Figure 2. The first panel is a visual drawing of the digit nine (9), while the next panel is the same digit but transformed by rotation of the image.

3.2. Encoding of Knowledge in Cognitive Systems

It is possible to hypothesize about a model of object representation in the brain and its artificial analog, a deep learning system. First, these cognitive systems are expected to encode objects by their parts, or elements, a topic that is covered above.^[3][4][5] Second, it is expected that this is a stochastic process, and in the artificial system the encoding scheme is in the weight values that are assigned to the interconnections among nodes of a network. It is further expected that the brain functions similarly at this level, given that the systems are based on nonlinear dynamics and distributed representations of objects.^{[5][18][20][21]}

These encoding schemes are expected to be abstract and not of a deterministic design based on a top-down only process. Since cognition is also considered a nonlinear dynamical system, the encoding of the representations is expected to be highly distributed among the parts of the neural network.^[18][21] This is testable in an artificial system and in the brain.

Further, a physical interpretation of cognition requires the matching of patterns to generalize knowledge of the outside world. This is consistent with a view of the cognitive systems as statistical machines with a reliance on sampling for achieving robustness in its output. With the advances in deep learning methods, such as the invention of the transformer architecture^[5][22], it is possible to sample and search for exceedingly complex sequence patterns. Also, the sampling of the world occurs within a sensory modality, such as from visual or language data, and this is complemented by a sampling among the modalities which potentially leads to increased robustness in the output.^[23]

3.3. Future Directions of Study

3.3.1 Dynamic Properties of Cognition

One question has been whether animal cognition is as interpretable as a deep learning system. This arose because of the difficulty in disentangling the mechanisms of the animal brain, whereas it is possible to record the changing states in an artificial system since the design is bottom-up. If the artificial system is similar enough, then it is possible to gain insight into the mechanisms of animal cognition.^[5][24] However, a problem in this assumption may occur. For example, it is known that the mammalian brain is highly dynamic, such as in the rates of sensory input processing and the downstream activation of the internal representations.^[18] These dynamic properties are not feasibly modeled in current artificial systems since there are constraints on hardware design and its efficiency.^[18] This is an impediment to design of an artificial system that is approximate of animal cognition. Having an artificial system that includes an overlay architecture with “fast weights” is expected to provide this form of true recursion in processing information from the outside world.^[5][18]

Since the artificial neural network systems continue to scale in capability, it is reasonable to continue to use an empirical approach to explore any sources of error, whether inherent in the method or a result that is not expected. This requires a thorough understanding on how these models work at all levels. One strategy for producing robust output has been to combine the various kinds of sensory information, such as both visual and language data. Another strategy has been to establish unbiased measures of the reliability of output from a model. It should be noted that animal cognition is not immune to error either. In the case of human cognition, there is a bias problem in perception of speech.^[25]

3.3.2 Generalization of Knowledge

Another area of importance is the property of generalization in the case of a model of cognition. This goal could be approached by processing the particular levels of representation of sensory input, the presumed process that occurs in animals and their ability to generalize knowledge.^[4][26][27] In a larger context, this generalizability is based on the premise that information of the outside world is compressible, such as in the repeatability of patterns in the information.

There is also the question of how to reuse knowledge outside the environment where it is learned, "being able to factorize knowledge into pieces which can easily be recombined in a sequence of computational steps, and being able to manipulate abstract variables, types, and instances".^[5] It seems relevant to have a model of cognition that describes high level representations of these "pieces" of the whole, even in the case of an abstract object. However, the dynamic states of internal representations in cognition may contribute to the processes of abstract reasoning.

3.3.3 General Abstract Reasoning

A model of high level of cognition includes the process of abstract reasoning.^[5] This is a pathway or pathways that are expected to learn the high level representations in sensory information, such as visual or auditory, so that novel input generates output that is based on a set of rules. These rule sets are also expected to have generalized applicability. The rule set may include a single rule or multiple rules that occur in a sequence. One method for a solution is to have a deep learning system learn the rule set, such as in the case of a visual puzzle which is solved by use of a logical operation.^[28] This is likely similar to one of the major ways that a person masters the game of chess, a memorization of priors for patterns and events of chess pieces on the game board.

Another kind of visual puzzle is a Rubik's Cube. However, in this case the puzzle has a known final state where each face of the cube shares a unique color. In the general case of visual puzzles, if there is no detectable rule set to solve the puzzle, then a person or a machine system should conclude that no rule set exists. If there is a detectable rule set, then there must be patterns of information, including missing information, that allow detection of the rule set. It is also possible that a particular rule set or those with many steps are not solvable by a person.

The pathway to a solution should include repeated testing of potential rule sets against an intermediate or final state of the puzzle. This iterative process may be approached by an heuristic search algorithm.^[5] However, these puzzles are typically low dimensional as compared to abstract verbal problems, such as in the general process of inductive reasoning. The acquisition of the rule sets for verbal reasoning require a search for patterns in this higher dimensional space. In either of these cases of pattern searching, whether complex or simple, they are dependent on the detection of patterns that represent the rule sets.

It is simpler to imagine a logical operation as the pattern that provides a solution, but it is expected that a process of inductive reasoning involves higher dimensional representations than an operator that combines boolean values. It is also probable that these representations are dynamic in a person, so that there is a possibility to sample the space of valid representations.

3.3.4 Phenomenon of Embodiment and Cognition

Lastly, there is a question on the dependence of animal cognition on the outside world. This dependence has been characterized as the phenomenon of embodiment, so the cognition is an embodied cognition, even in the case where the outside world is a machine simulation of it.^[18][29][30] This is essentially a property of a robot, where its functioning is dependent on input and output from the outside world. Although a natural system would receive input, produce output, and thus learn from the world along some constrained time scale, a somewhat alternative approach in an artificial system is reinforcement learning,^[30][31] a method that has been used to approximate the sensorimotor capability of animals.

A paper by Deepmind^[30] describes artificial agents in a three-dimensional space where they learn from a world that is undergoing change over time. The method uses a deep reinforcement learning approach combined with a dynamic generation of environments that comprise each world. Each world has artificial agents that learn to undergo tasks for completing an objective. Knowledge of these tasks is sufficiently generalizable that the agents are often adapted to handle tasks that are not yet known in a newly generated world. This overall approach reflects an animal that is embodied within its three-dimensional world and learns to interact in the world by performing and learning tasks. It is known that animals navigate and learn from the world around them, so it is a thoughtful experiment to create similar circumstances in a virtual one.

3.3.5 Embodiment in a Virtual and Abstract World

While the above section reflects on the importance of modeling the phenomenon of embodiment in its three-dimensional world, this is not necessarily a model for reasoning about abstract concepts. It is very plausible that the visual concepts in the abstract are modeled by a virtual world in three-dimensions, and the paper on this topic by Deepmind^[30] shows evidence of solving visual problems in its set of possible three-dimensional worlds.

The population of tasks and its distribution are constructed by Deepmind's machine learning approach. They show that learning a large distribution of tasks can provide sufficient knowledge to solve tasks that are not necessarily within the confines of the original task distribution. This furthers shows a generalizability in solving tasks and the promise that increasingly complex worlds will lead to a greater knowledge of task handling.

However, the problem of abstract concepts extends beyond the visual and conventional sensory representations as formed by the processes of cognition. Examples include visual puzzles with solutions that are abstract and require the association of patterns that extend beyond the visual realm, and the symbolic representations and their relationships in mathematics.^[32]

Combining these two approaches, it is possible to construct a world that is not a reflection of the three-dimensional space inhabited by animals, but instead to construct a virtual world that consists of abstract objects and the performance of tasks. The visual and symbolic puzzles, such as in the case of chess and related boardgames^[31], have been solved by deep learning approaches, but the machine reasoning is not generalized across a space of abstract environments and objects. The question is whether the abstract patterns to solve chess are also used in solving other puzzles. It seems a valid hypothesis that there is at least overlap in the use of abstract reasoning between these kinds of puzzles and synthesizing knowledge from abstract objects, such as in the synthesis of ideas and in solving problems by use of mathematics symbols and operations. Since we are capable of abstract thought, it is plausible that generating a set and distribution of general abstract tasks will lead to a working system that solves abstract problems in general.

If instead of a dynamic generation of three-dimensional worlds and objects, there was a vast and dynamic generation of worlds of abstract puzzles, for example, then the deep reinforcement learning approach could train on solving those abstract problems. The question is whether the distribution of these tasks is generalizable to unknown problems, those unrelated to this task distribution, and likewise the compressibility of the set of tasks. Since the advanced cognitive processes may involve a diverse set of dynamic representations, commonly referred to as mental representations, it is plausible that tasks are generalizable and may originate in the information systems of speech, vision, and memory. Therefore, the tasks may be expressed by different forms, although the lower dimensional representations are more generalizable, providing a better substrate for the recognition of patterns, and essential for any general process of abstract reasoning.