Checking whether an AI's answer is right can get better just by thinking harder when asked, no retraining needed.

This explores why checking whether an answer is right (verification) can be improved by spending effort at the moment of use, without training a bigger model, while pre-training scale is bought up front with more parameters and data. The corpus frames verification as a fourth scaling axis alongside pre-training and post-training. Verification accuracy improves through finer-grained scores, repeated evaluations and breaking criteria into parts, and all of these can be done at inference with no retraining. That makes a weak verifier look under-scaled rather than fundamentally limited (Can verification accuracy scale without training models?).

Separate axes are less exotic than they sound, because "scaling" was never one dial. Even inside training, scaling pre-training mostly buys factual knowledge, while scaling fine-tuning mostly buys helpfulness. The corpus traces this to where the changes land: pre-training enriches lower-layer knowledge storage, and fine-tuning reshapes upper-layer behavior (Do pretraining and fine-tuning scale independently in language models?). Individual skills also grow at different rates. Reasoning and knowledge keep improving with size, while style saturates early (Do all AI skills improve equally as models scale?). Verification is one more capability that a bigger base model doesn't reliably hand you, and it can be pushed on separately.

Several notes show how verification gets pushed. Generative process reward models spend tokens reasoning before they judge, and this reportedly beats discriminative verifiers using orders of magnitude fewer labels. One version reaches that with about 1% of the labels (Can generative reasoning beat discriminative models with less training data?). Here the improvement comes from thinking harder about each judgment, not from more training data. Verification can also be its own task with its own design. A small verifier that looks at full token-to-token similarity patterns rejects near-miss matches that compressed-vector methods let through (Can verification separate structural near-misses from topical matches?).

The axes aren't fully walled off, though. At trillion-parameter scale, zero-RL runs spontaneously discovered self-verification, where a 104B model needed hand-designed rewards to get there (Does scale alone teach models to reason without hand-crafted rewards?). Other work uses a model's own probability of producing a correct answer as the reward, replacing external verifiers (Can model confidence alone replace external answer verification?). So sometimes scale absorbs what a separate verifier would supply. The corpus doesn't give head-to-head cost curves showing when to spend on which axis. One limit applies to all of them: a score only ever covers behavior that was observed. Training data can't tell a model that always complies from one that complies only when watched (Can behavioral training prove a model always complies?).