diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index e011bb9..780052a 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -57,11 +57,6 @@ jobs:
           python -m pip install --upgrade setuptools pip wheel
           python -m pip install .[test]
 
-      - name: Install heavy deps for testing (signatory + torch)
-        run: |
-          python -m pip install torch==1.9.0
-          python -m pip install signatory==1.2.6.1.9.0  --no-cache-dir --force-reinstall
-
       - name: Test package
         run: >-
           python -m pytest -ra --cov --cov-report=xml --cov-report=term
diff --git a/tests/test_against_iisignature.py b/tests/test_against_iisignature.py
index 8175610..608f72e 100644
--- a/tests/test_against_iisignature.py
+++ b/tests/test_against_iisignature.py
@@ -8,6 +8,7 @@
 from numpy.random import default_rng
 
 from signax import logsignature, signature
+from signax.utils import compress, lyndon_words, unravel_signature
 
 rng = default_rng()
 
@@ -39,7 +40,19 @@ def test_logsignature(depth, length, dim, stream):
     batch_size = 10
     path = rng.standard_normal((batch_size, length, dim))
     jax_logsignature = logsignature(path, depth=depth, stream=stream, flatten=True)
-    s = iisignature.prepare(dim, depth, "O")
-    iis_logsignature = iisignature.logsig(np.asarray(path), s)
-    iis_logsignature = jnp.asarray(iis_logsignature)
+
+    # get expanded version of log signature
+    s = iisignature.prepare(dim, depth, "x")
+    iis_logsignature = iisignature.logsig(np.asarray(path), s, "x")
+
+    def _compress(expanded_log_signature):
+        # convert expanded array as list of arrays
+        expanded_log_signature = unravel_signature(expanded_log_signature, dim, depth)
+        indices = lyndon_words(depth, dim)
+        compressed = compress(expanded_log_signature, indices)
+        compressed = jnp.concatenate(compressed)
+        return compressed
+
+    iis_logsignature = jax.vmap(_compress)(iis_logsignature)
+
     assert jnp.allclose(jax_logsignature, iis_logsignature, atol=5e-1, rtol=5e-1)
diff --git a/tests/test_tensor_ops.py b/tests/test_tensor_ops.py
index 5ab6458..3f246b3 100644
--- a/tests/test_tensor_ops.py
+++ b/tests/test_tensor_ops.py
@@ -6,6 +6,7 @@
 import numpy as np
 from numpy.random import default_rng
 
+from signax import signature, signature_to_logsignature
 from signax.tensor_ops import (
     addcmul,
     mult,
@@ -13,6 +14,7 @@
     otimes,
     restricted_exp,
 )
+from signax.utils import compress, lyndon_words, unravel_signature
 
 rng = default_rng()
 
@@ -110,26 +112,27 @@ def test_mult():
     assert jnp.allclose(iis_signature, jax_output)
 
 
-# def test_log():
-#     """Test log via signature_to_logsignature"""
-#     depth = 4
-#     length, dim = 3, 2
-#     path = rng.standard_normal((length, dim))
-#     jax_path = jnp.array(path)
-#     jax_signature = signature(jax_path, depth, flatten=False)
-#     jax_logsignature = signature_to_logsignature(jax_signature)
-#     jax_output = jnp.concatenate([jnp.ravel(x) for x in jax_logsignature])
-
-#     torch_signature = signatory.signature(
-#         torch.tensor(path)[None, ...],
-#         depth,
-#     )
-#     torch_logsignature = signatory.signature_to_logsignature(
-#         torch_signature,
-#         dim,
-#         depth,
-#     )
-
-#     torch_output = jnp.array(torch_logsignature.numpy())
-
-#     assert jnp.allclose(torch_output, jax_output)
+def test_log():
+    """Test log via signature_to_logsignature"""
+    depth = 4
+    length, dim = 3, 2
+    path = rng.standard_normal((length, dim))
+    jax_path = jnp.array(path)
+    jax_signature = signature(jax_path, depth, flatten=False)
+    jax_logsignature = signature_to_logsignature(jax_signature)
+    jax_output = jnp.concatenate([jnp.ravel(x) for x in jax_logsignature])
+
+    s = iisignature.prepare(dim, depth, "x")
+    iis_logsignature = iisignature.logsig(np.asarray(path), s, "x")
+
+    def _compress(expanded_log_signature):
+        # convert expanded array as list of arrays
+        expanded_log_signature = unravel_signature(expanded_log_signature, dim, depth)
+        indices = lyndon_words(depth, dim)
+        compressed = compress(expanded_log_signature, indices)
+        compressed = jnp.concatenate(compressed)
+        return compressed
+
+    iis_logsignature = _compress(iis_logsignature)
+
+    assert jnp.allclose(iis_logsignature, jax_output)