Search

Random features are a powerful technique for rewriting positive-definite kernels as linear products. They bring linear tools to bear in important nonlinear domains like KNNs and attention. Unfortunately, practical implementations require approximating an expectation, usually via sampling. This has led to the development of increasingly elaborate representations with ever lower sample error. We resolve this arms race by deriving an optimal sampling policy. Under this policy all random features representations have the same approximation error, which we show is the lowest possible. This means that we are free to choose whatever representation we please, provided we sample optimally.

Spatiotemporal datasets, which consist of spatially-referenced time series, are ubiquitous in diverse applications, such as air pollution monitoring, disease tracking, and cloud-demand forecasting. As the scale of modern datasets increases, there is a growing need for statistical methods that are flexible enough to capture complex spatiotemporal dynamics and scalable enough to handle many observations. This article introduces the Bayesian Neural Field (BayesNF), a domain-general statistical model that infers rich spatiotemporal probability distributions for data-analysis tasks including forecasting, interpolation, and variography. BayesNF integrates a deep neural network architecture for high-capacity function estimation with hierarchical Bayesian inference for robust predictive uncertainty quantification. Evaluations against prominent baselines show that BayesNF delivers improvements on prediction problems from climate and public health data containing tens to hundreds of thousands of measurements. Accompanying the paper is an open-source software package (https://github.com/google/bayesnf) that runs on GPU and TPU accelerators through the JAX machine learning platform., Comment: 29 pages, 7 figures, 2 tables, 1 listing

How do we infer a 3D scene from a single image in the presence of corruptions like rain, snow or fog? Straightforward domain randomization relies on knowing the family of corruptions ahead of time. Here, we propose a Bayesian approach-dubbed robust inverse graphics (RIG)-that relies on a strong scene prior and an uninformative uniform corruption prior, making it applicable to a wide range of corruptions. Given a single image, RIG performs posterior inference jointly over the scene and the corruption. We demonstrate this idea by training a neural radiance field (NeRF) scene prior and using a secondary NeRF to represent the corruptions over which we place an uninformative prior. RIG, trained only on clean data, outperforms depth estimators and alternative NeRF approaches that perform point estimation instead of full inference. The results hold for a number of scene prior architectures based on normalizing flows and diffusion models. For the latter, we develop reconstruction-guidance with auxiliary latents (ReGAL)-a diffusion conditioning algorithm that is applicable in the presence of auxiliary latent variables such as the corruption. RIG demonstrates how scene priors can be used beyond generation tasks., Comment: ICML submission. Reworked main body, new appendix figures

Large language models (LLMs) solve problems more accurately and interpretably when instructed to work out the answer step by step using a ``chain-of-thought'' (CoT) prompt. One can also improve LLMs' performance on a specific task by supervised fine-tuning, i.e., by using gradient ascent on some tunable parameters to maximize the average log-likelihood of correct answers from a labeled training set. Naively combining CoT with supervised tuning requires supervision not just of the correct answers, but also of detailed rationales that lead to those answers; these rationales are expensive to produce by hand. Instead, we propose a fine-tuning strategy that tries to maximize the \emph{marginal} log-likelihood of generating a correct answer using CoT prompting, approximately averaging over all possible rationales. The core challenge is sampling from the posterior over rationales conditioned on the correct answer; we address it using a simple Markov-chain Monte Carlo (MCMC) expectation-maximization (EM) algorithm inspired by the self-taught reasoner (STaR), memoized wake-sleep, Markovian score climbing, and persistent contrastive divergence. This algorithm also admits a novel control-variate technique that drives the variance of our gradient estimates to zero as the model improves. Applying our technique to GSM8K and the tasks in BIG-Bench Hard, we find that this MCMC-EM fine-tuning technique typically improves the model's accuracy on held-out examples more than STaR or prompt-tuning with or without CoT., Comment: 23 pages, 37th Conference on Neural Information Processing Systems (NeurIPS 2023)

This paper presents a new approach to automatically discovering accurate models of complex time series data. Working within a Bayesian nonparametric prior over a symbolic space of Gaussian process time series models, we present a novel structure learning algorithm that integrates sequential Monte Carlo (SMC) and involutive MCMC for highly effective posterior inference. Our method can be used both in "online" settings, where new data is incorporated sequentially in time, and in "offline" settings, by using nested subsets of historical data to anneal the posterior. Empirical measurements on real-world time series show that our method can deliver 10x--100x runtime speedups over previous MCMC and greedy-search structure learning algorithms targeting the same model family. We use our method to perform the first large-scale evaluation of Gaussian process time series structure learning on a prominent benchmark of 1,428 econometric datasets. The results show that our method discovers sensible models that deliver more accurate point forecasts and interval forecasts over multiple horizons as compared to widely used statistical and neural baselines that struggle on this challenging data., Comment: 17 pages, 8 figures, 2 tables. Appearing in ICML 2023

Large language models (LLMs) can learn to perform a wide range of natural language tasks from just a handful of in-context examples. However, for generating strings from highly structured languages (e.g., semantic parsing to complex domain-specific languages), it is challenging for the LLM to generalize from just a few exemplars. We propose \emph{grammar prompting}, a simple approach to enable LLMs to use external knowledge and domain-specific constraints, expressed through a grammar in Backus--Naur Form (BNF), during in-context learning. Grammar prompting augments each demonstration example with a specialized grammar that is minimally sufficient for generating the particular output example, where the specialized grammar is a subset of the full DSL grammar. For inference, the LLM first predicts a BNF grammar given a test input, and then generates the output according to the rules of the grammar. Experiments demonstrate that grammar prompting can enable LLMs to perform competitively on a diverse set of DSL generation tasks, including semantic parsing (SMCalFlow, Overnight, GeoQuery), PDDL planning, and SMILES-based molecule generation., Comment: camera-ready version

The problem of inferring object shape from a single 2D image is underconstrained. Prior knowledge about what objects are plausible can help, but even given such prior knowledge there may still be uncertainty about the shapes of occluded parts of objects. Recently, conditional neural radiance field (NeRF) models have been developed that can learn to infer good point estimates of 3D models from single 2D images. The problem of inferring uncertainty estimates for these models has received less attention. In this work, we propose probabilistic NeRF (ProbNeRF), a model and inference strategy for learning probabilistic generative models of 3D objects' shapes and appearances, and for doing posterior inference to recover those properties from 2D images. ProbNeRF is trained as a variational autoencoder, but at test time we use Hamiltonian Monte Carlo (HMC) for inference. Given one or a few 2D images of an object (which may be partially occluded), ProbNeRF is able not only to accurately model the parts it sees, but also to propose realistic and diverse hypotheses about the parts it does not see. We show that key to the success of ProbNeRF are (i) a deterministic rendering scheme, (ii) an annealed-HMC strategy, (iii) a hypernetwork-based decoder architecture, and (iv) doing inference over a full set of NeRF weights, rather than just a low-dimensional code., Comment: 18 pages, 18 figures, 1 table; submitted to the 26th International Conference on Artificial Intelligence and Statistics (AISTATS 2023)

Prompted models have demonstrated impressive few-shot learning abilities. Repeated interactions at test-time with a single model, or the composition of multiple models together, further expands capabilities. These compositions are probabilistic models, and may be expressed in the language of graphical models with random variables whose values are complex data types such as strings. Cases with control flow and dynamic structure require techniques from probabilistic programming, which allow implementing disparate model structures and inference strategies in a unified language. We formalize several existing techniques from this perspective, including scratchpads / chain of thought, verifiers, STaR, selection-inference, and tool use. We refer to the resulting programs as language model cascades., Comment: Presented as spotlight at the Beyond Bases workshop at ICML 2022 (https://beyond-bayes.github.io)

Language models demonstrate both quantitative improvement and new qualitative capabilities with increasing scale. Despite their potentially transformative impact, these new capabilities are as yet poorly characterized. In order to inform future research, prepare for disruptive new model capabilities, and ameliorate socially harmful effects, it is vital that we understand the present and near-future capabilities and limitations of language models. To address this challenge, we introduce the Beyond the Imitation Game benchmark (BIG-bench). BIG-bench currently consists of 204 tasks, contributed by 450 authors across 132 institutions. Task topics are diverse, drawing problems from linguistics, childhood development, math, common-sense reasoning, biology, physics, social bias, software development, and beyond. BIG-bench focuses on tasks that are believed to be beyond the capabilities of current language models. We evaluate the behavior of OpenAI's GPT models, Google-internal dense transformer architectures, and Switch-style sparse transformers on BIG-bench, across model sizes spanning millions to hundreds of billions of parameters. In addition, a team of human expert raters performed all tasks in order to provide a strong baseline. Findings include: model performance and calibration both improve with scale, but are poor in absolute terms (and when compared with rater performance); performance is remarkably similar across model classes, though with benefits from sparsity; tasks that improve gradually and predictably commonly involve a large knowledge or memorization component, whereas tasks that exhibit "breakthrough" behavior at a critical scale often involve multiple steps or components, or brittle metrics; social bias typically increases with scale in settings with ambiguous context, but this can be improved with prompting., Comment: 27 pages, 17 figures + references and appendices, repo: https://github.com/google/BIG-bench

Markov chain Monte Carlo (MCMC) is widely regarded as one of the most important algorithms of the 20th century. Its guarantees of asymptotic convergence, stability, and estimator-variance bounds using only unnormalized probability functions make it indispensable to probabilistic programming. In this paper, we introduce the TensorFlow Probability MCMC toolkit, and discuss some of the considerations that motivated its design., Comment: Based on extended abstract submitted to PROBPROG 2020

Humans do not acquire perceptual abilities in the way we train machines. While machine learning algorithms typically operate on large collections of randomly-chosen, explicitly-labeled examples, human acquisition relies more heavily on multimodal unsupervised learning (as infants) and active learning (as children). With this motivation, we present a learning framework for sound representation and recognition that combines (i) a self-supervised objective based on a general notion of unimodal and cross-modal coincidence, (ii) a clustering objective that reflects our need to impose categorical structure on our experiences, and (iii) a cluster-based active learning procedure that solicits targeted weak supervision to consolidate categories into relevant semantic classes. By training a combined sound embedding/clustering/classification network according to these criteria, we achieve a new state-of-the-art unsupervised audio representation and demonstrate up to a 20-fold reduction in the number of labels required to reach a desired classification performance., Comment: This extended version of a ICASSP 2020 submission under same title has an added figure and additional discussion for easier consumption

We present a general approach to batching arbitrary computations for accelerators such as GPUs. We show orders-of-magnitude speedups using our method on the No U-Turn Sampler (NUTS), a workhorse algorithm in Bayesian statistics. The central challenge of batching NUTS and other Markov chain Monte Carlo algorithms is data-dependent control flow and recursion. We overcome this by mechanically transforming a single-example implementation into a form that explicitly tracks the current program point for each batch member, and only steps forward those in the same place. We present two different batching algorithms: a simpler, previously published one that inherits recursion from the host Python, and a more complex, novel one that implemenents recursion directly and can batch across it. We implement these batching methods as a general program transformation on Python source. Both the batching system and the NUTS implementation presented here are available as part of the popular TensorFlow Probability software package., Comment: 10 pages; Machine Learning and Systems 2020

In recent years, deep networks have led to dramatic improvements in speech enhancement by framing it as a data-driven pattern recognition problem. In many modern enhancement systems, large amounts of data are used to train a deep network to estimate masks for complex-valued short-time Fourier transforms (STFTs) to suppress noise and preserve speech. However, current masking approaches often neglect two important constraints: STFT consistency and mixture consistency. Without STFT consistency, the system's output is not necessarily the STFT of a time-domain signal, and without mixture consistency, the sum of the estimated sources does not necessarily equal the input mixture. Furthermore, the only previous approaches that apply mixture consistency use real-valued masks; mixture consistency has been ignored for complex-valued masks. In this paper, we show that STFT consistency and mixture consistency can be jointly imposed by adding simple differentiable projection layers to the enhancement network. These layers are compatible with real or complex-valued masks. Using both of these constraints with complex-valued masks provides a 0.7 dB increase in scale-invariant signal-to-distortion ratio (SI-SDR) on a large dataset of speech corrupted by a wide variety of nonstationary noise across a range of input SNRs.

We explore a variety of neural networks configurations for one- and two-channel spectrogram-mask-based speech enhancement. Our best model improves on previous state-of-the-art performance on the CHiME2 speech enhancement task by 0.4 decibels in signal-to-distortion ratio (SDR). We examine trade-offs such as non-causal look-ahead, computation, and parameter count versus enhancement performance and find that zero-look-ahead models can achieve, on average, within 0.03 dB SDR of our best bidirectional model. Further, we find that 200 milliseconds of look-ahead is sufficient to achieve equivalent performance to our best bidirectional model.

We describe a simple, low-level approach for embedding probabilistic programming in a deep learning ecosystem. In particular, we distill probabilistic programming down to a single abstraction---the random variable. Our lightweight implementation in TensorFlow enables numerous applications: a model-parallel variational auto-encoder (VAE) with 2nd-generation tensor processing units (TPUv2s); a data-parallel autoregressive model (Image Transformer) with TPUv2s; and multi-GPU No-U-Turn Sampler (NUTS). For both a state-of-the-art VAE on 64x64 ImageNet and Image Transformer on 256x256 CelebA-HQ, our approach achieves an optimal linear speedup from 1 to 256 TPUv2 chips. With NUTS, we see a 100x speedup on GPUs over Stan and 37x over PyMC3., Comment: Appears in Neural Information Processing Systems, 2018. Code available at http://bit.ly/2JpFipt

In this paper, we present a novel system that separates the voice of a target speaker from multi-speaker signals, by making use of a reference signal from the target speaker. We achieve this by training two separate neural networks: (1) A speaker recognition network that produces speaker-discriminative embeddings; (2) A spectrogram masking network that takes both noisy spectrogram and speaker embedding as input, and produces a mask. Our system significantly reduces the speech recognition WER on multi-speaker signals, with minimal WER degradation on single-speaker signals., Comment: To appear in Interspeech 2019

We present an extension to the Tacotron speech synthesis architecture that learns a latent embedding space of prosody, derived from a reference acoustic representation containing the desired prosody. We show that conditioning Tacotron on this learned embedding space results in synthesized audio that matches the prosody of the reference signal with fine time detail even when the reference and synthesis speakers are different. Additionally, we show that a reference prosody embedding can be used to synthesize text that is different from that of the reference utterance. We define several quantitative and subjective metrics for evaluating prosody transfer, and report results with accompanying audio samples from single-speaker and 44-speaker Tacotron models on a prosody transfer task.

In this work, we propose "global style tokens" (GSTs), a bank of embeddings that are jointly trained within Tacotron, a state-of-the-art end-to-end speech synthesis system. The embeddings are trained with no explicit labels, yet learn to model a large range of acoustic expressiveness. GSTs lead to a rich set of significant results. The soft interpretable "labels" they generate can be used to control synthesis in novel ways, such as varying speed and speaking style - independently of the text content. They can also be used for style transfer, replicating the speaking style of a single audio clip across an entire long-form text corpus. When trained on noisy, unlabeled found data, GSTs learn to factorize noise and speaker identity, providing a path towards highly scalable but robust speech synthesis.

Inspired by recent work on neural network image generation which rely on backpropagation towards the network inputs, we present a proof-of-concept system for speech texture synthesis and voice conversion based on two mechanisms: approximate inversion of the representation learned by a speech recognition neural network, and on matching statistics of neuron activations between different source and target utterances. Similar to image texture synthesis and neural style transfer, the system works by optimizing a cost function with respect to the input waveform samples. To this end we use a differentiable mel-filterbank feature extraction pipeline and train a convolutional CTC speech recognition network. Our system is able to extract speaker characteristics from very limited amounts of target speaker data, as little as a few seconds, and can be used to generate realistic speech babble or reconstruct an utterance in a different voice., Comment: Accepted to ICASSP 2018

This paper describes Tacotron 2, a neural network architecture for speech synthesis directly from text. The system is composed of a recurrent sequence-to-sequence feature prediction network that maps character embeddings to mel-scale spectrograms, followed by a modified WaveNet model acting as a vocoder to synthesize timedomain waveforms from those spectrograms. Our model achieves a mean opinion score (MOS) of $4.53$ comparable to a MOS of $4.58$ for professionally recorded speech. To validate our design choices, we present ablation studies of key components of our system and evaluate the impact of using mel spectrograms as the input to WaveNet instead of linguistic, duration, and $F_0$ features. We further demonstrate that using a compact acoustic intermediate representation enables significant simplification of the WaveNet architecture., Comment: Accepted to ICASSP 2018

Progress in deep learning is slowed by the days or weeks it takes to train large models. The natural solution of using more hardware is limited by diminishing returns, and leads to inefficient use of additional resources. In this paper, we present a large batch, stochastic optimization algorithm that is both faster than widely used algorithms for fixed amounts of computation, and also scales up substantially better as more computational resources become available. Our algorithm implicitly computes the inverse Hessian of each mini-batch to produce descent directions; we do so without either an explicit approximation to the Hessian or Hessian-vector products. We demonstrate the effectiveness of our algorithm by successfully training large ImageNet models (Inception-V3, Resnet-50, Resnet-101 and Inception-Resnet-V2) with mini-batch sizes of up to 32000 with no loss in validation error relative to current baselines, and no increase in the total number of steps. At smaller mini-batch sizes, our optimizer improves the validation error in these models by 0.8-0.9%. Alternatively, we can trade off this accuracy to reduce the number of training steps needed by roughly 10-30%. Our work is practical and easily usable by others -- only one hyperparameter (learning rate) needs tuning, and furthermore, the algorithm is as computationally cheap as the commonly used Adam optimizer.

The TensorFlow Distributions library implements a vision of probability theory adapted to the modern deep-learning paradigm of end-to-end differentiable computation. Building on two basic abstractions, it offers flexible building blocks for probabilistic computation. Distributions provide fast, numerically stable methods for generating samples and computing statistics, e.g., log density. Bijectors provide composable volume-tracking transformations with automatic caching. Together these enable modular construction of high dimensional distributions and transformations not possible with previous libraries (e.g., pixelCNNs, autoregressive flows, and reversible residual networks). They are the workhorse behind deep probabilistic programming systems like Edward and empower fast black-box inference in probabilistic models built on deep-network components. TensorFlow Distributions has proven an important part of the TensorFlow toolkit within Google and in the broader deep learning community.

Even in the absence of any explicit semantic annotation, vast collections of audio recordings provide valuable information for learning the categorical structure of sounds. We consider several class-agnostic semantic constraints that apply to unlabeled nonspeech audio: (i) noise and translations in time do not change the underlying sound category, (ii) a mixture of two sound events inherits the categories of the constituents, and (iii) the categories of events in close temporal proximity are likely to be the same or related. Without labels to ground them, these constraints are incompatible with classification loss functions. However, they may still be leveraged to identify geometric inequalities needed for triplet loss-based training of convolutional neural networks. The result is low-dimensional embeddings of the input spectrograms that recover 41% and 84% of the performance of their fully-supervised counterparts when applied to downstream query-by-example sound retrieval and sound event classification tasks, respectively. Moreover, in limited-supervision settings, our unsupervised embeddings double the state-of-the-art classification performance., Comment: Submitted to ICASSP 2018

Prosodic modeling is a core problem in speech synthesis. The key challenge is producing desirable prosody from textual input containing only phonetic information. In this preliminary study, we introduce the concept of "style tokens" in Tacotron, a recently proposed end-to-end neural speech synthesis model. Using style tokens, we aim to extract independent prosodic styles from training data. We show that without annotation data or an explicit supervision signal, our approach can automatically learn a variety of prosodic variations in a purely data-driven way. Importantly, each style token corresponds to a fixed style factor regardless of the given text sequence. As a result, we can control the prosodic style of synthetic speech in a somewhat predictable and globally consistent way., Comment: Submitted to NIPS ML4Audio workshop and ICASSP

Recent work in unsupervised representation learning has focused on learning deep directed latent-variable models. Fitting these models by maximizing the marginal likelihood or evidence is typically intractable, thus a common approximation is to maximize the evidence lower bound (ELBO) instead. However, maximum likelihood training (whether exact or approximate) does not necessarily result in a good latent representation, as we demonstrate both theoretically and empirically. In particular, we derive variational lower and upper bounds on the mutual information between the input and the latent variable, and use these bounds to derive a rate-distortion curve that characterizes the tradeoff between compression and reconstruction accuracy. Using this framework, we demonstrate that there is a family of models with identical ELBO, but different quantitative and qualitative characteristics. Our framework also suggests a simple new method to ensure that latent variable models with powerful stochastic decoders do not ignore their latent code., Comment: 21 pages, 9 figures

A text-to-speech synthesis system typically consists of multiple stages, such as a text analysis frontend, an acoustic model and an audio synthesis module. Building these components often requires extensive domain expertise and may contain brittle design choices. In this paper, we present Tacotron, an end-to-end generative text-to-speech model that synthesizes speech directly from characters. Given pairs, the model can be trained completely from scratch with random initialization. We present several key techniques to make the sequence-to-sequence framework perform well for this challenging task. Tacotron achieves a 3.82 subjective 5-scale mean opinion score on US English, outperforming a production parametric system in terms of naturalness. In addition, since Tacotron generates speech at the frame level, it's substantially faster than sample-level autoregressive methods., Comment: Submitted to Interspeech 2017. v2 changed paper title to be consistent with our conference submission (no content change other than typo fixes)

We propose Edward, a Turing-complete probabilistic programming language. Edward defines two compositional representations---random variables and inference. By treating inference as a first class citizen, on a par with modeling, we show that probabilistic programming can be as flexible and computationally efficient as traditional deep learning. For flexibility, Edward makes it easy to fit the same model using a variety of composable inference methods, ranging from point estimation to variational inference to MCMC. In addition, Edward can reuse the modeling representation as part of inference, facilitating the design of rich variational models and generative adversarial networks. For efficiency, Edward is integrated into TensorFlow, providing significant speedups over existing probabilistic systems. For example, we show on a benchmark logistic regression task that Edward is at least 35x faster than Stan and 6x faster than PyMC3. Further, Edward incurs no runtime overhead: it is as fast as handwritten TensorFlow., Comment: Appears in International Conference on Learning Representations, 2017. A companion webpage for this paper is available at http://edwardlib.org/iclr2017

Developers of text-to-speech synthesizers (TTS) often make use of human raters to assess the quality of synthesized speech. We demonstrate that we can model human raters' mean opinion scores (MOS) of synthesized speech using a deep recurrent neural network whose inputs consist solely of a raw waveform. Our best models provide utterance-level estimates of MOS only moderately inferior to sampled human ratings, as shown by Pearson and Spearman correlations. When multiple utterances are scored and averaged, a scenario common in synthesizer quality assessment, AutoMOS achieves correlations approaching those of human raters. The AutoMOS model has a number of applications, such as the ability to explore the parameter space of a speech synthesizer without requiring a human-in-the-loop., Comment: 4 pages, 2 figures, 2 tables, NIPS 2016 End-to-end Learning for Speech and Audio Processing Workshop

Convolutional Neural Networks (CNNs) have proven very effective in image classification and show promise for audio. We use various CNN architectures to classify the soundtracks of a dataset of 70M training videos (5.24 million hours) with 30,871 video-level labels. We examine fully connected Deep Neural Networks (DNNs), AlexNet [1], VGG [2], Inception [3], and ResNet [4]. We investigate varying the size of both training set and label vocabulary, finding that analogs of the CNNs used in image classification do well on our audio classification task, and larger training and label sets help up to a point. A model using embeddings from these classifiers does much better than raw features on the Audio Set [5] Acoustic Event Detection (AED) classification task., Comment: Accepted for publication at ICASSP 2017 Changes: Added definitions of mAP, AUC, and d-prime. Updated mAP/AUC/d-prime numbers for Audio Set based on changes of latest Audio Set revision. Changed wording to fit 4 page limit with new additions

Modern retrieval systems are often driven by an underlying machine learning model. The goal of such systems is to identify and possibly rank the few most relevant items for a given query or context. Thus, such systems are typically evaluated using a ranking-based performance metric such as the area under the precision-recall curve, the $F_\beta$ score, precision at fixed recall, etc. Obviously, it is desirable to train such systems to optimize the metric of interest. In practice, due to the scalability limitations of existing approaches for optimizing such objectives, large-scale retrieval systems are instead trained to maximize classification accuracy, in the hope that performance as measured via the true objective will also be favorable. In this work we present a unified framework that, using straightforward building block bounds, allows for highly scalable optimization of a wide range of ranking-based objectives. We demonstrate the advantage of our approach on several real-life retrieval problems that are significantly larger than those considered in the literature, while achieving substantial improvement in performance over the accuracy-objective baseline.

Robust and far-field speech recognition is critical to enable true hands-free communication. In far-field conditions, signals are attenuated due to distance. To improve robustness to loudness variation, we introduce a novel frontend called per-channel energy normalization (PCEN). The key ingredient of PCEN is the use of an automatic gain control based dynamic compression to replace the widely used static (such as log or root) compression. We evaluate PCEN on the keyword spotting task. On our large rerecorded noisy and far-field eval sets, we show that PCEN significantly improves recognition performance. Furthermore, we model PCEN as neural network layers and optimize high-dimensional PCEN parameters jointly with the keyword spotting acoustic model. The trained PCEN frontend demonstrates significant further improvements without increasing model complexity or inference-time cost.