Modelling Strava Fitness and Freshness

Since my blog about Strava Fitness and Freshness has been very popular, I thought it would be interesting to demonstrate a simple model that can help you use these metrics to improve your cycling performance.

As a quick reminder, Strava’s Fitness measure is an exponentially weighted average of your daily Training Load, over the last six weeks or so. Assuming you are using a power meter, it is important to use a correctly calibrated estimate of your Functional Threshold Power (FTP) to obtain an accurate value for the Training Load of each ride. This ensures that a maximal-effort one hour ride gives a value of 100. The exponential weighting means that the benefit of a training ride decays over time, so a hard ride last week has less impact on today’s Fitness than a hard ride yesterday. In fact, if you do nothing, Fitness decays rate is about 2.5% per day.

Although Fitness is a time-weighted average, a simple rule of thumb is that your Fitness Score equates to your average daily Training Load over the last month or so. For example, a Fitness level of 50 is consistent with an average daily Training Load (including rest days) of 50. It may be easier to think of this in terms of a total Training Load of 350 per week, which might include a longer ride of 150, a medium ride of 100 and a couple of shorter rides with a Training Load of 50.

How to get fitter

The way to get fitter is to increase your Training Load. This can be achieved by riding at a higher intensity, increasing the duration of rides or including extra rides. But this needs to be done in a structured way in order be effective. Periodisation is an approach that has been tried and tested over the years. A four-week cycle would typically include three weekly blocks of higher training load, followed by an easier week of recovery. Strava’s Fitness score provides a measure of your progress.

Modelling Fitness and Fatigue

An exponentially weighted moving average is very easy to model, because it evolves like a Markov Process, having the following property, relating to yesterday’s value and today’s Training Load.
F_{t} = \lambda * F_{t-1}+\left ( 1-\lambda  \right )*TrainingLoad_{t}
where
F_{t} is Fitness or Fatigue on day t and
\lambda = exp(-1/42) \approx 0.976 for Fitness or
\lambda = exp(-1/7) \approx 0.867 for Fatigue

This is why your Fitness falls by about 2.5% and your Fatigue eases by about 13.5% after a rest day. The formula makes it straightforward to predict the impact of a training plan stretching out into the future. It is also possible to determine what Training Load is required to achieve a target level of Fitness improvement of a specific time period.

Ramping up your Fitness

The change in Fitness over the next seven days is called a weekly “ramp”. Aiming for a weekly ramp of 5 would be very ambitious. It turns out that you would need to increase your daily Training Load by 33. That is a substantial extra Training Load of 231 over the next week, particularly because Training Load automatically takes account of a rider’s FTP.

Interestingly, this increase in Training Load is the same, regardless of your starting Fitness. However, stepping up an average Training Load from 30 to 63 per day would require a doubling of work done over the next week, whereas for someone starting at 60, moving up to 93 per day would require a 54% increase in effort for the week.

In both cases, a cyclist would typically require two additional hard training rides, resulting in an accumulation of fatigue, which is picked up by Strava’s Fatigue score. This is a much shorter term moving average of your recent Training Load, over the last week or so. If we assume that you start with a Fatigue score equal to your Fitness score, an increase of 33 in daily Training Load would cause your Fatigue to rise by 21 over the week. If you managed to sustain this over the week, your Form (Fitness minus Fatigue) would fall from zero to -16. Here’s a summary of all the numbers mentioned so far.

Impact of a weekly ramp of 5 on two riders with initial Fitness of 30 and 60

Whilst it might be possible to do this for a week, the regime would be very hard to sustain over a three-week block, particularly because you would be going into the second week with significant accumulated fatigue. Training sessions and race performance tend to be compromised when Form drops below -20. Furthermore, if you have increased your Fitness by 5 over a week, you will need to increase Training Load by another 231 for the following week to continue the same upward trajectory, then increase again for the third week. So we conclude that a weekly ramp of 5 is not sustainable over three weeks. Something of the order of 2 or 3 may be more reasonable.

A steady increase in Fitness

Consider a rider with a Fitness level of 30, who would have a weekly Training Load of around 210 (7 times 30). This might be five weekly commutes and a longer ride on the weekend. A periodised monthly plan could include a ramp of 2, steadily increasing Training Load for three weeks followed by a recovery week of -1, as follows.

Plan of a moderate rider

This gives a net increase in Fitness of 5 over the month. Fatigue has also risen by 5, but since the rider is fitter, Form ends the month at zero, ready to start the next block of training.

To simplify the calculations, I assumed the same Training Load every day in each week. This is unrealistic in practice, because all athletes need a rest day and training needs to mix up the duration and intensity of individual rides. The fine tuning of weekly rides is a subject for another blog.

A tougher training block

A rider engaging in a higher level of training, with a Fitness score of 60, may be able to manage weekly ramps of 3, before the recovery week. The following Training Plan would raise Fitness to 67, with sufficient recovery to bring Form back to positive at the end of the month.

A more ambitious training plan

A general plan

The interesting thing about this analysis is that the outcomes of the plans are independent of a rider’s starting Fitness. This is a consequence of the Markov property. So if we describe the ambitious plan as [3,3,3,-2], a rider will see a Fitness improvement of 7, from whatever initial value prevailed: starting at 30, Fitness would go to 37, while the rider starting at 60 would rise to 67.

Similarly, if Form begins at zero, i.e. the starting values of Fitness and Fatigue are equal, then the [3,3,3,-2] plan will always result in a in a net change of 6 in Fatigue over the four weeks.

In the same way, (assuming initial Form of zero) the moderate plan of [2,2,2,-1] would give any rider a net increase of Fitness and Fatigue of 5.

Use this spreadsheet to experiment.

Predicting the World Champion

A couple of years ago I built a model to evaluate how Froome and Dumoulin would have matched up, if they had not avoided racing against each other over the 2017 season. As we approach the 2019 World Championships Road Race in Yorkshire, I have adopted a more sophisticated approach to try to predict the winner of the men’s race. The smart money could be going on Sam Bennett.

Deep learning

With only two races outstanding, most of this year’s UCI world tour results are available. I decided to broaden the data set with 2.HC classification European Tour races, such as the OVO Energy Tour of Britain. In order to help with prediction, I included each rider’s weight and height, as well as some meta-data about each race, such as date, distance, average speed, parcours and type (stage, one-day, GC, etc.).

The key question was what exactly are you trying to predict? The UCI allocates points for race results, using a non-linear scale. For example, Mathieu Van Der Poel was awarded 500 points for winning Amstel Gold, while Simon Clarke won 400 for coming second and Jakob Fuglsang picked up 325 for third place, continuing down to 3 points for coming 60th. I created a target variable called PosX, defined as a negative exponential of the rider’s position in any race, equating to 1.000 for a win, 0.834 for second, 0.695 for third, decaying down to 0.032 for 20th. This has a similar profile to the points scheme, emphasising the top positions, and handles races with different numbers of riders.

A random forest would be a typical choice of model for this kind of data set, which included a mixture of continuous and categorical variables. However, I opted for a neural network, using embeddings to encode the categorical variables, with two hidden layers of 200 and 100 activations. This was very straightforward using the fast.ai library. Training was completed in a handful of seconds on my MacBook Pro, without needing a GPU.

After some experimentation on a subset of the data, it was clear that the model was coming up with good predictions on the validation set and the out-of-sample test set. With a bit more coding, I set up a procedure to load a start list and the meta-data for a future race, in order to predict the result.

Predictions

With the final start list for the World Championships Road Race looking reasonably complete, I was able to generate the predicted top 10. The parcours obviously has an important bearing on who wins a race. With around 3600m of climbing, the course was clearly hilly, though not mountainous. Although the finish was slightly uphill, it was not ridiculously steep, so I decided to classify the parcours as rolling with a flat finish

PositionRiderPrediction
1Mathieu Van Der Poel0.602
2Alexander Kristoff0.566
3Sam Bennett0.553
4Peter Sagan0.540
5Edvald Boasson Hagen0.507
6Greg Van Avermaet0.500
7Matteo Trentin0.434
8Michael Matthews0.423
9Julian Alaphilippe0.369
10Mike Teunissen0.362

It was encouraging to see that the model produced a highly credible list of potential top 10 riders, agreeing with the bookies in rating Mathieu Van Der Poel as the most likely winner. Sagan was ranked slightly below Kristoff and Bennett, who are seen as outsiders by the pundits. The popular choice of Philippe Gilbert did not appear in my top 10 and Alaphilippe was only 9th, in spite of their recent strong performances in the Vuelta and the Tour, respectively. Riders in positions 5 to 10 would all be expected to perform well in the cycling classics, which tend to be long and arduous, like the Yorkshire course.

For me, 25/1 odds on Sam Bennett are attractive. He has a strong group of teammates, in Dan Martin, Eddie Dunbar, Connor Dunne, Ryan Mullen and Rory Townsend, who will work hard to keep him with the lead group in the hillier early part of the race. Then he will then face an extremely strong Belgian team that is likely to play the same game that Deceuninck-QuickStep successfully pulled off in stage 17 of the Vuelta, won by Gilbert. But Bennett was born in Belgium and he was clearly the best sprinter out in Spain. He should be able to handle the rises near the finish.

A similar case can be made for Kristoff, while Matthews and Van Avermaet both had recent wins in Canada. Nevertheless it is hard to look past the three-times winner Peter Sagan, though if Van Der Poel launches one of his explosive finishes, there is no one to stop him pulling on the rainbow jersey.

Appendix

After the race, I checked the predicted position of the eventual winner, Mads Pedersen. He was expected to come 74th. Clearly the bad weather played a role in the result, favouring the larger riders, who were able to keep warmer. The Dane clearly proved to be the strongest rider on the day.

References

Code used for this project

Sunflowers

Image in the style of @grandtourart

Last year, I experimented with using style transfer to automatically generate images in the style of @grandtourart. More recently I developed a more ambitious version of my rather simple bike identifier. The connection between these two projects is sunflowers. This blog describes how I built a flower identification app.

In the brilliant fast.ai Practical Deep Learning for Coders course, Jeremy Howard recommends downloading a publicly available dataset to improve one’s image categorisation skills. I decided to experiment with the 102 Category Flower Dataset, kindly made available by the Visual Geometry Group at Oxford University. In the original 2008 paper, the researchers used a combination of techniques to segment each image and characterise its features. Taking these as inputs to a Support Vector Machine classifier, their best model achieved an accuracy of 72.8%.

Annoyingly, I could not find a list linking the category numbers to the names of the flowers, so I scraped the page showing sample images and found the images in the labelled data.

Using exactly the same training, validation and test sets, my ResNet34 model quickly achieved an accuracy of 80.0%. I created a new branch of the GitHub repository established for the Bike Image model and linked this to a new web service on my Render account. The huge outperformance of the paper was satisfying, but I was sure that a better result was possible.

The Oxford researchers had divided their set of 8,189 labelled images into a training set and a validation set, each containing 10 examples of the 102 flowers. The remaining 6,149 images were reserved for testing. Why allocate less that a quarter of the data to training/validation? Perhaps this was due to limits on computational resources available at the time. In fact, the training and validation sets were so small that I was able to train the ResNet34 on my MacBook Pro’s CPU, within an acceptable time.

My plan to improve accuracy was to merge the test set into the training set, keeping aside the original validation set of 1,020 images for testing. This expanded training set of 7,261 images immediately failed on my MacBook, so I uploaded my existing model onto my PaperSpace GPU, with amazing results. Within 45 minutes, I had a model with 97.0% accuracy on the held-out test set. I quickly exported the learner and switched the link in the flowers branch of my GitHub repository. The committed changes automatically fed straight through to the web service on Render.

I discovered, when visiting the app on my phone, that selecting an image offers the option to take a photo and upload it directly for identification. Having exhausted the flowers in my garden, I have risked being spotted by neighbours as I furtively lean over their front walls to photograph the plants in their gardens.

Takeaways

It is very efficient to use smaller datasets and low resolution images for initial training. Save the model and then increase resolution. Often you can do this on a local CPU without even paying for access to a GPU. When you have a half decent model, upload it onto a GPU and continue training with the full dataset. Deploying the model as a web service on Render makes the model available to any device, including a mobile phone.

My final model is amazing… and it works for sunflowers.

References

Automated flower classification over a large number of classes, Maria-Elena Nilsback and Andrew Zisserman, Visual Geometry Group, Department of Engineering Science, University of Oxford, United Kingdom, men,az@robots.ox.ac.uk

102 Flowers Jupyter notebook

Strava – Tour de Richmond Park Clockwise

Screenshot 2019-05-22 at 15.24.51

Following my recent update on the Tour de Richmond Park leaderboard, a friend asked about the ideal weather conditions for a reverse lap, clockwise around the park. This is a less popular direction, because it involves turning right at each mini-roundabout, including Cancellara corner, where the great Swiss rouleur crashed in the 2012 London Olympics, costing him a chance of a medal.

An earlier analysis suggested that apart from choosing a warm day and avoiding traffic, the optimal wind direction for a conventional anticlockwise lap was a moderate easterly, offering a tailwind up Sawyers Hill. It does not immediately follow that a westerly wind would be best for a clockwise lap, because trees, buildings and the profile of the course affect the extent to which the wind helps or hinders a rider.

Currently there are over 280,000 clockwise laps recorded by nearly 35,000 riders, compared with more than a million anticlockwise laps by almost 55,000 riders. As before, I downloaded the top 1,000 entries from the leaderboard and then looked up the wind conditions when each time was set on a clockwise lap.

In the previous analysis, I took account of the prevailing wind direction in London. If wind had no impact, we would expect the distribution of wind directions for leaderboard entries to match the average distribution of winds over the year. I defined the wind direction advantage to be the difference between these two distributions and checked if it was statistically significant. These are the results for the clockwise lap.

RoseSegmentBarSegmentclockwise

The wind direction advantage was significant (at p=1.3%). Two directions stand out. A westerly provides a tailwind on the more exposed section of the park between Richmond Gate and Roehampton, which seems to be a help, even though it is largely downhill. A wind blowing from the NNW would be beneficial between Roehampton and Robin Hood Gate, but apparently does not provide much hindrance on the drag from Kingston Gate up to Richmond, perhaps because this section of the park is more sheltered. The prevailing southwesterly wind was generally unfavourable to riders setting PBs on a clockwise lap.

The excellent mywindsock web site provides very good analysis for avid wind dopers. This confirms that the wind was blowing predominantly from the west for the top ten riders on the leaderboard, including the KOM, though the wind strength was generally light.

The interesting thing about this exercise is that it demonstrates a convergence between our online and our offline lives, as increasing volumes of data are uploaded from mobile sensors. A detailed analysis of each section of the million laps riders have recorded for Richmond Park could reveal many subtleties about how the wind flows across the terrain, depending on strength and direction. This could be extended across the country or globally, potentially identifying local areas where funnelling effects might make a wind turbine economically viable.

References

Jupyter notebook for calculations

Can self-driving cars detect cyclists?

Screenshot 2019-05-10 at 14.05.59

Self-driving cars employ sophisticated software to interpret the world around them. How do these systems work? And how good are they at detecting cyclists? Can cyclists feel safe sharing roads with an increasing number of vehicles that make use of these systems?

How hard is it to spot a cyclist?

Vehicles can use a range of detection systems, including cameras, radar and lidar.  Deep learning techniques have become very good at identifying objects in photographic images. So one important question is how hard is it to spot a cyclist in a photo taken from a moving vehicle?

Researchers at Tsinghua University, working in collaboration with Daimler, created a publicly available collection of dashboard camera photos, where humans have painstakingly drawn boxes around other road users. The data set is used by academics to benchmark the performance of their image recognition algorithms. The images are rather grey and murky, reflecting the cloudy and polluted atmosphere of the Chinese city location. It is striking that, in the majority of cases, the cyclists are very small, representing around 900 pixels out of the 2048 x 1024 images, i.e. less than 0.05% of the total area. For example, the cyclist in the middle of the image above is pretty hard to make out, even for a human.

Object-detecting neural networks are typically trained to identify the subject of a photo, which normally takes up are significant portion of the image. Finding a tall, thin segment containing a cyclist is significantly more difficult.

If you think about it, the cyclist taking up the largest percentage of a dash cam image will be riding across the direction of travel, directly in front of the vehicle, at which point it may be too late to take action. So a crucial aspect of any successful algorithm is to find more distant cyclists, before they are too close.

Setting up the problem

Taking advantage of skills acquired on the fast.ai course on deep learning, I decided to have a go at training a neural network to detect cyclists. Many of the images in the Tsinghua Daimler data set include multiple cyclists. In order to make the problem more manageable, I set out to find the single largest cyclist in each image.

If you are not interested in the technical bit, just scroll down to the results.

The technical bit

In order to save space on my drive, I downloaded about a third of the training set. The 3209 images were split 80:20 to create a training and validation sets. I also downloaded 641 unseen images that were excluded from training and used only for testing the final model.

I used transfer learning to fine-tune a neural network using a pre-trained ResNet34 backbone, with a customised head designed to generate four numbers representing the coordinates of a bounding box around the largest object in each image. All images were scaled down to 224 pixel squares, without cropping. Data augmentation added variation to the training images, including small rotations, horizontal flips and adjustments to lighting.

It took a couple of hours to train the network on my MacBook Pro, without needing to resort to a cloud-based GPU, to produce bounding boxes with an average error of just 12 pixels on each coordinate. The network had learned to do a pretty good job at detecting cyclists in the training set.

Results

The key step was to test my neural network on the set of 641 unseen images. The results were impressive: the average error on the bounding box coordinates was just 14 pixels. The network was surprisingly good at detecting cyclists.

oosImages

The 16 photos above were taken at random from the test set. The cyan box shows the predicted position of the largest cyclist in the image, while the white box shows the human annotation. There is a high degree of overlap for eleven cyclists 2, 3, 4, 5, 6, 8, 11, 12, 14, 15 and 16. Box 9 was close, falling between two similar sized riders, but 7 was a miss. The algorithm failed on the very distant cyclists in 1, 10 and 13. If you rank the photos, based on the size of the cyclist, we can see that the network had a high success rate for all but the smallest of cyclists.

In conclusion, as long as the cyclists were not too far away, it was surprisingly easy to detect riders pretty reliably, using a neural network trained over an afternoon.  With all the resources available to Google, Uber and the big car manufacturers, we can be sure that much more sophisticated systems have been developed. I did not consider, for example, using a sequence of images to detect motion or combining them with data about the motion of the camera vehicle. Nor did I attempt to distinguish cyclists from other road users, such as pedestrians or motorbikes.

After completing this project, I feel reassured that cyclists of the future will be spotted by self-driving cars. The riders in the data set generally did not wear reflective clothing and did not have rear lights. These basic safety measures make cyclists, particularly commuters, more obvious to all road users, whether human or AI.

Car manufacturers could potentially develop significant goodwill and credibility in their commitment to road safety by offering cyclists lightweight and efficient beacons that would make them more obvious to automated driving systems.

References

“A new benchmark for vision-based cyclist detection”, X. Li, F. Flohr, Y. Yang, H. Xiong, M. Braun, S. Pan, K. Li and D. M. Gavrila, in proceedings of IEEE Intelligent Vehicles Symposium (IV), pages 1028-1033, June 2016

Link to Jupyter notebook

Strava: Richmond Park leaderboard update

Screenshot 2019-04-27 at 16.15.55

An extended version of this blog was published by cyclist.co.uk

If you have ever had the feeling that it is becoming harder to rise up the Strava leaderboards and that KOMs are ever more elusive, you are right. I took a snapshot of the top 1000 entries for the Tour de Richmond Park segment in April 2019 and compared it with the leaderboard from February 2017 that I used for an earlier series of blogs.

The current rankings are led by a team of Onyx RT riders, who rode as a group at 6:02am on 25 July 2018, beating Rob Sharland’s solo effort by 6 seconds, with a time of 13:51. Some consider that targeting a KOM by riding as a team time trial is a kind of cheating. Having said that, many riders have achieved their best laps around Richmond Park while riding in the popular Saturday morning and Wednesday evening chain gang rides. In fact, if the Onyx guys had checked my blogs on the optimal wind direction and weather conditions, and chosen a warm evening with a moderate Easterly wind, they would have probably gone faster.

Survival of the fittest

The Darwinian nature of Strava leaderboards ensures that the slowest times are continually culled. Over the two year gap, the average time of the top 1000 riders improved by 35 seconds, which equates to an increase in speed of about 1.6% per annum. In 2017, a time of 17:40 was good enough to reach the top 1000. You now need to complete the rolling 10.8km course in less than 17:07, averaging over 37.8kph, to achieve the same ranking. The rider currently ranked 1000th would have been 503rd on the 2017 leaderboard, making the turnover about 50%.

Speed20172019

Strava inflation produces a right shift in the speeds at which riders complete the segment. Rider speeds exhibit “long tailed” distributions, with just a few riders producing phenomenal performances: although many people can hold an average of 38kph, it remains very hard to complete this segment at over 42kph.

More faster riders

A total of 409 names dropped off the bottom of the 2017 leaderboard, to be replaced by new faster riders. Some of these quicker times were set by cyclists who had improved enough to rise up the leaderboard into the top 1000, while others were new riders who had joined Strava or not previously done a lap of Richmond Park.

Riders riding faster

Of the 591 riders who appeared on both leaderboards, 229 improved their times by an average of 53 seconds. These included about 90 riders who would have dropped out of the top 1000, had they not registered faster times.

Getting faster without doing anything

One curious anomaly arose from the analysis: 32 efforts appearing on the 2019 leaderboard were recorded on dates that should have shown up on the 2017 leaderboard. Nine of these appeared to be old rides uploaded to Strava at a later date, but that left 23 efforts showing faster times in 2019 than 2017 for exactly the same segments completed by the same cyclists on the same rides.

For example, Gavin Ryan’s ride on 25 August 2016 appeared 8th on the 2017 leaderboard with a time of 14:23, but now he appears as 16th on the 2019 leaderboard with a time of 14:20! It seems that Strava has performed some kind of recalculation of historic times, resulting a new “effort_id” being assigned to the same completed segment. If you want to see a list of other riders whose times were recalculated, click here and scroll down to the section entitled “Curious anomaly”.

Summer is the time to go faster

Strava leaderboards were never designed to rank pure solo TT efforts. Although it is possible to filter by sex, age, weight and date, it remains hard to distinguish between team versus solo efforts, road versus TT bikes and weather conditions. The nature of records is that they are there to be broken, so the top times will always get faster. The evidence from this analysis suggests that there are more faster cyclists around today than two years ago.

As the weather warms up, perhaps you can pick a quiet time to move up the leaderboard on your favourite segment, while showing courtesy to other road users and respecting the legal speed limit.

 

 

 

 

Learning the language of the Giro

Fausto_Coppi

Computers are becoming ever better at natural language processing (NLP). I set up a neural network as a language model and loaded a set of pre-trained weights on my MacBook Pro, to see what it could do. After priming it with some text about the Giro d’Italia, this is what the model produced as a continuation.

Priming text: The Giro d’ Italia (Italian pronunciation: [ˈdʒiːro diˈtaːlja]; English: Tour of Italy; also known as the Giro) is an annual multiple-stage bicycle race primarily held in Italy, while also occasionally passing through nearby countries. The first race was organized in 1909 to increase sales of the newspaper La Gazzetta dello Sport; however it is currently run by RCS Sport. The race has been held annually since its first edition in 1909, except when it was stopped for the two world wars. As the Giro gained prominence and popularity the race was lengthened, and the peloton expanded from primarily Italian participation to riders from all over the world.

Computer generated continuation:  the race was won by the italian rider , giovanni di u_n , who won the race in the first leg of the race . the race was won by italian rider giovanni u_n , who won the race by a margin of two lengths .
= = = world tour = = =
the tour de france was the first of the tour de france . the tour de france was won by the reigning world champion , the reigning world champion , who had won the tour de france in the previous year ‘s race …

The output may not make a lot of sense, but the point is that it looks like English (in lower case). The grammar is reasonable, with commas, fullstops and a header inserted in  a logical way. Furthermore, the model has demonstrated some understanding of the context by suggesting that the Giro could be won by an Italian ride called Giovanni. The word “u_n” stands for unknown, which is consistent with the idea that an Italian surname may not be a familiar English word. It turns out that a certain Giovanni Di Santi raced against Fausto Coppi (pictured above) in the 1940 Giro, though he did not win the first stage. In addition to this, the model somehow knew that the Giro, in common with the Tour the France, is a World Tour event that could be won by the reigning world champion.

I found this totally amazing. And it was not a one off: further examples on random topics are included below. This neural network is just an architecture, defining a collection of matrix multiplications and transformations, along with a set of connection weights. Admittedly there are a lot of connection weights: 115.6 million of them, but they are just numbers. It was not explicitly provided with any rules about English grammar or any domain knowledge.

How could this possibly work?

In machine learning, language models are assessed on a simple metric: accuracy in predicting the next word of a sentence. The neural network approach has proved to be remarkably successful. Given enough data and a suitable architecture, deep learning now far outstrips traditional methods that relied on linguistic expertise to parse sentences and apply grammatical rules that differ across languages.

I was experimenting with an AWD-LSTM model originally created by Stephen Merity. This is a recurrent neural network (RNN) with three LSTM layers that include dropout. The pre-trained weights for the wt103 model were generated by Jeremy Howard of fast.ai, using a large corpus of text from Wikipedia.

Jeremy Howard converted the Wikipedia text into tokens. A tokeniser, such as spaCy,  breaks text into words and punctuation, resulting in a vocabulary of tokens that are indexed as integers. This allows blocks of text to be fed into the neural network as lists of numbers. The outputs are numbers that can be converted back into the predicted words.

The wt103 model includes a linear encoder that creates embeddings of word tokens. These are passed through three LSTM layers whose states are able to retain a memory of previous words or context. The result is passed through a decoder, employing the same weights as the encoder, to produce a softmax output that can be treated as a set of probabilities, across the vocabulary, to predict the next word token. Special forms of dropout were employed, as described in the paper, to limit overfitting and make the model more robust.

The network was trained by minimising cross-entropy loss using stochastic gradient descent. A technique called back propagation through time (BPTT) introduced some random variation into the length of the blocks of text employed in each training batch. The connection weights were iteratively improved towards optimal values.

OK, but so what?

Impressive as it may be for a neural network to spout highly plausible but nonsensical English, what possible use could this have? Well, suppose you want to automate the separation of texts into different categories, for example, distinguish different authors or determine the sentiment of tweets or predict the reaction of the stock market to news items or identify the sentiment of movie reviews. Fine-tuning a neural network that already has a good knowledge of English provides a huge advantage over starting from scratch. In lesson 10 of the fast.ai course, Jeremy Howard demonstrates how this approach can be used to achieve state of the art results on the widely used IMDB movie review data set.

Further examples

In the first example, the network finishes the sentence about a hurricane in perfect English.  Next, it comes up with the name of a critic (actually a rock music critic rather than a book reviewer, but heh!) and it makes use of its LSTM to open and close quotation marks. In the bean example, it amazingly starts describing flowers and correctly converts their dimensions from centimetres to inches!

My code can be found here.

Priming text: Hurricane Ivan was a large long Cape Verde hurricane that caused widespread damage in the Caribbean and United States The cyclone was

Computer generated continuation:  the first hurricane to strike the united states since hurricane katrina in 2005 .

Priming text: The book was widely acclaimed by the critics.

Computer generated continuation: the book was published in the united states by the american library association on june 1 , 2006 .

= = = critical response = = =

the book received mixed reviews from critics . the new york times reviewer robert christgau called it ” a great book ” and ” a great book ” . he praised the book ‘s ” strong , strong , and well – written ” prose , and the ” excellent ” prose .

Priming text: Most varieties of bean grow either as an erect bush or as a climbing plant, but a few important kinds are of intermediate form. Dwarf and semiclimbers are grown extensively. When the climbing type is grown for its immature pods, artificial supports are necessary to facilitate harvesting. Varieties differ greatly in size, shape, colour, and fibrousness or tenderness of the immature pods. In general, varieties grown for dry mature seeds produce pods that are too fibrous to be eaten at any state of development. Most edible-podded beans produce relatively low yields of mature seeds, or seeds that are of low eating quality. Seed colours range from white through green, yellow, tan, pink, red, brown, and purple to black in solid colours and countless contrasting patterns. Seed shapes range from nearly spherical to flattened, elongated, and kidney-shaped. Pods are of various shades of green, yellow, red, and purple and splashed with red or purple; pod shapes range from flat to round, smooth to irregular, and straight to sharply curved; length ranges from 75 to 200 millimetres (3 to 8 inches) or more.

Computer generated continuation:  the most common form of the flower is the flower spike , which is a characteristic of the flower spike . the flower is made up of a series of small , cylindrical , cylindrical , cylindrical , cylindrical stems that are up to 10 cm ( 3.9 in ) long and 2.5 cm ( 0.98 in ) wide . the flower spikes are arranged in a series of three or four pairs of flowers