This is just a consequence of the fact that bfloat16 has a very high dynamic range which is not all used. People like hyperparameters that look like 0.01 not 10^10, even though there is the same fractional precision available at each exponent and if you multiplied everything - hyperparameters, initialized weights, training data, etc in a network by 10^6 things will still work more or less the same since the upper range is hardly used (with the possible exception of some small number of special functions).

Typical entropy of bfloat16 values seen in weights (and activations) are about 10-12 bits (only 65-75% or so of the value range is used in practice). Sign and mantissa bits tend to be incompressible noise.

This has been exploited several times before in the context of both classical HPC and AI, with lossless compression work from Martin Burtscher's lab (https://userweb.cs.txstate.edu/~burtscher/), fpzip from LLNL (https://computing.llnl.gov/projects/fpzip) and my library dietgpu from 2021 (https://github.com/facebookresearch/dietgpu) which we used to speed training on a large GPU cluster by about 10% wall clock time overall by losslessly compressing all data prior to send and decompressing upon receive (e.g., gradients, weights from backup, etc), which is still computing the same thing as it did before as it is lossless.

Also, rANS is more efficient and easier to implement in SIMD-like instruction sets than Huffman coding. It would reduce the performance latency/throughput penalties as well with DFloat11 (since we have to decompress before we do the arithmetic).