### Introduction

* Knowledge Bases (KBs) are effective tools for Question Answering (QA) but are often too restrictive (due to fixed schema) and too sparse (due to limitations of Information Extraction (IE) systems).
* The paper proposes Key-Value Memory Networks, a neural network architecture based on [Memory Networks](https://gist.github.com/shagunsodhani/c7a03a47b3d709e7c592fa7011b0f33e) that can leverage both KBs and raw data for QA.
* The paper also introduces MOVIEQA, a new QA dataset that can be answered by a perfect KB, by Wikipedia pages and by an imperfect KB obtained using IE techniques thereby allowing a comparison between systems using any of the three sources.
* [Link to the paper](https://arxiv.org/abs/1606.03126).

### Related Work

* TRECQA and WIKIQA are two benchmarks where systems need to select the sentence containing the correct answer, given a question and a list of candidate sentences. 
* These datasets are small and make it difficult to compare the  systems using different sources.
* Best results on these benchmarks are reported by CNNs and RNNs with attention mechanism.

### Key-Value Memory Networks

* Extension of [Memory Networks Model](https://gist.github.com/shagunsodhani/c7a03a47b3d709e7c592fa7011b0f33e).
* Generalises the way context is stored in memory.
* Comprises of a memory made of slots in the form of pair of vectors $(k_{1}, v_{1})...(k_{m}, v_{m})$ to encode long-term and short-term context.

#### Reading the Memory

* **Key Hashing** - Question, *x* is used to preselect a subset of array $(k_{h1}, v_{h1})...(k_{hN}, v_{hN})$ where the key shares atleast one word with *x* and frequency of the words is less than 1000.
* **Key Addresing** - Each candidate memory is assigned a relevance probability:
    * $p_hi$ = softmax($Aφ_X(x).Aφ_K (k_{hi}))$
    * φ is a feature map of dimension *D* and *A* is a *dxD* matrix.
* **Value Reading** - Value of memories are read by taking their weighted sum using addressing probabilites and a vector *o* is returned.
* $o = sum(p_{hi} A\phi_V(v_{hi}))$
* Memory access process conducted by "controller" neural network using $q = Aφ_X (x)$ as the query.
* Query is updated using
    * $q_2 = R_1 (q+o)$
* Addressing and reading steps are repeated using new $R_i$ matrices to retrieve more pertinent information in subsequent access.
* After a fixed number of hops, H, resulting state of controller is used to compute a final prediction.
* $a = \text{argmax}(\text{softmax}(q_{H+1}^T B\phi_Y (y_i)))$
where $y_i$ are the possible candidate outputs and $B$ is a $dXD$ matrix.
* The network is trained end-to-end using a cross entropy loss, backpropogation and stochastic gradient.
* End-to-End Memory Networks can be viewed as a special case of Key-Value Memory Networks by setting key and value to be the same for all the memories.

#### Variants of Key-Value Memories

* $φ_x$ and $φ_y$ - feature map corresponding to query and answer are fixed as bag-of-words representation.

##### KB Triple

* Triplets of the form "subject relation object" can be represented in Key-Value Memory Networks with subject and relation as the key and object as the value.
* In standard Memory Networks, the whole triplet would have to be embedded in the same memory slot.
* The reversed relations "object is_related_to subject" can also be stored.

##### Sentence Level

* A document can be split into sentences with each sentence encoded in the key-value pair of the memory slot as a bag-of-words.

##### Window Level

* Split the document in the windows of W words and represent it as bag-of-words. 
* The window becomes the key and the central word becomes the value.

##### Window + Centre Encoding

* Instead of mixing the window centre with the rest of the words, double the size of the dictionary and encode the centre of the window and the value using the second dictionary.

##### Window + Title

* Since the title of the document could contain useful information, the word window can be encoded as the key and document title as the value.
* The key could be augmented with features like "_window_" and "_title_" to distinguish between different cases.

### MOVIEQA Benchmark

#### Knowledge Representation

* Doc - Raw documents (from Wikipedia) related to movies.
* KB - Graph-based KB made of entities and relations.
* IE - Performing Information Extraction on Wikipedia to create a KB.
* The QA pairs should be answerable by both raw document and KB so that the three approaches can be compared and the gap between the three solutions can be closed.
* The dataset has more than 100000 QA pairs, making it much larger than most existing datasets.

### Experiments

#### MOVIEQA

##### Systems Compared

* [Bordes et al's QA system](TBD)
* [Supervised Embeddings](TBD)(without KB)
* [Memory Networks](TBD)
* Key-Value Memory Networks

##### Observations

* Key-Value Memory Networks outperforms all methods on all data sources.
* KB > Doc > IE
* The best memory representation for directly reading documents uses "Window Level + Centre Encoding + Title".

##### KB vs Synthetic Document Analysis

* Given KB triplets, construct synthetic "Wikipedia" articles using templates, conjunctions and coreferences to determine the causes for the gap in performance when using KB vs doc.
* Loss in One Template sentences are due to the difficulty of extracting subject, relation and object from the artificial docs. 
* Using multiple templates does not deteriorate performance much. But conjunctions and coreferences cause a dip in performance.

#### WIKIQA

* Given a question, select the sentence (from Wikipedia document) that best answers the question.
* Key-Value Memory Networks outperforms all other solutions though it is only marginally better than LDC and attentive models based on CNNs and RNNs.

Zantedschi et al. propose Gaussian data augmentation in conjunction with bounded $\text{ReLU}$ activations as defense strategy against adversarial examples. Here, Gaussian data augmentation refers to the practice of adding Gaussian noise to the input during training.

Luo et al. Propose a method to compute less-perceptible adversarial examples compared to standard methods constrained in $L_p$ norms. In particular, they consider the local variation of the image and argue that humans are more likely to notice larger variations in low-variance regions than vice-versa. The sensitivity of a pixel is therefore defined as one over its local variance, meaning that it is more sensitive to perturbations. They propose a simple algorithm which iteratively sorts pixels by their sensitivity and then selects a subset to perturb each step. Personally, I wonder why they do not integrate the sensitivity into simple projected gradient descent attacks, where a Lagrange multiplier is used to enforce the $L_p$ norm of the sensitivity weighted perturbation. However, qualitative results show that their approach also works well and results in (partly) less perceptible changes, see Figure 1.

https://i.imgur.com/M7Ile8Y.png
Figure 1: Qualitative results including a comparison to other state-of-the-art attacks.

Also find this summary at [davidstutz.de](https://davidstutz.de/category/reading/).

Meng and Chen propose MagNet, a combination of adversarial example detection and removal. At test time, given a clean or adversarial test image, the proposed defense works as follows: First, the input is passed through one or multiple detectors. If one of these detectors fires, the input is rejected. To this end, the authors consider detection based on the reconstruction error of an auto-encoder or detection based on the divergence between probability predictions (on adversarial vs. clean example). Second, if not rejected, the input is passed through a reformed. The reformer reconstructs the input, e.g., through an auto-encoder, to remove potentially undetected adversarial noise.

Also find this summary at [davidstutz.de](https://davidstutz.de/category/reading/).

The paper introduces a new framework called Spark which focuses on use cases where MapReudce fails. While a lot of applications fit the MapReduce’s acyclic data flow model, there are use cases requiring iterative jobs where MapReduce is not greatly efficient. Many machine learning algorithms fall into this category. Secondly with MapReduce, each query incurs a significant overhead because it is effectively a different job each time. So MapReduce is not the ideal solution for doing interactive analysis. This is the space which Spark intends to fill in. Spark is implemented in Scala and now supports API in Java, Python, and R

#### Programming Model
The model supports RDDs, parallel operations and 2 type of shared variables. A driver program implements the high-level control flow and launches different operations in parallel.

Resilient Distributed Datasets (RDDs) are a read-only collection of objects, partitioned across a set of machines in a cluster. A handle to RDD contains enough information to compute the RDD from data in case of partition failure. RDDs can be constructed:

1. From a file in a Hadoop supported file system.
2. By “parallelizing” a Scala collection.
3. By transforming an existing RDD using operations like flatMap, map, and filter.
4. By changing persistence of an existing RDD.

flatMap, map and filter are standard operations as supported by various functional programming languages. For example map will take as input a list of items and return a new list of items after applying a function to each item of the original list.

RDDs are lazy and ephemeral. They are constructed on demand and discarded after use. The persistence can be changed to cache which means they are still lazy but are kept in memory (or disk if they can not fit memory) or to save where they are saved to disk only.

Some supported parallel operations(at time of writing the paper) include:

1. reduce: Combines dataset elements using an associative function to produce a result at the driver program.
2. collect: Sends all elements of the dataset to the driver program.
3. foreach: Passes each element through a user-provided function

Since the paper was authored, Spark has come a long way and support much more transformations (sample, union, distinct, groupByKey, reduceByKey, sortByKey, join, cartesian, etc), parallel operations (shuffle, count, first, take, takeSample etc), and persistence options (memory only, memory and disk, disk only, memory only serialized, etc).

Spark supports 2 kinds of shared variables:

Broadcast variables — These are read-only variables that are distributed to worker nodes for once and can be used multiple times (for reading). A use case of this variable would be training data which can be sent to all the worker nodes once and can be used for learning different models instead of sending the same data with each model.

Accumulators — These variables are also shared with workers, the different being that the driver program can only read them and workers can perform only associative operations on them. A use case could be when we want to count the total number of entries in a data set, each worker fills up its count accumulator and sends it to the driver which adds up all the received values.

#### Implementation
The core of Spark is the implementation of RDDs. Suppose we start by reading a file, then filtering the lines to get lines with the word “ERROR” in them, then we cache the results and then count the number of such lines using the standard map-reduce trick. RDDs will be formed corresponding to each of these steps and these RDDs will be stored as a link-list to capture the lineage of each RDD.

https://cdn-images-1.medium.com/max/800/1*6I7aiD2bPrsw32U76Q5q2g.png

Lineage chain for distributed dataset objects
Each RDD contains a pointer to its parent and information about how it was transformed. This lineage information is sufficient to reconstruct any lost partition and checkpointing of any kind is not required. There is no overhead if no node fails and even if some nodes fails, only select RDDs need to be reconstructed.

Internally an RDD object implements a simple interface consisting of three operations:

1. getPartitions, which returns a list of partition IDs.
2. getIterator(partition), which iterates over a partition.
3. getPreferredLocations(partition), which is used for task scheduling to achieve data locality.

Spark is similar to MapReduce — it sends computation to data instead of the other way round. This requires shipping closures to workers — closures to define and process a distributed dataset. This is easy given Scala uses Java serialization. However unlike MapReduce, operations are performed on RDDs that can persist across operations.

Shared variables are implemented using classes with custom serialization formats. When a broadcast variable b is created with a value v, v is saved to a file in the shared file system. The serialized form of b is a path to this file. When b’s value is queried, Spark checks if v is in the local cache. If not, it is read from the file system. For accumulators, each accumulator is given a unique ID upon creation and its serialized form contains its ID and the “zero” value. On the workers, a separate copy of the accumulator is created for each thread and is reset to “zero” value. Once the task finishes, the updated value is sent to the driver program.

#### Future Work
The paper describes how an early stage implementation performs on Logistic Regression, Alternating Least Square, and interactive mode. The results seem to outperform MapReduce largely because of caching the results of previous computations. This makes Spark a good alternative for use cases where same data is read into memory again and again (iterative jobs fit the category.) Spark has come a long way since the paper was written. It now supports libraries for handling SQL-like queries (SparkSQL), streaming data (Spark streaming), graphs (GraphX) and machine learning (MLlib) along with more transformations and parallel operations. I came across Spark while working at Adobe Analytics and have been reading about it to learn more. The cool thing about Spark is that it supports interactive analysis and has APIs in Python, R and Java thus making it easy to adopt. While I have not done some much work around Spark, I am looking forward to making something on top of it.