Posts in category: Google AI

Posted by Dustin Tran and Balaji Lakshminarayanan, Research Scientists, Google Research

Deep learning models have made impressive progress in vision, language, and other modalities, particularly with the rise of large-scale pre-training. Such models are most accurate when applied to test data drawn from the same distribution as their training set. However, in practice, the data confronting models in real-world settings rarely match the training distribution. In addition, the models may not be well-suited for applications where predictive performance is only part of the equation. For models to be reliable in deployment, they must be able to accommodate shifts in data distribution and make useful decisions in a broad array of scenarios.

In “Plex: Towards Reliability Using Pre-trained Large Model Extensions”, we present a framework for reliable deep learning as a new perspective about a model’s abilities; this includes a number of concrete tasks and datasets for stress-testing model reliability. We also introduce Plex, a set of pre-trained large model extensions that can be applied to many different architectures. We illustrate the efficacy of Plex in the vision and language domains by applying these extensions to the current state-of-the-art Vision Transformer and T5 models, which results in significant improvement in their reliability. We are also open-sourcing the code to encourage further research into this approach.

Uncertainty — Dog vs. Cat classifier: Plex can say “I don’t know” for inputs that are neither cat nor dog. Robust Generalization — A naïve model is sensitive to spurious correlations (“destination”), whereas Plex is robust. Adaptation — Plex can actively choose the data from which it learns to improve performance more quickly.

Framework for Reliability
First, we explore how to understand the reliability of a model in novel scenarios. We posit three general categories of requirements for reliable machine learning (ML) systems: (1) they should accurately report uncertainty about their predictions (“know what they don’t know”); (2) they should generalize robustly to new scenarios (distribution shift); and (3) they should be able to efficiently adapt to new data (adaptation). Importantly, a reliable model should aim to do well in all of these areas simultaneously out-of-the-box, without requiring any customization for individual tasks.

• Uncertainty reflects the imperfect or unknown information that makes it difficult for a model to make accurate predictions. Predictive uncertainty quantification allows a model to compute optimal decisions and helps practitioners recognize when to trust the model’s predictions, thereby enabling graceful failures when the model is likely to be wrong.
• Robust Generalization involves an estimate or forecast about an unseen event. We investigate four types of out-of-distribution data: covariate shift (when the input distribution changes between training and application and the output distribution is unchanged), semantic (or class) shift, label uncertainty, and subpopulation shift.

  Types of distribution shift using an illustration of ImageNet dogs.

• Adaptation refers to probing the model’s abilities over the course of its learning process. Benchmarks typically evaluate on static datasets with pre-defined train-test splits. However, in many applications, we are interested in models that can quickly adapt to new datasets and efficiently learn with as few labeled examples as possible.

Reliability framework. We propose to simultaneously stress-test the “out-of-the-box” model performance (i.e., the predictive distribution) across uncertainty, robust generalization, and adaptation benchmarks, without any customization for individual tasks.

We apply 10 types of tasks to capture the three reliability areas — uncertainty, robust generalization, and adaptation — and to ensure that the tasks measure a diverse set of desirable properties in each area. Together the tasks comprise 40 downstream datasets across vision and natural language modalities: 14 datasets for fine-tuning (including few-shot and active learning–based adaptation) and 26 datasets for out-of-distribution evaluation.

Plex: Pre-trained Large Model Extensions for Vision and Language
To improve reliability, we develop ViT-Plex and T5-Plex, building on large pre-trained models for vision (ViT) and language (T5), respectively. A key feature of Plex is more efficient ensembling based on submodels that each make a prediction that is then aggregated. In addition, Plex swaps each architecture’s linear last layer with a Gaussian process or heteroscedastic layer to better represent predictive uncertainty. These ideas were found to work very well for models trained from scratch at the ImageNet scale. We train the models with varying sizes up to 325 million parameters for vision (ViT-Plex L) and 1 billion parameters for language (T5-Plex L) and pre-training dataset sizes up to 4 billion examples.

The following figure illustrates Plex’s performance on a select set of tasks compared to the existing state-of-the-art. The top-performing model for each task is usually a specialized model that is highly optimized for that problem. Plex achieves new state-of-the-art on many of the 40 datasets. Importantly, Plex achieves strong performance across all tasks using the out-of-the-box model output without requiring any custom designing or tuning for each task.

The largest T5-Plex (top) and ViT-Plex (bottom) models evaluated on a highlighted set of reliability tasks compared to specialized state-of-the-art models. The spokes display different tasks, quantifying metric performance on various datasets.

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The largest T5-Plex (top) and ViT-Plex (bottom) models evaluated on a highlighted set of reliability tasks compared to specialized state-of-the-art models. The spokes display different tasks, quantifying metric performance on various datasets.

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Plex in Action for Different Reliability Tasks
We highlight Plex’s reliability on select tasks below.

Open Set Recognition
We show Plex’s output in the case where the model must defer prediction because the input is one that the model does not support. This task is known as open set recognition. Here, predictive performance is part of a larger decision-making scenario where the model may abstain from making certain predictions. In the following figure, we show structured open set recognition: Plex returns multiple outputs and signals the specific part of the output about which the model is uncertain and is likely out-of-distribution.

Structured open set recognition enables the model to provide nuanced clarifications. Here, T5-Plex L can recognize fine-grained out-of-distribution cases where the request’s vertical (i.e., coarse-level domain of service, such as banking, media, productivity, etc.) and domain are supported but the intent is not.

Label Uncertainty
In real-world datasets, there is often inherent ambiguity behind the ground truth label for each input. For example, this may arise due to human rater ambiguity for a given image. In this case, we’d like the model to capture the full distribution of human perceptual uncertainty. We showcase Plex below on examples from an ImageNet variant we constructed that provides a ground truth label distribution.

Plex for label uncertainty. Using a dataset we construct called ImageNet ReaL-H, ViT-Plex L demonstrates the ability to capture the inherent ambiguity (probability distribution) of image labels.

Active Learning
We examine a large model’s ability to not only learn over a fixed set of data points, but also participate in knowing which data points to learn from in the first place. One such task is known as active learning, where at each training step, the model selects promising inputs among a pool of unlabeled data points on which to train. This procedure assesses an ML model’s label efficiency, where label annotations may be scarce, and so we would like to maximize performance while minimizing the number of labeled data points used. Plex achieves a significant performance improvement over the same model architecture without pre-training. Compared to the state-of-the-art in literature, BASE achieves around 63% accuracy at 100K examples, achieving a lower accuracy and requiring more examples.

Active learning on ImageNet1K. ViT-Plex L is highly label efficient compared to a baseline that doesn’t leverage pre-training. We also find that active learning’s data acquisition strategy is more effective than uniformly selecting data points at random.

Learn more
Check out our paper here and an upcoming contributed talk about the work at the ICML 2022 pre-training workshop on July 23, 2022. To encourage further research in this direction, we are open-sourcing all code for training and evaluation as part of Uncertainty Baselines. We also provide a demo that shows how to use a ViT-Plex model checkpoint. Layer and method implementations use Edward2.

Acknowledgements
We thank all the co-authors for contributing to the project and paper, including Andreas Kirsch, Clara Huiyi Hu, Du Phan, D. Sculley, Honglin Yuan, Jasper Snoek, Jeremiah Liu, Jie Ren, Joost van Amersfoort, Karan Singhal, Kehang Han, Kelly Buchanan, Kevin Murphy, Mark Collier​​, Mike Dusenberry, Neil Band, Nithum Thain, Rodolphe Jenatton, Tim G. J. Rudner, Yarin Gal, Zachary Nado, Zelda Mariet, Zi Wang, and Zoubin Ghahramani. We also thank Anusha Ramesh, Ben Adlam, Dilip Krishnan, Ed Chi, Rif A. Saurous, and Sharat Chikkerur for their helpful feedback, and Tom Small and Ajay Nainani for helping with visualizations.

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Posted by Soravit Beer Changpinyo and Doron Kukliansky‎, Senior Software Engineers, Google Research

Visual Question Answering (VQA) is a useful machine learning (ML) task that requires a model to answer a visual question about an image. What makes it challenging is its multi-task and open-ended nature; it involves solving multiple technical research questions in computer vision and natural language understanding simultaneously. Yet, progress on this task would enable a wide range of applications, from assisting the blind and the visually-impaired or communicating with robots to enhancing the user’s visual experience with external knowledge.

Effective and robust VQA systems cannot exist without high-quality, semantically and stylistically diverse large-scale training data of image-question-answer triplets. But, creating such data is time consuming and onerous. Perhaps unsurprisingly, the VQA community has focused more on sophisticated model development rather than scalable data creation.

In “All You May Need for VQA are Image Captions,” published at NAACL 2022, we explore VQA data generation by proposing “Visual Question Generation with Question Answering Validation” (VQ²A), a pipeline that works by rewriting a declarative caption into multiple interrogative question-answer pairs. More specifically, we leverage two existing assets — (i) large-scale image-text data and (ii) large-capacity neural text-to-text models — to achieve automatic VQA data generation. As the field has progressed, the research community has been making these assets larger and stronger in isolation (for general purposes such as learning text-only or image-text representations); together, they can achieve more and we adapt them for VQA data creation purposes. We find our approach can generate question-answer pairs with high precision and that this data can successfully be used for training VQA models to improve performance.

The VQ2A technique enables VQA data generation at scale from image captions by rewriting each caption into multiple question-answer pairs.

VQ²A Overview
The first step of the VQ²A approach is to apply heuristics based on named entity recognition, part-of-speech tagging and manually defined rules to generate answer candidates from the image caption. These generated candidates are small pieces of information that may be relevant subjects about which to ask questions. We also add to this list two default answers, “yes” and “no”, which allow us to generate Boolean questions.

Then, we use a T5 model that was fine-tuned to generate questions for the candidate, resulting in [question, candidate answer] pairs. We then filter for the highest quality pairs using another T5 model (fine-tuned to answer questions) by asking it to answer the question based on the caption. was . That is, we compare the candidate answer to the output of this model and if the two answers are similar enough, we define this question as high quality and keep it. Otherwise, we filter it out.

The idea of using both question answering and question generation models to check each other for their round-trip consistency has been previously explored in other contexts. For instance, Q² uses this idea to evaluate factual consistency in knowledge-grounded dialogues. In the end, the VQ²A approach, as illustrated below, can generate a large number of [image, question, answer] triplets that are high-quality enough to be used as VQA training data.

VQ2A consists of three main steps: (i) candidate answer extraction, (ii) question generation, (iii) question answering and answer validation.

Results
Two examples of our generated VQA data are shown below, one based on human-written COCO Captions (COCO) and the other on automatically-collected Conceptual Captions (CC3M), which we call VQ²A-COCO and VQ²A-CC3M, respectively. We highlight the variety of question types and styles, which are critical for VQA. Overall, the cleaner the captions (i.e., the more closely related they are to their paired image), the more accurate the generated triplets. Based on 800 samples each, 87.3% of VQ²A-COCO and 66.0% VQ²A-CC3M are found by human raters to be valid, suggesting that our approach can generate question-answer pairs with high precision.

Generated question-answer pairs based on COCO Captions (top) and Conceptual Captions (bottom). Grey highlighting denotes questions that do not appear in VQAv2, while green highlighting denotes those that do, indicating that our approach is capable of generating novel questions that an existing VQA dataset does not have.

Finally, we evaluate our generated data by using it to train VQA models (highlights shown below). We observe that our automatically-generated VQA data is competitive with manually-annotated target VQA data. First, our VQA models achieve high performance on target benchmarks “out-of-the-box”, when trained only on our generated data (light blue and light red vs. yellow). Once fine-tuned on target data, our VQA models outperform target-only training slightly on large-scale benchmarks like VQAv2 and GQA, but significantly on the small, knowledge-seeking OK-VQA (dark blue/red vs. light blue/red).

VQA accuracy on popular benchmark datasets.

Conclusion
All we may need for VQA are image captions! This work demonstrates that it is possible to automatically generate high-quality VQA data at scale, serving as an essential building block for VQA and vision-and-language models in general (e.g., ALIGN, CoCa). We hope that our work inspires other work on data-centric VQA.

Acknowledgments
We thank Roee Aharoni, Idan Szpektor, and Radu Soricut for their feedback on this blogpost. We also thank our co-authors: Xi Chen, Nan Ding, Idan Szpektor, and Radu Soricut. We acknowledge contributions from Or Honovich, Hagai Taitelbaum, Roee Aharoni, Sebastian Goodman, Piyush Sharma, Nassim Oufattole, Gal Elidan, Sasha Goldshtein, and Avinatan Hassidim. Finally, we thank the authors of Q², whose pipeline strongly influences this work.

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Posted by Qihang Yu, Student Researcher, and Liang-Chieh Chen, Research Scientist, Google Research

Panoptic segmentation is a computer vision problem that serves as a core task for many real-world applications. Due to its complexity, previous work often divides panoptic segmentation into semantic segmentation (assigning semantic labels, such as “person” and “sky”, to every pixel in an image) and instance segmentation (identifying and segmenting only countable objects, such as “pedestrians” and “cars”, in an image), and further divides it into several sub-tasks. Each sub-task is processed individually, and extra modules are applied to merge the results from each sub-task stage. This process is not only complex, but it also introduces many hand-designed priors when processing sub-tasks and when combining the results from different sub-task stages.

Recently, inspired by Transformer and DETR, an end-to-end solution for panoptic segmentation with mask transformers (an extension of the Transformer architecture that is used to generate segmentation masks) was proposed in MaX-DeepLab. This solution adopts a pixel path (consisting of either convolutional neural networks or vision transformers) to extract pixel features, a memory path (consisting of transformer decoder modules) to extract memory features, and a dual-path transformer for interaction between pixel features and memory features. However, the dual-path transformer, which utilizes cross-attention, was originally designed for language tasks, where the input sequence consists of dozens or hundreds of words. Nonetheless, when it comes to vision tasks, specifically segmentation problems, the input sequence consists of tens of thousands of pixels, which not only indicates a much larger magnitude of input scale, but also represents a lower-level embedding compared to language words.

In “CMT-DeepLab: Clustering Mask Transformers for Panoptic Segmentation”, presented at CVPR 2022, and “kMaX-DeepLab: k-means Mask Transformer”, to be presented at ECCV 2022, we propose to reinterpret and redesign cross-attention from a clustering perspective (i.e., grouping pixels with the same semantic labels together), which better adapts to vision tasks. CMT-DeepLab is built upon the previous state-of-the-art method, MaX-DeepLab, and employs a pixel clustering approach to perform cross-attention, leading to a more dense and plausible attention map. kMaX-DeepLab further redesigns cross-attention to be more like a k-means clustering algorithm, with a simple change on the activation function. We demonstrate that CMT-DeepLab achieves significant performance improvements, while kMaX-DeepLab not only simplifies the modification but also further pushes the state-of-the-art by a large margin, without test-time augmentation. We are also excited to announce the open-source release of kMaX-DeepLab, our best performing segmentation model, in the DeepLab2 library.

Overview
Instead of directly applying cross-attention to vision tasks without modifications, we propose to reinterpret it from a clustering perspective. Specifically, we note that the mask Transformer object query can be considered cluster centers (which aim to group pixels with the same semantic labels), and the process of cross-attention is similar to the k-means clustering algorithm, which adopts an iterative process of (1) assigning pixels to cluster centers, where multiple pixels can be assigned to a single cluster center, and some cluster centers may have no assigned pixels, and (2) updating the cluster centers by averaging pixels assigned to the same cluster center, the cluster centers will not be updated if no pixel is assigned to them).

In CMT-DeepLab and kMaX-DeepLab, we reformulate the cross-attention from the clustering perspective, which consists of iterative cluster-assignment and cluster-update steps.

Given the popularity of the k-means clustering algorithm, in CMT-DeepLab we redesign cross-attention so that the spatial-wise softmax operation (i.e., the softmax operation that is applied along the image spatial resolution) that in effect assigns cluster centers to pixels is instead applied along the cluster centers. In kMaX-DeepLab, we further simplify the spatial-wise softmax to cluster-wise argmax (i.e., applying the argmax operation along the cluster centers). We note that the argmax operation is the same as the hard assignment (i.e., a pixel is assigned to only one cluster) used in the k-means clustering algorithm.

Reformulating the cross-attention of the mask transformer from the clustering perspective significantly improves the segmentation performance and simplifies the complex mask transformer pipeline to be more interpretable. First, pixel features are extracted from the input image with an encoder-decoder structure. Then, a set of cluster centers are used to group pixels, which are further updated based on the clustering assignments. Finally, the clustering assignment and update steps are iteratively performed, with the last assignment directly serving as segmentation predictions.

To convert a typical mask Transformer decoder (consisting of cross-attention, multi-head self-attention, and a feed-forward network) into our proposed k-means cross-attention, we simply replace the spatial-wise softmax with cluster-wise argmax.

The meta architecture of our proposed kMaX-DeepLab consists of three components: pixel encoder, enhanced pixel decoder, and kMaX decoder. The pixel encoder is any network backbone, used to extract image features. The enhanced pixel decoder includes transformer encoders to enhance the pixel features, and upsampling layers to generate higher resolution features. The series of kMaX decoders transform cluster centers into (1) mask embedding vectors, which multiply with the pixel features to generate the predicted masks, and (2) class predictions for each mask.

The meta architecture of kMaX-DeepLab.

Results
We evaluate the CMT-DeepLab and kMaX-DeepLab using the panoptic quality (PQ) metric on two of the most challenging panoptic segmentation datasets, COCO and Cityscapes, against MaX-DeepLab and other state-of-the-art methods. CMT-DeepLab achieves significant performance improvement, while kMaX-DeepLab not only simplifies the modification but also further pushes the state-of-the-art by a large margin, with 58.0% PQ on COCO val set, and 68.4% PQ, 44.0% mask Average Precision (mask AP), 83.5% mean Intersection-over-Union (mIoU) on Cityscapes val set, without test-time augmentation or using an external dataset.

Designed from a clustering perspective, kMaX-DeepLab not only has a higher performance but also a more plausible visualization of the attention map to understand its working mechanism. In the example below, kMaX-DeepLab iteratively performs clustering assignments and updates, which gradually improves mask quality.

kMaX-DeepLab’s attention map can be directly visualized as a panoptic segmentation, which gives better plausibility for the model working mechanism (image credit: coco_url, and license).

Conclusions
We have demonstrated a way to better design mask transformers for vision tasks. With simple modifications, CMT-DeepLab and kMaX-DeepLab reformulate cross-attention to be more like a clustering algorithm. As a result, the proposed models achieve state-of-the-art performance on the challenging COCO and Cityscapes datasets. We hope that the open-source release of kMaX-DeepLab in the DeepLab2 library will facilitate future research on designing vision-specific transformer architectures.

Acknowledgements
We are thankful to the valuable discussion and support from Huiyu Wang, Dahun Kim, Siyuan Qiao, Maxwell Collins, Yukun Zhu, Florian Schroff, Hartwig Adam, and Alan Yuille.

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Posted by Danijar Hafner, Student Researcher, Google Research

Research into how artificial agents can make decisions has evolved rapidly through advances in deep reinforcement learning. Compared to generative ML models like GPT-3 and Imagen, artificial agents can directly influence their environment through actions, such as moving a robot arm based on camera inputs or clicking a button in a web browser. While artificial agents have the potential to be increasingly helpful to people, current methods are held back by the need to receive detailed feedback in the form of frequently provided rewards to learn successful strategies. For example, despite large computational budgets, even powerful programs such as AlphaGo are limited to a few hundred moves until receiving their next reward.

In contrast, complex tasks like making a meal require decision making at all levels, from planning the menu, navigating to the store to pick up groceries, and following the recipe in the kitchen to properly executing the fine motor skills needed at each step along the way based on high-dimensional sensory inputs. Hierarchical reinforcement learning (HRL) promises to automatically break down such complex tasks into manageable subgoals, enabling artificial agents to solve tasks more autonomously from fewer rewards, also known as sparse rewards. However, research progress on HRL has proven to be challenging; current methods rely on manually specified goal spaces or subtasks, and no general solution exists.

To spur progress on this research challenge and in collaboration with the University of California, Berkeley, we present the Director agent, which learns practical, general, and interpretable hierarchical behaviors from raw pixels. Director trains a manager policy to propose subgoals within the latent space of a learned world model and trains a worker policy to achieve these goals. Despite operating on latent representations, we can decode Director’s internal subgoals into images to inspect and interpret its decisions. We evaluate Director across several benchmarks, showing that it learns diverse hierarchical strategies and enables solving tasks with very sparse rewards where previous approaches fail, such as exploring 3D mazes with quadruped robots directly from first-person pixel inputs.

Director learns to solve complex long-horizon tasks by automatically breaking them down into subgoals. Each panel shows the environment interaction on the left and the decoded internal goals on the right.

How Director Works
Director learns a world model from pixels that enables efficient planning in a latent space. The world model maps images to model states and then predicts future model states given potential actions. From predicted trajectories of model states, Director optimizes two policies: The manager chooses a new goal every fixed number of steps, and the worker learns to achieve the goals through low-level actions. However, choosing goals directly in the high-dimensional continuous representation space of the world model would be a challenging control problem for the manager. Instead, we learn a goal autoencoder to compress the model states into smaller discrete codes. The manager then selects discrete codes and the goal autoencoder turns them into model states before passing them as goals to the worker.

Left: The goal autoencoder (blue) compresses the world model (green) state (st) into discrete codes (z). Right: The manager policy (orange) selects a code that the goal decoder (blue) turns into a feature space goal (g). The worker policy (red) learns to achieve the goal from future trajectories (s1, …, s4) predicted by the world model.

All components of Director are optimized concurrently, so the manager learns to select goals that are achievable by the worker. The manager learns to select goals to maximize both the task reward and an exploration bonus, leading the agent to explore and steer towards remote parts of the environment. We found that preferring model states where the goal autoencoder incurs high prediction error is a simple and effective exploration bonus. Unlike prior methods, such as Feudal Networks, our worker receives no task reward and learns purely from maximizing the feature space similarity between the current model state and the goal. This means the worker has no knowledge of the task and instead concentrates all its capacity on achieving goals.

Benchmark Results
Whereas prior work in HRL often resorted to custom evaluation protocols — such as assuming diverse practice goals, access to the agents’ global position on a 2D map, or ground-truth distance rewards — Director operates in the end-to-end RL setting. To test the ability to explore and solve long-horizon tasks, we propose the challenging Egocentric Ant Maze benchmark. This challenging suite of tasks requires finding and reaching goals in 3D mazes by controlling the joints of a quadruped robot, given only proprioceptive and first-person camera inputs. The sparse reward is given when the robot reaches the goal, so the agents have to autonomously explore in the absence of task rewards throughout most of their learning.

The Egocentric Ant Maze benchmark measures the ability of agents to explore in a temporally-abstract manner to find the sparse reward at the end of the maze.

We evaluate Director against two state-of-the-art algorithms that are also based on world models: Plan2Explore, which maximizes both task reward and an exploration bonus based on ensemble disagreement, and Dreamer, which simply maximizes the task reward. Both baselines learn non-hierarchical policies from imagined trajectories of the world model. We find that Plan2Explore results in noisy movements that flip the robot onto its back, preventing it from reaching the goal. Dreamer reaches the goal in the smallest maze but fails to explore the larger mazes. In these larger mazes, Director is the only method to find and reliably reach the goal.

To study the ability of agents to discover very sparse rewards in isolation and separately from the challenge of representation learning of 3D environments, we propose the Visual Pin Pad suite. In these tasks, the agent controls a black square, moving it around to step on differently colored pads. At the bottom of the screen, the history of previously activated pads is shown, removing the need for long-term memory. The task is to discover the correct sequence for activating all the pads, at which point the agent receives the sparse reward. Again, Director outperforms previous methods by a large margin.

The Visual Pin Pad benchmark allows researchers to evaluate agents under very sparse rewards and without confounding challenges such as perceiving 3D scenes or long-term memory.

In addition to solving tasks with sparse rewards, we study Director’s performance on a wide range of tasks common in the literature that typically require no long-term exploration. Our experiment includes 12 tasks that cover Atari games, Control Suite tasks, DMLab maze environments, and the research platform Crafter. We find that Director succeeds across all these tasks with the same hyperparameters, demonstrating the robustness of the hierarchy learning process. Additionally, providing the task reward to the worker enables Director to learn precise movements for the task, fully matching or exceeding the performance of the state-of-the-art Dreamer algorithm.

Director solves a wide range of standard tasks with dense rewards with the same hyperparameters, demonstrating the robustness of the hierarchy learning process.

Goal Visualizations
While Director uses latent model states as goals, the learned world model allows us to decode these goals into images for human interpretation. We visualize the internal goals of Director for multiple environments to gain insights into its decision making and find that Director learns diverse strategies for breaking down long-horizon tasks. For example, on the Walker and Humanoid tasks, the manager requests a forward leaning pose and shifting floor patterns, with the worker filling in the details of how the legs need to move. In the Egocentric Ant Maze, the manager steers the ant robot by requesting a sequence of different wall colors. In the 2D research platform Crafter, the manager requests resource collection and tools via the inventory display at the bottom of the screen, and in DMLab mazes, the manager encourages the worker via the teleport animation that occurs right after collecting the desired object.

Future Directions
We see Director as a step forward in HRL research and are preparing its code to be released in the future. Director is a practical, interpretable, and generally applicable algorithm that provides an effective starting point for the future development of hierarchical artificial agents by the research community, such as allowing goals to only correspond to subsets of the full representation vectors, dynamically learning the duration of the goals, and building hierarchical agents with three or more levels of temporal abstraction. We are optimistic that future algorithmic advances in HRL will unlock new levels of performance and autonomy of intelligent agents.

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Posted by Been Kim, Research Scientist, Google Research, Brain Team, and Alison Lentz, Senior Staff Strategist, Google Research, Mural Team

Advances in computer vision and natural language processing continue to unlock new ways of exploring billions of images available on public and searchable websites. Today’s visual search tools make it possible to search with your camera, voice, text, images, or multiple modalities at the same time. However, it remains difficult to input subjective concepts, such as visual tones or moods, into current systems. For this reason, we have been working collaboratively with artists, photographers, and image researchers to explore how machine learning (ML) might enable people to use expressive queries as a way of visually exploring datasets.

Today, we are introducing Mood Board Search, a new ML-powered research tool that uses mood boards as a query over image collections. This enables people to define and evoke visual concepts on their own terms. Mood Board Search can be useful for subjective queries, such as “peaceful”, or for words and individual images that may not be specific enough to produce useful results in a standard search, such as “abstract details in overlooked scenes” or “vibrant color palette that feels part memory, part dream. We developed, and will continue to develop, this research tool in alignment with our AI Principles.”

Search Using Mood Boards
With Mood Board Search, our goal is to design a flexible and approachable interface so people without ML expertise can train a computer to recognize a visual concept as they see it. The tool interface is inspired by mood boards, commonly used by people in creative fields to communicate the “feel” of an idea using collections of visual materials.

With Mood Board Search, users can train a computer to recognize visual concepts in image collections.

To get started, simply drag and drop a small number of images that represent the idea you want to convey. Mood Board Search returns the best results when the images share a consistent visual quality, so results are more likely to be relevant with mood boards that share visual similarities in color, pattern, texture, or composition.

It’s also possible to signal which images are more important to a visual concept by upweighting or downweighting images, or by adding images that are the opposite of the concept. Then, users can review and inspect search results to understand which part of an image best matches the visual concept. Focus mode does this by revealing a bounding box around part of the image, while AI crop cuts in directly, making it easier to draw attention to new compositions.

Supported interactions, like AI crop, allow users to see which part of an image best matches their visual concept.

Powered by Concept Activation Vectors (CAVs)
Mood Board Search takes advantage of pre-trained computer vision models, such as GoogLeNet and MobileNet, and a machine learning approach called Concept Activation Vectors (CAVs).

CAVs are a way for machines to represent images (what we understand) using numbers or directions in a neural net’s embedding space (which can be thought of as what machines understand). CAVs can be used as part of a technique, Testing with CAVs (TCAV), to quantify the degree to which a user-defined concept is important to a classification result; e.g., how sensitive a prediction of “zebra” is to the presence of stripes. This is a research approach we open-sourced in 2018, and the work has since been widely applied to medical applications and science to build ML applications that can provide better explanations for what machines see. You can learn more about embedding vectors in general in this Google AI blog post, and our approach to working with TCAVs in Been Kim’s Keynote at ICLR.

In Mood Board Search, we use CAVs to find a model’s sensitivity to a mood board created by the user. In other words, each mood board creates a CAV — a direction in embedding space — and the tool searches an image dataset, surfacing images that are the closest match to the CAV. However, the tool takes it one step further, by segmenting each image in the dataset in 15 different ways, to uncover as many relevant compositions as possible. This is the approach behind features like Focus mode and AI crop.

Three artists created visual concepts to share their way of seeing, shown here in an experimental app by design invention studio, Nord Projects.

Because embedding vectors can be learned and re-used across models, tools like Mood Board Search can help us express our perspective to other people. Early collaborations with creative communities have shown value in being able to create and share subjective experiences with others, resulting in feelings of being able to “break out of visually-similar echo chambers” or “see the world through another person’s eyes”. Even misalignment between model and human understanding of a concept frequently resulted in unexpected and inspiring connections for collaborators. Taken together, these findings point towards new ways of designing collaborative ML systems that embrace personal and collective subjectivity.

Conclusions and Future Work
Today, we’re open-sourcing the code to Mood Board Search, including three visual concepts made by our collaborators, and a Mood Board Search Python Library for people to tap the power of CAVs directly into their own websites and apps. While these tools are early-stage prototypes, we believe this capability can have a wide-range of applications from exploring unorganized image collections to externalizing ways of seeing into collaborative and shareable artifacts. Already, an experimental app by design invention studio Nord Projects, made using Mood Board Search, investigates the opportunities for running CAVs in camera, in real-time. In future work, we plan to use Mood Board Search to learn about new forms of human-machine collaboration and expand ML models and inputs — like text and audio — to allow even deeper subjective discoveries, regardless of medium.

If you’re interested in a demo of this work for your team or organization, email us at cav-experiments-support@google.com.

Acknowledgments
This blog presents research by (in alphabetical order): Kira Awadalla, Been Kim, Eva Kozanecka, Alison Lentz, Alice Moloney, Emily Reif, and Oliver Siy, in collaboration with design invention studio Nord Projects. We thank our co-author, Eva Kozanecka, our artist collaborators, Alexander Etchells, Tom Hatton, Rachel Maggart, the Imaging team at The British Library for their participation in beta previews, and Blaise Agüera y Arcas, Jess Holbrook, Fernanda Viegas, and Martin Wattenberg for their support of this research project.

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Google’s AI Principles Review Process: How we assess new AI research and applications for alignment with our Principles

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Posted by Yundi Qian, Software Engineer, Google Research and Mircea Trofin, Software Engineer, Google Core

The question of how to compile faster and smaller code arose together with the birth of modem computers. Better code optimization can significantly reduce the operational cost of large datacenter applications. The size of compiled code matters the most to mobile and embedded systems or software deployed on secure boot partitions, where the compiled binary must fit in tight code size budgets. With advances in the field, the headroom has been heavily squeezed with increasingly complicated heuristics, impeding maintenance and further improvements.

Recent research has shown that machine learning (ML) can unlock more opportunities in compiler optimization by replacing complicated heuristics with ML policies. However, adopting ML in general-purpose, industry-strength compilers remains a challenge.

To address this, we introduce “MLGO: a Machine Learning Guided Compiler Optimizations Framework”, the first industrial-grade general framework for integrating ML techniques systematically in LLVM (an open-source industrial compiler infrastructure that is ubiquitous for building mission-critical, high-performance software). MLGO uses reinforcement learning (RL) to train neural networks to make decisions that can replace heuristics in LLVM. We describe two MLGO optimizations for LLVM: 1) reducing code size with inlining; and 2) improving code performance with register allocation (regalloc). Both optimizations are available in the LLVM repository, and have been deployed in production.

How Does MLGO Work? With Inlining-for-Size As a Case Study
Inlining helps reduce code size by making decisions that enable the removal of redundant code. In the example below, the caller function foo() calls the callee function bar(), which itself calls baz(). Inlining both callsites returns a simple foo() function that reduces the code size.

Inlining reduces code size by removing redundant code.

In real code, there are thousands of functions calling each other, and thus comprise a call graph. During the inlining phase, the compiler traverses over the call graph on all caller-callee pairs, and makes decisions on whether to inline a caller-callee pair or not. It is a sequential decision process as previous inlining decisions will alter the call graph, affecting later decisions and the final result. In the example above, the call graph foo() → bar() → baz() needs a “yes” decision on both edges to make the code size reduction happen.

Before MLGO, the inline / no-inline decision was made by a heuristic that, over time, became increasingly difficult to improve. MLGO substitutes the heuristic with an ML model. During the call graph traversal, the compiler seeks advice from a neural network on whether to inline a particular caller-callee pair by feeding in relevant features (i.e., inputs) from the graph, and executes the decisions sequentially until the whole call graph is traversed.

Illustration of MLGO during inlining. “#bbs”, “#users”, and “callsite height” are example caller-callee pair features.

MLGO trains the decision network (policy) with RL using policy gradient and evolution strategies algorithms. While there is no ground truth about best decisions, online RL iterates between training and running compilation with the trained policy to collect data and improve the policy. In particular, given the current model under training, the compiler consults the model for inline / no-inline decision making during the inlining stage. After the compilation finishes, it produces a log of the sequential decision process (state, action, reward). The log is then passed to the trainer to update the model. This process repeats until we obtain a satisfactory model.

Compiler behavior during training. The compiler compiles the source code foo.cpp to an object file foo.o with a sequence of optimization passes, one of which is the inline pass.

The trained policy is then embedded into the compiler to provide inline / no-inline decisions during compilation. Unlike the training scenario, the policy does not produce a log. The TensorFlow model is embedded with XLA AOT, which converts the model into executable code. This avoids TensorFlow runtime dependency and overhead, minimizing the extra time and memory cost introduced by ML model inference at compilation time.

Compiler behavior in production.

We trained the inlining-for-size policy on a large internal software package containing 30k modules. The trained policy is generalizable when applied to compile other software and achieves a 3% ~ 7% size reduction. In addition to the generalizability across software, generalizability across time is also important — both the software and compiler are under active development so the trained policy needs to retain good performance for a reasonable time. We evaluated the model’s performance on the same set of software three months later and found only slight degradation.

Inlining-for-size policy size reduction percentages. The x-axis presents different software and the y-axis represents the percentage size reduction. “Training” is the software on which the model was trained and “Infra[1|2|3]” are different internal software packages.

The MLGO inlining-for-size training has been deployed on Fuchsia — a general purpose open source operating system designed to power a diverse ecosystem of hardware and software, where binary size is critical. Here, MLGO showed a 6.3% size reduction for C++ translation units.

Register-Allocation (for performance)
As a general framework, we used MLGO to improve the register allocation pass, which improves the code performance in LLVM. Register Allocation solves the problem of assigning physical registers to live ranges (i.e., variables).

As the code executes, different live ranges are completed at different times, freeing up registers for use by subsequent processing stages. In the example below, each “add” and “multiply” instruction requires all operands and the result to be in physical registers. The live range x is allocated to the green register and is completed before either live ranges in the blue or yellow registers. After x is completed, the green register becomes available and is assigned to live range t.

Register allocation example.

When it’s time to allocate live range q, there are no available registers, so the register allocation pass must decide which (if any) live range can be “evicted” from its register to make room for q. This is referred to as the “live range eviction” problem, and is the decision for which we train the model to replace original heuristics. In this particular example, it evicts z from the yellow register, and assigns it to q and the first half of z.

We now consider the unassigned second half of live range z. We have a conflict again, and this time the live range t is evicted and split, and the first half of t and the final part of z end up using the green register. The middle part of z corresponds to the instruction q = t * y, where z is not being used, so it is not assigned to any register and its value is stored in the stack from the yellow register, which later gets reloaded to the green register. The same happens to t. This adds extra load/store instructions to the code and degrades performance. The goal of the register allocation algorithm is to reduce such inefficiencies as much as possible. This is used as the reward to guide RL policy training.

Similar to the inlining-for-size policy, the register allocation (regalloc-for-performance) policy is trained on a large Google internal software package, and is generalizable across different software, with 0.3% ~1.5% improvements in queries per second (QPS) on a set of internal large-scale datacenter applications. The QPS improvement has persisted for months after its deployment, showing the model’s generalizability across the time horizon.

Conclusion and Future Work
We propose MLGO, a framework for integrating ML techniques systematically in an industrial compiler, LLVM. MLGO is a general framework that can be expanded to be: 1) deeper, e.g., adding more features, and applying better RL algorithms; and 2) broader, by applying it to more optimization heuristics beyond inlining and regalloc. We are enthusiastic about the possibilities MLGO can bring to the compiler optimization domain and look forward to its further adoption and to future contributions from the research community.

Try it Yourself
Check out the open-sourced end-to-end data collection and training solution on github and a demo that uses policy gradient to train an inlining-for-size policy.

Acknowledgements
We’d like to thank MLGO’s contributors and collaborators Eugene Brevdo, Jacob Hegna, Gaurav Jain, David Li, Zinan Lin, Kshiteej Mahajan, Jack Morris, Girish Mururu, Jin Xin Ng, Robert Ormandi, Easwaran Raman, Ondrej Sykora, Maruf Zaber, Weiye Zhao. We would also like to thank Petr Hosek, Yuqian Li, Roland McGrath, Haowei Wu for trusting us and deploying MLGO in Fuchsia as MLGO’s very first customer; thank David Blaikie, Eric Christopher, Brooks Moses, Jordan Rupprecht for helping to deploy MLGO in Google internal large-scale datacenter applications; and thank Ed Chi, Tipp Moseley for their leadership support.

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Posted by Dan Walker and Dan Liebling, Software Engineers, Google Research

People don’t write in the same way that they speak. Written language is controlled and deliberate, whereas transcripts of spontaneous speech (like interviews) are hard to read because speech is disorganized and less fluent. One aspect that makes speech transcripts particularly difficult to read is disfluency, which includes self-corrections, repetitions, and filled pauses (e.g., words like “umm”, and “you know”). Following is an example of a spoken sentence with disfluencies from the LDC CALLHOME corpus:

It takes some time to understand this sentence — the listener must filter out the extraneous words and resolve all of the nots. Removing the disfluencies makes the sentence much easier to read and understand:

While people generally don’t even notice disfluencies in day-to-day conversation, early foundational work in computational linguistics demonstrated how common they are. In 1994, using the Switchboard corpus, Elizabeh Shriberg demonstrated that there is a 50% probability for a sentence of 10–13 words to include a disfluency and that the probability increases with sentence length.

The proportion of sentences from the Switchboard dataset with at least one disfluency plotted against sentence length measured in non-disfluent (i.e., efficient) tokens in the sentence. The longer a sentence gets, the more likely it is to contain a disfluency.

In “Teaching BERT to Wait: Balancing Accuracy and Latency for Streaming Disfluency Detection”, we present research findings on how to “clean up” transcripts of spoken text. We create more readable transcripts and captions of human speech by finding and removing disfluencies in people’s speech. Using labeled data, we created machine learning (ML) algorithms that identify disfluencies in human speech. Once those are identified we can remove the extra words to make transcripts more readable. This also improves the performance of natural language processing (NLP) algorithms that work on transcripts of human speech. Our work puts special priority on ensuring that these models are able to run on mobile devices so that we can protect user privacy and preserve performance in scenarios with low connectivity.

Base Model Overview
At the core of our base model is a pre-trained BERT_BASE encoder with 108.9 million parameters. We use the standard per-token classifier configuration, with a binary classification head being fed by the sequence encodings for each token.

Illustration of how tokens in text become numerical embeddings, which then lead to output labels.

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Illustration of how tokens in text become numerical embeddings, which then lead to output labels.

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We refined the BERT encoder by continuing the pretraining on the comments from the Pushrift Reddit dataset from 2019. Reddit comments are not speech data, but are more informal and conversational than the wiki and book data. This trains the encoder to better understand informal language, but may run the risk of internalizing some of the biases inherent in the data. For our particular use case, however, the model only captures the syntax or overall form of the text, not its content, which avoids potential issues related to semantic-level biases in the data.

We fine-tune our model for disfluency classification on hand-labeled corpora, such as the Switchboard corpus mentioned above. Hyperparameters (batch size, learning rate, number of training epochs, etc.) were optimized using Vizier.

We also produce a range of “small” models for use on mobile devices using a knowledge distillation technique known as “self training”. Our best small model is based on the Small-vocab BERT variant with 3.1 million parameters. This smaller model achieves comparable results to our baseline at 1% the size (in MiB). You can read more about how we achieved this model miniaturization in our 2021 Interspeech paper.

Streaming
Some of the latest use cases for automatic speech transcription include automated live captioning, such as produced by the Android “Live Captions” feature, which automatically transcribes spoken language in audio being played on the device. For disfluency removal to be of use in improving the readability of the captions in this setting, then it must happen quickly and in a stable manner. That is, the model should not change its past predictions as it sees new words in the transcript.

We call this live token-by-token processing streaming. Accurate streaming is difficult because of temporal dependencies; most disfluencies are only recognizable later. For example, a repetition does not actually become a repetition until the second time the word or phrase is said.

To investigate whether our disfluency detection model is effective in streaming applications, we split the utterances in our training set into prefix segments, where only the first N tokens of the utterance were provided at training time, for all values of N up to the full length of the utterance. We evaluated the model simulating a stream of spoken text by feeding prefixes to the models and measuring the performance with several metrics that capture model accuracy, stability, and latency including streaming F1, time to detection (TTD), edit overhead (EO), and average wait time (AWT). We experimented with look-ahead windows of either one or two tokens, allowing the model to “peek” ahead at additional tokens for which the model is not required to produce a prediction. In essence, we’re asking the model to “wait” for one or two more tokens of evidence before making a decision.

While adding this fixed look-ahead did improve the stability and streaming F1 scores in many contexts, we found that in some cases the label was already clear even without looking ahead to the next token and the model did not necessarily benefit from waiting. Other times, waiting for just one extra token was sufficient. We hypothesized that the model itself could learn when it should wait for more context. Our solution was a modified model architecture that includes a “wait” classification head that decides when the model has seen enough evidence to trust the disfluency classification head.

Diagram showing how the model labels input tokens as they arrive. The BERT embedding layers feed into two separate classification heads, which are combined for the output.

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Diagram showing how the model labels input tokens as they arrive. The BERT embedding layers feed into two separate classification heads, which are combined for the output.

–>

We constructed a training loss function that is a weighted sum of three factors:

1. The traditional cross-entropy loss for the disfluency classification head
2. A cross-entropy term that only considers up to the first token with a “wait” classification
3. A latency penalty that discourages the model from waiting too long to make a prediction

We evaluated this streaming model as well as the standard baseline with no look-ahead and with both 1- and 2-token look-ahead values:

Graph of the streaming F1 score versus the average wait time in tokens. Three data points indicate F1 scores above 0.82 across multiple wait times. The proposed streaming model achieves near top performance with much shorter wait times than the fixed look ahead models.

The streaming model achieved a better streaming F1 score than both a standard baseline with no look ahead and a model with a look ahead of 1. It performed nearly as well as the variant with fixed look ahead of 2, but with much less waiting. On average the model waited for only 0.21 tokens of context.

Internationalization
Our best outcomes so far have been with English transcripts. This is mostly due to resourcing issues: while there are a number of relatively large labeled conversational datasets that include disfluencies in English, other languages often have very few such datasets available. So, in order to make disfluency detection models available outside English a method is needed to build models in a way that does not require finding and labeling hundreds of thousands of utterances in each target language. A promising solution is to leverage multi-language versions of BERT to transfer what a model has learned about English disfluencies to other languages in order to achieve similar performance with much less data. This is an area of active research, but we do have some promising results to outline here.

As a first effort to validate this approach, we added labels to about 10,000 lines of dialogue from the German CALLHOME dataset. We then started with the Geotrend English and German Bilingual BERT model (extracted from Multilingual BERT) and fine-tuned it with approximately 77,000 disfluency-labeled English Switchboard examples and 1.3 million examples of self-labeled transcripts from the Fisher Corpus. Then, we did further fine tuning with about 7,500 in-house–labeled examples from the German CALLHOME dataset.

Diagram illustrating the flow of labeled data and self-trained output in our best multilingual training setup. By training on both English and German data we are able to improve performance via transfer learning.

Our results indicate that fine-tuning on a large English corpus can produce acceptable precision using zero-shot transfer to similar languages like German, but at least a modest amount of German labels were needed to improve recall from less than 60% to greater than 80%. Two-stage fine-tuning of an English-German bilingual model produced the highest precision and overall F1 score.

Conclusion
Cleaning up disfluencies from transcripts can improve not just their readability for people, but also the performance of other models that consume transcripts. We demonstrate effective methods for identifying disfluencies and expand our disfluency model to resource-constrained environments, new languages, and more interactive use cases.

Acknowledgements
Thank you to Vicky Zayats, Johann Rocholl, Angelica Chen, Noah Murad, Dirk Padfield, and Preeti Mohan for writing the code, running the experiments, and composing the papers discussed here. Wealso thank our technical product manager Aaron Schneider, Bobby Tran from the Cerebra Data Ops team, and Chetan Gupta from Speech Data Ops for their support obtaining additional data labels.

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Posted by Ethan Dyer and Guy Gur-Ari, Research Scientists, Google Research, Blueshift Team

Language models have demonstrated remarkable performance on a variety of natural language tasks — indeed, a general lesson from many works, including BERT, GPT-3, Gopher, and PaLM, has been that neural networks trained on diverse data at large scale in an unsupervised way can perform well on a variety of tasks.

Quantitative reasoning is one area in which language models still fall far short of human-level performance. Solving mathematical and scientific questions requires a combination of skills, including correctly parsing a question with natural language and mathematical notation, recalling relevant formulas and constants, and generating step-by-step solutions involving numerical calculations and symbolic manipulation. Due to these challenges, it is often believed that solving quantitative reasoning problems using machine learning will require significant advancements in model architecture and training techniques, granting models access to external tools such as Python interpreters, or possibly a more profound paradigm shift.

In “Solving Quantitative Reasoning Problems With Language Models” (to be released soon on the arXiv), we present Minerva, a language model capable of solving mathematical and scientific questions using step-by-step reasoning. We show that by focusing on collecting training data that is relevant for quantitative reasoning problems, training models at scale, and employing best-in-class inference techniques, we achieve significant performance gains on a variety of difficult quantitative reasoning tasks. Minerva solves such problems by generating solutions that include numerical calculations and symbolic manipulation without relying on external tools such as a calculator. The model parses and answers mathematical questions using a mix of natural language and mathematical notation. Minerva combines several techniques, including few-shot prompting, chain of thought or scratchpad prompting, and majority voting, to achieve state-of-the-art performance on STEM reasoning tasks. You can explore Minerva’s output with our interactive sample explorer!

Solving a multi-step problem: A question from the MATH dataset and Minerva’s solution. The model writes down a line equation, simplifies it, substitutes a variable, and solves for y.

A Model Built for Multi-step Quantitative Reasoning
To promote quantitative reasoning, Minerva builds on the Pathways Language Model (PaLM), with further training on a 118GB dataset of scientific papers from the arXiv preprint server and web pages that contain mathematical expressions using LaTeX, MathJax, or other mathematical typesetting formats. Standard text cleaning procedures often remove symbols and formatting that are essential to the semantic meaning of mathematical expressions. By maintaining this information in the training data, the model learns to converse using standard mathematical notation.

Example questions from the Joint Entrance Examination Main Math 2020 exam taken each year by almost 2M Indian high-school students intended to study engineering and similar fields (left), and the National Math Exam in Poland (May 2022) taken by approximately 270K high-school students every year (right).

A dataset for quantitative reasoning: Careful data processing preserves mathematical information, allowing the model to learn mathematics at a higher level.

Minerva also incorporates recent prompting and evaluation techniques to better solve mathematical questions. These include chain of thought or scratchpad prompting — where Minerva is prompted with several step-by-step solutions to existing questions before being presented with a new question — and majority voting. Like most language models, Minerva assigns probabilities to different possible outputs. When answering a question, rather than taking the single solution Minerva scores as most likely, multiple solutions are generated by sampling stochastically from all possible outputs. These solutions are different (e.g., the steps are not identical), but often arrive at the same final answer. Minerva uses majority voting on these sampled solutions, taking the most common result as the conclusive final answer.

Majority voting: Minerva generates multiple solutions to each question and chooses the most common answer as the solution, improving performance significantly.

Evaluation on STEM Benchmarks
To test Minerva’s quantitative reasoning abilities we evaluated the model on STEM benchmarks ranging in difficulty from grade school level problems to graduate level coursework.

• MATH: High school math competition level problems
• MMLU-STEM: A subset of the Massive Multitask Language Understanding benchmark focused on STEM, covering topics such as engineering, chemistry, math, and physics at high school and college level.
• GSM8k: Grade school level math problems involving basic arithmetic operations that should all be solvable by a talented middle school student.

We also evaluated Minerva on OCWCourses, a collection of college and graduate level problems covering a variety of STEM topics such as solid state chemistry, astronomy, differential equations, and special relativity that we collected from MIT OpenCourseWare.

In all cases, Minerva obtains state-of-the-art results, sometimes by a wide margin.

Evaluation results on MATH and MMLU-STEM, which include high school and college level questions covering a range of STEM topics.

What Minerva Gets Wrong
Minerva still makes its fair share of mistakes. To better identify areas where the model can be improved, we analyzed a sample of questions the model gets wrong, and found that most mistakes are easily interpretable. About half are calculation mistakes, and the other half are reasoning errors, where the solution steps do not follow a logical chain of thought.

It is also possible for the model to arrive at a correct final answer but with faulty reasoning. We call such cases “false positives”, as they erroneously count toward a model’s overall performance score. In our analysis, we find that the rate of false positives is relatively low (Minerva 62B produces less than 8% false positives on MATH).

Below are a couple of example mistakes the model makes.

Calculation mistake: The model incorrectly cancels the square root on both sides of the equation.

Reasoning mistake: The model computes the number of free throws at the fourth practice, but then uses this number as the final answer for the first practice.

Limitations
Our approach to quantitative reasoning is not grounded in formal mathematics. Minerva parses questions and generates answers using a mix of natural language and LaTeX mathematical expressions, with no explicit underlying mathematical structure. This approach has an important limitation, in that the model’s answers cannot be automatically verified. Even when the final answer is known and can be verified, the model can arrive at a correct final answer using incorrect reasoning steps, which cannot be automatically detected. This limitation is not present in formal methods for theorem proving (e.g., see Coq, Isabelle, HOL, Lean, Metamath, and Mizar). On the other hand, an advantage of the informal approach is that it can be applied to a highly diverse set of problems which may not lend themselves to formalization.

Future Directions
While machine learning models have become impressive tools in many scientific disciplines, they are often narrowly scoped to solve specific tasks. We hope that general models capable of solving quantitative reasoning problems will help push the frontiers of science and education. Models capable of quantitative reasoning have many potential applications, including serving as useful aids for researchers, and enabling new learning opportunities for students. We present Minerva as a small step in this direction. To see more samples from Minerva, such as the one below, please visit the interactive sample explorer!

Solving a problem using calculus and trigonoometry: A question from the MATH dataset asking for the speed of a particle in circular motion. Minerva finds a correct step-by-step solution. In the process, Minerva computes a time derivative and applies a trigonometric identity.

Acknowledgements
Minerva was a collaborative effort that spanned multiple teams in Google Research. We would like to thank our coauthors Aitor Lewkowycz, Ambrose Slone, Anders Andreassen, Behnam Neyshabur, Cem Anil, David Dohan, Henryk Michalewski, Imanol Schlag, Theo Gutman-Solo, Vedant Misra, Vinay Ramasesh, and Yuhuai Wu, as well as our collaborators Erik Zelikman and Yasaman Razeghi. Minerva builds upon the work of many others at Google, and we would like to thank the PaLM team, the T5X team, the Flaxformer team, and the JAX team for their efforts. We thank Tom Small for designing the animation in this post. We would also like to especially thank Vedant Misra for developing the Minerva sample explorer.

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