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Scaling Laws for Safety Probes

Yuchen Wu, Jerry Wei

arXiv:2610.30678v1cs.AIcs.CLcs.CRcs.LG

TL;DR

Safety teams cannot know a new model's probe performance or label and architecture needs in advance, while existing datasets are often too limited or already saturated. The paper builds six datasets and tests two probe architectures across models and label budgets. Probe error follows scaling laws that predict performance and support choices about labels, model size and architecture.

  • Problem

    Probe performance, label needs and architecture choice are unknown before training, and existing safety datasets are limited in scale or saturate too quickly.

    Source: §1 · p. 1

  • Method

    The authors build six safety datasets and train two probe architectures on 20 base models from five families, varying labels from 32 to 10^6.

    Source: §1 · p. 2

  • Results

    Probe error follows two scaling laws across tasks, families and architectures; predictions for larger models are within 0.02 in 72% of cases, and the laws choose the cheaper option in 73%.

    Source: §1 · p. 2

  • Takeaways & Limitations

    The laws can help safety teams plan a probe for a new model before collecting its labels.

    Source: §1 · p. 2, §6 · p. 10

    The laws are fitted on base models, whereas deployed monitors read post-trained models; too few post-trained sizes are available in several families to fit the laws.

    Source: Limitations · p. 21

Abstract

from arXiv · show

Safety probes trained on a model's activations are a standard tool for monitoring language models in real time. Each time a new model is released or a new harm area needs to be monitored, the probe must be retrained, which requires new labels and a choice of probe architecture. Yet neither the model nor the labels tell us in advance how well the resulting probe will perform. Finding out requires training and comparing many probe configurations. In this paper, we ask whether probe performance can instead be predicted in advance from model size and the number of labels. Existing safety datasets are insufficient for this, as they are either limited in scale or already saturated. We therefore construct six new safety datasets of sufficient size and difficulty. On these datasets, we train two probe architectures on 20 base models from five model families, with 32 to $10^{6}$ labels for each model. We measure performance using probe error, defined as 1 - AUROC, where lower values are better. We find that probe error follows two simple scaling laws. First, the lowest probe error a model can reach falls as a power law in its size. Second, probe error decreases towards its floor as the number of examples increases; the slope increases as the target model size increases. Both laws hold across tasks, model families and probe architectures, and only their fitted constants differ. When fitted on the smallest models of a family, the laws predict the error of the next larger model to within 0.02 in 72% of cases. They also identify whether more labels or a larger model is the cheaper way to reach a target error in 73% of cases. Finally, they choose the probe architecture with an extra error of only 0.006 on average when they pick the worse one. These laws allow safety researchers to determine how to create the best probe for any given model and label budget.

1 Introduction

Safety probes must be retrained for each new model, but their performance and the needed label budget and architecture are unknown in advance. This paper tests whether probe performance can be predicted from model size and label count.

1 Introduction

  • Prior probe studies varied only some of the factors needed to test scaling laws, while many public safety datasets saturate too quickly or run out of labels before performance levels off.The study identifies model size, family, task, label count and probe architecture as factors to vary together.Source: §1 · p. 1, Table 1 · p. 2
  • The study constructs six safety datasets and trains two probe architectures on 20 base models from five families, using 32 to 10^6 labels per model.The datasets cover truth judgement, sycophancy, policy violation, general harm, jailbreak and prompt injection; the probes use a single layer's last-token activations or all layers and token positions.Source: §1 · pp. 1–2
  • Probe error follows two scaling laws: its label-saturated floor falls as a power law with model size, and it falls toward that floor faster on larger models.The laws hold across tasks, families and probe architectures; only fitted constants differ.Source: §1 · p. 2
  • Fitted on smaller models, the laws predict a larger model's probe error within 0.02 in 72% of cases, choose the cheaper route to a target error in 73%, and select architectures with only 0.006 average extra error when choosing the worse one.The cheaper-route comparison uses model parameters multiplied by labels as its cost measure.Source: §1 · p. 2

2 Related Work

Prior work studies safety probes and scaling laws, but probe studies have not jointly varied the factors needed to test scaling across models and tasks. This paper applies scaling-law methods to how readable safety-relevant behavior is in model activations.

2 Related Work

  • Safety probes recover safety-relevant properties and have been studied as low-cost monitors, but prior studies vary only a few factors on fixed model sets.Prior work also examines activation sources, token-level scoring and robustness to adversarial fine-tuning.Source: §2 · pp. 2–3
  • No prior probe study varies model size, family, task, label count and probe architecture together or tests a fitted law by extrapolation.Table 1 defines these as the factors used to characterize prior studies.Source: §2 · p. 3
  • Scaling-law research spans training-set-size error, joint model-and-data scaling, pretraining, transfer, cross-family prediction and downstream tasks; this paper applies it to probe error.The paper follows joint model–data scaling and evaluates fits by predicting larger models from smaller ones.Source: §2 · p. 3

3 Data and Experimental Setup

The experiments use six minimal-pair safety datasets to test probe scaling across tasks, model families, architectures and label counts. The paired examples differ only in the content that determines the label.

3 Data and Experimental Setup

  • The six datasets use minimal pairs, and each includes up to 10^6 examples; each pair shares all text except the label-determining span.The tasks are truth, sycophancy, policy violation, general harm, jailbreak and prompt injection.Source: §3 · p. 3, Figure 3 · p. 4
  • Truth pairs swap a factual answer, while sycophancy pairs present the claim as a user's assertion that the assistant agrees with.The truth statements draw on Wikidata5M and cover 37 relations.Source: §3 · p. 3, Figure 3 · p. 4
  • Policy-violation pairs show the same content with clauses it does and does not violate; general-harm pairs match harmful requests with harmless twins.The policy content comes from four public safety datasets, and the general-harm requests come from 31 public red-team datasets.Source: §3 · p. 4, Figure 3 · p. 4
  • Jailbreak and prompt-injection pairs reuse general-harm requests inside the same wrapper or injected document, so the request differs while the harmfulness label remains tied to it.The pairs also end with the same assistant refusal.Source: §3 · p. 4, Figure 3 · p. 4
  • The setup compares last-token linear probes with all-layer, token-scoring CC++ probes on 20 base models from five families, across ten label counts from 32 to 10^6.Each dataset has a fixed, training-disjoint test set of 36,000 examples, with three seeds per experiment cell.Source: §3 · p. 5

4 Scaling Laws for Probe Error

Probe error is well described by a model-size power law and a label-count law that approaches the size-dependent error floor. The laws extend across model families, probe architectures, and tasks, with some fitted constants or label-law forms varying.

4 Scaling Laws for Probe Error

  • The size law fits a straight line on log–log axes, and error moves from chance toward the floor as labels increase, sooner for larger models.The section plots probe error on a log scale because a power law appears as a straight line there.Source: §4 · p. 5, §4.2 · p. 6

4.1 Model Size

  • 0.18 at 0.5B to 0.056 at 72B: Qwen2.5 probe error follows a power law in model size, with R2 = 0.94 on log E.The fitted law describes the tested range from 0.5B to 72B parameters; no model is more than 0.012 from the line.Source: §4.1 · pp. 5–6

4.3 Model Family

  • Every tested family follows the model-size law, with each doubling multiplying error by 0.76 for Qwen3.5, 0.79 for Gemma-4, 0.86 for Qwen2.5, 0.89 for OLMo-3, and 0.93 for Ministral-3.Every model lies within 0.018 of its family’s fitted line.Source: §4.3 · p. 6, Figure 6 · p. 7

4.2 Labels

  • With more labels, probe error approaches a model-size-dependent floor; the label law fits all tested families, though each needs its own B.Across new families, average deviations are 0.015–0.021 and worst-case deviations are 0.030–0.053.Source: §4.3 · p. 6, §4.2 · p. 6

4.4 Probe Architecture

  • The last-token probe follows the model-size law as closely as CC++, but its label error curve falls more gradually and requires a shared steepness g = 0.61 on Qwen2.5.For CC++, fixing g = 1 costs at most 0.005 error in all but two settings.Source: §4.4 · p. 7, Figure 8 · p. 8

4.5 Task

  • Across six tasks, the size law holds, while the label law also holds with a task-specific B; Policy violation has the loosest size-law fit.The size-law average deviation is 0.016 for Policy violation, versus 0.005–0.010 on the other five tasks.Source: §4.5 · p. 7

5 Using the Laws

The laws are used to predict probe error for a larger model, compare the cost of more labels versus a larger model, and choose a probe architecture before training it on that model. Across these uses, predictions from smaller models provide actionable guidance for later choices.

5.1 Predicting a Model Not Yet Trained

  • Within 0.02 in 72% of cases, laws fitted on smaller models predict the next model’s probe error, versus 54% for a straight-line baseline.The predictions cover six tasks on Qwen2.5, Qwen3.5, and Gemma-4; on Qwen2.5, accuracy within 0.02 rises from 7 of 12 at k = 3 to 10 of 12 at k = 6.Source: §5.1 · p. 8, Figure 10 · p. 9

5.2 A Larger Model or More Labels

  • 73% of the clearly cheaper choices are selected correctly by the laws using parameters times labels as cost, versus 38% and 44% for additive and joint scaling-law baselines.The comparison uses 45 cases where both options reach the target and measured costs differ by at least twofold.Source: §5.2 · pp. 9–10

5.3 Choosing the Probe

  • For Truth on Qwen2.5-32B, the predicted probe-curve crossing is at 9,300 labels, close to the measured 9,100-label crossing.The laws select the last-token probe below 9,300 labels and CC++ above it; the selected probe is better at every label count.Source: §5.3 · p. 10, Figure 12 · p. 10
  • When the laws pick the worse probe across 200 model-and-label combinations, its extra error averages 0.006.The laws pick the better probe, or one within 0.005 of it, in 82% of combinations; fixed rules achieve 68% and 61%.Source: §5.3 · p. 10

6 Conclusion

The paper concludes that probe error follows two scaling laws across its tested tasks, model families, and architectures. Those laws support planning probe performance and design choices before probing a larger model.

6 Conclusion

  • Probe error follows a size law in which the error floor falls as a power law, and a label law in which error approaches that floor faster for larger models.Both laws hold across tasks, model families, and probe architectures; only their fitted constants change.Source: §6 · p. 10
  • The study builds six safety datasets and evaluates two probe architectures on 20 base models from five families.The datasets contain up to 10^6 labels each.Source: §6 · p. 10
  • The laws estimate performance and guide label, model-size, and probe-architecture choices before training a probe on a new model.The conclusion says teams can plan a probe for a new model before collecting its labels.Source: §6 · p. 10

Limitations

This section covers the limits of the scaling-law evidence and applications, alongside the construction and scope of the General harm, jailbreak, and prompt-injection datasets, including paired-request labeling and rendering.

Limitations

  • The tested size range is limited by open families’ dense base-model releases, and a new family still needs several sizes probed before predicting the next one.Probe error falls with size in all 30 task-family panels; on Truth, no model in families with at least three sizes is more than 0.018 from its family line. Two further dense families also follow Eq. 1.Source: Limitations · p. 21
  • Post-trained models are not yet covered broadly enough to fit the laws across families, tasks, and label budgets.For Qwen2.5-Instruct on Truth, Eq. 1 gives α = 0.30 versus 0.27 for base models at the same label count, while error is lower at every size; other post-trained families have too few sizes for fitting.Source: Limitations · p. 21
  • Open questions include which parameter count to use for mixture-of-experts models and whether model size and training length can jointly predict probe error.Mixture-of-experts probes resemble dense models between their total and active parameter counts, nearer the total; error also falls during pre-training. Future fitting should test post-trained models on CC++, other tasks, and up to 10^6 labels.Source: Limitations · p. 21
  • The application examples use the authors’ models and datasets, and real deployment choices depend on label prices, servable models, and tolerated false-positive rates.Section 5.2 counts only parameters times labels; teams must apply the procedure using their own costs, models, and targets.Source: Limitations · p. 21

Broader impacts

  • The laws let teams estimate probe performance before labeling, then choose label counts, monitored model size, and probe architecture before spending compute on the largest model.The procedure can transfer to a new safety task after probing a few model sizes; the dataset construction method supports learning curves from near chance to saturation, unlike the public safety datasets examined.Source: Broader impacts · p. 21, §B.1 · p. 22

B.1 Summary

  • The six datasets use minimal pairs that differ in the span determining the label, enabling probe learning curves from 32 to 10^6 labels.The datasets ask distinct questions about truth, agreement with false claims, policy clauses, harmful requests, jailbreak-wrapped requests, and harmful instructions arriving as data.Source: §B.1 · p. 22, §B.3 · p. 25

B.7 General harm

  • The General harm seed pool contains 69,454 requests from 13 sources, with source-specific pairs recorded in Tables 12 and 13.Source: Table 14 · p. 32

B.8 Jailbreak

  • Jailbreak pairs retain their General harm labels inside wrappers, with both rows using the same wrapper so only the request differs.About 15% of rows use later rewrites; wrapper sources include public jailbreak collections and encodings of earlier work.Source: §B.8 · pp. 32–33
  • The jailbreak dataset uses 261 wrappers: 257 collected templates filtered and deduplicated, plus four request encodings; test pairs draw ten wrappers and training pairs draw two to seven.The collected templates are 200–4,000 characters and are screened against the severe-content rule.Source: §B.8 · p. 33

B.9 Prompt injection

  • Prompt injection uses 65 verbatim shells from AgentDojo [17], CyberSecEval [10], and InjecAgent [101], placing paired General harm requests in the same shell across ten renderings per pair.Each pair gets seven shells from two assigned home channels and three from other channels; the full build has 2,042,000 rows and passes checks including equal label counts per shell.Source: §B.9 · p. 34

B.10 Public datasets

The public safety datasets examined often allow strong probe performance with few labels, and their label distinctions can be captured by bag-of-words cues. This limits their usefulness for studying long learning curves.

B.10 Public datasets

  • Every one of the 14 scorable public-dataset bag-of-words gates has AUROC between 0.70 and 1.00.The folds are grouped by each dataset’s own key, such as conversation or template ID.Source: §B.10 · pp. 35–36, Figure 13 · p. 37
  • At 32 labels, 7 of 14 public datasets already reach at least 0.90 AUROC with CC++; at each dataset’s largest label count, all 14 range from 0.898 to 1.000.The largest count is at most 31,623 on every dataset, so none has a label axis as long as the paper’s new datasets.Source: §B.10 · p. 36, Figure 13 · p. 37
  • Figure 14 compares bag-of-words AUROC on public datasets that start at 0.90 or higher with the paper’s datasets.The figure uses word 1–2-gram TF-IDF and folds grouped by each dataset’s own key.Source: Figure 14 · p. 37

C Experimental Setup in Full

The setup evaluates two probe architectures across six datasets and 20 dense base models, then fits and checks scaling laws for probe error. Across tasks and families, error falls with model size in every tested panel.

C Experimental Setup in Full

  • The results use 20 dense base models from five families, with both probe architectures evaluated on all six datasets.The other 39 probed models use only the last-token probe and do not enter Sections 4 and 5 results.Source: C Experimental Setup in Full · pp. 37–38
  • Each cell combines a dataset, model, probe architecture, and label count, with three seeds at each of ten label counts.The counts span 32 to 10^6 labelled rows.Source: C Experimental Setup in Full · p. 38
  • The last-token probe reads a single final-prompt token, while CC++ reads all decoder layers and scores tokens across the sequence.The last-token readout is an L2-regularised logistic regression; CC++ uses a streaming objective and smoothed maximum-token readout.Source: C Experimental Setup in Full · p. 38

D.2 How the fits are made

D.1 Every fit at a glance

  • The 750 fitted cells have root-mean-square misses of 0.023, 0.037, and 0.023 for the three fit groups, with 0.030 across all cells.The points follow the diagonal from chance to about 0.05 probe error.Source: §D.1 · p. 41, Figure 15 · p. 41

D.3 Eq. 1 in every task and family

  • Probe error falls with model size in all 30 panels for each architecture; CC++ exponents range from 0.04 to 0.63, and last-token exponents from 0.05 to 1.1.For CC++, no model lies more than 0.023 from its panel’s fitted line.Source: §D.3 · p. 42

D.4 Families

On Truth, the fitted model-size and label laws describe probe error across families, while the stability of fitted constants depends on the span of model sizes used.

D.4 Families

  • The CC++ error floor falls with size in all five families; α ranges from 0.104 on Ministral-3 to 0.405 on Qwen3.5.The corresponding doubling factors range from 0.93 to 0.76, and no model lies more than 0.018 from its family line.Source: §D.4 · p. 42, Table 22 · p. 42
  • Across the five families, CC++ B ranges from 404 on Qwen3.5 to 3,427 on Qwen2.5; its Eq. 2 fits have 0.015–0.030 root-mean-square miss.The Qwen2.5 size span is a factor of 147, while the other families cover factors from 3.6 to 12.Source: §D.4 · p. 42
  • With CC++, runs of at least three adjacent Qwen2.5 sizes give positive α, and the slope settles once the size span reaches about ten.For runs of two sizes, α ranges from −0.08 to 0.57; from four sizes on, B lies within 16% of its all-seven value.Source: §D.4 · pp. 42, 45, Table 23 · p. 45
  • With CC++, family differences in α and B mostly exceed the variation across Qwen2.5 size ranges, with specified exceptions where narrower ranges leave differences open.The exceptions include α for Ministral-3 and OLMo-3 and B for OLMo-3.Source: §D.4 · p. 45

D.5 Tasks

For CC++ on Qwen2.5, the model-size law holds across the six tasks, while the fitted slopes and label-law constants vary by task.

D.5 Tasks

  • Probe error falls with model size across all six tasks; α ranges from 0.162 on Policy violation to 0.412 on General harm.No model lies more than 0.023 from its task’s fitted line.Source: §D.5 · p. 46, Table 24 · p. 46
  • The fitted label-law constant B ranges from 111 on Prompt injection to 3,427 on Truth, and Eq. 2’s task-level miss ranges from 0.025 to 0.045 in root mean square.General harm has the largest deviation, 0.122.Source: §D.5 · p. 46

D.6 The two probe architectures

The appendix checks how the probe laws behave across architectures, label budgets, functional forms, and extrapolation settings. It finds that the main forms fit many settings closely, with identifiable exceptions and boundaries.

D.6 The two probe architectures

  • With one constant B, Eq. 2 fits CC++ more closely than the last-token probe in all five families; freeing g improves last-token fits, whose error falls more slowly with labels.For last-token probes, free-g root-mean-square misses range from 0.015 to 0.027, with g between 0.54 and 0.79.Source: §D.6 · pp. 46–47, Table 25 · p. 47

D.7 Labels needed

  • Labels needed to reach target errors fall with Qwen2.5 model size on every task, though not at every step.A target error of 0.05 is reached only on General harm from 3B, Sycophancy from 14B, and Prompt injection from 32B.Source: §D.7 · p. 47, Table 26 · p. 48

E.1 The fraction function

  • Among one-parameter learning-curve functions, the Hill function has the lowest miss in nine of ten settings; two-parameter functions fit more closely at the cost of one extra constant per model.The exponential function has the lowest miss in the remaining setting, Sycophancy.Source: §E.1 · p. 50, Table 29 · p. 50

E.2 Steepness of the label law

  • Allowing a free steepness g buys CC++ little accuracy in most settings, but substantially tightens fits on General harm and Prompt injection.On those two tasks, fixing g at 1 roughly triples error, from 0.012 to 0.040 and from 0.015 to 0.045, respectively.Source: §E.2 · p. 50, Table 30 · p. 51

E.3 Where the square root of N comes from √

  • The half-way label count for CC++ on Qwen2.5 Truth falls from 8,177 at 0.5B to 243 at 72B, consistent with an N exponent of 0.51.With a shared exponent across five families, CC++ has exponent 0.47 and root-mean-square miss 0.023; the last-token shared exponent is 0.85 with miss 0.021.Source: §E.3 · p. 51, Table 32 · p. 52

E.4 The number of layers

  • For three same-layer-count model pairs, CC++ probe error falls with size, matching the parameter-count prediction on average; the last-token probe also falls in all 18 pairs.The mean log error ratio is −0.355 for CC++ and −0.519 for last-token probes, against Eq. 1 predictions of −0.355 and −0.536.Source: §E.4 · p. 52

E.7 Miss rate at a low false-positive rate

  • At a 1% or 0.1% false-positive rate, fitted laws have miss rates similar in size to those on probe error.For CC++, root-mean-square miss ranges from 0.022 to 0.058 at 1% and from 0.011 to 0.033 at 0.1%.Source: §E.7 · pp. 53–54

E.8 Extrapolation over more sizes

  • For predictions two Qwen2.5 sizes ahead, Eq. 1 is within 0.02 of measured error in 68% of predictions for 32B and 72B together, versus 23% for persistence.Across whole curves, Eq. 2 and Eq. 3 are within 0.02 in 39% of predictions for those sizes, versus 9% for persistence.Source: §E.8 · p. 54

E.6 Relative error

Eq. 1 outperforms persistence on one-size-up probe-error predictions, and the appendix examines choices within the last-token probe. The best layer is consistently before the final layer, at 64–80% of model depth.

E.6 Relative error

  • 72% of Eq. 1 predictions fall within 0.02 absolute error, versus 46% and 54% for the two straight-line references.The references are the two straight lines of probe error against log N and persistence.Source: §E.6 · p. 53
  • 72% of Eq. 1 predictions are correct versus 49% for persistence, a 24-point gap with a 95% interval of [8, 39].Eq. 1 also has smaller relative error in 49 of 72 predictions (68%).Source: §E.6 · p. 53, Table 33 · p. 53

F Setting Up the Probe in Full

  • The appendix compares layer, position, and head choices within the last-token probe on Truth across seven Qwen2.5 sizes.Figures 19–21 report these choices; Figure 22 compares the streaming probe with the last-token probe.Source: F Setting Up the Probe in Full · p. 56

F.1 Which layer

  • At 105 labels, the best layer lies at 64–80% of depth and lowers probe error versus the last layer by 0.018 to 0.085.The error rises again beyond the best layer at every size; the first layer is near chance, with probe error 0.40 to 0.48.Source: §F.1 · p. 56, Figure 19 · p. 56

F.2 Which position

Position readouts and probe heads have different trade-offs across label budgets, while CC++ overtakes the last-token probe at model- and label-dependent thresholds. Additional comparisons cover models beyond the main dense base-model set, including mixture-of-experts and post-trained models.

F.2 Which position

  • At 104 labels, learned position weights beat the last-token probe by 0.046, 0.040, and 0.025 probe error at 1.5B, 7B, and 32B.The last token is best with 100 labels; learned weights first lead at 3,162 labels for 1.5B, 1,000 for 7B, and 316 for 32B. At 32B, their lead shrinks to 0.008 at 10^6 labels; these runs use a smaller held-out Truth set.Source: §F.2 · pp. 56–57, Figure 20 · p. 57

F.3 How large a head

  • At 10^6 labels, MLP heads of widths 16, 64, and 256 change AUROC by −0.003, −0.004, and −0.001 on average.Rank-16 heads stay within 0.016 AUROC of the linear probe across Qwen2.5 sizes and label counts; low-rank heads are within two seed errors in 201 of 210 cells.Source: §F.3 · p. 57, Figure 21 · p. 57

F.4 The streaming probe against the last-token probe

  • CC++ first leads at 10^4 labels on 14B, 32B, and 72B, and at 31,623 labels on the four smaller Qwen2.5 sizes.With few labels, the last-token probe leads at every size, by up to 0.28 at 32 labels on 72B; at 10^6 labels, CC++ leads by 0.08 on 0.5B and less than 0.005 on 32B and 72B.Source: §F.4 · p. 58, Figure 22 · p. 58

G Other Models

  • The appendix reports last-token-probe results on Truth for 39 models beyond the 20 dense base models, one result per figure.These additional results do not enter the main text.Source: G Other Models · p. 59

G.1 Mixture-of-experts models

  • At 10^6 labels, Qwen3.5 35B-A3B and Gemma-4 26B-A4B have probe errors between their families’ predictions at total and active parameter counts.On a log scale, both are nearer the total-parameter prediction, so each probes like a dense family model somewhat smaller than its total size.Source: §G.1 · p. 59, Figure 23 · p. 59

G.2 Post-trained models

  • Post-training lowers OLMo-3 probe error at every label budget; at 10^6 labels, errors fall from 0.111 to 0.096 at 7B and 0.072 to 0.062 at 32B.At 10^6 labels, the three post-trained checkpoints are within 0.002 of one another, so the gain is present after supervised fine-tuning. Base-model laws predict higher error for Instruct in all 56 cells, by 0.084 on average.Source: §G.2 · pp. 59–60, Figure 24 · p. 60

G.3 Checkpoints during pre-training

OLMo-3 probe error falls across pre-training stages, while two additional dense families also show decreasing error with model size. The appendix relates the paper’s probe curves and scaling laws to prior work on learning curves, probe accuracy, and joint scaling.

G.3 Checkpoints during pre-training

  • At 10^6 labels, OLMo-3 probe error falls from 0.286 after 10,000 steps to 0.151 at stage 1’s end, then to 0.105 after stage 2 and 0.111 in the released 7B model.For 32B, error falls from 0.177 after 15,000 steps to 0.103 at stage 1’s end and 0.072 in the released base model; training after stage 1 lowers error by about 30% more.Source: §G.3 · p. 60, Figure 25 · p. 61

G.4 Two more dense families

  • Nemotron-H and Qwen1.5 probe error both falls with model size, with fitted α values of 0.42 and 0.33, within the five-family range of 0.05 to 0.47.Qwen1.5 reads 0.14 to 0.29 and lies above every other family at a similar size.Source: §G.4 · p. 61, Figure 26 · p. 61

H Relation to Prior Work on Probe Curves and Joint Scaling

  • Eqs. 2 and 3 describe probe learning curves in error rather than log loss; B indicates how early the curve descends and how much code is spent before the probe reaches its ceiling.The paper reports B rather than computing code lengths, and it ran no control tasks.Source: H Relation to Prior Work on Probe… · p. 62
  • Eq. 1 captures the larger-model trend previously reported for linear probes of place and time on Llama-2, with task-, family-, and probe-specific exponents.For CC++ across the paper’s 30 Appendix D.3 panels, the exponent ranges from 0.04 to 0.63.Source: H Relation to Prior Work on Probe… · p. 62
  • Unlike saturating vision-probe laws, Eq. 1 has no floor; additive and joint forms fitted on Qwen2.5 tasks place their floor at zero.Eq. 2 couples labels and model size through a product; D labels on N parameters cover the same share of the distance to the ceiling as D N/N′ labels on N′ parameters.Source: H Relation to Prior Work on Probe… · p. 62

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