Symmetrical SyncMap for Imbalanced General Chunking Problems
Authors: Heng Zhang
Danilo Vasconcellos Vargas
Venue: Submitted to ICLR 2023 (2023)
Keywords: Self-organization
Adaptive learning
Chunking
New learning paradigm
Bio-inspired learning
Structure learning

Abstract: Recently, SyncMap (2021) pioneered an approach to learn complex structures from sequences as well as adapt to any changes in underlying structures. Such approach, inspired by neuron group behaviors, is achieved by using self-organizing dynamical equations without any loss functions. Here we propose Symmetrical SyncMap that goes beyond the original work to show how to create dynamical equations and attractor-repeller points which are stable over the long run, even dealing with imbalanced continual general chunking problems (CGCPs). The main idea is to apply equal updates from positive and negative feedback loops by symmetrical activation. We then introduce the concept of memory window to allow for more positive updates. Our algorithm surpasses or ties other unsupervised state-of-the-art baselines in all 12 imbalanced CGCPs with various difficulties, including dynamical ones. To verify its performance in real-world scenarios, we conduct experiments on several well-studied structure learning problems. The proposed method surpasses substantially other methods in all scenarios, suggesting that symmetrical activation plays a critical role in uncovering topological structures and even hierarchies encoded in temporal data.

Under review as a conference paper at ICLR 2023
SYMMETRICAL SYNCMAP FOR IMBALANCED GENERAL CHUNKING PROBLEMS
Anonymous authors Paper under double-blind review
ABSTRACT
Recently, SyncMap (2021) pioneered an approach to learn complex structures from sequences as well as adapt to any changes in underlying structures. Such approach, inspired by neuron group behaviors, is achieved by using self-organizing dynamical equations without any loss functions. Here we propose Symmetrical SyncMap that goes beyond the original work to show how to create dynamical equations and attractor-repeller points which are stable over the long run, even dealing with imbalanced continual general chunking problems (CGCPs). The main idea is to apply equal updates from positive and negative feedback loops by symmetrical activation. We then introduce the concept of memory window allow for more positive updates. Our algorithm surpasses or ties other unsupervised sate-of-theeart baselines in all 12 imbalanced CGCPs with various difficulties, including dynamical ones. To verify its performance in real-world scenarios, we conduct experiments on several well-studied structure learning problems. The proposed method surpasses substantially other methods in all scenarios, suggesting that symmetrical activation plays a critical role in uncovering topological structures and even hierarchies encoded in temporal data.
INTRODUCTION
Human brains have been proved to have unsupervised abilities to detect repetitive patterns in se- quences involving texts, sounds and images (Orbán et al., |008 Buulf et al., 2011 Strauss al.) 2015)). In the field of neuroscience, part of this behavior is known as chunking. Chunking has been verified in many experiments to play an important role in a diverse range cognitive functions (Schapiro et al., 2013; Yokoi & Diedrichsen, 2019 Asabuki & Fukai 2020). Related to chunking problems, many sequence processing algorithms in machine learning have been proposed for time-series clustering (Aghabozorgi et al. 2015) based similarity measurements (Figure Ta)). Chunking sequences between state variables, however, is still underexplored (see Figure [b)()).
Recently, Vargas & Asabuki (2021) proposed the first learning of chunking based solely self- organization called SyncMap. The authors also extended chunking problems into one called Continual General Chunking Problem (CGCP), which includes problems with diverse structures that change dynamically throughout the experiments. For the first time, SyncMap was shown not only able uncover complex structures from sequential data, but also to adapt to continuously changing structures. It achieves this with self-organizing dynamics that maps temporal input correlations to spacial correlations. where the dynamics are always updating with negative/positive feedback loops. In this work, however, we identify problems in the original dynamics that lead to long-term instability, and we further show that performances in imbalanced CGCPs are poor given the asymmetric number of updates, i.e., the number of negative updates is much bigger than that of the positive ones.
Beyond identifying these problems, here we propose Symmetrical SyncMap, which can solve both of the problems above using symmetric selection of nodes and generalized memory window. Symmetrical SyncMap solves the instability of the dynamics efficiently, and goes beyond to propose solution to deal with imbalanced general chunking problems. As opposed to the original SyncMap that suffers from the uneven updates from positive/negative feedback loops, we propose symmetrical activation. and further introduce the concept of memory window, so that the system can have more updates from positive feedback loop while concurrnntyy reducing the number of negative updates. In fact, the symmetrical number of updates not only compensates when imbalanced chunks

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presented, but also makes the algorithm stable over the long and reaches equilibrium quickly in changing environments. By showing that equilibrium and self-orranizztion can appear only with dynamical equations and without optimization/loss functions, the biggest motivation from this paper realizing how the substantial improvements, beyond the self-organization inspiration, make the new learning paradigm very adaptive and precise. Moreover, the simplicity of the modifications here, as supported by the effectiveness in real-world scenarios of structure learning, solves the problem at the foundation, while keeping the final method concise and improving in both accuracy and stability.
2 RELATED WORKS
Chunking. Natural neural systems are well known for the unsupervised adaptivity, since they can self-organize by many mechanisms for several purposes on many timescales (Lukoševicius) (012). One of the mechanisms is chunking, which can be described as a biological process where the brain attains compact representation of sequences (Estes et al. [007 [aamkumar et al.) 2016). Specifically, long and complex sequences are first segmented into short and simple ones, while frequently repeated segments are concatenated into single umits (Asabuki & Fukai 2020). This can be seen as a complexity reduction for temporal information processing and associated cost (Ramkumar et al. (016).
Albeit our focus is more on ncuroscience and machine learning perspectives, earlier algorithms proposed for solving chunking problems are from linguistics and include PARSER (Perruchet & Vinter 1998). performs well in detecting simple chunks, but fails when the probability of state transition are uniform (Schapiro et al.) 2013). A neuro-inspired sequence learning model, Minimization of Regularized Information Loss (MRIL) was proposed by applying a family of competitive network of two compartment neuron models that aims to predict its own output in type of self-supervised neuron (Asabuki & Fukai 2020). Albeit the interesting paradigm, MRIL has been shown unstable even for problems in which it performs reasonably well. Very recently, self-organizing learning paradigm (called SyncMap) has been proposed, which surpassed MRIL in all scenarios (Vargas & Asabuki 202T).
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Figure 1: Explanation of the difference between time-series clustering and sequence chunking. (a) Process of time-series clustering. Homogenous time-series (S1-S3, S4-S5) are grouped together based on a certain similarity measure. (b) Chunking problems example. A fixed chunk (state variables A-B-C [blue]) and a probabilistic chunk (D-E-F [orange]) are repeated in the input sequence with equal probabilities. (c) Input-output map of problem structure in (b) over time. State transitioning by first-order Markov chain. (d) Examples of the structures of fixed chunk and probabilistic chunk.
Time-series Clustering. Time series data is defined as a sequence of continuous, real-valued elements, usually with high dimensionality and large data size (Aghabozorgi et al.] 2015)). As a subroutine unsupervised sequence processing, time-series clustering aims to uncover patterns, usually in very large sequential datasets that cannot be manually handled. This can be found in some articles applying competition based self- orgaaizigg maps (SOMs) (Kohonen) 1990) and their variations (Vannucci & Colla 2018 Fortuin et al. 2018 8), which are well-suited for clustering time series but not capable of chunking time series. other words, these SOMs were not designed find the underlying structures of sequences and correlation between variables, therefore, their objectives are different. A comparison of time-series clustering and sequence chunking is shown in Figure [
Word Embeddings. In the field of natural language processing, word embedding algorithms generally transforms texts and paragraphs into vector representations (Khattak et al.) 2019: Bojanowski et al. Peters et al. 2018). FastText enriched the word vector with subword information (Bojanowski ct al. 2017), whereas ELMo (Peters et al., 2018) and BERT (Devlin et al., 2018) aimed to represent word by contextualized word embeddings. Chunking problems presented here related to some
2017
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of them, such as prediction- based Word2vec embedding algorithm (Mikolov al. 2013) that transforms texts into a vector space representation and can be combined with clustering to deal with chunking problems. Therefore, Word2vec is used in the experiments.
Representation Learning and Communities Detection. The problem of finding probabilistic chunks refers to random walk over a graph with several chunk structures; in which the possibility of transition to an internal state within a chunk is higher than that of transition to an external state belonging to other chunks. Such graph structures mentioned above can be seen as communities (Radicchi et al. (2004), which are most-studied by recent representation learning algorithms such as Deep Walk (Perozzi et al., 2014) and Graph Neural Networks (GNNs) (Kipf & Welling 2016). More related, the Modularity Maximization (Newman & Girvan 2004 Tang & Liu (009) uses uggn-decommooition performed on the modularity matrix to learn vertex representation of community, By using the adjacency matrix (transition probability matrix) to convert sequential data to graph structure, Modularity Maximization can also deal with chunking problems via random walk over the generated graphs. Although there exists newer modularity-basee algorithms which try to optimize the pioneering work, such as Louvain method (Blondel et al. 20088,, their objective is mostly to reduce the computational cost. Therefore,
the original Modularity Maximization in the comparison.
3 CONTINUAL GENERAL CHUNKING PROBLEMS
Recently, a problem called Continual General Chunking Problem (CGCP) has been first proposed by Vargas & Asabuki| (2021). The paper generalized various problems from neuroscience to computer science, inc incluning chunking, causal and temporal communities and unsupervised feature learning of time sequences. Such problems are considered as extracting co-occurring states from time sequences, in which the generation process (i.e., data structure) can change over time. To illustrate, the input sequences of CGCP contain state variables where each state belongs to fixed chunk or a probabilistic chunk, transitioning by first-order Markov chain. The element of the transition matrix is given by:
Pab Pr[s++1 = b|8:- = a). where 8, is the state vector at t; and a and b are the label of states.
Specifically, the fixed chunk problem (see Figure (d) the blue chunk) refers to the situation that the next state 8,+1, with respect to the current state 8,, is deterministic within a chunk. For example, if a and b are two continuous elements of a fixed chunk with direction to b, then Pab = 1, E, Pas 1.
More realistically, the probabilistic chunk problem (see Figure (d)) the orange chunk) refers to input sequences which are generated by giving a random walk over graphs. The graphs are characterized by two types of degrees: internal degree kint and external degrees kent of state i. For every state, the following constrain holds: kime > keat for all i E A, where A is the set of all states in sequences. The above constraint is satisfied if the graph has dense connections within chunks but sparse connections between nodes in different chunks.
Beyond generalizing chunking problems to fixed and probabilistic chunks, CGCP also considers their continual variations. This is motivated by the constant adaptation observed by neural cells that can relatively switch behavior quickly in different environments (Dahmen et al. (2010). In this case, the data structure can change over time, conferring harder albeit realistic setting.
4 SYNCMAP
SyneMap is a sole self-organizati based algorithm proposed by Vargas & Asabuki (021)) It solves CGCP by creating a projected map that encodes the temporal correlation (chunks) as spatial distance between nodes. In SyncMap's dynamic, nodes which are activated together tend to be grouped as chunks, while nodes that do not activate together will be pulled away from each other. The algorithm is explained in detail in the following, with brief example shown in Figure 2(a).
Input Encoding. Consider an input sequence of state variables S = {81, $2... 81, 87). where T is the sequence length. 8, = {si, ..... sn,e) ) is vector at time step t, and its elements si,t, i l...., n hold constrain si, E (0,1) Σ Si, 1, where n is the number of states. The input is encoded as an exponentially decaying vector x; = {21,1) ..., In,3² ) having the same shape as 8y:
Si,ra -.11(())))) t- La <m * tslep
(1)
0,
otherwise
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where ta is the last state transition to state 8;, and m is the state memory. Specifically, state transitions happen every tstep step (also known as time delay), and variables that have their activation period greater than tstep are set to O. m and tstep are set at 2 and 10 in the original work. An example of the encoded exponentially decaying input is shown in Figure a
Training Dynamic. We generate weight nodes W in SyncMap's map space obtain pair tuple (Di,,, Wi.)). Nodes are first randomly initialized in a l dimensional map space. Note that weight node Wi, E IR is a point in SyncMap's 's map space, and it can also be considered as a vector.
In every iteration when new input vector æ; comes in, all its elements 25,,, together with the corresponding nodes wi,1, are divided into two sets according to the threshold value a: (1) activated
recently activated (positive) set PS, {ilær,, a} and (2) non-recently activated (negative) set NS {i| e I. a). The original SyncMap used a directly at 0.1. In this paper we introduce threshold value a which allows us to achieve more general state memory implementation.
Inside the space, the centroids of PS; and NS, sets are calculated as follows if and only if the cardinality of both sets are greater than one in this iteration (i.e., [PS|] and [NS, 1):
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where opt and cn2, are the centroids of PS₁ and NS, respectively, Finally, node wi,, corresponding to each input 2i, updated:
1, i PS,
a, i PS. 0, otherwise
,
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where is the learning rate and ||-|| is the Euclidean distance. Subsequently, updated nodes are normalized to be within a hyper-sphere having radius of 10 the end of the iteration.
Clustering Phase. SyncMap forms a map during dynamic training, which has the number of nodes equal to the number of input states n. After training, DBSCAN used (Schubert et al., 2017) 7) for clustering with the pre-defined density parameters epss and minimum cluster mc, as it does not require the number of clusters as input.
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Dynamies in SyneMap. (a) Chunking procedures using SyncMap. Sequences with state variables are first encoded as exponentially decaying input x; (top). Here, the state memory m=2. Weight nodes w; in SyncMap's 's dynamic are randomly initialized (bottom left). The dynamic is then trained by Equations 2 to 4 (bottom middle). Finally, in the clustering phase, DBSCAN is applied to obtain chunks/communities (bottom right). (b) Illustration of the instability in SyncMap. In the original work, the dynamical equations are strongly influenced by negative nodes, since the cardinality of all non activating nodes NS, are usually much greater than that of activating nodes PS, (e.g., 7: 2). (c) The proposed symmetrical activation. By applying stochastic selection, equal number of positive and negative nodes are activated in each iteration (e.g., 2: 2).
Figure 2:
Limitations of SyncMap. Although SyncMap shows capabilities to address all kinds of CGCP, one crucial issue is the instability of its dynamic in the long term. This is due to the asymmetric number of updates with respect to positive and negative nodes. Figure 2b shows how this happens with an example of nine nodes in 2-D SyncMap. The fixed state memory (m = 2) results in an uneven update of positive (2) and negative (7) nodes, i.c., the dynamic's 's update is more influenced by negative feedback loop, which causes undesirable convergence in the long run.
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Figure 3: General workflow of symmetrical activation. (a) Exponentially decaying input sequence. (b) Sequence after the process of positive and negative nodes' division (represented as logical vectors). (c) Comparison of the memory window between the original and Symmetrical SyncMap. State A,, B; and C, belong to three fixed chunks. The original SyncMap deterministically activates m most recent states (i.e., As and Ag), while Symmetrical SyncMap generalizes the state memory to have larger memory window (e.g., from A2 to As when m=5) for stochastically selecting and activating positive nodes. (d) Process of stochastic selection to achieve symmetrical activation. First, we randomly lose sight of some nodes in PSS set (i.e., instead of activating all positive nodes, we stochastically select some them to activate). This achieved by an AND operation to the input and a masking vector having random logical values each time step. Next, for stochastic selection of the negative nodes in N St set, we use a masking vector similarly to that in positive part, and end up with activating equal number of positive and negative nodes in every iteration.
SYMMETRICAL SAALSSYNE SYNCMAP
Inspired by how neural efficiency influences brain activation by focusing the energy on smaller brain areas NNubauer & Fink 2009); here we propose algorithm called Symmetrical SyncMap to better solve CGCP, particularly y the imbalanced chunking problems. The main idea is to use symmetrical positive and negative activations. In other words, try to reduce the number of activated negative nodes while selecting and activating more positive nodes in every iteration, thus balancing the updating rates in negative and positive feedback loops. To achieve symmetrical activation, we introduce stochastic selection and memory window.
5.1 MEMORY WINDOW: GENERALIZING THE STATE MEMORY
We introduce memory window to our algorithm by generalizing the state memory m. which allows a wider window for updates from the positive feedback loop, thus helping capture the bigger chunks. This is achieved by tuning the threshold value a as mentioned in SyncMap's definition, i.c., any nodes Wi, having its corresponding input value I, greater than will be divided into PS; set and vice versa (a true or false logical operation). With a pre-defined fstep, one can easily adjust threshold a to control the state memory (tstep=10, a=0.05 and m=3 in Figure 3a)).
5.2 SYMMETRICAL ACTIVATION
Symmetrical activation is the core of proposed algorithm, where equal number of positive and negative nodes are selected to activate at each time step. We propose stochastic selection to select nodes without bias in PS, and NS, sets. Details are shown in Figure 3
Stochastically select nodes into PS, set. With a pre-defined state memory m. we first obtain the temporary Pteemp set in way the original SyncMap obtains PS, (i.e., PStemp includes m
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positive nodes, and Pteemp C Wt, where W, {wr,li ...... n is the set including all nodes). Then, we apply stochastic selection to select positive nodes into PS, (i.e., a sampling process). Whether to enable stochastic selection at this particular time step is determined by probability parameter Pr E [0. 1]. In other word, stochastic selection were enabled, we randomly select positive nodes and "inhibit" (ignore) other m nodes in PSeem-- with the probability of Pr when state memory m > 2: otherwise we select all m nodes, When m = 2, stochastic selection is not used and two most-recent states are selected. Afterwards, PS, is updated, which only includes those activated positive nodes (PS, C PStemp). Additionally, we give an analysis of Pr in Appendix [
Stochastically select nodes into N set. After obtaining the above PS,, we define the temporary negative set N N. One may notice that there is a chance that some nodes in PStemp could potentially sampled as nodes in Stemp- This is desirable selection process and produces more robust results. Next, we again use the stochastic selection for sampling several negative nodes in Stmp set. The number of negative nodes being selected is symmetrically equal to the cardinality of PS; (i.e., N (PS))). After this step, the N S, set is updated (N C N Stemps see the right part of Figure d(d for example).
introduces a more uniform
The remaining steps follow the Equations
We calculate moving average of 10000 steps of nodes' position and use it for DBSCAN, instead of applying DBSCAN to the map at a "snapshot" time step in the original work. Algorithmic description is shown in Appendix
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Figure 4: Long term behavior analysis of the original SyncMap and Symmetrical SyneMap. (a) NMI over time of two models. Data are mean with s.t.d (error bar). Statistics are in Appendix H (b) For comparison, we show single trial performed by two models, initialized identically, (c)
Nodes' distribution at different time steps. Colors of the nodes indicate the true labels of chunks.
EXPERIMENTS OF CGCP PROBLEMS
We evaluate the proposed Symmetrical SyncMap with 13 tests, including (i) long-term behavior analysis, and (ii) 12 imbalanced CGCP with fixed, probabilistic and mixed chunks, as well as their continual variations. Among the large number of clustering quality measurements, Normalized Mutual Information (NMI) (Studholme et al.) 1999) for measurement (see Appendix Afror math detail). NMI ranges between 0 and 1, and the higher the score, the better the chunking performance. We did 30 trials for each experiment. Results of NMI are shown in Figure 4 and Table [ We used t-test with p-value of 0.05 verify if the best result is statistically significantly different from the others (statistical results are in Appendix H). An ablation study and computation time analysis are also investigated in Appendices [
used
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6.1 LONG TERM BEHAVIOR ANALYSIS EXPERIMENT
To evaluate the behavior of the algorithm over the long run, we set up this experiment. The problem considered here a continual changing environment with ten fixed chunks, each containing six different states. Transitions between chunks happen at the end of chunk sequence (i.e., after the sixth state variable presented inside a chunk). A chunk can transit to any other chunk with equal probability. Sequence length was set 7=600000. At time step t=0 the first environment was initialized. After t=300000 the problem changed to the second environment by re-assigning all 60 states into ten chunks. We applied the original SyneMap and the proposed one in this experiment.

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We used the same parameter settings of the two models, where a=0.001 *n, k=2, eps=1 and mc=2. Besides, m=3 and Pr=30% were used for Symmetrical SyneMap training.
Results in Figure 4 show that Symmetrical SyncMap reaches near the optimal performance in this experiment. By applying symmetrical activation, Symmetrical SyncMap can have long-term stability while keeping NMI near 1.0. In contrast, the NMI of the original SyneMap reaches the peak near 0.88 at t=70000 and decreases constantly afterwards. After environment changes, Symmetrical SyncMap detects new chunks and reaches to a new equilibrium quickly, while the original SyncMap performs poorer and becomes unstable in the long run.
6.2 IMBALANCED CGCP PROBLEMS
Baselines and Parameter Settings. We test several imbalanced CGCP problems and their continual variations by using Symmetrical SyncMap, SyncMap, Modularity Maximization (Modularity Max), Word2vec and MRIL. In detail, Symmetrical SyncMap's parameters were set to o=0.001 n. k=3, m=3, Pr=30%, eps=4.5 and mc=2. We conducted a parameter sensitivity analysis shown in Appendix [F] For the original SyncMap, we used k=3, m=2, eps=4.5 and mc=2. Regarding the Modularity Max, we first converted the input sequence to transition probability (TP) matrix, and then used the TP matrix to generate graph for communities detection. To evaluate how word embedding algorithm would fair in CGCP, a skip-gram Word2vec algorithm was modified to suit in the context of CGCP. Here, latent dimension of 3 and output layer with softmax were used, and the output size is equal to the inputs. Learning rate was set at 0.001 and batch size was 64 with a mean squared error as loss. A window of 100 steps (equivalent to 10 state transitions) of skip-gram. Regarding the MRIL, we used 5 output neurons for all experiments, with the learning rate of 0.001. We gathered the output neurons showing correlation larger than 0.5, detecting chunks by assigning an index of groups that maximally respond to each input. The input sequences of all baselines were the same exponential decaying input as used in Symmetrical SyncMap.
used to compute the output probability
We first consider several environments which consist of 3 different sizes of chunks: big, moderate and small chunks. Specifically, the big chunk has 20 state variables, while the moderate and small chunks have 10 and 5 respectively. Based on the chunk settings, we then designed three types of imbalanced problems: (i) Two big and one small chunks (20-20-5), (ii) One big, one moderate and one small chunks (20-10-5). (iii) One big and two small chunks (20-5-5). We tested these three types of imbalanced problems with three different structure settings: fixed, probabilistic and mixed chunks tests. The structures of the fixed and probabilistic environments are shown in Figure dd).. Please refer to Figure in Appendix [ for the examples of the complete structures. Regarding the mixed tests, two probabilistic chunks and one fixed chunk were presented in each environment, where the order of chunks in the input sequence was specified as: 1st probabilistic to fixed to 2nd probabilistic chunk. Sequence length 7 is set 200000 for all types of test.
Problem Settings (Appendix By
Dynamical Continual Variation. Three dynamical variations of the above-mentioned problems were presented: continual fixed, continual probabilistic and continual mixed. Sequence length was set to 2r. States were permuted between chunks: at time step t=0 the first type of problem was 15-15-5 (see the problem formalism in previous subsection), after t=r the second type of problem was 20-10
Algorithm
Fixed
Probabilistic
SBM Network 25-30-35
20-20-5
20-10-5
20-5-5
20-20-5
20-10-5
20-5-5
Medilarity Max
0.67400
0.7320.03
0.648002
0.96:4004
1,051L0
L020.0
0.99200022
WordZvec
0.4920.05
0.57200.07
0.5640.06
0.7020.04
0.77:01.9
0.6240.88
0.8420.03
MRIL
0.2510.09
0,3820.12
0.3610.11
0.43:0.14
0.3910.07
0.24:0.04
0.4620.10
Original SyncMap
0.93+0.12
0.75#0.08
0.63+0.11
1.000.0
0.8140.04
0.64:0.08
1.00,0
Ours: Symmetrical SyncMap
1.00..0
1.00.00
0.93+0.08
1.00.00
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Mixed
Continual
15-15-3 to 20-10-3
Algorithm
20-20-5
20-10-5
20-5-5
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Prob.
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Modulantt Max
0.6950005
0.7820.05
0.8910006
0.6920.02
0.70g0.05
0.62.0002
WordZvee
0.6620.07
0.60100066
0.7310.05
0.4520.04
0.6010.04
0.6520.04
MRIL
0.2020.05
0. 0.2020.05
0.1640.03
0.38.0.13 13
0.5920.02
0.55=0.04
Original SyncMap
0.8420018
0.8300.0
0.6420.07
0.72a0.07
0.8240044
0.8320.0
Ours: Symmetrical SyncMap
0.87:0.99
0.9020.06
0.95:0.04
1.000.0
1.020.0
0.95=0.06
Table 1: NMI results. A comparison is shown over Modularity Max, Word2vec, MRIL, original SyneMap and Symmetrical SyneMap in imbalanced and real-world CGCPs. The best and the non- statistically different results are in bold. Data are meants.t.d. Details of the statistical t-tests (p values) are presented in Appendix
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Results Overview. The proposed algorithm Symmetrical SyncMap learns nearly the optimal solutions in all imbalanced CGCPs. It surpasses or ties other algorithmss in all tests (Tables Tp. Modularity Max performs the second best, in which it wins or ties the others in 2 out of 3 probabilistic CGCP tests. Word2vec achieves relatively higher NMI in probabilistic CGCPs than other problem structures, whereas MRII performs the worst overall in all tests. The original SyneMap performs good in 20-20-5 CGCPs, yet performance decrease is witnessed as more chunks become smaller.
Symmetrical SyneMap, with its inherent adaptivity, performs significantly better than all other com- petitive algorithms, particularly in continual variations (i.e., dynamical CGCPs where environment can change). The proposed wider memory window and symmetrical activation allow capturing states in big chunks compactly, while at the same time the stochastic selection with suitable Pr helps to separate small chunks (See the learned maps and Pr analysis in Appendices [ and F., thus keeping the balance between dealing with small and big chunks. In all probabilistic CGCP tests, it produces very distinct chunks and learns the best solution (i.e., NMI=1.0). The performance downgrades slightly during the more challenging mixed CGCP tests, due to an extra imbalanced frequency issue: the fixed chunk inserted between two probabilistic chunks has lower frequency to appear in the sequences. Having said that, the proposed algorithm still outperforms the others in all mixed CGCPs with a very big lead.
Original SyncMap performs relatively better in 20-20-5 type CGCPs, with the steady decrease in 10-10-5 and 20-5-5 ones. In fixed CGCPs, it makes distinct clusters for smaller chunks, yet fails to group nodes of the big chunk together. In probabilistic and mixed tests, nodes belong to smaller chunks are merged into one cluster in almost every individual trial (see Figures in Appendix D)
Modularity Max shares the highest NMI score with Symmetrical SyncMap in two probabilistic CGCP tests. However, this graph-based algorithm does not perform well in other imbalanced CGCPs. possible reason that fixed chunks are less likely to appear in usual problems faced by Modularity Max, thus leading to problem bias. It is worth noting that comparing the results of Modularity Max the other algorithms in dynamical CGCPs is not fair, since TP matrix would record all the occurrence of state variables; thus, passing continual changing TP matrix is not inherently suitable for Modularity Max, leading to worse results in continual structures than that in static graphs
Word2vec creates maps in which nodes are more dispersed than that produced by SyncMap, thus making clustering difficult. It performs better in probabilistic chunk tests than fixed and mixed ones (see Figures in Appendix DD. For the continual problems, Word2vec lacks the ability of adaptation, thus showing the overall lower NMI scores. MRIL fails to detect imbalanced chunks with large number of state variables, and therefore it performs the worst in all tests. Increasing the number of output neurons may improve the performance of fixed chunk tests.
Ora. Surdhap with 2eee Ceprine
2na SuncMa with 2-bbe of Kanest (e)
Podben
Kande Olt
Ground Trath
Chunks 4 Chunna
14 Vic
0.550000
0.95u0.0e
0.02.0.00
Syschtap
Sprres
0.860007
Syues Syortii wihh
(a]
(h)
Sones Sycetta (Evatt)
Figure 5: Results of real-world scenarios with the original and Symmetrical SyncMap. (a) Dolphins network. Colors denote labels. Figure modified from Arenas et al. (2008). (b) and (f) The learned representations of the two models (Dolphins network). (c) NMI results. (d) The learned representation of the original SyncMap (Karate network). (e) Dendrograms by hierarchical clustering (ward linkage) in Karate problems by two models. (g) Karate network. Colors of nodes denote local communities while colored shadow areas define the global communities. Figure modified from Perozzi et al. (2014). (h) and (i) The learned representations of Symmetrical SyncMap (Karate network). Colors indicate the true labels of the communities. See Appendix C for more analysis.
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7 REAL-WORLD SCENARIOS
We study three real-world scenarios to verify the performance of Symmetrical SyneMap: (i) network of stochastic block model (SBM); and (ii) two social network datasets with well-established community structures. For the SBM, we test reference network introduced by Lee & Wilkinson (2019), where the network is considered as a graph which was then converted to high-dimensional CGCP (i.e., 3 sightly imbalanced communities with a total of 90 nodes and 1 1192 edges). The ground- truth is defined in Appendix C
Parameter settings of all models remained the same as in previous imbalanced CGCP experiments. As shown in Table [ both original and Symmetrical SyneMap yield the optimal solution, showing the capabilities to tackle with large-scale CGCP.
We then test two well-studied benchmark networks in community detection. Hierarchical clustering was applied to replace DBSCAN in the clustering phase, to produce dendrograms for the visualization of hierarchies (i.e.. by specifying the number of communities/chnnk)) Detailed settings and analysis for baselines are in Appendix C
NMI results are shown in Figure 5 ())
with statistics.
The first one is the Lusseau's 's network of bottlenose dolphins (Fortunato) 2010), an imbalanced structure with 2 ground-trute communities of sizes 20 and 42. Our algorithm yields much higher NMI than other algorithms. It avoids forming dense communities produced by the original SyncMap (see Figure ()) allowing local relationships be extracted, as verified in the following problem.
The second problem is the Zachary's 's karate club network which contains 34 nodes and 78 undirected and unweighted edges. We used two sets of ground-truth: (i) 2 chunks labeled by the original paper (achary 1977). and (ii) 4 chunks found through modularity-basee clustering (Perozzi et al. 2014).
Symmetrical SyncMap depicts the global graph structure while preserving the topology of local communities (Figure S (h)(()). In contrast, the original SyncMap can only separate two global communities with a very dense representation (Figure d))))) This unavoidable convergence is due to the stronger negative feedbacks over time, pulling away nodes from each community/chunk. Note that the representation learned by our method is comparable to node embeddings models with loss functions required and with more expensive training procedures such as DeepWalk (Perozzi jet al. 2014) and Graph Convolutional Networks (Kipf & Welling 2016). Unlike graph-based models, we achieve this by (i) mapping correlations from temporal input latent state space, (ii) keeping equilibrium by symmetrical activation (otherwise nodes would be locked in dense communities), and thus (iii) enabling hierarchies to be extracted from sequences. More importantly, the inherent adaptivity, as shown in previous experiments, suggests that our model a has potential usage in inductive applications, it does not require any additional optimizations when dealing with new (usttrssussstructtures,, while transductive methods such as DeepWalk cannot naturally generalize to unseen nodes or changed structures (Hamilton et al., 2017).
Having said that, we argue that these real-world scenarios usually (i) have no ground-truth and (ii) are strongly biased towards standard algorithms. To illustrate, the absence of ground-truth has to do with the fact that: it is not only difficult to define the social structures, but also hard to know the existence of real chunks in nature; thus, any answer would be guess at most. Besides, the bias is due to the output, used as tround-truth, is found by using standard algorithms in the original papers, which makes good results in real-world data more like "algorithms that perform similar to standard algorithms", rather than "algorithms that work with real-world data".
8 CONCLUSIONS
We propose Symmetrical SyncMap, brain inspired self-organizing algorithm built on top of the original work to solve continual general chunking problems (CGCP). Experiments of different CGCPs have illustrated how effective the concise modifications work on those challenging tasks. By applying symmetrical activation to the dynamical equations in which loss/optimization functions are not required, our algorithm not only learns imbalanced CGCP data structures with great long-term stability and adaptivity, but also shows the potentials to uncover complex hierarchical topologies encoded in temporal sequences. This reveals the self- oegf-orrgni ability of the proposed algorithm in analyzing the community structures of a broad class of temporal inputs. Future goals, advised by the results presented in this paper, will be to investigate CGCP problems with large scale, hierarchies and noisy environments, and tasks specific to representation learning in various real-world scenarios.

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9 REPRODUCIBILITY STATEMENT
We took every effort to make this work reproducible. Necessary codes are provided in supplementary materials, together with Python dependencies used build the experiment environments. Please refer to the README file zipped in the supplementary material for detailed instructions.
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A DEFINITION OF NORMALIZED MUTUAL INFORMATION (NMI)
Among the large number of clustering quality measurements, we used the Normalized Mutual Information (NMI) for measurement. Mathematically, NMI is defined as:
I(;Y)) NMI(Y,Y) (H()) H(Y))* NMI [0
(5)
where Y and Y are the output of algorithms and the truth labels, respectively. I(Y; Y) is the mutual information and (*) is the entropy. NMI ranges between 0 and 1, and the higher the score, the better the clustering performance (better correlation between Y and Y).
B EXAMPLES OF IMBALANCED CGCPS
Dyanmical Continaal
(a) Probablistic
15:15.5.
(4) 20-10-5.
Figure 6: Examples of imbalanced chunking problems used in the experiments. CGCP generalizes several problems, (a) Probabilistic chunks: a graph structure that allows random walking: (b) Fixed chunks: temporal chunks defined originated from neuroscience; (c) and (d) Mixed chunks: integration of fixed and probabilistic chunks. the continual setting. the causal structure can change over time. Dots inside each circle belong corresponding chunk. Lines connecting nodes without arrow indicate that the transition is bidirectional; for directional transitions, arrows specify the direction.
C ANALYSIS OF REAL-WORLD SCENARIOS
A
B
Figure 7: Stochastic block model (SBM) network used in experiments, (a) Graph introduced in Lee & Wilkinson 2019 which consists of 90 nodes and 1192 edges. The nodes are divided into groups, with groups 1, 2 and containing 25, and 35 nodes, respectively. The nodes within the same group more closely connected each other, than with nodes in another group. The connectivity of the nodes is considered uniform transition. (b) Corresponding adjacency matrix for graph in (a).
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(a)
(b)
Community
Community 2
Figure 8: Two community detection benchmarks used in experiments. (a) The Lusscau's network of bottlenose dolphins (Fortunato) 2010), modified from (Arenas et al., 2008). This network is considered as an imbalanced structure with 2 ground-truth communities of sizes 20 and 42. (b) The Zachary's karate club network, modified from (Perozzi et al. 2014). This contains 34 nodes and 78 undirected and unweighted edges. Colors within nodes denote local communities (i.e., the ground-truth found by the modularity-basse algorithm (Perozzi et al. 2014)), while colored shadow areas define the global communities (i.e., the ground -ruth collected from the original paper (Zachary 1977)).
C.I EXPERIMENT SETTINGS OF MODELS USED REAL-WORLD SCENARIOS
Here, we specify the detailed settings in the experiments of real-world problems.
Stochastic block model (SBM) network. The structure SBM network shown Figure As mentioned in the main text, all settings remained the same in previous imbalanced CGCP experiments (see Section 6.2).
Community detection benchmarks. In the two problems of the community detection benchmarks, MRIL was not used, since we focus on the investigation of how the given algorithms learn the topological and hierarchical structures underlying in input sequences, well as how well the structures are produced using such algorithms. MRIL cannnot encode input sequences into a map space, therefore was not considered as a baseline.
Regarding the Modularity Max, we again used TP matrices that produced by the graphs generated from the given input sequences, sequences. When finding the communities, we specify the "number of communities" to the algorithm. This can be found in the official documentation NetworkX (a Python library for analyzing graphs), where we set "a minimum number of communities below which the merging process stops. The process stops at this number of communities even if modularity not maximized." However, should be noted that the process will stop before the cutoff if it finds a maximum of modularity. Based on the given ground-truth,
focus is the ability of extracting information in input
the Lusseau's 's network of bottlenose dolphins, we set the "number of communities" at 2. In the Zachary's 's karate club network, we set the "number of communities" at and for computing NMI with two sets of ground truth, respectively.
Regarding the Word2vec, set the latent dimension equal 2, and kept all other parameter settings unchanged. This is to produce a 2-D representation the given community structures. Also, in the previous experiments, DBSCAN used to obtain chunks, where in the real-world problems we replaced it to hierarchical clustering as we are more interested in the topology as well as the hierarchical structures.
The original SyneMap and Symmetrical SyneMap shared the same changes with Word2vec, that is, only reduced the SyncMap space dimension from 3 to 2. Also, hierarchical clustering used.
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Regarding the hierarchical clustering, used "ward" as linkage method. And we specified the number of clusters when performing the algorithm. In details, for the Lusseau's network of bottlenose dolphins, set the "number of clusters" at 2. In the Zachary's 's karate club network, set the "number of clusters" at and for computing NMI with two sets of ground-truth, respectively.
C.2 RESULTS ANALYSIS
SBM network. Modularity Max performs nearly optimal in this scenario. Also, recall that it yields relatively low NMI in fixed CGCP. The differences of the performance observed here might be because the communities with many deterministic connections are less likely to appear in usual problems faced by Modularity Max, thus leading to a problem bias; that is, fixed chunk structures are not strictly meet the condition that the possibility of transition to an internal state within a chunk is higher than that of transition to an external state belonging to other chunks. This leads to a problem bias for Modularity Max.
Dolphins Network
Dendrograms
Karate Network
WortDvee with 2 CT (Dalttea)
Worshaee with 2label CT Marzo)
Word2vec
-2-
Orig. SynoMap
Orgy. SyrrMta with 2iabel (Dojenins)
Orl.. SyncHap with 2ibbel GT ocaane
Dentiggam: or Syneker (Gant))
-2-
Symm. SyncMap
Dandrogram Symm, Synchae (Dolesinn
Synclas Laabe
Summ Synchla labe nararn
42
Dentrogaa Symm Syccttap (Kanta)
-35
-59
-15-15 -26
300
12 75
Figure 9: Analysis of real-world problems used in the experiments. Here compare three algorithms, namely (i) Word2vec, (ii) original SyncMap, and (iii) Symmetrical SyncMap (the proposed one). Note that Modularity Max and MRIL do not encode input sequences into a map space. Thus, they not figuratively comparable.
Community detection benchmarks. Word2vec, as shown in Figure 9 always forms a latent representation with two long tails. This shape does harm when finding hierarchical structures.
We have analyzed the two models of SyncMap in the main text. It is worth noting here that from the dendrograms of the original SyncMap, we conclude that the original work is not possible to extract local relationships (i.e., hierarchies), as the nodes are all densely distributed in compact communities.
Regarding the Modularity Max, it does not encode temporal sequences into a map space. and thus it is not figuratively visualized. Meanwhile, although the datasets here are designed for modularity- based
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models, Modularity Max failed extract information and maximize the modularity from sequential data, thus showing lower NMI.
D MAPS LEARNED BY DIFFERENT ALGORITHMS
Chunking results: Node' distributions 20-10-5 problems.
Fixed Chunk Test
Probabilistic Chunk Test
Mixed Chunk Test
Original SyneMup
0-5-6
(0) NMI-883
(4) NMI-
(b) NM
Word2vee
(4) NMI--55
(0) NMI-9.777
(1
Sy Symettrial SyneMap
( NMI-1..
NMI--.
O NM
2
Figure 10: Chunking results of imbalanced 20- 10-5 fixed (left), probabilistic (middle) and mixed (right) problems using the original SyneMap (top), Word2vee (middle) and the proposed Symmetrical SyncMap (bottom). Colors of the nodes indicate the true labels of chunks. Specifically, purple for big chunk (20), yellow for moderate chunk (10), green for small chunk (5). Note that Modularity Max and MRIL do not encode input sequences into map space. Thus, they are not figuratively comparable.
E STABILITY ANALYSIS
The proposed Symmetrical SyncMap shows good stability over the long run in all imbalanced chunking problems. Figures [ [2] show the NMI average with error bar (s.t.d.) at every 10,000 time step during training in all imbalanced problems.
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A
B
4.0
Figure 11: NMI over time of imbalanced tests. (a) fixed 20-20-5, (b) fixed 20-10-5, (c) fixed 20-5-5,
(d) probabilistic 20-20-5, (e) probabilistic 20-10-5, (f) probabilistic 20-5-5.
B
C
450
400
10.00
Figure 12: NMI over time of imbalanced tests. (a) mixed 20-20-5, (b) mixed 20-10-5, (c) mixed
20-5-5, (d) continual fixed, (e) continual probabilistic, (f) continual mixed.
F PARAMETER SENSITIVITY ANAYLSIS
Table shows the performance of Symmetrical SyneMap on the same imbalanced experiments ffxee/probabllssiccmnnee 20- 10-1 test) but with different parameters settings. Results suggest that Symmetrical SyncMap is robust to changes in parameters, with mostly smooth changes.
Note that the parameter Pr is designed for solving small chunks. To illustrate, if Pr = 100%, then at every time step we apply state memory generalization to have a longer memory window. In this case, if the current chunk is too small (e.g., only having 3 states), then it would probably not be detected. Therefore, choosing Pr = 30% provides a trade-off between finding big and small chunks. In fact, in the future version of model, this parameter will longer be used, tiny chunk/communities are rarely appear alone, while they usually appear inside big chunk (i.e., hierarchies). Having said that, the results of using Pr 100% and Pr 30% are both adequate.
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Table 2: NMI of several Symmetrical SancMap variations in Fixed, Probabilistic and Mixed structures settings (20-104 10-5 tests).
Setting
Fixed
Probabilistic
Mixed
=
m= 3
Pr =30
1.0+0.0
1.0+0.0
0.9240.06
==3
m=
Pr 100%
0.95+0.08
0.98+0.02
0.86+0.03
k=3
m=3
Pr 100%
1.0+0.0
1.0+0.0
0.95+0.05
k=3
m=4
Pr %
0.96+0.08
1.00..0
0,95+0.05
k=2
m=2
Pr
0.90+0.10
1.00..0
0.87+0.07
m=3
Pr
0.98+0.07
1.0+0.0
0,90+0.08
Pr %
0.95+0.08
1.0+0.0
0,94
G ALGORITHMIC DESCRIPTION OF SYMMETRICAL SYNCMAP
Algorithm 1 Symmetrical SyncMap
Input:
input sequence X {mmli 1,,..,
Parameters: sequence length map dimension k. state memory probability parameter Pr, input
dimension ni learning rate
Output:
number of clusters
indicating
communities
and
chunks.
Initialize SyneMap by generating weight nodes W1 where 1...n
2: W; = (wa.el V 1...n,/ 0...r)
3: for / = 0 to r do
4: Initialize PS, and NS, as empty set
5: Randomly generate constant variable Pr: E [0,
Divide nodes into temporary PStemp
myey + m (Symmetrical activation)
8: if m 2 & Pr. < Pr then
9:
Stochastically select nodes in PSomm to activate Include these nodes into set PS;
10:
11:
mnag 2 (Symmetrical activation)
else if & Pr. Pr then
13:
PS. + PStemp
14:
end if
15:
Set temporary NSemmp +- W PS; Stochastically select maeg nodes in N Stemp activate
16:
Include these ming nodes into NS,
PS, N.S determined
19:
Calculate ept and cn,y by Eq.
20:
Update the nodes' position by Eqs. 3 and 4 Normalize nodes in hypersphere radius 10
21:
end for
Apply clustering algorithm as DBSCAN or Hierarchical clustering
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H STATISTICAL TESTS
We used a t-test with p-value of 0.05 to verify if the best result is statistically significantly different from other results. h the hypothesis test result (h=0 indicates failure reject the null hypothesis at the 5% significance level, and h=1 otherwise). is the two-tailed p value, and ci is the confidence interval for the difference in population means of two samples.
Table 3: Statistical Results.
Num. of Samples
Problems
Description
and M.dn-s..d.
Statistic
Long-term Analysis
30 each model
Two-sample
1= p=6.52288-22 27.
(Figure 5)
Orig. Symm.SyncMap
final time stop
1-test
ci=[0.3166x0..3
Prob. 20-20-5
30 each model
Two-sample
h= --4
(Table 1)
Maxax vs Symm.SyncMap
(0.96=0.04 and 1.0+0.0)
Hiees
ci=10.022000.0508
Frah. 20.20.3
30 each midal
Tap-sample
h- NaN, p-NaN.
(Table 1)
Orig. Symm.SyncMap
(1.0=0.0 and 1 L.040.0)
Hies
ci=[0.0:0.0]
Froh. T0.5
30 each model
Tam-sample
h-0, p-0.
(Table I)
M.Max vs Symm.SyncMap
(1.0=0.0 and 1.0+0.0)
1-test
ci [0.1-00003:000 0098)
Prob. 20-3-5
30 each model
Two-sample
h=0, p=0.3216.
(Table 1)
M.Max vs Symm.SyncMap
(1.00..0 and 1.0+0.0)
I-test
ci [-0.0042:0000123
Mixod 20-20-5
30 model
Two-sample
h=0, p=0.1568.
(Table I)
Orig. vs Symm.SyncMap
(0.84+0 08 and 0.87+0.09)
I-test
ci ci---0.0211000007
SBM Network
30 each model
Two-sample
b=0. p=0.09
(Table 1)
M.Max vs Symm.SyncMap
(0.9920.02 and 1 1.0,0.0)
biest
c= (000001;0000191
Network
Orig. vs Symm.SynMMap
model
lan-sample
PaNaN
(Table 1)
(1.020.0 and 1.000.0)
I-lst
c==[0.0:0.0]
I COMPUTATIONAL TIME ANAYLSIS
We analyze the computational time over Symmetrical SyncMap, SyncMap and Word2vec. In addition to Karate network, we introduced two larger scale imbalanced CGCP problems (i.e., problem with 300-D input and 1200-D input). More specifically, the structure of 300-D CGCP problem includes: Four chunks with 50 states + Two chunks with 20 states + Four chunks with 10 states + Four chunks with 5 states. We denote this problem as 300-D (50x4 20x2 + 10x4 5x4). Using the similar denotation, the 1200-D CGCP problem is 1200-D (300x2 + 150x2 + 50x4 + 20x2 + 10x4 + 5x4).
We ran all three problems 10-time per problem per algorithm with 200,000 sequence length. All tests were run on a MacBook Pro 2.4GHz Quad-Core Intel Core i5 16GB laptop as they demand little computational effort, and computation time [second] were obtained in meants.t.d. Results show that the proposed Symmetrical SyncMap is scalable. Although it is slower than the original one and Word2vec (mainly due to the stochastic selection process), the computation time does not become worse as the scale of the input increases. Note that both SyncMap and the proposed algorithm should improve considerably if parallelization, GPU programming and other techniques are employed. For example, all nodes in SyncMap can be updated at the same time.
Table 4: Computation time[s] comparison over Symmetrical SyncMap. SyncMap and Word2vec.
Problem Type
Symm. SyncMap
Orig. SyncMap
Word2vec
Karate (34-D)
90.227E1.297
30.17920.371
33.07720.429
Imbalanced 300-D
98.055+3.689
34.462+0.671
43.035=0.494
Imbalanced 1200-D
118.602+1.622
44.827+0.979
72.956#1.923
J ABLATION STUDY
The proposed method is composed of two parts compared to the original SyncMap: Symmetrical activation and genalized memory window. We perform an ablation study to evaluate the effect each of these two modifications. The ablation study investigated CGCP problem of mixed-20-100 10-5. The key feature of this problem is that there is a fixed chunk with 10 state in between two probabilistic chunks. The 10-time averaged NMI results shown in Table
From the NMI scores, is hard to image what happen inside the SyncMap space. However, a better visualization can be observed in the learned map comparison in Figure 13 To illustrate briefly, if
19

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Under review as a conference paper at ICLR 2023
Table 5: NMI score of ablation study.
Model Type
NMI Score
Original SyncMap (m=2)
0.84+0.07
SyncMap with Generalized Memory Window (m=3)
0.83+0.0
SyncMap with Symmetrical Activation (m=2)
0.84+0.03
Symmetrical SyneMap (m=3)
0.90+0.06
only applying symmetrical activation, the states (i.e., weight nodes in the map) of the given fixed chunk will be very sparely distributed (Figure c3,,,, i.e., the system cannot detect the fixed chunk because needs more memory to remember fxee chunks). On the other hand, if only applying generalized longer memory window, the strength of the negative feedback will still dominate the self-organizing process, thus resulting in the similar output with Original SyncMap (Figure (3) (b); that is, all weight nodes are squeezed into compact clusters. Therefore, by applying symmetrical activation and generalized memory window together, the system is stable and able to detect fixed chunk in more general cases (Figure 1 d).
s. Oviginal SyncMMap
Synehlap Geseralized Memory Window (m--))
c. Sysunetrical SyneMap without Geseralized Memory Window (mm22)
Symmetical SyncMMa
Figure 13: Learned map of (a) Original SyncMap, (b) SyncMap with Generalized Memory Window (m=3), (c) Symmetrical SyncMap without Generalized Memory Window (m=2), and (d) Symmetrical SyncMap. Note the nodes belong to fixed chunk is denoted by yellow color, which is slightly hard to visualize.
K RELATED WORKS
Chunking is an extremely multidisciplinary problem. In the main text, we attempt to cover a number of related topics from neuroscience machine learning and try to connect them to this work. Due the page limit, we review additional related works here for completeness.
Latent Variable Estimation. Some literature focusing latent variable estimation solve problems which are related to chunking (Fox et al., 2011; Qian & Aslin 2014 Pfau et al. 2010). However, they have different objectives, since chunking orgf-oiggni process over the variables of the problem with respect to their temporal correlation. Even if chunks of variables can be abstracted as set of variables, there still an inherent difference between chunks and latent variables.
Unsupervised Learning for Sequences. Feature extraction is commonly used to predict future input in unsupervised learning for sequences (Clark al. 2019 Lei et al., [017]] Mikolov et al.) 2013) Wu et al.) 2018). A peculiar learning algorithm called contrastive predictive encoding (CPE) has been proposed, which represents sequences by using a probabilistic contrastive loss in the latent space encode maximally useful information (Hjelm et al. (018)). CPE solves problems which complementary rather than competing with the problem presented here.
20


Reviews:
[{"review_id": "y_bgM7lFdo", "reviewer": "Reviewer_C5fg", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "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": "Symmetrical SyncMap builds upon SyncMap as an unsupervised clustering algorithm on graphs. To evaluate the behavior, chunking was formalized into CGCP (Continual General Chunking Problem) and becomes a graph clustering problem. Each node in the graph is assigned a weight vector. A key aspect of updating the weight vector are set the set of positive nodes and negative nodes. In the original SyncMap, these would become unbalanced. Symmetrical SyncMap proposals a sampling scheme so that the number of nodes in each set is equal. The method is then evaluated on both synthetic and real world data with very good results.", "summary_of_the_review": "The paper in its current state is hard to follow, but it does seem to have potential to be interesting. I think increased clarity and experiments on larger more interesting datasets would help a lot.", "strength_and_weaknesses": "The intuition of chunking and learning repetitive patterns and generalization as a graph clustering problem makes it easy to grasp the general thrust of the paper. The idea of balancing the positive and negative sets is well-motivated. The experimental results are strong, too.\n\nThe paper hurts the most on clarity. I found the description of SyncMap very hard to follow. In particular, it's still not clear to me how states transition and how $t_a$ is determined. May it would be helpful to explicitly walk through an iteration with a concrete example.\n\nReal-world experiments seems to be on datasets that are very small with few chunks. I would have expected to see something NLP-related  since Word2Vec and linguistics is mentioned.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "RfV01UjL6e", "reviewer": "Reviewer_SjDm", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "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": "This paper first identifies problems of SyncMap in Continual General Chunking Problem (CGCP) with long-term instability and poor performances given the asymmetric number of updates of nodes. To solve these issues, a variant of SyncMap, Symmetrical SyncMap is proposed using a symmetric selection of nodes, and a generalized memory window to avoid suffering from the uneven updates from positive/negative feedback loops, and helps the system have more updates from the positive feedback loop, respectively. The authors also show comparisons in 12 imbalanced CGCPs with various difficulties, indicating the proposed method surpasses or ties with other unsupervised SOTA baselines. The authors also verify the performance in real-world scenarios.\n\n", "summary_of_the_review": "Overall, I like this method, also the problem CGCP generated from neuroscience to computer science. I can see the potential of this problem and this method. The motivation, settings, and evaluations are clear, and all else aside, I felt a lot of insights from this paper. However, I'm just yet convinced by the current amount and set of experiments, also the ablations.\n", "strength_and_weaknesses": "Pros:\n\n- The paper is clearly written and well organized, the formulation of the problem is good, figures and descriptions help in understanding CGCP and SyncMap.\n- The idea of introducing even node updating is intuitive and interesting (also effective in results).\n- Competitive performance to SOTA methods, especially to vanilla SyncMap, and the results are even 1 in most cases.\n- Real-world scenarios evaluation helps understanding of the method, settings and formulations are clear.\n\nCons:\n\n- CGCP is a newly formulated problem, while few comparison methods are evaluated on this issue. Though this paper has listed some conventional and SOTA methods, there is still some space for comparison.\n- The author mentioned, “As opposed to the original SyncMap that suffers from the uneven updates …” in the Intro, and “the dynamic’s update is more influenced by negative feedback loop,” in Limitations of SyncMap. Though the motivation is intuitive that unbalanced negative samples may bring extra catastrophic information to the training phase, there do exist situations when there are more positive samples, and in that way, maybe even sampling strategy is no good as uneven does.\n- This novel method is composed of two parts compared to the vanilla SyncMap: symmetrical activation and memory window. I’m concerned that if the authors have evaluated the effect of each of these two components, i.e., does one of the components bring a big boost, or is it the combination of these two that helps much? The integration of both demands further explanation. \n\nMinor:\n\n- Extra “)” in Training Dynamic, page 4.\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "JvoMAphZgt", "reviewer": "Reviewer_7tpF", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "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": "This paper aims to address the problem of learning complex structures from sequences. \nThey improved an existing method called SyncMap by balancing the number of updates from positive and negative feedback loops. \nThey demonstrated the effectiveness of the proposed method on multiple synthetic and real-world datasets. ", "summary_of_the_review": "The paper address an interesting problem and proposed a method that works well in their experiments. \nBut I have concerns about their technical designs, experiments, and writing, so I tend to reject the paper. ", "strength_and_weaknesses": "Strength \n\nThe paper studies an interesting problem and its proposed method seems to be working well in multiple synthetic and real-world settings. \n\nWeakness\n\nThe technical contribution seems incremental. It turns a hard-code value of SyncMao into a hyperparameter and forces the positive set and negative set to be equally large. Both seem very minor tweak on the original SyncMap method. \n\nMoreover, they use a stochastic way to match the size of positive and negative sets, which introduces extra noise. I am concerned with it since the goal of this work is to make the original SyncMap method more stable. Although the experiments have shown that their method is better than original SyncMap, I would still like to see a more in-depth stability analysis that discusses why introducing this new noise is not an issue. \n\nThe technical definitions for fixed chunks and prob chunks are a little strange to me. It seems that all chunks are probabilistic but some of them have no branching structures inside them so the internal transition probability is always 1. \n\nI am also concerned with their evaluation. \nFrom my understanding of this problem setting, I think stochastic block model seems a natural baseline method. Actually, the authors used SBMs to synthesize some of their experiments. Then why not use SBM to learn this community structure? \n\nAnother reasonable baseline is to learn a markov model whose transition probability matrix is strongly regularized: it is sparse; it forms local high-prob structure. Why don't the authors consider baseline methods of this style? \n\nWriting needs improvements. \n\nThe technical part of the paper is not very self-contained. E.g., it is not clear how the positive set and negative set (or even eqn-2,3,4 in general) are related to the later stage of clustering. The clustering phase is introduced by simply citing DBSCAN without specifying how it works in this particular technical setting. \n\nThere are typos and errors. E.g., \"positive (7) nodes and negative (2) nodes\" is not consistent with the figure. \n\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "3WXFYg9Cl82", "reviewer": "Reviewer_hkor", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "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": "This paper proposes an improvement over the sync-map algorithm for imbalanced continual general chunking problems (CGCPs). The problem is effectively clustering on sequential data. The original sync-map samples positive pairs and negative nodes (any number), pull together positive pairs, and push apart negative nodes. The improvement is to only sample the same number of negative nodes. In addition, in order to find these negative pairs, the authors propose stochastic selection and memory window.\nExperimental results demonstrate the superior performance of the proposed methods over previous methods like Modularity Max, MRIL, and Word2vec.", "summary_of_the_review": "An effective improvement over syncmap algorithm for imbalance general chunking problems. The paper has limited scope as it's only proposed to solve these problems and not seem to be scalable.  ", "strength_and_weaknesses": "Strengths:\n1. The proposed method is well inspired by brain activity. It identifies the limitation of the previous syncmap algorithm and improves the algorithm with better sampling. It also proposes sampling tricks such as memory windows.\n2. The empirical advantage of the proposed method is strong. It outperforms previous methods.\n3. The balancing trick and memory window idea can be useful for other domains, e.g., contrastive learning. Hence, this paper may have an impact to out-of-domain topics.\n\nWeaknesses:\n1. All the experiments are conducted in a relatively small scale, including both model size and data size. It is questionable how fast this algorithm can converge. As a non-deep-learning algorithm, it is recommended to discuss convergence speed and overall computation/memory complexity. \n2. In addition, the discussion over 'Symmetrical SyncMap depicts the global graph structure while preserving the topology of local communities' seems not well supported. This further limits the scope that the proposed algorithm can apply to.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}]

Author rebuttal:

Decision: Reject