numr 0.5.2

High-performance numerical computing with multi-backend GPU acceleration (CPU/CUDA/WebGPU)
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196

//! Backward implementation for Fused Add + RMS Normalization

use crate::autograd::GradFn;
use crate::autograd::var::Var;
use crate::autograd::var_ops::{var_mean, var_mul, var_sub, var_sum};
use crate::error::Result;
use crate::ops::{BinaryOps, NormalizationOps, ReduceOps, ScalarOps, TensorOps, UnaryOps};
use crate::runtime::{Runtime, RuntimeClient};
use crate::tensor::{Tensor, TensorId};
use std::sync::Arc;

/// Backward for Fused Add + RMS Normalization: pre_norm = x + residual, output = rms_norm(pre_norm, weight, eps)
///
/// Gradients:
/// - d_input_residual = shared gradient for both x and residual (since d(x+r)/dx = d(x+r)/dr = 1)
/// - d_weight = sum(grad_out * x_norm, batch_dims)
pub struct FusedAddRmsNormBackward<R: Runtime> {
    input_ids: [TensorId; 3],
    saved_tensors: Vec<Tensor<R>>, // [pre_norm, weight]
    eps: f32,
    input_grad_fns: [Option<Arc<dyn GradFn<R>>>; 3],
}

impl<R: Runtime> FusedAddRmsNormBackward<R> {
    /// Create a new FusedAddRmsNormBackward
    pub fn new(
        x_id: TensorId,
        residual_id: TensorId,
        weight_id: TensorId,
        pre_norm: Tensor<R>,
        weight: Tensor<R>,
        eps: f32,
        x_grad_fn: Option<Arc<dyn GradFn<R>>>,
        residual_grad_fn: Option<Arc<dyn GradFn<R>>>,
        weight_grad_fn: Option<Arc<dyn GradFn<R>>>,
    ) -> Self {
        Self {
            input_ids: [x_id, residual_id, weight_id],
            saved_tensors: vec![pre_norm, weight],
            eps,
            input_grad_fns: [x_grad_fn, residual_grad_fn, weight_grad_fn],
        }
    }
}

impl<R: Runtime> GradFn<R> for FusedAddRmsNormBackward<R>
where
    R::Client: TensorOps<R> + ScalarOps<R> + BinaryOps<R> + ReduceOps<R> + UnaryOps<R>,
{
    fn backward(&self, grad_output: &Tensor<R>) -> Result<Vec<Option<Tensor<R>>>> {
        let client = R::default_client(grad_output.device());
        let pre_norm = &self.saved_tensors[0];
        let weight = &self.saved_tensors[1];

        let (d_input_residual, d_weight) =
            client.fused_add_rms_norm_bwd(grad_output, pre_norm, weight, self.eps)?;

        // x and residual share the same gradient
        Ok(vec![
            Some(d_input_residual.clone()),
            Some(d_input_residual),
            Some(d_weight),
        ])
    }

    fn backward_var(&self, grad_output: &Var<R>) -> Result<Vec<Option<Var<R>>>>
    where
        R::Client: RuntimeClient<R>
            + TensorOps<R>
            + ScalarOps<R>
            + BinaryOps<R>
            + ReduceOps<R>
            + UnaryOps<R>,
    {
        let client = R::default_client(grad_output.tensor().device());
        let pre_norm = &self.saved_tensors[0];
        let weight = &self.saved_tensors[1];
        let ndim = pre_norm.ndim();
        let last_dim = ndim - 1;

        // Recompute rstd and x_norm from pre_norm (treat as constants)
        let x_sq = client.mul(pre_norm, pre_norm)?;
        let mean_x_sq = client.mean(&x_sq, &[last_dim], true)?;
        let variance_eps = client.add_scalar(&mean_x_sq, self.eps as f64)?;
        let rms = client.sqrt(&variance_eps)?;
        let rstd = client.recip(&rms)?;
        let x_norm = client.mul(pre_norm, &rstd)?;

        // Wrap as non-differentiable Vars
        let rstd_var = Var::new(rstd, false);
        let x_norm_var = Var::new(x_norm, false);
        let weight_var = Var::new(weight.clone(), false);

        // d_input_residual = rstd * (grad_output * weight - x_norm * mean(grad_output * weight * x_norm))
        let gw = var_mul(grad_output, &weight_var, &client)?;
        let gw_xn = var_mul(&gw, &x_norm_var, &client)?;
        let mean_gw_xn = var_mean(&gw_xn, &[last_dim], true, &client)?;
        let correction = var_mul(&x_norm_var, &mean_gw_xn, &client)?;
        let inner = var_sub(&gw, &correction, &client)?;
        let d_input_residual = var_mul(&inner, &rstd_var, &client)?;

        // d_weight = sum(grad_output * x_norm, batch_dims)
        let g_xn = var_mul(grad_output, &x_norm_var, &client)?;
        let batch_dims: Vec<usize> = (0..last_dim).collect();
        let d_weight = if batch_dims.is_empty() {
            g_xn
        } else {
            var_sum(&g_xn, &batch_dims, false, &client)?
        };

        Ok(vec![
            Some(d_input_residual.clone()),
            Some(d_input_residual),
            Some(d_weight),
        ])
    }

    fn inputs(&self) -> &[TensorId] {
        &self.input_ids
    }

    fn input_grad_fns(&self) -> Vec<Option<Arc<dyn GradFn<R>>>> {
        self.input_grad_fns.to_vec()
    }

    fn saved_tensors(&self) -> &[Tensor<R>] {
        &self.saved_tensors
    }

    fn name(&self) -> &'static str {
        "FusedAddRmsNormBackward"
    }
}

#[cfg(test)]
mod tests {
    use super::*;
    use crate::runtime::cpu::{CpuDevice, CpuRuntime};

    #[test]
    fn test_fused_add_rms_norm_backward_basic() {
        let device = CpuDevice::new();
        let client = CpuRuntime::default_client(&device);

        let pre_norm = Tensor::<CpuRuntime>::from_slice(&[1.0f32, 2.0, 3.0, 4.0], &[1, 4], &device);
        let weight = Tensor::<CpuRuntime>::from_slice(&[1.0f32, 1.0, 1.0, 1.0], &[4], &device);
        let eps = 1e-5f32;

        let grad_out = Tensor::<CpuRuntime>::from_slice(&[1.0f32, 0.0, 0.0, 0.0], &[1, 4], &device);

        let (d_input_residual, d_weight) = client
            .fused_add_rms_norm_bwd(&grad_out, &pre_norm, &weight, eps)
            .unwrap();

        let di: Vec<f32> = d_input_residual.to_vec();
        let dw: Vec<f32> = d_weight.to_vec();

        for val in &di {
            assert!(val.is_finite(), "d_input_residual should be finite");
        }
        for val in &dw {
            assert!(val.is_finite(), "d_weight should be finite");
        }
    }

    #[test]
    fn test_fused_add_rms_norm_backward_shared_gradient() {
        let device = CpuDevice::new();

        let pre_norm = Tensor::<CpuRuntime>::from_slice(&[1.0f32, 2.0, 3.0], &[1, 3], &device);
        let weight = Tensor::<CpuRuntime>::from_slice(&[1.0f32, 1.0, 1.0], &[3], &device);

        let grad_out = Tensor::<CpuRuntime>::from_slice(&[1.0f32, 1.0, 1.0], &[1, 3], &device);

        let backward = FusedAddRmsNormBackward::<CpuRuntime>::new(
            TensorId::new(),
            TensorId::new(),
            weight.id(),
            pre_norm,
            weight,
            1e-5,
            None,
            None,
            None,
        );
        let grads = backward.backward(&grad_out).unwrap();

        assert_eq!(grads.len(), 3);
        // x and residual gradients should be identical
        let d_x: Vec<f32> = grads[0].as_ref().unwrap().to_vec();
        let d_r: Vec<f32> = grads[1].as_ref().unwrap().to_vec();
        for (a, b) in d_x.iter().zip(d_r.iter()) {
            assert!((a - b).abs() < 1e-10, "x and residual grads must match");
        }
    }
}