Title: From Synapses to Dynamics: Obtaining Function from Structure in a Connectome Constrained Model of the Head Direction Circuit
Venue: NeurIPS 2025
Accepted: yes
Keywords: computational neuroscience

connectome

neural dynamics

attractor dynamics

self-supervised learning

structure-function mapping
Abstract: How precisely does circuit wiring specify function? This fundamental question is particularly relevant for modern neuroscience, as large-scale electron microscopy now enables the reconstruction of neural circuits at single-synapse resolution across many organisms. To interpret circuit function from such datasets, we must understand the extent to which [measured] structure constrains dynamics. We investigate this question in the drosophila head direction (HD) circuit, which maintains an internal heading estimate through attractor dynamics that integrate self-motion velocity cues. This circuit serves as a sensitive assay for functional specification: continuous attractor networks are theoretically known to require finely tuned wiring, whereas connectomes reveal that biological wiring can be variable and omit key cellular parameters such as synaptic gains, neuronal thresholds, and time constants. 
We introduce a method that combines self-supervised and unsupervised learning objectives to estimate unknown parameters at the level of cell types, rather than individual neurons and synapses. Given the raw connectivity matrix, our approach recovers a network that robustly exhibits continuous attractor dynamics and accurately integrates a range of velocity inputs, despite  minimal parameter tuning on a connectome which notably departs from the symmetric regularity of an idealized ring attractor. We characterize how deviations from the original connectome shape the space of viable solutions. We also perform in-silico ablation experiments to probe the distinct functional roles of specific cell types in the circuit, demonstrating how connectome-derived structure, when augmented with minimal, biologically grounded tuning, can replicate known physiology and elucidate circuit function.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nAuthors conduct a computational study on the head direction circuit in fruit fly by using the recently published connectome dataset. They train networks that are constrained on the connectome and show that a continuous attractor (which is often studied with hand-picked models in the literature) emerges from a self-supervised training. Overall, the authors provide several distinct insights into the neurobiology of the head circuit with a rigorous and well-executed study.\n\nSTRENGTHS AND WEAKNESSES:\nThe methodology is sound, the ablation studies are on point, the training process is exceptionally clever. I am having trouble finding things that are wrong with this work, see my final point below for suggestions for improvements.\n\nQUESTIONS:\nI have the following suggestions:\n\n- Could you please make it clear in lines 182-192, which of these loss functions are your unique contributions and which ones are used in the literature. I also think linear consistency loss needs a bit more clarification for someone who is not immediately expert (i.e., why does this incentivize linear changes wrt input)? For instance, most of the setup seems very similar to this seminal work: https://openreview.net/forum?id=8ox2vrQiTF\n\n- Lines 159-160: I think you can also motivate this through gene expressions and more broadly biological motivations. For someone outside of neuroscience, it may not be clear why this is a smart choice.\n\n- There could be a better explanation for why the linear consistency is not considered supervised learning. I think that might also be more appreciated by the NeurIPS audience. \n\n- I do believe this study would be at a spotlight quality if there was an additional experiment with RELU or leaky-relu or selu or soft-plus nonlinearity. The choice of nonlinearity is arbitrary, as authors also point out. It would have been desirable to show the same results with a different nonlinearity, though I do not think this is absolutely necessary for acceptance.\n\nLIMITATIONS:\nNA.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 5, "CLARITY": 4, "IMPACT": 4, "ORIGINALITY": 4, "DATE": "2025-06-05"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper presents a computational framework to infer functional dynamics directly from a raw, synapse-level neural connectome, addressing the fundamental question of how anatomical structure specifies circuit function.  The authors use the Drosophila head direction (HD) circuit, a known continuous attractor network, as a testbed.  Their core contribution is a method that optimizes a small, biologically-interpretable set of parameters at the cell-type level (e.g., synaptic gains between cell types, neuronal biases) rather than for individual neurons or synapses.  The model is trained using a self-supervised objective that enforces linear velocity integration, without requiring any neural activity recordings or behavioral labels.  The resulting model successfully reproduces robust attractor dynamics, matching key experimental findings.  The authors then use this functional model to perform in silico ablation experiments, probing the specific roles of different cell types and generating new, testable hypotheses about the circuit's operation.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\nSignificance: The central idea of finding a \"middle ground\" of parameterization at the cell-type level is a powerful and important contribution.  It provides a principled approach to make connectomic data functional, moving beyond hand-tuned models without resorting to overly complex, unconstrained optimization. The self-supervised training paradigm, which obviates the need for large-scale neural recordings, is highly significant and enhances the scalability of this approach to other circuits where such data is unavailable. \n\n\n\nQuality: The manuscript is of high technical quality. The authors do not just show that their model can integrate velocity; they perform a rigorous analysis of the learned dynamics using PCA, intrinsic dimensionality analysis, and persistent homology to demonstrate that the model has indeed learned a low-dimensional ring attractor manifold.  The ablation studies are particularly strong, as they involve retraining the ablated networks, providing a much more compelling test for the necessity of a given cell type than simply removing it from a pre-trained model. \n\n\n\nClarity: The paper is exceptionally well-written, clear, and logically structured. The motivation is well-established, the methods are described precisely, and the figures are clean, informative, and directly support the claims made in the text. Figure 1, in particular, provides an excellent and intuitive schematic of the core methodology. \nOriginality: While connectome-constrained modeling is an active area of research, the specific combination of self-supervised learning with a cell-type level parameterization applied directly to a raw, asymmetric connectome is novel.  The approach successfully recovers function from a biologically realistic (i.e., noisy and imperfect) structure, which is a key departure from models that assume idealized connectivity. \n\n\nWeaknesses:\n\nDependence on A Priori Functional Knowledge: The self-supervised loss function is predicated on knowing that the circuit performs linear velocity integration.  This is a reasonable assumption for the well-studied HD system, but it limits the framework's applicability for true de novo discovery of function in less-understood circuits. The authors acknowledge this, but it remains a primary limitation on the generalizability of the current method.\n\nClarity on Preprocessing and Hyperparameters: The paper mentions a \"symmetrization process\" applied to the connectome synapse counts as a preprocessing step.  The details are deferred to an appendix, but this step could be critical. If the raw connectome requires significant \"correction\" to work, it slightly weakens the claim of obtaining function directly from the measured structure. Additionally, while the paper mentions that key global parameters were chosen via hyperparameter optimization, the sensitivity of the results to these choices, as well as the loss weights, is not explored. This leaves open the question of the model's robustness.\n\nQUESTIONS:\nOn Connectome Preprocessing and Robustness: The paper states that the connectome data underwent a \"symmetrization process\" (§11.7).  Could the authors please elaborate on the specifics of this procedure in the main text or a supplement? How essential is this step to achieving the reported results? A demonstration that the model is not overly sensitive to this specific preprocessing choice would strengthen the paper. My evaluation would improve if the authors can show that the symmetrization is a minor, justified correction and that the model's success is not brittle with respect to this choice or the key hyperparameters.\n\nOn Generalizing the Self-Supervised Objective: The paper suggests the framework could be extended to other functions like \"memory, or normalization\".  This is an exciting prospect. Could the authors provide a concrete example of how the self-supervised loss function could be formulated for a different computation, for instance, divisive normalization, without relying on target activity patterns? Clarifying this would help the reader understand the true scope and generalizability of the proposed methodology beyond integrator circuits.\n\nOn the Role of P-EN Subpopulations: The finding that ablating the P-ENb subpopulation has a more detrimental effect than ablating P-ENa is a specific and novel prediction.  Can the authors leverage their trained model to provide a more mechanistic hypothesis for this difference? For instance, do the learned synaptic gain parameters (Z_AB) or the underlying connectivity counts (C_ij) reveal a systematic difference in how these two populations contribute to the circuit that explains the ablation result? Linking the emergent functional difference back to the structural or parameterized weights would provide a deeper insight.\n\nOn the Level of Abstraction (Cell-Type vs. Sub-Type): The finding that a Delta7-ablated network can be partially rescued by tuning the weights of individual ring neuron subtypes is fascinating and seems to run counter to the main thesis that cell-type level tuning is sufficient.  Does this suggest that the optimal level of parameterization is circuit-dependent? Could the authors comment on the principles that might guide a researcher in choosing the right level of abstraction (e.g., cell-type, subtype, or even single-neuron) when applying this framework to a new circuit?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-06-12"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nIn this work, the Authors propose a model to specify a circuit's function based on its known connectivity. To this end, they use a standard model for the dynamics of neural activity and learn its parameters (gain, bias, time constant) individually for each cell type to optimize a regularized task-specific loss. The model is then applied to the fruit fly's head direction circuit data from the FlyEM dataset where the Atuhors recover some known properties if the circuit (integrator dynamics; ring attractor network) and confirm/refine the roles of individual cell types in this circuit.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\nThe work deals with a highly important neuroscience problem of understanding the function/dynamics of a circuit bases on (incomplete, noisy) data describing its connectivity. Indeed, the connectivity data, typically obtained with the electron microscopy, while providing the information about the connectivity graph between the cells, lacks other important information including the strength of connectivity and other neuronal property. Additionally, the data is often noisy, featuring only the synaptic connections that were established with high confidence.\n\nThis work is also timely: as more high-volume high-resolution connectivity data becomes available for different species (worm, fruit fly, mouse), an opportunity present to study various circuits using these datasets, necessitating an algorithm that goes from the connectivity graph to a dynamical system. This paper presents such an algorithm.\n\nThe approximations/assumptions made in this paper are reasonable. For the neuronal dynamics, a standard equation is used. The parameters for this equation are unified within each cell type. These assumptions are then tested by recovering the known dynamics of the studied neural circuit and the known roles of its constituent cell types.\n\nThe results of the ablation studies are interesting and novel. Alongside with recovering the known properties of the studied neural circuit and its cells, the ablation studies here have helped to propose some novel properties of the circuit's cell subtypes.\n\nThe text is mostly well-written, well-structured and easy to follow.\n\nWeaknesses.\n\nThe fruit fly's head direction circuit is a well-studied system, and substantial existing knowledge about this circuit seem to have been incorporated into the design of the loss function here. This includes the linear consistency, the stability, the minimum speed, and the entropy loss terms. I didn't see the ablation experiments for the components of the loss function but I assume that, since all of them are presented in the manuscript, all of them may be necessary to reproduce the known properties of the circuit in the proposed model. If that is true, then a successful model may require a substantial knowledge of the studied system -- something that it otherwise is supposed to provide. This property may also limit the application of the model to new, less studied systems.\n\nFor the loss function terms, I couldn't find the definition for capital theta.\n\nQUESTIONS:\nAre all the terms of the loss function required to reproduce the results of this work? If so then, upon omission of terms, what results are not reproduced? If the results regarding the known properties of the neural circuit depend on the selection of the terms of the cost function, how can we be certain that the same wouldn't happen to the predictions regarding the unknown properties of the circuit?\n\nHow to extend this model to other circuits? How much prior knowledge of the circuit's function is required for the successful deployment of this model?\n\nLIMITATIONS:\nThe loss function appears to require substantial information about the function of the neural circuit -- the property that the model has to predict.\n\nMy current scores on the paper reflect the uncertainty about how this cost function was formulated for the described task and how to formulate it for new tasks. I am happy to revisit my scores based on the interaction with the Authors.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-06-26"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors address the challenge of deriving functional network dynamics from incomplete and noisy connectomic data of the Drosophila head direction (HD) circuit. They propose a method to infer missing neuronal parameters—such as thresholds and time constants—and to correct potential errors in synaptic connectivity. The resulting model accurately integrates angular velocity inputs and exhibits continuous attractor dynamics. Importantly, the authors demonstrate that tuning parameters at the cell-type level suffices to achieve the desired dynamics. They also perform in silico ablation experiments to elucidate the functional roles of specific neuron types.\n\nSTRENGTHS AND WEAKNESSES:\nOverall, I found the question interesting, the analysis solid, the results convincing, and the paper well-written. \nWhile I am generally positive about the contribution, I outline some high-level concerns in the \"Limitations\" section below.\n\nQUESTIONS:\n- Can the authors elaborate on the \"noisy connectome measurements\" to help us better understand the problems? What are the potential sources of measurement errors? How likely are they to appear, and what will be the consequences?\n- What would the results be like if $Z$ and, therefore, synaptic connectivity are not tuned at all?\n- Much prior domain knowledge is used in the design of the method, which limits its application to other circuits. To explore its full potential, I wonder how the method would behave if all of this knowledge were removed. By domain knowledge, I mean 1. external inputs are only injected to left/ right GLNO neurons; 2. a single E-PG neuron's activity is initialized to 1 while others are set to 0; 3. location is decoded from the activity of E-PG neurons.\n- Can you explain in more detail the \"population coding\" you used to decode the location?\n- Can you elaborate on how the hyperparameters are optimized?\n- Can you elaborate on why the linear consistency loss encourages a *linear* readout of the velocity input?\n- The meaning of $\\Theta(\\cdot)$ used in the loss function is unexplained.\n- Can you elaborate on why $C_{ij}$ is used in L1 and L2 regularization? Are small synapse counts more subject to measurement errors?\n\nLIMITATIONS:\n- My primary concern lies in the generalizability of the proposed method. The approach—particularly the training objectives and input-output relationships—appears tailored specifically to the Drosophila head direction circuit. A broader discussion of the scope and limitations of this generalization would significantly strengthen the paper.\n\n- The authors argue that replicating idealized continuous attractor dynamics requires finely tuned connectivity with perfect rotational symmetry, which is not observed in the connectome. While this claim is common in theoretical models, I am not fully convinced that such symmetry and fine-tuning are strictly necessary in biological implementations. Dynamical systems with slow manifolds and discrete fixed points can exhibit ring-attractor-like behavior without strict rotational symmetry or extensive tuning. It is plausible that the Drosophila HD circuit leverages such robustness.\nThis raises an important question: how challenging is the problem if the system can function without the degree of tuning the authors assume? For example, what do the dynamics look like with the initial connectivity matrix and neuronal parameters? Including a comparison between this baseline model and the final optimized model would help clarify the extent to which the proposed optimization is necessary and what specific gains it affords.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-27"}