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227-0395-00L 6 Credits BSC , MSC , WBZ D-HEST , D-MAVT , D-MATH , D-PHYS , D-INFK , D-ITET

Neural Systems

Lecturers & Examiners: Prof. Dr. Richard Hahnloser, Prof. Dr. Mehmet Fatih Yanik, Prof. Dr. Benjamin Grewe, Prof. Dr. Timothée Proix, Dr. Katharina Anna Wilmes
VVZ CR 2.0

Last Updated: 2026-06-03 00:14:06

Abstract

Neural Systems 2026 links biophysical neuron models to computation and behavior. It covers action potentials and dynamical systems, population and neural-mass models, memory and associative networks, birdsong and language learning, predictive coding, Bayesian inference and information theory, dimensionality reduction, intrinsic motivation, and neuroeconomic decision making.

Objective

- Explain ionic equilibrium potentials, membrane equivalent circuits, and conductance-based spiking (Hodgkin–Huxley) - Simulate neural dynamics with numerical schemes (e.g., Euler and Runge–Kutta) and interpret refractoriness, rebound spiking, and noise effects - Reduce high-dimensional neuron models to 1D/2D systems and analyze phase portraits, nullclines, fixed points, basins of attraction, and bistability - Classify neuronal excitability and oscillatory regimes via bifurcations (saddle-node, SNIC, super/subcritical Hopf) and relate them to type I/II neurons, integrators/resonators, and threshold manifolds - Connect single-neuron dynamics to population descriptions (Fokker–Planck intuition, mean-field and neural mass models) and analyze Wilson–Cowan excitatory–inhibitory circuits, hysteresis, and limit cycles - Describe synaptic potentials, rate nonlinearities, integrate-and-fire models, and rate-based network equations - Interpret classic behavioral memory phenomena (free recall, forgetting curves, recognition capacity, amnesia) and relate them to computational accounts - Understand associative memory and attractor-network ideas (Hopfield-type networks) and their link to retrieval dynamics and scaling laws - Explain birdsong development as sensorimotor learning: templates, auditory feedback, social context, and separation of phonology and syntax learning - Describe song-system circuitry (HVC, RA, LMAN, Area X, VTA) and experimental methods (aligned population recordings, lesions, cooling, stimulation, antidromic identification) - Formulate forward models, corollary discharge, and prediction-error signaling in sensory cortex; relate these to predictive coding principles - Apply Bayesian estimation concepts (priors/posteriors, Bayes’ rule, decision theory, MAP vs ML) and causal inference in multisensory and sensorimotor settings - Use estimation theory tools (bias–variance trade-off, Cramér–Rao bound, Fisher information) to assess limits of neural and behavioral estimation - Apply Shannon entropy, conditional entropy, and MDL/model selection to neural coding and to information in language and vocal sequences - Understand predictive coding as redundancy reduction (spatial/temporal decorrelation; receptive fields in retina/LGN/cortex; hierarchical predictive coding) - Compare intrinsic-motivation mechanisms for exploration (softmax, exploration bonuses, counters, E-values) and curiosity via forward–inverse models; diagnose the “noisy TV” failure mode - Distinguish curiosity from playfulness/manipulation drives; interpret sensory substitution and empowerment as mutual-information-based control - Relate economic choice behavior to utility theory, marginal utility, dopamine prediction errors, and cumulative prospect theory

Content

The course develops a multi-scale view of neural systems from membrane biophysics to cognition and decision making. It begins with ionic concentration gradients, Nernst potentials, and the membrane equivalent circuit, leading to conductance-based Hodgkin–Huxley dynamics and numerical simulation (Euler, Runge–Kutta). Reduced neuron models are derived and analyzed using dynamical-systems tools: phase portraits, fixed points, stability, basins of attraction, bistability, and bifurcations. Two-dimensional reductions introduce nullclines, limit cycles, and transitions to periodic spiking through saddle-node, SNIC, and Hopf bifurcations, explaining type I/type II excitability, integrator vs resonator behavior, resonance, rebound and inhibition-induced spiking, depolarization block, and the impact of noise near criticality. The course then bridges to population descriptions via density and mean-field ideas, neural mass models, and Wilson–Cowan excitatory–inhibitory circuits, including hysteresis and oscillations, and motivates large-scale brain simulations. Computational themes include synaptic potentials, firing-rate nonlinearities, integrate-and-fire and rate-based network models, and neural coding with tuning curves. Memory is covered through classic experimental findings (free recall scaling laws, forgetting, recognition capacity, clinical deficits) and computational accounts of associative retrieval and attractor-like network ideas (Hopfield-type networks). A major systems module uses birdsong as a model for speech learning: template formation, the role of auditory feedback and social context, performance-error measurement (including optimal-transport style matching), and the organization of the song system (HVC–RA motor pathway and AFP basal-ganglia loop with LMAN/Area X). Key experiments (population recordings aligned to song, lesions, cooling, stimulation, antidromic identification) motivate circuit functions such as timing sequences, variability injection, and reinforcement-driven plasticity, including dopaminergic performance-error/prediction-error signals from VTA to Area X and closed-loop optogenetic manipulations. Predictive models unify sensory and sensorimotor computation via forward models, corollary discharge, and prediction-error neurons, and extend to predictive coding as redundancy reduction in natural signals (spatial/temporal decorrelation; receptive fields in retina, LGN, and cortex; hierarchical predictive coding). Statistical foundations include Bayesian estimation and decision theory (priors/posteriors, MAP vs ML), causal inference in multisensory perception and vocal adaptation, estimation theory (bias–variance, Cramér–Rao), Fisher information and behavioral optimality, and Shannon entropy/conditional entropy and MDL with links to language modeling and information rates. Later modules connect these principles to modern learning and behavior: dimensionality reduction and representation learning, intrinsic motivation for exploration (softmax, bonuses, counters, E-values), curiosity via forward–inverse models and the noisy-TV problem, playfulness/manipulation drives revealed by sensory substitution, and empowerment as mutual-information-based control. The course concludes with neuroeconomics, relating utility and prospect theory to neural mechanisms and dopamine prediction-error responses.

General Information

Language
English
Levels
BSC , MSC , WBZ
Frequency
Yearly recurring

Examination

Type
session examination
Mode
written 120 minutes
Aids
none (closed book exam)
The student's final grade is determined by a weighted average: 75% from the written exam grade and 25% from the project/exercise grade (compulsory continuous performance assessment).The project/exercises will be graded individually. If no project/exercise is submitted, this will result in a grade of 1. The total project/exercise grade for the course will comprise a weighted average, i.e. if a project or an exercise spans two lectures it will be weighted double. Students repeating the course can decide at the beginning of the semester if they want to keep the previous grade of their continuous performance assessment (project& exercises).

Course Components

Type Title Time & Place Hours
lecture Neural Systems
  • Mon 09:15-11:00 (ML D 28)
2 h weekly
exercise Neural Systems
  • Mon 11:15-12:00 (ML D 28)
1 h weekly
independent project Neural Systems No time listed 1 h weekly

Offered In