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整理神经网络部分

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qing committed 2026-08-25 10:59:41 +08:00
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commit d9b2359d25
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bot4cj/src/math/Af.cj
+82 -163
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@@ -1,33 +1,35 @@
package bot4cj.math
import std.math.*
import cangjie_tpc::matrix4cj.Matrix
/* -------- Activation Functions 激活函数族 --------
* TODO(20260516-qing): 增加序列化、反序列化工厂函数 */
/*
* -------- Activation Functions 激活函数族 --------
* TODO(20260516-qing): 增加序列化、反序列化工厂函数
* TODO(20260825-qing): 改为使用matrix4cj库
*/
public enum Af {
None | Sigmoid | ReLU | Leaky_ReLU(FP32) | Tanh | Softmax
None | Sigmoid | ReLU | Leaky_ReLU(Float64) | Tanh
/* -------- 执行激活函数 -------- */
public func forward(x: Matrix1) {
public func forward(x: Matrix) {
match(this) {
case None => none(x)
case Sigmoid => sigmoid(x)
case ReLU => relu(x)
case Leaky_ReLU(alpha) => leaky_relu(x, alpha)
case Tanh => tanh(x)
case Softmax => softmax(x)
}
}
/* -------- 激活函数的导数 -------- */
public func backward(y: Matrix1) {
public func backward(y: Matrix) {
match(this) {
case None => none_dot(y)
case Sigmoid => sigmoid_dot(y)
case ReLU => relu_dot(y)
case Leaky_ReLU(alpha) => leaky_relu_dot(y, alpha)
case Tanh => tanh_dot(y)
case Softmax => softmax_jacobian(y)
}
}
@@ -39,235 +41,152 @@ public enum Af {
case ReLU => "ReLU"
case Leaky_ReLU(alpha) => "Leaky_ReLU"
case Tanh => "Tanh"
case Softmax => "Softmax"
}
}
/* */
public func get_value(): FP32 {
/* NOTE(20260825-qing): 这个函数在序列化时可能会有用 */
public func get_value(): Float64 {
return match(this) {
case None => FP32(0.0f32)
case Sigmoid => FP32(0.0f32)
case ReLU => FP32(0.0f32)
case None => Float64(0.0f64)
case Sigmoid => Float64(0.0f64)
case ReLU => Float64(0.0f64)
case Leaky_ReLU(alpha) => alpha
case Tanh => FP32(0.0f32)
case Softmax => FP32(0.0f32)
case Tanh => Float64(0.0f64)
case Softmax => Float64(0.0f64)
}
}
/* -------- 空的激活函数 -------- */
private static func none(M: Matrix1) {
let row = M.get_row()
let col = M.get_col()
let N = Matrix1(row, col)
for (r in 0..row) {
for (c in 0..col) {
let x = M.get(r, c).getOrThrow()
let x1= x.getValue()
N.set(r, c, FP32(x1)) }
}
return N
private static func none(M: Matrix) {
return M.copy()
}
/* -------- 空激活函数的导数 -------- */
private static func none_dot(M: Matrix1) {
let row = M.get_row()
let col = M.get_col()
let N = Matrix1(row, col)
for (r in 0..row) {
for (c in 0..col) {
N.set(r, c, FP32(1.0f32)) }
}
return N
private static func none_dot(M: Matrix) {
let row = M.getRowDimension()
let col = M.getColumnDimension()
return Matrix(row, col, 1.0f64)
}
/* -------- S型生长曲线 -------- */
private static func sigmoid(M: Matrix1) {
let row = M.get_row()
let col = M.get_col()
let N = Matrix1(row, col)
private static func sigmoid(M: Matrix) {
let row = M.getRowDimension()
let col = M.getColumnDimension()
let N = Matrix(row, col)
for (r in 0..row) {
for (c in 0..col) {
let x = M.get(r, c).getOrThrow()
let x1= x.getValue()
let x2 = 1.0f32 / (1.0f32 + exp(-x1))
N.set(r, c, FP32(x2)) }
let x1 = M.get(r, c)
let x2 = 1.0f64 / (1.0f64 + exp(-x1))
N.set(r, c, x2)
}
}
return N
}
/* -------- S型生长曲线的导数 -------- */
private static func sigmoid_dot(M: Matrix1) {
let row = M.get_row()
let col = M.get_col()
let N = Matrix1(row, col)
private static func sigmoid_dot(M: Matrix) {
let row = M.getRowDimension()
let col = M.getColumnDimension()
let N = Matrix(row, col)
for (r in 0..row) {
for (c in 0..col) {
let x = M.get(r, c).getOrThrow()
let x1= x.getValue()
let x2 = 1.0f32 / (1.0f32 + exp(-x1))
let x3 = x2 * (1.0f32 - x2)
N.set(r, c, FP32(x3)) }
let x1 = M.get(r, c)
let x2 = 1.0f64 / (1.0f64 + exp(-x1))
let x3 = x2 * (1.0f64 - x2)
N.set(r, c, x3)
}
}
return N
}
/* -------- 线性整流单元 -------- */
private static func relu(M: Matrix1) {
let row = M.get_row()
let col = M.get_col()
let N = Matrix1(row, col)
private static func relu(M: Matrix) {
let row = M.getRowDimension()
let col = M.getColumnDimension()
let N = Matrix(row, col)
for (r in 0..row) {
for (c in 0..col) {
let x = M.get(r, c).getOrThrow()
let x1= x.getValue()
let x2 =if (x1 > 0.0f32) {x1} else{0.0f32}
N.set(r, c, FP32(x2))
let x1 = M.get(r, c)
let x2 =if (x1 > 0.0f64) { x1 } else{ 0.0f64 }
N.set(r, c, x2)
}
}
return N
}
/* -------- 线性整流单元的导数 -------- */
private static func relu_dot(M: Matrix1) {
let row = M.get_row()
let col = M.get_col()
let N = Matrix1(row, col)
private static func relu_dot(M: Matrix) {
let row = M.getRowDimension()
let col = M.getColumnDimension()
let N = Matrix(row, col)
for (r in 0..row) {
for (c in 0..col) {
let x = M.get(r, c).getOrThrow()
let x1= x.getValue()
let x2 =if (x1 > 0.0f32) {1.0f32} else{0.0f32}
N.set(r, c, FP32(x2))
let x1 = M.get(r, c)
let x2 =if (x1 > 0.0f64) { 1.0f64 } else{ 0.0f64 }
N.set(r, c, x2)
}
}
return N
}
/* -------- 带泄露的线性整流单元 -------- */
private static func leaky_relu(M: Matrix1, alpha: FP32) {
let row = M.get_row()
let col = M.get_col()
let N = Matrix1(row, col)
private static func leaky_relu(M: Matrix, alpha: Float64) {
let row = M.getRowDimension()
let col = M.getColumnDimension()
let N = Matrix(row, col)
for (r in 0..row) {
for (c in 0..col) {
let x = M.get(r, c).getOrThrow()
let x1= x.getValue()
let x2 =if (x1 > 0.0f32) {x1} else{x1 * alpha.getValue()}
N.set(r, c, FP32(x2))
let x1 = M.get(r, c)
let x2 =if (x1 > 0.0f64) { x1 } else{ x1 * alpha }
N.set(r, c, x2)
}
}
return N
}
/* -------- 带泄露的整流单元导数 -------- */
private static func leaky_relu_dot(M: Matrix1, alpha: FP32) {
let row = M.get_row()
let col = M.get_col()
let N = Matrix1(row, col)
private static func leaky_relu_dot(M: Matrix, alpha: Float64) {
let row = M.getRowDimension()
let col = M.getColumnDimension()
let N = Matrix(row, col)
for (r in 0..row) {
for (c in 0..col) {
let x = M.get(r, c).getOrThrow()
let x1= x.getValue()
let x2 =if (x1 > 0.0f32) { 1.0f32 } else{alpha.getValue()}
N.set(r, c, FP32(x2)) }
let x1 = M.get(r, c)
let x2 =if (x1 > 0.0f64) { 1.0f64 } else{ alpha }
N.set(r, c, x2)
}
}
return N
}
/* -------- 双曲正切函数 --------*/
private static func tanh(M: Matrix1) {
let row = M.get_row()
let col = M.get_col()
let N = Matrix1(row, col)
private static func tanh(M: Matrix) {
let row = M.getRowDimension()
let col = M.getColumnDimension()
let N = Matrix(row, col)
for (r in 0..row) {
for (c in 0..col) {
let x = M.get(r, c).getOrThrow()
let x1= x.getValue()
let x1 = M.get(r, c)
let x2 = tanh(x1)
N.set(r, c, FP32(x2)) }
N.set(r, c, x2)
}
}
return N
}
/* -------- 双曲正切函数的导数 -------- */
private static func tanh_dot(M: Matrix1) {
let row = M.get_row()
let col = M.get_col()
let N = Matrix1(row, col)
private static func tanh_dot(M: Matrix) {
let row = M.getRowDimension()
let col = M.getColumnDimension()
let N = Matrix(row, col)
for (r in 0..row) {
for (c in 0..col) {
let y = M.get(r, c).getOrThrow()
let y_val= y.getValue() /*---- NOTE(20260525-qing): 修复命名（x => y） ----*/
let rea = 1.0f32 - y_val * y_val
N.set(r, c, FP32(rea)) }
}
return N
}
/* -------- 归一化指数函数 -------- */
private static func softmax(M: Matrix1) {
let row = M.get_row()
let col = M.get_col()
let N = Matrix1(row, col)
var max_val = 0.0f32
for (r in 0..row) {
for (c in 0..col) {
let x = M.get(r, c).getOrThrow()
let x1= x.getValue()
if (x1 > max_val) {
max_val = x1 }
}
}
var sum = 0.0f32
for (r in 0..row) {
for (c in 0..col) {
let x = M.get(r, c).getOrThrow()
let x1= x.getValue()
let x2 = exp(x1 - max_val)
N.set(r, c, FP32(x2))
sum += x2
}
}
for (r in 0..row) {
for (c in 0..col) {
let x = N.get(r, c).getOrThrow()
let x1= x.getValue()
let x2 = x1 / sum
N.set(r, c, FP32(x2))
let y_val = M.get(r, c)
let rea = 1.0f64 - y_val * y_val
N.set(r, c, rea)
}
}
return N
}
/* -------- 计算Softmax的雅可比矩阵 --------
* 输入：已计算好的softmax输出（概率分布）
* 输出：雅可比矩阵 J[i][j] = ∂y_i/∂x_j */
private func softmax_jacobian(softmax_output: Matrix1) {
let row = softmax_output.get_row()
let col = softmax_output.get_col()
let n = row * col
var jacobian = Matrix1(n, n)
for (i in 0..n) {
for (j in 0..n) {
let row_i = i / col /* 需要将一维索引转换为二维索引来访问Matrix1 */
let col_i = i % col
let row_j = j / col
let col_j = j % col
let val_i = softmax_output.get(row_i, col_i).getOrThrow().getValue()
let val_j = softmax_output.get(row_j, col_j).getOrThrow().getValue()
if (i == j) { /* 对角线元素: y_i * (1 - y_i) */
jacobian.set(i, j, FP32(val_i * (1.0f32 - val_i))) }
else { /* 非对角线元素: -y_i * y_j */
jacobian.set(i, j, FP32(-val_i * val_j)) }
}
}
return jacobian
}
}