Trust, but Verify: Peeling Low-Bit Transformer Networks for Training Monitoring

We introduce a constrained optimization framework for training transformers that behave like optimization descent algorithms. Specifically, we enforce layerwise descent constraints on the objective function and replace standard empirical risk minimization (ERM) with a primal-dual training scheme. This approach yields models whose intermediate representations decrease the loss monotonically in expectation across layers. We apply our method to both unrolled transformer architectures and conventional pretrained transformers on tasks of video denoising and text classification. Across these settings, we observe constrained transformers achieve stronger robustness to perturbations and maintain higher out-of-distribution generalization, while preserving in-distribution performance.

Autoregressive transformers make confident errors that output-confidence monitoring cannot catch. Activation monitors catch them only when training leaves a decision-quality signal beyond what the output already exposes. This signal is an architectural property of the trained model, fixed upstream of any monitor. Controlling for output confidence removes 60.3% of the raw activation-probe signal on average across 14 models. Raw probe signal is mostly output confidence, and output-side readouts cannot recover the residual. What remains depends on architecture and training. In Pythia's controlled training, both matched-width configurations form the signal early. One preserves it through convergence while another erases it as perplexity continues to improve. Capability and observability are not inherently in tension. Across independently trained families this pattern persists, even as the collapse point shifts. Where the signal survives, monitoring catches what confidence cannot. On downstream QA, a WikiText-trained probe with no task-specific tuning catches about one in eight confident errors that output-confidence monitoring misses, at a 20% flag rate. These results establish signal engineering as a training-time design axis alongside loss and capability. Architecture sets the conditions for observability, and training determines what remains readable.

Reinforcement learning (RL) has become a central component of post-training large language models (LLMs), yet little is understood about how RL adaptation is distributed across transformer layers. Existing approaches typically update all model parameters uniformly, implicitly assuming that every layer contributes similarly to the gains obtained during RL post-training. In this work, we challenge this assumption through a systematic layer-wise study of RL training. Surprisingly, we find that training a single transformer layer can recover most of the gains achieved by full-parameter RL training, and in some cases even surpass it. To quantify this phenomenon, we introduce the quantity layer contribution, which measures the fraction of full RL improvement recovered by training a layer in isolation. Across seven models spanning two model families (Qwen3, Qwen2.5), three RL algorithms (GRPO, GiGPO, Dr. GRPO), and multiple task domains including mathematical reasoning, code generation, and agentic decision-making, we observe a remarkably stable pattern: RL gains are highly concentrated in a small subset of, and in many cases even a single, transformer layers. More strikingly, the same structural pattern consistently emerges: high-contribution layers concentrate in the middle of the transformer stack, while layers near the input and output ends contribute substantially less. The resulting layer rankings remain strongly correlated across datasets, tasks, model families, and RL algorithms.