TreeMoCo: Contrastive Neuron Morphology Representation Learning
Authors: Hanbo Chen
Jiawei Yang
Daniel Maxim Iascone
Lijuan Liu
Lei He
Hanchuan Peng
Jianhua Yao
Venue: NeurIPS 2022 Accept (2022)
Keywords: neuron morphology
cell types
contrastive learning
tree graph augmentation
tree-LSTM

Abstract: Morphology of neuron trees is a key indicator to delineate neuronal cell-types, analyze brain development process, and evaluate pathological changes in neurological diseases. Traditional analysis mostly relies on heuristic features and visual inspections. A quantitative, informative, and comprehensive representation of neuron morphology is largely absent but desired. To fill this gap, in this work, we adopt a Tree-LSTM network to encode neuron morphology and introduce a self-supervised learning framework named TreeMoCo to learn features without the need for labels. We test TreeMoCo on 2403 high-quality 3D neuron reconstructions of mouse brains from three different public resources. Our results show that TreeMoCo is effective in both classifying major brain cell-types and identifying sub-types. To our best knowledge, TreeMoCo is the very first to explore learning the representation of neuron tree morphology with contrastive learning. It has a great potential to shed new light on quantitative neuron morphology analysis. Code is available at https://github.com/TencentAILabHealthcare/NeuronRepresentation.

TreeMoCo: Contrastive Neuron Morphology Representation Learning
Hanbo Chen* + Tencent AI Lab
Jiawei Yang* University of California, Los Angeles jiawei maaxei11@uuca.eeo edu
hanbochen@tencent.ccom com
Daniel Maxim lascone
Lijuan Liu Southeast University, Nanjing edwiseeuuudud..e. cn
University of Pennsylvania, Philadelphia daniel. iac...iiiccooeeeeemeciiiiiiii. upenn. edu
Lei He
Hanchuan Peng
University of California, Los Angeles lheêee. ucla.
Southeast University, Nanjing h@braintell. org
Jianhua Yao
Tencent Al Lab
j Jaabhayaa@@eeneentccom
Abstract
Morphology of neuron trees a key indicator to delineate neuronal cell-types, ana- lyze brain development process, and evaluate pathological changes in neurological diseases. Traditional analysis mostly relies on heuristic features and visual inspec- tions. A quantitative, informative, and comprehensive representation of neuron morphology largely absent but desired. To fill this gap, in this work, we adopt a Tree-LSTM network to encode neuron morphology and introduce self-supervised learning framework named TreeMoCo to learn features without the need for labels. We test TreeMoCo on 2403 high-quality 3D neuron reconstructions of mouse brains from three different public resources. Our results show that TreeMoCo is effective in both classifying major brain cell-types and identifying sub-types. To our best knowledge, TreeMoCo is the very first to explore learning the representation neuron tree morphology with contrastive learning. It has great potential to shed new light on quantitative neuron morphology analysis. Code available at https: //github. com/ Tee./nt AILaiiea teeeeaaeeeeeeeoeeeeeeeeeeeee
Introduction
The central nervous system composed hundreds to thousands of neuronal subtypes. Subtype is the critical determinant of neuronal function within local and long-range circuits and is identified by a combination gene expression patterns, dendrite/axon morphology, synaptic connectivity, and clectrophysiological properties. In particular, dendritic morphology is central node of neuronal subtype identity, as dendritic branches receive the vast majority the presynaptic input onto each neuron and directly shape the clectrophysiological properties of the neuron that governs its firing output. Delineating neuron cell-types based on their dendritic morphology one of the core problems of neuroscience for the past century [51].
:: Equal contribution. 1, Work done when authors were at Tencent Al Lab. T Corresponding author.
36th Conference on Neural Information Processing Systems (NcurIPS 2022).

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Figure 1: Distribution neurons in the embedding space of TreeMoCo visualized by t-SNE [39].
Thumbnails of dendrites randomly colored. (b-e) Zoom-in view of regions in (a) showing clustering of isocortex layer 5 cells (b), layer 2/3 cells (c), basket cells (d), and Martinotti cells (c).
Neuron dendritic morphology can be digitally represented by a 3D neuron reconstruction (Fig. 2(a)), tree graph with 3D coordinates of each node; the root is placed at soma. With recent advances in imaging [9, 11, 47] and computational methods [20, 27, 42], 3D reconstruction whole neuron trees with high-throughput is now accessible for mouse brain [28, 44]. However, due to the lack of effective measurement, most analyses of these reconstructions are still largely based on biologists' visual inspection. Considering the enormous number of neurons in the brain and the 3D formation of neuron morphology, such visual inspection subjective, biased, and has low throughput.
The past decade has witnessed the success of deep learning in learning representations of almost all kinds of data such image, language, sound, and graph [2]. However, a special type of graph graphic data, most of the quantitative analysis of neuron trees is still based on simple heuristic features [33]. Only a few attempts have been made learning deep representations of neuron morphology. In [52], the authors proposed to encode neuron morphology with tree recurrent neural network (TRNN). However, this method relies on manual annotations, limiting its application to supervised training only. In [22], the authors proposed a generative self-supervised learning (SSL.) method for neuron morphology representation learning, named Morph reconstruct original neuron trees via a variational autoencoder and random walk sampling. Since this method

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cannot encode tree topology structure, its classification performance is limited and the method still relies on label information generate reasonable predictions. In [32], the authors adopt multi-view based SSL. to learn representations of neuron morphology. Though the work mainly focuses on the local components of neuron branch which is not available in whole neuron reconstruction data, its promising results advocate the possibility of learning morphology representation without labels.
Inspired by the contrastive learning successes in visual representation, we experiment with adapting MoCo for neuron morphology representation learning, namely TreeMoCo. It can learn embedding of 3D neuron reconstructions without needing prior knowledge such as cell type annotation. first maps neuron trees input to deep embedding space by our proposed neuron encoder, and then incorporates an SSL pipeline composed of neuron tree augmentations and a contrastive loss to learn representations. By testing the framework on 2403 neuron reconstructions from 3 different data resources, we are excited to find that TreeMoCo can clearly delineate neuron morphology in the embedding space (Fig. 1). Comparison with prior arts shows that TreeMoCo can achieve premium results than supervised methods even without annotations.
Background and Related Works
Heuristic features of neuron morphology. To quantitatively describe the neuron morphology, a set of heuristic features and related tools namely L-measure [33] has been proposed and widely used. These features can be summarized
categories including (1) distance-based measurements (e.g. branch length, distance to soma); (2) angle-based measurements (e.g., bifurcation angle); (3) topology-based measurements (e.g., number of bifurcations, branch order); and (4) size-based measurements (e.g., branch radius, surface area). Statistics of these features such as mean or standard deviation are usually adopted describe neuron morphology. Such representation is easy to compute and explain. However, they cannot differentiate complex morphologies (examples in Appx. A.
Cell-type and neuron morphology classification. As the primary function of dendritic branches is to compartmentalize functionally related synaptic inputs, dendritic morphology can be used to categorize neuronal subtypes based on total dendritic length, amount of branching across the dendritic trees, and localization of dendritic branch fields to different brain regions (such as layers of neocortex). Most existing cell-type classification algorithms rely on hand-crafted features [33] to predict or cluster cell types [40, 24]. In some recent works, researchers started to adopt tree- tree-hased model [52, 23] and sequence-baar -baed model [22] to classify neuron morphology. Despite competing performance than classic methods, training of these models requires manual annotations of cell types.
Contrastive learning. Contrastive learning (CL) is a SSL method that aims at bringing positive sample pairs closer and spreading away the negative sample pairs in the feature embedding space. This method dates back to [13] or carlier, and has recently drawn significant interest across different communities [45, 25, 17, 17,48, 48, 16, 6, 5]. Some research efforts have been made in graph contrastive learning (GCL) [37, 30, 15, 49, 46). Particularly, GraphCL. [49] studies the graph data augmentations systematically for GCL, and InfoGCL [46] provides theoretical analysis for it. However, to best knowledge, no work has studied the tree graph, a special instance of graph, within the context of CL.
3 Methods
3.1 Tree graph representation of neuron
We define a neuron reconstruction as T A (V, E), where V = (ux}ie (#R, yk: =x)) are nodes with 3D coordinates and E {ex}: e = (uk, o parrent) are edges connecting each node with its parent. As shown in Figure 2-(e), the number of 1 1-degree nodes could vary by reconstruction and image resolutions, while the bifurcation/tip nodes preserve major topology information. For computational efficiency, we remove 1 1-degree nodes and directly connect the root node, the bifurcation nodes, and the tip nodes in T (Fig. 2(b)). To preserve the shape information of 1-degree node sequences (branch in Fig. 2(e)), we calculate the related features and concatenate them with the coordinate property its downstream node, as illustrated in Figure 2-(e.f) The processed tree graph is defined as r Process(T) (T) A (), where G represents the tree topology and X {x*] is an N (3 + Q) matrix that is from N nodes with 3D coordinates and Q-dim branch features.
3

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Mituraationpppp node
6t
1-degron node
roct node
resolutionn resolution
Dr. Eutiitttn disance
DI2
processed
F.E.CC
whilt
(1) Original
(ii) Drapped
reomple
Fg edge vestor sequencee
(ii) Skipped
(iv) Swapped
Example neuron reconstruction
Processed neuran tree graph
Branch features
Topology augmentation
Figure 2: Illustration of (a) neuron reconstruction, (b) processed tree graph, (c) branch feature computation, (d) topology augmentations. (ii) to (iv) correspond to (9) to (11) in Table 1. (e) and (f) illustrate neuron tree processing for computation efficiency and resolution normalization purposes.
a
b
Nodes J.J
Parent
I~g
Contrasting
i~g
X
k
h(z)
Y= (X, 3)
Y==11
X = (X)
nx 3
l ll2
Input Tree
Augmentation
Neuron Encoder
Projection
LSTM-based Tree Path Processor
Figure 3: The overview of TreeMoCo: (a) TreeMoCo pipeline. (b) The zoom-in view of how the LSTM-based tree path processor 7 propagates information from child nodes i and j to parent node Blue and green colors denote the corresponding information flows for two LSTM cells, respectively. The symbol "Σ" denotes summation. The dashed rectangles mark our double-cell LSTM processor.
Branch feature is a Q-dim vector, of which two dimensions denote length and contraction. Length L is the accumulated distance between adjacent nodes along a branch: T. Σ. startSicend ||u; vi+1 1 22 which measures size. Contraction is the ratio between the Fuclidean distance = || Vena la and the length I. of branch: C D/ I,, which measures the curviness. Notably, both measurements are invariant to the order of edges and thus cannot differentiate certain patterns (details in Appx. A. To allow a comprehensive encoding of branch pattern, we resample each branch with a fixed number of vertices (8 in this paper) and take the sequence of the edge vectors E, = & 0i+1 as the its shape feature: Fg E R21 In addition, the branch orientation is unified before extracting feature vectors such that the start and end points are on the x-axis and the principle direction is aligned with y-axis (Fig, 2(c)), Together, there are 29 features for each neuron node: [z, y, C; FE).
3.2 Neuron Encoder
We next propose a neuron encoder f to project the neuron tree graph into feature space. Our model has two components: a trainable MLP (multi-layer perceptron) embedding layer (ω) that maps point coordinates and other node-related features into the embedding space, and L-SsM- tree-path processor (1)) that exploits tree topology information. Formally, we define the neuron encoder as o é. Figure 3 (a) shows an overview of our neuron encoder.
Embedding Layer (0). The embedding layer maps input features vector x into d-dim embedding vectors &. implemented by a three-layer perceptron with BatchNorm and ReLU attached to the input and hidden layers. We refer to the outputs of this embedding layer as node embeddings. Formally, compute āa o(xx), where x is the k-th node of neuron, or jointly X o(X).

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LSTM-based tree-path processor (1). The original LSTM [18] architecture applies for strictly sequential data. However, neuron tree structure more complicated than a simple sequence. Therefore, we adopt child-sum Tree-I.STM architecture, similar to [38], to process such data. Recall the hidden state and the cell state at time and layer are usually denoted as h and C, in LSTMs [18]. Here we denote them similarly, but indexed by tree node, as h and C, at node k. To aggregate information from multiple child nodes, we simply sum over the hidden states and cell states. The transition equations can be formulated as followings:
h = ΣSEC(H) h2, CL, = =EJEC(K) C₁.1
(1)
1g Cx,1 L.TM (8A. (h(,1,%(1))
(2)
h Σ)EO(H) h 2 = -jEc()) Z
(3)
hg.2, 2gg LSTM2(Ck,,1 (hk,2: 24)
where C(k) denotes the set of child nodes of node k, and 2y is the final cell state. We use two layers of LSTM cells (non-shared weights) to better capture the topology information (Eqns. 2, 4). Our tree-path processor designed
bottom-up manner where the information is aggregated from each individual leaf nodes and flowed to the root node. We then use the final cell state of the root node z, referred to as neuron representation, for downstream tasks, e.g., predicting class labels by an additional single linear layer classifier or projected by a projection head [5, 16] for contrastive learning. Formally, compute the representation of neuron tree by z ny XX 9) (the propagation path is determined by g). Figure 3 (b) demonstrates how information is propagated along the path.
3.3 Contrastive learning of tree graph
Recent progress in self-supervised contrastive learning, stemmed from visual representation learning [45, 16, 6, 5, 12]. has been seen in many other fields, including graph contrastive learning [46, 49] an overall under-explored direction. Attempts have been made to study self-supervised graph representation learning in terms of data augmentation [49], network architecture, and overall pipelines [46]. Although the neuron tree is a special case of graph structure, to share the same setups as traditional graphs in terms of contrastive learning [49]. Below we first introduce our TreeMoCo pipeline, then elaborate on the subtle but important difference between neuron tree and a general graph, subsequently introducing our data augmentations for tree structure.
argue that it is too special
Tree Contrastive Learning, Figure 3 illustrates the overall pipeline of TreeMoCo. The core idea of contrastive learning is to maximize the similarity between positive sample pairs and minimize it among negative sample pairs by optimizing contrastive loss function [45, 5, 13]. We follow successful exemplar, MoCo [16, 6]. in visual contrastive learning to build our framework.
Conceptually, MoCo [16] abstracts contrastive learning as dictionary look-up problem. For each encoded query q, there a set of encoded keys (kg, k1, k2,
dictionary. The task for a model is to pull closer q and its matched positive key k* in the dictionary while to spread away from all other negative keys k- To that end, we follow the successful experience in [5, 16] to use the dot-product as similarity measurement, and the InfoNCE [45] contrastive loss:
exp(q k* /T)
Lg = log
(5)
exp(q k+//)+++++- Σx- exp(q-k-/r)
where T is temperature hyper-parameter [45]. This loss defined for one input instance, and the total loss is averaged over batch.
To construct a pair of query and key, given a set of trees D and set of possible augmentations T. we first uniformly sample a tree T ~ D and transform it into two augmented views Y, t(T) and Tr (T),, referred as the query view and the key view, by applying two sampled augmentations t~ T, ~ T. Then, we compute their neuron representations using neuron encoder defined in Sec. 3.2, ie.. Zy f(Tg)) )) 2 = fT))). Following the improvement
SimCLR [6], we further map the neuron representations to another latent space using a non-linear projection head h(-) and normalize them by q = 11( ( (/l and k = h (zx2))/1l //Il1/(2. (22))22 Here, f' and h stand for the momentum copies of f and h. named momentum encoder [16]. Therefore, q and k+ in Equation 5 are naturally generated from single sample, and k 's are from a queue [16] that stores features from previous batches.
5

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Discussion: data augmentation on graphs, trees, and neuron morphology. Data augmentation essential for self-supervised contrastive learning [5]. Current successful data augmentations for graphs [49] mainly include (1) "node dropping" that randomly drops graph nodes and their associated edges, (2) "edge perturbation" that randomly adds or drops edges, (3) "attribute masking" that acts like dropout [36] to node features, and (4) "subgraph sampling" that uses random walk to sample a partial graph. These augmentations can apply to general graph data without loss of generality, However, some of them are unsuitable for tree-structure graphs without special consideration. For example, the node dropping at a rate of 0.2 (default in [49]) would produce a pruned tree since all the subtrees would be removed once their parent node dropped. Besides, edge perturbation is unlikely to be feasible in a tree structure if no strategical design is considered. Two nodes in a neuron tree may be spatially close to each other while having long "distance" in terms of topology (e.g., number of hops from one node to another) and vice versa. The perturbed edges would create cyclic graphs on the one hand, and break the consistency between space (3d coordinates) and structure (nodes connectivity) on the other hand. Therefore, we argue the special consideration is needed for the design of data augmentations on tree-structured data.
Data augmentation for neuron morphology representation learning. Regarding the characteris- ties of neuron data, we propose 11 available augmentations for neuron morphology representation learning, which are briefly summarized in Table I and some implementations are provided in Ap- pendix B.3. The rationale behind our design is that neuron representation should be invariant to augmentations - the golden rule applicable in many cases. For neuron data, such augmentations may occur in (i) node coordinates, (ii) overall morphology, (iii) attribute masking and (iv) topology. Thus can augment neuron data from different perspectives as Table shows. Jittering (4, 6) means adding random noise in a small range; deforming (7) means scaling each branch independently. We also include attribute masking (8) used in general graph augmentation. For (iv) topology, we propose three different augmentations. The first is (9) "truncated dropping subtrees" that recursively visits nodes from the root to leaves and drops subtree with a small probability (e.g., 0.05). The name "truncated"" means at most mn revisesubtrees will be dropped. Similarly, we have (10) "skipping parent node" that at most m parent nodes will be replaced by one of their subtrees (respectively), and (11) "swapping sibling child" that picks a subtree from a sibling node and swaps that subtree with another subtree in the current node; all pickings are random. For simplicity, we empirically use the same m 10 for ()) in this paper. Figure 2 (d) illustrates how topology augmentation acts like.
Table 1: Overview of data augmentations for neuron morphology representation learning.
Category
Target
Augmentations
(i) Point Transformation
Coordinates
1) Scaling, 2) Rotating, 3) Shifting, 4) Jittering 5) Flipping
(ii) Morphology
Branch feats
6) Jittering hranches, 7) Deforming branches
(iii) Attribute Masking
Branch feats
8) Masking attributes
9) Truncated dropping subtrees
(iv) Topology
Edges
10) Truncated skipping parent node
11) Truncated swapping sibling child
4 Experiments
4.1
Experiment setups
Data. We download data from 3 public resources: (1) BICCN fMOST data from Brain Image braimimagellbbrrry org/ httg//icc//eeeeee /eceeeenn///eeeeeeeeeeeeeeeeeeee (ooo/MMOT//) [28]. (2) Janelia MouseLight (JML, http::httt//mssli/eeeeeee///
Library (BIL,
j janelia ia.iaa.... org/) [44], and (3) Allen Cell Types (ACT, https://celltypes brain-map. org/) [1]. In total, 3358 three-dimensional mouse brain neuron reconstructions are collected (refer to Table 2 for details). To facilitate analysis, we exclude cell types with less than 50 reconstructions and the neurons with obvious reconstruction errors, yielding 2403 neurons in total. Some of the samples include both dendrite and axon reconstructions. For simplicity, we only keep dendritic arbors in this paper and leave the analysis of axons for future works. All three datasets have registered reconstructions to the 3D Allen mouse brain Common Coordinate Framework (CCFv3 [41]) and thus their scales are the same. Meanwhile, the absolute coordinates and orientations of registered neurons could also carry cell-type information that are

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related to brain anatomy instead of neuron morphology. To eliminate such potential information leakage, all dendrites are shifted and rotated such that the root is placed the origin and the X/Y/Z coordinates are determined based principle component analysis (PCA). Data are then processed and analyzed following the steps introduced in the Section 3.1. In the interest of evaluating TreeMoCo's capability of classifying known cell types across data sources, we specifically use the cell types with rich coverage among 3 datasets only (grayed cell types in Table 2). We denote these sub-datasets as BIL-6, JML-4 and ACT, respectively, For supervised training, 80% samples in each dataset are randomly picked as training set and 20% are reserved for testing. For TreeMoCo pre-training, we pre-train the joint training sets of 6 JML-4, and ACT when evaluating the supervised downstream tasks and train on all samples except those from class "others" when analyzing the embedding space.
Table 2: Demographic table of reconstructions. Refer to Appendix A.2 for full names of brain regions.
Number of neuron reconstructions each brain regions
Dataset
Total
1.2/3
1.4
1.5
1.6
VPM
CP
VPI.
SUB
PRE
MG
Others
BIL [28]
1741
126
56
315
93
378
311
80
4
50
328
JML [44]
1107
64
179
114
12
5
70
60
602
ACT [1]
510
111
123
164
97
15
Total
3358
301
179
658
304
390
311
85
74
50
945
Implementations and evaluation. We postpone the detailed implementations and settings of hyper-parametert parameters of TreeMoCo to Appendix B.I. For implementations of all the compared methods, we directly use the official codes and the default settings of MorphVAE [22], TRNN [52] and GraphCI. [52] to obtain the results. Please refer to Appendix B.2 for their implementation details. All models share the same 29-d input features and trained for 100 epochs. For evaluation, report the sample-wise accuracy. During pre-training, we evaluate models every 5 epochs via a K Nearest-Neiighor (KNN) classifier for unsupervised methods or their inherent classification heads for supervised methods and report the best test set performance for all the studied methods. This strategy mainly follows [45, 49]. We set the number of neighbors 20 for BIL-6 and ACT datasets and 5 for the JML-4 dataset since a minority class might only have 12 samples in total in JML-4.
4.2 Too delineates neuron morphology in the embedding space
Visual inspection of cell types delineation. We first demonstrate that TreeMoCo can learn neuron tree representations that manifest different characteristics of neuron morphology. Self-supervised training is conducted on the full dataset, and the distribution of the embeddings is visualized by t-SNE [39] in Figures 1 and 4. By visual inspection, it is evidenced that TreeMoCo can separate major cell-types such pyramidal neuron (Figs. 1(b-c)) and interneuron (Figs. I(d-e)). Pyramidal neurons are the primary long-range output neurons of the brain [35] while interneurons mainly sculpt local network dynamics through variety of circuit motifs. The asymmetric long projecting apical tuft is a unique feature that differentiates pyramidal neuron's 's morphology with interneuron's ss. TreeMoCo can further delineate subtypes of pyramidal neuron and interneurons. In Figure and 4(a), we can clearly see the separation of layer 2/3 (Fig. (c)) and layer 5 (Fig. I(b)) pyramidal neurons. Layer 2/3 neurons can be distinguished by their shorter apical dendrites with extensive oblique branching [43] while layer 5 neurons feature extended apical dendrites with extensive horizontal branching in layer I and sparse oblique branching in layer 2/3 [14]. The two primary classes of inhibitory interneurons (parvalbumineexpresss expressing basket cells and wwwaattstttti-expessisiii Martinotti cells) are also clearly distinguished with TreeMoCo. Parvalbumin-expei expresssin basket cells have extensive branching field Martinotti
that extends radially around the soma (Fig. ((d)) [29]. In contrast, comatostatin-exprsstt cells tend to have unipolar or bipolar dendritic branching that extends vertically above and below the soma (Fig. (())) [34]. It should be noted that such delineation is purely self-driven without any human labels or any prior knowledge of cell types. In contrast, the delincation is less clear in GraphCL's 's result and not observed in Morph VAE's result (details in Appx. D).
Quantitative evaluation. Here we quantitatively evaluate the quality of learned representations of different methods in classifying the known cell-types. For supervised methods, we directly train them on each dataset. For unsupervised methods, we pre-train them on the joint training sets. Table reports the results, with the best test KNN accuracy during unsupervised pre- pre-training or the best test
7

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Table 3: Comparisons to state-of-the-an neuron cell-type classification. We report the sample-we wise accuracy (%). The numbers of classes in BIL-6, JML-4 and ACT are 6, 4, and 4, respectively. Results obtained from officially released codes.
Table 4: Ablation on augmentations. We re- port the accuracy (%) of KNN on BIL-6 test set with models pre-trained on the full BIL-6 dataset with different augmentations.
Methods
BIL-6
JML-4
ACT
Pate-
Supervised training in individual datasets.
75
M6-27
TL
TE.L
MorphVVE [22]
66.80
40.00
41.05
TTRNN [52]
76.56
51,43
46.32
Drece
Unsupervised pre-training on joint training sets.
CCraphCL. [49] frozen KNN
69.14
54.29
58.95
60.45
71/19
13.23
1
15.84
TreeMoCo frozen KNN
78.91
64.29
55.79
TreeMoCo fine-tuned
83.98
67.14
68.42
Pall
Mab Mape:
Class Narre L25
[n) Classes
Average Length
Average Contraction
of Modees
VPM
CP
XPL
SUB
Delaset
[b] Datasets
Length
[h] Tree Height
BL
JML
ACT
Figure 4: Thumbnails of neurons in the same embedding space of Figure 1 colored by different attributes. It is evidenced TreeMoCo encodes cell types (a) and neuron morphology features (c)-(h), without human labels. Refer to Appendix D for high-resolution figures.
accuracy during supervised training included. It can be observed that TreeMoCo trained without label information can already achieve better performance than supervised Mor [22] and TRNN [52]. Fine-tuning the pre-trained neuron encoder further improves cell-type classification. This is mainly because Morph VAE [22] is based random walk to capture topology information, which ignores tree architecture. While TRNN [52] has less description power than our neuron encoder in capturing high-order interaction between features. GraphCI. [49] outperforms TreeMoCo in the ACT dataset but falls behind in BIL-6 and JMI.44 datasets. This coincides with the data quality differences (ACT reconstruction is less complete than BIL and JMI., more details in Appx. A.2). One explanation is that GraphCL pays more attention to local context and thus is less sensitive to global changes. It should be emphasized that although the overall test set performance is improved during training, we observe that the test KNN accuracy of both TreeMoCo and GraphCL fluctuates and suffers variations, especially for the smaller JML-4 and ACT datasets. GraphCL fails to improve models over time in the JML-4 dataset under some scenarios. Please refer to Appendix C for more details and discussions, where we provide the performance curves of different methods over training.
TreeMoCo manifests neuron morphology distribution. Figure 4 shows the t-SNE plots of neuron representations. Each plot is colored by different morphology feature, i.e., average/total branch length (c. d), average standard deviation of contraction (e, f), number of nodes in a neuron (g) and the height of neuron tree (h). Neurons that share similar morphology features are well clustered in
8

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the embedding space (see (1) to (7)), demonstrating the good representations learnt by TreeMoCo. These morphology attributes have not been explicitly provided as input features but turns out that TreeMoCo can mine such information by itself, without human labels. In addition, we can see it by cross-referencing Figure (a) and (b) that neurons of same class but from different datasets are clustered together in Tree.MoCo's representation space, showing TreeMoCo's os unbiasedness to data sources a much desirable property for neuron morphology representation learning.
4.3 Ablation on augmentation methods and network architectures
In this subsection, we first assess the importance of data augmentations in contrastive neuron morphology learning. Then we ablate on several design choices in our neuron encoder.
To systematically study the effects of different categories of data augmentations, we first group the proposed augmentations in Table by their categories, except for the topology augmentation, the one we are more interested in. Then, we apply them individually or in pairs to TreeMoCo framework with a higher applying probability due the reduced number of augmentations (details Appx. B.2.) when pre- training. Note that this ablation does not aim to figure out the best compositions of presented augmentations, but to unravel how different augmentations contribute to the final performance. For ablation purposes, in this experiment we train on the full BIL-6 dataset for 50 epochs. Table shows the KNN evaluation results under each individual category or a composition of data augmentations. Here we do not specify the order of augmentations, thus resulting symmetric performance matrix. Unlike the observation in visual or graph representation contrastive learning that no single augmentation performs the best [5, 49], we find in neuron morphology representation learning certain kinds of augmentations are good enough for pre-training (c.g., point transformation, skipping parent node). Topology augmentations do not necessarily bring better performance. This could be caused by the mechanism of Tree-LSTM which aggregates the whole tree to generate embeddings and thus is sensitive to the global changes caused by topology augmentation. Better neuron morphology representations might be excepted if a more proposer set of augmentations or a better network architecture were applied under the TreeMoCo framework.
Then, we study the effects of different components our neuron encoder. For this experiment, we train neuron encoders for 100 epochs three datasets and report their best test performance. Table 5 (left) shows the results, where a steady increasing trend of model performance can be observed. We also include the KNN accuracy (Tab. 5 right) for 50-epoch pre-training on the joint dataset and evaluated in BIL-6 dataset just for ablation interest. Here we find that batch normalization (BN) is beneficial for both contrastive sule-supe learning and supervised learning. No BÑ in the neuron encoder would give significantly worse results (first line of right table). Further adding BN in the projection head is helpful for TreeMoCo. This behavior has also been reported in non-contrastive SSL. methods before, egg., BYOL (12, 31J, where removing BN causes model collapse.
Table 5: Ablation on model designs. (left) Classification accuracy of supervised training for 100-epoch. (right) KNN accuracy of TreeMoCo pre-training for 50 epochs and evaluated in BIL-6 dataset. BN matters more in TreeMoCo. Gray rows indicate our default setting.
Settings
Classification Accuracy (%)
Encoder BN
Projector BN
KNN accuracy (%) BII.-6
BN
ML.
L.TM Cells
BlI.-
JMI.4
ACT
54.29
69.14
83.98
57.14
50.53
75.00
84.77
2
85.55
64,29
62.11
76.56
5
Conclusion and Limitations
In this work, we have explored contrastive learning for neuron morphology representation learning via TreeMoCo. Our results on 2403 neuron reconstructions show that TreeMoCo has the unique potential to identify unbiased cell-types. Modern cell-type classification is heavily dependent on transcriptomic data [50, 8). However, even neurons within the same mouse possessing identical genetic identity and birth-date demonstrate extremely variable dendritic morphology and synaptic distribution [19]. This variability underlies the need for high-throughput neuronal morphology classification techniques to probe for the existence of novel subtypes within classically established

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neuronal identities [3]. TreeMoCo has great potential to fill this need and to explore dendritic architecture. These findings could lead to more rigorous output measurements for drug discovery experiments and aid in the development of treatments for neurological disorders characterized by progressive dendrite degeneration such as Alzheimer's s disease and depression [10. 7].
We note that TreeMoCo is still a preliminary effort of its kind. Certain limitations can be observed and need to be solved in the future. For instance, Tree-LSTM aggregates the whole graph and thus is sensitive to global changes. This results in its performance decay on incomplete neuron reconstruction (ACT dataset) and its favor of node-feature-bue based augmentation over topology-basee bbsed augmentation. Moreover, compared to most image contrastive learning frameworks. TreeMoCo's 's performance on downstream tasks could oscillate after long training epochs on small datasets. An effective early stopping criterion is needed but absent when label information is not available.
Nevertheless, the graph common data structure representing objects varying from artery and lung vessels [21] to program source code [26] and HTML documents [4]. Another direction of our future work to extend TreeMoCo into more general framework for learning representations beyond neuron morphology. Following the success of contrastive learning in image analysis problems, we believe TreeMoCo could be powerful tool solve unsupervised and few-shot learning problems
related to a wide range of tree graph data.
Acknowledgments and Disclosure of Funding
Daniel Maxim lascone is sponsored by NIH (F32 MH125600-011
Lijuan Liu is sponsored by a MOST (China) Brain Research Project, "Mammalian Whole Brain Mesoscopic Stereotaxic 3D Atlas" (2022/D0200500, 20222ID0205044).
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Checklist
1. For all authors...
(a) Do the main claims made in the abstract and introduction accurately reflect the paper's
contributions and scope? [Yes]
(b) Did you describe the limitations of your work? [Yes]
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(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes]
2. If you are including theoretical results...
(a) Did you state the full set of assumptions of all theoretical results? [N/A]
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(a) Did you include the code, data, and instructions needed to reproduce the main experi- mental results (either the supplemental material or as URL)? [Yes]
(b) Did you specify all the training details (e.g., data splits. hyperparameters, how they were chosen)? [Yes]
(c) Did you report error bars (e.g.. with respect the random seed after running experi- ments multiple times)? [No]
(d) Did you include the total amount of compute and the type of resources used (c.g., type of GPUs, internal cluster, or cloud provider)? [Yes]
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5. If you used crowdsourcing or conducted research with human subjects...
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14


Reviews:
[{"review_id": "YDb7ielVFzC", "reviewer": "Reviewer_ZR1s", "summary": "The authors represent a neuron as a feature vector for each neuron node, and use an MLP and an Tree-LSTM to embed the neuron vectors in an embedding space using contrastive learning. Augmentations, dedicated to neuron morphology are proposed to enhance the contrastive learning procedure. ", "questions": "L108: V_i represents a 3D coordinate belonging to vertex i?\n\nL133: What are the input states here? Child nodes?\n\nEq 1-4: the second subscript of the h-variables was not formally defined. I assume it’s the first and second layer of a stacked LSTM?\n\nL170: are q and k the normalization factors, or the already normalized vectors. Looking at eq. 5 I guess, q and k are the normalized representations, but then the definitions in l170 seem incorrect and should be: q = h(z_q) / ||h(z_q)||_2 etc.\n\nL193: which perturbations are you pointing to here?\n\nL203: What is m?\n\nL301: BN = batch norm, I assume? Why do you find it apparent that this is more needed for self-supervised training? I don’t find this very surprising actually, as there is no label that guides the training, and therefore structure must be sought in the data itself, which might require proper normalization. \n", "limitations": "The training/testing strategy is doubtful (see the quality section above), and the authors did not present any limitations to their proposed work themselves. How is the model, e.g., dependent the type of features that were selected now?", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Originality:\n\nI don’t find the method very original or novel. The authors basically use SimCLR and adapt the architecture (inclusion of a Tree-LSTM) and augmentations to be suitable for tree structured data.\n \nQuality:\n\nI am doubting the validity of the performed experiments. There is no separate validation set, and the full training and test set is used to train CoNMoR. That results in two issues. How was the stopping criterium determined for CoNMoR training if no validation set was present? And second, the test set was already seen during CoNMoR pre-training which may highly boost the test set performance when subsequently training a supervised classifier. \nAlso, in line 264 the authors report the best KNN evaluation accuracy that was acquired during pre-training. So I understand this is not the value after the 100 epochs of pre-training? The authors propose this approach as fully unsupervised, however if labels are used to determine the epoch where KNN accuracy is highest, it is still not fully unsupervised. It would be more fair to report the KNN accuracy at the end of pretraining.\nLooking at Fig. 4, it seems that the L5 class is mostly very distinct from the other classes, since almost all metrics show ca clustering pattern around L5. So I’m not too sure whether the representations are really encoding all the features correctly, or simply distinguish L5 from the rest. \n\nClarity:\n\nSince the paper is aimed for NeurIPS audience, I think it deserves a bit better introduction in the field of neuron morphology and its analyses. Around line 44 I wondered, wat is the input to the model, a 3D reconstruction? But it’s a reconstruction of what? So try to give a better background about these reconstructions, what the data exactly is, how it is measured and what you are reconstructing here. Line 55: what is swc format? Better to explain that as well. \nReading further, the first paragraph of 3.1 is also very unclear to me (I’m a reader without much background in neuron morphology). So if you want to target a broader audience, try to explain the concepts better. Remarks like “Also, the number of such 1-degree\n nodes is biased to neuron reconstruction pipeline and raw data resolution.” need extra explanation.\nThe last few sentences of this first paragraph in 3.1 might be better understable if a figure was added to illustrate the concept. \n\nFig 3b is a bit hard to digest, and might need some improvement. Also, Table 4 could have a more descriptive caption. What is the meaning of the numbers and how should the reader compare them to Table 3?\n\nSignificance:\n\nThe idea of contrastive learning on tree structures is interesting in general. I think, however, that the paper could have had a broader signficance if it was written and tested as a more general method, for any type of tree-structured data. I also wonder whether it is needed to give this method a separate name CoNMoR, since it is basically SimCLR, adapted for tree structured data. \n", "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": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "X30MVniOuAp", "reviewer": "Reviewer_esRK", "summary": "This paper proposes to apply contrastive self-supervised representation learning to tree-structured neuron morphology data. The authors adopted Tree LSTM (Ref. [51]) and MOCO (Ref. [16]), and proposed tree topology data augmentation. The proposed method was demonstrated on three public datasets (BIL, JML, and ACT). Learned representation was visualized with 2D t-SNE and then qualitatively inspected and analyzed. For quantitative evaluation, cell-type classification accuracy was measured with (1) K Nearest-Neighbor (KNN) accuracy from self-supervised pre-training and (2) supervised fine-tuning.", "questions": "* (L224) Was the training/test set split only used in supervised fine-tuning? Why not in pre-training?\n* (L235-236) The choice of number of neighbors for KNN is very arbitrary. \n* (L264) \"..., with the best KNN evaluation accuracy during pre-training included.\"\n    * I do not understand what it exactly means. Do you record KNN evaluation accuracy when each epoch is done, and report the best among them? That doesn't seem very reasonable to me. I think if you were to report cell-type classification accuracy from pre-training, you should strictly use separate training and test sets, and report KNN evaluation accuracy on the test set **after** pre-training is done.\n* (L287-288) Why pre-training for 100 epochs for the main experiment and 50 epochs for the ablation study?", "limitations": "See \"Weaknesses\" in the above.", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "### Strengths\nThis paper is written clearly and presented well. The problem of interest (representation learning on unlabeled neuron morphology data) is clearly significant. \n\n\n### Weaknesses\nNovelty is limited. This paper has two novelties: (1) application of contrastive self-supervised learning to tree-structured neuron morphology data, and (2) topology data augmentation for tree data. However, the ablation study (Table 4 and Section 4.3) shows that the proposed topology data augmentation may not be effective nor important. Table 4 shows that the point transformation (\"point\") is the single-most effectective one, and the combination of \"point\" and attribute masking (\"mask\") achieved the best accuracy. The \"point\" and \"mask\" are both general graph augmentation, so the claimed novelty of the proposed tree topology augmentation becomes rather pointless.\n\nEvaluation contains multiple problems. First, I don't understand why the Allen Cell Types (ACT) dataset was included in the evaluation. As is shown in Figure A2, ACT's neuron reconstruction is largely incomplete. I see no point in using incomplete reconstructions which could only complicate representation learning. Second, training and evaluation seem quite arbitrary. Why was the training/test set split only used in supervised fine-tuning, but not in pre-training? It is very weird to compute KNN accuracy **during, not after, pre-training and report the best one** while not even having a separate test set. Also why pre-training for 100 epochs for the main experiment and 50 epochs for the ablation study? Third, it is unclear whether the two baselines (MorphVAE and TRNN) were faithfully reproduced. Without any evidence for this, the main quantitative result of this paper in Table 3 cannot be fully justified.", "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": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "NVTACWpWb3", "reviewer": "Reviewer_nMVE", "summary": "This paper presents self-supervised learning for neuron morphology representation. In this paper, the neuron morphology is represented as tree-structured data. Then, the Tree-LSTM is used to represent the tree-structured data. Finally, the representations are learned through contrastive learning with the proposed tree data augmentation techniques. ", "questions": "In line 203, $m$ is empirically set to 10. What does setting $m$ to 10 mean? Would not changing this value make a difference in performance?", "limitations": "Adding some baselines such as graph-based SSL in the quantitative evaluation help show the proposed method's superiority.", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "The proposed approach for representing neuron morphology is reasonable. Furthermore, this paper is well-written and easy to follow. Some experiments, including ablation studies, are well analyzed and discussed.\n\nHowever, this paper leaves some negative or uncertain points. \n1. First, the proposed framework is too weak from the novelty viewpoint. The proposed representation learning is based on the MoCO [16, 6], one of the visual contrastive learning methods. The differences are that the data is tree-structured and uses tree-data augmentation. Even if the tree data augmentation is novel, some techniques in the augmentation are directly derived from graph data augmentation. As a result, in lines 44 and 307-308, the statement ``this paper proposes a **new SSL framework** for tree structure representation learning'' is an overstatement for the reviewer. \n\n2. Since the tree is a special type of graph, it is necessary to include graph-based SSL [48] as a comparative model in the quantitative evaluation.  \n\n3. It would be better to mention/include details of baselines (morpheVAE and TRNN) used in the neuron cell-type classification experiment, such as how to implement and train the baselines. Without the details, it is hard to conclude that the proposed method achieves better performance than baselines.\n\n4. Delineating the learned representations using TSNE was meaningful. However, the reviewer thinks it is not enough to show only the representations of the proposed method. It would be better to include the representations of baselines.", "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": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ["I don’t know"]}, "extra_text": {}}, {"review_id": "MHprhaPylUt", "reviewer": "Reviewer_DfuA", "summary": "This paper proposed a contrastive framework to learn features from neuron trees. The authors have devised a carefully engineered set of augmentation suitable for tree-structured data sets. The learned features were used to classify cell types that yield superior performance compared to the previous methods.", "questions": "See the comments on weakness.", "limitations": "The authors have not adequately commented on the known limitations.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n1. The proposed method is technically sound and novel.\n2. The authors proposed several augmentations for the neuron trees, which turned out to be useful for self-supervised feature learning.\n3. The results are convincing across multiple datasets showing generalizability.\n\nWeaknesses:\n1. While the proposed method yields superior performance in particular problems for neuron morphology learning, my concern is that it is a niche problem. How could it benefit the general graph/topology learning community in general? The authors should comment on the applicability of the proposed tree representation learning in other domains, for example, molecular properties classification.\n2. The authors did not elaborate on the motivation for using InfoNCE loss over several other contrastive settings. Is there any particular reason to choose it?\n3. The authors mentioned a few contrastive learning on graphs. However, a direct comparison is missing to demonstrate the advantage over the previous approaches.\n4. It is unclear whether the baseline experiments [21,51] are performed in identical experimental settings. Further, if one has also to include the axons, would the tree structure assumption still hold? What is ‘m’ mentioned in the data augmentation?", "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": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}]

Author rebuttal:

Decision: Accept