1-Introduction

John Hopfield and Geoffrey Hinton

for foundational discoveries and inventions that enable machine learning with artificial neural networks

• combines biomedical experiments with theoretical models

• opens new avenues for scientific insights and technological applications

• researchers with different backgrounds identify principles of brain functions and translate them into mathematical representation

how structure and function of the brain can be studied on different levels

SPATIAL:

meters (entire body), cm (whole brain), mm (brain regions), micrometer (individual neurons), nanometer (cellular-level interactions and protein structures)

TEMPORAL:

years (aging), days (behavioral patterns), hours (learning/memory formation), minutes (synaptic plasticity - strengthening/weakening of synapses), seconds (neural signaling), milliseconds (actions potentials), microseconds (synaptic vesicle release), nanoseconds (molecular interactions), pikoseconds (extremly rapid molecular changes)

More than 100.000.000.000 neurons

More than 1.000.000.000.000.000 synapses (constantly added and removed)

Sound amplitude and temporal structure

Variability - ‘to spike or not to spike - and when’

introduces randomness into neural encoding process (action potential)

• Time code

  temporal strcuture matters

  —> information carried by exact timing and pattern of spike

  higer firing rate

• Frequency code

  number of action potentials per unit time

  —> information carried by overall spike frequency

  smaller firing rate

• Large system: more than 100 billion neurons (>10¹¹)

• densely connected: over one quadrillion connections between neurons (>10¹⁵)

Complex Properties:

• Massive feedback: neurons constantly send information back and forth —> feedback loops

• Strong longlinearities: relationship btw input and output not straightforward —> small changes can lead to large effects

• Collective Phenomena: neurons work together as networks —> cant understand behaviour by studying individual neurons alone

Many structural levels: brain operates across multiple scales (tiny ion channels to entire brain)

Many temporal scales: submilliseconds ionic changes to decade-long learning and memory develeopment

Human intuition fails —> mathematical modelling essential to analyze, simulate and understand brain functions

1. Detailed Compartmental Models:

   —> capture full anatomical and biophysical details of neuron

   —> dividing in multiple compartments representing dendrites, axons, soma

2. Reduced Compartmental Models:

   —> simplify neuron in smaller number of compartments

   —> retaining critical functional elements like dendritic integration or axonal output

3. Single-Compartment Models:

   —> models neuron as single electrical circuit, summarizing behaviour with key properties like ion channels

4. Cascade Models:

   —> abstract models that describe neuronal input-output relationships using nonlinear transformations

5. Black-box Models:

   —> focus only on input-output relationships without considering biological mechanisms

no ‘correct’ model for neurons, choice depends on research quesition and computational resources

Biophysically Realistic Models:

+ provide detailed and accurate representations

- require computationally expensive simulations

- highly parameter sensitive

Abstract Models:

+ facilitate mathematical understanding

+ more efficient for larger network simulations

- risk being oversimplified

- potentially missing critical biological details

instead of testing a hypotheses (true/false) —> experiments now designed to ensure predicitive models relaibly estimate missing data

—> solution to measure movement distances and add a metric to spatial maps (physical space) in hippocampus

Grid cells = activity patterns

= type of neuron involved in spatial navigation and encoding

—> play central role in forming spatial map of environment

Key features:

• Grid Cell Activity:

  firing in hexagonal patterns —> forming grid-like structures

• Neighboring Cell Properties:

  • Similar spatial frequency (scale of grid patterns similar)

  • Similar orientation (alignment of grid consistent)

  • Different spatial phases (patterns are offset related to each other)

• Grid scale increases from dorsal to ventral areas

grid cells share consistent orientation and scale, but their spatial phase differencese allow more environmental coverage

BUT: single grid cell cannot represent spatial location, bc it lacks necessary resolution and diversity in grid scales

Question: Why are axes aligned within module, when reduces models capacity to encode spatial location

= encode specific locations in environment with high precision

Grid cells encode broader spatial maps AND hexagonl patterns enable more general spatial navigation

Time coding:

encodes information in precise timing of action potentials (spikes)

—> temporal structure carries information

Frequency coding:

encodes information in rate of action potentials over time

—> overeall firing rate represents strength/intensity of stimiulus

• Hexagonal firing pattern

• Aligned orientation: neighboring grid cells within module share same orientation of hexagonal firing grids

• Similar grid scale: grid cells within module have similar spatial scales (distnace btw grid nodes)

• Spatial phase shifts: neighboring grid cells have different spatial phases —> hexagonal grids offset relative to each other —> broad spatial coverage