Optimize mHC for expansion rate 4 using convex combination of permutations and add enable_mhc_k4_shortcut feature gate

Author: dandragona

src/maxtext/configs/base.yml

@@ -1224,6 +1224,15 @@ force_q_layout: false
 mhc_expansion_rate: 1
 # The number of iterations for the Sinkhorn-Knopp algorithm.
 sinkhorn_iterations: 20
+# mHC-lite: https://openreview.net/pdf?id=5IJX6kvOif
+# - Controls whether to generate the MHC doubly stochastic matrix via
+#   permutation-based convex combination rather than Sinkhorn-Knopp.
+# - Practical only for a small mhc_expansion_rate (e.g., k=4), as the number
+#   of permutation matrices scales factorially (k!).
+# - Ideally, this should be used whenever expansion rate is small as it removes
+#   the expensive sinkhorn iterations, the downside to this approach is that
+#   it is factorial in k.
+enable_mhc_lite: False
 
 ################################## DeepSeek Engram ##################################
 # Indices of transformer layers where Engram are integrated; leave empty [] to disable.

src/maxtext/configs/types.py

@@ -1407,6 +1407,14 @@ class ManifoldConstrainedHyperConnections(BaseModel):
 
   mhc_expansion_rate: PositiveInt = Field(1, description="The number of parallel streams in Hyper Connection.")
   sinkhorn_iterations: PositiveInt = Field(20, description="The number of iterations for the Sinkhorn-Knopp algorithm.")
+  enable_mhc_lite: bool = Field(
+      False,
+      description=(
+          "Whether to generate the MHC doubly stochastic matrix via "
+          "permutation-based convex combination rather than Sinkhorn-Knopp. "
+          "Practical only for a small mhc_expansion_rate (e.g., k=4)."
+      ),
+  )
 
 
 class DilocoParams(BaseModel):

src/maxtext/layers/mhc.py

@@ -14,7 +14,10 @@
 
 """DeepSeek Manifold-Constrained Hyper Connections (mHC) Layer."""
 
+import itertools
+import math
 from typing import Callable
+
 from flax import nnx
 import jax
 import jax.numpy as jnp
@@ -25,6 +28,17 @@
 from maxtext.layers.normalizations import RMSNorm
 
 
+def get_permutation_matrices(k: int) -> Array:
+  """Generates all permutation matrices of size k.
+
+  Reference: mHC-lite: https://openreview.net/pdf?id=5IJX6kvOif
+  Shape: (k!, k, k)
+  """
+  perms = list(itertools.permutations(range(k)))
+  perms_array = jnp.array(perms)
+  return jnp.eye(k)[perms_array]
+
+
 def get_functions(expansion_rate: int):
   """Creates functions to broadcast a single feature stream into multiple
 
@@ -118,6 +132,17 @@ def __init__(
         out_sharding=(None,),
     )
 
+    if self.config.enable_mhc_lite:
+      num_perms = math.factorial(self.k)
+      res_out_dim = num_perms
+      res_beta_shape = (num_perms,)
+      res_beta_sharding = (None,)
+      self.permutation_matrices = get_permutation_matrices(self.k)
+    else:
+      res_out_dim = self.k * self.k
+      res_beta_shape = (self.k, self.k)
+      res_beta_sharding = (None, None)
+
     # Weight matrices
     scale_init = nd_dense_init(1.0, "fan_in", "normal")
     in_axis = 0
@@ -126,7 +151,7 @@ def __init__(
     self.res_alpha = nnx.Param(
         scale_init(
             self.rngs.params(),
-            (self.k * self.dim, self.k * self.k),
+            (self.k * self.dim, res_out_dim),
             self.weight_dtype,
             in_axis=in_axis,
             out_axis=out_axis,
@@ -156,8 +181,10 @@ def __init__(
 
     # Biases
     self.res_beta = nnx.Param(
-        default_bias_init(self.rngs.params(), (self.k, self.k), self.weight_dtype),
-        out_sharding=(None, None),
+        default_bias_init(
+            self.rngs.params(), res_beta_shape, self.weight_dtype
+        ),
+        out_sharding=res_beta_sharding,
     )
     self.pre_beta = nnx.Param(
         default_bias_init(self.rngs.params(), (self.k,), self.weight_dtype),
@@ -174,13 +201,36 @@ def res_mapping(self, x: Array):
     res_alpha = jnp.asarray(self.res_alpha[...], self.dtype)
     res_beta = jnp.asarray(self.res_beta[...], self.dtype)
     res_alpha_scale = jnp.asarray(self.res_alpha_scale[...], self.dtype)
-    # Apply projection: (b, s, k*d) @ (k*d, k*k) -> (b, s, k*k)
-    h_res = jnp.einsum("bsm,mn -> bsn", x, res_alpha, precision=self.matmul_precision)
-    b, s, _ = h_res.shape
-    h_res = jnp.reshape(h_res, (b, s, self.k, self.k))
-    intermediate = res_alpha_scale * h_res + res_beta[None, None, :, :]
-    output = sinkhorn(intermediate, self.sinkhorn_iterations)
-    return output
+
+    if self.config.enable_mhc_lite:
+      # Apply projection: (b, s, k*d) @ (k*d, k!) -> (b, s, k!)
+      h_res = jnp.einsum(
+          "bsm,mn -> bsn", x, res_alpha, precision=self.matmul_precision
+      )
+      intermediate = res_alpha_scale * h_res + res_beta[None, None, :]
+      # Use float32 for numerical stability during softmax
+      weights = jax.nn.softmax(
+          intermediate.astype(jnp.float32), axis=-1
+      ).astype(self.dtype)
+      # Sum the permutation matrices with the weights
+      permutation_matrices = self.permutation_matrices.astype(self.dtype)
+      output = jnp.einsum(
+          "bsn,nkm -> bskm",
+          weights,
+          permutation_matrices,
+          precision=self.matmul_precision,
+      )
+      return output
+    else:
+      # Apply projection: (b, s, k*d) @ (k*d, k*k) -> (b, s, k*k)
+      h_res = jnp.einsum(
+          "bsm,mn -> bsn", x, res_alpha, precision=self.matmul_precision
+      )
+      b, s, _ = h_res.shape
+      h_res = jnp.reshape(h_res, (b, s, self.k, self.k))
+      intermediate = res_alpha_scale * h_res + res_beta[None, None, :, :]
+      output = sinkhorn(intermediate, self.sinkhorn_iterations)
+      return output
 
   def mapping(self, x: Array, alpha_scale: Array, alpha: Array, beta: Array, scale: int):
     """Helper function for both pre and post mappings."""

tests/unit/mhc_test.py

@@ -15,21 +15,20 @@
 """Test for DeepSeek Manifold-Constrained Hyper Connections (mHC)."""
 
 import unittest
-import pytest
-
+from absl.testing import parameterized
 from flax import nnx
 from flax.linen import partitioning as nn_partitioning
 import jax
 import jax.numpy as jnp
 from jax.sharding import Mesh
-import numpy as np
-
-from maxtext.configs import pyconfig
 from maxtext.common.common_types import HyperConnectionType
+from maxtext.configs import pyconfig
 from maxtext.layers import attention_mla, linears, mhc, moe
 from maxtext.layers.initializers import nd_dense_init
 from maxtext.layers.normalizations import RMSNorm
 from maxtext.utils import maxtext_utils
+import numpy as np
+import pytest
 from tests.utils.test_helpers import get_test_config_path
 
 
@@ -86,14 +85,15 @@ def test_doubly_stochastic_property(self):
     np.testing.assert_allclose(col_sums, jnp.ones_like(col_sums), atol=1e-3)
 
 
-class TestMHC(unittest.TestCase):
+class TestMHC(parameterized.TestCase):
   """Test for MHC module"""
 
-  def setUp(self):
+  def _setup_mhc(self, rate, enable_mhc_lite=False):
+    """Sets up the common configurations and modules for MHC testing."""
     self.dim = 16
     self.config = pyconfig.initialize(
         [None, get_test_config_path()],
-        run_name="test_mhc",
+        run_name=f"test_mhc_k{rate}",
         enable_checkpointing=False,
         model_name="deepseek-custom",
         per_device_batch_size=jax.device_count(),
@@ -105,7 +105,8 @@ def setUp(self):
         # override
         override_model_config=True,
         base_emb_dim=self.dim,
-        mhc_expansion_rate=3,
+        mhc_expansion_rate=rate,
+        enable_mhc_lite=enable_mhc_lite,
         num_experts=4,
         num_experts_per_tok=2,
         engram_layers=[],
@@ -135,7 +136,10 @@ def setUp(self):
 
   # Skip GPU due to NotImplementedError: dynamic grid bounds not supported in the Triton backend
   @pytest.mark.tpu_only
-  def test_moe_layer_output_shape(self):
+  @parameterized.named_parameters(("Rate3", 3), ("Rate4", 4))
+  def test_moe_layer_output_shape(self, rate):
+    self._setup_mhc(rate)
+
     with nn_partitioning.axis_rules(self.config.logical_axis_rules):
       module = mhc.ManifoldConstrainedHyperConnections(self.config, self.dim, self.mesh, self.rngs)
       layer = moe.RoutedMoE(
@@ -154,12 +158,14 @@ def test_moe_layer_output_shape(self):
       b, s, k, d = self.x.shape
       output, metadata = module(self.pre_norm, layer, x=self.x, mhc_type=HyperConnectionType.MLP_MOE)
       # metadata includes load_balance_loss & moe_bias_updates
-      self.assertEqual(len(metadata), 2)
+      self.assertLen(metadata, 2)
       for key, value in metadata.items():
         self.assertIsNotNone(value, f"Key '{key}' has a value of None")
       self.assertEqual(output.shape, (b, s, k, d))
 
-  def test_dense_layer_output_shape(self):
+  @parameterized.named_parameters(("Rate3", 3), ("Rate4", 4))
+  def test_dense_layer_output_shape(self, rate):
+    self._setup_mhc(rate)
     with nn_partitioning.axis_rules(self.config.logical_axis_rules):
       module = mhc.ManifoldConstrainedHyperConnections(self.config, self.dim, self.mesh, self.rngs)
       layer = linears.MlpBlock(
@@ -180,8 +186,14 @@ def test_dense_layer_output_shape(self):
       self.assertDictEqual(metadata, {})
       self.assertEqual(output.shape, (b, s, k, d))
 
-  def test_attention_layer_output_shape(self):
-    inputs_shape = (self.config.per_device_batch_size, self.config.max_target_length, self.config.emb_dim)
+  @parameterized.named_parameters(("Rate3", 3), ("Rate4", 4))
+  def test_attention_layer_output_shape(self, rate):
+    self._setup_mhc(rate)
+    inputs_shape = (
+        self.config.per_device_batch_size,
+        self.config.max_target_length,
+        self.config.emb_dim,
+    )
     with nn_partitioning.axis_rules(self.config.logical_axis_rules):
       module = mhc.ManifoldConstrainedHyperConnections(self.config, self.dim, self.mesh, self.rngs)
       layer = attention_mla.MLA(
@@ -219,6 +231,69 @@ def test_attention_layer_output_shape(self):
       self.assertDictEqual(metadata, {})
       self.assertEqual(output.shape, (b, s, k, d))
 
+  def test_mhc_lite_doubly_stochastic(self):
+    """Verify that mHC-lite output is doubly stochastic (rows/cols sum to 1)."""
+    self._setup_mhc(4, enable_mhc_lite=True)
+    with nn_partitioning.axis_rules(self.config.logical_axis_rules):
+      module = mhc.ManifoldConstrainedHyperConnections(
+          self.config, self.dim, self.mesh, self.rngs
+      )
+
+      b, s, k, d = self.x.shape
+
+      # Generate random input X
+      random_x = jax.random.normal(jax.random.PRNGKey(42), (b, s, k * d))
+      norm_x = module.mhc_norm(random_x)
+
+      # Output from mHC-lite mapping
+      res_mapping_out = module.res_mapping(norm_x)
+
+      row_sums = jnp.sum(res_mapping_out, axis=-1)
+      col_sums = jnp.sum(res_mapping_out, axis=-2)
+
+      # Check if sums are close to 1.0
+      np.testing.assert_allclose(row_sums, jnp.ones_like(row_sums), atol=1e-2)
+      np.testing.assert_allclose(col_sums, jnp.ones_like(col_sums), atol=1e-2)
+
+  def test_feature_flag_gates_lite(self):
+    """Verify that setting enable_mhc_lite=False falls back to Sinkhorn."""
+    self.dim = 16
+    self.config = pyconfig.initialize(
+        [None, get_test_config_path()],
+        run_name="test_mhc_lite_gated",
+        enable_checkpointing=False,
+        model_name="deepseek-custom",
+        per_device_batch_size=4,
+        max_target_length=7,
+        max_prefill_predict_length=7,
+        attention="dot_product",
+        routed_bias_update_rate=0.01,
+        load_balance_loss_weight=0.02,
+        # override
+        override_model_config=True,
+        base_emb_dim=self.dim,
+        mhc_expansion_rate=4,
+        enable_mhc_lite=False,
+        num_experts=4,
+        num_experts_per_tok=2,
+        engram_layers=[],
+    )
+    devices_array = maxtext_utils.create_device_mesh(self.config)
+    self.mesh = Mesh(devices_array, self.config.mesh_axes)
+    self.rngs = nnx.Rngs(params=jax.random.key(0), dropout=jax.random.key(42))
+
+    with nn_partitioning.axis_rules(self.config.logical_axis_rules):
+      module = mhc.ManifoldConstrainedHyperConnections(
+          self.config, self.dim, self.mesh, self.rngs
+      )
+
+      # Shape of res_alpha should be (4*16, 4*4) = (64, 16) instead of (64, 24)
+      self.assertEqual(module.res_alpha.shape, (64, 16))
+      # Shape of res_beta should be (4, 4) instead of (24,)
+      self.assertEqual(module.res_beta.shape, (4, 4))
+      # Permutation matrices shouldn't be defined
+      self.assertFalse(hasattr(module, "permutation_matrices"))
+
 
 if __name__ == "__main__":
   unittest.main()