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Computational Neuroscience

Brains studied as dynamical information-processing systems using mathematical models that connect neural activity, computation, behavior and measurement.

neural data→model→computation→behavior→validation
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What can neural activity represent?

A representation claim links activity patterns to variables in the organism or environment and must specify how that link is tested.

01 · Tuning

Single units can vary systematically with features.

Tuning curves describe response structure without proving that one neuron alone carries the represented variable.

02 · Population code

Information can live across many units.

Distributed patterns can be more informative and robust than individual responses.

03 · Latent state

Observed activity may reflect lower-dimensional structure.

State-space models compress population activity into candidate dynamical variables.

04 · Readout

Representation requires an interpretable downstream use.

Decodability alone does not show that the nervous system itself uses the decoded variable.

Neural computation unfolds in time.

Recurrent interaction, integration and plasticity make temporal structure central to explanation.

01 · Integration

Evidence accumulates through changing states.

Integrator models connect noisy input to evolving decision variables.

02 · Attractors

Networks can stabilize recurring states.

Attractor models explain persistence, categorization and memory through dynamics rather than static storage.

03 · Oscillation

Rhythmic activity organizes timing.

Oscillations may coordinate communication, but frequency labels are not mechanisms by themselves.

04 · Plasticity

The system changes as it operates.

Learning rules alter weights, excitability and network organization across timescales.

Normative models ask what computation would make sense.

Bayesian, predictive and reinforcement-learning models specify computational objectives that can be compared with behavior and neural data.

01 · Bayesian inference

Combine prior expectations with evidence.

The framework separates what was expected from what the current signal contributes.

02 · Predictive processing

Use mismatch to update internal models.

Prediction-error accounts become informative only when predictions and update rules are specified.

03 · Reinforcement learning

Learn values from outcomes.

Prediction errors can update expected value and action policy over repeated experience.

04 · Decision variable

Compress evidence relevant to a choice.

Candidate neural decision signals must be distinguished from correlated motor or sensory activity.

Models compete through discriminating predictions.

Fitting existing data is weaker than predicting new conditions, perturbations or time courses.

01 · Parameter recovery

Can the data identify the model's parameters?

Poor identifiability can make precise-looking estimates meaningless.

02 · Out-of-sample prediction

Does the model generalize?

Held-out behavior and neural activity test whether fit exceeds memorization.

03 · Perturbation

Intervene on the system.

Stimulation, lesions or task changes can distinguish causal structure from correlation.

04 · Model comparison

Ask which alternative explains more with less.

Comparison should consider fit, complexity, robustness and whether models make genuinely different predictions.

A model is useful when it survives contact with data. Computational elegance is not enough; the model must clarify what is represented, how dynamics implement it, and which observations could distinguish it from alternatives.