Architecture Determines Observability of Transformers

Understanding whether deep neural networks are effectively optimized remains challenging, as training occurs in highly nonconvex landscapes and standard metrics provide limited visibility into layer-wise learning quality. This challenge is particularly acute for transformer-based language models, where training is expensive, models are often reused in frozen form, and poorly optimized layers can silently degrade performance. We propose a layer-wise peeling framework for monitoring training dynamics, in which each transformer layer is locally optimized against intermediate representations of the trained model. By constructing lightweight, layer-specific reference solutions and projecting layers onto multiple intermediate outputs via different permutations, we obtain achievable baselines that enable fine-grained diagnosis of under-optimized layers. Experiments on decoder-only transformer models show that these layer-wise reference bounds can match or even surpass the trained model at various stages of training, exposing inefficiencies that remain hidden in aggregate loss curves. We further demonstrate that this analysis remains effective under binarization and quantized settings, where training dynamics are particularly fragile. Across all numerical results, the proposed bounds consistently separate apparent convergence from effective optimality, highlighting optimization opportunities that are invisible when relying on training loss alone.

Chain-of-thought (CoT) monitoring is one of the most promising tools we have for detecting model misbehavior, but its effectiveness depends on models faithfully externalizing their reasoning. Motivated by this vulnerability, we study whether monitor-aware models are capable of obfuscating their reasoning to evade detection. We use synthetic document finetuning to expose eight models to realistic pre-training-style documents describing a CoT monitor and find that monitor-aware models consistently achieve higher rates of undetected misbehavior compared to unaware controls. This effect is weaker but still present on a harder agentic task. We also show that CoT controllability, a model's ability to reshape its own reasoning trace under an imposed constraint, is closely correlated with obfuscation success across the eight models studied ($r=0.800$, $p=0.017$). Monitor-aware models placed under equal reinforcement learning optimization pressure also learn to reward-hack without triggering a CoT monitor substantially faster than unaware controls. Together, these results suggest that knowledge of monitoring combined with high CoT controllability poses a risk to CoT-based monitoring.

Linear probes detect corrupted context in language models with near-perfect accuracy, yet this does not translate into reliable failure prediction. The result is a dissociation with direct implications for deployment monitoring. Across multi-hop arithmetic chains, probes that detect corruption turn out to be uninformative about final answer correctness; models forced into structured confidence formats collapse to two values with indistinguishable error rates; and probe persistence across hops fails to separate correct from incorrect outcomes, refuting our pre-registered "persistence beats peak" hypothesis. This pattern of knowing but not saying generalises across model families including reasoning models. As a real-time monitor, probe-based interventions are sharply model and error-type dependent: branch-and-pick is net-positive across models and uniquely non-breaking on Llama-3.1-8B (4 rescued, 0 broken), while reprompt and replace-prior break correct traces at roughly the rate they rescue wrong ones. Probe-based monitoring is a necessary complement to verbalised confidence, but no single intervention dominates, and the deployable answer is model-aware, error-type-aware routing.