diff --git a/internal/captcha/handler.go b/internal/captcha/handler.go
index f955418..b24606d 100644
--- a/internal/captcha/handler.go
+++ b/internal/captcha/handler.go
@@ -392,35 +392,24 @@ func preprocessMath(img image.Image) ([]float32, error) {
 }
 
 func decodeMathFromOutput(output []float32) string {
-	// Math 模型输出: [C, B, T] = [51, 1, 19]
-	// 需要转置为 [B, T, C] = [1, 19, 51]
-	numChars := 51
+	// Math 模型输出: [T, B, C] = [51, 1, 19]
+	// T = 51 个时间步, B = 1 batch, C = 19 个字符类别 (blank + 18 chars)
+	// 对每个 timestep 取 argmax，得到字符索引序列
+	timesteps := 51
 	batch := 1
-	timesteps := 19
-	
-	if len(output) != numChars*batch*timesteps {
-		timesteps = len(output) / numChars
-		if timesteps <= 0 {
+	numChars := 19  // blank(0) + 18 chars
+
+	if len(output) != timesteps*batch*numChars {
+		// 尝试推断
+		total := len(output)
+		if total%numChars != 0 {
 			return ""
 		}
+		timesteps = total / numChars
 	}
-	
-	// 转置: [C, B, T] -> [B, T, C]
-	// output[c*batch*timesteps + b*timesteps + t] -> data[b*timesteps*numChars + t*numChars + c]
-	data := make([]float32, batch*timesteps*numChars)
-	for c := 0; c < numChars; c++ {
-		for b := 0; b < batch; b++ {
-			for t := 0; t < timesteps; t++ {
-				srcIdx := c*batch*timesteps + b*timesteps + t
-				dstIdx := b*timesteps*numChars + t*numChars + c
-				if srcIdx < len(output) && dstIdx < len(data) {
-					data[dstIdx] = output[srcIdx]
-				}
-			}
-		}
-	}
-	
-	// CTC 解码: 对每个 timestep 取 argmax
+
+	// 对每个 timestep 取 argmax
+	// output[t*batch*numChars + b*numChars + c] 存储的是 timestep t, batch b 的字符 c 的概率
 	result := ""
 	lastIdx := -1
 
@@ -428,16 +417,18 @@ func decodeMathFromOutput(output []float32) string {
 		maxIdx := 0
 		maxProb := float32(-math.MaxFloat32)
 
+		// 对这个 timestep 的所有字符取最大值
 		for c := 0; c < numChars; c++ {
-			idx := t*numChars + c
-			if idx < len(data) && data[idx] > maxProb {
-				maxProb = data[idx]
+			idx := t*numChars + c  // 因为 batch=1，所以简化了
+			if idx < len(output) && output[idx] > maxProb {
+				maxProb = output[idx]
 				maxIdx = c
 			}
 		}
 
 		// CTC: 跳过 blank (index 0) 和重复
 		if maxIdx != 0 && maxIdx != lastIdx {
+			// 字符索引从 1 开始，对应 mathChars[0:]
 			if maxIdx-1 < len(mathChars) {
 				result += string(mathChars[maxIdx-1])
 			}