Computational Neuroscience Cheat Sheet

The core ideas of Computational Neuroscience distilled into a single, scannable reference — perfect for review or quick lookup.

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Quick Reference

Hodgkin-Huxley Model

A mathematical model that describes how action potentials in neurons are initiated and propagated, using a set of nonlinear ordinary differential equations representing ionic conductances across the cell membrane.

Neural Coding

The study of how neurons represent and transmit information through patterns of electrical activity, including rate coding (average firing frequency) and temporal coding (precise spike timing).

Synaptic Plasticity and Hebbian Learning

The ability of synapses to strengthen or weaken over time in response to activity. Hebbian learning, summarized as 'neurons that fire together wire together,' describes how correlated pre- and post-synaptic activity strengthens the connection between them.

Attractor Networks

Recurrent neural network models in which stable patterns of activity (attractors) represent stored memories or decision states. The network dynamics cause neural activity to converge toward these stable states.

Population Coding

The representation of information by the joint activity of a group of neurons rather than by any single neuron. The stimulus is decoded from the combined firing pattern of the population.

Bayesian Brain Hypothesis

The theory that the brain performs approximate Bayesian inference, combining prior expectations with incoming sensory evidence to form probabilistic estimates of the state of the world.

Predictive Coding

A theoretical framework proposing that the brain continuously generates predictions about incoming sensory input, and that neural processing primarily involves computing and propagating prediction errors between hierarchical levels.

Integrate-and-Fire Neuron Model

A simplified neuron model in which incoming synaptic inputs are summed (integrated) over time, and when the membrane potential reaches a threshold, the neuron emits a spike and resets. It captures essential spiking dynamics while remaining computationally efficient.

Spike-Timing-Dependent Plasticity (STDP)

A biological learning rule in which the direction and magnitude of synaptic change depend on the precise timing relationship between pre- and post-synaptic spikes. If the presynaptic spike precedes the postsynaptic spike, the synapse strengthens; if the order is reversed, it weakens.

Reinforcement Learning in the Brain

The computational framework linking dopaminergic neuron activity to reward prediction errors, mirroring the temporal difference (TD) learning algorithm from machine learning. Dopamine signals reflect the difference between received and expected reward.

Key Terms at a Glance

Action Potential:A rapid, transient reversal of membrane potential that propagates along axons, serving as the fundamental unit of neural communication.

Attractor:A stable state or set of states toward which a dynamical system evolves over time, used to model memory and decision-making in neural networks.

Bayesian Inference:A statistical method that updates the probability of a hypothesis as new evidence becomes available, using Bayes' theorem.

Brain-Computer Interface:A device that records neural signals and translates them into commands for computers or prosthetic devices.

Cable Equation:A partial differential equation describing voltage spread along a passive neurite, derived from the electrical cable properties of dendrites and axons.

Computational Psychiatry:The application of computational modeling to understand and characterize psychiatric disorders as aberrations in neural computation.

Connectome:A comprehensive map of all neural connections in a nervous system, ranging from individual synapses to large-scale fiber tracts.

Dendrite:A branching extension of a neuron that receives synaptic input from other neurons and conducts signals toward the cell body.

Dynamical System:A mathematical framework describing how the state of a system evolves over time according to fixed rules, widely used to model neural circuit dynamics.

Firing Rate:The average number of action potentials a neuron produces per unit time, commonly measured in spikes per second (Hz).

Free Energy Principle:A theoretical framework proposing that biological systems minimize variational free energy, a quantity bounding the surprise of sensory observations.

Gain Function:The input-output relationship of a neuron or neural circuit, describing how the response magnitude changes with input intensity.

Hebbian Plasticity:A synaptic learning rule in which concurrent activity of pre- and post-synaptic neurons leads to strengthening of their connection.

Information Theory:A mathematical framework quantifying information content, entropy, and channel capacity, applied in neuroscience to measure neural coding efficiency.

Ion Channel:A transmembrane protein that allows specific ions to flow across the cell membrane, governing neuronal excitability and signal propagation.

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