Title: Scalable inference of functional neural connectivity at submillisecond timescales
Venue: NeurIPS 2025
Accepted: yes
Keywords: Generalized linear model

functional connectivity

poisson point process

stochastic optimization
Abstract: The Poisson Generalized Linear Model (GLM) is a foundational tool for analyzing neural spike train data.
However, standard implementations rely on discretizing spike times into binned count data, limiting temporal resolution and scalability. Here, we develop stochastic optimization methods and polynomial approximations to the continuous-time analog of these models, and show them to be advantageous over their discrete-time counterparts. Further, we propose using a set of exponentially scaled Laguerre polynomials as an orthogonal temporal basis, which improves filter identification and yields closed-form integral solutions under the polynomial approximation. Applied to both synthetic and real spike-time data from rodent hippocampus, our methods demonstrate superior accuracy and scalability compared to traditional binned GLMs, enabling functional connectivity inference in large-scale neural recordings that are temporally precise on the order of synaptic dynamical timescales. We provide open-source implementations of both MC and PA estimators, optimized for GPU acceleration, to facilitate adoption in the neuroscience community.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper presents novel scalable inference methods for functional neural connectivity using continuous-time Poisson Generalized Linear Models (GLMs), directly addressing the limitations of traditional binned GLMs. Conventional GLMs struggle to capture submillisecond synaptic dynamics due to coarse binning and become computationally prohibitive for large-scale recordings.\n\nThe authors introduce two primary approaches that operate in continuous time: a Monte Carlo (MC) sampling-based method and a polynomial approximation (PA) method. Both methods demonstrate improved accuracy and computational tractability by avoiding the need for a large design matrix. A significant contribution is the proposal of exponentially scaled Laguerre polynomials as orthogonal temporal basis functions, which enhance filter identification and yield closed-form integral solutions for the PA approach.\n\nValidated on synthetic and real rodent hippocampal data, these continuous-time methods achieve high accuracy and scalability, enabling functional connectivity inference with submillisecond temporal precision. The recovered coupling filters align well with empirical cross-correlograms and established anatomical properties of hippocampal subregions, providing new opportunities for neural circuitry identification.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths \n- The work directly tackles the issues of coarse temporal resolution and scalability inherent in traditional binned Poisson GLMs, which struggle to capture submillisecond synaptic dynamics and become computationally prohibitive for large-scale recordings due to the need for a large design matrix.\n- High accuracy and temporal precision: The continuous-time approaches demonstrate superior accuracy and scalability in filter recovery, enabling accurate identification of monosynaptic coupling.\n- Efficient basis functions: exponentially scaled Laguerre polynomials as orthogonal temporal basis functions, which improve filter identification, provide closed-form integral solutions for the PA approach, and better capture biophysical synaptic dynamics compared to raised-cosine bases.\n\nWeaknesses\n-   The polynomial approximation methods (both PA-d and PA-c) are inherently less accurate compared to Monte Carlo (MC) or hybrid approaches. \n-   While the Monte Carlo (MC) approach improves stability compared to discrete batched GLMs, the paper identifies \"exploring variance reduction techniques for Monte Carlo sampling of the CIF\" as a key future direction. \n-   The current work primarily focuses on identifying functional connectivity using an exponential nonlinearity and restricts its analysis to spike history. \n-   Related work: existing work on continuous-time GLM e.g. https://doi.org/10.1109/IEMBS.2009.5334610 is not discussed in the paper.\n\nQUESTIONS:\n- It would be helpful to include more comparisons or discussion with other continuous-time GLM approaches.\n- Maximum likelihood estimation in autoregressive GLMs is often prone to instability issues, such as self-excitation. Does the proposed method encounter similar challenges?\n- How does the overall firing rate influence the performance of the method?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-22"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe manuscript proposes two new algorithms to optimize continuous-time Poisson Generalized Linear Models (GLM) on spike train data. This allows to infer dynamics at submillisecond timescales and scale this to long spike trains without the memory overhead that is introduced by binning the data into spike counts. For this the authors approximate the cumulative intensity function (CIF) that is part of the continuous-time GLM either using Monte Carlo (MC) or polynomial approximations (PA) of the integral. Using Laguerre polynomials as a basis function for the latter even admits a closed form solution. The method is demonstrated both on real and synthetic data, showing the proposed algorithms scale better in the number of neurons and time-steps. Using their algorithm they find functional connections in the hippocampus that are in line with what we know experimentally.\n\nSTRENGTHS AND WEAKNESSES:\n## Strengths\n- Using a continuous-time formulation of the GLM can take advantage of the sparse nature of spike trains. Instead of operating on discretized spike count arrays of size (1, num_time_bins), one can operatore on lists of spike times [t_1,t_2,...,t_N] whose size is independent of the discretization. While the idea to make these models tractable using polynomial approximations is not new, the authors propose to use a basis of Laguerre polynomials that permit a closed form solution and need fewer features to capture neural filters. Both of this improves computational efficiency, however accuracy does not seam to be effected (according to Fig. 4 and 5). Using a MC approximation is also a straight forward thing to try and gives the experimenter more options when deploying these methods. Both of these are small, but useful contributions in my view.\n- The fact that the authors are able apply this method on hippocampal data and show method can recover known connectivity structures is also a nice demonstration of why I think this method could generally be useful.\n\n## Weaknesses\n- The paper overall feels a bit rough around the edges in its current state and it can be hard at times to follow the thought-process of the authors. While the method and its derivation are sound, the presentation could in my opinion be improved. I found that a lot of information is left for the reader to piece together (see comments and as follows). For example, I find the there could be a more natural flow between paragraphs of the experiments section that makes it easier to follow. In addition I had trouble understanding the exact content of Fig. 3, despite the associated paragraph and figure caption. What is the point it is making? Why is the error increasing after optimization in panel C? If the authors could explain this to me again / make this more clear, I would be appreciate this.\n- Another issue I have with this method is that related work, while being mentioned, is barely discussed and no shortcomings are given.\n\n## Comments\n- L4 why not write Monte Carlo methods?\n- On my printed out version of the manuscript it is hard to tell apart the similar shades of pink and red within the same plot (I.e. Fig. 1 B and D, Fig. 4,). It would be great if the authors could make them more differentiable.\n- L142 The use of W here is a bit confusing, since it means something different from the W used elsewhere. Renaming this to $\\tau$ or $\\Delta T$ similar could make this less confusing.\n- What is $I$ in Eq. 10? Was this explained?\n- While I figured out what DB means in Fig. 3 from Fig 5.'s accompanying text it would be great to mention this somewhere earlier in the manuscript (or pot. the figure caption).\n- In Fig. 4 you plot convergence time, but while you do mention what this means in App. 1.4., this is not linked\n- The use and introduction of abbreviations (i.e. MC) is inconsistent and confusing. Sometimes abbrevs. are used, sometimes not, sometimes they are introduced multiple times. \n- The supplement is sometimes referenced, but it would be nice if the authors could ref. the specific sections directly, i.e. in L273 or in L188.\n\nQUESTIONS:\n- Do the authors know why the error in Fig. 2 is increasing with more > 3 basis functions and is this something expected? If yes, this is not obvious to me. Could the authors elaborate on this? Would tuning using a Bayesian information criterion make sense?\n- Something that is also not obvious to me is how the stratified sampling leads to lower variance compared to uniform sampling in L158? If the authors could explain this to me, that would be much appreciated.\n\nLIMITATIONS:\nMy feeling is that the authors insufficiently discuss potential shortcomings of their method.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-25"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper used continuous time Poisson process GLM to infer functional connectivity and proposed two methods to approximate the cumulative intensity function in the log likelihood equation: Monte Carlo stratified sampling, and polynomial approximation. They also used Laguerre polynomials as basis functions for GLM temporal filters. Empirical results show that these methods achieve better convergence with less runtime than discrete batched GLM. The methods can uncover some features of hippocampus connectivity after pre-selecting temporal filters within a certain timescale.\n\nSTRENGTHS AND WEAKNESSES:\nThe framework of this paper is clear, and the methods proposed in this paper achieve better performance than the discrete time batched GLM. However, continuous time Poisson process GLM is not a new concept and has been studied extensively in the field, as is pointed out in the introduction section with citations [1][14][15][16][17], and this paper has no direct comparison to these previous models or methods.\nAdditionally, there are several places that should be written more carefully:\nEquation (1) and (2) summarize methods for discrete time Poisson GLM, but the notations are not treated carefully: $X_t$ is never introduced, and I think the authors meant to write $x_t$ in (1), but then $W^T X_t^T$ will be confusing in (2). These equations directly correspond to equations (1) and (7) of the cited paper [8], which have very clear notations, so maybe the authors should just follow that.\nFigure 3A and B has no y-axis values, making it hard to assess whether batched discrete time GLM ‘converges poorly’ as stated in line 233. Line 237 references Figure 3C instead of Figure 3B as stated. Line 245 references Figure 3B instead of Figure 3A as stated.\nThe hybrid PA-MC model introduced in line 254 should be explained in more detail, especially given that it is the best performing method.\n\nQUESTIONS:\n1. What is the main difference between this paper and previous continuous time Poisson process GLM? \n\n2. Do methods in this paper outperform those in [1] and [15] when used to infer functional connectivity? \n\n3. If so, what is the individual contribution of Monte Carlo stratified sampling, polynomial approximation, choice of temporal filters and choice of nonlinearities?\n\n4. The authors pre-selected filters within a certain time scale (line 297) when using the model on a hippocampal dataset. In general, how much prior is required when using this method on a real dataset?\n\nLIMITATIONS:\nSee above.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 1, "DATE": "2025-06-29"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors address an important issue in the analysis of spiking neural data: how to reasonably apply Poisson GLM without discretizing into binned count data in order to estimate functional connectivity at the temporal scale of synaptic events. Current binning approaches degrade temporal resolution and for modern data sets leads to computational limitations. The authors continuous formulation uses two tractable surrogates for the intractable cumulative intensity integral: stratified Monte-Carlo quadrature (MC) and a quadratic polynomial approximation (PA-c) that gives a closed form MAP update. They further introduce an exponentially scaled Laguerre basis as an orthogonal alternative to the raised cosine basis.They validate their methods with one Neuropixels data set, showing that MC/PA-c run faster than batched discrete GLMS, recover filters more accurately than discrete or PA-d methods, and provide better estimates of hippocampal connectivity. They provide GPU-accelerated code.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**\n\nThis problem is of increasing importance as neural recording methods improve in speed and scale. \nThe quadratic PA-c derivation is elegant\nThe Laguerre function drop preserves biophysical realism\nThorough wall-time and memory comparisons\nGPU-optimized code provided\n\n**Weaknesses**\n\nThe paper would benefit from more comprehensive baselining. For example, it currently evaluates only against a binned Poisson-GLM variant (PA-d/SVRG) and one small Neuropixels data set. \nHow do things scale as the number of neurons increases? \n\n**Minor**\n\nNotation introduction could be made clearer: for example, not introducing what x_s is at line 140 well after it’s used in Eq 4. This is not the only case of late introduction of variables.\n\nQUESTIONS:\nHow novel is the Laguerre basis? Is this not used in earlier work?\n\nWhy not use public large-scale data sets such as Steinmetz et al. visual cortex data and baseline against previous continuous Hawkes process models and quadrature methods from Paninksi, Lindermann, and others?\n\nDoes MC becomes prohibitively slow for high firing rates or when PA-c becomes memory-bound (long recordings, hundreds or thousands of neurons)?\n\nLIMITATIONS:\nThe limitations could be better highlighted in the main paper.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}