How many assignments can a language model recall before it loses track of which value belongs to which entity? We measure this limit using continuous recall curves for 12 models at or below 3B parameters and a threshold sweep over 30 open models up to 12B. On the continuous curves, the load at which recall falls halfway to chance follows K50=cNα, with α=0.820 and R2=0.73. The broader sweep shows an eightfold range associated with pretraining recipe, although the continuous curves show no detectable recipe effect after controlling for scale, with few modern models in the fit. We derive why interference can lower measured capacity by reducing single-binding recall even when the load-dependent recall profile is unchanged. Direct task training also exceeds the extrapolated zero-shot law, but different measurement criteria prevent interpreting that comparison as a capacity gain. Its formation times follow a power-law form in two independent codebases, conditional on runs that succeed. Together, these results characterize capacity at the model's query interface. Bounds on joint recall and a decomposition of policy errors connect this measurement to working memory and instruction following, without treating recall as a measure of alignment. The controlled task also provides a baseline for testing whether binding limits constrain world-state tracking; the present experiments do not measure state updates or downstream transfer.
Figures & tables
Figure 1: The task and its two axes. Each trial presents K entity–obligation bindings, a D -token interference block, and a recall query; the model is correct iff its highest-logit obligation token matches the queried binding. Varying K probes capacity, varying D probes interference-robustness. Right: both capacity statistics are midpoint crossings of the recall curve between the model’s own K=1 ceiling and chance: k∗ on the measurement grid and K50 under a logistic fit to the continuous curves (Section 2 ).
quantity
old med.
modern med.
family-clustered 95% CI
family p
capacity k∗
3
16
[+10,+13]
0.012
packing efficiency k∗/ddecl
0.134
0.462
[+0.279,+0.473]
0.010
subspace dimension ddecl
24.86
33.23
[−0.003,+11.77]
0.114
interference
0.388
0.183
[−0.629,+0.013]
0.038
Table 1: Family-clustered comparisons. Medians by recipe with the family-clustered bootstrap interval and the family-level p -value for each quantity. Bold highlights capacity and its derived ratio. These are recipe contrasts, not tests of within-family capacity prediction.
The quality with which language models follow instructions falls as the load grows, yet there is still no quantity that expresses the limit of a model in units of load with an uncertainty. We propose an instrument in which the load consists of rules that replace single-token words in a text without meaning: such an instruction is atomic, the rules are independent by the construction of the task, and the outcome of every application of a rule is determined by a computable reference answer. Every occurrence of a word to be replaced becomes a Bernoulli trial with a known position in the answer and a known rule number. The statistical model first measures the shape of the dependence of the probability of a right replacement on the text length, the word position, the replacement density, the number of rules and the rule number, then describes it by smooth laws and restores a reference level that does not depend on the choice of the coding. The model yields the instruction capacity - the number of rules held at a given share of right replacements - with an uncertainty. A measurement of GPT-4o mini (2958 requests, 642,430 trials) gave regular laws for every load factor and for the collapse of the answer; the instruction capacity was about 37-38 rules at a share of right replacements of 0.95, and about 18-19 rules at the full replacement density. The code of the instrument, the measurement data and the passport are open, and every number of the passport is recomputed from the published points. The passport of a model serves as the calibration of a future meter of the instruction load of prompts.
We reproduce and stress-test the work of Yu et al. (2023), who characterize how language models (LMs) arbitrate between memorized knowledge and contradictory in-context statements. We replicate their world-capitals experiments on 31 models spanning Pythia, GPT-2, Qwen3, and Ministral families, including base and post-trained variants, and extend evaluations to five additional knowledge relation types from the ParaConflict dataset. We empirically confirm most of their original findings: larger models and higher-frequency entities tend to favor memorized answers, with substantial family-level variance. However, several conclusions do not generalize cleanly: entity-frequency effects disappear on Qwen3-14B and 32B; post-training shifts the memory-context trade-off inconsistently across families; question phrasing alone can change a model's reliance on memorized knowledge by up to 80 percentage points; and semantically unrelated prose can mimic coherent supporting context. Our results clarify where Yu et al.'s claims hold and to what extent they generalize to other prompts.
Guilhem Fouilhé, Nicholas Asher, Philippe Muller
IRIT ANITI · IRIT CNRS · IRIT Université de Toulouse
Models trained on a new task typically degrade on prior tasks, a phenomenon known as forgetting. Traditionally, mitigating forgetting has required replaying stored exemplars from prior tasks, which is often impractical. By contrast, language models can sample from their own training distribution, and we show that these self-generated samples serve as effective replay data, nearly eliminating forgetting. We find that forgetting nonetheless persists when the model has little remaining capacity: models pretrained close to saturation cannot absorb new information without overwriting prior knowledge. When capacity is not the limiting factor, low learning rates reduce forgetting but require substantially more training steps. Replay breaks this tradeoff, enabling fast, high-learning-rate finetuning without forgetting.