Humans excel at learning abstract patterns across different sequences, filtering out irrelevant details, and transferring these generalized concepts to new sequences. In contrast, many sequence learning models lack the ability to abstract, which leads to memory inefficiency and poor transfer. We introduce a non-parametric hierarchical variable learning model (HVM) that learns chunks from sequences and abstracts contextually similar chunks as variables. HVM efficiently organizes memory while uncovering abstractions, leading to compact sequence representations. When learning on language datasets such as babyLM, HVM learns a more efficient dictionary than standard compression algorithms such as Lempel-Ziv. In a sequence recall task requiring the acquisition and transfer of variables embedded in sequences, we demonstrate HVM’s sequence likelihood correlates with human recall times. In contrast, large language models (LLMs) struggle to transfer abstract variables as effectively as humans. From HVM’s adjustable layer of abstraction, we demonstrate that the model realizes a precise trade-off between compression and generalization. Our work offers a cognitive model that captures the learning and transfer of abstract representations in human cognition and differentiates itself from LLMs.

Neural networks are often described as black boxes, reflecting the significant challenge of understanding their internal workings and interactions. We propose a different perspective that challenges the prevailing view: rather than being inscrutable, neural networks exhibit patterns in their raw population activity that mirror regularities in the training data. We refer to this as the \textit{Reflection Hypothesis} and provide evidence for this phenomenon in both simple recurrent neural networks (RNNs) and complex large language models (LLMs). Building on this insight, we propose to leverage cognitively-inspired methods of \textit{chunking} to segment high-dimensional neural population dynamics into interpretable units that reflect underlying concepts. We propose three methods to extract these emerging entities, complementing each other based on label availability and neural data dimensionality. Discrete sequence chunking (DSC) creates a dictionary of entities in a lower-dimensional neural space; population averaging (PA) extracts recurring entities that correspond to known labels; and unsupervised chunk discovery (UCD) can be used when labels are absent. We demonstrate the effectiveness of these methods in extracting entities across varying model sizes, ranging from inducing compositionality in RNNs to uncovering recurring neural population states in large language models with diverse architectures, and illustrate their advantage to other interpretability methods. Throughout, we observe a robust correspondence between the extracted entities and concrete or abstract concepts in the sequence. Artificially inducing the extracted entities in neural populations effectively alters the network's generation of associated concepts. Our work points to a new direction for interpretability, one that harnesses both cognitive principles and the structure of naturalistic data to reveal the hidden computations of complex learning systems, gradually transforming them from black boxes into systems we can begin to understand. Implementation and code are publicly available at _https://github.com/swu32/Chunk-Interpretability_

This paper deals with finite-time stabilization (FTS) of nonlinear systems subject to actuator saturation. We present an analytical method to design the finite-time controller such that the FTS of the system can be guaranteed in the presence of actuator saturation. Moreover, a certain interrelation among the saturation bound, the system structure, and the controller parameters is established. Based on such a relationship, the settling time (ST) and the domain of attraction (DA) can both be estimated in an easily verifiable manner, which are ignored in many existing results of actuator saturation. Moreover, it is shown that the parameter of the designed controller can provide a tradeoff between the estimations of the ST and the DA by adjusting the controller parameters. All the results are illustrated in simulations. Note to Practitioners—Actuator saturation, a phenomenon where the control input exceeds the limits of an actuator, plays a crucial role in control theory and its applications. In control systems, actuator saturation can lead to performance degradation, instability, and even system failure if not properly addressed, such as Chornobyl nuclear power plant accident and the YF-22 crash incident. Note that in the presence of actuator saturation, most existing results focus on Lyapunov stability or finite-time boundedness, which makes it challenging to guarantee that the system converges to equilibrium within a finite time. This paper was motivated to break through this bottleneck and solve the FTS problem. Unlike the existing saturation results, we first decompose the system based on controllability. Then a straightforward controller design is proposed for the controllable part, while constraints on the system structure are provided for the uncontrollable part. Based on such conditions, not only is the estimation of the DA easily obtained, but the corresponding ST estimation is also derived. The obtained results in this paper are of great significance for providing a more general and easily achievable design for saturated control input. And these results are applied to various industries, such as aerospace, automotive, mobile robotics technology, and industrial automation.

This paper investigates the problems of finite-time stabilization ( FTS) and finite-time contractive stabilization ( FTCS) for nonlinear systems by designing a novel class of hybrid control consisting of aperiodically intermittent control ( APIC) and impulsive control ( IC). Different from the single APIC, our proposed hybrid control specifically introduces IC on the intervals without control input in APIC. It shows that IC in hybrid control may not only flexibly shorten the length of the intervals with continuous control input, but also alleviate the design pressure of gain of APIC. Based on the hybrid control, some Lyapunov-based criteria are derived to guarantee the FTS and FTCS, where a potential relationship between system structure, APIC law, and impulse actions is established. Specifically, some linear matrix inequalities ( LMIs) based criteria are presented to design the hybrid control gains. As an application, the theoretical results are extended to the finite-time state estimation of complex networks involving the unavailable network states. With the available measurement outputs, the hybrid state estimator involving both APIC and IC is proposed. Finally, three numerical examples are provided to illustrate the effectiveness of our results.Note to Practitioners—Unlike the Lyapunov stability results, the transient performances described by FTS and FTCS can be quantitatively guaranteed in the finite-time sense and have better applicability for the practical engineering requirements. This paper was motivated to solve FTS and FTCS problems. To guarantee the FTS and FTCS, a novel class of hybrid control is designed, which integrates the advantages of APIC and IC. Compared with the single APIC, the introduction of IC may reduce the dependence on the continuous control input in APIC, which significantly reduces the energy consumption of communication. The introduction of IC can also alleviate the design pressure of APIC to some extent. Hence, some easy-checked FTS and FTCS criteria are presented based on the proposed hybrid control. In practical applications, the theoretical results are extended to investigate the finite-time state estimation of complex networks considering unavailable network states. Utilizing the available measurement outputs, the corresponding hybrid state estimator consisting of APIC and IC is constructed. Finally, note that the impulsive transmission of ball motion is considered to further illustrate the practicability of our proposed results. In the future work, our proposed hybrid control strategy can be applied in other practical projects, such as the finite-time control of omnidirectional mobile robot.

This article investigates the local exponential stabilization (LES) for a class of nonlinear systems involving unmeasurable states subject to actuator saturation, where a novel kind of impulsive observer-based saturated impulsive control (SIC) is proposed. Some sufficient criteria for LES are derived drawing on impulsive control theory and saturated control methods. In order to ensure LES under the dual complexity of unmeasurable states and actuator saturation, an improved set inclusion condition for the convex combination approach is put forward, under which the saturation nonlinearity including the observer state can be linearized. Moreover, a convex optimal algorithm is given to estimate the domain of attraction as large as possible. As an application, the proposed theoretical results are applied to leader–follower synchronization of complex networks involving unmeasurable states and actuator saturation. The corresponding synchronization impulsive observer-based SIC strategy is presented. Finally, the efficacy of the results is illustrated by the proposed two examples.

In the framework of input saturation, this article studies the problem of finite-time synchronization (FTS) of a class of complex dynamical networks. By designing different classes of saturated controllers, two types of FTS criteria, including leader-follower synchronization and leaderless synchronization, are presented, respectively. A potential relationship between the saturation structure, the settling time, and the domain of attraction is established, which is crucial to achieve FTS. It shows that the saturation structure not only affects the estimation of domain of attraction but also possibly changes the settling time for FTS. Two numerical examples are presented to illustrate the effectiveness of the proposed results.

Finite-time stability (FTS) for nonlinear systems with delayed impulses is characterized in terms of Lyapunov method, where time delays in impulses occur between two consecutive impulse instants. Some Lyapunov-based sufficient conditions are presented to guarantee FTS, where a relationship among the system structure, the delayed impulses, and the settling time is established. For stabilizing impulses with time delays, the design of impulse time sequence is proposed, under which the estimation of settling time relying on the impulse jump, the time delays, and the initial condition is obtained. For destabilizing impulses with time delays, some constraints of the impulse time sequence affected by two different size scopes of time delays are put forward. Our results show that delayed impulses may contribute to or destroy the FTS and lead to different estimations of the settling time. The analysis is illustrated by two numerical examples.

From learning to play the piano to speaking a new language, reusing and recombining previously acquired representations enables us to master complex skills and easily adapt to new environments. Inspired by the Gestalt principle of \textit{grouping by proximity} and theories of chunking in cognitive science, we propose a hierarchical chunking model (HCM). HCM learns representations from non-i.i.d. sequential data from the ground up by first discovering the minimal atomic sequential units as chunks. As learning progresses, a hierarchy of chunk representations is acquired by chunking previously learned representations into more complex representations guided by sequential dependence. We provide learning guarantees on an idealized version of HCM, and demonstrate that HCM learns meaningful and interpretable representations in a human-like fashion. Our model can be extended to learn visual, temporal, and visual-temporal chunks. The interpretability of the learned chunks can be used to assess transfer or interference when the environment changes. Finally, in an fMRI dataset, we demonstrate that HCM learns interpretable chunks of functional coactivation regions and hierarchical modular and sub-modular structures confirmed by the neuroscientific literature. Taken together, our results show how cognitive science in general and theories of chunking in particular can inform novel and more interpretable approaches to representation learning.