Representation in a broad sense is how a particular object is presented in the space of internal states of the perceiving subject. Inspired by the works of V.A. Lefebvre, we call the formation and use of representations “reflection in a broad sense”. We study representations in extremely simple model objects – recurrent neural networks of small size (30 neurons). One of the simplest tasks that requires the presence of representations for solution is responding to fixed time series of stimuli, in which the neural network should recognize the series feeding to the input and thereby predict the next stimulus it will receive. The representation of a series is considered as a dynamic pattern of neural activity distinguishable from representations of other series. This pattern can be decoded, i.e., based on its type, it is possible to define the certain series fed to the input of the neural network. In this paper, we check whether there are differences in decoding of homogeneous and heterogeneous recurrent neural networks’ neural activity, considering decoding using feedforward networks and the K-nearest neighbors method. Configurations with temporal heterogeneity (DTRNN) demonstrate differences from homogeneous ones, while configurations with functional heterogeneity (RefNet) behave similarly to homogeneous configurations. This result is consistent with the literature data on the significance of temporal coding obtained on more complex systems. In the future, we plan to continue working models that have temporal heterogeneity in order to formulate a mathematically and neurobiologically substantiated measure of the neural activity decodability.

The functioning of a subject in a changing environment is most effective from the point of view of survival if the subject can form, maintain and use internal representations of the external world for decision-making. These representations are also called reflection in a broad sense. Using it, one can win in reflexive games since an internal representation of the enemy allows predicting their future moves. The goal is to assess the reflexive potential of heuristic model objects – artificial neural networks – in the reflexive games “Even-Odd” (or “Matching pennies”) and “Rock-Paper-Scissors”. We used homogeneous fully connected neural networks of small sizes (from 8 to 45 neurons). Games were played between neural networks with different configurations and parameters (size, step size for modifying weight coefficients). A set of reflexivity criteria is presented, corresponding to different levels of consideration: neuronal, behavioral, formal. The transitivity of formal success in the game is shown. The most successful configurations, however, may not meet other criteria of reflexivity. We hypothesize that the best compliance with the criteria and, as a consequence, universal success in reflection tasks is achievable for heterogeneous configurations with a structure in which the formation of hierarchical systems of attractors is possible.

Functioning in the flow of events is possible since the subject recognizes current events as familiar and acts in accordance with the representation of ​​them. The presence of internal representations is called reflection in a broad sense and can be regarded as a requirement for effective solving of some tasks, for example, winning in a reflexive game. We consider tasks that imitate Even-odd and Rock-scissors-paper games by replacing a playmate with fixed sequences of moves. In this paper, we investigate the question whether it is possible to identify which of the available fixed sequences of moves is currently receiving by model object – a simple recurrent neural network, by decoding signals on its neurons. We show that neural-network based decoding method allows recognizing the current sequence of moves by the neural activity of the playing network, separating data that does not correspond to any of the known sequences. Therefore, simple recurrent neural networks can form stable recognizable representations associated with fixed sequences of game events in the imitation of reflexive games. This result indicates that these model objects implement reflexive processing of information and can be used for studying reflection phenomenon.

The paper reports the assessment of the possibility to recover information obtained using an artificial neural network via inspecting neural activity patterns. A simple recurrent neural network forms dynamic excitation patterns for storing data on input stimulus in the course of the advanced delayed match to sample test with varying duration of pause between the received stimuli. Information stored in these patterns can be used by the neural network at any moment within the specified interval (three to six clock cycles), whereby it appears possible to detect invariant representation of received stimulus. To identify these representations, the neural network-based decoding method that shows 100% efficiency of received stimuli recognition has been suggested. This method allows for identification the minimum subset of neurons, the excitation pattern of which contains comprehensive information about the stimulus received by the neural network.

The study is concerned with question whether it is possible to identify the specific sequence of input stimuli received by artificial neural network using its neural activity pattern. We used neural activity of simple recurrent neural network in course of “Even-Odd” game simulation. For identification of input sequences we applied the method of neural network-based decoding. Multilayer decoding neural network is required for this task. The accuracy of decoding appears up to 80%. Based on the results: 1) residual excitation levels of recurrent network’s neurons are important for stimuli time series processing, 2) trajectories of neural activity of recurrent networks while receiving a specific input stimuli sequence are complex cycles, we claim the presence of neural activity attractors even in extremely simple neural networks. This result suggests the fundamental role of attractor dynamics in reflexive processes.

We tested the ability of simple recurrent neural networks to use the reflection of playmate during the “Even-Odd” reflexive game. Reflection is understood as an internal representation of an external environment. To determine if subject uses reflection in the game, three criteria were proposed and applied: formal, neuronal, behavioral. The formal criterion is a win in the game, the neuronal one is a dynamic attractor’s formation of the player’s neural activity, the behavioral one is the deviation of a move sequence from the natural strategy “win-stay, lose-shift”. Three configurations of simple recurrent neural networks were used: 1) the basic one; 2) the one with an additional input which receives information about the success of the last game move, 3) the one which has off-game cycles for processing the received stimulus and making instant decision. We considered the following game conditions: 1) round-robin tournaments of various neural network configurations with modifiable and fixed synapses, 2) playing against fixed sequences of moves. It was found that the simplest neural network model is able to play as good as and, in some cases, better than neural networks of a more complex configuration. The off-game cycles for processing the received stimuli contribute to the non-reflexive behavior of the neural network. The performance of neural networks in a reflexive game correlates 1) with the presence of a self-sustaining dynamic attractor and 2) with the use of moves other than the natural strategy.

We demonstrate the possibility of identification of certain stimuli time series, which is received by simple recurrent neural network while playing a reflexive game “Even-Odd” (Matching Pennies), using its neural activity patterns. For successful identification by the method of neural network-based decoding, a non-linear decoder with at least 6 neurons on the hidden layer is required. This result indicates the presence of attractors of neural activity, which allow the trained recurrent neural network to determine the type of the received stimuli sequence and form the right response.

Reflection, that in a general sense means internal representation of the external world, refers to one of awareness levels observed in animals. In this paper we demonstrate the ability of a homogeneous recurrent neural network to solve a problem that requires a reflection. The delayed matching to sample test was chosen as a task which is impossible to pass without an internal representation of an external world. Experiments showed that simple recurrent neural networks can form these representations and store them as neuron firing patterns for several clock cycles. Although the trained network was able to distinguish these patterns easily, the identification of certain stimulus by neuron firing was not practically possible due to minor differences in the level of synchronous firing of a given neuron for different stimuli. Neural networks were shown to be applicable for modeling reflexive abilities, so these simple models may also be used for creation of general technique that ultimately can be applied to recognizing neural correlates of human consciousness.

The study is concerned with the comparison of two methods for identification of stimulus received by artificial neural network using neural activity pattern that corresponds to the period of storing information about this stimulus in the working memory. We used simple recurrent neural networks learned to pass the delayed matching-to-sample test. Neural activity was detected at the period of pause between receiving stimuli. The analysis of neural excitation patterns showed that neural networks encoded variables that were relevant for the task during the delayed matching-to-sample test, and their activity patterns were dynamic. The method of centroids allowed identifying the type of the received stimuli with efficiency up to 75% while the method of neural network-based decoder showed 100% efficiency. In addition, this method was applied to determine the minimal set of neurons whose activity was the most significant for stimulus recognition.

Abstract Reflection understood as an internal representation of the external world by the subject is the key property of consciousness. In a refined form this property is manifested in reflective games. To win a reflective game a player has to use reflection of strictly one rank higher than the opponent. So it can be assumed that there are only two game modes - when only one player uses reflection and wins and when both players use reflection but one of them chooses incorrect reflection rank. The option of random move selection is not considered since firstly, starting the game for a draw is strange, and secondly, it is technically impossible to make random moves without a special device. Experiments with recurrent neural networks playing with each other showed that the entire set of game patterns (time series of the game score) is split into two sharply different groups that can be associated with two modes mentioned above. Experiments, in which a multilayer neural network, which is basically incapable of reflection, played against a recurrent neural network, showed that a recurrent neural network has a clear advantage winning confidently in more than 90% of the games. At the same time game patterns demonstrate splitting into two sharply different groups as was observed in experiments with the game of two recurrent neural networks and in the reflexive game of living people.