TensorFlow Lattice: Flexibility Empowered by Prior Knowledge

Wednesday, October 11, 2017

Crossposted on the Google Research Blog

Machine learning has made huge advances in many applications including natural language processing, computer vision and recommendation systems by capturing complex input/output relationships using highly flexible models. However, a remaining challenge is problems with semantically meaningful inputs that obey known global relationships, like “the estimated time to drive a road goes up if traffic is heavier, and all else is the same.” Flexible models like DNNs and random forests may not learn these relationships, and then may fail to generalize well to examples drawn from a different sampling distribution than the examples the model was trained on.

Today we present TensorFlow Lattice, a set of prebuilt TensorFlow Estimators that are easy to use, and TensorFlow operators to build your own lattice models. Lattices are multi-dimensional interpolated look-up tables (for more details, see [1--5]), similar to the look-up tables in the back of a geometry textbook that approximate a sine function.  We take advantage of the look-up table’s structure, which can be keyed by multiple inputs to approximate an arbitrarily flexible relationship, to satisfy monotonic relationships that you specify in order to generalize better. That is, the look-up table values are trained to minimize the loss on the training examples, but in addition, adjacent values in the look-up table are constrained to increase along given directions of the input space, which makes the model outputs increase in those directions. Importantly, because they interpolate between the look-up table values, the lattice models are smooth and the predictions are bounded, which helps to avoid spurious large or small predictions in the testing time.

How Lattice Models Help You

Suppose you are designing a system to recommend nearby coffee shops to a user. You would like the model to learn, “if two cafes are the same, prefer the closer one.”  Below we show a flexible model (pink) that accurately fits some training data for users in Tokyo (purple), where there are many coffee shops nearby.  The pink flexible model overfits the noisy training examples, and misses the overall trend that a closer cafe is better. If you used this pink model to rank test examples from Texas (blue), where businesses are spread farther out, you would find it acted strangely, sometimes preferring farther cafes!
Slice through a model’s feature space where all the other inputs stay the same and only distance changes. A flexible function (pink) that is accurate on training examples from Tokyo (purple) predicts that a cafe 10km-away is better than the same cafe if it was 5km-away. This problem becomes more evident at test-time if the data distribution has shifted, as shown here with blue examples from Texas where cafes are spread out more.
A monotonic flexible function (green) is both accurate on training examples and can generalize for Texas examples compared to non-monotonic flexible function (pink) from the previous figure.

In contrast, a lattice model, trained over the same example from Tokyo, can be constrained to satisfy such a monotonic relationship and result in a monotonic flexible function (green). The green line also accurately fits the Tokyo training examples, but also generalizes well to Texas, never preferring farther cafes.

In general, you might have many inputs about each cafe, e.g., coffee quality, price, etc. Flexible models have a hard time capturing global relationships of the form, “if all other inputs are equal, nearer is better, ” especially in parts of the feature space where your training data is sparse and noisy. Machine learning models that capture prior knowledge (e.g.  how inputs should impact the prediction) work better in practice, and are easier to debug and more interpretable.

Pre-built Estimators

We provide a range of lattice model architectures as TensorFlow Estimators. The simplest estimator we provide is the calibrated linear model, which learns the best 1-d transformation of each feature (using 1-d lattices), and then combines all the calibrated features linearly. This works well if the training dataset is very small, or there are no complex nonlinear input interactions. Another estimator is a calibrated lattice model. This model combines the calibrated features nonlinearly using a two-layer single lattice model, which can represent complex nonlinear interactions in your dataset. The calibrated lattice model is usually a good choice if you have 2-10 features, but for 10 or more features, we expect you will get the best results with an ensemble of calibrated lattices, which you can train using the pre-built ensemble architectures. Monotonic lattice ensembles can achieve 0.3% -- 0.5% accuracy gain compared to Random Forests [4], and these new TensorFlow lattice estimators can achieve 0.1 -- 0.4% accuracy gain compared to the prior state-of-the-art in learning models with monotonicity [5].

Build Your Own

You may want to experiment with deeper lattice networks or research using partial monotonic functions as part of a deep neural network or other TensorFlow architecture. We provide the building blocks: TensorFlow operators for calibrators, lattice interpolation, and monotonicity projections. For example, the figure below shows a 9-layer deep lattice network [5].

Example of a 9-layer deep lattice network architecture [5], alternating layers of linear embeddings and ensembles of lattices with calibrators layers (which act like a sum of ReLU’s in Neural Networks). The blue lines correspond to monotonic inputs, which is preserved layer-by-layer, and hence for the entire model. This and other arbitrary architectures can be constructed with TensorFlow Lattice because each layer is differentiable.

In addition to the choice of model flexibility and standard L1 and L2 regularization, we offer new regularizers with TensorFlow Lattice:
  • Monotonicity constraints [3] on your choice of inputs as described above.
  • Laplacian regularization [3] on the lattices to make the learned function flatter.
  • Torsion regularization [3] to suppress un-necessary nonlinear feature interactions.
We hope TensorFlow Lattice will be useful to the larger community working with meaningful semantic inputs. This is part of a larger research effort on interpretability and controlling machine learning models to satisfy policy goals, and enable practitioners to take advantage of their prior knowledge. We’re excited to share this with all of you. To get started, please check out our GitHub repository and our tutorials, and let us know what you think!

By Maya Gupta, Research Scientist, Jan Pfeifer, Software Engineer and Seungil You, Software Engineer


Developing and open sourcing TensorFlow Lattice was a huge team effort. We’d like to thank all the people involved: Andrew Cotter, Kevin Canini, David Ding, Mahdi Milani Fard, Yifei Feng, Josh Gordon, Kiril Gorovoy, Clemens Mewald, Taman Narayan, Alexandre Passos, Christine Robson, Serena Wang, Martin Wicke, Jarek Wilkiewicz, Sen Zhao, Tao Zhu


[1] Lattice Regression, Eric Garcia, Maya Gupta, Advances in Neural Information Processing Systems (NIPS), 2009
[2] Optimized Regression for Efficient Function Evaluation, Eric Garcia, Raman Arora, Maya R. Gupta, IEEE Transactions on Image Processing, 2012
[3] Monotonic Calibrated Interpolated Look-Up Tables, Maya Gupta, Andrew Cotter, Jan Pfeifer, Konstantin Voevodski, Kevin Canini, Alexander Mangylov, Wojciech Moczydlowski, Alexander van Esbroeck, Journal of Machine Learning Research (JMLR), 2016
[4] Fast and Flexible Monotonic Functions with Ensembles of Lattices, Mahdi Milani Fard, Kevin Canini, Andrew Cotter, Jan Pfeifer, Maya Gupta, Advances in Neural Information Processing Systems (NIPS), 2016
[5] Deep Lattice Networks and Partial Monotonic Functions, Seungil You, David Ding, Kevin Canini, Jan Pfeifer, Maya R. Gupta, Advances in Neural Information Processing Systems (NIPS), 2017

Google Code-in 2017 is seeking organization applications

Monday, October 9, 2017

We are now accepting applications for open source organizations who want to participate in Google Code-in 2017. Google Code-in, a global online contest for pre-university students ages 13-17, invites students to learn by contributing to open source software.

Working with young students is a special responsibility and each year we hear inspiring stories from mentors who participate. To ensure these new, young contributors have a great support system, we select organizations that have gained experience in mentoring students by previously taking part in Google Summer of Code.

Organizations must apply before Tuesday, October 24 at 16:00 UTC.

17 organizations were accepted last year, and over the last 7 years, 4,553 students from 99 different countries have completed more than 23,651 tasks for participating open source projects. Tasks fall into 5 categories:

  • Code: writing or refactoring 
  • Documentation/Training: creating/editing documents and helping others learn more
  • Outreach/Research: community management, outreach/marketing, or studying problems and recommending solutions
  • Quality Assurance: testing and ensuring code is of high quality
  • User Interface: user experience research or user interface design and interaction

Once an organization is selected for Google Code-in 2017 they will define these tasks and recruit mentors who are interested in providing online support for students.

You can find a timeline, FAQ and other information about Google Code-in on our website. If you’re an educator interested in sharing Google Code-in with your students, you can find resources here.

By Josh Simmons, Google Open Source

Announcing more Open Source Peer Bonus winners

Tuesday, October 3, 2017

We’re excited to announce 2017’s second round of Open Source Peer Bonus winners. Google Open Source established this program six years ago to encourage Googlers to recognize and celebrate external contributors to the open source ecosystem Google depends on.

The Open Source Peer Bonus program works like this: Googlers nominate open source contributors outside of the company who deserve recognition for their contributions to open source projects, including those used by Google. Nominees are reviewed by a volunteer team of engineers and the winners receive our heartfelt thanks and a small token of our appreciation.

To date, we’ve recognized nearly 600 open source contributors from dozens of countries who have contributed their time and talent to more than 400 open source projects. You can find past winners in recent blog posts: Fall 2016, Spring 2017.

Without further ado, we’d like to recognize the latest round of winners and the projects they worked on. Here are the individuals who gave us permission to thank them publicly:

Name Project Name Project
Mo JangdaAMP ProjectEric TangMaterial Motion
Osvaldo LopezAMP ProjectNicholas Tollerveymicro:bit, Mu
Jason JeanAngular CLIDamien GeorgeMicroPython
Henry ZhuBabelTom SpilmanMonoGame
Oscar BoykinBazel Scala rulesArthur EdgeNARKOZ/gitlab
Francesc AltedBloscSebastian BergNumPy
Matt HoltCaddyBogdan-Andrei IancuOpenSIPS
Martijn CroonenChromiumAmit AmbastaOR-tools
Raphael CostaChromiumMichael PowellOR-tools
Mariatta WijayaCPythonWestbrook JohnsonPolymer
Victor StinnerCPythonMarten Seemannquic-go
Derek ParkerDelveFabian HennekeSecure Shell
Thibaut CouroubledevdocsChris FillmoreShaka Player
David Lechnerev3devTakeshi KomiyaSphinx
Michael NiedermayerFFmpegDan KennedySQLite
Mathew HuuskoFirebaseJoe MistachkinSQLite
Armin RonacherFlaskRichard HippSQLite
Nenad StojanovskiForseti SecurityYuxin WuTensorpack
Solly RossHeapsterMichael Herzogthree.js
Bjørn Erik PedersenHugoTakahiro Aoyagithree.js
Brion VibberJS-InterpreterJelle ZijlstraTypeshed
Xiaoyu ZhangKubernetesVerónica LópezWomen Who Go
Anton KachurinMaterial Components for the Web

Thank you all so much for your contributions to the open source community and congratulations on being selected!

By Maria Webb, Google Open Source