Recently, SyncMap pioneered an approach to learn complex structures from sequences as well as adapt to any changes in underlying structures. This is achieved by using only nonlinear dynamical equations inspired by neuron group behaviors, i.e., without 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 negative and positive 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 dynamically changing 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 3 out of 4 scenarios, suggesting that symmetrical activation plays a critical role in uncovering topological structures and even hierarchies encoded in temporal data.

Self-organization is ubiquitous in nature and mind. However, machine learning and theories of cognition still barely touch the subject. The hurdle is that general patterns are difficult to define in terms of dynamical equations and designing a system that could learn by reordering itself is still to be seen. Here, we propose a learning system, where patterns are defined within the realm of nonlinear dynamics with positive and negative feedback loops, allowing attractor-repeller pairs to emerge for each pattern observed. Experiments reveal that such a system can map temporal to spatial correlation, enabling hierarchical structures to be learned from sequential data. The results are accurate enough to surpass state-of-the-art unsupervised learning algorithms in seven out of eight experiments as well as two real-world problems. Interestingly, the dynamic nature of the system makes it inherently adaptive, giving rise to phenomena similar to phase transitions in chemistry/thermodynamics when the input structure changes. Thus, the work here sheds light on how self-organization can allow for pattern recognition and hints at how intelligent behavior might emerge from simple dynamic equations without any objective/loss function.

Humans possess an inherent ability to chunk sequences into their constituent parts. In fact, this ability is thought to bootstrap language skills to the learning of image patterns which might be a key to a more animal-like type of intelligence. Here, we propose a continual generalization of the chunking problem (an unsupervised problem), encompassing fixed and probabilistic chunks, discovery of temporal and causal structures and their continual variations. Additionally, we propose an algorithm called SyncMap that can learn and adapt to changes in the problem by creating a dynamic map which preserves the correlation between variables. Results of SyncMap suggest that the proposed algorithm learn near optimal solutions, despite the presence of many types of structures and their continual variation. When compared to Word2vec, PARSER and MRIL, SyncMap surpasses or ties with the best algorithm on $77\%$ of the scenarios while being the second best in the remaing $23\%$.