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network science, a sparse network has much fewer links than the possible maximum number of links within that network (the opposite is a dense network)
Sparse_network
Topics referred to by the same term
theory Sparse matrix, in numerical analysis, a matrix populated primarily with zeros Sparse file, a computer file mostly empty Sparse network, a network with
Sparse_(disambiguation)
Neural network that learns efficient data encoding in an unsupervised manner
the network parameters so that p θ ( x ) = ∫ z p θ ( x , z ) d z {\displaystyle p_{\theta }(x)=\int _{z}p_{\theta }(x,z)dz} . Inspired by the sparse coding
Autoencoder
Matrix in which most of the elements are zero
In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. There is no strict
Sparse_matrix
Machine learning technique
network, and each expert is a linear-ReLU network. Since the output from the gating is not sparse, all expert outputs are needed, and no conditional
Mixture_of_experts
Concept in graph theory
finding, this implies that the network divides naturally into groups of nodes with dense connections internally and sparser connections between groups. But
Community_structure
Multicast routing protocol
(August 2006). Protocol Independent Multicast - Sparse Mode (PIM-SM): Protocol Specification (Revised). Network Working Group. doi:10.17487/RFC4601. RFC 4601
Protocol-Independent Multicast
Protocol-Independent_Multicast
Computer Networking Program
Médard, Muriel (June 2014). "Tunable sparse network coding for multicast networks". 2014 International Symposium on Network Coding (NetCod). pp. 1–6. doi:10
Linear_network_coding
Concept in mathematics
Sparse approximation (also known as sparse representation) theory deals with sparse solutions for systems of linear equations. Techniques for finding
Sparse_approximation
Rail yard and fueling station
BNSF locomotives and railcars. The facility was constructed due to the sparse network of fueling sites in the region before 2000, making it often necessary
Hauser_Refueling_Facility
Class of artificial neural network
Echo state networks (ESN) have a sparsely connected random hidden layer. The weights of output neurons are the only part of the network that can change
Recurrent_neural_network
Neural network based evaluation function
simple 8x8 grid, it uses a massive, sparse input layer, often called the HalfKP feature set. This means the network tracks the position of every piece
Efficiently updatable neural network
Efficiently_updatable_neural_network
Type of feedforward neural network
network to use all of its inputs a little rather than some of its inputs a lot. L1 regularization is also common. It makes the weight vectors sparse during
Convolutional_neural_network
Mode of transport
extensive rail networks, but some railways elsewhere in Africa and South America are isolated lines. Australia has a generally sparse network befitting its
Rail_transport
Computer networking that tolerates variable latency
projects. Disruption may occur because of the limits of wireless radio range, sparsity of mobile nodes, energy resources, attack, and noise. In the 1970s, spurred
Delay-tolerant_networking
Algorithm for finding shortest paths
of large constant factors. Graph structure also plays a major role. Sparse networks, such as road maps, allow Dijkstra's algorithm to operate efficiently
Dijkstra's_algorithm
Probabilistic graphical representation of causal relationships
Bayesian network can save considerable amounts of memory over exhaustive probability tables, if the dependencies in the joint distribution are sparse. For
Bayesian_network
Use of force or threat of war focused for political purposes
political strategies. Organizations such as Al-Qaeda may exist as a sparse network of groups lacking central coordination, making them more difficult to
Military_strategy
Type of information retrieval using LLMs
These methods focus on the encoding of text as either dense or sparse vectors. Sparse vectors, which encode the identity of a word, are typically dictionary-length
Retrieval-augmented generation
Retrieval-augmented_generation
Data-driven algorithm
Sparse identification of nonlinear dynamics (SINDy) is a data-driven algorithm for obtaining dynamical systems from data. Given a series of snapshots of
Sparse identification of non-linear dynamics
Sparse_identification_of_non-linear_dynamics
Academic field
Network science is an academic field which studies complex networks such as telecommunication networks, computer networks, biological networks, cognitive
Network_science
Distributed file system protocol
features including: server-side clone and copy, application I/O advise, sparse files, space reservation, application data block (ADB), labeled NFS with
Network_File_System
Country in North America
densities, with the majority residing in its urban areas and large areas being sparsely populated. Its capital is Ottawa and its three largest metropolitan areas
Canada
Biological theory of intelligence
neural networks has a long history dating back to early research in distributed representations and self-organizing maps. For example, in sparse distributed
Hierarchical_temporal_memory
Method by which information is represented in the brain
cell activity to maintain sparse, decorrelated odor coding and thus the odor-specificity of memories. Artificial neural network Autoencoder Biological neuron
Neural_coding
Exponentially decreasing bounds on tail distributions of random variables
for permutation routing problems which reduce network congestion while routing packets in sparse networks. Chernoff bounds are used in computational learning
Chernoff_bound
Knowledge base that represents semantic relations between concepts in a network
Semantic similarity network Semantic neural network SemEval – an ongoing series of evaluations of computational semantic analysis systems Sparse distributed memory
Semantic_network
Country primarily in North America
government-sponsored national passenger rail company, has a relatively sparse network compared to that of Western European countries. Service is concentrated
United_States
Mathematical model of memory
Sparse distributed memory (SDM) is a mathematical model of human long-term memory introduced by Pentti Kanerva in 1988 while he was at NASA Ames Research
Sparse_distributed_memory
Computational problem of graph theory
Johnson, Donald B. (1977). "Efficient algorithms for shortest paths in sparse networks". Journal of the ACM. 24 (1): 1–12. doi:10.1145/321992.321993. S2CID 207678246
Shortest_path_problem
Measure of network community structure
sparse connections between nodes in different modules. Modularity is often used in optimization methods for detecting community structure in networks
Modularity_(networks)
Form of artificial neural network
Vincent; JIANG, Xiaoran (2014). "A study of retrieval algorithms of sparse messages in networks of neural cliques". COGNITIVE 2014 : The 6th International Conference
Hopfield_network
Signal processing technique
Compressed sensing (also known as compressive sensing, compressive sampling, or sparse sampling) is a signal processing technique for efficiently acquiring and
Compressed_sensing
Network where the ties among nodes have weights assigned to them
weights, transcending the conventional constraints of sparser network configurations. Unlike sparse networks where the absence of links typically indicate lack
Weighted_network
Decentralized type of wireless network
random geometric graph. Early work included simulating ad hoc mobile networks on sparse and densely connected topologies. Nodes are firstly scattered in a
Wireless_ad_hoc_network
Classification of Artificial Neural Networks (ANNs)
Network". Advances in Neural Information Processing Systems 23 (NIPS 2010). Vol. 23. pp. 1–9. Ranzato, Marc Aurelio; Boureau, Y-Lan (2007). "Sparse Feature
Types of artificial neural networks
Types_of_artificial_neural_networks
Branch of machine learning
with fewer units than a similarly performing shallow network. For instance, it was proved that sparse multivariate polynomials are exponentially easier to
Deep_learning
Type of activation function
creates sparse representation naturally, because many hidden units output exactly zero for a given input. They also found empirically that deep networks trained
Rectified_linear_unit
Vehicle communication standard
V2R communication is beneficial because V2R provides better service sparse networks and long-distance communication, whereas V2V enables direct communication
Intelligent vehicular ad hoc network
Intelligent_vehicular_ad_hoc_network
Type of convolutional neural network
convolutional neural network that was developed for image segmentation. The network is based on a fully convolutional neural network whose architecture
U-Net
Mathematical structure
A sparsity matroid is a mathematical structure that captures how densely a multigraph is populated with edges. To unpack this a little, sparsity is a measure
Sparsity_matroid
Upland between England and Scotland
similar access for the public to the north of the border. In addition, a sparse network of public bridleways and footpaths stretches around the area, often
Cheviot_Hills
Trimming artificial neural networks to reduce computational overhead
Huanyu; Shen, Li; Pechenizkiy, Mykola; Wang, Zhangyang (2022-02-06). "Sparse Training via Boosting Pruning Plasticity with Neuroregeneration". arXiv:2106
Pruning (artificial neural network)
Pruning_(artificial_neural_network)
Partition of a graph's nodes into cliques
Mathieu; Kim, Ethan; Vetta, Adrian (January 2012), "Clique cover on sparse networks", 2012 Proceedings of the Fourteenth Workshop on Algorithm Engineering
Clique_cover
Matrix manipulation algorithm
ISBN 0-12-583850-6. Tinney, W. F.; Walker, J. W. (1967). "Direct solution of sparse network equations by optimally ordered triangular factorization". Proc. IEEE
Minimum_degree_algorithm
Representation learning method
Sparse dictionary learning (also known as sparse coding or SDL) is a representation learning method which aims to find a sparse representation of the
Sparse_dictionary_learning
Technique to solve partial differential equations
(2021-06-07). "Uncovering near-wall blood flow from sparse data with physics-informed neural networks". Physics of Fluids. 33 (7): 071905. arXiv:2104.08249
Physics-informed neural networks
Physics-informed_neural_networks
Method to find shortest paths
Johnson, Donald B. (1977), "Efficient algorithms for shortest paths in sparse networks", Journal of the ACM, 24 (1): 1–13, doi:10.1145/321992.321993, S2CID 207678246
Johnson's_algorithm
Reverse-engineering neural networks
such as AI misalignment. A sparse autoencoder (SAE) is a model trained to disentangle neural network activations into sparse representations. The learned
Mechanistic_interpretability
Technique combining machine learning and computer vision
the learning algorithms. D. Roth applied two learning algorithms: 1.Sparse Network of Winnows(SNoW) system SNoW-Train Initial step: initial the set of
Geometric_feature_learning
Most populous city in Canada
The TTC operates an extensive bus network that serves parts of the city many not served by the sparse subway network. The TTC bus system had an annual
Toronto
Network for fugitive slaves in 19th-century U.S.
granting them immunity to operate in free states. Because the law required sparse documentation to claim a person was a fugitive, slave catchers also kidnapped
Underground_Railroad
American data scientist and statistician
highly impactful seminal work on large-scale Bayesian dynamic modeling, sparse network models, and related development of efficient computational algorithms
Emily_B._Fox
Town in Hadhramaut, Yemen
broad plateau averaging around 1,400 m (0.87 miles) of altitude, with a sparse network of deeply sunk wadis (seasonal watercourses). Although the southern
Tarim,_Yemen
Country within the United Kingdom
an abrupt halt in the previous sheep farming boom. Scotland is the most sparsely populated country of the United Kingdom. In August 2012, the Scottish population
Scotland
Country in Eastern Europe and North Asia
square kilometre (22 inhabitants/mi2), Russia is one of the world's most sparsely populated countries, with the vast majority of its people concentrated
Russia
Country in Southern and Western Europe
Basilicata, and the island of Sardinia, as well as much of Sicily, are sparsely populated. Italy's population almost doubled during the 20th century, but
Italy
Species of spider
likened to a blind person with a cane would move while walking on a sparse network of aerial lines. Eberhard, William G (2007-09-07). "Miniaturized orb-weaving
Leucauge_mariana
Ability of a computer to receive and interpret intelligible handwritten input
2278–2324. "Sparse Networks Come to the Aid of Big Physics". Quanta Magazine. June 2023. Retrieved 17 June 2023. Graham, Benjamin. "Spatially-sparse convolutional
Handwriting_recognition
Methodic assignment of colors to elements of a graph
Alessandro; Rizzi, Romeo (2001), "Some simple distributed algorithms for sparse networks" (PDF), Distributed Computing, 14 (2), Berlin, New York: Springer-Verlag:
Graph_coloring
Topological index of a molecule
Johnson, Donald B. (1977), "Efficient algorithms for shortest paths in sparse networks", Journal of the ACM, 24 (1): 1–13, doi:10.1145/321992.321993, S2CID 207678246
Wiener_index
Species of large felid
10 individuals inhabit an area of 100 km2 (39 sq mi); in habitats with sparse prey, an area of 1,000 km2 (390 sq mi) usually supports only five individuals
Snow_leopard
statistically significant in networks with larger density, while it must be regarded as a less pronounced effect in sparser networks. Diego Garlaschelli; Loffredo
Reciprocity_(network_science)
2010 video game
resolution, shadows, and anti-aliasing, but felt improvements were otherwise sparse; Eurogamer's Oliver Mackenzie criticized the outdated user interface. Several
Red_Dead_Redemption
Supranational political and economic union
the "blue banana", while Sweden and Finland in the north are much more sparsely populated. The total population of the EU has been slightly decreasing
European_Union
Algorithm for modelling sequential data
Long Sequences with Sparse Transformers". arXiv:1904.10509 [cs.LG]. "Constructing Transformers For Longer Sequences with Sparse Attention Methods". Google
Transformer_(deep_learning)
military into constructing a packet switching network. Early international collaborations via the ARPANET were sparse. Connections were made in 1973 to Norway
History_of_the_Internet
an unweighted and typically sparse "backbone" network that can be more informative to analyze and visualize. Flavor network and the principles of food
Bipartite_network_projection
Finnish and American software engineer (born 1969)
License version 2. Dirk Hohndel became its head maintainer in late 2012. Sparse is a static analysis tool that flags constructs that are likely to be of
Linus_Torvalds
Country in North Africa
of the Sahara desert, which constitute most of Egypt's territory, are sparsely inhabited. About 43% of Egypt's residents live across the country's urban
Egypt
Province of Canada
densely populated Canada East, and Upper Canada became the anglophone and sparsely populated Canada West. This union, unsurprisingly, was the main source
Quebec
the network is still relatively sparse, as ( ln N N ) → 0 {\displaystyle {\left({\frac {\ln N}{N}}\right)\rightarrow 0}} for large N. The network turns
Evolution_of_a_random_network
Chinese artificial intelligence company
September 2025. V3.2-Exp was released on 29 September 2025. It uses DeepSeek Sparse Attention, a more efficient attention mechanism based on previous research
DeepSeek
Electronic communication subsystem on an integrated circuit
clock domain. NoC architectures typically model sparse small-world networks (SWNs) and scale-free networks (SFNs) to limit the number, length, area and power
Network_on_a_chip
Country in Central and Southeast Europe
72.9 inhabitants per square kilometre, making Croatia one of the more sparsely populated European countries. The overall life expectancy in Croatia at
Croatia
Subset of artificial intelligence
representation is low-dimensional. Sparse coding algorithms attempt to do so under the constraint that the learned representation is sparse, meaning that the mathematical
Machine_learning
Vice President of the United States since 2025
throughout the organization's existence. Our Ohio Renewal closed by 2021 with sparse achievements. According to Jivani, the organization's director of law and
JD_Vance
Country in Southeast Asia and Oceania
relies heavily on coal-fired generation. Extending the grid is difficult in sparsely populated and island areas, while reliability problems are reported even
Indonesia
Country in northern Europe
has sent athletes to compete in every Games since then, except for the sparsely attended 1904 Games and the 1980 Summer Olympics in Moscow when they participated
Norway
Collection of molecular regulators
that natural selection tends to favor networks with sparse connectivity. There are primarily two ways that networks can evolve, both of which can occur
Gene_regulatory_network
3D reconstruction technique
methods) and respective camera poses are reproducible and error-free. For each sparse viewpoint (image and camera pose) provided, camera rays are marched through
Neural_radiance_field
Fewest cliques covering a graph's edges
Blanchette, Mathieu; Kim, Ethan; Vetta, Adrian (2012), "Clique cover on sparse networks", in Bader, David A.; Mutzel, Petra (eds.), Proceedings of the 14th
Intersection number (graph theory)
Intersection_number_(graph_theory)
Network with non-trivial topological features
triangles in the network. For instance, sparse random graphs have a vanishingly small clustering coefficient while real world networks often have a coefficient
Complex_network
American social news and discussion site
Reddit released its official mobile app, called iReddit. This app was sparsely updated, and was superseded by a new mobile website in 2010. For several
Measure of connection disorder in a network
normalized network entropy is maximal H = 1 {\displaystyle {\mathcal {H}}=1} when the network is fully connected and decreases the sparser the network becomes
Network_entropy
Borough and county in New York, US
industrialization spread to Sunset Park (then coterminous with the city's sprawling, sparsely populated Eighth Ward) and adjacent Bay Ridge (hitherto a resort-like subsection
Brooklyn
Concept in network science
Lenka; Zhang, Pan (October 2013). "Spectral redemption in clustering sparse networks". Proceedings of the National Academy of Sciences. 110 (52): 20935–20940
Stochastic_block_model
Professional baseball team in Oakland, California (1968–2024)
season tickets a tough sell, while crowds as high as 30,000 often seemed sparse in such a venue. On December 21, 2005, the Athletics announced that seats
Oakland_Athletics
Country in the Caribbean
were enslaved people and 1,082 Indigenous people.[citation needed] The sparse settlement and slow rate of population-increase during Spanish rule (and
Trinidad_and_Tobago
Salafi jihadist militant organisation
from its own brutal brand of law enforcement. In fact, it is more of a network than a nation, having made canny use of social media to exert influence
Islamic_State
Artificial neural network that mimics neurons
clustering with spiking neurons by sparse temporal coding and multilayer RBF networks". IEEE Transactions on Neural Networks. 13 (2): 426–435. Bibcode:2002ITNN
Spiking_neural_network
Country in South America
Pacific coastal lowlands, backed by the Serranía de Baudó mountains, are sparsely populated and covered in dense vegetation. The principal Pacific port is
Colombia
Network
observed. A variant of a network telescope is a sparse darknet, or greynet, consisting of a region of IP address space that is sparsely populated with "darknet"
Network_telescope
County (län) of Sweden
lives in the namesake province, whereas the Lapland part of the county is sparsely populated. Norrbotten covers a larger land area than both Austria and Portugal
Norrbotten_County
Suite of algorithms
National Institutes of Health supported Biomedical Informatics Research Network. In a more general sense, diffeomorphic mapping is any solution that registers
Large deformation diffeomorphic metric mapping
Large_deformation_diffeomorphic_metric_mapping
Method of representing systems
A biological network is a method of representing systems as complex sets of binary interactions or relations between various biological entities. In general
Biological_network
Network of points with known positions used in geodesy and surveying
used in the field. Instead of using only sparse and much less accurate distance measurements some control networks were established or updated by using trilateration
Geodetic_control_network
Biblical figure and Israelite monarch
Silberman stated that the archaeological evidence shows that Judah was sparsely inhabited and Jerusalem no more than a small village. The evidence suggested
David
Country in Southeast-Central Europe
both countries. Due to configuration of the terrain, natural lakes are sparse and small; most of them are located in the lowlands of Vojvodina, like the
Serbia
Country in North Africa
portion of the country is in the Sahara Desert and as such is generally sparsely populated and unproductive economically. Most of the population lives to
Morocco
SPARSE NETWORK
SPARSE NETWORK
Surname or Lastname
English
English : from the Norman personal name Serlo, Germanic Sarilo, Serilo. This was probably originally a byname cognate with Old Norse Sorli, and akin to Old English searu ‘armor’, meaning perhaps ‘defender’, ‘protector’.
Surname or Lastname
English
English : variant of Spear.
Surname or Lastname
English
English : variant of Sparks.
Male
English
Short form of English unisex Paisley, PAISE means "church."Â
Surname or Lastname
English
English : patronymic from Spire 1.
Boy/Male
Afghan, Arabic, Iranian, Muslim, Parsi
Pious; Pure; Chaste; Holy
Surname or Lastname
English
English : patronymic from Spark 1.
Surname or Lastname
English
English : metonymic occupational name for someone who made bags or purses or for an official in charge of expenditure, from Middle English purse (via Old English from Latin bursa).Scottish : variant of Purser.
Surname or Lastname
Portuguese
Portuguese : occupational name from soeiro ‘swineherd’, Latin suerius.English : patronymic from a nickname for someone with reddish hair, from Anglo-Norman French sor ‘chestnut (color)’.
Girl/Female
Hindu, Indian
Touch
Surname or Lastname
English
English : variant spelling of Pass.French : possibly a nickname from passe ‘sparrow’.
Surname or Lastname
English
English : patronymic from Spear.
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Feel; Healthy; Touch
Boy/Male
Anglo Saxon Welsh
Spares.
Surname or Lastname
English (Suffolk)
English (Suffolk) : unexplained.
Surname or Lastname
English
English : variant of Speake.
Female
English
English variant form of French Cerise, SHARISE means "cherry."Â
Surname or Lastname
English
English : nickname for a frugal person, from Middle English spare ‘sparing’, ‘frugal’.
Surname or Lastname
Irish (Kerry)
Irish (Kerry) : Anglicized form of Gaelic Mac Saoghair, which in turn may be a patronymic from a Gaelicized form of the Old English personal name Saeger (see 2 below).English : patronymic from a Middle English personal name Saher or Seir (see Sayer 1).Americanized form of French Cyr.Richard Sears came to Plymouth, MA, from England about 1630.
Boy/Male
American, British, English
Gallant
SPARSE NETWORK
SPARSE NETWORK
Boy/Male
Indian, Punjabi, Sikh
Support of God's Love
Girl/Female
Gaelic
From the glen. Valley.
Girl/Female
Hindu
Perfume, Fragrance
Boy/Male
Hindu
Girl/Female
Hindu, Indian
Happiness
Boy/Male
Scottish
Anchor.
Girl/Female
Arabic, Chinese, Muslim
Splendid; Illuminous; Bright Shine of Light
Girl/Female
Hindu, Indian, Tamil
Lotus; Queen
Boy/Male
Muslim
Name of a companion of the prophet
Boy/Male
Muslim
Spring
SPARSE NETWORK
SPARSE NETWORK
SPARSE NETWORK
SPARSE NETWORK
SPARSE NETWORK
v. t.
Held in reserve, to be used in an emergency; as, a spare anchor; a spare bed or room.
n.
A fine sieve; a searce.
n.
One who parses.
v. t.
To sprinkle; to moisten by sprinkling; as, to sparge paper.
v. t.
To inclose in a hearse; to entomb.
n.
The right of bowling again at a full set of pins, after having knocked all the pins down in less than three bowls. If all the pins are knocked down in one bowl it is a double spare; in two bowls, a single spare.
adv.
In a scattered or sparse manner.
n.
One who spares.
imp. & p. p.
of Spare
v. t.
Scanty; not abundant or plentiful; as, a spare diet.
v. t.
To sift through a sarse.
n.
To emit sparks; to throw off ignited or incandescent particles; to shine as if throwing off sparks; to emit flashes of light; to scintillate; to twinkle; as, the blazing wood sparkles; the stars sparkle.
v. t.
To emit in the form or likeness of sparks.
superl.
Not refined; rough; rude; unpolished; gross; indelicate; as, coarse manners; coarse language.
imp. & p. p.
of Parse
superl.
Thinly scattered; set or planted here and there; not being dense or close together; as, a sparse population.
v. t.
Being over and above what is necessary, or what must be used or reserved; not wanted, or not used; superfluous; as, I have no spare time.
superl.
Large in bulk, or composed of large parts or particles; of inferior quality or appearance; not fine in material or close in texture; gross; thick; rough; -- opposed to fine; as, coarse sand; coarse thread; coarse cloth; coarse bread.
adv.
Sparsely; scatteredly; here and there.
n.
Brilliancy; luster; as, the sparkle of a diamond.