We need to talk about the current state of LLMs in development. For the last two years, most of us have been using these models for “vibes.” You prompt it, it spits out something that looks like a clean WooCommerce hook, and you ship it. But if you’ve spent any time in the trenches, you know that “looking correct” isn’t the same as “being correct.” We’ve all seen models hallucinate logic that works 90% of the time, only to fail spectacularly under a specific race condition or a weird edge case.
The solution isn’t just “bigger models.” It’s formal verification—moving from vibes-based generation to verifiable, step-by-step logic. This is where Reinforcement Learning LLM reasoning comes in. We’re finally seeing the same intuition that made AI master the game of Go being applied to how models think through mathematical and software proofs.
The Problem with Guessing
In Part 1 of this series, we looked at building a proof checker. The mental model is simple: as long as we have mechanical rules, we can verify if a proof is sound. But how do we actually train a model to follow those rules instead of just predicting the next most likely token? If you just fine-tune on a raw dataset, the model learns the “accent” of a mathematician, not the logic.
As recently highlighted in research like DeepSeek-R1, the breakthrough happens when you use a “Do or do not” reward system. You give the model a problem, let it generate multiple attempts, and run those attempts through a hard-coded verifier. Valid logic gets a reward of 1; everything else—hallucinations, syntax errors, or logical leaps—gets a 0. No partial credit.
Bootstrapping with Synthetic Data
You can’t start an RL loop from zero. You need a baseline. To build a robust training set, we use a mix of manual translations from textbooks (like forallx) and high-quality synthetic data generated by a powerhouse model like Claude 3.5 Sonnet.
The “gotcha” here? You can’t trust the synthetic data blindly. Every proof Sonnet generates must pass through our proof checker before it ever touches our training set. We’re using the AI to build the ladder, but we’re checking every rung for structural integrity.
Check out our previous discussion on how the AI revolution is shifting development workflows to see where this is heading.
The RL Loop: Sample, Verify, Reward
For the technical implementation, services like Tinker are abstracting the heavy infrastructure, allowing us to perform LoRA-style fine-tuning on open-source models (like Qwen or GPT-OSS) without wrestling with hardware bottlenecks. The logic of the training loop looks roughly like this:
# Conceptual RL Reward Logic
def bbioon_verify_proof_reward(attempt, premises, conclusion):
# 1. Parse the generated proof
parsed_proof = proof_parser.parse(attempt)
if not parsed_proof:
return 0 # Format error
# 2. Check logical consistency against rules
verifier = ProofVerifier(rules_engine)
is_valid = verifier.verify(parsed_proof)
# 3. Ensure it actually proves what we asked
if is_valid and parsed_proof.conclusion == conclusion:
return 1
return 0The model starts by failing almost everything. It’s messy. It’s frustrating. But slowly, the weights adjust. It starts to learn that nested subproofs and DeMorgan’s laws aren’t just patterns—they are rules that, when followed, lead to the “1” it’s incentivized to find.
The Reality Check: Where RL Struggles
I’ve spent 14 years in WordPress and WooCommerce development, and if there’s one thing I’ve learned, it’s that “simple” is a lie. Even in our RL runs, models that crushed basic proofs would often stumble on complex, nested logic. For example, proving (not A or not B) -> not (A and B) is relatively easy for a fine-tuned 20b model. But give it multiple premises and nested contradictions, and the logic often collapses.
This tells us that “Vibe Proving” isn’t a silver bullet. It’s an engineering discipline. We need better prompt optimization, curriculum learning (starting with easy proofs and ramping up), and eventually, migrating to more expressive languages like Lean.
Look, if this Reinforcement Learning LLM reasoning stuff is eating up your dev hours, let me handle it. I’ve been wrestling with WordPress and complex backend logic since the 4.x days.
Final Thoughts on Formal Verification
The goal isn’t just to make AI better at math. Verifiable proofs are the missing ingredient for building confidence in massive, distributed software systems. If we can train an LLM to prove its reasoning, we can finally stop “hoping” the code works and start knowing it does. AI is no longer about generating text; it’s about engineering correctness.
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