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@@ -44,7 +44,7 @@ OpenReservoirComputing (ORC) is a Python library for reservoir computing (RC) bu
 
 # Statement of Need
 
-Time-series prediction, classification, and control are fundamental tasks across science and engineering, arising in applications from climate modeling and fluid dynamics to robotics and neuroscience. Deep learning approaches to these tasks typically require large datasets, long training times, and expensive tuning of optimization hyperparameters. RC offers a compelling alternative. Since only the readout layer is trained via a single ridge regression, RC models can be trained in a fraction of the time required by comparable recurrent neural networks, often with less data and fewer hyperparameters to tune [@lukosevicius2009reservoir,@pathak2018model,@wyder2025common]. This makes RC particularly attractive for rapid prototyping, real-time applications, and data-limited settings. However, realizing these benefits in practice requires software that is both efficient and adaptable.
+Time-series prediction, classification, and control are fundamental tasks across science and engineering, arising in applications from climate modeling and fluid dynamics to robotics and neuroscience. Deep learning approaches to these tasks typically require large datasets, long training times, and expensive tuning of optimization hyperparameters. RC offers a compelling alternative. Since only the readout layer is trained via a single ridge regression, RC models can be trained in a fraction of the time required by comparable recurrent neural networks, often with less data and fewer hyperparameters to tune [@lukosevicius2009reservoir;@pathak2018model;@wyder2025common]. This makes RC particularly attractive for rapid prototyping, real-time applications, and data-limited settings. However, realizing these benefits in practice requires software that is both efficient and adaptable.
 
 ORC's built-in models provide an easy entry point for users new to the field. In particular, a new user can supply their own time-series data to instantiate, train, and forecast in three simple lines of code. 
 
@@ -86,7 +86,7 @@ Other open source libraries for RC include Pytorch-ESN [@nardo2018pytorchesn] an
 
 # Software Design
 
-![ORC three-layer pipeline architecture. Each reservoir computer (RC) is decomposed into (i) an ``embedding'' function that lifts a low-dimensional signal $u_t$ to the reservoir dimension, (ii) a ``driver'' function that propagates the reservoir state, and (iii) a ``readout'' that maps back to a target $y$. For control and forecasting RCs, the target $y$ is typically $u_{t+1}$ (either in the presence of a forcing term or not) and for classification the target $y$ is a label. \label{fig:architecture}](../imgs/architecture_paper.pdf)
+![ORC three-layer pipeline architecture. Each reservoir computer (RC) is decomposed into (i) an embedding function that lifts a low-dimensional signal $u_t$ to the reservoir dimension, (ii) a driver function that propagates the reservoir state, and (iii) a readout that maps back to a target $y$. For control and forecasting RCs, the target $y$ is typically $u_{t+1}$ (either in the presence of a forcing term or not) and for classification the target $y$ is a label. \label{fig:architecture}](../imgs/architecture_paper.pdf)
 
 ORC models are decomposed into three components, illustrated in \autoref{fig:architecture}: (i) an embedding $f_E$ that lifts a low-dimensional input signal $u_t$ to a high-dimensional space, (ii) a driver $f_R$ that propagates the high-dimensional state $r_t$, and (iii) a readout $f_O$ that maps the latent state back to an approximation of some low-dimensional signal $y_t$. Depending on the task at hand, $y_t$ may be a future time-step of $u_t$, a label associated with input data, or some other target signal. ORC differs from many existing approaches that unify (i) and (ii). Separating the embedding from the reservoir state propagation allows for cleaner application of RC to non-standard tasks, such as acting as a surrogate model for model predictive control.
 
@@ -113,3 +113,5 @@ Claude (Anthropic) was used for code assistance during code debugging, proofread
 
 # Acknowledgements
 The authors acknowledge support from the NSF AI Institute in Dynamic Systems (grant number 2112085). The authors also thank Anastasia Bizyaeva, Noa Kaplan, and Ling-Wei Kong for insightful conversations.
+
+# References
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