I am currently implementing a simple neural network and the backprop algorithm in Python with numpy. I have already tested my backprop method using central differences and the resulting gradient is equal.
However, the network fails to approximate a simple sine curve. The network hast one hidden layer (100 neurons) with tanh activation functions and a output layer with a linear activation function. Each unit hast also a bias input. The training is done by simple gradient descent with a learning rate of 0.2.
The problem arises from the gradient, which gets with every epoch larger, but I don't know why? Further, the problem is unchanged, if I decrease the learning rate.
EDIT: I have uploaded the code to pastebin: http://pastebin.com/R7tviZUJ
There are two things you can try, maybe in combination:
Use a smaller learning rate. If it is too high, you may be overshooting the minimum in the current direction by a lot, and so your weights will keep getting larger.
Use smaller initial weights. This is related to the first item. A smaller learning rate would fix this as well.
I had a similar problem (with a different library, DL4J), even in the case of extremely simple target functions. In my case, the issue turned out to be the cost function. When I changed from negative log likelihood to Poisson or L2, I started to get decent results. (And my results got MUCH better once I added exponential learning rate decay.)
Looks like you dont use regularization. If you train your network long enough it will start to learn the excact data rather than abstract pattern.
There are a couple of method to regularize your network like: stopped training, put a high cost to large gradients or more complex like e.g.g drop out. If you search web/books you probably will find many options for this.
A too big learning rate can fail to converge, and even DIVERGE, that is the point.
The gradient could diverge for this reason: when exceeding the position of the minima, the resulting point could not only be a bit further, but could even be at a greater distance than initially, but the other side. Repeat the process, and it will continue to diverge. in other words, the variation rate around the optimal position could be just to big compared to the learning rate.
Source: my understanding of the following video (watch near 7:30).
https://www.youtube.com/watch?v=Fn8qXpIcdnI&list=PLLH73N9cB21V_O2JqILVX557BST2cqJw4&index=10
Related
I am new to deep learning and I try to implement an RNN (with 2 GRU layers).
At first, the network seems to do it's job quite fine. However, I am currently trying to understand the loss and accuracy curve. I attached the pictures below. The dark-blue line is the training set and the cyan line is the validation set.
After 50 epochs the validation loss increases. My assumption is that this indicates overfitting. However, I am unsure why the validation mean absolute error still decreases. Do you maybe got an idea?
One idea I had in mind was that this could be caused by some big outliers in my dataset. Thus I already tried to clean it up. I also tried to scale it properly. I also added a few dropout layers for further regularization (rate=0.2). However these are just normal dropout layers because cudnn does not seem to support recurrent_dropout from tensorflow.
Remark: I am using the negative log-likelihood as loss function and a tensorflow probability distribution as the output dense layer.
Any hints what I should investigate?
Thanks in advance
Edit: I also attached the non-probabilistic plot as recommended in the comment. Seems like here the mean-absolute-error behaves normal (does not improve all the time).
What are the outputs of your model? It sounds pretty strange that you're using the negative log-likelihood (which basically "works" with distributions) as the loss function but the MAE as a metric, which is suited for deterministic continuous values.
I don't know what is your task and perhaps this is meaningful in your specific case, but perhaps the strange behavior comes out from there.
If I train an image caption model then stop to rename a few tokens:
Should I train the model from scratch?
Or can I reload the model and continue training from the last epoch with the updated vocabulary?
Will either approach effect model accuracy/performance differently?
I would go for option 2.
When training the model from scratch, you are initializing the model's weights randomly and then you fit them based on your problem. However, if, instead of using random weights, you use weights that have already been trained for a similar problem, you may decrease the convergence time. This option is kind similar to the idea of transfer learning.
Just to give the other team a voice: So what is actually the difference between training from scratch and reloading a model and continuing training?
(2) will converge faster, (1) will probably have a better performance and should thus be chosen. Do we actually care about training times when we trade them off with performance - do you really? See you do not.
The further your model is already converged to a specific problem, the harder it gets to get it back into another optimum. Now you might be lucky and the chance, that you are going down the right rabid hole, rises with similar tasks and similar data. Yet with a change in your setup this can not be guaranteed.
Initializing a few epochs on other than your target domain, definitely makes sense and is beneficial, yet the question arises why you would not train on your target domain from the very beginning.
Note: For a more substantial read I'd like to refer you to this paper, where they explain in more depth why domain is of the essence and transfer learning could mess with your final performance.
It depends on the number of tokens being relabeled compared to the total amount. Just because you mentioned there are few of them, then the optimal solution in my opinion is clear.
You should start the training from scratch but initialize the weights with the values they had from wherever the previous training stopped (again mentioning that it is crucial that the samples that are being re-labeled are not of substantial amount). This way, the model will likely converge faster than starting with random weights and also better than trying to re-fit ("forget") what it managed to learn from the previous training.
Topologically speaking you are initializing in a position where the model is closer to a global minimum but has not made any steps towards a local minimum.
Hope this helps.
I'm working with neural networks (NN) as a part of my thesis in geophysics, and is using TensorFlow with Keras for training my network.
My current task is to use a NN to approximate a thermodynamical model i.e a nonlinear regression problem. It takes 13 input parameters and outputs a velocity profile (velocity vs. depth) of 450 parameters. My data consists of 100,000 synthetic examples (i.e. no noise is present), split in training (80k), validation (10k) and testing (10k).
I've tested my network for a number of different architectures: wider (5-800 neurons) and deeper (up to 10 layers), different learning rates and batch sizes, and even for many epochs (5000). Basically all the standard tricks of the trade...
But, I am puzzled by the fact that the learning curve shows validation error lower than training error (for all my tests), and I've never been able to overfit to the training data. See figure below:
The error on the test set is correspondingly low, thus the network seems to be able to make decent predictions. It seems like a single hidden layer of 50 neurons is sufficient. However, I'm not sure if I can trust these results due to the behavior of the learning curve. I've considered that this might be due to the validation set consisting of examples that are "easy" to predict, but I cannot see how I should change this. A bigger validation set perhaps?
To wrap it up: Is is necessarily a bad sign if the validation error is lower than or very close to the training error? What if the predictions made with said network are decent?
Is it possible that overfitting is simply not possible for my problem and data?
In addition to trying a higher k fold and the additional testing holdout sample,perhaps mix it up when sampling from the original data set: Select a stratified sample when partitioning out the training and validation/test sets. Then partition the validation and test set without stratifying the sampling.
My opinion is that if you introduce more variation in your modeling methodology (without breaking any "statistical rules"), you can be more confident in the model that you have created.
You can achieve more trustworthy results by repeating your experiments on different data. Use cross validation with high fold (like k=10) to get better confidence of your solution performance. Usually neural networks easily overfit, if your solution has similar results on validation and test set its a good sign.
It is not that easy to tell when not knowing the exact way you have setup the experiment:
what cross-validation method did you use?
how did you split the data?
etc
As you mentioned, the fact that you observe validation error lower than training can be a result of the fact that either the training dataset contains many "hard" cases to learn or the validation set contains many "easy" cases to predict.
However, since generally speaking training loss is expected to underestimate the validation, to me the specific model appear to have unpredictable/unknown fit (perform better in predicting the unknown that the known feels indeed weird).
In order to overcome this, I would start experimenting by reconsidering the data splitting strategy, adding more data if possible, or even change your performance metric.
I just try to dive into TensorFlows Object Detection. I have a very small training set of circa 40 images yet. Each image can have up to 3 classes. But now the question came into my mind: Does every training image need every class? Is that important for efficient training? Or is it okay if an image may only have one of the object classes?
I get a very high total loss with ~8.0 and thought this might be the reason for this but I couldn't find an answer.
In general machine learning systems can cope with some amount of noise.
An image missing labels or having the wrong labels is fine as long as overall you have sufficient data for the model to figure it out.
40 examples for image classification sounds very small. It might work if you start with a pre-trained image network and there are few classes that are very easy to distinguish.
Ignore absolute the loss value, it doesn't mean anything. Look at the curve to see that the loss is decreasing and stop the training when the curve flattens out. Compare the loss value to a test dataset to check if the values are sufficiently similar (you are not overfitting). You might be able to compare to another training of the exact same system (to check if the training is stable for example).
I built a small conv net in tensorflow.What I noticed is that if I add a dropout probability to the fully connected layer, then I have to use lower learning rates or else I get gradient overshoots. Is there any explanation why this keeps happening?
Funnily in literature the opposite was observed. The original paper to dropout is here: http://www.jmlr.org/papers/volume15/srivastava14a.old/source/srivastava14a.pdf. In Appendix A.2: The authors explain that the learning rate should be increased by 10-100 times, while momentum should also be increased because many gradients cancel each other out. Maybe you are not using a high enough batch size.
Thie following part is my explanation, in contrast to the literature provided above, as to why your observed result happened.
By using 0.5 dropout only half of the neurons are active and contribute to the error. Still the error is similar in size. Therefore the error will be back propagated through the network to only half the neurons. So each neurons "part" in the error doubles.
By using the same learning rate the gradient updates double. Therefore you have the same problem as if you had used a larger learning rate in the first place. By lowering the learning rate the updates are again in the range, which you had previously used.