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Sequence memory is an essential attribute of natural and artificial intelligence that enables agents to encode, store, and retrieve complex sequences of stimuli and actions. Computational models of sequence memory have been proposed where…

Forgetting is often seen as an unwanted characteristic in both human and machine learning. However, we propose that forgetting can in fact be favorable to learning. We introduce "forget-and-relearn" as a powerful paradigm for shaping the…

We analyse large deviations of time-averaged quantities in stochastic processes with long-range memory, where the dynamics at time t depends itself on the value q_t of the time-averaged quantity. First we consider the elephant random walk…

A detailed analysis of three pendular motion models is presented. Inertial effects, self-oscillation, and memory, together with non-constant moment of inertia, hysteresis and negative damping are shown to be required for the comprehensive…

Structured learning is appropriate when predicting structured outputs such as trees, graphs, or sequences. Most prior work requires the training set to consist of complete trees, graphs or sequences. Specifying such detailed ground truth…

Fractional order differential and difference equations are used to model systems with memory. Variable order fractional equations are proposed to model systems where the memory changes in time. We investigate stability conditions for linear…

Continual learning is considered a promising step towards next-generation Artificial Intelligence (AI), where deep neural networks (DNNs) make decisions by continuously learning a sequence of different tasks akin to human learning…

There is an increasing need of continual learning in dynamic systems, such as the self-driving vehicle, the surveillance drone, and the robotic system. Such a system requires learning from the data stream, training the model to preserve…

A mass of traces of human activities show diverse dynamic patterns. In this paper, we comprehensively investigate the dynamic pattern of human attention defined by the quantity of interests on subdisciplines in an online academic…

Most of mathematic forgetting curve models fit well with the forgetting data under the learning condition of one time rather than repeated. In the paper, a convolution model of forgetting curve is proposed to simulate the memory process…

Motivated by modern observational studies, we introduce a class of functional models that expands nested and crossed designs. These models account for the natural inheritance of correlation structure from sampling design in studies where…

Lifelong machine learning or continual learning models attempt to learn incrementally by accumulating knowledge across a sequence of tasks. Therefore, these models learn better and faster. They are used in various intelligent systems that…

In many daily tasks we make multiple decisions before reaching a goal. In order to learn such sequences of decisions, a mechanism to link earlier actions to later reward is necessary. Reinforcement learning theory suggests two classes of…

In a sequential decision-making problem, the information structure is the description of how events in the system occurring at different points in time affect each other. Classical models of reinforcement learning (e.g., MDPs, POMDPs)…

Identifying and quantifying memory are often critical steps in developing a mechanistic understanding of stochastic processes. These are particularly challenging and necessary when exploring processes that exhibit long-range correlations.…

Time-dependent data-generating distributions have proven to be difficult for gradient-based training of neural networks, as the greedy updates result in catastrophic forgetting of previously learned knowledge. Despite the progress in the…

Temporal causal representation learning methods assume that causal mechanisms switch instantaneously between discrete domains, yet real-world systems often exhibit continuous mechanism transitions. For example, a vehicle's dynamics evolve…

Lifelong learning occurs on timescales ranging from minutes to decades. People can lose themselves in a new skill, practicing for hours until exhausted. And they can pursue mastery over days or decades, perhaps abandoning old skills…

Artificial autonomous agents and robots interacting in complex environments are required to continually acquire and fine-tune knowledge over sustained periods of time. The ability to learn from continuous streams of information is referred…

Friction is a phenomenon that manifests across all spatial and temporal scales, from the molecular to the macroscopic scale. It describes the dissipation of energy from the motion of particles or abstract reaction coordinates and arises in…