feat: fixed BP.

src/bqn/nn.bqn

@@ -4,19 +4,19 @@ M ← +˝∘×⎉1‿∞
 
 Minn ← {rt‿ly𝕊dat:
   A‿DA ← ⟨1÷1+⋆∘-, ⊢×1⊸-⟩
-  BP ← {ts‿we𝕊𝕩:
-    do ← <(-⟜ts×DA)⊢´𝕩
-    𝕩×⌜¨do∾do{d𝕊w‿z: z DA⊸×d M˜⍉w}`⋈¨´1⊸↓¨we⋈⌽𝕩
+  BP ← {fs‿ts‿we𝕊𝕩: 
+    do ← <(-⟜ts×DA)⊑hx‿tx ← 1(↑⋈↓)⌽𝕩
+    (fs<⊸∾tx)×⌜˜¨⌽do∾do{d𝕊w‿z: z DA⊸×d M˜⍉w}`⋈¨´tx⋈˜1↓we
   }
   FP ← {z𝕊b‿we: we‿z⋄A¨b+we M z}`⟜(⋈¨´)
   E ⇐ FP{⊢´𝕩𝔽 dat{𝕨𝕊bi‿we: fs‿ts ← 𝕨(↑⋈↓)˜⊑ly
-    bi⋈we-rt× ts‿we BP fs<⊸FP𝕩}˝˜(U⚇1-⟜1∘≠⋈·<∘⌽˘2⊸↕)ly}
+    bi⋈we-rt× fs‿ts‿we BP fs<⊸FP𝕩}˝˜(U⚇1-⟜1∘≠⋈·<∘⌽˘2⊸↕)ly}
 }
 
-n‿ri‿rf‿dr ← 100‿2.8‿4‿0.1
+n‿ri‿rf‿dr ← 10‿2.8‿4‿0.1
 ≠td ← ∾{𝕩∾˘2↕𝕩(⊣×1⊸-×⊢)⍟(↕n)•rand.Range 0}¨↕∘⌈⌾((ri+dr×⊢)⁼)rf
 
-lm ← 0.01‿⟨2, 10, 1⟩ Minn td
-lm.E 2.85
+lm ← 0.01‿⟨2, 5, 1⟩ Minn td
+≡lm.E 2.85
 
 )r Setplot "scatter" ⋄ •Out¨ Plot´  m {ns←≠⊑𝕨 ⋄ (>𝕨)⋈˜∘‿ns⥊ns/𝕩} r

src/nn.org

@@ -57,13 +57,13 @@ The original C implementation has 175 lines excluding the optimization loop. The
 #+begin_src bqn :tangle ./bqn/nn.bqn
   Minn ← {rt‿ly𝕊dat:
     A‿DA ← ⟨1÷1+⋆∘-, ⊢×1⊸-⟩
-    BP ← {ts‿we𝕊𝕩:
-      do ← <(-⟜ts×DA)⊢´𝕩
-      𝕩×⌜¨do∾do{d𝕊w‿z: z DA⊸×d M˜⍉w}`⋈¨´1⊸↓¨we⋈⌽𝕩
+    BP ← {fs‿ts‿we𝕊𝕩: 
+      do ← <(-⟜ts×DA)⊑hx‿tx ← 1(↑⋈↓)⌽𝕩
+      (fs<⊸∾tx)×⌜˜¨⌽do∾do{d𝕊w‿z: z DA⊸×d M˜⍉w}`⋈¨´tx⋈˜1↓we
     }
     FP ← {z𝕊b‿we: we‿z⋄A¨b+we M z}`⟜(⋈¨´)
     E ⇐ FP{⊢´𝕩𝔽 dat{𝕨𝕊bi‿we: fs‿ts ← 𝕨(↑⋈↓)˜⊑ly
-      bi⋈we-rt× ts‿we BP fs<⊸FP𝕩}˝˜(U⚇1-⟜1∘≠⋈·<∘⌽˘2⊸↕)ly}
+      bi⋈we-rt× fs‿ts‿we BP fs<⊸FP𝕩}˝˜(U⚇1-⟜1∘≠⋈·<∘⌽˘2⊸↕)ly}
   }
 #+end_src
 
@@ -122,29 +122,22 @@ Moreover, it is not so trivial to approximate: the recurrence lacks a [[https://
 the context of neural networks[fn:5]. First let's generate some reference data:
 
 #+begin_src bqn :tangle ./bqn/nn.bqn
-  n‿ri‿rf‿dr ← 100‿2.8‿4‿0.1
+  n‿ri‿rf‿dr ← 10‿2.8‿4‿0.1
   ≠td ← ∾{𝕩∾˘2↕𝕩(⊣×1⊸-×⊢)⍟(↕n)•rand.Range 0}¨↕∘⌈⌾((ri+dr×⊢)⁼)rf
 #+end_src
 
 #+RESULTS:
-: 1287
+: 117
 
 Then we can train =Minn=, and generate some approximated data with the perceptron:
 
 #+begin_src bqn :tangle ./bqn/nn.bqn
-  lm ← 0.01‿⟨2, 10, 1⟩ Minn td
-  lm.E 2.85
+  lm ← 0.01‿⟨2, 5, 1⟩ Minn td
+  ≡lm.E 2.85
 #+end_src
 
 #+RESULTS:
-: ⟨ ⟨ 10 1 ⟩ ⟨ 1 10 ⟩ ⟩
-: Error: Mapping: Expected equal shape prefix (10‿2 ≡ ≢𝕨, ⟨2⟩ ≡ ≢𝕩)
-: at     bi⋈we-rt× ts‿we BP fs<⊸FP𝕩}˝˜(U⚇1-⟜1∘≠⋈·<∘⌽˘2⊸↕)ly}
-:             ^
-: at   E ⇐ FP{⊢´𝕩𝔽 dat{𝕨𝕊bi‿we: fs‿ts ← 𝕨(↑⋈↓)˜⊑ly
-:                     ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
-: at lm.E 2.85
-:    ^^^^
+: 118
 
 Let’s see if we’ve gotten the numbers right after learning. But then again, what is a number that a man may know it[fn:6]...