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Posted by Chao Jia and Yinfei Yang, Software Engineers, Google Research

Learning good visual and vision-language representations is critical to solving computer vision problems — image retrieval, image classification, video understanding — and can enable the development of tools and products that change people’s daily lives. For example, a good vision-language matching model can help users find the most relevant images given a text description or an image input and help tools such as Google Lens find more fine-grained information about an image.

To learn such representations, current state-of-the-art (SotA) visual and vision-language models rely heavily on curated training datasets that require expert knowledge and extensive labels. For vision applications, representations are mostly learned on large-scale datasets with explicit class labels, such as ImageNet, OpenImages, and JFT-300M. For vision-language applications, popular pre-training datasets, such as Conceptual Captions and Visual Genome Dense Captions, all require non-trivial data collection and cleaning steps, limiting the size of datasets and thus hindering the scale of the trained models. In contrast, natural language processing (NLP) models have achieved SotA performance on GLUE and SuperGLUE benchmarks by utilizing large-scale pre-training on raw text without human labels.

In “Scaling Up Visual and Vision-Language Representation Learning With Noisy Text Supervision“, to appear at ICML 2021, we propose bridging this gap with publicly available image alt-text data (written copy that appears in place of an image on a webpage if the image fails to load on a user’s screen) in order to train larger, state-of-the-art vision and vision-language models. To that end, we leverage a noisy dataset of over one billion image and alt-text pairs, obtained without expensive filtering or post-processing steps in the Conceptual Captions dataset. We show that the scale of our corpus can make up for noisy data and leads to SotA representation, and achieves strong performance when transferred to classification tasks such as ImageNet and VTAB. The aligned visual and language representations also set new SotA results on Flickr30K and MS-COCO benchmarks, even when compared with more sophisticated cross-attention models. The representations also enable zero-shot image classification and cross-modality search with complex text and text + image queries.

Creating the Dataset
Alt-texts usually provide a description of what the image is about, but the dataset is “noisy” because some text may be partly or wholly unrelated to its paired image.

Example image-text pairs randomly sampled from the training dataset of ALIGN. One clearly noisy text label is marked in italics.

In this work, we follow the methodology of constructing the Conceptual Captions dataset to get a version of raw English alt-text data (image and alt-text pairs). While the Conceptual Captions dataset was cleaned by heavy filtering and post-processing, this work scales up visual and vision-language representation learning by relaxing most of the cleaning steps in the original work. Instead, we only apply minimal frequency-based filtering. The result is a much larger but noisier dataset of 1.8B image-text pairs.

ALIGN: A Large-scale ImaGe and Noisy-Text Embedding
For the purpose of building larger and more powerful models easily, we employ a simple dual-encoder architecture that learns to align visual and language representations of the image and text pairs. Image and text encoders are learned via a contrastive loss (formulated as normalized softmax) that pushes the embeddings of matched image-text pairs together while pushing those of non-matched image-text pairs (within the same batch) apart. The large-scale dataset makes it possible for us to scale up the model size to be as large as EfficientNet-L2 (image encoder) and BERT-large (text encoder) trained from scratch. The learned representation can be used for downstream visual and vision-language tasks.

Figure of ImageNet credit to (Krizhevsky et al. 2012) and VTAB figure credit to (Zhai et al. 2019)

The resulting representation can be used for vision-only or vision-language task transfer. Without any fine-tuning, ALIGN powers cross-modal search – image-to-text search, text-to-image search, and even search with joint image+text queries, examples below.

Evaluating Retrieval and Representation
The learned ALIGN model with BERT-Large and EfficientNet-L2 as text and image encoder backbones achieves SotA performance on multiple image-text retrieval tasks (Flickr30K and MS-COCO) in both zero-shot and fine-tuned settings, as shown below.

		Flickr30K (1K test set) R@1		MS-COCO (5K test set) R@1
Setting	Model	image → text	text → image	image → text	text → image
Zero-shot	ImageBERT	70.7	54.3	44.0	32.3
	UNITER	83.6	68.7	–	–
	CLIP	88.0	68.7	58.4	37.8
	ALIGN	88.6	75.7	58.6	45.6
Fine-tuned	GPO	88.7	76.1	68.1	52.7
	UNITER	87.3	75.6	65.7	52.9
	ERNIE-ViL	88.1	76.7	–	–
	VILLA	87.9	76.3	–	–
	Oscar	–	–	73.5	57.5
	ALIGN	95.3	84.9	77.0	59.9

Image-text retrieval results (recall@1) on Flickr30K and MS-COCO datasets (both zero-shot and fine-tuned). ALIGN significantly outperforms existing methods including the cross-modality attention models that are too expensive for large-scale retrieval applications.

ALIGN is also a strong image representation model. Shown below, with frozen features, ALIGN slightly outperforms CLIP and achieves a SotA result of 85.5% top-1 accuracy on ImageNet. With fine-tuning, ALIGN achieves higher accuracy than most generalist models, such as BiT and ViT, and is only worse than Meta Pseudo Labels, which requires deeper interaction between ImageNet training and large-scale unlabeled data.

Model (backbone)	Acc@1 w/ frozen features	Acc@1	Acc@5
WSL (ResNeXt-101 32x48d)	83.6	85.4	97.6
CLIP (ViT-L/14)	85.4	–	–
BiT (ResNet152 x 4)	–	87.54	98.46
NoisyStudent (EfficientNet-L2)	–	88.4	98.7
ViT (ViT-H/14)	–	88.55	–
Meta-Pseudo-Labels (EfficientNet-L2)	–	90.2	98.8
ALIGN (EfficientNet-L2)	85.5	88.64	98.67

ImageNet classification results comparison with supervised training (fine-tuning).

Zero-Shot Image Classification
Traditionally, image classification problems treat each class as independent IDs, and people have to train the classification layers with at least a few shots of labeled data per class. The class names are actually also natural language phrases, so we can naturally extend the image-text retrieval capability of ALIGN for image classification without any training data.

The pre-trained image and text encoder can directly be used in classifying an image into a set of classes by retrieving the nearest class name in the aligned embedding space. This approach does not require any training data for the defined class space.

On the ImageNet validation dataset, ALIGN achieves 76.4% top-1 zero-shot accuracy and shows great robustness in different variants of ImageNet with distribution shifts, similar to the concurrent work CLIP. We also use the same text prompt engineering and ensembling as in CLIP.

	ImageNet	ImageNet-R	ImageNet-A	ImageNet-V2
CLIP	76.2	88.9	77.2	70.1
ALIGN	76.4	92.2	75.8	70.1

Top-1 accuracy of zero-shot classification on ImageNet and its variants.

Application in Image Search
To illustrate the quantitative results above, we build a simple image retrieval system with the embeddings trained by ALIGN and show the top 1 text-to-image retrieval results for a handful of text queries from a 160M image pool. ALIGN can retrieve precise images given detailed descriptions of a scene, or fine-grained or instance-level concepts like landmarks and artworks. These examples demonstrate that the ALIGN model can align images and texts with similar semantics, and that ALIGN can generalize to novel complex concepts.

Image retrieval with fine-grained text queries using ALIGN’s embeddings.

Multimodal (Image+Text) Query for Image Search
A surprising property of word vectors is that word analogies can often be solved with vector arithmetic. A common example, “king – man + woman = queen”. Such linear relationships between image and text embeddings also emerge in ALIGN.

Specifically, given a query image and a text string, we add their ALIGN embeddings together and use it to retrieve relevant images using cosine similarity, as shown below. These examples not only demonstrate the compositionality of ALIGN embeddings across vision and language domains, but also show the feasibility of searching with a multi-modal query. For instance, one could now look for the “Australia” or “Madagascar” equivalence of pandas, or turn a pair of black shoes into identically-looking beige shoes. Also, it is possible to remove objects/attributes from a scene by performing subtraction in the embedding space, shown below.

Image retrieval with image text queries. By adding or subtracting text query embedding, ALIGN retrieves relevant images.

Social Impact and Future Work
While this work shows promising results from a methodology perspective with a simple data collection method, additional analysis of the data and the resulting model is necessary before the responsible use of the model in practice. For instance, considerations should be made towards the potential for the use of harmful text data in alt-texts to reinforce such harms. With regard to fairness, data balancing efforts may be required to prevent reinforcing stereotypes from the web data. Additional testing and training around sensitive religious or cultural items should be taken to understand and mitigate the impact from possibly mislabeled data.

Further analysis should also be taken to ensure that the demographic distribution of humans and related cultural items, such as clothing, food, and art, do not cause skewed model performance. Analysis and balancing would be required if such models will be used in production.

Conclusion
We have presented a simple method of leveraging large-scale noisy image-text data to scale up visual and vision-language representation learning. The resulting model, ALIGN, is capable of cross-modal retrieval and significantly outperforms SotA models. In visual-only downstream tasks, ALIGN is also comparable to or outperforms SotA models trained with large-scale labeled data.

Acknowledgement
We would like to thank our co-authors in Google Research: Ye Xia, Yi-Ting Chen, Zarana Parekh, Hieu Pham, Quoc V. Le, Yunhsuan Sung, Zhen Li, Tom Duerig. This work was also done with invaluable help from other colleagues from Google. We would like to thank Jan Dlabal and Zhe Li for continuous support in training infrastructure, Simon Kornblith for building the zero-shot & robustness model evaluation on ImageNet variants, Xiaohua Zhai for help on conducting VTAB evaluation, Mingxing Tan and Max Moroz for suggestions on EfficientNet training, Aleksei Timofeev for the early idea of multimodal query retrieval, Aaron Michelony and Kaushal Patel for their early work on data generation, and Sergey Ioffe, Jason Baldridge and Krishna Srinivasan for the insightful feedback and discussion.

Posted by Nachiappan Valliappan, Senior Software Engineer and Kai Kohlhoff, Staff Research Scientist, Google Research

Eye movement has been studied widely across vision science, language, and usability since the 1970s. Beyond basic research, a better understanding of eye movement could be useful in a wide variety of applications, ranging across usability and user experience research, gaming, driving, and gaze-based interaction for accessibility to healthcare. However, progress has been limited because most prior research has focused on specialized hardware-based eye trackers that are expensive and do not easily scale.

In “Accelerating eye movement research via accurate and affordable smartphone eye tracking”, published in Nature Communications, and “Digital biomarker of mental fatigue”, published in npj Digital Medicine, we present accurate, smartphone-based, ML-powered eye tracking that has the potential to unlock new research into applications across the fields of vision, accessibility, healthcare, and wellness, while additionally providing orders-of-magnitude scaling across diverse populations in the world, all using the front-facing camera on a smartphone. We also discuss the potential use of this technology as a digital biomarker of mental fatigue, which can be useful for improved wellness.

Model Overview
The core of our gaze model was a multilayer feed-forward convolutional neural network (ConvNet) trained on the MIT GazeCapture dataset. A face detection algorithm selected the face region with associated eye corner landmarks, which were used to crop the images down to the eye region alone. These cropped frames were fed through two identical ConvNet towers with shared weights. Each convolutional layer was followed by an average pooling layer. Eye corner landmarks were combined with the output of the two towers through fully connected layers. Rectified Linear Units (ReLUs) were used for all layers except the final fully connected output layer (FC6), which had no activation.

Architecture of the unpersonalized gaze model. Eye regions, extracted from a front-facing camera image, serve as input into a convolutional neural network. Fully-connected (FC) layers combine the output with eye corner landmarks to infer gaze x– and y-locations on screen via a multi-regression output layer.

The unpersonalized gaze model accuracy was improved by fine-tuning and per-participant personalization. For the latter, a lightweight regression model was fitted to the model’s penultimate ReLU layer and participant-specific data.

Model Evaluation
To evaluate the model, we collected data from consenting study participants as they viewed dots that appeared at random locations on a blank screen. The model error was computed as the distance (in cm) between the stimulus location and model prediction. Results show that while the unpersonalized model has high error, personalization with ~30s of calibration data led to an over fourfold error reduction (from 1.92 to 0.46cm). At a viewing distance of 25-40 cm, this corresponds to 0.6-1° accuracy, a significant improvement over the 2.4-3° reported in previous work [1, 2].

Additional experiments show that the smartphone eye tracker model’s accuracy is comparable to state-of-the-art wearable eye trackers both when the phone is placed on a device stand, as well as when users hold the phone freely in their hand in a near frontal headpose. In contrast to specialized eye tracking hardware with multiple infrared cameras close to each eye, running our gaze model using a smartphone’s single front-facing RGB camera is significantly more cost effective (~100x cheaper) and scalable.

Using this smartphone technology, we were able to replicate key findings from prior eye movement research in neuroscience and psychology, including standard oculomotor tasks (to understand basic visual functioning in the brain) and natural image understanding. For example, in a simple prosaccade task, which tests a person’s ability to quickly move their eyes towards a stimulus that appears on the screen, we found that the average saccade latency (time to move the eyes) matches prior work for basic visual health (210ms versus 200-250ms). In controlled visual search tasks, we were able to replicate key findings, such as the effect of target saliency and clutter on eye movements.

Example gaze scanpaths show the effect of the target’s saliency (i.e., color contrast) on visual search performance. Fewer fixations are required to find a target (left) with high saliency (different from the distractors), while more fixations are required to find a target (right) with low saliency (similar to the distractors).

For complex stimuli, such as natural images, we found that the gaze distribution (computed by aggregating gaze positions across all participants) from our smartphone eye tracker are similar to those obtained from bulky, expensive eye trackers that used highly controlled settings, such as laboratory chin rest systems. While the smartphone-based gaze heatmaps have a broader distribution (i.e., they appear more “blurred”) than hardware-based eye trackers, they are highly correlated both at the pixel level (r = 0.74) and object level (r = 0.90). These results suggest that this technology could be used to scale gaze analysis for complex stimuli such as natural and medical images (e.g., radiologists viewing MRI/PET scans).

Similar gaze distribution from our smartphone approach vs. a more expensive (100x) eye tracker (from the OSIE dataset).

We found that smartphone gaze could also help detect difficulty with reading comprehension. Participants reading passages spent significantly more time looking within the relevant excerpts when they answered correctly. However, as comprehension difficulty increased, they spent more time looking at the irrelevant excerpts in the passage before finding the relevant excerpt that contained the answer. The fraction of gaze time spent on the relevant excerpt was a good predictor of comprehension, and strongly negatively correlated with comprehension difficulty (r = −0.72).

Digital Biomarker of Mental Fatigue
Gaze detection is an important tool to detect alertness and wellbeing, and is studied widely in medicine, sleep research, and mission-critical settings such as medical surgeries, aviation safety, etc. However, existing fatigue tests are subjective and often time-consuming. In our recent paper published in npj Digital Medicine, we demonstrated that smartphone gaze is significantly impaired with mental fatigue, and can be used to track the onset and progression of fatigue.

A simple model predicts mental fatigue reliably using just a few minutes of gaze data from participants performing a task. We validated these findings in two different experiments — using a language-independent object-tracking task and a language-dependent proofreading task. As shown below, in the object-tracking task, participants’ gaze initially follows the object’s circular trajectory, but under fatigue, their gaze shows high errors and deviations. Given the pervasiveness of phones, these results suggest that smartphone-based gaze could provide a scalable, digital biomarker of mental fatigue.

Example gaze scanpaths for a participant with no fatigue (left) versus with mental fatigue (right) as they track an object following a circular trajectory.

The corresponding progression of fatigue scores (ground truth) and model prediction as a function of time on task.

Beyond wellness, smartphone gaze could also provide a digital phenotype for screening or monitoring health conditions such as autism spectrum disorder, dyslexia, concussion and more. This could enable timely and early interventions, especially for countries with limited access to healthcare services.

Another area that could benefit tremendously is accessibility. People with conditions such as ALS, locked-in syndrome and stroke have impaired speech and motor ability. Smartphone gaze could provide a powerful way to make daily tasks easier by using gaze for interaction, as recently demonstrated with Look to Speak.

Ethical Considerations
Gaze research needs careful consideration, including being mindful of the correct use of such technology — applications should obtain explicit approval and fully informed consent from users for the specific task at hand. In our work, all data was collected for research purposes with users’ explicit approval and consent. In addition, users were allowed to opt out at any point and request their data to be deleted. We continue to research additional ways to ensure ML fairness and improve the accuracy and robustness of gaze technology across demographics, in a responsible, privacy-preserving way.

Conclusion
Our findings of accurate and affordable ML-powered smartphone eye tracking offer the potential for orders-of-magnitude scaling of eye movement research across disciplines (e.g., neuroscience, psychology and human-computer interaction). They unlock potential new applications for societal good, such as gaze-based interaction for accessibility, and smartphone-based screening and monitoring tools for wellness and healthcare.

Acknowledgements
This work involved collaborative efforts from a multidisciplinary team of software engineers, researchers, and cross-functional contributors. We’d like to thank all the co-authors of the papers, including our team members, Junfeng He, Na Dai, Pingmei Xu, Venky Ramachandran; interns, Ethan Steinberg, Kantwon Rogers, Li Guo, and Vincent Tseng; collaborators, Tanzeem Choudhury; and UXRs: Mina Shojaeizadeh, Preeti Talwai, and Ran Tao. We’d also like to thank Tomer Shekel, Gaurav Nemade, and Reena Lee for their contributions to this project, and Vidhya Navalpakkam for her technical leadership in initiating and overseeing this body of work.

Posted by Zarana Parekh, Software Engineer and Jason Baldridge, Staff Research Scientist, Google Research

The past decade has seen remarkable progress on automatic image captioning, a task in which a computer algorithm creates written descriptions for images. Much of the progress has come through the use of modern deep learning methods developed for both computer vision and natural language processing, combined with large scale datasets that pair images with descriptions created by people. In addition to supporting important practical applications, such as providing descriptions of images for visually impaired people, these datasets also enable investigations into important and exciting research questions about grounding language in visual inputs. For example, learning deep representations for a word like “car”, means using both linguistic and visual contexts.

Image captioning datasets that contain pairs of textual descriptions and their corresponding images, such as MS-COCO and Flickr30k, have been widely used to learn aligned image and text representations and to build captioning models. Unfortunately, these datasets have limited cross-modal associations: images are not paired with other images, captions are only paired with other captions of the same image (also called co-captions), there are image-caption pairs that match but are not labeled as a match, and there are no labels that indicate when an image-caption pair does not match. This undermines research into how inter-modality learning (connecting captions to images, for example) impacts intra-modality tasks (connecting captions to captions or images to images). This is important to address, especially because a fair amount of work on learning from images paired with text is motivated by arguments about how visual elements should inform and improve representations of language.

To address this evaluation gap, we present “Crisscrossed Captions: Extended Intramodal and Intermodal Semantic Similarity Judgments for MS-COCO“, which was recently presented at EACL 2021. The Crisscrossed Captions (CxC) dataset extends the development and test splits of MS-COCO with semantic similarity ratings for image-text, text-text and image-image pairs. The rating criteria are based on Semantic Textual Similarity, an existing and widely-adopted measure of semantic relatedness between pairs of short texts, which we extend to include judgments about images as well. In all, CxC contains human-derived semantic similarity ratings for 267,095 pairs (derived from 1,335,475 independent judgments), a massive extension in scale and detail to the 50k original binary pairings in MS-COCO’s development and test splits. We have released CxC’s ratings, along with code to merge CxC with existing MS-COCO data. Anyone familiar with MS-COCO can thus easily enhance their experiments with CxC.

Crisscrossed Captions extends the MS-COCO evaluation sets by adding human-derived semantic similarity ratings for existing image-caption pairs and co-captions (solid lines), and it increases rating density by adding human ratings for new image-caption, caption-caption and image-image pairs (dashed lines).*

Creating the CxC Dataset
If a picture is worth a thousand words, it is likely because there are so many details and relationships between objects that are generally depicted in pictures. We can describe the texture of the fur on a dog, name the logo on the frisbee it is chasing, mention the expression on the face of the person who has just thrown the frisbee, or note the vibrant red on a large leaf in a tree above the person’s head, and so on.

The CxC dataset extends the MS-COCO evaluation splits with graded similarity associations within and across modalities. MS-COCO has five captions for each image, split into 410k training, 25k development, and 25k test captions (for 82k, 5k, 5k images, respectively). An ideal extension would rate every pair in the dataset (caption-caption, image-image, and image-caption), but this is infeasible as it would require obtaining human ratings for billions of pairs.

Given that randomly selected pairs of images and captions are likely to be dissimilar, we came up with a way to select items for human rating that would include at least some new pairs with high expected similarity. To reduce the dependence of the chosen pairs on the models used to find them, we introduce an indirect sampling scheme (depicted below) where we encode images and captions using different encoding methods and compute the similarity between pairs of same modality items, resulting in similarity matrices. Images are encoded using Graph-RISE embeddings, while captions are encoded using two methods — Universal Sentence Encoder (USE) and average bag-of-words (BoW) based on GloVe embeddings. Since each MS-COCO example has five co-captions, we average the co-caption encodings to create a single representation per example, ensuring all caption pairs can be mapped to image pairs (more below on how we select intermodality pairs).

Top: Text similarity matrix (each cell corresponds to a similarity score) constructed using averaged co-caption encodings, so each text entry corresponds to a single image, resulting in a 5k x 5k matrix. Two different text encoding methods were used, but only one text similarity matrix has been shown for simplicity. Bottom: Image similarity matrix for each image in the dataset, resulting in a 5k x 5k matrix.

The next step of the indirect sampling scheme is to use the computed similarities of images for a biased sampling of caption pairs for human rating (and vice versa). For example, we select two captions with high computed similarities from the text similarity matrix, then take each of their images, resulting in a new pair of images that are different in appearance but similar in what they depict based on their descriptions. For example, the captions “A dog looking bashfully to the side” and “A black dog lifts its head to the side to enjoy a breeze” would have a reasonably high model similarity, so the corresponding images of the two dogs in the figure below could be selected for image similarity rating. This step can also start with two images with high computed similarities to yield a new pair of captions. We now have indirectly sampled new intramodal pairs — at least some of which are highly similar — for which we obtain human ratings.

Top: Pairs of images are picked based on their computed caption similarity. Bottom: Pairs of captions are picked based on the computed similarity of the images they describe.

Last, we then use these new intramodal pairs and their human ratings to select new intermodal pairs for human rating. We do this by using existing image-caption pairs to link between modalities. For example, if a caption pair example ij was rated by humans as highly similar, we pick the image from example i and caption from example j to obtain a new intermodal pair for human rating. And again, we use the intramodal pairs with the highest rated similarity for sampling because this includes at least some new pairs with high similarity. Finally, we also add human ratings for all existing intermodal pairs and a large sample of co-captions.

The following table shows examples of semantic image similarity (SIS) and semantic image-text similarity (SITS) pairs corresponding to each rating, with 5 being the most similar and 0 being completely dissimilar.

Examples for each human-derived similarity score (left: 5 to 0, 5 being very similar and 0 being completely dissimilar) of image pairs based on SIS (middle) and SITS (right) tasks. Note that these examples are for illustrative purposes and are not themselves in the CxC dataset.

Evaluation
MS-COCO supports three retrieval tasks:

1. Given an image, find its matching captions out of all other captions in the evaluation set.
2. Given a caption, find its corresponding image out of all other images in the evaluation set.
3. Given a caption, find its other co-captions out of all other captions in the evaluation set.

MS-COCO’s pairs are incomplete because captions created for one image at times apply equally well to another, yet these associations are not captured in the dataset. CxC enhances these existing retrieval tasks with new positive pairs, and it also supports a new image-image retrieval task. With its graded similarity judgements, CxC also makes it possible to measure correlations between model and human rankings. Retrieval metrics in general focus only on positive pairs, while CxC’s correlation scores additionally account for the relative ordering of similarity and include low-scoring items (non-matches). Supporting these evaluations on a common set of images and captions makes them more valuable for understanding inter-modal learning compared to disjoint sets of caption-image, caption-caption, and image-image associations.

We ran a series of experiments to show the utility of CxC’s ratings. For this, we constructed three dual encoder (DE) models using BERT-base as the text encoder and EfficientNet-B4 as the image encoder:

1. A text-text (DE_T2T) model that uses a shared text encoder for both sides.
2. An image-text model (DE_I2T) that uses the aforementioned text and image encoders, and includes a layer above the text encoder to match the image encoder output.
3. A multitask model (DE_I2T+T2T) trained on a weighted combination of text-text and image-text tasks.

CxC retrieval results — a comparison of our text-text (T2T), image-text (I2T) and multitask (I2T+T2T) dual encoder models on all the four retrieval tasks.

From the results on the retrieval tasks, we can see that DE_I2T+T2T (yellow bar) performs better than DE_I2T (red bar) on the image-text and text-image retrieval tasks. Thus, adding the intramodal (text-text) training task helped improve the intermodal (image-text, text-image) performance. As for the other two intramodal tasks (text-text and image-image), DE_I2T+T2T shows strong, balanced performance on both of them.

CxC correlation results for the same models shown above.

For the correlation tasks, DE_I2T performs the best on SIS and DE_I2T+T2T is the best overall. The correlation scores also show that DE_I2T performs well only on images: it has the highest SIS but has much worse STS. Adding the text-text loss to DE_I2T training (DE_I2T+T2T) produces more balanced overall performance.

The CxC dataset provides a much more complete set of relationships between and among images and captions than the raw MS-COCO image-caption pairs. The new ratings have been released and further details are in our paper. We hope to encourage the research community to push the state of the art on the tasks introduced by CxC with better models for jointly learning inter- and intra-modal representations.

Acknowledgments
The core team includes Daniel Cer, Yinfei Yang and Austin Waters. We thank Julia Hockenmaier for her inputs on CxC’s formulation, the Google Data Compute Team, especially Ashwin Kakarla and Mohd Majeed for their tooling and annotation support, Yuan Zhang, Eugene Ie for their comments on the initial versions of the paper and Daphne Luong for executive support for the data collection.

* All the images in the article have been taken from the Open Images dataset under the CC-by 4.0 license.

Posted by Jonathan Mallinson and Aliaksei Severyn, Research Scientists, Google Research

Sequence-to-sequence (seq2seq) models have become a favoured approach for tackling natural language generation tasks, with applications ranging from machine translation to monolingual generation tasks, such as summarization, sentence fusion, text simplification, and machine translation post-editing. However these models appear to be a suboptimal choice for many monolingual tasks, as the desired output text often represents a minor rewrite of the input text. When accomplishing such tasks, seq2seq models are both slower because they generate the output one word at a time (i.e., autoregressively), and wasteful because most of the input tokens are simply copied into the output.

Instead, text-editing models have recently received a surge of interest as they propose to predict edit operations – such as word deletion, insertion, or replacement – that are applied to the input to reconstruct the output. However, previous text-editing approaches have limitations. They are either fast (being non-autoregressive), but not flexible, because they use a limited number of edit operations, or they are flexible, supporting all possible edit operations, but slow (autoregressive). In either case, they have not focused on modeling large structural (syntactic) transformations, for example switching from active voice, “They ate steak for dinner,” to passive, “Steak was eaten for dinner.” Instead, they’ve focused on local transformations, deleting or replacing short phrases. When a large structural transformation needs to occur, they either can’t produce it or insert a large amount of new text, which is slow.

In “FELIX: Flexible Text Editing Through Tagging and Insertion”, we introduce FELIX, a fast and flexible text-editing system that models large structural changes and achieves a 90x speed-up compared to seq2seq approaches whilst achieving impressive results on four monolingual generation tasks. Compared to traditional seq2seq methods, FELIX has the following three key advantages:

• Sample efficiency: Training a high precision text generation model typically requires large amounts of high-quality supervised data. FELIX uses three techniques to minimize the amount of required data: (1) fine-tuning pre-trained checkpoints, (2) a tagging model that learns a small number of edit operations, and (3) a text insertion task that is very similar to the pre-training task.
• Fast inference time: FELIX is fully non-autoregressive, avoiding slow inference times caused by an autoregressive decoder.
• Flexible text editing: FELIX strikes a balance between the complexity of learned edit operations and flexibility in the transformations it models.

In short, FELIX is designed to derive the maximum benefit from self-supervised pre-training, being efficient in low-resource settings, with little training data.

Overview
To achieve the above, FELIX decomposes the text-editing task into two sub-tasks: tagging to decide on the subset of input words and their order in the output text, and insertion, where words that are not present in the input are inserted. The tagging model employs a novel pointer mechanism, which supports structural transformations, while the insertion model is based on a Masked Language Model. Both of these models are non-autoregressive, ensuring the model is fast. A diagram of FELIX can be seen below.

An example of FELIX trained on data for a text simplification task. Input words are first tagged as KEEP (K), DELETE (D) or KEEP and INSERT (I). After tagging, the input is reordered. This reordered input is then fed to a masked language model.

The Tagging Model
The first step in FELIX is the tagging model, which consists of two components. First the tagger determines which words should be kept or deleted and where new words should be inserted. When the tagger predicts an insertion, a special MASK token is added to the output. After tagging, there is a reordering step where the pointer reorders the input to form the output, by which it is able to reuse parts of the input instead of inserting new text. The reordering step supports arbitrary rewrites, which enables modeling large changes. The pointer network is trained such that each word in the input points to the next word as it will appear in the output, as shown below.

Realization of the pointing mechanism to transform “There are 3 layers in the walls of the heart” into “the heart MASK 3 layers”.

The Insertion Model
The output of the tagging model is the reordered input text with deleted words and MASK tokens predicted by the insertion tag. The insertion model must predict the content of MASK tokens. Because FELIX’s insertion model is very similar to the pretraining objective of BERT, it can take direct advantage of the pre-training, which is particularly advantageous when data is limited.

Example of the insertion model, where the tagger predicts two words will be inserted and the insertion model predicts the content of the MASK tokens.

Results
We evaluated FELIX on sentence fusion, text simplification, abstractive summarization, and machine translation post-editing. These tasks vary significantly in the types of edits required and dataset sizes under which they operate. Below are the results on the sentence fusion task (i.e., merging two sentences into one), comparing FELIX against a large pre-trained seq2seq model (BERT2BERT) and a text-editing model (LaserTager), under a range of dataset sizes. We see that FELIX outperforms LaserTagger and can be trained on as little as a few hundred training examples. For the full dataset, the autoregressive BERT2BERT outperforms FELIX. However, during inference, this model takes significantly longer.

A comparison of different training dataset sizes on the DiscoFuse dataset. We compare FELIX (using the best performing model) against BERT2BERT and LaserTagger.

Latency in milliseconds for a batch of 32 on a Nvidia Tesla P100.

Conclusion
We have presented FELIX, which is fully non-autoregressive, providing even faster inference times, while achieving state-of-the-art results. FELIX also minimizes the amount of required training data with three techniques — fine-tuning pre-trained checkpoints, learning a small number of edit operations, and an insertion task that mimics masked language model task from the pre-training. Lastly, FELIX strikes a balance between the complexity of learned edit operations and the percentage of input-output transformations it can handle. We have open-sourced the code for FELIX and hope it will provide researchers with a faster, more efficient, and more flexible text-editing model.

Acknowledgements
This research was conducted by Jonathan Mallinson, Aliaksei Severyn (equal contribution), Eric Malmi, Guillermo Garrido. We would like to thank Aleksandr Chuklin, Daniil Mirylenka, Ryan McDonald, and Sebastian Krause for useful discussions, running early experiments and paper suggestions.

Posted by Thao Nguyen, AI Resident, Google Research

A common practice to improve a neural network’s performance and tailor it to available computational resources is to adjust the architecture depth and width. Indeed, popular families of neural networks, including EfficientNet, ResNet and Transformers, consist of a set of architectures of flexible depths and widths. However, beyond the effect on accuracy, there is limited understanding of how these fundamental choices of architecture design affect the model, such as the impact on its internal representations.

In “Do Wide and Deep Networks Learn the Same Things? Uncovering How Neural Network Representations Vary with Width and Depth”, we perform a systematic study of the similarity between wide and deep networks from the same architectural family through the lens of their hidden representations and final outputs. In very wide or very deep models, we find a characteristic block structure in their internal representations, and establish a connection between this phenomenon and model overparameterization. Comparisons across models demonstrate that those without the block structure show significant similarity between representations in corresponding layers, but those containing the block structure exhibit highly dissimilar representations. These properties of the internal representations in turn translate to systematically different errors at the class and example levels for wide and deep models when they are evaluated on the same test set.

Comparing Representation Similarity with CKA
We extended prior work on analyzing representations by leveraging our previously developed Centered Kernel Alignment (CKA) technique, which provides a robust, scalable way to determine the similarity between the representations learned by any pair of neural network layers. CKA takes as input the representations (i.e., the activation matrices) from two layers, and outputs a similarity score between 0 (not at all similar) and 1 (identical representations).

We apply CKA to a family of ResNets of varying depths and widths, trained on common benchmark datasets (CIFAR-10, CIFAR-100 and ImageNet), and use representation heatmaps to illustrate the results. The x and y axes of each heatmap index the layers of the model(s) in consideration, going from input to output, and each entry (i, j) is the CKA similarity score between layer i and layer j.

We use CKA to compute the representation similarity for all pairs of layers within a single model (i.e., when network 1 and network 2 are identical), and across models (i.e., when network 1 and network 2 are trained with different random initializations, or have different architectures altogether).

Below is an example of the resulting heatmap when we compare representations of each layer to every other layer within a single ResNet of depth 26 and width multiplier 1. In the design convention used here, the stated depth only refers to the number of convolutional layers in the network, but we analyze all layers present, and the width multiplier applies to the number of filters in each convolution. Notice the checkerboard pattern in the heatmap, which is caused by skip connections (shortcuts between layers) in the architecture.

The Emergence of the Block Structure
What stands out from the representation heatmaps of deeper or wider networks is the emergence of a large set of consecutive layers with highly similar representations, which appears in the heatmaps as a yellow square (i.e., a region with high CKA scores). This phenomenon, which we call the block structure, suggests that the underlying layers may not be as efficient at progressively refining the network’s representations as we expect. Indeed, we show that the task performance becomes stagnant inside the block structure, and that it is possible to prune some underlying layers without affecting the final performance.

Block structure — a large, contiguous set of layers with highly similar representations — emerges with increasing width or depth. Each heatmap panel shows the CKA similarity between all pairs of layers within a single neural network. While its size and position can vary across different training runs, the block structure is a robust phenomenon that arises consistently in larger models.

With additional experiments, we show that the block structure has less to do with the absolute model size, than with the size of the model relative to the size of the training dataset. As we reduce the training dataset size, the block structure starts to appear in shallower and narrower networks:

With increasing network width (towards the right along each row) and decreasing dataset size (down each column), the relative model capacity (with respect to a given task) is effectively inflated, and the block structure begins to appear in smaller models.

Through further analysis, we are also able to demonstrate that the block structure arises from preserving and propagating the dominant principal components of its underlying representations. Refer to our paper for more details.

Comparing Representations Across Models
Going further, we study the implications of depth and width on representations across models of different random initializations and different architectures, and find that the presence of block structure makes a significant difference in this context as well. Despite having different architectures, wide and deep models without the block structure do exhibit representation similarity with each other, with corresponding layers broadly being of the same proportional depth in the model. However, when the block structure is present, its representations are unique to each model. This suggests that despite having similar overall performance, each wide or deep model with the block structure picks up a unique mapping from the input to the output.

For smaller models (e.g., ResNet-38 1×), CKA across different initializations (off the diagonal) closely resembles CKA within a single model (on the diagonal). In contrast, representations within the block structure of wider and deeper models (e.g., ResNet-38 10×, ResNet-164 1×) are highly dissimilar across training runs.

Error Analysis of Wide and Deep Models
Having explored the properties of the learned representations of wide and deep models, we next turn to understanding how they influence the diversity of the output predictions. We train populations of networks of different architectures and determine on which test set examples each architecture configuration tends to make errors.

On both CIFAR-10 and ImageNet datasets, wide and deep models that have the same average accuracy still demonstrate statistically significant differences in example-level predictions. The same observation holds for class-level errors on ImageNet, with wide models exhibiting a small advantage in identifying classes corresponding to scenes, and deep networks being relatively more accurate on consumer goods.

Per-class differences on ImageNet between models with increased width (y-axis) or depth (x-axis). Orange dots reflect differences between two sets of 50 different random initializations of ResNet-83 (1×).

Conclusions
In studying the effects of depth and width on internal representations, we uncover a block structure phenomenon, and demonstrate its connection to model capacity. We also show that wide and deep models exhibit systematic output differences at class and example levels. Check out the paper for full details on these results and additional insights! We’re excited about the many interesting open questions these findings suggest, such as how the block structure arises during training, whether the phenomenon occurs in domains beyond image classification, and ways these insights on internal representations can inform model efficiency and generalization.

Acknowledgements
This is a joint work with Maithra Raghu and Simon Kornblith. We would like to thank Tom Small for the visualizations of the representation heatmap.

Posted by Jaqui Herman, Research Specialist and Tim Herrmann, Program Manager

The 9th International Conference on Learning Representations (ICLR 2021), a virtual conference focused on deep learning, kicked off this week, offering conference and workshop tracks that present some of the latest research in deep learning and its applications to areas such as computer vision, computational biology, speech recognition, text understanding, and more.

As a Platinum Sponsor of ICLR 2021, Google will have a strong presence with over 100 accepted publications and participation on organizing committees and in workshops. If you have registered for ICLR 2021, we hope you’ll watch our talks and learn about the work at Google that goes into solving interesting problems for billions of people. Learn more about our research being presented in the list below (Googlers in bold).

Officers and Board Members
Includes: Hugo Larochelle, Tara Sainath

Organizing Committee
Includes: Sanmi Koyejo, Chelsea Finn

Area Chairs
Includes: Abhishek Kumar, Aditya Menon, Aleksandra Faust, Alexey Dosovitskiy, Andrew Cotter, Andrew Dai, Augustus Odena, Been Kim, Behnam Neyshabur, Ben Poole, Bo Dai, Bo Li, Branislav Kveton, Ce Liu, Claudio Gentile, Colin Raffel, Danny Tarlow, David Ha, Dengyong Zhou, Dumitru Erhan, Dustin Tran, Felix Hill, George Tucker, Hanie Sedghi, Heinrich Jiang, Hossein Mobahi, Izhak Shafran, Jascha Sohl-Dickstein, Jasper Snoek, Jean-Philippe Vert, Jeffrey Pennington, Justin Gilmer, Kevin Swersky, Marco Cuturi, Mario Lucic, Marlos C. Machado, Mathieu Blondel, Matt Johnson, Matthieu Geist, Mohammad Norouzi, Naman Agarwal, Navdeep Jaitly, Nicolas Le Roux, Niki Parmar, Olivier Bachem, Olivier Pietquin, Philip Long, Quentin Berthet, Razvan Pascanu, Rodolphe Jenatton, Samy Bengio*, Sebastian Nowozin, Silvio Lattanzi, Slav Petrov, Srinadh Bhojanapalli, Suman Ravuri, Tim Salimans, Vitaly Kuznetsov, William Cohen, Yann Dauphin, Yujia Li

Publications
Scalable Learning and MAP Inference for Nonsymmetric Determinantal Point Processes
Mike Gartrell, Insu Han, Elvis Dohmatob, Jennifer Gillenwater, Victor-Emmanuel Brunel

An Image is Worth 16×16 Words: Transformers for Image Recognition at Scale (see the blog post)
Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, Jakob Uszkoreit, Neil Houlsby

Share or Not? Learning to Schedule Language-Specific Capacity for Multilingual Translation
Biao Zhang*, Ankur Bapna, Rico Sennrich, Orhan Firat

Evolving Reinforcement Learning Algorithms (see the blog post)
John D Co-Reyes, Yingjie Miao, Daiyi Peng, Esteban Real, Quoc V Le, Sergey Levine, Honglak Lee, Aleksandra Faust

Score-Based Generative Modeling through Stochastic Differential Equations
Yang Song*, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, Ben Poole

What Matters for On-Policy Deep Actor-Critic Methods? A Large-Scale Study
Marcin Andrychowicz, Anton Raichuk, Piotr Stańczyk, Manu Orsini, Sertan Girgin, Raphaël Marinier, Leonard Hussenot, Matthieu Geist, Olivier Pietquin, Marcin Michalski, Sylvain Gelly, Olivier Bachem

When Do Curricula Work?
Xiaoxia Wu, Ethan Dyer, Behnam Neyshabur

Sharpness-aware Minimization for Efficiently Improving Generalization
Pierre Foret*, Ariel Kleiner, Hossein Mobahi, Behnam Neyshabur

Gradient Vaccine: Investigating and Improving Multi-task Optimization in Massively Multilingual Models Zirui Wang*, Yulia Tsvetkov, Orhan Firat, Yuan Cao

Mathematical Reasoning via Self-supervised Skip-tree Training
Markus Norman Rabe, Dennis Lee, Kshitij Bansal, Christian Szegedy

Long-Tail Learning via Logit Adjustment
Aditya Krishna Menon, Sadeep Jayasumana, Ankit Singh Rawat, Himanshu Jain, Andreas Veit, Sanjiv Kumar

Are Neural Rankers Still Outperformed by Gradient Boosted Decision Trees?
Zhen Qin, Le Yan, Honglei Zhuang, Yi Tay, Rama Kumar Pasumarthi, Xuanhui Wang, Michael Bendersky, Marc Najork

LambdaNetworks: Modeling Long-Range Interactions without Attention
Irwan Bello

Contrastive Behavioral Similarity Embeddings for Generalization in Reinforcement Learning
Rishabh Agarwal, Marlos C. Machado, Pablo Samuel Castro, Marc G Bellemare

BUSTLE: Bottom-Up Program Synthesis Through Learning-Guided Exploration
Augustus Odena, Kensen Shi, David Bieber, Rishabh Singh, Charles Sutton, Hanjun Dai

Practical Real Time Recurrent Learning with a Sparse Approximation
Jacob Menick, Erich Elsen, Utku Evci, Simon Osindero, Karen Simonyan, Alex Graves

LEAF: A Learnable Frontend for Audio Classification (see the blog post)
Neil Zeghidour, Olivier Teboul, Félix de Chaumont Quitry, Marco Tagliasacchi

Batch Reinforcement Learning Through Continuation Method
Yijie Guo, Shengyu Feng, Nicolas Le Roux, Ed Chi, Honglak Lee, Minmin Chen

Scalable Transfer Learning with Expert Models
Joan Puigcerver, Carlos Riquelme Ruiz, Basil Mustafa, Cedric Renggli*, André Susano Pinto, Sylvain Gelly, Daniel Keysers, Neil Houlsby

Contrastive Behavioral Similarity Embeddings for Generalization in Reinforcement Learning
Rishabh Agarwal, Marlos C. Machado*, Pablo Samuel Castro, Marc G Bellemare

Scaling Symbolic Methods Using Gradients for Neural Model Explanation
Subham Sekhar Sahoo, Subhashini Venugopalan, Li Li, Rishabh Singh, Patrick Riley

Primal Wasserstein Imitation Learning (see the blog post)
Robert Dadashi, Leonard Hussenot, Matthieu Geist, Olivier Pietquin

Reset-Free Lifelong Learning with Skill-Space Planning
Kevin Lu, Aditya Grover, Pieter Abbeel, Igor Mordatch

Teaching Temporal Logics to Neural Networks
Christopher Hahn, Frederik Schmitt, Jens U. Kreber, Markus Norman Rabe, Bernd Finkbeiner

Shape-Texture Debiased Neural Network Training
Yingwei Li, Qihang Yu, Mingxing Tan, Jieru Mei, Peng Tang, Wei Shen, Alan Yuille, Cihang Xie

Rethinking Embedding Coupling in Pre-trained Language Models
Hyung Won Chung, Thibault Fevry*, Henry Tsai, Melvin Johnson, Sebastian Ruder

Overparameterisation and Worst-Case Generalisation: Friend or Foe?
Aditya Krishna Menon, Ankit Singh Rawat, Sanjiv Kumar

Single-Photon Image Classification
Thomas Fischbacher, Luciano Sbaiz

Into the Wild with AudioScope: Unsupervised Audio-Visual Separation of On-Screen Sounds
Efthymios Tzinis*, Scott Wisdom, Aren Jansen, Shawn Hershey, Tal Remez, Daniel P. W. Ellis, John R. Hershey

Adaptive Federated Optimization
Sashank J. Reddi, Zachary Charles, Manzil Zaheer, Zachary Garrett, Keith Rush, Jakub Konečný, Sanjiv Kumar, Hugh Brendan McMahan

Share or Not? Learning to Schedule Language-Specific Capacity for Multilingual Translation
Biao Zhang*, Ankur Bapna, Rico Sennrich, Orhan Firat

Off-Dynamics Reinforcement Learning: Training for Transfer with Domain Classifiers
Benjamin Eysenbach, Shreyas Chaudhari, Swapnil Asawa, Sergey Levine, Ruslan Salakhutdinov

Open Question Answering over Tables and Text
Wenhu Chen*, Ming-Wei Chang, Eva Schlinger, William Yang Wang, William W. Cohen

Practical Real Time Recurrent Learning with a Sparse Approximation
Jacob Menick, Erich Elsen, Utku Evci, Simon Osindero, Karen Simonyan, Alex Graves

IDF++: Analyzing and Improving Integer Discrete Flows for Lossless Compression
Rianne van den Berg, Alexey A. Gritsenko, Mostafa Dehghani, Casper Kaae Sønderby, Tim Salimans

A Universal Representation Transformer Layer for Few-Shot Image Classification
Lu Liu, William L. Hamilton, Guodong Long, Jing Jiang, Hugo Larochelle

Tradeoffs in Data Augmentation: An Empirical Study
Raphael Gontijo-Lopes, Sylvia Smullin, Ekin Dogus Cubuk, Ethan Dyer

Coping with Label Shift via Distributionally Robust Optimisation
Jingzhao Zhang, Aditya Krishna Menon, Andreas Veit, Srinadh Bhojanapalli, Sanjiv Kumar, Suvrit Sra

Rethinking Attention with Performers (see the blog post)
Krzysztof Marcin Choromanski, Valerii Likhosherstov, David Dohan, Xingyou Song, Andreea Gane, Tamas Sarlos, Peter Hawkins, Jared Quincy Davis, Afroz Mohiuddin, Lukasz Kaiser, David Benjamin Belanger, Lucy J Colwell, Adrian Weller

Teaching with Commentaries
Aniruddh Raghu*, Maithra Raghu, Simon Kornblith, David Duvenaud, Geoffrey Hinton

Anatomy of Catastrophic Forgetting: Hidden Representations and Task Semantics
Vinay Venkatesh Ramasesh, Ethan Dyer, Maithra Raghu

Model-Based Offline Planning
Arthur Argenson, Gabriel Dulac-Arnold

The Geometry of Integration in Text Classification RNNs
Kyle Aitken*, Vinay Venkatesh Ramasesh, Ankush Garg, Yuan Cao, David Sussillo, Niru Maheswaranathan

On the Origin of Implicit Regularization in Stochastic Gradient Descent
Samuel L Smith, Benoit Dherin, David Barrett, Soham De

Score-Based Generative Modeling through Stochastic Differential Equations
Yang Song*, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, Ben Poole

The Deep Bootstrap Framework: Good Online Learners are Good Offline Generalizers (see the blog post)
Preetum Nakkiran*, Behnam Neyshabur, Hanie Sedghi

Learning Energy-Based Models by Diffusion Recovery Likelihood
Ruiqi Gao, Yang Song, Ben Poole, Ying Nian Wu, Diederik P Kingma

Latent Skill Planning for Exploration and Transfer
Kevin Xie, Homanga Bharadhwaj, Danijar Hafner, Animesh Garg, Florian Shkurti

PseudoSeg: Designing Pseudo Labels for Semantic Segmentation
Yuliang Zou*, Zizhao Zhang, Han Zhang, Chun-Liang Li, Xiao Bian, Jia-Bin Huang, Tomas Pfister

WaveGrad: Estimating Gradients for Waveform Generation
Nanxin Chen*, Yu Zhang, Heiga Zen, Ron J Weiss, Mohammad Norouzi, William Chan

One Network Fits All? Modular versus Monolithic Task Formulations in Neural Networks
Atish Agarwala, Abhimanyu Das, Brendan Juba*, Rina Panigrahy, Vatsal Sharan*, Xin Wang, Qiuyi Zhang

Long Range Arena : A Benchmark for Efficient Transformers
Yi Tay, Mostafa Dehghani, Samira Abnar, Yikang Shen, Dara Bahri, Philip Pham, Jinfeng Rao, Liu Yang, Sebastian Ruder, Donald Metzler

Explainable Deep One-Class Classification
Philipp Liznerski, Lukas Ruff, Robert A. Vandermeulen, Billy Joe Franks, Marius Kloft, Klaus Robert Muller

Net-DNF: Effective Deep Modeling of Tabular Data
Liran Katzir, Gal Elidan, Ran El-Yaniv

Deployment-Efficient Reinforcement Learning via Model-Based Offline Optimization
Tatsuya Matsushima, Hiroki Furuta, Yutaka Matsuo, Ofir Nachum, Shixiang Gu

Auxiliary Task Update Decomposition: The Good, the Bad and the Neutral
Lucio M. Dery, Yann Dauphin, David Grangier

Long-Tail Learning via Logit Adjustment
Aditya Krishna Menon, Sadeep Jayasumana, Ankit Singh Rawat, Himanshu Jain, Andreas Veit, Sanjiv Kumar

Average-Case Acceleration for Bilinear Games and Normal Matrices
Carles Domingo-Enrich, Fabian Pedregosa, Damien Scieur

OPAL: Offline Primitive Discovery for Accelerating Offline Reinforcement Learning
Anurag Ajay*, Aviral Kumar, Pulkit Agrawal, Sergey Levine, Ofir Nachum

Training Independent Subnetworks for Robust Prediction
Marton Havasi*, Rodolphe Jenatton, Stanislav Fort, Jeremiah Zhe Liu, Jasper Snoek, Balaji Lakshminarayanan, Andrew Mingbo Dai, Dustin Tran

Benchmarks for Deep Off-Policy Evaluation
Justin Fu, Mohammad Norouzi, Ofir Nachum, George Tucker, Ziyu Wang, Alexander Novikov, Mengjiao Yang, Michael R Zhang, Yutian Chen, Aviral Kumar, Cosmin Paduraru, Sergey Levine, Thomas Paine

TropEx: An Algorithm for Extracting Linear Terms in Deep Neural Networks
Martin Trimmel, Henning Petzka, Cristian Sminchisescu

Mastering Atari with Discrete World Models (see the blog post)
Danijar Hafner, Timothy P Lillicrap, Mohammad Norouzi, Jimmy Ba

Exploring the Uncertainty Properties of Neural Networks’ Implicit Priors in the Infinite-Width Limit
Danijar Hafner, Timothy P Lillicrap, Mohammad Norouzi, Jimmy Ba

Graph Traversal with Tensor Functionals: A Meta-Algorithm for Scalable Learning
Ben Adlam, Jaehoon Lee, Lechao Xiao, Jeffrey Pennington, Jasper Snoek

Anchor & Transform: Learning Sparse Embeddings for Large Vocabularies
Paul Pu Liang*, Manzil Zaheer, Yuan Wang, Amr Ahmed

Sharpness-Aware Minimization for Efficiently Improving Generalization
Pierre Foret*, Ariel Kleiner, Hossein Mobahi, Behnam Neyshabur

HyperGrid Transformers: Towards A Single Model for Multiple Tasks
Yi Tay, Zhe Zhao, Dara Bahri, Donald Metzler, Da-Cheng Juan

Federated Learning via Posterior Averaging: A New Perspective and Practical Algorithms
Maruan Al-Shedivat*, Jennifer Gillenwater, Eric Xing, Afshin Rostamizadeh

BUSTLE: Bottom-Up Program Synthesis Through Learning-Guided Exploration
Augustus Odena, Kensen Shi, David Bieber, Rishabh Singh, Charles Sutton, Hanjun Dai

Are Neural Rankers Still Outperformed by Gradient Boosted Decision Trees?
Zhen Qin, Le Yan, Honglei Zhuang, Yi Tay, Rama Kumar Pasumarthi, Xuanhui Wang, Michael Bendersky, Marc Najork

Do Wide and Deep Networks Learn the Same Things? Uncovering How Neural Network Representations Vary with Width and Depth
Thao Nguyen, Maithra Raghu, Simon Kornblith

A Unifying View on Implicit Bias in Training Linear Neural Networks
Chulhee Yun*, Shankar Krishnan, Hossein Mobahi

Implicit Under-Parameterization Inhibits Data-Efficient Deep Reinforcement Learning
Aviral Kumar, Rishabh Agarwal, Dibya Ghosh, Sergey Levine

Mathematical Reasoning via Self-Supervised Skip-Tree Training
Markus Norman Rabe, Dennis Lee, Kshitij Bansal, Christian Szegedy

Lipschitz Recurrent Neural Networks
N. Benjamin Erichson, Omri Azencot, Alejandro Queiruga, Liam Hodgkinson, Michael W. Mahoney

Autoregressive Dynamics Models for Offline Policy Evaluation and Optimization
Michael R Zhang*, Thomas Paine, Ofir Nachum, Cosmin Paduraru, George Tucker, ziyu wang, Mohammad Norouzi

The Importance of Pessimism in Fixed-Dataset Policy Optimization
Jacob Buckman, Carles Gelada, Marc G Bellemare

Monotonic Kronecker-Factored Lattice
William Taylor Bakst, Nobuyuki Morioka, Erez Louidor

What Matters for On-Policy Deep Actor-Critic Methods? A Large-Scale Study
Marcin Andrychowicz, Anton Raichuk, Piotr Stańczyk, Manu Orsini, Sertan Girgin, Raphaël Marinier, Leonard Hussenot, Matthieu Geist, Olivier Pietquin, Marcin Michalski, Sylvain Gelly, Olivier Bachem

Adversarially Guided Actor-Critic
Yannis Flet-Berliac, Johan Ferret, Olivier Pietquin, Philippe Preux, Matthieu Geist

Scalable Learning and MAP Inference for Nonsymmetric Determinantal Point Processes
Mike Gartrell, Insu Han, Elvis Dohmatob, Jennifer Gillenwater, Victor-Emmanuel Brunel

GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding
Dmitry Lepikhin, HyoukJoong Lee, Yuanzhong Xu, Dehao Chen, Orhan Firat, Yanping Huang, Maxim Krikun, Noam Shazeer, Zhifeng Chen

Revisiting Hierarchical Approach for Persistent Long-Term Video Prediction
Wonkwang Lee, Whie Jung, Han Zhang, Ting Chen, Jing Yu Koh, Thomas Huang, Hyungsuk Yoon, Honglak Lee*, Seunghoon Hong

Gradient Vaccine: Investigating and Improving Multi-task Optimization in Massively Multilingual Models
Zirui Wang, Yulia Tsvetkov, Orhan Firat, Yuan Cao

Dataset Meta-Learning from Kernel Ridge-Regression
Timothy Nguyen, Zhourong Chen, Jaehoon Lee

Dual-Mode ASR: Unify and Improve Streaming ASR with Full-Context Modeling
Jiahui Yu, Wei Han, Anmol Gulati, Chung-Cheng Chiu, Bo Li, Tara N Sainath, Yonghui Wu, Ruoming Pang

Implicit Gradient Regularization
David Barrett, Benoit Dherin

Contrastive Behavioral Similarity Embeddings for Generalization in Reinforcement Learning
Rishabh Agarwal, Marlos C. Machado, Pablo Samuel Castro, Marc G Bellemare

Deconstructing the Regularization of BatchNorm
Yann Dauphin, Ekin Dogus Cubuk

C-Learning: Learning to Achieve Goals via Recursive Classification
Benjamin Eysenbach, Ruslan Salakhutdinov, Sergey Levine

Evolving Reinforcement Learning Algorithms
John D Co-Reyes, Yingjie Miao, Daiyi Peng, Esteban Real, Quoc V Le, Sergey Levine, Honglak Lee, Aleksandra Faust

Colorization Transformer
Manoj Kumar, Dirk Weissenborn, Nal Kalchbrenner

Control-Aware Representations for Model-based Reinforcement Learning
Brandon Cui, Yinlam Chow, Mohammad Ghavamzadeh

Evaluations and Methods for Explanation through Robustness Analysis
Cheng-Yu Hsieh, Chih-Kuan Yeh, Xuanqing Liu, Pradeep Kumar Ravikumar, Seungyeon Kim, Sanjiv Kumar, Cho-Jui Hsieh

Learning and Evaluating Representations for Deep One-Class Classification
Kihyuk Sohn, Chun-Liang Li, Jinsung Yoon, Minho Jin, Tomas Pfister

No MCMC for Me: Amortized Sampling for Fast and Stable Training of Energy-Based Models
Will Sussman Grathwohl, Jacob Jin Kelly, Milad Hashemi, Mohammad Norouzi, Kevin Swersky, David Duvenaud

Neural Thompson Sampling
Weitong ZHANG, Dongruo Zhou, Lihong Li, Quanquan Gu

A Design Space Study for LISTA and Beyond
Tianjian Meng, Xiaohan Chen, Yifan Jiang, Zhangyang Wang

i-Mix: A Domain-Agnostic Strategy for Contrastive Representation Learning
Kibok Lee, Yian Zhu, Kihyuk Sohn, Chun-Liang Li, Jinwoo Shin, Honglak Lee

Factorizing Declarative and Procedural Knowledge in Structured, Dynamical Environments
Anirudh Goyal, Alex Lamb, Phanideep Gampa, Philippe Beaudoin, Charles Blundell, Sergey Levine, Yoshua Bengio, Michael Curtis Mozer

Calibration of Neural Networks using Splines
Kartik Gupta, Amir Rahimi, Thalaiyasingam Ajanthan, Thomas Mensink, Cristian Sminchisescu, Richard Hartley

Extreme Memorization via Scale of Initialization
Harsh Mehta, Ashok Cutkosky, Behnam Neyshabur

Molecule Optimization by Explainable Evolution
Binghong Chen, Tianzhe Wang, Chengtao Li, Hanjun Dai, Le Song

Combining Ensembles and Data Augmentation Can Harm Your Calibration
Yeming Wen, Ghassen Jerfel, Rafael Muller, Michael W Dusenberry, Jasper Snoek, Balaji Lakshminarayanan, Dustin Tran

Workshops
Science and Engineering of Deep Learning
Speakers and Panelists include: Alex Hanna
Moderator and Advisors include: Emily Denton
Organizers include: Negar Rostemzadeh, Samy Bengio*

Synthetic Data Generation: Quality, Privacy, Bias
Speakers include: Jinsung Yoon, Emily Denton
Program Committee includes: Syed Ashrafulla

Enormous Language Models: Perspectives and Benchmarks
Speakers and Panelists include: Noam Shazeer, Natalie Schluter
Organizers include: Colin Raffel, Adam Roberts, Jascha Sohl-Dickstein, Katherine Lee, William Fedus, Aitor Lewkowycz

The Role of Mathematical Reasoning in General Artificial Intelligence
Speakers and Panelists include: Markus Rabe, Christian Szegedy

Weakly Supervised Learning
Invited Speakers include: Lu Jiang

Learning to Learn
Organizers include: Yevgen Chebotar

Embodied Multimodal Learning (EML)
Invited Speakers includes: Sergey Levine

Distributed and Private Machine Learning
Program Committee includes: Peter Kairouz, Ananda Theertha Suresh

S2D-OLAD: From Shallow to Deep, Overcoming Limited and Adverse Data
Invited Speakers include: Alex Hanna, Hugo Larochelle
Organizers include: Vincent Dumoulin

Responsible AI (RAI)
Speakers include: Been Kim

Energy-Based Models: Current Perspectives, Challenges, and Opportunities
Organizers include: Adji Bousso Dieng, Igor Mordatch

A Roadmap to Never-Ending RL
Invited Session Panelists include: Aleksandra Faust
Program Committee includes: Coline Devin, Karol Hausman, Ben Eysenbach, Ofir Nachum, Ryan Julian, Tianhe Yu, Dumitru Erhan, Marc Pickett, Shixiang Gu

2nd Workshop on Practical ML for Developing Countries: Learning Under Limited/low Resource Scenarios
Program Committee includes: Pablo Samuel Castro

Beyond Static Papers: Rethinking How We Share Scientific Understanding in ML
Speakers include: David Ha, Hugo Larochelle
Organizers include: Sara Hooker

* Indicates work done while at Google

Posted by Martin Mladenov, Research Scientist and Chih-wei Hsu, Software Engineer, Google Research

Recommender systems are the primary interface connecting users to a wide variety of online content, and therefore must overcome a number of challenges across the user population in order to serve them equitably. To this end, in 2019 we released RecSim, a configurable platform for authoring simulation environments to facilitate the study of RL algorithms (the de facto standard ML approach for addressing sequential decision problems) in recommender systems. However, as the technology has progressed, it has become increasingly important to address the gap between simulation and real-world applications, ensuring that models are flexible and easily extendible, enabling probabilistic inference of user dynamics, and addressing computational efficiency.

To address these issues, we recently released RecSim NG, the “Next Generation” of simulators for recommender systems research and development. RecSim NG is a response to a set of use cases that have emerged as important challenges in the application of simulation to real-world problems. It addresses the gap between simulation and real-world applications, ensures the models are flexible and easily extendible, enables probabilistic inference of user dynamics, and addresses computational efficiency.

Overview of RecSim NG
RecSim NG is a scalable, modular, differentiable simulator implemented in Edward2 and TensorFlow. It offers a powerful, general probabilistic programming language for agent-behavior specification.

RecSim NG significantly expands the modeling capabilities of RecSim in two ways. First, the story API allows the simulation of scenarios where an arbitrary number of actors (e.g., recommenders, content consumers, content producers, advertisers) interact with one another. This enables the flexible modeling of entire recommender ecosystems, as opposed to the usual isolated user-recommender interaction setting. Second, we introduced a library of behavioral building blocks that, much like Keras layers, implement well-known modeling primitives that can be assembled to build complex models quickly. Following the object-oriented paradigm, RecSim NG uses entity patterns to encapsulate shared parameters that govern various agent behaviors, like user satisfaction, and uses templates to define large populations of agents concisely in a way that abstracts agent “individuality” without duplicating invariant behaviors.

Apart from the typical use of simulators to generate Monte Carlo samples, RecSim NG directly enables various other forms of probabilistic reasoning. While domain knowledge and intuition are key to modeling any recommendation problem, the simulation fidelity needed to bridge the so-called “sim2real” gap can only be achieved by calibrating the simulator’s model to observed data. For data-driven simulation, RecSim NG makes it easy to implement various model-learning algorithms, such as expectation-maximization (EM), generative adversarial training, etc.

Also available within RecSim NG are tools for probabilistic inference and latent-variable model learning, backed by automatic differentiation and tracing. RecSim NG exposes a small set of Edward2 program transformations tailored to simulation-specific tasks. Its log-probability module can evaluate the probabilities of trajectories according to the probabilistic graphical model induced by the simulation. This, together with the automatic differentiation provided by the TensorFlow runtime, enables the implementation of maximum-likelihood estimation and model learning within the simulation itself. RecSim NG can readily use the Markov-chain Monte Carlo (MCMC) machinery provided by TensorFlow Probability to power posterior inference and latent-variable model learning. For example, a simulation model that describes how latent user attributes (e.g., preferences, intents, satisfaction) are translated into observational data (e.g., clicks, ratings, comments) can be “run in reverse,” that is, real observational data generated by a recommender system can be used to identify the most likely configuration of latent user attributes, which in turn can be used to assess the quality of the user experience. This allows for a simulation model to be integrated directly into the full data-science and model-development workflow.

Assessing recommender ecosystem health, i.e., the long-term impact of recommendation strategies on aspects such as overall satisfaction, collective fairness, and safety, requires the simulation of large multi-agent systems in order to plausibly reproduce the interactions between the different participants of the ecosystem. This, along with the computational load of probabilistic inference tasks, requires an efficient simulation runtime. For computational performance, RecSim NG offers a TensorFlow-based runtime for running simulations on accelerated hardware. The simulation takes advantage of all optimizations offered by TensorFlow’s AutoGraph compiler, including accelerated linear algebra (XLA) if available. The simulation will automatically exploit all available cores on the host machine as well as specialized hardware (if run accordingly), such as Tensor Processing Units (TPUs). The core RecSim NG architecture is back-end independent, enabling applications to be developed within other computational frameworks (such as JAX or PyTorch).

Ecosystem Modeling as an Application
To demonstrate the capabilities of RecSim NG, we present a very simplified model of multi-agent interactions among users and content providers in a stylized recommender ecosystem¹. The simulation captures the dynamics of a recommender system that mediates the interaction between users and content providers by recommending slates of those providers’ content items to users over time. We adopt a simplified user model whereby each user is characterized by a static, observable “user interest vector.” This vector determines a user’s affinity with a recommended item, which are then used as inputs to a choice model that determines a user’s item selection from a recommended slate. A user’s utility for any selected item is simply their affinity for the item, perturbed with Gaussian noise.

The aim of the recommender is to maximize cumulative user utility, over all users, over a fixed horizon. However, interesting ecosystem effects make this challenging, and emerge because of content provider behavior. Like users, each provider has an “interest vector” around which the content items it makes available are centered, reflecting that provider’s general expertise or tendencies. Providers have their own incentives for making content available: their utility is measured by the number of their items selected by any user over the recent past. Moreover, providers with higher utility generate or make available a greater number of items, increasing the “catalog” from which users (and the recommender) can choose.

We compare two different recommender policies in this setting. The first is a standard “myopic” policy that, for any user, always recommends the items that have the greatest predicted affinity for that user. Under such a policy, the behavior of providers has the potential to give rise to “rich-get-richer” phenomena: providers that initially attract users produce more items at subsequent periods, which increases the odds of attracting even further future engagement. This gradual concentration of available items around “mainstream” content providers has a negative impact on overall user utility over time. The second recommender policy is aware of these provider dynamics, which it counteracts by promoting under-served providers.² While a simple heuristic, the provider-aware policy increases overall user utility over extended horizons.

The number of agents in the simulation is large and we templatize both users and content providers with reusable modeling blocks offered by RecSim NG. Determining how to execute the simulation in parallel is non-trivial, so it is critical to utilize TF’s AutoGraph and other computational optimizations.

Conclusion
Our hope is that RecSim NG will make it easier for both researchers and practitioners to develop, train and evaluate novel algorithms for recommender systems, especially algorithms intended to optimize system behavior over extended horizons, capture complex multi-agent interactions and incentives, or both. We are also investigating the release of increasingly realistic user models that can serve as benchmarks for the research community, as well as methods that can facilitate “sim2real” transfer using RecSim NG.

Further details regarding the RecSim NG framework can be found in the associated white paper, while code and colabs/tutorials are available here. A video about RecSim NG presented at RecSys-2020 is shown below:

Acknowledgements
We thank our collaborators and early adopters of RᴇᴄSɪᴍ NG, including the other members of the RecSim NG team: Vihan Jain, Eugene Ie, Chris Colby, Nicolas Mayoraz, Hubert Pham, Dustin Tran, Ivan Vendrov and Craig Boutilier.

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¹ This model is a much simpler version of that presented in this ICML-20 paper. ^↩

² This simple heuristic policy is used only to demonstrate RecSim NG’s capabilities. More sophisticated algorithms that compute policies that explicitly maximize long-term user utility are discussed in this ICML-20 paper. ^↩

Posted by Rose E. Wang, Student Researcher and Aleksandra Faust, Staff Research Scientist, Google Research

As robots become more ubiquitous in day-to-day life, the complexity of their interactions with each other and with the environment grows. In a controlled environment, such as a lab, multiple robots can coordinate their actions and efforts through a centralized planner that facilitates communication between individual agents. And while much research has been done to address reliable sensor-informed goal navigation, in many real-world applications aligning goals across independent robotic agents must be done without a centralized planner, which poses non-trivial challenges.

An example of such a challenging decentralized task is the rendezvous task, in which multiple agents must agree upon a time and place at which they can meet, without explicitly communicating with one another. This goal alignment task plays an important role in real world multiagent and human-robot settings, e.g., performing object handovers or determining goals on the fly. Solving the decentralized rendezvous task in this situation depends not just on the obstacles in the environment, but also the policies and dynamics of each agent. Addressing potential miscoordination and dealing with noisy sensor data depends on the agents’ ability to model the motions of other agents as well as their own, and to adapt to diverging intentions while using limited information.

An example of two independently controlled robots separated by obstacles that share the objective of meeting each other. How should they move in order to meet? Example trajectories are illustrated in red and blue arrows for each robot. Each robot makes an independent decision of where to go based on their own observations.

In “Model-based Reinforcement Learning for Decentralized Multiagent Rendezvous”, presented at CoRL 2020, we propose an holistic approach to address the challenges of the decentralized rendezvous task, which we call hierarchical predictive planning (HPP). This is a decentralized, model-based reinforcement learning (RL) system that enables agents to align their goals on the fly in the real world. We evaluate HPP in a mixture of real-world and simulated environments and compare it to several learning-based planning and centralized baselines. In those evaluations, we show that HPP is able to more effectively predict and align trajectories, avoid miscoordinations, and directly transfer to the real world without additional fine-tuning.

Putting Together Prediction, Planning and Control
Akin to a standard navigation pipeline, our learning-based system consists of three modules: prediction, planning, and control. Each agent employs the prediction model to learn agent motion and to predict the future positions of itself (the ego-agent) and others based on its own observations (e.g., from LiDAR and team position information) of other agents’ behaviors and navigation patterns. So, each agent learns two prediction models, one for its own motion and one for the other agent. These motion predictors constitute the prediction module, and are used by each agent’s planning module.

The output of the prediction module — the estimate of where each agent, both the ego-agent and the other agents, is most likely to be given the ego-agent’s own sensor observations — is useful information for the planning module, which evaluates different goal locations and maintains a belief distribution over where the team should converge. The belief distribution is periodically updated using evaluations provided by the prediction model. An agent samples from this belief distribution to update the goal to which it should navigate.

The selected goal is passed to the agent’s control module, which is equipped with a pre-trained, imperfect navigation policy that can navigate to a given location in the obstacle-laden environment. The control policy then determines what action the robot should execute.

This process of observing other agents, updating belief distributions and navigating to an updated goal repeats until agents have successfully rendezvoused. While the hierarchical planning and control setup are not unusual, our work closes the loop between the control and planning for decentralized multiagent systems by use of the sensor-informed prediction module.

Training the Prediction Models
HPP trains motion predictors in simulation, assuming that each agent is controlled by a hidden, perhaps suboptimal, control policy capable of avoiding obstacles. The key difficulty lies in training prediction models without access to other agents’ sensor observations and control policies.

The predictors are trained via self-supervision. To collect the training data, we randomly place all the agents and obstacles in an environment, and each agent is given a random goal (unknown to other agents). As the agents move toward their respective goals, each agent records the experience — its sensor observations and the poses of all agents (itself and other agents). Next, from the recorded experience, the agent learns a separate predictor for each agent in the team including itself (target agent). The training dataset consists of ego-agent initial sensor observations, target agent’s pose and goal, labeled with future ego-observations and target agent poses. The goal and labels are inferred from the recorded experience.

As a result, the predictors learn temporal causality of the present and future ego-agent’s observations and target agent’s poses, conditioned on the target agent’s assumed goals — in other words the models predict where each agent will be in the future based on the present. The predictor training is done only with the information available to agents at the runtime, and in environments independent from the deployment environments.

The training environment for the model prediction models. The environment is filled with randomly filled obstacles. All agents (left in blue, upper right in red) are given the same random goal (center in green) and move with their own control modules towards it.

Selecting Goals for Alignment
A model-based RL planner for each agent uses the learned predictors in the deployment environments to guide the agents towards the rendezvous point. The planner takes into account what it believes the other agents would do when also completing the rendezvous task.

HPP illustration. Each robot independently considers several potential rendezvous points, and evaluates each point based how close it believes that the agents can get.

To perform this reasoning, each agent independently samples a series of potential goals and selects the goal that it believes it would be the most likely to succeed. This process effectively simulates a centralized planner for fictitious agents by using the prediction models to predict trajectories of those agents moving to a fixed goal. Conditioned on a proposed goal, the algorithm predicts the poses of the agents in the future, which are generated from sequential roll outs of the prediction models. Each goal is then evaluated by scoring the anticipated system state using the task reward favoring goals that bring agents closer together. We use the cross-entropy method (CEM) to convert these goal evaluations into belief updates over potential rendezvous points. Finally, the agent’s planner selects a goal for itself from this new belief distribution and passes this goal to the agent’s control module.

A simple illustration of the goal evaluation. At the end of a simulated trajectory, the agents (red, left, and blue, right) are either far (top) or close (bottom) to each other. The goal in the bottom image is better than the goal on top because agents end up closer to each other.

Results
We compare HPP against several baselines — MADDPG (learning-based), RRT (planning) with CEM, and centralized baselines that use heuristics for selecting the agent’s rendezvous point — in a mixture of real-world and simulated environments.

Evaluation environments, each of which are independent of the training environment for the agent’s control policy and prediction modules.

There are two main takeaways from our results. One is that HPP enables agents to predict and align trajectories, avoiding miscoordinations. For example:

The second takeaway is that HPP transfers directly into the real world without additional training. For example:

Conclusion
This work presents HPP, a model-based RL approach for decentralized multiagent coordination. Agents first learn to predict where they and their teammates are going to be from their own sensors and decide and navigate to a common goal. Our experiments demonstrate the method generalizes to new environments and handles miscoordination while making no assumptions about the dynamics of other agents. This may be of interest to the larger multiagent research community as a real-world example of a decentralized task using noisy sensors and imperfect controllers, to the motion planning community as an example of a learning-based planning system that closes the loop between the planner and controller, and to the RL community as an example of model-based RL as feedback in a hierarchical, self-supervised prediction setting.

Acknowledgements
This research was done by Rose E. Wang, J. Chase Kew, Dennis Lee, Tsang-Wei Edward Lee, Tingnan Zhang, Brian Ichter, Jie Tan, Aleksandra Faust with special thanks to Michael Everett, Oscar Ramirez and Igor Mordatch for the insightful discussions.

Torch is not just for deep learning. Its L-BFGS optimizer, complete with Strong-Wolfe line search, is a powerful tool in unconstrained as well as constrained optimization.