Parametric models deployed in non-stationary environments degrade as the underlying data distribution evolves over time (a phenomenon known as temporal domain drift). In the current work, we present KOMET (Koopman Operator identification of Model parameter Evolution under Temporal drift), a model-agnostic, data-driven framework that treats the sequence of trained parameter vectors as the trajectory of a nonlinear dynamical system and identifies its governing linear operator via Extended Dynamic Mode Decomposition (EDMD). A warm-start sequential training protocol enforces parameter-trajectory smoothness, and a Fourier-augmented observable dictionary exploits the periodic structure inherent in many real-world distribution drifts. Once identified, KOMET's Koopman operator predicts future parameter trajectories autonomously, without access to future labeled data, enabling zero-retraining adaptation at deployment. Evaluated on six datasets spanning rotating, oscillating, and expanding distribution geometries, KOMET achieves mean autonomous-rollout accuracies between 0.981 and 1.000 over 100 held-out time steps. Spectral and coupling analyses further reveal interpretable dynamical structure consistent with the geometry of the drifting decision boundary.

Neural Information Processing Systems http://nips.cc/

That is,we optimize for theα and β hyperparameters while fixing theσ to a negligible amount (σ = 2 32 specifically).

Our method efficiently infers the trial-to-trial changes inananimal'spolicy,and decomposes those changes into a learning component and a noise component.

A vast swath of modern neuroscience research requires training animals to perform specific tasks.

We calculate the AIC for each of the 16 models fit.

Learning and memory in the brain are implemented by complex, time-varying changes in neural circuitry. The computational rules according to which synaptic weights change over time are the subject of much research, and are not precisely understood. Until recently, limitations in experimental methods have made it challenging to test hypotheses about synaptic plasticity on a large scale. However, as such data become available and these barriers are lifted, it becomes necessary to develop analysis techniques to validate plasticity models. Here, we present a highly extensible framework for modeling arbitrary synaptic plasticity rules on spike train data in populations of interconnected neurons. We treat synaptic weights as a (potentially nonlinear) dynamical system embedded in a fully-Bayesian generalized linear model (GLM). In addition, we provide an algorithm for inferring synaptic weight trajectories alongside the parameters of the GLM and of the learning rules. Using this method, we perform model comparison of two proposed variants of the well-known spike-timing-dependent plasticity (STDP) rule, where nonlinear effects play a substantial role. On synthetic data generated from the biophysical simulator NEURON, we show that we can recover the weight trajectories, the pattern of connectivity, and the underlying learning rules.

Understanding how animals learn is a central challenge in neuroscience, with growing relevance to the development of animal- or human-aligned artificial intelligence. However, most existing approaches assume specific parametric forms for the learning rule (e.g., Q-learning, policy gradient) or are limited to simplified settings like bandit tasks, which do not involve learning a new input-output mapping from scratch. In contrast, animals must often learn new behaviors de novo, which poses a rich challenge for learning-rule inference. We target this problem by inferring learning rules directly from animal decision-making data during de novo task learning, a setting that requires models flexible enough to capture suboptimality, history dependence, and rich external stimulus integration without strong structural priors. We first propose a nonparametric framework that parameterizes the per-trial update of policy weights with a deep neural network (DNN), and validate it by recovering ground-truth rules in simulation. We then extend to a recurrent variant (RNN) that captures non-Markovian dynamics by allowing updates to depend on trial history. Applied to a large behavioral dataset of mice learning a sensory decision-making task over multiple weeks, our models improved predictions on held-out data. The inferred rules revealed asymmetric updates after correct versus error trials and history dependence, consistent with non-Markovian learning. Overall, these results introduce a flexible framework for inferring biological learning rules from behavioral data in de novo learning tasks, providing insights to inform experimental training protocols and the development of behavioral digital twins.

Despite explosive expansion of artificial intelligence based on artificial neural networks (ANNs), these are employed as "black boxes'', as it is unclear how, during learning, they form memories or develop unwanted features, including spurious memories and catastrophic forgetting. Much research is available on isolated aspects of learning ANNs, but due to their high dimensionality and non-linearity, their comprehensive analysis remains a challenge. In ANNs, knowledge is thought to reside in connection weights or in attractor basins, but these two paradigms are not linked explicitly. Here we comprehensively analyse mechanisms of memory formation in an 81-neuron Hopfield network undergoing Hebbian learning by revealing bifurcations leading to formation and destruction of attractors and their basin boundaries. We show that, by affecting evolution of connection weights, the applied stimuli induce a pitchfork and then a cascade of saddle-node bifurcations creating new attractors with their basins that can code true or spurious memories, and an abrupt disappearance of old memories (catastrophic forgetting). With successful learning, new categories are represented by the basins of newly born point attractors, and their boundaries by the stable manifolds of new saddles. With this, memorisation and forgetting represent two manifestations of the same mechanism. Our strategy to analyse high-dimensional learning ANNs is universal and applicable to recurrent ANNs of any form. The demonstrated mechanisms of memory formation and of catastrophic forgetting shed light on the operation of a wider class of recurrent ANNs and could aid the development of approaches to mitigate their flaws.