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The FOSDEM conference on February 3rd, 2024, featured a presentation on Manticore Vector Search by Peter Zaitsev, co-founder of Manticore, and Sergey Nikolaev, CEO of Manticore. This event showcased the latest about vector search in databases. For a closer look, a recording of Zaitsev’s talk is available above. Below, you can see a more detailed summary of the topic in the form of an article. https://youtu.be/sHwUgxztcqs?si=uqOUnQoaopRodgbL&embedable=true Introduction In the past two to three years, the database landscape has seen several key changes: A new category of ‘vector databases’ has emerged, featuring open-source platforms such as Milvus in 2019, Vespa in 2020, Weaviate in 2021, and Qdrant in 2022, as well as cloud solutions like Pinecone, introduced in 2019. These databases are dedicated to vector search, focusing on the use of various machine learning models. However, they may lack traditional database capabilities such as transactions, analytics, data replication, and so on. Elasticsearch added vector search capabilities in 2019. Then, from 2022 to 2023, established databases, including Redis, OpenSearch, Cassandra, ClickHouse, Oracle, MongoDB, and Manticore Search, in addition to cloud services from Azure, Amazon AWS, and Cloudflare, started offering vector search functionality. Other well-known databases, like MariaDB, are in the process of integrating vector search capabilities*. For PostgreSQL users, there is the ‘pgvector’ extension, which has implemented this functionality since 2021. While MySQL has not announced plans for native vector search functionality, proprietary extensions from providers such as PlanetScale and AlibabaCloud are available. Vector space and vector similarity Let’s discuss why so many databases recently enabled vector search functionality and what it is at all. Let’s begin with a tangible example. Consider two colors: red, with an RGB code of (255, 0, 0), and orange, with an RGB code of (255, 200, 152). To compare them, let’s plot them on a three-dimensional graph, where each point represents a different color, and the axes correspond to the red, green, and blue components of the colors. We then draw vectors from the origin of the graph to the points representing our colors. Now, we have two vectors: one representing red and the other - orange. If we want to find the similarity between these two colors, one approach could be to simply measure the angle between the vectors. This angle can vary from 0 to 90 degrees, or if we normalize it by taking the cosine, it will vary from 0 to 1. However, this method does not consider the magnitude of the vectors, which means that the cosine will yield the same value for colors A, A1, and A2 even though they represent different shades. To address this issue, we can use the cosine similarity formula, which accounts for vector lengths - the vector’s dot product divided by the product of their magnitudes. This concept is the essence of vector search. It’s straightforward to visualize with colors, but now imagine that, instead of three color axes, we have a space with hundreds or thousands of dimensions, where each axis represents a specific feature of an object. While we can’t easily depict this on a slide or fully visualize it, mathematically, it is feasible, and the principle remains the same: you have vectors in a multi-dimensional space, and you compute the similarity between them. There are a few other formulas to find vector similarity: for example, the dot product similarity and the Euclidean distance, but as the OpenAI API docs say, the difference between them typically doesn’t matter much. Vector features: sparse vectors So, an object may have various features. The color with Red, Green, and Blue components is the simplest example. In real life, it’s typically more complex. In text search, for instance, we may represent documents as high-dimensional vectors. This leads us to the concept of “Bag of Words.” This model transforms text into vectors where each dimension corresponds to a unique word, and the value may be a binary indicator of the word’s presence, a count of occurrences, or a word weight based on its frequency and inversed document frequency (called TF-IDF), which reflects how important a word is to a document in a collection. This is so called sparse vector since most values are zero as most documents don’t have many words. When talking about full-text search in libraries and search engines like , , and , sparse vectors help make searches faster. Basically, you can make a special kind of index that ignores documents without the search term. So you don’t have to check every single document against your search each time. The sparse vectors are also easily understandable. They can be, in a sense, reverse-engineered. Each dimension corresponds to a specific, clear feature, so we can trace back from our vector representation to the original text. This concept has already existed for about 50 years. Lucene Elasticsearch Manticore Search Vector features: dense vectors Traditional text search methods like , which have been around for decades, produce sparse word vectors that depend on term frequency. The main issue? They typically overlook the context in which words are used. For instance, the term “apple” could be associated with both fruit and the technology company without distinction, potentially ranking them similarly in a search. TF-IDF But consider this analogy: In a vector space, which two objects would have closer proximity: a cat and a dog or a cat and a car? Traditional methods that generate sparse vectors — like the one shown at the top of the image below - may struggle to provide a meaningful answer. Sparse vectors are often high-dimensional, with most values being zero, representing the absence of most words in a given document or context. Then came the revolution of deep learning, introducing . These are dense vector representations, as illustrated by the lower part of the image. In contrast to sparse vectors, which may have tens of thousands of dimensions, dense vectors are lower-dimensional (such as 784 dimensions in the image) but packed with continuous values that capture nuanced semantic relationships. This means the same word can have different vector representations depending on its context, and different words can have similar vectors if they share contexts. Technologies like and use these dense vectors to capture complex language features, including semantic relationships, distinguishing synonyms from antonyms, and comprehending irony and slang — tasks that were quite challenging for earlier methods. contextual embeddings BERT GPT Moreover, deep learning extends beyond text, enabling the processing of complex data like images, audio, and video. These can also be transformed into dense vector representations for tasks such as classification, recognition, and generation. The rise of deep learning coincided with the explosion in data availability and computational power, allowing the training of sophisticated models that uncover deeper and subtler patterns in data. Embeddings The vectors such models provide are called “embeddings.” It’s important to understand that unlike the sparse vectors shown previously, where each element can represent a clear feature like a word present in the document, each element of an embedding also represents a specific feature, but in most cases, we don’t even know what the feature is. For example, and used the GloVe model to vectorize Wikipedia and then visualized the values for some words with different colors. We can see here that: Jay Alammar made an interesting experiment A consistent red line appears across various words, indicating similarity in one dimension, though the specific attribute it represents remains unidentified. Terms like “woman” and “girl” or “man” and “boy” display similarities across multiple dimensions, suggesting relatedness. Interestingly, “boy” and “girl” share similarities distinct from “woman” and “man,” hinting at an underlying theme of youth. Except for one instance involving the term “water,” all analyzed words pertain to people, with “water” serving to differentiate between conceptual categories. Distinct similarities between “king” and “queen,” apart from other terms, may suggest an abstract representation of royalty. So, dense vector embeddings, generated through deep learning, capture a vast amount of information in a compact form. Unlike sparse vectors, every dimension of a dense embedding is generally non-zero and carries some semantic significance. This richness comes with a cost - with dense embeddings, since each dimension is densely populated with values, we can’t simply skip documents that don’t contain a specific term. Instead, we face the computational intensity of comparing the query vector with every document vector in the dataset. It’s a brute-force approach that is naturally resource-intensive. However, specialized indexes tailored for dense vectors have been developed. These indexes, such as KD-trees, Ball trees, or more modern approaches like (Hierarchical Navigable Small World) graphs, are pretty smart, but they sometimes have to guess a bit to be fast. This guessing can mean they don’t always get the answer 100% right. The most popular index that databases adopt is HNSW, which stands for Hierarchical Navigable Small World. It’s used by the extension for Postgres, , , , , , , and . Its algorithm builds a multi-layered graph structure. Each layer is a graph where each node (representing a data point) is connected to its closest neighbors. HNSW pgvector Lucene Opensearch Redis SOLR Cassandra Manticore Search Elasticsearch The bottom layer contains all nodes (data points), and each successive upper layer contains a subset of the nodes from the layer below. The topmost layer has the fewest nodes. Searching starts from the upper layers and gradually moves down to the lower layers. This hierarchical approach makes the search process efficient. In a nutshell, HNSW, like any other index, just pregenerates some shortcuts that you then can use for faster query processing. There are other vector indexes, such as maintained by Spotify and others, each with its own set of pros and cons in terms of performance, resource consumption, and accuracy loss. Annoy Image: https://cdn.sanity.io/images/vr8gru94/production/d6e3a660654d9cb55f7ac137a736539e227296b6-1920x1080.png K-nearest neighbours Vector search is actually an umbrella term that includes various tasks such as clustering and classification and others. But commonly, the first feature a database adds for vector search is the ‘K-nearest neighbor search’ (KNN), or its close relative, the ‘Approximate nearest neighbor search’ (ANN). It is appealing because it enables databases to find documents that are most similar to a given document’s vector, which enhances databases with the powerful capabilities of a search engine, which they previously lacked. Traditional search engines like Lucene, Elasticsearch, SOLR, and Manticore Search handle various natural language processing tasks — such as morphology, synonyms, stopwords, and exceptions — all aimed at finding documents that match a given query. KNN accomplishes a similar goal but through different means - just comparing the vectors associated with documents in the table that are usually provided by an external machine-learning model. Let’s explore what a typical vector search looks like in databases, taking as our example. Manticore Search First, we create a table with a column titled : image_vector create table test ( title text, image_vector float_vector knn_type='hnsw' knn_dims='4' hnsw_similarity='l2' ); This vector is of a , which is important because databases that don’t support this data type must first add it, since dense vectors are usually stored in float arrays. At this time, you also usually configure the field by specifying the vector dimension size, vector index type, and its properties. For instance, we specify that we want to use the HNSW index, the vector will have a dimensionality of 5, and the similarity function will be , which is the Euclidean distance. float type l2 Then, we insert a few records into the table: insert into test values ( 1, 'yellow bag', (0.653448,0.192478,0.017971,0.339821) ), ( 2, 'white bag', (-0.148894,0.748278,0.091892,-0.095406) ); Each record has a title and a corresponding vector, which, in a real-world scenario, could be the output from a deep learning model that encodes some form of high-dimensional data, such as an image or sound, an embedding from text, or something else from the OpenAI API. This operation stores the data in the database and may trigger rebuilding or adjusting the index. Next, : we perform a vector search by utilizing the KNN function select id, knn_dist() from test where knn ( image_vector, 5, (0.286569,-0.031816,0.066684,0.032926) );

+------+------------+
| id   | knn_dist() |
+------+------------+
|    1 | 0.28146550 |
|    2 | 0.81527930 |
+------+------------+
2 rows in set (0.00 sec) Here, we’re querying the database to locate the vectors that are closest to our specified input vector. The numbers in parentheses define the particular vector we’re seeking the nearest neighbors for. This step is critical for any database that aims to implement vector search capabilities. At this step, the database can either utilize specific indexing methods, such as HNSW or perform a brute-force search by comparing the query vector against each vector in the table to find the closest matches. The results returned show the titles of the nearest vectors to our input vector and their respective distances from the query. Lower distance values indicate closer matches to the search query. Embedding computation Most databases and search engines so far rely on external embeddings. This means that when you insert a document, you must obtain its embedding from an external source beforehand and include it with the document’s other fields. The same applies when searching for similar documents: if the search is for a user query rather than an existing document, you need to use a machine learning model to calculate an embedding for it, which is then passed to the database. This process can lead to compatibility issues, the need to manage additional data processing layers, and potential inefficiencies in search performance. The operational complexity of this approach is also higher than necessary. Along with the database, you may have to keep another service running to generate embeddings. Some search engines like OpenSearch, Elasticsearch, and Typesense are now making things easier by automatically creating embeddings. They can even use tools from other companies, like OpenAI, to do this. I think we’ll see more of this soon. More databases will start to make embeddings on their own, which could really change how we search for and analyze data. This change means that databases will do more than just store data; they’ll actually understand it. By using machine learning and AI, these databases will be smarter and able to predict, adapt, and handle data in more advanced ways. Hybrid search approaches Some search engines have adopted a method known as hybrid search, which combines traditional keyword-based search with advanced neural network techniques. Hybrid search models excel in situations that require both exact keyword matches, as provided by traditional search techniques, and broader context recognition, as offered by vector search capabilities. This balanced approach can enhance the accuracy of search results. For example, measured by comparing it to the classical BM25 ranking and the ColBERT model individually. In their approach, they used the classical BM25 as the first-phase ranking model and calculated the hybrid score only for the top-ranking K documents according to the BM25 model. It was found that the hybrid search mode outperformed each of them in most tests. Vespa the accuracy of their hybrid search Another simpler method is Reciprocal Rank Fusion (RRF), a technique that combines rankings from different search algorithms. RRF calculates a score for each item based on its rank in each list, where higher rankings receive better scores. The score is determined by the formula 1 / (rank + k), where ‘rank’ is the item’s position in the list, and ‘k’ is a constant used to adjust the influence of lower rankings. By summing these modified reciprocal ranks from each source, RRF emphasizes consensus among different systems. This method blends the strengths of various algorithms, leading to more robust and comprehensive search results. Conclusion Vector search is more than just a concept or a niche functionality of search engines; it’s a practical tool transforming how we retrieve data. In recent years, the database field has seen major changes, with the rise of new vector-focused databases and established ones adding vector search features. This reflects a strong need for more advanced search functions, a need that vector search can meet. Advanced indexing methods, like HNSW, have made vector search faster. Looking ahead, we expect databases to do more than just support vector search; they’ll likely create embeddings themselves. This will make databases simpler to use and more powerful, turning them from basic storage spaces into smart systems that can understand and analyze data. In short, vector search is a significant shift in data management and retrieval, marking an exciting development in the field. Also published . here

Vector Search in Databases: FOSDEM's Presentation on Manticore Vector Search

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A Treatise on Painting by da Vinci Leonardo, is part of the HackerNoon Books Series. You can jump to any chapter in this book . LANDSCAPE. here MISCELLANEOUS OBSERVATIONS. LANDSCAPE. Chap. CCCXXIII.— Of Objects seen at a Distance. Any dark object will appear lighter when removed to some distance from the eye. It follows, by the contrary reason, that a dark object will appear still darker when brought nearer to the eye. Therefore the inferior parts of any object whatever, placed in thick air, will appear farther from the eye at the bottom than at the top; for that reason the lower parts of a mountain appear farther off than its top, which is in reality the farthest. Chap. CCCXXIV.— Of a Town seen through a thick Air. The eye which, looking downwards, sees a town immersed in very thick air, will perceive the top of the buildings darker, but more distinct than the bottom. The tops detach against a light ground, because they are seen against the low and thick air which is beyond them. This is a consequence of what has been explained in the preceding chapter. Chap. CCCXXV.— How to draw a Landscape. Contrive that the trees in your landscape be half in shadow and half in the light. It is better to represent them as when the sun is veiled with thin clouds, because in that case the trees receive a general light from the sky, and are darkest in those parts which are nearest to the earth. Chap. CCCXXVI.— Of the Green of the Country. Of the greens seen in the country, that of trees and other plants will appear darker than that of fields and meadows, though they may happen to be of the same quality. Chap. CCCXXVII.— What Greens will appear most of a blueish Cast. Those greens will appear to approach nearest to blue which are of the darkest shade when remote. This is proved by the seventh proposition, which says, that blue is composed of black and white seen at a great distance. Chap. CCCXXVIII.— The Colour of the Sea from different Aspects. When the sea is a little ruffled it has no sameness of colour; for whoever looks at it from the shore, will see it of a dark colour, in a greater degree as it approaches towards the horizon, and will perceive also certain lights moving slowly on the surface like a flock of sheep. Whoever looks at the sea from on board a ship, at a distance from the land, sees it blue. Near the shore it appears darkish, on account of the colour of the earth reflected by the water, as in a looking-glass; but at sea the azure of the air is reflected to the eye by the waves in the same manner. Chap. CCCXXIX.— Why the same Prospect appears larger at some Times than at others. Objects in the country appear sometimes larger and sometimes smaller than they actually are, from the circumstance of the air interposed between the eye and the horizon, happening to be either thicker or thinner than usual. Of two horizons equally distant from the eye, that which is seen through the thicker air will appear farther removed; and the other will seem nearer, being seen through a thinner air. Objects of unequal size, but equally distant, will appear equal if the air which is between them and the eye be of proportionable inequality of thickness, viz. if the thickest air be interposed between the eye and the smallest of the objects. This is proved by the perspective of colours, which is so deceitful that a mountain which would appear small by the compasses, will seem larger than a small hill near the eye; as a finger placed near the eye will cover a large mountain far off. Chap. CCCXXX.— Of Smoke. Smoke is more transparent, though darker towards the extremities of its waves than in the middle. It moves in a more oblique direction in proportion to the force of the wind which impels it. Different kinds of smoke vary in colour, as the causes that produce them are various. Smoke never produces determined shadows, and the extremities are lost as they recede from their primary cause. Objects behind it are less apparent in proportion to the thickness of the smoke. It is whiter nearer its origin, and bluer towards its termination. Fire appears darker, the more smoke there is interposed between it and the eye. Where smoke is farther distant, the objects are less confused by it. It encumbers and dims all the landscape like a fog. Smoke is seen to issue from different places, with flames at the origin, and the most dense part of it. The tops of mountains will be more seen than the lower parts, as in a fog. Chap. CCCXXXI.— In what Part Smoke is lightest. Smoke which is seen between the sun and the eye will be lighter and more transparent than any other in the landscape. The same is observed of dust, and of fog; while, if you place yourself between the sun and those objects, they will appear dark. Chap. CCCXXXII.— Of the Sun-beams passing through the Openings of Clouds. The sun-beams which penetrate the openings interposed between clouds of various density and form, illuminate all the places over which they pass, and tinge with their own colour all the dark places that are behind: which dark places are only seen in the intervals between the rays. Chap. CCCXXXIII.— Of the Beginning of Rain. When the rain begins to fall, it tarnishes and darkens the air, giving it a dull colour, but receives still on one side a faint light from the sun, and is shaded on the other side, as we observe in clouds; till at last it darkens also the earth, depriving it entirely of the light of the sun. Objects seen through the rain appear confused and of undetermined shape, but those which are near will be more distinct. It is observable, that on the side where the rain is shaded, objects will be more clearly distinguished than where it receives the light; because on the shady side they lose only their principal lights, whilst on the other they lose both their lights and shadows, the lights mixing with the light part of the rain, and the shadows are also considerably weakened by it. Chap. CCCXXXIV.— The Seasons are to be observed. In Autumn you will represent the objects according as it is more or less advanced. At the beginning of it the leaves of the oldest branches only begin to fade, more or less, however, according as the plant is situated in a fertile or barren country; and do not imitate those who represent trees of every kind (though at equal distance) with the same quality of green. Endeavour to vary the colour of meadows, stones, trunks of trees, and all other objects, as much as possible, for Nature abounds in variety . ad infinitum Chap. CCCXXXV.— The Difference of Climates to be observed. Near the sea-shore, and in southern parts, you will be careful not to represent the Winter season by the appearance of trees and fields, as you would do in places more inland, and in northern countries, except when these are covered with ever-greens, which shoot afresh all the year round. Chap. CCCXXXVI.— Of Dust. Dust becomes lighter the higher it rises, and appears darker the less it is raised, when it is seen between the eye and the sun. Chap. CCCXXXVII.— How to represent the Wind. In representing the effect of the wind, besides the bending of trees, and leaves twisting the wrong side upwards, you will also express the small dust whirling upwards till it mixes in a confused manner with the air. Chap. CCCXXXVIII.— Of a Wilderness. Those trees and shrubs which are by their nature more loaded with small branches, ought to be touched smartly in the shadows, but those which have larger foliage, will cause broader shadows. Chap. CCCXXXIX.— Of the Horizon seen in the Water. By the sixth proposition, the horizon will be seen in the water as in a looking-glass, on that side which is opposite the eye. And if the painter has to represent a spot covered with water, let him remember that the colour of it cannot be either lighter or darker than that of the neighbouring objects. Chap. CCCXL.— Of the Shadow of Bridges on the Surface of the Water. The shadows of bridges can never be seen on the surface of the water, unless it should have lost its transparent and reflecting quality, and become troubled and muddy; because clear water being polished and smooth on its surface, the image of the bridge is formed in it as in a looking-glass, and reflected in all the points situated between the eye and the bridge at equal angles; and even the air is seen under the arches. These circumstances cannot happen when the water is muddy, because it does not reflect the objects any longer, but receives the shadow of the bridge in the same manner as a dusty road would receive it. Chap. CCCXLI.— How a Painter ought to put in Practice the Perspective of Colours. To put in practice that perspective which teaches the alteration, the lessening, and even the entire loss of the very essence of colours, you must take some points in the country at the distance of about sixty-five yards from each other; as trees, men, or some other remarkable objects. In regard to the first tree, you will take a glass, and having fixed that well, and also your eye, draw upon it, with the greatest accuracy, the tree you see through it; then put it a little on one side, and compare it closely with the natural one, and colour it, so that in shape and colour it may resemble the original, and that by shutting one eye they may both appear painted, and at the same distance. The same rule may be applied to the second and third tree at the distance you have fixed. These studies will be very useful if managed with judgment, where they may be wanted in the offscape of a picture. I have observed that the second tree is less by four fifths than the first, at the distance of thirteen yards. Chap. CCCXLII.— Various Precepts in Painting. The superficies of any opake body participates of the colour of the transparent medium interposed between the eye and such body, in a greater or less degree, in proportion to the density of such medium and the space it occupies. The outlines of opake bodies will be less apparent in proportion as those bodies are farther distant from the eye. That part of the opake body will be the most shaded, or lightest, which is nearest to the body that shades it, or gives it light. The surface of any opake body participates more or less of the colour of that body which gives it light, in proportion as the latter is more or less remote, or more or less strong. Objects seen between lights and shadows will appear to have greater relievo than those which are placed wholly in the light, or wholly in shadow. When you give strength and precision to objects seen at a great distance, they will appear as if they were very near. Endeavour that your imitation be such as to give a just idea of distances. If the object in nature appear confused in the outlines, let the same be observed in your picture. The outlines of distant objects appear undetermined and confused, for two reasons: the first is, that they come to the eye by so small an angle, and are therefore so much diminished, that they strike the sight no more than small objects do, which though near can hardly be distinguished, such as the nails of the fingers, insects, and other similar things: the second is, that between the eye and the distant objects there is so much air interposed, that it becomes thick; and, like a veil, tinges the shadows with its own whiteness, and turns them from a dark colour to another between black and white, such as azure. Although, by reason of the great distance, the appearance of many things is lost, yet those things which receive the light from the sun will be more discernible, while the rest remain enveloped in confused shadows. And because the air is thicker near the ground, the things which are lower will appear confused; and . vice versâ When the sun tinges the clouds on the horizon with red, those objects which, on account of their distance, appear blueish, will participate of that redness, and will produce a mixture between the azure and red, which renders the prospect lively and pleasant; all the opake bodies which receive that light will appear distinct, and of a reddish colour, and the air, being transparent, will be impregnated with it, and appear of the colour of lilies. The air which is between the earth and the sun when it rises or sets, will always dim the objects it surrounds, more than the air any where else, because it is whiter. It is not necessary to mark strongly the outlines of any object which is placed upon another. It ought to detach of itself. If the outline or extremity of a white and curved surface terminate upon another white body, it will have a shade at that extremity, darker than any part of the light; but if against a dark object, such outline, or extremity, will be lighter than any part of the light. Those objects which are most different in colour, will appear the most detached from each other. Those parts of objects which first disappear in the distance, are extremities similar in colour, and ending one upon the other, as the extremities of an oak tree upon another oak similar to it. The next to disappear at a greater distance are, objects of mixed colours, when they terminate one upon the other, as trees, ploughed fields, walls, heaps of rubbish, or of stones. The last extremities of bodies that vanish are those which, being light, terminate upon a dark ground; or being dark, upon a light ground. Of objects situated above the eye, at equal heights, the farthest removed from the eye will appear the lowest; and if situated below the eye, the nearest to it will appear the lowest. The parallel lines situated sidewise will concur to one point. Those objects which are near a river, or a lake, in the distant part of a landscape, are less apparent and distinct than those that are remote from them. Of bodies of equal density, those that are nearest to the eye will appear thinnest, and the most remote thickest. A large eye-ball will see objects larger than a small one. The experiment may be made by looking at any of the celestial bodies, through a pin-hole, which being capable of admitting but a portion of its light, it seems to diminish and lose of its size in the same proportion as the pin-hole is smaller than the usual apparent size of the object. A thick air interposed between the eye and any object, will render the outlines of such object undetermined and confused, and make it appear of a larger size than it is in reality; because the linear perspective does not diminish the angle which conveys the object to the eye. The aerial perspective carries it farther off, so that the one removes it from the eye, while the other preserves its magnitude. When the sun is in the West the vapours of the earth fall down again and thicken the air, so that objects not enlightened by the sun remain dark and confused, but those which receive its light will be tinged yellow and red, according to the sun’s appearance on the horizon. Again, those that receive its light are very distinct, particularly public buildings and houses in towns and villages, because their shadows are dark, and it seems as if those parts which are plainly seen were coming out of confused and undetermined foundations, because at that time every thing is of one and the same colour, except what is enlightened by the sun. Any object receiving the light from the sun, receives also the general light; so that two kinds of shadows are produced: the darkest of the two is that which happens to have its central line directed towards the centre of the sun. The central lines of the primitive and secondary lights are the same as the central lines of the primitive and secondary shadows. The setting sun is a beautiful and magnificent object when it tinges with its colour all the great buildings of towns, villages, and the top of high trees in the country. All below is confused and almost lost in a tender and general mass; for, being only enlightened by the air, the difference between the shadows and the lights is small, and for that reason it is not much detached. But those that are high are touched by the rays of the sun, and, as was said before, are tinged with its colour; the painter therefore ought to take the same colour with which he has painted the sun, and employ it in all those parts of his work which receive its light. It also happens very often, that a cloud will appear dark without receiving any shadow from a separate cloud, according to the situation of the eye; because it will see only the shady part of the one, while it sees both the enlightened and shady parts of the other. Of two objects at equal height, that which is the farthest off will appear the lowest. Observe the first cloud in the cut, though it is lower than the second, it appears as if it were higher. This is demonstrated by the section of the pyramidical rays of the low cloud at M A, and the second (which is higher) at N M, below M A. This happens also when, on account of the rays of the setting or rising sun, a dark cloud appears higher than another which is light. Chap. CCCXLIII.— The Brilliancy of a Landscape. The vivacity and brightness of colours in a landscape will never bear any comparison with a landscape in nature when illumined by the sun, unless the picture be placed so as to receive the same light from the sun itself. About HackerNoon Book Series: We bring you the most important technical, scientific, and insightful public domain books. This book is part of the public domain. da Vinci Leonardo (2014). A Treatise on Painting. Urbana, Illinois: Project Gutenberg. Retrieved https://www.gutenberg.org/cache/epub/46915/pg46915-images.html This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at , located at . www.gutenberg.org https://www.gutenberg.org/policy/license.html

Of Objects seen at a Distance

Let's learn about via these 51 free stories. They are ordered by most time reading created on HackerNoon. Visit the to find the most read stories about any technology. Gamedev /Learn Repo 1. Frank Morgan on Writing, Hospitality, and Web3 Learn how tech writers can create viral content about web3, scrum, agile, hospitality tech, The Sandbox, FTX, NFT, and the metaverse on Hackernoon or anywhere! 2. The Jinn: My Storyline for my first Game Project in Unity The daylight dims, its 3:00 pm, almost afternoon. It feels humid as the moisture in the air has increased. The skin feels all damp and sticky. My little room is getting all hot as I start sweating. It was supposed to be an ordinary afternoon on a summer day. “Lets go outside…” I talked to myself. 3. Creating a Notification-Based Game via Unity and Courier I built a notification-based game with Unity Engine, Courier, Twilio, and Mailjet. This post discusses how I used Courier to build Rain Spikes. 4. Getting Started With Game Development How to begin developing video games? 5. What To Do When Your 12-Year-Old Son Has a Girlfriend in Fortnite I recently had a chat with a parent. He said his 12-year-old son came home and announced that he has met someone in Fortnite —  and that someone is now his girlfriend. 6. 6 Software Tools I Use to Make Game Art Without Being an Artist Being a programmer doesn't stop me from making game art assets. If you go for a minimalism style and use good colors that fit well together you can make a game look good. I will show you the programs I use and the games I used it for. 7. Phaser 3 Game Framework: My Honest Review I've been using Phaser 3 for a couple of months now, and I'm really enjoying it, but sometimes it makes shake my head 'why?' , only not in a 'bad way', making games is weird, js itself is weird, so it's only logical that Phaser, a game engine js-based... is weird. That's why I opted for the following way to address this review, I'm gonna be giving you something that I liked, next to why/how it was weird, in what's gonna be my attempt to look impartial. But first... 8. A Podcast with NIS America: How has COVID Changed the Gaming Industry? In this episode of the Hacker Noon Podcast, I talked to Erin Kim from NIS America. For those of you that don't know, NIS America is the America-based counterpart of the Japanese game development company NIS (Nippon Ichi Software). 9. Making A Spooky Quantum Game in 15 Hours or Less It’s no longer news that many organizations and even NASA are in a race to reach what is known as quantum supremacy or the quantum advantage. This means they are investing in resources to develop new computers that are able to solve problems that current (classical) computers cannot; and of course perform faster at already solved problems. If you’re reading this article, you may have heard about Quantum Computing and all it promises to deliver and are curious to learn about the technology. 10. Wednesday Addiction: Why Less Is More In Games I’ve played many games that try to be too many things at once and they always fail. My favorite ones are those that take a simple concept and play with it. 11. How To Integrate App Tracking Transparency with your iOS Unity Project ByteSyze SDK covers iOS 14 compliant bases by integrating a custom App Tracking Transparency handler into your Unity iOS project for your ATT-dependent SDK's. 12. Oh You're Going to Your First Game Jam? Read Me First I have participated in quite a few game jams over the years and now I want to share my experiences with you. I participated in both online as offline jams like Ludum Dare and Global Game Jam. Game jams are fun and can be a great learning experience but they can also be stressful and tiring. 13. Blockchain Tech In the Gaming Industry: Major Players To Spark Mass Adoption? While the blockchain and crypto industry participants never stop developing and exploring new possible applications of the tech, major global industries are now turning for answers in this unique technology when it comes to innovations in their field. 14. Learn to Code with Pico-8 Games There are a lot of reasons to learn to code with games. Games are fun. Unlike to-do apps, games are something you are excited to show to your friend because it is something they will engage with. There is a misconception among some developers that games are difficult to code, and unapproachable to beginner developers. I couldn’t disagree more, especially if you learn to code with Pico-8 games. 15. Quest Arrest: Shipping a Physical Game Boy Game in 2021 In this article, I'll talk about Quest Arrest, a digital and physical Game Boy game I developed and shipped in 2020 and continue to sell today in 2021. 16. From 3D Rendering to Motion Capture: What's Next for Game Development? The past few decades have been game-changing for our daily lives as a whole range of industries transformed into what we see today. The world does not function the way it used to just a few decades ago and that is thanks to technological advancements, occurring throughout this timeframe. 17. Game Development in 2022: Top 6 Programming Languages Do you want to become a game developer? Then, you need to learn a gaming programming language. So, check out this blog to know more about these languages. 18. The Importance of Music in Video Games Think back to the year of 1986. You are an excited child sprinting through the arcade so you can be the first to get to the amazing new game, ”Outrun”. What was it that was so special about this game? The cars? The quirky characters? The endless crashing into things? Probably. But I recently played it for the first time, and the one thing that stood out to me was the music. 19. How to Improve Customer Care Today customer care is one of the most popular and widely discussed topics in the IT industry. 20. My Experience as A Team Lead For Unity3D Gamedev Team Recently I became the team lead in the company I am working for and here I want to share a few lessons that I already managed to learn. 21. Demographics of the Gaming Industry: Reading Between the Lines An overview of recent developments in the gaming industry and what they mean for publishers and developers. 22. Indie Game Marketing on YouTube: a Guide by Developers for Developers With the growth of YouTube, potential for promotion arises. But the marketing of indie games is not easy. How to avoid a chaotic struggle and achieve success? 23. On Weapon Design in Video Games After introducing you to the game characters' initial conceptualization in the previous DevBlog, it is now time to design the weapons that the characters use. 24. How I Let an AI Code a Game For Me! What if I would ask an artificial intelligence to writa game for me? Is it hard? Will it work? I'm using Github Copilot to try it out. 25. Build a Game Engine from Scratch in C++ So you want to learn more about game engines and write one yourself? That's awesome! To help you on your journey, here are some recommendations of C++ libraries 26. 'Seed' by Klang Games: Part 1 of The Game AI Series I spoke to their excellent game AI engineer Alessia Nigretti to get some insights into the team’s development process and the technology unpinning the game. 27. Game Coding for Dummies: A Quick Guide for Newbies If you’re a complete newbie or already have a bit of a programming background, you can’t go wrong with Java for game development. 28. What I Learned Developing Games from Scratch on Flutter "Dart engineers exploring Stack Overflow 'Flutter gamedev' section", Photo by Elena Zhuravleva. 29. Blockchain Games Hold More Potential Than Previously Understood Blockchain technology is step by step penetrating many areas of our lives, not just becoming an innovation, but shaping the approach and requirements for market products. 30. Wanna Get Great At Making Indie Games? Make Lots Of Them It's simple, really: ff you want to become a good game developer, you need to make lots of games. Let’s first start with why you need to be productive: the more games you make the better and faster you become at making games. Every new game you make is a new addition to your portfolio. Publish your games on different portals to see what the players think about your game, see what works, and what kind of ideas don’t. 31. What AI Game Developers Do and How to Become One Depending on the genre and purpose of the game, different technologies and approaches are used in the development of AI. 32. 5 Steps You Should Take To Launch A Cool Game The key steps of the game development process, how each of them functions, and what roles and operations they consist of. 33. 5 Things You Should Know Before Developing CTV Games Learn 5 main steps that CTV developers should take into account when they are creating a new game. 34. 5 Best Game Engines for Beginner Indie Developers With so many game engines to choose from it can be difficult to focus on only one. Especially without any experience in the world of game development. That is why I made this list of game engines each with a summary of why it is a great option for beginners. 35. Dedicated Game Server: How To Choose The Right Infrastructure The importance of high-performance dedicated game server in the gaming sector is too high to ignore, especially since cloud gaming has begun to steal the show. Super-high latency is what gamers need to experience the real gut of a game. And customized dedicated servers are the best solution to provide such a short/zero latency. 36. 18 Misconceptions Gamers have about NFTs Western gamers and developers, and this is predominantly a Western issue, have come out strongly against NFTs. 37. Advantages of AI in Gaming: How We're Creating Smarter Competition Why artificial intelligence is being introduced into competitive and cooperative games today, and how the development teams of such games use AI. 38. The Future of Multiplayer Game Architecture is Hybrid This multiplayer game architecture, if technically and economically feasible can reshape the future of gaming. 39. Code a Java Game with (almost) Zero Coding Skills Everyone, well, almost everyone, loves video games. So even if you are not going to be a professional game developer or just don’t know for sure, to learn a programming language through practice and creating your own video game project is an excellent idea. Furthermore, it could be a good motivation for your learning. 40. IoT as a Multi-Faceted Game Changer in 2021 and Beyond There is no second-guessing the predominance of the IT industry, despite the catastrophic effects of the pandemic felt across diverse verticals. 41. What I've Learned By Making And Promoting A Game To Help Stray Cats At the beginning of summer 2019, I've got an idea to make a cat-themed game to help stray cats by donating all the revenue to cat charities. 42. How To Make Your Own Game in Python Hi there ! 43. What is Cloud Gaming and How is Google Leading the Industry? Most games today are downloaded and played on smartphones, gaming consoles, and PCs. Network connections support player accounts and in-game purchases, but the games themselves run on players' devices. Game companies build services around top game titles, enabling them to deliver continuous updates that add new gameplay and respond to the public feedback on social streaming services. 44. An Introduction to LÖVE the 2D Game Engine If you are looking into starting with LÖVE, this guide compiles a lot of information that will help you to get started and save you hours of research. 45. How to Get Your First Job as a Video Game Designer How many of us have thought to ourselves “how cool would it be to become a game designer!” It might seem like a pipe dream at first, but with the right approach, it’s possible, even for someone in their 30s with a completely unrelated education or background. 46. Adventures in Assembly #2 As I've continued my dive down the rabbit hole that is assembly, I've found a buoy to grab onto: NES programming. 47. How to Create Promotional Assets: An Insider's Guide into the World of Graphic Design I offer you to go through the evolutionary stages of promo materials. 48. Bugs from the 90's: The Code of Command and Conquer [Volume 2] The American company Electronic Arts Inc (EA) has opened the source code of the games Command & Conquer: Tiberian Dawn and Command & Conquer: Red Alert publicly available. Several dozen errors were detected in the source code using the PVS-Studio analyzer, so, please, welcome the continuation of found defects review. 49. How I Remade 2048 Using React Today you will learn how to build your own clone of the 2048 game in React. 50. Bugs From the 90's: The Code of the Command & Conquer Game The American company Electronic Arts Inc (EA) has made the source code of the games Command & Conquer: Tiberian Dawn and Command & Conquer: Red Alert publicly available. This code should help the game community to develop mods and maps, create custom units, and customize the gameplay logic. We all now have a unique opportunity to plunge into the history of development, which is very different from the modern one. 51. Is It Hard to Develop a MMORPG? How we built a MMORPG in just about 2 years (actually, it’s more). Thank you for checking out the 51 most read stories about Gamedev on HackerNoon. to find the most read stories about any technology. Visit the /Learn Repo

51 Stories To Learn About Gamedev

How LLMs Have Transformed Working with Computers

Integral Neural Networks (INNs) are flexible architectures that trained once can be transformed to arbitrary user-defined size without any fine-tuning. As sound waves (music) can be sampled at any desired sampling rate (sound quality) INNs can change data and parameters shape (DNN quality) dynamically. The team of presented their paper, “Integral Neural Networks,” at the IEEE/CVF CVPR 2023 conference. This work was recognized as one of only 12 ‘Award Candidate’ papers featured at the event. INNs are a new class of neural networks that combine continuous parameters and integral operators to represent basic layers. During the inference stage, INNs convert to a vanilla DNN representation by discrete sampling from continuous weights. Parameters of such networks are continuous along filter and channel dimensions which leads to structured pruning without fine-tuning just by re-discretization along those dimensions. TheStage.ai In this article, we will guide you through the process of transforming a 4x image super-resolution EDSR model to an INN, then show how to achieve structured pruning of the model. Finally, we will convert the INN back to a discrete DNN and deploy it on an Nvidia GPU for efficient inference. This article will proceed as follows: A brief introduction to INNs. Overview of EDSR network for super-resolution task. TorchIntegral framework application to obtain integral EDSR in a single line of code. Structural pruning of INN without INN fine-tuning (fast pipeline). Deploy pruned models on Nvidia GPUs. For further information and updates, please check the following resources: INN project site INN project Github Support code of this article INNs for DNNs pruning without fine-tuning Layers in INNs are replaced by integral operators, but the practical evaluation of integral operators requires the discretization of input signals for the usage of numerical integration methods. It turns out that the layers in INNs are designed in such a way as to coincide with classical DNN layers (fully-connected, convolutions) after discretization. EDSR 4x Image Super-Resolution pruning Image super-resolution is a well-known computer vision task where an image should be enhanced with a known or unknown degradation operator. We consider classical super-resolution form using bicubic downsampling as a degradation operator. Many architectures can be used for image super-resolution tasks, including high-end neural networks based on diffusion models and transformers. In this document, we will focus on the 4x EDSR architecture. EDSR architecture is well-suited for our demonstration as it comprises ResNet (which is widely used in many deep learning problems) and a 4x upsampling block at the end. A schematic description of EDSR can be found in the following figures. Specifics of EDSR architecture pruning Structured pruning, which involves deleting entire filters or channels, has unique implications for residual blocks, which serve as the primary building blocks in EDSR. Since each state is updated by adding a Conv -> ReLU -> Conv block to the input, the input and output signals must have the same number of parameters. This can be efficiently managed in TorchIntegral by creating a . The figure below illustrates that the second convolution of each residual block forms a single group. pruning dependency graph To prune the second convolution in a residual block, it is necessary to prune all second convolutions in each residual block. However, for a more flexible setup, we prune filters of the first convolutions, and therefore channels of the second convolutions, in all residual blocks. Conversion of EDSR model to INN EDSR For conversions from the pre-trained DNNs, we utilize our special filter-channels permutation algorithm with further smooth interpolation. The permutation algorithm preserves model quality while making the weights of the DNNs look like sampled from continuous functions. import torch
import torchintegral as inn
from super_image import EdsrModel

# creating 4x EDSR model
model = EdsrModel.from_pretrained("eugenesiow/edsr", scale=4).cuda()

# Transform model layers to integral.
# continous_dims and discrete dims define which dimensions
# of parameters tensors should be parametrized continuously
# or stay fixed size as in discrete networks.
# In our case we make all filter and channel dimensions
# to be continuous excluding convolutions of the upsample block.
model = inn.IntegralWrapper(init_from_discrete=True)(
    model, example_input, continuous_dims, discrete_dims
).cuda() Integration grid tuning: structured post-training pruning of DNNs Integration grid tuning is the operation that selects smoothly (under SGD optimization) parameter tensors whose filters should be sampled for user-defined numbers. Unlike the filter/channel deletion methods, INNs generate filters that can combine several discrete filters because of interpolation operation. INNs introduce on the tensor of parameters along filter and channel dimensions. soft select-by-index operation # Set trainable gird for each integral layer
# Each group should have the same grid
# During the sum of continuous signals
# We need to sample it using the same set of points

for group in model.groups:
    new_size = 224 if 'operator' in group.operations else 128 
    group.reset_grid(inn.TrainableGrid1D(new_size))

# Prepare model for tuning of integration grid
model.grid_tuning()
# Start training
train(model, train_data, test_data) Integration grid tuning is a that can be carried out on a small calibration set. The result of this optimization is a structurally compressed DNN. Tests on a single Nvidia A4000 show that integration grid tuning on the full Div2k dataset . A distributed setup on 4x A4000 demonstrates almost a 4x speedup, resulting in an optimization time of . fast optimization process requires 4 minutes just 1 minute During our experiments, we found that 500 images give the same result as a full train set Div2k of 4000 images. Performance The resulting INN model can be easily converted to a discrete model and deployed on any NVIDIA GPU. We provide frames per second (FPS) on the RTX A4000 with an input resolution of 64x64. The compressed model achieves almost a 2x speedup. To convert the pruned INN model to a discrete model the following line of code can be used: model = model.transform_to_discrete()
# then model can be compiled, for instance
# compilation can add an additional 1.4x speedup for inference
model = torch.compile(model, backend='cudagraphs') Model Size FP16 FPS RTX A4000 PSNR EDSR orig. 75 MB 170 30.65 INN EDSR 30% 52 MB 230 30.43 INN EDSR 40% 45 MB 270 30.34 INN EDSR 50% 37 MB 320 30.25 Conclusion In this article, we have presented an overview of the CVPR2023 award candidate paper, “Integral Neural Networks”. It was applied for the post-training pruning of the 4x EDSR model, achieving nearly a 2x speedup with a single line of code and 1-minute fine-tuning of the integration grid. In our future articles, we will present more applications of the INNs and will cover more details on efficient model deployment. Stay tuned: INN project site INN project Github Support code of this article Thank you for your attention! Also published . here

Unleashing 2x Acceleration for DNNs: Transforming Models with Integral Neural Networks in Just 1 Min

DNN-এর জন্য 2x ত্বরণ আনলিশ করা: মাত্র 1 মিনিটে ইন্টিগ্রাল নিউরাল নেটওয়ার্ক সহ মডেলগুলিকে রূপান্তর করা

Entfesseln Sie die doppelte Beschleunigung für DNNs: Transformieren Sie Modelle mit integralen neuronalen Netzen in nur 1 Minute

Liberando una aceleración 2x para DNN: transformando modelos con redes neuronales integrales en solo 1 minuto

Libérer une accélération 2x pour les DNN : transformer des modèles avec des réseaux de neurones intégraux en seulement 1 minute

डीएनएन के लिए 2x एक्सेलेरेशन जारी करना: केवल 1 मिनट में इंटीग्रल न्यूरल नेटवर्क के साथ मॉडल को बदलना

DNN の 2 倍の高速化を解き放つ: 統合ニューラル ネットワークを使用してわずか 1 分でモデルを変換

DNN을 위한 2배 가속 실현: 단 1분 만에 통합 신경망을 사용하여 모델 변환

Liberando aceleração 2x para DNNs: transformando modelos com redes neurais integrais em apenas 1 minuto

DNN'ler için 2 Kat Hızlanmayı Ortaya Çıkarma: Sadece 1 Dakikada Entegre Sinir Ağlarıyla Modelleri Dönüştürme

Giải phóng khả năng tăng tốc gấp 2 lần cho DNN: Chuyển đổi mô hình với Mạng thần kinh tích hợp chỉ trong 1 phút

为 DNN 释放 2 倍加速：只需 1 分钟即可使用集成神经网络转换模型

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