The equation library

Every recovered mathematical record has an individual page. Browse original equations, code expressions, indexed components, parameter definitions, and explicitly unresolved source slots.

2,910 recordsSource snapshot 2026-10-17

Counts refer to mathematical records, including implemented expressions and generated instances. They are not counts of independently validated theories. Exact occurrences and unresolved slots remain traceable. Read the complete 1–516 source index ↗ · Inspect the scan decisions ↗

2,910 records · page 4 of 59Search the source archive ↗

donor-deepseek-yarn-correction

Solve for the rotary frequency index at a chosen rotation count

At index i, the unscaled angular frequency is base^(−2 i/dim). Over orig_max positions it completes orig_max*base^(−2 i/dim)/(2π) rotations. Setting that count equal to rot and solving logarithmically for i gives the displayed correction coordinate. The caller rounds and clamps coordinates to form…

Donor architecture mathematicshistorical source recovered; expression not executed in this website audit

yarn_find_correction_dim(rot, dim, base, orig_max) = dim * ln( orig_max / (rot * 2 * pi) ) / ( 2 * ln(base) )

donor-deepseek-attention-scale

Square the YaRN multiplier in the attention coefficient

The baseline coefficient is 1/√192. Multiplying it by the squared magnitude adjustment yields(1+0.1 ln 40)²/√192≈0.1352337788608801, a factor 1.8738542071 above the baseline. The dossier’s 0.135237 is an approximate decimal. In this configuration the sine/cosine cache’s separate ratio of equal…

Donor architecture mathematicshistorical source recovered; expression not executed in this website audit

softmax_scale = 192^-0.5 * mscale * mscale = 0.0721688 * 1.3688879^2 = 0.135237 This is NOT 1/sqrt(192) = 0.0721688. The 1.874x factor is load-bearing.

donor-deepseek-moe-weighted-sum

Sum the selected expert outputs with their routing weights

Each chosen expert evaluates the same input representation h. Its output vector is multiplied by the associated routing weight, and the selected vectors are added. The implementation groups tokens by expert for efficient evaluation and restores their original order before summing; those…

Donor architecture mathematicshistorical source recovered; expression not executed in this website audit

y = moe_infer(h, topk_idx, topk_weight) # sum_i w_i * Expert_i(h)

donor-deepseek-attention-value

Use attention weights to average value vectors

Matrix multiplication sums the value vector at each key position weighted by that query’s attention probability. A 128-component value vector per head gives a 128-component output per head. This is a convex combination before subsequent dropout or projection when the supplied probabilities are…

Donor architecture mathematicshistorical source recovered; expression not executed in this website audit

out = probs @ v -> 128 per head

donor-deepseek-yarn-blend-overview

YaRN prose blend with the ramp orientation reversed

If ramp is the increasing yarn_linear_ramp_mask defined in the embedded source, this prose reverses the blend. The body defines inv_freq_mask=1−ramp and returns interp*(1−inv_freq_mask)+extra*inv_freq_mask, equivalent to interp*ramp+extra*(1−ramp). At a zero ramp the code retains the original high…

Donor architecture mathematicshistorical source recovered; expression not executed in this website audit

inv_freq = interp * (1 - ramp) + extrap * ramp

donor-eq-1181af70ef9682

Add an always-active shared expert

The shared expert processes identity, the input representation saved before the routed expert computation. Its output is added to the weighted routed sum. It therefore contributes a parallel transformation of the original input; it does not take the routed output as its input.