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 among matrices. We demonstrate that this approach yields more than two times 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.
Sensory pathways differ widely across species and modalities in anatomy and function. Yet many solve variants of the same ancient, pervasive problem: quickly detecting meaningful changes in the world. Sometimes animals need to make these detections from noisy signals with millisecond precision to survive. We suggest how a single spiking neuron can address this selection pressure for quick detection. We present a simple relationship linking neural voltage dynamics to online hypothesis testing that we call the time constant rule. Assume that a neuron's membrane time constant equals the inverse of a change in its input rate. We show that this rule is then necessary and sufficient for its subthreshold membrane potential to represent a likelihood ratio of that rate change. Thresholding that likelihood ratio makes the neuron an online detector of input rate increases and, by extension, stimulus onset when rapid reaction is required. We tested the time constant rule by reanalyzing published recordings from eight second-order sensory neurons spanning olfaction, mechanoreception, electroreception, and audition, across both insects and vertebrates. In all cases, the measured membrane time constants were consistent with the predicted inverse relationship. These examples are intended as cross-system and cross-phyla consistency checks rather than a population-level validation study. When the time constant rule holds, it yields a direct and intuitive interpretation of neural computation. A neuron's voltage is an online likelihood ratio: its time constant sets the decay of statistical evidence, its threshold is a decision line, and each output spike is a time-stamped declaration that its input statistics have changed. The rule links membrane biophysics with the statistical computation and ecological function of a neuron. Its falsifiability invites direct experimental tests to determine whether it extends more broadly across sensory pathways and neuron classes.
Hyperdimensional computing (HDC) is gaining popularity as a lightweight alternative computing paradigm, where data are represented as long vectors (commonly of dimension 10,000) and processed using simple algebraic operations. In the two-part HDC classification pipeline, data are first encoded as a high-dimensional representation, then classified based on their similarity to a set of prototypes. Conventionally, the prototypes are trained while the encoder remains static. In this work, we propose a method of training a binary/bipolar HDC encoder, relying exclusively on native HDC integer and binary operations. Evaluations with our method show an average accuracy improvement of 2.13% over the untrained encoder on several classification data sets commonly used in HDC research, with no increase in model size or inference complexity.
