Cramming 1568 Tokens into a Single Vector and Back Again: Exploring the
  Limits of Embedding Space Capacity
Authors: name: Yuri Kuratov, name: Mikhail Arkhipov, name: Aydar Bulatov, name: Mikhail Burtsev

A range of recent works addresses the problem of compression of sequence of
tokens into a shorter sequence of real-valued vectors to be used as inputs
instead of token embeddings or key-value cache. These approaches allow to
reduce the amount of compute in existing language models. Despite relying on
powerful models as encoders, the maximum attainable lossless compression ratio
is typically not higher than x10. This fact is highly intriguing because, in
theory, the maximum information capacity of large real-valued vectors is far
beyond the presented rates even for 16-bit precision and a modest vector size.
In this work, we explore the limits of compression by replacing the encoder
with a per-sample optimization procedure. We show that vectors with compression
ratios up to x1500 exist, which highlights two orders of magnitude gap between
existing and practically attainable solutions. Furthermore, we empirically show
that the compression limits are determined not by the length of the input but
by the amount of uncertainty to be reduced, namely, the cross-entropy loss on
this sequence without any conditioning. The obtained limits highlight the
substantial gap between the theoretical capacity of input embeddings and their
practical utilization, suggesting significant room for optimization in model
design.