This slide is used to do an introduction for the matplotlib library and this will be a very basic introduction. As matplotlib is a very used and famous library for machine learning this will be very helpful to teach a student with no coding background and they can start the plotting of maps from the ending of the slide by there own.
In this paper we propose Regularised Cross-Modal Hashing
(RCMH) a new cross-modal hashing model that projects
annotation and visual feature descriptors into a common
Hamming space. RCMH optimises the hashcode similarity
of related data-points in the annotation modality using an
iterative three-step hashing algorithm: in the first step each
training image is assigned a K-bit hashcode based on hyperplanes learnt at the previous iteration; in the second step the binary bits are smoothed by a formulation of graph regularisation so that similar data-points have similar bits; in the third step a set of binary classifiers are trained to predict the regularised bits with maximum margin. Visual descriptors are projected into the annotation Hamming space by a set of binary classifiers learnt using the bits of the corresponding annotations as labels. RCMH is shown to consistently improve retrieval effectiveness over state-of-the-art baselines.
This slide is used to do an introduction for the matplotlib library and this will be a very basic introduction. As matplotlib is a very used and famous library for machine learning this will be very helpful to teach a student with no coding background and they can start the plotting of maps from the ending of the slide by there own.
In this paper we propose Regularised Cross-Modal Hashing
(RCMH) a new cross-modal hashing model that projects
annotation and visual feature descriptors into a common
Hamming space. RCMH optimises the hashcode similarity
of related data-points in the annotation modality using an
iterative three-step hashing algorithm: in the first step each
training image is assigned a K-bit hashcode based on hyperplanes learnt at the previous iteration; in the second step the binary bits are smoothed by a formulation of graph regularisation so that similar data-points have similar bits; in the third step a set of binary classifiers are trained to predict the regularised bits with maximum margin. Visual descriptors are projected into the annotation Hamming space by a set of binary classifiers learnt using the bits of the corresponding annotations as labels. RCMH is shown to consistently improve retrieval effectiveness over state-of-the-art baselines.
A Hough Transform Based On a Map-Reduce AlgorithmIJERA Editor
This paper presents a method that proposes the composition of the Map-Reduce algorithm and the Hough
Transform method to research particular features of shape in the Big Data of images. We introduce the first
formal translation of the Hough Transform method into the Map-Reduce pattern. The Hough transform is
applied to one image or to several images in parallel. The context of the application of this method concerns Big
Data that requires Map-Reduce functions to improve the processing time and the need of object detection in
noisy pictures with the Hough Transform method.
Interaction Networks for Learning about Objects, Relations and PhysicsKen Kuroki
For my presentation for a reading group. I have not in any way contributed this study, which is done by the researchers named on the first slide.
https://papers.nips.cc/paper/6418-interaction-networks-for-learning-about-objects-relations-and-physics
Effective Numerical Computation in NumPy and SciPyKimikazu Kato
Presented at PyCon JP 2014.
Video is available at
http://bit.ly/1tXYhw6
This talk explores case studies of effective usage of Numpy/Scipy and shows that the computational speed sometimes improves drastically with the appropriate derivation of formulas and performance-conscious implementation. I especially focus on scipy.sparse, the module for sparse matrices, which is often useful in the areas of machine learning and natural language processing.
Image Retrieval with Fisher Vectors of Binary Features (MIRU'14)Yusuke Uchida
Recently, the Fisher vector representation of local features has attracted much attention because of its effectiveness in both image classification and image retrieval. Another trend in the area of image retrieval is the use of binary feature such as ORB, FREAK, and BRISK. Considering the significant performance improvement in terms of accuracy in both image classification and retrieval by the Fisher vector of continuous feature descriptors, if the Fisher vector were also to be applied to binary features, we would receive the same benefits in binary feature based image retrieval and classification. In this paper, we derive the closed-form approximation of the Fisher vector of binary features which are modeled by the Bernoulli mixture model. In experiments, it is shown that the Fisher vector representation improves the accuracy of image retrieval by 25% compared with a bag of binary words approach.
Spectroscopy or hyperspectral imaging consists in the acquisition, analysis, and extraction of the spectral information measured on a specific region or object using an airborne or satellite device. Hyperspectral imaging has become an active field of research recently. One way of analysing such data is through clustering. However, due to the high dimensionality of the data and the small distance between the different material signatures, clustering such a data is a challenging task.In this paper, we empirically compared five clustering techniques in different hyperspectral data sets. The considered clustering techniques are K-means, K-medoids, fuzzy Cmeans, hierarchical, and density-based spatial clustering of applications with noise. Four data sets are used to achieve this purpose which is Botswana, Kennedy space centre, Pavia, and Pavia University. Beside the accuracy, we adopted four more similarity measures: Rand statistics, Jaccard coefficient, Fowlkes-Mallows index, and Hubert index. According to accuracy, we found that fuzzy C-means clustering is doing better on Botswana and Pavia data sets, K-means and K-medoids are giving better results on Kennedy space centre data set, and for Pavia University the hierarchical clustering is better
Fast Object Recognition from 3D Depth Data with Extreme Learning MachineSoma Boubou
Object recognition from RGB-D sensors has recently emerged as a renowned and challenging research topic. The current systems often require large amounts of time to train the models and to classify new data. We proposed an effective and fast object recognition approach from 3D data acquired from depth sensors such as Structure or Kinect sensors.
Our contribution in this work} is to present a novel fast and effective approach for real-time object recognition from 3D depth data:
- First, we extract simple but effective frame-level features, which we name as differential frames, from the raw depth data.
- Second, we build a recognition system based on Extreme Learning Machine classifier with a Local Receptive Field (ELM-LRF).
Reversible Data Hiding in the Spatial and Frequency DomainsCSCJournals
Combinational lossless data hiding in the spatial and frequency domains is proposed. In the spatial domain, a secret message is embedded in a host medium using the min-max algorithm to generate a stego-image. Subsequently, the stego-image is decomposed into the frequency domain via the integer wavelet transform (IWT). Then, a watermark is hidden in the low-high (LH) and high-low (HL) subbands of the IWT domain using the coefficient-bias approach. Simulations show that the perceptual quality of the image generated by the proposed method and the method¡¦s hiding capability are good. Moreover, the mixed images produced by the proposed method are robust against attacks such as JPEG2000, JPEG, brightness adjustment, and inversion.
We report on cosmological N-body
simulations which run over up to 4
supercomputers across the globe. We
achieved to run simulations on 60 to 750
cores distributed over a variety of
supercomputers. Regardless of the
network latency of 0.32 s and the
communication over 30.000 km of optical
network cable we are able to achieve up
to 92% of the performance compared to
an equal number of cores on a single
supercomputer.
A Hough Transform Based On a Map-Reduce AlgorithmIJERA Editor
This paper presents a method that proposes the composition of the Map-Reduce algorithm and the Hough
Transform method to research particular features of shape in the Big Data of images. We introduce the first
formal translation of the Hough Transform method into the Map-Reduce pattern. The Hough transform is
applied to one image or to several images in parallel. The context of the application of this method concerns Big
Data that requires Map-Reduce functions to improve the processing time and the need of object detection in
noisy pictures with the Hough Transform method.
Interaction Networks for Learning about Objects, Relations and PhysicsKen Kuroki
For my presentation for a reading group. I have not in any way contributed this study, which is done by the researchers named on the first slide.
https://papers.nips.cc/paper/6418-interaction-networks-for-learning-about-objects-relations-and-physics
Effective Numerical Computation in NumPy and SciPyKimikazu Kato
Presented at PyCon JP 2014.
Video is available at
http://bit.ly/1tXYhw6
This talk explores case studies of effective usage of Numpy/Scipy and shows that the computational speed sometimes improves drastically with the appropriate derivation of formulas and performance-conscious implementation. I especially focus on scipy.sparse, the module for sparse matrices, which is often useful in the areas of machine learning and natural language processing.
Image Retrieval with Fisher Vectors of Binary Features (MIRU'14)Yusuke Uchida
Recently, the Fisher vector representation of local features has attracted much attention because of its effectiveness in both image classification and image retrieval. Another trend in the area of image retrieval is the use of binary feature such as ORB, FREAK, and BRISK. Considering the significant performance improvement in terms of accuracy in both image classification and retrieval by the Fisher vector of continuous feature descriptors, if the Fisher vector were also to be applied to binary features, we would receive the same benefits in binary feature based image retrieval and classification. In this paper, we derive the closed-form approximation of the Fisher vector of binary features which are modeled by the Bernoulli mixture model. In experiments, it is shown that the Fisher vector representation improves the accuracy of image retrieval by 25% compared with a bag of binary words approach.
Spectroscopy or hyperspectral imaging consists in the acquisition, analysis, and extraction of the spectral information measured on a specific region or object using an airborne or satellite device. Hyperspectral imaging has become an active field of research recently. One way of analysing such data is through clustering. However, due to the high dimensionality of the data and the small distance between the different material signatures, clustering such a data is a challenging task.In this paper, we empirically compared five clustering techniques in different hyperspectral data sets. The considered clustering techniques are K-means, K-medoids, fuzzy Cmeans, hierarchical, and density-based spatial clustering of applications with noise. Four data sets are used to achieve this purpose which is Botswana, Kennedy space centre, Pavia, and Pavia University. Beside the accuracy, we adopted four more similarity measures: Rand statistics, Jaccard coefficient, Fowlkes-Mallows index, and Hubert index. According to accuracy, we found that fuzzy C-means clustering is doing better on Botswana and Pavia data sets, K-means and K-medoids are giving better results on Kennedy space centre data set, and for Pavia University the hierarchical clustering is better
Fast Object Recognition from 3D Depth Data with Extreme Learning MachineSoma Boubou
Object recognition from RGB-D sensors has recently emerged as a renowned and challenging research topic. The current systems often require large amounts of time to train the models and to classify new data. We proposed an effective and fast object recognition approach from 3D data acquired from depth sensors such as Structure or Kinect sensors.
Our contribution in this work} is to present a novel fast and effective approach for real-time object recognition from 3D depth data:
- First, we extract simple but effective frame-level features, which we name as differential frames, from the raw depth data.
- Second, we build a recognition system based on Extreme Learning Machine classifier with a Local Receptive Field (ELM-LRF).
Reversible Data Hiding in the Spatial and Frequency DomainsCSCJournals
Combinational lossless data hiding in the spatial and frequency domains is proposed. In the spatial domain, a secret message is embedded in a host medium using the min-max algorithm to generate a stego-image. Subsequently, the stego-image is decomposed into the frequency domain via the integer wavelet transform (IWT). Then, a watermark is hidden in the low-high (LH) and high-low (HL) subbands of the IWT domain using the coefficient-bias approach. Simulations show that the perceptual quality of the image generated by the proposed method and the method¡¦s hiding capability are good. Moreover, the mixed images produced by the proposed method are robust against attacks such as JPEG2000, JPEG, brightness adjustment, and inversion.
We report on cosmological N-body
simulations which run over up to 4
supercomputers across the globe. We
achieved to run simulations on 60 to 750
cores distributed over a variety of
supercomputers. Regardless of the
network latency of 0.32 s and the
communication over 30.000 km of optical
network cable we are able to achieve up
to 92% of the performance compared to
an equal number of cores on a single
supercomputer.
Distance oracle - Truy vấn nhanh khoảng cách giữa hai điểm bất kỳ trên đồ thịHong Ong
Bài review cách tính nhanh khoảng cách giữa hai điểm bất kỳ trên đồ thị. Ứng dụng trong nhiều lĩnh vực như: telecome, internet routing, social network analysis, etc.
International Journal of Engineering and Science Invention (IJESI)inventionjournals
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
https://github.com/telecombcn-dl/lectures-all/
These slides review techniques for interpreting the behavior of deep neural networks. The talk reviews basic techniques such as the display of filters and tensors, as well as more advanced ones that try to interpret which part of the input data is responsible for the predictions, or generate data that maximizes the activation of certain neurons.
Introduction To Machine Learning and Neural Networks德平 黄
It's a slideshow given by myselft, a simple introduction to machine learning and neurals . It's mainly about how neural networks work and some basic inductions to Backpropagation Algorithm. Moreover, something abount Convolutional Neural Networks was given in the last few slides.
Random Chaotic Number Generation based Clustered Image EncryptionAM Publications
Image encryption process is one of secure communication techniques to get confidentiality and authority of reading data. Encryption techniques should be improved with technological progress to overcome the security problems like the existence of penetration of the network. This paper develop an image encryption technique by encrypt the clusters of image using the generated keys from propose a modified of standard map. In decryption process, a recover image can be obtained by reverse the encryption process and utilize adding instead of clustering. Exploratory results check and demonstrate that the proposed procedure is secure and quick.
Classification of Iris Data using Kernel Radial Basis Probabilistic Neural N...Scientific Review SR
Radial Basis Probabilistic Neural Network (RBPNN) has a broader generalized capability that been
successfully applied to multiple fields. In this paper, the Euclidean distance of each data point in RBPNN is
extended by calculating its kernel-induced distance instead of the conventional sum-of squares distance. The
kernel function is a generalization of the distance metric that measures the distance between two data points as the
data points are mapped into a high dimensional space. During the comparing of the four constructed classification
models with Kernel RBPNN, Radial Basis Function networks, RBPNN and Back-Propagation networks as
proposed, results showed that, model classification on Iris Data with Kernel RBPNN display an outstanding
performance in this regard
Classification of Iris Data using Kernel Radial Basis Probabilistic Neural Ne...Scientific Review
Radial Basis Probabilistic Neural Network (RBPNN) has a broader generalized capability that been successfully applied to multiple fields. In this paper, the Euclidean distance of each data point in RBPNN is extended by calculating its kernel-induced distance instead of the conventional sum-of squares distance. The kernel function is a generalization of the distance metric that measures the distance between two data points as the data points are mapped into a high dimensional space. During the comparing of the four constructed classification models with Kernel RBPNN, Radial Basis Function networks, RBPNN and Back-Propagation networks as proposed, results showed that, model classification on Iris Data with Kernel RBPNN display an outstanding performance in this regard.
Similar to [ICLR/ICML2019読み会] A Wrapped Normal Distribution on Hyperbolic Space for Gradient Based Learning (ICML2019) (20)
Salas, V. (2024) "John of St. Thomas (Poinsot) on the Science of Sacred Theol...Studia Poinsotiana
I Introduction
II Subalternation and Theology
III Theology and Dogmatic Declarations
IV The Mixed Principles of Theology
V Virtual Revelation: The Unity of Theology
VI Theology as a Natural Science
VII Theology’s Certitude
VIII Conclusion
Notes
Bibliography
All the contents are fully attributable to the author, Doctor Victor Salas. Should you wish to get this text republished, get in touch with the author or the editorial committee of the Studia Poinsotiana. Insofar as possible, we will be happy to broker your contact.
Slide 1: Title Slide
Extrachromosomal Inheritance
Slide 2: Introduction to Extrachromosomal Inheritance
Definition: Extrachromosomal inheritance refers to the transmission of genetic material that is not found within the nucleus.
Key Components: Involves genes located in mitochondria, chloroplasts, and plasmids.
Slide 3: Mitochondrial Inheritance
Mitochondria: Organelles responsible for energy production.
Mitochondrial DNA (mtDNA): Circular DNA molecule found in mitochondria.
Inheritance Pattern: Maternally inherited, meaning it is passed from mothers to all their offspring.
Diseases: Examples include Leber’s hereditary optic neuropathy (LHON) and mitochondrial myopathy.
Slide 4: Chloroplast Inheritance
Chloroplasts: Organelles responsible for photosynthesis in plants.
Chloroplast DNA (cpDNA): Circular DNA molecule found in chloroplasts.
Inheritance Pattern: Often maternally inherited in most plants, but can vary in some species.
Examples: Variegation in plants, where leaf color patterns are determined by chloroplast DNA.
Slide 5: Plasmid Inheritance
Plasmids: Small, circular DNA molecules found in bacteria and some eukaryotes.
Features: Can carry antibiotic resistance genes and can be transferred between cells through processes like conjugation.
Significance: Important in biotechnology for gene cloning and genetic engineering.
Slide 6: Mechanisms of Extrachromosomal Inheritance
Non-Mendelian Patterns: Do not follow Mendel’s laws of inheritance.
Cytoplasmic Segregation: During cell division, organelles like mitochondria and chloroplasts are randomly distributed to daughter cells.
Heteroplasmy: Presence of more than one type of organellar genome within a cell, leading to variation in expression.
Slide 7: Examples of Extrachromosomal Inheritance
Four O’clock Plant (Mirabilis jalapa): Shows variegated leaves due to different cpDNA in leaf cells.
Petite Mutants in Yeast: Result from mutations in mitochondrial DNA affecting respiration.
Slide 8: Importance of Extrachromosomal Inheritance
Evolution: Provides insight into the evolution of eukaryotic cells.
Medicine: Understanding mitochondrial inheritance helps in diagnosing and treating mitochondrial diseases.
Agriculture: Chloroplast inheritance can be used in plant breeding and genetic modification.
Slide 9: Recent Research and Advances
Gene Editing: Techniques like CRISPR-Cas9 are being used to edit mitochondrial and chloroplast DNA.
Therapies: Development of mitochondrial replacement therapy (MRT) for preventing mitochondrial diseases.
Slide 10: Conclusion
Summary: Extrachromosomal inheritance involves the transmission of genetic material outside the nucleus and plays a crucial role in genetics, medicine, and biotechnology.
Future Directions: Continued research and technological advancements hold promise for new treatments and applications.
Slide 11: Questions and Discussion
Invite Audience: Open the floor for any questions or further discussion on the topic.
Observation of Io’s Resurfacing via Plume Deposition Using Ground-based Adapt...Sérgio Sacani
Since volcanic activity was first discovered on Io from Voyager images in 1979, changes
on Io’s surface have been monitored from both spacecraft and ground-based telescopes.
Here, we present the highest spatial resolution images of Io ever obtained from a groundbased telescope. These images, acquired by the SHARK-VIS instrument on the Large
Binocular Telescope, show evidence of a major resurfacing event on Io’s trailing hemisphere. When compared to the most recent spacecraft images, the SHARK-VIS images
show that a plume deposit from a powerful eruption at Pillan Patera has covered part
of the long-lived Pele plume deposit. Although this type of resurfacing event may be common on Io, few have been detected due to the rarity of spacecraft visits and the previously low spatial resolution available from Earth-based telescopes. The SHARK-VIS instrument ushers in a new era of high resolution imaging of Io’s surface using adaptive
optics at visible wavelengths.
Nutraceutical market, scope and growth: Herbal drug technologyLokesh Patil
As consumer awareness of health and wellness rises, the nutraceutical market—which includes goods like functional meals, drinks, and dietary supplements that provide health advantages beyond basic nutrition—is growing significantly. As healthcare expenses rise, the population ages, and people want natural and preventative health solutions more and more, this industry is increasing quickly. Further driving market expansion are product formulation innovations and the use of cutting-edge technology for customized nutrition. With its worldwide reach, the nutraceutical industry is expected to keep growing and provide significant chances for research and investment in a number of categories, including vitamins, minerals, probiotics, and herbal supplements.
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Slides from:
11th International Conference on Electrical, Electronics and Computer Engineering (IcETRAN), Niš, 3-6 June 2024
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https://www.etran.rs/2024/en/home-english/
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In this book, we use conservation of energy techniques on a fluid element to derive the Modified Bernoulli equation of flow with viscous or friction effects. We derive the general equation of flow/ velocity and then from this we derive the Pouiselle flow equation, the transition flow equation and the turbulent flow equation. In the situations where there are no viscous effects , the equation reduces to the Bernoulli equation. From experimental results, we are able to include other terms in the Bernoulli equation. We also look at cases where pressure gradients exist. We use the Modified Bernoulli equation to derive equations of flow rate for pipes of different cross sectional areas connected together. We also extend our techniques of energy conservation to a sphere falling in a viscous medium under the effect of gravity. We demonstrate Stokes equation of terminal velocity and turbulent flow equation. We look at a way of calculating the time taken for a body to fall in a viscous medium. We also look at the general equation of terminal velocity.
Deep Behavioral Phenotyping in Systems Neuroscience for Functional Atlasing a...Ana Luísa Pinho
Functional Magnetic Resonance Imaging (fMRI) provides means to characterize brain activations in response to behavior. However, cognitive neuroscience has been limited to group-level effects referring to the performance of specific tasks. To obtain the functional profile of elementary cognitive mechanisms, the combination of brain responses to many tasks is required. Yet, to date, both structural atlases and parcellation-based activations do not fully account for cognitive function and still present several limitations. Further, they do not adapt overall to individual characteristics. In this talk, I will give an account of deep-behavioral phenotyping strategies, namely data-driven methods in large task-fMRI datasets, to optimize functional brain-data collection and improve inference of effects-of-interest related to mental processes. Key to this approach is the employment of fast multi-functional paradigms rich on features that can be well parametrized and, consequently, facilitate the creation of psycho-physiological constructs to be modelled with imaging data. Particular emphasis will be given to music stimuli when studying high-order cognitive mechanisms, due to their ecological nature and quality to enable complex behavior compounded by discrete entities. I will also discuss how deep-behavioral phenotyping and individualized models applied to neuroimaging data can better account for the subject-specific organization of domain-general cognitive systems in the human brain. Finally, the accumulation of functional brain signatures brings the possibility to clarify relationships among tasks and create a univocal link between brain systems and mental functions through: (1) the development of ontologies proposing an organization of cognitive processes; and (2) brain-network taxonomies describing functional specialization. To this end, tools to improve commensurability in cognitive science are necessary, such as public repositories, ontology-based platforms and automated meta-analysis tools. I will thus discuss some brain-atlasing resources currently under development, and their applicability in cognitive as well as clinical neuroscience.
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What are greenhouse gasses how they affect the earth and its environment what is the future of the environment and earth how the weather and the climate effects.
Richard's aventures in two entangled wonderlandsRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
[ICLR/ICML2019読み会] A Wrapped Normal Distribution on Hyperbolic Space for Gradient Based Learning (ICML2019)
1. A Wrapped Normal Distribution on Hyperbolic Space
for Gradient Based Learning
ICML’19, Jun 12th, 2019
Yoshihiro Nagano1), Shoichiro Yamaguchi2), Yasuhiro Fujita2), Masanori Koyama2)
1) Department of Complexity Science, The University of Tokyo, Japan
2) Preferred Networks, Inc., Japan
Paper: proceedings.mlr.press/v97/nagano19a.html
Code: github.com/pfnet-research/hyperbolic_wrapped_distribution
ICLR/ICML2019 , Jul 21st, 2019
3. Motivation
ARTICLERESEARCH
Figure 3 | Monte Carlo tree search in AlphaGo. a, Each simulation
traverses the tree by selecting the edge with maximum action value Q,
plus a bonus u(P) that depends on a stored prior probability P for that
is evaluated
a rollout to
Selectiona b cExpansion Evaluation
p
p
Q + u(P)
Q + u(P)Q + u(P)
Q + u(P)
P P
P P
r
P
max
max
P
[Silver+2016]
Mammal
Primate
Human Monkey
Rodent
4. Motivation
Mammal
Primate
Human Monkey
Rodent
ARTICLECH
Monte Carlo tree search in AlphaGo. a, Each simulation
he tree by selecting the edge with maximum action value Q,
is evaluated in two ways: using the value network vθ
a rollout to the end of the game with the fast rollout
Selection b c dExpansion Evaluation Backup
p
p
Q + u(P)
Q + u(P)Q + u(P)
Q + u(P)
P P
P P
Q QQ
Q
rr r
P
max
max
P
[Silver+2016]
Hierarchical Datasets Hyperbolic Space
[Image: wikipedia.org]
[Nickel & Kiela, 2017]
5. Motivation
Mammal
Primate
Human Monkey
Rodent
ARTICLECH
Monte Carlo tree search in AlphaGo. a, Each simulation
he tree by selecting the edge with maximum action value Q,
is evaluated in two ways: using the value network vθ
a rollout to the end of the game with the fast rollout
Selection b c dExpansion Evaluation Backup
p
p
Q + u(P)
Q + u(P)Q + u(P)
Q + u(P)
P P
P P
Q QQ
Q
rr r
P
max
max
P
[Silver+2016]
Hierarchical Datasets Hyperbolic Space
Volume increases exponentially
with its radius
6. Motivation
Mammal
Primate
Human Monkey
Rodent
ARTICLECH
Monte Carlo tree search in AlphaGo. a, Each simulation
he tree by selecting the edge with maximum action value Q,
is evaluated in two ways: using the value network vθ
a rollout to the end of the game with the fast rollout
Selection b c dExpansion Evaluation Backup
p
p
Q + u(P)
Q + u(P)Q + u(P)
Q + u(P)
P P
P P
Q QQ
Q
rr r
P
max
max
P
[Silver+2016]
Hierarchical Datasets Hyperbolic Space
[Nickel+2017]
7. Motivation
Mammal
Primate
Human Monkey
Rodent
ARTICLECH
Monte Carlo tree search in AlphaGo. a, Each simulation
he tree by selecting the edge with maximum action value Q,
is evaluated in two ways: using the value network vθ
a rollout to the end of the game with the fast rollout
Selection b c dExpansion Evaluation Backup
p
p
Q + u(P)
Q + u(P)Q + u(P)
Q + u(P)
P P
P P
Q QQ
Q
rr r
P
max
max
P
[Silver+2016]
Hierarchical Datasets Hyperbolic Space
[Nickel+2017]
How can we extend these works to
probabilistic inference?
15. Hyperbolic Wrapped Distribution(b)
Figure 3: The heatmaps of log-likelihood of the pesudo-
hyperbolic Gaussians with various µ and Σ. We designate
the origin of hyperbolic space by the × mark. See Ap-
pendix B for further details.
Since the metric at the tangent space coincides with the Eu-
clidean metric, we can produce various types of Hyperbolic
distributions by applying our construction strategy to other
distributions defined on Euclidean space, such as Laplace
and Cauchy distribution.
to a
rep
gra
wor
β-V
a sc
In H
is i
cod
µ
As
allo
dien
of t
rep
4.2
We
bili
lum
tual
wor
on
ing
wri
Density:
Projection:
(910 1
(;2 2 ; 9120 +
) 0 2 9 2 92 (
≃ ℝ* 2
16. Numerical Evaluations: VAEs on Synthetic Data
Hyperbolic VAE
Yoshihiro Nagano 1
Shoichiro Yamaguchi 2
Yasuhiro Fujita 2
Masanori Koyama 2
Abstract
rbolic space is a geometry that is known to
ell-suited for representation learning of data
an underlying hierarchical structure. In this
r, we present a novel hyperbolic distribution
d pseudo-hyperbolic Gaussian, a Gaussian-
distribution on hyperbolic space whose den-
can be evaluated analytically and differen-
d with respect to the parameters. Our dis-
ion enables the gradient-based learning of
robabilistic models on hyperbolic space that
d never have been considered before. Also,
an sample from this hyperbolic probability
bution without resorting to auxiliary means
ejection sampling. As applications of our
bution, we develop a hyperbolic-analog of
tional autoencoder and a method of prob-
tic word embedding on hyperbolic space.
emonstrate the efficacy of our distribution
rious datasets including MNIST, Atari 2600
kout, and WordNet.
duction
hyperbolic geometry is drawing attention as a
geometry to assist deep networks in capturing
tal structural properties of data such as a hi-
Hyperbolic attention network (G¨ulc¸ehre et al.,
proved the generalization performance of neural
on various tasks including machine translation
ng the hyperbolic geometry on several parts of
(a) A tree representation of the
training dataset
(b) Normal VAE (β = 1.0) (c) Hyperbolic VAE
Figure 1: The visual results of Hyperbolic VAE applied to
an artificial dataset generated by applying random pertur-
bations to a binary tree. The visualization is being done
on the Poincar´e ball. The red points are the embeddings
of the original tree, and the blue points are the embeddings
of noisy observations generated from the tree. The pink
× represents the origin of the hyperbolic space. The VAE
was trained without the prior knowledge of the tree struc-
ture. Please see 6.1 for experimental details
determines the properties of the dataset that can be learned
from the embedding. For the dataset with a hierarchical
stribution on Hyperbolic Space for
sed Learning
2
Yasuhiro Fujita 2
Masanori Koyama 2
(a) A tree representation of the
training dataset
(b) Normal VAE (β = 1.0) (c) Hyperbolic VAE
Figure 1: The visual results of Hyperbolic VAE applied to
(