Based on the visual evidence described in the case study, what is the most probable reason for the discrepancy in the visualization, and what fundamental limitation of the model does this reveal?

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A visual representation of positional encoding failure can be seen when a model is trained on sequences up to a certain length, for instance, 1,024 positions. When this model is then required to generate positional values for a longer sequence, such as up to 2,048, the output remains coherent within the original training range but becomes chaotic and meaningless for all positions beyond 1,024. This visualization clearly demonstrates the model's inability to generalize its understanding of position.

Visual Example of Positional Encoding Failure

An engineer generates a visualization of the positional values for a sequence of 4,096 positions using a pre-trained language model. The visualization displays a coherent, structured pattern for the first 2,048 positions. However, for all positions from 2,049 to 4,096, the pattern becomes chaotic and nonsensical. What is the most logical inference that can be drawn from this visualization?

Interpreting a Positional Value Visualization

Imagine a language model was trained exclusively on text sequences with a maximum length of 512 positions. You are tasked with creating a visualization that plots the positional values generated by this model for a new sequence that is 1,024 positions long. Describe the expected appearance of this visualization, specifically contrasting the first half (positions 1-512) with the second half (positions 513-1,024).

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