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This article is from WeChat public account:Jizhi Club (ID: swarma_org), the original title of “Figure learning: how the network structure of the impact of emerging leading human cognition”, author: Yan Peng high, editor: Zhang Shuang, cover: Oriental IC

Introduction: The human brain has many advanced functions. It can accept information, store information and exchange information. So how does humanity learn? In a preprinted paper published on arxiv.org on September 16, 2019, the author explored how network structures affect human cognition by introducing an evolving interdisciplinary field, graph learning.

The human brain has many advanced functions, one of which is to learn the rules of things based on past experience, so that we can understand the language, abstract reasoning, and classify visual patterns. Even children who are only 8 months old can find statistical rules in spoken language to determine the boundaries between words.

Every event can be seen as a complex network structure, and this ability of the human brain allows us to learn these network structures quickly and accurately.

How does humanity learn?

To understand how humans learn, let’s start with a simple experiment. Build a series of contiguous sequences of four pseudo words, each of which has three syllablesComposition, as shown in Figure 1A. The syllable order of each pseudo word is fixed, and each pseudo word in the sequence appears randomly, that is, the transition probability of the syllable in the word is 1, and the probability of transition between words is 1/3.

The researcher asked the baby to listen to the sequence. After a while, the baby being tested was able to detect the difference in syllable transition probability. The experiment revealed a word recognition mechanism in the language learning process. This ability to detect changes in metastatic probability is a central and universal feature of human learning.

Figure 1

Although the transition probability contains important information in the stimulus sequence, they do not represent all of the information. Due to the existence of transition probabilities, a complex network structure is formed between each syllable. To describe this structure, the researcher transforms the sequence of Figure 1A into the network structure shown in Figure 1B, where each syllable is a node, node The edges between them represent possible transfer relationships between them, at which point the sequence in Figure 1A can be represented as a random walk of the network in Figure 1B.

As seen in Fig. 1B, these syllables naturally form four clusters, each cluster corresponding to a pseudo word. This phenomenon raises an important question: when parsing the word (or performing any other statistical learning task), people learn a single transition in the network. The difference in probability, or learned the characteristics of the larger scale of the network?

The impact of network structure on human learning

The network has many local structures, mesoscale structures, and global structures. As shown in Figure 2, these structures are often related to nodes and edges of the network, as follows:

• Local Structure: Degree of Node

• Mesoscale structure: clustering coefficient, modularity

• Global Structure: Audit, Centrality, Propagation

Figure 2

In order to study the impact of network structure on human learning, the researchers designed a series of time-reflecting experiments, as shown in Figure 3. During the experiment, the subject received a series of stimulation sequences, which were required to be pressed on the keyboard according to the stimulus. The corresponding key. The shorter the reflection time, the stronger the expectation of the transfer, and the weaker the opposite.

By using different network structures, we can study the effects of local, mesoscale, and global structures on human learning.

Figure 3

The effect of local structure on human learning

In order to study the effects of local structures on human learning, the researchers used a random network for reaction time experiments. As shown in Figure 4, each node in the network represents a stimulus, and the random walk of the network constitutes a stimulus sequence. Reaction timeThe change in the previous node degree during the transfer process is shown in Figure 4: the greater the degree of the previous node, the longer the reaction time.

Because the transition probability of random walk can be represented by the reciprocal of the previous node, the experimental results show that the greater the transition probability, the shorter the reaction time. This result indicates that humans are sensitive to the local structure of the network.

Figure 4

Mesoscale and global scale, the impact of structure on human learning

A series of studies have shown that the mesoscale and large-scale structures of the network have an impact on human learning.

For mesoscale structures, studies have shown that low-cluster words are easier to identify in long-term memory; for large-scale structures, in experiments with reaction time tests, for nodes with low intermediateity The response is faster; more research has shown that it is easier for children to capture and speak low-nuclear words.

But in order to establish the causal relationship between network structure and human learning, we must also prove that the above phenomenon is not affected by the local structure of the network, so the researchers used the control variable method to design a new set of reaction time experiments. In the experiment process, the networks with the same degree but different topological structures are used, and they are used as the transfer network of the stimulus sequence. As shown in Fig. 5, the two networks are the module network and the lattice network respectively, and the degrees of all nodes are 4, so The local structure of the two networks is the same.

Figure 5

In the module network, the reaction time of the intra-cluster and inter-cluster transfer is measured separately. By calculating the difference between the reaction time between the clusters and the reaction time in the cluster, the result of Fig. 6 (the upper part) is obtained. The reaction time between clusters is longer than that in clusters, which indicates that people respond more quickly to intra-cluster transfer, and the mesoscale structure of the network has a significant impact on human learning.

In addition, by measuring the response time of people on the grid network and the module network, the difference between the two is shown in Figure 6 (lower part) shows that the average response time of the grid network is longer, which indicates that the global structure of the network has a significant impact on human learning.

Figure 6

The above experiments show that humans can not only learn the individual’s transition probability, but also explore the structural characteristics of potential networks. These features include not only local features, but also the characteristics of the network’s mesoscale and global scale. . But how do humans learn this high-level network feature? Modeling human graph learning gives the answer.

Human mechanism for graph learning

First consider a simple model, assuming that the probability of transition of the stimulus sequence isThe transfer matrix Pij determines that we can calculate the frequency at which the stimulus element i is transferred to j, thereby estimating the transition probability of i to j by frequency. In fact, this estimate is the maximum likelihood estimate for Pij. However, when we estimate, we do not consider the topology of the network. However, the previous experiments show that the topology of the network has an impact on human learning. Therefore, the estimation of the direct use frequency cannot reflect the mechanism of human graph learning.

Considering the impact of the network structure, the researchers proposed a mechanism: when accepting a series of stimuli, humans will integrate the network’s transfer structure over time. In a nutshell, human response to stimuli is not only related to current stimuli, but also to one, two or more stimuli. The mechanism can be expressed by the following equation, where t represents the time point, f(t) represents the integral weight at different time points, C is the normalized constant, and P is the true transition probability matrix of the network, < Em>P represents the estimated transition probability matrix.

In order to further elaborate this learning mechanism, the researchers performed the experiment shown in Figure 7. When f(t) is an impulse function (left of Figure 7A), the learner only focuses on the current stimulus, at which point the learner simply uses the maximum likelihood estimate, and the final estimated transition structure P Convergence to the real transfer structure P(Fig. 7B left). When f(t) is a uniformly distributed function (Fig. 7A right), the learner will integrate all time steps, then estimate The P of the transfer structure deviates far from the real structure (Fig. 7B right).

Figure 7

However, when f(t) decays with time step (in Figure 7A), the learner will moderate the transfer structure The length of the integral, the final estimated transfer structure P will reflect some global features (in Figure 7B), for example tight The communities formed by connected nodes are becoming more visible, and some local structures, such as the borders of communities and communities, are degraded. This time integration mechanism has proven to be biologically feasible and is ubiquitous in current cognitive theory.

Expanding graph learning paradigm

The problems of most graph learning studies, such as the reactive test studies mentioned above, can all be seen as random walks on the transfer network. In the language of a random process, this is a smooth Markov process.

Although graph learning based on random walk provides a natural research perspective, it is still limited by three assumptions: (1) The transfer structure does not change over time (stationary); (2) future stimuli only depend on the current stimulus (Markov sex); 3) The stimulation sequence is predetermined and will not be affected by the observer. By studying these limitations, future research will expand the paradigm of existing graph learning.

(1) Stationarity

Most of the graph learning studies are directed at static network structures, but most networks in real life change over time. For example, the process shown in Figure 8.The edges in the network will be reconnected over time. Studies have shown that when observing a series of stimuli that change from one transitional structure to another, the learning representation of the first network affects their response to the second network, but as time goes by, These effects will gradually weaken. Future graph learning studies can focus more on the characteristics of time-varying network structures.

Figure 8

(2) Markovity

In the current study of graph learning, we always focus on the stimulus sequence with Markovity, that is, the future stimulus depends only on the current stimulus. However, the actual stimulation sequences mostly have long-term correlation and dependence.

This long-term dependency can be represented by Figure 9. Due to the existence of long-term dependencies, the next state of path 1(Figure 9 left) There are two possibilities, while path 2 (Figure 9 right) has three possibilities. For example, each word in spoken language is not only related to the previous word, but also related to the earlier words in the sentence. There are also complex long-term dependencies between the musical notes. So can the time integration mechanism mentioned above infer this non-Markov process? These issues are waiting to be solved in future graph studies.

Figure 9

(3)Information Search

Stimulation sequences are often designed to be independent of the observer, but the structure of the stimulation sequence can also be determined by the observer. For example, when people search for information online, people will actively choose a path that traverses the link network. In this case, people have subjective initiative to obtain information rather than passively accept pre-customized information.

As shown in FIG. 10, by actively searching for information, people finally obtain a new sub-network from the original network. This proactive information search brings many interesting questions: Is the path of active search enabling people to learn the topology of the network more effectively? Or does this ability to actively search lead to a prejudice against the structure of the real network? These problems need to be resolved.

Figure 10

Research the structure of a real network

There is a close connection between human cognition and the network. People rely on the network system to perform various tasks, such as using language to communicate (Fig. 11A) , invented music (Fig. 11B) and stored and retrieved information on the network (Fig. 11C), many of which evolve as humans evolve or are designed directly by humans. We must not makeDoubt: Some networks are built to support human learning and cognition.

Figure 11

Graphics learning provides quantitative models and experimental tools to study these issues. We find that many real-world transitional networks have two distinct structural features: (1) heterogeneous, hub nodes with unusually high degrees, and degree distributions with power laws (Fig. 12D); (2) modular, that is, there are closely connected clusters, and the connections between the clusters are sparse ( Figure 12E). So do these structural characteristics have a common purpose, that is, to promote human learning and communication?

Figure 12

Research shows that modular structures improve people’s responsiveness, and hub nodes in heterogeneous networks can help people search for information. These results show that graph learning provides a unique and constructive perspective through which to explore the transitional networks of the world around us.

summary

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Human behavior, cognition, and neural activity are heavily dependent on the topology of the transitional network. By studying this unified framework, we can scientifically explore the impact of network architecture on human cognition.

Graphics learning is an emerging field of research that offers a wealth of interdisciplinary research opportunities. From new cognitive modeling techniques, to the extension of existing graph learning paradigms, to the use of real-world networks, graph learning will change our thinking about human cognition, complex networks, and the interaction between them.

Thesis title: Graph learning: How humans infer and represent networks

Thesis address: https://arxiv.org/abs/1909.07186

This article is from WeChat public account:Jizhi Club (ID: swarma_org), author: Yan Peng high, editor: Zhang Shuang