Abstract We derive a lower bound on the error of parameter inference from invasive measurement in recurrent adaptive networks with online plasticity. The bound decomposes into a variance contribution and a bias contribution, arising from physically distinct components of measurement back-action: stochastic fluctuations injected into the state dynamics and the systematic shift of the state operating point under repeated observation. Under generic measurement families, the bias term and the measurement-dependent component of the variance channel increase with measurement precision through distinct mechanisms and cannot generally be traded off against each other. Near marginal stability, both contributions are amplified by resolvent operators that diverge as their corresponding spectral radii approach unity, so that the bound becomes more restrictive in the regime in which cortical circuits are believed to operate. Evaluated at biologically realistic scale, the bound implies that the per-neuron disturbance required for noninvasiveness falls orders of magnitude below ambient biological fluctuations, making the constraint plausibly operative for standard invasive measurement modalities. Beyond the stationary regime, a finite-time analysis converts the bound into an experimentally relevant timescale, distinguishing the ballistic accumulation of measurement-induced bias from intrinsic representational drift and yielding testable temporal and geometric signatures for optogenetic and chronic-recording protocols. The result identifies a structural limit on parameter inference in adaptive recurrent systems, induced by the dynamical coupling between measurement, recurrent amplification, and online plasticity.
Abstract Exact gaussian process (GP) inference scales cubically in data size, posing a severe bottleneck for applications that require repeated GP kernel inversions, such as time series models like gaussian process factor analysis (GPFA), where data size can vary across trials. To address this, we introduce an algorithmic variant of GPFA that shares computations across trials of different lengths. It does so by leveraging block-matrix identities to incrementally reuse inverses and determinants from smaller GP kernel matrices to accelerate computations on larger ones without sacrificing numerical precision. By casting successive trial-length extensions as Schur-complement updates, our method reduces the cost of each new inversion to depend only on the size difference between matrices. We demonstrate that this approach yields more than twofold speed-ups over direct and persymmetric inversion baselines on both synthetic data sets and data from neural recordings. In an additional comparison to sparse inducing-point GPFA, sparse inference reduced inference time for small inducing sets at the expense of worse model fits, while optimizing inducing locations was slower than our exact GPFA variant when the optimization cost was included. We also provide a scikit-learn–compatible Python GPFA package, BlockInverseGPFA, and introduce a variance–explained metric for model evaluation.
Abstract Positive psychology interventions, such as gratitude practice, aim to improve well-being through simple techniques. One widely used practice involves reflecting daily on three things one is grateful for. Although this practice is promising, empirical evidence for its efficacy is mixed, and the underlying mechanisms remain poorly understood. Here, we develop a computational model of gratitude practice to gain insight into the potential mechanisms of the practice. Employing the active inference framework, we present three simulation studies. First, we formalize gratitude practice as the deliberate allocation of high precision (i.e., attention) to three positive observations. This allows us to show how agents form beliefs about their environment and how these beliefs shift following gratitude practice. Second, to link the model to empirical findings, we simulate an optimism assessment task before and after the intervention, demonstrating an increase in optimism following gratitude practice. Finally, we simulate an abstract proof-of-concept task inspired by the Yarbus paradigm to model attention and find that gratitude practice may affect habitual attention patterns, where agents attend to positive elements over neutral or negative elements in a painting. Our model provides a conceptual understanding of gratitude practice that can be used in future research to gain insights into who may benefit from gratitude practice.
This article presents a cortically motivated framework for geometry-aware sparse reservoir computing with efficient online readout adaptation. The architecture is based on FitzHugh-Nagumo units coupled through sparse connectivity motifs informed by cortical statistics (reciprocity, triadic closure, and Dale’s law), resulting in a structured and biologically plausible recurrent matrix. The readout weights are trained by means of an anchor-proximal ridge objective applied to streaming time windows, ensuring temporally stable online learning with a low memory footprint. It presents the results of numerical experiments on a temporal decision-making benchmark and an image-based long-range segmentation task. The proposed sparse reservoir, combined with the windowed proximal readout, is shown to achieve competitive accuracy while substantially reducing recurrent and state-storage requirements. A favorable trade-off of biological plausibility, predictive performance, and computational efficiency is thereby demonstrated.
A key challenge in biophysically detailed modeling is determining functionally effective synaptic weights. Here, we introduce a dendritic voltage surrogate that couples passive dendritic transfer impedances with the exact active currents computed from the original model, yielding explicit, differentiable approximations of membrane voltage. The resulting gradients can achieve effective synaptic learning in active dendrites under transient conditions. In detailed pyramidal neuron models with somatic bursting and dendritic calcium plateau, the surrogate enables reconstruction of subthreshold and bursting membrane potentials and supports supervised fitting of target responses. At network scale, we train a detailed 136-neuron model of Caenorhabditis elegans to match an experimentally measured whole-brain correlation matrix using a multi-GPU framework. Our approach links interpretable dendritic computation with scalable optimization, providing an effective synaptic learning framework for detailed neurons and networks.
