Cross-Entropy Is Load-Bearing: A Pre-Registered Scope Test of the K-Way Energy Probe on Bidirectional Predictive Coding
Cacioli (2026) showed that the K-way energy probe on standard discriminative predictive coding networks reduces approximately to a monotone function of the log-softmax margin. The reduction rests on five assumptions, including cross-entropy (CE) at the output and effectively feedforward inference dynamics. This pre-registered study tests the reduction's sensitivity to CE removal using two conditions: standard PC trained with MSE instead of CE, and bidirectional PC (bPC; Oliviers, Tang & Bogacz, 2025). Across 10 seeds on CIFAR-10 with a matched 2.1M-parameter backbone, we find three results. The negative result replicates on standard PC: the probe sits below softmax (Delta = -0.082, p < 10...
| Authors | Jon-Paul Cacioli |
|---|---|
| Primary category | cs.CL |
| Published | 23 April 2026 |
| Last updated at source | 23 April 2026 |
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