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Unlike the classic first-order distributed optimization method, the second-order distributed optimization method utilizes gradient information and second-order information (i.e., curvature information) to find a “better” descent direction to update the global model iteratively.
However, previous work {{cite:2f41fcb5d29a48ba747b6aad2daa6653270c3ea1}} pointed out that the complex inverse matrix-vector product involved in the calculation of curvature information is not suitable for distributed environments.
To this end, in {{cite:37e0f06ee6115c6ef7e5a6c8fdfcd050ca8cb2b3}}, {{cite:27375ed3ebe0a483e8bb0aacbe7ac76c5098e514}}, {{cite:86eb8444bc3ec858fd9e78e40caf3ef0fe236d17}}, the authors designed DANE, DONE, and GIANT, respectively, to overcome this problem.
Specifically, DANE circumvented the challenges mentioned above by designing a well-designed local optimization problem, while DONE proposed a distributed approximate Newton method based on the Richardson iteration.
GIANT used the harmonic mean Hessian matrix to approximate the true Hessian matrix, significantly reducing communication costs.
Similar to GIANT, we focus on how to approximate the Hessian matrix to reduce communication costs efficiently. This paper develops a variant of the L-BFGS algorithm that uses the Fisher information matrix to approximate the Hessian matrix to achieve fast convergence.
| m | 8a16ff24a4d3f0a8e617a745a32435f0 |
According to the end-to-end differentiable property of AutoLoss, we update {{formula:eb1773c1-28c6-4f39-836f-4d48515c449b}} and {{formula:0277c190-07fe-4ad0-bb04-76f109a750ac}} through gradient descent utilizing the differentiable architecture search (DARTS) techniques {{cite:8d169fb4085d30b663d9226476df81e40ddc1641}}. To be specific, {{formula:25e840b6-a253-4cec-b821-e904ad369dc1}} and {{formula:422c78c1-48ea-4125-917d-523280a66c81}} are alternately updated on training and validation batches by minimizing the training loss {{formula:27c3042c-b65a-4d1b-a6a6-8fb14b47516b}} and validation loss {{formula:e11a0467-aecf-49da-94eb-a7d7b390fdd7}} , respectively. This forms a bi-level optimization problem {{cite:0d9faf049f92b6fb5e91010a9b34ccab97576cc6}},
where controller parameters {{formula:38799060-09bc-404f-830a-3e13b9a6a5e1}} and DRS parameters {{formula:cbd9113b-d110-4b76-865f-412e0ee0bb35}} are considered as the upper- and lower-level variables:
{{formula:1c25a193-a405-4e39-9608-7dc85888ebd0}}
| m | be0ea8a93f7f231b74a56f5f14a34096 |
In this paper, we use a simple yet powerful residual-like decoder with a new loss function for pixel-wise gaze prediction. The architecture is similar to the architecture in {{cite:9acc0f42baf7d5458567c5636c50d68c93c48c25}}, but we dispense with the GAN training and instead propose a simpler, residual decoder. We demonstrate that the model although simpler, achieves better performance on most metrics and datasets. Additionally, we propose a novel method to visualize and analyze the representations learnt by deep saliency models. To the best of our knowledge, this is the first work which looks inside deep saliency models.
| i | f6a1f2657c64a14a6e5df402f477f023 |
where, {{formula:eec59cdf-5a2d-4c7f-84aa-a79907791d71}} denotes the first two rows of the rotation matrix. Note that if the origin of the 3D world coordinate system gets mapped to the origin of the 2D image coordinate system then {{formula:329d781d-f592-41a2-9b70-b098e3e43f51}} ; this is usually implemented by centering the 2D and 3D poses. Authors used a sparse representation of the 3D poses similar to {{cite:bf416e87ecc1a5af00b028770342a93074bb471c}} where the 3D pose is represented by a sparse linear combination of bases selected using the Orthogonal Matching Pursuit (OMP) algorithm {{cite:c2fb8faebb2ddd5e1591de8c355adcd8fb84ece1}} from an overcomplete dictionary of pose atoms, namely {{formula:6901c0a7-6441-4bf4-9529-ccf0614402d6}} , where {{formula:c848c334-529a-42e4-b20f-59a55d58eac1}} is the mean pose obtained by averaging poses from the CMU motion capture dataset {{cite:6ee998240a8789c7e773e3751e7ec4515b9a98b1}} and {{formula:d020bf45-1cd4-496b-b58b-70e3f6afda53}} denotes the indices of selected bases using OMP with weights {{formula:5dfae6c9-35c3-4485-afda-659ea560348b}} . An overcomplete dictionary of bases was built by concatenating PCA bases from poses of different action classes in the CMU dataset after bone length normalization and Procrustes aligned. The second term {{formula:139cb973-63ba-4da8-b2a6-ea74da180e1c}} in equation (REF ) is equal to zero if the estimated pose {{formula:6e3b09aa-2cc0-4eb9-809c-e39683cb8270}} has valid joint angles for limbs and infinity otherwise. According to the pose-conditioned constraints in {{cite:1de5dae93fb403bcea5ad23c6fe674b1a472161b}} a pose has valid joint angles if the upper arms/legs' joint angles map to a 1 in the corresponding occupancy matrix (learned from the ABCD dataset) and the lower arms/legs satisfy two conditions that prevent these bones from bending beyond feasible joint-angle limits (inequalities (REF ) and (REF )). The term {{formula:a1dd1cc9-7e49-4f99-a1d7-ee05b38deb77}} in equation (REF ) penalizes the difference between the squares of the estimated {{formula:d208c0c2-30f0-4e03-ad2b-659aeb521eae}} bone length {{formula:6ffcab69-1306-4179-8ffa-5f17f7bfd0b2}} and the normalized mean bone length {{formula:20498b8d-ed84-4023-a180-3c5f26048481}} , {{formula:b2c741f4-58f6-48b0-b716-62f8d1152925}} (normalized mean bones calculated from the CMU dataset) with weight {{formula:ca70bd29-e157-4682-b06b-60b4eb603d86}} . Note that {{cite:1de5dae93fb403bcea5ad23c6fe674b1a472161b}} does not introduce any generative pose model.
| m | a4b827d2fa85580bc15d7f15713c5556 |
In Section REF we found that while AGN with relatively weak radio jets compared to the radiative emission from the nucleus (with {{formula:87e38392-4d8c-4b9b-a1d4-fbbcbf352ecf}} ) are found in galaxies with SMBH masses across the full range found in our sample ({{formula:14f381f6-81d6-4021-89e8-df0b5374a270}} ), all galaxies hosting jets with {{formula:d2c43b71-586f-4218-b069-995c76eea9eb}} have black hole masses {{formula:94b22d6d-9ddd-4350-88f2-b85d29850e2d}} . This suggests that a large black hole mass is required to launch and sustain a powerful radio jet. Our results show that this holds out to at least {{formula:8721efcd-c43a-4580-8fcf-c65f3df9ef18}} . This is in agreement with {{cite:0cd33d95f46a20077ff4ed49988e484c9c3bb895}}, who found that the radio-loudness of quasars is dependent on black hole mass, with all the genuinely radio-loud quasars in their sample having M{{formula:368afa8b-68fc-4036-8cd2-a3835618a4e4}} . {{cite:807d3f541cb70a2d5dbf06fa492d4c9e4bd4caef}} also found that radio luminosity scales with black hole mass.
{{cite:32df989f655fd350e0fd1e2c3e193d8ba34a4a3a}} suggest that only when a supermassive black hole has both a high mass and high spin is it able to sustain powerful radio jets for long enough to produce an extended radio galaxy. This could explain why in our sample a large black hole mass seems to be required to sustain a powerful radio jet, but only a fraction of the radio-loud AGN which have large black hole masses produce powerful jets.
| d | 9aaa2b177e94f2c2e52601aebde9eadb |
Range of applicability.
The optimization framework introduced here can applied to any steady-state meso-scale system that can be modeled by a stationary Markovian (or Langevin-type) dynamics,
for which the rate of entropy production is related to the relative probability of forward and reverse
trajectories {{cite:320503d16dd00c43d2022f7a64f315fbbe6256e6}}, {{cite:470710436f5800c53a0a0e2ce54d85d0e1f7cee9}}, {{cite:d06270ac5c15670b1d1cc66117afad9376fcb0e7}}. These minimal assumptions are fulfilled by many living and active
systems, from single molecules and biomolecular networks {{cite:470710436f5800c53a0a0e2ce54d85d0e1f7cee9}}, to molecular motors {{cite:d06270ac5c15670b1d1cc66117afad9376fcb0e7}},
and active sensors {{cite:42720ae67dd2dc925dfb3c653174da0e225119fd}}. A practical advantage of our method lies in the fact that the coarse-graining level can be adapted to the quality and volume
of the available experimental data. Here, we focused coarse-graining to a small network with only 3 remaining states, which make it easier to collect precise
statistics for the transition rates. In general, with increasing data resolution and trajectory length, finer coarse-graining of space and time will lead to better bounds.
Extrapolating the impressive progress of imaging techniques over the last decade, one can expect that {{formula:160f0911-3213-4a2e-8a88-321007f7e7b3}} -based estimation applied to
higher-resolution data will enable rapidly improving entropy production rate estimates in the near future.
| d | e7353e88e1ac98000473124602923612 |
Positional encoding.
We observe that the proper positional encoding improve the quality of the generated images. In Table REF , we experimented with three different positional encoding schemes: sinusoidal {{cite:804a4f66498391641f4c447b78bd170d18203136}} encoding {{formula:c6982f68-88c3-4614-9a5c-59b0e2c34127}} in Eq. (REF ), Fourier {{cite:627f37988bfd4d13f8659ce90e27d2b7b4a5ff38}}It is defined as:
{{formula:dd62322a-9fc0-4e15-9bcb-ff849253647a}} ,
where {{formula:6badad41-5a05-4e7b-93c1-4610ec2ae658}} is random vector sampled from normal distribution {{formula:efebb536-f587-4c86-a442-dbb9c98ddbd9}} ., and nonlinear embedding {{formula:376acb9a-56c6-4bac-a3e8-dba6232bfa27}} in Eq. (REF ). The value in parenthesis in the encoding function are the output dimension of the function.
The baseline is the generator with no positional encoding (without using {{formula:9c770da8-d24e-4b41-bb6f-f3e2858e45d9}} and {{formula:deaae29c-4142-478d-a41d-c58e9a5d58ff}} ).
Finally, we found that using {{formula:1b31e11c-5949-490f-849c-5ef1b0ed0e7a}} shows lower FID than that of Fourier or the baseline.
In detail, using only sinusoidal or Fourier encoding induces an artifact in the resulting image. As shown in Figure REF (c), sinusoidal encoding with a high number of dimensions shows a grid-like artifact. The number of dimension of {{formula:5975c07c-0e23-4556-b6ab-62c04137ebe3}} significantly affect the result. When the number of dimensions is high, the frequency of features gets high. Such phenomenon makes each position cannot be clearly distinguished. When we reduce the number of dimensions of {{formula:4de961bd-bba1-4dd3-8fff-e55d4b086f98}} , as shown in Figure REF (b), the generated images do not show the artifact. When we compensate the low dimension with {{formula:d577aefb-34af-44e0-b67a-c76115509afa}} that has proper output dimension, the mIoU and FID score are improved.
Figure REF (d) results from Fourier encoding, and it shows sinusoidal artifact.
{{table:fb6f36af-7588-43c6-9057-de2f2b0af63c}} | r | 05e25960c6f0db6c387d4f334afa0794 |
MF-BPR {{cite:a3b1f572a132a4022bac440a598757f648f33928}}: This is matrix factorization with Bayesian Personal Ranking (BPR) as the loss function.
FM {{cite:70c2c355656ffb267685f252333235220d0e0d1a}}: Factorization Machine (FM) is a content-based model
which uses feature interactions to model user preferences. We take the side information as additional input features in both datasets.
NFM {{cite:33656311c8babd30e8ec089e6013a92d270d8cc7}}: Neural Factorization Machine applies an MLP to model the high-order feature interactions.
FISM {{cite:aa2a38d8d62dfd0e27732cb050a25d30482752bc}}: This is an item collaborative filtering (ICF) model which learns the user embedding by aggregating the item embeddings that she has interacted with.
CKE {{cite:9c593851644a008e2d4023c33670e4d8ca12cc71}}: It models the items with a knowledge graph that connects items with their features and then learns the embeddings of items that can be used in CF models.
LightGCN {{cite:4c239e08571ca376e9c4512693a79a46188b5902}}: It simplifies GNN based recommender systems like NGCF {{cite:33656311c8babd30e8ec089e6013a92d270d8cc7}} to make them linear models and achieve better performance.
KGPolicy{{cite:5f4d536955ca1eac59f0b656d63f28b90814960c}}: Knowledge Graph Policy Network is to explore high-quality negatives via reinforcement learning. We take features of users and items as nodes in the knowledge graph.
RCF {{cite:31e4ecbda1d29f6f8dfb460f76cff32aacd49890}}: Relational Collaborative Filtering (RCF) considers the multi-relational pattern in the items. It utilizes the attention mechanism to combine the multi-relational pattern with the collaborative relation.
| m | 2bcea793893994522054f8a9ad5dc702 |
The band structure and Fermi surfaces are studied with the full potential, all-electron code fplo {{cite:6aa5422e82df74b254ad5d865e5fcf0c99837e64}} using the semi-local generalized gradient approximation (GGA) {{cite:685a2f155d71f63ad06c8e5f657c6de5edb7ed70}} exchange-correlation functional. This code uses a basis of pre-determined atomic orbital-like functions, with various numerical techniques to handle the full potential and general charge density of the crystal. These calculations use valence and virtual {{formula:99893d82-5dcd-4ab8-b586-1f5611a23556}} and {{formula:f8a186b1-f28c-4d11-ab9b-769e11eac9fb}} orbitals for B, and valence and virtual {{formula:eba085ed-befa-4635-8917-08b3b9ed8acd}} and {{formula:3130d21e-a695-4181-afd7-f91e67c274d4}} orbitals and {{formula:bb82f03b-27f9-4a01-bfe2-996c4a173e77}} orbitals for Mo.
| m | 5369ee7ba234ac9ee327b3223c6813d2 |
Several feature extraction methods, as well as classifiers, have been explored in the medical image processing area such as bag-of-visual-words {{cite:e96559a46a042245df3fcfa049cd9cefe356c4d7}}, the Gaussian filter, the Gabor filter {{cite:b64727c34289c2af039bd6838c40f5f56ddd358b}} as feature extractors; and K-Nearest Neighbors (K-NN), Random Forest, Support Vector Machine (SVM), Artificial Neural Networks (ANN), as classifier amongst the others. On the other hand, deep learning based methods have the ability to skip the feature extraction part of the traditional machine learning based methods and focus on the final goal (e.g. classify vessel pixels) by learning from the raw data without using handcrafted features {{cite:0b3c81a104b321cf7626ebd0df280ce900835418}}.
| m | 035ceeb730a997507017dd83c62c0480 |
We implement a neural language model (NLM) using an existing encoder-decoder LSTMhttps://github.com/pytorch/examples/tree/master/word_language_model with 2 layers of size 200. We randomly split the dataset of each community into training (70%), validation (15%), and test (15%) sets and train one NLM per community using the word embeddings previously learned for that community with the vector space model described in Section REF . We train the models for 40 epochs, using Adam estimation {{cite:ccb077d83cae7fe3f83b8f5e75ea198f3c3ae6ae}} for parameter update and dropout for regularisation. The same procedure is also carried out for the global community. All the community language models reached an average test perplexity between 45 and 67 on the task of predicting the upcoming word given the preceding word (window size = 1) — a performance in line with the state of the art, (e.g., {{cite:071fb99a3dfa7b9b069f7dc1736778cf7a5f31db}}).
| m | 0558829761d1b752bd1850a0b464cce8 |
The starting point for the proof of Theorem REF comes from the prior articles {{cite:076ba875dddc9f3e1631ace49908d7173f64beb0}}, {{cite:1c76a6788ce157b618bae7b534b078d65d60cf5b}}, {{cite:8473d860c5f3b2133ca287769bda0a98a5a3fc90}}, which obtained an insightful “function space” interpretation of {{formula:407e6e9c-2761-4a53-af70-a75adf18fcaa}} as a subset of {{formula:6fb617aa-adb3-4cf8-9a38-8e4726786921}} . Specifically, a simple computation (cf e.g. Theorem {{formula:195872c8-15eb-40ff-8b4d-87eeae041625}} in {{cite:1c76a6788ce157b618bae7b534b078d65d60cf5b}} and also Lemma REF below) shows that {{formula:3405d663-79d4-4669-8f61-b301dd05be59}} achieves the smallest value of the total variation {{formula:3103740e-a962-4b49-980c-6e32c1b3decb}} for the derivative {{formula:fb86ab90-86b5-459d-b4b7-bda77f49cfcb}} among all {{formula:b764886b-072e-458d-a0a4-ed198c018d81}} (The function {{formula:229618d2-eb0c-481b-97c9-13823c0ef51c}} is piecewise constant and {{formula:de5ff903-22fc-42e1-b1e2-ec3504983493}} is the sum of absolute values of its jumps.) Part of the content of the prior work {{cite:076ba875dddc9f3e1631ace49908d7173f64beb0}}, {{cite:1c76a6788ce157b618bae7b534b078d65d60cf5b}}, {{cite:8473d860c5f3b2133ca287769bda0a98a5a3fc90}} is the following result
| r | 8e7214547e2e4ae1767fa9b004d8e83b |
Comparisons on Market-1501.
As shown in Table REF , the proposed the proposed hierarchical similarity graph network (HSGNet) obtains the highest 95.0% Rank1, 98.9% Rank5 and 86.6% mAP.
For example, compared with two partition-based methods, i,e, SpindleNet {{cite:a691fdb77524dd394835247da668367ad8a04c42}} and PAR {{cite:9a5d6175c264bd36e9d509c58d93f828f6a30d88}}, the HSGNet is higher than 17.9% and 13.8% on Rank1, respectively.
Considering the partition-free methods, i.e., AANet {{cite:1b72d3178b9ba1b1eef1cbb4102975ed7e31fb86}} and IANet {{cite:263b0dac61ea3f758d5bdfd08b88e8a50a3edbb8}}, it is still defeated 4.2% and 3.5% on mAP, respectively.
Although our method is slightly lower on Rank1 than P{{formula:c714e859-5ed2-4479-b788-4a4792940615}} -Net {{cite:344cad42daec89d9c59d2960996b68f5d51ba858}}, which uses an additional semantic segmentation model, we defeat it by 1.0% on mAP. Therefore, integrating Rank and mAP retrieval comparison results into account, our method remains competitive on Market-1501.
| m | b5246472807e3d280fbb95af99116649 |
Positional Encoding Module (PEM). In the standard transformer{{cite:518ba724e3c5de57b57dc0f8733d6579afe7282f}}, {{cite:f3acbeb30e517f45837524dd4389f030fca6065c}} design, encoding spatial information has proved useful for recognition tasks. However, it is non-trivial for WSIs due to varying sizes. In this work, we employ a conditional position encoder (PEM){{cite:fe2e8c69c62782197a38546fc79347565fb759f4}} that takes re-calibrated features {{formula:2af57ea6-bcfa-4ec2-8a49-143fa9dadd96}} , performs zero-padding to provide absolute position for a convolution {{formula:353c91ba-4543-43c7-a8cf-0dc8b4c2922c}} , and later concatenates the output with a class token {{formula:574e3628-2538-4c30-b5d7-92a51ac7d853}} initialized from the normal distribution. Here, features {{formula:c2037eb1-bb77-49c5-a613-e3bcc61be9a4}} are re-shaped into a 2D image by first computing {{formula:d24c3ef5-6737-4439-9c5f-0ca35fbc341d}} i.e., {{formula:04193002-851f-4b16-9f59-2f577339d7ab}} , where {{formula:5a823f64-8445-49cb-ac95-aacddfc3f5a2}} is the number of instances in a bag. Thus,
{{formula:1b6e3b9b-5853-4b6c-8869-e025ca8452bf}}
| m | f1724b35da230d525b98b7271a5a1f08 |
Despite these benefits, there are situations and applications where alternative approaches might be better suited. In particular, autoregressive constructions that decompose the joint distribution into its telescoping univariate marginals {{cite:42be9100d82ce02abb248caec7da9609ed80d6f3}}, {{cite:91c4e8d62c2ca8ccba86ddb77429eb23a57add38}}, {{cite:787c7a7054cd375ea706673edcb9653bfa34a53c}}, {{cite:cd42cb26899d7f1582f9bcdc10567b99db1d3e43}}, {{cite:62ea548466cacbf7838298093c9370d784181e3b}}, allow the quantile levels to retain their classical probabilistic interpretation (e.g. for the construction of univariate prediction intervals) and provide direct access to certain conditional distributions of interest (future conditioned on past). Similarly, multi-horizon approaches provide direct access to the univariate marginal distributions, which in our approach can only be obtained through sampling. In fact, an interesting avenue for future work is to explore whether a multivariate quantile function model can be constructed that retains the ability to access marginal and conditional distributions without resorting to sampling.
Future work could further extend our approach to the practically important case of count distributions and assess the quality of our approach for quantile functions jointly over the time and item dimensions. Finally, more suitable forecasters in domain adaptation {{cite:eb8e7583ac412bfc31e495c95277df62a0bf8f40}} with faster training schemes {{cite:949431ba5a7066afaa7a9a1856837ddf39e50996}} can be developed, ultimately being able to be incorporated for downstream decision makings, e.g., planning cloud computing and vehicle controllers {{cite:f3d2531fb9a590f78ab9970a38144ab9d861ca70}}, {{cite:71536133a0b36d6bae7fadf439ee95624c034d3d}}, {{cite:366d6d2aae1f970738527cfb773b8498f6c6139c}}.
| d | e341d89908d6ed817f3b5cbfcef7bc2b |
Finding short motifs presents significant challenges because many of the apparent relationships between short fragments could have arisen by chance and thus have no functional significance. Furthermore, most widely available tools for sequence database search and motif finding were designed with longer motifs in mind. For example, Watt and Doyle {{cite:afc5f4bc1362e566a7e21c752dee6a0a259ea7c9}} recently observed that the NCBI BLAST {{cite:0592d31f19daff1ee7eeb69d24a1eb4dee5b06b4}} family of programs, the best known set of tools for searching biological sequence datasets, is not suitable for
identifying shorter sequences with particular constraints and proposed
a pattern search tool to find DNA or protein fragments that match a
given sequence or a pattern exactly. This paper outlines
the Protein Fragment Motif Finder (PMFind), a new tool that uses database search to
identify the conserved short peptide motifs of a query sequence and associates them with the available functional annotations.
| i | c6ad7958f2aa5168f0e1ff97f8b5b5a0 |
When designing models for EEG signal processing, we must take characteristics of EEG (e.g., non-stationarity and small amplitude) into consideration, as well as external circumstances such as electrode layout, interferences introduced by the surrounding environment during data collection. A possible instance may be tensor deep learning, as it can utilise comprehensive information (time, channels, frequencies, etc.) and stored the information in tensor. These novel deep models are expected to update dynamically in response to data collection over time. Appropriate data retraining schemes or parameter tuning strategies should also be developed to promote the advance of deep learning in EEG. Models can be updated in a real-time manner by tuning parameters or even changing architecture. Another concern that meets our needs is to develop general models that can be applied to different applications of EEG. A prominent advance we need to mention is the development of EEGNet {{cite:c75ab8b9e7800008508432b0a144f021f7c05a42}}, which is proven effective and accurate in different BCI paradigms. Another promising model is SincNet, which was initially proposed for speaker recognition and also well for the classification of EEG signal {{cite:085afc0c3b6b449ff66aaed61a93d0325b1d57e7}}. New deep learning architectures, such as capsule network {{cite:c37507bf30ad4b859db0476470671ac2c793b52c}}, {{cite:8329f606889b4b49474ea4efd7541b7f78bffccf}}, are also required to enhance the chance of success of EEG applications.
| d | f74cc58018bc99fcb400a617815091f7 |
Using the condition on probabilities {{formula:7e0f678a-c85e-4f8a-b209-84fb94bf30e7}} and
the first Borel-Cantelli lemma; see e.g., {{cite:4aff1991ddbbfc176dff9e6d3675dbd201b67508}}, we see that for
any {{formula:cf06bfa7-dbd3-4204-9d50-ac3815dd4f7e}}
{{formula:b5305a36-7e8c-4e56-b31a-f8feb8095c25}}
| r | ed30de359ca22b480bb2092460d03166 |
RotNet: Rotation prediction, proposed by Gidaris et al. {{cite:72b0bf6c9e4cb275dc7acd0ac6beec7c160be848}}, has been one of the most successful pretext tasks for the learning of useful semantic representations. In this approach, every image is transformed using all four rotation transformations, and the network is trained to predict the corresponding rotation angle used for transforming the image.
Due to its simplicity and effectiveness, the rotation task has been used to improve the training of GANs {{cite:83146e8e9235c7ee97f3e855604da5593356399e}}, {{cite:5fe393c5acf8916aa0a7c096a148f2b2ecc2d8d1}} as well.
| m | 8540eff5c8a6277ac87f065a349b82af |
For {{formula:50767fca-e478-4981-9336-88c5fd32874a}} , {{formula:d135c2de-59d2-4687-8cf3-60f666ea12ea}} are defined in (REF ).
We call this method the Procrustes parareal method since
{{formula:cc690567-6f1c-4fd7-a2a0-315e4d9ca851}} is constructed by solving the Orthogonal Procrustes Problem {{cite:7a62482d64392c21f4d0249e112e3dc2d1fbe1bd}}.
| m | 98a46f5a22eed5dc7e4f63a370c69fa7 |
The three-dimensional simulations are performed in a cubic domain of dimensions {{formula:53418594-7e57-4108-b06e-d6ead8416957}} . The numerical method {{cite:b4eb121cbf3467b8e8beddc3178c0b1d233bd06b}} combines the phase-field method {{cite:51247aeeb259bcdef13a8d9e6ca31586a609a720}}, {{cite:3d6210888eabf10042eaa3c9cdcad359a3c8a813}}, {{cite:d160735796821ecabef2a4af87725a8d8a617f28}} and an advanced finite difference direct numerical simulation solver for the Navier-Stokes equations {{cite:f3c2f3f3cc8112b69ee88736602560ac005aa0d1}}, {{cite:8108abeff2dbf4fb76f73a11439ebb31acb08c6f}}, called AFiD. Numerical details, validation cases, and convergence tests were already presented in our previous study {{cite:b4eb121cbf3467b8e8beddc3178c0b1d233bd06b}}.
| m | b470474fd3e5a850c620a789b816783c |
Recently, many spectral GNN variants have been proposed, e.g., {{cite:710dcf473df7f1a83bbd9b54cc6e4f8d3b4b37eb}}, {{cite:4128b32f17a7fae0dc556019fca278ade9ad78c0}}. The main workflow of spectral GNNs follows four main steps: 1) transform the graph to the spectral domain using the graph Laplacian eigenfunctions (see Eq. REF ); 2) perform the same transformation on the graph convolutional filters; 3) apply convolutions in the spectral domain; 4) transform from the spectral domain back to the original graph domain (see Eq. REF ).
{{formula:5eb16b20-781d-4062-b17c-8c804beafbf4}}
{{formula:f27ee109-a336-49df-af15-c5487c34b293}}
| m | 2ba2abe3983bd5b1618b975a23db5093 |
where {{formula:ddd06ee1-7076-4842-b3eb-66ff672a7269}} is the number of independent fitting parameters and {{formula:081eba65-ebd9-464b-9590-8aead408db78}} the number of data points.
The larger are the differences {{formula:13786f8b-8392-4dc1-ab08-2e1904130f69}} AIC ({{formula:187504cf-bfde-4a6f-85e3-c40f78d0cd26}} BIC) with respect to the model that carries smaller value of AIC (BIC) the higher is the evidence against the model with larger value of AIC (BIC) – the {{formula:0cdb5a0a-10cd-414d-992c-697efdb3ae1f}} CDM in all the cases considered in Tables 2-3.
The rule applied to our case is the following {{cite:9eaed187bd3f6383bc50c64822df9de90b2a2edf}}, {{cite:6445ad6cee25e2224ee70df2a78c8e7a026587dc}}, {{cite:8c52ed716f4f667255494001d50c7599ed753635}}: for {{formula:abc518ac-31f4-48c9-9d2d-92a333a99cbe}} AIC and {{formula:7a932cda-e69d-4796-becb-15d194e18e80}} BIC in the range {{formula:ac6007d5-0870-40ce-98d1-5ebce1212f35}} we can speak of “strong evidence” against the {{formula:1c5bfc63-94a9-4753-8524-c4d24fb3165f}} CDM, and hence in favor of the given nonstandard model. Above 10, one speaks of “very strong evidence”. Notice that the Bayes factor is {{formula:f1db858a-a88b-4dbd-971e-a64ca0e06a57}} , and hence near 150 in such case.
| d | 4c408ff7d312f82e00417b68349fe12d |
Time-series prediction plays an important role in many fields, such as sensor network monitoring{{cite:48575c194f5ac1f2e4196b3d6955f9b408dec5cd}},energy and smart grid management,economics and finance{{cite:8b4560c058b9f2ad13a00b524867caf8101e7170}},and disease propagation analysis{{cite:fcb70f364fa5667f171f0151ddb7fbb1c88df490}}. In each of the previous scenarios, we can make long-term predictions using a large number of past time series,namely long sequence time-series forecastin(LSTF). Multidimensional time series prediction is an important part of it. The so-called multidimensional time series prediction refers to the generation of multiple kinds of data at the same time, using this datas at the historical moment to predict the data at the future moment. This paper mainly discusses the different types of time series data detected in the same place at the same time. However, existing models cannot learn the hidden relationship between different dimensions well. In the previous period,vector autoregression(VAR) is arguably the most widely used models in multivariate time series{{cite:b8be81769e3ca11c9e391dbede47071d618010d5}}{{cite:3e2e8fb0fedb63cf1ccc7a66311bc873292bb926}}{{cite:5c106e5a9035622ceb6f39f03da4a449abfd2916}} due to its simplicity. In recent years, various VAR models have made significant progress,including the elliptical VAR{{cite:5348d5236a7eed078b5d56d3f477fe89bab8ec39}} model for heavy-tail time series and structured VAR{{cite:5ca275b1f782f8bbcc56abb4350ef0a6c16f1a28}} model in order to better explain the dependence between high dimensional variables. However,the model capacity of VAR grows linearly over the temporal window size and quadratically over the number of variables. This means that the model is easy to overfit when it deals with long time series. In order to alleviate this problem,{{cite:696ad39eaf967045dac7a2b48750ce963a6ea7f2}}proposed to reduce the original high-dimensional signal to low-dimensional implicit representation, and then use VAR to perform a variety of regularization prediction.
| i | ced327d4aa58c2bf39c8c45de7581616 |
Software.
All experiments are done in Python 3.7.10. We used Scikit-learn 0.24.2 {{cite:1e9faea8b8d1c974f79cdea7ce441316ac1abb1b}} for machine learning models and PyTorch Geometric 1.6.3 {{cite:1897a2639c69d0b16bbeb0e960b43f4a6b4b32f6}} for graph neural network implementations.
For Riemannian geometric computations in the SPD space, we used the SPD class from the Morphomatics package of {{cite:999267dc1901cc11361f8bf032e2fc0057ac1693}}. To extract the graph topological features from the tangent matrices we used NetworkX {{cite:e3a05ddd2d77c5baf43dd9c86c7b6b7a0b77f85e}}.
| r | 718915eeeda7acac8908ae2cf2b37b6f |
Other cases of interest include arbitrary {{formula:6ea212c6-4a5b-4135-9b5f-e2ece022c1eb}} and {{formula:9806b22e-e3be-47ff-980d-3e335de6babb}} . These are the partition function for {{formula:cd7534fb-bf44-407b-b36b-9a4994b88da2}} -spin structures of type {{formula:7b93faf3-59c6-49f1-8a66-169782406694}} (here {{formula:917f3b75-d150-4c11-a4a1-892fc28edd69}} ). These were introduced by Witten {{cite:aaa8ec90aa30c232bf1a95b176aad92e36246a85}} who also formulated the conjecture that the corresponding intersection theory is governed by the model (REF ) with {{formula:23065c9f-c3de-432f-98d5-f70a536db789}} and {{formula:a938b152-9ba9-4fff-af12-fd8a37448b68}} . The conjecture was proved in {{cite:f72046712ae6e512668f20402e559a318bb4bb94}}.
| d | 95934892a8675dc88767570f41c373ce |
There are several accounts of numerical treatment of energy balance models. The early simulations were based on spectral Legendre decomposition in space and the first order implicit Euler scheme in time {{cite:b965cbdc715403fb41a2c34457af340a3ce2a983}}. As was also noted in {{cite:ac6ead23e0c2f8f0a600c4a73652fb6310fa1797}} the model is amenable for such a treatment due to rapid convergence of the orthogonal series. Recently, several papers concerning finite element method were published. In {{cite:53b00d41ffb3d8c4ee99e4c537faac65a14d6d91}}, {{cite:a49190e61237c78805979d62d982c29ecff85a81}} the situation set on a two-dimensional Riemannian manifold was solved in the case of nonlinear diffusivity modelled by a p-Laplacian. On the other hand, in {{cite:4f49775f8550af04e24485d4319b511b06eab5fd}} a finite volume WENO method has been applied to solve the problem where the surface of the Earth is split into land and ocean fractions. Similar analysis but with emphasis on equilibrium solutions was given in {{cite:a486e1104f17e9ad78ce0841539cbc6cab471731}}. Since our model involves a nonlocal operator we would also like to point the interested reader to a expository literature concerning these {{cite:95a1b4922f913b0ff5b25763bd44d041bfaa3e3e}}, {{cite:792355cd3069581d9b48aa6b942877ded0d60dab}}, {{cite:b6536b5117a98cc855e54822fc9b6fda1a10ed10}}, {{cite:f52089a665abc2a0788e53aa2cc3f64a5e1ffbfb}}
| i | 6cea8b73290eae3920360c3d059f7eb9 |
Since Richard Feynman's original and ground-breaking proposal in {{cite:4eb4f0605e08d53fb2650a0db98d4b437d96b3e7}} of constructing computers that follow the laws of quantum mechanics to simulate physical systems that obey said laws, the scientific community has gone to extraordinary lengths in order to build an operational quantum computer. Following the introduction of these novel ideas about constructing quantum machines, research has shown that application of quantum physics theory is not only useful for simulation of complex quantum mechanical systems such as macromolecules for drug discovery {{cite:d3c50053f5fc04ec8e81401f35c575cc254a78c4}}, {{cite:8e658752b9ee0574303d47e0880f41467046f6a0}}, {{cite:37487aeb36e939fb87c23b3300cbbe512e02e749}}, {{cite:7dfdb47518a10a3ab114401d9a37131caaf6f599}}, but also to efficiently solve tasks which are computationally unmanageable in a reasonable amount of time for classical computers. The most prominent of these tasks are the factorization of prime numbers and the discrete logarithm problem {{cite:6a11b9b4825cfa9c9f9d405ac582a613e12f4abe}}, Byzantine agreement {{cite:c596cb5cc6ed9659c01262c139b3b7e25b906908}}, or searching an unstructured database or an unordered list {{cite:8a7d1d78aef237b9f0c4631b44f78bdd6eeadd60}}, {{cite:dae1f065eb04c7854c64edc75d4299dba80a586c}}. This way, quantum machines are thought to have the potential to revolutionize the modern industry with applications such as the design of medicines optimized to cure specific diseases, the optimization of materials, more accurate weather forecasting or advanced artificial intelligence among others.
| i | 9ff01d462b3ff5b7e5eb251e1450def0 |
An important implication of our analysis is that while the
shapes of halos (and by extension elliptical galaxies) become more
oblate (especially at small radii), following the growth of a baryonic
component, the majority of their orbits are not S-tubes as might be
predicted from their shapes. Instead our analysis shows that orbits
prefer to maintain their orbital characteristics, and the majority of
the orbits are those which would be generally found in triaxial
galaxies. This is particularly important for studies of the internal
dynamics of elliptical galaxies since the fact that their shapes
appear nearly axisymmetric need not imply that their orbital structure
is as simple as the structure of oblate elliptical galaxies. Modifying
the shapes to slightly triaxial could result in significant changes in
their orbit populations and consequently could affect both the
inferred dynamical structure as well as the estimates of the masses
components such as the supermassive black holes in these galaxies
{{cite:843e9b4b1e496e92cbc40da5940210b1dc64e96b}}.
| d | 837c022253b320306d0ff3ce32b29c7a |
The eigenvalue problem is solved with the FEAST library {{cite:4b7c1413f0d24764c4b00ebb61a96b4df121d36a}} which allows to solve for a specific region of the spectrum. We also use the MUMPS library {{cite:e1d4fb4d3b24ae5a75f64784039e3837916ca452}}, {{cite:d1d730950d4b14b350c73817d4f81590cfbdf4f8}} for performing matrix multiplications and factorizations as well as the solution of linear systems needed by the FEAST eigenvalue solver.
| m | fd5250ba224eac06004a8a2408a1f7ed |
In addition, we demonstrate that using a weighted adjacency matrix can lead to better performance of the graph neural network. In our solution, the weights for the edges are defined using a handcrafted formula. An alternative approach is to learn the edge weights with deep neural networks. For example, we can employ the graph attention network (GAT) {{cite:8daaf6bdefb8300f36169956c015a657fd50983d}} to dynamically learn the edge weights through an attention mechanism. Given sufficient amounts of training data, we typically find handcrafted features to be outperformed by the representations learned with deep neural networks.
| d | 6947f09fb10c56e824003e244ac6501c |
AutoAugment and Model EMA show a decrease in accuracy. {{cite:9844fab048238004b1bcda051b1a5ee40120fcff}} mentions that Model EMA does not increase performance, so my findings fall in line with the original paper. Whereas AutoAugment, I did not put in the time to try to optimize the parameters so perhaps with some tuning it could be useful.
| r | 5962644f4ad564635ebdafb38c1d9b6f |
Questions raise themselves for future explorations. Is it possible to further generalize our results to RL with general function approximation under bounded Bellman Eluder dimensions {{cite:dded2336326c0745aabb62aa82cb86974d713283}}? Can we optimize the dependence on horizon {{formula:ac9e2ecc-8b2a-41bd-82df-024021a54468}} and feature dimension {{formula:11c14d2a-6a3e-4937-bb4f-e3274ec1f804}} ? We leave these interesting questions as potential next steps.
| d | 3a03e8f21217b9f8ee696b6b2304373c |
Proof. The inequality (REF ) can be derived from Lemma 2B.1 in {{cite:4b16d8d6c9bfd3ebf2c2e106c3164abc268288dd}}.
| r | 6565ffa69f2d9e304d1019d4fa912a79 |
The second group consists of sentence encoders from the Sentence-Transformers library trained using multilingual knowledge distillation method {{cite:ccb79c628cfb876c52490062dfd95001eb191403}}. These models offer varying performance on Polish language tasks. However, two of them stand out: paraphrase-xlm-r-multilingual-v1 and paraphrase-multilingual-mpnet-base-v2. Both achieved an average score on all tasks above 81%. The former was particularly good on the semantic retrieval tasks while scoring lower on typical classification tasks. The latter, on the other hand, obtained balanced scores on all types of tasks.
| r | e6cde92e9382186a738cc90371810079 |
For multi-organ segmentation, where multiple organs are segmented simultaneously, networks should be designed to own more powerful ability of discriminating the pixel-wise features.
OAN {{cite:23e55cc679887e4cdeb434de93151b99a54060e7}} designs a fusion network that takes 2D multi-view images as input and reconstructs the 3D segmentation result finally.
DenseVNet {{cite:33ce80e09e1fad6fc4896a64f1009d99674e09fd}} proposes a dense 3D network for performance improvement.
Besides, due to the data insufficiency, a blackseries of works {{cite:5f8a97f722942a8c218175d3011a0333e9fa529f}}, {{cite:a77551379b88b4d24af04369f96e3e706147e324}}, {{cite:625362068729f3c8ecf347dc04ec751b7ff616a5}} propose different training paradigms and achieve multi-organs segmentation using partially label annotations from single organ datasets.
In this group of work {{cite:bf418e1264774e7862f4783ff5330b8f0b93b766}}, {{cite:76ef49a7837b560992132b8050dcf26b48e0ec61}}, {{cite:a90bc646cf74f2e0892fc19e294b59477c947992}}, {{cite:411b0eb128ebf149ec9042a7fd7e992f211568e1}}, the features patch or image patch are treated as tokens, which are used to conduct efficient non-local context modeling among arbitrary positions, making them achieve SOTA performance on the most popular dataset {{cite:f1ce5675baf2df3be9055d4d325b50d13ab535e4}}.
However, we empirically found that developing and validating methods with limited data still hinders the potential power of modern deep models, leading to unfair/inaccurate comparisons and estimates of different methods.
| m | 4a337dc8dd7f90dc749cf932e2cdfab3 |
In terms of future directions given that the core renormalization group
functions of QCD are known at five loops in the {{formula:252bfa09-7fd1-4798-8a05-31b9b1039976}} scheme,
{{cite:d8ad8dcf57ef1bda6815751bce34319451a8176b}}, {{cite:2ca855621c9754af165dd9f9f152b053c84b8bf6}}, {{cite:627a81e6ecced5ae46c25d72959561800c33f1aa}}, {{cite:ede39b79c0a3bedf68b3741781fc61acea1a1c0b}}, the techniques are already available in principle to deduce
the next term in the series for {{formula:603746c8-5c13-4639-8a21-046938e5ae4c}} . This would require a five loop
computation of the {{formula:12e90b08-4e6c-4411-8e64-71aa5b41c98e}} correlation function. In addition the approach of
{{cite:627a81e6ecced5ae46c25d72959561800c33f1aa}} to renormalize QCD using a vacuum bubble expansion means that all the
core four loop Feynman integrals that are necessary to compute the four loop
graphs of the effective potential are known. Therefore extending our analysis
to the next loop order would seem viable in the foreseeable future. From
another point of view it would be interesting to apply the LCO Lagrangian to
other problems such as the evaluation of 2- and 3-point functions akin to
that studied in {{cite:5c4d22f09ea4a9641a0ef11c7a3ecd93ffeca482}}, {{cite:cd38c1e4d71bd670e9f8d2d30c3ed1137bf6c27d}}, {{cite:192a085d5c805d3ce70edfa41cfca5bb3509d003}}, {{cite:a98ead6a490855f168e1ee4de9cff4c2430e298b}}. The reasoning would be to see if the mass
estimate extracted here was consistent with lattice data as well as testing
the effect the extra interactions present in (REF ) have. Finally we
recall that one of the early observations that led to the interest in studying
the value of {{formula:dc7c1d3e-5d5a-4148-b168-db266eb7705e}} in the Landau gauge
arose in lattice and other studies, {{cite:815e56c158995ef8b965f4b61a30fb0562aad618}}, {{cite:92d8f64ee4c60f23bb20629898ccd0bc776af6d2}}, {{cite:175f558207c72c0519de878ef072305dc3a51a29}}, {{cite:77a9da7328dae09223f87bb723cf43c5c4e4bbb9}}, {{cite:027c6219f646ec0821c2a60cf55c5981424c4740}}. It was noted that
{{formula:64caca64-e48c-430b-b694-0e576cafa92d}} power corrections arose in operator product expansion measurements.
This ran counter to expectations that the leading correction would be
{{formula:e4a114e3-e8f4-4ce9-ad93-bd37c282997b}} . With the general acceptance that an effective gluon mass lurks
in Yang-Mills theory the LCO Lagrangian might be the tool to formally
re-examine the operator product expansion.
| d | 5b6dcabd608e595901e18a441ccf82fd |
Matrix completion, whose central goal is to recover a large low-rank matrix based on a limited number of observable entries, has been widely studied in the last decade. Among various methods for matrix completion, spectral method is fast, easy to implement and achieves good performance {{cite:fada36ec08b3c215931d0cf0e43cfbb9ee5553c5}}, {{cite:0391f54ca7a327278d20761834ab85800abf448b}}, {{cite:0b8e4cba20a080ef9317b9caa5a0a1681b3c4df2}}. The new perturbation bounds can be potentially used for singular space estimation under the matrix completion setting to yield better results.
| d | 1819c5dc00967a880d7971ef2c0f9929 |
Many other models use supervised learning rules {{cite:633b3b1d3c96b11a5e0c8ec906b3b0ba48a5ddad}}, {{cite:19092eed5b29beb37b36156f05a0c08a14065270}}, sometimes reaching impressive performance on natural image classification tasks {{cite:19092eed5b29beb37b36156f05a0c08a14065270}}. The main drawback of these supervised methods, however, is that learning is slow and requires numerous labeled samples (e.g., about 1 million in {{cite:19092eed5b29beb37b36156f05a0c08a14065270}}), because of the credit assignment problem {{cite:a8f026d54397dabc687d91cf5a3b63386d2a5804}}, {{cite:cbde9208fc371ae3917c4b0ab3b74021f9a751e9}}. This contrasts with humans who can generalize efficiently from just a few training examples {{cite:b33b28b977325f75cbb50ff2a95d3c35f339bed6}}. We avoid the credit assignment problem by keeping the {{formula:20bbb035-591a-4a7b-a46a-931c2c2f9de1}} features fixed when training the final classifier (that being said, fine-tuning them for a given classification problem would probably increase the performance of our model {{cite:275d2084fa11b7cdb77198421085d7e6bd5e8820}}, {{cite:d3f6d153ef0a13b6b95ce15fb00664d4cdeba3df}}; we will test this in future studies). Even if the efficiency of such hybrid unsupervised-supervised learning schemes has been known for a long time, few alternative unsupervised learning algorithms have been shown to be able to extract complex and high-level visual features (see {{cite:43df2e9f5040a43b6e4bc17e55807afa08d3b57c}}, {{cite:275d2084fa11b7cdb77198421085d7e6bd5e8820}}). Finding better representational learning algorithms is thus an important direction for future research and seeking for inspiration in the biological visual systems is likely to be fruitful {{cite:b33b28b977325f75cbb50ff2a95d3c35f339bed6}}. We suggest here that the physiological mechanism known as STDP is an appealing start point.
| d | d504adb3b658fe01c228f3dfcc4c0932 |
In HDNNPs{{cite:905fd6127e7b4b334e1c8f423d93d9f92c142ece}}, {{cite:3bb7b4cafd21812d7b8ff289edc1c0170cef5e9e}}, which we use to compute the energies and forces driving the molecular dynamics (MD) simulations, the potential energy is constructed as a sum of atomic energy contributions {{formula:ca72c310-d984-46e9-9a81-fec43d8d6555}} ,
{{formula:67953342-42a1-422a-9559-6154df24b374}}
| m | 705100c8040e1a628d719baf84a6cd61 |
Here, {{formula:9168d51f-7d18-4420-a04b-6c5e39a2c3ed}} is the observational uncertainty, and
{{formula:1bd62b53-5f70-4a39-92ba-6f8db811aa6f}} is the uncertainty associated with the
model itself, for the {{formula:1a321e67-47a0-45f2-b3fc-7aec0181cac2}} filter. {{cite:6e66db71ae92491baaf1b8154aeee65ce4d22d95}} estimated
the uncertainty associated with the term {{formula:d652ed67-2852-494e-a690-ce0fa66e90cb}} by
comparing the colors obtained from different stellar evolutionary
tracks and spectral libraries. Following {{cite:d97a9722ed6b259b3796f62dd4daf1be4f40c6dd}}, we adopt
{{formula:b806a3d9-0d9d-465c-a2fb-653183e4132b}} .
| r | 218bf9acf4fcdef3edb07dd9790c412f |
Input {{cite:716ceedf02f19b4eaed10d6ca2c4a480835e4f27}}.
We sample historical flow videos from recent time to near history and distant history according to three corresponding temporal views: closeness, period, and trend.
We select hours, daily, and weekly as the key timesteps to construct the three views.
For each of temporal views, we fetch a list of key timesteps’ flow matrices and concatenated them, to construct the input as:
{{formula:b857942e-cec8-40c0-9ecf-87d594279063}}
| m | cfcf72a783acc5e7bcc7bb9803fe4381 |
In SNFs, MCMC is combined with normalizing flows by introducing sampling layers between the standard flow layers {{cite:8058a1e85827f93f65335a2a264e0d7582df9c34}}, {{cite:99eb6ff0e51c763f978c9ad34a681511c978f25d}}. They are usually trained with samples from the target and perform poorly when trained with samples from the flow, see section REF . Instead, we use AIS to improve the training procedure. However, the two contributions are orthogonal, so SNFs could be trained with FAB as well. Similarly, FAB works with other flow architectures {{cite:d3adbb27d602795906f4fbe557c1919eacf596fa}}, {{cite:a51fd08eba8fa16a8663241b732adfbd239c95eb}} and base distributions {{cite:c07a6eacfa02c14744bbfc5d725b3284a71d1a91}}, {{cite:e5a41d6b6898caa8be31b6febb951d5755bf8369}} than those we used.
In {{cite:e3a0fb0329320ddbbf357451b3959ce2f3b74295}} AIS is applied in the context of variational inference to improve estimation of the marginal likelihood gradient for varitational autoencoders' decoder. This approach may be extended by FAB to also improve the encoder training, through minimising the FAB loss with respect to the parameters of the encoder, with the latent posterior as the target distribution.
This would be advantageous relative to {{cite:e3a0fb0329320ddbbf357451b3959ce2f3b74295}}, as well as MCMC based approaches like {{cite:e37710929ae5beec763766fbaefdf1a0241a00bd}} for training the decoder, because if the flow-based encoder can learn a good approximation of the latent posterior, then this alleviates the requirement to run MCMC for long in order to obtain good samples for the decoder.
| d | 9a9946b03e8397647c3116e7b24aaf6c |
Motivated by the possibility of Planck-scale departures from known physics in the form of spacetime-symmetry breaking, a substantial research effort has been put towards highly accurate tests of Lorentz and CPT symmetry in gravity.{{cite:ec81de776bb89af54af470a24a4c54f926cf4446}}, {{cite:b8503622b0b67b91585c36391fd2591686de9530}} By using the test framework called the Standard-Model Extension (SME), sensitive tests in the weak-gravity limit have been devised, for example within the Solar System, short-range gravity, gravitational waves, and more.{{cite:d69acf30ecf619569a9e3c05610b81f38d16536a}}, {{cite:aaab7d53332cd1d59e96d8cb590a98085311289b}}, {{cite:e4ca0a79895e6ef93f08fa6ed7df8c01e1fde24b}} Also, some specific models of spacetime-symmetry breaking have been studied in the context of gravity as well as future astrophysical observations.{{cite:7c9b88f97d4f1d781a1fe6d1b4cb5d7a2ef15388}}
| i | cce786aad82eb1f48fabab03a05e1b28 |
An alternative approach could be to consider the axions as inflaton candidates, as opposed to the saxions described above. However, these models are also in tension with the swampland programme and in particular with the axionic weak gravity conjecture (aWGC) {{cite:ce449f6a5785b7db8364bf502252d3c206fb54a3}}. The aWGC implies the existence of at least one instanton coupling electrically to an axion such that {{formula:ac236758-746f-47ae-8a6c-2bb20014850f}} , where {{formula:89750085-2dc0-4192-9de6-2e853158d6b2}} is the axion decay constant and {{formula:8dfd9fa1-1d7a-42e9-9c39-8cdbc3ca2ad2}} is the instanton action. If the instanton couples to the inflaton, which requires a super-Planckian field range, {{formula:9f21c957-23e1-4cf8-9eca-e2611c641380}} and we lose parametric control of the low-energy theory. We can get around this by assuming the existence of heavy spectator axions that do not contribute to the inflationary dynamics and that satisfy the aWGC bound. However, stronger forms of the aWGC claim that spectator axions are not enough, imposing further hurdles on axion inflation models which remain unsolved {{cite:b5d82873bcb5397ec83b1d86d646a32600d19d45}}, {{cite:4f9cd168a1afd1e6932350bfe1ce9e973e77b8c4}}, {{cite:6933bf5870b52bc05f512e91543e9a83bb100261}}, {{cite:fa3c1d3a2c9ffaaaed88725bf9122c83a1d9dc97}}.
| d | 996c1cfe6d2443d2264861dc71a67832 |
Thus, {{formula:445cf8d4-9181-43be-a957-f8b44d681c9b}} is an infinite tree in which every vertex has finite degree. By König's infinity lemma (see {{cite:f19bfc26a1437360175e39b8187e9981333699eb}}), there exists an infinite path {{formula:7963e646-9ad4-434b-88f6-8a94ed5a76cb}} in {{formula:647fa469-0df4-4492-93c2-a4777c538c12}} with {{formula:632bb5c1-b058-4d5b-b680-02e739fc02e5}} . Thus, there exists {{formula:98d229c2-c7b2-46ba-aea0-5ba8a34d757c}} restricting to {{formula:c0d9f66a-4f6d-4468-97de-0ce8c8878ec3}} for all {{formula:3e92383d-530b-4117-a5ba-57875c6875be}} , so {{formula:bc7396c1-ba94-4c4d-b632-e8b2faa780a4}} is a solution of the K-hexahedron equations that agrees with {{formula:c4081586-8959-4cc9-bbec-ff4ba3addf9d}} on {{formula:b6778139-2f73-47e5-a4a2-2d942a7dfb96}} .
| r | e5c70b224ef4d4c47b63707506927403 |
All methods included in the vision and language understanding experiments are summarized in Table REF . Specifically, we evaluate SNGP on a Wide ResNet 28-10 {{cite:37d4d4206d7e3555cb603739c167e9fcf313c574}} for image classification, and BERT{{formula:3c46b739-fc28-4914-a78e-7a265ec01825}} {{cite:74cc6165503e28fda8e8e4be6b57e7e1c9c0755e}} for language understanding. We compare against a deterministic baseline and two ensemble approaches:
MCD (with 10 dropout samples) and deep ensembles (with 10 models), all trained with a dense output layer and no spectral regularization. We consider three single-model approaches: MCDGP (with 10 samples), DUQ (see Section ). For all models that use GP layer, we keep {{formula:e0f1ae35-d3ed-4332-aaaf-de0ea7c1b1a3}} and compute predictive distribution by performing Monte Carlo averaging with 10 samples. We also include two ablated version of SNGP: DNN-SN which uses spectral normalization on its hidden weights and a dense output layer (i.e. distance preserving hidden mapping without distance-aware output layer), and DNN-GP which uses the GP as output layer but without spectral normalization on its hidden layers (i.e., distance-aware output layer without distance-preserving hidden mapping). Further experiment details
and recommendations for practical implementation
are in Appendix . All baselines are built on the uncertainty_baselines framework.
{{table:5ac4a92a-aeab-4f3a-b8ed-a9166d8a24fa}} | m | fb304debdd5d4eaa94de1f89c92681f8 |
Each task {{formula:76850150-0cec-4a76-82aa-cf789c4e0f1b}} is represented by a corresponding vector representation {{formula:3190523c-13a0-412f-bfb7-99fdb9d8ab6c}} . Our framework allows any fixed-length vector representation for this task descriptor, including semantic embeddings such as GloVe {{cite:20761d08f1f5687e210cffa22ce20b43159e3e78}} or Word2Vec {{cite:a462084edaa99f2bb7a1d667af2f7327aa459269}}, or simply a one-hot encoding of the task. A richer embedding such as Task2Vec {{cite:ba0fc04d3e0fc02b3cf8b434085a0f6a2f3ab63d}}, which takes into account task correlations, may also be used. Details of our implementation are deferred to Sec .
We consider {{formula:0507fbb3-9afd-47cd-b947-483f9ff1db60}} , the weights of a neural network which can solve a task {{formula:ce53a89c-c77b-4c0a-a3ae-45c4e707c5da}} , as generated by a random process given by a continuous latent variable {{formula:930358eb-0cad-47cb-89dc-2d449b5ca70b}} , i.e.
{{formula:c697d714-f345-43d5-875a-fe6d7ea33c1b}} is generated from {{formula:d11f0aac-e0c7-449f-be9f-914d5a67f39b}} , where {{formula:97eef590-b6b3-4b1a-b082-22141a513e00}} is sampled from a conditional prior distribution {{formula:f853b689-bff3-4e54-a354-c905f8fb445c}} (We denote the {{formula:cf3e67cb-7a58-4e3d-8c37-d543e157fea9}} task, {{formula:07c73233-7000-4bf0-95b4-60d9a150f9a8}} as {{formula:4f5a1d8d-2936-4bab-b0fd-271fadf01da5}} for simplicity of explaining the model in this subsection). {{formula:24baaac2-ff4f-450f-9817-5f0f7b777b99}} refers to the unknown optimal parameters of the weight-generating distribution, which we seek to find. We achieve this objective using a VAE-like formulation {{cite:840876995715d70d3f39d5d3e426aa12fadab94a}}, adapted for this problem.
Computing the marginal likelihood of the weight distribution {{formula:1e266b54-44ec-4c54-a6e3-0162bb0710f2}} is intractable as its true posterior {{formula:bcb86530-b669-405f-bff3-21585411e02b}} is intractable to compute. We introduce the approximate posterior {{formula:e5ddcd9b-12cf-4e23-a658-149ea65b8fd7}} , parametrized by {{formula:2202d55d-2e9e-4571-aa9a-2387fe6f9d56}} , as a variational distribution for the intractable true posterior {{formula:2c0b68c9-a85e-4d16-ab87-059d7938b3d7}} .
The marginal likelihood of the parameter distribution, {{formula:3559f4a8-1c9f-4b6e-aa85-915b2eb6f8af}} , can then be written as (please refer the Appendix for the complete derivation):
| m | ad6b7b3428a849a29745026893e152d0 |
In the uplink of a communication network, several BSs may be able to measure the CSI of a UE. With the CSI from the available BSs, the UE localization can be performed with an early fusion or late fusion approach. In early fusion, the combined CSI of all the multiple BSs is considered as a single fingerprint that is used as input of a DL model trained for the UE localization. In late fusion, the CSI of each BS is taken as an input of a separate DL model, to obtain an estimate of the UE position at each BS. Afterwards, the position estimates of all BSs are combined to obtain an overall estimate of the UE position. For DL based applications, there is no conclusive evidence as to which type of fusion is better {{cite:ded33c915019c95aa87b6ae615f43dea4d6cfc0e}}, as this is usually problem dependent.
| i | d47c0c0a680e5b83c0fffb00f3556fe9 |
The simple but naïve way to identify discussion topics is to look directly for keywords in posts (see visualisations in the Appendix). A better but more complex approach is topic modelling. We use a probabilistic generative model called Latent Dirichlet Allocation (LDA) {{cite:dc4821ea3ca413272516b60a17a1419564dcd1ff}} to uncover hidden topics in the forum discussion. The intuitive idea behind LDA is that the underlying hidden patterns within the corpus can be learned by observing the co–occurrence probability of terms, thus forming `topics'. We consider all posts within each category of our forums as a corpus, and see each post as a document containing an unordered set of keywords. The LDA estimation process requires us to decide the number of topics beforehand – one of the most important hyperparameters affecting model quality. To decide the optimal number, we trained several models spanning 10 to 100 topics with incremental steps of 10, then selected the best based on coherence scores {{cite:a6008886ecdc18d0b5dd914d26fcb225847703c0}} (see the Appendix). Our experiment uses the LDA implementation from Mallet {{cite:6b172ad3461861be9fe294729e9ef7571d086968}}.
| d | 1a5f5dcf89ff91e79086dfeac55831fa |
1. The nearest neighbor search is a greedy one. As a result it is possible for it to stop at the local optimum {{cite:6633d9b69084647a7611ba8180f7bd678bf39a6f}}.
| r | 97274a0f348234cb7a45ac4d33fd2d52 |
We visualize these two metrics on a sample CT volume in Fig. REF , along with the segmentation labels. For patches that are not relevant to the labels, {{formula:dc7cf560-9314-4814-98de-4804d735602c}} generates very similar {{formula:0e351d07-1663-41f7-9abf-5081675a4cb9}} ; on the other hand, patches that contain labels yield significantly different weights. Furthermore, {{formula:966937ed-c333-4a25-b3b2-56eab8129ee6}} is also significant on foreground patches, and minimum on background patches. This suggests that {{formula:88d29927-c45b-468e-a2cc-ef7271beff65}} and {{formula:3c96a721-aaa1-4c05-b3c2-b3e440e140ab}} implicitly partitions potential foreground regions, which is a strategy similar to foreground oversampling used in methods like nnU-Net {{cite:27e299992b605852bfe2806babd14b5b6b316630}}. While our method does not employ explicit foreground oversampling, the HyperNet design appears to automate such a strategy. For more details on the visualization of {{formula:99f6a3c9-232c-49f0-96ba-c42f2068afb7}} , please refer to the Supplemental Material.
| m | 1d7d4be3db9aeba255d61da6a44d4ec8 |
We point out that the low Mach number limit is an interesting topic
in fluid dynamics and applied mathematics. Now we briefly review
some related results on the Euler, Navier-Stokes and MHD equations.
In {{cite:6ed7012679ca9ca59ac1ed67b6eacb604e6f78ac}}, Schochet obtained the convergence of the non-isentropic
compressible Euler equations to the incompressible non-isentropic
Euler equations in a bounded domain for local smooth solutions and well-prepared initial data.
As mentioned above, in {{cite:00d2bd5d46d3b3be08992b76388aa5f9a26c7732}} Métivier and Schochet proved
rigorously the incompressible limit of the compressible non-isentropic
Euler equations in the whole space with general initial data, see also {{cite:7b8832030ee4196796d37086c6f94d46c7840a60}}, {{cite:b13e60f2344ae88161bf4c234265e0480cc7bbbf}}, {{cite:6141cca0e20326acd7a8ab045e6a100e74733dee}}
for further extensions. In {{cite:c7e6370470d36a58dad1c10f1925555db25e819d}} Métivier and Schochet
showed the incompressible limit of the one-dimensional non-isentropic Euler equations
in a periodic domain with general data. For compressible heat-conducting flows,
Hagstrom and Lorenz established in {{cite:614fbac8097596250287a8baf24c5626d5b2ebb1}} the low Mach number limit
under the assumption that the variation of the density and temperature is small.
In the case of without heat conductivity, Kim and Lee {{cite:49e0b1a92f4b4bbe9c30325c09655127c976708e}} investigated the incompressible limit
to the non-isentropic Navier-Stokes equations in a periodic domain with well-prepared data, while
Jiang and Ou {{cite:f614d33eddff3f64f8c834bda1f31dbc54052c8f}} investigated the incompressible limit in three-dimensional
bounded domains, also for well-prepared data. The justification of the low Mach number limit for
the non-isentropic Euler or Navier-Stokes equations with general initial
data in bounded domains or multi-dimensional periodic domains is still open.
We refer the interested reader to {{cite:4c3dd84014890590b986a85692b531d1cc441503}} on formal computations for viscous
polytropic gases, and to {{cite:c7e6370470d36a58dad1c10f1925555db25e819d}}, {{cite:81a730d47d11bbd2766c60a39672568901d10132}} for the study on the
acoustic waves of the non-isentropic Euler equations in periodic domains.
Compared with the non-isentropic case, the description of
the propagation of oscillations in the isentropic case is simpler
and there are many articles on this topic (isentropic flows) in the literature, see, for example,
Ukai {{cite:bba2926db2daabe8d8e822141a05af9e3e7ec14a}}, Asano {{cite:f42a4fea903bff9ce0f6a69cd0495b9433b66799}}, Desjardins and Grenier {{cite:33a91ff1bbc0cdf41148722abb635c9c2404b04d}} in
the whole space case; Isozaki {{cite:e7af501bd7c2ebb6f9ee97564ae31b28a27c055a}}, {{cite:b02ad56b1d49df15afc5caf71e3c45bc3f0591e8}} in the case of exterior domains;
Iguchi {{cite:59010f05e72cb5953b7fb00e454828b02a455464}} in the half space case; Schochet {{cite:1e258c7559839201ea9f9acf320e8b0ef1c95d3b}} and
Gallagher {{cite:ce4477a529ea28e16ab03f42baa4c256c759f094}} in the case of periodic domains; and Lions and Masmoudi
{{cite:05c7a58b4cc2d58f326d5ec0585c74c53f8ab5bd}}, and Desjardins, et al. {{cite:8fccbb024007809134397ba7640957827a4f7219}} in the case of bounded domains.
| i | 41baf1e63e9681d218b42573cfec8340 |
Some works proposed the learning-based sampling methods, which learn the sampling strategies through the lightweight neural networks. SampleNet {{cite:fd3ab7f60ba256f41f94736a1cc396460d4251a5}} and S-NET learn a subset of a point cloud by the neural networks. In these methods, other heuristic sampling methods (such as FPS) have to be used to provide the baseline for learning. Then the sampling points generated by the learning-based methods have to be compared with the points in the original point cloud, which introduces extra computations. CAE {{cite:643c3f7e0fc54eb970cc693a3962f8acda3ff919}} and PAT {{cite:2042d3e714badaf0b81f366eefe1b63ba2d9375e}} use the reparameterization trick to calculate the sampling weight matrix according to the relationship among all points. CP-Net{{cite:518f96eb0039126fccc6cb4ff40552a50f9825fb}} evaluated the contribution to the aggregated features and selected Critical Points (CP) as the sampling points. The learning-based methods are optimized for both the task and the deep network in sampling to improve the effectiveness of the sampling. However, these methods do not perform local grouping. Rather, the traditional local grouping methods such as kNN or ball query have to be used to complete the data structuring.
| m | 800f0256759ecd1b0b999582da9b8e42 |
Data Explanation: We employ two data sets of epidemic dynamics.
The real data set is collected from the Social Evolution experiment
{{cite:9647f3283e8decedc3e2d401f46cf078b3d2f8a4}}. This study records “common cold” symptoms of 65
students living in a university residence hall from January 2009 to
April 2009, tracking their locations and proximities using mobile
phones. In addition, the students took periodic surveys regarding
their health status and personal interactions. The synthetic data
set was collected on the Dartmouth College campus from April 2001
to June 2004, and contains the movement history of 13,888 individuals
{{cite:bdba353969fb41842286f029a5c4461434323a41}}. We synthesized disease transmission along a timeline
using the popular susceptible-infectious-susceptible (SIS) epidemiology
model {{cite:8bcf9e5449f4ab233324b42caef183e530f0c52b}}, then applied the VISKM to calibrate performance.
We selected this data set because we want to demonstrate that our
model works on data with a large number of people over a long period
of time.
| r | 2ce6eeb3292ae74077b83b44ee7bce96 |
The alternating direction method of multipliers (ADMM) is an important variant of ALM and has been widely applied in machine learning, data analysis and signal processing. The studies of ADMM in the convex setting is comprehensive and clear, see, for instance, {{cite:cd59a62d4f945238a22c91cffe7c7818399e8462}}, {{cite:f0fd6e0b71e8448a568d0c1515ba6cd1c48d4fe2}}, {{cite:98dac0f85f7c43da5d41adc5febb530e8fdc61d8}}. In recent years, there are some works addressing the convergence of ADMM in nonconvex setting.
In {{cite:82ddad98b0d511e6dc2e42232a0ea60385d44c09}}, a proximal ADMM (P-ADMM) is proposed for minimizing the sum of a smooth function and the composition of a lower semi-continuous (l.s.c.) function with a linear operator. The algorithm is convergent under the assumption that {{formula:e0f792fe-2749-4e32-b9f7-fc128ef5271b}} is full row rank and the objective function is semialgebraic and its smooth term has a bounded Hessian. For the same problem as that of {{cite:82ddad98b0d511e6dc2e42232a0ea60385d44c09}}, {{cite:259b71356ee33088462b8e4d127043f2ff84a9a6}} establish the global convergence of a P-ADMM under the assumption that {{formula:c3de9de5-36f4-4ead-add3-1a5869472b30}} is full row rank and the objective function is semialgebric. {{cite:78a489c765022aed021f314bb0513dd64bd51141}} considered a more general model than that of {{cite:82ddad98b0d511e6dc2e42232a0ea60385d44c09}}, {{cite:259b71356ee33088462b8e4d127043f2ff84a9a6}}, where the objective function has an additional l.s.c. term and the smooth term has two variables. In {{cite:78a489c765022aed021f314bb0513dd64bd51141}}, a proximal linearized ADMM (PL-ADMM) is proposed and the global convergence is established under the assumption that {{formula:8c3c7099-1fd7-4ea1-b19c-cf534868cc0e}} is full row rank, the objective function is semialgebraic. Some papers focus on solving the nonconvex composition problem with two variables and linear constraints which are general model including (REF ). Most of these works established the convergence of ADMM-type algorithms under the assumption that the objective function satisfies Kurdyka-{{formula:8ffb0bfb-8e23-471c-acbe-24bd891825c2}} ojasiewicz (K{{formula:262096b4-dd28-4de1-824c-aecb91e2c76c}} ) property. Furthermore, when it comes to the the global convergence analysis of the special case (REF ), {{cite:1ab5cc8f2318547b82dda35932e11e533b5d0eeb}}, {{cite:64ed5f362d1c631d074337543ce17b4a021b1e21}} requires that {{formula:0bfa3945-23a9-477b-866d-ca943acbc98b}} is nonsingular. The convergence analysis for multi-block ADMM in nonconvex setting can refer to {{cite:ca958ff454e30002a66cbd21ba6ff2df49cc014a}}, {{cite:d679d938728c094048a47b2ef52326306668fa10}}, {{cite:d10b809033238389e803ab48fbea7d56c3091d7b}}.
| i | d9c03f2d829688b76a6f5ce66873457d |
We compared our models with the state-of-the-art systems on English{{cite:b7501b12562b601ce61eaaedeabe460c0475fd4c}}'s results are different since their implementation did not convert the predicted BIOES tags back to BIO2 during evaluation. For fair comparison, we only report the results of the standard evaluation., Dutch and Spanish. For Dutch and Spanish, we used cross-lingual embedding as a way to exploit lexical information. The results are shown in Tab. REF and Tab. REFWe thank reviewers for pointing out a paper {{cite:591cfe9c87497b81dccda0f9234ab3dbe9f4c74d}} obtains the new state-of-the-art result on Dutch with comparable results on Spanish.. Our best-performing model outperform all the competing systems.
{{table:607983ca-114f-4f0f-91c9-4539d49d2873}}{{table:831d20a6-b950-4144-8c40-cd770ca173c6}} | r | 3538301a1895089a083f4f1e4939add1 |
The V-QCD baryon solution we present here has several advantages with
respect to similar constructions in the literature, as well as some
limitations. In order to discuss them, we shall compare the results of
this work with the two main models of holographic QCD in which
single-baryon solutions were analyzed. These are the top-down Witten-Sakai-Sugimoto model (WSS) {{cite:03b87bb0d5071ea880ab970510d438282b745532}}, {{cite:11b89b7a89bb4275315bb84dc0a158ef569648ba}} and the bottom-up Hard-Wall model (HW) {{cite:5ec59236027e3a7e89b0332618e0e6db3475bd31}}, {{cite:4a2598359a52f9ea6b5b7e64c1efeab43110025a}}.
| d | 061f83cedefa6dbc0589cb67e03bdcf4 |
We have assumed {{formula:23f70cc4-139d-4169-b0bf-eb167ce2c9e4}} is real, and that the different components
have equal number and mass. The second term contains
both the exchange and anomalous term, which couples {{formula:d9ecf841-1e03-47d1-af89-430aa69acb70}} to {{formula:d3a13c6e-3b37-49ee-bcc5-cfbfc451c05a}} and
{{formula:099be594-0670-4b10-a5bd-12da32b4d040}} to {{formula:1d177c46-0e3d-4a60-90e6-e3275bba720c}} , respectively. These terms would be non-local if the interaction
was finite range. These excitations are normalized in the
standard way: {{formula:24405d21-0516-4a9d-9873-ff587994853c}} -{{formula:6d9fa382-1194-49eb-873a-05b4a46dc7d8}} {{cite:fe3de84b9ae0475037beb0692fd58e2f39019e4c}}.
| m | b965d8d9aafa445867ac0e99425f6b7d |
Statistical Comparisons of the Different {{formula:e658682b-9527-4cfa-853f-2e72ba2cad31}} Variants for Window Size 300ms: To examine the importance and significance of {{formula:5422ae3e-5440-49a5-b0e4-f721ed35064b}} variants, we perform statistical tests for all models considering {{formula:b37ef6a6-0c57-4dfe-ac72-c9f05fd426b8}} . By following {{cite:0bec180b13d26f71a0c899292e270ab191437b20}}, the Wilcoxon signed-rank test {{cite:e7e8e80d43ddb4af58579177e21f02e787fb952a}} is used in which each user is considered as a separate dataset. As illustrated in Fig. REF , we conduct comparison between the model with the least number of parameters (i.e., Model 1) and other models. (i.e., Model 2, 3, and 4). Using Wilcoxon signed-rank test, it can be mentioned that no statistical significance was observed comparing Model 1 and Model 3 in Fig. REF . However,
Model 1 is significant versus Model 2 (or Model 4) because the {{formula:348f81e1-9113-48f8-9b98-a775887b46d6}} -value is less than {{formula:95c4b657-80a2-4ba5-957f-82c051fed2ab}} . Further details are provided in Fig. REF where the {{formula:68cbaeb3-8676-4a92-8e11-b724630e4df6}} -value is indicated by the following symbols:
| r | 0641fd52ee035a65a25e83c83a84f140 |
Large data sets and giant models, together with advances in deep learning algorithms and hardware, enable researchers to push the limit of many machine learning tasks {{cite:c5a4ee8534df1adb3e96bddf3b161b58a5303c29}}, {{cite:5d352fca4d766ffe62d5eefa1edfc980700ecb13}}, {{cite:1329a66a6347a173bc54523e2a1c7337b17c2fe0}} including speech {{cite:bfc6bad02984d4fd70a783242e955db81cd92942}}. It brings renewed interests in building universal automatic speech recognition (ASR) systems that can recognize speech from any language. Traditionally, a predefined language agnostic representation is required for building multilingual models such as a global phoneme set like International Phonetic Alphabet (IPA) {{cite:f9bd30efab4e25806a6bcd796eb755349279bdc3}}, Speech Assessment Methods Phonetic Alphabet (SAMPA) {{cite:85f8f9e41e672892dafd73277cf2b40e2e54c4d6}} and Worldbet {{cite:b26bf20f7ecb4b8fad6c99eca82e1e313277f97c}} or a universal speech representation like articulations {{cite:f1a996b90f1b6b8f8942b6b3f9c6a46d391059aa}}, which all require expert knowledge. In the past decade, deep neural networks have been widely adopted in the speech community {{cite:b2eede108e01983ed77f3216630861057b2b6ed9}}, especially the recently developed end-to-end (E2E) models that merges the modeling of acoustics, lexicon and language into a single neural network {{cite:17ba6f5af77a700b1a8731b980804613af999ba9}}, {{cite:70916b49aa506b1f14494b041f2034b48b31185f}}, {{cite:e61e0ba21538ecee0ba1e3baac96aab40cb36591}}, {{cite:18fddb85c2cec55a18df46d21a6ec364f677038b}}, {{cite:1a6399cdeda13d67f3f2aa7b9700d04b01f7dc46}}.
It largely simplifies the building of multilingual models by learning shared representation directly from data. This also speeds up the sharing of techniques between ASR and other machine learning fields such as neural machine translation {{cite:443f73ef2bf26ee85624ba29136402d805e7bf0a}}. Experiments on less than 10 languages have shown promising capabilities of such E2E models in modeling dialects of a particular language {{cite:bebe0f4822143aa5d83c33673f3fe168bd1470f9}}, languages from the same family {{cite:b567b6ed5bc2264adac7677d78ccbb8480058b26}} and languages from different families {{cite:5412b7f94d42a96e19a4ccf760126387b23ef523}}, {{cite:cf76e9647319d4aa7d1643d18774e2471f45937b}}, {{cite:9434172597b713bd3dc023e8a404f40ecca3f671}}, {{cite:5b49b4cec28eba5ed2d3a035927d162492084877}}. Recently, massively multilingual experiments using more than 50 languages {{cite:5b49b4cec28eba5ed2d3a035927d162492084877}}, {{cite:cf76e9647319d4aa7d1643d18774e2471f45937b}}, {{cite:9434172597b713bd3dc023e8a404f40ecca3f671}} also show comparable or better performance compared to monolingual systems.
| i | dfb9907af0a21ef1accc5ef161a69529 |
Thus, we show that the inversion bias guarantee for LESS embeddings
matches our result for sub-gaussian sketches up to a logarithmic
factor. This additional factor is standard in the analysis of fast
sketching methods. It comes from the fact that, as an artifact of the
matrix concentration bounds {{cite:53fe26c641e608154eef431a821b78121fa02017}} we use in our analysis of LESS embeddings, a sketch of size {{formula:25f27306-516e-45e2-abce-87308e634ed0}} is needed to satisfy
the subspace embedding property, which is one of our two
structural conditions for small inversion bias (see
Section REF ). As a corollary, we obtain
an improved guarantee for averaging i.i.d. sketched inverse
covariance estimates which also matches the corresponding statement
for sub-gaussian sketches (Corollary REF ) up to
logarithmic factors.
| r | ec9da7c3970f703ce4890804b3485916 |
The following word association and word similarity datasets are used throughout experimentation: Simlex {{cite:1d71206d2b8cf775ca8cd64e3e3ed967d55fde64}}, WordSim-353 {{cite:89bb314d0be760554de1b381ef73228b7da7b620}}, RG {{cite:4fee3827dfb0202867788aa7178b85ee9939987e}}, MTurk (MechanicalTurk-771) {{cite:ccd79329d0d77a3b72ebf94084d570fd967cb1e9}}, rare word (RW) {{cite:81b1adc6d562c392275acc5daeb96cb1881b6721}} and MEN {{cite:71d2c8102e7fc24825d145084bd1e89abaec082b}}.
Table REF shows the results, where (1) shows the single embedding performance, (2) results for standard meta-embedding approaches that either apply a single mathematical operation or use a linear projection as an encoding, (3) results using AE schemes by Bollegala and Bao {{cite:403350c6688230d2e2c791e7db82ec90cacec453}} and (4) results of our proposed TAE embedding.
Results in red shading indicate the best performing meta-embedding for all presented approaches, while black shading indicates the best performing meta-embedding for the respective section.
| r | cb3b7b687908d35123679a41129b994c |
for some fixed {{formula:85ee782a-44a9-412e-8436-59de77fa65f0}} {{cite:7a89b9e1484c6b71bf133dc2dd4ddaa666929262}}, {{cite:9b7ab0041aaa7242ab0803b09cdb1a10b55b8b4b}}, {{cite:0835c5846b4c5811d1a94e92e9fbd4cdcd59a490}}, {{cite:6e9225b07ce005d6b92e0ed2950f54fa79783967}}, {{cite:dc5f815831e73de7fc121a564ea8c2d13caa19a7}}. The name “truncated” Newton method has also been used for the specific case when the inexactness comes from the use of iterative linear system solvers like GMRES {{cite:ba75a3d719c62129f91d59a5ba2088b3a4fabaa2}}, {{cite:de99bd695ee43ffadb213a988f92c09720e7b89c}} or BiCGSTAB {{cite:fa9c5a3ff97896075bc92f8cff017e7faea43eba}}, {{cite:23780e3175e0eeb88112d0b53a48d9bd1b4f3052}}. We focus on GMRES, a particularly simple yet strong iterative method for general linear systems that has been consistently used in the context of solving nonlinear systems {{cite:9b7ab0041aaa7242ab0803b09cdb1a10b55b8b4b}}.
| m | 7a5e6657dd46a1c979fdb1e6c4e23820 |
Trends in sea level at long time-scales also impact changes in weather-like extremes. Recently, many studies have focused on quantification of current and future changes in sea level extremes driven by storms, tides and waves {{cite:0a73f37f605956893891a5b9eda23b76727a48b9}}, {{cite:e45d4fc8f1fe5b06690f700b5e5e48728c246cdf}}, {{cite:8ac7c60b7cd80f043cc60ccdd8724838ac844aee}}, {{cite:c0478e04a6fb2dda44b3af1b716a359a0388a64f}}, {{cite:87c1da15b5c85a8ff1d3b68f0e1365eceeb6aec1}}. Such studies aim to characterize tails of sea level distributions in recent periods or in future scenarios via Extreme Value Theory (EVT) {{cite:09e0447d7996b1e6bfed493d323e3f5b1aeaefd0}}, and often quantify changes in extremes solely as a function of changes in distributional mean {{cite:87c1da15b5c85a8ff1d3b68f0e1365eceeb6aec1}}. A shift in the mean sea level is in fact recognized to be the primary driver of changes in tails of the distributions {{cite:bb830c8089636f5b01a6b3a5048d51d1baf36a0e}}, {{cite:2e27a95d1a39836de6aa869684699beaf427cbf6}}
| i | 3f4dc1796abeb30e2b24bd2f2807ff6d |
where the authors utilized the mapping {{formula:74faf65c-aab0-44ad-8bc0-fc644e9ac453}} with step length {{formula:c2b664d8-3533-4d5a-8131-2d244eb02efa}} and the forcing terms {{formula:0a03219b-1f27-4b14-ae49-76b843dff7ec}} and {{formula:4ea53655-b6fe-4b77-bcfe-23427a3052fd}} to control the level of accuracy of the approximate solution to the SNE. In comparison to Eq. (REF ), the mapping {{formula:8d6cb18d-2c27-4327-ae66-9388b185cbad}} replaces the tensor term {{formula:608b95c7-3616-41a0-9d1d-1551b7103b1b}} while still preserving a third-order rate of convergence. As shown in the algorithm above, each iteration only requires approximately solving two linear systems. Eustaquio et al. utilized Saad and Schultz's Generalized Minimum Residual method (GMRES) {{cite:ee2e9e9b9811d56fbca3a306343c146934c7748a}} to solve the two linear systems and obtain the inexact Newton steps {{formula:ceab01ad-3e03-4818-b866-f14227aa2d6e}} and {{formula:6133f862-06d3-435b-9e31-47c5e1b33fe6}} .
| m | 5128e565cb7b541bc9165aa08be6754b |
The sum of all terms beyond quadratic order in the density expansion is known as the
`bridge functional' {{cite:7cc176748b103ebc9bd3c43ae73e95460b792509}}, {{cite:657f868c24cfe34c8264b0563d9c20b922ec5d21}}.
Rosenfeld has shown that the quadratic functional can be much improved by replacing the true bridge
functional of the fully interacting system with that of the hard-sphere system
(often referred to as either the `reference functional' or `universal bridge functional' method)
{{cite:0ca1dae823912b6b26aa784a6e1e5edc87023fdf}}.
This approach is somewhat similar in spirit to our inhomogeneous BH theory, for which
the total correlation function {{formula:12625e73-3574-499e-afab-32addab37ae8}} is assumed `universal' for
any attractive interaction.
On the positive side, the universal bridge functional method can make very accurate predictions
in certain cases and has the convenient feature that only one-body functions
are required {{cite:0ca1dae823912b6b26aa784a6e1e5edc87023fdf}}, {{cite:6dad7c588265ee37f2228c0538516d101a034faa}}, {{cite:86c5c74994f188e8a327017dd48534a0b745f8a0}}, {{cite:be21120f101a845bfe579273ce4658f928c7ccc7}}.
However, compared with the BH functional we observe two fundamental disadvantages of the
Bridge functional approach:
(i) Despite resumming higher order terms, the theory is still a density expansion and thus cannot escape
the need to identify a bulk reference state. This is problematic for confined fluids.
(ii) To yield accurate results the hard-sphere reference functional has to be evaluated at some
effective hard-sphere diameter. This introduces a free parameter for which an optimization criterion
must be specified.
In our view, the assumption that {{formula:d280e4f5-876d-40be-8cf9-cf5b9aec8c8e}} is `universal' constitutes a
physically clear generalization of van der Waals vision of the liquid state, whereas
the universal bridge functional seems to be a more obscure formal object.
| d | 15917058fa36e7c892563c062a57cbc2 |
In this paper, we will present two different proofs of the regularity of the compactified metrics near the conformal infinity for the cases when {{formula:5d71e1a9-528f-4a62-a0a4-d1ae145b3746}} is even and when {{formula:b09103cf-9ff5-4744-9fa0-da7593061de9}} is arbitrary. When {{formula:40bace37-c7ce-460e-a601-71288de024bb}} is even, we will take advantage that for the CCE manifold {{formula:bb8cef37-4f3d-400a-af87-ba70ea56fa4e}} , the {{formula:b1114f9b-12c5-494f-b5bd-0c799c61f5df}} -th order obstruction tensor ({{cite:f6b6e9ea3c5e0040379bb8fa45f9cfa0ef7d13d6}}, {{cite:c6d6e25327b6e2a04a6995635d9eebc2b0f9a62b}}, see the definition in section ) vanishes. Thus the 4-th Bach tensor for the compactified metric {{formula:21e16358-5539-40df-b4d5-931acafb8fc6}} satisfies an elliptic PDE (see (REF )); this would lead to a gain of the regularity
of the metric of {{formula:3a45ddcc-8d6a-4b9e-9ad0-05ee9ea0c953}} near the conformal infinity. We will describe this process in section .
| r | 7866aeae388537d2f73d581c30a5f8d0 |
In the absence of the constraint {{formula:23465510-dd31-4d80-9858-763f73a41d06}} , if we set {{formula:6cf4ece9-150e-48ab-a7fe-fa913f227b5f}} , then solving problem (REF ) via
IG-involved descent method (REF )
will reduce to the ordinary IG-absent method that solves problem (REF ).
This is a known BLO result (e.g. {{cite:6e011af9a57ba1f0a7c3c82be3282802f3d28fbf}}) and can be readily proven using the stationary condition. To be specific, based on the stationary condition of unconstrained lower-level optimization, we have {{formula:c5578486-2c93-4e11-8144-b827a8b60a6b}} . Since {{formula:bbf17ee2-5c8f-4747-a294-147461111327}} , we have {{formula:4d5b215e-7eb1-4915-8bdd-242c5f263b07}} . As a result, the second term in (REF ) becomes {{formula:d3f3d8cc-c8ae-447e-8d2c-68ac157b399d}} and solving problem (REF ) becomes identical to solving the min-max problem (REF ).
In the presence of the constraint {{formula:70e1b192-7548-45ec-8b7f-e73801661f7e}} , the stationary condition cannot be applied since the stationary point may not be a feasible point in the constraint. In other words, {{formula:60559548-ee46-4a38-9879-3a271209de26}} does not hold in the case of {{formula:3d06ffbb-c1da-4b59-8491-040cc036e3b1}} . As a matter of fact, one has to resort to KKT conditions instead of the stationary condition for a constrained lower-level problem. Similar to our proof in Proposition REF , the implicit gradient (and thus the second term of (REF )) cannot be omitted in general. This makes the optimization routine to solve problem (REF ) different from solving problem (REF ).
| d | 53d2fb5307855a4c74efdce9957432b7 |
The loop model and the Potts model can be studied by means of representation theory of the affine Temperley-Lieb algebra {{cite:f03153d5c5b97c65708ee45d88070315b67735fb}}, {{cite:e135d436fc55247ea45198595e598834888b0eb3}}, {{cite:af21b0123545543d04c4054fdcbd10ccf627bfc4}}, and more precisely a quotient thereof, known as the Jones-Temperley-Lieb algebra {{cite:8a600eb344ebe805177ee1ed1a6fc3523f5e9e14}}, {{cite:6e86e0d55a402b173281ff828a0ce53aa2cdc82f}}, that we shall define precisely below.
Our goal is to study the torus partition function for these models. It is computed by taking the Markov traces {{cite:9e1fa89841d957645a6792a20a048015f3f751dd}} of the transfer matrix in the so-called standard modules of the aTL algebra, denoted {{formula:f71cf41a-572e-4ff1-8f0c-5bab4cdeee5f}} , which can be constructed in the basis of link patterns. The parameters {{formula:957d74da-833e-4b48-9ba4-094c5d8aeb98}} and {{formula:700730e1-f249-4191-9ea8-b4c0120be051}} are defined by choosing a quantization scheme, in which one principal direction of the torus is taken as `space' and the other as (imaginary) `time'. Then {{formula:efc13835-34b2-4731-b38a-8b3d444588c0}} is the number of non-contractible loop strands, henceforth called through-lines, running along the time direction, while {{formula:3114de10-87c3-4c35-a769-b11044ec5896}} is the pseudo-momentum corresponding to the movement of through-lines across the periodic space direction.
The transfer matrices in the aTL standard modules are related to the transfer matrices of the XXZ spin chain with a diagonal twist, which can be solved by Bethe ansatz. The correct twist is related to {{formula:b15999a9-5564-4913-b2a9-2b5a0cb4a54c}} , so this parameter enters the Bethe equations.
In the framework of the Bethe ansatz, the eigenvalues of the transfer matrix are functions of Bethe roots which are physical solutions of the Bethe equations. Therefore one can expect physical solutions of the Bethe equations to contain information about the representation theory of the aTL algebra.
| i | 9606b1751993744190acf622b86c9a15 |
Finally, we observe that among the three ArtLM variants, FT-Art-BERT has the best performance, surpassing the both smaller FT-Art-DistilBERT and the larger FT-Art-RoBERTa, although RoBERTa reports a superior performance than BERT on most of the NLP tasks {{cite:1f02d362375634e00c6da1d817bab8e86c64b149}}.
A possible cause is that the RoBERTa model removes the NSP task in the pre-training process, as mentioned in Section REF and in Table REF .
However, our artist pair classification usage is similar to the idea behind the NSP task, which leads to the performance degradation after its removal.
Another possible explanation is that the RoBERTa is trained on a much larger corpus than BERT, it may require more art-related data in this second pre-training process in order to be significant.
| r | 3244c0dc06da62b524c22348e403e44c |
In this work, we propose a stereo superpixel segmentation method with a decoupling mechanism of spatial information,
the framework is illustrated in Fig. REF .
In general, the proposed method can be divided into the following steps:
First, stereo image pairs with Lab color space are input
into fully convolutional network to extract the deep features.
Then, the deep features of left and right views are fed to the Decoupled Stereo Fusion Module (DSFM),
which integrates the features from both views.
Moreover, Dynamic Spatiality Embedding Module (DSEM) is proposed
to adaptively combine the spatial information with deep features.
Finally, a soft clustering algorithm {{cite:7955586fe0e8cabb50ea0809bbdb955f6fc58935}} is adopted to generate the superpixels.
| m | 1ab34b0b15f2235458ff01d42aae3e3e |
We focus on attribute features as input in this paper. An input instance is a vector {{formula:808cf4d9-057a-4f12-aab0-79a652f7666a}} where each entry {{formula:d909004d-7ba0-4345-aa56-57266c94bd2f}} denotes a raw feature (like age, occ., edu., etc.). If {{formula:c3f415fd-c56f-41c4-a8cd-f38ce1fa6c5c}} is a discrete/categorical raw feature with {{formula:eed940e1-e32d-4664-91ad-268879b44720}} possible values, its space is an integer set {{formula:7b2f2698-eb0e-4d79-9585-417f99591d65}} . If {{formula:1b45b318-3445-4ea1-8922-cecbed87d160}} is a continuous one, a common practice is to convert it into a discrete feature within space {{formula:6015b7d4-d182-4599-8a84-1d576a515caf}} by evenly division {{cite:df7f50535e8fd7a3b1b0aa8d09ad126106a78810}} or log transformation {{cite:df7f50535e8fd7a3b1b0aa8d09ad126106a78810}}. We call {{formula:aed66ba6-2548-4aef-b9d5-e41b1c49824d}} as cardinality for {{formula:f3d17ff6-9ff1-4d48-a5ec-b55254b2165a}} -th raw feature.
| m | d77ef169221754a0c264d98871cb06d6 |
Given the scale of {{formula:1fa2eeb6-8cf4-4543-9570-967a94a519f6}} , it is only at galactic length
scales or longer where the impact of the extended
GEOM is expected to be seen, and in {{cite:c9ae8531c1674eb9a574d887706113615dfc58a6}} we applied this
extension to the analysis of the motion of bodies at these
scales. Using a spherical model for galaxies, we calculated the
density profile of a stationary galaxy given the radius
{{formula:249089e1-4e43-4393-bcf0-7b9a0fbef6b7}} kpc of a typical
galactic hub and the velocity {{formula:e1e827a1-6b2e-485e-a051-d8b2617b968a}} km/s of a
typical rotational velocity curve (RVC) at this radius
{{cite:c9ae8531c1674eb9a574d887706113615dfc58a6}}. This {{formula:22606299-2bb1-4c37-87e5-f3c9e57f63df}} and {{formula:bc1f114f-1694-4b84-ba0a-bec296113066}} were determined from the
observed motion of stars in 1,393 spiral galaxies {{cite:6c74ac53d88f43ddad3213c2a25df6f4212c274c}} -
{{cite:608d9f6e62e70ae56b2c673a399d5678e580c5b0}}. The density profile for the model galaxy was
determined using the extended GEOM and the following model of the RVC
of the galaxy,
{{formula:1168a19e-7148-4562-bb70-678ff54a2c35}}
| i | 9959c28a4205d6f1c39107e9aefc8588 |
We further report the quantitative results compared with the prior DG methods, as shown in Table REF .
We implement these approaches on the task of liver segmentation based on the official public codes with some necessary modifications.
When the source domains are BTCV, CHAOS, IRCAD and the unseen test domain is LITS, the proposed ETTA-SE method does not outperforms MASF {{cite:b3f4530ef645f13374959a22cf42361dc761e41e}}.
However, our method can still achieve the state-of-the-art performance on all the remaining settings.
The proposed method also surpasses other advanced methods on the average Dice score.
As shown in Figure REF , some over-segmented and under-segmented results produced by prior methods can be refined by our method.
| m | 63cb912ea94565b6d9440b2e252069c4 |
Data science and machine learning have an increasingly prominent role in our science, as is evident from any recent particle physics conference and this Snowmass process. In recent years, machine learning techniques for detector and accelerator control {{cite:f4eb6548674df5e1df17368c14a74ef8535322a6}}, data simulation {{cite:9eb8e103c25394001be4242d759583756bee999d}}, parton distribution functions {{cite:0b476acd15e69edfbb427dbd8f19be07cfb10d35}}, reconstruction {{cite:d06d2237af6b0be618a7b7a8062d8edf3249ef82}}, {{cite:34f9fa618c91ec46e69b771e44bc5776a2030940}}, {{cite:56a712f231a406e886f691294159cf1e50b32d66}}, anomaly detection {{cite:6fa1dab0a323f925d99a235a8b7f08865570bed6}}, {{cite:7d3b922499b7aa48b20103e3de923b086c8ec7b5}} and data analysis are increasing being applied to particle physics research. Recent reviews of these techniques applied to particle physics research can be found in {{cite:84fc088433327b82f66688dbd13807f125973fdb}}, {{cite:d08d120a4f03b827fdcfb2b804e8f7fe3b4af093}}, {{cite:9f44af16e0dd70459345c3f588ef927c683b63fe}}, {{cite:1bb28e1ee22a70d61ee5750f60568324e4634f84}}, {{cite:bed4907cd5778976f45e7996c5adad976fafefca}}, {{cite:52095c81e53b4a834ca33a6fe0c3d38801bab270}}, {{cite:2248f2591f2feede7e03a2e65473aeb87396852f}}, {{cite:97cebb021fa3ea4ecabdc3de8eec1f915f944139}}, {{cite:ff5e66b046b7652f5f836530eddc902f22aa819f}}, {{cite:5d529f5b33e15a0637f71ae247aff095a056d819}}.
A “living review” aiming to provide a comprehensive list of citations for those in the particle physics community developing and applying machine learning approaches to experimental, phenomenological, or theoretical analyses can be found in {{cite:9ec9882a94138a2d540c381e61457afa4d407276}}.
| i | 1ab47c88fdd7b87f412c14cbb28adaf0 |
The north-south asymmetries in velocity dispersions are detected in this work, though the differences between {{formula:d0b54a41-8cb0-42d4-b52f-8b43764ec791}} stars and {{formula:bb096046-eb34-4822-83d7-3c94d0eab50c}} stars are less pronounced than those for the mean velocities. It is interesting to find that the {{formula:b9ea7c1b-81b1-41cf-afd3-49a622659b19}} in the south disk is larger than that in the north. The velocity dispersions are probes for the secular heating process in the disk, which are principally generated by spirals and giant molecular clouds (GMCs). The variation in {{formula:1e9c130c-f22c-4ae0-a412-474daa4f00c8}} is a measure of the variation of the importance of the GMC as heating agents relative to spirals, since spirals heat mainly within the plane while GMCs heat both in-plane and vertically ({{cite:c0f51c211d92fd01fa13aa42c4d60c8549f73c4b}}; {{cite:74829fc8906f7803f62ef688fcf8c4ce850b3287}}; {{cite:bb7d4049a575ff03c4c40bc5ba86b3d0eeafa72a}}). The increasing {{formula:a20fff89-3e53-4cb3-b922-6166e065021c}} with increasing {{formula:3089dc0f-1e10-4ae2-8174-31ace9649256}} indicates that the relative strength of spiral to GMC heating decreases with the distance to the plane within {{formula:3be90f24-4418-4f86-afe2-319a5e31b1fa}} . Meanwhile, the larger {{formula:b9c7cb64-4dca-4a86-97e9-58a4586d83d8}} below the plane than above suggests either a weaker spiral heating agent or a larger number of GMCs at {{formula:39dfebe9-9c3c-4243-aef3-fec9857f2a09}} . Moreover, the interactions between a satellite galaxy and the disk could also heat the disk and cause north-south differences in velocity dispersions {{cite:bb7d4049a575ff03c4c40bc5ba86b3d0eeafa72a}}.
| d | 7aaf629803766d136b9d10d782c5058c |
At last, the critical assumptions of the present approach and its realization merit a discussion. Our methodology is based on the hierarchical distribution of the attached eddies, and the hypothesis that the characteristic velocity scales carried by the attached eddies with different wall-normal heights are identical with their scale interactions omitted. That's to say, the attached eddies in each hierarchy contribute equally to the streamwise wall-shear fluctuations on the wall surface and the streamwise turbulence intensity in the lower bound of the logarithmic region. Only in this way, both {{formula:e4c13530-4274-48df-bd2e-df8f6236e0d8}} and {{formula:88e577f6-89eb-44b1-a584-c0859cc884f6}}
approximately reflect the characteristics of the attached eddies at {{formula:9bc7f83a-b4ad-4956-a22c-27837e5748fb}} .
In fact, these assumptions are also the key elements when developing the attached-eddy model {{cite:bd7f49cf7c7a5a3130a89c089c6d65ca8ac94e43}}, {{cite:67a2220b9e3588e9a2e44f528819f0ece8beeec0}}, {{cite:5b8c75af294b569f5bb8f650a020d9bca818a9ad}}, {{cite:1b9671fda33e6136d05b85357f3dc6b32a63519c}}, {{cite:80cb355cc95515160a5e1a96a0b377ff047e65a9}}, {{cite:db404aebc786ffe07fdd40180117a243b691abcb}}, and some of them may be valid only in high-Reynolds number wall turbulence. For example, the hierarchical distribution of the multi-scale attached eddies is prominent at high-Reynolds number turbulence {{cite:7a57cc4cecab86072dd9c4147c04b4cec14545ba}}, {{cite:d8005f08a60fc6ccdb2a623cd939eced159b5847}}, {{cite:2252a6892c45d39cb2a32d26a0a21fe3a34c1f03}}.
However, when the DNS data listed in Table REF are utilized to study the characteristics of the attached eddies, the finite Reynolds-number effects and the intricate scale interactions would take effects inevitably. Besides, the VLSMs, which can not be depicted by the attached-eddy model, would also impose non-trivial impacts {{cite:1ceb5e1adf7a02900c1f11b4f46964c77fb495ab}}, {{cite:3929eddfbb5b6c7e47e6ff84a515f5ba935a42f8}}, {{cite:7b068868174d86c88a559c2b0742cd8c1d5fa62b}}. Accordingly, the subtraction between {{formula:a75c2c13-fb7d-4327-aeff-3d7357f1c939}} and {{formula:361146d6-6bd3-4f44-af20-04e16fdafd4f}} can not achieve a sharp cut-off at the targeted scale in the spectral space, and hereby the spectrum of {{formula:5dfc7bce-76a5-495e-867c-0dbe5adc77fc}} would be comparatively small but not negligible at the smaller and larger scales of the targeted one.
The finiteness of {{formula:456675d4-b3fa-45cd-86e6-8d1682fd58c5}} is another factor, which is worth attention in some scenarios. Due to the limitations of numerical simulation, {{formula:9a717530-c300-4074-9f0f-762f37d8787b}} is a finitely small quantity. When assessing the SIA of the attached eddies at a given wall-normal height, treating {{formula:7ea09a26-6ecf-4509-aec3-c9428f084b2a}} as their characteristic scales (therefore, neglecting the effects of the narrowband between {{formula:79cfea47-10e2-4dfb-a33e-0d84e3e38fbc}} and {{formula:1bfa51c5-9480-4f64-94cf-00a73791bf81}} ) is acceptable, because {{formula:8e6b2130-ca77-4c1a-b5dd-dbb02013a32f}} is rather small compared to the spanning of the whole logarithmic region. The linear growth of the typical length scales of {{formula:02a9d606-b7e9-46bb-9988-8f3c84127c52}} and {{formula:73d768e0-9c80-4986-90cb-391c8788712d}} shown in Fig. REF ({{formula:8717a831-550c-4d6c-9d62-842537aa7ada}} ) can verify this validity. On the other hand, when the spectral characteristics of {{formula:c1632334-0753-4b52-b118-2a89033e96d7}} are considered, {{formula:718ef380-cc85-414a-9e41-501bbc003ae4}} should be interpreted as the additive outcomes of the attached eddies with their wall-normal heights within {{formula:5e272a95-0d27-430b-b703-c43c474cac48}} and {{formula:8c41ae49-c0d2-478a-96e9-600ea77ad770}} , strictly speaking. Under this circumstance, the spectral energy distribution that corresponds to the self-similar attached eddies within this range should be observed to peak around the dominate wavelength and vary continuously and locally. The results shown in Fig. REF confirm our proposition. Details will be discussed in the following section.
| m | f4f338b2def3ed60357201fd1a196829 |
We compare our CT3D with state-of-the-art methods on both the KITTI test and val sets with 0.7 IoU threshold. For our test submission, all the released training data is used to train the model. Following {{cite:31489bcd7b68bab28c7ac373a7ceffce0678e69d}}, {{cite:1cd641a548f184e2fd4862fdab99c28e06f74b4f}}, {{cite:10a0f9872164865a2e7e0c92f13ce7961ba25b7c}}, {{cite:956c96b1a83c8566c367c4b7ce9384cb3fcb34d0}}, the average precision (AP) for test set is calculated with 40 recall positions, while the AP for val set is calculated with 11 recall positions when compared to the previous methodsThe setting of AP calculation is modified from 11 recall positions to 40 recall positions on 08.10.2019. For fair comparison with previous methods, we exploit the 11 recall setting on val set..
| r | eb4f0661f9467732e1eb250cff30818e |
where {{formula:323a87fe-da92-4875-9928-3754a034381f}} denotes the eddy viscosity. Although it is named as viscosity, {{formula:3a4b7b09-8914-4439-8731-8f69d02c7d5e}} is an artificial parameter different from the molecular viscosity in the original equations. Similar idea has been adopted to the large eddy simulation (LES), where sub-grid eddy viscosity {{formula:120ce644-3616-4c0e-b8ee-918b1ed7a347}} is introduced to model the subgrid scale turbulent flow. For hybrid RANS/LES such as detach eddy simulation (DES) and scale adaptive simulation (SAS), {{formula:6a0779ae-0900-4c27-b2ad-47212b3b6b45}} in the control system has different meaning in different region of the computational domain, depending on the resolution of the turbulence scales. Normally, {{formula:231d2de7-5e89-47b1-af81-5d0a64649c97}} is flow dependent. In the turbulence community, various modeling of the parameter {{formula:99f296ef-0010-476b-9ebe-2da5f5ab49fd}}
has been studied for several decades. With the big data and machine learning, model constants of the RANS equations are tuned by fitting {{cite:def246aeffb42fb083c80c225279771e9bf0bfff}}, {{cite:7a633c77f453bd4182ee210fa596fd59648c9fb9}}, {{cite:f46d7afcd3b3c3dd487cb6949eb0dbddabc84fa1}}, {{cite:2d980ba47931eb0b6df6d90c63f39d0b172d6afb}}. However, compared with small data sets, observed discrepancies are not explained any better with big ones {{cite:f46d7afcd3b3c3dd487cb6949eb0dbddabc84fa1}}, and modelling {{formula:2a366160-007f-4faa-87ed-7241f4bff5ea}} so as the {{formula:482558ef-f750-4719-8397-25d6cf1dc448}} in a universal sense still remains as a persistent challenging because of the case-by-case dependence. Luckily, engineering practices demonstrate that predictions of the RANS equations for complex flows are mostly quite satisfactory. It indicates that utilization of {{formula:839640ef-c9b1-466b-bf9f-22d35c35a3e6}} as an extra parameter can be a reliable way to establish the fitting between averaged/filtered experiment data and solutions of the corresponding control equations.
| m | 50864a22027b7091d74bdb76322c99f7 |
Our proposed framework (Figure REF ) employs transfer learning {{cite:14369e600d59ced9468e78b81269e5fc3f5317ac}} of a pre-trained convolutional neural network (CNN) for fast adaptation to the Mel-spectrograms extracted from speech inputs. Transfer learning is an analysis technique in machine learning that used to solve a problem by reusing knowledge gained from solving another but similar problem. Extracted spectrograms are fed into the deep convolutional neural network in which the speech signals are classified as bona fide or spoofed. In the following subsections, we describe the three major components of our system: Transfer Learning {{cite:14369e600d59ced9468e78b81269e5fc3f5317ac}}, Mel-spectrograms {{cite:449c232c74510247f172b2812a7510559f076904}} and ResNet {{cite:9b053c1a9bc28f075fcbb7dd1be687b4c848dbaf}}, followed by a functional overview of our proposed framework.
| m | f710da587f34e08afe7ecad84bd3e0c3 |
We refer to {{cite:3fcc87b7a3ad33f633f7a4f8a4f6408bd79047fc}} for the following definition and results. Given a Banach space {{formula:7f2f0827-452f-4a07-8140-708e974a3d12}} , set
{{formula:1fb5fc0b-a472-479a-88e9-2725dd7e4bbc}}
| r | ed665f20e6ddb45b89f1166a9029d9db |
We now consider the numerical performance of our proposed procedure. In sec:sims we provide simulation results for several examples, including varying levels of heteroskedasticity. We then apply our algorithm to three different flight data sets – the first is the data described in {{cite:5dd30a60ccf31b28f6f8b69df2314c79487765f6}}, which measures global flights, the second is USA flight data, available from the Bureau of Transportation Statisticshttps://www.transtats.bts.gov/, and the third is a global trade dataset, available from {{cite:3b0ce6a09dfc8ca82039bb17b5b77d032c61ba81}}.
| r | 541a44b0830e10260b10f54d070e0cda |
In recent years much attention has been given to the field of high dimensional expanders which are high dimensioanl analogues of expander graphs.
One extremely useful property of high dimensional expanders is that higher dimensional random walks (which are higher dimensional analogues of random walks on graphs) converge rapidly (For example, this property was used in {{cite:ffcf2f1cf54ba171237e403b713315867601894e}}, {{cite:d228511a5e24a6a3d4641d91133cb2ea3af86472}}, {{cite:bd184baa445123f82f69050d1d942a346b775ef0}}, {{cite:32acaa05446ec5be594b4fbcd98d4307976cd525}} and more).
Consequently here has been some work studying the convergence of higher dimensional random walks {{cite:ffcf2f1cf54ba171237e403b713315867601894e}}, {{cite:4439ca593d3db1eaa07d59f9e87c9c9420e1842e}}, {{cite:17808d8a1e67f8147827f3e566b74bb18eb2492e}}, {{cite:ec2b87499ec35885def58a4d2c670ed8b575444e}}.
In this paper we aim to improve upon these convergence results by relating the structure of the function to its expansion.
Specifically we present the following improvements:
| i | d635be68a7b3452c0705747e30058be9 |
The importance of these tools has been seen in many places, such as those used for signaling games{{cite:a44a0b77c0e12b8a65a4f912bb0d8ff2dc90a604}}, population dynamics and biomolecular networks, mesh network topologies{{cite:ca09e199c02f5e9e257f2a2df1d5358e6cda1fb9}}, 3-D neural imaging reconstruction{{cite:0f808bc2e43e57dccf0f6a0c04ccf17c1e37ca18}}, etc. These techniques work directly in complement to the notions from deep neural networks by providing an explainable AI which can then be used as a hyperparameter in designing the DNNs by affecting their layer hierarchies, activation functions, dropout scenarios and memory length estimates.
| i | 691f85b2ec2fa42ff2184f31b527b70f |
BH: the vanilla BH procedure {{cite:7388ca0cb45180661e8ba8ac7da3394ed11bc6b6}}
oracle: The oracle procedure {{formula:c01b9228-29e8-4833-9498-db44eb3bfaea}}
SABHA: Structure adaptive BH procedure with {{formula:e98c311e-8313-4afb-92ee-e27f398cab71}} , {{formula:870eae45-1b52-4051-9d29-fceef9ec02e4}} and stepwise constant weights {{cite:38c99acee96cd7a512faaa4ec466ce19310c6fa7}}
BL: Boca and Leek procedure {{cite:1de8bc45a5d57e9d3cdde579d1ddac38790fc421}}.
| r | bcc9c389324b9930f5ae0b42a0dd8685 |
We make comparison with the latest document representation methods, which achieve strong performances on tasks like web search and question answering. 1) DPR {{cite:6a840cd9e1f02fd656ee11562af5b53ef6cbbd6d}}, where in-batch negative samples are used for the training of siamere BERT based document encoders. It achieves competitive dense retrieval performance on open domain QA tasks. 2) DE-BERT {{cite:82b8958222280542b82e1621d888d21764ab4937}}, which adapts DPR by introducing extra hard negative samples. 3) ANCE {{cite:7071beacdc3f531d66fa0bb210aced2059cc057e}}, which iteratively mines hard negatives globally from the entire corpus. It is one of the strongest dense retrieval baselines on MS MARCO benchmark. 4) STAR {{cite:9f1ae30ad271d8cf1f8f5dab414f77ac2c40d14e}}, which improves ANCE by introducing in-batch negatives for stabilized and more accurate document representation. We use the following ANN indexes in the experiments. To evaluate the massive-scale EBR performance, the SOTA scalable ANN algorithm DiskANN {{cite:9cb520d69b151e3ef6d7910477f47d5f89de7945}} is leveraged. To evaluate the generic EBR performance, we adopt HNSW {{cite:365e166afea48a5edf410bc7ccd9eba41c7f3586}}, which is one of the most effective ANN algorithms in practice.
| m | 3a80390af9daa4e205784b6ae6f9677f |
The recent discovery of coherent elastic neutrino-nucleus scattering{{cite:6474a91fb37257029a7903b89250f26d33009c94}} (CE{{formula:77b7e549-a1df-4d98-8647-652e024c25d2}} NS) offers a new intriguing detection channel for SNe neutrinos. Driven by a Z-boson exchange, CE{{formula:01c4a903-53c3-4121-ac47-a8bae611dfb8}} NS is a neutral current process and, as such, offers equal sensitivity to all neutrino flavors. It is a low energy scattering where an impinging neutrino with energy of {{formula:974a553b-d05e-4787-836e-bada735bf53d}} (10MeV) transfers {{formula:67f0ba2b-7a66-4097-900d-ed93f42a148f}} (1keV) momentum to the recoiling nucleus{{cite:dd0fc26e6a907fd2ab76e158da095fc8384f9fc1}}. The appeal of this process as detection channel comes from the fact that at such low energy the momentum transfer is of the same order of the de Broglie wavelength of the target nucleus and, therefore, the cross-section gets coherently enhanced. This coherence enhancement results in a cross-section that is orders of magnitude larger than the ones of Inverse Beta Decay (IBD) and Electron Scattering (ES), allowing relatively small detectors to assess SNe emission properties with the same precision as the one of gigantic neutrino telescopes, provided that they achieve a detection threshold capable of assessing these low energy recoils{{cite:e68b60184be9653b49c77ba4aa3b6ec442ba2290}}.
| i | c5372c6d428adc61e9fe6918b3897229 |
Recently diffusion models have outperformed other generative models in the task of image generation {{cite:4cbf714c245eed47325752a09db8e78d06448674}}, {{cite:29f38a99110dd10eb5f3805f59ec2d3b487d24be}}. This is due to the ability of diffusion models to perform exact sampling from very complex distributions {{cite:06710b7512e18bfeb1540d9b26818e85842a5138}}. A unique quality of the diffusion models compared to other generative processes is that the model performs generation through a tractable Markovian process, which happens over many time steps. The output at each timestep is easily accessible. Therefore, the model is more flexible than other generative models, and this form of generation allows manipulation of images by adjusting latents {{cite:e477f7026a446653f78872f009a9dcd26652be1b}}, {{cite:4cbf714c245eed47325752a09db8e78d06448674}}, {{cite:858b4d0069bfa69cba3c6b2da6bd255d1287e91d}}. Various techniques have used this interesting property of diffusion models for low-level vision tasks such as image editing {{cite:e477f7026a446653f78872f009a9dcd26652be1b}}, {{cite:91791ebf6b95714745c77cec4e49121b32352614}}, image inpainting {{cite:c6170315c3cd9ecbdf18ffb790b317f704f11c1e}}, image super-resolution {{cite:e2ea7fb54e26bf90968e6868a88bacd6737326a4}}, and image restoration problems {{cite:5dc98e028f375f70bc23f865c34886e29dd647b6}}.
| i | 7491cdbcccab9a87091017c09260440e |
In conclusion, selected tasks are on a completely novel dataset and are sensitive with respect to lexical and syntactic information. Yet, pre-trained Transformers seem not to be able to solve these tasks, although these Transformers are able to deal with
lexical and syntactic information {{cite:890cbeec5ded470e650112f244df539eeac157d6}}, {{cite:dd5f92320ea70d37fb611e7d914e8d956b8265ea}}, {{cite:51e9f66f56eead6a8f09a9466d4ac4b172db1215}}. This contradiction seems to be a possible evidence of the fact that large pre-training may force Transformers to overfit on seen data. This overfitting possibly happens at the sentence level so they cannot capture stylistic and syntactic differences.
| r | cc36d2d9ff713979e173fc2e3401fd07 |
HeadPosr is compared to state-of-art-methods as shown in Table REF and REF . These compared networks are as follows. 3DDFA {{cite:8a85809f02a9ba8450747fb2153f61e37c1fec8c}} utilizes CNNs to correspond the 3D model into an image. It is shown to work quite efficiently with occlusion scenes. KEPLER {{cite:438ddc9d0e3b7041f1fe4248be41fc4c76ffb9f9}} uses modified GoogleNet network to predict landmarks and pose simultaneously. Dlib {{cite:1e269db58bbd3289375d3dad0bca80ebd3ae8bdc}} is a well known library which is used for landmark prediction, HPE, face detection, etc. FAN {{cite:8f1d1eec3a44bcaee32348e61776e9fca9a18a85}} uses multi-scale features by merging features from multiple layers at multiple stages. Hopenet {{cite:98f59fe879242abc43f854d89e2abf597395e116}} uses ResNet, similar to HeadPosr, but is trained on mean squared error and cross entropy loss. Shao {{cite:fd18215f0d0dc577177db5c61531e411c4cd6b10}} uses CNN based network by adjusting the margins of detected face bounding box. SSR-Net-MD {{cite:96ecec63ccaa26242535eb3f34c6372b6aa324b3}}, FSA-Caps-Fusion {{cite:b34bf705c7968d1b52a64876bc8af2455ce8d3c6}}, and TriNet {{cite:ea270a976715350d166587b299e657fb81b9997b}} use the same basic technique of network having multiple stages using soft stage-wise regression. VGG16 {{cite:9c4cfaec6dc79cfa46f83a308e832de04d4b792d}} is a network having combination of CNN and RNN using Bayesian filters analysis. DeepHeadPose {{cite:244b3231162396c5b837ae07317bace384ab85de}} uses low resolution depth images applying regression and classification to predict the pose. Martin {{cite:a32b411d78683b1374e603d06c43edae3d8e0fde}} uses depth images for predicting head pose and uses registration between depth images and 3D model. WHENet {{cite:d4adcf437645cd739ed5ea948163fe96fb7e58b6}} uses efficientNet as backbone with multi-loss approaches and with changes to loss functions.
| r | f97d05573e8bae927aaaaa18f4b26a94 |
for all {{formula:474fb044-0b98-44e6-b5e7-7f24fe93f81a}} and {{formula:e44d169e-4194-4f30-a2e5-2dee5ad9d582}} , where the notation {{formula:0422fc53-5139-4534-a109-8f61e00511b2}} is used to
denote the ball of radius {{formula:48a25c64-1b19-4728-98f2-bb2abe261adc}} and centered at the point {{formula:f02ba8e8-250c-41ff-b926-cc2b9fec49a7}} . If this
condition is satisfied then {{formula:a24ea5df-116d-4d62-9b2b-bc7c03122fbb}} is said to be a
space of homogeneous type, in the sense of Coifman
and Weiss {{cite:2281e0459ddb3f6840d3be9b11a3df0c65285423}}, whilst any space that does
not satisfy this condition is called non-homogeneous.
| i | 72632cffb5f0e80cf253fe00ef710796 |
The ratio of the theoretical predictions to data based on jetphox at NLO with different PDF sets, including MMHT14 {{cite:06e93ebab647abfe41e13ff8e1fe3b5f1f621597}}, CT14 {{cite:8ce537cc149864cc8e82b08d941471c70e61aac2}}, and HERAPDF2.0 {{cite:58740988448079b827df0f3f4b49557688689ee9}} together with NNPDF3.0, are shown in Fig. REF . The differences between jetphox predictions using different PDF sets are small, within the theoretical uncertainties estimated with NNPDF3.0.
| r | 770a9616846cd104661e5a96a22878e0 |
The canonical form proposed in ref. {{cite:4bb5bdce6d9abc1c8326d2f41f9e16ac03f30f7f}} not only implied an epsilon-factorized form for the differential equations of eq. (REF ), but further imply that the distinct differential equations for each kinematic variable are joined in one differential of dlog-form {{formula:6407e5b4-6400-40bf-8ca2-8bc968cee79a}} where {{formula:bbbeb280-4b11-4b3e-bf9a-e05d39a28203}} is a matrix containing only logarithms of rational functions of the kinematic variables. An obvious question is if the differential equations found here can likewise be unified into one differential form {{formula:854798e4-8e11-42b4-a039-117c3de64723}} , but where {{formula:082084de-70f8-4cdd-9f61-b8ed61c3bb91}} obviously no longer will contain solely logarithms. In the polylogarithmic case, the arguments of those logarithms are the symbol letters {{cite:e9778230fe6af5a3cbe9221759449727edc0960c}}, {{cite:d137a6b2d71212168f9e8fe501e5f25c25cead7a}} of the problem, so an obvious open question is if the entries of {{formula:1ee77ade-2399-4f05-b0d4-cb5fa5f372d0}} in the elliptic case, if it even exists, will be related to the entries of the elliptic generalization of the coaction {{cite:264615b419364be9411a2a3035dea6e7c69fe46e}} in a similar straight forward fashion. For the polylogarithmic case, the fact that the algorithm discussed in this paper works in the first place, may be seen as following from the existence of an iterated dlog representation for the whole integral {{cite:993ae7484f6d67e18ae8c072f02d5caec7fcf1fc}}, {{cite:fea704c87627f3c60e931b32fc578e84f8674021}}, {{cite:51857a4f423af9a3855f57a0706881704dfb58b7}}, {{cite:f6f4597af9c451ba6c69e479b1ce681a2143091f}}, and the question of how such a representation may generalize to the elliptic case is presumably also linked to the above.
| d | ad270563944263115e33c38f6082eda4 |
In classical PINN, a second-order optimizer, L-BFGS-B, is used after the Adam optimizer to speed up the PINN convergence, thus requiring considerably fewer iterations {{cite:d5e5e98db0975bc939f89af1e32137977aafe001}}, {{cite:f3aec1d8ed96af6036d3e9076d60c904ad025239}}. In classical PINN, L-BFGS-B is not used from the start of the training, as it would quickly converge to a local minimum of the training landscape without escaping it. As in the classical case, we deploy an L-BFGS-B optimizer after 80 optimizer iterations. While L-BFGS-B can reduce the cost function evaluation in both cases, we note that the final error is approximately the same for plain SGD optimizers and SGD combined with L-BFGS-B. As additional tests, we also implemented a multi-step SGD and L-BFGS-B, e.g., a succession of SGD and L-BFGS-B, without achieving a final performance improvement. In classical fully-connected PINNs, Adam and L-BFGS-B optimizers are widely employed and successful for PINNs {{cite:d5e5e98db0975bc939f89af1e32137977aafe001}}, {{cite:f3aec1d8ed96af6036d3e9076d60c904ad025239}}, while in quantum PINN SGD provides better performance than Adam and L-BFGS-B. In quantum PINN, the optimization landscape is more diverse, and its optimizer exploration is more challenging.
| r | 641f5787ec9cfa92bc83ae47c4ec0407 |
Approaches to “information augmentation" can include customized data augmentation, as well as transfer learning from related data domains. For this category, we choose MixUp {{cite:6fcec70c39dc0b54ac968f055faeed2f99a6f576}} and Balanced-MixUp {{cite:770982933d810f18deaf356ace54a430532fc1ea}}. MixUp is an augmentation technique that linearly mixes pairs of input images and labels according to a Beta distribution, producing a strong regularizing effect. Balanced-MixUp, as explained earlier, is an extension of MixUp that linearly mixes pairs of images and labels, where one image is drawn from a batch of instance-balanced (naturally distributed) data and the other from class-balanced (resampled) data.
| m | 2f18bd0a1799fd4eecb8f102a6db42bf |
{{table:09906beb-6535-4f24-b8db-357803c948ed}}{{table:1cf5e844-d41d-486e-8249-fb5bc88f43c6}}{{table:48356abe-4f20-40b2-a205-6c0cb86489ed}}{{table:8b8fed3d-9757-4627-b608-63b01249edd7}}{{figure:3b36c442-a9c2-4da2-a939-5fbade123e90}}{{figure:fa58d29c-c050-40b0-a21f-8ac9206606e4}}
Additional Experimental Materials
This section contains additional information that supplements
technical details presented in the main text.
Model architecture & training configuration.
Tables REF , REF , REF ,
REF , REF , and REF
list the architectures of the different models
used in our experiments. For all six tasks, we use
convolutional network networks. We vary the number of layers,
channels, and filter sizes in the models to accommodate different
tasks. Table REF describes the details of the
training configurations used for each task.
Description of §'s experiments on existing
watermark designs.
We provide additional details on our experiments in
§, which study the performance of two existing watermark designs ({{cite:68eed6dfb124fac0008a721b92ff7bbe21657be9}} and
{{cite:9125086e4671869d75d85dc78ceae58dc6cf7a66}}) under piracy attacks. We describe the
watermark triggers and model training
configurations used in our experiments.
Watermark Triggers.
For {{cite:68eed6dfb124fac0008a721b92ff7bbe21657be9}}, the original trigger set we
use is the same as the trigger set used in {{cite:68eed6dfb124fac0008a721b92ff7bbe21657be9}}. To
collect the pirate trigger set, we randomly choose 100 images of abstract
art from Google Images, resize them to fit our model, and assign
labels for each of them. Note that both the
original and pirate trigger sets contain exactly 100
images. For {{cite:9125086e4671869d75d85dc78ceae58dc6cf7a66}}, we use a trigger very similar
to one used in their paper – the word "TEXT" written in black pixels
at the bottom of an image. The pirate trigger is the word “HELLO”
written in white pixels at the top. Figure REF shows
triggers used
for {{cite:9125086e4671869d75d85dc78ceae58dc6cf7a66}}, and one sample
from both original and pirate trigger sets {{cite:68eed6dfb124fac0008a721b92ff7bbe21657be9}}.
For completeness, we tried several triggers for the piracy attack
on {{cite:9125086e4671869d75d85dc78ceae58dc6cf7a66}} and found that all are successful (>
95% pirate trigger accuracy). These are shown in Figure REF .
Training Configurations.
To train the original watermarked models for both methods, we use the
training configurations shown in Table REF and the
watermark injection ratios in Table REF .
For all tasks, we assume the attacker only has 5k
training data for MNIST, YTFaces, GTSRB, and CIFAR-10. The same
configuration is used for the piracy experiments on
our own watermarking system.
Additional results for §REF .
Table REF provides the detailed numerical results on Figure REF (a)-(b), in terms of normal classification accuracy (NC), owner's
watermark classification accuracy and pirate watermark
classification accuracy. For the latter two, we also provide the
individual accuracy of null and true embeddings.
Experimental setup for transfer learning in §.
The dataset for the student task is LISA
(3,987 training images and 340 testing images of 17 US traffic signs). We resize all the
images to (48, 48, 3) to allow transfer learning. During transfer learning, we fine tune
the student model for 200 epochs using student training data,
using SGD optimizer with 0.01 learning rate and 0 decay.
Additional details on countermeasures in
§.
We list the detailed configurations
and discussion for countermeasures.
Model Extraction Attack.
To launch an attack on GTSRB,
we create a substitute model with the same model architecture in Table REF .
To train the substitute model from scratch we use the same training
configurations for GTSRB in Table REF but do not
add watermarks to any training data.
We include the In-distribution data requirements for {{cite:cd515ad5f6c1858d2bfa37996485bf0e91bd0054}} in
Table REF . Even with
12.75x input data from ImageNet, the normal classification
accuracy for substitute models is still lower than that of the original model (94.1% vs. 96.1%).
{{table:fd122cc3-8525-4abc-a9ad-93d12fdd73ac}} Model Distillation Attack {{cite:320192ab306101093daa73d07102e9d37517c959}}.
Distillation is similar to the model extraction attack, but it introduces
temperatures when using the target model to label the data. Prior work
suggests that model distillation can train accurate models using smaller
datasets (compared to datasets used to train models from scratch).
However, we believe this conclusion was due in large part to
unnecessarily large training datasets used to train models from scratch.
We performed detailed experiments, (on GTSRB), where we varied parameters
(different temperatures) to find the optimal (smallest) training subset
that would produce (via distillation) a model with accuracy within 3% of
the ideal model. The result was a small training sample (12.8% of the
original) that produced accuracy of 95.4%. Our tests show that the same
exact dataset, when used to train GTSRB models from scratch, produces a
model with 95.0% accuracy. We also validated this on MNIST and
CIFAR-10, where the distilled dataset, when used to train a model from
scratch, produced a model with accuracy matching that of the distilled
model.
| d | b9ffdb14b7230380583503745d28c883 |
Proposition 1.2 (Propositions 1-2, {{cite:42886aff56b0aa6aa526461937fd9ab65c8836b3}})
Let {{formula:b18d3a65-d57e-489f-9707-397d2553e2f7}} be a cycle set. Then the pair {{formula:74ea8062-13a3-422f-9893-f1b9c1b539cc}} , where {{formula:8cf06615-0076-427b-a2f3-615cce4ae963}} , for all {{formula:bb947874-9b21-4dc1-972b-ffe2b9b487e4}} , is a solution of the Yang-Baxter equation which we call the associated solution to {{formula:859d9e18-599b-40b3-8c42-ab70fc786795}} . Moreover, this correspondence is one-to-one.
| r | 8eac4964a110efb17976282eecebe85f |
where {{formula:75935b66-9476-430c-acc2-236520dc0abe}} is a normalization constant, and {{formula:dff60e05-5e8c-4bd7-a626-944f14ed555d}} is the
weight function, and satisfies the following equation {{cite:20d67d6eaed0d36bda7b9bed723ac5de4927e02c}}
{{formula:485d3c02-8c4a-457a-814b-4e066eef3037}}
| m | 80d99c75f76ca8796bde88ad498b4c02 |
Replicating real physical spaces in their full fidelity in a digital form is a longstanding goal across multiple areas in science and engineering.
Digitizing real environments has many future use cases, such as virtual telepresence.
The combination of replicas of real environments with powerful
simulators such as AI Habitat {{cite:f32e366ee0ef64f4e8081c9b26556e85e78df88c}} enables scalable machine learning
that may yield models that can be directly deployed in the real world to perform tasks like embodied navigation {{cite:7b4ebac6221c80ee54d3f3bed22f8e2c0b5d6c10}}, instruction following {{cite:950d8b03fadba6135ed5a10939f00b3042b5c118}}, and question answering {{cite:24e579f0e0f901bbc2e143a3ef384d04518d4cce}}.
Via parallelization, reality simulators enable faster-than-realtime and more
scalable training of AI agents in comparison with training real robots in the
wild.
Additionally, simulation from Replica can be leveraged in egocentric computer
vision, semantic segmentation in 2D and 3D and geometry inference.
More realistic replicas lead to more realistic virtual
telepresence, more accurate computation over them, and a smaller
domain gap between simulation and reality.
{{figure:ccfac0e0-309f-4c7e-900f-d2ccec68476a}} | i | 55bea2d55ede8570975b58cf1da5a161 |
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