hanyuy/prior-shift-diagnostic

Prior-shift diagnostic

When a derived language model (instruction-tuned, preference-tuned, or continued-pretrained) gets worse on text its base model was trained on, how much of the loss increase can a context-free correction of its logits, a token bias and/or a temperature, take back?

This deposit holds the diagnostic (code/prior_shift.py), per-document results for 14 released base/derived pairs, and a CPU script (reproduce.sh) that re-runs the synthetic tests and recomputes every point estimate from the per-document sums.

Result

The scoring text is one million tokens of web text from one DCLM shard of the OLMo-2 pretraining mix. For the OLMo-2 pairs it is probably training data, since OLMo-2 saw that mix about once. SmolLM2's model card lists DCLM among its sources, so for it the text comes from the same source family. For Qwen2.5 it is a proxy for web pretraining data. Whether any particular document was seen is unknown for every model.

• The context-free biases fitted here recover little of the loss increase. The main out-of-sample measurement is a bias fitted on the 4,096 most frequent tokens. Its symmetric share is at most 0.098, on Qwen2.5-7B-Instruct, and below 0.07 on every other pair. A one-step closed-form bias fitted on the scoring text itself gives at most 0.158, on the same pair. That in-sample figure is not an upper bound: an optimally fitted bias can recover more than one step does. So the result is that these fitted bias corrections stay below 0.20 on all 14 pairs, not that no bias could do better. On the headline pair the top-4K fit hit its 20-iteration cap while its held-out FIT-slice loss was still falling by about 2·10⁻⁵ nats per step. The measured EVAL share is 0.098; what further iterations would do on EVAL was not measured.
• Adding a temperature recovers more, most of all in the OLMo-2 preference-tuned models. Most derived models are overconfident on this text: the fitted T is up to 1.22, against 1.00–1.01 for their bases (for Qwen2.5-Coder-1.5B the difference is within the search resolution). Within OLMo-2, the bias-plus-temperature share S_sym^aff rises from SFT to DPO: OLMo-2-1B is at 0.06 after SFT and 0.16 after DPO, and OLMo-2-7B-Instruct reaches 0.26 (0.36 with the top-4K bias), where the top-4K bias alone gives 0.04. The gap between the two fits is an incremental contrast between fitting procedures, not a decomposition: no temperature-only correction is fitted. This is two within-family contrasts with one recipe. Other instruction-tuned models are far lower (SmolLM2-1.7B-Instruct 0.021, Qwen2.5-1.5B-Instruct 0.018), so it is not a general property of preference tuning.
• Continued pretraining on math forgets a lot and recovers almost nothing. Qwen2.5-Math loses 0.49 (7B) and 0.80 (1.5B) nats/token. Every out-of-sample correction recovers ≤ 0.031 of it, and the in-sample one-step closed form ≤ 0.055. The Coder models lose less (0.13), with similarly near-zero shares.

The full table is data/summary.md, with 95% document-bootstrap intervals in data/summary.json. These intervals resample EVAL documents with the fitted corrections held fixed. They are much narrower than the spread from fitting choices: for example, the closed-form share of Qwen2.5-7B-Instruct ranges from 0.077 to 0.120 over the three smoothing strengths in result.json, and the top-4K bias interval for that pair reaches 0.104.

Why the closed-form bias is not the headline

The smoothed closed-form correction (cf, METHODS.md) gives every token unseen in FIT a fixed negative bias. At the reported smoothing strength this makes every base model worse on EVAL (R_cf_old from −0.022 to −0.030 nats/token), and 12 of 14 derived models too. Its symmetric share therefore partly measures which model the smoothing hurts more. The same tail penalty is a likely reason the full-vocabulary fitted bias early-stopped at b = 0 on every model. The top-4K bias moves only frequent tokens. Its fit stays at b = 0 for all six bases, so for it S_sym equals S_card. The in-sample one-step figure comes from jensen_in_sample_E in each result.json.

A caveat for any "a simple correction explains X%" claim

How much an affine correction recovers does not identify what caused the loss. In one synthetic known-answer case, the derived model's output weights get random, context-dependent damage, and the construction adds no global bias and no temperature. The fitted bias-plus-temperature correction still recovers 0.29 of the loss increase, and the bias alone 0.08 (code/test_prior_shift.py, case ctx; reproduce.sh prints both). The damage changes the model's calibration as a side effect, and a temperature partly undoes that.

This is one construction at one damage scale, not a calibrated threshold. It is a counterexample to reading a combined share of that size as evidence for a global prior or temperature change. It does not imply that a genuine temperature change must show up in the bias share: the temp case is a pure temperature change, which the affine correction recovers almost entirely and the bias alone does not.

Quantities

For a base model (old) and a derived model (new) sharing a tokenizer, scored on the same EVAL documents, Δ = CE_new − CE_old (nats/token). For a correction x fitted separately to each model on FIT documents, with R^x the cross-entropy it removes:

S_card^x = R_new^x / Δ                  share recovered on the derived model
S_sym^x  = (R_new^x − R_old^x) / Δ      net change in what the correction recovers

S_sym is reported because S_card overstates the share when the base itself gains from the correction on this text: the synthetic case proxy shows S_card 0.47 against S_sym 0.30. S_sym is a difference of two gains. It can cancel when the two models gain for different reasons, e.g. a bias the derived model removed and a new one it introduced. A small S_sym is therefore not evidence that no new prior error exists. For the top-4K bias, R_old = 0 on every base, so no cancellation occurs there. Corrections, fitting and statistics are in METHODS.md.

Pairs

Group	Base	Derived	Regime
g1	OLMo-2-0425-1B	-SFT, -DPO, -Instruct	post-training
g2	OLMo-2-1124-7B	-SFT, -DPO, -Instruct	post-training
g3	Qwen2.5-7B	-Instruct, Qwen2.5-Math-7B, Qwen2.5-Coder-7B	post-training; continued pretraining
g4	Qwen2.5-1.5B	-Instruct, Qwen2.5-Math-1.5B, Qwen2.5-Coder-1.5B	post-training; continued pretraining
g5	SmolLM2-1.7B	-Instruct	post-training
g6	OLMo-2-0425-1B at branch stage1-step1907359-tokens4001B (commit 9d3e43659f00, as listed on 2026-10-09)	OLMo-2-0425-1B (final)	mid-training anneal

Every model is pinned to a Hugging Face commit; the full SHAs are in each result.json (revisions) and inputs.json (args).

Layout

code/prior_shift.py        the diagnostic (GPU; one base, one or more derived models)
code/summarize.py          table and descriptive flags from a results directory
code/test_prior_shift.py   synthetic known-answer tests (CPU, about a minute on an idle machine)
data/<group>/inputs.json   document indices, SHA-256 of each document's text, token counts
data/<group>/<model>/result.json   estimates, intervals, fitted temperatures, bias-fit traces
data/<group>/<model>/docsums.npz   per-document loss sums under every correction, both models
data/<group>.log           run log
data/summary.{json,md}     the full table of results
verify_data.py             recomputes the point estimates from docsums.npz
test_verify_data.py        negative controls: verify_data.py must reject corrupted inputs
reproduce.sh               runs all checks on a CPU

The data contain no corpus text: documents are identified by index and SHA-256 within one public shard (inputs.json, field data). The fitted bias vectors are not saved.

Checking this deposit

./reproduce.sh     # Python 3 with numpy and torch; a few minutes on a CPU

It does four things: verifies the checksums; runs the synthetic tests and prints the values cited above; recomputes every point estimate in each result.json from the per-document sums, checking that all 14 pairs are present and that the sums are finite and consistent, and shows that the verifier rejects corrupted inputs; and regenerates the summary table. It exits non-zero on any failure.

It does not recompute the confidence intervals, the fitted temperatures, the in-sample figures or the fit traces; those need the models. Nor does it tie data/ to the code, which needs the GPU re-run below. code/ is the code that produced data/; only docstrings, comments and the test's import name differ.

Re-running the models

On a GPU (all pairs ran on one A100-80GB; Colab's resource monitor, read by hand and not recorded, showed ≈ 21 GB GPU and ≈ 26 GB host memory on the 7B pairs):

python code/prior_shift.py --base Qwen/Qwen2.5-7B --base_rev d149729398750b98c0af14eb82c78cfe92750796 \
    --new Qwen/Qwen2.5-7B-Instruct --new_rev a09a35458c702b33eeacc393d103063234e8bc28 --out out/g3

The run used Python 3.13 and torch 2.11 (recorded in each result.json) and transformers 5.18 (not recorded), with numpy, zstandard and requests. The sweep took about 13.5 A100-hours, mostly the temperature search. Model revisions are pinned. The data shard is read from the dataset's main branch, not a pinned commit. Every document's SHA-256 is in inputs.json, but the code does not compare a re-run against it, so drift has to be checked by hand. Results are deterministic up to GPU floating-point nondeterminism.

What is not claimed

• Scope. One web shard, one million EVAL tokens, 14 pairs from three model families, all at or below 7B. Nothing here speaks to larger models, to other old-distribution text, or to benchmark forgetting.
• No bound on bias recoverability. The shares are those of the fitted procedures (smoothing, early stopping, top-4,096 support). The in-sample one-step figure is not a ceiling. A differently fitted bias might recover more. K = 4,096, the IPF step (undamped, no line search) and the early-stopping split were not varied. That every base fit stays at b = 0 is a property of this procedure, not of the models. The symmetric in-sample share (0.158 at most) differs from the per-model in-sample share S_card, which is large (e.g. 0.78 on Qwen2.5-7B-Instruct), because the base gains in sample too.
• Excluded tokens are not measured. Special and added tokens (EOS, chat-template tokens) are removed from the softmax, so all losses are conditional on the regular vocabulary. A prior shift onto excluded tokens, e.g. more EOS mass, would raise a model's full-vocabulary loss and be invisible here.
• A small S_sym does not rule out an introduced prior error (see Quantities). Format- and position-specific shifts fall on the context-dependent side of this split by definition.
• The flags in code/summarize.py are descriptive thresholds. The 0.20 bias bar and the 0.39 combined-share bar (0.29 from the synthetic ctx case plus 0.10) are fixed numbers, not calibrated tests. No flag firing is not evidence against a mechanism.
• The affine fit is not a certified optimum. The temperature is chosen by golden-section search over early-stopped inner fits; the profile is not shown to be unimodal, and T = 1 is not explicitly among the candidates.
• Same tokenizer, same targets. Base and derived models are scored on the base tokenizer's ids. Tokenizer agreement is checked on one probe sentence, and per-document target counts are taken from the base model, not cross-checked.
• The scoring text is not held out for every model. For OLMo-2 it is likely training data.
• The temperature finding is not new in kind. Post-training is known to hurt calibration on benchmarks; this measures the same effect as a share of web-text loss.

Citation and licence

Archived on Zenodo: 10.5281/zenodo.23304208 (this version; all versions: 10.5281/zenodo.23304207). See CITATION.cff. Everything, data included, is CC BY 4.0 (LICENSE-DOCS). The code (code/, reproduce.sh, verify_data.py, test_verify_data.py) is additionally offered under MIT (LICENSE); GitHub's sidebar shows only the latter.

Source data: documents from one DCLM shard of allenai/olmo-mix-1124 (ODC-BY; its DCLM-Baseline part is CC BY 4.0). No corpus text is redistributed here, only document indices, SHA-256 hashes, token counts and per-document loss sums.