Bayesian Optimization via Continual Variational Last Layer Training

Gaussian Processes (GPs) are widely seen as the state-of-the-art surrogate models for Bayesian optimization (BO) due to their ability to model uncertainty and their performance on tasks where correlations are easily captured (such as those defined by Euclidean metrics) and their ability to be efficiently updated online. However, the performance of GPs depends on the choice of kernel, and kernel selection for complex correlation structures is often difficult or must be made bespoke. While Bayesian neural networks (BNNs) are a promising direction for higher capacity surrogate models, they have so far seen limited use due to poor performance on some problem types. In this paper, we propose an approach which shows competitive performance on many problem types, including some that BNNs typically struggle with. We build on variational Bayesian last layers (VBLLs), and connect training of these models to exact conditioning in GPs. We exploit this connection to develop an efficient online training algorithm that interleaves conditioning and optimization. Our findings suggest that VBLL networks significantly outperform GPs and other BNN architectures on tasks with complex input correlations, and match the performance of well-tuned GPs on established benchmark tasks.

Training Language Models on the Knowledge Graph: Insights on Hallucinations and Their Detectability

While many capabilities of language models (LMs) improve with increased training budget, the influence of scale on hallucinations is not yet fully understood. Hallucinations come in many forms, and there is no universally accepted definition. We thus focus on studying only those hallucinations where a correct answer appears verbatim in the training set. To fully control the training data content, we construct a knowledge graph (KG)-based dataset, and use it to train a set of increasingly large LMs. We find that for a fixed dataset, larger and longer-trained LMs hallucinate less. However, hallucinating on $\leq5$% of the training data requires an order of magnitude larger model, and thus an order of magnitude more compute, than Hoffmann et al. (2022) reported was optimal. Given this costliness, we study how hallucination detectors depend on scale. While we see detector size improves performance on fixed LM's outputs, we find an inverse relationship between the scale of the LM and the detectability of its hallucinations.

Variational Bayesian Last Layers

We introduce a deterministic variational formulation for training Bayesian last layer neural networks. This yields a sampling-free, single-pass model and loss that effectively improves uncertainty estimation. Our variational Bayesian last layer (VBLL) can be trained and evaluated with only quadratic complexity in last layer width, and is thus (nearly) computationally free to add to standard architectures. We experimentally investigate VBLLs, and show that they improve predictive accuracy, calibration, and out of distribution detection over baselines across both regression and classification. Finally, we investigate combining VBLL layers with variational Bayesian feature learning, yielding a lower variance collapsed variational inference method for Bayesian neural networks.

Beyond Human Data: Scaling Self-Training for Problem-Solving with Language Models

Fine-tuning language models~(LMs) on human-generated data remains a prevalent practice. However, the performance of such models is often limited by the quantity and diversity of high-quality human data. In this paper, we explore whether we can go beyond human data on tasks where we have access to scalar feedback, for example, on math problems where one can verify correctness. To do so, we investigate a simple self-training method based on expectation-maximization, which we call ReST$^{EM}$, where we (1) generate samples from the model and filter them using binary feedback, (2) fine-tune the model on these samples, and (3) repeat this process a few times. Testing on advanced MATH reasoning and APPS coding benchmarks using PaLM-2 models, we find that ReST$^{EM}$ scales favorably with model size and significantly surpasses fine-tuning only on human data. Overall, our findings suggest self-training with feedback can substantially reduce dependence on human-generated data.

Kernel Regression with Infinite-Width Neural Networks on Millions of Examples

Neural kernels have drastically increased performance on diverse and nonstandard data modalities but require significantly more compute, which previously limited their application to smaller datasets. In this work, we address this by massively parallelizing their computation across many GPUs. We combine this with a distributed, preconditioned conjugate gradients algorithm to enable kernel regression at a large scale (i.e. up to five million examples). Using this approach, we study scaling laws of several neural kernels across many orders of magnitude for the CIFAR-5m dataset. Using data augmentation to expand the original CIFAR-10 training dataset by a factor of 20, we obtain a test accuracy of 91.2\% (SotA for a pure kernel method). Moreover, we explore neural kernels on other data modalities, obtaining results on protein and small molecule prediction tasks that are competitive with SotA methods.

Plex: Towards Reliability using Pretrained Large Model Extensions

A recent trend in artificial intelligence is the use of pretrained models for language and vision tasks, which have achieved extraordinary performance but also puzzling failures. Probing these models' abilities in diverse ways is therefore critical to the field. In this paper, we explore the reliability of models, where we define a reliable model as one that not only achieves strong predictive performance but also performs well consistently over many decision-making tasks involving uncertainty (e.g., selective prediction, open set recognition), robust generalization (e.g., accuracy and proper scoring rules such as log-likelihood on in- and out-of-distribution datasets), and adaptation (e.g., active learning, few-shot uncertainty). We devise 10 types of tasks over 40 datasets in order to evaluate different aspects of reliability on both vision and language domains. To improve reliability, we developed ViT-Plex and T5-Plex, pretrained large model extensions for vision and language modalities, respectively. Plex greatly improves the state-of-the-art across reliability tasks, and simplifies the traditional protocol as it improves the out-of-the-box performance and does not require designing scores or tuning the model for each task. We demonstrate scaling effects over model sizes up to 1B parameters and pretraining dataset sizes up to 4B examples. We also demonstrate Plex's capabilities on challenging tasks including zero-shot open set recognition, active learning, and uncertainty in conversational language understanding.

Pre-training helps Bayesian optimization too

Bayesian optimization (BO) has become a popular strategy for global optimization of many expensive real-world functions. Contrary to a common belief that BO is suited to optimizing black-box functions, it actually requires domain knowledge on characteristics of those functions to deploy BO successfully. Such domain knowledge often manifests in Gaussian process priors that specify initial beliefs on functions. However, even with expert knowledge, it is not an easy task to select a prior. This is especially true for hyperparameter tuning problems on complex machine learning models, where landscapes of tuning objectives are often difficult to comprehend. We seek an alternative practice for setting these functional priors. In particular, we consider the scenario where we have data from similar functions that allow us to pre-train a tighter distribution a priori. To verify our approach in realistic model training setups, we collected a large multi-task hyperparameter tuning dataset by training tens of thousands of configurations of near-state-of-the-art models on popular image and text datasets, as well as a protein sequence dataset. Our results show that on average, our method is able to locate good hyperparameters at least 3 times more efficiently than the best competing methods.

A Simple Approach to Improve Single-Model Deep Uncertainty via Distance-Awareness

Accurate uncertainty quantification is a major challenge in deep learning, as neural networks can make overconfident errors and assign high confidence predictions to out-of-distribution (OOD) inputs. The most popular approaches to estimate predictive uncertainty in deep learning are methods that combine predictions from multiple neural networks, such as Bayesian neural networks (BNNs) and deep ensembles. However their practicality in real-time, industrial-scale applications are limited due to the high memory and computational cost. Furthermore, ensembles and BNNs do not necessarily fix all the issues with the underlying member networks. In this work, we study principled approaches to improve uncertainty property of a single network, based on a single, deterministic representation. By formalizing the uncertainty quantification as a minimax learning problem, we first identify distance awareness, i.e., the model's ability to quantify the distance of a testing example from the training data, as a necessary condition for a DNN to achieve high-quality (i.e., minimax optimal) uncertainty estimation. We then propose Spectral-normalized Neural Gaussian Process (SNGP), a simple method that improves the distance-awareness ability of modern DNNs with two simple changes: (1) applying spectral normalization to hidden weights to enforce bi-Lipschitz smoothness in representations and (2) replacing the last output layer with a Gaussian process layer. On a suite of vision and language understanding benchmarks, SNGP outperforms other single-model approaches in prediction, calibration and out-of-domain detection. Furthermore, SNGP provides complementary benefits to popular techniques such as deep ensembles and data augmentation, making it a simple and scalable building block for probabilistic deep learning. Code is open-sourced at https://github.com/google/uncertainty-baselines

Predicting the utility of search spaces for black-box optimization: a simple, budget-aware approach

Black box optimization requires specifying a search space to explore for solutions, e.g. a d-dimensional compact space, and this choice is critical for getting the best results at a reasonable budget. Unfortunately, determining a high quality search space can be challenging in many applications. For example, when tuning hyperparameters for machine learning pipelines on a new problem given a limited budget, one must strike a balance between excluding potentially promising regions and keeping the search space small enough to be tractable. The goal of this work is to motivate -- through example applications in tuning deep neural networks -- the problem of predicting the quality of search spaces conditioned on budgets, as well as to provide a simple scoring method based on a utility function applied to a probabilistic response surface model, similar to Bayesian optimization. We show that the method we present can compute meaningful budget-conditional scores in a variety of situations. We also provide experimental evidence that accurate scores can be useful in constructing and pruning search spaces. Ultimately, we believe scoring search spaces should become standard practice in the experimental workflow for deep learning.

Sparse MoEs meet Efficient Ensembles

Machine learning models based on the aggregated outputs of submodels, either at the activation or prediction levels, lead to strong performance. We study the interplay of two popular classes of such models: ensembles of neural networks and sparse mixture of experts (sparse MoEs). First, we show that these two approaches have complementary features whose combination is beneficial. Then, we present partitioned batch ensembles, an efficient ensemble of sparse MoEs that takes the best of both classes of models. Extensive experiments on fine-tuned vision transformers demonstrate the accuracy, log-likelihood, few-shot learning, robustness, and uncertainty calibration improvements of our approach over several challenging baselines. Partitioned batch ensembles not only scale to models with up to 2.7B parameters, but also provide larger performance gains for larger models.