diff --git a/jax_scaled_arithmetics/__init__.py b/jax_scaled_arithmetics/__init__.py
index 803aee4..5a42b7e 100644
--- a/jax_scaled_arithmetics/__init__.py
+++ b/jax_scaled_arithmetics/__init__.py
@@ -1,2 +1,4 @@
 # Copyright (c) 2023 Graphcore Ltd. All rights reserved.
+from . import lax
 from ._version import __version__
+from .core import ScaledArray, autoscale  # noqa: F401
diff --git a/jax_scaled_arithmetics/core/__init__.py b/jax_scaled_arithmetics/core/__init__.py
index 61e13fa..d6f4c6a 100644
--- a/jax_scaled_arithmetics/core/__init__.py
+++ b/jax_scaled_arithmetics/core/__init__.py
@@ -1,2 +1,3 @@
 # Copyright (c) 2023 Graphcore Ltd. All rights reserved.
 from .datatype import ScaledArray  # noqa: F401
+from .interpreters import autoscale, register_scaled_op  # noqa: F401
diff --git a/jax_scaled_arithmetics/core/datatype.py b/jax_scaled_arithmetics/core/datatype.py
index 759e2ba..cfcc518 100644
--- a/jax_scaled_arithmetics/core/datatype.py
+++ b/jax_scaled_arithmetics/core/datatype.py
@@ -78,3 +78,7 @@ def to_array(self, dtype: DTypeLike = None) -> GenericArray:
     def __array__(self, dtype: DTypeLike = None) -> NDArray[Any]:
         """Numpy array interface support."""
         return np.asarray(self.to_array(dtype))
+
+    @property
+    def aval(self):
+        return self.data * self.scale
diff --git a/jax_scaled_arithmetics/core/interpreters.py b/jax_scaled_arithmetics/core/interpreters.py
new file mode 100644
index 0000000..503cb1d
--- /dev/null
+++ b/jax_scaled_arithmetics/core/interpreters.py
@@ -0,0 +1,59 @@
+# Copyright (c) 2023 Graphcore Ltd. All rights reserved.
+
+from functools import wraps
+from typing import Dict
+
+import jax
+from jax import core
+from jax._src.util import safe_map
+
+from ..core import ScaledArray
+
+_scaled_ops_registry = {}
+
+
+def register_scaled_op(lax_func, scaled_func):
+    _scaled_ops_registry[lax_func] = scaled_func
+
+
+def autoscale(fun):
+    @wraps(fun)
+    def wrapped(*args, **kwargs):
+        aval_args = safe_map(lambda x: x.aval, args)
+        # get jaxpr of unscaled graph
+        closed_jaxpr = jax.make_jaxpr(fun)(*aval_args, **kwargs)
+        # convert to scaled graph
+        out = autoscale_jaxpr(closed_jaxpr.jaxpr, closed_jaxpr.literals, *args)
+        return out
+
+    return wrapped
+
+
+def autoscale_jaxpr(jaxpr, consts, *args):
+    env: Dict[core.Var, ScaledArray] = {}
+
+    def read(var):
+        if type(var) is core.Literal:
+            return var.val
+        return env[var]
+
+    def write(var, val):
+        env[var] = val
+
+    safe_map(write, jaxpr.invars, args)
+    safe_map(write, jaxpr.constvars, consts)
+
+    for eqn in jaxpr.eqns:
+        invals = safe_map(read, eqn.invars)
+        if eqn.primitive not in _scaled_ops_registry:
+            raise NotImplementedError(f"{eqn.primitive} does not have an implementation for ScaledArray inputs yet")
+        outvals = _scaled_ops_registry[eqn.primitive](*invals)
+        if not eqn.primitive.multiple_results:
+            outvals = [outvals]
+        safe_map(write, eqn.outvars, outvals)
+
+    outvals = safe_map(read, jaxpr.outvars)
+    if len(outvals) == 1:
+        return outvals[0]
+    else:
+        return outvals
diff --git a/jax_scaled_arithmetics/lax/__init__.py b/jax_scaled_arithmetics/lax/__init__.py
index 9dc9fcb..65b52cc 100644
--- a/jax_scaled_arithmetics/lax/__init__.py
+++ b/jax_scaled_arithmetics/lax/__init__.py
@@ -1 +1,2 @@
 # Copyright (c) 2023 Graphcore Ltd. All rights reserved.
+from .scaled_ops import *  # noqa: F401, F403
diff --git a/jax_scaled_arithmetics/lax/scaled_ops.py b/jax_scaled_arithmetics/lax/scaled_ops.py
new file mode 100644
index 0000000..d1106f8
--- /dev/null
+++ b/jax_scaled_arithmetics/lax/scaled_ops.py
@@ -0,0 +1,15 @@
+# Copyright (c) 2023 Graphcore Ltd. All rights reserved.
+
+from jax import lax
+
+from jax_scaled_arithmetics import core
+from jax_scaled_arithmetics.core import ScaledArray
+
+
+def scaled_mul_p(A: ScaledArray, B: ScaledArray) -> ScaledArray:
+    return ScaledArray(A.data * B.data, A.scale * B.scale)
+
+
+core.register_scaled_op(lax.mul_p, scaled_mul_p)
+
+__all__ = ["scaled_mul_p"]
diff --git a/tests/interpreters/test_interpreter.py b/tests/interpreters/test_interpreter.py
new file mode 100644
index 0000000..5bbb4ad
--- /dev/null
+++ b/tests/interpreters/test_interpreter.py
@@ -0,0 +1,54 @@
+# Copyright (c) 2023 Graphcore Ltd. All rights reserved.
+
+import chex
+import jax
+import jax.numpy as jnp
+
+from jax_scaled_arithmetics.core import ScaledArray, autoscale
+
+
+class AutoScaleInterpreterTests(chex.TestCase):
+    def test__identity(self):
+        def func(x):
+            return x
+
+        asfunc = autoscale(func)
+
+        scale = jnp.array(1.0)
+        inputs = jnp.array([1.0, 2.0])
+        expected = jnp.array([1.0, 2.0])
+
+        scaled_inputs = ScaledArray(inputs, scale)
+        scaled_outputs = asfunc(scaled_inputs)
+
+        assert jnp.allclose(scaled_outputs.aval, expected)
+
+        jaxpr = jax.make_jaxpr(asfunc)(scaled_inputs).jaxpr
+
+        # Vars need to be primitive data types (e.g., f32) -> 2 Vars per ScaledArray
+
+        assert jaxpr.invars[0].aval.shape == inputs.shape
+        assert jaxpr.invars[1].aval.shape == ()
+
+        assert jaxpr.outvars[0].aval.shape == expected.shape
+        assert jaxpr.outvars[1].aval.shape == ()
+
+    def test__mul(self):
+        def func(x, y):
+            return x * y
+
+        asfunc = autoscale(func)
+
+        x_in = jnp.array([-2.0, 2.0])
+        x_scale = jnp.array(0.5)
+        x = ScaledArray(x_in, x_scale)
+
+        y_in = jnp.array([1.5, 1.5])
+        y_scale = jnp.array(2.0)
+        y = ScaledArray(y_in, y_scale)
+
+        expected = jnp.array([-3.0, 3.0])
+
+        out = asfunc(x, y)
+
+        assert jnp.allclose(out.aval, expected)