Tracing Computation Density in LLMs

Transformer-based large language models (LLMs) are comprised of billions of parameters arranged in deep and wide computational graphs, but it is not clear that they exploit their full capacity for all inputs. We introduce the s-Trace method to efficiently estimate the subgraph of size s that best approximates a full model output. With this method, we find the computation in a variety of LLMs to be organized in two distinct phases. A small subgraph mostly composed of early-layer nodes can reconstruct the head of the full model output distribution. Adding further nodes, mostly located in later layers and increasingly consisting of attention heads, leads to incremental refinements in approximating the full output distribution. We find moreover that the amount of necessary computation per input correlates with model uncertainty, and that sparser subgraphs encode shallow statistics, such as unigram frequency. Overall, our results suggest a consistent modular organization in effective LLM computation, with a sparse early-layer core providing a rough prediction that is further refined through denser computations in later layers.

Sparse or Dense? A Mechanistic Estimation of Computation Density in Transformer-based LLMs

Transformer-based large language models (LLMs) are comprised of billions of parameters arranged in deep and wide computational graphs. Several studies on LLM efficiency optimization argue that it is possible to prune a significant portion of the parameters, while only marginally impacting performance. This suggests that the computation is not uniformly distributed across the parameters. We introduce here a technique to systematically quantify computation density in LLMs. In particular, we design a density estimator drawing on mechanistic interpretability. We experimentally test our estimator and find that: (1) contrary to what has been often assumed, LLM processing generally involves dense computation; (2) computation density is dynamic, in the sense that models shift between sparse and dense processing regimes depending on the input; (3) per-input density is significantly correlated across LLMs, suggesting that the same inputs trigger either low or high density. Investigating the factors influencing density, we observe that predicting rarer tokens requires higher density, and increasing context length often decreases the density. We believe that our computation density estimator will contribute to a better understanding of the processing at work in LLMs, challenging their symbolic interpretation.