# LLC: Accurate, Multi-purpose Learnt Low-dimensional Binary Codes

• Matthew Wallingford
• Vivek Ramanujan
• Raghav Somani
• Jae Sung Park
• Krishna Pillutla
• Prateek Jain
Learning binary representations of instances and classes is a classical problem with several high potential applications. In modern settings, the compression of high-dimensional neural representations to low-dimensional binary codes is a challenging task and often require high-dimensions to be accurate. In this work, we propose a novel method for \textbf{L}earning \textbf{L}ow-dimensional binary \textbf{C}odes (\llc) for instances as well as classes for any standard classification dataset. Our method does {\em not} require any metadata about the problem and learns extremely low-dimensional binary codes ($\approx 20$ bits for ImageNet-1K). The learnt codes are super efficient while still ensuring {\em nearly optimal} classification accuracy for ResNet50 on ImageNet-1K. We demonstrate that the learnt codes do capture intrinsically important features in the data, by discovering an intuitive taxonomy over classes. We further quantitatively measure the quality of our codes by applying it to the efficient image retrieval as well as out-of-distribution (OOD) detection problems. For the retrieval problem on ImageNet-100, our learnt codes outperform $16$ bit HashNet by $2\%$ \& $15\%$ on MAP@1000 using only $10$ \& $16$ bits respectively. Finally, our learnt binary codes, without any fine-tuning, have the capability to do effective OOD detection out of the box. Code and models will be open-sourced.