RoPE with frequencies as optional input (#1337)

* start rope with freq input

* rope with frequencies

* nits

* fix bug

* fix bug + test

* cleanup

* optional base

mlx/backend/metal/kernels/rope.metal

@@ -4,23 +4,20 @@
 
 #include "mlx/backend/metal/kernels/bf16.h"
 #include "mlx/backend/metal/kernels/utils.h"
-
 template <typename T, bool traditional, bool forward>
-[[kernel]] void rope_single(
+void rope_single_impl(
-    const device T* in [[buffer(0)]],
+    const device T* in,
-    device T* out [[buffer(1)]],
+    device T* out,
     constant const int& offset,
-    constant const float& base,
+    const float inv_freq,
     constant const float& scale,
     constant const size_t& stride,
-    uint2 pos [[thread_position_in_grid]],
+    uint2 pos,
-    uint2 grid [[threads_per_grid]]) {
+    uint2 grid) {
-  // Figure out L and d.
   float L = scale * static_cast<float>(offset);
-  float d = static_cast<float>(pos.x) / static_cast<float>(grid.x);
 
   // Compute costheta, sintheta
-  float theta = L * metal::exp2(-d * base);
+  float theta = L * inv_freq;
   float costheta = metal::fast::cos(theta);
   float sintheta = metal::fast::sin(theta);
 
@@ -55,24 +52,54 @@ template <typename T, bool traditional, bool forward>
   out[out_index_2] = static_cast<T>(rx2);
 }
 
-template <typename T, bool traditional, bool forward, int N = 4>
+template <typename T, bool traditional, bool forward>
-[[kernel]] void rope(
+[[kernel]] void rope_single(
     const device T* in [[buffer(0)]],
     device T* out [[buffer(1)]],
     constant const int& offset,
-    constant const float& base,
+    constant const float& scale,
+    constant const size_t& stride,
+    constant const float& base [[buffer(10)]],
+    uint2 pos [[thread_position_in_grid]],
+    uint2 grid [[threads_per_grid]]) {
+  float d = static_cast<float>(pos.x) / static_cast<float>(grid.x);
+  float inv_freq = metal::exp2(-d * base);
+  rope_single_impl<T, traditional, forward>(
+      in, out, offset, inv_freq, scale, stride, pos, grid);
+}
+
+template <typename T, bool traditional, bool forward>
+[[kernel]] void rope_single_freqs(
+    const device T* in [[buffer(0)]],
+    device T* out [[buffer(1)]],
+    constant const int& offset,
+    constant const float& scale,
+    constant const size_t& stride,
+    const device float* freqs [[buffer(10)]],
+    constant const size_t& freq_stride [[buffer(11)]],
+    uint2 pos [[thread_position_in_grid]],
+    uint2 grid [[threads_per_grid]]) {
+  float inv_freq = 1.0 / (freqs[freq_stride * pos.x]);
+  rope_single_impl<T, traditional, forward>(
+      in, out, offset, inv_freq, scale, stride, pos, grid);
+}
+
+template <typename T, bool traditional, bool forward, int N = 4>
+void rope_impl(
+    const device T* in,
+    device T* out,
+    constant const int& offset,
+    const float inv_freq,
     constant const float& scale,
     constant const size_t strides[3],
     constant const size_t out_strides[3],
     constant const size_t& n_batch,
-    uint3 pos [[thread_position_in_grid]],
+    uint3 pos,
-    uint3 grid [[threads_per_grid]]) {
+    uint3 grid) {
-  // Figure out L and d.
   float L = scale * static_cast<float>(pos.y + offset);
-  float d = static_cast<float>(pos.x) / static_cast<float>(grid.x);
 
   // Compute costheta, sintheta
-  float theta = L * metal::exp2(-d * base);
+  float theta = L * inv_freq;
   float costheta = metal::fast::cos(theta);
   float sintheta = metal::fast::sin(theta);
 
@@ -116,17 +143,85 @@ template <typename T, bool traditional, bool forward, int N = 4>
   }
 }
 
+template <typename T, bool traditional, bool forward, int N = 4>
+[[kernel]] void rope(
+    const device T* in [[buffer(0)]],
+    device T* out [[buffer(1)]],
+    constant const int& offset,
+    constant const float& scale,
+    constant const size_t strides[3],
+    constant const size_t out_strides[3],
+    constant const size_t& n_batch,
+    constant const float& base [[buffer(10)]],
+    uint3 pos [[thread_position_in_grid]],
+    uint3 grid [[threads_per_grid]]) {
+  float d = static_cast<float>(pos.x) / static_cast<float>(grid.x);
+  float inv_freq = metal::exp2(-d * base);
+  rope_impl<T, traditional, forward, N>(
+      in,
+      out,
+      offset,
+      inv_freq,
+      scale,
+      strides,
+      out_strides,
+      n_batch,
+      pos,
+      grid);
+}
+
+template <typename T, bool traditional, bool forward, int N = 4>
+[[kernel]] void rope_freqs(
+    const device T* in [[buffer(0)]],
+    device T* out [[buffer(1)]],
+    constant const int& offset,
+    constant const float& scale,
+    constant const size_t strides[3],
+    constant const size_t out_strides[3],
+    constant const size_t& n_batch,
+    const device float* freqs [[buffer(10)]],
+    constant const size_t& freq_stride [[buffer(11)]],
+    uint3 pos [[thread_position_in_grid]],
+    uint3 grid [[threads_per_grid]]) {
+  float inv_freq = 1.0 / (freqs[freq_stride * pos.x]);
+  rope_impl<T, traditional, forward, N>(
+      in,
+      out,
+      offset,
+      inv_freq,
+      scale,
+      strides,
+      out_strides,
+      n_batch,
+      pos,
+      grid);
+}
+
+// clang-format off
 #define instantiate_rope_g(name, type, traditional, forward) \
   template [[host_name("rope_" #name)]] [[kernel]] void      \
   rope<type, traditional, forward>(                          \
       const device type* in [[buffer(0)]],                   \
       device type* out [[buffer(1)]],                        \
       constant const int& offset,                            \
-      constant const float& base,                            \
       constant const float& scale,                           \
       constant const size_t strides[3],                      \
       constant const size_t out_strides[3],                  \
       constant const size_t& n_batch,                        \
+      constant const float& base [[buffer(10)]],             \
+      uint3 pos [[thread_position_in_grid]],                 \
+      uint3 grid [[threads_per_grid]]);                      \
+  template [[host_name("rope_freqs_" #name)]]                \
+  [[kernel]] void rope_freqs<type, traditional, forward>(    \
+      const device type* in [[buffer(0)]],                   \
+      device type* out [[buffer(1)]],                        \
+      constant const int& offset,                            \
+      constant const float& scale,                           \
+      constant const size_t strides[3],                      \
+      constant const size_t out_strides[3],                  \
+      constant const size_t& n_batch,                        \
+      const device float* freqs [[buffer(10)]],              \
+      constant const size_t& freq_stride [[buffer(11)]],     \
       uint3 pos [[thread_position_in_grid]],                 \
       uint3 grid [[threads_per_grid]]);
 
@@ -136,9 +231,20 @@ template <typename T, bool traditional, bool forward, int N = 4>
       const device type* in [[buffer(0)]],                       \
       device type* out [[buffer(1)]],                            \
       constant const int& offset,                                \
-      constant const float& base,                              \
       constant const float& scale,                               \
       constant const size_t& stride,                             \
+      constant const float& base [[buffer(10)]],                 \
+      uint2 pos [[thread_position_in_grid]],                     \
+      uint2 grid [[threads_per_grid]]);                          \
+  template [[host_name("rope_single_freqs_" #name)]]             \
+  [[kernel]] void rope_single_freqs<type, traditional, forward>( \
+      const device type* in [[buffer(0)]],                       \
+      device type* out [[buffer(1)]],                            \
+      constant const int& offset,                                \
+      constant const float& scale,                               \
+      constant const size_t& stride,                             \
+      const device float* freqs [[buffer(10)]],                  \
+      constant const size_t& freq_stride [[buffer(11)]],         \
       uint2 pos [[thread_position_in_grid]],                     \
       uint2 grid [[threads_per_grid]]);
 
@@ -146,7 +252,6 @@ template <typename T, bool traditional, bool forward, int N = 4>
   instantiate_rope_s(name, type, traditional, forward)     \
   instantiate_rope_g(name, type, traditional, forward)
 
-// clang-format off
 instantiate_rope(traditional_float16, half, true, true)
 instantiate_rope(traditional_bfloat16, bfloat16_t, true, true)
 instantiate_rope(traditional_float32, float, true, true)

mlx/backend/metal/rope.cpp

@@ -67,8 +67,10 @@ void RoPE::eval_gpu(
   // Special case for inference (single time step and contiguous)
   bool single = in.flags().row_contiguous && (mat_size == in.shape(-1));
 
+  bool with_freqs = inputs.size() == 2;
   std::ostringstream kname;
-  kname << "rope_" << (single ? "single_" : "") << (forward_ ? "" : "vjp_")
+  kname << "rope_" << (single ? "single_" : "")
+        << ((with_freqs) ? "freqs_" : "") << (forward_ ? "" : "vjp_")
         << (traditional_ ? "traditional_" : "") << type_to_name(in);
   auto kernel = d.get_kernel(kname.str());
   auto& compute_encoder = d.get_command_encoder(s.index);
@@ -78,27 +80,36 @@ void RoPE::eval_gpu(
   compute_encoder.set_input_array(donated ? out : in, 0);
   compute_encoder.set_output_array(out, 1);
   compute_encoder->setBytes(&offset_, sizeof(int), 2);
-  compute_encoder->setBytes(&base, sizeof(float), 3);
+  compute_encoder->setBytes(&scale_, sizeof(float), 3);
-  compute_encoder->setBytes(&scale_, sizeof(float), 4);
 
   size_t n_batch = in.size() / mat_size;
+  MTL::Size group_dims;
+  MTL::Size grid_dims;
   if (single) {
-    compute_encoder->setBytes(&out_strides[1], sizeof(size_t), 5);
+    compute_encoder->setBytes(&out_strides[1], sizeof(size_t), 4);
     uint32_t dim0 = dims_ / 2;
-    auto group_dims = get_block_dims(dim0, n_batch, 1);
+    group_dims = get_block_dims(dim0, n_batch, 1);
-    auto grid_dims = MTL::Size(dim0, n_batch, 1);
+    grid_dims = MTL::Size(dim0, n_batch, 1);
-    compute_encoder.dispatchThreads(grid_dims, group_dims);
   } else {
-    compute_encoder->setBytes(&strides, 3 * sizeof(size_t), 5);
+    compute_encoder->setBytes(&strides, 3 * sizeof(size_t), 4);
-    compute_encoder->setBytes(&out_strides, 3 * sizeof(size_t), 6);
+    compute_encoder->setBytes(&out_strides, 3 * sizeof(size_t), 5);
-    compute_encoder->setBytes(&n_batch, sizeof(size_t), 7);
+    compute_encoder->setBytes(&n_batch, sizeof(size_t), 6);
     uint32_t dim0 = dims_ / 2;
     uint32_t dim1 = in.shape(-2);
     uint32_t dim2 = (n_batch + n_per_thread - 1) / n_per_thread;
-    auto group_dims = get_block_dims(dim0, dim1, dim2);
+    group_dims = get_block_dims(dim0, dim1, dim2);
-    auto grid_dims = MTL::Size(dim0, dim1, dim2);
+    grid_dims = MTL::Size(dim0, dim1, dim2);
-    compute_encoder.dispatchThreads(grid_dims, group_dims);
   }
+
+  if (with_freqs) {
+    auto& freqs = inputs[1];
+    compute_encoder.set_input_array(freqs, 10);
+    auto freq_stride = freqs.strides()[0];
+    compute_encoder->setBytes(&freq_stride, sizeof(size_t), 11);
+  } else {
+    compute_encoder->setBytes(&base, sizeof(float), 10);
+  }
+  compute_encoder.dispatchThreads(grid_dims, group_dims);
 }
 
 } // namespace mlx::core::fast

mlx/fast.cpp

@@ -1,5 +1,4 @@
 // Copyright © 2023-2024 Apple Inc.
-
 #include <cassert>
 #include <numeric>
 
@@ -323,7 +322,7 @@ bool LayerNormVJP::is_equivalent(const Primitive& other) const {
 }
 
 array rope(
-    const array& x,
+    std::vector<array> inputs,
     int dims,
     bool traditional,
     float base,
@@ -331,15 +330,23 @@ array rope(
     int offset,
     bool forward,
     StreamOrDevice s) {
+  auto& x = inputs[0];
   if (x.ndim() < 3) {
     std::ostringstream msg;
     msg << "[rope] Input must have at least 3 dimensions but got input with "
         << x.ndim() << " dimensions.";
     throw std::invalid_argument(msg.str());
   }
+  if (inputs.size() == 2 &&
+      (inputs[1].ndim() != 1 || inputs[1].shape(0) != dims / 2)) {
+    std::ostringstream msg;
+    msg << "[rope] freqs must be one dimensional with size " << dims
+        << " but got shape " << inputs[1].shape() << ".";
+    throw std::invalid_argument(msg.str());
+  }
 
   auto fallback = [dims, traditional, base, scale, offset, forward, s](
-                      const std::vector<array>& inputs) {
+                      std::vector<array> inputs) {
     auto& shape = inputs[0].shape();
     int ndim = shape.size();
     auto x = reshape(inputs[0], {-1, shape[ndim - 2], shape[ndim - 1]}, s);
@@ -348,10 +355,20 @@ array rope(
     // Compute sines and cosines
     auto half_dims = dims / 2;
     auto positions = multiply(arange(offset, N, t, s), array(scale, t), s);
-    auto freqs = negative(arange(0, half_dims, t, s), s);
+
-    freqs = exp(multiply(freqs, array(std::log(base) / half_dims, t), s), s);
+    auto default_inv_freqs = [&inputs, &s, &t, base, half_dims]() {
+      return exp(
+          multiply(
+              arange(0, -half_dims, -1, t, s),
+              array(std::log(base) / half_dims, t),
+              s),
+          s);
+    };
+
+    auto inv_freqs =
+        inputs.size() == 2 ? reciprocal(inputs[1], s) : default_inv_freqs();
     auto theta =
-        multiply(expand_dims(positions, 1, s), expand_dims(freqs, 0, s), s);
+        multiply(expand_dims(positions, 1, s), expand_dims(inv_freqs, 0, s), s);
     auto coss = cos(theta, s);
     auto sins = sin(theta, s);
 
@@ -409,20 +426,39 @@ array rope(
         x.dtype(),
         std::make_shared<RoPE>(
             stream, fallback, dims, traditional, base, scale, offset, forward),
-        {x});
+        std::move(inputs));
   }
-  return fallback({x})[0];
+  return fallback(std::move(inputs))[0];
 }
 
 array rope(
     const array& x,
     int dims,
     bool traditional,
-    float base,
+    std::optional<float> base,
     float scale,
     int offset,
+    const std::optional<array>& freqs /* = std::nullopt */,
     StreamOrDevice s /* = {} */) {
-  return rope(x, dims, traditional, base, scale, offset, true, s);
+  std::vector<array> inputs = {x};
+  if (freqs) {
+    inputs.push_back(astype(*freqs, float32, s));
+    if (base) {
+      throw std::invalid_argument(
+          "[rope] Only one of base or freqs can have a value.");
+    }
+  } else if (!base) {
+    throw std::invalid_argument("[rope] Neither base nor freqs has a value.");
+  }
+  return rope(
+      std::move(inputs),
+      dims,
+      traditional,
+      base.has_value() ? *base : 1.0,
+      scale,
+      offset,
+      true,
+      s);
 }
 
 std::vector<array> RoPE::vjp(
@@ -438,16 +474,27 @@ std::vector<array> RoPE::vjp(
                    offset = offset_,
                    forward = forward_,
                    s](std::vector<array> inputs) {
-    return std::vector<array>{
+    return std::vector<array>{rope(
-        rope(inputs[0], dims, traditional, base, scale, offset, !forward, s)};
+        std::move(inputs),
+        dims,
+        traditional,
+        base,
+        scale,
+        offset,
+        !forward,
+        s)};
   };
 
+  auto inputs = cotangents;
+  if (primals.size() == 2) {
+    inputs.push_back(primals[1]);
+  }
   return {array(
       cotangents[0].shape(),
       cotangents[0].dtype(),
       std::make_shared<RoPE>(
           s, fallback, dims_, traditional_, base_, scale_, offset_, !forward_),
-      cotangents)};
+      std::move(inputs))};
 }
 
 bool RoPE::is_equivalent(const Primitive& other) const {

mlx/fast.h

@@ -25,9 +25,10 @@ array rope(
     const array& x,
     int dims,
     bool traditional,
-    float base,
+    std::optional<float> base,
     float scale,
     int offset,
+    const std::optional<array>& freqs = std::nullopt,
     StreamOrDevice s = {});
 
 /** Computes: O = softmax(Q @ K.T) @ V **/

python/src/fast.cpp

@@ -79,12 +79,13 @@ void init_fast(nb::module_& parent_module) {
       "dims"_a,
       nb::kw_only(),
       "traditional"_a,
-      "base"_a,
+      "base"_a.none(),
       "scale"_a,
       "offset"_a,
+      "freqs"_a = nb::none(),
       "stream"_a = nb::none(),
       nb::sig(
-          "def rope(a: array, dims: int, *, traditional: bool, base: float, scale: float, offset: int, stream: Union[None, Stream, Device] = None) -> array"),
+          "def rope(a: array, dims: int, *, traditional: bool, base: Optional[float], scale: float, offset: int, freqs: Optional[array] = None, stream: Union[None, Stream, Device] = None) -> array"),
       R"pbdoc(
         Apply rotary positional encoding to the input.
 
@@ -94,11 +95,13 @@ void init_fast(nb::module_& parent_module) {
               is larger than dims then the rest is left unchanged.
             traditional (bool): If set to ``True`` choose the traditional
               implementation which rotates consecutive dimensions.
-            base (float): The base used to compute angular frequency for
+            base (float, optional): The base used to compute angular frequency for
-                each dimension in the positional encodings.
+              each dimension in the positional encodings. Exactly one of ``base`` and
+             ``freqs`` must be ``None``.
             scale (float): The scale used to scale the positions.
             offset (int): The position offset to start at.
-
+            freqs (array, optional): Optional frequencies to use with RoPE.
+              If set, the ``base`` parameter must be ``None``. ``Default: None``.
         Returns:
             array: The output array.
       )pbdoc");
@@ -115,7 +118,7 @@ void init_fast(nb::module_& parent_module) {
       "memory_efficient_threshold"_a = nb::none(),
       "stream"_a = nb::none(),
       nb::sig(
-          "def scaled_dot_product_attention(q: array, k: array, v: array, *, scale: float,  mask: Union[None, array] = None, stream: Union[None, Stream, Device] = None) -> array"),
+          "def scaled_dot_product_attention(q: array, k: array, v: array, *, scale: float,  mask: Optional[array] = None, stream: Union[None, Stream, Device] = None) -> array"),
       R"pbdoc(
         A fast implementation of multi-head attention: ``O = softmax(Q @ K.T, dim=-1) @ V``.
 

python/tests/test_fast.py

@@ -7,13 +7,18 @@ import mlx.core as mx
 import mlx_tests
 
 
-def rope_orig(x, dims, traditional, base, scale, offset):
+def rope_orig(x, dims, traditional, base, scale, offset, freqs=None):
     N = x.shape[1] + offset
     dtype = x.dtype
     half_D = dims // 2
     positions = mx.arange(offset, N, dtype=dtype) * scale
-    freqs = mx.exp(-mx.arange(0.0, half_D, dtype=dtype) * (math.log(base) / half_D))
+    if freqs is None:
-    theta = mx.reshape(positions, (-1, 1)) * mx.reshape(freqs, (1, -1))
+        inv_freqs = mx.exp(
+            -mx.arange(0.0, half_D, dtype=dtype) * (math.log(base) / half_D)
+        )
+    else:
+        inv_freqs = 1 / freqs
+    theta = mx.reshape(positions, (-1, 1)) * mx.reshape(inv_freqs, (1, -1))
     costheta, sintheta = mx.cos(theta), mx.sin(theta)
     if traditional:
         x1 = x[..., :dims:2]
@@ -138,6 +143,84 @@ class TestFast(mlx_tests.MLXTestCase):
                 )
                 self.assertLess(mx.abs(rx - rx_fast).max(), tolerances[dtype])
 
+    def test_rope_with_freqs(self):
+        # Check throws
+        T = 4
+        dims = 8
+        x = mx.random.uniform(shape=(2, T, dims))
+
+        with self.assertRaises(ValueError):
+            freqs = mx.random.uniform(shape=(dims - 1,))
+            mx.fast.rope(
+                x,
+                dims,
+                traditional=False,
+                base=None,
+                scale=1.0,
+                offset=0,
+                freqs=freqs,
+            )
+        with self.assertRaises(ValueError):
+            freqs = mx.random.uniform(shape=(1, dims))
+            mx.fast.rope(
+                x,
+                dims,
+                traditional=False,
+                base=None,
+                scale=1.0,
+                offset=0,
+                freqs=freqs,
+            )
+
+        freqs = mx.random.uniform(shape=(dims // 2,))
+
+        rx = rope_orig(x, dims, False, None, 1.0, 0, freqs)
+        rx_fast = mx.fast.rope(
+            x,
+            dims,
+            traditional=False,
+            base=None,
+            scale=1.0,
+            offset=0,
+            freqs=freqs,
+        )
+        self.assertLess(mx.abs(rx - rx_fast).max(), 1e-5)
+
+        # Test single vector
+        x = mx.random.uniform(shape=(1, 1, dims))
+        rx = rope_orig(x, dims, False, None, 1.0, 0, freqs)
+        rx_fast = mx.fast.rope(
+            x,
+            dims,
+            traditional=False,
+            base=None,
+            scale=1.0,
+            offset=0,
+            freqs=freqs,
+        )
+        self.assertLess(mx.abs(rx - rx_fast).max(), 1e-5)
+
+        # Test grad with freqs
+        f1 = lambda x, y: (rope_orig(x, dims, False, None, 1.0, 0, freqs) * y).sum()
+        f2 = lambda x, y: (
+            mx.fast.rope(
+                x,
+                dims,
+                traditional=False,
+                base=None,
+                scale=1.0,
+                offset=0,
+                freqs=freqs,
+            )
+            * y
+        ).sum()
+
+        x = mx.random.uniform(shape=(2, 4, dims))
+        y = mx.random.uniform(shape=(2, 4, dims))
+        g1 = mx.grad(f1)(x, y)
+        g2 = mx.grad(f2)(x, y)
+        self.assertLess(mx.abs(g1 - g2).max(), 1e-5)
+
     def test_rope_grad(self):
         D = 32
         defaults = (D, 10000.0, 1.0, 0, False)