Here is a preliminary analysis of applying WeightWatcher to study how LLMs memorize random inputs. When we deliberately corrupt part of the training data with random labels, the model eventually memorizes those labels—and its clean test accuracy begins to deteriorate. We monitored the weight spectra throughout training and found a surprisingly strong, layer-specific signal. The clearest effect occurs in the attention K matrix. Across multiple independent seeds, the WeightWatcher power-law exponent α falls toward and then below the critical value α = 2 as random-label memorization becomes extensive. The relationship is remarkably reproducible, with a mean rank correlation of roughly ρ ≈ −0.90 between K α and memorization. The effect survives WeightWatcher’s fix_fingers correction, suggesting it is not simply an artifact of a few anomalous eigenvalues. Importantly, this is not a universal α < 2 rule Other layers behave quite differently. The emerging picture is that memorization involves a layer-selective spectral reorganization, with the K matrix providing an especially strong marker of the transition from generalization toward memorization and overtraining. These are still small NanoGPT experiments and the analysis is preliminary, but the multi-seed results are encouraging. The next step is to determine whether the same spectral signature survives at larger scale and across optimizers. If anyone is interested in getting involved or trying it themselves, please reach out here or on the weightwatcher ai community Discord

Reinforcement Learning is the key to getting LLMs to appear to reason. If you know some statistical mechanics, you may, like I did, immediately recognize that the basic REINFORCE algorithm is essentially non-Equilibrium Monte Carlo, where the RL updates follow a gradient that looks exactly like a linear relaxation described the Fluctuation-Dissipation theorem. Here, I have vibed up a short document and explainer video to help explain the idea. I hope it is useful and is sparks some new ideas. Join us on the weightwatcher.ai discord to discuss

🔥Hot take: RL algos like REINFORCE and PPO are effectively non-equilibrium Monte Carlo. You perturb the system (prompt) and follow the gradient of the (generated) response along the linear response dictated by the fluctuation-dissipation theorem.

𝗔𝗱𝗮𝗺𝗪 𝘃𝘀. 𝗠𝘂𝗼𝗻: α, 𝗢𝘃𝗲𝗿𝗳𝗶𝘁𝘁𝗶𝗻𝗴, 𝗮𝗻𝗱 𝗠𝗲𝗺𝗼𝗿𝗶𝘇𝗮𝘁𝗶𝗼𝗻. A quick update on our WeightWatcher experiments comparing AdamW with the newer Muon optimizer. We trained a single-head nanoGPT model with both optimizers across five seeds. We then used WeightWatcher to study the weight-matrix spectra and several forms of memorization. The top plot shows the average raw α. AdamW produces relatively stable α values. Muon is much noisier. Its ESDs vary substantially across layers, which makes α harder to estimate reliably. But the average hides something important: 👉 Individual layers do fall below α = 2. Our spectral/RG theory predicts that this regime can be associated with pathological, example-specific learning. So we tested that prediction directly. We inserted random sequences into the training set and measured whether the model remembered them using exact extraction, token recall, teacher-forced recall, and canary exposure. The result was striking. • AdamW memorized the planted sequences strongly. Earlier in training it reached ~96% exact recall of 32-token canaries. • Muon strongly suppressed this kind of memorization. At 10,000 steps, teacher-forced recall was ~62% for AdamW versus <1% for Muon. There is also a surprise: some Muon layers have α < 2 as well. So α < 2 by itself is not sufficient to explain memorization. This is why we recommend examining individual WeightWatcher layers and their ESDs—not simply average α. Muon appears to suppress memorization while also producing unusual ESDs that make conventional WeightWatcher analysis more difficult. We are now running Muon much longer to understand how these spectra evolve. If you are using WeightWatcher and trying to analyze models trained with Muon, feel free to reach out for help. #talkToChuck 𝗔𝗱𝗮𝗺𝗪 𝘃𝘀. 𝗠𝘂𝗼𝗻: α, 𝗢𝘃𝗲𝗿𝗳𝗶𝘁𝘁𝗶𝗻𝗴, 𝗮𝗻𝗱 𝗠𝗲𝗺𝗼𝗿𝗶𝘇𝗮𝘁𝗶𝗼𝗻. A quick update on our WeightWatcher experiments comparing AdamW with the newer Muon optimizer. We trained a single-head nanoGPT model with both optimizers across five seeds. We then used WeightWatcher to study the weight-matrix spectra and several forms of memorization. The top plot shows the average raw α. AdamW produces relatively stable α values. Muon is much noisier. Its ESDs vary substantially across layers, which makes α harder to estimate reliably. But the average hides something important: 👉 Individual layers do fall below α = 2. Our spectral/RG theory predicts that this regime can be associated with pathological, example-specific learning. So we tested that prediction directly. We inserted random sequences into the training set and measured whether the model remembered them using exact extraction, token recall, teacher-forced recall, and canary exposure. The result was striking. • AdamW memorized the planted sequences strongly. Earlier in training it reached ~96% exact recall of 32-token canaries. • Muon strongly suppressed this kind of memorization. At 10,000 steps, teacher-forced recall was ~62% for AdamW versus <1% for Muon. There is also a surprise: some Muon layers have α < 2 as well. So α < 2 by itself is not sufficient to explain memorization. This is why we recommend examining individual WeightWatcher layers and their ESDs—not simply average α. Muon appears to suppress memorization while also producing unusual ESDs that make conventional WeightWatcher analysis more difficult. We are now running Muon much longer to understand how these spectra evolve. If you are using WeightWatcher and trying to analyze models trained with Muon, feel free to reach out for help. #talkToChuck