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Wonyeol Lee

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4 papers

1 author row

TMLR Journal 2023 Journal Article

Training with Mixed-Precision Floating-Point Assignments

Wonyeol Lee
Rahul Sharma
Alex Aiken

When training deep neural networks, keeping all tensors in high precision (e.g., 32-bit or even 16-bit floats) is often wasteful. However, keeping all tensors in low precision (e.g., 8-bit floats) can lead to unacceptable accuracy loss. Hence, it is important to use a precision assignment—a mapping from all tensors (arising in training) to precision levels (high or low)—that keeps most of the tensors in low precision and leads to sufficiently accurate models. We provide a technique that explores this memory-accuracy tradeoff by generating precision assignments for convolutional neural networks that (i) use less memory and (ii) lead to more accurate convolutional networks at the same time, compared to the precision assignments considered by prior work in low-precision floating-point training. We evaluate our technique on image classiﬁcation tasks by training convolutional networks on CIFAR-10, CIFAR-100, and ImageNet. Our method typically provides > 2× memory reduction over a baseline precision assignment while preserving training accuracy, and gives further reductions by trading off accuracy. Compared to other baselines which sometimes cause training to diverge, our method provides similar or better memory reduction while avoiding divergence.

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AAAI Conference 2020 Conference Paper

Differentiable Algorithm for Marginalising Changepoints

Hyoungjin Lim
Gwonsoo Che
Wonyeol Lee
Hongseok Yang

We present an algorithm for marginalising changepoints in time-series models that assume a ﬁxed number of unknown changepoints. Our algorithm is differentiable with respect to its inputs, which are the values of latent random variables other than changepoints. Also, it runs in time O(mn) where n is the number of time steps and m the number of changepoints, an improvement over a naive marginalisation method with O(nm ) time complexity. We derive the algorithm by identifying quantities related to this marginalisation problem, showing that these quantities satisfy recursive relationships, and transforming the relationships to an algorithm via dynamic programming. Since our algorithm is differentiable, it can be applied to convert a model non-differentiable due to changepoints to a differentiable one, so that the resulting models can be analysed using gradient-based inference or learning techniques. We empirically show the effectiveness of our algorithm in this application by tackling the posterior inference problem on synthetic and real-world data.

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NeurIPS Conference 2020 Conference Paper

On Correctness of Automatic Differentiation for Non-Differentiable Functions

Wonyeol Lee
Hangyeol Yu
Xavier Rival
Hongseok Yang

Differentiation lies at the core of many machine-learning algorithms, and is well-supported by popular autodiff systems, such as TensorFlow and PyTorch. Originally, these systems have been developed to compute derivatives of differentiable functions, but in practice, they are commonly applied to functions with non-differentiabilities. For instance, neural networks using ReLU define non-differentiable functions in general, but the gradients of losses involving those functions are computed using autodiff systems in practice. This status quo raises a natural question: are autodiff systems correct in any formal sense when they are applied to such non-differentiable functions? In this paper, we provide a positive answer to this question. Using counterexamples, we first point out flaws in often-used informal arguments, such as: non-differentiabilities arising in deep learning do not cause any issues because they form a measure-zero set. We then investigate a class of functions, called PAP functions, that includes nearly all (possibly non-differentiable) functions in deep learning nowadays. For these PAP functions, we propose a new type of derivatives, called intensional derivatives, and prove that these derivatives always exist and coincide with standard derivatives for almost all inputs. We also show that these intensional derivatives are what most autodiff systems compute or try to compute essentially. In this way, we formally establish the correctness of autodiff systems applied to non-differentiable functions.

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NeurIPS Conference 2018 Conference Paper

Reparameterization Gradient for Non-differentiable Models

Wonyeol Lee
Hangyeol Yu
Hongseok Yang

We present a new algorithm for stochastic variational inference that targets at models with non-differentiable densities. One of the key challenges in stochastic variational inference is to come up with a low-variance estimator of the gradient of a variational objective. We tackle the challenge by generalizing the reparameterization trick, one of the most effective techniques for addressing the variance issue for differentiable models, so that the trick works for non-differentiable models as well. Our algorithm splits the space of latent variables into regions where the density of the variables is differentiable, and their boundaries where the density may fail to be differentiable. For each differentiable region, the algorithm applies the standard reparameterization trick and estimates the gradient restricted to the region. For each potentially non-differentiable boundary, it uses a form of manifold sampling and computes the direction for variational parameters that, if followed, would increase the boundary’s contribution to the variational objective. The sum of all the estimates becomes the gradient estimate of our algorithm. Our estimator enjoys the reduced variance of the reparameterization gradient while remaining unbiased even for non-differentiable models. The experiments with our preliminary implementation confirm the benefit of reduced variance and unbiasedness.

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