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Title: Meta-Learning Neural Bloom Filters

Paper content:
There has been a recent trend in training neural networks to replace data structures that have been crafted by hand, with an aim for faster execution, better accuracy, or greater compression.
In this setting, a neural data structure is instantiated by training a network over many epochs of its inputs until convergence.
In many applications this expensive initialization is not practical, for example streaming algorithms --- where inputs are ephemeral and can only be inspected a small number of times.
In this paper we explore the learning of approximate set membership over a stream of data in one-shot via meta-learning.
We propose a novel memory architecture, the Neural Bloom Filter, which we show to be more compressive than Bloom Filters and several existing memory-augmented neural networks in scenarios of skewed data or structured sets.
One of the simplest questions one can ask of a set of data is whether or not a given query is contained within it.
Is q, our query, a member of S, our chosen set of observations?
This set membership query arises across many computing domains; from databases, network routing, and firewalls.
One could query set membership by storing S in its entirety and comparing q against each element.
However, more space-efficient solutions exist.The original and most widely implemented approximate set membership data-structure is the Bloom Filter BID2 .
It works by storing sparse distributed codes, produced from randomized hash functions, within a binary vector.
The Bloom-filter trades off space for an allowed false positive rate, which arises due to hash collisions.
However its error is one-sided; if an element q is contained in S then it will always be recognized.
It never emits false negatives.One can find Bloom Filters embedded within a wide range of production systems; from network security BID16 , to block malicious IP addresses; databases, such as Google's Bigtable BID7 , to avoid unnecessary disk lookups; cryptocurrency BID19 , to allow clients to filter irrelevant transactions; search, such as Facebook's typeahead search BID0 , to filter pages which do not contain query prefixes; and program verification BID13 , to avoid recomputation over previously observed states.While the main appeal of Bloom Filters is favourable compression, another important quality is the support for dynamic updates.
New elements can be inserted in O(1) time.
This is not the case for all approximate set membership data structures.
For example, perfect hashing saves ≈ 40% space over Bloom Filters but requires a pre-processing stage that is polynomial-time in the number of elements to store BID12 .
Whilst the static set membership problem is interesting, it limits the applicability of the algorithm.
For example, in a database application that is serving a high throughput of write operations, it may be intractable to regenerate the full data-structure upon each batch of writes.We thus focus on the data stream computation model BID27 , where input observations are assumed to be ephemeral and can only be inspected a constant number of timesusually once.
This captures many real-world applications: network traffic analysis, database query serving, and reinforcement learning in complex domains.
Devising an approximate set membership data structure that is not only more compressive than Bloom Filters, but can be applied to either dynamic or static sets, could have a significant performance impact on modern computing applications.
In this paper we investigate this problem using memory-augmented neural networks and meta-learning.We build upon the recently growing literature on using neural networks to replace algorithms that are configured by heuristics, or do not take advantage of the data distribution.
For example, Bloom Filters are indifferent to the data distribution.
They have near-optimal space efficiency when data is drawn uniformly from a universe set BID5 (maximal-entropy case) but (as we shall show) are sub-optimal when there is more structure.
Prior studies on this theme have investigated compiler optimization BID11 , computation graph placement , and data index structures such as b-trees BID22 .In
the latter work, BID22 explicitly consider the problem of static set membership. By
training a neural network over a fixed S (URLs from Google's Transparency Report) with negative examples in the form of held-out URLs, they observe 36% space reduction over a conventional Bloom Filter 1 . Crucially
this requires iterating over the storage set S a large number of times to embed its salient information into the weights of a neural network classifier. For a new
S this process would have to be repeated from scratch.Instead of learning from scratch, we draw inspiration from the few-shot learning advances obtained by meta-learning memory-augmented neural networks BID30 BID34 . In this setup
, tasks are sampled from a common distribution and a network learns to specialize to (learn) a given task with few examples. This matches
very well to applications where many Bloom Filters are instantiated over different subsets of a common data distribution. For example,
a Bigtable database usually contains one Bloom Filter per SSTable file. For a large
table that contains Petabytes of data, say, there can be over 100, 000 separate instantiated data-structures which share a common row key format and query distribution. Meta-learning
allows us to exploit this common redundancy.The main contributions of this paper are (1) A new sparse memory-augmented neural network architecture, the Neural Bloom Filter, which learns to write to memory using a distributed write scheme, and (2) An empirical evaluation of the Neural Bloom Filter meta-learned on one-shot approximate set membership problems of varying structure.We compare with the classical Bloom Filter alongside other memory-augmented neural networks such as the Differentiable Neural Computer and Memory Networks BID33 . We find when
there is no structure, that differentiates the query set elements and queries, the Neural Bloom Filter learns a solution similar to a Bloom Filter derivative (a Bloom-g filter BID28 ), but when there is a lot of structure the solution can be considerably more space-efficient.
In many situations neural networks are not a suitable replacement to Bloom Filters and their variants.
The Bloom Filter is robust to changes in data distribution, and adversarial attacks, because it delivers a bounded false positive rate for any sampled subset, unlike a neural network.
However in this paper we consider the questions, "When might a neural network provide better compression than a Bloom Filter?" and "What kind of neural architecture is practical?".
We see that a model which uses an external memory with an adaptable capacity, avoids BPTT with a feed-forward write scheme, and learns to address its memory, is the most promising option in contrast to popular memory models such as DNCs and LSTMs.
We term this model the Neural Bloom Filter due to the analogous incorporation of a hashing scheme, commutative write scheme, and multiplicative read mechanism.The Neural Bloom Filter relies on settings where cost of learning to query is possible and will be a net benefit to a population of existing bloom filters.
That is, because we rely on meta-learning, we need situations where we have an off-line dataset (both of stored elements and queries) that is similar enough to future data that we wish to store.
In the case of a large database we think this is warranted, a database with 100, 000 separate set membership data structures will benefit from a single (or periodic) meta-learning training routine that can run on a single machine and sample from the currently stored data, generating a large number of efficient data-structures.
We envisage the space cost of the network to be amortized by sharing it across many neural bloom filters, and the time-cost of executing the network to be offset by the continuous acceleration of dense linear algebra on modern hardware, and the ability to batch writes and queries efficiently.
A promising future direction would be to investigate the feasibility of this approach in a production system.

assistant: text: We investigate the space efficiency of memory-augmented neural nets when learning set membership.