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This states that the flattened input-side factor has 13824 real coordinates in the selected module. It defines the column dimension of the effective rank-one update. The vector dimension describes the inspected adapter module, not the total size of the base model.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| a_t | Input-side factor |
How it works
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Original context
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Each segment contains at least 20 observations. The selected k is the last step in the first segment, not the onset of a newly observed physiological process. This fit is kept on its original 300-step domain rather than silently extending its meaning to all 792 steps. It has no independence-based significance test: sequential training observations are autocorrelated and the split is selected after viewing the trajectory. A smooth nonlinear curve can also describe a rise and decline. 4.3 Effective weight update and factorization invariance For a rank-one adapter, let at∈R13824 and bt∈R5120 be the flattened input and output factors. The learned contribution to the layer is Ut=s btatT, s=64, and the adapted layer acts as W0+Uth. This is the usual low-rank update structure [4]. Rank-stabilized and ordinary rank denominators coincide at rank one; inspecting the configuration is nevertheless necessary [9]. The factorization is not unique. For nonzero ct, replacing bt by ctbt and at by at/ct preserves Ut. In particular, simultaneous sign reversal changes both factor directions but not the effective operator. Consequently, we calculate factor metrics and corresponding effective-update metrics. This checks for a purely representational explanation of a factor change without assuming that the source study’s finding is such an artifact.
Exact original notation
{a}_{t}\in {R}^{13824}