General science

Posted on General science, Teaching

Training Time Speed Ups

The training time of a neural network is a topic that is under discussed in machine learning academic literature, but is super important in practice. By making training time faster, one reaps the benefits of (A) reducing their compute budget and (B) being able to test hypothesis faster.

For the purposes of this post, I’m assuming the neural network of interest has already achieved the inference runtime and performance requirements, and now the focus is purely on optimizing the training time. When I am speeding up training time, I usually find myself alternating between solutions that are either primarily software or hardware related.

Software Solutions

1. Optimizer and Schedules

The software solution that I tune the most is definitely the optimizer and its associated hyper parameters. I find that after almost any other change it is worth double checking that your optimizer and its hyperparameters are still optimal for your new setup.

When first prototyping a network, I prefer to use SGD with a constant learning rate and momentum. This reduces the number of optimizer hyperparameters to just setting the learning rate.

Once a network prototype is achieved, a reliable trick to boost performance is to introduce learning rate step drops when the learning appears to have stalled out. However, determining the exact iteration at which to perform the learning rate step can be nuanced.

I personally have had great success with the One Cycle learning rate policy. However, it opens up a lot of new knobs to potentially tune (min/max lr, exact lr curve, etc). I strongly recommend using AdamW + Fast.ai One Cycle schedule (which follows a cosine annealing) as a starting policy and tuning from there.

2. Initialization

The proper initialization of a neural network can have a large impact on the training speed. There are three major options:
1. Random initialization. A standard choice is Kaiming initialization with Focal Loss bias.
2. Pretraining w/ other datasets. This includes data from other tasks (ie use ImageNet for backbone pretraining when doing object detection) or from same task but different source (ie always doing object detection, but generalizing from COCO to nuScenes).
3. Pretraining w/ same dataset. If one has determined that some subset of a dataset is less valuable for training, it could still serve a useful role in pretraining. See next section on Curriculum for ideas on how to determine the usefulness of data.

3. Curriculum

Given a fixed dataset, there is still an open question on the best way to present the data to the neural network. While the default to define an epoch as one random pass through the dataset works great as a starting point, there are lots of potential improvements in the selection and presentation of a curriculum for the neural network.

Some ideas in this area include:
1. Sampling of data. Not all data samples are equally valuable, for example repeat factor sampling can be used to prioritize rare annotations.
2. Multitask prioritization. When teaching a neural network multiple tasks, one strategy is to teach those tasks from easiest to hardest.
3. Progressive resizing. When training image based tasks with a fully convolution neural network, one approach is to start with small resolution images and progressively increase the size.

I have found that the effort to reward ratio favors spending a significant amount of time on tuning the curriculum.

4. Architecture

Since I am assuming that one has already achieved the required inference runtime, the neural network architecture may not need to be optimized further. However, if you are using a stochastic step during training like drop out, the removal of this step can significantly speed up your training time. Otherwise, tuning the architecture for training speed is usually not worth a large time investment.

Hardware Specific Solutions

1. Better Hardware

If you just sit still, your training time likely will go down from the continued advances in CPUs, GPUS, RAM, etc. A great way to set yourself up for these changes is by not owning your own hardware but instead training in the cloud.

2. Data Serving

The goal is to keep your GPUs fed, so one should push your non-GPU code to be slightly faster than your GPU step so that your GPUs are always busy. Be prepared to often revisit this step as you make advances in optimizing other parts of your training time. There is no way around it, solving this step is often difficult since there is no one size fits all solution. Instead, you will constantly need to find a nuanced solution that depends on your specific hardware and dataset.

3. GPU Utilization

Modern neural network architectures favor 2D CNNs which are highly optimized for GPUs. And if you can show how to simplify a complicated architecture to a 2D CNN, you might get a paper out of it ;).

So personally I have found the effort to be put into GPU utilization to be highly bimodal. If you have an architecture that is not GPU efficient, go all in on making it more efficient, the rewards are huge! But if you have already optimized for inference runtime, you likely already have a modern architecture that efficiently utilizes GPUs. Once you have the right architecture, then you often only need to make minor tweaks to the batch size to fully utilize the GPU.

4. Mixed Precision Training

With the correct hardware, training with mixed precision (float32 and float16) is an easy way to cut training time in half, and modern libraries make it as simple as a single setting. The only catch is that you may make your training more unstable. But if you can tame the extra training noise, this is a no brainer.

5. Multiple GPUs

Eventually, once you have pulled off all the other speedups, you will be left with one real option: scale up your compute! If you can really push the number of GPUs you can leverage, you can pull off crazy headlines like:

Distributed computing has been and will continue to be a hot topic for years to come.

Conclusion

I hope this helps shed light on some of the potential ways to speed up your neural network training. Let me know what type of training speedups you can achieve with this advice!

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1 Comment Posted on Everybody, General science, Teaching

NSF GRFP 2018-2019

Thanks to everyone who has been sending me new essays to host. Its crazy that my advice page went from only my essays and thoughts to 93 different examples!

I have to give a disclaimer that I haven’t been following changes to the NSF GRFP as closely this past year, but I think that my general advice still holds. If something seems outdated or wrong, please let me know. I always highly recommend getting multiple opinions and I’m glad that many people who have shared their essays are also writing about their experiences. Also check out the Grad Cafe for useful discussions.

Good luck everyone!

Posted on General science, Research

Deep Learning Tips

I thought I would write up some general tips and tricks that I have learned by experimenting with neural networks. My focus is on tips that apply to any problem and any neural network architecture, and in fact, some of these tips apply more generally to any machine learning algorithm. So what I have learned over the years?

Data Splits

Before doing anything else, you need to split the dataset into training and testing. But how much data should go into each split? This depends on your number of samples and the number of classes. For example, MNIST has only 10 digits with little variation in each digit, so the standard split is around 80% train and 20% test. ImageNet has over a million samples of 1000 diverse classes, so they use around 50% train and 50% test. So if you have an easy problem and/or a small dataset, I would suggest 80% train and 20% test. If you have a very tough problem and/or a large dataset, I would suggest 50% train and 50% test.

The test data should now be put in a lock box and only used on your final model.

Next you also should set aside some of the training data for validation which is used to determine generalization results when tuning hyperparameters. I would suggest around 20% of the training data to be used as a validation.

Finally, I do a little bit of cheating and I data snoop. I usually take a very tiny amount of the data, maybe 1-5% and play around with it. I will inspect the data to make sure that it looks good, and use the small number of samples to debug my initial code and very roughly tune the hyperparameters. This saves you the headache of doing a long training session only to find out that you had a bug in your code or grossly misunderstood where to start your hyperparameter search.

Data Preprocessing

As a general rule, the data should be standardized by preprocessing. I’ll discuss some specific standardizations below, but a general issue is whether to standardize by the whole dataset, per sample, or per feature. I tend to default to per sample, but I don’t have a good scientific reason why that is the best. If you standardize by the whole dataset or per feature, you need to make sure you only use the training data to set the scales. If you standardize per feature, make sure that all of your features have significant variation before doing so (see MNIST for an example where per feature standardization can lead to weird results since many features have a standard deviation of zero).

Mean

All numerical data should be mean centered, no questions asked. If you classes can be robustly classified just by the mean difference, then you don’t need a neural network. You have a very simple problem and should just use a simple threshold discriminator.

Scaling

I highly recommend scaling the data so that it is all order 1. This can speed up training because most initialization schemes of weights assume that the data is mean centered and has values around the size of 1. But there are two possible ways to scale your data: standard deviation or by the range. If you data looks normally distributed, then standard deviation makes sense. Otherwise I just divide by the maximum of the absolute value.

Correlations

In theory, it can also be helpful to remove correlations between features by using PCA or ZCA whitening. However, in practice you may run into numerical stability issues since you will need to invert a matrix. So this is worth considering, but takes some more careful application.

Data Augmentation

More training data is always better, but obtaining that data can be expensive. So I always try hard to find a way to do data augmentation. However, the correct data augmentation is usually problem specific, so I won’t go into details here.

Early Stopping

The no free lunch theorem of machine learning states that there is no general learning algorithm that will solve all problems. However, Geoff Hinton has pointed out that early stopping is as close to a free lunch as we can get. Early stopping is the easiest way for any machine learning algorithm to avoid overfitting, and you can read more about the technical justifications for it at Distill’s momentum article.

Optimizer

SGD vs Adam

In practice, all optimizers for neural networks involve some form of stochastic gradient descent (SGD). The only questions is whether you need to manually tune the learning rate and other parameters, or whether you use an adaptive version of SGD that automatically adjusts the learning rates. I think the best adaptive method is Adam (and Nadam when possible, see later subsection on momentum). So for me the choice is simple: either plain SGD or Adam/Nadam. For a more complete comparison of SGD variants, I highly recommend this blog post.

Learning Rate

If  you are using Adam, you will rarely need to tune the learning rate. But for SGD, the learning rate is by far the most important parameter to tune. A nice tip from Yoshua Bengio is this: the optimal learning rate is often an order of magnitude lower than the smallest learning rate that blows up the loss. So this means, start with a high learning rate and work your way down a half order of magnitude at a time (for example: 1, 0.3, 0.1, …). Then start your fine grained learning rate search about an order of magnitude below the last time the loss blew up.

Another useful tweak on the learning rate is to have it decay over the course of training. I find that this slightly improves the final performance, but more importantly leads to consistent training results. There are a variety of ways to implement the decay, but I’m not sure they make that much of a difference. My standard implementation is

l_{batch} = \frac{l_{start}}{1+decay*(N_{batches})}

where N_{batches} is the number of minibatches seen so far during training. I then set decay so that the final learning rate at the end of all the epochs is 1/10th the starting learning rate.

Momentum

Momentum is very useful for neural networks, but in practice I spend minimal time tuning the momentum rate because I have a few default settings that I strongly recommend.

First, I really only consider three possible momentum values: 0.5, 0.9, and 0.99. Since the maximum effect of momentum is \frac{1}{1-momentum}, my default values are roughly spaced by an order of magnitude. I always start with 0.9 and go from there.

Also, I always choose Nesterov momentum whenever possible. Most packages, like Keras, have Nesterov as an option for SGD, and Keras also has Nadam, which is Adam with Nesterov momentum. For more details on Nesterov, see here. The short explanation is that it leads to the same maximum effect of \frac{1}{1-momentum}, but it does so in a more gradual manner. In practice, this means that while standard momentum gets very unstable above 0.9, Nesterov momentum can be safely set to 0.99.

Another useful tip is to set the momentum to a smaller value (say half your standard value) for the final few epochs (maybe the last 5-10% of epochs). The intuition for why this is helpful is that hopefully by the end of training, the neural network is close to good weights, but it might be rocking back and forth around the optimal weights. Since the neural network weight space is highly non-convex, by tuning down the momentum, you force the neural network to settle down into these non-convex “valleys” that may contain the best weights.

The final tip, originally suggested here, is to exponentially ramp up and down the momentum anytime you want to change the momentum rate during training. This gives the weights updates time to adjust to the new momentum rates. I personally have found this gives a very slight improvement in performance, but more importantly it leads to consistent training results.

Summary of my momentum tips:

  • Peak momentum values of: 0.5, 0.9, or 0.99
  • Always choose Nesterov momentum if possible
  • Start momentum initially at half the desired peak value and exponentially ramp up
  • Towards the end of training, exponentially ramp down momentum to half the desired peak value.
  • Train for 5-10% of epochs at the desired smaller momentum.

Initialization

All weights should be initialized to an orthogonal matrix. This is extremely important for recurrent neural networks (as explained here), but I have also found it to be useful for all neural networks.

Activation Function

The standard is that all hidden layers are ReLUs unless you need the hidden layers to be a valid probability, in which case you should use a sigmoid.

Loss

Choosing the right loss function is very problem dependent, so I will leave that for another day. However, whatever loss function you do choose, make sure the output layer activation function is complimentary to that loss, see Michael Nielsen’s book for details on why sigmoid outputs and crossentropy losses are complimentary.

Regularization

Weights

Weight regularization is almost always a requirement to prevent overfitting and to get good generalization. The two main choices are L1 or L2 regularization. L1 will ensure that small weights are set to zero, and hence will lead to a sparser set of weights. L2 prevents weights from becoming too large, but does not sparsify the weights. Personally, rather than choosing between the two, I tend to default to both. I set L1 to be very small so that I at least get slightly sparser weights, but then I mainly focus on tuning L2 to control overfitting.

Activity

Dropout and batch normalization are not regularizers in the traditional sense, but in practice they help reduce overfitting by controlling the activation outputs. Additionally, it is extremely difficult to train very deep neural networks without using either dropout or batchnorm. Dropout was the standard for several years, but now it is usually replaced by batchnorm.

Parameter Tuning

Neural networks have a lot of interdependent hyperparameters to tune, so picking which ones to tune first is kind of a chicken and the egg problem. Personally, I start off with an adaptive optimizer (like Adam or Nadam) and then tune the architecture. Next I will roughly tune the regularization. Once that leads to acceptable results, I will switch the optimizer to SGD and only focus on tuning the learning rate. If SGD seems promising, I will then tune other parameters like decay and momentum. Hopefully by this point, you are achieving pretty good results. I will then use this neural network as the starting point for a systematic hyperparameter search to truly find the best results.

Final Tips

Don’t take my word for anything, try it out yourself! I strongly recommend experimenting with every option you can find in Keras and see for yourself what actually will work. I also suggest getting opinions from as many people as possible (see Yoshua Bengio’s tips). I think that about 90% of the advice will overlap, but everyone has their own bias. So hopefully be reading enough independent sources, you can average out all our mistakes. Good luck!

Posted on General science, Teaching

Temporal Difference Learning

How can humans or machines interact with an environment and learn a strategy for selecting actions that are beneficial to their goals? Answers to this question fall under the artificial intelligence category of reinforcement learning. Here I am going to provide an introduction to temporal difference (TD) learning, which is the algorithm at the heart of reinforcement learning.

I will be presenting TD learning from a computational neuroscience background. My post has been heavily influenced by Dayan and Abbott Ch 9, but I have added some additional points. The ultimate reference for reinforcement learning is the book by Sutton and Barto, and their chapter 6 dives into TD learning.

Conditioning

To start, let’s review conditioning. The most famous example of conditional is Pavlov’s dogs. The dogs naturally learned to salivate upon the delivery of food, but Pavlov realized that he could condition dogs to associate the ringing of a bell with the delivery of food. Eventually, the ringing of the bell on its own was enough to cause dogs to salivate.

The specific example of Pavlov’s dogs is an example of classical conditioning. In classical conditioning, no action needs to be taken. However, animals can also learn to associate actions with rewards and this is called operant conditioning.

Before I introduce some specific conditioning paradigms, here are the important definitions:

  • s = stimulus
  • r = reward
  • x = no reward
  • v = value, or expected reward (generally a function of r, x)
  • u = binary, indicator variable, of stimulus (1 if stimulus present, 0 otherwise)

Here are the conditioning paradigms I want to discuss:

  • Pavlovian
  • Extinction
  • Blocking
  • Inhibitory
  • Secondary

For each of these paradigms, I will introduce the necessary training stages and the final result. The statement, a \rightarrow b, means that a becomes associated (\rightarrow) with b.

Pavlovian

Training: s \rightarrow r. The stimulus is trained with a reward.

Results: s \rightarrow v[r]. The stimulus is associated with the expectation of a reward.

Extinction

Training 1: s \rightarrow r. The stimulus is trained with a reward. This eventually leads to successful Pavlovian training.

Training 2: s \rightarrow x. The stimulus is trained with a no reward.

Results: s \rightarrow v[x]. The stimulus is associated with the expectation of no reward. Extinction of the previous Pavlovian training.

Blocking

Training 1: s_1 \rightarrow r. The first stimulus is trained with a reward. This eventually leads to successful Pavlovian training.

Training 2: s_1 + s_2 \rightarrow r. The first stimulus and a second stimulus is trained with a reward.

Results: s_1 \rightarrow v[r], and s_2 \rightarrow v[x]. The first stimulus completely explains the reward and hence “blocks” the second stimulus from being associated with the reward.

Inhibitory

Training: s_1+s_2 \rightarrow x, and s_1 \rightarrow r. The combination of two stimuli leads to no reward, but the first stimuli is trained with a reward.

Results: s_1 \rightarrow v[r], and s_2 \rightarrow -v[r]. The first stimuli is associated with the expectation of the reward while the second stimuli is associated with the negative of the reward.

Secondary

Training 1: s_1 \rightarrow r. The first stimulus is trained with a reward. This eventually leads to successful Pavlovian training.

Training 2: s_2 \rightarrow s_1. The second stimulus is trained with the first stimulus.

Results: s_2 \rightarrow v[r]. Eventually the second stimulus is associated with the reward despite never being directly associated with the reward.

Rescorla-Wagner Rule

How do we turn the various conditioning paradigms into a mathematical framework of learning? The Rescorla Wagner rule (RW) is a very simple model that can explain many, but not all, of the above paradigms.

The RW rule is a linear prediction model that requires these three equations:

  1. v=w \cdot u
  2. \delta = r-v
  3. w_{new} = w_{old}+\epsilon \delta u

and introduces the following new terms:

  • w = weights associated with stimuli state
  • \epsilon = learning rate, with 0 \le \epsilon \le 1

What do each of these equations actually mean?

  1. The expected reward, v, is a linear dot product of a vector of weights, w, associated with each stimuli, u.
  2. But there may be a mismatch, or error, between the true actual reward, r, and the expected reward, v.
  3. Therefore we should update our weights of each stimuli. We do this by adding a term that is proportional to a learning rate \epsilon, the error \delta, and the stimuli u.

During a Pavlovian pairing of stimuli with reward, the RW rule predicts an exponential approach of the weight to w = \langle ru\rangle over the course of several trials for most values of \epsilon (if \epsilon=1 it would instantly update to the final value. Why is this usually bad?). Then if the reward stops being paired with the stimuli, the weight will exponential decay over the course of the next trials.

The RW rule will also continue to work when the reward/stimulus pairing is stochastic instead of deterministic and the will will still approach the final value of w = \langle ru\rangle.

How does blocking fit into this framework? Well the RW rule says that after the first stage of training, the weights are w_1 = r and w_2 = 0 (since we have not presented stimulus two). When we start the second stage of training and try and associate stimulus two with the reward, we find that we cannot learn that association. The reason is that there is no error (hence \delta = 0) and therefore w_2 = 0 forever. If instead we had only imperfectly learned the weight of the first stimulus, then there is still some error and hence some learning is possible.

One thing that the RW rule incorrectly predicts is secondary conditioning. In this case, during the learning of the first stimulus, s_1, the learned weight becomes w_1 >0. The RW rule predicts that the second stimulus, s_2, will become w_2 <0. This is because this paradigm is exactly the same as inhibitory conditioning, according to the RW rule. Therefore, a more complicated rule is required to successfully have secondary conditioning

One final note. The RW rule can provide an even better match to biology by assuming a non-linear relationship between v and the animal behavior. This function is often something that exponentially saturates at the maximal reward (ie an animal is much more motivated to go from 10% to 20% of the max reward rather than from 80% to 90% of the max reward). While this provides a better fit to many biological experiments, it still cannot explain the secondary conditioning paradigm.

Temporal Difference Learning

To properly model secondary conditioning, we need to explicitly add in time to our equations. For ease, one can assume that time, t, is discrete and that a trial lasts for total time T and therefore 0 \le t \le T.

The straightforward (but wrong) extension of the RW rule to time is:

  1. v[t]=w[t-1] \cdot u[t]
  2. \delta[t] = r[t]-v[t]
  3. w[t] = w[t-1]+\epsilon \delta[t] u[t]

where we will say that it takes one time unit to update the weights.

Why is this naive RW with time wrong? Well, psychology and biology experiments show that animals expected rewards does NOT reflect the past history of rewards nor just reflect the next time step, but instead reflects the expected rewards during the WHOLE REMAINDER of the trial. Therefore a better match to biology is:

  1. v[t]=w[t-1] \cdot u[t]
  2. R[t]= \langle \sum_{\tau=0}^{T-t} r[t+\tau] \rangle
  3. \delta[t] = R[t]-v[t]
  4. w[t] = w[t-1]+\epsilon \delta[t] u[t]

where R[t] is the full reward expected over the remainder of the trial while r[t] remains the reward at a single time step. This is closer to biology, but we are still missing a key component. Not all future rewards are treated equally. Instead, rewards that happen sooner are valued higher than rewards in the distant future (this is called discounting). So the best match to biology is the following:

  1. v[t]=w[t-1] \cdot u[t]
  2. R[t]= \langle \sum_{\tau=0}^{T-t} \gamma^\tau r[t+\tau] \rangle
  3. \delta[t] = R[t]-v[t]
  4. w[t] = w[t-1]+\epsilon \delta[t] u[t]

where 0 \le \gamma \le 1 is the discounting factor for future rewards. A small discounting factor implies we prefer rewards now while a large discounting factor means we are patient for our rewards.

We have managed to write down a set of equations that accurately summarize biological reinforcement. But how can we actually learn with this system? As currently written, we would need to know the average reward over the remainder of the whole trial. Temporal difference learning makes the following assumptions in order to solve for the expected future rewards:

  1. Future rewards are Markovian
  2. Current observed estimate of reward is close enough to the typical trial

A Markov process is memoryless in that the next future step only depends on the current state of the system and has no other history dependence. By assuming rewards follow this structure, we can make the following approximation:

  • R[t]= \langle r[t+1] \rangle + \gamma \langle \sum_{\tau=1}^{T-t} \gamma^{\tau-1} r[t+\tau]
  • R[t]= \langle r[t+1] \rangle + \gamma R[t+1]

The second approximation is called bootstrapping. We will use the currently observed values rather than the full estimate for future rewards. So finally we end up at the temporal difference learning equations:

  1. v[t]=w[t-1] \cdot u[t]
  2. R[t] =  r[t+1] + \gamma v[t+1]
  3. \delta[t] =r[t+1] + \gamma v[t+1]-v[t]
  4. w[t] = w[t-1]+\epsilon \delta[t] u[t]

 

Screen Shot 2017-05-15 at 5.06.51 PM.png

Dayan and Abbott, Figure 9.2. This illustrates TD learning in action.

I have included an image from Dayan and Abbott about how TD learning evolves over consecutive trials, please read their Chapter 9 for full details.

Finally, I should mention that in practice, people often use the TD-Lambda algorithm. This version introduces a new parameter, lambda, which controls how far back in time one can make adjustments. Lambda 0 implies one time step only, while lambda 1 implies all past time steps. This allows TD learning to excel even if the full system is not Markovian.

Dopamine and Biology’s TD system

So does biology actually implement TD learning? Animals definitely utilize reinforcement learning and there is strong evidence that temporal difference learning plays an essential role. The leading contender for the reward signal is dopamine. This is a widely used neurotransmitter that evolved in early animals and remains widely conserved. There are a relatively small number of dopamine neurons (in the basal ganglia and VTA in humans) that project widely throughout the brain. These dopamine neurons can produce an intense sensation of pleasure (and in fact the “high” of drugs often comes about either through stimulating dopamine production or preventing its reuptake).

There are two great computational neuroscience papers that highlight the important connection between TD learning and dopamine that analyze two different biological systems:

Both of these papers deserved to be read in detail, but I’ll give a brief summary of the bee foraging paper here. Experiments were done that tracked bees in an controlled environment consisting of “yellow flowers” and “blue flowers” (which were basically just different colored cups). These flowers had the same amount of nectar on average, but were either consistent or highly variable. The bees quickly learned to only target the consistent flowers. These experimental results were very well modeled by assuming the bee was performing TD learning with a relatively small discount factor (driving it to value recent rewards).

TD Learning and Games

Playing games is the perfect test bed for TD learning. A game has a final objective (win), but throughout play it can be difficult to determine your probability of winning. TD learning provides a systematic framework to associate the value of a given game state with the eventual probability of learning. Below I highlight the games that have most significantly showcased the usefulness of reinforcement learning.

Backgammon

Backgammon is a two person game of perfect information (neither player has hidden knowledge) with an element of chance (rolling dice to determine one’s possible moves). Gerald Tesauro’s TD-Gammon was the first program to showcase the value of TD learning, so I will go through it in more detail.

Before getting into specifics, I need to point out that there are actually two (often competing) branches in artificial intelligence:

Symbolic logic tends to be a set of formal rules that a system needs to follow. These rules need to be designed by humans. The connectionist approach uses artificial neural networks and other approaches like TD learning that attempt to mimic biological neural networks. The idea is that humans set up the overall architecture and model of the neural network, but the specific connections between “neurons” is determined by the learning algorithm as it is fed real data examples.

Tesauro actually created two versions of a backgammon program. The first was called Neurogammon. It was trained using supervised learning where it was given expert games as well as games Tesauro played against himself and told to learn to mimic the human moves. Neurogammon was able to play at an intermediate human level.

Tesauro’s next version of a backgammon program was TD-Gammon since it used the TD learning rule. Instead of trying to mimic the human moves, TD-Gammon used to the TD learning rule to assign a score to each move throughout a game. The additional innovation is that the TD-Gammon program was trained by playing games against itself. This initial version of TD-Gammon soon matched Neurogammon (ie intermediate human level). TD-Gammon was able to beat experts by both using a supervised phase on expert games as well as a reinforcement phase.

Despite being able to beat experts, TD-Gammon still had a weakness in the endgame. Since it only looked two-moves ahead, it could miss key moves that would have been found by a more thorough analytical approach. This is where symbolic logic excels and hence TD-Gammon was a great demonstration of the complimentary strength and weaknesses of symbolic vs connectionist logic.

Go

Go is a two person game of perfect information with no element of chance. Despite this perfect knowledge, the game is complex enough that there are around 10^170 possible games (for reference, there are only about 10^80 atoms in the whole universe). So despite the perfect information, there are just too many possible games to determine the optimal move.

Recently AlphaGo made a huge splash by beating one of the world’s top players of Go. Most Go players, and even many artificial intelligence researchers, thoughts an expert level Go program was years away. So the win was just as surprising as when DeepBlue beat Kasparov in chess. AlphaGo is a large program with many different parts, but at the heart of it is a reinforcement learning module that utilizes TD learning (see here or here for details).

Poker

The final frontier in gaming is poker, specifically multi-person No-Limit Texas Hold’em. The reason this is the toughest game left is that it is a multi-player game with imperfect information and an element of chance.

Last winter the computer systems won against professionals for the first time in a series of heads up matches (computer vs only one human). Further improvements are needed to actually beat the best professionals at a multi-person table, but these results seem encouraging for future successes. The interesting thing to me is that both AI system seems to have used only a limited amount of reinforcement learning. I think that fully embracing reinforcement and TD learning should be the top priority for these research teams and might provide the necessary leap in ability. And they should hurry since others might beat them to it!

Posted on Academia, General science, Research

Research Experience for Undergrads (REU)

This National Science Foundation program is designed to give undergraduates, especially those from smaller schools, a chance to gain real research experience for a summer. Personally I participated in one official REU and one program modeling on REUs. I learned a lot (and they were tons of fun!). The best part is not the specific topic you research, but the opportunity to learn how to be a researcher.
Most of the applications are due in February. Check out the the official NSF REU website for the latest details.
 
When you are ready to apply, go here to search for programs of REUs in various subjects. Also, search the internet for other research opportunities; Harvard has a nice list of research programs for undergrads. For more detailed tips on applications, I recommend this site. 
 
If you want to get an idea of what an REU is like, here are some interviews of past Math REU participants. And also keep in mind these research tips for undergrads if you do get an REU.
4 Comments Posted on General science, Research, Teaching

NSF GRFP 2016-2017

For a couple of years now, I have had a website with my thoughts on the National Science Foundation Graduate Research Fellowship (NSF GRFP) and examples of successful essays. The popularity of the site in the past few years has grown well beyond what I expected, so this year I’m going to use this blog to try out a few new things.

 

Questions from You

I end up getting lots of emails asking for advice. While sometimes the advice really does merit an individualized result, many of the questions are applicable to everyone. So in the interest of efficiently answering questions, here is my plan this year.

  1. Before asking me, make sure you’ve read my advice, checked out the NSF GRFP FAQ, skimmed GradCafe, read my FAQ (next section), and checked out the comments for this blog post.
  2. I will not answer any questions about eligibility due to gaps in graduate school because I am honestly clueless on it.
  3. If you feel comfortable asking the question publicly, post it by commenting below.
  4. If you want to ask me privately, send me an email (my full name at gmail.com, include NSF GRFP Question in subject line). I will try and answer you and also work with you on a public question/answer that I can include here.

 

FAQ

Here are some past questions I have been asked and/or questions I anticipate being asked this year.

  • My research is closely related to medicine. Am I still eligible?
    • I think the best test for this is to ask your advisor if they would apply to NSF or NIH for grants on this topic. If NSF you are definitely good, but if NIH, you will need to reframe the research to fit into NSF.
  • I am a first year graduate student. Should I apply this year or wait until my second year? (New issue this year since incoming graduate students can only apply once).
    • This is the toughest question for me since no one has had to make this choice yet. However, here is how I would personally decide. The important thing to remember is that undergrads and graduate students are each separately graded. So you really need to decide how you currently rank relative to your peers versus how you will rank next year. If you did a bunch of undergrad research, have papers, etc, definitely apply as a first year. If you didn’t, it might payoff to wait, but only if your program lets you get right into research. If you will just be taking classes, I’m less confident your relative standing will improve. Good luck to everyone with this tough choice!

 

Requests for Essay Reading

Unfortunately, I now get more requests to read essays than I can reasonably accomplish. But I am still willing to read over a few and here is how I will decide on the essays to read.

  1. If you are in San Diego, and you think I am a better fit for you than the other local people on the experienced resource list,  send me an email with the subject NSF GRFP Experienced Resource List.
  2. If you are not in San Diego, first check out the experienced resource list and also ask around your school for other resources.
  3. If you can’t find anyone to read your essays, fill out this form. I will semi-randomly select essays to read.

What do I mean by semi-randomly? Well, in the interest of supporting the NSF GRFP’s goal of increasing the diversity of graduate school, I will give priority to undergrads who are without a local person on the experienced resource list and/or are from underrepresented groups. The NSF GRFP specifically “encourages women, members of underrepresented minority groups, persons with disabilities, and veterans to apply”, and I am willing to extremely loosely define minority group by race, ethnicity, sexual orientation, family socio-economic status, geography, colleges that traditionally send few students to graduate school, etc. The form is fill in the blank, so feel free to justify your inclusion in any other underrepresented group that I did not explicitly list.

I’ll then take the prioritized list and make some random selection. The number of people I select this way will depend on the number of local people I end up advising, but I will definitely read at least 2 non-local applications.

 

Here is a my time-line for essay reading:

  • Sept 16th – Random drawing number 1
  • Sept 30th Extended to Oct 5th – Random drawing number 2 (I’ll include everyone again, so early birds get double the chances of being selected)
  • Oct 21st – Last day I will help people (sorry I’m traveling near the deadline)

 

 

Posted on General science, Research, Teaching

Best Machine Learning Resources

Machine learning is a rapidly evolving field that is generating an intense interest from a wide audience. So how can you get started?

For now, I’m going to assume that you already have the basic programming (ie general introduction to programming and experience with matrices) and mathematical skills (calculus and some probability and linear algebra).

These are the best current books on machine learning:

These are some out of date books that still contain some useful sections (for example, Murphy several times refers you to Bishop or MacKay for more details).

Here is a list of other potential resources:

 

Posted on General science, Research, Teaching

I3: International Institute for Intelligence

While I was previously discussing my opinion of Open AI, I mentioned that I would do something different if I was in charge. Here is my dream.

 

What OpenAI is Missing

Helping everyday people throughout the whole world.

OpenAI’s stated goal is:

OpenAI is a non-profit artificial intelligence research company. Our goal is to advance digital intelligence in the way that is most likely to benefit humanity as a whole, unconstrained by a need to generate financial return.

In the short term, we’re building on recent advances in AI research and working towards the next set of breakthroughs.

However, based on their actions so far, this interview with Ilya Sutskever, and popular press articles, the main focus of OpenAI appears to be advanced research in an artificial intelligence by stressing open source, as well as thinking longterm about the impacts of letting advanced artificial intelligence systems control large aspects of our life. While I strongly support these goals, in reality, these will not benefit all of humanity. Instead, it only benefits those with either the necessary training (which is a minimum of a bachelors, but usually means a masters or PhD) or money (to hire top people, buy the required computing resources, etc) to take advantage of the advanced research. So this leaves out the developing world as well as the poor in developed countries, ie contrary to their stated goal, OpenAI is missing the vast majority of humanity.

While one can argue that by making OpenAI’s research open source, eventually it will trickle down and help a wider swath of humanity. However, the current trend suggests that large corporations are best poised to benefit the most from the next revolution (I mean, who is more likely to invent a self driving car, Google, or someone in a developing country?). Additionally, these innovations focus on first world problems (since these are the highest paying customers). And finally, each round of innovation ends up creating fewer and fewer jobs (so the number of unemployed in developed countries may expand). I firmly believe that unless there is a global educational effort (and probably an implementation of basic income), the benefits of AI will be directed towards a tiny sliver of the world’s population.

 

My Proposal: I3

Here I lay out my proposal for a new institute that would actually expand the benefits of recent and future advances in machine learning / artificial intelligence to a wider swath of humanity. I don’t claim that it would truly benefit all of humanity (again, see basic income), but it is a way for research advances to reach a larger proportion of it.

I propose a new education and research institute focused on artificial intelligence, machine learning, and computational neuroscience which I’ll call the International Institute for Intelligence. I like alliterations, and since I think it should focus on three types of intelligence, I especially like the idea of calling it I3 or I-Cubed for short.

Why these three research areas? Well, machine learning is currently revolutionizing how companies use data and is facilitating new technological advances everyday. Designing artificial intelligence systems on top of these machine learning algorithms seems like a realistic possibility in the near future. The less conventional choice is computational neuroscience. I think it is important to include for two reasons. First, the brain is the best example we have of an intelligent system, so until we actually design an artificial intelligence, it seems best to understand and mimic the best example (this is the philosophy of Deep Mind according to Demis Hassabis). Second, the US Brain Initiative  and similar international efforts are injecting significant resources into neuroscience, with the hopes of sparking a revolution similar in spirit and magnitude to the widespread effect the Human Genome Project had on biotechnology and genomics. So I figure we might as well prepare everyone for this future.

So what would be the actual purpose of I3? Sticking with the theme of threes, I propose three initiatives that I will list in my order of importance as well as some bonus points.

 

1. International PhD Education

The central goal is to similar program to ICTP (International Centre for Theoretical Physics) but with a different research emphasis. So what is ICTP? It was founded by Nobel Prize Winner Abdus Salam and it has several programs to promote research in developing countries, including:

  • Predoctoral program – students get a 1 year course to prep them for PhDs
  • Visiting PhD program – students in a developing nation PhD program get to spend a couple of months each year for 3 years at ICTP to participate in their research
  • Conferences
  • Regional offices (currently Sao Paolo, Brazil, but more in the planning)

So the idea is to implement a similar program but with the research emphasis now focused on machine learning, artificial intelligence, and computational neuroscience. While I think the main thing is to get the predoctoral program and visiting PhD program started, eventually it would be great to have 5 regional offices spread throughout the developing world. For example, I think one is needed in South America (Lima, Peru?), one in Africa (Nairobi, Kenya?), and 2 in Asia (India, and China, but not in a traditional technological center). And assuming I3 is based in the US (see my case for San Diego below), it would be great to have an affiliate office in Europe, maybe in Trieste next to ICTP.

One additional initiative that I think could be useful would be paying people to not leave their country and instead help them establish a research center at their local universities. This could also wait until later because it might be easiest to convince some of the future alumni of the predoctoral or visiting PhD programs to return/stay in their home country.

A second additional initiative would be to encourage professors from developed and developing countries to take their sabbatical at I3. This would provide a fresh stream of mentors and set up potential future collaborations. This is a blend of two programs at KITP (this and that).

 

2. US Primary School Education

The science pipeline analogy is overused, but I don’t have a better one yet. So currently, the researchers in I3 focused areas are predominately male, white or Asian, and middle to upper class. So not a very representative sample of the US (or world) population. Therefore, the best longterm solution is to get a more diverse set of students interested in the research at a young age.

Technically this should have a higher priority over the next initiative (US College Education), but since there are other non-profits interested in this (for example, CodeNow), maybe I3 does not need to be a leader in this and instead can play a supporting role.

 

3. US College Education

And again back to science pipeline analogy, if we are to have a more diverse set of researchers, we need to encourage a diverse set of undergrads to pursue relevant majors and continue on into graduate programs. This won’t be solved by any single program, but here are some potential ideas.

  • US underrepresented students could apply for the same 1 year program that is offered to international students.
  • Assist universities in establishing bridge programs that partner research universities with colleges that have significant minority populations. A great example of this is the Vanderbilt-Fisk Physics program.
  • US colleges would also benefit from the proposed sabbatical program offered to international researchers. I also like the KITP idea of extending it to undergraduate only institutes (especially those with large minority populations) as a way to get more undergrads interested in research.
  • Establish a complete set of free college curriculum for machine learning, artificial intelligence, and computational neuroscience. While there are many useful MOOCs on these topics, I still don’t think they beat an actual course.

 

Bonus #1 : Research

ICTP has proven that it is possible to further global educational goals and still succeed at research. I would argue that the people working at I3 should mainly be evaluated for tenure based on their mentorship and teaching of students. Research of course will play a role (otherwise it would be poor mentorship of future researchers), but I think there shouldn’t be huge pressure to bring in grants, high-profile publications, etc. But even without that emphasis, there is no way that a group of smart people with motivated students will not lead to great research.

 

Bonus #2: International Primary and College Education

This is longer term, but if there are successful programs in improving the US primary and college education, international regional offices, and PhD alumni who are in their home countries, it seems like there should be possible to leverage those connections into a global initiative to improve primary and college education.

 

Final Thoughts

So Elon Musk, Peter Thiel, and friends, if you have another billion you want to donate (or Open AI funds to redirect), here is my proposal. In reality, implementing all of my ideas would probably cost several billions, but once you got the center founded, I think that it would be easy to get tech companies, the US government, and even UNESCO to help provide funding.

My final point is that I think San Diego would be a perfect location. I know I’m biased since I live here now, but there a many legitimate reasons San Diego is great for this institute.

  1. UCSD already partners with outside research institutes (Salk, Scripps, etc)
  2. UCSD (and Salk, etc) are leaders in all of these research areas
  3. It is extremely easy to convince people to take a sabbatical in San Diego

While there are many other great potential locations, I strongly suggest that I3 is not in the Bay Area, Seattle, Boston, or New York City. These cities already have plenty of tech jobs, please spread the wealth to other parts of the US.

Anyways, I’ll keep dreaming that someday I’ll get to work at a place like the one I just described.

 

Posted on General science, Research

General Programming Tips

I thought I would put together some useful programming tips that I have learned over the years. Most of these are general tips, but they are tailored towards Python.

  1. Zen of Python. Even if you don’t use Python, these are good ideas to internalize.
  2. The language documentation (Python’s standard library), StackOverflow, and Google searches are your best friends.
  3. Utilize modern IDEs (like Spyder for Python) and tab-completion to reduce the number of basic errors.
  4. Comments are not optional. The general logic of functions and objects should be understandable from the comments. Every block of code logic should have a short comment to aid future changes. If you find a chunk of code confusing now, it will be just as confusing if not worse in the future!
  5. Use sensible variable names. This cuts down on the number/length of comments.
  6. Try to adhere to the language standards (Python’s), but don’t obsess over it.
  7. Set your own consistent standards (Do variable names end in s or not? Do boolean variables have similar style names? Etc).
  8. When starting a project, do you best to get quickly get up to a basic working prototype. Working but incomplete code is always better than non-working code. Quick coding is aided by the next point…
  9. Outline your code before starting. My tips for outlining in Python are detailed after this list.
  10. Write modular code. Common tasks should be made into functions or objects.
  11. Avoid magic numbers and hard coded values. Better to include a set of named parameters in one section of your code where the basic logic of these variables is explained.
  12. Avoid multiple inheritance (check out this fun explanation of why this is bad).
  13. A program should have a standard interface, I like to call it main, and a way to run the standard interface with some default values. In Python, utilize if __name__ == ‘__main__’: to define standard parameters and then call main(parameters). This aids the goal of always having working code, as well as making it easier to interact with different programs.
  14. Check out these Python tricks (1-23 are the best, rest are more advanced).

 

Here are details on how I outline code in Python. I try my best to have running code at all times, even if it does absolutely nothing. If it isn’t real code, I leave it as a comment. Therefore, my programming tends to proceed as follows.

  1. Outline the general logic of the code in comments. Define needed functions, but at first have it take no actual variables (utilize pass to keep it as functioning Python code). In the comments inside a function, list the data type you think it should take in, what it should do, and what it should return.
  2. If you start to code a function or series of logic, you can safely leave it incomplete by having it raise NotImplementedError.
  3. Use assert to check any of your assumptions. A custom assert statement will save you lots of time later.
  4. While the Pythonic way is to utilize duck typing, I still prefer to do some type checking if there is potential for confusion. So I like to utilize things like isinstance or implement checks on attributes.
  5. Take advantage of your IDE’s additional formatting options. For example, Spyder specially highlights comments that start with TODO: with a little checkmark. Additionally, it supports code blocks and defines them by #%%. This lets you quickly run small chunks of a larger code.

What is the major advantages of coding like this?

  1. If your code always runs, it allows you to quickly find syntax errors and typos.
  2. You avoid implementing unused code. It sucks to really work on a code section to only realize later that you didn’t actually need it.
  3. You spend your time on the standard case and can add certain options or take care of edge cases when the appropriate time arises. Because sometimes that time will never arise…

Anyways, enough advice, start coding!

 

 

 

 

Posted on Everybody, General science, Research

Thoughts on OpenAI

OpenAI was started just over 6 months ago, and I feel like they have done enough to warrant a review of what they have done so far, and my thoughts of what they should do next.

What is OpenAI?

OpenAI was announced in December 2015 and their stated mission is:

OpenAI is a non-profit artificial intelligence research company. Our goal is to advance digital intelligence in the way that is most likely to benefit humanity as a whole, unconstrained by a need to generate financial return.

In the short term, we’re building on recent advances in AI research and working towards the next set of breakthroughs.

 

What have they done so far?

  1. Started a new, small (so far) research center
  2. Experimented with a novel organization of the research center
  3. Hired a variety of smart people
  4. Released a toolkit for reinforcement learning (RL)

Since it has only been six months and they are still getting setup, it is still difficult to assess how well they have done. But here are my first impressions of the above points.

  1. Always great to have more places hiring researchers!
  2. Way too early to assess. I’m always intrigued by experiments of new ways to organize research, since there are three dominant types of organizations today (academia, industry focused on development, and industry focused on longterm research).
  3. Bodes well for their future success.
  4. I have yet to use it, but the it looks awesome. Supervised learning was sped along by datasets such as UC Irvine’s Machine Learning Repository, MNIST, and Imagenet, and I think their toolkit could have a similar impact on RL.

 

What do I think they should do?

This blog post was motivated by me having a large list of things that I think OpenAI should be doing. After I started writing, I realized that many of the things on my wish list would probably be better run by a new research institute, which I will detail in a future post. So here, I focus on my research wish-list for OpenAI.

Keep the Data Flowing

As Neil Lawrence pointed out shortly after OpenAI’s launch, data is king. So I am very happy with OpenAI’s RL toolkit. I hope that they keep adding new datasets or environments that machine learners can use. Some future ideas include supporting new competitions (maybe in partnership with Kaggle?), partnering with organizations to open up their data, and introducing datasets for unsupervised learning.

Unsupervised Learning

But maybe I’m putting the cart (data) before the horse (algorithms and understanding). Unsupervised learning is tough for a series of interconnected issues:

  • What are good test cases / datasets for unsupervised learning?
  • How does one assess learning success?
  • Are our current algorithms even close to the “best”?

The reason supervised learning is easier is that algorithms require data with labels, there are lots of established metrics for evaluating success (for example, accuracy of label predictions), and we know for most metrics what is the best (100% correct label predictions). Reinforcement learning has some of that (data and a score), but is much less well defined that supervised learning.

So while I think the progress on reinforcement learning will definitely lead to new ideas for unsupervised learning, more work needs to be done directly on unsupervised learning. And since they have no profit motives or tenure pressure, I really hope OpenAI focuses on this extremely tough area.

Support Deep Learning Libraries

We currently have a very good problem: lots of deep learning libraries, to the point of almost being too many. A few years ago, everyone had to essentially code their own library, but now one can choose from Theano and TensorFlow for low end libraries, to Lasagne and Keras for high end libraries, just to name a few examples from Python.

I think that OpenAI could play a useful role in standardization and testing of libraries. While there are tons of great existing libraries, their documentation quality varies significantly, and in general is sub par (for example compared to NumPy). Additionally, besides choosing a language (I strongly advocate Python), one usually needs to choose a backend library (Theano vs TensorFlow), and then a high end library.

So my specific proposal for OpenAI is the following initiatives:

  1. Help establish some deep learning standards so people can verify the accuracy of a library and assess its quality and speed
  2. Set up some meetings between Theano, TensorFlow, and others to help standardize the backend (and include them in the settings of standards)
  3. Support initiatives for developers to improve documentation of their libraries
  4. Support projects that are agnostic to the backend (like Keras) and/or help other packages that are backend specific (like Lasagne) become backend agnostic

As a recent learning of deep learning, and someone who interacts extensively with non-machine learners, I think the above initiatives would allow a wider population of researchers to incorporate deep learning in their research.

Support Machine Learning Education

I believe this is the crucial area that OpenAI is missing, and it will prevent them from their stated mission to help all of humanity.

Check out a future post for my proposed solution…