Log-based anomaly detection is increasingly dominated by large pretrained models, from BERT-scale encoders to 8B-parameter language models, which require GPUs at inference time and are difficult to deploy on the monitoring nodes where logs are produced. We present LogCDM, a compact detector that scores each log session using three complementary signals: the next-event surprise of a small causal Transformer, the distance between a graph-attention embedding of the session's own transition graph and that of a normal reference graph, and a transition-drift statistic that we show is exactly a frequency-weighted chi-squared divergence between transition kernels.

The divergence view yields an asymptotic null distribution, a length-standardized score, and a per-edge decomposition that explains each alarm. A sigmoid gate fuses the three signals; under a shared-covariance Gaussian model, this gate is the Bayes posterior, and its learned weights indicate which signal each dataset relies on.

With 8.1-8.8M parameters and no GPU required at inference, LogCDM reaches F1 scores of 0.984 on HDFS, 0.870 on chronologically split BGL, and 0.850 on Thunderbird, within 0.013-0.12 of an 8.1B-parameter LLM detector evaluated under the same protocol and above all compact baselines on BGL. It scores a session in 5.5-10.5 ms on a CPU.

Ablations show that the structural signals add 0.025-0.030 F1 on BGL and Thunderbird but almost nothing on HDFS, consistent with the learned fusion weights.