many updates from Jang et al paper (updated with comments) including BTSP update in syn. plast; added reservoir computing, stability-plasticity dilemma.

Author: rcoreilly

citedrefs.json

@@ -41,7 +41,7 @@ Another linear algebra framing of this operation is in terms of the synaptic wei
 
 Furthermore, this basis space can help with the [[curse of dimensionality]] by using fewer basis vectors to capture most of the important dimensions of variance, relative to the high dimensionality of the original space. For example, original dimensions that are largely redundant (e.g., the shapes of the eyes and the mouth used in expressing different emotions) can be combined together into one basis vector.
 
-## Eigenvectors and singular value decomposition
+## Eigenvectors
 
 The process of [[principal components analysis]] (PCA) provides a way of selecting a new set of basis vectors to project the input space into, based on the linear algebra process of **eigenvector** decomposition, where the eigenvector is a special vector that keeps pointing in the same direction when multiplied by the matrix that it is an eigenvector of:
 

content/jang-et-al-2026.md

@@ -4,6 +4,7 @@ Title = "This is how the Neocortex Learns"
 Authors = "Randall C. O'Reilly"
 Affiliations = "Astera Institute, Department of Psychology and Center for Neuroscience, University of California Davis"
 Abstract = "A sufficient account of how the neocortex learns must meet three criteria: 1. Computationally, it must approximate a powerful, general-purpose learning algorithm known to scale to human-level intelligence; 2. Algorithmically, it must be implementable using known, well-established neural circuits within the neocortex and associated brain structures; 3. Implementationally, there must be a detailed account for how all of the algorithmic mechanisms actually function at a neurochemical level. At present, there is only one framework that meets all of these criteria: error-driven predictive learning via temporal derivatives, driven by corticothalamic circuits, based on competitive kinase synaptic plasticity induction mechanisms. This has been implemented in the Axon neural simulation framework using spiking neurons, and demonstrated to learn across a wide range of challenging cognitively-motivated tasks."
+Reference = "Preprint: O'Reilly, R.C. (2026). This is how the Neocortex Learns. bioRxiv. <a href=\"https://doi.org/10.111/ejn.13949\">doi:10.11/ejn.13949</a>."
 Date = "2026-05-16"
 Categories = ["Papers"]
 bibfile = "ccnlab.json"

content/linear-algebra.md

@@ -11,9 +11,13 @@ There have been various attempts to understand at a more abstract, principled le
 
 A useful starting point for understanding these differences is in terms of [[linear algebra#non-negative factorization]] vs. sign-unconstrained factorization (i.e., principal components analysis or PCA). Read the section at the above link (and the earlier part of that page on PCA if otherwise unfamiliar with that) before proceeding.
 
-In short, classical probabilities are like non-negative factors: they can only be 0 or positive, and thus they define a purely _additive_ set of factors, which must ultimately sum to 1 across all relevant possibilities. As with the case of non-negative factorization, these probabilities align directly and uniquely with the discrete, mutually-exclusive outcomes that they are associated with (heads vs. tails in a coin flip, for example).
+In short, classical probabilities are like non-negative factors (see Kolmogorov's [probability axioms](https://en.wikipedia.org/wiki/Probability_axioms)): they can only be 0 or positive, and thus they define a purely _additive_ set of factors, which must ultimately sum to 1 across all relevant possibilities. As with the case of non-negative factorization, these probabilities align directly and uniquely with the discrete, _mutually-exclusive_ outcomes that they are associated with (heads vs. tails in a coin flip, for example).
 
-By contrast, quantum probabilities are defined in terms of a [Hilbert space](https://www.intoquantum.pub/p/an-introduction-to-the-hilbert-space) in terms of orthogonal basis vectors, with probability amplitudes that are _complex_ numbers (i.e., a combination of a real and an imaginary number). To understand this, we need a brief digression on complex numbers.
+By contrast, quantum probabilities are defined in terms of a [Hilbert space](https://www.intoquantum.pub/p/an-introduction-to-the-hilbert-space) in terms of orthogonal basis vectors, with probability amplitudes that are _complex_ numbers (i.e., a combination of a real and an imaginary number). The fact that complex numbers are two-dimensional (2D) entities mathematically implies that they are in general **non-commutative**, for the same reason that matrix multiplication is non-commutative: values can "mix" across dimensions, and the order of these mixing processes actually _matters_: $AB \neq BA$ in general.
+
+Physically, this non-commutative property of quantum physics is associated with Heisenberg's _uncertainty principle_: measuring information along one dimension (e.g., position) necessarily makes the other dimension (e.g., momentum or velocity) _less_ certain. In other words, measuring something about a quantum system necessarily _changes_ the system being measured, so that the _order_ of such measurement operations matters (and commutativity is all about the order of such operations).
+
+To understand all this more concretely, we need a brief digression on complex numbers.
 
 The imaginary number: $i = \sqrt{-1}$ seems very mysterious, but really it is just an efficient way to represent an orthogonal additional dimension relative to real numbers, thereby providing an efficient way to represent a 2D value with a complex number (real + imaginary). Furthermore, because of the -1 in there, complex numbers "intrinsically" have positive and negative components, and thus violate the non-negativity constraint.