The modern connectivist framing of neural computation emphasizes the primacy of synaptic communication at the risk of neglecting the influence of the surrounding neuromodulatory environment --- a neuron's 'biophysical context.' Decades of experimental work has established two views of neuromodulatory (NMs) influence: 1) NMs significantly alter circuit dynamics and 2) NMs gate synaptic plasticity, acting as a 'third factor' in learning. Here, we unify these perspectives, proposing that neuromodulation via volume transmission implements a powerful computational principle: context factorization. We derive an endogenously neuromodulated Recurrent Neural Network (e-nmRNN) from a rate reduction of NM release, showing how NM concentrations dynamically factorize network connectivity. This framework reveals how multiplicative NM gating distinctly influences dynamical regimes compared to additive input. Crucially, this context factorization enables targeted online credit assignment: learning rules derived for the e-nmRNN are naturally gated by NM concentrations, localizing updates to relevant contexts. We demonstrate that e-nmRNN dynamics can learn to approximate gradient descent, facilitating rapid in-context adaptation akin to meta-learning. Empirically, e-nmRNNs achieve strong compositional generalization in sequence-to-sequence tasks, outperforming baselines and exhibiting greater hyperparameter robustness. Furthermore, when trained on complex multitasking benchmarks, e-nmRNNs develop emergent properties mirroring biological observations, including modularity, cell-type specialization based on NM release, and distinct neuromodulatory timescales encoding task context. The model's interpretability allows us to reverse engineer these emergent structures. Notably, in reinforcement learning tasks, the e-nmRNN learns to encode context and signals like Reward Prediction Error (RPE) within its neuromodulator dynamics, demonstrating a mechanism for RPE-gated online credit assignment essential for learning how to learn. By bridging biophysical mechanisms with computational principles and empirical validation, our work presents e-nmRNNs as a performant, interpretable model for understanding the computational role of neuromodulation in flexible and compositional learning.

Recent advances in techniques for monitoring and perturbing neural populations have greatly enhanced our ability to study circuits in the brain. In particular, two-photon holographic optogenetics now enables precise photostimulation of experimenter-specified groups of individual neurons, while simultaneous two-photon calcium imaging enables the measurement of ongoing and induced activity across the neural population. Despite the enormous space of potential photostimulation patterns and the time-consuming nature of photostimulation experiments, very little algorithmic work has been done to determine the most effective photostimulation patterns for identifying the neural population dynamics. Here, we develop methods to efficiently select which neurons to stimulate such that the resulting neural responses will best inform a dynamical model of the neural population activity. Using neural population responses to photostimulation in mouse motor cortex, we demonstrate the efficacy of a low-rank linear dynamical systems model, and develop an active learning procedure which takes advantage of low-rank structure to determine informative photostimulation patterns. We demonstrate our approach on both real and synthetic data, obtaining in some cases as much as a two-fold reduction in the amount of data required to reach a given predictive power. Our active stimulation design method is based on a novel active learning procedure for low-rank regression, which may be of independent interest.