  Large Language Models (LLMs) are often criticized for lacking true
"understanding" and the ability to "reason" with their knowledge, being seen
merely as autocomplete systems. We believe that this assessment might be
missing a nuanced insight. We suggest that LLMs do develop a kind of empirical
"understanding" that is "geometry"-like, which seems adequate for a range of
applications in NLP, computer vision, coding assistance, etc. However, this
"geometric" understanding, built from incomplete and noisy data, makes them
unreliable, difficult to generalize, and lacking in inference capabilities and
explanations, similar to the challenges faced by heuristics-based expert
systems decades ago.
  To overcome these limitations, we suggest that LLMs should be integrated with
an "algebraic" representation of knowledge that includes symbolic AI elements
used in expert systems. This integration aims to create large knowledge models
(LKMs) that not only possess "deep" knowledge grounded in first principles, but
also have the ability to reason and explain, mimicking human expert
capabilities. To harness the full potential of generative AI safely and
effectively, a paradigm shift is needed from LLM to more comprehensive LKM.
