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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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
Academic field
Network science is an academic field which studies complex networks such as telecommunication networks, computer networks, biological networks, cognitive
Network_science
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
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
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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)
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
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
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
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
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
generalize and extend sparsity regularization methods, by allowing for optimal selection over structures like groups or networks of input variables in
Structured sparsity regularization
Structured_sparsity_regularization
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
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
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
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
Problem in computer networking
Waylon Brunette. Data MULEs: Modeling a Three-tier Architecture for Sparse Sensor Networks. In Proc. IEEE SNPA Workshop, May 2003. Aruna Balasubramanian, Brian
Routing in delay-tolerant networking
Routing_in_delay-tolerant_networking
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
American football season
original on May 25, 2023. Retrieved May 10, 2025. "While details remain sparse, the NFL's TV packages on CBS and Fox will seemingly look much different
2026_NFL_season
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
Neural network coding model
The convolutional sparse coding paradigm is an extension of the global sparse coding model, in which a redundant dictionary is modeled as a concatenation
Convolutional_sparse_coding
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
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
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
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
Challenges in Geographic Routing: Sparse Networks, Obstacles, and Traffic Provisioning. In DIMACS Workshop on Pervasive Networking, Piscataway, NJ, May 2001 B
Greedy Perimeter Stateless Routing in Wireless Networks
Greedy_Perimeter_Stateless_Routing_in_Wireless_Networks
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
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
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
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
American football season
original on May 25, 2023. Retrieved May 10, 2025. "While details remain sparse, the NFL's TV packages on CBS and Fox will seemingly look much different
2025_NFL_season
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
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
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
Sparse graph with strong connectivity
In graph theory, an expander graph is a sparse graph that has strong connectivity properties, quantified using vertex, edge or spectral expansion. Expander
Expander_graph
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
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
Pandemic caused by SARS-CoV-2
levels of 'hybrid immunity' and low case numbers. Due to its remoteness and sparse population, Antarctica was the last continent to have confirmed cases of
COVID-19_pandemic
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
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
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
Country in West Asia
date palms, acacia, and eucalyptus trees. In the desert, the flora is very sparse and consists of grasses and thorn bushes. The indigenous fauna had come
United_Arab_Emirates
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)
Japanese high-speed rail system
'new main line'), colloquially known in English as the bullet train, is a network of high-speed railway lines in Japan. The system was developed to provide
Shinkansen
Television content transmitted via signals on coaxial or fibre-optic cable
little success in Africa, as it is not cost-effective to lay cables in sparsely populated areas. Multichannel multipoint distribution service, a microwave-based
Cable_television
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
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
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
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
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
Algorithm for modelling sequential data
Generating Long Sequences with Sparse Transformers, arXiv:1904.10509 "Constructing Transformers For Longer Sequences with Sparse Attention Methods". Google
Transformer_(deep_learning)
Species of plant
depression is the leading cause of death from opioid use. Although evidence is sparse, the risk of respiratory depression caused by taking kratom appears to be
Mitragyna_speciosa
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
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
Set of learning techniques in machine learning
data point (to enable sparse representation of data), and an L2 regularization on the parameters of the classifier. Neural networks are a family of learning
Feature_learning
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
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
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
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)
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
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
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
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
undirected, scale-free network where the degree distribution follows a power law with an exponential cutoff – most authors are sparsely connected while a few
Scientific collaboration network
Scientific_collaboration_network
SPARSE NETWORK
SPARSE NETWORK
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.
Boy/Male
Anglo Saxon Welsh
Spares.
Surname or Lastname
English (Suffolk)
English (Suffolk) : unexplained.
Surname or Lastname
English
English : patronymic from Spark 1.
Surname or Lastname
English
English : variant of Spear.
Surname or Lastname
English
English : variant of Speake.
Surname or Lastname
English
English : patronymic from Spire 1.
Male
English
Short form of English unisex Paisley, PAISE means "church."Â
Girl/Female
Hindu, Indian
Touch
Surname or Lastname
English
English : variant of Sparks.
Surname or Lastname
English
English : nickname for a frugal person, from Middle English spare ‘sparing’, ‘frugal’.
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’.
Boy/Male
American, British, English
Gallant
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)’.
Surname or Lastname
English
English : variant spelling of Pass.French : possibly a nickname from passe ‘sparrow’.
Female
English
English variant form of French Cerise, SHARISE means "cherry."Â
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Feel; Healthy; Touch
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.
Surname or Lastname
English
English : patronymic from Spear.
Boy/Male
Afghan, Arabic, Iranian, Muslim, Parsi
Pious; Pure; Chaste; Holy
SPARSE NETWORK
SPARSE NETWORK
Girl/Female
Tamil
Devotee
Girl/Female
Indian
Zilay: shadow, Share Urooj
Boy/Male
Arabic
Planet; North
Boy/Male
Muslim
Girl/Female
Gaelic
Slender. (French) 'from the forest.
Girl/Female
Arabic, Bengali, Gujarati, Hindu, Indian, Kannada, Marathi, Muslim, Telugu
Salute of Paradise
Boy/Male
Indian
Servant of the all-hearing (Allah)
Female
English
French form of Latin Clara, CLAIRE means "clear, bright."
Girl/Female
Hindu, Indian, Marathi, Tamil
Peace
Boy/Male
Arabic, Muslim, Sindhi
Teacher
SPARSE NETWORK
SPARSE NETWORK
SPARSE NETWORK
SPARSE NETWORK
SPARSE NETWORK
imp. & p. p.
of Spare
adv.
Sparsely; scatteredly; here and there.
n.
One who spares.
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.
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.
superl.
Thinly scattered; set or planted here and there; not being dense or close together; as, a sparse population.
n.
Brilliancy; luster; as, the sparkle of a diamond.
adv.
In a scattered or sparse manner.
v. t.
To inclose in a hearse; to entomb.
n.
A fine sieve; a searce.
n.
One who parses.
imp. & p. p.
of Parse
superl.
Not refined; rough; rude; unpolished; gross; indelicate; as, coarse manners; coarse language.
v. t.
Held in reserve, to be used in an emergency; as, a spare anchor; a spare bed or room.
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.
v. t.
To sift through a sarse.
v. t.
Scanty; not abundant or plentiful; as, a spare diet.
v. t.
To emit in the form or likeness of sparks.
v. t.
To sprinkle; to moisten by sprinkling; as, to sparge paper.
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.