Deep Learning Models Also Recall Features

While scaling laws govern aggregate large language model performance, no scaling law has linked factual recall to both model size and training-data composition. We evaluated 38 models on over 8,900 scholarly references evaluated by an automated reference verification system. Recall quality follows a sigmoid in the log-linear combination of model parameter count and topic representation in training data. These two variables alone explain 60% of the variance across 16 dense models from four families, rising to 74-94% within individual families. The form matches a superposition-inspired account in which recall is gated by a signal-to-noise ratio: signal strength scales with concept frequency and the noise floor with model capacity.

Not all facts a language model can recall support further learning equally well. We distinguish active facts, which support generalization beyond their own recall, from inert facts, which can be recalled but do not support such generalization in a given task. We study this distinction by constructing new relations from existing ones. Take the relation that maps a place to its continent (Paris -> Europe) and assign each of its answers an arbitrary new label (Europe -> crab, Asia -> zebra). The new relation then maps Paris -> crab. We fine-tune the model on the new relation for a subset of subjects, without telling it the original relation or the relabeling rule, and test whether it assigns the corresponding labels to held-out subjects that share an answer in the original relation. Having learned Paris -> crab, does it answer Munich -> crab? Across eleven language models and 70 relations, how linearly readable the original relation is in pretrained representations strongly predicts this generalization. Within each model, the two correlate across relations at Pearson r = 0.87 to 0.92. This association persists when controlling, separately and jointly, for the number of fine-tuning subjects and answers, the model's accuracy on the original relation, and how often the subjects occur in pretraining text. It is also robust to re-randomizing the label assignment and fine-tuning seed, and to replacing the animal labels with labels from thirteen other semantic categories. When we map a fine-tuned model's wrong label back to the original answer it was assigned to, Munich -> zebra becomes Munich -> Asia. Answers recovered this way are more often among the linear probe's top answers for the subject than among the pretrained model's own. Whether a new relation generalizes depends less on whether its facts can be recalled than on how readily their shared structure can be read out linearly.

Activation space and parameter space provide complementary views of model computation. Activations represent information, while weights read, transform, and write that information. Yet existing interpretability methods largely study the two spaces separately, leaving the connection between represented information and parameter-level computation underexplored. We introduce Activation-Supported Parameter Decomposition (ASPD), which jointly decomposes activation and parameter spaces and grounds each learned weight component in the activation features it reads or writes. This grounding constrains otherwise non-unique parameter decompositions using the model's internal activations, while an internal reconstruction objective provides a local learning signal at the weight matrix being analyzed. Together, these properties enable scalable, interpretable, and causally editable parameter decomposition in pretrained large language models, demonstrated on Qwen-3-8B. The learned read--write components can also be composed into parameter-level mechanism circuits. We use ASPD to recover mechanisms underlying the classic IOI circuit and trace semantic transformations through model weights.