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In this work, we present the marginalizable density model approximator (MDMA), a novel deep network architecture preserving most of the expressive power of neural models for density estimation, while providing closed form expressions for the probabilities, marginals and conditionals of any subset of the variables.
In a nutshell, the MDMA learns many deep
scalar representations for each individual variable
and combines them using hierarchical tensor decompositions {{cite:b0523f0b98e0146f4cb0ecb565570eacb39d7887}}, {{cite:0329383ba7fc1076879e7786bd2438324b34a2c2}} into a tractable multivariate CDF that can be fitted using stochastic gradient descent.
Additionally, sampling from MDMA can be parallelized along the input dimension, resulting in
a very low space complexity and a time complexity that scales only logarithmically with the number of variables in the problem (as opposed to linearly in naive autoregressive sampling, see below in sec:related).
| i | efe8c8967aeaf6bff7cc1234fa358d21 |
Another important tool for modelling and verification is stochasticity.
Probability is often essential to effectively quantify uncertain aspects of systems,
from the presence of hardware failures to the unreliability of physical sensors.
Stochastic games {{cite:b2e899728827be5d9c02c19f7d60d4ae6317832e}}, {{cite:1324fa6b7cfd83ad7940730fafe57313033b2f12}}, {{cite:67cc05b149c656f98951014518a0d621e13a42d8}} are a well studied model
for the dynamic execution of multiple players in a probabilistic setting.
Results and algorithms for many verification problems on such
models have also been presented, e.g., {{cite:51ab1597ca000c19e6c7ab39d2a8f5d7c4224ee9}}, {{cite:77c0b496b35323aab6fe439fbbd88e3bf62797e5}}.
| i | 9027fa78cee6f986a49eb86e4069bef7 |
The superaccretor SS 433 belongs to a typical class of ULXs. The apparent X-ray luminosity is about {{formula:04976f25-1310-4153-9bac-66d6fd229ab6}} erg s{{formula:65d28a6c-9ac4-4c0b-9557-4242726062a4}} but the intrinsic luminosity is considered to be probably
{{formula:4524872f-1e1a-4ce6-8250-426183bb3b42}} erg {{formula:ae148078-d28e-431a-abb6-6846a3ff2255}} because we observe the source edge-on (Fabrika 2004, Fabrika, Vinokurov and Atapin 2018).
In our models Thick4 and 5, the luminosities are very high as {{formula:4708ad45-edea-4b9b-a377-05f3561b1e09}} erg s{{formula:e1f46651-d424-4148-ace4-a4354a187148}} and
the radiation shows a strongly anisotropic distribution around the rotational axis.
In addition, the edge-on luminosity through the outer radial boundary is very low as {{formula:a79d8766-ba03-4e72-895b-bc8257a972d1}} erg s{{formula:971a5128-e201-4bb2-9bdc-b0ed47140d05}} .
The large mass outflow rates {{formula:b9eab4be-888d-4e9a-acb6-1cf0ce94dc13}} – {{formula:741554c6-2178-4cba-8f9f-ddf377f67ff7}}
yr{{formula:36d1ab0c-6348-48e1-9f20-ae130eb095a2}} are originated in the wide wind region. However, the relativistically high velocity jets
along the rotational axis are not found in the funnel region, as is detected in SS 433. This may be due to that the outer boundary used here is small as {{formula:ec755fa7-ee9b-4fb6-a085-6810ffd0c4a2}} = 100
and the outflow gas in the funnel region is not still sufficiently accelerated by powerful radiation
pressure force.
In SS 433 which consists of a close binary system,
the mass transfer rate from the second companion and the wind mass outflow rate from the primary
are observationally estimated to be {{formula:16f04583-858a-4411-968a-76d3ec9b6e82}} – {{formula:2e347a8a-2aba-4cd6-846f-f11172e1d95a}} yr{{formula:5b62e9af-1507-4a4a-ab37-b498487a0055}}
and {{formula:025014fe-7ecc-4de9-9903-84a34d0116a7}} – {{formula:d7c11e92-9fd5-4bef-8c73-33ab507ccaa4}} yr{{formula:7ed2dfa2-9902-4344-8553-36a62c681f91}} , respectively {{cite:cddc54113eb2d0ce188c3854b43541b6dbae7d93}}.
Their values agree well to the input mass
accretion rates and the mass outflow rates in models Thick4 and 5.
In the close binary system with high luminosity, it is conceivable that the companion
transports not only high mass outflow but also high angular momentum to the primary through critical
Roche lobe, differently from small angular momentum by stellar wind in detached binary system.
Then, one may wonder if the inviscid flow used in this paper is valid under such close binary system with the super-Eddington luminosity or not.
This is justified as the viscous flow can achieve specific angular momentum of Keplerian value at the outer boundary while behaving as a sub-Keplerian, low angular momentum
flow with shock in the inner region {{cite:ccaa6bb80d69af5c5d892a6899f55c8dfdc055eb}}. Actually they find the global accretion solution that the viscous Keplerian flow with the viscosity parameter {{formula:9515ac34-4561-47a3-82cf-bd90d913344f}} ({{formula:e29c845e-e7bc-49ee-a1e6-0b9f5aafe877}} 0.15) at the outer boundary beyond distance of {{formula:bbec4baa-4d5a-4653-b20f-436cb899199a}} connects to the low angular momentum sub-Keplerian flow below the inner region of a few hundreds {{formula:c944ee48-63e2-4898-b4dc-a37f6166313c}} .
| d | 9e3729b8f41d8bdac4381d66f32b35c8 |
In a previous article {{cite:329e6057f086b4f336565d4585f0a9c180567428}} by the second and third authors, we proved the long-time existence of Yamabe flow (REF ) on asymptotically flat manifolds. Moreover, we showed that the flow converges in a global weighted sense (defined by {{cite:ee5bd2ae1895f3f0b82ce59d9693985047b45e6d}}) if and only if the Yamabe constant {{formula:eb6680c2-e03f-4e6d-9f60-7e1c8a50b249}} is positive. Long-time existence was also studied independently by {{cite:5c6e6f87e12f52a254c6a12bfcfc7843783c2cf6}}, who also considered local convergence assuming nonnegative scalar curvature.
The convergence/divergence behavior of the Yamabe flow on
asymptotically flat metrics is quite different from that of the Ricci flow; see for example {{cite:89489357ce7c318edfa90af39efaa8d2aa72d97f}} regarding the Ricci flow in this setting in dimension {{formula:cc9af3a7-68bd-4cb9-a1b8-137f4cccbe8d}} . We also refer readers to related results on the Ricci flow in {{cite:fd4891eb6c3454894129421ff0e116cec3052ac3}}, {{cite:ae79a17cd3bd7830cbc8ede7ee1b1d22e2b16bc2}}.
| i | f05750ede9f5ef6f6a34223e2086e4b0 |
Our method also benefits from the learners’ diversity. Co-training will fall into self-training without diversity, and consistency training on the same prediction will also be meaningless for the lack of diversity. The diversity inherently comes from the randomness in the strong augmentation function (the unlabeled examples for two heads are differently augmented and pseudo-labeled) and different learners’ initialization. Copy-Paste (CP) is also an alternative way to boost training samples’ diversity, and recent work {{cite:be6b7bbdb73572705db66a98b71819dc0c0d9ea6}} has proved its effectiveness. However, the plain CP has its inherent drawback caused by two problems. The first is the distribution mismatch between labeled data and unlabeled data. The second is the class imbalance problem, most current semantic segmentation datasets{{cite:be812a9edbbf8ad2c25208c11051d12b801fe267}}, {{cite:c360ba8f3d4dfea11fc4f7294557a6e833e1c770}} contain long-tailed categories. By extending Copy-Paste (CP) into Dynamic Cross-Set Copy-Paste (DCSCP), our method could not only boost consistency training samples’ diversity but also reduce the misalignment between two sets’ samples and address the class imbalance problem via preserving long-tailed samples. Meanwhile, to reduce the negative effect of noisy predictions brought by self-training, Uncertainty Guided Re-weight Module (UGRM) is applied to unsupervised loss to dynamically give more weight to reliable samples while suppressing the noisy pseudo labels in self-training.
| i | c3b8118c6a27c7aac1819d64cf3b35b4 |
It might seem possible to generalise the techniques presented here to study chimeras on rings
of nonlocally coupled general oscillators {{cite:87bbd826e5b8e2d3e76ec21cd7c7779cf15ea921}}, {{cite:7a63919b32b726c8888d76d1b41bb2f51b743041}}. However, while the locked
oscillators would be described by ODEs and the asynchronous ones by PDEs, one would need to know
(or to automatically find) the boundaries between such groups of oscillators, in order to
determine whether an ODE or a PDE was needed to describe the dynamics
at a particular position on the ring. Also, these boundary points would move as parameters
were varied.
| d | 1278b795450da3979dd9b5159c527115 |
This conjecture was proved in {{cite:981602c5e785eb20215266185a180dcf2e6b9949}} for {{formula:a3d829f6-f787-40e4-841f-18fafeaffbad}} , but for {{formula:c7fabaa2-7e8b-478d-ad4f-ed0176ed2db1}} , it is not even
known if these functions are minimizers of {{formula:907d66b4-d5e8-443d-8dd0-1a3d478600c6}} . As in {{cite:2f6d5d7fc04df4386275bc0fb87c8d588ae7771f}}, {{cite:7e00b02363013e71be1960399e920060d5752cf7}}, we can overcome this difficulty by the optimal asymptotic behavior of minimizers, which was obtained in {{cite:fd1206dfb639b9f4ecbca3b16e8de1cb22af214e}}.
| i | 36fdcf39e55a82aecb1bcb7dfe2dda9f |
nce is a powerful tool to predict mi and has been used in recent works like cpc {{cite:d8da07574bb9232a3d2f61f1c8d03fe7bf0641d7}} that rely on the nce objective to distinguish pairs of context vectors from the same or different time segments. This approach is similar to Time Contrastive Learning tcl {{cite:d3529c552ed7bc478862ce3966391f950b42ee67}} which is an algorithm for nonlinear ica. Although tcl has only been shown to work for univariate cases and cpc fails to model independent subspaces explicitly, they serve as a strong motivation for our approach which addresses both concerns.
| m | 1410503e60213e89cbe2590e9d4d08e2 |
{{cite:9728075e15452043d81f35a21cb8f7685a0d8237}}, {{cite:835500c48b6b790599eb9018d5c3e6553744a0ff}}, {{cite:dcb2657793cc0d22aa359723391ba6d72ed7baac}}
Assume that the minimizer of the extended Parisi functional for {{formula:a0adccb9-6f62-40d1-9c00-3ce08ac90f82}} exists. For all {{formula:3af02db5-3bc5-4f45-aa59-26892fde5767}} , then there is an efficient algorithm that outputs a solution with value {{formula:c407149d-b73b-4d8c-b2f3-28995b37241b}} on almost all instances.
{{cite:363bfac4ae024076bb9564a68a50854ebf1cee15}} Assume the mixture polynomial {{formula:f4e691d2-8e00-4e1d-b8f2-6ea4265a294f}} is even. For all {{formula:455d4945-3620-477c-9308-ff853e9eb190}} , there is a branching OGP with value {{formula:99d692e8-a14d-498d-b5f4-f5dce629d029}} , which therefore obstructs overlap-concentrated algorithms from achieving this value on almost all instances.
| r | fb2fe7f5b8d4640bf5e1d7851914c4b6 |
Batch Normalization for FedNST:
As reported in other works {{cite:2e6375e09e3a2e4bca9c7b430205ffc362846056}}, {{cite:2e7c5ead5a3614abdb0fa375ac56a4439ee75a3a}}, {{cite:5f28cc16374d217078dbfa88a88c5abaa701277c}}, we find that using standard Batch Normalization (BN) for FL gives rise to convergence issues due to data heterogeneity.
To address this issue, we replace all BN layers with a modified version of static Batch Normalization (sBN) {{cite:2e7c5ead5a3614abdb0fa375ac56a4439ee75a3a}}. sBN does not keep track of running statistics, i.e., the moving-average mean and variance associated with BN layers, during FL training. At the end of FL training, it queries all clients sequentially to produce global BN statistics which can then be used to evaluate the trained model.This post-processing step has computational and privacy concerns {{cite:2e7c5ead5a3614abdb0fa375ac56a4439ee75a3a}} and it makes it difficult to perform model evaluation during training.
| m | 736e3c5a98eb99272f28b12fcd3d43a6 |
where {{formula:4bbadc1c-370b-4e31-887b-45d1bf40b3fc}} denotes the timestep at which {{formula:4da86414-5949-4dfc-a297-1d3f01a7840e}} is visited while
following a policy {{formula:5f800504-e999-4307-909d-93d0a3473695}} , assuming that {{formula:c50b7605-81f0-4d2b-bb42-b3f0b8942aa2}} is a recurrent state under all policies.
This is used by {{cite:ab80a73bd546928a9d1752108f19f58150246bac}}, and {{cite:c711330588eb322d6b2fe354bdb868af5c4ac76c}}.
Another batch approximation technique is based on the inverse-propensity scoring
{{cite:0638a24ea38843934dcfb085f3817126a938526a}}.
| m | 739cec936031e6b0fa0d53e21d9752d1 |
Then, we compare DCEN with recent generative methods.
Notably, the generative methods utilize prior unseen domain semantics to synthesize extra unseen visual data for training, e.g., powerful GANs, while DCEN only uses the seen domain data.
From Table REF , DCEN outperforms most generative methods by a large margin, which is encouraging for embedding-based methods because no synthesized unseen domain data is used for training.
Compared to recent TF-VAEGAN {{cite:24dd81347c7fa370524bc4077cb4ed91fa9976d7}}, DCEN obtains comparable results on CUB using only seen domain data.
This is due to introducing task-independent knowledge from instance discrimination, and it proves that the embedding-based methods have much potential.
| m | 98b98c43573434520ae667bf92946b5a |
For transforms that are trained end-to-end,
there is evidence that the Jacobian of {{formula:cea56d07-5427-4bf3-a5d0-286c14428ad5}} ,
when viewed as a {{formula:ab69de20-14bc-4393-a832-21aecf383a91}} -by-{{formula:4f73fa91-8301-4533-b591-fca280d74e32}} matrix, has orthonormal
rows with high probability {{cite:5eee1c04782b7b41a47d3dcabf32704ba508c468}}.
If the gradient {{formula:e0ee7fb6-666e-45fb-ba10-f52fe4e2b80d}} is
also zero, then the first term in (REF )
vanishes and the Hessian is proportional to the identity
matrix, eliminating the need for distortion universality. A number
of nonlinear transforms have been proposed for compression
that are not trained in this fashion, however {{cite:e63a65158f94ebbf01fc186ee59736acb31b654f}}, {{cite:4f4fc81dfc8e6fce5a8edd4d4a8584ad62d5c6cc}}, {{cite:dd64afd1601bfc5bfe8bdc4ab3eb274eac3274c2}}, {{cite:a99b706213251a82760056f1600a89bacbc4dfe0}}, {{cite:0dee36f33204ed6b2736f36b51d7ce67e0e4461e}}.
Even for those that are, employing a quantizer that minimizes
the objective in (REF ) could allow for
reduced capacity
in the neural networks comprising the analysis and synthesis
transforms, with a concomitant reduction in training requirements.
Application to nonlinear transform coding was the original
motivation for this work.
| i | 989548c4bd3771c11b4ae200533c5792 |
The E12 isochrone (high rotation) fittings to HRD/CMD derive turn-off age, 85{{formula:7a521c46-c77e-427f-948e-007d017fa0e0}} 13 Myr of Be 55, by taking care five RSGs/RBGs. For this age, the masses of five RSGs/RBGs from the E12 isochrone are about 6 {{formula:6a9c1171-4f34-4587-8204-056bc29923e7}} (Col. 6 of Table 5). The 70 Myr G13 isochrone with moderate rotation does not provide a good fit to the RSGs/RBGs on the {{formula:d8cd5687-5cba-4903-9a3e-9dd03e34aa7c}} -{{formula:8502b8e7-971b-4a9c-9b04-f0764b289011}} (Fig.12). The age 85 Myr is somewhat older than N12, L18, and A20 (Table 7) but falls in the range of 30–100 Myr of {{cite:8fcff1ff050e5276a725f9878c2c7febff87f21c}}. From the non-rotating PARSEC isochrones, A20 give its age as {{formula:c50fb243-3781-4756-bf12-a50d0b79ebdd}} Myr (see their fig. 6 and table 1), by considering evolved members. The age 85 Myr also falls in the range of 63–105 Myr, which is found from the period-age relations in table 14 of A20 for Cepheid {{formula:f80242fd-5868-4609-be4f-4906be02af01}} /{{formula:dd25c60a-1258-4f9b-b702-30519164d07e}} . Note that N12 apply two isochrones of {{cite:2d15265dbb9e75a04bbb561e7ea0e2f0f071160e}}; {{formula:cc9bb453-425d-4c42-93ac-e287b7880451}} (40 Myr) and {{formula:4884d7e2-b3c2-4b36-b603-07be9fecf71c}} (50 Myr) on {{formula:2c5b823e-c0f1-449e-b90f-6e2c03e0c62b}} . By taking {{formula:2db6d3b5-318f-4ff6-acf4-5e356c943900}} mag, N12 also apply the same isochrones to {{formula:91feee8f-1026-40ce-887f-c62bdead4c98}} , and give an age 50 Myr. The other literature values find more old ages (Table 7), than this paper.
| d | 1819ebb8f2823617f0872c39e9c695fa |
In astrophysics, gas and dust mixtures have been predominantly studied with grid-based codes. The gas phase is computed as usual whereas the dust is treated by using superparticles (e.g. {{cite:24835cffe7dc3fd7f4e65a2812b5fa689584ec1b}}, {{cite:8495a8e8a1bd08be1963c244b582f222eba4d2bd}}). Computing the drag is usually divided into three steps: i) interpolation of the gas velocities at the particle positions, ii) calculation of the drag force on the particles and iii) attribution of the back-reaction from the particles onto the nearby cells.
| d | 9d18e47ea350230ad903f3d8d20409e6 |
To further illustrate the effectiveness of personalized conversational response generation, we report random selected cases in Table REF . The SEQ2SEQ represent the standard sequence-to-sequence model, Persona represent the persona-based Speaker Model proposed in {{cite:464c0c7e9bf72d9339bc261d98bc53dd47df1356}}, and FedNLG represent personalized conversational model with federated learning technique.
As can be seen, the standard SEQ2SEQ produces the same response to the given question for different characters, which is intuitive that no persona was learned in this model.
In contrast, we observe that Persona model and our proposed FedNLG are both sensitive to the identity of the character, generating diversified responses which contains persona and humanity. For example, the model produces "You're not gonna be a genius?" in response to "What if i smack my head on the concrete?", which could be recognized as "Ross" style.
Both Persona and FedNLG predicts diversified responses with persona in two movie datasets, Friends and The Big Bang Theory.
We also test our model on consistency by generating some similar questions, empirically our persona-based models successfully produce consistent responses compared to standard SEQ2SEQ model, which is consistent with results in {{cite:464c0c7e9bf72d9339bc261d98bc53dd47df1356}}.
| m | 16b20ea157a93bd4dc4754724d5d8920 |
Step 2: We prove that the system of SDEs (REF ) has a unique strong solution before its first collision time by approximating the singular drift with regular functions. For the existence and uniqueness of SDE, we refer to {{cite:8c66509ae0b2d0b9cbd373fedc81be7f9bf6c617}}.
| r | 64239f0fb70a12e118363a690840a5f1 |
Colored dots and a star in Figure REF and Figure REF illustrate the CIFAR-10 models proposed in {{cite:ec5af6d1da79ecce4c204f9e94fbe989630e29b0}} and {{cite:2c8aa9cf9d9a216614e1b81d3d922b6680823a4b}}, where the accuracy and robustness values are taken from corresponding publications. We see in Figure REF that for these values and the chosen {{formula:845ca075-a0bc-4b15-9553-1fc2e1cee83a}} an adversary would always attack, independent of the strategy the defender chooses (Case 1).
Similarly in Figure REF , we can see that for the given values and the chosen {{formula:022a9a85-b877-4cb9-9603-9946dbdff7ae}} and {{formula:b78af532-8697-4754-b84e-2cf9bd81fa7b}} , the defender is always in Case C, meaning that she might use both models.
Keep in mind that values of {{formula:bf88e31e-d171-4b8d-99c2-eecb843fa524}} and {{formula:6686439e-6f83-4fcf-bd02-60a5561d25f1}} are arbitrarily chosen and the defender will play a model with higher {{formula:63cf887b-3bad-4bba-8d27-3bf7e0a5504e}} for that given attack rate (recall that the adversary will likely attack). Needless to say that our chosen value {{formula:ee3c66c2-773c-40c9-bcbe-6d1d6ee23274}} is very high as it means that the adversary can influence up to {{formula:0023db16-df5b-41ed-b8e3-ed5116c4bc21}} of samples. Realistically {{formula:7ef6ab69-f0b6-4ebc-a2a6-5e6e93c3cf87}} will be much lower, even as low as one percent, which means that the defender might opt to use the non-robust model, although the adversary will always attack.
| r | 44fe98569afd40e668d4da58905528db |
The risk measure CVaR was first studied in the context of portfolio optimisation problems by {{cite:577e576991961a9f4653d213d3b8ee3168b92824}}, {{cite:078f25ee61d9a31c1c4d287d71fe939dee054d34}}. They showed that a mean-CVaR optimisation problem can be transformed into a linear programming problem that improves the efficiency of solving portfolio optimization problems associated with CVaR significantly. However, closed form approximate formulas are still more convenient and efficient and therefore we will discuss such formulas for them below.
| r | 0c8d49658f5e59ace598841085f63207 |
Coronal mass ejections (CMEs; {{cite:443f76aa134ba4b06be7c1a56fdcab9049729c01}}, {{cite:443f76aa134ba4b06be7c1a56fdcab9049729c01}}) are enormous expulsions of plasma and magnetic flux from the Sun into the heliosphere. The basic structure of the magnetic field of a CME as it erupts is that of a large-scale magnetic flux rope (FR). In interplanetary space, CME-associated FRs that have enhanced magnetic field intensities, smoothly rotating magnetic field vectors, and low proton temperature {{cite:615751a9ea3d5a2e0c12750a48378e809f41e52c}}, {{cite:f1c145f5ea6ce0e28aafb392b7d0a725ee5fed89}}, {{cite:ea97bcfab45dc6147b5c8a7a2e3b2e7a14ef27ec}} are called magnetic clouds (MCs). Due to their strong magnetic field intensities, high speed and potential for supporting sustained southward magnetic fields, MCs drive the most intense geomagnetic storms {{cite:0f2a8b5028ce4b3d12d2b4819cddf7a0f2ea2784}}. The coherent rotation of magnetic field vector observed inside MCs as it passes the spacecraft represents the systematic twist of the field lines as they wind around the FR central axis. Twist is an intrinsic property of magnetic flux ropes that is related to the stability of FRs. The distribution of twist has important consequences for energetic particle propagation inside FRs because the twist modifies the length of the FR field lines {{cite:703130fbcae3ac927cbbde47cf563779903beb54}}. Along with magnetic field intensity, axis orientation, the field line twist – winding of magnetic field lines around MC axis, and chirality – the right-handed or left-handed sense of twist of FRs are also important FR properties affecting their geoeffectiveness.
| i | 4f852f6c16500bcc0d804c6d2fcc55f1 |
BERT {{cite:858f4834f0652de2048ed046c8806ea572f52133}}, a Transformer-based model, has now become one of the most popular and outperforming models for hate speech detection tasks, or in general, text classification tasks, and it is proved to be the most effective performing model in a similar subtask {{cite:8658836cfddedb1954787c70b0c44fd188030504}}. In this paper, the fine-tuned BERT will be used for the hate speech detection task.
| m | 0891ef4a7f9ca45a3f1fee14fa8e7b64 |
Theorem 9.3 (Perron-Frobenius){{cite:8c843bacfb5b52d34218a329dc39c291da3f4df2}}
Let {{formula:6d261685-e0b3-495c-9158-e8d57fd63a3b}} be a non-negative, irreducible matrix. Then, {{formula:3fb2e22c-f806-4e56-93ab-4fe956f79c4b}} is a strictly positive real number, and the corresponding eigenvector {{formula:55db4e5f-386c-4a47-b668-539b51b25f57}} where {{formula:ddf60026-384d-455e-9680-81da738f96b2}} is also strictly positive. We call {{formula:fc5121d6-3e25-4383-a4ea-41dfcae33437}} and {{formula:220cb2ea-91e1-4f4d-9484-a243c273d0aa}} the PF eigenvalue and PF eigenvector of the matrix respectively.{{formula:2b2087b2-9c67-46cd-ad64-311dbf336590}}
| r | c25bc801425c8274844a429dd4f34b8c |
Multi-modal synthesis.
Following SPADE {{cite:8da3e9e3c490c74e3b694d6c5a3690d9081693ac}}, we train an additional encoder for multi-modal synthesis or style-guided image with the KL Divergence loss in the way of VAE {{cite:6d6faaaacd74e85c11bf806c65e2329268f3c606}}. By controlling the mean and variance vector to sample different random noises, our generator can also synthesize images with diverse and photo-realistic appearances for the given input segmentation mask, as shown in Fig. REF .
| r | 4c7772c66bab679661749bdc09408ae0 |
Interest in this direction has been fanned by a series of anomalous experimental measurements, especially since the mid-1990's, which suggested the existence of new, light neutrino states.
At the LSND experiment {{cite:4a9903e4d49e3abbcd70ddfe86be272d0b06b709}}, an unexpected 3.8{{formula:4686253d-8998-40fc-9ab4-59e0c2d314a9}} excess of electron antineutrino events was observed from a meson decay-at-rest neutrino source, while at the MiniBooNE experiment {{cite:9720e765a99c2603d1435bb1c0b8bf81244ca002}}, a 4.8{{formula:87e3e591-12a0-4874-abc3-9c6b08352c5c}} excess of electron-anti/neutrino-like events was observed in a muon-anti/neutrino-pure beam from meson decay-in-flight.
Additionally, many reactor neutrino experiments performed over many decades and at different baselines below 100 m observed a {{formula:3f73ded6-3ce8-42d1-a67e-a6cce837ddbf}} (5%) deficit of electron antineutrino interactions with respect to theoretical predictions {{cite:34423fb0c90b9a9a3c8399e2a7275d0213256cfc}}, while radiochemical experiments have observed a consistent {{formula:54e0fd51-391a-4a98-91c6-a7b088147485}} (20%) deficit in the electron neutrino rate expected from nearby intense electron capture radioactive sources {{cite:306913957a8c03f3fba1737e535150572c066d71}}, {{cite:cdcba4480ee76e29cbc76ea17c74c16edc91bee3}}, {{cite:97635fad27cdfcff07d8eef4237aee91bca5193b}}, with the most recent verification of this deficit provided by the BEST experiment, at {{formula:81cb078c-ea75-44fa-a559-b3c95f146a74}} {{cite:4e40d752899eaf655f0774e5304bd7f99cbd0723}}. This series of indications of neutrino phenomena deviating from the three-neutrino paradigm have commonalities of being observed primarily in electron (anti)neutrino observations, from either electron (anti)neutrino or muon (anti)neutrino sources, with either Cherenkov or scintillator detectors, and at relatively “short baselines” from these neutrino sourcesNote that the term “short baseline” refers to a ratio of neutrino propagation distance relative to neutrino energy of {{formula:181e5366-3481-4ecf-9453-494583d6633e}} km/GeV or {{formula:e5c33541-cb3b-4ad0-9381-5901b12300a6}} m/MeV, corresponding to a neutrino oscillation frequency {{formula:a726dc5a-1552-4347-b793-51dda02938ad}} m{{formula:17b6df3b-5a50-4d0e-a067-98800e1608ea}} of {{formula:7828e0a8-9f7f-4302-add3-f23b0869664d}} eV{{formula:6883e8bc-4a14-4cce-a4d4-b731c9de0b6e}} ..
| i | 9df2c224a61079bd06f64c8f78e4147f |
Having approximate analytic tools at hand is beneficial not only for theoretical studies but also for inflationary model building and PBH phenomenology. Using various shapes for the power spectra, we analyse the potential of future GW experiments for probing the GW background induced by the large scalar perturbations in single-field inflation, showing that the windows where the PBHs could constitute all DM and where they could contribute to the LIGO-Virgo GW events, can be probed with the future GW interferometers and pulsar timing arrays, respectively {{cite:7f34d50783f62f4740669fe5a7e804aa440fbb72}}, {{cite:3384eb8619b303e5456f0f4c8c6c775371acd4ad}}, {{cite:c8a4174235570c8194d341a5a290c91b775c559d}}, {{cite:cd4c30b98c3f2bfd9c00503a3d22ed2abb1422fe}}, {{cite:7de7d5f6644809cc8aed182ec76ab647de8242fc}}, {{cite:6d0a36daf8a314f1948a5ee825f293fbd36ed7d1}}, {{cite:3a6e55f84603be4f309856b054791e9e240c208d}}, {{cite:d8620f41425af4e483a1db3b9dc5f3f40546d83c}}, {{cite:5279015968f68ef2b389f19b617ce43c790f4190}}, {{cite:3662679f72be775c3e71075607bac93c4cbf4ff6}}, {{cite:5b0f2b29d991abec2cc9fbc54f6a632d322c946f}}, {{cite:6b65f181063ebcab97079fb1ebb7659457b613f4}}, {{cite:95156474541fb92b80db89bfa9284d5adb472751}}. These analytical tools can also be applied to improve limits on heavy PBH scenarios, e.g., by using COBE/Firas {{formula:eebeb17c-8432-49b6-856b-d3c3ec89c4e0}} -distortion constraints {{cite:4329a3af538cc34636e2fb838419083717b94121}}, {{cite:0afc58ebd4f283d73587bcf46f032471cb95abfd}}, {{cite:833bd96dbebf0c052a6988738e39e9bf02177f4e}}.
| i | e2a2e2bb99dade79edde1eee94e085d9 |
Besides SNe Ia data, compilation of measurements
of differential ages of the galaxies in GDDS, SPICES and VDSS surveys
gives measured values of Hubble parameter at 15 different redshift values
{{cite:eb29a9b2e0c958f6dadbf2c4714faf5a193ed569}}, {{cite:8de816390125a6acd88e3e2b9f9d3c279cda45fa}}, {{cite:43ddbadfcd32587e42674abcd8b83dc39afb706d}}, {{cite:2a96005a534a3d67f97e6c1f1f981ab4f6fd60a0}}
The {{formula:23ae71e8-2640-49eb-a330-3aa98373bfad}} function for the analysis of this observational
Hubble data (OHD) may be defined as
{{formula:8f45d50e-c986-4a0f-9ab6-fab9694422cb}}
| m | a1bb00ad37491b7e6de3729d2ca36446 |
Additionally, enabling stable multi-agent training without centralized training could open up future opportunities for legible {{cite:36e0ef66f825a7a9188c9cdd9fc87d7e42fa4cfb}} agents in human environments. Agents with interpretable actions can induce more faithful human mental models, improving human-AI interaction; however, predictability does not imply legibility. Future work could explore the role of legibility in designing intrinsic rewards.
| d | a2ce9f445d3c82db4a573adae165a563 |
For PAMAP2, we adopt a CNN for training and predicting. The network is composed of two convolutional layers, two pooling layers, two batch normalization layers, and two fully connected layers. For three MedMNIST datasets, we all adopt LeNet5 {{cite:5d14b5bcda8f11ee3938c6601f084d6f29cb5207}}. For COVID-19, we adopt Alexnet {{cite:fcbafaf521ef97cbeda9656f9ee9f7ca53dd0d41}}. We use a three-layer fully connected neural network as the classifier with two BN layers after the first two fully connected layers following {{cite:9f4cc4f4da50eb15b847101d3bc551d8ca058abd}}.
For model training, we use the cross-entropy loss and SGD optimizer with a learning rate of {{formula:00ea1b79-6d09-4336-ac4b-e92d6977aa8c}} .
If not specified, our default setting for local update epochs is {{formula:eb797f78-3ae4-4796-b120-ec6c5781b698}} where {{formula:0d3fb79b-d0e3-457f-8bc6-3b627a625c48}} means training epochs in one round.
And we set {{formula:957f4171-fabe-415c-900a-291ddbcdcfcf}} for our method, since we can see that {{formula:fc061b21-c5e5-40fa-af2f-0e51984ee9be}} has few influences on accuracy and it only affects convergence speeds in the appendix.
In addition, we randomly select {{formula:b686a890-6709-4bd5-be89-ff8c2f3b7064}} of the data to train a model of the same architecture as the pre-trained model.
We run three trials to record the average results.
| m | 2a47315851c0c63b62357742020f4945 |
Centralized Training for Decentralized Execution (CTDE), where agents are trained offline using centralized information but execute in a decentralized manner online, has seen widespread adoption in multi-agent reinforcement learning (MARL) {{cite:78c9367b194421087c044af5867616f3630c0842}}, {{cite:908dca84a20e60347502af33933374662ca3c98b}}, {{cite:b28300fa3aad9e2c209df7f966d30ffd4208ead5}}.
In particular, actor-critic methods with centralized critics have become popular after being proposed by {{cite:6180c17a1b772c69c039662572223085586b2956}} and {{cite:cc48a1c271c1d0f78bb90464243326e486e99c1b}}, since the critic can be discarded once the individual actors are trained.
Despite the popularity of centralized critics, the choice is not discussed extensively
and its implications for learning remain largely unknown.
| i | c77f1ff883fa69141c4a92da3c83c594 |
In this section, we evaluate the performance of different variants of PRIMA on eight tasks from the family tree and graph benchmarks {{cite:b98d0b8c826ce97987445b6125aaa9c8f1f42835}}, including 1-Outdegree, AdjacentToRed, HasFather, HasSister, 4-Connectivity, IsGrandparent, IsUncle, IsMGUncle.
These tasks are widely used benchmarks for inductive logic programming {{cite:84a3b40ada8c38e715b7e76334476b46f16572c4}}, {{cite:eb049f3437fefc72c5e19d1c96559a891306b4fb}}. Detailed descriptions about those tasks can be found in Appendix REF .
We evaluate their testing accuracy and reasoning cost (measured in FLOPs: the number of floating-point operations executed {{cite:d7051d9198b17f4d2a04f5c3c7aa040c978fcc87}}) on these tasks and compare them to several baselines. Furthermore, detailed case studies are conducted on the reasoning path, which indicates the operator sharing among different tasks. All the results demonstrate the graceful capability-efficiency tradeoff of PRIMA in MTR.
| r | 55211c97065ef501ed85fa8388931c49 |
We have performed the Riccati-type pseudo-potential approach to deformations of the AKNS model in sec. , such that the modified NLS is obtained through a certain reduction. In this framework it has been constructed infinite towers of quasi-conservation laws and discussed their properties and relationships with the MNLS model. This construction reproduced the tower of NLS-type quasi-conserved charges obtained in the anomalous zero-curvature approach of {{cite:9dc5e52986ec94e0c982256c2d959546bf8caedb}}. Moreover, in sec. we have introduced a dual Riccati-type pseudo-potential approach and uncovered, in that framework, a novel set of infinite number of quasi-conservation laws, such that it encompasses the quasi-conservation laws obtained by a direct method starting from the eqs. of motion in sec. 3 of the companion paper {{cite:b8603effc5883ffbf3512496b70fced53a1b7ad3}}.
| d | a1cc4e437060295591a2f1737aed15ff |
The study of representations of a polynomial {{formula:cf1ed540-4cfc-4ca3-8988-53e0413b165b}} non-negative on a basic semi-algebraic set {{formula:b1b7ff98-a355-4773-bad7-9bf52353afa5}} (also called Nichtnegativstellensätz) is a central interest in real algebraic geometry with influential applications in polynomial optimization.
We refer the readers to {{cite:a1418db161682af2ea647456a3e4b9b0cce8eac8}}, {{cite:d5afea0e978a02c9956eba83fb6629fa2c76ccfe}}, {{cite:73595a348bfbc9ecbc670eaef5eb46cba4d66f4d}}, {{cite:7a1d44effcf835578dfbcf58408f7231f0d4465a}}, {{cite:7053f5368ba91078388b3e3d449f6246b73566bc}}, {{cite:df086eab1deb9377d7e91448ee2e6f514487a1bb}}, {{cite:02ec1e5e77d736e07b0cd63bbf15cdf24f3471aa}}, {{cite:a5689846bf4a99d404c78c91a14c318111ef1c43}}, {{cite:154949bfd9c425c08b8d04c97bb35a8094f9b424}}, {{cite:273ff2301713119c7a51265aca19574d2abac9c4}}, {{cite:f12f7b4e8a5ff194115378ae92e7401d9fddf61c}}, {{cite:d0d88390a248966fde181950e07620a2ec8b52f7}}
for extensive discussions of various aspects of this subject.
Accordingly, it is important, difficult and challenging to provide Nichtnegativstellensätz, which have the same forms as Putinar's and Schmüdgen's Positivstellensatz, in cases where: (i) polynomial {{formula:ff7c7e56-36be-4835-beb3-b15f982236b1}} is non-negative with infinitely many zeros on basic semi-algebraic sets {{formula:123ad02f-06fd-49a3-bbea-ee8b685ca6bc}} or (ii) the Karush–Kuhn–Tucker conditions do not hold for {{formula:c9f129b0-f09c-4ddd-8c72-2c7f04c0cc5e}} at any zero of {{formula:de1ae409-49c7-4c24-aa9a-17bc12f978c3}} on {{formula:8606aed9-8fd6-46d0-8f91-2aa66f77e526}} .
Initially developed by Demmel, Nie and Powers in their celebrated work {{cite:154949bfd9c425c08b8d04c97bb35a8094f9b424}}, the techniques in {{cite:2118db2022fb1c79d2183f028b39e6f0de6fc601}} enable us to deal with above cases, and hence obtain exact semidefinite programs for a polynomial optimization problem in these cases.
Roughly speaking, we utilize a variety {{formula:d3a908b8-4ed3-4c1b-9fa6-d6c950ac8763}} , generated by polynomials in the Fritz John conditions for {{formula:bea8ed7e-6238-4df7-bd80-fec25713a6bd}} , whose intersection with {{formula:8962cefe-eb87-4039-8460-fc1ab0192998}} contains the zeros of {{formula:4884bd99-3a12-4fd0-ae36-f9df1578dde1}} .
It turns out that {{formula:30e8d916-d0f5-472d-8731-2ce3d6277493}} has finitely many values on {{formula:fc1e607a-a735-4c5e-b3fc-a60abb70553d}} , so has nice representations without denominator involving quadratic module and preordering associated with {{formula:218ec217-4176-48c6-8385-f8b9a638712b}} under a generic condition.
Following the same research line as in {{cite:2118db2022fb1c79d2183f028b39e6f0de6fc601}} our main results in this paper based on this approach state some Nichtnegativstellensätz under more general conditions.
In particular, {{formula:90d053e8-ce90-47eb-be1f-37c2a39d2b08}} still has the representation involving preordering when {{formula:8e985b62-d1fd-4448-bc5e-acf1ee879f2c}} has finitely many values on the intersection {{formula:6a12989c-b0d1-48f6-be7b-08726858b4c6}} (instead of only {{formula:e8776fff-68ab-4958-8b61-32bf115d7ef7}} as above) under the more general condition.
| i | 0f0e3dca2f9ba3372bf693252c5af899 |
where {{formula:35638605-b675-4e8d-9049-329baaf2d431}} is the permutation group of size {{formula:4bdd1cf2-a0ef-40e2-8bee-113f236c0141}} . Surprisingly, although these two matrix functionals have the same number of terms and are defined in a very similar manner they behave very differently and, on particular, have strikingly different computational complexity: While the determinant of an {{formula:e2eab55e-d677-45b4-b28b-b4a10c362f6f}} matrix can be computed in {{formula:4ff1006d-c491-4beb-9f1d-b9873c3a95a2}} time {{cite:d95f136376442e81f881e10870ee62021d80530a}}, {{cite:6aadbd93d861b67c18375f12bb46e7b35d1d6a52}}, computing the permanent is #P-hard {{cite:cb8f8dcb6cebd4749bb6b75f87ca32d34f9c633a}}. Well-before the seminal paper by Valiant, mathematicians investigated the difference between computing the determinant and the permanent. For example, in 1913 Pólya {{cite:5c81309603db5964ec5c5479bd344dff4d25a6cc}} asked for which matrices it is impossible to convert the permanent into the determinant by just multiplying the entries of the matrix in any uniform way, and it was shown by Szegő {{cite:91005250c45b7fc071e7ad3f7ef4d609f9b0880d}} that this is generally impossible for matrices of size greater {{formula:c3dd6ad0-4e1e-465d-801e-46913a94ec49}} .
| i | 6bb34e521e59274e1115de83371690f4 |
the lifting {{formula:8cdc3ed5-29cb-4667-91bf-081535e030cc}} can be approximated by {{formula:0d4f0212-e2d4-467d-8a27-4a43f70f96e6}} sinusoids whose {{formula:fba31c99-dac2-4665-a0b6-a26ce7653592}} -dimensional frequencies {{formula:669799ab-a9dc-4e9f-9bd8-39a8db92c728}} are sampled from a Gaussian distribution in the input space with zero mean and spherical covariance with variances proportional to {{formula:1d05cd1a-a8c1-4b4b-91c9-26bf41de6954}} {{cite:972a7f448a113e3adfbdd2f48d0d802cadbff30a}}. In other words, the {{formula:16991a8d-74da-46cf-80be-cc9bb3bdf897}} -th component of mapping {{formula:62157fd4-3a00-4643-be0c-6fe0532c68fb}} is:
{{formula:73666abb-d928-4805-a73b-8ceacec57c50}}
| m | 7328a218d490e79043eba138042e295b |
As an alternative to MCMC, others have embraced variational inference (VI) in
which the intractable DGP posterior (REF ) is approximated with a
simpler family of distributions, which are often also Gaussian
{{cite:7609996f264fedddc2e7b5e0bb51970aae6bcfc9}}. Inspired by deep neural networks, {{cite:1188828f739f7ebed164966496d79686abfb0eff}}
proposed an Expectation Propogation (EP) scheme for DGPs, which is closely
related to VI. {{cite:c5481381809b9f85feaf49f1ee31ffb19b15934f}} broadened previous VI-like
approaches for DGPs by allowing intra-layer dependencies, naming their method
“doubly stochastic variational inference” (DSVI). The main advantage of
these approaches is that integration is replaced by optimization, which
requires less work. The disadvantage is that optimization ignores uncertainty;
the fidelity of a VI approximation is linked to the choice of variational
family, rather than directly to computational effort. More MCMC always
improves posterior resolution; more VI does not. Hyperparameters
don't neatly fit into variational families otherwise preferred for latent
nodes, so they often get ignored, or their tuning is left to external
validation schemes. By contrast, extra Metropolis easily accommodates a few
more hyperparameters without hassle.
| m | 2662b299d1719c74f29e96f418c076df |
Since it is relatively narrow and is seen as clear signals in both {{formula:77f7e9f3-5779-42e7-b13b-9110121bccd1}} -meson decays and {{formula:79d891b8-ae6d-4310-85cc-f5d5160b4da0}}
fusion reactions, the {{formula:b13f0735-d952-4423-8eca-c0b188902b6b}} is one of the most intriguing of the {{formula:4dfc6117-6a5d-4559-b8e8-65fca3681b51}} exotic meson candidates.
However, significant progress in our understanding of its underlying nature will probably not be
forthcoming until larger data samples are available in future experiments such as
BelleII {{cite:108322a35cca822211a574dc36e9043ee9d187cb}}. With the order-of-magnitude larger event samples that are expected for
BelleII, we can expect definitive {{formula:ac87366e-c471-4acc-b6b0-c5ea72329605}} determinations and measurements of, or more stringent limits
on, the strengths of the {{formula:9db7825f-d92c-406b-8cd6-a43ec6630faf}} and {{formula:72314073-ae5f-4483-9d24-a801d7e9680a}} decay channels for both the {{formula:4e9da0c2-b05b-4ead-971f-23b80b049ac8}} -meson-decay and
{{formula:faba9824-b162-482c-82e6-1f3d7bb4d38a}} -fusion production modes.
The LHCb experiment has demonstrated ability to detect {{formula:d3ca42be-4349-45a1-9fdc-dcf8790b498c}} mesons in {{formula:e0b2464f-de0f-49a3-a19f-9c170f2b33eb}} decays {{cite:6c4b3ef5c24abf5464b98572dbedf66fc87b9f66}}
and should also be able to probe the {{formula:e3dd51ee-75bf-4f46-a092-d9c5b6c03666}} quantum numbers.
| d | bb41cc1fbfd3644dc09f0d90ff8e3078 |
Irreversibly also increases the complexity of decoding the diary in the radiation. In section , using the conjecture of {{cite:c9f1a5147aadf3e570af6687e0acdcdec998c61c}}, which relates the complexity {{formula:3eeadff1-117f-4903-9fd0-0c0e57fff64d}} to the size of the python's lunch, we found {{formula:17e5d99b-df59-418c-ad8d-a483d456c1d7}} , where {{formula:a5b48bde-c660-461d-aa6c-83a98bd8ba5d}} is the estimate based on reversible qubit models {{cite:b602210073b7eb92e03cb9c00491356460555d93}}.
| d | 1d40694a9df6d5a78e5171684cc8584d |
Here, we briefly describe the general trends of Model S. We discuss the results as functions of various parameters in the following sections.
First, we find that the surface brightness profiles become more extended as the total H1 column density ({{formula:59329afb-be17-427b-82bf-71eb5fed0970}} ) increases (Figure REF , left column).
Second, the polarization patterns are concentric due to the spherical symmetry and increase radially outward (Figure REF , second column). These predictions are consistent with previous findings {{cite:8e4a99e42c2b184d437f6ff6f47663ed6e99a8f8}}, {{cite:3ad003679467c87a8faa0723c0dff4349f75bb0b}}.
Third, the degree of polarization (DoP) does not behave monotonically as a function of {{formula:719652ba-9933-468f-9530-dc59693a37a1}} . The overall DoP peaks at {{formula:5134732a-8729-452b-810b-9624779cbba1}} relative to {{formula:e0879a31-4f47-41ae-ae8c-c72ca7f51738}} , {{formula:5286de39-c025-48bc-ad25-d04d127307e8}} , and {{formula:9c34c461-c72a-475d-9cea-b8a7e5089282}} .
Lastly, at {{formula:e2a5c5cd-8e5b-4c84-b7b9-224f3f0b32e6}} , the degree of polarization increases steeply from nearly 0% at the center of the halo to 20%.
Throughout the paper, we will refer to this behavior as a “polarization jump.” This discontinuous DoP profile is one of the most surprising results from our simulations.
| r | 9029de6b1667da224f07d07c76b83b1b |
We conclude by remarking that the next step in our line of work concerns electron-ion ({{formula:c785e65a-70df-43d1-b888-cadfc9919bd3}} ) simulations. Studying the case of large mass ratio, and especially the energy partition between particle species, is fundamental for the correct interpretation of data from current and future observations targeting RIAFs ({{cite:486de535cd8b63a032bee0f279c97effc447d21d}}). In these collisionless astrophysical environments, electrons and ions are decoupled and a two-temperature state can originate from turbulence and/or radiation-reaction dynamics ({{cite:b990115e1db9e9accbf455c4a4624e3e12c0e1fa}}, {{cite:04c33b89772f029b2ba7f4f4851b5e49c432c7dd}}, {{cite:fc065cdd92cc5d4bc6822b14dc9d8788196f0eb6}}, {{cite:ac80cf04c796e73b794adc0c018611f2cbb6d95a}}, {{cite:b7d1ff9ccef6cea7d4a9083f55990dbb838c80b4}}). With our simulations, we will be able to study the process of temperature decoupling (and possibly the dynamics of radiation) during the MRI from first principles. Moreover, information from fully kinetic simulations can be used as input for global fluid simulations of accretion around compact objects employing subgrid models to account for the missing microphysics ({{cite:b84571248371b3ce419715719295f1e411752470}}, {{cite:73185f4e06d26badb6f0f647e846f8b3304f5124}}, {{cite:358b1c23aa94c683b16ac4f620f0525b691f710b}}). Given the ever-growing interest in understanding the dynamics of collisionless accretion disks around SMBHs, we believe that this work has the potential to substantially impact our insight into the physics of such space environments.
| d | b62ccc20f989c2091fe14d9ca2b0b9b8 |
A natural but impractical idea to tackle the discontinuity problem is to let each client inherit its own client optimizer states from previous rounds. However, these previous states can be stale and inaccurate because they are evaluated at point {{formula:acfe6c48-e20b-4a06-b8c3-7a515adb8d8f}} and do not take account of the possibly dramatic changes from {{formula:7c1ea3c4-94d9-4b06-9619-f024924bb7ab}} to the current iterate {{formula:934760d0-5c82-4827-9ac2-5dbbdd6435fb}} . When the server only selects a random subset of clients at each round, the staleness will be further exacerbated, as one client may be disconnected from the server for multiple rounds. Besides, this solution is impossible in many applications of FL (e.g., the cross-device setting) that requires clients to be stateless and not to maintain any persistent states across rounds, due to privacy and system constraints {{cite:ca126777e9486b993e429b02ee703ddd5bff9e02}}.
Furthermore, one can also choose to synchronize the local optimizer states at the end of each round and use the synchronized states as the initial value for next round. For example, {{cite:62f338aa41a922ed28e9933e01d27e70424096cf}} has used a similar strategy to synchronize momentum buffer when the clients use momentum SGD. However, in order to aggregate and broadcast the additional optimizer states, this strategy would incur doubled or tripled communication costs compared to FedOpt with vanilla SGD client optimizer.
| m | 5fcb80f8d6343de5f6c3dab45d3298b8 |
Kernels have been found to be fruitful in a variety of domains, and the presented results on kernels on non-standard spaces are likely to be of interest to extend the applicability of kernel methods.
In particular, we enrich the collection of kernels on Hilbert and Banach spaces with classes enjoying proven integrally strictly positive definiteness, which may be relevant in functional two-sample testing {{cite:1a0303e2b5d2d7eb2702d5b6729ea99c3cb92453}} and further endeavors in functional data analysis.
Kernels on measures are of special interest for machine learning with set- and distributional data {{cite:e53d6a3f7819159dea9b413b7a6fb52ba3519446}}, {{cite:fda79a5739d924146ac65cf0cdbe74d457eeea06}}, {{cite:80f2512d0874cfe64133f666ac81f359a280fa11}}, {{cite:edc74c404bb5781b73b1ddbbfedd0ab28c7b0f93}}, as well as in the evaluation of probabilistic forecasts {{cite:bbdc3bccf628846f6ddf31f3de4451518a9c3577}} with kernel scores associated with characteristic kernels providing a versatile source of strictly proper scoring rules. To give a concrete example of a new avenue of research, scoring rules for point processes are just in their infancy {{cite:3b211f9ba99eb248dad57bc9e10039b57d158cb4}}, {{cite:0131c521e11ff7c947c74f152da6d266ed5beb46}}, and results established in the present paper pave the way to novel classes of strictly proper (kernel) scoring rules on such objects.
| d | db2892ddfffa85c1859d42fe5ce5648d |
After showing the details of these traditional adaptive gradient methods and Adam-type methods, we introduce their convergence properties as well as their further variants. {{cite:414766654c630d67c8c6efe5380d6cdbadceed79}} shows that Adam does not converge in some settings where large gradient information is rarely encountered and it will die out quickly because of the “short memory” property of the exponential moving average. However, under some conditions, the convergence proofs of adaptive gradient methods have been obtained. {{cite:1e461cc4901e994aeb7f0adf9848c4a2e6d91417}} proved the convergence rate of RMSprop and Adam when using deterministic gradients instead of stochastic gradients. {{cite:c5781aa9bc1159e00814a6d0bde144df2bcd3dc8}} analyzed the convergence rate of AdaGrad under both convex and non-convex settings. All the papers above provide theoretical guarantee for the convergence of different types of adaptive gradient descent. After that, {{cite:8f6c2c47faaa9d4b88c1714fbed3716e65496b1c}} extends Adam to a broader class of Adam-type algorithms and provides its convergence analysis for non-convex optimization problems. In order to combine the fast convergence of adaptive methods and better generalization with momentum based methods, a number of new algorithms are proposed, such as SC-AdaGrad / SC-RMSprop {{cite:0b5fd8b395299e495781100019e7a6b766f772dc}}, AdamW {{cite:8bf4ed3b31e7bcd8754eb67286c0a6aff4ff8818}}, AdaBound {{cite:e449030d32847161ab71e11599c3a166b918c0f8}} etc..
| m | b9d49209d7e5a30a0bc707198e8d4c4c |
In this work, we consider a left-right symmetric framework with the simplest Higgs sector consisting of only two Higgs doublets, a left-handed and a right-handed under the two {{formula:acb1bf4a-90e2-42af-9508-8a68dbcf4a9e}} group factors. This leads to only two neutral physical Higgs states, one of them being the SM Higgs boson of mass 125 GeV. Due to the minimality of the Higgs sector, vector-like fermions are introduced to generate masses of the SM fermions via universal seesaw mechanism {{cite:f35f3e2703d6554a529906d870002c6ed8936818}}, {{cite:dfd1ee8daf9952ee3a4e4019e35a493bc220550f}}, {{cite:34727f52ff7620f61d0df8f00df13fced1c194c0}}, {{cite:97c3f7406a5ad294d03aae2a7aff5d46da6c3f47}}, {{cite:619d58cd02c9186582f4df6a0f672153426d7881}}, {{cite:641ff0dd0403f37cb7251f3f24d13599a04caafa}}, {{cite:ee853a2020aed1aa2609ead34394331004f45a33}}. One of the most attractive features of this class of models is, strong hierarchical structure of the SM fermions is naturally realized without the requirement of fine-tuning of the Yukawa couplings. Unlike the SM, where the Yukawa couplings lie in the range {{formula:77396b66-8bfb-48e3-a769-28bca222069d}} - 1, a smaller range of {{formula:fcd91034-3921-429b-b80f-9f5aa115a78d}} - 1 is sufficient to explain fermion mass hierarchy in this model. The observed mass hierarchies of the SM fermions are naturally explained via the heaviness of the vector-like fermions having inverse mass ordering. Another motivation of this framework is to solve the strong CP problem based on parity symmetry {{cite:619d58cd02c9186582f4df6a0f672153426d7881}}, {{cite:641ff0dd0403f37cb7251f3f24d13599a04caafa}} (for a recent study, see also Ref. {{cite:0f1d3a3a7995da7207513c57d902343c8d989a67}}), which does not require the implementation of Peccei-Quinn symmetry {{cite:50091952d765b5a1daab09a25378de383fa2e400}}. In this work, we, however, do not impose parity symmetry. As will be shown, parity symmetric solution that demands the left and the right couplings to be identical (for example, {{formula:b3d806e6-ab19-4574-9f7b-24d01f3640f4}} ) fails to correspond to the strong first-order phase transition. From the phenomenological point of view, an advantage of this setup over the conventional left-right symmetric model that utilizes Higgs triplets is the possibility of incorporating lighter gauge boson {{formula:2fb03365-4d46-4703-9ead-1b6e627a0b5b}} that may address flavour anomalies, see for example Ref. {{cite:d30ea56880ff01335dd7e3265a0e6a27b55d9678}}.
| i | f20cc68cb895ae2540c6693fccd4f088 |
A popular method for computing the DRT involves the use of the
Fast Fourier Transform (FFT).
The basic approach is to sample the 2-D FFT
along different radial lines through the origin
and then use the 1-D inverse FFT along each line to estimate the DRT.
This direct approach suffers from many artifacts that have been discussed in {{cite:32c87c5498e2e6eba999b023a47f7725318e3b27}}.
Assuming that the DRT is computed directly, Beylkin proposed an exact inversion algorithm
in {{cite:d9859d1078cdb891546ba8ad0f695c63d8fc4f3d}}.
A significant improvement to this approach was proposed by
Kelley and Madisetti by eliminating interpolation calculations {{cite:f4673aa307458bed99723928df3aa6ddea46574e}}.
A common way to address this complexity
is to use Graphic Processing Unit (GPU) implementations as described in
{{cite:fda76b914eeaa3501399c8d94fd511ba12d545ba}}.
Unfortunately, this earlier work on the DRT requires the use of expensive floating point units
for implementing the FFTs.
Floating point units require significantly larger amounts of hardware resources than
fixed point implementations that will be discussed next.
| i | e9ff47efc01d9e6b7b5e1a4c5c917d1e |
Therefore, in this paper, we evaluate the effect of using different learned feature descriptors in the pose estimation of a hybrid monocular VSLAM pipeline, shown in Figure REF . We evaluate two learned descriptors on the same VSLAM traditional back-end, similar to the proposed in the well-known ORB-SLAM {{cite:707d70936f2ce3502f8d9142e53fa9be2f8b9583}} algorithm. We adopted the following learned feature extractors and descriptors: Learned Invariant Feature Transform (LIFT) {{cite:85bc5b25b8b14e3355e63492f7a6bedd5c477d86}} and Local Feature Network (LF-Net) {{cite:2b8cf6a179b1aa8873030f4d033b1c61297c7c90}}.
{{figure:b0ed07ba-ebe9-4566-982b-6f7ab77a8e09}} | i | 7acb9ba48e9adb1a2a18f5f5b85ffb66 |
FigureREF illustrates the framework of our proposed CLIP4Caption++ for video captioning. First, we use the pre-trained model of CLIP and SlowFast to extract visual features from origin video (REF ) (higher part in Fig. REF ). Second, we sampled the extracted frame features using TSN {{cite:f1dda6f63f781d505a6744ad27b9379077d8f223}} sampling (REF ). And then, video feature and text, as well as the token type, were embedded by embedding layer for bimodal feature fusion (REF ) (lower part in Fig. REF ). For ensemble, we train multiple caption models with the different settings and ensemble the output of multiple models for a final strong result (REF ). Details will be elaborated as follows.
| m | 763361dfd953974d5c6b878e96c5b7ba |
The second method is to use GAN {{cite:4a0ae18a313f560612dc78b24de1781b77d918f9}} to generate training images.
By using conditional GAN, we can generate images with specified labels,
Once we train conditional GAN on an existing small dataset,
we can generate any number of realistic images.
This method has been used as a data generation method in medical image processing
where it is not possible to collect large scale data such as MRI and CT {{cite:eae5274763b5bd1c2e9f8cb9e67343492996552e}}, {{cite:100b034f9ae2963181386dc50094d8b3354a11b1}}.
GANs are good at generating images with specific structures
such as faces, human bodies, animals, and indoor images.
But it is still difficult to generate various scenes
and videos {{cite:77eaf65a3b9f0f974f0833030a787b262280e3e6}}, {{cite:a5acf13bb4ad0f3fd9bf9d327c623ba90194fa23}}
such as those appear in videos for action recognition.
| i | 4e7f79991de0bcae7907d62febb5e3fc |
WebVision. WebVision {{cite:26d947258db06b89923afd30275d6156413a2b0c}} contains 2.4 million images crawled from Google and Flickr using 1,000 labels shared with the ImageNet dataset. Its training set is both heteroskedastic label noise and class imbalanced (more detailed statistics can be found in {{cite:26d947258db06b89923afd30275d6156413a2b0c}}), and it is considered as a popular benchmark for robust learning in the presence of heavy label noises.
We trained Inception-ResNet v2 {{cite:a6280814afd54cc0b360fe4292514c6741189acf}} with softmax cross-entropy loss by SGD with a momentum 0.9, a weight decay {{formula:56db3ade-e6dc-4e26-91be-33a41a0496d1}} , an initial learning rate 0.1 and a batch size of 256. The learning rate is divided by 10 after 30 and 40 epoch (for a total 50 epochs). The transferred CMW-Net is used at every iteration to produce proper sample weights for robust training.
The test performance on full WebVision and ILSVRC12 dataset are presented in Table REF .
| r | b35eccea615dfadf7e74bdf31baf7881 |
where {{formula:e7166527-7b90-4338-898b-af8e61fe53a6}} and {{formula:b486aa3d-4907-4687-aca1-21d4fcae0e70}} are iteratively increased, in order to find solutions that minimize {{formula:9aefc680-af31-4076-adcd-7452d4660ed2}} (see {{cite:6df3d1820c5479f97f7f0df2ed890506dbca3321}} for the full details).
Asymptotically, this leads to an (approximate) DAG structure for {{formula:ca525bf5-f905-41bd-9555-2d615a803eb3}} .
The whole algorithm can then be seen as an outer update step, where {{formula:b89990b0-a86e-48b3-875b-287b1e7bc98e}} and {{formula:10a1811d-fba7-477a-9f7e-25ebfb1c6216}} are
increased, as well as an inner update step, which can e.g. be solved with a second order Newton method, such as L-BFGS-B {{cite:5f30e5ac50cdf384c6342e4f2556c03f2af91e34}}.
There are a few points worth noting here:
| m | 8d019345c7b1c579535ccd548a6bc331 |
In bulk, it is prestablished that a short flexible chain exhibits weak compression under direct field{{cite:80910312d3f32dad18fce7dd5503fd9b085d22b1}}, {{cite:d5148b7413b5a30b129a91864bcd53cec307c415}}. Figure REF elucidates the structural response of a confined semiflexible polymer ({{formula:1fb08f3b-9918-45d3-962c-07bef1cdeff0}} ) under subjection to a constant DC field. This is parametrized in terms of average radius of gyration, given as {{formula:aef1d16d-6908-42e5-8121-c0266f292546}} , where {{formula:963708d4-2f60-47e3-b350-3bd05c81612b}} is the center-of-mass of the chain. The retrieved curve exhibits a non-monotonic dependence over {{formula:69530d43-31d7-4c68-a233-bfeb453ab7e2}} , where within a moderate field strength chain exhibits a significant structural compression, followed by a stretching at higher field strengths{{cite:d5148b7413b5a30b129a91864bcd53cec307c415}}. This is qualitatively similar to the stretching response reported for the flexible chain in bulk, with the exception that there chain compaction was seen only for smaller chain lengths and weak field{{cite:3ec9ba997a7c1c3bd9c088b744753a22bd9cf038}}, {{cite:98e6a4da7596e49d84b9a9e542c3bd8cea93630f}}. However, for a confined chain, not only the compaction becomes prominent for {{formula:1f194caa-5737-4f40-ad39-bdb91c853756}} , the favourability of the induced compression shifts toward higher fields with increasing persistence length. Also, the relative compaction gets more pronounced for higher bending rigidities such as, for {{formula:0998f584-e386-41c3-8159-21f630aa99cc}} it is roughly {{formula:025ea681-acb9-4c81-8edc-23e49ebb9ca5}} , while for {{formula:cc2043d0-6401-4818-baf6-b6a668b88060}} , {{formula:49a5d040-8159-4dec-84ed-59793cdd859a}} , with {{formula:24adb5ba-991f-442e-bb7e-f8cac6a09e81}} being the radius of gyration of the chain in equilibrium. This is particularly fascinating considering the long and semiflexible nature of a typical DNA molecule{{cite:4eb3d474813d973f4d72d4250df99fa9552ad48a}}, which reportedly exhibits collapse under applied fields{{cite:4949d0f0648d51b22b88aaffecf4c771a4f76a62}}, {{cite:7677fb343fad4d6d88ff6428876fa32e25ccb1c0}}, {{cite:83fc2f0dcecac638ba486f29b0858f8101ed6df4}}.
| r | 6c3762a912a63ea4a986ba88d9283206 |
In Fig. REF , we show the results of this comparison for both datasets. For VOC07+12, in Fig. REF a, we observe that starting from the first two active learning cycle, our method has a relative improvement over the random baseline by {{formula:ce788592-2254-4a60-b2c4-1b3927833c75}} , over the best overall active learning method {{cite:3f9e891cfc193488f7e234fada2be671b4b8204e}} by {{formula:f88b9700-ac50-4e25-b999-4d0b351e4468}} , and it outperforms the semi-supervised method of {{cite:613e7232dc98b75d890f1f63785e021f81f3c89e}} by {{formula:5df36a5f-8647-49ec-8093-6ba05cb817de}} . We see that the performance improvement of our method is maintained in the other active learning cycles. In the last one, where we use {{formula:c7168fbb-0028-4f5f-87bc-6f47c8d28800}} samples, {{formula:18ec2ada-b077-4638-8429-89393cb1f8d4}} of which are actively sampled, our method outperforms the random baseline by {{formula:a45469fc-a67a-4cc7-b62c-c9ecf804a5a3}} , best existing active learning methods by more than {{formula:b81c67cd-af0f-4fe6-80d5-37682fd013b8}} {{cite:5abac42b53d15e2e7402a829fcc8da6638c873d4}}, and the semi-supervised learning approach by {{formula:31743d90-18ba-4345-a260-cc94f3a5f547}} .
Multi-model active learning networks, namely, ensemble {{cite:3fabcc12c98d01f72f96baa838458fba483ac6f6}} or MC-dropout {{cite:e785387be4b5811d567ad72c3de0805b873bae47}} typically outperform single models at the cost of longer training and active learning time, and in the case of the ensemble has 3 times more training parameters. Nonetheless, our proposed single model still reaches better results than multi-model methods, outperforming the ensembles by {{formula:664ac09c-e138-453c-b3f7-60364c443084}} in the first AL cycle, and {{formula:fcfdd052-d18c-49fc-b4b5-5034bc6ff812}} in the last cycle.
| m | a1cd5a05a8c111e0de8d16e23734475b |
The performance of the proposed framework is compared with nine state-of-the-art learning-based and classic deformable registration algorithms including SimpleElastix (Elastix) {{cite:d6dfe020884284cb5f049a64d1564841d65b3b32}}, Moving Mesh (MM) {{cite:5de5d6cd2fc29f53428da165bc5d21c7eac46ac6}}, Real-Time Image-based Tracker (RTT) {{cite:4e66754c7c3c8953b1965d86088c914ce2adf6e8}}, Demons {{cite:b01265c76660a5a0e77e57f878998a1a841ee74e}}, LCC-Demons (LCC-D) {{cite:820174366fc1011ca62510df490508d4d5fcad93}}, Symmetric Normalization (SYN) {{cite:77ef0508c9640f2f4b6025c4625b2607af944190}}, {{cite:006a51fa00b037e861fbc6071e54d676ad45a970}}, {{cite:54b0f22b3040c1004330ab27407b595972f88960}} and DIRNet {{cite:bbbcfb53023694a666f22a4bbb00e78c28601c59}}.
| r | 3372ae663e860ba8639fd6a2a996db8c |
In this section, we describe the details of the proposed network and the motivation behind the design ideas while connecting these with literature and hardware limitations. As mentioned before, we designed our proposed architecture by hand and adopted an efficient building block for SISR problem inspired from {{cite:4e1ac803bd0b2a90bd900a1319f0ff28837606a6}}, {{cite:5779b99972f9cb6549060566574581299a87cdee}}, {{cite:8a298becfe7e5c7a02160863b759243cb4dc59f5}}.
| m | 7c678801b7cf4cef5ca93d31666406b5 |
For the LM to understand language in the context of suicidal thought patterns it needs to be fine-tuned on such a data. For this we word2vec representations on corpus of suicide related subreddits as as well as fine-tune LMs during training on the same corpus. Thus we obtain embeddings of the text contextualized to suicidal conversation in order to accurately infer yes or no from similarity. To implement the word2vec model, we use the gensim library and the Continuous Bag of Words (CBOW) model {{cite:a3348659976963019e48475c29949a93793cdca5}}. Note that in the word2vec model due to lack of tokenization coverage as in LMs, we chunk the string one letter at a time and check against the list of words and their vectors. The LMs we fine-tune are:
| r | c782bd50d3060487b812c1f06a978d56 |
In this work, we introduced Smoothed-AND (SAND)-masking technique that improves the performance of the current state-of-the-art OOD methods over a variety of datasets. In fact, SAND-mask aims at addressing the failure modes that we identified for a recent major contributions in the field of OOD generalization, i.e., Reference {{cite:a63f1a169f89031852550087c6cfa70221fbafdf}}. As it is supported by a rigorous and exhaustive set of results on the DomainBed benchmark, SAND-mask outperforms its counterparts and significantly enhances the classification accuracy over the Colored MNIST dataset for about {{formula:4d3697c3-5153-464e-98f4-3299514afc49}} . Despite the superior performance of SAND-mask over different datasets, in what follows, we elaborate on its limitations and potential direction to be pursued in future.
| d | 66250a5785bb142b7debecf944309160 |
We show {{formula:fc3759e5-31ea-4dd6-b84f-b02149a459e5}} versus {{formula:0637b5f0-6e49-44cb-bde2-5e8989f42630}} in Figs. REF , REF ,
and REF for different parameters of the system. We can
see that {{formula:a34b34f5-ac3e-4b76-8c6b-4e4370361f0a}} reaches its maximal values in a plateau which spans
from {{formula:983c9233-0d86-49e1-9767-2bb9b4d5cf80}} to {{formula:30149c2b-a9ee-4811-b137-072e4116bfe1}} . It matches the frequency
range probed in Ref. {{cite:5cf20d297e452a2c80d83779dd848c3c0ceb9acc}} in the search of a stochastic
GW background. The observational upper bound established in in Ref. {{cite:5cf20d297e452a2c80d83779dd848c3c0ceb9acc}}
is {{formula:dd482848-2a81-4cf8-ac94-8b11f7e28c4c}} , which is also depicted in
Figs. REF , REF , and REF .
For the convenience, we summarize the parameters of the plateaus in
Table REF .
{{table:469823f1-a529-4387-9ecb-9afde5a2f3d8}} | r | 4078dc3e5cde0ca9fd63c7b227b6ca7d |
Our treatment of the AGN IR emission has also glossed over much of
what it constitutes an altogether distinct subfield of AGN study. It
has been suggested that clouds are also involved in this component
of the AGN spectra, however with different properties and at radii
larger than those of the UV and optical line emitting clouds
{{cite:416364ba8e21b7433f5ac1296776b675e105590e}}. This is clearly a point that will have to be
looked upon with greater care. A complicating factor in this
direction is that of star formation in the AGN environment, whose IR
contribution introduces additional parameters in such a study.
Finally, with respect to the IR and far-IR AGN spectra, we would
like to point to the synergy between X-ray spectroscopy and far-IR
observations discussed in §5.1 that would help establish the
consistency of this scheme across two very different frequency
bands.
| d | 99bd944652a8e7afc7054fd34d815849 |
To best address, the above question, a method based on Fourier optics (FO) and vector spherical harmonics (VSH) is used to computationally explore longitudinal coupling in structures resembling cornea. The VSH is the vector solution of the wave equation in spherical coordinates. In 1908, Gustave Mie was one of the pioneers who used VHS to address the incident and scattered field from a sphere illuminated by a plane wave {{cite:265752271899532f0e1209d202fd8e3dd8dcb6a3}}. Later, Davis modified the theory for Gaussian beam illumination {{cite:0c83ef1396e380ffa3acaa4dc7259e183537dd1f}}. The early proposed method was quite intricate and cumbersome. In 1993, Khaled et al. {{cite:4522a93d1104aae960ac1991bbd5277c7a5f30cd}} presented a method using Fourier analysis {{cite:0974944eca98ecc80d14f3d72e610c37c0a76c2d}} to model Gaussian beam as the angular spectrum of plane waves, and for computing scattering coefficients, they employed the T-matrix method {{cite:2479e723c2daebd1a05dd5d0bd099593790f316f}}.
| i | dc7f6ace8d5081a7857e347a22dbdb7a |
Their values are not completely restricted by the theoretical constraint in {{cite:a8035f5b0e602f2d9b2647352bf85962f745706d}}, but merely focus on the actual FLOPs budgets in each scaling stage. This means the searching process of ours is more fair.
| d | 287934cdfc0a075eaf3df721558ccafa |
Motion deblur. Corresponding to Case 3 in Fig. REF , we compare our DMR results with state-of-the-art, Event-based Double Integral (EDI) {{cite:a29a13d1752551b2e02a991356703f2358f08abf}}, shown in Fig. REF . Compared to EDI, our results preserves sharp edges while alleviating event noise.
{{figure:85059c12-7127-4189-a0cd-2203ce55f077}} | r | e43ef4fd3ad1f54490d3a737fd0e113f |
The ground and first excited states of {{formula:391b0efb-caa7-4675-8a25-9480d28f4022}} have been computed in a recent paper by a variational method using the ground and first excited states of the harmonic oscillator Hamiltonian as trial states {{cite:0fcbeea9ad441b2f32c73f898279362fc8ec88ce}}. The results from this paper are compared with the ET results in Fig. REF as a function of {{formula:ca5b053b-66c4-41da-8872-90e28187996e}} . Let us mention that the dimensionless numbers obtained with the formulas in {{cite:0fcbeea9ad441b2f32c73f898279362fc8ec88ce}} must be divided by 2 to be compared with our results, because the energies are given in unit of {{formula:b2048bf7-4794-46fa-885b-04e75b89816e}} , while they are given in unit of {{formula:f4a53b09-a78a-4019-ace7-20dd7304deb5}} in this paper (see (REF )). It is clear that the variational upper bounds are better that the upper bounds given by the ET. Nevertheless, the ET can give the whole spectra with the same computational cost. This is not the case in {{cite:0fcbeea9ad441b2f32c73f898279362fc8ec88ce}}, where different integrations must be performed to compute ground and first excited states. Moreover, the variational principle states that the expectation value of a Hamiltonian for an arbitrary trial state always gives an upper bound of the ground state. But an upper bound of an excited state can be reliably computed with a trial state if it is orthogonal to all exact states below this excited state {{cite:1a867fdabeb3ac5b98f7786e2d8baee702418ec5}}. So, for a one dimensional system, an upper bound of the ground state can be computed with an even trial wave function and an upper bound of the first excited state with an odd trial wave function. The computation of the other excited states is much more complicated and requires the expansion of trial states in an (orthonormal) basis {{cite:d2287ef6e844456f1108d73979c4458fb8749665}}.
{{figure:0ef54f73-fe3e-4280-bb0d-655a56efb0ac}} | m | dbe1ef944da6d6b1126196a3ed78efe5 |
Existing studies on analyzing privacy leakages focus on either general machine learning models {{cite:0bf245cefbd6a7b4d86feaea5770c4eb2586e590}}, {{cite:d9306cd23e019d7d0dfa8a4d0613b56ccb4092f8}} or in a federated learning setting where model is collaboratively trained by multiple clients by sharing and aggregating the gradients via a server{{cite:2ede20e87ba1fa737c36af385d1df759e4403799}}, {{cite:d9306cd23e019d7d0dfa8a4d0613b56ccb4092f8}}.
However, there no such study on transfer learning paradigms.
To this end, we are the first to provide a general categorization for deep transfer learning models based on the potential information leakages.
This is not trivial since there are numerous methods
for deep transfer learning {{cite:cd858dff9c0e447d9c35a6fce8d21ae7fd6901a8}}, {{cite:81b4e3a52b3b500a7790868555788c64f07af11d}}, {{cite:362e77b903e520bdd7f6e7584fe00812895bc61a}}.
Given the goal of privacy leakage analysis, we care more about the interaction manner between source and target domains.
Thus, we divide previous works into three categories, as illustrated in Figure 1: (1) model-based paradigm where the whole model structure and parameters are shared (2) mapping-based where the hidden features are shared (3) parameter-based where the parameter gradients are shared.
Based on that, the previous works can fall into the above categories or a hybrid of them.
For example, fine-tuning based approaches obviously belong to the first category.
The prior work {{cite:38dac53ea411590110d3582ca2b26624c06825ae}} is based on the mapping-based paradigm, since it uses the correlation alignment loss which further depends on the shared hidden features. Similarly, previous works that minimize the domain representation difference by variants of distribution divergence metrics such as maximum mean discrepancy also fall into the second category {{cite:e3e49dd974adbc4574e9ec56b6f1eebfd8252018}}, {{cite:c74478407128a692e7ce1cc3a977f9f9ff3a74f0}}, {{cite:33bb1fd7476990ee63a8b586734a5c962b92b52d}}. Fully-shared and shared-private transfer learning models {{cite:fd4f372cbc32df79d4609dcbb7e6da8697b081a8}} can be regarded as parameter-based, as they both jointly train a shared network via gradient updates in a multi-task fashion, just to name a few.
{{figure:48ec9097-34b1-4134-a40b-e16be678c445}} | i | d2a1798dd89e3982f760f4ebaea9c0a9 |
Where M is the number of simplified input features, {{formula:4e8844c0-e71f-4a9a-9364-b289cf34a878}} is the number of non-zero entries in {{formula:2537afeb-497c-4929-9340-15b823189ccd}} and {{formula:26f09b61-0719-41dd-8dcc-28d505279e6f}} represents all {{formula:cff8cbf7-a5e5-4205-83c3-af5892c192ce}} vectors where the non-zero entries are a subset of the non-zero entries in {{formula:f58104fa-aac0-4b22-ba39-9f11564e30bd}} , and S is the set of non-zero indexes in {{formula:e16fbe8f-d9a4-435f-9682-f46bddd8a030}} . The SHAP explanations were generated from code by {{cite:59213a4a363c3dd065f1239b18c02f13533801e8}}.
| m | 4b5155d3ef535751026be6789a24a696 |
To demonstrate the performance of C-VTON, we first analyze Fréchet Inception Distances (FID {{cite:535e54ab82f6bd903a65c0d76a13db233752b7ec}}) and Learned Perceptual Image Patch Similarities (LPIPS) {{cite:eee24115062e3ab84e2c7389622835980d655bf7}} over processed VITON and MPV test images and conduct a human perceptual study (similarly to {{cite:128493416243e38e43dab51a669141e3855a2802}}, {{cite:2c6c4ece1f874bcb4975fe7e0d546f399a37ae6f}}, {{cite:b22068a278e834355fffc65072c6813482180fb8}}) on the MTurk platform. For comparison purposes, we also report result for multiple state-of-the-art models, i.e., CP-VTON {{cite:b22068a278e834355fffc65072c6813482180fb8}}, CP-VTON+ {{cite:577aa446c35ca92762c9c478e8a2394e70330f75}}, ACGPN {{cite:1f47fb434a02323c768fd9e91bec5cfb12ab2046}}, PF-AFN {{cite:128493416243e38e43dab51a669141e3855a2802}} and S-WUTON {{cite:90f75697a1f3025cc18c79d6291cc58c0eb9d148}}. Pretrained (publicly released) models are used for the experiments to ensure a fair comparison, except for S-WUTON, where synthesized test images were made available for scoring by the authors of the model.
| r | f47aa5f9c5b468e2f9e50526748a68a2 |
Once we have constructed the closed string field theory, we may couple the closed
string field to various {{formula:600fbe4e-d37d-4adc-8eb9-431db9fa6fc6}} -branes, which play a role of sources for the closed string
field. Solving the classical equation of motion for the closed string field, may leads us to {{formula:1d2a26bf-e7d1-4427-973a-89b9658021c0}} -brane classical solutions in terms of massless fields at large distance. It implies that the double copy technique is also useful to study classical solutions of gravity theory
{{cite:61cd7c62406a986fc49afe4705efc5ba0054606f}}, {{cite:d59b9c81fd15a45ec234d247eeba14880e304905}} and the closed
string field theory may be the unified framework behind the double copy theory.
| d | ab704e3371fbdb0e4cfe4fcdaf8aac77 |
The first approach requires having a large-resolution photograph (like satellite images) and produces pictures whose variations in style and semantics are limited to the given imagery.
The second solution can only perform some limited extrapolation since using a single global latent code cannot encompass the diversity of an infinite scenery (as also confirmed by our experiments).
The third approach is the most recent and principled one, but the autoregressive inference is dramatically slow {{cite:9c3fe6f4d62db9580ac660c71c0a66f3aa9c3766}}: generating a single {{formula:1d9b7a8c-7f8d-4a7c-b103-ca3c1cfafd91}} image with {{cite:010f08f0377270f7dae439ec55f7b9b84f413374}}'s method takes us {{formula:04cd5c3f-45c2-4ae4-8f33-143375b669ef}} 10 seconds on a single V100 GPU.
| i | 3b07d2751dc6b7711c73a1fcc83f51ef |
It is recognized that CNNs are generally more efficient for their intrinsically-biased architecture designs, such as parameter sharing, local information aggression, and spatial reduction. Therefore, to enhance the light-weight property of ViTs, recent works mainly borrow the inductive bias from CNNs to develop various counterparts in a hybrid or heterogeneous manner, i.e. integrating convolutions into transformer blocks as a plug-and-play module. For example,
ResT {{cite:ae971195194a23894612ac0bbb44fdad00a2ace8}} proposes to leverage convolutions to reduce the spatial dimensions of key and values in self-attention; LVT {{cite:aa5a4ddbf46ee804c8e018fd10eeae61d9e2b009}} adopts convolutions to perform local self-attention for low-level features and multi-scale attentions for high-level features. Moreover, some methods {{cite:5769d35daa1949837a05383ccf3d284abd10cf36}}, {{cite:2098b8cc680141968816ce51512c569c066ef427}}, {{cite:5f93286ff3d86684b896ab16ef27d763de62b90c}} aim to improve CNNs via interpreting self-attentions into existing CNN blocks. A recent study MobileViT {{cite:5f93286ff3d86684b896ab16ef27d763de62b90c}} incorporates transformer into MobileNetV2 {{cite:4019786794687a29aa3181637c7f7cb66812e2f5}} to obtain global representations in the upper stages.
| i | 8782e0aaf6280d3216a39cb7ef0377aa |
Both Monte Carlo Dropout and Quantile Graph WaveNet require an additional calibration step, however the advantage of the latter is that we can re-map every tau value, as suggested by {{cite:214ab0281ab78b3d0872ae9606275b1a668f1f1b}}. The underestimation that is present in many Bayesian Neural networks {{cite:214ab0281ab78b3d0872ae9606275b1a668f1f1b}} is not present in the Quantile Graph WaveNet. However, recalibration by reassigning the Quantiles is not perfect either since exploring the region outside of what is learned may cause the density to decrease rather than increase as wished. We do assume the CDF to start with 0.0 and end with 1.0, but there is no mathematical law that requires this start- and endpoint. In theory we can shrink and expand our space if needed, but retraining on these areas with remapped tau values may help prevent reversal of the density.
| r | 22b4c3d42499968a6228f2b0a9678770 |
To eliminate the impact caused by distortion, one strategy {{cite:c08209f5fb9c52ff1464cd51f8b864b573a065d4}}, {{cite:282d9b388dd66500404d82e2a48993e6f3ac6dfa}}, {{cite:8351667de0a6dd5c6aa0c1efc22da615ff631fbf}}, {{cite:8ef5f5504dc61dc76a7de40d28a27d05624c5daf}} is to convert the 360-degree video into multiple perspective views and process them with traditional CNN on each perspective view. However, this approach does not eliminate distortion, but only minimizes its impact. For example, {{cite:282d9b388dd66500404d82e2a48993e6f3ac6dfa}} proposed a saliency prediction network for 360-degree videos, taking video frames and optical flows in CMP format as input, and then performing saliency prediction of these features by decoder and bidirectional convolutional LSTM. Because these views are processed separately, the face boundaries introduce an additional boundary problem that may require subsequent processing to merge the face outputs, which can affect saliency prediction performance. Another strategy is to counteract the effect of distortion by changing the convolution method, as in {{cite:7bfc24a58b0f44da4b53f8f2a25ac0b98fbad3b5}}, {{cite:1480a6efb4704fc12bf3f3e55ed13dcbe4870b3c}}, {{cite:7f188fd3f0c6eaf9e32dbc718b11378949e13e2f}}. For example, {{cite:7bfc24a58b0f44da4b53f8f2a25ac0b98fbad3b5}} proposed a new framework, SphereNet, which adjusts the sampling grid position of the convolution filter according to the geometry of the spherical image representation and wraps the filter around the sphere to avoid the effect of image distortion.
| m | b29caa87ed8107a4f169386b350a4c29 |
There have been benchmarks and datasets for interpretability of machine learning models {{cite:e6d8b751e07565104d4f7755cc5a62843b6e234e}}, {{cite:82c13fbfc26794ed8360fae3c55389b82ae87f9a}}. The rising number of applications of GNNs in several sensitive domains like medicine and healthcare {{cite:33c6ec67ea2ffb720ec5107f9294d6ef3e0d7118}}, {{cite:a34b23046554b1ab0bdcb94ff971672482a6e2e1}} necessitates the need to explain their decision-making process. GNNs are inherently black-box and non-interpretable. Moreover, due to the complex interplay of node features and neighborhood structure in the decision-making process, general explanation approaches {{cite:6ca2e01813ccb65d48a5836229b9c303957771b4}}, {{cite:00352a0ff5c27e04bda85f0ac4822ee3bc8a4247}}, {{cite:8655b8d7cb7094c6fbc073409948a138a51ad4e7}} cannot be trivially applied for graph models.
Consequently, several explanation techniques {{cite:e26671f331784169edf26fb797be8558542147cd}}, {{cite:f75fa7d3696f32df0149d03b2feec1483a703720}}, {{cite:043e75603b64ba231ee23b3537af1d4325c85d8f}}, {{cite:75e8d7c8e46fece486f2bbf08b915feaefff0b01}} have been proposed for GNNs in the last few years.
Unlike standard machine learning models, in GNNs, the explanation methods return a combination of feature and data attributions as explanations given a trained GNN model.
For example, in a node classification task, an explanation of a class prediction for a certain node could be a subset of the responsible features in addition to a subset of responsible nodes/edges in its computational graph.
A known challenge in developing explanation techniques is that of evaluation of the quality of explanations.
This challenge also extends to the evaluation of explainability approaches for GNNs and is the focus of this work.
| i | 1dcb14216f72615edf5a65c7920c4dd4 |
We also use a Transformer-XL style cache, which holds the keys and values from the previous training step. When doing self-attention, the cached keys and values are prepended to the current keys and values, and we use a sliding-window causal mask {{cite:b0488cf0261f435a2373c282cd7bb5c50ae75180}} so that each token has a local context that includes the previous 512 tokens.
| m | 6272492ff5adeefc7d7e0f843e85d80c |
In this section, we test the performance of state-of-the-art baseline feature selection algorithms in their feature identification capabilities in control. We choose eight strong feature selection baselines, including classic methods, gradient boosting methods and recent population-wise methods. We also provide one instance-wise feature selection method. Implementation of these algorithms are either by the scikit-learn package{{cite:f8616b1ad21ec0957e5ed6977fd7070a76d9a669}} or from codes with their original papers. F&S {{cite:1b1110a42a4e499c645793bea2fc740e6ccaab4f}}, short for Fisher Score, a similarity-based method, which selects each feature independently according to their scores under the fisher criterion. XGB{{cite:3d4b52a5e020b8d9b29b080782b0766efa13f502}}, short for XGBoost, an optimized distributed gradient boosting library that can calculate the feature importance across many trees. LGB{{cite:e81c36032dfa39ccb456c4f97ecb18e18614da3d}}, short for LightGBM, gradient boosting framework that uses tree based learning algorithms. RF{{cite:525fd2dfea3414a6d65cea286844134226e1e7f1}}, short for Random Forest, operates by constructing a multitude of decision trees at training time. FIR{{cite:ff7876d0736becaa03b35547ac9847dbd88fb73e}}, a novel dual-net architecture consisting of operator and selector for discovery of an optimal feature subset. CCM{{cite:8055f098213ad5221cd7c37e583f7271c55dd35f}}, employs kernel-based measures of independence to find a subset of covariates that is maximally predictive of the response. SAN{{cite:652e10efc78b4898f1f221ebc7e442712bc18f0e}}, explores the use of attention-based neural networks mechanism for estimating feature importance. We use both the local/global variants: SAN-local and SAN-global. L2X{{cite:da6c320de552c8d97a3d875358a5a99862a0d1b0}}, an instance-wise feature selection method that extract a subset of features that are most informative for each given example.
| m | d46f78c28843fc8e2ef254c181a52271 |
Several applications of sparsifying transform (ST) learning and various extensions have been demonstrated in the field of medical image reconstruction such as magnetic resonance image reconstruction and computed tomography (CT) image reconstruction {{cite:5e887ca614e8c771372cd65fea8af6dacef3157d}}, {{cite:b607315bdd8167a0ab9bd30018fb5dd49a46b1a9}}. The conventional method for regular-dose CT image reconstruction is the analytical filtered back-projection (FBP) {{cite:26cc8fb2b5be37c5edcfd5c12d3b56c22de11c3f}}. However, with reduced/low X-ray dose, severe artifacts and noise can degrade the quality of the reconstructed image.
A class of reconstruction methods takes the physics model of the imaging system into account along with statistical models of measurements and noise and often simple object priors. These methods are referred to as model-based image reconstruction methods (MBIR) {{cite:197517d82215df740534325d10ac54e05b091766}}.
| i | 70d8aa73ab0a7b465402e444277c50e3 |
For the Bardeen spacetime, the Hayward spacetime and the solution of Ref. {{cite:357ce2570285dbda81a28e99394debea540fc5ef}}, increasing of the spacetime charge parameter implies monotonic decreasing of the imaginary part of QNM frequency; For the two solutions of Ref. {{cite:660580b9c1c3e6f2e0cf1e11fe0a26d282f255da}}, the imaginary part of QNM frequency increases when the charge parameter increases; However, for the two solutions of Ref. {{cite:bedf1989ac49a90d2c9a7acd728823334756c366}}, {{cite:85359b248fcfac49458d284cce6481f4c8aa6844}}, there exists a maximum of the imaginary part in the charge parameter interval.
{{table:6787894d-4e66-49ea-b38f-191874fd3ef0}}{{table:01622c59-7e8d-4d33-8287-11d581b124a3}}{{table:3b7aa81e-ebbe-4946-b383-a1a5407d8b79}}{{table:21f4de6b-0aa4-4110-bb3c-4ba8e47cf0d3}}{{table:92251111-a5aa-41b8-ad9a-fda01e7ee939}}{{table:f827707a-ebd8-4e3d-bf7a-825e462f40c9}}{{table:1460589b-1c75-4a5e-a95b-a43991eee897}} | m | ceb95d9ce87ab5ed554404e53acaa211 |
In this sectionOur code is available at https://github.com/anonymouswater/HAML, we challenge the capabilities of HAML in practice by testing HAA2C and HADDPG on the most challenging MARL benchmarks—we use StarCraft Multi-Agent Challenge {{cite:524fc552dc4d53bab9225c94c2994cfd618ab5a2}} and Multi-Agent MuJoCo {{cite:2cca4777cff5e16ce71f499514cd768f8f7c8230}}, for discrete (only HAA2C) and continuous action settings, respectively.
| r | c16c93a3d9eddc303f49a53fdfbabc2c |
Analyzing the behavior of coupled oscillators is hard even in the absence of uncertainties, due to the non-linear nature of their dynamics. One approach to reduce the complexity of analyses is to map the oscillators' models to their phase dynamics. Such a transformation is feasible under particular conditions {{cite:52f5b11ee4a23379c1b203afc187467c9a792888}}, {{cite:ae3b222c3b90898480fe8baa33a9a685b84db9ad}}, {{cite:d535f697200f3dbffc49ab2f2d044929b53a1c74}}. The framework has been employed in studying the collective behavior of some classes of nonlinear coupled oscillators, for instance, van der Pol oscillators, Andronov-Hopf oscillators, and the neuron models of Hodgkin-Huxley and Fitzhugh-Nagumo {{cite:ba535e6656637ae8cc34538391d793d4278f6770}}, {{cite:bbaff01984ed4863a1e0f85d0d5256b2f5cc7fc5}}. The most studied model for phase-coupled oscillators is the Kuramoto model {{cite:4cb0b16e319c499b641641d9c8d4d45b0bb936a8}}. The continuous-time deterministic Kuramoto model has been widely employed to study synchronization in various problem settings {{cite:63bfc8792fcb117a4d49e85c8246bb41f9fed8b7}}, {{cite:d398a1e14b7ec194a65ac73b09d071b87fffa47d}}, {{cite:4c6748608b2d50b6d42c1898d1cce5743996aa6e}}, {{cite:55ceafa7e892ec7211902aeebfbfdf73d71f3ed0}}, {{cite:7615c0a97fe27a51c622134a9c4311c4eb14bb25}}, {{cite:a44fa8457eb321de7586ecbe2d07891b3d57878b}}. The coupling law in the Kuramoto model is a sine function, which is the first term in an odd Fourier expansion of a general nonlinear function. This approximation is not accurate in some applications {{cite:e43072f1d8298eb280e6e9cb443ecafe453ebb69}}. For instance, studies of some particular neuronal oscillatory networks have shown that the coupling function is more involved {{cite:ba535e6656637ae8cc34538391d793d4278f6770}}, {{cite:50f928f105049995a89497725608df913d0ee6fd}}, which motivates us to study more general couplings.
| i | 3e5afa4c00cf2e524f549dbb2e22a166 |
Here we highlight the keys differences between the CGCT and PGL {{cite:79bc3e8185d422cb25194fc1d40640335fcb9f30}} as well as the dual classifier-based methods {{cite:8d429b776fc854e48a1f760676f1424b85fd41d7}}, {{cite:ace0a2ba3b775d6cd2d576e66311f939d72e9e4b}}. The PGL {{cite:79bc3e8185d422cb25194fc1d40640335fcb9f30}} exploits the graph learning framework in an episodic fashion to obtain pseudo-labels for the unlabeled target samples, which are then used to bootstrap the model by training on the pseudo-labeled target data. While our proposed method is similar in spirit to the episodic training in {{cite:79bc3e8185d422cb25194fc1d40640335fcb9f30}}, we do not solely rely on the GCN to obtain the pseudo-labels. We conjecture that due to the fully-connected nature of the graph and lack of target labels, the GCN will be prone to accumulate features of dissimilar neighbours, thereby, resulting in the erroneous label propagation. To address this peculiarity, we propose to resort to the co-teaching paradigm, where the {{formula:00c40d26-8f80-4f40-8603-d22b70de5727}} is exploited to train the {{formula:70cd1623-1b45-4588-b2ad-77c1cefe337c}} network. As the two classifiers will capture different aspects of training {{cite:8d429b776fc854e48a1f760676f1424b85fd41d7}}, it will prevent the {{formula:c71aaab8-0587-439e-b95f-b683fe11026c}} to be trained with the same erroneous pseudo-labels as the {{formula:07a5fdfc-cb65-48be-92f6-388bd7f73d39}} . We validate this conjecture empirically, where a network with a single GCN classifier with pseudo-labels performs sub-optimally compared to CGCT (see Tab. 5 row 7 of the main paper). Finally, the dual classifier-based methods maintain two classifiers to identify and filter either harder target samples {{cite:ace0a2ba3b775d6cd2d576e66311f939d72e9e4b}} or noisy samples {{cite:8d429b776fc854e48a1f760676f1424b85fd41d7}}. Contrarily, we maintain {{formula:de9c2ca6-cf65-4853-8648-291a8338a291}} and {{formula:bb33f9ad-287f-4021-8e7c-bb11cc542024}} to provide feedback to each other by exploiting the key observation that each classifier learns different patterns during training. Furthermore, given the intrinsic design of the {{formula:81899ab3-4cdb-4e0e-abdb-220ab0478924}} , we also do away with an extra adhoc loss of keeping the weights of two networks different.
| d | 4f5ad3aa1e4359b8c8745db0cc9c4ccf |
In the past decade, we have seen the emergence of various Knowledge Graphs (KGs), such as YAGO {{cite:4de54cb845a58931cdd9f76ebd7e4b03968c3684}} and DBPedia {{cite:e88770968c4b3bd054d631a7fbc63976a049b7b3}}. They have achieved great success in both academic and industrial applications, ranging from recommendation {{cite:acd4ddb27da7c194cd5485fbf538b43e0fb18a5b}} to Question Answering {{cite:588b90bc653483eb525f699c38872ad06bed2f90}}. However, these KGs are far from complete, which limits the benefits of transferred knowledge. Relation Extraction (RE) is a vital step to complete KGs by extracting the relations between entities from texts. It is nontrivial since the same relation type may have various textual expressions, and meanwhile, different types of relations can also be described with the same words. Such ambiguity between relations and texts challenges the supervision of RE models.
| i | 8fa32a61504054b8c5b3f2898477c5ae |
where {{formula:32e53c4d-998e-4cc3-ab58-6c1af4388c39}} is the two-loop coefficient of the QCD {{formula:1a4fd2bc-89cc-467d-a82b-a857bc397067}} -function. According to {{formula:2427803f-e076-4f51-801d-60fcf228d74b}} {{cite:39bbe387fc19aac40d5daa875d507e4c87f2de36}}, we obtain {{formula:66c45744-bc9c-4c4a-a5ba-c8ea6d8bfb38}} and {{formula:753f6299-6552-45bf-95aa-838f791f2286}} .
{{figure:c24f3391-aeba-4d47-808e-3aaa01c8dc74}} | r | d381890e7d758a08a533c9c53aedb743 |
Our proposed scheme focuses on improving the accuracy of absolute pose regression. As such, we evaluate it on multiple
contemporary datasets used for benchmarking camera pose regressors, and
compare the results to recent state-of-the-art regression-based absolute
localization methods. Other classes of localization schemes, described in section REF , which utilize additional data at inference time (localization pipelines {{cite:eccb29bb1d11cd8d30bfa670066730427843cf81}}, {{cite:ae9692b50706e83165a5b0cf639a13fe4a960f98}}, {{cite:8e44572e21b54d1425f09f3febe6f7caeb431b66}}, {{cite:f04909f9bc2ac926e64374d13da90b30d94ae75a}} and relative
pose regression {{cite:59364db1e58c2d32b80cb026b6296cc670ed2de0}}, {{cite:90d20b7de05740cbeb1a42a5681f45bd1774d4cc}}, {{cite:911fa089e291e50bb753c910a8b16009e71271a1}}) or that are an order of magnitude slower (3D-based scene coordinate regression {{cite:8845271117d16b9171ada63bbd202e6623d0a4b8}}, {{cite:a2ac99c52b129714fe7058986cd009d15097def0}}) are not considered for this analysis.
| r | 034e03abe1f8fbbe7110bef6f816ab39 |
In terms of classical {{formula:54e0ed31-49ee-48d1-b5fa-3ece533a2cc7}} -SAT, as mentioned above, in stark contrast to {{formula:506ee89b-9e79-4b25-ac2f-2348e84c8178}} -QSAT, solutions to {{formula:dcbde4af-e6d4-49e3-8ed1-3214682c06dd}} -SAT instances with an SDR can be trivially computed. As for parameterized complexity, classically it is a well-established field of study (see, e.g., {{cite:7aad101ba41dd65ff53b871cca9422ebadc7341a}} for an overview). The parameterized complexity of SAT and {{formula:f75b0a1f-b68c-4f33-8771-500ae3d845bd}} SAT, in particular, has been studied by a number of works, such as {{cite:fb1707b5411dda7f5781f64b9a3a8fcc6b79563d}}, {{cite:74bec3ecc6f3f50f356364d0cab608f0635f66e8}}, {{cite:f1a1529cdb0999eaabdf7ccaa225cfd0c274115c}}, {{cite:99dd42678a6b5f0e20e8b35d752092a578ae073f}}, {{cite:cc475cd88c1eace52930251f742ecf90616110bd}}, {{cite:4f14518d4ee34324524115408a9322d3a2b6993d}}, {{cite:bd0765ce4cd8b837dd1fdd471af8efcbbf6d9f37}}, which consider a variety of parameterizations including based on tree-width, modular tree-width, branch-width, clique-width, rank-width, and incidence graphs which are interval bipartite graphs. Regarding parameterized complexity of Quantum SAT, as far as we are aware, our work is the first to initiate a “formal” study of the subject; however, we should be clear that existing works in Quantum Hamiltonian Complexity {{cite:5f55bc7813574df31ebfbdb538bf7b2a76e03cf2}}, {{cite:1404b30b55f4aa9d9b9caa6cf6e2e86fafe0f92a}} have long implicitly used “parameterized” ideas (e.g. in tensor network contraction, the bond dimension can be viewed as a parameter constraining the complexity of the contraction).
| d | 22c05eb2af8d9b1abd36c44b72af64e5 |
We can immediately recover the proposed Lyapunov function in {{cite:9657d1a93f126c12dbace92e89a6cef805327b12}} by setting {{formula:2b3de27a-7c27-4be0-8eba-532e1f1beb59}} to
{{formula:e98531ec-96f9-4c8e-b537-0be528a9df14}}
| m | 599a6d88531e9044add0e6ae52926da6 |
To formalize the encoding process with solid physics backgrounds, we try to find an appropriate way to derive the thermodynamics of encoding based on the nonequilibrium second law of thermodynamics. One can find a reverse derivation process from information quantities to the nonequilibrium second law of thermodynamics and fluctuation theorem {{cite:15355fef557924c666486fb82550dd31e9da1991}}, {{cite:bf4d8cb2795b242e67427175c564d0bf951e0c48}}. Although our proposed encoding process is suggested as a possible generalization of the measurement process {{cite:2e53be90d6045bf9c2749468cd957810431dcdad}}, {{cite:55e2b7fee4bee6744202cb74093c16e82699b6f7}}, {{cite:0220fc7882dde06294446985db9f8356836f457a}}, {{cite:f1ab08c461f420694b87f70cb4544a77b08aa2a0}}, {{cite:15355fef557924c666486fb82550dd31e9da1991}}, {{cite:2dd789a4b84e07bdffeed74674b131e8616f4c31}}, {{cite:d8af8eb4edf5e78263fcc1e8ee9af07fbf0f1b27}}, we need to emphasize that there exist essential consistency between these two concepts. Given the thermodynamic definition of encoding, a fundamental law is suggested that the mutual information {{formula:4e502a2f-31ab-4dbf-9ded-62fe10077e8b}} (the encoded information of {{formula:f165b565-ee5d-4ad1-8d1b-18518724770f}} by system {{formula:86a2f87e-223a-46ac-9514-aa1e2cc046b6}} entirety) is bounded by the irreversible work {{formula:2b023dc0-8204-43c2-bb36-65f0eb57e183}} from system {{formula:9c1bd557-438b-4fc0-90ca-accf4840d8d4}} based on (). This upper bound is implied by the nonequilibrium second law of thermodynamics intrinsically {{cite:d8af8eb4edf5e78263fcc1e8ee9af07fbf0f1b27}}.
| d | 42a879b5d5f8767c333d64127da0792d |
Among the deep learning literature, medical image segmentation has emerged as a specific research topic, owing to the typical size of the available training datasets. Bridging the gap between few-shot and data-heavy learning-based segmentation methods, the infamous U-Net architecture {{cite:c0ad1cf985948c812444e0f8837609ef2d94ca6d}} has founded a new family of convolutional neural networks (CNNs) with relative data frugality (typically between a few dozens and a few thousands training examples).
In this data regime, data augmentation plays a major role to prevent over-fitting and improve generalization capabilities of the CNNs. As such, a plethora of augmentation techniques have been designed, using both simple geometric transformations such as rotations, reflections and elastic deformations as well as more advanced approaches. Most of these techniques modify the shape, color or contrast of the images while preserving the texture {{cite:04e0a221ed41fc6c9103a499125e7a8a18c9ddbc}}.
However, recent works strongly suggest that CNNs are biased towards texture {{cite:8faf2b2cd1fe817c525becb7e8beaa917a897bfd}}, {{cite:94d3c76969ce76dc9f34c13459d9f8def3d1e639}}. Quantitative experiments demonstrated that style augmentation, which randomizes texture, contrast and color, improves classification performance on several benchmark datasets {{cite:7e0763a45856b1d628b479597bebc53aceca2258}}, {{cite:8faf2b2cd1fe817c525becb7e8beaa917a897bfd}}.
Despite these appealing performance boosts in classification tasks, the interest of style augmentation has not yet been evaluated on segmentation tasks. Medical segmentation seems particularly adapted to this kind of experiment. Indeed, small medical training datasets are not always sufficiently representative of the full spectrum of textures the network might encounter during evaluation. As such, changes of imaging devices, acquisition setups, or tissue characteristics might lead to performance drops with a texture-biased network.
In this work, the interest of style augmentation for segmentation tasks is evaluated on the MoNuSeg dataset. Using the recent UNeXt architecture with reduced number of parameters, the conducted experiments show that style augmentation strongly prevents over-fitting and improves segmentation performance.
| i | d9c34ca4f459841c27bfd20d570b019a |
Methods for inter-frame (temporal) prediction have been proposed to achieve efficient compression of dynamic point clouds. These methods can be grouped into three main categories.
In voxel-based schemes {{cite:4ab839a95671bb95e0d79d77a523f7d4031e1a4d}}, where a motion vector (MV) is estimated for each voxel, a few points in both the prediction and reference frames are selected as anchors to establish correspondence via spectral matching, leading to a set of sparse MVs. Then, using a smoothness constraint, a dense set of MVs can be obtained from the sparse set to provide motion for all remaining points.
In patch-based techniques {{cite:c87f38a8d81520e100132883ef105cf069e77452}}, motion estimation (ME) is considered as an unsupervised 3D point registration process wherein a MV is estimated by iterative closest point (ICP) {{cite:e0241f9947d2112f97bbef47a26df4cb0e029b4b}} for each patch generated by K-means clustering.
In this paper we focus on block-based methods, where frames to be predicted are partitioned into several non-overlapping 3-dimensional blocks of a given size. For each block, the best matching block in a reference frame is selected according to specific matching criteria, which can be based purely on geometry, e.g., an ICP-based approach that generates rigid transforms {{cite:213038ad4fbb5fb8a05538c897d1937f8441ef26}}, or can use a combination of geometry and color attribute information {{cite:202db285d296b210fb7945e94a81a59e559db481}}.
Recent work has also focused on block-based motion search speedup, including both efficient search pattern design and search window reduction {{cite:60598547b16c8ca4c28e6e9892dce03389ec8f05}}, {{cite:a883b028c2204ec98f76e2be6ad2f29e0c0d2bba}}, {{cite:fc97827c055b4e1272f4e5dbd29afe9645ebad2d}}, {{cite:41bcdba7d5518e4e3e3996c81201d152f8c4d78d}}.
| i | f3b284922d8407b7fa419c8fbefb984c |
Dust thermal emission in PNe peaks between 20 and 30 {{formula:82d8b989-494f-4cdb-87d1-67fc461094fb}} m and represents most of the integrated intensity across both SWS and LWS ISO spectra.
In cooler media dust emission shifts towards the longer wavelengths and can be estimated from LWS spectra alone {{cite:993ce8d3a709a603dfaa46eaa09630aa89e44fe9}}.
Figures 3 and 4 in {{cite:993ce8d3a709a603dfaa46eaa09630aa89e44fe9}} show that in the {{formula:3aba524d-47c0-47a9-a8d4-edb8e8569efa}} -Oph cloud (peak of thermal emission close to 100 {{formula:f91a3454-42cc-485e-8d3f-706e3a176757}} m) weakly illuminated by HD147889, {{formula:7cbbb376-03d4-44ff-b7cd-444b11494cca}} is in the range 0.02-0.04, which is much larger than generally observed in PNe (Figure REF ).
C05's PNe observations may thus support Onaka et al.'s conclusion that {{formula:d4134412-4d52-4ff1-a3fe-8465378830fd}} tends to diminish in strongly ionized regions or under harsh radiation fields, which, again (see Section ), casts doubts on the possibility that C-rich PNe are a privileged site for synthesizing UIB carriers.
| d | 7db0f8587d78e3ee467c74d855e5af42 |
Figure REF
plots a 95% confidence interval on mean log-regret versus the budget used thus far. We perform experiments using a single budget in each problem; the goal
is to minimize regret at the point when the budget is fully exhausted at the right-hand edge of each plot. To focus attention on these budgets, we plot results over the range from 20% to 100% of this overall budget.
The results for {{formula:11671d28-48e2-48b6-ac2a-203c8270ba84}} look-ahead steps are deferred Section to the supplementary material to improve readability and also because they are outperformed by the {{formula:7ebb08c5-c2bd-493f-ba55-d165a5552422}} counterparts for most problems.
All implementations use BoTorch {{cite:760ed1c609f4eba3d833c978c49967f46a017e33}}. The objective and log-cost functions are modeled using independent GPs. Additional details and runtimes can also be found in Section of the supplementary material. An implementation of our algorithms and numerical experiments can be found at https://github.com/RaulAstudillo06/BudgetedBO.
| r | e5c5c4765e40b53d237812f0ae396ca7 |
The purpose of the present article is to investigate inflationary cosmological solutions consistent with latest Planck and BICEP2/Keck Array data in the framework of mimetic {{formula:d0a634ce-b87c-4ada-9450-f7aba44730f0}} gravity with Lagrange multiplier and mimetic potential. {{formula:9c5728f2-ad64-4ccc-b126-c026baf2485f}} gravity was introduced in {{cite:73076f5e02f852b13679c28c864305362d60a158}} and has been extremely successful in the understanding of the flat rotation curves {{cite:f87d277c4b1df2281350e21aeef933dc2f691d50}}, late-time acceleration {{cite:73076f5e02f852b13679c28c864305362d60a158}}, baryogenesis {{cite:9982a2dcaee02678d8b54888dd7fe23925aca0df}}, bouncing cosmology {{cite:e475e2e7e4704a512832deee4c2afb1e0f8ad732}}, {{cite:dd9990e63b13f6eca8e77799a6722521ccfee4c9}}, evolution of density perturbations {{cite:4582294fcef8118111fccd0c14c4dd7caddde1ba}}, redshift drift {{cite:b5616e27f40a2b2221aec1cad1c9989235b70599}}, Big bang nucleosynthesis {{cite:7c1c87df05635ac638b08947fa529d583fc0d337}}, temporally varying physical constants {{cite:32e44d35cc6ff377ecca0997a3c9c9ce19c03237}}, inflation {{cite:41d2d179bf7e9b25766051ee7c79b333df9c7b39}}, {{cite:6806f32b56c43341d1b90f14ad77e446b905a51f}}, and viscous cosmology {{cite:baa272b112534c93e4bb50489ae662381c01c2a2}}.
| i | 9bde696db721abfc4f5d024ac1b23590 |
One challenge in federated learning, as noted by {{cite:88098a6196fbebdf0cc0227bff74acbc5ca68647}}, is the quality and data distribution of the sources being used for the training tasks. A related challenge is the
potential for random failures or adversarial parties to disrupt the federated training.
For these reasons, robust federated learning has seen a flurry of activity {{cite:28e95a92764a5b8059c449d6efa6bcffa6936320}}, {{cite:fcc8eda8fe65aa27392e3c5d3d1e1b4760ac3016}}, {{cite:87b28175edac81fd461b34906a070680fe4e4758}}, {{cite:5d7987755131831b2e6fe25ff9fc86bb11918f5c}}, {{cite:d09762fce6fefb686fda07f9c3abf37a2a141163}}.
Some, like {{cite:62b19f2adbce3d284bc186a56e59f7da989f2f44}}, {{cite:fcc8eda8fe65aa27392e3c5d3d1e1b4760ac3016}}, {{cite:c4d19c2ed52f09dece307b5e56284dedf6f6c99b}} focus on the adversarial setting, and others, like {{cite:d09ed2f0f608c75956a5f50af09acb6ead19945b}}, {{cite:d09762fce6fefb686fda07f9c3abf37a2a141163}}, focus on the general setting of distributed learning under different source distributions.
In both cases, this requires identifying the weight with which to include each party in the aggregation.
| i | d822879b3c95e6a1da5bcfb9a5b71f4e |
In high energy experiments, the power-law or intermittency behavior can be measured by calculations of SFMs of baryon number density {{cite:79c8bc9c0f64b46b162234c063d2547c9766b58e}}, {{cite:02d61bb146f3e06315e2f1c97d98ab911ce7a2e5}}, {{cite:99ea7b3f5e03ed0e7b7f38f7f5fbbe8306237a0d}}. For this purpose, an available region of momentum space is partitioned into {{formula:46474647-ee9c-4d89-b7e5-a268b913a0e6}} equal-size bins, {{formula:0f58e887-77bb-423e-a854-0272da0a9215}} is defined as:
{{formula:5d091f3d-0c87-4085-81c0-745c34fbe288}}
| m | 3db8e4c1ef57b83c20ab9a0d3a20ba46 |
Batch-independent normalization methods, such as GroupNorm {{cite:3ff430ad04a76ec2bf374a80ef77d562a54be80f}},
Filter Response Normalization {{cite:a6c451cb7a9a973703ac5dbe59dc8cfc8225dc16}}, EvoNorm {{cite:db3dae15ccf2cf7f5c827e2aab6931c12ae1d484}}
do not suffer from training noise and have competitive accuracy.
However, unlike BatchNorm, they all incur extra cost of normalization in inference.
| d | de165d489521652dbdc9642eec3976c9 |
In many clinical applications medical image segmentation is an essential step that foregoes quantitative analysis of clinical features and diagnosis. DCNNs showed state-of-the-art performance for segmentation tasks in case when the training sets are large, representative and correctly annotated. In case of noisy annotations, DCNNs easily overfits to them during training, resulting in mediocre performance on the test sets {{cite:66ca25e541677c257f8c0a6e0eac2266298dda75}}. Compared to consumer photography, obtaining large datasets consisting of accurately labeled medical images is expensive and much more time-consuming. It is therefore essential to devise methods that will produce stable results while training on relatively cheap and unreliable annotations.
| i | 58ba2ecabd4b82231a53181d03ae29d2 |
Theorem 3 (Positivstellensatz {{cite:7d8152c35647dcca350a32809687b078fdaf2537}})
Consider a collection of polynomials {{formula:f373be6a-1d1b-4bef-b358-01f1038c34e1}} , {{formula:728db01a-1256-406b-a576-b2414d2a226d}} and {{formula:3017a920-0a48-458e-bfcb-68acb3eec2ca}} . Then the set
{{formula:76a74a2f-b2e5-45e7-a624-9de637d5e728}}
| r | d07a154962b0c764e04f63ff905c3167 |
In the experiments, we used the RSICD {{cite:4054fa5236834e61af047c5e8956b20280f4252e}} and the UC Merced Land Use (denoted as UCM) {{cite:a1d79d832cf3512b268282b9d963ab65ca5702ce}} datasets. RSICD includes 10921 aerial images, each of which is a section of {{formula:5b2b1c42-b564-4180-82f5-efa99de3ba9f}} pixels and has 5 corresponding captions. UCM consists of 2100 aerial images, each of which is a section of {{formula:215867ca-d389-41d1-9c96-88461892038e}} pixels and has 5 captions per image. For both datasets, we used only one randomly selected caption associated to each image for training. The datasets were split randomly into train, query and retrieval sets. We applied a Gaussian blur, random rotation, and center cropping for the image augmentation, while the text augmentation was performed by the rule-based replacement {{cite:8570394993e5c3da9471dff8938e30137b67a52a}} of noun and verb tokens with semantically similar ones. The original training sets are clean but in our experiments, we fixed 20% and 30% of training set for RSICD and UCM, respectively as clean training set {{formula:fafb62bd-1078-467c-89f4-2e1a108d7e15}} , while we inject noise to the rest.
| r | b0c48cad70f28b852dd0b54993b20989 |
Despite the motivation for using margin-free classification, we also explored the possibility of using multivariate Gaussian densities in a similarly constructed Two-Stage Gaussian Mixture (TSGM) model. We used the R package mclust {{cite:e40e6f0a88e88549dab4600e046f349a844d8912}} to fit the data
which gave a lower accuracy of 59.52%. This model also tended to classify the larger classes, with more than 50 data points in the training dataset, like LPV, DCEP, DSCTC, EA and EB, well. However, 13 out of 23 classes including DSCT, ACV, GDOR, RRC and BCEP were not detected at all. With low detection ability of the smaller classes, the TSGM model would exhibit low classification accuracy for new class detection.
| d | be4d89f7cf67629c8d07e2c7d95ccb70 |
Many traditional ZSL methods rely on a predefined class hierarchy for explicit knowledge propagation. ImageNet, whose classes are a subset of WordNet, becomes the ideal benchmark for these works. With 400M image text pairs, CLIP{{cite:22153572cbdcb96b37b39751e91b90462cf3da38}} vastly outperforms previous methods. Our method uses Conceptual Captions{{cite:eb01d1bc07076bc054b9a8a3daf24a2175a21b1b}} 3M, which is on the same order of magnitude as ImageNet 1k, and outperforms the previous SoTA, HZSL{{cite:8ccdc5f35b0da29e8f1884d555fc73e8cfa3ce68}}, by 73% relatively. In table REF , we demonstrate good performance on a variety of image and sentence encoder architectures. The gap between our method and CLIP may be caused by the fact that ImageNet classes contain many uncommon words, such as scientific names of animals or medical terms. CLIP's dataset is much larger and thus covers much more uncommon words. EMA distillation also slightly decreases the performance compared to using only contrastive loss. We hypothesize that this is because ImageNet only has one "gold" label per image during evaluation. However, EMA distillation encourages the model to output a softer probability output for multiple classes, which can be present but just not labeled.
| r | 58914637a3d2debdb1c0fd3b68c4a366 |
We conclude by showing how quantum volume relates to – and can be shown within – the VB visualization framework. Obviously, making a rigorous connection to quantum volume as defined in Ref. {{cite:b490002224c41635557b4d2bc9507b58f9f27de2}} requires choosing and performing a specific benchmark (the one proposed in that work)! But even for that benchmark, there are advantages to the richer reporting that we propose. They are illustrated in Fig. REF . In this example, the quantum volume experiments are explicitly highlighted along the diagonal, as is a region of implied success (those circuits with width and depth less than or equal to the quantum volume). This particular hypothetical device has a quantum volume of {{formula:b68f6199-fe8d-4bd8-af33-92ad50f6f00c}} , which is clear in the plot – but it's capable of implementing significantly deeper circuits if restricted to slightly fewer qubits. As usual, logarithmic axes allow the display of a much wider range of circuit shapes, as shown in Fig. REF (b).
| r | ea7f41805a612245725cc01dc95a240a |
The previous experiments performed within range 0.48-0.68K have only shown the general features for returning the crystal facet growth kinetics to the normal regime {{cite:57ada1ee5952952ff41bb8aa6706fac7f3dac3cf}}.
It is shown that the significant relaxation takes place for time {{formula:2b667eb0-1672-42e0-addc-50d93eb484d1}} 20 ms after ending the fast growth stage. Next, the slow relaxation is observed to the normal magnitudes of the kinetic growth coefficient. The details of this process have not been clarified due to experimental limitations indicated in the Introduction.
| d | 21ea9d7566034f928dec710bc2f0ec6c |
where {{formula:2bb3948d-bac1-464c-9830-dff13099ea75}} is the advantage function associated to {{formula:c43cff5d-1aca-468b-82aa-fc0d32ea9faa}} , and where {{formula:a6adbe13-983d-4c28-a113-403cb3c5e010}} and {{formula:d0ee769c-1da6-4acf-b506-80ac4c500b52}} are the action-value and value functions for the policy {{formula:d990d419-8479-4009-9c56-c5a6eb2402b9}} , respectively. Under some conditions detailed in {{cite:ba970900dbdadd1b95e42c9887ba49e0239a3ff5}}, the action-value function {{formula:8d5cbf5b-a20d-433c-8689-7342adae7e31}} in (REF ) can be replaced by an approximation {{formula:16fc1ebf-414e-457e-b3d6-bde1b722572f}} without affecting the policy gradient. Such an approximation is labelled compatible and can, e.g., take the form:
{{formula:138066a0-5073-4a54-90e5-0480aea2aeb2}}
| m | 0cab29f0e11a0db855e3aad5f06fa955 |
Our method outperforms the conventional method in two aspects:
(1) information of subsamples at high-redshifts is conserved. To pair subsamples with a slight difference of redshift is a simple and commonly used method. For example, {{formula:50f028e4-9551-41c0-a3d6-92252db922ec}} {{cite:792392fd8098f479437a13eea8117a9b82284ad4}}, {{cite:82bf72a2d168207e71a038dbb5746d2392d893e5}}, {{cite:3f6924d5cc22f1aef21e47be79330474efa087e1}}, {{cite:98b86f624335e49bc0c28fc5d69ba6f65d95626a}}, {{cite:1cd74619af517e4d2257a398ebb6f62ea24d033f}}, {{formula:a60bccca-3e07-4e6b-a197-d0775bafc247}} {{cite:bb955a1fe21776ee7a02a7819231102917465f62}}, and {{formula:54ef1bf8-2dc5-47fb-9e16-899685da89d4}} {{cite:f146cc4198e19d5f0a20d84343090a19d3e2b448}}. Gaussian Process (GP) reconstruction is also a usable method {{cite:114f9c1fa8b63136a54611ebb25a97290ee1aa2b}}, {{cite:4160824cb920be171f8f29bb844a9335bc1d6d6a}}. The linear interpolation method is also taken by some researchers {{cite:56e61ae485f852120e8f411ac13765dd0448ff5e}}, {{cite:ba535ed022c70f5a546f1c1676335157f1afc1b9}}. These methods reduce the systematic error to an extent but do not consider the distance-deviation consistency. The relation between the distance and the redshift is non-linear: the same redshift deviation at the higher redshift has a smaller distance deviation. For example, some researchers set the {{formula:ca90d2c4-c6f9-469c-88f7-cf1b5ac8364d}} , the uncertainty of dimensionless distance is 5% at {{formula:287ed8ec-20af-4193-a130-aa7db516b29d}} , the minimum redshift of the subsample we select, but small than 1% at {{formula:aad3b753-9282-4513-8603-f5a9f6a8125d}} for selecting data with a general cosmology model, so the selecting uncertainty is not the consistency of distance-deviation. The selecting uncertainty of their methods are all ignoring, and if they were taking them into account in their fitting, they had to introduce a cosmological model so that their methods were no longer model-independent. In our approach, although two cosmological models are introduced, they are used to jointly pick the data, breaking the dependence on a single cosmological model when picking the data, and are not introduced into the {{formula:66167398-c1ca-4b31-96fb-73f847f33897}} function, in other words, the final parameter fit results are independent of the cosmological model. {{cite:5ba585ba3e61cbfd73e13fe2c3941b816b390867}}used a similar method for selecting the data with a {{formula:c18cd74b-a61d-4d94-adb0-b828e96c55d5}} CDM model to fitting the parameters of the ultra-compact radio quasars. At high redshift, in general, subsamples are sparse and matching pairs of subsamples is difficult if a fixed {{formula:09cc9474-7856-4033-89ad-2822555753f3}} is used. The distance deviation consistency method selects more subsamples at high-redshifts.
| m | 8c054df374d11481e7658cf76075dcdf |
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