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The temporal smoothness term introduced by Sultani et al. minimizes the difference in anomaly scores between temporally adjacent segments {{cite:ddc9447aa181d78aa6f44d218ef34b96d5b8652f}}. However, from the above results, we infer that this term has the regularization effect of ensuring that all segments in a video have similar anomaly scores, rather than constraining the temporal order between segments.
Zaheer et al. reported a decrease in accuracy without this term {{cite:eb8d013967d39f8fc64c12c7b790c5b279195660}}, {{cite:61e6d11becdb062d511a849a7929a553aa72dad0}}, which may indicate the importance of the regularization effect that the temporal smoothness term brings.
Although the MTN and top-{{formula:b331abaa-df87-4b54-b83e-110da3478cc2}} strategies used in Tian et al.'s method {{cite:b8f4dbed27eac75ed5b93992fd9cc71dcc89a443}} are more complex, and we would expect them to analyze more complex temporal relationships than just temporal order, the above results indicate that temporal order is not important.
Based on the above observations, we hypothesized that the high anomaly detection accuracy achieved by these methods is due to the fact that they have a mechanism that allows all segments from the video to be trained together and extracts salient features that are important for determining normal/abnormal.
| m | a6bfa12da3ac6392c46694b5103dba48 |
A natural next step is to study the regimes in which catastrophic forgetting is most problematic. This includes the setting where tasks do not have a nearly orthogonal relationship but also when data does not necessarily live on a low-dimensional manifold. We are also interested in understanding how the ideas of this paper generalize to other continual learning benchmarks and for more general neural network architectures. Prior work found experimental evidence that catastrophic forgetting is most severe not when tasks are very dissimilar but when they only have an intermediate level of similarity {{cite:efd5267d83e21838e8e33f4caf6f32e540a7d233}}. Using orthogonality as a proxy for task similarity, this agrees with our work that shows that nearly orthogonal tasks are less prone to catastrophic forgetting. An interesting future work would be to formalize this notion of task similarity for our model. Moving forward, one goal of theory in continual learning is to be able to analytically compare algorithms. Our work provides a foundation of understanding this behavior in a simple linear regression setting. In order to push this work forward, either non-linear models need to be studied or tasks that are related by something more complex than permutations.
| d | 29f8a8f1ec1cc82618ff18f63c865cb9 |
Sparse vs. Transformer GNNs. When we compare the performance of sparse GNNs (GatedGCN, PNA) against Transformer GNNs (SAN, GraphiT) augmented with LSPE in Table REF , the performance of the sparse GNNs is surprisingly better than the latter, despite Transformer GNNs being theoretically well-posed to counter the limitations of long-range interactions of the former. Notably, the evaluation of our proposed architecture, in this work, is on molecular graphs on which the information among local structures seems to be the most critical, diminishes the need of full attention. This also aligns with the insight put forward in {{cite:9c7e07b7f47985d6e69e885c5ed1eae46a1742e6}} where the SAN, a Transformer model, benefited less from full attention on molecules. Beyond molecular graphs, there may be other domains where Transformer GNNs could give better performance, but still these would not scale in view of the quadratic computational complexity. Indeed, it is important to notice the much lesser training times of sparse GNNs compared to Transformer GNNs in Table REF .
| r | 620c6d17d0afd66e0afb69f628ff0eea |
at time {{formula:8ec68f80-4a01-429f-bf4a-f456f6f2eb47}}
(e.g., in the general setting without decision-dependence this follows from {{cite:af37f22c443565af257874526c64ee7c11dda75a}}).
The reason for projecting onto the set {{formula:fcc5b081-5f10-440a-b279-66f750aa23a1}} is to ensure that in the next iteration, the decision is in the feasible set.
| m | e5a679b6401f28416d791a0da72eac45 |
Our approach towards Theorem REF relies on an argument introduced in {{cite:59116ee8a4407ad107e21841564510e1d2aa0c38}}. By double-counting the number of solutions to a tautological equation, we derive an inequality involving second and fourth moments of certain representation functions. In {{cite:59116ee8a4407ad107e21841564510e1d2aa0c38}}, these energies are bounded individually, using the point-plane incidences bound of Rudnev {{cite:6cf8331592b7a1f731d1589202d6e421dfc85b47}} and the point-line incidences bound of Stevens and de Zeeuw {{cite:4bbdde6a1d68b027a5067443cb84d448858135ff}} respectively, yielding the final estimate. Here, we proceed differently. Firstly, relying on the basic observation that the arguments of {{cite:59116ee8a4407ad107e21841564510e1d2aa0c38}} do not distinguish between addition and multiplication, we obtain an inequality involving both multiplicative and additive energies. Utilising a recent regularisation technique of Rudnev, as recorded by Xue {{cite:4f168122a4ddcba69ad67fb402bf9830f98a2983}}, we can efficiently bound these mixed energies. This facilitates a more optimal application of the incidence results to the double-counting argument of {{cite:59116ee8a4407ad107e21841564510e1d2aa0c38}}.
| i | 8eb6cc5bd2a0e20f06f13408c882ed5f |
Our earlier studies found that the anisotropy of polarized synchrotron intensity could be used to estimate the direction of projected magnetic field roughly. This is still a complementary method to synchrotron gradient techniques that can trace projected magnetic field directions more accurately. The advantage of structure functions of synchrotron and polarization intensities is that their statistical methods have been described in detail in LP12 and LP16, which establishes a theoretical basis of synchrotron statistical analysis and provides possibilities to distinguish contribution of three basic MHD modes, i.e. Alfvén, slow and fast modes. The spatially separated configurations were first proposed in Zhang, Lazarian & Xiang ({{cite:6d2c193ccdfb4707f5b0d47fb1af2e7a12dae545}}) to simulate complex ISM for recovering the spectral properties of MHD turbulence at different wavelengths. Similarly, the anisotropy of polarized synchrotron intensity at different wavelengths was studied in Lee, Cho & Lazarian ({{cite:f4c397e1dcb589596dbb70d49a5d174ddd017407}}) using structure function and quadrupole moment. The purpose of the current work is furthering new gradient techniques for more realistic astrophysical scenario. The accumulation of large amounts of observational data facilitates the application of new magnetic field measurement techniques. For instance, the gradient techniques proposed in our series studies have been applied to realistic observational data from Plank (Yuen & Lazarian {{cite:0683201d6243d9251ee6aad7b6a61ccb4f92cbc7}}) and Canadian Galactic Plane Survey (Zhang, Liu & Lazarian {{cite:f30f9c0e5e5be4fbd4da5ec5fda8115efdb73baa}}). Recently, observations from Urumqi 6 cm polarization survey has been used to identify different plasma modes in the Galactic turbulence (Zhang et al {{cite:a64650f017aad2a8c8b430c66f4578484dd9ee7b}}).
| d | d656848e8d3c9f5efec8d246c9c0065f |
When (REF ) varies regularly with an index different from {{formula:c29a8898-de9e-4889-9e1b-bf8754bff2b2}} , the questions we address here have already been answered, see, e.g. {{cite:9f7ffe3b2c293039361bb06ca75099dc790d3b92}}, {{cite:d53122e3ae43b35a5fb819c7d7b41865f329e8c0}}, {{cite:fa79aeaa3477480d133a2dfbca6a5db0b8726ac8}}. However, no-one we asked seemed aware of those results we needed for the case of index {{formula:bc2724d2-f153-441d-9bc9-6c870acfa1c2}} . The {{formula:8487e176-5de8-46ee-9156-3b230c90c606}} 's we consider belong to the family of subexponential random variables. See ({{cite:11ad3ab3abfd910e1f99e5f62a1cf7871c22d897}}, section 3.2) for necessary and sufficient conditions for a real-valued random variable to be subexponential.
| r | 41e2fc39ad336d6c86f709b59ee70f35 |
In a core collapse supernova, neutrinos are trapped in the neutrino
sphere and slowly diffuse out. These neutrinos have self-interactions
that lead what is known as collective neutrino
oscillations{{cite:ee4c67c08f2b19095a7a6216fec5cae034dcce5a}}.
These phenomena can also occur in the hot plasma of the Early
Universe{{cite:412492f544af8edf0f83950228910ef88822d9ff}} before the neutrinos decouple. In the presence of the
type of neutrino-scalar interaction we have considered, the collective
oscillations could be modified.
| d | e65a2c563d401fdc39109c29d827a2d6 |
Lastly, the data illustrations have utilized a pre-specified set of regions for functional connectivity analysis {{cite:b79e32b6397c5ee059e508c0c350c62218044546}}. This approach relies on a predefined brain parcellation, commonly in form of an atlas, to determine regions of interest. As a result, different subjects are also assumed to have the same functional network nodes. Recently, data-driven methods for functional connectivity analysis have been proposed {{cite:60619118f89dbd777ef0e551534cc3d327a4bc10}}, {{cite:1820cca3dc5effdbdb271a92d212404255a76575}}, thus allowing nodes in functional networks to be subject-specific {{cite:e220d04fe871c844b442b376c77fe6a27c6ef968}}, {{cite:f679e4ab23cd329c2871e094b71302018f31e4c1}}. It will be interesting to investigate if our proposed methods for quantifying functional connectivity can be combined with subject-specific region discovery in order to simultaneously study variability in the spatial distribution of functional connectivity nodes as well as connections between them.
| d | 7fbc8e338e625d81b3bc26e70af57b20 |
It is apparent that the outcomes of Data Analytics [DA] and Machine Learning [ML] are often perpetuating the human bias present in the datasets and therefore enacting illegal discrimination. Constraining the DA/ML outcomes to be fair is problematic as there is no universally accepted definition of fairness while at the same time many of the notions of fairness are very hard to implement, disrupting DA pipelines and putting a significant extra load on DA resources. One apparent solution is to remove bias from the data before proceeding with DA as usual; however, these methods generally, cannot account for non-linear, non-binary and/or multivariate relationships between race (or other biasing factor) and the rest of the data {{cite:3281c8bb1dc7f9832243fc977868c0006136970e}}. This paper introduced Fair Adversarial Networks [FANs] as a method that compensates for these shortcomings and provides a very significant improvement in both fairness and ease of use.
| d | 4fad7f1eb98825223f790e4aa7cc46b3 |
For QA, the computational advantage of incoherent tunneling over certain classical methods (typically SA{{cite:385f86d1f0185223ff6d1ed349f84c100f4fbc3f}} and the Hamze–de Freitas–Selby algorithm{{cite:358c84222e2fc58e083e0fc9fc150208fadf03cf}}, {{cite:991d41ad6f7432a929c0f665d58ae9a682193e65}}) for certain classes of problems has been shown {{cite:7a88fae88139a9b951867926a7ed0c6d3ae09cdd}}, {{cite:0f36512cb557287f255c6620e94cea63f288b53b}}, {{cite:d5f8b74ea5a4836339e809d1947de0c4a90524d8}}, {{cite:b7e3f2588152c2441ff5d6250917f7f4cd2c8232}}, {{cite:4b8bc797919224c64d14bb0e993dee1081defa81}}, {{cite:3ed20bb983d5466a1848888492c6c6db281dc8d2}}. However, for any real-world problem of interest, no evidence of an unqualified quantum speedup (as defined in Ref. {{cite:368c8d76df938a708948e6ddcb18329f13171825}}) has been found. Perhaps the most compelling results with the D-Wave QA so far are for a specially crafted problem class, deceptive cluster loops, for which the QA was found to outperform in terms of time-to-solution for all classical heuristics that were tested, including parallel tempering {{cite:9f12430c980e06b46ab428d187719670e854e0de}}. The speedup was of an approximately constant-factor nature, with no strong evidence of a scaling advantage {{cite:3ed20bb983d5466a1848888492c6c6db281dc8d2}}. Another disadvantage of quantum annealing is that they cannot sample uniformly all low-lying states in contrast to other heuristic algorithms such as SA-based algorithms {{cite:95992bc4efa60981385501146a2731329d73208d}}, {{cite:6d5889c90b4a62036d8484ef60de663785a7e46a}}. In SA, after many repetitions and starting from different initial states one can record all the configurations that minimize the problem Hamiltonian. For an optimization machine, such an ability to sample fairly is beneficial as having different solutions for a problem is often useful. Furthermore, it is not yet well-understood what the role of entanglement in QA is and whether it contributes to a quantum speedup {{cite:b4ee105ffdb07868967e98cb96659df542d93265}}. While various aspects of quantumness, including entanglement, might or might not aid the performance of CIMs or QAs, this uncertainty has inspired the proposal of interesting quantum-inspired classical algorithms related to CIMs and QAs, which is a fruitful development in its own right.
| d | ffc11ee5bc0465f45022bcc1f001ff69 |
For readability purposes, we refer to convolutional layers with x feature maps as CONVx layers, and
max pooling layers as POOL. The convolutional model has the following architecture:
a CONV128 layer, a {{formula:0da527a2-d84a-4d97-a362-7bc69514c620}} POOL layer (max pooling only on the time dimension), again a CONV128 layer and a {{formula:13948fae-9b8f-4d18-a816-3bfdbf899d94}} POOL layer,
a CONV256 layer and a fully connected layer providing the prediction score for each class.
Activation functions are ReLU{{cite:907032d3ebef4b468fc823a18a3369978c4b0842}}, all convolutional kernels are
{{formula:96591796-f6cf-4c73-9990-a7ec2dfeeae7}} . The fully connected layer is linear (no activation function).
Dropout is set to 0.5.
The network is further normalized using batch normalization {{cite:98eac42ba63578a1232aed549dc035a60bde92dd}}.
The model has been trained for about 400 epochs using a learning rate of 0.001
and an Adam optimizer with decay rates of 0.9 (beta1) and 0.999 (beta2).
The LSTM used in Table REF is the standard version of {{cite:c44e35ac39be9dc72634bb91c3ed54886648e1b2}},
trained for 300 epochs.
For this model all 3 {{formula:b615c72b-49a8-4b0f-933b-4b9ee1e87c13}} coordinate pairs are concatenated to produce
a 6 dimensional feature vector. There are 128 hidden units for a cell, and a fully connected
layer is used to linearly activate the output.
For the 2D Spatio-Temporal LSTM we used the variation of {{cite:fe9996f33bdcdf4ab4b278b834ea0585cc9624fc}}, which is itself a variant of the Multi-dimensional LSTM{{cite:9108aa2e1e5ff438e616e02ef129c1d39b46929e}}. {{cite:fe9996f33bdcdf4ab4b278b834ea0585cc9624fc}} uses a “trust-gate”, which filters the input in order to compensate for noise.
We apply recurrent dropout as defined in {{cite:65b9541b8859e9b25dfd771881bda3a826d23ab7}}. It is trained for 150 epochs.
In our model, each cell possesses 64 hidden units and the trust parameter is set to 0.5.
An activation layer takes all cell outputs (from the whole grid) to compute predictions.
| r | 080d473a53efd15e58e4580a4a9e0c37 |
where {{formula:6c0d62e7-88d1-48a2-8443-d086a4a666af}} is an undetermined function, and {{formula:05572547-7378-4946-acf0-4260d4607931}} and {{formula:4ad7f457-6678-411c-ac40-6dda91057b8e}} are the critical exponents. The constant {{formula:eec21394-b7de-44bb-985c-f00b35b86ca2}} , which vanishes in the standard power-law scaling ansatz {{cite:f6ea885cbe360ebd0f829ba33eb7af14ed28a4b0}}, accommodates the fact that the interaction distance is bounded from above, {{formula:ed06290b-67d1-46e5-8e85-1e2aaba50d0d}} .
A simple scaling analysis (see Methods) shows that {{formula:ad45dbc8-1478-4e1c-b79d-6256e939f824}} is the correlation length exponent, while {{formula:61eb6340-fe77-40d6-b85d-846b237a8c56}} determines the effect of interactions in the renormalisation group sense.
For example, when interactions are relevant, {{formula:40d03410-b9d9-4d84-ae6c-59dd77ca3d15}} should remain non-zero as {{formula:1dfff4fe-285d-4524-ad84-2b73d324b602}} increases, which dictates {{formula:2ff96e8a-b9af-432c-979a-0b252663c26a}} .
On the other hand, when interactions are irrelevant, it is expected that {{formula:f2fc4b13-a206-46c7-b744-061a81b4d746}} decreases with {{formula:b6e76660-f519-4363-8e7b-2ef235843eab}} near the critical regions, in which case {{formula:1852c03a-2972-4d05-9da4-ac3aab391670}} . Note, however, that it is possible for interactions to be irrelevant and still yield finite {{formula:0759acb2-88f6-4f56-8244-4cc17eaffd6f}} in the thermodynamic limit. This is because, {{formula:8c519e21-8d49-498c-8e27-0358c3993a66}} may be sensitive to non-universal (short distance) properties of the system, which can give a residual non-zero contribution parametrised by {{formula:1130a316-10e9-4d26-b4e6-bf9556d72998}} .
| r | 5c483cc7259e51b67156a7809eb3ba89 |
To address this, recent works have explored the joint optimization of machine learning models and explanation methods to improve the reliability of explanations {{cite:ee9a21595e0401edbef5ef6414278793c6b6c7c7}}, {{cite:4ece91239e8b9d19576275302c4022de66b3079c}}. Zhou et al. {{cite:4ece91239e8b9d19576275302c4022de66b3079c}} proposed DropEdge as a technique to drop random edges (similar to generating random edge explanations) during training to reduce overfitting in GNNs. More recently, Spinelli et al. {{cite:ee9a21595e0401edbef5ef6414278793c6b6c7c7}} used meta-learning frameworks to generate GNN explanations and show an improvement in the performance of specific GNN explanation methods. While these works make an initial attempt at jointly optimizing explainers and predictive models, they are neither generalizable nor exhaustive. They fail to show improvement in the downstream GNN performance {{cite:ee9a21595e0401edbef5ef6414278793c6b6c7c7}} and degree of explainability {{cite:4ece91239e8b9d19576275302c4022de66b3079c}} across diverse GNN architectures and explainers. Further, there is little to no work done on either theoretically analyzing the effect of GNN explanations on the neural message framework in GNNs or on important GNN properties like oversmoothing {{cite:c086863d90c9483c9c05909eb219d249d43988d7}}.
| i | c8289dcb57ed9b04a0cbd602c197501b |
Transformers:
We fine-tuned a BERT {{cite:e9040feaad74659eb9ea0624ab193f2cbb367bfd}} and SBERT {{cite:25c59f05008465e4bb74ea8bed9c48d72950acdc}} based encoder with a dense output layer.
We used a pretrained BERT-Base model from the huggingface https://huggingface.co/transformers/ library.
For SBERT, we used an all-mpnet-base-v2 layer, pretrained using a billion sentence pairs from multiple datasets.
Both transformer encoders have a hidden state dimension of 768.
We did not perform any text preprocessing.
In our transformer-based experiments, we calculated the class weights using: {{formula:f85d83fa-1414-4952-b013-1d99075b98e9}} , where {{formula:32257d41-548f-429a-874d-a40fa47793c1}} and {{formula:e5861bc7-95c2-419f-8196-ed48f17057a5}} are the number of negative and positive examples of emotion class {{formula:cd52d9fa-2950-4e10-8f21-d192668b8ef0}} , respectively.
The square root dampens the impact of the negative to positive ratio, which otherwise over-corrects the class imbalance.
| m | 571b478fe3ab54ebdc6d96c3436e91a1 |
There are a few points about this framework that need to be further clarified. In general, turbulent flows have universal behavior in their smallest scales {{cite:aab708205ef0dafe7695321917049fc5274ada3a}}, {{cite:41fc124d107875b61580e0ea158bdc6fdd7a6131}} and vary in large scales due to forcing and geometry. This might seem to suggest that TL will always need to learn changes in large scales between a base and a target turbulent flow. This is not necessarily true, as even in Cases 1-2 here, in which the base and target flows are different in forcing and {{formula:be6fb332-9483-4c0f-9e11-5a1d158fa5e2}} number, there are differences in small-scales of {{formula:e1fef77a-624e-4d03-b573-dfbe7b8a754f}} too. Furthermore, in the broader applications of TL (e.g., in blending different datasets) and beyond just single-physics turbulent flows, there might be differences between the base and target systems at any scales. Step 1 is intended to identify these differences.
| d | 84bd13215f41081f4c55f8e06ad8261c |
When the data is independent and identically distributed, the learning results of FL and CL are similar. For instance, the work {{cite:0d8e075a9e84cee36fbbd6832d46e1e9a220443b}}, {{cite:425ac8f336c4a0ce83604ac5bd85ec095c839c45}}, {{cite:7fb7fb9d0b97b7e224f2a321106f0de052e74c81}}, {{cite:18573778f79dab575426c7ee7f1352f7063bab2a}} showed that when the training data is independent and identically distributed (IID), the difference between FL and CL is within 3%. If the amount of data on each client is small, FL's effect is better than CL because FL expands the number of IID data samples {{cite:3f2526ddf2924dac0e1275af66dcb1e03731b755}}, {{cite:c78df55fad0046dedf621e635b6dc1f74331c249}}, {{cite:6bc5fdf41366f876491de9e93703666f0434ebbc}}, {{cite:8e7a47114e3e6146a017be5e4f383de6e594c750}}, {{cite:a18d4ded793377d3dc03b3479e57370d9948f346}}, {{cite:2b00fed14ac1d8294a55c2ac85030735bf8f0f56}}.
When the training data is unevenly distributed, FL may not achieve the same effect as CL {{cite:83ac79f43c5a44a75ca57816f496d38cad4ea0e6}}, {{cite:08bfac2d04ea57c12f91e6b16bd83fb010f9561e}}, {{cite:bcd9321d5a3c511188c243fdce285ce241aaa6c6}}, {{cite:3f47b57983be7a56a13844a34c015b99f52bc462}}, {{cite:1e96791ab4caa03d346aecd41075fcb5e770d2df}}, {{cite:425ac8f336c4a0ce83604ac5bd85ec095c839c45}}, {{cite:d6209aa5ed0d842b17c47c81c72f1a06b96520ca}}, {{cite:7fb7fb9d0b97b7e224f2a321106f0de052e74c81}}. The review article {{cite:febd0da967fc60b46e78660d51e92e7ca34f9520}} claimed that if the amount of data on a client is small, the CL model may be better than the FL model trained using data on multi-clients in the case of uneven distribution of training data.
| d | c9313b3c7fca5247cd8b8db72e7bfb4d |
The paper {{cite:d83d81fdfdf52fa15a353fe2042aa10bbbf908e0}} constructs metastable states where the graph is close to {{formula:1a7877f7-1e35-457d-9c0a-86ebada781e5}} for some {{formula:1b0a5f9c-62c1-435e-a111-30d5322a06d2}} which is a local maximizer of {{formula:6c4e9f47-20ca-4198-8c22-04ae053cd939}} , from which any local Markov chain takes {{formula:4bceba7f-e70c-4f44-aa4e-353910482d0e}} time to escape. The large deviations theory based results established in {{cite:6328b31a622e7157b119cd3c9a203dcaa66d5b76}} show that when {{formula:24dabb5d-40ec-4627-882d-4527d8dc3187}} is not the global minimizer of {{formula:978ff3ff-5ef1-4762-ba8c-5cd8517e9bf7}} , then these metastable states collectively have mass {{formula:2e64bbf0-54ca-4f53-96c2-a555f4928300}} . One might hypothesize that the metastable states can be fully characterized by the behavior of local maximizers of {{formula:671144f1-1d89-4830-b5b4-1642c8739091}} and the cut-metric neighborhoods, and moreover that they have total mass {{formula:f8e8ef3c-db8c-43cf-bb9e-c1a7d2067818}} .
| r | 6fc15cb1d8ae039ca825a088d11ed13d |
Our method is superior to state-of-the-art unsupervised approaches and gives comparable results to supervised techniques for image manipulation and image-to-image translation. We showed that incorporating the proposed auxiliary module as part of the training encourages better disentanglement of the structure from the texture and better feature embedding. This opens up new applications for image editing and style transfer, such as balancing existing datasets by generating images from underrepresented classes, expanding semantic segmentation datasets, creating multi-view datasets, etc. Previous works {{cite:26b06291f09438c7390b09f269e75f794336412a}} explored the effect of combining multiple loss functions with different weights in a single model using {{cite:8375b945b2bc09713e4643607ae162c23e5431be}} to achieve better optimization. We believe the same can be applied as a future step on our pipeline for image manipulation. The importance of structure versus texture may differ from one application to another. By designing an architecture in which one can specify the percentage of structure versus texture for image generation, our method can address even broader range of challenges.
| d | c7cd40d3b4b7f793e0dd9ecabead3206 |
Our method falls within the category of federated learning algorithms. This means it can be implemented for situations when data mining is to be performed over remote devices or siloed data centers {{cite:9290c4fc8aebb412d2893d9da5046d7f4ce10b56}}, where aggregating the data tables is prohibitively expensive in terms of time, computation, or storage costs. This work aligns with several recent contributions that seek to exploit the privacy-preserving aspects of federated learning algorithms {{cite:467ff1e700da4f9bda51df5e955a27f1b5863f42}}, {{cite:6f4bde890d2988abd9ddd741d1c6a772c4cd50ec}}.
| d | 38041c14daec58dda99b6f68b4084dc2 |
Concerning the number of CG iteration we want to point out several observations. First, we generally observed for various parameters that the number of CG iterations increases as we emphasize the singularity, i.e., as {{formula:5e20800f-31fa-40c4-b71e-2b5ce8f6bfab}} . This coincides with Theorem 6.3 in {{cite:b38fa8330019d5a356d8425f7f48e7a505412100}}, stating that for shape-regular and quasi-uniform meshes the following estimate for the condition number {{formula:1a73e617-029b-4236-8e12-371d546a8303}} holds:
{{formula:8b3e9d43-ab1d-4ded-9613-2a6a46dc9c58}}
| d | 9e2cdef9342bad47fcd5df8c82b62d04 |
We end this section by comparing our results with existing works on private value-iteration RL, i.e., {{cite:b8d635d9fba7037b732bd955db309f3a2160662c}} on LDP and {{cite:468b5d33cc9b8da89e7b44d1c1f87462fab170c7}} on JDP.
| d | d499a639064718501dfdff51c755e53d |
Our goal is to localize objects that make characteristic sounds in videos, without using any manual annotation.
Similar to prior work {{cite:b383b83055cba5b25842c82276737c387c1ecff5}}, we use a two-stream network to extract visual and audio representations from unlabelled video.
For localization, we compute the cosine similarity between the audio representation and the visual representations extracted convolutionally at different spatial locations in the images.
In this manner, we obtain a positive signal that pulls together sounds and relevant spatial locations.
For learning, we also need an opposite negative signal.
A weak one is obtained by correlating the sound to locations in other, likely irrelevant videos.
Compared to prior work {{cite:b383b83055cba5b25842c82276737c387c1ecff5}}, {{cite:9d169842d01aa8d191dfd6ee876e13df2631f1a3}},
our key contribution is to also explicitly seek for hard negative locations that contain background or non-sounding objects in the same images that contain the sounding ones, leading to more selective and thus precise localization. An overview of our architecture can be found in Fig-model.
| m | ca2c9ce25d69d825daacafb0cdda0d82 |
In this paper we studied hyperbolic codes for two-dimensional topological states, where {{formula:5b6afd52-bf88-4dda-ae22-9af6ad717825}} .
However better codes exist, such as the hypergraph product codes {{cite:a34683a58f9a428b54f49f8fb734d349540f5b38}}, {{cite:e41a20c7e691e1fbdbc98fd8fb41b9d772ef1d27}}
or homological codes associated with four-dimensional hyperbolic manifolds {{cite:888aac8142e870828a32abed5bf7b6270fbb8a13}}. These
codes also have constant space overhead (and finite error thresholds because they are LDPC), but with the
improved scaling of {{formula:34ae1933-6bb6-413a-a80e-d36bf0179256}} for the hypergraph product codes and {{formula:2c9ede8a-34be-4483-aff5-170fc15735a0}} ({{formula:e37921fa-b725-4125-b921-e15cde94d737}} )
for the four-dimensional hyperbolic codes. However, due to Mostow rigidity, the mapping class
group of higher dimensional hyperbolic manifolds is necessarily finite. It is therefore a fundamental
question whether there exist codes with constant space overhead and {{formula:8920fce1-abe6-4e1e-9641-443aae435cf3}} (with {{formula:a80dc326-567e-40f8-932a-de778d13aafe}} ),
and which also admit a universal logical gate set through constant depth unitary circuits.
| d | 525cac6285706d36ae94875d4fc8183f |
A plethora of clustering methods {{cite:35814b38afc51f00a2996812bb0282128c74d687}}, {{cite:e329109ad0426bdf15db40ade0c3bf8dfa4db891}}, {{cite:80596db47ab32d5f2b11d35fd3597c489851dcc3}}, {{cite:4909e666aadfcecfef56532ee54cf6c977c492aa}}, {{cite:43af7e46dd029ae71a315b383bfe931a60fafce0}}, {{cite:fcee46698d51ca4a85e5188110447e5c7fd5079a}}, {{cite:c453cde511238bbb034e15ba8927a6843e5b4612}}, {{cite:4ccb26a893753b961dfff8d78bded1501f08433a}}, {{cite:dabf426c13b5a0d6e5aacbf6a614e7695ac38178}} based on autoencoder have been proposed. One of the most critical problems with deep clustering is how to design a proper clustering loss function. Methods such as DEC {{cite:80596db47ab32d5f2b11d35fd3597c489851dcc3}} and IDEC {{cite:fcee46698d51ca4a85e5188110447e5c7fd5079a}} minimize the Kullback-Leibler (KL) divergence between the cluster distribution and an auxiliary target distribution. The basic idea is to refine the clusters by learning from their high confidence assignments. However, the auxiliary target distribution is hard to choose for better clustering results. Other methods such as DCN {{cite:43af7e46dd029ae71a315b383bfe931a60fafce0}} and DKM {{cite:dabf426c13b5a0d6e5aacbf6a614e7695ac38178}} combine the objective of K-means with that of autoencoder and jointly optimize them. However, the discrimination of clusters in the embedding space is not directly related to the reconstruction loss of auoencoder. Thus, in this paper, after using an autoencoder to generate an embedding space, we discard the decoder and do not optimize the reconstruction loss anymore. Because no matter what we do to the embddding space, we can separately train the decoder to reconstruct the input data from their embeddings.
| i | bc72b87a768e57dedb3520104e5984f9 |
We first introduce some preliminary concepts which are needed in the
exposition. To that end, we follow {{cite:2de2df9dce6f97231faf89c1a591ceee6ef5c3c7}} and {{cite:4673f24d19529360ffae22f4b7d1ed30c3d35727}}, see also {{cite:e26ad356d507a33e453a14a3208f406d0e311fa9}} and {{cite:77bc8d3862a9a678aabd0843d10d158f54ebccf5}}.
| m | 68987c821efe752562af813a4bbc8441 |
Probabilistic programming languages enrich classical imperative or functional languages with native primitives to draw samples from random distributions, such as Bernoulli, Uniform, and Normal distributions.
The resulting probabilistic programs (PPs) {{cite:6068090e9890eeb04a91b9fb14e5a868902e8f92}}, {{cite:792dec3466187f8d3be3fefffe6e167318436b15}} embed uncertain quantities, represented by random variables, within standard program control flows.
As such, PPs offer a unifying framework to naturally encode probabilistic machine learning models {{cite:9cde9873cbf10b2784cfbc4facdf64cad058c35c}}, for example Bayesian networks {{cite:72fca1e255cceca3a5c21c675a553ddfab0a7de4}}, into programs. Moreover, PPs enable programmers to handle uncertainty resulting from sensor measurements and environmental perturbations in cyber-physical systems {{cite:9d3cee96818e00dab7b2c46eba8ddbde2b47f6f2}}, {{cite:23d1a09477c5593650c8b251d3390cb46009232c}}.
Other notable examples of PPs include the implementation of cryptographic {{cite:16201ea57a12703adaae1aa58a342322a44e314a}} and privacy {{cite:e41ba662521289ea8e506c5752f8bc87d1ed83a9}} protocols, as well as randomized algorithms {{cite:5de2e27e25ee71a1f5be5650ef20f3c56be508c2}} such as
Herman's self-stabilization protocol {{cite:b51581bb2acad1033df599d1a8741cd7714e9002}} for recovering from faults in a process token ring — see our example in Figure REF .
| i | 46f2deb2641b2ee2d0e6e30f82b6715a |
At {{formula:858d3295-b66a-4431-84ce-ec15fbea5ae0}} , rest-frame 1500 Å falls in
the optical to near-IR spectral range in the observer frame, and is
accessible with ground-based as well as space-based
instruments. Again, luminosity functions which extend several
magnitudes fainter than {{formula:a9e233e4-f37e-4d6e-bcb2-90377ffb2e41}} have been produced for the redshift
range {{formula:6eedb434-d8c4-4d1d-ba32-52fda9294a65}} {{cite:f072018eb0af71678fff560cd1f75b51aa7a4c32}}, {{cite:5ce107b55fb0c9092fc3b18edce8987d1fdf70d0}}.
| i | 19001fd0ff5afc87b3c6a74a9a22fa30 |
The persistence of TBM characteristics can form the basis for a strategy to extend TBM features long after the topological system that supports it is gone: namely, by quenching to a large gap wherein postquench eigenstates are energetically inaccessible. Since the persistent TBM PD arises from the fast postquench Larmor precession enforced by large {{formula:308048a9-11e5-471f-8101-fd6e1b273692}} , we expect that it is robust against inelastic scattering with energies far smaller than the gap scale as well as slowly varying disorder with typical lengths longer than the TBM width. The frozen and melting quenched PD regimes can be readily prepared and measured in ultra-cold atom optical lattices {{cite:ff92aa368a0d40f87d61ced8eefcc3354d429763}}, {{cite:f4e733bfd9494f50690462d77762f8e6188de947}}, {{cite:19b68d5b3b771823ad29331b3a9970062b069157}}, {{cite:d8a706e98f5f15d0e44c91f32c63a0cb00c232f8}}, {{cite:781ed38b7291625c68dc5fd219f5396dd13f841a}} with its pseudospin components of the wavepacket independently extracted {{cite:d8a706e98f5f15d0e44c91f32c63a0cb00c232f8}}, {{cite:781ed38b7291625c68dc5fd219f5396dd13f841a}}, and its real-space dynamics tracked {{cite:19b68d5b3b771823ad29331b3a9970062b069157}}.
| r | 194c5a6a134cce8ca2423c50b7c95815 |
In the previous sections the variation of material parameters was used to model structural details like areas of lower densities or void regions with (close to) zero density. This approach is conceptually similar to immersed boundary methods (IBM), where a known structure is embedded in a larger, simply shaped 'fictitious domain', and an indicator function {{formula:0da4bf41-8e4b-47b8-a894-380146709ad6}} discriminates between the fictitious and physical part of the computation (see Figure REF ). While ‘fictitious domain methods’ were suggested already in the 1960ies for a numerical approximation of boundary value problems {{cite:d7fc8a06778903e77e30c3011f9ab40d213d9317}}, they have become very popular again during the last decade, in particular as they offer attractive opportunities for closely integrating geometric modeling and numerical analysis. Many variants of immersed boundary methods have been proposed. Among these are the finite cell method (FCM {{cite:cb36f5f4588647f345cc79269124ad81252df3ff}}), its IGA-based variant immersogeometric analysis {{cite:98a29d16ee23172a7ab8b69caae3ed77c325e9f4}}, CutFEM {{cite:baf5f705d2b44335ac78c935d4f4ceb91c87e966}}, IBRA {{cite:4a38f8cf5e4a314f577cb1dfaa34a1700108724a}}, the aggregated finite element method {{cite:598354bd1d2946ad7fb9b1c13b7b68d3114ffb92}}, the cgFEM {{cite:debb6799af504effb10c7f642880d3b6bcfac79e}} or the shifted boundary method {{cite:eb741dfbc3cb007565d1dfe1f9057945bc2c6711}}, {{cite:b1a2ee96105f9abaf6ba44b541bc0720406d1bb2}}. CutFEM {{cite:ef434677d4f731f11553150a1708368ae566383a}} and the finite cell method have also been extended to scalar and elastic wave equations. The spectral cell method {{cite:03aa77c03fea9ab34effff7784e3e3f6fd236733}}, {{cite:917afffae0eaab833093ca753488bf4de07bbf09}}, {{cite:ea47580f82a47af30ccc1dd421874e79c8a9f99d}} concentrates on an efficient combination of immersed boundary approaches and explicit time integration for wave equations. We will exemplify the application of full waveform inversion for immersed boundary approaches concerning in particular the finite cell method.
{{figure:943acd21-b555-475f-8f5b-83e2858ce5cb}} | m | 5170f3695e4d2ceba3cc007b6b919cfc |
Decoding strategies are crucial and directly impact output quality. In general, Beam Search {{cite:c6eff3c125e455d3cf3175ae3bd4dac0cac3d926}} is the most common algorithm, in addition to some other sampling techniques such as Nucleus sampling (Top-p) {{cite:a3f01ca4695761770f9bcd384fc5105841d6558e}}. In Beam Search, the output of a model is found by maximizing the model probability. On the other hand, Nucleus sampling selects the smallest possible set of tokens whose cumulative probability exceeds the probability p. Experimentally, we found that using the top-p (p=0.9) algorithm yields the best results in terms of the used scoring metrics, thus we use it in all of our experiments.
| m | 2254dbc726a00ad31d76ac2ffd41d408 |
We tested the accuracy of the QGCN on the datasets above, as measured by the test accuracy and compared it to several baselines that can be divided into four groups:
Graph Kernel Methods. Shortest-Path Kernel (SP) {{cite:05a9b41f5715a4b1427bfe886062234e72a42217}}, Weisfeiler-Lehman Kernel (WL) {{cite:1e515eb5444bdf12db1eb5e98b108d2bc9f016aa}} and GRAPHLET {{cite:095f5af9dd0f2a999ee01bb21226578032bfd47b}}. Graph Pooling Models. Models that combine GNNs with pooling operator for graph level representation learning: HaarPool {{cite:bc280355218946e04bb89bc5fe3e033513640c14}}, HPG-SL {{cite:7a989e2ef05e7f857d781766c41507f4e8deaafc}}, G-Inception {{cite:1a23542797d4ddfdbe2c3d67d0efb8381306277d}}, WKPI {{cite:037cfb65a1335118752dc2313fd4119f1d753901}}, EigenGCN {{cite:9a40b491f99d497f41d089b51f25b897998b65c0}} and DGCNN {{cite:1ac2f203125b0733e1b51939ed52ab811688278a}}.Attention based methods. DAGCN {{cite:ff0145ee5fda1cb7505f7806d274f3da749d3196}}, SAG-Pool {{cite:29e6f7efa498be29b456812157bf5b14d7c43514}} and GAT-GC {{cite:10513e533de50f85741dec659d4ac170807c454a}}. Self-supervised Methods. CSSL {{cite:9e7e1464da695a309bc1bb2c80331167fe5499fe}}.
| r | 7917b725db335b3f80c05be9c763a113 |
The following two theorems were conjectured by Fomin-Zelevinsky {{cite:71d4e5d51815b8f7ff6e5430d3ab14a80026ae81}}, {{cite:7aa8f4ccc2b0aeda1cece9261c9b868c44f9ccbe}}
and proved by Gross-Hacking-Keel-Kontsevich by the scattering diagram method.
| r | c9c0c11a0b8e5a49b49fe04846b57fd0 |
In this section, we present our salient objects detection model's
results. In order to obtain the LTP{{formula:3021c72c-d425-40ce-9ec3-1376434013b2}} pixel's code (LTP code
for simplification), we used an adaptive threshold. Let a pixel at
position {{formula:4aefc223-ce05-4d2c-9b24-22b28c447c85}} with value {{formula:9b9f6e80-feb7-427c-9ab5-742667ebc00e}} , the threshold for its LTP code
is the tenth of the pixel's value: {{formula:0f464293-c022-4467-9fe2-7bb7c5a5646c}} (see
Eq. REF ). We chose this threshold because empirically it
is this value that has given better results. The number of neighbours
P around the pixel on a radius R used to find its LTP code in our
model is {{formula:77c8d812-8caa-48c2-bcb0-b8f1493b93aa}} and {{formula:1bd5fe11-739d-4d01-89d9-abc0ac9d7042}} . Thus the maximum value of the LTP code in
our case is {{formula:4ab06078-5bb3-4e41-8fb2-89d7cbaba764}} . This makes the maximum size of the histogram characterizing the micro-texture in an opposing color pair
to be {{formula:b466fe69-a789-4da2-8f7c-92e4f8a2da4d}} which is then requantized with levels/classes of 75 bins (see Section REF ). The superpixels that we use as adaptive windows to characterize the color micro-textures are obtained thanks to SLICO (Simple Linear Iterative Clustering with zero
parameter) algorithm which is faster and exhibits state-of-the-art
boundary adherence. Its only parameter is the number of superpixels
desired and is set to 100 in our model (which is also the value
recommended by the author of the SLICO algorithm). Finally, we use in
the combination to obtain the final saliency map the color spaces RGB,
HSL, LUV and CMY.
We chose, for our experiments, images from public datasets, the most
widely used in the salient objects detection field
{{cite:0c32db5aefa1f97771631978a4c510073231317f}} such as Extended Complex Scene Saliency
Dataset (ECSSD) and Microsoft Research Asia 10,000 (MSRA10K). The
ECSSD contains 1000 natural images and their ground truth. Many of
its images are semantically meaningful, but structurally complex for
saliency detection {{cite:6be602f8b4153362b51b26d59d4eeeb8e38c4be2}}. The MSRA10K contains
{{formula:a5a7651d-e56e-4528-b854-7d2f62303013}} images and {{formula:79e6f074-7284-48d7-955c-9e6d366d2631}} manually obtained binary saliency
maps corresponding to their ground truth {{cite:16c91e2caf220f3f1e8ab7d5f50f84b703c6ade8}}, {{cite:0c32db5aefa1f97771631978a4c510073231317f}}.
| r | f91133e4e7047b519e028b93a36c888d |
Beyond the four challenging image semantic segmentation benchmarks above, we also test MCIBI++ on other benchmarks, including PASCAL-Context {{cite:4bf185bc431fbeb0850b91d359eaf7ee926b78a9}} and PASCAL VOC 2012 {{cite:9ddedc4be75a1f940e5db52e351293391d0d829e}}, {{cite:dde7e964ed50c51d6e16b2b6e854b93e1bdf81f4}}.
| r | 6143778ad59a668438e875a78621dc47 |
Data augmentation mechanisms are often used as regularization methods for
deep learning classifiers. The study of data augmentation mechanisms in
ensembles of simple classifiers have achieved state-of-the-art performance not
only 10 years ago {{cite:fa494fcb45281f0a4bff30e05db8ab8ce25d79a4}}, {{cite:c8a19fd7b347ae37187699fe742af3d79b93b1e4}}, but also when compared to
modern deep learning architectures {{cite:10556af57842c116984f5d80c6ecc1c2b65fce18}}, {{cite:14f190a90fb73eaed10db7d68f4c2bb1098332cd}}, {{cite:46cb3ee5da18651a1a10332f0a4e41d62505258a}}. However, the implementation of different data augmentation methods
shows a promising path to improve the performance of simple classifiers
(and/or recent ensemble architectures) and requires further research.
| d | 3ca5f0cb76f870d037423f439eb47b4c |
System Architecture. We build upon the recently proposed dense indirect VO method of Min et al.
{{cite:0fe2793349462f0f9d2b646bb17a71583be2c7e0}}, which addressed the joint probabilistic estimation of camera motion, 3D structure and track reliability from a set of input dense OF estimates. As standard practice in SLAM literature {{cite:6a4fa7ce864d2f8d6ba3d35d2f67b2b4041a1484}}, {{cite:ed776d2b09b7231db4fcc7bee3140678bf6d3f64}}, our proposal VOLDOR{{formula:5cfcec24-2c68-4342-aae7-a20a0ad0b17f}} SLAM has a VO front-end and a mapping back-end. The front-end operates over small sequential batches (i.e. temporal sliding window) of dense OF estimates. We adaptively determine keyframe selection and stride among subsequent batches based on visibility-coverage metrics designed for our dense SLAM system. To enforce consistency within a larger geometric scope, while enabling online operation, the back-end adaptively prioritizes the analysis and establishment pose constraints between keyframe pairs balancing the search for loop closure connections and the reinforcement of local keyframe connectivity. VOLDOR{{formula:412dcf36-16f2-411e-bdda-8b879f0b0d07}} SLAM also implements a loop closure scheme based on an image retrieval and geometric verification module {{cite:a016836de6db512a9d137c06f898088379c0f24c}}. Finally, all pairwise camera pose constraints are managed within a {{formula:11b90844-1fa2-41a0-8433-1d2bae02556b}} -based pose graph {{cite:97a528d31f8937acf56fa3dbd4a863e3da34cf6c}}. Module dependencies and data flow of our system are illustrated in Fig.REF . The resulting dense SLAM implementation enables online operation at {{formula:9f286fca-d085-4ea8-88cf-42b1c170b9ec}} FPS on a single GTX1080Ti GPU.
| m | 8267b4e77015bdcaee6b23f851dd1210 |
To solve the inverse problem involving the two data sets just described, we use a sequential data assimilation method {{cite:755052552fdb97deded180881633416042419ee6}} based on the ensemble Kalman inversion {{cite:37de100774cc27aa8955da1f8050a3a2389a7662}}, a methodology pioneered in the oil reservoir community {{cite:6bc42e91ee26ef9d745b03ca17da355a8052b678}}, {{cite:74e19f23f83d6cb2da6e4588493472785739b71c}}. We provide the details of this algorithm and successful inclusion of a priori knowledge in a form of inequality and equality constraints in {{cite:338a6cfc70e5c8762f25bff10f0c4416d2dec971}}, {{cite:12bcd181215d5d7fb82009fc08dfa7413df1a726}}. Therefore, for brevity, next we only discuss the main steps of the adopted algorithm formulated in the range of the covariance. In this algorithm, we first generate an initial ensemble of {{formula:c2ded981-831d-46cb-9022-4c778f021ca2}} particles {{formula:28281b18-974a-4cb8-b67c-360d01107709}} at iteration {{formula:7ecd12c7-9ba7-421e-9a8d-d9f009793ef5}} . Considering a horizontally layered soil with {{formula:fdab2508-3019-4fc7-b2e1-0b04d24a7433}} layers, each particle is an array of size {{formula:df5091d8-7274-4fc2-8898-135779145cc8}} including P and S wave velocity of each layer and a damping ratio. We note that in this study we assume that the damping ratio is depth independent. To generate the initial ensemble of {{formula:7bc1ca22-39f4-49a2-9a25-c71ef33bcf64}} particles, we consider uniform distribution for each parameter. Then, at each iteration {{formula:c9d06f59-7ab2-43f0-b6f7-a0775c151dac}} , we use the forward model predictions {{formula:bac7fe00-7605-48bd-9eb4-8848ac5a75df}} and the observation data {{formula:52a69774-f5e1-46c6-b3fc-958faafa92be}} to update these particles sequentially. We have two forward models: {{formula:c0dd6c7e-618d-4ac9-bde6-db48f40c15b6}} uses the {{formula:e92d66df-2f98-4943-9a51-34c2895778d8}} th {{formula:fbc4ff74-160c-4796-8b68-9c840bcbd3bd}} profiles and damping ratio to perform 1D site response analysis and compute the acceleration time series at different depths. On the other hand, {{formula:c600b3c2-2eac-4a93-8475-27c86648abf4}} uses the {{formula:96403e62-31d3-4033-9fc0-79306d97e7d2}} th {{formula:054fc16b-b78d-4826-8e6e-722e048bd2e2}} and {{formula:af66b889-f70d-4150-8503-59996e8661f8}} profiles to compute the theoretical dispersion curve. For each particle, we concatenate the forward models' prediction results to form {{formula:84ac147e-b3d7-4170-b055-7e8e9f22e9fe}} and compute the prediction error {{formula:c2d531e0-fe20-4798-922e-c6f765c2634c}} . Then, we use the modeling error along with the Kalman gain {{formula:b8b96e66-fb23-48e3-9e9f-1a59bc005c21}} to correct each particle as follows:
{{formula:5f2923f3-e9d1-47cd-acee-f63f47c1c5be}}
| m | 8d9e5e312aba7b78ac5f353f4dabac81 |
We first analyze the role of two key parameters {{formula:7c0bb557-0124-49c1-8722-e194e8602cd3}} and
{{formula:fc67a761-3054-4336-83f1-52f153463c83}} in determining the strength of the effective field
{{formula:d8f6fb73-58dc-4455-b6b5-a54bd09994c4}} and the torque efficiency of the system. Figs.
REF and REF show that, with a fixed {{formula:47ab85a6-8a12-4258-b417-5d1437840552}} and
{{formula:264f7f8d-caf4-4729-ad6b-bdeaeb6eeb92}} respectively, {{formula:e382257f-bc6b-4c71-a138-3189988926af}} increases linearly with
{{formula:5ba1db8b-d683-43dd-90da-2110cb19e7c3}} . This trend is consistent with the prediction that
Heff=R P0B(zje),
derived from either gauge formulation {{cite:e7ae12432a52a0edad86371867da5c479f0ecf81}} or from
semiclassical (Boltzmann) transport equation {{cite:ed7414bbe8b03c15c156a51f2f6afc4a415945f7}} in
the strong coupling limit. Eq. () is a global expression of spin torque under linear response. In the gauge formulation, the factor {{formula:e341fa58-0c0b-416e-af2c-e8ace6d80aef}}
assumes a value of {{formula:6a39d0ca-c5d0-45b8-b0fa-d88c8bcc9de4}} in the adiabatic limit, while in the
Boltzmann model, it refers to the spin polarization of current. We
now consider the torque efficiency, which is given by the gradient
of {{formula:11a6b2bc-4c1e-4947-82cd-c93c972d9b6a}} with respect to {{formula:eeb8cdc4-4349-4d0a-9b97-51c3dd106236}} . As can be seen from
Figs. REF and REF , the torque efficiency is
generally enhanced with increase in either {{formula:ddaa36d6-b4b4-4f28-9c3b-770d67e5c62d}} and {{formula:15a97c1a-a64f-47d3-a3c3-409e1a2f9e63}} .
However, in our non-equilibrium spatial treatment, it is clear from the plot in Fig. REF that the
torque efficiency does not vary linearly with {{formula:690c71d2-67bf-40cd-b980-9395c07c80b7}} , unlike the
prediction of Eq. (). The difference can be
accounted for by noting that the global expression of Eq. () is derived in
the limit of large coupling {{formula:38b41ae2-4bd0-488d-822d-ccf6ad884b76}} , i.e., up to only the linear
order in {{formula:20f9c8fa-087e-4821-b91e-e176f8a32413}} . In our model, as can be seen from Fig.
REF , the torque efficiency shows a slight oscillatory
dependence superimposed upon a general increase with respect to
{{formula:813463d9-f064-4b73-a24a-7bfb5e04b296}} , especially at the region of {{formula:01abbecf-9af4-4c02-860f-632a558fb313}} eVm. However, at the region where {{formula:6f28d669-6f11-4449-b79c-9d8d674b06d0}} eVm, its behavior is similar to the prediction derived from the Boltzmann semiclassical model for arbitrary coupling strength
{{cite:ed7414bbe8b03c15c156a51f2f6afc4a415945f7}}. From the effective field {{formula:666984ec-f314-47d3-b5d2-eb3bfabf7e4a}} ,
one can estimate the critical current density required for
magnetization switching. In Figs. REF and REF , we
consider RSOC strengths ranging from {{formula:ed0f8e66-edce-419f-8cf8-f2f638ba201b}} to {{formula:f9d8160b-5dd6-41a6-9a83-f644af281e6b}} eVm,
which roughly corresponds to the practical values observed at the
interfaces with heavy metal or oxide layers. Assuming an exemplary
spin polarization of {{formula:85548096-d340-42eb-9078-b0ac097e7b45}} , RSOC strength
of {{formula:85b0c8a0-d0be-45e1-895d-982142f40918}} eVm, and a switching field of
{{formula:cd670cd3-e70c-47ee-87f5-df8ff812e050}} T applicable for Co nanowire structures
{{cite:c06641ada31149a30c368558ae15ca39f30e39fc}}, we find that the critical current density
for switching is approximately {{formula:329c19a8-a191-4821-b7f9-341fbab03253}} A/{{formula:bbe52e14-4e06-410a-8fbe-2a05978059a0}} [see Fig.
REF ]. This is significantly lower than the critical current
density of the order of {{formula:f64f4bba-013c-4afb-a55f-61ec2ce1e3ee}} A/{{formula:98164b85-620e-414d-8d74-eeb48407873c}} for the case of the
conventional Slonczewski spin torque in spin valve structures
{{cite:27475e36e8c9019c43e6908a46dacd6f32d7ab58}}, {{cite:88b29befc00760c9d80f3ab63710962327889587}}.
{{figure:6e2695fc-1c71-43be-b00f-df507588389f}} | r | 0041a1083fa093124af734a5fbc07d6f |
High-quality embedding of words can help boost the performance of many machine learning models in NLP tasks.
Recent work about word embedding can be categorized into two genres, i.e., neural network based methods {{cite:f162bd7b53fe723cd03f7290e9296757ca597671}}, {{cite:54d210e36d8d01d551da2da6514c395fb4ebd343}}, {{cite:0f9b69f51578f85b23db0ec719ec288ac7220e94}} and global matrix factorization based methods {{cite:48084247cb0c787f5c89050731f089382450f0eb}}, {{cite:476d581fc01fec97f7602cfb4ef7858b6089539a}}, {{cite:d8b884a36486a6729fd7bf1abf942302e1772905}}. Word2Vec, GloVe and fasttext are the most popular neural network based methods.
Most of the existing methods focus on improving the performance of word embedding.
However, it is computationally expensive to obtain such word embedding — it takes several days and, typically, around a hundred CPU cores to attain decent quality representation of words
{{cite:f162bd7b53fe723cd03f7290e9296757ca597671}}, {{cite:b64bc5effba32718440ba0c8c773f5c5fa250537}}, {{cite:0f9b69f51578f85b23db0ec719ec288ac7220e94}}, {{cite:5bf9c4a031a18679bfb2d258b38954431f52b80e}}.
Global matrix factorization based methods for generating word embedding have roots stretching as far back as LSA{{cite:48084247cb0c787f5c89050731f089382450f0eb}}. These methods utilize low-rank approximations to decompose large matrices that capture statistical information about a corpus.
Previous work has shown that both the word2vec and GloVe methods can be viewed as implicit factorization of special information matrices{{cite:476d581fc01fec97f7602cfb4ef7858b6089539a}}, {{cite:d8b884a36486a6729fd7bf1abf942302e1772905}}.
Although global matrix factorization based method is more efficient than the neural network based methods, it still needs to factorize a large {{formula:3c8ab14b-1652-49e6-a77f-9e735abd3e4e}} information matrix for large-scale vocabulary, where {{formula:fd913670-5643-4c21-8c9b-e82fcbf63533}} is the size of vocabulary.
This makes it highly expensive to directly factorize and calculate for large-scale word embedding learning.
| i | cd39a6e5f53aa1924fbb5a843cd39107 |
Our method is compared with several baseline methods, including IQL, VDN {{cite:7b44534cabff9626e2f3da659c317f1ff4456d5b}}, QMIX {{cite:a18699a276848c71662c8fd485d4c185d6bcc10c}}, QTRAN {{cite:a3c3359fa2d0440550620188eea4620c361703c9}}, QPLEX {{cite:f61ff830136be4d821ae751171d2c6adadd67af1}}, CWQMIX and OWQMIX {{cite:b8f2de3678a832bcc44d77f488cf321c99a36a5c}}.
Our S2RL implementation uses VDN, QMIX and QPLEX as an integrated architecture to verify its performance, called S2RL (VDN), S2RL (QMIX) and S2RL (QPLEX).
These three SOTA methods are chosen for their robust performance in different multi-agent scenarios, while S2RL can also be easily applied to other frameworks.
| m | 3530707d7c971b9e77801bec4cc5cb2a |
This section introduces the proposed AA-TransUNet model which uses the TransUNet {{cite:05a7f97adbd6e39e990449b6eebe97a7601c3954}} as the core model and extends it to reduce its parameters and improve its forecasting performance. We then investigate the application of the proposed model in precipitation nowcasting tasks.
{{figure:415c4884-d527-4228-b3e4-f0639d1413a9}} | m | 69b6240e7ef0bec12a9e15cd532b7de6 |
Studies of word embeddings range from word similarity {{cite:ecc97b6584eafa24e1c6533b4e24c01689fb5b47}}, {{cite:0c2278065d00dab8097fa169c28c7f4fb148b43f}}, over the ability to capture derivational relations {{cite:bc5f27a2436adb1dcbfa2827af4fddbbd92267e0}}, linear superposition of multiple senses {{cite:92ece05a82bcf40120f21e26b225df6cf3f93c58}}, the ability to predict semantic hierarchies
{{cite:adac649a4e7f8d20c1bfd2a13f181bf4c145e92e}} or POS tags {{cite:240667eef40d10dd50be5bf4f8c8aed458c84035}} up to data efficiency
{{cite:a3e5bfbdd03c584425711e8a736bd219acafb911}}.
{{table:4c2b4ecc-7ac0-42ce-98c8-5f8848554c67}} | i | d5459787c095b7e2c4891a302b731852 |
To verify GraspPF quantitatively, a comparison experiment is conducted with baseline algorithms to predict grasp. We adopt GraspNet{{cite:a35ceba54d8ce409fa3c2d631c9bb1f43f714e12}}, Contact-GraspNet (abbreviated to Con-GraspNet){{cite:4272079fce2a369061ccc2db52b025f7e42890be}}, and GG-CNN{{cite:865d1629265253f371416d4177783a141f90c96a}} as baselines because they are reported to show good performance in a cluttered environment, and the original implementations are provided.
GG-CNN is executed in a closed-loop manner, whose implementation reproduces the original Kinova Mico experiment.
Throughout all baselines, we filter out grasp candidates by {{formula:45a9fd12-3e30-4669-b76b-8735847d1fd4}} .
GraspPF is executed in two versions: GraspPF-ol, GraspPF-cl. GraspPF-ol is an open-loop version of GraspPF, which uses the particle filter as a refinement with a fixed observation. On the other hand, GraspPF-cl runs in a closed-loop manner and continuously refines grasps during approaching motion.
| r | b8ee156262aa5ee13b004db604131398 |
PINN challenges. The training of PINN, however, is far from simple, especially for nonlinear systems of equations. To construct the multi-layer perceptron, non-linearities should be applied to each element of the output of the linear transformation. This is unlike the finite element method, which is a more entrenched framework with clear strategies and established mathematical analysis that guarantees convergence and stability for both the solution and weighting functions in predetermined finite-dimensional spaces. Furthermore, for both forward and inverse problems, the physical constraints or controlling equations could be expressed in several ways; for instance, the collocation-based loss function, which evaluates the solution at specific collocation points, or the energy-based method that can reduce the order of the derivatives in governing equations despite requiring numerical integrations. A large number of tunable hyperparameters, such as the configurations of the neural network, the types of activation functions, and the neuron weight initialization, as well as different techniques to impose boundary conditions while providing significant flexibility, may bewilder researchers who are unacquainted with neural networks {{cite:4bed8f49fa4951ec05933c442c3fe5d3796584fe}}, {{cite:02a96bcc36edc11b180d3ec3802dc0a44bf9b0d5}}, {{cite:2fa8ad71a70474f2a45ed1195c4884c63f1b4904}}.
| i | f78fbd64b834990f81c2be3464a1f517 |
Previous works on quantum cosmology have shown that the aforementioned phantom rip-like doomsdays, namely the BR, the LR and the LSBR, can be avoided due to quantum effects rising up as the universe approaches the classical singularity {{cite:17560477a2dea9e68161ab259f0762e042d3e3de}}, {{cite:33798dc3d708c8a1545aa83e2d409c2be1daba84}}, {{cite:cfcf3e2242a7bbf353ce854d7edf1917e66790a8}}. Since the background late-time cosmology can be equivalently described in the context of GR or by alternative theories of gravity, it is natural to wonder whether these singularities are still avoided in the quantum realm for a different underlying theory of gravity. Following this line of thought, it has already been established that the BR and the LSBR can be avoided due to quantum effects in {{formula:2b1fac12-9a79-47da-9f9e-6f0730fe9b64}} cosmology {{cite:4b53f567b9585e121d03bd56c5c4aec66c9cf444}}, {{cite:2d431aec94a3066e17663087eb10863c1212c814}}. However, up-to our knowledge, no results for the LR abrupt event in quantum {{formula:d78b227d-43d5-4df0-98e7-2011e192c93d}} cosmology have been published so far. Thus, in this work we address the missing quantum fate of the LR in metric {{formula:6433595d-9ed7-4606-81fa-ea6b03ed3e97}} theories of gravity. To do so, we consider a group of {{formula:a2e5e7e4-c633-4ec3-8d71-9d1a254b714b}} theories of gravity that predict the occurrence of the LR abrupt event at the classical level. (For previous works on the LR cosmology in alternative theories of gravity see Refs. {{cite:3c27fac2f94da128a00fd8351950bb363d1639c6}}, {{cite:589d2d702f3bb4c96f7b1abf4f7cc14fb64d4fc9}}, {{cite:127732e6c2569c6e57ec86080ac3bf23aa67f437}}.) The quantum analysis is performed in the framework of {{formula:d842899d-8c22-47bf-bd96-e268b16a2615}} quantum geometrodynamics, with the Wheeler-DeWitt equation {{cite:2b11176416697888c87b94e652acda523ebc7e2b}} being adapted to the {{formula:71bd2270-469b-421f-ad5b-b088d98d7db2}} gravity case {{cite:4b8442e1b86228c153937363f2ad51613fa41052}}. Consequently, we explore the possibility of avoiding the LR cosmic doomsday in {{formula:372be479-5a70-4898-bbbc-bc114387a5d5}} quantum cosmology.
| i | 2cbb0337ad0251f0cde6fa3d8ab590bc |
Due to the good structure {{cite:4f3d79a808cea3ba010216c48437f1a899467877}}, {{cite:bf794b235d4e646151a410d53e7318db70a67e65}}, {{cite:c8ff8dfbe248fccd6dff4a7db66bf85dd18efe48}} and the excellent learning method {{cite:53025733b07b20dcd0a03d342d9179688f5c2e9b}}, {{cite:6dee091926af4c7d4b65ed34e437f330f396e93f}}, the convolutional neural network (CNN) is widely used in traffic speed prediction and autonomous driving and other urban traffic tasks. It is also well done in vehicle re-identification task {{cite:054caefc11a3dc97ef08640e52e5caf5d108efad}}. The purpose of vehicle re-identification is to find the same vehicle from non-overlapping camera scenes {{cite:31addf6d0274b3823e357890f5f10a601882248e}}.
| i | 95dc971435c367ccd6e15b4e6cd51585 |
A third possible field of future work involves the knowledge and
competence of the researchers themselves.
Researchers in the field of
software engineering should follow best practices
with respect to research methods.
Guidelines, e.g. the books by
Kitchenham et al. {{cite:24ea147743279b4f53a15c01e980f0c07620af9f}},
Runeson et al. {{cite:e8adbf7901273d078bd052207999fcb73c73cdef}},
and Shull et al. {{cite:98b953324796ddfd527f5522df0d8edb7fa41f80}}
instruct a researcher on how to do research.
We would welcome research providing instructions;
e.g. a checklist for researchers, supervisors, or reviewers;
on when not to conduct research,
such that we may avoid doing research blindly.
| d | 4d08c22a94c3fb615c2d11ae3fc5abe3 |
Classical black hole solutions of general relativity contain spacetime singularities {{cite:bdab1c0b1ffd0795bb9f713c427b56593608c6a6}},
which are expected to be removed in the quantum theory of the gravitational collapse of
a compact source (see, e.g., Refs. {{cite:28f0dbd7d6de633977a9fda755c38fb753f2fee8}}).
Moreover, charged and rotating classical black holes also contain a inner Cauchy horizon,
which signals a potential loss of predictability and also gives rise to mass inflation
at the perturbative level (see, e.g., Refs. {{cite:1e526013ef03574d45020af6a984d5346fadd9ca}}).
These latter considerations are the underlying motivations for the
strong cosmic censorship conjecture {{cite:149754945704e49d66c7e8cb031a4e885549e34d}}, {{cite:eb335132f31ac3a80369bf8740a56c41fa765665}},
which can be simply phrased as the fact that the evolution of some sufficiently regular
initial data should always give rise to a globally hyperbolic spacetime {{cite:b9e803ec04f19f17fc34677e32063aa34db545f9}}.
In particular, this conjecture implies that perturbations of the inner Cauchy horizon should
turn it into a curvature singularity.
| i | 3805b3405cbd8c871fab0d50d64c440f |
As empirical findings suggest that the image feature is more vulnerable, we first employ an existing image-based defense method that removes high-frequency component through JPEG compression {{cite:dae105c46c5cce0f1fff4b044303561fb23f7609}}.
In addition, we conduct adversarial training against the attacker.
Since generating a strong adversary is extremely expensive due to the simulation pipeline, we employ a strategy similar to Free Adversarial Training {{cite:8fea1ef4bb50f02d746fddc35e265bef7dcc07c9}} and reuse past perturbations by continuously updating the same adversarial object.
Specifically, we perform 5 updates to the adversary per one update to the model.
We combine the feature denoising {{cite:05e193dbfe458f37848d57a8e895caec4b7e0595}} with the adversarial training to further enhance robustness against image perturbations in particular.
We report the success rates as well as the average precision (AP) at 0.7 IoU to study the trade-off between adversarial robustness and performance on benign data {{cite:a612c69a6eb01e6af4a886737e9beaa05c2c65f0}}.
| m | 76853df45fb0add78c1b0a1089ebd335 |
RL. The RL group uses PPO ({{cite:6f7ce4ee91c5ef7ebbdce7b4b1dde570bfd0cb64}}) with GAE ({{cite:41d5e067712c7506b35b94505bc7609db6887b02}}), and use collision as its feedback. Every iteration contains 10,000 frames of data and 20 epochs of training. The test is performed after each training epoch. We ran the training process up to 1 million frames.
| m | e83b1c8d08d80fb4dbfc810a15f3c35e |
and hence {{formula:1157aee4-04a2-483b-b8c5-cbb1f68a1d01}} -a.s. that {{formula:7501a5c3-ce52-4abb-9866-6ffc7b84cf2a}} by (REF ) and {{cite:761d93f7958b8052c094c09459e845ec07590602}}, thus giving
{{formula:3b3b08fd-4ad8-4b7b-a1d3-1803b2dd0473}}
| r | 1545a3aed894f3345b07c67ce45dcd08 |
In this paper, we consider the general class of single-field inflation models in which an Einstein frame can be defined. We outline the essential qualitative features of these scenarios and propose a novel, analytically solvable model capable of capturing these features. Our analytic method uses the Wands duality {{cite:43d593dbc724e973aa3166276e03b27694f7edca}} between the USR and the subsequent constant-roll (CR) (or SR) phase, which is present in most single-field models for PBHs. Thus, it improves upon existing analytic approaches built around specific ansätze for the second SR parameter {{cite:5279015968f68ef2b389f19b617ce43c790f4190}}, {{cite:2b33eb873f57cca480495d2b0e9b940c6f9aaf19}}, {{cite:1d751df3f241866070d0a21f4e57e766680316aa}}. Moreover, we show that our analytic model corresponds to a continuous potential constructed by glueing together two parabolas and can thus be seen as a limiting case of realistic inflationary scenarios. It can also be thought of as a generalization of the Starobinsky model {{cite:17bf2b27be45bb0cf37f5be6320204607dab1959}}, in which the potential consists of two linear segments with different slopes.
| i | c6476b6740e104d90ca313d3c9196303 |
In 1847, Stokes {{cite:3749a73c3b2b0af1dad5ee7d4bee61ff7489d3c7}} derived a formal asymptotic expansion for the small-amplitude, periodic traveling wave solutions of the full water wave equations in infinite depth, see Figure REF for a schematic. Seventy-five years later, Nekrasov {{cite:b1ee718f3c2db47c14dbb6c90e83506378cf7cda}} and Levi-Civita {{cite:490c1ef93696b0e08a23664c5a41d80075afc5b6}} proved the validity of these expansions if the amplitude {{formula:4641879e-62d3-4d82-9d02-4276beb50e91}} of the waves is sufficiently small. Not long after, Struik {{cite:de3bb932d7d8392d3010ffce5a7552d542543f90}} extended this analysis to finite depth. The stability with respect to sideband perturbations of these solutions, now known as Stokes waves, was investigated first experimentally by Benjamin & Feir {{cite:92ba2f66d4182e86d483f939f1def4c4b61641a0}} in the late 1960s and immediately after supported by independent formal calculations by Benjamin {{cite:2207ca91f34b92ef8bffbc006545ad10fcbc9f17}} and Whitham {{cite:d81f2938e7bb77725a1c6decac2e5b29ce1d61d8}} using distinct methods. Both calculations suggest that Stokes waves are modulationally unstable with respect to longitudinal sideband perturbations provided {{formula:53f64238-5e42-47ca-a9da-94ec65ffff83}} , where {{formula:50f53576-a364-4818-b9af-dd8591d23279}} is the wavenumber of the Stokes waves, {{formula:06fb5eba-b553-47a2-8dec-7656825499c0}} is the constant depth of the water, and {{formula:2a79c5c3-a047-47e2-a691-87c00a4d5d21}} . This instability is now known as the Benjamin-Feir or modulational instability.
| i | 24fd52ebdc33695ef49a7e305874d56d |
Theorem 4 ({{cite:cea2cfd3408d989f9158cfc4dc5951a7f16c3f0e}}, {{cite:3e9f55f2758ff64a039bb744e5acee2869024899}}, {{cite:8a84e45d4cfbb3275c43d29b83ffcdf0be261c4f}})
{{formula:3f99e227-337a-43a9-8a7c-f07dd3bbfe83}} ,
{{formula:2a4fd9a8-381c-4388-b050-ad730bcc3a5c}} ,
{{formula:cdfa668b-71b4-4cb7-85f9-63cd7eb2e2a8}} ,
{{formula:1b454f9e-e4c4-4850-8b23-e4cfb27e412a}} ,
{{formula:34c55936-b3fa-4002-b730-40e5d6cb3151}} .
| r | ad70374a5da590eaf7ec54104a89a60c |
We first compare our PlaneMVS with a SOTA single-view plane reconstruction method PlaneRCNN {{cite:71d1f2f1168934792541547f2a612b28846995ac}}, which also serves as the baseline of our model. We test it on our re-implemented version with plane semantic predictions with the same training and testing data as ours. Tab. REF shows that our method outperforms PlaneRCNN in terms of both plane geometry and 3D plane detection by a large margin. As shown in Fig. REF , PlaneRCNN does well in obtaining geometrically smooth planar depth maps, but their plane parameters are far from accurate (e.g., the 2nd and 4th row of Fig. REF ), which rely on single-view regression and suffer from the depth scale ambiguity issue (e.g., the 1st and 3rd row of Fig. REF ). For AP without considering depth, we also get considerable improvements benefiting from multi-task learning and the proposed soft-pooling loss. Although PlaneRCNN is a strong baseline, Fig. REF clearly shows that our method better perceives plane boundaries, and our segmentation aligns better with 3D plane geometry. For mAP evaluation which considers plane semantic accuracy with detection, our method also outperforms PlaneRCNN by a nontrivial margin.
| m | 7bcdf193f4bee2f169a863fe57d37397 |
During cross-validation, the training set was split into five folds at every iteration, where one fold was kept as a validation set to test the performance with the trained parameters.
For the classification of Musky OC, we applied an oversampling method to the training data, excluding the validation set, to reduce the imbalance in the data distribution. The weighted F1 score was used as an evaluation metric because of the imbalanced characteristic of the datasets.
We configured the hyperparameter search space consistent with the models of {{cite:4723a96de748062215d0a8469764d9e2d6b196b5}} and a specific range for the regularization term {{formula:c9fc983c-1979-4695-93ac-a7a2f89be7da}} for our model. We utilized the Optuna framework {{cite:9e6f8fe422252a95ab4416cfac9eae2492062187}} by repeating the cross-validation 100 times.
After finding the best-performing number of hidden nodes of the KCNet, we set it as the number of hidden nodes for both the DOA-applied model and the Ensemble-DOA-applied model, and we used the same value of the regularization term {{formula:2f9f95a2-24ae-41ea-be9d-a246c054707e}} as was used for KCNet. Details of the methods, hyperparameter search spaces, and implementations are given in Appendix REF .
| m | 5b226dd157c0589bc4ced7da3486c9fb |
where {{formula:edff551c-6af5-426e-9b76-b5da6d474500}} is a 2-dimensional copula, see for instance {{cite:f6c81d5a43f68aafddc80d0551f4252069236c93}}.
To measure assortativity of a graph, {{cite:005eedb10b344d680f32bc2e1678110caa6985d6}} introduced
the assortativity coefficient of {{formula:09011665-1b70-435a-a326-5be2277adf51}} given by
{{formula:385aead3-a739-4cae-84fd-b84fe8073a5c}}
| d | 4466676b37669b60eca8814f697114de |
The presence of a coupling in the dark sector may not be ruled out a priori {{cite:9e6b446eb83021a89fa73cd5699ae09c08b5a7f7}}, {{cite:62b205364a4d00477f01a45ce234e296441ab642}}, {{cite:53eb5ceef1d8a3616d8c8490de9b436fc1afd9e1}}, {{cite:2f219977c1a30ea779ca0dd27d3cebaa858eecc7}}, {{cite:a0ade98cb168f3290312e1310343e8525c1ee264}}, {{cite:90a6cf44fa2dbdfca195e6d5594f7921dc98d4bd}}, {{cite:a10eff38c92689f0220bebf4379bf4cb4bf341e8}}, {{cite:64bb5be57e1137f64ece0a7b3befc83eca27fda7}}, {{cite:1bc9730b5868aad3a306d752359d329d96cbbe43}}, {{cite:1f3943951466e93cc227e1fa10a4010dbfc4d2f2}}, {{cite:e0bebbe92b783531114e37cd5e229efadca15110}}, {{cite:716db2ef5b73f5351c91526aff8e582992c73e6f}}, {{cite:9a19568cd27ec06b1857a4db81225a95131c352a}}, {{cite:cac6d3e3051ce1d3cb6da31d24c0c129ed3ad6d4}}, {{cite:46ce8a25c7049dad252ba2a43cf3c0a724b673e5}}, {{cite:f7ed9a8a6bff219c0ef8fc2aee86ccb996db592e}}, {{cite:c3ba1214e2d6d806eff84cc85d899273dc942579}}, {{cite:1babacc8bd507abc3fcb884a49cabb7a6d739472}}, {{cite:77c42b858b01efb73f880f2282fa2ccaba4897fe}}, {{cite:ce89d0e6e87558c8168ceeb42874fa7d5210ecd7}}, {{cite:3e0ffdfbe69b0a390393990be4398ffc75d47e85}}, {{cite:3bdb4913dbfbf2e460f5047a1b616fdf67845d10}}, {{cite:65cc2515256884f4de2ace23603d548b0c1e8058}}, {{cite:8e58ec1d5578f7731d58543d1011cdc9ec651876}}, {{cite:b06027d90188e236f478bc9647fb54b288f90e98}}, {{cite:6fffaf6ba9ba25e7a566567740e6bff82d608a72}}, {{cite:8ea96dc093d5d7fb97e2bed552f50333d2254585}}, {{cite:6f911f79755a279fd0a8e4be93721e85082f99a2}}, {{cite:5ff37006c3428586f6484b0c59902a9c32ba9d33}}. It naturally raises the question whether the interaction was there from the beginning of the Universe and exists through its evolution or is a recent phenomenon, or it was entirely an early phenomenon and not at all present today. A modification of the phenomenological interaction term by an evolving coupling parameter instead of its being a constant, may answer this question. A constant coupling parameter indicates the interaction is present throughout the evolution of the Universe {{cite:90a6cf44fa2dbdfca195e6d5594f7921dc98d4bd}}, {{cite:d3ebe19ad8bef8a156d4ce575089df687695a391}}. In this work, we have considered the coupling parameter to be evolving with the scale factor. Interaction with an evolving coupling parameter is not studied much in literature and warrants a detailed analysis. Rosenfeld {{cite:1a02436f1f89a4c319576032d8362b7b8f20c481}} and Yang {{cite:95300dce9899418d33d1944fa23ea0e476967947}} have considered the dynamical coupling parameter, but the motivation as well as the analytical form of the parameter used in the present work are different.
| i | 2c2b55ee1c7d26b0375bc126a2fbaf24 |
This work could also shed light on the double copy theory {{cite:1803817dffe1f53da7cd8b060c7e9104b1593de9}}, {{cite:584a9c3bc308e64e5ebf1d80294be5dd05543d1c}}, {{cite:079a096804cdddf91d76469371dfa48ec447c905}}, {{cite:4242e9042eea22e440846eef14430f423df63a03}}, which is based on the proposal “gravity = gauge {{formula:81c4932f-869e-431b-9b78-35f2bee5d599}} gauge". A classical solution to Einstein gravity could possibly be obtained as a product of two copies of the non-Abelian gauge theory. In this approach,
the ghost sector could help us understand the relationship between the general covariance of gravity theory and local gauge invariance of non-Abelian gauge theory.These issues will be discussed in subsequent papers.
| d | 84e1d58dd2ce8c6311e0b03f4fbcb169 |
WKB method. The Schrödinger-like wave equation (REF ) with the effective potential (REF ) containing the lapse function f(r) related to the regular black holes is not solvable analytically. Many numerical methods are developed to compute QNMs of various black hole spacetimes in the literature.
One of these standard methods is the WKB approximative method that was applied for the first time by Schutz and Will {{cite:2255ebfc3ffd885642c516b62bb008b8144e0e4a}}.
Iyer and his coworkers developed the WKB method up to third order {{cite:ddf77040acbed24a2292b3a2ca85bb31f8cbcbb0}} and later, Konoplya developed it up to sixth order {{cite:78d418be8b504b0488c30d3d4a27aa2f823f25d7}}. This semianalytic method has been applied extensively in numerous black hole spacetime cases, which has been proved to be accurate up to around one percent for the real and the imaginary parts of the quasinormal frequencies for low-lying modes with {{formula:e3a6c632-3c6d-4860-8922-a34a35785cc4}} , where {{formula:2c4a8e01-3eb6-429b-811b-3b0ef9f77fc9}} is the mode number and {{formula:49ccc68f-6fc3-4540-9205-ab35232384c6}} is the angular momentum quantum number. In this paper, the third order WKB formalism is applied since the 6th order WKB method consumes too much CPU power for some cases of regular black holes.
| m | a7842893233f50bbf05e4e603530d893 |
One promising direction for improving our proposed methods is to improve the narrative coherence evaluator.
For more accurate coherence evaluation, the coherence evaluator needs to have world knowledge and common sense reasoning skills.
Imagine the story of Cinderella.
To be able to identify that the absence of event The prince falls in love with Cinderella leads to coherence reduction, an ideal coherence evaluator needs to recognize that this event has a strong causal relation (in this case, precondition) with the next event Cinderella marries the prince.
Recently, several techniques have been proposed to provide language models with more world knowledge {{cite:a518647e6b86c6ff04b91ae3af8953a752e36e23}} and to enhance the common sense reasoning skills of language models {{cite:1085f05ed957d983c3d636a7ebaa234b12077f40}}.
Evaluating the coherence of a narrative using these LMs can potentially improve our proposed methods.
| d | eed7fe95b3cd8eaf1bb932b4d27b9102 |
For the ease of use, we define MNACR, EF-0ACR, and EF-3ACR which are MobileNetV2 {{cite:573ebf801473cd24ba9887a2d05ee1bf6333413c}}, EfficientNet-B0 {{cite:8f0c0362f11c32e3add7cb2b4d47ffefda44e671}}, and EfficientNet-B3 {{cite:8f0c0362f11c32e3add7cb2b4d47ffefda44e671}} being trained using our ACR Loss versus the corresponding MNbase,EF-0base, and EF-3base being trained using the widely used L2 loss. We uses 300W {{cite:fe4de6d8711102e00fceda76ed2078f900283db1}}, and COFW {{cite:8ff69aa792862c09a3000e1570518f02527cce1f}} dataset for our experiments.
| r | fdc123d1c1442c643a01e76c3920930d |
(i). Task masking. This approach masks a subset of neurons at each layer for a task (identified by task-id). Since the mask can indicate what neurons have been used by previous tasks, in learning the new task, the system can freeze the used neurons to prevent CF of the previously learned knowledge. The most popular system is HAT {{cite:8c8e3b82ee639b377d5cc4072798ac212f385cb0}} in CV. HAT initializes a task embedding {{formula:659827cf-7942-4ada-a403-f1ec82cebd59}} for each task {{formula:c699cc4d-62b8-420d-a2f8-07449c2463a2}} and each layer {{formula:bfb3486e-3788-4137-814c-336e4e7dc247}} in the network. A {{formula:0c2a9cc7-dad3-442f-a635-915baf282551}} function is used as a pseudo-gate/step function along with a large positive number {{formula:acae1b1b-90e4-43cf-a5a0-9df5f660151e}} (hyper-parameter). A mask {{formula:fdf12e93-1a8d-4932-ba22-637d6defc4b0}} is given by {{formula:87b33881-ff29-4a0d-ab7b-4012d334d609}} .
During training, the mask is element-wise multiplied with the output of each layer {{formula:d0ce16fc-fb49-41cf-b965-87bec5906fb6}} . In backward propagation, HAT blocks the used neurons (indicated by the mask) by previous tasks via multiplication of the inverse of the mask with the gradient to avoid CF.
In NLP, this task masking mechanism has been mainly used in the adapter layer to prevent CF, including,
| m | 492cb0dfce14d2f10aab9d99f1f7964e |
Our construction differs from the T-dual field redefinition of the NS-NS bosonic closed string action {{cite:df3ba2fd441596ca0b82a59f51ff2b9bd93f5f75}}, its Lie algebroid description {{cite:32ae7ce7d24aa3b5c2405081fa6e95d61f01b6a2}}, {{cite:cb3715fef4822528cd558c57a4d11aed73c2b272}} and their respective generalized Ricci scalars, for example because of our different choice of the basis of the fiber, that treats equally the metric and the antisymmetric field, and also because of the introduction of the generalized Lie bracket. Another big difference is due to the simultaneous presence in the ansatz for the vielbein of {{formula:29b32990-acc5-4421-89ef-5b74d5cc083f}} and {{formula:7588cee9-ac5b-44c4-9873-e11c133de15f}} , so that the anchor map is forced to be {{formula:c4173447-f252-41a6-a4d3-97c007cecbea}} , while so far just {{formula:bc3f31db-f35e-4ff6-bf86-5970367f6217}} was employed as anchor in the above references. Clearly if we had to choose just {{formula:18e9591e-54ad-4bc3-9ef0-99227a135289}} as new basis for the 1-forms we would not get a block diagonal generalized metric on the CA {{formula:95f35593-3cf6-49a0-986d-aa255ead675d}} . Notice that our systematic method returns a well-defined connection on generalized vectors, provided that a generalized Lie bracket is given, and it is simple to define a curvature tensor in our framework. This is not so obvious in Generalized Geometry. We did not double the dimension of the base manifold. A further analysis on the relations with DFT is beyond the scopes of this work: however it is rather reasonable to expect our action functional to be some limit of the DFT invariant action of Hohm, Hull and Zwiebach {{cite:99a66298c1bc7e4853efa8b47ba93f6734bf3f50}} when the section condition is applied. A similar setting, namely a graded Poisson algebra with the trivector {{formula:147f1fb5-173d-4ccc-ad2d-01d8c3618eaf}} , was related to the section condition of DFT in {{cite:3a2e4cf674379792e742b9a740ae8695ffd1fe38}}.
| d | 9a94a85af2b9a66b30622a59d03cf5e0 |
This question has been the subject of a substantial body of literature. One line of works considered the case where gradient methods converge to minimal norm solutions on kernel regression {{cite:613c4f3a45fee75787d44ae13dd43cddb01121a7}}, {{cite:e0c249f1f5201ceacc81041767fc240bb8c0425c}}, {{cite:a09504b9b9a9da1ea7a06b6949823a99c16e6e12}}, {{cite:db812e28a53d45546e9566858e2fc77be04430e1}}, and then analyzed the generalization properties of those minimal norm solutions. However, the phenomenon of norm minimization has only been proven to occur with the quadratic loss with an appropriate initialization scheme. Another line of works focused on overparameterized models, e.g., neural networks under the Neural Tangent Kernel (NTK) regime {{cite:c8cad8846e42ba9e6fb440e933afe7ec02ac2aac}}, {{cite:6bc6d98cd23cb95d54aa703c9e5cff1fa4bcacae}}, {{cite:5bdaae8bcd23fdd6f849e4a7c800a9c0565dc2b3}}, {{cite:9ada204cad4a85d9eff508c6edc5294683e16857}}, {{cite:cf5444ee27d4c37c06741a96d802f194677505e9}}, proving that overparameterized neural networks trained by (stochastic) gradient descent ((S)GD) have good generalization properties on certain target functions, e.g. polynomial functions. All of these works have made significant progress on the interplay of optimization and generalization. However, they focused on studying specific settings, such as the NTK and models possessing minimal norm solutions. In this paper, we propose to study general loss function conditions that induce direct connections between optimization and generalization.
| i | 787fb88563b35ed16ae1b70f35462d7d |
More information about neutrino-nuclear CCQE interaction can be obtained from
the analysis of the charged-current QE event
distributions and {{formula:7bca6525-ac83-4057-8d4a-b4c1506cf718}} differential cross sections as functions of
{{formula:bad876e6-4ca1-40a2-820a-82d08ddba7f2}} (squared four-momentum transfer) {{cite:cd301e2096a1bea0a772410761f50fd05aa2fe14}}. The shape of these
distributions is sensitive to the {{formula:b934eed6-2b08-40f8-ba7b-8fd66b0645a6}} dependence of two vector,
{{formula:ae0fe085-a260-4066-9cd1-663a28cd4312}} , one axial-vector {{formula:d1c1eb5c-154e-47de-87c6-a3e5e5e41f3c}} form factors and nuclear effects.
The vector form factors are well-known from electron scattering. For the
axial-vector form factors the dipole parametrization with one free parameter
{{formula:3f51aabb-e509-446c-ad1d-5c90a1037924}} (axial mass) is mainly used. This parameter controls the {{formula:4ece175a-e499-462b-a56e-285515f09ece}}
dependence of {{formula:d1490cef-8c03-4df0-8a42-5634f8767bdc}} , and ultimately, the normalization of the predicted
cross sections. The dipole parametrization has no strict theoretical basis and
the choice of this parametrization is made by the analogy with
electroproduction. To describe the nuclear effects, neutrino CCQE models
typically employ a relativistic Fermi gas model (RFGM) {{cite:8c5d05dc721b4bbde421572997b2dcefbb18e921}} in which
the nucleons with a flat nucleon momentum distribution up to the same Fermi
momentum {{formula:b649312e-42f2-4dfa-9a8b-46ffddf1ceb1}} and nuclear binding energy {{formula:0a3cd0f1-ff0b-4aac-8768-a426b28fc61a}} .
The experimental values of {{formula:91a77299-8d3a-4cb1-9770-8d8bef63ed32}} extract from the (anti)neutrino CCQE
scattering data, i.e. from the analysis of the shape of the
{{formula:e7106829-c11c-456d-876e-b4dc03207a6f}} - distributions and from the direct measurements of the total cross
sections. They show very wide spread from roughly 0.7 to 1.2 GeV and the
resulting world-average {{formula:7e0f35fa-fb1c-4f72-853b-455f73c7c0fe}} GeV {{cite:20e51d2de297ccd5be99693134b48d633f25278d}}.
| i | 65cbebd74fbc72201b4d21a442528a8c |
So what is the reason for the sign problem in Eq. (REF )?
The answer lies in the linear constitutive relations (REF )
defined in the lab frame. This is valid for a static medium and not
for a moving medium. The linear constitutive relations should be defined
in the medium's comoving frame as the relations for three-vector fields
and get modified in the lab frame in a nontrivial way {{cite:20ea68e8cc72fba1e30a7e59750af3227ee63f59}}, {{cite:4f8ecdec290005316d19d6a32e7386e59b1463b2}}.
The covariant form of the constitutive relations (REF )
meets this requirement and therefore leads to Eq. (REF )
having an implicit Lorentz covariance in the SVA.
| d | dd332f1ca37353c859ecdb04bd22f1d0 |
The Cityscapes dataset {{cite:f5fbbb7ee51b843466cf5af899bcfe4a7ca41cc9}} has 19 classes. Its fine set contains high quality pixel-level annotations of 5,000 images, where there are 2,975, 500 and 1,525 images in the Training, Validation, and Test sets, respectively.
Like other works {{cite:48a104863bf5183d64d2deb2c75716023031039a}}, {{cite:3d12866c9f7c2d95752241102432ca69d492b0ef}}, we crop the training images to 769{{formula:1476458d-2f1a-4a5c-a0c8-c2af4d73bbb9}} 769 during training, and keep full-resolution 1025{{formula:310263fa-cbe6-4e23-8375-7ef820cc97ed}} 2049 during inference. We report our results https://www.cityscapes-dataset.com/anonymous-results/?id=86b37... in Table REF and also visualize our feature maps and results in Fig. REF (the bottom two rows).
{{table:3abdfb51-d21c-4de5-b4e6-c1e2965bd26a}} | r | 517b62540b50406c3330c9f897dc42f6 |
Thanks to their low cost and high mobility,
uncrewed aerial vehicles (UAVs) may soon take over important tasks including search and rescue, delivery, and remote sensing.
In the next decade,
UAV taxis may also redefine how we commute and, in turn, where we live and work.
For these and other applications,
UAVs will transfer real-time data to and from the mobile network,
requiring reliable connectivity for command and control (C&C) and mission-specific data payloads {{cite:1557de0451ffe70e358628f8b02323ba4a000fba}}, {{cite:89c01df426bf359423ade87e27aa585b085587cf}}, {{cite:27d7712205d498fcbc2438d8de3f8b260cbf2a4c}}, {{cite:c57c9afbee3512013d7287be4f43f173b41a05b0}}, {{cite:27c9adfec8303e86b364136e8a7977b7dd653726}}, {{cite:d7aff3fcb6063fb8e2e216cc7f4abf7c1bbb2522}}, {{cite:92752e93c663d55e54ac99e6e9abfedd71da5ecf}}.
| i | fa45dae8c5c695e33011910074847fb6 |
It should be noted that reachable accuracy using the transfer learning method with two base models and two classifiers is reasonable, while the high-tech deep learning methods using complicated structures are able to reach an accuracy of more than 99.79% {{cite:39595794f924b73e586bc44041af2a793193cbf7}}, {{cite:fdb58c67e63d91a8691a94fb5dbfc276d06c9aab}}, {{cite:f299b0f422f3d2e25035f2025e64fd0faf22e9ed}}, {{cite:72e83b3dfa513941b171fee4ef07b90453248dec}}, {{cite:13bab088617cb731460cf3630f04c9b2abb86c96}}, {{cite:bd8f594ecfd0429140b0a311b6d0c2414999de6b}}. The developed codes are available on the Kaggle server with execution details{{formula:4e7ed78d-cc02-4220-a311-82db2b957e4f}} .
{{table:04c18e1a-07c3-4df5-b766-72269bdc0c8a}}{{table:10a16fc6-7f60-4ef5-b083-553c44a8affb}} | r | 0e2f24d5feaa50d44d002c8630a28bf2 |
Fixing {{formula:c60f9a4d-c998-4f2c-bc48-6f3b5202140e}} and following the standard notations of {{cite:fe72d360ddb3a45c92e6571209342b60606eef9b}}, {{cite:1dd28207ae33a306bc747b3515ca7cb03b76571a}}, the {{formula:5f273a22-e295-49ca-8714-4533b054e1e0}} -shifted factorial for a finite positive integer {{formula:901ed085-c19f-472f-b519-fa2218ab865a}} is defined by
{{formula:b2617fc1-4d10-4816-9deb-6c4950b6ab97}}
| r | a87a2235cb4709f52cf14194c826eb0a |
From the beginning to the present, two-stage approaches
{{cite:1a7e551c54e8be0407ec02f6719bd0789ce37c8e}}, {{cite:f8adcb0afcaf995c04be6d2673a966b250ec3083}}, {{cite:ce782536345e6bfa42cd3e6f42b7b7aa6cfa8b7d}}, {{cite:203d20bdee9f3e186ae3c5dc1cf7c1241a428216}}, {{cite:7d9580fb3917e95a03fa419a722576882309ae3f}}, {{cite:40b2b70eb0e16c2cdc4729621b281519c8334a93}}, {{cite:874f2b913e9f4dc6c4a43dd295d01dbd8e8c0ce6}}, {{cite:ccdfe88299f0b327f5a480676aa607c92645e271}}, {{cite:acd45d7f0e7f9f0f63dcb749e73d32cdd3e6951d}}, {{cite:adb1aef11ce8379e6dc8ca7bf9a2b6712704bfe9}}, {{cite:ab2be403903e2878c7bef5d3af08c94afcb40068}}, {{cite:f6351aa4b0819d2b96a0184a2f26cbaccafcd3e3}}, {{cite:8b5660a3a9b6895548a5165f7ae4f480435e031e}}
as an intuitive approach build the method upon the off-the-shelf object detector {{cite:a249db3e7f66e973914ff47d775c92cb8165e3e2}}.
In the first stage, the object detector selects some of high scoring human and object bounding boxes from detection results and extracts appearance features or crops images of the selected bounding boxes.
In the second stage, for each of the human-object pairs, the human and object appearance features are used to predict the action class scores separately or fused with supplementary semantic information as a pairwise interaction feature to predict action class scores directly.
For the two-stage approaches, the difficulty lies in the integration of semantic information of human-object pairs. With the split human-object pairs, spatial information can be extracted to enhance the appearance features
{{cite:1a7e551c54e8be0407ec02f6719bd0789ce37c8e}}, {{cite:ce782536345e6bfa42cd3e6f42b7b7aa6cfa8b7d}}, {{cite:203d20bdee9f3e186ae3c5dc1cf7c1241a428216}}, {{cite:40b2b70eb0e16c2cdc4729621b281519c8334a93}}, {{cite:874f2b913e9f4dc6c4a43dd295d01dbd8e8c0ce6}}, {{cite:ccdfe88299f0b327f5a480676aa607c92645e271}}, {{cite:acd45d7f0e7f9f0f63dcb749e73d32cdd3e6951d}}, {{cite:adb1aef11ce8379e6dc8ca7bf9a2b6712704bfe9}}, {{cite:ab2be403903e2878c7bef5d3af08c94afcb40068}}, {{cite:f6351aa4b0819d2b96a0184a2f26cbaccafcd3e3}}, {{cite:8b5660a3a9b6895548a5165f7ae4f480435e031e}}.
Furthermore, fine-grained information like human pose can be used as supplementary semantic information {{cite:203d20bdee9f3e186ae3c5dc1cf7c1241a428216}}, {{cite:7d9580fb3917e95a03fa419a722576882309ae3f}}, {{cite:874f2b913e9f4dc6c4a43dd295d01dbd8e8c0ce6}}, {{cite:f6351aa4b0819d2b96a0184a2f26cbaccafcd3e3}}, {{cite:8b5660a3a9b6895548a5165f7ae4f480435e031e}}, and graph-based methods {{cite:f8adcb0afcaf995c04be6d2673a966b250ec3083}}, {{cite:7d9580fb3917e95a03fa419a722576882309ae3f}}, {{cite:ccdfe88299f0b327f5a480676aa607c92645e271}}, {{cite:adb1aef11ce8379e6dc8ca7bf9a2b6712704bfe9}}, {{cite:ab2be403903e2878c7bef5d3af08c94afcb40068}} are also well suited to the understanding of complex semantic relationships between humans and objects.
Without considering the object detection process, the two-stage approach can design a complex model to fuse abundant semantic information of human-object pairs and achieve high accuracy.
However, processing all of the human-object pairs is time-consuming, and the appearance features limited in the bounding box are lack contextual information when the human and the object are far apart.
As shown in Figure REF , the spatial distribution of a widely used HOI detection dataset, HICO-DET {{cite:1a7e551c54e8be0407ec02f6719bd0789ce37c8e}}, HOI instances with the center distance between the human and object bounding box more than a third of the image size commonly exist.
| i | 6c5da8f173430024915a0514827c89c2 |
The first rigorous study on data compression was published by Claude Shannon in 1948 {{cite:7d5658f44e088c2d910a77086a76de8c13504570}}, in a seminal paper that constituted a firm setting in the foundations of classical information theory. In that work it was considered a {{formula:1a1eb495-9d09-46ca-8f0f-b209c7c2cde0}} -ary alphabet as well as a collection of uncorrelated random sources of letters (whose probabilities depend only on the {{formula:8ebcf36a-afd4-432b-889d-6fc03dd4374b}} letters that immediately precede them) with the aim to examine to what extent could one compress {{formula:6ea73c86-19b1-48c1-bae9-ce9baa0bb252}} symbols emitted from a particular source. Shannon found that any process of data compression results limited by the entropy itself such that a codeword whose average length attains the entropy can be regarded as optimal. In other words, this result led to quantify the average amount of information (absence of redundancy) by simply measuring the entropy.
| i | 1d06c5ac71a5720b237b3bea8b113893 |
From the Tensorflow dataset, 10 keywords: "Yes", "No", "Stop", "Seven", "Zero", "Nine", "Five", "One", "Go" and "Two", have been chosen to explore the functionality of the pipeline using some basic command words. Considering other works comparing NN based pipelines, 10 keywords is the maximum used {{cite:e6867fb4eb34e4c18856a4b811caf61f9befe45b}}, {{cite:1221b4764553789afc0b94ba78dc1e9ab9618250}}. Among the keywords chosen, there is an acoustic similarity between "No" and "Go", therefore, we explore the impact of 9 keywords together (without "Go") and then the effect of "No" and "Go" together. The approximate ratio of training data, testing data and validation data is given as 8:1:1 respectively with a total of 3340 datapoints per class. Using this setup, we will conduct a series of experiments to examine the impact of the various parameters of the KWS-TM pipeline discussed earlier. The experiments are as follows:
| r | 3695c0367db27101c2277d44dafad8ce |
As we have discussed earlier, in the analysis we have performed
we kept {{formula:4a148f61-4bb5-4163-89cf-bd26a9d740e2}} and {{formula:afd41458-0fd5-40f7-9da3-669926dd2f37}} fixed to certain values.
We have obtained results for {{formula:dcfa49bd-746c-4a52-a65c-61a0e2f50d7e}}
and eleven values of {{formula:a8e23132-470a-4863-9a72-f34b6af75b43}} from the interval
[0.40,0.60]. In what follows we present results for three reference values
of {{formula:e30ca686-9565-46d9-bf19-548ed249e340}} , 0.50 and 0.58,
which belong to, and essentially span, the {{formula:86a46a0e-21c8-4121-8a6c-8762d052c672}} range of
allowed values of {{formula:05ff2d26-45b8-42c2-a077-a27f3a7de286}} obtained in the latest global
neutrino data analyses {{cite:33fcf0d66a827611b5e20ad3ff72bd9cce2237a8}}, {{cite:86d3662d2c6564f8224d4613c1f5de77a6e20921}}.
All results are obtained assuming 10 years of ORCA operation.
In subsections 3.1-3.4 we present results for NO neutrino mass spectrum.
Results for IO spectrum are reported in subsection 3.5.
| r | e15a7c2450ad18652ac2b9eaa0672bee |
The other class of the noise based methods introduces adversarial noise as well as adversarial training to improve the model robustness {{cite:79b068652c7b9d0d3b386dc942ba69e200b4f8dc}}, {{cite:a9d170a79896474940380d8471a199efc832cc63}}, {{cite:540def64d311bfdadd03b0e416e87c355fab5279}}, {{cite:7540ddfde83fe59ef14cbb4edca986413331392f}}. He et al. propose an Adversarial Personalized Ranking (APR) model which can enhance the pairwise ranking method BPR {{cite:bfec70e09fda40f31f379f4660d4f2a9b88953ca}} by performing adversarial training {{cite:a9d170a79896474940380d8471a199efc832cc63}}. Tang et al. propose an Adversarial Multimedia Recommendation (AMR) model for robust recommendation of images, which is trained to defend an adversary of perturbations to the target image {{cite:540def64d311bfdadd03b0e416e87c355fab5279}}. Yuan et al. propose a general adversarial training framework, which can improve both the robustness and the overall performance of NN-based recommendation models {{cite:7540ddfde83fe59ef14cbb4edca986413331392f}}.
| m | b92ce2085638d6397d3422f65750e0a9 |
Shared bipartite quantum systems, and in particular shared entangled states, are among the most basic resources in quantum information theory. Several developments have demonstrated the usefulness of entangled states in completing tasks that are constrained by the causal structure of spacetime. Two cases of interest are summoning (and its variants) {{cite:b3aa352000bee50f48ab1c04ca51495d3eaf4a23}}, {{cite:095488d9f8deb96a48e4b88b1b53ac1f6157dc11}}, {{cite:581d4a8415888fcd94aaefec9bbd5f5360eb5b4e}} and position-based cryptography {{cite:0c1abd79f081fdc8190f148bbb4a522bb5e4943e}}, {{cite:63502f45325784bd00d97fc1ddabfff35e2fae2d}}.
Fig. REF describes an instance of a summoning task, which highlights an interesting use of a maximally entangled state. Note that this entangled state must be distributed between two spacetime regions—if the entanglement between the relevant spatial regions is established too late, the summoning task cannot be completed. Similarly, entangled states must be distributed between two spacetime regions in order to perform certain position-based cryptographic tasks {{cite:63502f45325784bd00d97fc1ddabfff35e2fae2d}}, {{cite:40f695cc75bc2b36793c0c0f71327c5cda1e6268}}, {{cite:e69559d5faf12a0c99e79da0a90c1ddfba9740db}}, {{cite:7b2d4c07dcfb201765745dd518601239995e3276}}.
{{figure:8e52c4e1-85e7-4fa1-99b2-ab2bed4a5821}} | i | 3d3d919640c0e91d37ebd3cb9436c9fc |
BC with policy improvement. This algorithm utilizes the entire dataset to estimate the Q-value of the behavior policy, {{formula:8ea0ff1c-9615-4d66-9d54-5b23eeb2d0db}} , and performs one step of policy improvement using the estimated Q-function, typically via an advantage-weighted update: {{formula:06b75d82-abcd-4d23-8989-5e5dd3bbb59d}} . When would this algorithm perform poorly compared to offline RL? Intutively, this would happen when multiple steps of policy improvement are needed to effectively discover high-advantage actions under the behavior policy. This is the case when the the behavior policy puts low density on high-advantage transitions.
In Theorem REF , we show that more than one step of policy improvement can improve the policy under Condition REF , for the special case of the softmax policy parameterization {{cite:36af428846fcc35ae187267adab6d4dbc69b11d9}}.
| m | 9c606cb4b5f0b8f3b209e827edc6cec3 |
The PDFs resulting from SM NLO fit are presented in Fig. REF demonstrating the contributions of the fit, model, and parameterisation uncertainties. The NLO values of {{formula:6e5e4c2c-2690-4d42-82d3-71d21e9cadc4}} and of {{formula:f1c77134-5a95-4ff4-8486-b2251048ba8c}} are determined simultaneously with the PDFs as
{{formula:0a6d0891-b437-4154-8458-3537f55ce552}} ,
and
{{formula:82f9d260-2ebc-40ab-9aaa-39318e351add}} .
These are consistent with earlier CMS results {{cite:97aec3a6fa6384309bdd06e984ce3ab44a62c8bd}} and Ref. {{cite:e8503066985d872aa71ceff9c955d6b380e59139}}, respectively. The uncertainty in the value of {{formula:64f63c0b-7774-4a8a-8b17-17a79313e5c2}} is dominated by the scale variation, which is significantly larger than in the NNLO result of Eq. (REF ).
{{figure:2d1680ce-ce64-4d04-b4c6-2604c32677b1}} | r | 6636aab3e889af5d22dd1d71a8d76cac |
We name Algorithm the extrapolated proportional-integral projected gradient method for the following reasons. First, if {{formula:711dd733-1d8d-4660-ab10-2a91499deb95}} , then Algorithm reduces to the proportional-integral projected gradient method (PIPG) {{cite:0160423d7b30a1ef7c715f894e09d852c5027e62}}, {{cite:8b5d5355bfb78bfea0f1fe79aec67ebf7b0bbde1}}, {{cite:eaab2a4e40b8bb3fd075b96a42e9e49b6879b3fd}}, which has been used in distributed optimization {{cite:4a21bdb719c75d924aa82933b90b204e35ac8c35}}, {{cite:5a9177ade3f18f2d1450223fcab59a1215f43aef}} and optimal control {{cite:8b5d5355bfb78bfea0f1fe79aec67ebf7b0bbde1}}, {{cite:c25ff035eb6efd7915ab8c6f020c4bf6129f1dac}}. Second, lines – define an interpolation step if {{formula:cbee172d-aa2f-40c5-85cf-c486f4f3de66}} and an extrapolation step if {{formula:68f9f913-610e-4541-90e9-4db816e3d30c}} ; see Fig. REF for an illustration. Since extrapolation improves practical convergence {{cite:b64e09ea5577ee48dc7ca2d60718d075279e101c}}, {{cite:0160423d7b30a1ef7c715f894e09d852c5027e62}}, we will let {{formula:e6deb90c-8019-4308-a3be-7c03fcd009ab}} in Algorithm , hence the name “extrapolated PIPG".
| m | e25cee5400785f2539f8fc5fe111b00f |
We compare {{formula:6da46a6e-df28-41de-b9b9-d93e869a53f7}} with supervised data valuation methods, LOO (Eq. REF and Truncated Monte Carlo (TMC) version of Data Shapley (Eq. REF ) {{cite:1c468cc3f15f46df76f74d3193703f33b8144c76}}, as well as a baseline method that randomly assigns data values. All these methods are applied on Assessed Set's features extracted by the pre-trained MAE.
We design four experiments to evaluate how selecting data using the different data assessment methods
can affect the classification accuracy. We report the averaged test accuracy on Validation Set using logistic regression models (LRM).
| m | 1e2071e8c604bf7b3749fdc53ced54b4 |
Fig. REF shows the performance of the proposed angle-based beamforming algorithm. For comparison, the algorithm in {{cite:24ad07f87910cfad38cc48382c22b7478db7c60d}} which assumes full CSI is presented as “Benchmark 1”, while a beamforming algorithm based on angles estimated by the MUSIC method is presented as “Benchmark 2”.
As can be seen, our proposed angle-based algorithm achieves nearly the same performance as both benchmark algorithms.
The beamforming algorithm corresponding to “Benchmark 1 ” achieves the best performance, but requires full CSI. Although the angle-based beamforming algorithm corresponding to “Benchmark 2 ” is slightly better than the proposed algorithm, it adopts the MUSIC method to estimate angle information and thus has higher training overhead and computational complexity than the proposed angle-domain estimation method.
{{figure:e062e6fe-e70b-4266-b77b-6f8b4a720500}} | r | f35922e66e81353aafea831f54278cb4 |
Table REF shows the fraction of valid molecules generated by GRASSY, GSAE {{cite:de0a2431adffc6fdc271a30a96c59148764cb316}}, GraphAF {{cite:184f2c341612b4cf734c1a0dac47c2841fc4a5ca}} and MolGANhttps://github.com/nicola-decao/MolGAN (full RL version with hyperparameter {{formula:cd99d036-5d17-4402-958a-b2d2e633aa58}} {{cite:2fc717eb2fec9647056decf41221c21f816be74d}}, according to the criteria above. The minimum and maximum number of atoms in the training molecules are listed to justify the choice of the validity threshold used to mark small generated molecules as invalid.
| r | 996795b1f003af92b785598d1ad0fa9b |
Before our transit searches we: (i) rejected data with quality flag values {{formula:88ee69de-d5c8-4c2b-8f4f-036987347d7a}} {{cite:ff3b3ff58ac4f77f588417fc0b100e2ba2c00bd4}} leaving 14827 cadences; (ii) recursively removed
outliers exceeding the median flux (of the entire light curve) by more than three standard deviations (`sigma-clipping'),
rejecting 69 data points (c.f. 20 points if the data were Gaussian distributed);
(iii) detrended
this cleaned
light curve using
Gaussian Processes (GP)
as described below. Sigma-clipping was implemented using lightkurve {{cite:7151892511c30b6cf0be44230b138881e6884456}}.
| m | 9c1c8fcdb6cce996ab4cc21536d7693a |
We evaluate the proposed approach on three publicly competitive fine-grained visual classification datasets, including CUB-200-2011 {{cite:ea8114aef6f118de9d84db11464b066d62ebce25}}, Stanford Cars {{cite:b6966ca8486de8fc81e26e6ca6dea1ba71144dc9}}, and FGVC Aircraft {{cite:dbfb7b395e120f10758d4a4244e515c4f5cff350}}. The detailed statistics with category numbers and the standard training/testing splits are summarized in Table REF . We employ top-1 accuracy as evaluation metric.
{{figure:0eaacffe-c6fa-4345-a42d-6bee32d37521}} | d | 25ad308ffd587621719d898e7aefe593 |
Let {{formula:09c8ec79-38ac-49ef-9c70-e2dfe25301f7}} be a Hilbert modular form congruent to {{formula:23c1354f-2b59-4485-9351-97c79dce2259}} modulo {{formula:80e3f1f9-4809-46cb-b9a9-865018124603}} which satisfies {{formula:61589c84-82b8-45fb-9695-29acd357ae46}} and {{formula:8d8806b3-7934-48d1-bb30-02b8382038a2}} . Notice the existence of such {{formula:b27928e2-9e6d-487c-88c0-d96df1d87a7a}} is guaranteed by level-lowering {{cite:577eeb05effea7f1b8ffde3216620c08df4ff04a}}.
Then the theorem for {{formula:840ac0af-5eb0-4161-a1e8-3491fd7639e5}} follows immediately from Theorem REF and the main result of {{cite:e5f3bef1857b4c54ac68a1207332ec300869bdb1}} concerning the analytic {{formula:fffa7e80-d692-43b7-a1ff-e886cd6091d6}} -invariant. Since all primes dividing {{formula:c4f44660-47f8-499f-a98c-76ae4928d2c1}} splits in {{formula:49a672c2-2fae-42bd-bf6b-65b526d20ea5}} , we can apply the same method as {{cite:5f98972a51337e3ef311f67508414a2c568e01b2}} and conclude that {{formula:12a13b20-65bf-4ae0-b513-85d0cc1874a8}} is {{formula:3d746461-c0f1-40ba-9319-a5c29aedbde1}} -cotorsion with vanishing {{formula:be6ef005-1fcf-4278-b762-f854951ffede}} -invariant. Since {{formula:147826c9-7712-4977-94d5-d1dd01785433}} is obtained from {{formula:62ea5a99-9098-469c-8dc2-a1da7dbae49d}} by level lowering, an adaption of the method of {{cite:5f98972a51337e3ef311f67508414a2c568e01b2}} shows that {{formula:5c534a36-65b8-4f70-9c99-7ad49346e25a}} . The point is that when we relaxed the local condition at {{formula:39f61133-c64d-46fd-877c-f3eb1df6452e}} for our Selmer groups{{formula:abe354b4-f268-476e-a968-6d84f94eeb0a}} (resp.{{formula:14aead05-fd42-4578-9ae2-810fc92176b6}}{{formula:b9b52b7b-40b6-401f-8cd9-7648fcc9baa3}} ) only depends on the residual representation {{formula:faa9cc0f-a7e4-4feb-9aca-a91f8e101a7e}} . Since {{formula:1ed501ce-76c5-4ea9-ba0e-fc190fa9c6aa}} is known to be cotorsion with vanishing {{formula:a68a450f-a113-48bf-bf6f-e1df1bc79fd4}} -invariant, {{formula:b496495a-7c7c-4647-b97f-d53fe8de60d3}} is finite. This implies in turn that {{formula:fc65778a-3dba-4c53-9654-7396d41a3676}} is finite. Then we can conclude that {{formula:41d913d7-d67e-4512-b553-90fc3fb2e0ec}} is cotorsion with vanishing {{formula:a603b685-dff7-4e99-b73c-460b139c833f}} -invariant. Now the same reasoning as in {{cite:5f98972a51337e3ef311f67508414a2c568e01b2}} allows us to conclude that {{formula:3e015f1e-6e95-405b-a938-b5844b451197}} has the same properties.
| m | 0bd76b7fe23a7e0b7def222b08181fb1 |
We have shown how a two-step learning approach can result in efficient and accurate solutions to the HJB PDE. In our setting, the output of the neural network was set to directly be the value function {{formula:099399ed-d88d-479f-b579-9e0f9ed29013}} . However, as in the SDRE derivation, it is possible to assume that {{formula:54f9a15d-c971-40a9-a762-8e1d076c4d26}} and adapt the neural network architecture accordingly. Depending on the problem this can result in an efficient solver; we will address the choice of architecture for HJB PDE solvers in future work. Our results show that in a setting where the residual is sufficiently low for multiple solutions, the neural network converges to the one closest to initialization, which can be analyzed in the context of implicit bias {{cite:0d3443a58e148f365c87536898b8630766266bbb}}.
| d | 2a3675befc5bc635f1b0724a69ea6a3a |
The labeling challenges in ImageNet were identified by the research community {{cite:9a4652a5d45b9f6326ea0c312b85efc6ac84479e}}, {{cite:4b2771369208cd722a78250322501644fb932133}}, {{cite:2d084b4ab0f7d243181922ae54761c7612ef9313}} and initial attempts were made for mitigation. Northcutt et al {{cite:4b2771369208cd722a78250322501644fb932133}} removed wrong samples detected by confident learning up to 10 % of the training set and they could achieve 0.5 % accuracy improvement with ResNet-50 on the ILSVRC2012 validation set. Beyer et al {{cite:9a4652a5d45b9f6326ea0c312b85efc6ac84479e}} used pretrained models and crowdsourcing to relabel the ImageNet validation set (ReaL) with more possible classes per image. They removed appr. 10 % of the training set, and after training for 90 epochs, the accuracy of ResNet50 improved by 0.3-0.4 %. Some works developed new validation sets to test out-of-distribution samples. In {{cite:bd31803f8e6ac5e5f6f7041651291dea853a1aef}}, artistic images were collected to form ImageNet-R validation set, while in {{cite:9134f282f0fc2ea10d2104de8e55b56ccd1f9dc8}}. new natural pictures were gathered by replicating the original labeling process to create ImageNetV2 validation sets. All these researches involved extensive human supervision in their processes except {{cite:4b2771369208cd722a78250322501644fb932133}}. When images were removed by automated clean-up methods from the training set during the experiments in {{cite:4b2771369208cd722a78250322501644fb932133}} and {{cite:9a4652a5d45b9f6326ea0c312b85efc6ac84479e}}, the improvements were 0.3-0.4 % for the original and ReaL validation sets. The author implemented a new process with label fixes and image removal. The former is beneficial to correct wrong labels without human intervention, the latter targets the deletion of noisy pictures for the training process. Namely, images with minuscule objects (e.g. fig1-c), quality issues (e.g. fig1-d) and too many categories (e.g. fig1-f).
| m | f4c2811fdf657b195c1b8df408be4346 |
There are many plausible extensions to this line of work. We have assumed a rigid model for treatment effect heterogeneity in this paper: treatment effects vary according to a known stratification on observed covariates. More modern work {{cite:f65e0778e07c51427edbf3f8e0593d25f9004bea}}, {{cite:98ac01c2fa0c6353a87ad7e7a12d3e57bca0fb7f}} focuses on estimating heterogeneous treatment effects empirically, allowing for greater flexibility in how the effects differ across units. Incorporating such ideas into this work, we might imagine using some of the observational data in a first stage to estimate a stratification scheme, and using the remaining data for shrinkage in a second stage. Alternatively, we could consider modeling the causal effect explicitly as a function of the covariates, e.g. defining {{formula:c1d93194-5406-4944-bf10-4112087f922c}} rather than a vector of true treatment effects {{formula:8df2396e-7869-4370-a0f3-28a7808c847c}} . We could then define a flexible shrinker to trade off between estimates not within strata, but within nearby values of the covariates themselves.
| d | 67c24af74ced3165248eb28aa5b4ee4e |
where {{formula:feae4c96-38a0-49d0-9d44-dd18ff72abc2}} is the film thickness,
{{formula:3e90502f-fc5b-41f1-a51d-1be1d44074d3}} , and {{formula:137a42f5-225e-4258-bd2e-9dc44d40d7f6}} , see Ref. {{cite:27394d0d139b13f709a9b7819ad7c9c33ed722a1}}.
| m | 28df54e81af4f1d2b52f43f12a87d5e4 |
It should be noted that we have ignored saturation mechanisms other than the axion emission to infinity, such as the spin-down of the BH {{cite:6af8070ba2825bfc7df16b622212f35b9e39a648}} and the energy dissipation due to the existence of the multiple superradiant modes {{cite:942fccc6dbabdb3fb7f0a44f91b0cdd32e445ad1}}.
If another saturation mechanism works before the onset of instability,
we cannot expect an explosive phenomenon to happen. We can assess whether the spin-down of the BH can be effective or not by looking at the angular momentum of the cloud. Let us first analyze with unstable case, i.e. {{formula:168fbfbe-f4e7-4191-8700-a658430e2a84}} . For {{formula:8e3cb660-1306-44fb-a437-0ed58a9f00cc}} case, the angular momentum of the cloud at around the maximum of the energy is
{{formula:99449a68-4405-4007-91ce-6003811f9491}}
| d | 458f69022a100c5448083db0912c2887 |
When comparing with the experiments {{cite:95f9d9654aa0fe435015fb96711ac78a9866b86f}}, {{cite:eccbefcce18a50a4241a149e4bb5cb2a74c8508d}}, {{cite:49e7302ee60bd72e52796b378ebf1070df219a8e}}, we find that the typical electric potential performed on TDBG is higher than that used in our theoretical calculations. This may be attributed to the fact that in our model, the uniform electric potential drop is assumed between neighboring layers, but in real samples, the uniform electric potential drop cannot exist, because the separation between the double bilayer graphene is evidently larger than the separation between the two layers of one bilayer graphene. Nevertheless, the effect of the electric potential in TDBG can still be qualitatively captured by the theoretical model.
| d | 7bc1963506fe172c109eb07827b3054f |
The posterior distributions estimated using the proposed algorithm, although close to the MCMC results, nevertheless differ slightly. The results are slightly noisy when estimating stochastic volatility, while in the DSGE model they are biased. This signals an opportunity for further improvements of the neural networks by increasing the flexibility of the neural network architecture, the number of simulations or by modifying the training procedure. It is well known that for a certain learning rate schedule, stochastic optimization procedures converge to one of the local optima in the asymptotics (see Chapter 5 in {{cite:926f49efc18b7e52b3a29b70254d8a60872d4e78}}). The exact (even local) optimum is not achieved with a finite number of iterationsThis usually means that the learning rate does not tend to zero.,{{cite:9057268887e8acd14a88fc91cbb0f1ae9617416b}} provide intuitions about the behavior of the estimation procedure at non-zero learning rates.. An insufficiently flexible network and/or a small number of observations in the neighborhood of real data can lead to a situation where the model is unable to predict the posterior distribution accurately, even at the optimumA good example of such type an improvement in the field of text analysis is the GPT-3 model (see {{cite:da2e65a053fbfa39d7a854d05217bf07aacd82fc}}). It has reached a fundamentally new level compared to previous models due to an order of magnitude more parameters than previously used and a huge dataset.. Moreover, the quality of the posterior distribution approximation is likely to deteriorate with increasing problem dimensionality. Hence, one of the main tasks for the future is to study the relationship between scalability, approximation quality and neural network training time.
| d | 1d68b1c9292a3b13283f58016339185c |
There are many real-world challenges in computer vision, aiming to solve the problems of the COVID-19 dataset described above and classify slices. For example, Fang et al.{{cite:943515e5b14832983f4c73c4f5bf18f72511b559}} proposed enhanced local features based on convolution and deconvolution in CT images to improve the classification accuracy. Singh et al.{{cite:33deed8487d68a97f5340efc659853a92145b50c}} use multi-objective differential evolution–based convolutional neural networks to resolve the difference between infected patients. Pathak et al.{{cite:33f08e41a556b11534da6c115b77e2ddd4e2571c}} proposed a transfer learning model to classify COVID-19 patients via the semantic features extracted by ResNet{{cite:0695295a3a2a292994c2b144846d15bdb8dea7a2}}, in which the weights in the ResNet were pretrained by the ImageNet dataset.
| i | aaa3f100acecd4a59e52f03b1f60b235 |
We compare our method to an RNN {{cite:18e3b639ae48075803e90fe4879af5b0798384f7}} and a Transformer {{cite:55689e1788a0e36d42dcd9bee8fcd1a294c0ef78}} baseline and present some ablations for the proposed novel components of our model on HumanAct12 and NTU13 in tab:HumanAct12NTU13 and UESTC in tab:UESTC.
Furthermore, we present a new state-of-the-art with the results for our Transformer-based and MLP-based models.
We also investigate the contribution of variational INR by comparing them to a non-variational version and the contribution of the decomposed representations by comparing to a version with no action code.
Note that by construction our motion generation procedure can generate high-quality motions for arbitrarily specified sequence lengths (as in Table 1) within the variation of training sequence lengths, whereas previous works reported a performance drop for variable-length generation.
| r | 8e313ec7fff91b66feea5c8ad805d26d |
Like RNNs, transformers are designed to handle sequential input data. However, unlike the latter, they do not necessarily process the data in order. Rather, the attention mechanism provides context for any position in the input sequence, and self-attention itself identifies/learns the weights of attention. In the case of spatio-temporal data, the attention can be applied to the spatial as well as the temporal sequence to attend to or pay attention to. The vanilla transformers in their original form are pure sequence to sequence models, as they learn a target output sequence from an input sequence, i.e. they perform transformation at the sequence level. Their limitations, such as disrupting temporal coherence and failing to capture long-term dependencies, were reached for sentence completion of language generation tasks, where difficulties were noted while generating texts with a model which learns sequences without the knowledge of full-sequences {{cite:8074fd4cb2272ab97c1f56753bcc521198583d17}}, {{cite:49c7b18b88b9ebc731bc7629d9b39343ee2b12e8}}, {{cite:96d090eb28379a8cd6b9150130a084b51c82c6f7}}. Several studies were performed, such as that of Dai et al. {{cite:74d2926f4c9f1fb2c278fb43ad07b483e4e1dcb0}}, to address this inability to capture long-term dependencies by attending to memories from previously learned parameters, yet at the expense of computing costs. To deal with some of these issues, autoregressive transformers were proposed by {{cite:ed2d6f37d45954a23e51459c79fbe4a1fa4ad77d}} for sentence and image completion tasks. Although not explicitly stated in some works, the Generative Pre-trained Transformer (GPT) family of models {{cite:51303c8374d71f76830e6b62105ca1264448d711}}, {{cite:6ae9b3015a67f709e790e11f43f0e013ff52825e}}, {{cite:e9c6792254d5124904c2d51bae6f1217ffeaa822}} are in fact autoregressive transformers inspired by the decoder part of the original transformers. In {{cite:ed2d6f37d45954a23e51459c79fbe4a1fa4ad77d}}, Katharopoulous et al. showed that a self-attention layer trained in an autoregressive fashion can be seen as a recurrent neural network. Transformers can be combined with the classic convolutional encoder-decoder type models to harness their full potential when the input and target output tensors are in a spatio-temporal form. As locality is more important in learning small-scale features, this combination serves as a powerful method for a variety of computer-vision problems, including video-frame prediction. The self-attention mechanism on convolutional layers not only attends or focuses on a sequence of significance, but it also improves the representation of spatially-relevant regions by focusing on important features and suppressing less-important ones {{cite:052a10da80ef73810f5f4dc90044323c453fb0e3}}.
| m | 4bcdba029d7c91404864a5933fffe9a6 |
Due to the very different energy and time scales involved in prompt charmonium production, phenomenological models assume that the cross section factorises into a hard term, describing the initial production of the {{formula:8cac89f7-9aee-4bd5-8c9d-9632a50290fe}} pair, and a soft term accounting for the subsequent evolution into a bound state. While the production of {{formula:b9b6fb9b-2e5e-4915-bf23-bff8cd929cec}} pairs can be computed within perturbative QCD, their evolution to a bound state involves long-distance physics which are non-perturbative. Their determination relies largely on fits to experimental measurements. A detailed overview of this field of study can be found in Refs. {{cite:c25bef10e84a2b5ff6d3c50999cb46ea8fb5a0ef}}, {{cite:20981a15ff43a802d9685b7797d7f9e6d62fa9db}}, {{cite:be436318defdfeababa4b815d1cb051fbe710cec}}. There are a few different approaches employed for the description of quarkonium production, namely the Colour Singlet Model (CSM) {{cite:5a485ec08531b7abbaf063956bc06af070e5bd37}}, the Colour Evaporation Model (CEM) {{cite:e491e79295feea76d126cf0aa7d03f79819982ed}}, {{cite:3f128df6e21283f2b12ca651095e7774ab06ad65}}, and the Non-Relativistic QCD model (NRQCD) {{cite:120769302aaed8fa40c742a3fc0294a1aa0f5815}}.
While the CSM model is known to underestimate the production cross sections {{cite:5047f0c31cb385a5a1872a40af6823c6b43004f8}}, both the NRQCD and improved CEM models provide a better description of the measured cross sections {{cite:8b119c938b9f24407ad977ba1b6e9dfbcc772a75}}, {{cite:71039158eb56230023c49f0fcb0beab97eb81a8f}}, {{cite:971e831f3076b51380051e0c66442dbeac4cba25}}. However, the simultaneous description of the differential production cross sections and the charmonium state polarisation is still not achieved {{cite:4ddeadb7fe5d885f3c81b6f336ced1e42cd0f350}}, {{cite:788b9ac6529264e9d80a0d5348ff488a4d5119e0}}, although recent calculations within the {{formula:6fdd7fe3-8b33-4bba-b4ec-f99d4399d092}} -factorisation approach seem to improve the agreement with polarisation measurements {{cite:f53930174705f7535853b7ad07fe8603ea1e7594}}.
| i | 8cc9dbaac83c86fb7ae9e53a192b6ece |
In earlier work, {{cite:164b38e24fc7daf01ec86c338d5c1b4907faefd1}} proved that the binned empirical estimator {{formula:099b062c-c22a-401c-8e3b-a13edb7c93e3}} consistently underestimates the true ECE, and showed by construction that this gap can approach 0.5. Our results complement this work in that we are concerned with the true theoretical relationship between two different measures of calibration, namely ECE and VECE, whereas {{cite:164b38e24fc7daf01ec86c338d5c1b4907faefd1}} relate the estimate {{formula:779b80dd-78c8-467d-a7a4-092506a9fb4d}} (Equation REF ) with the true ECE (Equation REF ).
| r | 46a371a2a42cc8b87b3d12ac5625f665 |
If the integrand can be extended into a region in the complex plane, each univariate rule can achieve an exponential convergence rate. Hence, this choice of quadrature rule exploits the smooth dependence of the solution on the parameters {{formula:a8dfe13d-7c43-40ca-91e1-aa1931b1ab42}} for {{formula:e1b64037-eae0-4aff-bdb4-065eaeba384f}} , which is shown in {{cite:ec13309a03edfb9d3a2f84b13fb972755685f81d}}, {{cite:acf075f9ee1c4189b1ae711d629d5a891f5bda2f}}, {{cite:9aa0661746c41cb9799fea50410e0c17bdd030e8}}.
However, the combination of the {{formula:0461ae75-77fe-4029-8696-4898865c60ae}} quadrature rules in a full isotropic tensor product, i.e., with {{formula:1affe76b-13a0-4c2e-83fe-a2df6b389adc}} , suffers from the curse of dimensionality as the number of quadrature points grows exponentially in the dimension {{formula:764ed74c-95b2-4ccb-8116-cc11cf48cc05}} .
Instead, an anisotropic version, as discussed in {{cite:2b06ef180e684c59e4349ea63d8693b617237f07}}, can be used which combines the {{formula:935ca99b-0c08-4e80-94a7-741f851a0aad}} rules with different approximation power and which can exploit the decreasing influence of the parameters {{formula:8e479fdf-f519-4806-99a1-284afa0857f9}} on the PDE solution {{formula:bfb82884-18fd-4da6-bda8-cf28ef1885c0}} by choosing the numbers {{formula:1ba9acbe-b45f-48ab-b98a-216975d11862}} according to the anisotropy.
If the decrease of influence of the stochastic parameters {{formula:8ba58e23-e138-4488-9736-15e0fc66dd38}} is sufficiently fast, for example such that the errors of the univariate rules are balanced when {{formula:8f772aa4-9d3c-43c8-9297-f1aef879b217}} with {{formula:2b15cacc-fc41-4eb6-b5e7-be983242811a}} , the curse of dimensionality can be broken.
Moreover, we combine such an anisotropic approach with a sparse grid quadrature which leads to an anisotropic sparse grid quadrature similar to {{cite:b0ed4e7ffb03d13b17f4e4c91a90c8990be9267e}}, {{cite:8382b56007f338b4f7454dc75f77a084eb2f8197}}.
The bounds in {{cite:2b06ef180e684c59e4349ea63d8693b617237f07}}, {{cite:acf075f9ee1c4189b1ae711d629d5a891f5bda2f}}, {{cite:9aa0661746c41cb9799fea50410e0c17bdd030e8}} on the derivatives of {{formula:25670c8c-879b-4885-a043-7f22dff603b4}} with respect to the parameters {{formula:fcb389ed-62bf-4765-bc2b-591a2dbaf3f7}} justify that a sufficiently anisotropic sparse grid in the parametric variables is a sound approach.
The construction of this anisotropic sparse grid quadrature is coupled with the KL-truncation and the spatial approximation which will become clearer in a moment.
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