Editing Psionics (section)

== Neural Network Equations ==
=== McCulloch-Pitts Neuron Model ===
<math>y = \begin{cases} 1 & \text{if } \sum_i w_i x_i + b > \text{threshold} \\ 0 & \text{otherwise} \end{cases}</math>
* Describes a simple model of neural activation, potentially relevant for modeling the neural correlates of psychic experiences.
* Offers insights into the computational mechanisms underlying psychic abilities, including information processing and decision-making.
* Provides mathematical tools for simulating the behavior of neural networks involved in psi-related processes.

=== Perceptron Learning Rule ===
<math>\Delta w_i = \eta (d - y) x_i</math>
* Describes a learning algorithm for adjusting weights in a perceptron model, potentially relevant for studying the development of psychic abilities.
* Offers insights into the adaptive processes underlying psychic learning and skill acquisition.
* Provides mathematical formalism for training neural networks to recognize patterns and make predictions in psi research.

=== Backpropagation Algorithm ===
<math>\delta^L = \nabla_a C \odot \sigma'(z^L)</math>
* Describes a training algorithm for multi-layer neural networks, potentially relevant for modeling the hierarchical organization of cognitive processes in psychic experiences.
* Offers insights into the mechanisms underlying the refinement and optimization of psychic abilities through feedback and practice.
* Provides mathematical tools for optimizing the performance of neural networks involved in psi-related tasks.

=== Long Short-Term Memory (LSTM) Equations ===
<math>\begin{aligned} f_t &= \sigma(W_f \cdot [h_{t-1}, x_t] + b_f) \\ i_t &= \sigma(W_i \cdot [h_{t-1}, x_t] + b_i) \\ o_t &= \sigma(W_o \cdot [h_{t-1}, x_t] + b_o) \\ g_t &= \tanh(W_c \cdot [h_{t-1}, x_t] + b_c) \\ c_t &= f_t \odot c_{t-1} + i_t \odot g_t \\ h_t &= o_t \odot \tanh(c_t) \end{aligned}</math>
* Describes the behavior of LSTM units in recurrent neural networks, potentially relevant for modeling the temporal dynamics of psychic experiences.
* Offers insights into the mechanisms underlying memory formation and retention in psi-related processes.
* Provides mathematical formalism for capturing the context-dependent and long-range dependencies observed in psychic phenomena.

=== Hopfield Network Energy Function ===
<math>E(\mathbf{x}) = -\frac{1}{2} \mathbf{x}^T \mathbf{W} \mathbf{x}</math>
* Describes an energy function used in associative memory models, potentially relevant for modeling the retrieval of psychic information from memory.
* Offers insights into the storage and retrieval processes underlying psychic abilities, including telepathic communication and remote viewing.
* Provides mathematical tools for simulating the dynamics of neural networks involved in psi-related memory tasks.