Q: Is Tensorflow RNN implemented to ouput Elman Network's hidden state?
cells = tf.contrib.rnn.BasicRNNCell(4)
outputs, state = tf.nn.dynamic_rnn(cell=cells, etc...)
I'm quiet new to TF's RNN and curious about meaning of outputs, and state.
I'm following stanford's tensorflow tutorial but there seems no detailed explanation so I'm asking here.
After testing, I think state is hidden state after sequence calculation and outputs is array of hidden states after each time steps.
so I want to make it clear. outputs and state are just hidden state vectors so to fully implement Elman network, I have to make V matrix in the picture and do matrix multiplication again. am I correct?
I believe you are asking what the output of a intermediate state and output is.
From what I understand, the state would be intermediate output after a convolution / sequence calculation and is hidden, so your understanding is in the right direction.
Output may vary as how you decide to implement your network model, but on a general basis, it is an array where any operation (convolution, sequence calc etc) has been applied after which activation & downsampling/pooling has been applied, to concentrate on identifiable features across that layer.
From Colah's blog ( http://colah.github.io/posts/2015-08-Understanding-LSTMs/ ):
Finally, we need to decide what we’re going to output. This output will be based on our cell state, but will be a filtered version. First, we run a sigmoid layer which decides what parts of the cell state we’re going to output. Then, we put the cell state through tanhtanh (to push the values to be between −1−1 and 11) and multiply it by the output of the sigmoid gate, so that we only output the parts we decided to.
For the language model example, since it just saw a subject, it might want to output information relevant to a verb, in case that’s what is coming next. For example, it might output whether the subject is singular or plural, so that we know what form a verb should be conjugated into if that’s what follows next.
Hope this helps.
Thank you
Related
I want to predict stock price.
Normally, people would feed the input as a sequence of stock prices.
Then they would feed the output as the same sequence but shifted to the left.
When testing, they would feed the output of the prediction into the next input timestep like this:
I have another idea, which is to fix the sequence length, for example 50 timesteps.
The input and output are exactly the same sequence.
When training, I replace last 3 elements of the input by zero to let the model know that I have no input for those timesteps.
When testing, I would feed the model a sequence of 50 elements. The last 3 are zeros. The predictions I care are the last 3 elements of the output.
Would this work or is there a flaw in this idea?
The main flaw of this idea is that it does not add anything to the model's learning, and it reduces its capacity, as you force your model to learn identity mapping for first 47 steps (50-3). Note, that providing 0 as inputs is equivalent of not providing input for an RNN, as zero input, after multiplying by a weight matrix is still zero, so the only source of information is bias and output from previous timestep - both are already there in the original formulation. Now second addon, where we have output for first 47 steps - there is nothing to be gained by learning the identity mapping, yet network will have to "pay the price" for it - it will need to use weights to encode this mapping in order not to be penalised.
So in short - yes, your idea will work, but it is nearly impossible to get better results this way as compared to the original approach (as you do not provide any new information, do not really modify learning dynamics, yet you limit capacity by requesting identity mapping to be learned per-step; especially that it is an extremely easy thing to learn, so gradient descent will discover this relation first, before even trying to "model the future").
I am modeling a perceptual process in tensorflow. In the setup I am interested in, the modeled agent is playing a resource game: it has to choose 1 out of n resouces, by relying only on the label that a classifier gives to the resource. Each resource is an ordered pair of two reals. The classifier only sees the first real, but payoffs depend on the second. There is a function taking first to second.
Anyway, ideally I'd like to train the classifier in the following way:
In each run, the classifier give labels to n resources.
The agent then gets the payoff of the resource corresponding to the highest label in some predetermined ranking (say, A > B > C > D), and randomly in case of draw.
The loss is taken to be the normalized absolute difference between the payoff thus obtained and the maximum payoff in the set of resources. I.e., (Payoff_max - Payoff) / Payoff_max
For this to work, one needs to run inference n times, once for each resource, before calculating the loss. Is there a way to do this in tensorflow? If I am tackling the problem in the wrong way feel free to say so, too.
I don't have much knowledge in ML aspects of this, but from programming point of view, I can see doing it in two ways. One is by copying your model n times. All the copies can share the same variables. The output of all of these copies would go into some function that determines the the highest label. As long as this function is differentiable, variables are shared, and n is not too large, it should work. You would need to feed all n inputs together. Note that, backprop will run through each copy and update your weights n times. This is generally not a problem, but if it is, I heart about some fancy tricks one can do by using partial_run.
Another way is to use tf.while_loop. It is pretty clever - it stores activations from each run of the loop and can do backprop through them. The only tricky part should be to accumulate the inference results before feeding them to your loss. Take a look at TensorArray for this. This question can be helpful: Using TensorArrays in the context of a while_loop to accumulate values
I saw this video online, it shows a "neural network" with three inputs and three outputs, although the inputs are not changing, I believe there is enough similarity between this network and those of other evolutionary algorithms to make the question valid.
My question is, since it is possible for all three input nodes shown in the video to "exert influence" on the output nodes with controlled weight, why is the four intermediate nodes necessary? Why not connect the input nodes directly to the outputs?
An artificial neural network consisting only of inputs and outputs is a (single-layer) perceptron. Realizing these networks would not solve many problems set back the use of artificial neural networks for over a decade!
For simplicity, imagine only one output neuron (many outputs can be considered many similar problems in parallel). Furthermore, let's consider for the moment only one input. The neurons use an activation function, which determines the activity (output) of this neuron depending on the input it receives. For activation functions used in practice*, the more input, the higher output (or the same in some ranges, but let's forget about that). And chaining two of these also results in "the more input, the more final output".
With one output neuron you interpret the results as "if output is over threshold, then A, otherwise B". (Where "A" and "B" can mean different things). Because both our neurons produce more signal the more input they receive, then our network can only answer easy linear problems of type "if input signal is over threshold, then A, otherwise B".
Using two inputs is very similar: we combine the output of two input-neurons. Now we are in the situation "if inputs to input neurons 1 and 2 are, together, high enough that our final output is over a threshold, then A, otherwise B". Graphically this means we can decide A or B by drawing a line (allow curvature) on the input 1-input 2 plane:
But there are problems that cannot be solved this way! Consider the XOR problem. Our goal is to produce this:
As you can see, it is impossible to draw a line that gets all the A's on one side and all the B's on the other. And these lines represent all the possible one-layer perceptrons! We say that the XOR problem is not linearly separable (and this is why the XOR is a traditional test for neural networks).
Introducing at least one hidden layer allows to solve this problem. In practice this is like combining the result of two one-layer perceptrons:
Adding more neurons to the hidden layer means being able to solve more and more complex problems. In fact, any function f(A,B).
However, you may know other networks use more layers (see deep learning), but in this case the motivation is not a theoretical limitation, but rather searching for networks that perform better.
*Using weird hand-crafted activation functions will not make things better. You may be able to solve an specific problem, but still not all, and you need to know how to design this activation function.
I'm using an open source version of a3c implementation in Tensorflow which works reasonably well for atari 2600 experiments. However, when I modify the network for Mujoco, as outlined in the paper, the network refuses to learn anything meaningful. Has anyone managed to make any open source implementations of a3c work with continuous domain problems, for example mujoco?
I have done a continuous action of Pendulum and it works well.
Firstly, you will build your neural network and output mean (mu) and standard deviation (sigma) for selecting an action.
The essential part of the continuous action is to include a normal distribution. I'm using tensorflow, so the code is looks like:
normal_dist = tf.contrib.distributions.Normal(mu, sigma)
log_prob = normal_dist.log_prob(action)
exp_v = log_prob * td_error
entropy = normal_dist.entropy() # encourage exploration
exp_v = tf.reduce_sum(0.01 * entropy + exp_v)
actor_loss = -exp_v
When you wanna sample an action, use the function tensorflow gives:
sampled_action = normal_dist.sample(1)
The full code of Pendulum can be found in my Github. https://github.com/MorvanZhou/tutorials/blob/master/Reinforcement_learning_TUT/10_A3C/A3C_continuous_action.py
I was hung up on this for a long time, hopefully this helps someone in my shoes:
Advantage Actor-critic in discrete spaces is easy: if your actor does better than you expect, increase the probability of doing that move. If it does worse, decrease it.
In continuous spaces though, how do you do this? The entire vector your policy function outputs is your move -- if you are on-policy, and you do better than expected, there's no way of saying "let's output that action even more!" because you're already outputting exactly that vector.
That's where Morvan's answer comes into play. Instead of outputting just an action, you output a mean and a std-dev for each output-feature. To choose an action, you pass your inputs in to create a mean/stddev for each output-feature, and then sample each feature from this normal distribution.
If you do well, you adjust the weights of your policy network to change the mean/stddev to encourage this action. If you do poorly, you do the opposite.
I would like to see how the learning rate changes during training (print it out or create a summary and visualize it in tensorboard).
Here is a code snippet from what I have so far:
optimizer = tf.train.AdamOptimizer(1e-3)
grads_and_vars = optimizer.compute_gradients(loss)
train_op = optimizer.apply_gradients(grads_and_vars, global_step=global_step)
sess.run(tf.initialize_all_variables())
for i in range(0, 10000):
sess.run(train_op)
print sess.run(optimizer._lr_t)
If I run the code I constantly get the initial learning rate (1e-3) i.e. I see no change.
What is a correct way for getting the learning rate at every step?
I would like to add that this question is really similar to mine. However, I cannot post my findings in the comment section there since I do not have enough rep.
I was asking myself the exact same question, and wondering why wouldn't it change. By looking at the original paper (page 2), one sees that the self._lr stepsize (designed with alpha in the paper) is required by the algorithm, but never updated. We also see that there is an alpha_t that is updated for every t step, and should correspond to the self._lr_t attribute. But in fact, as you observe, evaluating the value for the self._lr_t tensor at any point during the training returns always the initial value, that is, _lr.
So your question, as I understood it, is how to get the alpha_t for TensorFlow's AdamOptimizer as described in section 2 of the paper and in the corresponding TF v1.2 API page:
alpha_t = alpha * sqrt(1-beta_2_t) / (1-beta_1_t)
BACKGROUND
As you observed, the _lr_t tensor doesn't change thorough the training, which may lead to the false conclusion that the optimizer doesn't adapt (this can be easily tested by switching to the vanilla GradientDescentOptimizer with the same alpha). And, in fact, other values do change: a quick look at the optimizer's __dict__ shows the following keys: ['_epsilon_t', '_lr', '_beta1_t', '_lr_t', '_beta1', '_beta1_power', '_beta2', '_updated_lr', '_name', '_use_locking', '_beta2_t', '_beta2_power', '_epsilon', '_slots'].
By inspecting them through training, I noticed that only _beta1_power, _beta2_power and the _slots get updated.
Further inspecting the optimizer's code, in line 211, we see the following update:
update_beta1 = self._beta1_power.assign(
self._beta1_power * self._beta1_t,
use_locking=self._use_locking)
Which basically means that _beta1_power, which is initialized with _beta1, will be multiplied by _beta_1_t after every iteration, which is also initialized with beta_1_t.
But here comes the confusing part: _beta1_t and _beta2_t never get updated, so effectively they hold the initial values (_beta1and _beta2) through the whole training, contradicting the notation of the paper in a similar fashion as _lr and lr_t do. I guess this is for a reason but I personally don't know why, in any case this are protected/private attributes of the implementation (as they start with an underscore) and don't belong to the public interface (they may even change among TF versions).
So after this small background we can see that _beta_1_power and _beta_2_power are the original beta values exponentiated to the current training step, that is, the equivalent to the variables referred with beta_tin the paper. Going back to the definition of alpha_t in the section 2 of the paper, we see that, with this information, it should be pretty straightforward to implement:
SOLUTION
optimizer = tf.train.AdamOptimizer()
# rest of the graph...
# ... somewhere in your session
# note that a0 comes from a scalar, whereas bb1 and bb2 come from tensors and thus have to be evaluated
a0, bb1, bb2 = optimizer._lr, optimizer._beta1_power.eval(), optimizer._beta2_power.eval()
at = a0* (1-bb2)**0.5 /(1-bb1)
print(at)
The variable at holds the alpha_t for the current training step.
DISCLAIMER
I couldn't find a cleaner way of getting this value by just using the optimizer's interface, but please let me know if it exists one! I guess there is none, which actually puts into question the usefulness of plotting alpha_t, since it does not depend on the data.
Also, to complete this information, section 2 of the paper also gives the formula for the weight updates, which is much more telling, but also more plot-intensive. For a very nice and good-looking implementation of that, you may want to take a look at this nice answer from the post that you linked.
Hope it helps! Cheers,
Andres