#![allow(clippy::approx_constant)] use anyhow::{Context, Result}; use candle_core::{test_device, test_utils, Device, Shape, Tensor, Var}; fn simple_grad(device: &Device) -> Result<()> { let x = Var::new(&[3f32, 1., 4.], device)?; let x = x.as_tensor(); let y = (((x * x)? + x * 5f64)? + 4f64)?; let grads = y.backward()?; let grad_x = grads.get(x).context("no grad for x")?; assert_eq!(x.to_vec1::()?, [3., 1., 4.]); // y = x^2 + 5.x + 4 assert_eq!(y.to_vec1::()?, [28., 10., 40.]); // dy/dx = 2.x + 5 assert_eq!(grad_x.to_vec1::()?, [11., 7., 13.]); Ok(()) } fn sum_grad(device: &Device) -> Result<()> { let x = Var::new(&[3f32, 1., 4.], device)?; let x = x.as_tensor(); let y = (x.sqr()?.sum_keepdim(0)? * 2.)?; let grads = y.backward()?; let grad_x = grads.get(x).context("no grad for x")?; assert_eq!(y.to_vec1::()?, [52.]); // y = 2.x^2 so dy/dx = 4.x assert_eq!(grad_x.to_vec1::()?, &[12., 4., 16.]); // Same test as before but squeezing on the last dimension. let y = (x.sqr()?.sum_keepdim(0)? * 2.)?.squeeze(0)?; let grads = y.backward()?; let grad_x = grads.get(x).context("no grad for x")?; assert_eq!(y.to_scalar::()?, 52.); // y = 2.x^2 so dy/dx = 4.x assert_eq!(grad_x.to_vec1::()?, &[12., 4., 16.]); Ok(()) } fn matmul_grad(device: &Device) -> Result<()> { let data: Vec<_> = (0..12).map(|i| i as f32).collect(); let x = Var::from_slice(&data, (2, 2, 3), device)?; let data: Vec<_> = (0..12).map(|i| i as f32).collect(); let y = Var::from_slice(&data, (2, 3, 2), device)?; let c = x.matmul(&y)?; let grads = c.backward()?; let grad_x = grads.get(&x).context("no grad for x")?; let grad_y = grads.get(&y).context("no grad for y")?; assert_eq!(grad_x.shape(), &Shape::from((2, 2, 3))); assert_eq!(grad_y.shape(), &Shape::from((2, 3, 2))); assert_eq!( &*grad_x.to_vec3::()?, &[ [[1., 5., 9.], [1., 5., 9.]], [[13., 17., 21.], [13., 17., 21.]] ] ); assert_eq!( &*grad_y.to_vec3::()?, &[ [[3., 3.], [5., 5.], [7., 7.]], [[15., 15.], [17., 17.], [19., 19.]] ] ); Ok(()) } // The simplest gradient descent, using scalar variable. fn grad_descent(device: &Device) -> Result<()> { let x = Var::new(0f32, device)?; let learning_rate = 0.1; for _step in 0..100 { let xt = x.as_tensor(); let c = ((xt - 4.2)? * (xt - 4.2)?)?; let grads = c.backward()?; let x_grad = grads.get(&x).context("no grad for x")?; x.set(&(xt - x_grad * learning_rate)?)? } assert_eq!(x.to_scalar::()?, 4.199999); Ok(()) } fn unary_grad(device: &Device) -> Result<()> { let x = Var::new(&[3f32, 1., 4., 0.15], device)?; let x = x.as_tensor(); let y = (x.log()? + 1.)?; let grads = y.backward()?; let grad_x = grads.get(x).context("no grad for x")?; assert_eq!( test_utils::to_vec1_round(&y, 4)?, [2.0986, 1.0, 2.3863, -0.8971] ); assert_eq!( test_utils::to_vec1_round(grad_x, 4)?, [0.3333, 1.0, 0.25, 6.6667] ); let y = x.exp()?; let grads = y.backward()?; let grad_x = grads.get(x).context("no grad for x")?; assert_eq!( test_utils::to_vec1_round(&y, 4)?, [20.0855, 2.7183, 54.5982, 1.1618] ); assert_eq!( test_utils::to_vec1_round(grad_x, 4)?, [20.0855, 2.7183, 54.5982, 1.1618] ); let y = x.exp()?.sqr()?; let grads = y.backward()?; let grad_x = grads.get(x).context("no grad for x")?; assert_eq!( test_utils::to_vec1_round(&y, 3)?, [403.429, 7.389, 2980.958, 1.35] ); // exp(x)^2 = exp(2*x) assert_eq!( test_utils::to_vec1_round(grad_x, 2)?, [806.86, 14.78, 5961.92, 2.7] ); let y = x.sin()?; let grads = y.backward()?; let grad_x = grads.get(x).context("no grad for x")?; assert_eq!( test_utils::to_vec1_round(&y, 4)?, [0.1411, 0.8415, -0.7568, 0.1494], ); assert_eq!( test_utils::to_vec1_round(grad_x, 4)?, [-0.99, 0.5403, -0.6536, 0.9888], ); let y = x.cos()?; let grads = y.backward()?; let grad_x = grads.get(x).context("no grad for x")?; assert_eq!( test_utils::to_vec1_round(&y, 4)?, [-0.99, 0.5403, -0.6536, 0.9888], ); assert_eq!( test_utils::to_vec1_round(grad_x, 4)?, [-0.1411, -0.8415, 0.7568, -0.1494], ); let y = x.sqr()?; let grads = y.backward()?; let grad_x = grads.get(x).context("no grad for x")?; assert_eq!(y.to_vec1::()?, [9.0, 1.0, 16.0, 0.0225]); assert_eq!(grad_x.to_vec1::()?, [6.0, 2.0, 8.0, 0.3]); let y = x.sqr()?.sqrt()?; let grads = y.backward()?; let grad_x = grads.get(x).context("no grad for x")?; assert_eq!(y.to_vec1::()?, [3.0, 1.0, 4.0, 0.15]); assert_eq!(test_utils::to_vec1_round(grad_x, 4)?, [1.0, 1.0, 1.0, 1.0]); let y = x.neg()?; let grads = y.backward()?; let grad_x = grads.get(x).context("no grad for x")?; assert_eq!(y.to_vec1::()?, [-3.0, -1.0, -4.0, -0.15]); assert_eq!(grad_x.to_vec1::()?, [-1.0, -1.0, -1.0, -1.0]); let y = x.affine(0.2, 1.)?; let grads = y.backward()?; let grad_x = grads.get(x).context("no grad for x")?; assert_eq!(y.to_vec1::()?, [1.6, 1.2, 1.8, 1.03]); assert_eq!(grad_x.to_vec1::()?, [0.2, 0.2, 0.2, 0.2]); let y = Tensor::new(1f32, device)?.broadcast_div(x)?; let grads = y.backward()?; let grad_x = grads.get(x).context("no grad for x")?; assert_eq!( test_utils::to_vec1_round(&y, 4)?, [0.3333, 1.0, 0.25, 6.6667] ); assert_eq!( grad_x.to_vec1::()?, [-0.11111111, -1.0, -0.0625, -44.444443], ); let y = x.broadcast_div(&Tensor::new(0.5f32, device)?)?; let grads = y.backward()?; let grad_x = grads.get(x).context("no grad for x")?; assert_eq!(y.to_vec1::()?, [6., 2., 8., 0.3]); assert_eq!(grad_x.to_vec1::()?, [2., 2., 2., 2.]); let x = Var::new(&[3f32, 1., 4., 0.15], device)?; let y = x.powf(2.5)?; let grads = y.backward()?; let grad_x = grads.get(&x).context("no grad for x")?; assert_eq!(test_utils::to_vec1_round(&y, 2)?, [15.59, 1.0, 32.0, 0.01]); assert_eq!( test_utils::to_vec1_round(grad_x, 2)?, [12.99, 2.5, 20.0, 0.15] ); let y = x.tanh()?; let grads = y.backward()?; let grad_x = grads.get(&x).context("no grad for x")?; assert_eq!(test_utils::to_vec1_round(&y, 2)?, [1.0, 0.76, 1.0, 0.15]); assert_eq!( test_utils::to_vec1_round(grad_x, 2)?, [0.01, 0.42, 0.0, 0.98], ); // testing compared to pytorch nn.GELU(approximate = 'tanh') let y = x.gelu()?; let grads = y.backward()?; let grad_x = grads.get(&x).context("no grad for x")?; assert_eq!( test_utils::to_vec1_round(&y, 4)?, [2.9964, 0.8412, 3.9999, 0.0839] ); assert_eq!( test_utils::to_vec1_round(grad_x, 4)?, [1.0116, 1.0830, 1.0003, 0.6188], ); // Testing compared to pytorch torch.erf // // import torch // x = torch.tensor([3.0, 1.0, 4.0, 0.15], requires_grad=True) // y = x.erf() // print(y) // loss = y.sum() // loss.backward() // print(x.grad) let y = x.erf()?; let grads = y.backward()?; let grad_x = grads.get(&x).context("no grad for x")?; assert_eq!(test_utils::to_vec1_round(&y, 4)?, [1.0, 0.8427, 1.0, 0.168]); assert_eq!( test_utils::to_vec1_round(grad_x, 4)?, [0.0001, 0.4151, 0.0, 1.1033], ); // Testing compared to pytorch nn.GELU(approximate = 'none') // // import torch // import torch.nn.functional as F // x = torch.tensor([3.0, 1.0, 4.0, 0.15], requires_grad=True) // y = F.gelu(x, approximate='none') // print(y) // loss = y.sum() // loss.backward() // print(x.grad) let y = x.gelu_erf()?; let grads = y.backward()?; let grad_x = grads.get(&x).context("no grad for x")?; assert_eq!( test_utils::to_vec1_round(&y, 4)?, [2.9960, 0.8413, 3.9999, 0.0839] ); assert_eq!( test_utils::to_vec1_round(grad_x, 4)?, [1.0119, 1.0833, 1.0005, 0.6188], ); // Testing compared to pytorch elu // // import torch // import torch.nn.functional as F // x = torch.tensor([-1.0, 0.0, -2.0, 3.0], requires_grad=True) // y = F.elu(x, alpha=2.0) // print(y) // loss = y.min // loss = y.sum() // loss.backward() // print(x.grad) let elu_x = Var::new(&[-1.0f32, 0., -2., 3.], device)?; let y = elu_x.elu(2.)?; let grads = y.backward()?; let grad_x = grads.get(&elu_x).context("no grad for x")?; assert_eq!( test_utils::to_vec1_round(&y, 4)?, [-1.2642, 0.0000, -1.7293, 3.0000] ); assert_eq!( test_utils::to_vec1_round(grad_x, 4)?, [0.7358, 2.0000, 0.2707, 1.0000] ); // testing compared to pytorch nn.Silu() let y = x.silu()?; let grads = y.backward()?; let grad_x = grads.get(&x).context("no grad for x")?; assert_eq!( test_utils::to_vec1_round(&y, 4)?, [2.8577, 0.7311, 3.9281, 0.0806] ); assert_eq!( test_utils::to_vec1_round(grad_x, 4)?, [1.0881, 0.9277, 1.0527, 0.5747], ); if device.is_cpu() { let x = Var::new(&[[[1f32, 2., 3.], [4., 5., 6.], [7., 8., 9.]]], device)?; let y = x.interpolate1d(12)?.reshape(36)?; let z = Tensor::new( &[ 1_f32, 02., 03., 04., 05., 06., 07., 08., 09., 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., ], device, )?; let loss = y.unsqueeze(1)?.transpose(0, 1)?.matmul(&z.unsqueeze(1)?)?; let grads = loss.backward()?; let grad_x = grads.get(&x).context("no grad for x")?; assert_eq!( test_utils::to_vec3_round(grad_x, 4)?, [[[10_f32, 26., 42.], [58., 74., 90.], [106., 122., 138.]]] ); } // manually checked: see comments let x = Var::new(&[[[[1f32, 2., 3.], [4., 5., 6.], [7., 8., 9.]]]], device)?; let y = x.interpolate2d(6, 6)?.reshape(36)?; let z = Tensor::new( &[ 1_f32, 02., 03., 04., 05., 06., 07., 08., 09., 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., ], device, )?; // gradient should be // row 1 // 1+2+7+8 = 18 // 3+4+9+10 = 26 // 5+6+11+12 = 34 // row 2 // 13+14+19+20 = 66 // 15+16+21+22 = 74 // 17+18+23+24 = 82 // row 3 // 25+26+31+32 = 114 // 27+28+33+34 = 122 // 29+30+35+36 = 130 let loss = y.unsqueeze(1)?.transpose(0, 1)?.matmul(&z.unsqueeze(1)?)?; let grads = loss.backward()?; let grad_x = grads.get(&x).context("no grad for x")?; assert_eq!( test_utils::to_vec2_round(&grad_x.flatten(0, 2)?, 4)?, [[18_f32, 26., 34.], [66., 74., 82.], [114., 122., 130.]] ); // manually checked: see comments let x = Var::new(&[[[[1f32, 2.], [4., 5.]]]], device)?; let y = x.interpolate2d(6, 6)?.reshape(36)?; let z = Tensor::new( &[ 1_f32, 02., 03., 04., 05., 06., 07., 08., 09., 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., ], device, )?; // gradient should be // row 1 // 1+2+3+7+8+9+13+14+15 = 72 // 4+5+6+10+11+12+16+17+18 = 99 // row 2 // 19+20+21+25+26+27+31+32+33 = 234 // 22+23+24+28+29+30+34+35+36 = 243 let loss = y.unsqueeze(1)?.transpose(0, 1)?.matmul(&z.unsqueeze(1)?)?; let grads = loss.backward()?; let grad_x = grads.get(&x).context("no grad for x")?; assert_eq!( test_utils::to_vec2_round(&grad_x.flatten(0, 2)?, 4)?, [[72_f32, 99.], [234., 261.]] ); // manually checked: see comments let x = Var::new(&[[[[1f32, 2.], [4., 5.]], [[6f32, 7.], [8., 9.]]]], device)?; let y = x.interpolate2d(4, 4)?.reshape(32)?; #[rustfmt::skip] let z = Tensor::new( &[ 1_f32, 02., 03., 04., 05., 06., 07., 08., 09., 10., 11., 12., 13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25., 26., 27., 28., 29., 30., 31., 32. ], device, )?; // gradient should be // m1r1 // 1+2+5+6=14 // 3+4+7+8=22 // m1r2 // 9+10+13+14=46 // 11+12+15+16=54 // m2r1 // 17+18+21+22=78 // 19+20+23+24=86 // m2r2 // 25+26+29+30=110 // 27+28+31+32=118 let loss = y.unsqueeze(1)?.transpose(0, 1)?.matmul(&z.unsqueeze(1)?)?; let grads = loss.backward()?; let grad_x = grads.get(&x).context("no grad for x")?; assert_eq!( test_utils::to_vec3_round(&grad_x.flatten(0, 1)?, 4)?, [[[14_f32, 22.], [46., 54.]], [[78., 86.], [110., 118.]]] ); // manually checked: see comments let x = Var::new( &[[[[1f32, 2.], [4., 5.]]], [[[6f32, 7.], [8., 9.]]]], device, )?; let y = x.interpolate2d(4, 4)?.reshape(32)?; #[rustfmt::skip] let z = Tensor::new( &[ 1_f32, 02., 03., 04., 05., 06., 07., 08., 09., 10., 11., 12., 13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25., 26., 27., 28., 29., 30., 31., 32. ], device, )?; // gradient should be // m1r1 // 1+2+5+6=14 // 3+4+7+8=22 // m1r2 // 9+10+13+14=46 // 11+12+15+16=54 // m2r1 // 17+18+21+22=78 // 19+20+23+24=86 // m2r2 // 25+26+29+30=110 // 27+28+31+32=118 let loss = y.unsqueeze(1)?.transpose(0, 1)?.matmul(&z.unsqueeze(1)?)?; let grads = loss.backward()?; let grad_x = grads.get(&x).context("no grad for x")?; assert_eq!( test_utils::to_vec3_round(&grad_x.flatten(0, 1)?, 4)?, [[[14_f32, 22.], [46., 54.]], [[78., 86.], [110., 118.]]] ); Ok(()) } fn binary_grad(device: &Device) -> Result<()> { let x = Var::new(&[3f32, 1., -4., -1.], device)?; let x = x.as_tensor(); // leaky relu let y = x.maximum(&(x * 0.1)?)?; let grads = y.backward()?; let grad_x = grads.get(x).context("no grad for x")?; assert_eq!(x.to_vec1::()?, [3., 1., -4., -1.]); assert_eq!(y.to_vec1::()?, [3., 1., -0.4, -0.1]); assert_eq!(grad_x.to_vec1::()?, [1., 1., 0.1, 0.1]); let y = x.minimum(&(x * 0.1)?)?; let grads = y.backward()?; let grad_x = grads.get(x).context("no grad for x")?; assert_eq!(y.to_vec1::()?, [0.3, 0.1, -4., -1.]); assert_eq!(grad_x.to_vec1::()?, [0.1, 0.1, 1., 1.]); // This one is easy to mess up, we want the gradient to be one as it is the identity function. let y = x.minimum(x)?; let grads = y.backward()?; let grad_x = grads.get(x).context("no grad for x")?; assert_eq!(y.to_vec1::()?, [3., 1., -4., -1.]); assert_eq!(grad_x.to_vec1::()?, [1., 1., 1., 1.]); let x_var = Var::new(&[3f32, 1., -4., -1., 5., 9.], device)?; let x = x_var.as_tensor(); let y_var = Var::new(&[2f32, 7., 1.], device)?; let y = y_var.as_tensor(); let ss = x .reshape((2, 3))? .slice_scatter0(&y.reshape((1, 3))?, 1)? .sqr()?; let grads = ss.backward()?; let grad_x = grads.get(x).context("no grad for x")?; let grad_y = grads.get(y).context("no grad for y")?; assert_eq!(ss.to_vec2::()?, [[9., 1., 16.], [4., 49., 1.]]); assert_eq!(grad_x.to_vec1::()?, [6.0, 2.0, -8.0, 0.0, 0.0, 0.0]); assert_eq!(grad_y.to_vec1::()?, [4.0, 14.0, 2.0]); Ok(()) } test_device!( simple_grad, simple_grad_cpu, simple_grad_gpu, simple_grad_metal ); test_device!(sum_grad, sum_grad_cpu, sum_grad_gpu, sum_grad_metal); test_device!( matmul_grad, matmul_grad_cpu, matmul_grad_gpu, matmul_grad_metal ); test_device!( grad_descent, grad_descent_cpu, grad_descent_gpu, grad_descent_metal ); test_device!(unary_grad, unary_grad_cpu, unary_grad_gpu, unary_grad_metal); test_device!( binary_grad, binary_grad_cpu, binary_grad_gpu, binary_grad_metal );