SimSort: A Data-Driven Framework for Spike Sorting by Large-Scale Electrophysiology Simulation

Thank you for your detailed and thoughtful review. We appreciate your suggestions regarding the evaluation and the need for a more thorough discussion of the limitations. We address your concerns point by point below.

1. Real-data comparison with Kilosort and detection of low-amplitude spikes (W1, Q1)

SimSort may capture only "easy" spikes?

Thank you for raising this important question. We agree that evaluating a spike sorting method’s sensitivity to low-amplitude events is essential. To assess this, we compared the total number of spikes detected by SimSort and Kilosort2.5 across six real tetrode recordings. We report the overall number of detected spikes per recording as a preliminary comparison:

SimSort detected a comparable or higher number of spikes in four out of six recordings. In recordings 5 and 6, however, SimSort detected fewer spikes than Kilosort. Upon manual inspection, we found that many of the Kilosort-only units in these recordings were detected primarily on a single channel, with no corresponding activity on adjacent channels.

This detection pattern may reflect the statistical structure of the simulated data used during SimSort pretraining. In our simulation framework, most spikes are generated by neurons whose extracellular potentials are visible across several nearby electrodes. Although we included randomized channel-wise noise augmentation during training, it remains uncommon for simulated spikes to be confined to a single channel while others contain only background fluctuations. This may have led SimSort to be less sensitive to spatially sparse spikes. We consider this a potential limitation of the current framework, which we will discuss in the revised limitations section, and improve in the future version.

To further investigate whether SimSort is biased toward high-amplitude spikes, we analyzed the SNR distribution of all spikes detected by SimSort in the six real recordings:

These results show that SimSort detects a wide range of spikes in terms of SNR, including many low-amplitude events with SNR below 2.0. This indicates that the model is not limited to high-SNR spikes and is capable of recovering lower-amplitude spikes in real recordings.

The training dataset also seems to have very high SNR (figure S10). Why not increase the noise here to match real recordings?

Thank you for pointing this out. The trace shown in Figure S10 was selected primarily for visualization purposes and may not reflect the full range of signal-to-noise ratios (SNR) in our training dataset. To address the concern that our training data might have uniformly high SNR, we clarify that the simulated dataset includes a broad spectrum of SNRs, encompassing a substantial number of low-SNR spikes. SNR was computed using a robust method based on the median absolute deviation (MAD). A summary of the SNR distribution is provided below:

2. Some questions about the preprocessing steps of real recordings (Q2, Q3)

Is there drift in the real recordings?

The real recordings in this study are relatively short (∼250 seconds), during which significant drift is unlikely to occur. We did not observe noticeable drift patterns in the data and therefore did not apply drift correction. We agree, however, that drift can be a critical factor in longer or high-density recordings. We appreciate the suggestion to consider tools such as DREDGE, and plan to incorporate drift quantification and, if necessary, correction modules into future versions of the pipeline.

SimSort’s current contrastive learning framework does not include augmentation for drift. This was a deliberate design choice: for tetrode data, the concept of drift is inherently ambiguous due to the small number of channels and limited spatial resolution. As a result, we did not apply channel invariances during training. Nonetheless, we see drift modeling as an important direction when adapting SimSort to high-density probes.

Should the whitening step be included in the preprocessing pipeline?

Thank you for the suggestion. In this work, we followed the preprocessing pipeline used in established spike sorting methods such as Kilosort and MountainSort, which includes spatial whitening in signal preprocessing.

To assess its impact, we conducted an ablation study by replacing spatial whitening with data standardization. As shown below, sorting performance decreased consistently across both datasets:

The results show a consistent decrease in accuracy, recall, and precision when spatial whitening is removed from the preprocessing pipeline.

3. Full pipeline evaluation on IBL Neuropixels data (Q4

Why not have tried the full spike sorting pipeline on IBL Neuropixels dataset?

We appreciate your suggestion to evaluate SimSort as a full spike sorting pipeline on IBL Neuropixels recordings.

SimSort was originally developed and pretrained on tetrode recordings, and directly applying it to high-density Neuropixels data would require adapting the detection model to handle broader spatial input. In this submission, we focused on evaluating the performance of identification model using neuropixels waveforms extracted by Kilosort2.5, following the CEED protocol for fair comparison of contrastive learning approaches.

We thank for your helpful suggestion to incorporate localization features into the contrastive representation. We agree this could further enhance the model’s applicability to high-density recordings and will test it in future extensions.

4. Whether SimSort find additional units in hybrid dataset? (L1)

Could the authors clarify whether or not the sorter learns additional units, and evaluate the quality of these units?

Thank you for raising this important point. To examine whether SimSort is limited to detecting only the injected ground-truth spikes, we compared the total number of detected spikes on the hybrid-static dataset. The results are summarized below:

To better address this question, we respectfully refer you to Figures S11 and S13. Figure S11 shows the identification results based solely on spikes with ground-truth annotations, while Figure S13 shows the output when SimSort performs both detection and identification on the raw hybrid recordings. In Figure S13, more units are identified than in Figure S11, including additional clusters that are not part of the injected ground-truth set. Many of these clusters exhibit well-formed waveforms, suggesting that they likely correspond to meaningful neural activity.

A similar observation can be made from the comparison between Figures S12 and S14. These results indicate that SimSort is capable of discovering additional spike events beyond the injected ground-truth units.

6. Statistical significance in Table S4 (L2)

Thank you for pointing out this important issue, and we apologize for the omission. The comparison between SimSort and CEED yields p = 0.0012, indicating a statistically significant difference (p < 0.05). The comparison between SimSort and CEED_UMAP yields p = 0.0554 and is not statistically significant. We will include these results in Table S4 and move the table to the main text in the final version.

We sincerely appreciate your thoughtful and constructive review. We understand that a key concern is the comparison with existing spike sorters on real-world data. Due to the format constraints of the rebuttal stage, we have presented as much comparative analysis with Kilosort as possible to address this point. We also plan to include a more comprehensive discussion of these issues in the limitations section of the final version. We hope these efforts help clarify the performance of SimSort. If we have misunderstood any part of your feedback, or if you have further questions or suggestions, we would be happy to continue the discussion.

Thank you for the careful follow-up and for holding us to a high standard on transferability and practicality. To avoid over-claim, we first restate scope: this submission targets tetrodes, which are widely used by neuroscientists (Many recent studies on Cell/Nature/Science still used tetrodes [1-5]). Our end-to-end pipeline (detection → identification/clustering) and all claims are calibrated to 4-channel recordings. Results on Neuropixels were identification-only (following the CEED protocol) to show representation transfer, not a full HD-probe pipeline claim.

Transferability beyond tetrodes

While we do not claim a Neuropixels detector in this paper, our identification-only evaluation on IBL waveforms shows that the learned representation out of domain performs on par with CEED (which is trained in domain). Combined with the scaling-with-data analysis in the paper, this supports the thesis that broader training coverage (including new geometries and event types) will improve generalization. If accepted, our immediate next steps are: (i) extend simulation to spatially sparse/single-channel events, (ii) add channel-drop/geometry-aware invariances to contrastive training, and (iii) train on multi-geometry corpora (tetrodes + high-density probes) to support a Neuropixels detector.

What the community gets today (within scope).

For tetrodes, SimSort offers (i) zero-shot improvements on Hybrid (best Accuracy & Precision in static; best Accuracy & Recall under drift) and WaveClus-difficult, (ii) physiologically meaningful real-data units (clear refractory structure; tuning), and (iii) a data-driven pretraining recipe that scales with additional, more diverse training data.

Concrete commitments:

1. Configurable preprocessing in the released code (whitening on/off; alternatives).
2. Diagnostics for isolation and merge/split in the camera-ready + repo.
3. Simulator/augmentation extensions to cover single-channel sparsity and multi-geometry data; document this plan in the limitations/future-work.

Clarifying scope (NeurIPS vs. Top Journal)

Our submission meets NeurIPS criteria -- introducing a novel paradigm of simulation-pretraining, demonstrating robust zero-shot transfer, rigorous validation, and reproducibility through public code/data release. While extensive multi-probe evaluation fits top-journal-level work (like Nature Methods, Neuron, Nature Neuroscience etc.), we believe the current submission clearly surpasses the NeurIPS acceptance bar.

Thank you again for strengthening our work through your valuable feedback, and we'd appreciate if you can reconsider the evaluation.

[Reference]

[1] Eliav et al., Fragmented replay of very large environments in the hippocampus of bats. Cell (2025).

[2] Harkin et al., A prospective code for value in the serotonin system. Nature (2025).

[3] Chen et al., Brain region–specific action of ketamine as a rapid antidepressant. Science (2024).

[4] Jun et al., Prefrontal and lateral entorhinal neurons co-dependently learn item–outcome rules. Nature (2024).

[5] Aldarondo et al., A virtual rodent predicts the structure of neural activity across behaviours. Nature (2024).

Thank you for letting us know that we have clarified the scope of the paper and its contribution to the community. We’re glad that our rebuttal helped explain why we chose to evaluate clustering on Neuropixels data.

We also appreciate your recognition of the following contribution:

(i) Zero-shot improvements on Hybrid → This is demonstrated in the paper.

Regarding (ii) and (iii), we fully agree that additional evaluation on published real-world datasets would provide stronger evidence to support adoption by experimental neuroscientists. SimSort is not an incremental extension of existing sorters, but a new framework, and we recognize that building community trust takes time and sustained efforts. In this submission, we present evidence that SimSort generalizes across simulated, hybrid, and real tetrode recordings (Fig. 5), which we believe is an essential step to start. Just like KiloSort, which recently presented its fourth version, SimSort will continue to evolve, and your feedback is an important part for us to improve.

I think a proper spike sorter should be evaluated when run end-to-end on a real dataset (non-hybrid).

We agree. In this submission, we evaluated SimSort end-to-end on tetrode recordings collected in our own lab (Fig. 5), using a classic visual neuroscience paradigm. Please kindly let us know if you have any question about this real data. At the same time, we recognize that reproducing published findings from existing datasets would further strengthen the practical relevance. We appreciate the suggestion.

We sincerely appreciate your thoughtful feedback and will carefully reflect it in the final version.

I thank the authors for clarifying the scope of the paper and the contribution to the community.

I now understand why the authors chose to evauate the clustering on Neuropixels data to show that the learned representation out of domain performs on par with CEED (which is trained in domain).

However, if the contribution is for tetrodes, why not focus the paper on tetrodes and make sure that each of the contribution is clear? More precisely:

(i) zero-shot improvements on Hybrid --> This is shown in the paper

(ii) physiologically meaningful real-data units --> Why not run the sorter on the data from some of the 5 papers cited in the response above and show reproducibility (or even improvement) of the downstream task? This would also adress my concerns related to generalization across multiple brain regions / cell types.

(iii) data-driven pretraining recipe that scales with additional, more diverse training data --> Show how the pipeline can be used "end-to-end" on one or more real datasets + downstream task.

To summarize, I think given the clarified scope and contribution of the paper, it is important to show the full output of the pipeline on a real tetrode dataset (i.e. non hybrid). This can then be evaluated by looking at a downstream task (similar to papers cited above) or hand validation. This is similar to the "Full pipeline evaluation" comment in my original response. I think a proper spike sorter should be evaluated when run end-to-end on a real dataset (non hybrid).

I believe that such an analysis is also needed to convince the neuroscience community of the usefulness of SimSort.

Also, I think either showing (ii) or (iii) should be sufficient, but it seems that authors tried to show both (either a spike sorter that lead to meaningful units in tertrode recordings; or a recipe that generalize to many datasets), without properly showing one or the other. I would recommend focusing on one application either a general spike sorting recipe or a tetrode pipeline that allows efficient and accurate processing of tetrode recordings to stregthen the paper.

Thank you for your detailed and constructive review. We sincerely appreciate your positive assessment of SimSort’s clarity, reproducibility, and potential impact, as well as your thoughtful comments regarding the simulation dataset. Below we address your concerns point by point:

1. Clarification on morphology and modeling assumptions (B1–B5, Q4)

Thank you for your insightful comments regarding the dataset design. We appreciate your careful reading and the suggestion to clarify several important modeling assumptions in the main text.

We confirm that the morphologies used in our simulations were 2D multi-compartmental neuron models. While the models include detailed dendritic and axonal arbors, these structures were embedded in two-dimensional space. Recurrent synaptic connections were omitted, and each neuron was independently driven by pink noise inputs injected at the soma.

We agree that omitting 3D morphology and recurrent connections limits the biophysical realism of the simulation. As you noted, this simplification may reduce spike synchrony and constrain waveform variability that arises from complex spatial arrangements of neurons. We will explicitly acknowledge this limitation in the revised manuscript.

We will also add the following clarifications to the revised paper:

• Each 10-minute trial includes five neurons placed in a 100 μm × 100 μm × 100 μm volume surrounding the tetrode, with random rotations and placements.
• Extracellular signals are generated using the line-source approximation, then summing contributions from all neurons.
• Neurons were simulated independently with no recurrent connections.
• Pink noise was the only driving input.

We will also move key simulation details from the appendix to the main text to improve accessibility.

2. Resolving overlapping spikes across neuron (B5)

Is it possible/frequent that two neurons in the same time bin can emit a spike in the same time bin?

Good point! In simulation, spike overlap is possible (multiple neurons to emit spikes within the same time bin), particularly under high firing rate conditions. Since the extracellular voltage is the linear sum of contributions from all active neurons, SimSort’s detection module is trained to identify spike events from such composite waveforms, while the task of assigning spikes to their respective source neurons is handled by the subsequent identification module. Overlapping spikes represent one of the key challenges that our contrastive representation learning framework is designed to address.

How is this handled?

Even when two spikes occur within the same time bin, they typically originate from different spatial positions, resulting in distinct waveforms across channels due to spatial variation in the extracellular potential. This difference in waveform shape across channels provides useful cues for distinguishing overlapping events. An example of such spatial variation can be seen in Figure 5c, where spikes from different neurons exhibit different waveform patterns across the 4 channels.

In practice, we observed that SimSort can often detect and separate overlapping spikes when their peak times differ by more than 15 sampling points (~0.5 ms), with both events typically detected and identified correctly. We will include these observations in the revised manuscript.

3. What additional benefits or difficulties should we encounter with more complex and detailed models? (Q1)

We agree that more biologically detailed models -- such as those with 3D morphologies, synaptic connectivity, and realistic network dynamics can offer valuable potential for spike sorting research. For example, recurrent connectivity can lead to spike time correlations and population synchrony, which increase the difficulty of resolving temporally overlapping events. In addition, incorporating diverse neuronal morphologies, spatial arrangements can result in more complex and variable extracellular waveforms, placing higher demands on the model’s ability to distinguish and represent waveform features robustly.

Importantly, features such as spike-time correlations can naturally emerge in large-scale simulations even with simplified neuron models. When many independent units are simulated over extended durations, spikes from different neurons may occur closely in time by chance. This exposes the model to temporally ambiguous cases without requiring explicit connectivity or coordinated input.

On the other hand, highly detailed and complex neuron models present substantial challenges. They are not only computationally expensive, but also make it considerably more difficult to accurately compute and model extracellular potentials because of the increased complexity of morphology, and signal propagation. In this work, we adopt a relatively simplified yet biophysically grounded simulation approach as a foundational step toward developing robust and generalizable spike sorting methods using synthetic data.

We appreciate the suggestion to include references to more advanced neuron modeling efforts such as Laquitaine et al. (2025), Markram et al. (2015), and Billeh et al. (2019). We agree that incorporating more biologically realistic 3D morphologies and connectivity patterns holds strong potential to further enhance deep learning methods for spike sorting. Such advances may also benefit broader applications in neuroscience and brain–computer interfaces. We will incorporate these references and expand our discussion accordingly in the revised manuscript.

4. Failure modes and validation challenges (Q2, Q3)

This is a valuable comment. Our model may fail in several challenging scenarios. The detector may misclassify noise events with spike-like waveforms as spikes. Under extremely low SNR conditions, the identification model may struggle to extract stable and discriminative features, even with noise augmentation during training. In long-term recordings with drift, spikes from the same neuron may be split into separate clusters, as the model does not explicitly account for waveform invariance across channels. Additionally, when two spikes occur within a short temporal window (e.g., less than 15 sampling points apart), the smaller one is often ignored to avoid false positives, potentially leading to missed detections. We will add more discussions about failure cases in the revised manuscript.

Validating the model remains challenging, particularly due to the lack of ground-truth labels in real in vivo recordings. While paired intracellular–extracellular recordings or optogenetic tagging provide gold-standard validation, they are difficult to scale. As a practical alternative, we perform indirect validation by analyzing the sensory tuning of sorted V1 neurons, where consistent and selective response patterns support the reliability of the sorting results.

To better evaluate the model’s limitations, diverse datasets will be valuable. Hybrid datasets with real background noise and drift, long-term recordings, paired ground-truth data, and more realistic simulations with recurrent dynamics can expose specific failure cases and challenge the model’s temporal resolution and representational robustness. Such benchmarks will be essential for future improvements in generalizability and reliability.

5. Figure readability and expanded discussion of related work (A1-A2, C)

We apologize for the small font size in Figures 5 and 6. In the revision, we will enlarge label fonts to improve readability. We will also reference the relevant appendix sections more clearly within the main text to guide the reader. Additionally, we will expand the discussion of prior deep learning models for spike detection and waveform representation in the revised version, to better contextualize our approach within the existing literature.

We greatly appreciate the time and effort you put into reviewing our work. Please feel free to raise any additional points during the discussion—we are happy to clarify or expand as needed.

Thank you for addressing my review. I am still favorable to the publication of this paper. If the authors state how they plan to integrate a better comparison with Kilosort 4 (at least conceptual), I am willing to upgrade my grade to 5.

The response is very useful, and the suggested clarification regarding the simulation details is very useful and interesting. It could be interesting to review in passing how other works like Kilosort are generating synthetic data for training.

Regarding the response to another reviewer about KiloSort 3.5 and 4. I agree with the other reviewer that this should be reported. Plus, the Kilosort 4 is a deep learning first Spike Sorting method, and it would be fair and important to highlight that SimSort is not the only one of this type. On this topic, I am not satisfied with the response provided to the other reviewer:

First, KiloSort 3.5 and 4.0 introduced enhancements primarily optimized for high-density Neuropixels recordings. Since our current study focuses on tetrode recordings, we did not include KiloSort 3.5 and 4 in our comparisons.

Therefore, KiloSort 4 should be "rather bad" when applied to Tetrode instead of Neuropixels? First, it would be good to verify this statement. Second, if true, a comparison with KiloSort 4 is still needed. At minima, a summary of the technical differences in the deep learning method, or the applicability (if Kilosort4 cannot be applied, should we therefore understand that transferability from tetrode to neuropixels is also impossible with your possible?).

Thank you for your positive feedback and helpful suggestions. Below, we respond in detail to the concerns you raised:

1. Generalization to other datasets and recording techniques (W1 & Q1)

We agree that evaluating SimSort on a broader range of datasets and recording configurations is an important direction. In this work, we focused on tetrode recordings as an initial step toward validating simulation-pretrained models on real data. Extending SimSort to higher-density recordings like Neuropixels presents additional engineering and algorithmic challenges (e.g., larger input dimensionality, probe geometry encoding), which we are actively working to address in future versions.

2. Comparison with KiloSort 3.5 and 4.0 (W2 & Q2)

Thank you for raising this important point. There are two keys reasons that we did not include Kilosort 3.5 and 4.0 in our comparisons.

First, KiloSort 3.5 and 4.0 introduced enhancements primarily optimized for high-density Neuropixels recordings. Since our current study focuses on tetrode recordings, we did not include KiloSort 3.5 and 4 in our comparisons.

Moreover, the goal of our work is to demonstrate, for the first time, that large-scale, simulation-driven pretraining provides a potentially practical and generalizable strategy for robust spike sorting.

3. Ablation study on model architecture and detection method (W3 & Q3)

We appreciate your suggestion. We further conduct ablation experiments to analyze the contribution of different components in SimSort to the overall performance. First, we replaced the detection module with a simple threshold detector and kept the spike identification module unchanged. The results on the hybrid dataset are summarized in Table 1.

Table 1. Sorting Results with Threshold Detector vs SimSort (Hybrid Dataset)

From Table 1, we can see that SimSort consistently performs well, whereas the threshold-based method is sensitive to the choice of voltage threshold.

Then, we tested whether a simpler GRU-based detection model can replace the Transformer-based detector in the spike detection stage. As shown in Table 2, the detection performance drops significantly.

Table 2. Detection Performance Comparison Between GRU and Transformer

Transformers are particularly well-suited for spike detection due to their ability to model long-range dependencies and contextual interactions between time points, without the limitations of recurrence or fixed receptive fields. Furthermore, the self-attention mechanism allows the model to adaptively weigh different parts of the signal for detecting spike events under varying background conditions.

To evaluate the role of encoder architecture and representation learning objective in the spike identification model, we compared three configurations:
(1) a GRU encoder trained with contrastive loss (SimSort), (2) a Transformer encoder with the same loss, (3) a GRU encoder trained with a non-contrastive supervised objective.

Table 3. Identification performance across objectives, encoders, and denoising

As shown in Table 3, the contrastive approach yields substantially better performance, indicating its critical role in robust spike identification. Among the contrastive models, the GRU encoder slightly outperforms the Transformer.

We also conducted an ablation study to evaluate the impact of the denoising module. By removing the denoiser while keeping the GRU encoder and contrastive learning unchanged, we observed a modest drop in performance, particularly in the drift setting. This indicates that while SimSort’s identification performance is primarily driven by contrastive learning, denoising contributes to robustness under more challenging conditions.

Thanks again for your valuable suggestions, we will include these results in the revised manuscript.

4. How different data types (for example, spikes from different areas) influence the model performance? (Q4)

Thank you for the insightful question, we also have considered this problem. The follows are our answers.

For general spike sorting tasks, the specificity of the brain region or neuron type play a relatively limited role. Spike detection primarily relies on identifying temporally localized voltage deflections that exceed background noise -- a process more strongly influenced by signal-to-noise ratio and electrode geometry than by regional differences. For spike identification, our contrastive learning framework is designed to distinguish waveforms based on relative similarity, without relying on prior knowledge of cell types or waveform templates.

We also have shown empirical results about the generalizability of SimSort to different brain regions and animals (Figure 5). we constructed our simulation dataset using morphologically detailed neuron models from the rat somatosensory cortex. For real-data evaluation, we successfully applied SimSort to the tetrode recordings from the mouse primary visual cortex. This implies the specificity of the brain region or neuron type play a relatively limited role.

To further investigate the influence of brain-region variability on model performance, we plan to incorporate additional regions into the simulation dataset and the test dataset in future work.

We sincerely thank you again for your thoughtful and constructive feedback. We hope our response has addressed your concerns, and we would be happy to further discuss any remaining questions during the discussion phase.

Thank you for addressing part of my concerns.

1. About Kilosort comparison: Whether the method is general enough could not be quantified without extending tetrode into neuropixel. As the authors mention that the goal is to provide a practical and generalizable stratege. The comparison is necessery. "Moreover, the goal of our work is to demonstrate, for the first time, that large-scale, simulation-driven pretraining provides a potentially practical and generalizable strategy for robust spike sorting."

2. In the reply to reviewer 1rAH, the authors emphaze the zero-shot generalization with large-scale, biolophysically simulations. The large-scale simulation is the authors' contribution. However, the advantages of the models are not significant if they are resulted from the large simulated dataset, because YASS and CEED could also be trained based on the large-scale simulation dataset (the dataset is not limited to be used only by Sim-Sort. Then, the question raised here is: whether the main contribution comes from Sim-Sort or the dataset? If the contribution is from Sim-Sort, the YASS and CEED frameworks should also be trained by the large-scale training dataset for a fair comparison. Moreover, since the training dataset are from simulation, then transferring to Neuropixel data should be achievable. "We see the key novelty of SimSort not merely in the use of deep learning, but in the scientific finding that large-scale, biophysically realistic simulations alone can enable zero-shot generalization to real-world spike sorting tasks. While previous deep learning-based methods such as YASS and CEED have shown promising results, their reliance on relatively small training datasets has limited their generalization ability. To our knowledge, SimSort is the first demonstration that simulation-driven pretraining alone can achieve generalizable and reliable spike sorting, highlighting a new paradigm for scalable and data-efficient modeling in this field."

We appreciate your thoughtful comments and suggestions, which helped improve the clarity and quality of our work. Below, we address your concerns and questions in detail:

1. Model design and architectural novelty (W1)

The main contribution of our study is to reveal the potential of simulation-driven pretraining to enhance the robustness and scalability of spike sorting in experimental neuroscience. Although our architecture is based on well-established components such as Transformers and GRUs, the novelty of our work lies in how these components are integrated and tailored specifically for spike sorting, particularly in the context of simulation-based pretraining.

2. Inference speed evaluation and practicality (W2 & Q3)

This is a nice point. SimSort is actually fast and we will update our paper to clarify its inference speed. As shown in the demonstration video included in our originally submitted supplementary material, SimSort processes a 30-second tetrode recording in 9.5 seconds for the whole process including data pre-processing, spike detection, spike identification and visualization on a single A100 GPU. This pipeline has not undergone dedicated speed optimization. We believe that techniques such as batching, GPU-based preprocessing and clustering could further improve runtime. Even in its current form, SimSort demonstrates practical inference speed on tetrode recording and exhibits potential for efficient large-scale spike sorting. The following Table 1 shows the detailed computational speed.

Table 1: Computational Requirements of SimSort models

3. Scaling law of the training data size (W3)

discussion on data scale-up laws

Thank you for your careful review. Are you suggesting that detection accuracy is exhibiting signs of saturation? We note, however, that the other two metrics—Sorting Accuracy and Identification ARI (solid green and purple curves in Fig. 7)—do not show comparable saturation.

Consider the Hybrid (static) dataset. When the data size increases from $2^{12}$ to $2^{13}$, Sorting Accuracy rises by ≈ 0.02 and Identification ARI by ≈ 0.04. Although these absolute gains may appear modest, they are meaningful because the metrics are approaching their upper bounds. The similar pattern holds for the Hybrid (drift) dataset.

Regarding detection accuracy (dashed purple curves), we agree that the trend is approaching saturation. Importantly, though, enlarging the dataset never degrades detection performance, so increasing sample size remains advantageous—even if the marginal gains taper off.

We appreciate your suggestion about adding more discussion about the results regarding the scaling law, which will be reflected in the revision.

more diversified simulation data or improvements in the model architecture

Thank you for raising this thoughtful question. We agree that a critical direction for future improvement lies in examining how the composition and diversity of synthetic datasets influence model generalization.

As you suggested, merely increasing the volume of data from a single simulation paradigm may yield diminishing returns, especially if the additional data do not introduce novel variability in waveform structure or network-level dynamics.

Further performance gains are more likely to come from increasing simulation diversity rather than scale alone. This includes:

• Incorporating neuron models from different brain regions, which can differ in cell-type composition, firing patterns, and background activity.
• Including recurrent connectivity of neuron models, which can introduce spike synchrony and temporal correlations—important challenges for realistic spike sorting.
• Utilizing 3D neuron morphologies (rather than 2d) and more realistic tissue conductivity, which can generate more heterogeneous extracellular waveforms.

At the same time, improvements in model architecture, particularly mechanisms that account for temporal overlap or drift (e.g., invariant representations across waveform deformations), are also promising directions.

In short, we see this work as a first step demonstrating the viability of simulation-based pretraining, and we fully agree that diversifying simulation conditions and evolving model design will be key to further advancing generalization. We plan to pursue both directions in future work.

4. factors in the simulation process that are key to zero-shot transfer (Q1)

This is a thoughtful question. Several aspects of our simulation design contributed to the observed generalization:

• Electrode geometry and neuron positioning. We explicitly model the 3D spatial configuration of electrodes and surrounding neurons. The relative distance, orientation, and density of nearby cells strongly influence extracellular signals. This spatial variability is essential for training a detection model to distinguish spikes from noise across diverse waveform shapes and amplitudes.
• Biophysical realism of neuron models. We use morphologically and electrophysiologically realistic neurons with diverse firing properties, generating a wide range of biologically plausible waveforms.
• Naturalistic noise-driven activity. Temporally correlated stochastic current injection introduces realistic subthreshold fluctuations and irregular spike timing, enhancing robustness to background noise and temporal variability.
• Large-scale, ground-truth-labeled training data. The volume and diversity of training samples help the model learn generalizable features and avoid overfitting to specific conditions.

Our results suggest that combining spatial modeling, biophysical diversity, and statistical variability can help bridge the sim-to-real gap. Supporting high-density probes is part of our ongoing efforts.

5. Model architecture design intention(Q2)

For spike detection, the task is formulated as a sequence labeling problem over long, continuous voltage traces. Here, temporal context is critical—not only to suppress noise and artifacts, but also to accurately detect overlapping or low-amplitude spikes that are temporally modulated. Transformers are particularly well-suited for this setting due to their ability to model long-range dependencies and contextual interactions between time points, without the limitations of recurrence or fixed receptive fields. Furthermore, the self-attention mechanism allows the model to adaptively weigh different parts of the signal for detecting spike events under varying background conditions.

For spike identification, the input consists of short waveform segments (~2 ms, typically 60 samples), where the objective is to learn compact, discriminative embeddings of spike shapes for clustering. In this case, we chose a GRU-based encoder after empirical comparison with Transformer. GRUs have significantly fewer parameters and lower computational cost than Transformer.

To validate these design choices, we conducted an ablation study comparing different combinations of detection and identification architectures.

First, we replaced the detection module with a simple threshold detector and kept the spike identification module unchanged. Please kindly refer to our response to reviewer jc2X's W3 & Q3 for the results. We observed that SimSort's detection model consistently performs well, whereas the threshold-based method is sensitive to the choice of voltage threshold.

Then, we tested whether a simpler GRU-based detection model can replace the Transformer-based detector in the spike detection stage. As shown in Table 2, the detection performance drops significantly.

Table 2. Detection Performance Comparison Between GRU and Transformer

Transformers are particularly well-suited for spike detection due to their ability to model long-range dependencies and contextual interactions between time points, without the limitations of recurrence or fixed receptive fields. Furthermore, the self-attention mechanism allows the model to adaptively weigh different parts of the signal for detecting spike events under varying background conditions.

To evaluate the role of encoder architecture and representation learning objective in the spike identification model, we compared different encoder backbones and learning algorithms as follows.

Table 3. Identification performance across objectives, encoders, and denoising

As shown in Table 3, the contrastive approach yields substantially better performance, indicating its critical role in robust spike identification. Among the contrastive models, the GRU encoder slightly outperforms the Transformer. We also noticed a modest performance drop when denoiser is not applied.

The font size in the tables in Figures 5 and 6 is too small.

We appreciate and will revise.

Thanks again for your valuable suggestions which have helped us improve the clarity and rigor of our work, we will include these results in the revised manuscript. We welcome any further questions and are happy to engage in continued discussion.