Connect with us

AI

Navigating with grid-like representations in artificial agents

Most animals, including humans, are able to flexibly navigate the world they live in exploring new areas, returning quickly to remembered places, and taking shortcuts. Indeed, these abilities feel so easy and natural that it is not immediately obvious how complex the underlying processes really are. In contrast, spatial navigation remains a substantial challenge for artificial agents whose abilities are far outstripped by those of mammals.In 2005, a potentially crucial part of the neural circuitry underlying spatial behaviour was revealed by an astonishing discovery: neurons that fire in a strikingly regular hexagonal pattern as animals explore their environment. This lattice of points is believed to facilitate spatial navigation, similarly to the gridlines on a map. In addition to equipping animals with an internal coordinate system, these neurons – known as grid cells – have recently been hypothesised to support vector-based navigation. That is: enabling the brain to calculate the distance and direction to a desired destination, as the crow flies, allowing animals to make direct journeys between different places even if that exact route had not been followed before.The group that first discovered grid cells was jointly awarded the 2014 Nobel Prize in Physiology or Medicine for shedding light on how cognitive representations of space might work.

Published

on

More broadly, our work reaffirms the potential of utilising algorithms thought to be used by the brain as inspiration for machine learning architectures. The extensive previous neuroscience research into grid cells makes the agent’s interpretability – which is itself a major topic in AI research – significantly easier, by giving us clues about what to look for when trying to understand its internal representations. The work also showcases the potential of using artificial agents actively engaging in complex behaviours within realistic virtual environments to test theories of how the brain works.

Taking this principle further, a similar approach could be used to test theories concerning brain areas that are important for perceiving sound or controlling limbs, for example. In the future such networks may well provide a new way for scientists to conduct ‘experiments’, suggesting new theories and even complementing some of the work that is currently conducted in animals.

UPDATE 14.05.18: We’d encourage you to read The emergence of grid-like representations by training recurrent neural networks to perform spatial localization by Cueva and Wei, which was published contemporaneously at ICLR. While different in scope and findings, it shows interesting results. In brief, the authors found periodic firing that conformed to the shape of the enclosure, e.g rectangular grids in a square environment and triangular in a triangular environment (fig. 2 of Cueva and Wei). This differs from our study, where we found grid-like units whose firing pattern closely resembles rodent grid cells which typically show hexagonal firing patterns across different shaped environments (e.g. square and circular arena).

This work was done by Andrea Banino, Caswell Barry, Benigno Uria, Charles Blundell, Timothy Lillicrap, Piotr Mirowski, Alexander Pritzel, Martin Chadwick, Thomas Degris, Joseph Modayil, Greg Wayne, Hubert Soyer, Fabio Viola, Brian Zhang, Ross Goroshin, Neil Rabinowitz, Razvan Pascanu, Charlie Beattie, Stig Petersen, Amir Sadik, Stephen Gaffney, Helen King, Koray Kavukcuoglu, Demis Hassabis, Raia Hadsell, and Dharshan Kumaran.


Read the Nature paper: [PDF]

Download the original paper (unformatted): [PDF]

Read Nobel Prize Laureate Edvard Moser’s review of the paper.

Source: https://deepmind.com/blog/article/grid-cells

AI

Graph Convolutional Networks (GCN)

In this post, we’re gonna take a close look at one of the well-known graph neural networks named Graph Convolutional Network (GCN). First, we’ll get the intuition to see how it works, then we’ll go deeper into the maths behind it. Why Graphs? Many problems are graphs in true nature. In our world, we see many data are graphs, […]

The post Graph Convolutional Networks (GCN) appeared first on TOPBOTS.

Published

on

graph convolutional networks

In this post, we’re gonna take a close look at one of the well-known graph neural networks named Graph Convolutional Network (GCN). First, we’ll get the intuition to see how it works, then we’ll go deeper into the maths behind it.

Why Graphs?

Many problems are graphs in true nature. In our world, we see many data are graphs, such as molecules, social networks, and paper citations networks.

Tasks on Graphs

  • Node classification: Predict a type of a given node
  • Link prediction: Predict whether two nodes are linked
  • Community detection: Identify densely linked clusters of nodes
  • Network similarity: How similar are two (sub)networks

Machine Learning Lifecycle

In the graph, we have node features (the data of nodes) and the structure of the graph (how nodes are connected).

For the former, we can easily get the data from each node. But when it comes to the structure, it is not trivial to extract useful information from it. For example, if 2 nodes are close to one another, should we treat them differently to other pairs? How about high and low degree nodes? In fact, each specific task can consume a lot of time and effort just for Feature Engineering, i.e., to distill the structure into our features.

graph convolutional network
Feature engineering on graphs. (Picture from [1])

It would be much better to somehow get both the node features and the structure as the input, and let the machine to figure out what information is useful by itself.

That’s why we need Graph Representation Learning.

graph convolutional network
We want the graph can learn the “feature engineering” by itself. (Picture from [1])

If this in-depth educational content on convolutional neural networks is useful for you, you can subscribe to our AI research mailing list to be alerted when we release new material. 

Graph Convolutional Networks (GCNs)

Paper: Semi-supervised Classification with Graph Convolutional Networks (2017) [3]

GCN is a type of convolutional neural network that can work directly on graphs and take advantage of their structural information.

it solves the problem of classifying nodes (such as documents) in a graph (such as a citation network), where labels are only available for a small subset of nodes (semi-supervised learning).

graph convolutional network
Example of Semi-supervised learning on Graphs. Some nodes dont have labels (unknown nodes).

Main Ideas

As the name “Convolutional” suggests, the idea was from Images and then brought to Graphs. However, when Images have a fixed structure, Graphs are much more complex.

graph convolutional network
Convolution idea from images to graphs. (Picture from [1])

The general idea of GCN: For each node, we get the feature information from all its neighbors and of course, the feature of itself. Assume we use the average() function. We will do the same for all the nodes. Finally, we feed these average values into a neural network.

In the following figure, we have a simple example with a citation network. Each node represents a research paper, while edges are the citations. We have a pre-process step here. Instead of using the raw papers as features, we convert the papers into vectors (by using NLP embedding, e.g., tf–idf).

Let’s consider the green node. First off, we get all the feature values of its neighbors, including itself, then take the average. The result will be passed through a neural network to return a resulting vector.

graph convolutional network
The main idea of GCN. Consider the green node. First, we take the average of all its neighbors, including itself. After that, the average value is passed through a neural network. Note that, in GCN, we simply use a fully connected layer. In this example, we get 2-dimension vectors as the output (2 nodes at the fully connected layer).

In practice, we can use more sophisticated aggregate functions rather than the average function. We can also stack more layers on top of each other to get a deeper GCN. The output of a layer will be treated as the input for the next layer.

graph convolutional network
Example of 2-layer GCN: The output of the first layer is the input of the second layer. Again, note that the neural network in GCN is simply a fully connected layer (Picture from [2])

Let’s take a closer look at the maths to see how it really works.

Intuition and the Maths behind

First, we need some notations

Let’s consider a graph G as below.

graph convolutional network
From the graph G, we have an adjacency matrix A and a Degree matrix D. We also have feature matrix X.

How can we get all the feature values from neighbors for each node? The solution lies in the multiplication of A and X.

Take a look at the first row of the adjacency matrix, we see that node A has a connection to E. The first row of the resulting matrix is the feature vector of E, which A connects to (Figure below). Similarly, the second row of the resulting matrix is the sum of feature vectors of D and E. By doing this, we can get the sum of all neighbors’ vectors.

graph convolutional network
Calculate the first row of the “sum vector matrix” AX
  • There are still some things that need to improve here.
  1. We miss the feature of the node itself. For example, the first row of the result matrix should contain features of node A too.
  2. Instead of sum() function, we need to take the average, or even better, the weighted average of neighbors’ feature vectors. Why don’t we use the sum() function? The reason is that when using the sum() function, high-degree nodes are likely to have huge v vectors, while low-degree nodes tend to get small aggregate vectors, which may later cause exploding or vanishing gradients (e.g., when using sigmoid). Besides, Neural networks seem to be sensitive to the scale of input data. Thus, we need to normalize these vectors to get rid of the potential issues.

In Problem (1), we can fix by adding an Identity matrix I to A to get a new adjacency matrix Ã.

Pick lambda = 1 (the feature of the node itself is just important as its neighbors), we have Ã = A + I. Note that we can treat lambda as a trainable parameter, but for now, just assign the lambda to 1, and even in the paper, lambda is just simply assigned to 1.

By adding a self-loop to each node, we have the new adjacency matrix

Problem (2)For matrix scaling, we usually multiply the matrix by a diagonal matrix. In this case, we want to take the average of the sum feature, or mathematically, to scale the sum vector matrix ÃX according to the node degrees. The gut feeling tells us that our diagonal matrix used to scale here is something related to the Degree matrix D̃ (Why , not D? Because we’re considering Degree matrix  of new adjacency matrix Ã, not A anymore).

The problem now becomes how we want to scale/normalize the sum vectors? In other words:

How we pass the information from neighbors to a specific node?

We would start with our old friend average. In this case, D̃ inverse (i.e., D̃^{-1}) comes into play. Basically, each element in D̃ inverse is the reciprocal of its corresponding term of the diagonal matrix D.

For example, node A has a degree of 2, so we multiple the sum vectors of node A by 1/2, while node E has a degree of 5, we should multiple the sum vector of E by 1/5, and so on.

Thus, by taking the multiplication of D̃ inverse and X, we can take the average of all neighbors’ feature vectors (including itself).

So far so good. But you may ask How about the weighted average()?. Intuitively, it should be better if we treat high and low degree nodes differently.

We’re just scaling by rows, but ignoring their corresponding columns (dash boxes)
Add a new scaler for columns.

The new scaler gives us the “weighted” average. What are we doing here is to put more weights on the nodes that have low-degree and reduce the impact of high-degree nodes. The idea of this weighted average is that we assume low-degree nodes would have bigger impacts on their neighbors, whereas high-degree nodes generate lower impacts as they scatter their influence at too many neighbors.

graph convolutional network
When aggregating feature at node B, we assign the biggest weight for node B itself (degree of 3), and the lowest weight for node E (degree of 5)
Because we normalize twice, we change “-1” to “-1/2”

For example, we have a multi-classification problem with 10 classes, F will be set to 10. After having the 10-dimension vectors at layer 2, we pass these vectors through a softmax function for the prediction.

The Loss function is simply calculated by the cross-entropy error over all labeled examples, where Y_{l} is the set of node indices that have labels.

The number of layers

The meaning of #layers

The number of layers is the farthest distance that node features can travel. For example, with 1 layer GCN, each node can only get the information from its neighbors. The gathering information process takes place independentlyat the same time for all the nodes.

When stacking another layer on top of the first one, we repeat the gathering info process, but this time, the neighbors already have information about their own neighbors (from the previous step). It makes the number of layers as the maximum number of hops that each node can travel. So, depends on how far we think a node should get information from the networks, we can config a proper number for #layers. But again, in the graph, normally we don’t want to go too far. With 6–7 hops, we almost get the entire graph which makes the aggregation less meaningful.

graph convolutional network
Example: Gathering info process with 2 layers of target node i

How many layers should we stack the GCN?

In the paper, the authors also conducted some experiments with shallow and deep GCNs. From the figure below, we see that the best results are obtained with a 2- or 3-layer model. Besides, with a deep GCN (more than 7 layers), it tends to get bad performances (dashed blue line). One solution is to use the residual connections between hidden layers (purple line).

graph convolutional network
Performance over #layers. Picture from the paper [3]

Take home notes

  • GCNs are used for semi-supervised learning on the graph.
  • GCNs use both node features and the structure for the training
  • The main idea of the GCN is to take the weighted average of all neighbors’ node features (including itself): Lower-degree nodes get larger weights. Then, we pass the resulting feature vectors through a neural network for training.
  • We can stack more layers to make GCNs deeper. Consider residual connections for deep GCNs. Normally, we go for 2 or 3-layer GCN.
  • Maths Note: When seeing a diagonal matrix, think of matrix scaling.
  • A demo for GCN with StellarGraph library here [5]. The library also provides many other algorithms for GNNs.

Note from the authors of the paper: The framework is currently limited to undirected graphs (weighted or unweighted). However, it is possible to handle both directed edges and edge features by representing the original directed graph as an undirected bipartite graph with additional nodes that represent edges in the original graph.

What’s next?

With GCNs, it seems we can make use of both the node features and the structure of the graph. However, what if the edges have different types? Should we treat each relationship differently? How to aggregate neighbors in this case? What are the advanced approaches recently?

In the next post of the graph topic, we will look into some more sophisticated methods.

graph convolutional network
How to deal with different relationships on the edges (brother, friend,….)?

REFERENCES

[1] Excellent slides on Graph Representation Learning by Jure Leskovec (Stanford):  https://drive.google.com/file/d/1By3udbOt10moIcSEgUQ0TR9twQX9Aq0G/view?usp=sharing

[2] Video Graph Convolutional Networks (GCNs) made simple: https://www.youtube.com/watch?v=2KRAOZIULzw

[3] Paper Semi-supervised Classification with Graph Convolutional Networks (2017): https://arxiv.org/pdf/1609.02907.pdf

[4] GCN source code: https://github.com/tkipf/gcn

[5] Demo with StellarGraph library: https://stellargraph.readthedocs.io/en/stable/demos/node-classification/gcn-node-classification.html

This article was originally published on Medium and re-published to TOPBOTS with permission from the author.

Enjoy this article? Sign up for more computer vision updates.

We’ll let you know when we release more technical education.

Continue Reading

AI

Microsoft BOT Framework — Loops

Published

on

Loops is one of the basic programming structure in any programming language. In this article, I would demonstrate Loops within Microsoft BOT framework.

To follow this article clearly, please have a quick read on the basics of the Microsoft BOT framework. I wrote a couple of articles sometime back and the links are below:

Let’s Get Started.

I would be using the example of a TaxiBot described in one of my previous article. The BOT asks some general questions and books a Taxi for the user. In this article, I would be providing an option to the user to choose there preferred cars for the ride. The flow will look like below:

Create a new Dialog Class for Loops

We would need 2 Dialog classes to be able to achieve this task:

  1. SuperTaxiBotDialog.cs: This would be the main dialog class. The waterfall will contains all the steps as defined in the previous article.
  2. ChooseCarDialog.cs: A new dialog class will be created which would allow the user to pick preferred cars. The loop will be defined in this class.

The water fall steps for both the classes could be visualized as:

The complete code base is present on the Github page.

Important Technical Aspects

  • Link between the Dialogs: In the constructor initialization of SuperTaxiBotDialog, add a dialog for ChooseCarDialog by adding the line:
AddDialog(new ChooseCarDialog());

1. 8 Proven Ways to Use Chatbots for Marketing (with Real Examples)

2. How to Use Texthero to Prepare a Text-based Dataset for Your NLP Project

3. 5 Top Tips For Human-Centred Chatbot Design

4. Chatbot Conference Online

  • Call ChooseCarDialog from SuperTaxiBotDialog: SuperTaxiBotDialog calls ChooseCarDialog from the step SetPreferredCars, hence the return statement of the step should be like:
await stepContext.BeginDialogAsync(nameof(ChooseCarDialog), null, cancellationToken);
  • Return the flow back from ChooseCarDialog to SuperTaxiBotDialog: Once the user has selected 2 cars, the flow has to be sent back to SuperTaxiBotDialog from the step LoopCarAsync. This should be achieved by ending the ChooseCarDialog in the step LoopCarAsync.
return await stepContext.EndDialogAsync(carsSelected, cancellationToken);

The complete code base is present on the Github page.

Once the project is executed using BOT Framework Emulator, the output would look like:

Hopefully, this article will help the readers in implementing a loop with Microsoft BOT framework. For questions: Hit me.

Regards

Tarun

Source: https://chatbotslife.com/microsoft-bot-framework-loops-fe415f0e7ca1?source=rss—-a49517e4c30b—4

Continue Reading

AI

The Bleeding Edge of Voice

This fall, a little known event is starting to make waves. As COVID dominates the headlines, an event called “Voice Launch” is pulling…

Published

on

Tapaan Chauhan

This fall, a little known event is starting to make waves. As COVID dominates the headlines, an event called “Voice Launch” is pulling together an impressive roster of start-ups and voice tech companies intending to uncover the next big ideas and start-ups in voice.

While voice tech has been around for a while, as the accuracy of speech recognition improves, it moves into its prime. “As speech recognition moves from 85% to 95% accuracy, who will use a keyboard anymore?” says Voice Launch organizer Eric Sauve. “And that new, more natural way to interact with our devices will usher in a series of technological advances,” he added.

Voice technology is something that has been dreamt of and worked on for decades all over the world. Why? Well, the answer is very straightforward. Voice recognition allows consumers to multitask by merely speaking to their Google Home, Amazon Alexa, Siri, etc. Digital voice recording works by recording a voice sample of a person’s speech and quickly converting it into written texts using machine language and sophisticated algorithms. Voice input is just the more efficient form of computing, says Mary Meeker in her ‘Annual Internet Trends Report.’ As a matter of fact, according to ComScore, 50% of all searches will be done by voice by 2020, and 30% of searches will be done without even a screen, according to Gartner. As voice becomes a part of things we use every day like our cars, phones, etc. it will become the new “norm.”

The event includes a number of inspiration sessions meant to help start-ups and founders pick the best strategies. Companies presenting here include industry leaders like Google and Amazon and less known hyper-growth voice tech companies like Deepgram and Balto and VCs like OMERS Ventures and Techstars.

But the focus of the event is the voice tech start-ups themselves, and this year’s event has some interesting participants. Start-ups will pitch their ideas, and the audience will vote to select the winners. The event is a cross between a standard pitchfest and Britain’s Got Talent.

Source: https://chatbotslife.com/the-bleeding-edge-of-voice-67538bd859a9?source=rss—-a49517e4c30b—4

Continue Reading
AI3 hours ago

Graph Convolutional Networks (GCN)

AI4 hours ago

Microsoft BOT Framework — Loops

AI4 hours ago

The Bleeding Edge of Voice

AI19 hours ago

Using Amazon SageMaker inference pipelines with multi-model endpoints

AI19 hours ago

Using Amazon SageMaker inference pipelines with multi-model endpoints

AI19 hours ago

Using Amazon SageMaker inference pipelines with multi-model endpoints

AI19 hours ago

Using Amazon SageMaker inference pipelines with multi-model endpoints

AI19 hours ago

Using Amazon SageMaker inference pipelines with multi-model endpoints

AI19 hours ago

Using Amazon SageMaker inference pipelines with multi-model endpoints

AI19 hours ago

Using Amazon SageMaker inference pipelines with multi-model endpoints

AI19 hours ago

Using Amazon SageMaker inference pipelines with multi-model endpoints

AI19 hours ago

Using Amazon SageMaker inference pipelines with multi-model endpoints

AI19 hours ago

Using Amazon SageMaker inference pipelines with multi-model endpoints

AI19 hours ago

Using Amazon SageMaker inference pipelines with multi-model endpoints

AI19 hours ago

Using Amazon SageMaker inference pipelines with multi-model endpoints

AI19 hours ago

Using Amazon SageMaker inference pipelines with multi-model endpoints

AI19 hours ago

Using Amazon SageMaker inference pipelines with multi-model endpoints

AI19 hours ago

Using Amazon SageMaker inference pipelines with multi-model endpoints

AI19 hours ago

Using Amazon SageMaker inference pipelines with multi-model endpoints

AI19 hours ago

Using Amazon SageMaker inference pipelines with multi-model endpoints

Trending