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Jack Richter-Powell, Luca Thiede, Alán Asparu-Guzik, David Duvenaud

Molecular modeling at the quantum level requires choosing a parameterization of the wavefunction that both respects the required particle symmetries, and is scalable to systems of many particles. For the simulation of fermions, valid parameterizations must be antisymmetric with respect to the exchange of particles. Typically, antisymmetry is enforced by leveraging the anti-symmetry of determinants with respect to the exchange of matrix rows, but this involves computing a full determinant each time the wavefunction is evaluated. Instead, we introduce a new antisymmetrization layer derived from sorting, the $\textit{sortlet}$, which scales as $O(N \log N)$ with regards to the number of particles -- in contrast to $O(N^3)$ for the determinant. We show numerically that applying this anti-symmeterization layer on top of an attention based neural-network backbone yields a flexible wavefunction parameterization capable of reaching chemical accuracy when approximating the ground state of first-row atoms and small molecules.

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Mrinank Sharma, Meg Tong, Tomasz Korbak, David Duvenaud, Amanda Askell, Samuel R. Bowman, Newton Cheng, Esin Durmus, Zac Hatfield-Dodds, Scott R. Johnston, Shauna Kravec, Timothy Maxwell, Sam McCandlish, Kamal Ndousse, Oliver Rausch, Nicholas Schiefer, Da Yan, Miranda Zhang, Ethan Perez

Human feedback is commonly utilized to finetune AI assistants. But human feedback may also encourage model responses that match user beliefs over truthful ones, a behaviour known as sycophancy. We investigate the prevalence of sycophancy in models whose finetuning procedure made use of human feedback, and the potential role of human preference judgments in such behavior. We first demonstrate that five state-of-the-art AI assistants consistently exhibit sycophancy across four varied free-form text-generation tasks. To understand if human preferences drive this broadly observed behavior, we analyze existing human preference data. We find that when a response matches a user's views, it is more likely to be preferred. Moreover, both humans and preference models (PMs) prefer convincingly-written sycophantic responses over correct ones a non-negligible fraction of the time. Optimizing model outputs against PMs also sometimes sacrifices truthfulness in favor of sycophancy. Overall, our results indicate that sycophancy is a general behavior of state-of-the-art AI assistants, likely driven in part by human preference judgments favoring sycophantic responses.

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Dami Choi, Yonadav Shavit, David Duvenaud

It is important that consumers and regulators can verify the provenance of large neural models to evaluate their capabilities and risks. We introduce the concept of a "Proof-of-Training-Data": any protocol that allows a model trainer to convince a Verifier of the training data that produced a set of model weights. Such protocols could verify the amount and kind of data and compute used to train the model, including whether it was trained on specific harmful or beneficial data sources. We explore efficient verification strategies for Proof-of-Training-Data that are compatible with most current large-model training procedures. These include a method for the model-trainer to verifiably pre-commit to a random seed used in training, and a method that exploits models' tendency to temporarily overfit to training data in order to detect whether a given data-point was included in training. We show experimentally that our verification procedures can catch a wide variety of attacks, including all known attacks from the Proof-of-Learning literature.

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Paul Vicol, Jonathan Lorraine, Fabian Pedregosa, David Duvenaud, Roger Grosse

Many problems in machine learning involve bilevel optimization (BLO), including hyperparameter optimization, meta-learning, and dataset distillation. Bilevel problems consist of two nested sub-problems, called the outer and inner problems, respectively. In practice, often at least one of these sub-problems is overparameterized. In this case, there are many ways to choose among optima that achieve equivalent objective values. Inspired by recent studies of the implicit bias induced by optimization algorithms in single-level optimization, we investigate the implicit bias of gradient-based algorithms for bilevel optimization. We delineate two standard BLO methods -- cold-start and warm-start -- and show that the converged solution or long-run behavior depends to a large degree on these and other algorithmic choices, such as the hypergradient approximation. We also show that the inner solutions obtained by warm-start BLO can encode a surprising amount of information about the outer objective, even when the outer parameters are low-dimensional. We believe that implicit bias deserves as central a role in the study of bilevel optimization as it has attained in the study of single-level neural net optimization.

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Aniruddh Raghu, Jonathan Lorraine, Simon Kornblith, Matthew McDermott, David Duvenaud

Pre-training (PT) followed by fine-tuning (FT) is an effective method for training neural networks, and has led to significant performance improvements in many domains. PT can incorporate various design choices such as task and data reweighting strategies, augmentation policies, and noise models, all of which can significantly impact the quality of representations learned. The hyperparameters introduced by these strategies therefore must be tuned appropriately. However, setting the values of these hyperparameters is challenging. Most existing methods either struggle to scale to high dimensions, are too slow and memory-intensive, or cannot be directly applied to the two-stage PT and FT learning process. In this work, we propose an efficient, gradient-based algorithm to meta-learn PT hyperparameters. We formalize the PT hyperparameter optimization problem and propose a novel method to obtain PT hyperparameter gradients by combining implicit differentiation and backpropagation through unrolled optimization. We demonstrate that our method improves predictive performance on two real-world domains. First, we optimize high-dimensional task weighting hyperparameters for multitask pre-training on protein-protein interaction graphs and improve AUROC by up to 3.9%. Second, we optimize a data augmentation neural network for self-supervised PT with SimCLR on electrocardiography data and improve AUROC by up to 1.9%.

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Jonathan Lorraine, David Acuna, Paul Vicol, David Duvenaud

We generalize gradient descent with momentum for learning in differentiable games to have complex-valued momentum. We give theoretical motivation for our method by proving convergence on bilinear zero-sum games for simultaneous and alternating updates. Our method gives real-valued parameter updates, making it a drop-in replacement for standard optimizers. We empirically demonstrate that complex-valued momentum can improve convergence in adversarial games - like generative adversarial networks - by showing we can find better solutions with an almost identical computational cost. We also show a practical generalization to a complex-valued Adam variant, which we use to train BigGAN to better inception scores on CIFAR-10.

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Winnie Xu, Ricky T. Q. Chen, Xuechen Li, David Duvenaud

We perform scalable approximate inference in a recently-proposed family of continuous-depth Bayesian neural networks. In this model class, uncertainty about separate weights in each layer produces dynamics that follow a stochastic differential equation (SDE). 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 approaches the true posterior. This approach further inherits the memory-efficient training and tunable precision of neural ODEs.

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Will Grathwohl, Kevin Swersky, Milad Hashemi, David Duvenaud, Chris J. Maddison

We propose a general and scalable approximate sampling strategy for probabilistic models with discrete variables. Our approach uses gradients of the likelihood function with respect to its discrete inputs to propose updates in a Metropolis-Hastings sampler. We show empirically that this approach outperforms generic samplers in a number of difficult settings including Ising models, Potts models, restricted Boltzmann machines, and factorial hidden Markov models. We also demonstrate the use of our improved sampler for training deep energy-based models on high dimensional discrete data. This approach outperforms variational auto-encoders and existing energy-based models. Finally, we give bounds showing that our approach is near-optimal in the class of samplers which propose local updates.

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