reaperdoesntknow commited on
Commit
be3ed35
·
verified ·
1 Parent(s): e97c886

Add DISC Mathematical Foundations, update portfolio stats (49 models, 22,598 total downloads)

Browse files
Files changed (1) hide show
  1. README.md +17 -0
README.md CHANGED
@@ -148,6 +148,23 @@ Companion paper: **[Three Teachers to Dual Cognition](https://doi.org/10.57967/h
148
 
149
  Apache 2.0 — same as the base Qwen3 model.
150
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
151
  ## Citation
152
 
153
  ```bibtex
 
148
 
149
  Apache 2.0 — same as the base Qwen3 model.
150
 
151
+
152
+ ## Mathematical Foundations: Discrepancy Calculus (DISC)
153
+
154
+ This model's training pipeline is grounded in Discrepancy Calculus — a measure-theoretic framework that treats singularities as primary structure rather than pathology. Full theory: *"On the Formal Analysis of Discrepancy Calculus"* (Colca, 2026; Convergent Intelligence LLC: Research Division).
155
+
156
+ **The Core Operator:**
157
+
158
+ $$Df(x) = \lim_{\varepsilon \downarrow 0} \frac{1}{\varepsilon} \int_x^{x+\varepsilon} \frac{|f(t) - f(x)|}{|t - x|}\, dt$$
159
+
160
+ For smooth $f$: $Df(x) = |f'(x)|$. For rough $f$: $D$ localizes irregularity to null sets while preserving integral structure.
161
+
162
+ **The Mesh Fundamental Identity** — every BV function decomposes as:
163
+
164
+ $$f(b) - f(a) = \underbrace{\int_a^b f'(x)\,dx}_{\text{smooth (AC)}} + \underbrace{\sum_{x \in J_f} \Delta f(x)}_{\text{jumps}} + \underbrace{D^c f(I)}_{\text{Cantor drift}}$$
165
+
166
+ Standard knowledge distillation captures only term 1. Topological Knowledge Distillation (TKD) preserves all three by treating the teacher's output distribution as a BV function and computing discrepancy energy, jump sets, and gap energy density before training begins.
167
+
168
  ## Citation
169
 
170
  ```bibtex