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Title: Adaptive Posterior Learning: few-shot learning with a surprise-based memory module

Paper content:
The ability to generalize quickly from few observations is crucial for intelligent systems.
In this paper we introduce APL, an algorithm that approximates probability distributions by remembering the most surprising observations it has encountered.
These past observations are recalled from an external memory module and processed by a decoder network that can combine information from different memory slots to generalize beyond direct recall.
We show this algorithm can perform as well as state of the art baselines on few-shot classification benchmarks with a smaller memory footprint.
In addition, its memory compression allows it to scale to thousands of unknown labels.
Finally, we introduce a meta-learning reasoning task which is more challenging than direct classification.
In this setting, APL is able to generalize with fewer than one example per class via deductive reasoning.
Consider the following sequential decision problem: at every iteration of an episode we are provided with an image of a digit (e.g. MNIST) and an unknown symbol.
Our goal is to output a digit Y = X + S where X is the value of the MNIST digit, and S is a numerical value that is randomly assigned to the unknown symbol at the beginning of each episode.
After seeing only a single instance of a symbol an intelligent system should not only be able to infer the value S of the symbol but also to correctly generalize the operation associated with the symbol to any other digit in the remaining iterations of that episode.Despite its simplicity, this task emphasizes three cognitive abilities that a generic learning algorithm should display:
1. the algorithm can learn a behaviour and then flexibly apply it to a range of different tasks using only a few context observations at test time;
2. the algorithm can memorize and quickly recall previous experiences for quick adaptation; and
3. the algorithm can process these recalled memories in a non-trivial manner to carry out tasks that require reasoning.The first point is commonly described as "learning to learn" or meta-learning, and represents a new way of looking at statistical inference BID22 BID2 BID1 .
Traditional neural networks are trained to approximate arbitrary probability distributions with great accuracy by parametric adaptation via gradient descent BID13 BID23 .
After training that probability distribution is fixed and neural networks can only generalize well when the testing distribution matches the training distribution BID16 .
In contrast, meta-learning systems are trained to learn an algorithm that infers a function directly from the observations it receives at test time.
This setup is more flexible than the traditional approach and generalizes better to unseen distributions as it incorporates new information even after the training phase is over.
It also allows these models to improve their accuracy as they observe more data, unlike models which learn a fixed distribution.The second requirement -being able to memorize and efficiently recall previous experience -is another active area of research.
Storing information in a model proves especially challenging as we move beyond small toy-examples to tasks with higher dimensional data or real-world problems.Current methods often work around this by summarizing past experiences in one lower-dimensional representation BID7 BID10 or using memory modules BID6 .
While the former approach can produce good results, the representation and therefore the amount of information we can ultimately encode with such models will be of a fixed and thus limited size.
Working with neural memory modules, on the other hand, presents its own challenges as learning to store and keep the right experiences is not trivial.
In order to successfully carry out the task defined at the beginning of this paper a model should learn to capture information about a flexible and unbounded number of symbols observed in an episode without storing redundant information.Finally, reasoning requires processing recalled experiences in order to apply the information they contain to the current data point being processed.
In simple cases such as classification, it is enough to simply recall memories of similar data points and directly infer the current class by combining them using a weighted average or a simple kernel BID26 BID24 , which limits the models to performing interpolation.
In the example mentioned above, more complex reasoning is necessary for human-level generalisation.In this paper we introduce Approximate Posterior Learning (APL, pronounced like the fruit), a self-contained model and training procedure that address these challenges.
APL learns to carry out few-shot approximation of new probability distributions and to store only as few context points as possible in order to carry out the current task.
In addition it learns how to process recalled experiences to carry out tasks of varying degrees of complexity.
This sequential algorithm was inspired by Bayesian posterior updating BID8 in the sense that the output probability distribution is updated as more data is observed.We demonstrate that APL can deliver accuracy comparable to other state-of-the-art algorithms in standard few-shot classification benchmarks while being more data efficient.
We also show it can scale to a significantly larger number of classes while retaining good performance.
Finally, we apply APL to the reasoning task introduced as motivation and verify that it can perform the strong generalization we desire.The main contributions of this paper are:• A simple memory controller design which uses a surprise-based signal to write the most predictive items to memory.
By not needing to learn what to write, we avoid costly backpropagation through memory which makes the setup easier and faster to train.
This design also minimizes how much data is stored, making our method more memory efficient.•
An integrated external and working memory architecture which can take advantage of the best of both worlds: scalability and sparse access provided by the working memory; and all-to-all attention and reasoning provided by a relational reasoning module.•
A training setup which steers the system towards learning an algorithm which approximates the posterior without backpropagating through the whole sequence of data in an episode.
We introduced a self-contained system which can learn to approximate a probability distribution with as little data and as quickly as it can.
This is achieved by putting together the training setup which encourages adaptation; an external memory which allows the system to recall past events; a writing system to adapt the memory to uncertain situations; and a working memory architecture which can efficiently compare items retrieved from memory to produce new predictions.We showed that the model can:• Reach state of the art accuracy with a smaller memory footprint than other meta-learning models by efficiently choosing which data points to remember.•
Scale to very large problem sizes thanks to the use of an external memory module with sparse access.•
Perform fewer than 1-shot generalization thanks to relational reasoning across neighbors.

assistant: text: We introduce a model which generalizes quickly from few observations by storing surprising information and attending over the most relevant data at each time point.