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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
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
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
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 mathematics
Sparse approximation (also known as sparse representation) theory deals with sparse solutions for systems of linear equations. Techniques for finding
Sparse_approximation
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
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
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
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. One of the first
Delay-tolerant_networking
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
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
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
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
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
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
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
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
Neural network based evaluation function
simple 8×8 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
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
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
Academic field
Network science is an academic field which studies complex networks such as telecommunication networks, computer networks, biological networks, cognitive
Network_science
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
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
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)
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Right of public access to land or bodies of water
this means is not further explicated on in the constitution, and only sparsely in other legislation. In practice, allemansrätten is defined as actions
Freedom_to_roam
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
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
Ecoregion that covers parts of the Russian Far East
The Kamchatka-Kurile meadows and sparse forests ecoregion (WWF ID: PA0603) covers the coastal zones of the Kamchatka peninsula, northern section of the
Kamchatka–Kurile meadows and sparse forests
Kamchatka–Kurile_meadows_and_sparse_forests
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
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
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
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
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
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
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
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
Maurizio, Mazzoleni; Reyne, Ugay (2019). "Flood Inundation Mapping of the Sparsely Gauged Large-Scale Brahmaputra Basin Using Remote Sensing Products". Remote
List_of_rivers_by_discharge
Australian drama series
"atmospherically... very well-judged, with a faded, weather-beaten look – sparse but evocative". David Knox of TV Tonight rated the series 4 out 5 stars
Treasure_&_Dirt
Chinese artificial intelligence company
X.; Wang, Lean (27 February 2025), Native Sparse Attention: Hardware-Aligned and Natively Trainable Sparse Attention, arXiv:2502.11089 "deepseek-ai/DeepSeek-V3
DeepSeek
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
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)
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
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)
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
Purported ancient tribal confederation of the Late Bronze Age
hypothesized that the Shekelesh have some connection to Sicily, though evidence is sparse, and proposals vary as to whether Sicily was their original homeland, or
Sea_Peoples
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
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
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
Algorithm for modelling sequential data
In deep learning, the transformer is a family of artificial neural network architectures based on the multi-head attention mechanism, in which text is
Transformer_(deep_learning)
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
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
a very weather-active region. Forecasts had to be made from a very sparse network of observing stations in mainland Asia and over the western Pacific
John_A._Day
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 South America
communities. Until the period of European colonisation, Argentina was relatively sparsely populated by a wide number of diverse cultures with different social organisations
Argentina
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
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
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
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
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
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
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
American computer scientist
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
Donald_B._Johnson
Earthquake near the China–Kyrgyzstan border
assigned mb (body wave magnitude) 7.9 and Ms 8.6, respectively. Due to the sparse network of seismic instruments to record the mainshock, its magnitude was greatly
1902_Turkestan_earthquake
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
Aircraft crash in United States
successfully executed a loop before purposely crashing the aircraft on the sparsely populated Ketron Island in Puget Sound with the intent to die by suicide
2018 Horizon Air Bombardier Q400 incident
2018_Horizon_Air_Bombardier_Q400_incident
East Asian ethnic group
settlement by Chinese of lands previously regarded as part of the empire's sparsely populated frontier or periphery. Guangdong and Fujian, hitherto regarded
Han_Chinese
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
Large language model developed by Google
like Anthropic, xAI, or OpenAI held advantages. Gato, a multimodal neural network developed by DeepMind Gemini Robotics Reasoning model List of large language
Gemini_(language_model)
Phenomenon in neural networks
interpretable structure from polysemantic representations is to train a sparse autoencoder on the activations of the model being studied. The autoencoder
Polysemanticity
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
2025 operating system version
disc image format, formerly RAW, has been replaced by the new format Apple Sparse Image Format (ASIF), which Apple claims is significantly faster and more
MacOS_Tahoe
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