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Position interpolation maps the positions in a new, longer sequence to match the original position range observed during training. If the training sequence lengths ranged from $${}0$$ to $$m_l$$, and the new sequence has a length $$m$$, position interpolation compresses all points in the expanded range $$[0, m]$$ into the original learned range $$[0, m_l]$$.

Position Interpolation Mapping for Longer Sequences

The linear scaling of position ranges in position interpolation can be practically realized by directly modifying the input to the positional embedding model. This adjusts how the sequence positions are processed without changing the core embedding architecture.

Implementing Linear Scaling by Modifying Embedding Model Input

An AI development team has a language model that was trained exclusively on documents with a maximum length of 4096 tokens. When they try to use this model for summarizing new, longer documents of up to 16384 tokens, they observe a significant drop in quality. The model seems to lose coherence and disregard information from the beginning of the longer documents. The team cannot afford to retrain the model from scratch. Based on this scenario, explain the fundamental issue with how the model is processing the positions of tokens in the longer documents. Then, describe the core mechanism of a technique that could resolve this issue by re-mapping the token positions.

Adapting a Language Model for Longer Documents

A language model was trained with a maximum context window of 4096 positions. If this model is now used to process a sequence of 16384 positions using an interpolation technique, explain how the position for the 8192nd token in the new sequence would be re-scaled to fit within the model's original learned range. Describe the calculation and state the resulting scaled position.

Calculating Scaled Positional Indices

A language model was originally developed to process text sequences with a maximum length of 2048 positions. To enable it to handle a longer input sequence of 8192 positions, a technique is applied that linearly scales down the new position indices to fit within the model's original learned range. Given this scenario, what would be the scaled-down position index that corresponds to the token at position 6144 in the new, longer sequence?

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