Source
Kirsanov, Chou, Cho and Chung (2025), LIT-946, read in full in NOTE-789: §4.1 (“Task performance”, “Last-token effects”, “Sensitivity to the choice of demonstrations”), Figure 6, and §5.
What was actually shown
Manifold capacity, P / D* for P classes where D* is the critical projection dimension for linear separability, measures how separable the class point clouds are to an ideal linear decoder.
- Example choice. With five demonstrations, accuracy over random draws of examples runs “from below 0.1 to approximately 0.6”. Final-layer capacity of the last token changes little, the worst runs still exceed the instruction prompt’s capacity, and their layer profile is “nearly identical” to the best runs (Fig. 6).
- Relabelled categories. When labels are consistently swapped (“Joy” → “Anger”), accuracy is low on both the new and the original labels, while last-token capacity is “similar to the gold label setting”.
- The contrast case. Letter-code labels lower capacity as well as accuracy, so capacity does track some failures.
Each result could have come out the other way: low-accuracy runs could have had low capacity, as the letter-code case does.
What this does not say
- The readout is not measured. The paper infers misalignment of the unembedding from high capacity with low accuracy. It proposes, and does not run, the comparison with a trained linear classifier.
- Not order effects. Only which examples were drawn was varied, not their order, so Lu et al.’s order sensitivity is not explained by this.
- Not instruction-tuned models. Base models only.
- Not open-ended tasks. Capacity is defined for fixed label sets.
- Not that the representation is the “real” task state. High capacity means an ideal linear decoder could separate the classes; it does not mean the model represents the intended task.
Connections
No relations are declared.
- CLAIM-029. Its defeater cites surface-form sensitivity as evidence against a stable frame. This account locates one such sensitivity in the readout, with the representation the context sets left nearly unchanged.
- CLAIM-118. It adds a third place where interpretation can fail, beside context and interpreter: between what is decodable and what the model’s own decoder reads.
- QUESTION-020. A receiver whose representation already separates the classes and whose readout fails is a case where improving the interpreter’s readout, not the signal, would recover the loss. The paper does not test that.
- THEORY-264, from the same reading and LIT-942, holds the representation-side finding that demonstrations and instructions act differently.