open source library for differentiable nonlinear least squares (DNLS) optimization built on PyTorch, providing a common framework for end-to-end structured learning in robotics and vision. Existing DNLS implementations are application specific and do not always incorporate many ingredients important for efficiency. Theseus is application-agnostic, as we illustrate with several example applications that are built using the same underlying differentiable components, such as second-order optimizers, standard costs functions, and Lie groups. For efficiency, Theseus incorporates support for sparse solvers, automatic vectorization, batching, GPU acceleration, and gradient computation with implicit differentiation and direct loss minimization. We do extensive performance evaluation in a set of applications, demonstrating significant efficiency gains and better scalability when these features are incorporated. Project page: https://sites.google.com/view/theseus-ai

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arXiv2022

Latent Discretization for Continuous-time Sequence Compression

Neural compression offers a domain-agnostic approach to creating codecs for lossy or lossless compression via deep generative models. For sequence compression, however, most deep sequence models have costs that scale with the sequence length rather than the sequence complexity. In this work, we instead treat data sequences as observations from an underlying continuous-time process and learn how to efficiently discretize while retaining information about the full sequence. As a consequence of decoupling sequential information from its temporal discretization, our approach allows for greater compression rates and smaller computational complexity. Moreover, the continuous-time approach naturally allows us to decode at different time intervals. We empirically verify our approach on multiple domains involving compression of video and motion capture sequences, showing that our approaches can automatically achieve reductions in bit rates by learning how to discretize.

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arXiv2022

Semi-Discrete Normalizing Flows through Differentiable Tessellation

Mapping between discrete and continuous distributions is a difficult task and many have had to resort to heuristical approaches. We propose a tessellation-based approach that directly learns quantization boundaries in a continuous space, complete with exact likelihood evaluations. This is done through constructing normalizing flows on convex polytopes parameterized using a simple homeomorphism with an efficient log determinant Jacobian. We explore this approach in two application settings, mapping from discrete to continuous and vice versa. Firstly, a Voronoi dequantization allows automatically learning quantization boundaries in a multidimensional space. The location of boundaries and distances between regions can encode useful structural relations between the quantized discrete values. Secondly, a Voronoi mixture model has near-constant computation cost for likelihood evaluation regardless of the number of mixture components. Empirically, we show improvements over existing methods across a range of structured data modalities.

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arXiv2022

Neural Conservation Laws: A Divergence-Free Perspective

We investigate the parameterization of deep neural networks that by design satisfy the continuity equation, a fundamental conservation law. This is enabled by the observation that any solution of the continuity equation can be represented as a divergence-free vector field. We hence propose building divergence-free neural networks through the concept of differential forms, and with the aid of automatic differentiation, realize two practical constructions. As a result, we can parameterize pairs of densities and vector fields that always exactly satisfy the continuity equation, foregoing the need for extra penalty methods or expensive numerical simulation. Furthermore, we prove these models are universal and so can be used to represent any divergence-free vector field. Finally, we experimentally validate our approaches by computing neural network-based solutions to fluid equations, solving for the Hodge decomposition, and learning dynamical optimal transport maps.

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arXiv2022

Matching Normalizing Flows and Probability Paths on Manifolds

Continuous Normalizing Flows (CNFs) are a class of generative models that transform a prior distribution to a model distribution by solving an ordinary differential equation (ODE). We propose to train CNFs on manifolds by minimizing probability path divergence (PPD), a novel family of divergences between the probability density path generated by the CNF and a target probability density path. PPD is formulated using a logarithmic mass conservation formula which is a linear first order partial differential equation relating the log target probabilities and the CNF's defining vector field. PPD has several key benefits over existing methods: it sidesteps the need to solve an ODE per iteration, readily applies to manifold data, scales to high dimensions, and is compatible with a large family of target paths interpolating pure noise and data in finite time. Theoretically, PPD is shown to bound classical probability divergences. Empirically, we show that CNFs learned by minimizing PPD achieve state-of-the-art results in likelihoods and sample quality on existing low-dimensional manifold benchmarks, and is the first example of a generative model to scale to moderately high dimensional manifolds.

stat.ML↗

arXiv2022

Infinitely Deep Bayesian Neural Networks with Stochastic Differential Equations

We perform scalable approximate inference in continuous-depth Bayesian neural networks. In this model class, uncertainty about separate weights in each layer gives hidden units that follow a stochastic differential equation. We demonstrate gradient-based stochastic variational inference in this infinite-parameter setting, producing arbitrarily-flexible approximate posteriors. We also derive a novel gradient estimator that approaches zero variance as the approximate posterior over weights approaches the true posterior. This approach brings continuous-depth Bayesian neural nets to a competitive comparison against discrete-depth alternatives, while inheriting the memory-efficient training and tunable precision of Neural ODEs.

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arXiv2021

Fully differentiable optimization protocols for non-equilibrium steady states

In the case of quantum systems interacting with multiple environments, the time-evolution of the reduced density matrix is described by the Liouvillian. For a variety of physical observables, the long-time limit or steady state solution is needed for the computation of desired physical observables. For inverse design or optimal control of such systems, the common approaches are based on brute-force search strategies. Here, we present a novel methodology, based on automatic differentiation, capable of differentiating the steady state solution with respect to any parameter of the Liouvillian. Our approach has a low memory cost, and is agnostic to the exact algorithm for computing the steady state. We illustrate the advantage of this method by inverse designing the parameters of a quantum heat transfer device that maximizes the heat current and the rectification coefficient. Additionally, we optimize the parameters of various Lindblad operators used in the simulation of energy transfer under natural incoherent light. We also present a sensitivity analysis of the steady state for energy transfer under natural incoherent light as a function of the incoherent-light pumping rate.

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arXiv2021

Learning Neural Event Functions for Ordinary Differential Equations

The existing Neural ODE formulation relies on an explicit knowledge of the termination time. We extend Neural ODEs to implicitly defined termination criteria modeled by neural event functions, which can be chained together and differentiated through. Neural Event ODEs are capable of modeling discrete and instantaneous changes in a continuous-time system, without prior knowledge of when these changes should occur or how many such changes should exist. We test our approach in modeling hybrid discrete- and continuous- systems such as switching dynamical systems and collision in multi-body systems, and we propose simulation-based training of point processes with applications in discrete control.

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arXiv2021

"Hey, that's not an ODE": Faster ODE Adjoints via Seminorms

Neural differential equations may be trained by backpropagating gradients via the adjoint method, which is another differential equation typically solved using an adaptive-step-size numerical differential equation solver. A proposed step is accepted if its error, \emph{relative to some norm}, is sufficiently small; else it is rejected, the step is shrunk, and the process is repeated. Here, we demonstrate that the particular structure of the adjoint equations makes the usual choices of norm (such as $L^2$) unnecessarily stringent. By replacing it with a more appropriate (semi)norm, fewer steps are unnecessarily rejected and the backpropagation is made faster. This requires only minor code modifications. Experiments on a wide range of tasks -- including time series, generative modeling, and physical control -- demonstrate a median improvement of 40% fewer function evaluations. On some problems we see as much as 62% fewer function evaluations, so that the overall training time is roughly halved.

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arXiv2021

Neural Spatio-Temporal Point Processes

We propose a new class of parameterizations for spatio-temporal point processes which leverage Neural ODEs as a computational method and enable flexible, high-fidelity models of discrete events that are localized in continuous time and space. Central to our approach is a combination of continuous-time neural networks with two novel neural architectures, i.e., Jump and Attentive Continuous-time Normalizing Flows. This approach allows us to learn complex distributions for both the spatial and temporal domain and to condition non-trivially on the observed event history. We validate our models on data sets from a wide variety of contexts such as seismology, epidemiology, urban mobility, and neuroscience.

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arXiv2021

Convex Potential Flows: Universal Probability Distributions with Optimal Transport and Convex Optimization

Flow-based models are powerful tools for designing probabilistic models with tractable density. This paper introduces Convex Potential Flows (CP-Flow), a natural and efficient parameterization of invertible models inspired by the optimal transport (OT) theory. CP-Flows are the gradient map of a strongly convex neural potential function. The convexity implies invertibility and allows us to resort to convex optimization to solve the convex conjugate for efficient inversion. To enable maximum likelihood training, we derive a new gradient estimator of the log-determinant of the Jacobian, which involves solving an inverse-Hessian vector product using the conjugate gradient method. The gradient estimator has constant-memory cost, and can be made effectively unbiased by reducing the error tolerance level of the convex optimization routine. Theoretically, we prove that CP-Flows are universal density approximators and are optimal in the OT sense. Our empirical results show that CP-Flow performs competitively on standard benchmarks of density estimation and variational inference.

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arXiv2020

Inverse design of dissipative quantum steady-states with implicit differentiation

Inverse design of a property that depends on the steady-state of an open quantum system is commonly done by grid-search type of methods. In this paper we present a new methodology that allows us to compute the gradient of the steady-state of an open quantum system with respect to any parameter of the Hamiltonian using the implicit differentiation theorem. As an example, we present a simulation of a spin-boson model where the steady-state solution is obtained using Redfield theory.

quant-ph↗

arXiv2020

Self-Tuning Stochastic Optimization with Curvature-Aware Gradient Filtering

Standard first-order stochastic optimization algorithms base their updates solely on the average mini-batch gradient, and it has been shown that tracking additional quantities such as the curvature can help de-sensitize common hyperparameters. Based on this intuition, we explore the use of exact per-sample Hessian-vector products and gradients to construct optimizers that are self-tuning and hyperparameter-free. Based on a dynamics model of the gradient, we derive a process which leads to a curvature-corrected, noise-adaptive online gradient estimate. The smoothness of our updates makes it more amenable to simple step size selection schemes, which we also base off of our estimates quantities. We prove that our model-based procedure converges in the noisy quadratic setting. Though we do not see similar gains in deep learning tasks, we can match the performance of well-tuned optimizers and ultimately, this is an interesting step for constructing self-tuning optimizers.

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arXiv2020

Scalable Gradients for Stochastic Differential Equations

The adjoint sensitivity method scalably computes gradients of solutions to ordinary differential equations. We generalize this method to stochastic differential equations, allowing time-efficient and constant-memory computation of gradients with high-order adaptive solvers. Specifically, we derive a stochastic differential equation whose solution is the gradient, a memory-efficient algorithm for caching noise, and conditions under which numerical solutions converge. In addition, we combine our method with gradient-based stochastic variational inference for latent stochastic differential equations. We use our method to fit stochastic dynamics defined by neural networks, achieving competitive performance on a 50-dimensional motion capture dataset.

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arXiv2020

Residual Flows for Invertible Generative Modeling

Flow-based generative models parameterize probability distributions through an invertible transformation and can be trained by maximum likelihood. Invertible residual networks provide a flexible family of transformations where only Lipschitz conditions rather than strict architectural constraints are needed for enforcing invertibility. However, prior work trained invertible residual networks for density estimation by relying on biased log-density estimates whose bias increased with the network's expressiveness. We give a tractable unbiased estimate of the log density using a "Russian roulette" estimator, and reduce the memory required during training by using an alternative infinite series for the gradient. Furthermore, we improve invertible residual blocks by proposing the use of activation functions that avoid derivative saturation and generalizing the Lipschitz condition to induced mixed norms. The resulting approach, called Residual Flows, achieves state-of-the-art performance on density estimation amongst flow-based models, and outperforms networks that use coupling blocks at joint generative and discriminative modeling.

stat.ML↗

arXiv2020

SUMO: Unbiased Estimation of Log Marginal Probability for Latent Variable Models

Standard variational lower bounds used to train latent variable models produce biased estimates of most quantities of interest. We introduce an unbiased estimator of the log marginal likelihood and its gradients for latent variable models based on randomized truncation of infinite series. If parameterized by an encoder-decoder architecture, the parameters of the encoder can be optimized to minimize its variance of this estimator. We show that models trained using our estimator give better test-set likelihoods than a standard importance-sampling based approach for the same average computational cost. This estimator also allows use of latent variable models for tasks where unbiased estimators, rather than marginal likelihood lower bounds, are preferred, such as minimizing reverse KL divergences and estimating score functions.

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