From 183fe79644e9eaeee2d758f277a3d4b7ac02aa64 Mon Sep 17 00:00:00 2001 From: Gurshaant Malik Date: Thu, 6 May 2021 16:06:04 -0300 Subject: [PATCH 1/3] Add trainable theta and discretization options Co-authored-by: Daniel Rasmussen --- CHANGES.rst | 15 ++- keras_lmu/layers.py | 235 +++++++++++++++++++++++++++------ keras_lmu/tests/test_layers.py | 230 +++++++++++++++++++++++++++----- keras_lmu/version.py | 2 +- 4 files changed, 407 insertions(+), 75 deletions(-) diff --git a/CHANGES.rst b/CHANGES.rst index d6ba7c89..e489fa36 100644 --- a/CHANGES.rst +++ b/CHANGES.rst @@ -19,7 +19,7 @@ Release history - Removed - Fixed -0.3.2 (unreleased) +0.4.0 (unreleased) ================== **Added** @@ -29,8 +29,21 @@ Release history uses this implementation for all values of ``memory_d`` when feedforward conditions are satisfied (no hidden-to-memory or memory-to-memory connections, and the sequence length is not ``None``). (`#40`_) +- Added ``trainable_theta`` option, which will allow the ``theta`` parameter to be + learned during training. (`#41`_) +- Added ``discretizer`` option, which controls the method used to solve for the ``A`` + and ``B`` LMU matrices. This is mainly useful in combination with + ``trainable_theta=True``, where setting ``discretizer="euler"`` may improve the + training speed (possibly at the cost of some accuracy). (`#41`_) + +**Changed** + +- The ``A`` and ``B`` matrices are now stored as constants instead of non-trainable + variables. This can improve the training/inference speed, but it means that saved + weights from previous versions will be incompatible. (`#41`_) .. _#40: https://github.com/nengo/keras-lmu/pull/40 +.. _#41: https://github.com/nengo/keras-lmu/pull/41 0.3.1 (November 16, 2020) ========================= diff --git a/keras_lmu/layers.py b/keras_lmu/layers.py index d98bac14..7a624cca 100644 --- a/keras_lmu/layers.py +++ b/keras_lmu/layers.py @@ -4,7 +4,6 @@ import numpy as np import tensorflow as tf -from scipy.signal import cont2discrete from tensorflow.python.keras.layers.recurrent import DropoutRNNCellMixin @@ -28,16 +27,20 @@ class to create a recurrent Keras layer to process the whole sequence. Calling The number of degrees in the transfer function of the LTI system used to represent the sliding window of history. This parameter sets the number of Legendre polynomials used to orthogonally represent the sliding window. - theta : int + theta : float The number of timesteps in the sliding window that is represented using the LTI system. In this context, the sliding window represents a dynamic range of data, of fixed size, that will be used to predict the value at the next time step. If this value is smaller than the size of the input sequence, only that - number of steps will be represented at the time of - prediction, however the entire sequence will still be processed in order for - information to be projected to and from the hidden layer. + number of steps will be represented at the time of prediction, however the + entire sequence will still be processed in order for information to be + projected to and from the hidden layer. If ``trainable_theta`` is enabled, then + theta will be updated during the course of training. hidden_cell : ``tf.keras.layers.Layer`` Keras Layer/RNNCell implementing the hidden component. + trainable_theta : bool + If True, theta is learnt over the course of training. Otherwise, it is kept + constant. hidden_to_memory : bool If True, connect the output of the hidden component back to the memory component (default False). @@ -47,6 +50,12 @@ class to create a recurrent Keras layer to process the whole sequence. Calling input_to_hidden : bool If True, connect the input directly to the hidden component (in addition to the connection from the memory component) (default False). + discretizer : str + The method used to discretize the A and B matrices of the LMU. Current + options are "zoh" (short for Zero Order Hold) and "euler". + "zoh" is more accurate, but training will be slower than "euler" if + ``trainable_theta=True``. Note that a larger theta is needed when discretizing + using "euler" (a value that is larger than ``4*order`` is recommended). kernel_initializer : ``tf.initializers.Initializer`` Initializer for weights from input to memory/hidden component. If ``None``, no weights will be used, and the input size must match the memory/hidden size. @@ -73,9 +82,11 @@ def __init__( order, theta, hidden_cell, + trainable_theta=False, hidden_to_memory=False, memory_to_memory=False, input_to_hidden=False, + discretizer="zoh", kernel_initializer="glorot_uniform", recurrent_initializer="orthogonal", dropout=0, @@ -86,11 +97,13 @@ def __init__( self.memory_d = memory_d self.order = order - self.theta = theta + self._init_theta = theta self.hidden_cell = hidden_cell + self.trainable_theta = trainable_theta self.hidden_to_memory = hidden_to_memory self.memory_to_memory = memory_to_memory self.input_to_hidden = input_to_hidden + self.discretizer = discretizer self.kernel_initializer = kernel_initializer self.recurrent_initializer = recurrent_initializer self.dropout = dropout @@ -98,9 +111,15 @@ def __init__( self.kernel = None self.recurrent_kernel = None + self.theta_inv = None self.A = None self.B = None + if self.discretizer not in ("zoh", "euler"): + raise ValueError( + f"discretizer must be 'zoh' or 'euler' (got '{self.discretizer}')" + ) + if self.hidden_cell is None: for conn in ("hidden_to_memory", "input_to_hidden"): if getattr(self, conn): @@ -116,20 +135,78 @@ def __init__( self.hidden_output_size = self.hidden_cell.units self.hidden_state_size = [self.hidden_cell.units] - Q = np.arange(order, dtype=np.float64) - R = (2 * Q + 1)[:, None] / theta - j, i = np.meshgrid(Q, Q) - A = np.where(i < j, -1, (-1.0) ** (i - j + 1)) * R - B = (-1.0) ** Q[:, None] * R - C = np.ones((1, order)) - D = np.zeros((1,)) - self._A, self._B, _, _, _ = cont2discrete((A, B, C, D), dt=1.0, method="zoh") - self.state_size = tf.nest.flatten(self.hidden_state_size) + [ self.memory_d * self.order ] self.output_size = self.hidden_output_size + @property + def theta(self): + """ + Value of the ``theta`` parameter. + + If ``trainable_theta=True`` this returns the trained value, not the initial + value passed in to the constructor. + """ + if self.built: + return 1 / tf.keras.backend.get_value(self.theta_inv) + + return self._init_theta + + def _gen_AB(self): + """Generates A and B matrices.""" + + # compute analog A/B matrices + Q = np.arange(self.order, dtype=np.float64) + R = (2 * Q + 1)[:, None] + j, i = np.meshgrid(Q, Q) + A = np.where(i < j, -1, (-1.0) ** (i - j + 1)) * R + B = (-1.0) ** Q[:, None] * R + + # discretize matrices + if self.discretizer == "zoh": + # save the un-discretized matrices for use in .call + self._base_A = tf.constant(A.T, dtype=self.dtype) + self._base_B = tf.constant(B.T, dtype=self.dtype) + + self.A, self.B = LMUCell._cont2discrete_zoh( + self._base_A / self._init_theta, self._base_B / self._init_theta + ) + else: + if not self.trainable_theta: + A = A / self._init_theta + np.eye(self.order) + B = B / self._init_theta + + self.A = tf.constant(A.T, dtype=self.dtype) + self.B = tf.constant(B.T, dtype=self.dtype) + + @staticmethod + def _cont2discrete_zoh(A, B): + """ + Function to discretize A and B matrices using Zero Order Hold method. + + Functionally equivalent to + ``scipy.signal.cont2discrete((A.T, B.T, _, _), method="zoh", dt=1.0)`` + (but implemented in TensorFlow so that it is differentiable). + + Note that this accepts and returns matrices that are transposed from the + standard linear system implementation (as that makes it easier to use in + `.call`). + """ + + # combine A/B and pad to make square matrix + em_upper = tf.concat([A, B], axis=0) + em = tf.pad(em_upper, [(0, 0), (0, B.shape[0])]) + + # compute matrix exponential + ms = tf.linalg.expm(em) + + # slice A/B back out of combined matrix + discrt_A = ms[: A.shape[0], : A.shape[1]] + discrt_B = ms[A.shape[0] :, : A.shape[1]] + + return discrt_A, discrt_B + def build(self, input_shape): """ Builds the cell. @@ -161,6 +238,18 @@ def build(self, input_shape): f" must equal `memory_d` ({self.memory_d})." ) + # when using euler, 1/theta results in better gradients for the memory + # update since you are multiplying 1/theta, as compared to dividing theta + if self.trainable_theta: + self.theta_inv = self.add_weight( + name="theta_inv", + shape=(), + initializer=tf.initializers.constant(1 / self._init_theta), + constraint=tf.keras.constraints.NonNeg(), + ) + else: + self.theta_inv = tf.constant(1 / self._init_theta, dtype=self.dtype) + if self.memory_to_memory: self.recurrent_kernel = self.add_weight( name="recurrent_kernel", @@ -177,19 +266,8 @@ def build(self, input_shape): with tf.name_scope(self.hidden_cell.name): self.hidden_cell.build((input_shape[0], hidden_input_d)) - self.A = self.add_weight( - name="A", - shape=(self.order, self.order), - initializer=tf.initializers.constant(self._A.T), # note: transposed - trainable=False, - ) - - self.B = self.add_weight( - name="B", - shape=(1, self.order), # system is SISO - initializer=tf.initializers.constant(self._B.T), # note: transposed - trainable=False, - ) + # generate A and B matrices + self._gen_AB() def call(self, inputs, states, training=None): """ @@ -233,7 +311,25 @@ def call(self, inputs, states, training=None): u = tf.expand_dims(u, -1) # update memory - m = tf.matmul(m, self.A) + tf.matmul(u, self.B) + if self.discretizer == "zoh" and self.trainable_theta: + # apply updated theta and re-discretize + A, B = LMUCell._cont2discrete_zoh( + self._base_A * self.theta_inv, self._base_B * self.theta_inv + ) + else: + A, B = self.A, self.B + + _m = tf.matmul(m, A) + tf.matmul(u, B) + + if self.discretizer == "euler" and self.trainable_theta: + # apply updated theta. this is the same as scaling A/B by theta, but it's + # more efficient to do it this way. + # note that when computing this way the A matrix does not + # include the identity matrix along the diagonal (since we don't want to + # scale that part by theta), which is why we do += instead of = + m += _m * self.theta_inv + else: + m = _m # re-combine memory/order dimensions m = tf.reshape(m, (-1, self.memory_d * self.order)) @@ -272,11 +368,13 @@ def get_config(self): dict( memory_d=self.memory_d, order=self.order, - theta=self.theta, + theta=self._init_theta, hidden_cell=tf.keras.layers.serialize(self.hidden_cell), + trainable_theta=self.trainable_theta, hidden_to_memory=self.hidden_to_memory, memory_to_memory=self.memory_to_memory, input_to_hidden=self.input_to_hidden, + discretizer=self.discretizer, kernel_initializer=self.kernel_initializer, recurrent_initializer=self.recurrent_initializer, dropout=self.dropout, @@ -317,16 +415,20 @@ class LMU(tf.keras.layers.Layer): The number of degrees in the transfer function of the LTI system used to represent the sliding window of history. This parameter sets the number of Legendre polynomials used to orthogonally represent the sliding window. - theta : int + theta : float The number of timesteps in the sliding window that is represented using the LTI system. In this context, the sliding window represents a dynamic range of data, of fixed size, that will be used to predict the value at the next time step. If this value is smaller than the size of the input sequence, only that - number of steps will be represented at the time of - prediction, however the entire sequence will still be processed in order for - information to be projected to and from the hidden layer. + number of steps will be represented at the time of prediction, however the + entire sequence will still be processed in order for information to be + projected to and from the hidden layer. If ``trainable_theta`` is enabled, then + theta will be updated during the course of training. hidden_cell : ``tf.keras.layers.Layer`` Keras Layer/RNNCell implementing the hidden component. + trainable_theta : bool + If True, theta is learnt over the course of training. Otherwise, it is kept + constant. hidden_to_memory : bool If True, connect the output of the hidden component back to the memory component (default False). @@ -336,6 +438,12 @@ class LMU(tf.keras.layers.Layer): input_to_hidden : bool If True, connect the input directly to the hidden component (in addition to the connection from the memory component) (default False). + discretizer : str + The method used to discretize the A and B matrices of the LMU. Current + options are "zoh" (short for Zero Order Hold) and "euler". + "zoh" is more accurate, but training will be slower than "euler" if + ``trainable_theta=True``. Note that a larger theta is needed when discretizing + using "euler" (a value that is larger than ``4*order`` is recommended). kernel_initializer : ``tf.initializers.Initializer`` Initializer for weights from input to memory/hidden component. If ``None``, no weights will be used, and the input size must match the memory/hidden size. @@ -365,9 +473,11 @@ def __init__( order, theta, hidden_cell, + trainable_theta=False, hidden_to_memory=False, memory_to_memory=False, input_to_hidden=False, + discretizer="zoh", kernel_initializer="glorot_uniform", recurrent_initializer="orthogonal", dropout=0, @@ -380,11 +490,13 @@ def __init__( self.memory_d = memory_d self.order = order - self.theta = theta + self._init_theta = theta self.hidden_cell = hidden_cell + self.trainable_theta = trainable_theta self.hidden_to_memory = hidden_to_memory self.memory_to_memory = memory_to_memory self.input_to_hidden = input_to_hidden + self.discretizer = discretizer self.kernel_initializer = kernel_initializer self.recurrent_initializer = recurrent_initializer self.dropout = dropout @@ -392,6 +504,24 @@ def __init__( self.return_sequences = return_sequences self.layer = None + @property + def theta(self): + """ + Value of the ``theta`` parameter. + + If ``trainable_theta=True`` this returns the trained value, not the initial + value passed in to the constructor. + """ + + if self.built: + return ( + self.layer.theta + if isinstance(self.layer, LMUFFT) + else self.layer.cell.theta + ) + + return self._init_theta + def build(self, input_shapes): """ Builds the layer. @@ -409,13 +539,15 @@ def build(self, input_shapes): not self.hidden_to_memory and not self.memory_to_memory and input_shapes[1] is not None + and not self.trainable_theta ): self.layer = LMUFFT( memory_d=self.memory_d, order=self.order, - theta=self.theta, + theta=self._init_theta, hidden_cell=self.hidden_cell, input_to_hidden=self.input_to_hidden, + discretizer=self.discretizer, kernel_initializer=self.kernel_initializer, dropout=self.dropout, return_sequences=self.return_sequences, @@ -425,11 +557,13 @@ def build(self, input_shapes): LMUCell( memory_d=self.memory_d, order=self.order, - theta=self.theta, + theta=self._init_theta, hidden_cell=self.hidden_cell, + trainable_theta=self.trainable_theta, hidden_to_memory=self.hidden_to_memory, memory_to_memory=self.memory_to_memory, input_to_hidden=self.input_to_hidden, + discretizer=self.discretizer, kernel_initializer=self.kernel_initializer, recurrent_initializer=self.recurrent_initializer, dropout=self.dropout, @@ -461,11 +595,13 @@ def get_config(self): dict( memory_d=self.memory_d, order=self.order, - theta=self.theta, + theta=self._init_theta, hidden_cell=tf.keras.layers.serialize(self.hidden_cell), + trainable_theta=self.trainable_theta, hidden_to_memory=self.hidden_to_memory, memory_to_memory=self.memory_to_memory, input_to_hidden=self.input_to_hidden, + discretizer=self.discretizer, kernel_initializer=self.kernel_initializer, recurrent_initializer=self.recurrent_initializer, dropout=self.dropout, @@ -502,19 +638,25 @@ class LMUFFT(tf.keras.layers.Layer): The number of degrees in the transfer function of the LTI system used to represent the sliding window of history. This parameter sets the number of Legendre polynomials used to orthogonally represent the sliding window. - theta : int + theta : float The number of timesteps in the sliding window that is represented using the LTI system. In this context, the sliding window represents a dynamic range of data, of fixed size, that will be used to predict the value at the next time step. If this value is smaller than the size of the input sequence, only that - number of steps will be represented at the time of - prediction, however the entire sequence will still be processed in order for - information to be projected to and from the hidden layer. + number of steps will be represented at the time of prediction, however the + entire sequence will still be processed in order for information to be + projected to and from the hidden layer. hidden_cell : ``tf.keras.layers.Layer`` Keras Layer implementing the hidden component. input_to_hidden : bool If True, connect the input directly to the hidden component (in addition to the connection from the memory component) (default False). + discretizer : str + The method used to discretize the A and B matrices of the LMU. Current + options are "zoh" (short for Zero Order Hold) and "euler". + "zoh" is more accurate, but training will be slower than "euler" if + ``trainable_theta=True``. Note that a larger theta is needed when discretizing + using "euler" (a value that is larger than ``4*order`` is recommended). kernel_initializer : ``tf.initializers.Initializer`` Initializer for weights from input to memory/hidden component. If ``None``, no weights will be used, and the input size must match the memory/hidden size. @@ -532,6 +674,7 @@ def __init__( theta, hidden_cell, input_to_hidden=False, + discretizer="zoh", kernel_initializer="glorot_uniform", dropout=0, return_sequences=False, @@ -547,6 +690,7 @@ def __init__( self.theta = theta self.hidden_cell = hidden_cell self.input_to_hidden = input_to_hidden + self.discretizer = discretizer self.kernel_initializer = kernel_initializer self.dropout = dropout self.return_sequences = return_sequences @@ -558,9 +702,11 @@ def __init__( order=order, theta=theta, hidden_cell=None, + trainable_theta=False, input_to_hidden=False, hidden_to_memory=False, memory_to_memory=False, + discretizer=discretizer, kernel_initializer=None, trainable=False, ), @@ -594,7 +740,9 @@ def build(self, input_shape): impulse = tf.reshape(tf.eye(seq_len, 1), (1, -1, 1)) self.impulse_response = tf.signal.rfft( - tf.squeeze(tf.transpose(self.delay_layer(impulse)), axis=-1), + tf.squeeze( + tf.transpose(self.delay_layer(impulse, training=False)), axis=-1 + ), fft_length=[2 * seq_len], ) @@ -694,6 +842,7 @@ def get_config(self): theta=self.theta, hidden_cell=tf.keras.layers.serialize(self.hidden_cell), input_to_hidden=self.input_to_hidden, + discretizer=self.discretizer, kernel_initializer=self.kernel_initializer, dropout=self.dropout, return_sequences=self.return_sequences, diff --git a/keras_lmu/tests/test_layers.py b/keras_lmu/tests/test_layers.py index 967ff178..bbbde129 100644 --- a/keras_lmu/tests/test_layers.py +++ b/keras_lmu/tests/test_layers.py @@ -3,14 +3,16 @@ import numpy as np import pytest import tensorflow as tf +from scipy.signal import cont2discrete from keras_lmu import layers -def test_multivariate_lmu(rng): +@pytest.mark.parametrize("discretizer", ("zoh", "euler")) +def test_multivariate_lmu(rng, discretizer): memory_d = 4 order = 16 - n_steps = 10 + n_steps = 10 * order input_d = 32 input_enc = rng.uniform(0, 1, size=(input_d, memory_d)) @@ -23,6 +25,7 @@ def test_multivariate_lmu(rng): memory_d=memory_d, order=order, theta=n_steps, + discretizer=discretizer, kernel_initializer=tf.initializers.constant(input_enc), hidden_cell=tf.keras.layers.SimpleRNNCell( units=memory_d * order, @@ -39,6 +42,7 @@ def test_multivariate_lmu(rng): memory_d=1, order=order, theta=n_steps, + discretizer=discretizer, kernel_initializer=tf.initializers.constant(input_enc[:, [i]]), hidden_cell=tf.keras.layers.SimpleRNNCell( units=order, @@ -58,19 +62,21 @@ def test_multivariate_lmu(rng): for i in range(memory_d): assert np.allclose( - results[0][..., i * order : (i + 1) * order], results[i + 1], atol=2e-6 - ) + results[0][..., i * order : (i + 1) * order], results[i + 1], atol=2e-5 + ), np.max(abs(results[0][..., i * order : (i + 1) * order] - results[i + 1])) @pytest.mark.parametrize("has_input_kernel", (True, False)) @pytest.mark.parametrize("fft", (True, False)) -def test_layer_vs_cell(has_input_kernel, fft, rng): +@pytest.mark.parametrize("discretizer", ("zoh", "euler")) +def test_layer_vs_cell(rng, has_input_kernel, fft, discretizer): n_steps = 10 input_d = 32 kwargs = dict( memory_d=4 if has_input_kernel else input_d, order=12, - theta=n_steps, + theta=n_steps * (8 if discretizer == "euler" else 1), + discretizer=discretizer, kernel_initializer="glorot_uniform" if has_input_kernel else None, memory_to_memory=not fft, ) @@ -97,12 +103,15 @@ def test_layer_vs_cell(has_input_kernel, fft, rng): ): assert np.allclose(w0.numpy(), w1.numpy()) - atol = 2e-6 if fft else 1e-8 - assert np.allclose(cell_out, lmu_cell(inp), atol=atol) - assert np.allclose(cell_out, layer_out, atol=atol) + assert np.allclose(cell_out, lmu_cell(inp)) + assert np.allclose(cell_out, layer_out, atol=3e-6 if fft else 1e-8), np.max( + np.abs(cell_out - layer_out) + ) -def test_save_load_weights(rng, tmp_path): +@pytest.mark.parametrize("discretizer", ("zoh", "euler")) +@pytest.mark.parametrize("trainable_theta", (True, False)) +def test_save_load_weights(rng, tmp_path, discretizer, trainable_theta): memory_d = 4 order = 12 n_steps = 10 @@ -116,6 +125,8 @@ def test_save_load_weights(rng, tmp_path): order, n_steps, tf.keras.layers.SimpleRNNCell(units=64), + discretizer=discretizer, + trainable_theta=trainable_theta, return_sequences=True, )(inp) model0 = tf.keras.Model(inp, lmu0) @@ -126,6 +137,8 @@ def test_save_load_weights(rng, tmp_path): order, n_steps, tf.keras.layers.SimpleRNNCell(units=64), + discretizer=discretizer, + trainable_theta=trainable_theta, return_sequences=True, )(inp) model1 = tf.keras.Model(inp, lmu1) @@ -140,12 +153,24 @@ def test_save_load_weights(rng, tmp_path): assert np.allclose(out0, out2) +@pytest.mark.parametrize("discretizer", ("zoh", "euler")) +@pytest.mark.parametrize("trainable_theta", (True, False)) @pytest.mark.parametrize("mode", ("cell", "lmu", "fft")) -def test_save_load_serialization(mode, tmp_path): +def test_save_load_serialization(mode, tmp_path, trainable_theta, discretizer): + if mode == "fft" and trainable_theta: + pytest.skip("FFT does not support trainable theta") + inp = tf.keras.Input((10 if mode == "fft" else None, 32)) if mode == "cell": out = tf.keras.layers.RNN( - layers.LMUCell(1, 2, 3, tf.keras.layers.SimpleRNNCell(4)), + layers.LMUCell( + 1, + 2, + 3, + tf.keras.layers.SimpleRNNCell(4), + trainable_theta=trainable_theta, + discretizer=discretizer, + ), return_sequences=True, )(inp) elif mode == "lmu": @@ -156,6 +181,8 @@ def test_save_load_serialization(mode, tmp_path): tf.keras.layers.SimpleRNNCell(4), return_sequences=True, memory_to_memory=True, + trainable_theta=trainable_theta, + discretizer=discretizer, )(inp) elif mode == "fft": out = layers.LMUFFT( @@ -163,6 +190,7 @@ def test_save_load_serialization(mode, tmp_path): 2, 3, tf.keras.layers.SimpleRNNCell(4), + discretizer=discretizer, return_sequences=True, )(inp) @@ -194,8 +222,15 @@ def test_save_load_serialization(mode, tmp_path): ), ) @pytest.mark.parametrize("memory_d", [1, 4]) -def test_fft(return_sequences, hidden_cell, memory_d, rng): - kwargs = dict(memory_d=memory_d, order=2, theta=3, hidden_cell=hidden_cell()) +@pytest.mark.parametrize("discretizer", ("zoh", "euler")) +def test_fft(return_sequences, hidden_cell, memory_d, discretizer, rng): + kwargs = dict( + memory_d=memory_d, + order=2, + theta=12, + hidden_cell=hidden_cell(), + discretizer=discretizer, + ) x = rng.uniform(-1, 1, size=(2, 10, 32)) @@ -208,7 +243,7 @@ def test_fft(return_sequences, hidden_cell, memory_d, rng): fft_layer = layers.LMUFFT(return_sequences=return_sequences, **kwargs) fft_layer.build(x.shape) fft_layer.kernel.assign(rnn_layer.cell.kernel) - fft_out = fft_layer(x) + fft_out = fft_layer(x, training=None) assert np.allclose(rnn_out, fft_out, atol=2e-6) @@ -229,29 +264,30 @@ def test_validation_errors(): @pytest.mark.parametrize( - "hidden_to_memory, memory_to_memory, memory_d, steps", + "should_use_fft, hidden_to_memory, memory_to_memory, steps, trainable_theta", [ - (False, False, 1, 5), - (True, False, 1, 5), - (False, True, 1, 5), - (False, False, 2, 5), - (False, False, 1, None), + (True, False, False, 5, False), + (False, True, False, 5, False), + (False, False, True, 5, False), + (False, False, False, None, False), + (False, False, False, 5, True), ], ) -def test_fft_auto_swap(hidden_to_memory, memory_to_memory, memory_d, steps): +def test_fft_auto_swap( + should_use_fft, hidden_to_memory, memory_to_memory, steps, trainable_theta +): lmu = layers.LMU( - memory_d, + 4, 2, 3, tf.keras.layers.Dense(5), hidden_to_memory=hidden_to_memory, memory_to_memory=memory_to_memory, + trainable_theta=trainable_theta, ) lmu.build((32, steps, 8)) - assert isinstance(lmu.layer, tf.keras.layers.RNN) == ( - hidden_to_memory or memory_to_memory or steps is None - ) + assert isinstance(lmu.layer, layers.LMUFFT) == should_use_fft @pytest.mark.parametrize( @@ -396,16 +432,24 @@ def test_dropout( assert np.allclose(y0, y1) +@pytest.mark.parametrize("trainable_theta", (True, False)) +@pytest.mark.parametrize("discretizer", ("zoh", "euler")) @pytest.mark.parametrize("fft", (True, False)) -def test_fit(fft): +def test_fit(fft, discretizer, trainable_theta): + if fft and trainable_theta: + pytest.skip("FFT does not support trainable theta") + lmu_layer = layers.LMU( memory_d=1, order=256, - theta=784, - hidden_cell=tf.keras.layers.SimpleRNNCell(units=10), + theta=784 if discretizer == "zoh" else 2000, + trainable_theta=trainable_theta, + hidden_cell=tf.keras.layers.SimpleRNNCell(units=30), hidden_to_memory=not fft, memory_to_memory=not fft, input_to_hidden=not fft, + discretizer=discretizer, + kernel_initializer="zeros", ) inputs = tf.keras.layers.Input((5 if fft else None, 10)) @@ -420,7 +464,7 @@ def test_fit(fft): y_test = tf.ones((5, 1)) model.compile( loss=tf.keras.losses.SparseCategoricalCrossentropy(from_logits=True), - optimizer=tf.keras.optimizers.RMSprop(), + optimizer=tf.keras.optimizers.Adam(), metrics=["accuracy"], ) @@ -447,3 +491,129 @@ def test_no_input_kernel_dimension_mismatch(fft): with pytest.raises(ValueError, match="no input kernel"): lmu_layer(tf.ones((4, 10, 2))) + + +def test_discretizer_types(): + with pytest.raises(ValueError, match="discretizer must be 'zoh' or 'euler'"): + layers.LMUCell( + memory_d=1, order=256, theta=784, hidden_cell=None, discretizer="test" + ) + + +@pytest.mark.parametrize("trainable_theta", (True, False)) +def test_discretizer_equivalence(trainable_theta, rng): + # check that zoh and euler produce approximately the same output + layer_zoh = layers.LMU( + memory_d=2, + order=8, + theta=256, + hidden_cell=None, + discretizer="zoh", + return_sequences=True, + kernel_initializer=None, + trainable_theta=trainable_theta, + ) + layer_euler = layers.LMU( + memory_d=2, + order=8, + theta=256, + hidden_cell=None, + discretizer="euler", + return_sequences=True, + kernel_initializer=None, + trainable_theta=trainable_theta, + ) + + x = rng.uniform(-1, 1, size=(32, 10, 2)) + + zoh = layer_zoh(x) + euler = layer_euler(x) + + assert np.allclose(zoh, euler, atol=0.02), np.max(np.abs(zoh - euler)) + + +def test_cont2discrete_zoh(rng): + A = rng.randn(64, 64) + B = rng.randn(64, 1) + C = np.ones((1, 64)) + D = np.zeros((1,)) + + scipy_A, scipy_B, *_ = cont2discrete((A, B, C, D), dt=1.0, method="zoh") + tf_A, tf_B = layers.LMUCell._cont2discrete_zoh(A.T, B.T) + + assert np.allclose(scipy_A, tf.transpose(tf_A)) + assert np.allclose(scipy_B, tf.transpose(tf_B)) + + +@pytest.mark.parametrize("discretizer", ("euler", "zoh")) +@pytest.mark.parametrize("trainable_theta", (True, False)) +def test_theta_update(discretizer, trainable_theta, tmp_path): + # create model + theta = 10 + lmu_cell = layers.LMUCell( + memory_d=2, + order=3, + theta=theta, + trainable_theta=trainable_theta, + hidden_cell=tf.keras.layers.SimpleRNNCell(units=4), + discretizer=discretizer, + ) + + inputs = tf.keras.layers.Input((None, 20)) + lmu = tf.keras.layers.RNN(lmu_cell)(inputs) + model = tf.keras.Model(inputs=inputs, outputs=lmu) + + model.compile( + loss=tf.keras.losses.MeanSquaredError(), optimizer=tf.keras.optimizers.Adam() + ) + + # make sure theta_inv is set correctly to initial value + assert np.allclose(lmu_cell.theta_inv.numpy(), 1 / theta) + + # fit model on some data + model.fit(tf.ones((64, 5, 20)), tf.ones((64, 4)), epochs=1) + + # make sure theta kernel got updated if trained + assert np.allclose(lmu_cell.theta_inv.numpy(), 1 / theta) != trainable_theta + + # save model and make sure you get same outputs, that is, correct theta was stored + model.save(str(tmp_path)) + + model_load = tf.keras.models.load_model( + str(tmp_path), custom_objects={"LMUCell": layers.LMUCell} + ) + + assert np.allclose( + model.predict(np.ones((32, 10, 20))), + model_load.predict(np.ones((32, 10, 20))), + ) + + +@pytest.mark.parametrize("mode", ("cell", "rnn", "fft")) +def test_theta_attribute(mode): + theta = 3 + + # check LMUCell theta attribute + if mode == "cell": + layer = layers.LMUCell(1, 2, theta, None, trainable_theta=True) + elif mode == "rnn": + layer = layers.LMU(1, 2, theta, None, trainable_theta=True) + elif mode == "fft": + layer = layers.LMU(1, 2, theta, None, trainable_theta=False) + + assert not layer.built + assert layer.theta == theta + + layer.build((1, 1)) + assert layer.built + assert np.allclose(layer.theta, theta) + + if mode == "fft": + # fft doesn't support trainable theta + assert isinstance(layer.layer, layers.LMUFFT) + else: + # check that updates to the internal variable are reflected in the theta + # attribute + cell = layer if mode == "cell" else layer.layer.cell + cell.theta_inv.assign(10) + assert np.allclose(layer.theta, 0.1) diff --git a/keras_lmu/version.py b/keras_lmu/version.py index eda5ed50..4b17531c 100644 --- a/keras_lmu/version.py +++ b/keras_lmu/version.py @@ -7,7 +7,7 @@ """ name = "keras_lmu" -version_info = (0, 3, 2) # (major, minor, patch) +version_info = (0, 4, 0) # (major, minor, patch) dev = 0 # set to None 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