Repository for the Term Project of Machine Learning, Fall 2024, PKU

Problem

For dimensions $n$, design Lattice such that the normalized quantization error is small.

Run

You can run the following command to search for the best Lattice for a given dimension. Please refer to the examples directory for the configuration file. Feel free to modify the configuration file to suit your needs.

python sgd.py --config examples/medium.yml 12 # dimension

You can run the following command to compute Normalized Second Moment (NSM) of a given lattice. We set the number of samples to $10^9$ defaultly.

python check_nsm.py --basis "<dir_to_your_lattice>" --num_samples <the_number_of_samples>

And we use draw_figs.py to draw the figures of the comparison of the NSM of different lattices. You can refer to draw_figs.py for more details.

Results

We put all the results in the data directory, including the generation matrix of the lattices with settings:

• dimension $[1,25]$, batch size = $1$, default scheduler, i.e. the reproduction of the results in Optimization and Identification of Lattice Quantizers
• dimension $[1,25]$, batch size = $8$, default scheduler.
• dimension $[1,25]$, batch size = $8$, cosine scheduler.

And comparison of 12-dimensional and 16-dimensional lattice convergence across three setups: medium mode with batch size 1, medium mode with batch size 8, both using the default scheduler, and cosine mode with batch size 8 using a cosine scheduler. The illustration of the comparison is shown in the data/compare_12_16.pdf file.