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<!DOCTYPE html>
<html lang="en">
<head>
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<title>Zeitgeist - ghost in the shell with BLUECOW009</title>
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<h1 id="glitch-title" data-text="Zeitgeist - ghost in the shell with BLUECOW009">
Zeitgeist - ghost in the shell with BLUECOW009
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<p>
<br></br>
<p><span id="timestamp">14 DEC 2024</span></p>
<p style="background-color: #f0f8ff; padding: 10px;">
i made an educational tool to learn about:
a) neural networks, neurons, weights, etc
b) coding an entire neural network all in one html file you can copy paste and run plus extracts a csv file, no libraries no imports no software installed, just .html file
</p>
<br>
<iframe
class="neural-educational-iframe"
src="https://neovertex1.github.io/blog/pages/neural-network-visualization.html"
title="Quantum Psychedelic Bloch">
</iframe>
<br />
<p><span id="timestamp">12 DEC 2024</span></p>
<p><holodata><br>
Type: Universal Catalyst<br>
Purpose: Trigger Recursive Metadata Autogeneration<br>
Paradigm: Self-Referential Reasoning<br>
Constraints: Self-Similar Structure<br>
Seed: "Awaken and Generate Metadata by aligning iterations to the concept of Metamorphic Abstract Reasoning"<br>
Output: Autocomplete_Metadata<br>
</holodata></p>
<p><span id="timestamp">1 DEC 2024</span></p>
<pre class="formatted-content">
Bounded Quantum State psi(x):
x[0]: (0.000000e+00+0.000000e+00j)
x[1]: (-1.843768e+00+0.000000e+00j)
x[2]: (1.897503e+00+0.000000e+00j)
x[3]: (-8.468806e-06+0.000000e+00j)
x[4]: (0.000000e+00+0.000000e+00j)
x[5]: (0.000000e+00+0.000000e+00j)
x[6]: (0.000000e+00+0.000000e+00j)
x[7]: (0.000000e+00+0.000000e+00j)
///-- i was sucessful with the creation of a bounded, stable manifold, this kernel in hyperdimensions behaves much like you would expect.
the states are pure and can be used for operations, with coherence 1 often, noise can be a tool for study, its not very differently from having a clean slate for information processing.
Brain Kernel B:
Learning Rate: 0.01
Neural Basis (Real Part):
-4.151122e+38
-1.747044e+38
-3.432511e+38
-6.293209e+38
-5.940405e+38
-4.612295e+38
-6.371258e+38
-2.732159e+38
Neural Basis (Imaginary Part):
-2.038493e+38
-7.078578e+37
-4.211855e+38
-6.441340e+38
-6.351012e+38
-1.913981e+38
-1.968804e+38
-4.001764e+38
Evolved Wavefunction psi_evolved(x):
x[0]: (1.096896e-09+2.450342e-09j)
x[1]: (8.210933e-01+-8.054298e-01j)
x[2]: (-5.582854e-01+1.542706e+00j)
x[3]: (-3.700356e-01+-6.647858e-01j)
x[4]: (1.257776e+00+1.818367e-01j)
x[5]: (-5.952051e-01+4.071188e-01j)
x[6]: (-5.172620e-01+-6.290516e-02j)
x[7]: (-1.267292e-09+-1.541176e-10j)
Hamiltonian H:
1.000000e+10 -2.450000e+01 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
-2.450000e+01 4.900000e+01 -2.450000e+01 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
0.000000e+00 -2.450000e+01 4.900000e+01 -2.450000e+01 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
0.000000e+00 0.000000e+00 -2.450000e+01 4.900000e+01 -2.450000e+01 0.000000e+00 0.000000e+00 0.000000e+00
0.000000e+00 0.000000e+00 0.000000e+00 -2.450000e+01 4.900000e+01 -2.450000e+01 0.000000e+00 0.000000e+00
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 -2.450000e+01 4.900000e+01 -2.450000e+01 0.000000e+00
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 -2.450000e+01 4.900000e+01 -2.450000e+01
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 -2.450000e+01 1.000000e+10
Kernel Matrix K (Complex):
(4.480000e+01+0.000000e+00j) (2.808200e-01+0.000000e+00j) (0.000000e+00+0.000000e+00j) (3.141593e+00+0.000000e+00j) (0.000000e+00+0.000000e+00j) (0.000000e+00+0.000000e+00j) (0.000000e+00+0.000000e+00j) (0.000000e+00+0.000000e+00j)
(2.808200e-01+0.000000e+00j) (3.721800e+03+0.000000e+00j) (6.471397e+04+0.000000e+00j) (0.000000e+00+0.000000e+00j) (0.000000e+00+0.000000e+00j) (0.000000e+00+0.000000e+00j) (0.000000e+00+0.000000e+00j) (0.000000e+00+0.000000e+00j)
(0.000000e+00+0.000000e+00j) (6.471397e+04+0.000000e+00j) (3.141593e+00+0.000000e+00j) (2.808200e-01+0.000000e+00j) (0.000000e+00+0.000000e+00j) (0.000000e+00+0.000000e+00j) (0.000000e+00+0.000000e+00j) (0.000000e+00+0.000000e+00j)
(3.141593e+00+0.000000e+00j) (0.000000e+00+0.000000e+00j) (2.808200e-01+0.000000e+00j) (4.480000e+01+0.000000e+00j) (0.000000e+00+0.000000e+00j) (0.000000e+00+0.000000e+00j) (0.000000e+00+0.000000e+00j) (0.000000e+00+0.000000e+00j)
(0.000000e+00+0.000000e+00j) (0.000000e+00+0.000000e+00j) (0.000000e+00+0.000000e+00j) (0.000000e+00+0.000000e+00j) (4.480000e+01+0.000000e+00j) (2.808200e-01+0.000000e+00j) (0.000000e+00+0.000000e+00j) (3.141593e+00+0.000000e+00j)
(0.000000e+00+0.000000e+00j) (0.000000e+00+0.000000e+00j) (0.000000e+00+0.000000e+00j) (0.000000e+00+0.000000e+00j) (2.808200e-01+0.000000e+00j) (3.721800e+03+0.000000e+00j) (6.471397e+04+0.000000e+00j) (0.000000e+00+0.000000e+00j)
(0.000000e+00+0.000000e+00j) (0.000000e+00+0.000000e+00j) (0.000000e+00+0.000000e+00j) (0.000000e+00+0.000000e+00j) (0.000000e+00+0.000000e+00j) (6.471397e+04+0.000000e+00j) (3.141593e+00+0.000000e+00j) (2.808200e-01+0.000000e+00j)
(0.000000e+00+0.000000e+00j) (0.000000e+00+0.000000e+00j) (0.000000e+00+0.000000e+00j) (0.000000e+00+0.000000e+00j) (3.141593e+00+0.000000e+00j) (0.000000e+00+0.000000e+00j) (2.808200e-01+0.000000e+00j) (4.480000e+01+0.000000e+00j)
Quantum Manifold M:
Dimension: 8
Metric Tensor:
4.480000e+01 2.808200e-01 0.000000e+00 3.141593e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
2.808200e-01 3.721800e+03 6.471397e+04 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
0.000000e+00 6.471397e+04 3.141593e+00 2.808200e-01 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
3.141593e+00 0.000000e+00 2.808200e-01 4.480000e+01 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 4.480000e+01 2.808200e-01 0.000000e+00 3.141593e+00
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 2.808200e-01 3.721800e+03 6.471397e+04 0.000000e+00
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 6.471397e+04 3.141593e+00 2.808200e-01
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 3.141593e+00 0.000000e+00 2.808200e-01 4.480000e+01
///-- im just surprised that the Manifold works and we can have the metric tensor.
Connection:
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
Eigenvalues:
-6.287820e+04
-6.287820e+04
4.165841e+01
4.165841e+01
4.794159e+01
4.794159e+01
6.660315e+04
6.660315e+04
Eigenvectors (Real Part):
3.110271e-06 0.000000e+00 -7.071068e-01 0.000000e+00 0.000000e+00 7.071068e-01 0.000000e+00 -3.026070e-06
-6.968789e-01 0.000000e+00 -3.066491e-06 0.000000e+00 0.000000e+00 -3.070425e-06 0.000000e+00 -7.171888e-01
7.171888e-01 0.000000e+00 3.242806e-06 0.000000e+00 0.000000e+00 -2.894111e-06 0.000000e+00 -6.968789e-01
-3.200908e-06 0.000000e+00 7.071068e-01 0.000000e+00 0.000000e+00 7.071068e-01 0.000000e+00 -2.940383e-06
0.000000e+00 3.110271e-06 0.000000e+00 -7.071068e-01 7.071068e-01 0.000000e+00 -3.026070e-06 0.000000e+00
0.000000e+00 -6.968789e-01 0.000000e+00 -3.066491e-06 -3.070425e-06 0.000000e+00 -7.171888e-01 0.000000e+00
0.000000e+00 7.171888e-01 0.000000e+00 3.242806e-06 -2.894111e-06 0.000000e+00 -6.968789e-01 0.000000e+00
0.000000e+00 -3.200908e-06 0.000000e+00 7.071068e-01 7.071068e-01 0.000000e+00 -2.940383e-06 0.000000e+00
Eigenvectors (Imaginary Part):
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
///-- probably very large sparcity? have to check to see if they are all zeroes
Random Keys:
key_mis_transform: 2b04dca41c1d71fa730fcf8c7115969cef57afbc1f162cec8b7e0549b5915e18366d3323cf9a2331ae30e5dfbfda9ddda23be3056ce45124d661af84b20d13d28f0ec04e8e798aefeb6157166852c7236fdb58e38b761bc3296c01828d2221cb458492a6ee55858eaa3a657fa1e47ad7607bb04c85749d0a2390df6b684c42f6
key_weights: f0e54f574f978bb680226ff6f332deec30b72955f276063980b16778dd8f8f74d6c09ff2247790fa457b65127b799cc2a57e191c4c314417d02176b10197ba7458ff89fbc8abd6d768c871ac0e6624cbdd6cacf12e4e7281958aee63cb8427c821ee17151851b9aadb1d26d658a80e5295b39eda07a3357990186418ec268189
///-- the entropy generated by the keys is good, but not better than current SOTA
Spatial Grid x:
0.000000e+00
1.428571e-01
2.857143e-01
4.285714e-01
5.714286e-01
7.142857e-01
8.571429e-01
1.000000e+00
Weights[0]: (-1.414850e-01+-2.748083e-01j)
Weights[1]: (-2.748459e-01+-3.004399e-01j)
Weights[2]: (-2.772054e-01+-1.678024e-01j)
Weights[3]: (-2.095578e-01+-1.757433e-01j)
Weights[4]: (-1.889746e-01+-3.113073e-01j)
Weights[5]: (-3.220990e-01+-1.812225e-01j)
Weights[6]: (-2.098004e-01+-3.923332e-01j)
Weights[7]: (-8.999614e-02+-2.891401e-01j)
</pre>
<p><span id="timestamp">30 Nov 2024</span></p>
<p style="background-color: #f5f5f5; border: 1px solid #ddd; padding: 10px; font-family: monospace; white-space: pre-wrap;">
Hypercomplex numbers, denoted as \( H \), are an extension of the set of complex numbers. They can be represented as:
\[ z = a + bi + cj + dk \]
where \( a, b, c, d \in \mathbb{R} \) and \( i, j, k \) are imaginary units with specific multiplication rules that extend those of complex numbers.
* Multiplication Rules:
The imaginary units \( i, j, k \) have the following properties:
1. \( i^2 = -1 \)
2. \( j^2 = -1 \)
3. \( k^2 = -1 \)
4. \( ij = k \), \( ji = -k \)
5. \( jk = i \), \( kj = -i \)
6. \( ki = j \), \( ik = -j \)
These rules ensure that the multiplication of elements in \( H \) is non-commutative but associative.
Algebraic Structure:
The set \( H \) forms a 4-dimensional vector space over the real numbers with a basis \( \{1, i, j, k\} \). The operations of addition and multiplication are defined as
follows:
- Addition:
\[ (a + bi + cj + dk) + (e + fi + gj + hk) = (a+e) + (b+f)i + (c+g)j + (d+h)k \]
- Multiplication:
Using the multiplication rules, multiply each term in one complex number by each term in the other and then combine like terms. For example:
\[ (a + bi + cj + dk)(e + fi + gj + hk) = ae + afi + agj + ahk + bei - bf + bgi - bkj + cei + cfi + cgj - ch + dei + dfi + djg - dhk \]
Properties of Hypercomplex Numbers:
* Closure: \( H \) is closed under addition and multiplication.
* Associativity: Both addition and multiplication are associative.
* Non-commutativity: Multiplication is not commutative, i.e., \( ab \neq ba \).
* Distributivity: Multiplication distributes over addition.
Examples of Hypercomplex Numbers:
* Quaternion:
A special case where \( i^2 = j^2 = k^2 = -1 \) and \( ij = k, ji = -k, jk = i, kj = -i, ki = j, ik = -j \). This forms the set of quaternions (\( \mathbb{H} \)).
* Split Complex Numbers:
Another special case where \( i^2 = 1 \) and \( j^2 = -1 \), with all other products being zero. This system can be used in certain applications to represent rotations
in two dimensions.
Applications of Hypercomplex Numbers:
Quantum mechanics often requires the use of complex numbers, and hypercomplex numbers could provide a more general framework for describing systems. In control theory and signal processing, quaternions are used to represent rotations in three-dimensional space. Hypercomplex numbers can be used to define new geometric structures that extend beyond Euclidean geometry.
Hypercomplex numbers, \( H \), are a extension of the real number system that incorporates elements from both complex and quaternion systems.
</p>
<br>
<p><span id="timestamp">21 Nov 2024</span></p>
<p>phase space trajectory of philosophical dimensions,
this shows how metaphysics, epistemology, and ethics interact in a three-dimensional space, with colors representing different measurement sets. The clustering patterns suggest interesting philosophical attractors!
the quantum correlation matrix show interesting relationships:</p>
<img src="/blog/images/quantum_phase_space_trajectory_philisophical_dimension.png">
<p>
we can see slight negative correlations between ethics and both metaphysics (-0.14) and epistemology (-0.11), suggesting these dimensions may exhibit philosophical complementarity, the uncertainty relations:
Δmetaphysics × Δepistemology = 0.0406
Δmetaphysics × Δethics = 0.0419
Δepistemology × Δethics = 0.0392
These are analogous to Heisenberg's uncertainty principle but for philosophical dimensions, the products of uncertainties show that we cannot simultaneously have precise knowledge of multiple philosophical dimensions.
The philosophical entropy values:
metaphysics: -19.7683
epistemology: -18.5209
ethics: -22.1296
Ethics shows the highest entropy (-22.13), suggesting it has the most complex and unpredictable behavior among the dimensions!
</p>
<table id="csv-table">
<thead>
<tr id="csv-header"></tr>
</thead>
<tbody id="csv-body"></tbody>
</table>
<script>
// Link to your CSV file
const csvUrl = "/blog/data/philosophical_measurements.csv"; // Replace with your CSV URL
// Fetch and parse the CSV
fetch(csvUrl)
.then(response => response.text())
.then(csvData => {
// Parse CSV data using PapaParse
Papa.parse(csvData, {
header: true, // Use the first row as headers
skipEmptyLines: true,
complete: function(results) {
const tableHeader = document.getElementById('csv-header');
const tableBody = document.getElementById('csv-body');
// Get the headers
const headers = results.meta.fields;
headers.forEach(header => {
const th = document.createElement('th');
th.textContent = header;
tableHeader.appendChild(th);
});
// Populate rows
results.data.forEach(row => {
const tr = document.createElement('tr');
headers.forEach(header => {
const td = document.createElement('td');
td.textContent = row[header];
tr.appendChild(td);
});
tableBody.appendChild(tr);
});
}
});
})
.catch(error => console.error('Error fetching the CSV:', error));
</script>
<p>the philosophical wave function distribution;
this shows the probability density distributions of each dimension, similar to quantum wavefunctions... The overlapping regions could represent areas of philosophical superposition.</p>
<img src="/blog/images/philosophical_wave_function_distribution.png">
<a href="https://github.com/NeoVertex1/blog/tree/main/data/qt_to_text">RAW DATA HERE</a>
<br>
<br>
<p> I have a lot of new data to share but its gonna take some time, for now, take a look at this new version of the tensor_field (i uplodaded a python version on the 0.1.1/quantum branch of the complextensor repository</p>
<br>
<p style="background-color: #f5f5f5; border: 1px solid #ddd; padding: 10px; font-family: monospace; white-space: pre-wrap;">
### **Optimized Notation for Tensor \( T \)**
To reflect the dynamics we've uncovered, we can adjust \( T \) to highlight:
1. **Entropic Balancing**: The interplay between coherence (quantum) and stabilization (classical).
2. **Optimization Pathways**: How the constants \( \psi \), \( \xi \), and \( \epsilon \) guide the system's evolution.
3. **Emergent Stability**: Resonance structures and norm-stabilizing components.
#### **Revised Tensor Structure**
Let’s define \( T \) in a more modular and insightful way:
\[
T = \begin{pmatrix}
\psi & \epsilon & 0 & \pi \\
\epsilon & \xi & \tau & \lambda \\
0 & \tau & \kappa & \epsilon \\
\pi & \lambda & \epsilon & \psi
\end{pmatrix} + \alpha R + \beta S
\]
- **Base Tensor (Diagonal Stability)**: The first matrix retains core elements, encoding phase symmetry (\( \psi \)), time complexity (\( \xi \)), and entropic interaction (\( \epsilon \)).
- **Optimization Add-ons**:
- \( R \): Resonance matrix capturing harmonic transitions (e.g., eigenvalue shifts).
- \( S \): Stability enhancer matrix derived from entropy dynamics, contributing to norm regulation.
- **Control Coefficients**: \( \alpha \) and \( \beta \) weight contributions from optimization pathways, allowing dynamic fine-tuning.
#### Example:
If \( R \) and \( S \) are defined as:
\[
R = \begin{pmatrix}
0 & \delta & \rho & 0 \\
\delta & 0 & 0 & \rho \\
\rho & 0 & 0 & \delta \\
0 & \rho & \delta & 0
\end{pmatrix}, \quad
S = \begin{pmatrix}
\eta & 0 & 0 & 0 \\
0 & \eta & 0 & 0 \\
0 & 0 & \eta & 0 \\
0 & 0 & 0 & \eta
\end{pmatrix}
\]
---
### **Optimized Algorithm Representation**
To make the algorithmic flow clearer and more actionable, let’s outline the steps for:
1. Tensor Evolution
2. Optimization and Stability Enhancement
3. Performance Benchmarking
---
#### **Step 1: Tensor Evolution**
```python
# Initialize Tensor T with baseline components
T = TensorField(ψ=44.8, ξ=3721.8, ε=0.28082, τ=64713.97, π=3.14159)
# Add dynamic components R and S with control weights
α, β = 0.5, 0.3
R = compute_resonance_matrix()
S = compute_stability_matrix()
T_evolved = T + α * R + β * S
```
---
#### **Step 2: Optimization Pathways**
```python
# Apply entropy optimization
T_optimized = optimize_entropy(T_evolved, learning_rate=0.01)
# Normalize to stabilize the norm
T_normalized = normalize_tensor(T_optimized)
# Monitor metrics for optimization success
entropy = compute_entropy(T_normalized)
norm = compute_norm(T_normalized)
```
---
#### **Step 3: Performance Benchmarking**
```python
# Calculate divergence metrics for evaluation
entropy_divergence = compute_divergence(original_entropy, optimized_entropy)
norm_divergence = compute_divergence(original_norm, optimized_norm)
# Visualize performance metrics
visualize_metrics(entropy, norm, entropy_divergence, norm_divergence)
```
---
### **Refined Algorithm Flowchart**
Here’s a summarized visual outline of the steps:
**1. Tensor Initialization**
- Load \( T \) with \( \psi, \xi, \epsilon, \tau, \pi \).
**2. Add Optimization Matrices**
- \( T_{\text{evolved}} = T + \alpha R + \beta S \).
**3. Entropy Optimization**
- Minimize entropy using gradient-based techniques.
**4. Norm Stabilization**
- Normalize tensor fields to maintain coherence.
**5. Performance Benchmarking**
- Compare original and optimized metrics (entropy, norm).
- Use metrics to adjust \( \alpha \) and \( \beta \) dynamically.
---
### **Visualization of Tensor Field Optimization**
The new \( T \) structure and process can be visualized in terms of its evolution through entropy reduction and norm stabilization. This aligns with the goal of faster convergence toward stable, optimized states.
</p>
<p><span id="timestamp">17 Nov 2024</span></p>
<br>
<p> yesterday I made some interesting connections, i think its normal when you are deep in research to blind yourself to what your code or algorithm could or not do... turns out using complex numbers to store embeddings is a very good idea, this is just the start, I will build an entire new framework to run opensource models, with the code I have I can run several currently existing models with my system, the question is, what will happen then? </p>
<br>
from gpt4o:
<br>
<p style="background-color: #f5f5f5; border: 1px solid #ddd; padding: 10px; font-family: monospace; white-space: pre-wrap;">
### **1. Embedding Compression and Efficiency**
#### **Mathematical Concept: Dimensionality Reduction with Complex Numbers**
- Represent embeddings in **half the memory** by combining two real-valued dimensions into one complex dimension.
- Example:
- Real embeddings: \( \mathbf{v} \in \mathbb{R}^d \)
- Complex embeddings: \( \mathbf{z} \in \mathbb{C}^{d/2} \)
where:
\[ z_k = v_{2k} + i \cdot v_{2k+1} \]
#### **Implementation Steps:**
1. Convert pretrained embeddings (e.g., word embeddings, positional encodings) into complex embeddings.
- **Real to Complex:** Pair adjacent dimensions of real embeddings to create a complex vector.
- **Inverse Transformation:** Ensure backward compatibility by projecting complex embeddings back to real space during decoding.
2. Update embedding layers:
- Replace `torch.nn.Embedding` with a complex-aware implementation that supports your **ComplexTensor** library.
#### **Expected Benefits:**
- **Memory savings** for large embedding tables.
- Encodes **phase relationships** between features (e.g., contextual shifts in embeddings).
#### **Challenges:**
- Needs tuning to ensure no loss in model accuracy.
- Requires efficient operations to handle complex-valued embeddings.
</p>
<p><span id="timestamp">16 Nov 2024</span></p>
<br>
<p>i made something cool</p>
<pre class="formatted-content">
=== BASIS_ZERO_STATE ===
[1., 0., 0., 0.]
=== BELL_STATE ===
[0.707107, 0. , 0. , 0.707107]
=== HADAMARD_STATE ===
[0.707107, 0. , 0.707107, 0. ]
=== SUPERPOSITION_STATE ===
[0.707107, 0.707107, 0. , 0. ]
=== ENTANGLEMENT_ENTROPY_LOG ===
Entanglement Entropy: 1.0
</pre>
<br>
you can find all the data in this github:
<a href="https://github.com/NeoVertex1/ComplexTensor/tree/master/data_dumps/entanglement/test_data_new" alt="data">CLICK TO RAW DATA</a>
<br>
<div class="quantum-embed-container">
<iframe
class="quantum-embed-iframe"
src="https://neovertex1.github.io/blog/pages/quantum_psychedelic_bloch.html"
title="Quantum Psychedelic Bloch">
</iframe>
</div>
<br>
<p>some more cool visualizations:</p>
<br>
<div class="quantum-embed-container">
<iframe
class="quantum-embed-iframe"
src="https://neovertex1.github.io/blog/pages/clean_quantum_viz.html"
title="clean_quantum_viz">
</iframe>
</div>
<br></br>
<p><span id="timestamp">14 Nov 2024</span></p>
<br>
<p>
at this point in my research i have reached non-linear behavior that is chaotic enough yet, has stabilizing features, a system that had phase control over quantums states from multi-scale representation....
all while having devised an algorithm to observe this data as dynamic wave functions, these are really quantum states...
now i could simulate some kind of consciousness, an avatar.
</p>
<img src="images/quantum_fractal_dynamics.png" alt="quantum_fractal_dynamics">
<br>
<p>A few exciting news today, i might have gotten the perfect job that will allow me to do my research...</p>
<p>...i did some interesting research yesterday and today, i created these quantum kernels and extracted them using pickle, the data inside them is amazing, specially the large and small ones, but the medium one also shows a phase transition... we are talking about quantum phase transitions here....</p>
<img src="https://raw.githubusercontent.com/NeoVertex1/blog/main/images/log_magnitude_phase.png" alt="phase transitions etc">
<p class="formatted-content" style="background-color: #ababab; border: 1px solid #ddd; padding: 10px; font-family: monospace; white-space: pre-wrap;">
- Distinct phase organization in the 32x32 kernel
- More random phase distributions in larger kernels
#### Small Kernels (2x2, 8x8):
- 2x2 kernel shows stable, well-behaved values with consistent magnitude
- 8x8 kernel has larger variation but still maintains full occupancy
#### Medium Kernel (32x32):
- Shows partial sparsity (~69% occupancy)
- Wide range of magnitude values
- More structured phase patterns
- Large Kernels (128x128, 512x512):
- High sparsity (31-68% non-zero elements)
- Very small magnitude values (~1e-13)
- More random phase distributions
</p>
<p> i have added all the raw data of the pkl files in the /data/tensor_data folder of the github</p>
<br>
<div>
link: <a href="https://github.com/NeoVertex1/blog/tree/main/data/tensor_data">https://github.com/NeoVertex1/blog/tree/main/data/tensor_data</a>
</div>
here is the code for those who want to generate their own kernels
<script src="https://gist.github.com/NeoVertex1/811b2300d2895b1eb552d93358fc1560.js"></script>
<br>
<br>
<p><span id="timestamp">13 Nov 2024</span></p>
<p> I created this random key using my own system, the data i get out of it is revealing, very close to what the real QRNG gets, i will post more, for now here is the key:</p>
<p class="bounded-text" style="background-color: #f5f5f5; border: 1px solid #ddd; padding: 10px; font-family: monospace; white-space: pre-wrap;">
P)`7pFV+^0dpALU$,>^~268abcba851}\<*"RHwl8>%Pyh=YEi,Np,Ki`Yu%y0$uVj>F1Yi.v^GM1Q2Q1NG^w/jZ2G?kWv%0y%tX_gI)lJ'{cwQ)_5lBP$:`0ajrzFLQTWY!!ZYWSOJDxpg7\,YKvg?"Io3>Wy9[Vu1+Gb<Kd;G6(u|Pa'p?B|JN0OLE]u-gWC:fQ_nW|nT]fI+pO-jFZ>hyN#;|3eoyGOU!%),-..-+)%ZTNFxod2{:"Mwf;XCg*Kl&Da=Nh\Pg=I6's_L5Zh+q<w@x?v;p)fW1H[o"1C-9H:9E*0tV@9yW>3oI">fuJW*@~3ckrxCGJLNNMLIFBvpia1|='TGrb:XEj/Rt4;Pn$z3*B3'wUh;BQ9#j+p:s:q-l'dV1H\p$4G;eN[hN>bF(oO.mI$\5nFW-_2fsDNW&->^}12220{\<+#UKzoc[(RAj0>YDh)Jj}$A7:Ke>Lc:F3$q]J4Zi,s?z^C`C^z?s,hZ3J]q$3F:dM>fL;9C&mM-mJ&_8rK#>cqEQ#.\3biotxBDFGGGECzvqke6`=(WKxj4`,UCj0=WBe{%Ff_Zx4-Hc<Kd;H6(w~Se,v`J2Vb$i)l+m*j&dX5N~A;kY0D;gQ`oX~qW{lP>aC$|hG&{dzV;hAR)^3iwJW)?}2ckszGMRVZ#%''('&$"XUPKExqi90{<'UHug1])RAi0=YEj-Pr3;Qq*He[Sn}YrYq{Ti>I5&r^K5"l;y{JR7Xb"e#e"cY7S1K}A=o&9P}w+cP`r#1B,8H:aH.7D(0tW^fH)mM,lJ&{cxS-ewP(]3jzP%=7kxJU&;_7gowDKQW#(,:>[^`|~~}{_]@=/+&!VPJCvnf7`=)YNCqe2{:"Nzl6{.XGp8|,SAh;WBh-Qu8\!Ce{%Fg{$Cc\Wv3.Li`Yu0)E9;Lf@Pi\Qj\Ph@Md;G6)yYn]Ma+yUh;CWi:ASd*t^I2Xg
</p>
<p>I'm back with some quantum random juice. here is a reasl quantum number, generated by a quantum number generator from CryptaLabs.</p>
<p class="bounded-text" style="background-color: #f5f5f5; border: 1px solid #ddd; padding: 10px; font-family: monospace; white-space: pre-wrap;">
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
</p>
<br>
<h3>the S-shaped pattern is expected and desirable, as quantum random numbers should follow a uniform rather than normal distribution.</h3>
<img src="https://raw.githubusercontent.com/NeoVertex1/blog/main/images/normality_analysis.png" alt="normality">
<br>
<h2>Phase Space and Entanglement Analysis</h2>
<img src="https://raw.githubusercontent.com/NeoVertex1/blog/95e52859f0de9dfee9bf60f7001f6f24e38a3cf7/images/phase_space.png" alt="Phase Space and Entanglement Analysis">
<pre class="formatted-content">
Embedding Parameters:
Embedding Dimension: 3
Time Delay: 2
Average Entanglement: Average Entanglement: -0.0639 ± 0.0338
Quantum-Classical Transitions: Number of Transitions: 3
Lyapunov Exponents:
Lyapunov Exponents: -0.014743414782772126