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A checkpoint is eligible when the larger of the two declared factor-change magnitudes reaches η. This excludes bends formed from very small displacements under the study’s chosen filter. Because its inputs are factor magnitudes, eligibility can change under reciprocal LoRA rescaling even when the operator-based cosine is invariant.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| E_t | Eligibility indicator |
| M_A | Input-factor displacement magnitude |
| M_B | Output-factor displacement magnitude |
| eta | Magnitude threshold |
| k | Comparison lag |
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Original context
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I evaluate lags of five, ten, and 15 training steps on the regular grid. Each lag uses every center with both required neighbors. This preserves the training step offsets and does not impose the longest lag’s edge trimming on shorter lags.
A sharp angle can accompany a tiny movement. I therefore also apply the amplitude eligibility rule in the source plotting code. Let MA(t;k) be the larger of the norms ∥at−k−at∥2 and ∥at+k−at∥2, with MB(t;k) defined analogously. A center is eligible when
Et(k,η)=1{max(MA(t;k),MB(t;k))≥η}.
(4.6)
The six thresholds are zero, 0.0001, 0.0005, 0.001, 0.002, and 0.005. The value 0.002 appears in the inspected source plotting call. I retain all 18 combinations of lag and threshold rather than select only the result nearest the region previously reported.
Although the effective matrix cosine is invariant under reciprocal factor rescaling, this inherited factor amplitude filter is not. Applying an invariant metric after that filter does not make the complete event selection invariant. A future invariant detector would need an amplitude rule in effective matrix space or in the operator’s action on specified inputs. I do not silently substitute that alternative here.Exact original notation
{E}_{t}(k,\eta )=1{max({M}_{A}(t;k),{M}_{B}(t;k))\ge \eta }.Related builds
Sources & provenance
{E}_{t}(k,\eta )=1{max({M}_{A}(t;k),{M}_{B}(t;k))\ge \eta }.
{E}_{t}(k,\eta )=1{max({M}_{A}(t;k),{M}_{B}(t;k))\ge \eta }.
{E}_{t}(k,\eta )=1{max({M}_{A}(t;k),{M}_{B}(t;k))\ge \eta }.
{E}_{t}(k,\eta )=1{max({M}_{A}(t;k),{M}_{B}(t;k))\ge \eta }.