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When training deep learning models, the performance depends largely on the selected hyperparameters. However, hyperparameter optimization (HPO) is often one of the most expensive parts of model design. Classical HPO methods treat this as a black-box optimization problem. However, gray-box HPO methods, which incorporate more information about the setup, have emerged as a promising direction for more efficient optimization. For example, using intermediate loss evaluations to terminate bad selections. In this work, we propose an HPO method for neural networks using logged checkpoints of the trained weights to guide future hyperparameter selections. Our method, Forecasting Model Search (FMS), embeds weights into a Gaussian process deep kernel surrogate model, using a permutation-invariant graph metanetwork to be data-efficient with the logged network weights. To facilitate reproducibility and further research, we open-source our code at https://github.com/NVlabs/forecasting-model-search., Comment: See the project website at https://research.nvidia.com/labs/toronto-ai/FMS/

Recent text-to-3D generation approaches produce impressive 3D results but require time-consuming optimization that can take up to an hour per prompt. Amortized methods like ATT3D optimize multiple prompts simultaneously to improve efficiency, enabling fast text-to-3D synthesis. However, they cannot capture high-frequency geometry and texture details and struggle to scale to large prompt sets, so they generalize poorly. We introduce LATTE3D, addressing these limitations to achieve fast, high-quality generation on a significantly larger prompt set. Key to our method is 1) building a scalable architecture and 2) leveraging 3D data during optimization through 3D-aware diffusion priors, shape regularization, and model initialization to achieve robustness to diverse and complex training prompts. LATTE3D amortizes both neural field and textured surface generation to produce highly detailed textured meshes in a single forward pass. LATTE3D generates 3D objects in 400ms, and can be further enhanced with fast test-time optimization., Comment: See the project website at https://research.nvidia.com/labs/toronto-ai/LATTE3D/

Neural networks efficiently encode learned information within their parameters. Consequently, many tasks can be unified by treating neural networks themselves as input data. When doing so, recent studies demonstrated the importance of accounting for the symmetries and geometry of parameter spaces. However, those works developed architectures tailored to specific networks such as MLPs and CNNs without normalization layers, and generalizing such architectures to other types of networks can be challenging. In this work, we overcome these challenges by building new metanetworks - neural networks that take weights from other neural networks as input. Put simply, we carefully build graphs representing the input neural networks and process the graphs using graph neural networks. Our approach, Graph Metanetworks (GMNs), generalizes to neural architectures where competing methods struggle, such as multi-head attention layers, normalization layers, convolutional layers, ResNet blocks, and group-equivariant linear layers. We prove that GMNs are expressive and equivariant to parameter permutation symmetries that leave the input neural network functions unchanged. We validate the effectiveness of our method on several metanetwork tasks over diverse neural network architectures., Comment: 29 pages. v2 updated experimental results and details

Text-to-3D modelling has seen exciting progress by combining generative text-to-image models with image-to-3D methods like Neural Radiance Fields. DreamFusion recently achieved high-quality results but requires a lengthy, per-prompt optimization to create 3D objects. To address this, we amortize optimization over text prompts by training on many prompts simultaneously with a unified model, instead of separately. With this, we share computation across a prompt set, training in less time than per-prompt optimization. Our framework - Amortized text-to-3D (ATT3D) - enables knowledge-sharing between prompts to generalize to unseen setups and smooth interpolations between text for novel assets and simple animations., Comment: 22 pages, 20 figures

Sim2Real domain adaptation (DA) research focuses on the constrained setting of adapting from a labeled synthetic source domain to an unlabeled or sparsely labeled real target domain. However, for high-stakes applications (e.g. autonomous driving), it is common to have a modest amount of human-labeled real data in addition to plentiful auto-labeled source data (e.g. from a driving simulator). We study this setting of supervised sim2real DA applied to 2D object detection. We propose Domain Translation via Conditional Alignment and Reweighting (CARE) a novel algorithm that systematically exploits target labels to explicitly close the sim2real appearance and content gaps. We present an analytical justification of our algorithm and demonstrate strong gains over competing methods on standard benchmarks.

Calibration is a fundamental property of a good predictive model: it requires that the model predicts correctly in proportion to its confidence. Modern neural networks, however, provide no strong guarantees on their calibration -- and can be either poorly calibrated or well-calibrated depending on the setting. It is currently unclear which factors contribute to good calibration (architecture, data augmentation, overparameterization, etc), though various claims exist in the literature. We propose a systematic way to study the calibration error: by decomposing it into (1) calibration error on the train set, and (2) the calibration generalization gap. This mirrors the fundamental decomposition of generalization. We then investigate each of these terms, and give empirical evidence that (1) DNNs are typically always calibrated on their train set, and (2) the calibration generalization gap is upper-bounded by the standard generalization gap. Taken together, this implies that models with small generalization gap (|Test Error - Train Error|) are well-calibrated. This perspective unifies many results in the literature, and suggests that interventions which reduce the generalization gap (such as adding data, using heavy augmentation, or smaller model size) also improve calibration. We thus hope our initial study lays the groundwork for a more systematic and comprehensive understanding of the relation between calibration, generalization, and optimization., Comment: Appeared at ICML 2022 Workshop on Distribution-Free Uncertainty Quantification

Modern deep learning systems require huge data sets to achieve impressive performance, but there is little guidance on how much or what kind of data to collect. Over-collecting data incurs unnecessary present costs, while under-collecting may incur future costs and delay workflows. We propose a new paradigm for modeling the data collection workflow as a formal optimal data collection problem that allows designers to specify performance targets, collection costs, a time horizon, and penalties for failing to meet the targets. Additionally, this formulation generalizes to tasks requiring multiple data sources, such as labeled and unlabeled data used in semi-supervised learning. To solve our problem, we develop Learn-Optimize-Collect (LOC), which minimizes expected future collection costs. Finally, we numerically compare our framework to the conventional baseline of estimating data requirements by extrapolating from neural scaling laws. We significantly reduce the risks of failing to meet desired performance targets on several classification, segmentation, and detection tasks, while maintaining low total collection costs., Comment: Accepted to NeurIPS 2022

Given a small training data set and a learning algorithm, how much more data is necessary to reach a target validation or test performance? This question is of critical importance in applications such as autonomous driving or medical imaging where collecting data is expensive and time-consuming. Overestimating or underestimating data requirements incurs substantial costs that could be avoided with an adequate budget. Prior work on neural scaling laws suggest that the power-law function can fit the validation performance curve and extrapolate it to larger data set sizes. We find that this does not immediately translate to the more difficult downstream task of estimating the required data set size to meet a target performance. In this work, we consider a broad class of computer vision tasks and systematically investigate a family of functions that generalize the power-law function to allow for better estimation of data requirements. Finally, we show that incorporating a tuned correction factor and collecting over multiple rounds significantly improves the performance of the data estimators. Using our guidelines, practitioners can accurately estimate data requirements of machine learning systems to gain savings in both development time and data acquisition costs., Comment: Accepted to CVPR 2022

Modern computer vision applications rely on learning-based perception modules parameterized with neural networks for tasks like object detection. These modules frequently have low expected error overall but high error on atypical groups of data due to biases inherent in the training process. In building autonomous vehicles (AV), this problem is an especially important challenge because their perception modules are crucial to the overall system performance. After identifying failures in AV, a human team will comb through the associated data to group perception failures that share common causes. More data from these groups is then collected and annotated before retraining the model to fix the issue. In other words, error groups are found and addressed in hindsight. Our main contribution is a pseudo-automatic method to discover such groups in foresight by performing causal interventions on simulated scenes. To keep our interventions on the data manifold, we utilize masked language models. We verify that the prioritized groups found via intervention are challenging for the object detector and show that retraining with data collected from these groups helps inordinately compared to adding more IID data. We also plan to release software to run interventions in simulated scenes, which we hope will benefit the causality community., Comment: In submission at JMLR; 0xe5110eA3B5014cd9a585Dc76c74Ee509F504Be14

Linear interpolation between initial neural network parameters and converged parameters after training with stochastic gradient descent (SGD) typically leads to a monotonic decrease in the training objective. This Monotonic Linear Interpolation (MLI) property, first observed by Goodfellow et al. (2014) persists in spite of the non-convex objectives and highly non-linear training dynamics of neural networks. Extending this work, we evaluate several hypotheses for this property that, to our knowledge, have not yet been explored. Using tools from differential geometry, we draw connections between the interpolated paths in function space and the monotonicity of the network - providing sufficient conditions for the MLI property under mean squared error. While the MLI property holds under various settings (e.g. network architectures and learning problems), we show in practice that networks violating the MLI property can be produced systematically, by encouraging the weights to move far from initialization. The MLI property raises important questions about the loss landscape geometry of neural networks and highlights the need to further study their global properties., Comment: 15 pages in main paper, 4 pages of references, 24 pages in appendix. 29 figures in total

Despite impressive progress in deep learning, generalizing far beyond the training distribution is an important open challenge. In this work, we consider few-shot classification, and aim to shed light on what makes some novel classes easier to learn than others, and what types of learned representations generalize better. To this end, we define a new paradigm in terms of attributes -- simple building blocks of which concepts are formed -- as a means of quantifying the degree of relatedness of different concepts. Our empirical analysis reveals that supervised learning generalizes poorly to new attributes, but a combination of self-supervised pretraining with supervised finetuning leads to stronger generalization. The benefit of self-supervised pretraining and supervised finetuning is further investigated through controlled experiments using random splits of the attribute space, and we find that predictability of test attributes provides an informative estimate of a model's generalization ability., Comment: Technical report, 26 pages

Machine learning models have traditionally been developed under the assumption that the training and test distributions match exactly. However, recent success in few-shot learning and related problems are encouraging signs that these models can be adapted to more realistic settings where train and test distributions differ. Unfortunately, there is severely limited theoretical support for these algorithms and little is known about the difficulty of these problems. In this work, we provide novel information-theoretic lower-bounds on minimax rates of convergence for algorithms that are trained on data from multiple sources and tested on novel data. Our bounds depend intuitively on the information shared between sources of data, and characterize the difficulty of learning in this setting for arbitrary algorithms. We demonstrate these bounds on a hierarchical Bayesian model of meta-learning, computing both upper and lower bounds on parameter estimation via maximum-a-posteriori inference., Comment: 12 pages in main paper,22 pages in appendix,4 figures total

Our understanding of learning input-output relationships with neural nets has improved rapidly in recent years, but little is known about the convergence of the underlying representations, even in the simple case of linear autoencoders (LAEs). We show that when trained with proper regularization, LAEs can directly learn the optimal representation -- ordered, axis-aligned principal components. We analyze two such regularization schemes: non-uniform $\ell_2$ regularization and a deterministic variant of nested dropout [Rippel et al, ICML' 2014]. Though both regularization schemes converge to the optimal representation, we show that this convergence is slow due to ill-conditioning that worsens with increasing latent dimension. We show that the inefficiency of learning the optimal representation is not inevitable -- we present a simple modification to the gradient descent update that greatly speeds up convergence empirically.

Posterior collapse in Variational Autoencoders (VAEs) arises when the variational posterior distribution closely matches the prior for a subset of latent variables. This paper presents a simple and intuitive explanation for posterior collapse through the analysis of linear VAEs and their direct correspondence with Probabilistic PCA (pPCA). We explain how posterior collapse may occur in pPCA due to local maxima in the log marginal likelihood. Unexpectedly, we prove that the ELBO objective for the linear VAE does not introduce additional spurious local maxima relative to log marginal likelihood. We show further that training a linear VAE with exact variational inference recovers an identifiable global maximum corresponding to the principal component directions. Empirically, we find that our linear analysis is predictive even for high-capacity, non-linear VAEs and helps explain the relationship between the observation noise, local maxima, and posterior collapse in deep Gaussian VAEs., Comment: 11 main pages, 10 appendix pages. 13 figures total. Accepted at 33rd Conference on Neural Information Processing Systems (NeurIPS 2019)

Lipschitz constraints under L2 norm on deep neural networks are useful for provable adversarial robustness bounds, stable training, and Wasserstein distance estimation. While heuristic approaches such as the gradient penalty have seen much practical success, it is challenging to achieve similar practical performance while provably enforcing a Lipschitz constraint. In principle, one can design Lipschitz constrained architectures using the composition property of Lipschitz functions, but Anil et al. recently identified a key obstacle to this approach: gradient norm attenuation. They showed how to circumvent this problem in the case of fully connected networks by designing each layer to be gradient norm preserving. We extend their approach to train scalable, expressive, provably Lipschitz convolutional networks. In particular, we present the Block Convolution Orthogonal Parameterization (BCOP), an expressive parameterization of orthogonal convolution operations. We show that even though the space of orthogonal convolutions is disconnected, the largest connected component of BCOP with 2n channels can represent arbitrary BCOP convolutions over n channels. Our BCOP parameterization allows us to train large convolutional networks with provable Lipschitz bounds. Empirically, we find that it is competitive with existing approaches to provable adversarial robustness and Wasserstein distance estimation., Comment: 9 main pages, 31 pages total, 3 figures. Accepted at 33rd Conference on Neural Information Processing Systems (NeurIPS 2019)

The vast majority of successful deep neural networks are trained using variants of stochastic gradient descent (SGD) algorithms. Recent attempts to improve SGD can be broadly categorized into two approaches: (1) adaptive learning rate schemes, such as AdaGrad and Adam, and (2) accelerated schemes, such as heavy-ball and Nesterov momentum. In this paper, we propose a new optimization algorithm, Lookahead, that is orthogonal to these previous approaches and iteratively updates two sets of weights. Intuitively, the algorithm chooses a search direction by looking ahead at the sequence of fast weights generated by another optimizer. We show that Lookahead improves the learning stability and lowers the variance of its inner optimizer with negligible computation and memory cost. We empirically demonstrate Lookahead can significantly improve the performance of SGD and Adam, even with their default hyperparameter settings on ImageNet, CIFAR-10/100, neural machine translation, and Penn Treebank., Comment: Accepted to Neural Information Processing Systems 2019. Code available at: https://github.com/michaelrzhang/lookahead

Training neural networks under a strict Lipschitz constraint is useful for provable adversarial robustness, generalization bounds, interpretable gradients, and Wasserstein distance estimation. By the composition property of Lipschitz functions, it suffices to ensure that each individual affine transformation or nonlinear activation is 1-Lipschitz. The challenge is to do this while maintaining the expressive power. We identify a necessary property for such an architecture: each of the layers must preserve the gradient norm during backpropagation. Based on this, we propose to combine a gradient norm preserving activation function, GroupSort, with norm-constrained weight matrices. We show that norm-constrained GroupSort architectures are universal Lipschitz function approximators. Empirically, we show that norm-constrained GroupSort networks achieve tighter estimates of Wasserstein distance than their ReLU counterparts and can achieve provable adversarial robustness guarantees with little cost to accuracy., Comment: 8 main pages, 21 pages total, 17 figures. Accepted at ICML 2019

When assessing student work, graders will often find that some students will leave one or more problems blank on assessments. Since there is no work shown, the grader has no means to evaluate the student's understanding of a particular problem, and thus awards 'zero' points. This practice punishes the student behavior of leaving a problem blank, but this zero is not necessarily an accurate assessment of student understanding of a particular topic. While some might argue that this practice is 'fair' in that students are aware that they can't receive points for problems they don't attempt, we share evidence that this practice unequally impacts different student groups. We analyze 10 years of UC Davis introductory physics course databases to show that different groups of students (by gender, racial/ethnic group, first generation, etc.) skip problems, and entire exams at different rates. We also share some implications for grading and teaching practices.

Bayesian neural networks (BNNs) allow us to reason about uncertainty in a principled way. Stochastic Gradient Langevin Dynamics (SGLD) enables efficient BNN learning by drawing samples from the BNN posterior using mini-batches. However, SGLD and its extensions require storage of many copies of the model parameters, a potentially prohibitive cost, especially for large neural networks. We propose a framework, Adversarial Posterior Distillation, to distill the SGLD samples using a Generative Adversarial Network (GAN). At test-time, samples are generated by the GAN. We show that this distillation framework incurs no loss in performance on recent BNN applications including anomaly detection, active learning, and defense against adversarial attacks. By construction, our framework not only distills the Bayesian predictive distribution, but the posterior itself. This allows one to compute quantities such as the approximate model variance, which is useful in downstream tasks. To our knowledge, these are the first results applying MCMC-based BNNs to the aforementioned downstream applications., Comment: accepted at ICML 2018

Momentum is a simple and widely used trick which allows gradient-based optimizers to pick up speed along low curvature directions. Its performance depends crucially on a damping coefficient $\beta$. Large $\beta$ values can potentially deliver much larger speedups, but are prone to oscillations and instability; hence one typically resorts to small values such as 0.5 or 0.9. We propose Aggregated Momentum (AggMo), a variant of momentum which combines multiple velocity vectors with different $\beta$ parameters. AggMo is trivial to implement, but significantly dampens oscillations, enabling it to remain stable even for aggressive $\beta$ values such as 0.999. We reinterpret Nesterov's accelerated gradient descent as a special case of AggMo and analyze rates of convergence for quadratic objectives. Empirically, we find that AggMo is a suitable drop-in replacement for other momentum methods, and frequently delivers faster convergence., Comment: 11 primary pages, 11 supplementary pages, 12 figures total