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Karan Goel

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13 papers

2 author rows

ICLR Conference 2023 Conference Paper

Effectively Modeling Time Series with Simple Discrete State Spaces

Michael Zhang
Khaled Kamal Saab
Michael Poli
Tri Dao
Karan Goel
Christopher Ré

Time series modeling is a well-established problem, which often requires that methods (1) expressively represent complicated dependencies, (2) forecast long horizons, and (3) efficiently train over long sequences. State-space models (SSMs) are classical models for time series, and prior works combine SSMs with deep learning layers for efficient sequence modeling. However, we find fundamental limitations with these prior approaches, proving their SSM representations cannot express autoregressive time series processes. We thus introduce SpaceTime, a new state-space time series architecture that improves all three criteria. For expressivity, we propose a new SSM parameterization based on the companion matrix---a canonical representation for discrete-time processes---which enables SpaceTime's SSM layers to learn desirable autoregressive processes. For long horizon forecasting, we introduce a "closed-loop" variation of the companion SSM, which enables SpaceTime to predict many future time-steps by generating its own layer-wise inputs. For efficient training and inference, we introduce an algorithm that reduces the memory and compute of a forward pass with the companion matrix. With sequence length $\ell$ and state-space size $d$, we go from $\tilde{O}(d \ell)$ naïvely to $\tilde{O}(d + \ell)$. In experiments, our contributions lead to state-of-the-art results on extensive and diverse benchmarks, with best or second-best AUROC on 6 / 7 ECG and speech time series classification, and best MSE on 14 / 16 Informer forecasting tasks. Furthermore, we find SpaceTime (1) fits AR($p$) processes that prior deep SSMs fail on, (2) forecasts notably more accurately on longer horizons than prior state-of-the-art, and (3) speeds up training on real-world ETTh1 data by 73% and 80% relative wall-clock time over Transformers and LSTMs.

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ICLR Conference 2022 Conference Paper

Efficiently Modeling Long Sequences with Structured State Spaces

Albert Gu
Karan Goel
Christopher Ré

A central goal of sequence modeling is designing a single principled model that can address sequence data across a range of modalities and tasks, particularly on long-range dependencies. Although conventional models including RNNs, CNNs, and Transformers have specialized variants for capturing long dependencies, they still struggle to scale to very long sequences of $10000$ or more steps. A promising recent approach proposed modeling sequences by simulating the fundamental state space model (SSM) $ x'(t) = Ax(t) + Bu(t), y(t) = Cx(t) + Du(t) $, and showed that for appropriate choices of the state matrix $ A $, this system could handle long-range dependencies mathematically and empirically. However, this method has prohibitive computation and memory requirements, rendering it infeasible as a general sequence modeling solution. We propose the Structured State Space sequence model (S4) based on a new parameterization for the SSM, and show that it can be computed much more efficiently than prior approaches while preserving their theoretical strengths. Our technique involves conditioning $ A $ with a low-rank correction, allowing it to be diagonalized stably and reducing the SSM to the well-studied computation of a Cauchy kernel. S4 achieves strong empirical results across a diverse range of established benchmarks, including (i) 91\% accuracy on sequential CIFAR-10 with no data augmentation or auxiliary losses, on par with a larger 2-D ResNet, (ii) substantially closing the gap to Transformers on image and language modeling tasks, while performing generation $60\times$ faster (iii) SoTA on every task from the Long Range Arena benchmark, including solving the challenging Path-X task of length 16k that all prior work fails on, while being as efficient as all competitors.

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ICML Conference 2022 Conference Paper

It's Raw! Audio Generation with State-Space Models

Karan Goel
Albert Gu
Chris Donahue
Christopher Ré

Developing architectures suitable for modeling raw audio is a challenging problem due to the high sampling rates of audio waveforms. Standard sequence modeling approaches like RNNs and CNNs have previously been tailored to fit the demands of audio, but the resultant architectures make undesirable computational tradeoffs and struggle to model waveforms effectively. We propose SaShiMi, a new multi-scale architecture for waveform modeling built around the recently introduced S4 model for long sequence modeling. We identify that S4 can be unstable during autoregressive generation, and provide a simple improvement to its parameterization by drawing connections to Hurwitz matrices. SaShiMi yields state-of-the-art performance for unconditional waveform generation in the autoregressive setting. Additionally, SaShiMi improves non-autoregressive generation performance when used as the backbone architecture for a diffusion model. Compared to prior architectures in the autoregressive generation setting, SaShiMi generates piano and speech waveforms which humans find more musical and coherent respectively, e. g. 2{\texttimes} better mean opinion scores than WaveNet on an unconditional speech generation task. On a music generation task, SaShiMi outperforms WaveNet on density estimation and speed at both training and inference even when using 3{\texttimes} fewer parameters

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NeurIPS Conference 2022 Conference Paper

On the Parameterization and Initialization of Diagonal State Space Models

Albert Gu
Karan Goel
Ankit Gupta
Christopher Ré

State space models (SSM) have recently been shown to be very effective as a deep learning layer as a promising alternative to sequence models such as RNNs, CNNs, or Transformers. The first version to show this potential was the S4 model, which is particularly effective on tasks involving long-range dependencies by using a prescribed state matrix called the HiPPO matrix. While this has an interpretable mathematical mechanism for modeling long dependencies, it also requires a custom representation and algorithm that makes the model difficult to understand and implement. On the other hand, a recent variant of S4 called DSS showed that restricting the state matrix to be fully diagonal can still preserve the performance of the original model when using a specific initialization based on approximating S4's matrix. This work seeks to systematically understand how to parameterize and initialize diagonal state space models. While it follows from classical results that almost all SSMs have an equivalent diagonal form, we show that the initialization is critical for performance. First, we explain why DSS works mathematically, as the diagonal approximation to S4 surprisingly recovers the same dynamics in the limit of infinite state dimension. We then systematically describe various design choices in parameterizing and computing diagonal SSMs, and perform a controlled empirical study ablating the effects of these choices. Our final model S4D is a simple diagonal version of S4 whose kernel computation requires just 3 lines of code and performs comparably to S4 in almost all settings, with state-of-the-art results in image, audio, and medical time-series domains, and 85\% average on the Long Range Arena benchmark.

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NeurIPS Conference 2022 Conference Paper

S4ND: Modeling Images and Videos as Multidimensional Signals with State Spaces

Eric Nguyen
Karan Goel
Albert Gu
Gordon Downs
Preey Shah
Tri Dao
Stephen Baccus
Christopher Ré

Visual data such as images and videos are typically modeled as discretizations of inherently continuous, multidimensional signals. Existing continuous-signal models attempt to exploit this fact by modeling the underlying signals of visual (e. g. , image) data directly. However, these models have not yet been able to achieve competitive performance on practical vision tasks such as large-scale image and video classification. Building on a recent line of work on deep state space models (SSMs), we propose \method, a new multidimensional SSM layer that extends the continuous-signal modeling ability of SSMs to multidimensional data including images and videos. We show that S4ND can model large-scale visual data in $1$D, $2$D, and $3$D as continuous multidimensional signals and demonstrates strong performance by simply swapping Conv2D and self-attention layers with \method\ layers in existing state-of-the-art models. On ImageNet-1k, \method\ exceeds the performance of a Vision Transformer baseline by $1. 5\%$ when training with a $1$D sequence of patches, and matches ConvNeXt when modeling images in $2$D. For videos, S4ND improves on an inflated $3$D ConvNeXt in activity classification on HMDB-51 by $4\%$. S4ND implicitly learns global, continuous convolutional kernels that are resolution invariant by construction, providing an inductive bias that enables generalization across multiple resolutions. By developing a simple bandlimiting modification to S4 to overcome aliasing, S4ND achieves strong zero-shot (unseen at training time) resolution performance, outperforming a baseline Conv2D by $40\%$ on CIFAR-10 when trained on $8 \times 8$ and tested on $32 \times 32$ images. When trained with progressive resizing, S4ND comes within $\sim 1\%$ of a high-resolution model while training $22\%$ faster.

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NeurIPS Conference 2021 Conference Paper

Combining Recurrent, Convolutional, and Continuous-time Models with Linear State Space Layers

Albert Gu
Isys Johnson
Karan Goel
Khaled Saab
Tri Dao
Atri Rudra
Christopher Ré

Recurrent neural networks (RNNs), temporal convolutions, and neural differential equations (NDEs) are popular families of deep learning models for time-series data, each with unique strengths and tradeoffs in modeling power and computational efficiency. We introduce a simple sequence model inspired by control systems that generalizes these approaches while addressing their shortcomings. The Linear State-Space Layer (LSSL) maps a sequence $u \mapsto y$ by simply simulating a linear continuous-time state-space representation $\dot{x} = Ax + Bu, y = Cx + Du$. Theoretically, we show that LSSL models are closely related to the three aforementioned families of models and inherit their strengths. For example, they generalize convolutions to continuous-time, explain common RNN heuristics, and share features of NDEs such as time-scale adaptation. We then incorporate and generalize recent theory on continuous-time memorization to introduce a trainable subset of structured matrices $A$ that endow LSSLs with long-range memory. Empirically, stacking LSSL layers into a simple deep neural network obtains state-of-the-art results across time series benchmarks for long dependencies in sequential image classification, real-world healthcare regression tasks, and speech. On a difficult speech classification task with length-16000 sequences, LSSL outperforms prior approaches by 24 accuracy points, and even outperforms baselines that use hand-crafted features on 100x shorter sequences.

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ICML Conference 2021 Conference Paper

Mandoline: Model Evaluation under Distribution Shift

Mayee F. Chen
Karan Goel
Nimit Sharad Sohoni
Fait Poms
Kayvon Fatahalian
Christopher Ré

Machine learning models are often deployed in different settings than they were trained and validated on, posing a challenge to practitioners who wish to predict how well the deployed model will perform on a target distribution. If an unlabeled sample from the target distribution is available, along with a labeled sample from a possibly different source distribution, standard approaches such as importance weighting can be applied to estimate performance on the target. However, importance weighting struggles when the source and target distributions have non-overlapping support or are high-dimensional. Taking inspiration from fields such as epidemiology and polling, we develop Mandoline, a new evaluation framework that mitigates these issues. Our key insight is that practitioners may have prior knowledge about the ways in which the distribution shifts, which we can use to better guide the importance weighting procedure. Specifically, users write simple "slicing functions" {–} noisy, potentially correlated binary functions intended to capture possible axes of distribution shift {–} to compute reweighted performance estimates. We further describe a density ratio estimation framework for the slices and show how its estimation error scales with slice quality and dataset size. Empirical validation on NLP and vision tasks shows that Mandoline can estimate performance on the target distribution up to 3x more accurately compared to standard baselines.

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ICLR Conference 2021 Conference Paper

Model Patching: Closing the Subgroup Performance Gap with Data Augmentation

Karan Goel
Albert Gu
Yixuan Li 0001
Christopher Ré

Classifiers in machine learning are often brittle when deployed. Particularly concerning are models with inconsistent performance on specific subgroups of a class, e.g., exhibiting disparities in skin cancer classification in the presence or absence of a spurious bandage. To mitigate these performance differences, we introduce model patching, a two-stage framework for improving robustness that encourages the model to be invariant to subgroup differences, and focus on class information shared by subgroups. Model patching first models subgroup features within a class and learns semantic transformations between them, and then trains a classifier with data augmentations that deliberately manipulate subgroup features. We instantiate model patching with CAMEL, which (1) uses a CycleGAN to learn the intra-class, inter-subgroup augmentations, and (2) balances subgroup performance using a theoretically-motivated subgroup consistency regularizer, accompanied by a new robust objective. We demonstrate CAMEL’s effectiveness on 3 benchmark datasets, with reductions in robust error of up to 33% relative to the best baseline. Lastly, CAMEL successfully patches a model that fails due to spurious features on a real-world skin cancer dataset.

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NeurIPS Conference 2021 Conference Paper

Personalized Benchmarking with the Ludwig Benchmarking Toolkit

Avanika Narayan
Piero Molino
Karan Goel
Willie Neiswanger
Christopher Ré

The rapid proliferation of machine learning models across domains and deployment settings has given rise to various communities (e. g. industry practitioners) which seek to benchmark models across tasks and objectives of personal value. Unfortunately, these users cannot use standard benchmark results to perform such value-driven comparisons as traditional benchmarks evaluate models on a single objective (e. g. average accuracy) and fail to facilitate a standardized training framework that controls for confounding variables (e. g. computational budget), making fair comparisons difficult. To address these challenges, we introduce the open-source Ludwig Benchmarking Toolkit (LBT), a personalized benchmarking toolkit for running end-to-end benchmark studies (from hyperparameter optimization to evaluation) across an easily extensible set of tasks, deep learning models, datasets and evaluation metrics. LBT provides a configurable interface for controlling training and customizing evaluation, a standardized training framework for eliminating confounding variables, and support for multi-objective evaluation. We demonstrate how LBT can be used to create personalized benchmark studies with a large-scale comparative analysis for text classification across 7 models and 9 datasets. We explore the trade-offs between inference latency and performance, relationships between dataset attributes and performance, and the effects of pretraining on convergence and robustness, showing how LBT can be used to satisfy various benchmarking objectives.

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RLDM Conference 2019 Conference Abstract

PLOTS: Procedure Learning from Observations using Subtask Structure

Tong Mu
Karan Goel
Emma Brunskill

In many cases an intelligent agent may want to learn how to mimic a single observed demon- strated trajectory. In this work we consider how to perform such procedural learning from observation, which could help to enable agents to better use the enormous set of video data on observation sequences. Our approach exploits the properties of this setting to incrementally build an open loop action plan that can yield the desired subsequence, and can be used in both Markov and partially observable Markov domains. In addition, procedures commonly involve repeated extended temporal action subsequences. Our method optimistically explores actions to leverage potential repeated structure in the procedure. In comparing to some state-of-the-art approaches we find that our explicit procedural learning from observation method is about 100 times faster than policy-gradient based approaches that learn a stochastic policy and is faster than model based approaches as well. We also find that performing optimistic action selection yields substantial speed ups when latent dynamical structure is present.

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AAMAS Conference 2019 Conference Paper

PLOTS: Procedure Learning from Observations using subTask Structure

Tong Mu
Karan Goel
Emma Brunskill

In many cases an intelligent agent may want to learn how to mimic a single observed demonstrated trajectory. In this work we consider how to perform such procedural learning from observation, which could help to enable agents to better use the enormous set of video data on observation sequences. Our approach exploits the properties of this setting to incrementally build an open loop action plan that can yield the desired subsequence, and can be used in both Markov and partially observable Markov domains. In addition, procedures commonly involve repeated extended temporal action subsequences. Our method optimistically explores actions to leverage potential repeated structure in the procedure. In comparing to some state-of-the-art approaches we find that our explicit procedural learning from observation method is about 100 times faster than policy-gradient based approaches that learn a stochastic policy and is faster than model based approaches as well. We also find that performing optimistic action selection yields substantial speed ups when latent dynamical structure is present.

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RLDM Conference 2017 Conference Abstract

Sample Efficient Policy Search for Optimal Stopping Domains

Karan Goel
Christoph Dann
Rika Antonova
Emma Brunskill

Arising naturally in many fields, optimal stopping problems consider the question of deciding when to stop an observation-generating process. Classical examples include house-selling, the problem of deciding whether to sell a house given a bid and a history of past offers, and the secretary problem of deciding whether to hire an applicant or not, given that future applicants may be of higher quality. We examine the problem of simultaneously learning and planning in optimal stopping domains with unknown dynamics, when data is collected directly from the environment, as is common in real-world applications, rather than from a simulator. We propose Gather Full, Search and Execute, a simple and flexible model-free policy search method that leverages problem structure to improve efficiency of data reuse. Using a simple policy evaluation trick, GFSE evaluates every policy in an input policy class using all of the collected data and outputs a policy that has a near-optimal value in the policy class. To achieve this, we bound the sample complexity of GFSE to guarantee that policy value estimates are uniformly close to their true values with high probability. Our results tighten existing PAC bounds for general Partially Observable Markov Decision Processes (POMDPs) to achieve logarithmic dependence on horizon length for our setting, in contrast to the exponential horizon length dependence for learning in general POMDPs. We demonstrate the benefit of our method against prevalent model-based and model-free approaches on a simulated student tutoring domain, and a ticket purchase domain with real airline pricing data.

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IJCAI Conference 2017 Conference Paper

Sample Efficient Policy Search for Optimal Stopping Domains

Karan Goel
Christoph Dann
Emma Brunskill

Optimal stopping problems consider the question of deciding when to stop an observation-generating process in order to maximize a return. We examine the problem of simultaneously learning and planning in such domains, when data is collected directly from the environment. We propose GFSE, a simple and flexible model-free policy search method that reuses data for sample efficiency by leveraging problem structure. We bound the sample complexity of our approach to guarantee uniform convergence of policy value estimates, tightening existing PAC bounds to achieve logarithmic dependence on horizon length for our setting. We also examine the benefit of our method against prevalent model-based and model-free approaches on 3 domains taken from diverse fields.

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