Forrest Iandola

Jay Zhangjie Wu, Xiuyu Li, Difei Gao et al. · berkeley

Humans watch more than a billion hours of video per day. Most of this video was edited manually, which is a tedious process. However, AI-enabled video-generation and video-editing is on the rise. Building on text-to-image models like Stable Diffusion and Imagen, generative AI has improved dramatically on video tasks. But it's hard to evaluate progress in these video tasks because there is no standard benchmark. So, we propose a new dataset for text-guided video editing (TGVE), and we run a competition at CVPR to evaluate models on our TGVE dataset. In this paper we present a retrospective on the competition and describe the winning method. The competition dataset is available at https://sites.google.com/view/loveucvpr23/track4.

Yang Li, Liangzhen Lai, Yuan Shangguan et al.

Transformer-based models excel in speech recognition. Existing efforts to optimize Transformer inference, typically for long-context applications, center on simplifying attention score calculations. However, streaming speech recognition models usually process a limited number of tokens each time, making attention score calculation less of a bottleneck. Instead, the bottleneck lies in the linear projection layers of multi-head attention and feedforward networks, constituting a substantial portion of the model size and contributing significantly to computation, memory, and power usage. To address this bottleneck, we propose folding attention, a technique targeting these linear layers, significantly reducing model size and improving memory and power efficiency. Experiments on on-device Transformer-based streaming speech recognition models show that folding attention reduces model size (and corresponding memory consumption) by up to 24% and power consumption by up to 23%, all without compromising model accuracy or computation overhead.

Yangyang Shi, Gael Le Lan, Varun Nagaraja et al.

This paper presents an innovative approach to enhance control over audio generation by emphasizing the alignment between audio and text representations during model training. In the context of language model-based audio generation, the model leverages input from both textual and audio token representations to predict subsequent audio tokens. However, the current configuration lacks explicit regularization to ensure the alignment between the chosen text representation and the language model's predictions. Our proposal involves the incorporation of audio and text representation regularization, particularly during the classifier-free guidance (CFG) phase, where the text condition is excluded from cross attention during language model training. The aim of this proposed representation regularization is to minimize discrepancies in audio and text similarity compared to other samples within the same training batch. Experimental results on both music and audio generation tasks demonstrate that our proposed methods lead to improvements in objective metrics for both audio and music generation, as well as an enhancement in the human perception for audio generation.

Ernie Chang, Sidd Srinivasan, Mahi Luthra et al.

Text-to-audio generation (TTA) produces audio from a text description, learning from pairs of audio samples and hand-annotated text. However, commercializing audio generation is challenging as user-input prompts are often under-specified when compared to text descriptions used to train TTA models. In this work, we treat TTA models as a ``blackbox'' and address the user prompt challenge with two key insights: (1) User prompts are generally under-specified, leading to a large alignment gap between user prompts and training prompts. (2) There is a distribution of audio descriptions for which TTA models are better at generating higher quality audio, which we refer to as ``audionese''. To this end, we rewrite prompts with instruction-tuned models and propose utilizing text-audio alignment as feedback signals via margin ranking learning for audio improvements. On both objective and subjective human evaluations, we observed marked improvements in both text-audio alignment and music audio quality.

Ernie Chang, Pin-Jie Lin, Yang Li et al.

Distributional shift is a central challenge in the deployment of machine learning models as they can be ill-equipped for real-world data. This is particularly evident in text-to-audio generation where the encoded representations are easily undermined by unseen prompts, which leads to the degradation of generated audio -- the limited set of the text-audio pairs remains inadequate for conditional audio generation in the wild as user prompts are under-specified. In particular, we observe a consistent audio quality degradation in generated audio samples with user prompts, as opposed to training set prompts. To this end, we present a retrieval-based in-context prompt editing framework that leverages the training captions as demonstrative exemplars to revisit the user prompts. We show that the framework enhanced the audio quality across the set of collected user prompts, which were edited with reference to the training captions as exemplars.

Zechun Liu, Changsheng Zhao, Forrest Iandola et al.

This paper addresses the growing need for efficient large language models (LLMs) on mobile devices, driven by increasing cloud costs and latency concerns. We focus on designing top-quality LLMs with fewer than a billion parameters, a practical choice for mobile deployment. Contrary to prevailing belief emphasizing the pivotal role of data and parameter quantity in determining model quality, our investigation underscores the significance of model architecture for sub-billion scale LLMs. Leveraging deep and thin architectures, coupled with embedding sharing and grouped-query attention mechanisms, we establish a strong baseline network denoted as MobileLLM, which attains a remarkable 2.7%/4.3% accuracy boost over preceding 125M/350M state-of-the-art models. Additionally, we propose an immediate block-wise weight-sharing approach with no increase in model size and only marginal latency overhead. The resultant models, denoted as MobileLLM-LS, demonstrate a further accuracy enhancement of 0.7%/0.8% than MobileLLM 125M/350M. Moreover, MobileLLM model family shows significant improvements compared to previous sub-billion models on chat benchmarks, and demonstrates close correctness to LLaMA-v2 7B in API calling tasks, highlighting the capability of small models for common on-device use cases.

Bichen Wu, Alvin Wan, Forrest Iandola et al.

Object detection is a crucial task for autonomous driving. In addition to requiring high accuracy to ensure safety, object detection for autonomous driving also requires real-time inference speed to guarantee prompt vehicle control, as well as small model size and energy efficiency to enable embedded system deployment. In this work, we propose SqueezeDet, a fully convolutional neural network for object detection that aims to simultaneously satisfy all of the above constraints. In our network, we use convolutional layers not only to extract feature maps but also as the output layer to compute bounding boxes and class probabilities. The detection pipeline of our model only contains a single forward pass of a neural network, thus it is extremely fast. Our model is fully-convolutional, which leads to a small model size and better energy efficiency. While achieving the same accuracy as previous baselines, our model is 30.4x smaller, 19.7x faster, and consumes 35.2x lower energy. The code is open-sourced at \url{https://github.com/BichenWuUCB/squeezeDet}.

Matthew Moskewicz, Forrest Iandola, Kurt Keutzer

The popularity of neural networks (NNs) spans academia, industry, and popular culture. In particular, convolutional neural networks (CNNs) have been applied to many image based machine learning tasks and have yielded strong results. The availability of hardware/software systems for efficient training and deployment of large and/or deep CNN models has been, and continues to be, an important consideration for the field. Early systems for NN computation focused on leveraging existing dense linear algebra techniques and libraries. Current approaches use low-level machine specific programming and/or closed-source, purpose-built vendor libraries. In this work, we present an open source system that, compared to existing approaches, achieves competitive computational speed while achieving higher portability. We achieve this by targeting the vendor-neutral OpenCL platform using a code-generation approach. We argue that our approach allows for both: (1) the rapid development of new computational kernels for existing hardware targets, and (2) the rapid tuning of existing computational kernels for new hardware targets. Results are presented for a case study of targeting the Qualcomm Snapdragon 820 mobile computing platform for CNN deployment.

Forrest N. Iandola, Song Han, Matthew W. Moskewicz et al.

Recent research on deep neural networks has focused primarily on improving accuracy. For a given accuracy level, it is typically possible to identify multiple DNN architectures that achieve that accuracy level. With equivalent accuracy, smaller DNN architectures offer at least three advantages: (1) Smaller DNNs require less communication across servers during distributed training. (2) Smaller DNNs require less bandwidth to export a new model from the cloud to an autonomous car. (3) Smaller DNNs are more feasible to deploy on FPGAs and other hardware with limited memory. To provide all of these advantages, we propose a small DNN architecture called SqueezeNet. SqueezeNet achieves AlexNet-level accuracy on ImageNet with 50x fewer parameters. Additionally, with model compression techniques we are able to compress SqueezeNet to less than 0.5MB (510x smaller than AlexNet). The SqueezeNet architecture is available for download here: https://github.com/DeepScale/SqueezeNet

Forrest N. Iandola, Anting Shen, Peter Gao et al.

Recently, there has been a flurry of industrial activity around logo recognition, such as Ditto's service for marketers to track their brands in user-generated images, and LogoGrab's mobile app platform for logo recognition. However, relatively little academic or open-source logo recognition progress has been made in the last four years. Meanwhile, deep convolutional neural networks (DCNNs) have revolutionized a broad range of object recognition applications. In this work, we apply DCNNs to logo recognition. We propose several DCNN architectures, with which we surpass published state-of-art accuracy on a popular logo recognition dataset.

Forrest Iandola, Matt Moskewicz, Sergey Karayev et al.

Convolutional Neural Networks (CNNs) can provide accurate object classification. They can be extended to perform object detection by iterating over dense or selected proposed object regions. However, the runtime of such detectors scales as the total number and/or area of regions to examine per image, and training such detectors may be prohibitively slow. However, for some CNN classifier topologies, it is possible to share significant work among overlapping regions to be classified. This paper presents DenseNet, an open source system that computes dense, multiscale features from the convolutional layers of a CNN based object classifier. Future work will involve training efficient object detectors with DenseNet feature descriptors.

Peihao Wang, Dejia Xu, Zhiwen Fan et al.

Despite the remarkable performance of score distillation in text-to-3D generation, such techniques notoriously suffer from view inconsistency issues, also known as "Janus" artifact, where the generated objects fake each view with multiple front faces. Although empirically effective methods have approached this problem via score debiasing or prompt engineering, a more rigorous perspective to explain and tackle this problem remains elusive. In this paper, we reveal that the existing score distillation-based text-to-3D generation frameworks degenerate to maximal likelihood seeking on each view independently and thus suffer from the mode collapse problem, manifesting as the Janus artifact in practice. To tame mode collapse, we improve score distillation by re-establishing the entropy term in the corresponding variational objective, which is applied to the distribution of rendered images. Maximizing the entropy encourages diversity among different views in generated 3D assets, thereby mitigating the Janus problem. Based on this new objective, we derive a new update rule for 3D score distillation, dubbed Entropic Score Distillation (ESD). We theoretically reveal that ESD can be simplified and implemented by just adopting the classifier-free guidance trick upon variational score distillation. Although embarrassingly straightforward, our extensive experiments successfully demonstrate that ESD can be an effective treatment for Janus artifacts in score distillation.

Peihao Wang, Zhiwen Fan, Dejia Xu et al.

Score distillation has emerged as one of the most prevalent approaches for text-to-3D asset synthesis. Essentially, score distillation updates 3D parameters by lifting and back-propagating scores averaged over different views. In this paper, we reveal that the gradient estimation in score distillation is inherent to high variance. Through the lens of variance reduction, the effectiveness of SDS and VSD can be interpreted as applications of various control variates to the Monte Carlo estimator of the distilled score. Motivated by this rethinking and based on Stein's identity, we propose a more general solution to reduce variance for score distillation, termed Stein Score Distillation (SSD). SSD incorporates control variates constructed by Stein identity, allowing for arbitrary baseline functions. This enables us to include flexible guidance priors and network architectures to explicitly optimize for variance reduction. In our experiments, the overall pipeline, dubbed SteinDreamer, is implemented by instantiating the control variate with a monocular depth estimator. The results suggest that SSD can effectively reduce the distillation variance and consistently improve visual quality for both object- and scene-level generation. Moreover, we demonstrate that SteinDreamer achieves faster convergence than existing methods due to more stable gradient updates.

Yunyang Xiong, Chong Zhou, Xiaoyu Xiang et al.

Segment Anything Model 2 (SAM 2) has emerged as a powerful tool for video object segmentation and tracking anything. Key components of SAM 2 that drive the impressive video object segmentation performance include a large multistage image encoder for frame feature extraction and a memory mechanism that stores memory contexts from past frames to help current frame segmentation. The high computation complexity of multistage image encoder and memory module has limited its applications in real-world tasks, e.g., video object segmentation on mobile devices. To address this limitation, we propose EfficientTAMs, lightweight track anything models that produce high-quality results with low latency and model size. Our idea is based on revisiting the plain, nonhierarchical Vision Transformer (ViT) as an image encoder for video object segmentation, and introducing an efficient memory module, which reduces the complexity for both frame feature extraction and memory computation for current frame segmentation. We take vanilla lightweight ViTs and efficient memory module to build EfficientTAMs, and train the models on SA-1B and SA-V datasets for video object segmentation and track anything tasks. We evaluate on multiple video segmentation benchmarks including semi-supervised VOS and promptable video segmentation, and find that our proposed EfficientTAM with vanilla ViT perform comparably to SAM 2 model (HieraB+SAM 2) with ~2x speedup on A100 and ~2.4x parameter reduction. On segment anything image tasks, our EfficientTAMs also perform favorably over original SAM with ~20x speedup on A100 and ~20x parameter reduction. On mobile devices such as iPhone 15 Pro Max, our EfficientTAMs can run at ~10 FPS for performing video object segmentation with reasonable quality, highlighting the capability of small models for on-device video object segmentation applications.

Xiaoyu Xiang, Liat Sless Gorelik, Yuchen Fan et al.

We present Make-A-Texture, a new framework that efficiently synthesizes high-resolution texture maps from textual prompts for given 3D geometries. Our approach progressively generates textures that are consistent across multiple viewpoints with a depth-aware inpainting diffusion model, in an optimized sequence of viewpoints determined by an automatic view selection algorithm. A significant feature of our method is its remarkable efficiency, achieving a full texture generation within an end-to-end runtime of just 3.07 seconds on a single NVIDIA H100 GPU, significantly outperforming existing methods. Such an acceleration is achieved by optimizations in the diffusion model and a specialized backprojection method. Moreover, our method reduces the artifacts in the backprojection phase, by selectively masking out non-frontal faces, and internal faces of open-surfaced objects. Experimental results demonstrate that Make-A-Texture matches or exceeds the quality of other state-of-the-art methods. Our work significantly improves the applicability and practicality of texture generation models for real-world 3D content creation, including interactive creation and text-guided texture editing.

Balakrishnan Varadarajan, Bilge Soran, Forrest Iandola et al.

The Segment Anything Model (SAM) has been a cornerstone in the field of interactive segmentation, propelling significant progress in generative AI, computational photography, and medical imaging. Despite its ability to process arbitrary user input and generate corresponding segmentation masks, SAM's 600 million parameter architecture, based on ViT-H, is not compatible with current mobile hardware due to its high computational demands and large model size. Our research aims to adapt SAM for use in mobile photography applications. To this end, we have developed a fully convolutional SqueezeSAM model architecture, which is 62.5 times faster and 31.6 times smaller than the original SAM, making it a viable solution for mobile applications. Furthermore, our tiny model achieves an mIOU within 1% of the original VIT-H architecture. Automated segmentation holds significant value in the creation flow for photography applications, as evidenced by its adoption by leading industry players like apple and capcut. To facilitate this automation, we employ salient object detection and simulate potential user clicks for foreground object selection, generating an initial segmentation mask that users can subsequently edit interactively. A common user expectation is that a click on a specific part of an object will result in the segmentation of the entire object. For example, a click on a person's t-shirt in a photo should ideally segment the entire person, not just the t-shirt. However, SAM typically only segments the clicked area. We address this limitation through a novel data augmentation scheme. Consequently, if a user clicks on a person holding a basketball, both the person and the basketball are segmented together, aligning with user expectations and enhancing the overall user experience.

Forrest Iandola, Stanislav Pidhorskyi, Igor Santesteban et al.

Gaussian-based human avatars have achieved an unprecedented level of visual fidelity. However, existing approaches based on high-capacity neural networks typically require a desktop GPU to achieve real-time performance for a single avatar, and it remains non-trivial to animate and render such avatars on mobile devices including a standalone VR headset due to substantially limited memory and computational bandwidth. In this paper, we present SqueezeMe, a simple and highly effective framework to convert high-fidelity 3D Gaussian full-body avatars into a lightweight representation that supports both animation and rendering with mobile-grade compute. Our key observation is that the decoding of pose-dependent Gaussian attributes from a neural network creates non-negligible memory and computational overhead. Inspired by blendshapes and linear pose correctives widely used in Computer Graphics, we address this by distilling the pose correctives learned with neural networks into linear layers. Moreover, we further reduce the parameters by sharing the correctives among nearby Gaussians. Combining them with a custom splatting pipeline based on Vulkan, we achieve, for the first time, simultaneous animation and rendering of 3 Gaussian avatars in real-time (72 FPS) on a Meta Quest 3 VR headset. Demo videos are available at https://forresti.github.io/squeezeme.

Forrest N. Iandola, Albert E. Shaw, Ravi Krishna et al.

Humans read and write hundreds of billions of messages every day. Further, due to the availability of large datasets, large computing systems, and better neural network models, natural language processing (NLP) technology has made significant strides in understanding, proofreading, and organizing these messages. Thus, there is a significant opportunity to deploy NLP in myriad applications to help web users, social networks, and businesses. In particular, we consider smartphones and other mobile devices as crucial platforms for deploying NLP models at scale. However, today's highly-accurate NLP neural network models such as BERT and RoBERTa are extremely computationally expensive, with BERT-base taking 1.7 seconds to classify a text snippet on a Pixel 3 smartphone. In this work, we observe that methods such as grouped convolutions have yielded significant speedups for computer vision networks, but many of these techniques have not been adopted by NLP neural network designers. We demonstrate how to replace several operations in self-attention layers with grouped convolutions, and we use this technique in a novel network architecture called SqueezeBERT, which runs 4.3x faster than BERT-base on the Pixel 3 while achieving competitive accuracy on the GLUE test set. The SqueezeBERT code will be released.

Paden Tomasello, Sammy Sidhu, Anting Shen et al.

Convolutional neural networks (CNNs) have become increasingly popular for solving a variety of computer vision tasks, ranging from image classification to image segmentation. Recently, autonomous vehicles have created a demand for depth information, which is often obtained using hardware sensors such as Light detection and ranging (LIDAR). Although it can provide precise distance measurements, most LIDARs are still far too expensive to sell in mass-produced consumer vehicles, which has motivated methods to generate depth information from commodity automotive sensors like cameras. In this paper, we propose an approach called Deep Sensor Cloning (DSC). The idea is to use Convolutional Neural Networks in conjunction with inexpensive sensors to replicate the 3D point-clouds that are created by expensive LIDARs. To accomplish this, we develop a new dataset (DSDepth) and a new family of CNN architectures (DSCnets). While previous tasks such as KITTI depth prediction use an interpolated RGB-D images as ground-truth for training, we instead use DSCnets to directly predict LIDAR point-clouds. When we compare the output of our models to a $75,000 LIDAR, we find that our most accurate DSCnet achieves a relative error of 5.77% using a single camera and 4.69% using stereo cameras.

Forrest Iandola, Kurt Keutzer

Over the last five years Deep Neural Nets have offered more accurate solutions to many problems in speech recognition, and computer vision, and these solutions have surpassed a threshold of acceptability for many applications. As a result, Deep Neural Networks have supplanted other approaches to solving problems in these areas, and enabled many new applications. While the design of Deep Neural Nets is still something of an art form, in our work we have found basic principles of design space exploration used to develop embedded microprocessor architectures to be highly applicable to the design of Deep Neural Net architectures. In particular, we have used these design principles to create a novel Deep Neural Net called SqueezeNet that requires as little as 480KB of storage for its model parameters. We have further integrated all these experiences to develop something of a playbook for creating small Deep Neural Nets for embedded systems.

Forrest Iandola

In recent years, the research community has discovered that deep neural networks (DNNs) and convolutional neural networks (CNNs) can yield higher accuracy than all previous solutions to a broad array of machine learning problems. To our knowledge, there is no single CNN/DNN architecture that solves all problems optimally. Instead, the "right" CNN/DNN architecture varies depending on the application at hand. CNN/DNNs comprise an enormous design space. Quantitatively, we find that a small region of the CNN design space contains 30 billion different CNN architectures. In this dissertation, we develop a methodology that enables systematic exploration of the design space of CNNs. Our methodology is comprised of the following four themes. 1. Judiciously choosing benchmarks and metrics. 2. Rapidly training CNN models. 3. Defining and describing the CNN design space. 4. Exploring the design space of CNN architectures. Taken together, these four themes comprise an effective methodology for discovering the "right" CNN architectures to meet the needs of practical applications.

Peter H. Jin, Qiaochu Yuan, Forrest Iandola et al.

Training time on large datasets for deep neural networks is the principal workflow bottleneck in a number of important applications of deep learning, such as object classification and detection in automatic driver assistance systems (ADAS). To minimize training time, the training of a deep neural network must be scaled beyond a single machine to as many machines as possible by distributing the optimization method used for training. While a number of approaches have been proposed for distributed stochastic gradient descent (SGD), at the current time synchronous approaches to distributed SGD appear to be showing the greatest performance at large scale. Synchronous scaling of SGD suffers from the need to synchronize all processors on each gradient step and is not resilient in the face of failing or lagging processors. In asynchronous approaches using parameter servers, training is slowed by contention to the parameter server. In this paper we compare the convergence of synchronous and asynchronous SGD for training a modern ResNet network architecture on the ImageNet classification problem. We also propose an asynchronous method, gossiping SGD, that aims to retain the positive features of both systems by replacing the all-reduce collective operation of synchronous training with a gossip aggregation algorithm. We find, perhaps counterintuitively, that asynchronous SGD, including both elastic averaging and gossiping, converges faster at fewer nodes (up to about 32 nodes), whereas synchronous SGD scales better to more nodes (up to about 100 nodes).

Khalid Ashraf, Bichen Wu, Forrest N. Iandola et al.

The ability to automatically detect other vehicles on the road is vital to the safety of partially-autonomous and fully-autonomous vehicles. Most of the high-accuracy techniques for this task are based on R-CNN or one of its faster variants. In the research community, much emphasis has been applied to using 3D vision or complex R-CNN variants to achieve higher accuracy. However, are there more straightforward modifications that could deliver higher accuracy? Yes. We show that increasing input image resolution (i.e. upsampling) offers up to 12 percentage-points higher accuracy compared to an off-the-shelf baseline. We also find situations where earlier/shallower layers of CNN provide higher accuracy than later/deeper layers. We further show that shallow models and upsampled images yield competitive accuracy. Our findings contrast with the current trend towards deeper and larger models to achieve high accuracy in domain specific detection tasks.

Forrest N. Iandola, Khalid Ashraf, Matthew W. Moskewicz et al.

Long training times for high-accuracy deep neural networks (DNNs) impede research into new DNN architectures and slow the development of high-accuracy DNNs. In this paper we present FireCaffe, which successfully scales deep neural network training across a cluster of GPUs. We also present a number of best practices to aid in comparing advancements in methods for scaling and accelerating the training of deep neural networks. The speed and scalability of distributed algorithms is almost always limited by the overhead of communicating between servers; DNN training is not an exception to this rule. Therefore, the key consideration here is to reduce communication overhead wherever possible, while not degrading the accuracy of the DNN models that we train. Our approach has three key pillars. First, we select network hardware that achieves high bandwidth between GPU servers -- Infiniband or Cray interconnects are ideal for this. Second, we consider a number of communication algorithms, and we find that reduction trees are more efficient and scalable than the traditional parameter server approach. Third, we optionally increase the batch size to reduce the total quantity of communication during DNN training, and we identify hyperparameters that allow us to reproduce the small-batch accuracy while training with large batch sizes. When training GoogLeNet and Network-in-Network on ImageNet, we achieve a 47x and 39x speedup, respectively, when training on a cluster of 128 GPUs.

Hao Fang, Saurabh Gupta, Forrest Iandola et al.

This paper presents a novel approach for automatically generating image descriptions: visual detectors, language models, and multimodal similarity models learnt directly from a dataset of image captions. We use multiple instance learning to train visual detectors for words that commonly occur in captions, including many different parts of speech such as nouns, verbs, and adjectives. The word detector outputs serve as conditional inputs to a maximum-entropy language model. The language model learns from a set of over 400,000 image descriptions to capture the statistics of word usage. We capture global semantics by re-ranking caption candidates using sentence-level features and a deep multimodal similarity model. Our system is state-of-the-art on the official Microsoft COCO benchmark, producing a BLEU-4 score of 29.1%. When human judges compare the system captions to ones written by other people on our held-out test set, the system captions have equal or better quality 34% of the time.

Ross Girshick, Forrest Iandola, Trevor Darrell et al.

Deformable part models (DPMs) and convolutional neural networks (CNNs) are two widely used tools for visual recognition. They are typically viewed as distinct approaches: DPMs are graphical models (Markov random fields), while CNNs are "black-box" non-linear classifiers. In this paper, we show that a DPM can be formulated as a CNN, thus providing a novel synthesis of the two ideas. Our construction involves unrolling the DPM inference algorithm and mapping each step to an equivalent (and at times novel) CNN layer. From this perspective, it becomes natural to replace the standard image features used in DPM with a learned feature extractor. We call the resulting model DeepPyramid DPM and experimentally validate it on PASCAL VOC. DeepPyramid DPM significantly outperforms DPMs based on histograms of oriented gradients features (HOG) and slightly outperforms a comparable version of the recently introduced R-CNN detection system, while running an order of magnitude faster.