How HERMES OPTIMUS Works

Neural Network Architecture

HERMES OPTIMUS employs a precisely calibrated feedforward neural network with a 4-60-12 architecture, structured as follows:

• Input Layer: 4 neurons (one for each character in a word)
• Hidden Layer: 60 neurons with sigmoid activation
• Output Layer: 12 neurons (one for each target word)

This architectural configuration was selected after careful consideration to optimize the balance between computational performance and the stringent memory constraints of the calculator hardware. The implementation of 4 input neurons enables the network to process words with a maximum length of 4 characters, which proves sufficient for the targeted vocabulary set while maintaining operational efficiency.

Neuron Activation Patterns

The neural network demonstrates sophisticated pattern recognition capabilities through its activation response to different letter inputs. The heatmap below visualizes how each letter in the alphabet, when placed at different positions in a word, activates the network's output neurons for each of the 12 target words.

The heatmap reveals how different letters in different positions trigger specific word recognitions. Brighter colors (yellow) indicate stronger activation, while darker colors (purple) indicate weaker activation. This visualization demonstrates how the neural network has learned to associate specific letter patterns with target words, enabling it to correct misspelled or scrambled inputs.

Data Representation

The lexical data undergoes the following encoding process:

• Each character is converted to a value between 0 and 1 by mapping A-Z to 1/26 through 26/26
• Words shorter than 4 characters are padded with zeros
• The network outputs confidence scores for each of the 12 target words

The 12 target words are: "BACK", "DARK", "EACH", "FROM", "JUST", "BEEN", "GOOD", "MUCH", "SOME", "TIME", "LIKE", and "ONLY".

Activation Function

The network implements the sigmoid activation function, mathematically expressed as:

This mathematical function effectively maps any numerical input to a value constrained between 0 and 1, providing ideal characteristics for classification tasks. To mitigate potential overflow errors on the calculator hardware, the implementation incorporates precise numerical safeguards that appropriately constrain extreme values: