Editing Openai/69371729-f090-8004-b69b-aa9f25ca0b40 (section)

== gpt-5-1 ==
=== User: Matrix multiplication in neural networks does not use the hebbian "fire together wire together". ===
Matrix multiplication in neural networks does not use the hebbian "fire together wire together". Correct? Tgere can be abundant calculations within matrices

=== Assistant: Short answer: yes, that’s basically correct—standard matrix multiplication in neural networks is not Hebbian learning. ===
Short answer: yes, that’s basically correct—standard matrix multiplication in neural networks is not Hebbian learning.

Let’s unpack it a bit, because there’s an important subtlety.

==== When a neural network computes ====

y=Wx\mathbf{y} = \mathbf{W}\mathbf{x}y=Wx
that’s just inference:
* x\mathbf{x}x: input activations
* W\mathbf{W}W: weights
* y\mathbf{y}y: output activations

This step is pure calculation. There is no learning rule here at all. You’re just combining signals efficiently using linear algebra. So yes, you can have tons of internal matrix calculations without any Hebbian principle involved.

==== Hebbian learning is a weight update rule, not a forward computation: ====

: 

In math form (classic version):

Δwij∝xiyj\Delta w_{ij} \propto x_i y_jΔwij∝xiyj
Key point:
* Hebbian learning updates weights based on correlated activity
* It does not describe how activations are combined during inference

So Hebbian learning answers:

: 

Matrix multiplication answers:

: 

Different questions, different roles.

==== Most modern NNs use: ====
* Matrix multiplication for forward passes ✅
* Backpropagation + gradient descent for learning ✅
* Not Hebbian learning in the strict biological sense ❌

Backprop requires:
* Global error signals
* Weight symmetry (or approximations)
* Credit assignment across layers

All of which violate classic Hebbian locality.

==== You can rewrite parts of backprop so that individual weight updates look Hebbian-like: ====

Δwij∝(errorj)⋅(xi)\Delta w_{ij} \propto (\text{error}_j) \cdot (x_i)Δwij∝(errorj)⋅(xi)
That resembles Hebbian correlation, but the error term is non-local, so it’s not truly Hebbian.

This is why you’ll sometimes hear:

: 

Which is fair, but only at an abstract level.

==== - ✅ Matrix multiplication ≠ Hebbian learning ====
* ✅ You can have massive matrix computations with no learning rule at all
* ✅ Hebbian learning is about how weights change, not how activations are computed
* ✅ Modern deep learning mostly abandoned Hebb in favor of backprop

If you want, I can also explain:
* Why Hebbian learning struggles with deep networks
* How biologically plausible learning tries to replace backprop
* Or how STDP relates to all this

Just say the word 👀