TRAKR – A reservoir-based tool for fast and accurate classification of neural time-series patterns
Authors: Muhammad Furqan Afzal
Christian D Marton
Erin L. Rich
Kanaka Rajan
Venue: ICLR 2022 Submitted (2022)
Keywords: neuroscience
recurrent neural networks
reservoir networks
time series classification
neural data
electrophysiological recordings

Abstract: Neuroscience has seen a dramatic increase in the types of recording modalities and complexity of neural time-series data collected from them. The brain is a highly recurrent system producing rich, complex dynamics that result in different behaviors. Correctly distinguishing such nonlinear neural time series in real-time, especially those with non-obvious links to behavior, could be useful for a wide variety of applications. These include detecting anomalous clinical events such as seizures in epilepsy, and identifying optimal control spaces for brain machine interfaces. It remains challenging to correctly distinguish nonlinear time-series patterns because of the high intrinsic dimensionality of such data, making accurate inference of state changes (for intervention or control) difficult. Simple distance metrics, which can be computed quickly do not yield accurate classifications. On the other end of the spectrum of classification methods, ensembles of classifiers or deep supervised tools offer higher accuracy but are slow, data-intensive, and computationally expensive. We introduce a reservoir-based tool, state tracker (TRAKR), which offers the high accuracy of ensembles or deep supervised methods while preserving the computational benefits of simple distance metrics. After one-shot training, TRAKR can accurately, and in real time, detect deviations in test patterns. By forcing the weighted dynamics of the reservoir to fit a desired pattern directly, we avoid many rounds of expensive optimization. Then, keeping the output weights frozen, we use the error signal generated by the reservoir in response to a particular test pattern as a classification boundary. We show that, using this approach, TRAKR accurately detects changes in synthetic time series. We then compare our tool to several others, showing that it achieves highest classification performance on a benchmark dataset–sequential MNIST–even when corrupted by noise. Additionally, we apply TRAKR to electrocorticography (ECoG) data from the macaque orbitofrontal cortex (OFC), a higher-order brain region involved in encoding the value of expected outcomes. We show that TRAKR can classify different behaviorally relevant epochs in the neural time series more accurately and efficiently than conventional approaches. Therefore, TRAKR can be used as a fast and accurate tool to distinguish patterns in complex nonlinear time-series data, such as neural recordings.

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TRAKR A RESERVOIR-BASED TOOL FOR FAST AND ACCURATE CLASSIFICATION OF NEURAL TIME-SERIES PATTERNS
Anonymous authors Paper under double-bling review
ABSTRACT
Neuroscience has seen dramatic increase in the types of recording modalities and complexity of neural time-series data collected from them. The brain is a highly recurrent system producing rich, complex dynamics that result in different behaviors. Correctly distinguishing such nonlinear neural time series in real-time, especially those with non-obvious links behavior, could be useful for a wide variety of applications. These include detecting anomalous clinical events such as seizures epilepsy, and identifying optimal control spaces for brain machine in- terfaces. It remains challenging to correctly distinguish nonlinear time-series pat- terns because of the high intrinsic dimensionality of such data, making accurate inference of state changes (for intervention control) difficult. Simple distance metrics, which can be computed quickly do not yield accurate classifications. On the other end of the spectrum of classification methods, ensembles of classifiers deep supervised tools offer higher accuracy but are slow, data-intensive, and com- putationally expensive train and deploy. We introduce reservoir-based tool, state tracker (TRAKR), which offers the high accuracy of ensembles or deep su- pervised methods while preserving the computational benefits of simple distance metrics. After one-shot training. TRAKR can accurately, and in real time, detect deviations in test patterns. By forcing the weighted dynamics of the reservoir fit desired pattern directly, we avoid many rounds of expensive optimization. Then, keeping the output weights frozen, we use the error signal generated by the reservoir in response to particular test pattern as a classification boundary. We show that using this approach, TRAKR accurately detects changes in synthetic time series. We then compare our tool to several others, showing that it achieves classification performance on par with supervised deep networks on a benchmark sequsettsequntiall MNIST-, while outperforming all other approaches. When the samples are corrupted by noise, our approach maintains relatively high per- formance, while supervised deep networks show sharp decline in performance. We also apply TRAKR to electrocorticograply (ECoG) data from the macaque orbitofrontal cortex (OFC), a higher-order brain region involved in encoding the value of expected outcomes. We show that TRAKR can classify different behav- iorally relevant epochs in the neural time series with high accuracy. Altogether, we show that TRAKR is high performing tool for distinguishing patterns in complex nonlinear Lime-series data, such as neural recordings. With its high per- formance, robustness to noise, low train- and inference-time, and ease-of-use, it offers a viable alternative to more complex state-of-the the art approaches, particu- larly for real-time applications.
INTRODUCTION
The size and complexity of neural data collected has increased greatly (Marblestone et al. (2013) Neural data display rich dynamics in the firing patterns of neurons across time, resulting from the recurrently connected circuitry in the brain. As our insight into these dynamics increases through new recording modalities, so does the desire to understand how dynamical patterns change across time and, ultimately, give rise to different behaviors.

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A lot of work in computational neuroscience over the past decade has focused modeling the collective dynamics of a population of neurons in order to gain insight into how firing patterns are related to task variables (Márton et al. (2020); Richards et al. (2019); Yang et al. (2018); Remington
eet al. g Kell et al. (2018): Zeng et al. (2018); Pandarinath et al. (2018); Durstewitz| (2017);
Chaisangmongkar kon al. (0017); Rajan et al. (016)) (ussillo al. (2015) Mante (2013)) (Sus-
sillo & Barak (2013): Barak et al. (2013) 3); Sussillo & Abbott (2009). These approaches, however, rely on fitting the whole dynamical system through many rounds of optimization, either indirectly by modeling the task inputs and outputs (Márton et al. (2020); Kell et al. (2018); Chaisangmongkoon al.) (2017); [ussiilo et al. (2013); ; Mante et al. (2013): : Sussillo & Barak (2013). or directly by fit- ting the weights of neural network to recorded firing patterns (Pandarinath et al. (2018); Durstewitz for certain applications. e.g. in clinical settings where decisions need to be taken based on recordings in real-time. In these settings, neural sime-series patterns need to be accurately distinguished in order to, say, detect the onset of seizures, or distinguish different mental states.
(2017)) Thus, these approaches can be too time- and computation-intentn
Previous approaches to classifying time series lic on a spectrum from simple distance metrics (c.g.. Euclidean) to more computationally intensive approaches such dynamic time warping (Xing al. (2010), ) ensembles of classifiers (Bagnall et al.)) or deep supervised learning (Jeong) (2020); Fawaz al. (2019). Computing simple distance metries is fast and straightforward, but does not always yield high accuracy results because the patterns may not be perfectly aligned in time. On the other end of the spectrum, ensembles of classifiers and deep learning- based approaches (Bagnall et a Jeong (2020); /Faazz et al. (2019)) have been developed that can offer high accuracy results, but at high computational cost. Dynamic time warping (DTW) has been consistently found to offer good results in practice relative to computational cost (Fawaz et al. 2019); [Bagnall et al. (2016); Serra & Arcos (0144) and is currently routinely used to measure the similarity of time-series patterns.
Previous work in reservoir computing has shown that networks of neurons can be used as reser- voirs of useful dynamics, so called echo-state networks (ESNs), without the need to train recurrent weights through successive rounds of expensive optimization (Vlachas et al.] (2020); Pathak et al. 20188; Vincent-Lamare et al. (2016); Buonomano & Maass (2009); Jaeger & Haas (2004); Jaeger a ba Maass al. (2002)). This suggests reservoir networks could offer a computationally cheaper alternative to deep supervised approaches in the classification of neural time-series data. However, the training of reservoir networks has been found to be more unstable compared to methods that also adjust the recurrent connections (e.g., via backpropagation through time, BPTT) in the case of reduced-order data (Vlachas et al.. (2020)). Even though ESNs have been shown to yield good results when fine-tuned (Tanisaro & Heidemann (2016); Aswolinskiy et al.] (2016)) convergence represents a significant problem when training ESNs end-to-end to perform classification on com- plex time-series datasets, and is a hurdle to their wider adoption.
Here, we propose fitting the reservoir output weights to a single time series thus avoiding many rounds of training that increase training time and could potentially cause instabilities. We use the error generated through the output unit in response to particular test pattem as input to classi- fier. We show that using this approach, we obtain high accuracy results on benchmark dataset sequential MNIST- outperforming other approaches such as simple distance metrics (e.g., based on Euclidean distance or Mutual Information) and a previous approach based on echo-state networks, while performing on par with deep supervised networks. We also show that our approach is more robust to noise than other approaches, in particular deep supervised networks. At the same time, TRAKR achieves high performance while keeping training and inference time low.
We also apply our tool, TRAKR, to neural data from the macaque orbitofrontal cortex (OFC), higher-order brain region involved in encoding expectations, and inducing changes in behavior dur- ing unexpected outcomes (Rich & Wallis (2016); Rudebeec & Rich| (2018); Jones al. (2012) 2): Wallis 2012);; [Scheenbaum (2009): Burke et al. (2009): Wallis & Miller (2003): y [Schoenbaum et al. recordings obtained from the macaque OFC, including anterior and posterior areas 11 and 13, during a reward expecta- tion task. The task was designed to understand if and how expectations encoded OFC are updated by unexpected outcomes. TRAKR is able to distinguish three different behaviorally relevant epochs based on the neural time-series with high accuracy, revealing that OFC units differentiate between different task episodes. This shows it can be used as a reliable tool to gain further insight into the information encoded in neural circuits.
(1998) This data consists of 128-channel clectrocorticographyy (micro-ECCOL
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Taken together, make the following contributions:
We show that by fitting single time series and working with the error signal reservoirs can perform par with supervised deep networks in time series classification
We show that this approach, while easy to use, outperforms other commonly used approaches,
such Dynamic Time Warping (DTW), and other distance measures embraced for their simplicity
We show that our approach is more robust to noise than other approaches
Our approach is computationally less expensive than other approaches, achieving high perfor- mance at low train- and inference- time
is able detect differences between neural patterns with high accuracy
Altogether, this shows that TRAKR is a viable alternative state-of-the-art approaches for time series classification.
2 METHODS
2.1 MODEL DETAILS
TRAKR (Figure IA) a reservoir-based recurrent neural network (RNN) with N recurrently con- nected neurons. Recurrent weights, J, are initialized randomly and remain aplastic over time [Buonomano & Maass (2009); Jaeger (b); Maass et al. (2002)). The readout unit, Routs is con- nected to the reservoir through set of output weights, Wout, which are plastic and adjusted during training. The reservoir also receives an input signal, I((), through an aplastic set of weights
Win.
A
B
input
input wts (aplassicc)
STATE TRACKER (TRAKR)
Reservoir
reservoir unit activity, x(()
x,/dt(()) -xx(t) + 9 9,(1) Σ, w,
recurrent (aplastic)
overall output
Z., (f)= L, Wer x(1)
output (plastic)
neural time series
recurrent wts aplastic)
state tracker error, Aw(()
Aw oz 1(0) (,0 ()
output wts
learning rete
regularizer
(Train: plastic,
W
Test: frazen)
readout
Figure 1: A) TRAKR setup overview. TRAKR consist reservoir connected to input and readout units via dedicated weights. Recurrent weights J and input weights win. are aplastic. Only the output weights Wont are subject to training. B) TRAKR equations for single unit activity, readout unit activity and error term.
The network is governed by the following equations:
dx.(1) =x((t) + Σ (1) Wiinn T(t)

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Zont (1)
Σ Wout, Wout, (1)
Here, (t) is the activity of single neuron in the reservoir, is the integration time constant, is the gain setting the scale for the recurrent weights, and J is the recurrent weight matrix of the
N 3 (t) denotes the strength of input to a particular neuron from other reservoir. The term 9 ==1
neurons in the reservoir and I(t) is the imput signal (Equation 1). Sout (t) denotes the activity of the readout unit together with the output weights, Wout (Equation 2). In our notation, Wij denote the weight from neuron j to i, and so Wout, means the weight from 1th unit in the reservoir to the readout unit. the activation function given by:
(t) = (a))((;((t)
We use recursive least squares (RLS) to adjust the output weights, Wout during training (Haykin, Simon S. (1996). The algorithm and the update rules given by:
AWout, (1) (Zows (1) f(t)) Σ (o(O0(())
Wout, (t) Wout, (t 1) + Awout,
(5)
Here, 7) is the learning rate, f(t) is the target function, and the term E, Pij (t) acts as a reg- ularizer where the inverse cross-correlation matrix of the network firing rates. For details on setting hyperparamcters, see Appendix A.
2.2 ADJUSTING RESERVOIR DYNAMICS
During training, the output weights, Wonts are optimized using RLS based on the instantaneous difference between the output, Zout (t), and the target function, f()). This optimization is performed in one shot (without the need for multiple optimization rounds). Here. we use the reservoir to autoencode the input signal, thus ft) I(t). The instantaneous difference gives rise to an error term, E(t), calculated as:
N
E(t) = Σ A
(6)
2.3 OBTAINING THE FRROR SIGNAL
After training, the output weights, Wont are frozen. The test pattern is fed the network via the input, T(t), and the network is iterated to obtain the error, E(t) over the duration of the test signal. The error, E(t) is computed as the difference between the test signal and the network output (Equa- [ion 6). The error may vary depending on the similarity of given test signal to the learned time series. The error used as input to a classifier.
2.4 CLASSIFICATION OF THE ERROR SIGNAL
The error, E(t). is used input to support vector machine (SVM) classifier with a Gaussian radial basis function (rbf) kernel. The classifier is trained using 10-fold stratified cross-validation. The same classifier and training procedure was used in comparing the different approaches. Naive Bayes as well as the neural network- based approaches (multilayer perceptron (MLP) and time warping invariant echo state network (ESN)) are directly used as classifiers, again with 10-fold stratified cross-validation. Accuracy and area under the curve (AUC) are computed measure of classifi- cation performance. MacBook Pro CPU was used for all the comparisons.
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2.5
NEURAL RECORDINGS
2.5.1
TASK DESIGN
Neural recordings were obtained from the macaque OFC using a custom designed 128-channel Micro-ECOG array (NeuroNexus), with coverage including anterior and posterior subregions (areas 11/13). During preliminary training, the monkey learned to associate unique stimuli (natural images) with rewards different values. Rewards were small volumes of sucrose or quinine solutions, and values were manipulated by varying their respective concentrations.
The behavioral task design is shown in (Figure 4J).. During the task, the monkey initiated a trial by contacting touch-sensitin bar and holding gaze central location. On each trial, either one or two images were presented, and the monkey selected one by shifting gaze to it and releasing the bar. At this point, small amount of fluid was delivered, and then neutral cue appeared (identical across all trials) indicating the start of a 5s response period where the macaque could touch the bar briefly activate the fluid pump. By generating repeated responses, it could collect as much of the available reward as desired. There were two types of these trials. Match (mismatch) trials were those where the initial image accurately (did not accurately) signal the type of reward delivered on that trial. Behavioral performance and neural time series were recorded in 11 task sessions across 35 days. For further details on trials and data preprocessing, see Appendix
RESULTS
3.1
DETECTING PATTERN CHANGES SYNTHETIC TIME SERIES
A
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Figure 2: A) (Blue) Wont plastic for 15 Hz sin-ffunction and frozen for a 5 Hz rhythm. (Orange) Test pattern with the same frequencies but the signal order reversed. (Red) TRAKR output. (Green) The error signal, (t), is showing an increase for the part of the test pattern which was not learned during training. B) Similar to A but Wout were plastic during the second half of the training signal (5Hz rhythm).
First, we trained TRAKR on idealized, synthetic signals using sin-functions of two different fre- quencies (Figure 2). Reservoir output weights were fitted to the signal using recursive least squares (RLS; see subsectiion 2.1. In Figure 2/A, the network was trained on the first half of the signal (blue) while the output weights, Wouts remained frozen during the second half. Then with Wout frozen, a fed to the reservoir. The network output, Zout Zoue(t), (t), in red and the error signal,
test signal (orange) E(t), in green are depicted in(Figure 2 The network correctly detects the deviation of the test pattern (orange, 1st half of the signal) from the learned pattern (blue, 1st half of the signal), which results in an increase in the error signal (green, 1st half of the signal, FFgure 2A).. The second half of the test signal (orange) aligns with the trained signal (blue, 1st half) and thus yields error (green, 2nd half). In Figure 2B, the order of the training procedure was reversed in that output weights remained frozen for the first half of the signal (blue) and were plastic during the second half. As expected,
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the increase in the error signal (green) now occurs during the second half of the test signal (orange). Thus, TRAKR correctly detects, via the error signal E(t), when a new frequency pattern occurs in the test signal that deviates from the trained pattern.
3.2 CLASSIFYING DIGITS SEQUENTIAL MNIST
We then applied TRAKR to the problem of classifying the ten digits from sequential MNIST, benchmark dataset for time-series problems (Le et al. (2015) Kerg al. (2019)
A
B
TRAKR
Naive Bayes
AUC
Accuracy
MLP
DTW
1
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Mutual Information
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Euclidean Distance
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Figure 3: Classification performance the sequential-MNIST dataset Le et al. (2015). A MLP:
Multi-layer perceptron (as in Fawaz et al. (2019)): ESN: echo-state network (twiESN, as in Fawaz al. (2019);; NB: Naive Bayes; DTW: Dynamic Time Warping (as in Rakthanmanon et al. (2012)); MI: Mutual Information; Euc: Euclidean distance metric. TRAKR performs on par with MLPs, while outperforming all other methods (99% AUC; * P < 0.001, (Bofeerroni-corrected) B Classification performance under increasing amount of noise. TRAKR performance declines grad- ually with noise intensity, while MLP performance degrades abruptly at higher noise levels. Chance level is at 10%.
For training, we used the entire dataset of 1000 sequential MNIST digits including 100 samples for each digit (0-9). We fed each sequential digit (28 x 28 pixel image flattened into vector of length 784) as a one-shot training signal to TRAKR, Reservoir output weights were again fitted to a single digit using recursive least squares (RLS; see subsectiion 2.1. After fitting TRAKR to one time series corresponding to one of the samples of a particular digit, we froze the output weights and fed all the other digits test samples with the magnitude of the error varying depending on the similarity with the learned digit. The error signal then fed into classifier which was trained to differentiate the digits based the terms (see juuseection 2.4 more details). We repeated this procedure for all digits and samples in the dataset to obtain the averaged classification performance for TRAKR (Figure 3A).
TRAKR. We obtained an error signal, E(t), from every test sample,
We found that TRAKR achieves a performance of AUC = 99% on this dataset (Figure A We compared our approach with other commonly used methods for the classification of time series. We compared our results against supervised deep neural networks (MLP: as in Fawaz et al. (2019)), re- cent echo-state network based approach (twiESN; as Fawaz al. (2019)). distance measures such as Dynamic Time Warping (DTW; Rakthanmanon et al. (2122). Euclidean distance Euc), Mutual information (MT), and a naive Bayes classifier (NB). With the exception of MIPPs, which showed performance on par with TRAKR, we found that all other approaches performed significantly worse than TRAKR (p 0.001; see subsection 2.4 further details).
We also tested the performance of TRAKR under different noise levels added to training digits (Figure 3B, Appendix C). We again compared TRAKR against all the other approaches and found higher noise levels: performance decays gradually as the noise is increased and is at AUC = 75% even at higher noise levels (a = 1). particular, we found TRAKR performs better than MLPs at higher noise levels.
TRAKR to perform the best, particularly

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Table 1: Computational cost compared
Method
Training time (ms) [mean + sd]
Inference time (ms) [mean + sd]
MLP
110200.00 8700000
92.50 +88.40
twiESN
105500.00 -:200.000
250.35 10.25
TRAKR
1..11 train time
(45.40 11138)+--vv) test time
DTW
(0.30 =0. train time
(0.30 + test time
MI
(0.20 + train time
(0.20 =0) +vv test time
Euc
(0.02 +0.01)+ train time
(0.02 +0.01) + sym test time
NB
252.60 11015
(5.22 +1.41)
SVM
15200.00 135000.0
80.60 :120.30
We also measured training and inference time, comparing TRAKR to the other approaches intro- duced above (Table I). We found that training time for TRAKR is situated at the lower end of the spectrum, slower than it takes to obtain measure of the distance between two traces using DTW, MI or Euc, but significantly faster than it takes to train the MLP or twiESN. While it does require upfront fitting, our approach has the advantage that it does not require multiple rounds of optimiza- tion (like MLP or twiESN) because the signal is fit in one shot (see subssecioo 2.2 for details). This yields relatively fast training time.
After fitting, TRAKR can detect deviations from the learned signal in real-time. The inference time of our approach again lies in between computationally relatively more expensive approaches such as MLP and twiESN and less intensive approaches such as DTW, MI and Euc. We also measured the train and inference time of the classifier we use (SVM) and found that it does not significantly impact training or inference time; other, relatively more simple classifiers such as kNN (k-Nearest Neigh- bors) may also be used instead, for further gains in speed. We compared all of these approaches under the same conditions (see subsection 2.4). Also, see Appendix D for details on calculation of training and inference time.
3.3 PERFORMANCE ON NEURAL TIME SERIES RECORDED FROM THE MACAQUE OFC
The OFC is involved in encoding and updating affective expectations. We used a behavioral task designed to study the neural mechanisms of how such expectations are encoded in the OFC of pri- mates and how they may guide behavior under different conditions. The goal here was determine whether TRAKR can be used to reliably distinguish complex neural time series patterns (Figure 4/A; see also subsubsection 2 for more details).
A recording from single electrode is shown together with three different behaviorally relevant epochs (rest, choice and reward periods; FFgurre 4B). We compared the performance of TRAKR with all other previously introduced methods on the task of trying to distinguish the neural time series patterns in these three epochs, important to note that we did not know a priori whether there is enough information encoded in the OFC recordings to allow for differentiating the three epochs. Thus, a high performing classifier can offer clues here as to what type of information is encoded in the brain.
We trained TRAKR on the neural time series corresponding to rest period from a particular trial, and used the other complete trials as test signals to obtain the error, E(t). The error signal was used as input to classifier. We repeated this procedure for all trials in the dataset to obtain the averaged classification performance. We also calculated the Fast Fourier transform (FFT) of the signals and obtained the magnitude (power) in the (0 12Hz), ,3 (13 35H²), and y (36- - 80Hz) 2) bands within the 3 epochs. We compared TRAKR against this FFT based classification too.
Again, with the exception of MLP which performed on par with TRAKR, we found that TRAKR outperformed all the other methods (AUC 94%; p 0.001: Figure 4C). TRAKR was able to distinguish the three epochs with high accuracy based on the neural signal, showing that there is enough information in the OFC differentiate these patterns. It is important to note that based on the performance of lower performing approaches, such as DTW or Euc, one might have (wrongly) concluded that the OFC lacks enough information to solve this task. Overall, with its high per-
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A
Free-choloe (selection)
5s interval collect as much fluid as desired
Single picture
fluid delivered (250ms)
Instrumental response
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Recording Sessions
Figure 4: A) Neural task design (see subsubsection 2.5.1 for detailed description). B) Example neural time series from single trial, with three behaviorally relevant epochs (rest, choice and in- strumental reward seeking period). C) MLP: Multi-layer perceptron (as in Fawaz et al. (2019));
ESN: echo-state network (twiESN, as in Fawaz et al. (2019)): NB: Naive Bayes; DTW: Dynamic Time Warping (as in Rakthannmano al. (2012)); MI: Mutual Information; Euc: Euclidean distance metric. TRAKR performs on par with MLP. while outperforming all other methods in classifying the different neural epochs (* methods perform at chance-level (50% AUC) in distinguishing match/mismatch trials, suggesting that the OFC does not encode enough information to distinguish between the two conditions. E) Classification performance (TRAKR) decreases over 11 recording sessions (35 days).
0.001, Bonferroni-correcter chance-level at 33%). D) All
formance, TRAKR can be used as a reliable tool to differentiate time series patterns and generate hypotheses on the type of information represented in neural circuits.
We also investigated whether any of the methods could distinguish between match and mismatch trials based on the OFC signals (Figure 4D). For this purpose, we trained TRAKR the neural time series corresponding to choice period from particular trial, and used the other complete trials test signals obtain the error, Ett). We found that all methods performed at chance-level, indicating there is not enough information in the OFC recordings to differentiate the two. We also observed that the classification performance for the three epochs degrades days (Figure 4B; blue & red solid lines), while that for match/mismatch trials consistently stays around chance-level (Fiuure 4E; blue red dotted lines).
Lastly, we visualized different electrodes in the space spanned by the first three principal compo- nents of the reservoir's activations (Appendix E). We fitted the reservoir to signal obtained from particular electrode, froze the output weights, and projected other electrodes onto the first three prin- cipal components of reservoir activity. We found that electrodes trace out different paths in reservoir space. Thus, as proof-of-concept, projections onto reservoir space can be used to visually inspect
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the similarity of recordings from different electrodes, and identify differences that may be indicative of functionally meaningful sub uub-groupings that represent functionally coherent modules in the brain.
4 DISCUSSION
We have shown that TRAKR can distinguish time series patterns with high accuracy. TRAKR outperforms other approaches in classifying time-series data benchmark dataset, sequential MNIST, and in differentiating neural time series signals obtained from recordings in the macaque OFC. It performs on par with supervised neural networks (MLPs), while outperforming other types of echo state networks (twiESN) and commonly used distance measures such as Dynamic Time Warping (DTW). Meanwhile, found that our approach is more robust noise than other ap- proaches, in particular supervised neural networks, and offers good performance in terms of training and inference time.
We found that TRAKR offers high accuracy at relatively lower training and inference times than other approaches with comparable accuracy such as supervised multi-layer neural networks. While TRAKR relies on a classifier on top of the error traces to perform the classification task, other classifiers such as kNN may be used maximize training and inference speed, instead of the SVM classifier employed here. All approaches were compared in the same environment, but all neural network-based approaches may equally benefit from further gains in training and inference speed by optimising the code for deployment on GPUs. For this purpose, TRAKR can readily be implemented in JAX, a high-peerformance computing framework (Bradbury et al. (2018).
Mcanwhile, other approaches based on echo-state networks, such twiESN (Fawaz et al. 2019 performed worse than TRAKR and showed higher train and inference times. This suggests our contribution is key to making reservoir networks viable alternative state-of-the-art approaches in time series classification.
While TRAKR and most other methods could distinguish three behaviorally relevant epochs based on the OFC signal, none of the methods were able to accurately distinguish match and mismatch tri- als. This indicates that there enough information in the OFC to distinguish the three task periods, but not enough to differentiate match and mismatch trials. It is possible that receiving better or worse reward than expected affected the neural signal in distinct/opposite ways, such that the effect was cancelled out average. It is also possible that the difference in neural time-series patterns was only discernible if the reward was maximally different (much better or worse than expected). In the current task design, there were 4 different levels of reward (flavors) that the macaque asso- ciated with different pictures (subsubsection 2.5.T). The number of trials in which obtained was maximally different from expected reward was low and possibly not sufficient for accurate classifi- cation. Another possibility, supported by our results and corroborated by several studies (Stalnaker ct al. (2018); McDannald et al. 20144; Takaaashi al. (2013); Kennerley et al. (2II)), is that OFC neural activity signals reward values but not reward prediction errors, which instead are mediated through the ventral tegmental area (VTA) in the midbrain.
We found that the classification performance decreased over recording sessions. This could mean that the difference between task epochs being classified decreased because of increased familiarity with the task. That is less likely, however, because the subject was well-trained prior to recordings. Instead, since the signal was recorded over a period of 35 days, the decrease in the classification performance could be a result of degrading signal quality, perhaps due to electrode impedance issues Kozzi et (2055a b): Holson et al. (1998): Robinson & Camp (199T)).
CONCLUSION
There is a need for and strong interest in tools for the analysis of time-series data (Bhatnagar et al. (2211). We show that TRAKR is a fast, accurate and robust tool for the classification of time-series patterns. Through its ease of use and low training and inference time, it is particularly suited for real- time applications where accurate decisions need to be made quickly and signal degradation or other artifacts necessitate frequent re-calibration, such as clinical settings. TRAKR can also be used to distinguish neural time series patterns in the brain, shedding light on the information encoded in neural circuits and thus generating hypotheses for new experiments.

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A TRAKR HYPERPARAMETERS
The recurrent weights J.y are weights from unit j to i. The recurrent weights are initially chosen independently and randomly from a Gaussian distribution with mean of and variance given by g² /2/ The input weights Win are also chosen independently and randomly from the standard normal distribution.
An integration time constant T = Ims is used. We use gain = 1.2 for all the networks.
The matrix P is not explicitly calculated but updated follows:
P(t - (1-1))(())((((((1)
P(t) = P(t-
1 (+
The learning rate y is given by 1 ((())(())(())
The number of units used in the reservoir is generally N = 30.
B MACAQUE TRIAL DETAILS & DATA PRE-PROCESSING
Each trial was approximately 6.5s long, including different behaviorally relevant epochs and cues. The macaque performed approximately 550 trials within each task session (mean + sd 562 72). Of note, 80% of the trials were match trials within each task session.
ECOG data were acquired by a neural processing system (Ripple) at 30 and then resampled at 1 The 128-channel data were first 7-score normalized. Second-order butterworth bandstop IIR filters were used to remove 60Hz line noise and harmonics from the signal. We also used second-order Savitzky-oolay filters of window length 99 to smooth the data and remove very high frequency juice pump artifacts (> 150H2). For most of the analysis here, we used the average of the 1 228-channel time series input TRAKR.
C DETAILS ON SEQUENTIAL MNIST CLASSIFICATION
For measuring noise robustness, added random independent Gaussian noise to the training digits
(j4 = and varying standard deviation (a)). The actual noise that was added (noise levels as depicted
in Figure 3) can be calculated 255, with [0, 1J. The number 255 represents the maximal pixel value in the sequential digits.
D CALCULATION OF TRAINING AND INFERENCE TIME
The calculation of training time for TRAKR includes the time taken to train one sequence through TRAKR along with 10-fold cross validation time using SVM. For all the other methods, is also the time taken to train using 10-fold cross validation. For MLP, the training is done using Keras which optimized, whereas TRAKR has further room for optimization by implementing
JAX etc.
The calculation of inference time for TRAKR includes the time taken to feed one test sequence into TRAKR and making predictions on test set using SVM. For all the other methods, the time includes making predictions on the same test set.
E VISUALIZATION OF RESERVOIR ACTIVATIONS
Single electrode recordings were projected into the space spanned by the first three principal compo- nents reservoir activations. The four electrodes trace out different trajectories in reservoir space, suggesting they capture potentially different neural dynamics, as shown in the figure below.
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Electrode Electrode 13
Electrode 76
Electrode 127
PC3
3
-10
PC2
PC1
10
16


Reviews:
[{"review_id": "uhNijOVnI74", "reviewer": "Reviewer_dzZZ", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "Strengths:\n\n1. The manuscript is straightforward and well-written\n2. The notion of using the error signal as the input to a classifier as new and potentially interesting\n3. The classification results are possibly compelling\n\nMajor issues:\n\n1. A central claim of the paper is that echo state networks are both performant and computationally efficient. Firstly, to properly contextualize the accuracy of their technique, the authors should compare TRAKR against more state of the art methods. For instance, the author should consider implementing some of the methods from the Fawaz review they cite. Moreover, while deep-learning methods may be more expensive to train, they can be used as a more up-to-date benchmark. Additionally, this could present the authors with an opportunity to compare the performance of TRAKR with deep learning methods as a function of the size of the training dataset (I suspect TRAKR might look more favorable here).\n\n2. Another major claim is that TRAKR is more \"lightweight\" than ensemble or deep-learning methods. Deep learning methods, especially for large network sizes, are particularly data-hungry in the training phase. However, inference with deep networks can be extremely fast, to the point of being sufficient for real-time applications. If one were to compare the inference time of a deep network on a GPU vs TRAKR, it is possible that TRAKR is not significantly faster than a better-performing deep network. This must be clarified since computational efficiency is touted as a major feature of TRAKR.  \n\nMinor issues:\n\n1. Figure 4 what do the error bars repesent", "summary_of_the_paper": "Here, the authors propose a reservoir-computing based framework for time-series applications. The proposed methodology involves training the output units of the echo state network to recapitulate, or autoencode, a test signal. Next, time-series are fed to the network and the error signal between the time-series and the network's response is used as input to an SVM that is used for classification.  Effectively the error signal is used as a distance metric.\n\nThe authors report that the network performs well on sequential MNIST and decoding of neural data. Additionally, they argue that a key advantage of their approach is that it is computationally lightweight – both training and inference are fast. ", "summary_of_the_review": "While the manuscript is well-written and the ideas presented are fairly straightforward, the authors need to address the primary competitor to TRAKR, deep nets, head-on. First, it is likely that deep nets are on par if not better-performing than TRAKR, which the authors readily admit.  However, the authors also need to perform analysis of inference speed with deep networks.  If deep nets can run almost as quickly as TRAKR, then this complicates a central pillar of the paper.  ", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "O4W_DLpUbtg", "reviewer": "Reviewer_xpen", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "Strengths: The method is reasonably presented. The method seems novel, and valuable because it requires very little training to create a representation of the input that can be used for further tasks. \n\nWeaknesses:\nThe experiments proposed in the paper do not seem sufficient to assess the strengths of the proposed method. The proposed method is not compared against other reservoir-based methods, against random-projection methods, or against deep neural networks.\n___\nSinusoid toy dataset:\n1. The frozen section of the train set is confusing. Why include this section in the train set if the learned weights are frozen ? Wouldn't it be clearer to remove the frozen section of the training set ?\n\nMNIST experiment:\n\n2. MNIST is composed on images, which are not naturally represented as sequential time-series. Why use MNIST as a dataset for time-series classification ? \n3. Why is the comparison limited to the four baseline methods? Why not include other models known to be good at classifying MNIST (such as CNNs)? Why not include other methods based on reservoir computing ? Why not include other random-projection methods ?\n4. How were these baseline methods applied? Were the distance metrics used as input of the RBF kernel? How is Naive Bayes used in conjunction with the SVM ?\n5. Is the classification task a one-vs-one, one-vs-all, or multinomial task? If multinomial, how is the AUC computed ?\n6. How are the error bars computed in Figure 3A ? How is the shaded area computed in Figure 3B ? Assuming this is some sort of standard deviation around a mean value, why does the mean AUC for TRAKR fluctuates more than the standard deviation (e.g. trough at noise level = 0.7)?\n7. How much time does the method requires to (a) train the reservoir, (b) train the SVM, (c) predict a sample ? Which computational time is reported in Table 1?\n\nThe OFC experiment raises the same questions as the MNIST experiment in terms of choice of the baseline methods. Additionally, it is not clear how the task of predicting behavioral states is useful to understand how the brain works. The TRAKR method does not seem to give particularly interpretable representations. The TRAKR+PCA embedding presented in Figure 5 also lacks a comparison with other embeddings, such as PCA directly on the electrode signals.", "summary_of_the_paper": "The paper proposes a new method to classify neural time-series. The method is based on a recurrent reservoir, which includes a black box function (here a fixed random RNN) and a linear readout. The black box function produces an state vector at each time point of an input time-series. This state vector is then transformed with a linear readout, trained to reconstruct the input signal. In other words, the reservoir is an auto-encoder with a fixed random RNN encoder and a linear decoder trained to minimize the reconstruction error. The method then uses the reconstruction error of the reservoir as a representation of the signal, to be used in a RBF-kernel SVM classifier and perform a given task.\n\nOn a simple toy example, the authors show that the reservoir can learn to reconstruct a sinusoid signal, and that it fails to reconstruct a sinusoid with a frequency different than during training. This failure can be considered useful to identify regimes different that the ones seen during training. The method is then used on a small MNIST datasest, training the reservoir on one sample, and then training an SVM classifier on all samples based on the reconstruction error of the reservoir. The method is then compared with four baseline methods. Finally, the method is applied to neural recordings of a macaque OFC, training the reservoir on one epoch, and then training a classifier to predict behavioral states.", "summary_of_the_review": "The comparison with other methods seems rather incomplete.", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "Mj_aod35W8y", "reviewer": "Reviewer_m9nG", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "Strength\n1. The paper is clearly written and easy to follow.\n2. The proposed approach is simple, easy to implement, and already provides a gain over conventional methods.\n\nWeaknesses\n1. The technical contribution is unclear, since reservoir computing is not new. Would be interesting to see if we learn an embedding space (using simpler methods) with a given set of reference time segments and use that embedding to reconstruct other segments to generate error signals, whether we could achieve the same gain as reservoir computing. This experiment can help highlight the need for reservoir computing.\n2. It is unclear what would be a good choice of “reference” time segments/sequences. For ECoG, rest period would make sense, but is there a way to decide in the general setting? Is the contribution of this work actually the use of a reference to generate error signals for classification, which tends to increase accuracy?\n3. It is unclear what the simulated timeseries experiment is demonstrating. If we overfit the training time segments, by construction, we would get huge error signals on test segments, which would enable us to distinguish the two. \n4. For the sequential MNIST experiment, it is not clear which digit would be a good reference and how results change with this choice. Nevertheless, getting an AUC of 99% with such a simple approach is quite impressive. If we use 10-fold cross validation, does the high AUC stays? Sometimes leave-one-out provides error estimates similar to training errors. \n5. Though TRAKR is fitted in one shot, does performance improve with a few more rounds? In general, when deploying a model real time, we care more about the amount of time it takes to generate a prediction from the model, and not so much its training time (unless the amount of training time is impractical). Hence, comparisons with other DL models are needed to show TRAKR’s performance is at least on par.\n6. Overall, seems like TRAKR works well for relatively simple classification tasks but breaks down on harder tasks like match vs. mismatch.\n", "summary_of_the_paper": "This paper proposes using reservoir computing for classifying time segments. The key advantage is less training time. The approach, TRAKR, is evaluated on simulated timeseries, sequential MNIST, and ECoG with increased accuracy over conventional methods shown.", "summary_of_the_review": "My score is mainly based on TRAKR not evaluated on harder classification tasks, lack of comparison with state-of-the-art DL models, and unclear technical novelty.\n\nPost-revision summary\nThe authors addressed some of my comments. However, the motivation as written remains to be faster runtime for real world applications, but accuracy is lower than MLP and runtime is not that much shorter. A little surprising, but would expect the state-of-the-art to be some form of transformers as opposed to MLP. Given MLP provides higher performance, I will keep my score.", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}]

Author rebuttal:

Meta-review: Authors propose an autoencoding echo state machine for a one-shot one-class time series classification task. Their approach feeds a (one-dimensional) error signal over time relative to a reference training datum to SVMs. Training is very fast by design. OFC signal analysis has practical value in neuroscience. But only one benchmark (seq-MNIST) was used to evaluate their method. While the performance seem impressive, no explanation of why the internal representation learned by the proposed system is superior and robust to noise was provided. No sequential autoencoders or latent neural trajectory inference methods were compared. Although the manuscript has greatly improved through the review-rebuttal process, there are missing key details (e.g. length of E(t) used for classification--important for real-time application, initial state for the reservoir, choice of W_in --important since it seems to be a chaotic network that's driven by strong input). While there is novelty in the approach, there is a general lack of enthusiasm among the reviewers for the manuscript as is. The reviewers and AC strongly encourage the authors to further developed these ideas and add thorough analyses for another conference.

(BTW, perhaps it's worth citing https://doi.org/10.1109/IJCNN.2016.7727309, since autoencoder combined with reservoir computing has been used for anomaly detection.)
Decision: Reject