Talk by Simon Hughes at the Haystack search conference in 2019. Discussing how to implement semantic search within an inverted index using vectors.

1. Searching with Vectors
Simon Hughes
Chief Data Scientist, Dice.com
Twitter: @hughes_meister

2. Who Am I?
• Chief Data Scientist at DHI (owns Dice.com)
• Key Projects:
• Search and Match
• Dice Recommender Systems
• Dice Job Search
• Dice Talent Search 3.0 and 4.0
• Dice Skill Center
• Dice Career Advisory Pages
• Dice Salary Predictor
• Dice Career Paths
• PhD Candidate DePaul University
• Subject Area – Machine Learning and NLP
• Thesis – Extracting Causal Relations from Scientific Essays
• Contact Info:
• Email: simon.hughes@dhigroupinc.com
• Twitter: https://twitter.com/hughes_meister

3. Motivation
• Dice.com - leading US technology professional job board
• Jobs marketplace
• We connect technology talent with employers
• High quality searching and matching are critical to our value proposition, for both our customers
and our clients
• Need – high quality content-based recommender engine
• Automatically determine how well a job seeker matches a particular position, and vice versa
• Requirements:
• A semantic matching engine – goes beyond keyword search, to extracting semantic
information from job postings and resume
• Deployed at scale using existing search infrastructure (Solr and ElasticSearch)
• Github Repository for Talk:
• https://github.com/DiceTechJobs/VectorsInSearch

4. Agenda
• Why a Vector Representation?
• Learning Vector Representations
• Vector Based Search in an Inverted Index

5. Understanding Textual Data
Key Challenges:
• Synonymy – Multiple Words with the Same Meaning
• Related – typos, miss-spellings, acronyms, metonyms
• E.g. QA, Quality Assurance, Tester
• Polysemy – Ambiguity, a word has multiple meanings
• E.g. Bank, Book, Ape
• Hypernyms/Hyponyms – ‘type of’ relationships
• E.g. a dog (hyponym) is a type of animal (hypernym)
• Meronyms/Holonyms – ‘part of’ relationships
• E.g. finger (meronym) is a ‘part of’ a hand (holonym)
• What Words / Phrases are More Important?
• Named Entity Extraction (NER), Controlled Vocabularies
• Colocation (phrases) detection – e.g. “data scientist” vs “scientist who works with data”
• Stop words
• Term weighting schemes - e.g. tf.idf

6. How to Solve these Problems?
• Map documents and queries to a semantic space
• “From Strings to Things”?
• Google KG marketing
• Map words into concepts / semantics
• From strings to concepts
• How to represent?
Java
Technologies
Big Data Tools
Javascript
Frameworks

7. Representations
Java
• Local representation
• Non distributed
• Sparse
• E.g. one-hot-vector
• One vector component per unique word
• Similar items have different representations

8. Representations
• Distributed Representation
• Dense vector
• Components of the vector represent learned concepts / latent variables
• Similar items have similar representations
• Most existing approaches produce dense vectors
Java
Java
• Local representation
• Non distributed
• Sparse
• E.g. one-hot-vector
• One vector component per unique word
• Similar items have different representations

9. Agenda
• Why a Vector Representation?
• Learning Vector Representations
• Vector Based Search in an Inverted Index

10. The Importance of Context
How do we learn the meaning (semantics) of words?
• Distributional Hypothesis
• Words occurring in similar contexts have similar meanings
• Harris 1954
• “a word is characterized by the company it keeps”
• Firth 1957
• Ignores word order, grammar and syntax
• Latent Relation Hypothesis
• Pairs of words occurring in similar patterns have similar semantic relations
• Turney et al, 2003
• Patterns – X cuts Y, X works with Y, etc
• Word order and grammatical relations matter
• Further reading - Distributional approaches to word meanings

11. Learning Meaning from Context
Bag of Words Approaches – ignore word order
• Latent Models
• Context - Documents
• LSA
• LDA
• Semantic Vector Space Model
• Word Embeddings
• Context – word window
• Word2vec
• Glove
• Simple linear language models
• History - http://blog.aylien.com/a-review-of-the-recent-history-of-natural-language-processing/
• For document embeddings
• Average or idf weighted average of word vectors
• Sentence / Document Embeddings
• Context – document + word window
• E.g. Doc2vec
• Context – surrounding sentences
• E.g. skip-thought vectors

12. Word2Vec
• By Aelu013 [CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0) ], from Wikimedia Commons

13. Limitations of BOW Approaches:
• Shallow representation
• Word embeddings – limited to the word level
• Latent models – document level but doesn’t encode relational information
• Synonymy - learn relatedness, not true synonyms
• E.g. Antonyms have similar vectors
• Polysemy – cannot encode different meanings of same word
• Global model not a local model

14. Beyond BOW - Deep Language Models
• Deep Language Model Embeddings
• Derived from the internal state of a deep LM
• Learns deep representation of sequences of
words in context
• Can adjust word vectors based on their current
context
• “NLP’s imagenet moment”
• Achieved state of the art results on many NLP tasks
• Consistently out-perform word embedding models
• Example models - ELMO, BERT, ULMFit, OpenAI
Transformer
• Used for encoding sentences not whole
documents
• Hard to scale

15. Deep Language Models
p(w1,w2,w3, w4,…,wn) = p(wn|w1,w2,…,wn-1)
…..
…..
…..
p(w1) p(w2|W1) p(w3|w1,w2) p(w4|w1,w2,w3)
Begin w1 w2 w3
LSTM LSTM LSTM LSTM

16. Embedding Models for Search
• Word Embedding Approaches
• Cluster Word Embeddings
• “Representing Documents and Queries as Sets of Word Embedded Vectors for Information
Retrieval”
• Clustered word2vec vectors using k-means
• Documents represented as clusters of word vectors
• Query - map query vectors as similarity to cluster centroids
• Out performed Jelinek Mercer LM similarity using VSM
• Average Word Embeddings
• From Chapter 5 of Deep Learning for Search
• Author - Tommaso Teofili
• Query and document represented as average of word2vec vectors
• Computing a weighted average using idf worked best
• Outperformed BM25 using cosine similarity
• BM25 + word2vec – highest NDCG score

17. Embedding Models for Search
• Dual Embedding Space Model (DESM)
• Research from Microsoft
• Extends word2vec
• Learns a dual embedding for queries and documents
• Paper - https://arxiv.org/pdf/1602.01137.pdf
• Evaluation
• Compared BM25, LSA and DESM on Bing Query Log Data
• Metrics - NDCG@1, NDCG@3, NDCG@5
• Results
• LSA and DESM both out-performed BM25
• DESM out-performed LSA
• DESM + BM25 out-performed all other approaches

18. Agenda
• Why a Vector Representation?
• Learning Vector Representations
• Vector Based Search in an Inverted Index

19. Vectors in Search
• Dense Embedding Vector:
• Dense
• D dimensional
• D = 50-1000
• Inverted index:
• Sparse
• Pivoted by term
• V = Vocabulary
• |V| =100k+
• Fast because sparse
[+0.12, -0.34, -0.12, +0.27, +0.63]
Term Posting List
Java 1,5,100,102
.NET 2,4,600,605,1000
C# 2,88,105,800
SQL 130,433,648,899,1200
Html 1,2,10,30,55,202,252,30,598,

20. Searching with Word Embeddings
Approaches for using word embeddings:
• Top N terms
• Expand query using top n terms from model
• Boost expansions by cosine similarity
• Can use as a boost query, a re-rank query or a straight term expansion
• Q = “java developer”^10
OR ”java j2ee developer”^0.91 OR “java architect”^0.89
OR “lead java developer”^0.87 OR “j2ee developer”^0.86
OR “java engineer”^0.86
• Term Clustering
• Cluster embeddings using a clustering algorithm
• E.g. k-means
• Compute different sized clusters, k=100,1000,10000
• Map clusters to tokens and index
• Different fields for each k
• Larger k fields – bigger boost or rely on idf scoring
• Query expands to top clusters, boosted by similarity
• Q = “java developer”^10
OR cluster_k1000:5894^5
OR cluster_k100:23^2.5
OR cluster_k10:8^1.25
• See https://github.com/DiceTechJobs/ConceptualSearch

21. Searching Vectors – k-NN Search
• K-NN search
• Find the k closest neighbors to query vector according to similarity metric
• Usually cosine similarity or Euclidean distance
• Definitions
• D = number of components in the vector
• N = number of documents
• Brute Force Search:
• O(ND) = linear
• What if N AND/OR D is(are) very large?
• Vs. Inverted Index
• Sublinear - makes uses of sparsity of terms
• BTree or Distributed Hash Table lookup for terms, iterate posting list, re-rank
matches - O(n log n)

22. Optimal Vector Representation In An Inverted Index?
What properties would such a representation have?
• For Performance
• Sparse representation necessary to leverage inverted index
• For Relevancy
• Distributed representation
• Each document should be a collection of tokens
• Tokens represent some semantic feature of the space
• Similarity is preserved
• Similar vectors must also be similar under this new representation
• Zipfian distribution of tokens
• “We need a Zipfian Distribution” – John Berryman (Co-author of ‘Relevant Search’)
• Tokenizing Embedding Spaces

23. Zipf’s Law
• The frequency of terms in a
corpus follow a power law
distribution
• Small number of tokens are
very common - filter out
irrelevant docs
• A large number of tokens
are very rare - discriminate
between similar matches
• Distribution of last names - By Thekohser [CC BY-SA 3.0
(https://creativecommons.org/licenses/by-sa/3.0 )], from Wikimedia Commons

24. Approximate Nearest Neighbor Search
• Faster than full k-NN, with some loss in accuracy
• Approaches can be either:
• Data Dependent
• Learns and adjusts from the data
• Makes indexing new documents hard
• Data Independent
• Some Approaches:
• KD Tree
• LSH
• Heuristic Methods
• K-Means Tree
• Randomized KD Forest
• Paper: https://arxiv.org/abs/1603.09596
• HNSW (Hierarchical Navigable Small World Graphs – Top on http://ann-benchmarks.com/
• Paper: https://arxiv.org/pdf/1603.09320.pdf
• Vector Thresholding
• Choice of similarity metric is important in choosing an algorithm

25. KD Trees
• Construction
• Constructs a binary search tree by partitioning the search space along each vector dimension using the
dimensions
• Partitions are chosen orthogonal to each dimension
• Usually the median
• Querying
• Described here - https://en.wikipedia.org/wiki/K-d_tree#Complexity
• Limitations
• How to implement efficiently in an inverted index?
• Lucene 6.0 dimensional points
• See also - https://www.elastic.co/blog/lucene-points-6.0
• Not exposed in Solr and Elastic Search AFAIK
• Tree needs rebalancing on each insertion
• Curse of dimensionality
• N >> 2d - for N points and D dimensions
• Complexity essentially linear for real world vectors (D>= 50)
• Approximate KNN Search
• Possible with KD tree – limit the number of searched nodes
• Typically out-performed by other ANNs approaches

26. Locality Sensitive Hashing
• LSH hashes items to discrete buckets
• More buckets – slower but more accurate
• Locality Preserving
• Maximizes the probability that similar items occupy the same buckets
• Random Projection LSH (sim Hash)
• LSH variant for cosine similarity
• Generate a random d-dimensional unit vector r, and for each vector v
• ℎ𝑎𝑠ℎ 𝑣 = 𝑠𝑖𝑔𝑛(𝑣. 𝑟)
• Produces a binary encoding, one bit for each hash function (random vector)
• Probability 2 vectors’ hashes match - proportional to cosine similarity
• Output of hash function can be indexed and searched using Hamming Distance
• Intuition - Van Durme and Lall - http://www.cs.jhu.edu/~vandurme/papers/VanDurmeLallACL10-slides.pdf
• Data independent, although data dependent variations exist
• However, for real data, it is typically out-performed by heuristic methods like k-means trees, and randomized KD-
trees
• https://lear.inrialpes.fr/pubs/2011/JDS11/jegou_searching_with_quantization.pdf

27. Encoding LSH Hash into the Index
• Hash into Bits
• Store hash fingerprint as a single token • Store each bit as a token using it’s position and value
• Use mm parameter to speed up search
• Or store shingles of the binary tokens
• This is not sparse!
[+0.08, -0.16, -0.12, +0.27, +0.63, -0.01, +0.16, -0.48]
[1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1]
[“10110110100101”] ["00_1","01_0","02_1","04_1","04_0","05_1","06_1","07_0","08_1","09_0","10_0","11_1","12_0","13_1”]
OR

28. Hamming Similarity
Class
• Custom similarity class
• Computes the number of
matching tokens

29. K-Means Tree
• Hierarchical Clustering Algorithm
• Recursively partitions vector space using k-Means clustering
• Fast - k-means runs in linear time using Lloyd’s heuristic
• Most other clustering algorithms run in quadratic time or worse
• Tree Construction
• For some branching factor b create b clusters
• Create b nodes, store centroid for each node
• For each new cluster, cluster its members into b smaller clusters
• These form child nodes of their parent clusters, forming a tree structure
• Continue until < b members per cluster
• Paper
• "Scalable Nearest Neighbor Algorithms for High Dimensional Data" - Marius Muja,
2014 – implemented in the FLANN library

30. K-Means Tree
Second Layer
(Leaf Nodes)
Root Node
First Layer
…. ….…..
….
Documents
• Depth 3 K-Means Tree

31. Lucene Implementation Details
• Pre-train a k-means tree on a representative subset of the index
• Indexing:
• Convert all nodes from tree into unique tokens
• For each vector, find the closest matching leaf node
• Index vector with tokens for that leaf node, and all parent nodes
• Querying
• Find top n matching nodes from tree
• Convert nodes into a query, boosted by similarity to query vector
• 'q': 'clusters:(“121”^0.9 “909”^0.88 ”523”^0.91)’
• Create a re-rank query to brute force re-rank the top matching documents
• 'rq’: '{!rerank reRankQuery=$rqq reRankDocs=1000 reRankWeight=99}’
• 'rqq': '{!payloadEdismax v=$vq}’
• ‘vq’: vector:(”0”^-0.0136 ”1”^0.05387 ”2”^0.070476 ”3”^0.14529 …)
• Uses a special payload query parser (payload_score is insufficient)
• See https://github.com/DiceTechJobs/VectorsInSearch
• *Better approach – use doc values field or Lucene dimensional points
• Trade speed for accuracy depending on depth of tree search, and how many vectors are re-ranked
• Tree nodes follow a Zipfian distribution

32. Lucene Implementation Details
• Cluster Field – stores cluster tokens
• Turn off all norms, tf and idf weighting, custom hamming similarity class
• Vector Field – stores vectors for re-ranking
• Stores components plus payloads, custom similarity class using payloads
• Similarity classes: https://github.com/DiceTechJobs/SolrPlugins

33. Lucene Implementation Details
Vector field analysis chain: Cluster fields:

34. Other Heuristic Methods
• Randomized KD Forest
• Constructs a number of KD trees choosing axis to split on randomly
• Searches all trees in parallel to a fixed number of leaf nodes
• KD Trees are very deep
• How to implement efficiently in an inverted index?
• Hierarchical Navigable Small World Graphs
• Hierarchical graph based model - https://arxiv.org/pdf/1603.09320.pdf
• Consistently out-performs other ANNs methods on the ANNs benchmarks
page - http://ann-benchmarks.com/

35. Distribution of Vector
Components
• Distribution of components
from our vectors is Gaussian
• Mean is 0
• This means that most vector
components are very small
• These components will have
minimal impact on cosine
score
Histogram of components taken from 350k vectors
Mean = 0.0

36. Vector Thresholding with Tokenization
[+0.08, -0.16, -0.12, +0.27, +0.63, -0.01, +0.16, -0.48]
[ 0, 0, 0, 0, +0.63, 0, 0, -0.48]
• Drop all but the largest components
[“04i+0.6”, “07i-0.5”]
• Round weight to lower precision
• Encode position and weight as a single token
• Paper: “Semantic Vector Encoding and Similarity Search Using Fulltext Search Engines”

37. Vector Thresholding with Payloads
[+0.08, -0.16, -0.12, +0.27, +0.63, -0.01, +0.16, -0.48]
[ 0, 0, 0, 0, +0.63, 0, 0, -0.48]
• Drop all but the largest components
• I modified the previous idea, using payload score queries
• Indexing: Store remaining (non zero) tokens in index with payloads
• Querying: Uses custom payload query parser + similarity class
• See Github repo, and solr config in Kmeans tree section
Q=vector:(”3”^-0.0136 ”14”^0.05387 ”56”^-0.070476 ”71”^0.14529 …)
&defType=payloadEdismax

38. Performance Comparison - Initial Results
• Hardware - Mac Book Pro, 2.6Ghz i7 CPU, 16G Ram, SSD
• Search Engine:
• Solr 7.5, single shard
• Index: 700k documents
• 1000 sample vector queries, requests were single threaded
• Metric – precision @10 compared to brute force
• Updated results – check https://github.com/DiceTechJobs/VectorsInSearch

39. Performance Comparison - Initial Results
• Each algorithm was ran over a range of different parameter values, to show recall – speed trade off

40. Performance Comparison - Initial Results
Algorithm Precision@10 Queries Per Sec
(Mean Qry Time)
LSH (Hamming Similarity) 0.69 1.3 qps (757 ms)
Kmeans Tree (trained on index) 0.88 9.2 qps (170 ms)
Kmean Tree (trained on sample) 0.85 9.5 qps (105 ms)
Vector Thresholding with Tokenization
(top 40% of components)
0.85 3.5 qps (312 ms)
Vector Threshold with Payloads
(top 40% of components)
0.94 1.8 qps (547 ms)

41. The Ultimate Solution - Sparse Coding?
• Also called ‘Dictionary Learning’
• Learns a sparse ‘overcomplete’ representation of a vector
• Example Algorithms:
• Sparse Auto-Encoder
• K-SVD
• Encoding needs to preserve the Metric Space
• Similar items need to remain similar after encoding
Other Relevant Approaches
• Word2bits - learns binary quantized word vectors
• https://github.com/agnusmaximus/Word2Bits

42. Block Max WAND
• https://www.elastic.co/blog/faster-retrieval-of-top-hits-in-elasticsearch-with-
block-max-wand
• ‘Weak AND’ algorithm to be integrated into Lucene 8.0 and ES 7.0
• Speeds up large OR queries by pruning clauses that won’t occur in top N
matches
• Speed up can be 40% to 13x
• Can help address performance of these larger OR queries

43. Thank you!
Github Repository:
https://github.com/DiceTechJobs/VectorsInSearch
Simon Hughes
Chief Data Scientist, Dice.com
@hughes_meister