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Although, surrogate gradient learning is one of the best direct learning algorithms for spiking neural networks {{cite:4e9cd9d8a77a77c0fefdfb44965650afe339657c}}, but it suffers from the challenges of backpropagation through time, especially for longer simulation times, including vanishing/exploding gradients and high computational cost and memory demand. However, in our proxy learning method we do not confront with such issues, as the backpropagation is done with the proxy CANN that is a time-free network.
| d | 5e0033aa432c7dff511f35f76d4bda5e |
Given such a setting, in this paper, we are interested in addressing two questions: given a large, unlabelled clinical database, (1) how do we extract attribute information from such unlabelled instances? and (2) how do we reliably search for and retrieve relevant instances? To address the former, the task of clustering holds value. In this setting, a centroid groups together instances that share some similarities. Recent research has focused on exploiting existing clustering algorithms, such as {{formula:9275421b-94dd-40f5-bfc9-fab1c9b059b5}} -means, to group similar patients from electronic heath record (EHR) data {{cite:ce1ce6fce7f4603337817155d32ec79e19c5d277}}, {{cite:731dc20b7df7d3c3fe85486b3e227a21f88cbed4}}. Such methods, however, are exclusively unsupervised; they do not exploit patient attribute information. To address the second question, the task of information retrieval holds promise. In this setting, a query associated with a set of desired attributes is exploited to retrieve a relevant instance. Recent research has focused predominantly on retrieving medical images {{cite:2576cebad8c9b0de3205f398773488eac3b49f96}}, clinical text {{cite:90737abef79776fa4abfa831cd302862d0e97197}}, and EHR data {{cite:67b97e813d2b1a8c6fa30053bd3d61a379ef8403}}, with minimal emphasis on medical time-series data {{cite:9d2ad5ac35eec0e95fee3fe18cb2a96d160e18ff}}. These methods do not extend to cardiac time-series data nor do they account for search based on multiple patient attributes. Most notably, previous work performs either clustering or retrieval, and not both.
| i | 141e1f1d007ba36b6efaaaecb4b23847 |
We conduct our experiment on a real-world dataset CIFAR10{{cite:ba1c9fa1f32223dc80e52987d3ad79f98796c534}}. The CIFAR10 dataset consists of 60,000 images in 10 classes, including 50,000 training images and 10,000 test images. Learning on the image dataset simulates the real edge computing scenarios such as traffic flow monitoring and image recognition of smart cameras. We consider a wireless network with 1 MBS, 5 BSs, and 100 end users. The users are randomly distributed in the coverage area of BSs, as shown in Fig. REF . The CIFAR10 dataset is shuffled and assigned to the end users randomly. Thus the training data of federated learning is Independent and Identically Distributed (IID) in our experiment. The Convolutional Neural Network (CNN) {{cite:9d440364b902cade4a33b2dad5977a788e91b323}} is adopted as the machine learning model for federated learning. The CNN model has two {{formula:880cd9b9-0f1c-4388-9f20-827f99f67746}} convolution layers (with 32 channels and 64 channels, respectively) and {{formula:649fd9d0-d45f-412a-84bd-dbaf183c0a36}} max-pooling layers, followed by a fully connected layer with 512 units.
The maximum CPU frequencies of five BSs are 2.6GHz, 1.8GHz, 3.6GHz, 2.4GHz, and 2.4GHz, respectively. The transmission power of RSUs and the MBS is 34dBm and 42dBm, respectively. The bandwidth of the subchannel is set as 30MHz. {{formula:49e71764-84b9-4db6-8e86-2cbaf341863e}} is set to -174 dBm.
{{figure:81fed02a-fece-4e4b-867b-e1dea7744406}} | r | 6289d54346911481cff8b9ec50eb22d1 |
The algorithms we consider are deterministic. An interesting direction for
future research is to adapt SMR synchronizers to emulate asynchronous rounds, as
required by randomized consensus
algorithms {{cite:bb76fe20c84a611cb08abb6545231e560335c56d}}, {{cite:3613527891319d77b58e63835a700056dea31600}}, {{cite:709fa285f62c138f1e6f5d0512496b55ccf455db}}, {{cite:f4501260f162a06554a1f39c071603b8004dd105}}.
| d | b7ac54692d4e761a96bc5b7ea8fb568d |
These images are then assessed by a scorer. Specifically, the fitness of an image is calculated by either (a) the loss against a specific ImageNet class under a trained MobileNetV3 model {{cite:f085fc63597cb63bda7686190126fbbea25e050a}}, or (b) the similarity to a caption under the CLIP model {{cite:2e80092c357ad30056b30f136f2e09cc7f94244e}}.
As the rendering proecss is non-differentiable, we optimize the 15 parameters in a genetic algorithm -based optimization loop.
The parameters are mutated at a rate of 0.1 and a selection rate of 0.5 while using the roulette wheel selection strategy. We keep a population size of 40 at every iteration.
| m | 66542435fb91fba63e9b9c7aa4beaddd |
We compare the proposed FL scheme with the FL FDMA scheme with equal bandwidth {{formula:32a39262-f6a3-42e7-9d5b-1b848f173928}} (labelled as `EB-FDMA'),
the FL FDMA scheme with fixed local accuracy {{formula:6677f708-8a26-4f52-aa4a-b647361e774c}} (labelled as `FE-FDMA'), and the FL time division multiple access (TDMA) scheme in {{cite:268d1a74cbef1023b74506df1543849c2c45906d}} (labelled as `TDMA').
Fig. REF shows how the delay changes as the maximum average transmit power of each user varies.
We can see that the delay of all schemes decreases with the maximum average transmit power of each user.
This is because a large maximum average transmit power can decrease the transmission time between users and the BS.
We can clearly see that the proposed FL scheme achieves the best performance among all schemes.
This is because the proposed approach jointly optimizes bandwidth and local accuracy {{formula:70ec362e-736b-4b77-ba75-ce9841d9a9c2}} , while the bandwidth is fixed in EB-FDMA and {{formula:8d970aac-a4f9-467d-aed6-6a9c68619b59}} is not optimized in FE-FDMA.
Compared to TDMA, the proposed approach can reduce the delay by up to 27.3%.
| r | e64eeed68ffcf58cc06d727061956635 |
Next, Theorem REF gives a lower Lipschitz bound for max filter banks when {{formula:3d89ac1a-871a-44e2-8648-67e31a2d93fa}} is finite.
Furthermore, by Lemma REF , this bound is optimal for several choices of {{formula:13396456-d04d-404e-807e-00937ef23d8b}} .
It would be interesting to determine a lower Lipschitz bound in cases where {{formula:bd533ff0-85bb-4970-896f-658389a01a26}} is infinite.
However, such a bound is also an open problem in the same complex phase retrieval setting where {{formula:d56ed1ec-03e4-4e17-bddd-d21c70ec3efa}} {{cite:dd660c7f2919def80f8be4cb51a7c165cecd4688}}.
Another open problem in this neighborhood is Problem 19 in {{cite:a21184d1bcb587ea17ab259aa683dbc8ddd55ee2}}, which asks whether an injective max filter bank is necessarily bilipschitz.
We note that while explicit lower Lipschitz bounds are not known in the setting of complex phase retrieval, a compactness argument gives that injectivity implies bilipschitz; see Proposition 1.4 in {{cite:4bb5e798d2f23acfa96d027b0417542216ef452a}}.
| d | 7777f859e686e24e574f5dedf9213bc4 |
Recent developments show that, Transformer {{cite:279e33a441d30c3c39b93fe47d3655846c565716}} based pre-trained language models like BERT {{cite:02a3e949e71fa76306c9d2969795b711ae99b6e2}}, RoBERTa {{cite:b793e514b16da38109b5c0e8cebe2ec7d3ab3db8}}, ALBERT {{cite:65a4ca3e96dae13c033fe60d5d98d2133362f41f}}, and DeBERTa {{cite:84ba71f1e71f70c5272e929d8942c376f07bf78f}}, have proven to be very successful in learning robust context-based representations of lexicons and applying these to achieve state of the art performance on a variety of downstream tasks such as document classification in our case.
| r | 3cd42f4b4ac75f90b595a31e636ed924 |
We are interested in solving the nonlinear system of equations. The nonlinear complementarity problem, is identified as an important mathematical programming problem can be converted into nonlinear system of equations.The idea of nonlinear complementarity problem is based on the concept of linear complementarity problem. For recent study on this problem and applications see {{cite:fd95af60e734d0f6cffa218dec3d7c8cec407f1b}}, {{cite:d37f719614015886b70059de3f9f014eb4c77b03}}, {{cite:5228ffa7cae0c70ad63d148fed6bf8114c075762}}, {{cite:85c94b097fd03fd14570164013baa6bf8c08f9ef}} and references therein. For details of several matrix classes in complementarity theory, see {{cite:709265920bda2a18089ae88236b85e9ce2051dd7}}, {{cite:b56d3861c46b3a6972cb1d589bcddc820e3c54e1}}, {{cite:826731b8de2182a0fa0195d280c3c3eec871d458}}, {{cite:576a2382505b1832436dbf160b511f10ff07de93}}, {{cite:423346e600d7a669f6af4fd02210074660bd5cad}}, {{cite:0ca4430bc10978a4f5271f2eca0e5cc3cd899f19}}, {{cite:7bfbce21656d8a357154e8ee5d1082ba6579af6e}}, {{cite:36492d78b380a97b03c4c34f037e03e62142e00e}}, {{cite:40eb91f0bfcc648e4727fb8973dc3e325eb72d09}} and references cited therein. The problem of computing the value vector and optimal stationary strategies for structured stochastic games for discounted and undiscounded zero-sum games and quadratic Multi-objective programming problem are formulated as linear complementary problems. For details see {{cite:c1e60c8626b02aa402d0237f748ebdb75d3e3688}}, {{cite:4f00d9fa416168f309fe6ce5ad82d23201a4295a}}, {{cite:30b5afcac7824eff88bb3eaccd9b80277b605a7e}} and {{cite:f90c4f3f21f7f2e7f0aca51f256d66e1fb70bdac}}. The complementarity problems are considered with respect to principal pivot transforms and pivotal method to its solution point of view. For details see {{cite:eec983f52dd13a5251369552b2fcec0c3439dab0}}, {{cite:022650b13dc20b689db57abbdb62ade0e8579aa5}}, {{cite:cd1e7c89d8313b8fa28bc1d414bdde933efda4c2}} and {{cite:4f555a1106df19fde2c1d04bd8b9edb3ec9817e6}}.
| i | 0f280ef719bd3991db46aefcc4fbcd5f |
Systems are compared in terms of BLEU {{cite:4256c75cdd9db8ddbc80c8759b2db4f54c472e52}} (as implemented in multi-bleu.perl A script from the Moses SMT toolkithttp://www.statmt.org/moses) and TER {{cite:ed5158c3ae432897e0cc302fa50442bac9c55524}} scores, on the single references of the official IWSLT test sets.
| m | 4f4a1e8125291b61b7b06dbd8c251ad5 |
Several of our experimental outcomes were unexpected and need additional investigation. Our results for the convolutional model were initially very promising, so why, at a high dimensionality did our attempt to regularize the network fail, when it succeeded at a low dimensionality? While one might assume that dropout would be ineffective at improving convolutional networks because of how few parameters there are, Srivastava and Hinton have found this to be false {{cite:66ee9d10d73a04d5b84710d99aa1127f83d4afbb}}.
| d | dbb7e70c98c4a5355a7b3ad8d844fc48 |
In this section, we summarize our experimental analysis, resulting from more than 500 experiments. In our experiments, we primarily explore the effect of temporal misalignment on GPT2 {{cite:5f22cc014e77603d8a89891f282935750d6b2021}}, a PLM often used for generation.In our preliminary results, we found that BERT, RoBERTa, and GPT2 models showed similar patterns.
We report the macro {{formula:9c7c704c-adb7-4ad1-a0a7-a268d0aee7fd}} score for classification tasks and Rouge-L {{cite:d01ef596d59edf1dc61f14485688d0a978c68f80}} for NewSum.
| r | eee30400517759afebf9d96aa1778882 |
In this paper, we build a novel pessimism-based Bayesian learning framework for offline optimal DTRs. We propose to combine the pessimism principle with Thompson sampling and
Bayesian machine learning to optimize the degree of pessimism. Theoretically, we derive the upper bound for the regret of the proposed method and demonstrate its explicit form in a specific case of parametric model. Empirically, even though BML often requires additional computational cost, we develop a highly efficient and scalable computational algorithm based on variational inference and conduct extensive experiments to illustrate the superior performance of our method.
Additional Theories
In this section, we generalize the previous theoretical results into DTR settings. We first introduce the following notations. For any {{formula:babff903-89e1-43fc-a729-aa2bad62a3af}} , {{formula:c04eb513-df47-4027-b083-22746c1a4ff8}} is the model at stage {{formula:1538928d-662b-426c-8c81-79077beb3326}} used to fit the response of pseudo-reward {{formula:bb286c6a-1c01-4f8c-ab1a-9a52032dfa6b}} . For {{formula:188a1f60-bee0-4f58-808f-f4a73118183e}} , {{formula:59d62dbb-c00d-4625-9c41-102046cbfc6f}} is the model at final stage {{formula:9de3ae3c-65bb-4488-9395-5650ca42d463}} for fitting {{formula:87f9a7d9-5243-4832-95c6-4a345ec2f146}} . We denote {{formula:3873e89b-d2ee-4fd9-b503-a02e211d140a}} as the conditional density of the pseudo-reward given the history information under the model {{formula:2d423f9d-1881-4395-a113-3c780ebf102e}} so that
{{formula:a12e4dd8-7cce-4120-9044-8f71ba9bdbe8}}
We consider the following assumptions for {{formula:59dca9e6-0a67-4688-9085-f62a149b25af}} :
Assumption 2
The realization condition holds, i.e., there exists some {{formula:2bd69224-472f-4a75-883f-85217271ce09}} such that {{formula:7e4734c2-075c-472d-89e4-28cf9b4976f7}} is the oracle conditional pseudo-reward density function.
The parameter space of {{formula:861db411-febd-438b-8dcb-d02be400ab4c}} is compact and {{formula:c2939425-fa98-4141-b190-9847b9977187}} is continuous and identifiable in {{formula:97aae99b-4ac9-456b-8970-d232e84f0395}} .
{{formula:0ae1677e-a988-42b9-8d62-fb8acca5c945}} is differentiable in quadratic mean at the oracle parameter {{formula:e91bdb8a-a192-4e98-bdfd-04630cb787fb}} with non-singular Fisher information matrix.
The prior measure of {{formula:04acfa2d-9863-4b16-8c74-2715cfabfbd8}} is absolutely continuous in a neighborhood of {{formula:10e98310-84e8-4a35-9ae0-892154f0c07a}} with a continuous positive density at {{formula:7250ad74-324e-4062-aff8-6dc7ae3d7a7b}} .
Assumption 3
Suppose the data used for fitting {{formula:5cea1a85-e509-46d7-9239-8199ce31e828}} for {{formula:4ef0e15b-e017-46fc-8b44-7732841b551a}} are independent.
Assumption REF imposes the cross-fitting condition to simplify our theoretical analysis. Without such an independence assumption, we need to impose certain entropy condition on the function class to prove Theorem REF {{cite:bbaee5c37792f6689a0b22f5a81c4b2d3abb049d}}.
With the assumptions above, we derive the following proposition guarantees that the {{formula:a306ef68-7346-41cf-ae6d-074b9e318896}} based on the Gaussian approximation and Monte Carlo sampling provides a valid uniform lower bound from the frequentist point of view.
Proposition 3
Suppose Assumptions REF and REF hold true. Then,
{{formula:c8d8bb0a-db05-4d07-aca0-5c1ce20bbc26}}
Finally, we establish the theoretical guarantee that characterizes the average regret of the proposed policy from Algorithm REF , i.e., the difference between the value function under the optimal policy and that under the proposed policy.
Theorem 2
Suppose Assumptions REF and REF sequentially hold for each stage {{formula:9e0540f0-9907-4e38-9ee3-d6913f93bb7a}} . Assume that we set the significant level {{formula:e8584d27-0390-4a6e-bc73-0f581b0e905f}} following the Bonferroni correction. Then, as {{formula:35e6037e-c255-4f43-a79a-aa37c84a2a8e}} , with probability at least {{formula:903d7b2a-4985-4c1b-a130-402f94c03944}} , the average regret is upper bounded by
{{formula:77d1c849-412e-4c3f-b099-54ceeafec237}}
Specifically, if {{formula:a2104963-8831-4e1c-a886-ffd4ded46f4a}} is the BLBM with {{formula:943465db-08d3-4e3e-bb51-c8c80a0ac1fb}} numbers of basis functions in Section REF . We can derive the explicit upper bound for the average regret in terms of the sample size {{formula:5dab6989-c5a4-4d83-83a5-92218760cc31}} as {{formula:88e2ae9c-e447-4de1-9517-63bb5709f615}} , where {{formula:94fa8d1f-e6dc-4a99-b380-69e2115c1f5d}} is a constant.
Proofs
In this sections, we provide the proofs for Appendix . As a special case by setting {{formula:bb207833-8fcb-47c5-81b6-a2a6afba5c19}} , it can be also regarded as the proofs for Section .
Proof of Proposition REF
If we denote {{formula:1a7a8c76-59ef-49a8-a96e-0d00a337a5fb}} as the space for the history information. According to the definition that for any {{formula:db468202-6422-463c-8f92-9c4d03539a2c}} , {{formula:3b8b8c5c-1b96-4ecd-ae7f-4cf30e01cdd8}} is the model at stage {{formula:1fa21961-a0d3-481a-8cae-815726f2a6ac}} used to fit the response {{formula:a3e8a9fe-ca32-417d-81e3-4610e168dd4b}} and by Equation REF , we know that for any {{formula:79dcb2de-6d65-45db-98a3-5e5ec6cdbe73}} and {{formula:dd3dce07-313e-4e70-9601-26eb23d67f20}} ,
{{formula:2beb773b-371e-43ca-8205-b7008851a668}}
For {{formula:c7a4d9ce-5677-4cfb-8610-5c338aeb1303}} , we obtain that
{{formula:e0037539-ce64-4f31-b18d-a053b5352202}}
We have the assumptions that the parameter space is compact and the likelihood function {{formula:f01f62ce-9bc8-471a-9fa0-fe8aa7f27695}} is continuous and identifiable in {{formula:f5b48531-4b46-4a43-8ef0-6a74e098b042}} . Furthermore, suppose that {{formula:09561818-e526-460b-8b2e-c047d5f382af}} is differentiable in quadratic mean at {{formula:331e241f-0d99-4b95-a417-92e50e9be40b}} with non-singular Fisher information matrix, and the prior measure of {{formula:b872d3ad-7a18-4956-8649-da3ad96c06a6}} is absolutely continuous in a neighborhood of {{formula:b01a9fe6-88a7-4c13-9f22-559e9407cebd}} with a continuous positive density at {{formula:65db54a3-960e-4595-819b-0a60b32a5c9a}} . Then with Corollary 7 of {{cite:d97c70879c7a93c787ee5f524f8f64ee7ba3fc24}}, we have,
{{formula:3e4cf287-5a20-403c-8a86-8290dd152853}}
We denote {{formula:1b672d6d-b4fe-4ea6-b357-d66680264f7b}} , which is the solution to the optimzation problem in equation REF for a given {{formula:092e9f82-68a4-48a7-802b-a0788e3563f6}} and {{formula:8d69f5f2-00c3-49ab-a8a3-babe1f40d87c}} . Let {{formula:b5a9a740-7dec-462e-a13e-5e33892eeb51}} denote some positive constant such that {{formula:1a352235-395f-4f5c-bd6e-bb5f1d34d25f}} for {{formula:0d2c6a87-b5a9-47e8-b62a-685e76db07ad}} . The value of {{formula:8fd91c8a-73a8-4d0e-923c-ee100dd28119}} will be determined later. Since {{formula:552faf4f-4577-4af2-abdf-47682e4484e8}} is Lipschitz continuous in {{formula:9a557576-b8f3-4f58-8f08-4d062f18c989}} , there exists certain constant {{formula:8a7afa1d-0281-4b20-99d0-cdf5cc1410db}} such that for {{formula:5f0656fc-7901-4bc5-a525-cc0ddd950e2c}} ,
{{formula:d1b81069-3fc8-45f8-8b4f-ae5ea68660d4}}
Consider the interval {{formula:fc5b5c9c-f258-4360-97b8-4b6f96711c6a}} , we have
{{formula:83c9a78d-c5a5-439f-9aae-34bbe8414ca1}}
In our proposal, we adopt a Gaussian distribution to approximate the posterior distribution. Hence, {{formula:3fae6a16-afdf-4191-89f5-c13c25ba9bde}} is Lipschitz continuous in {{formula:c60bde14-096e-4e38-baf8-af197fb0c534}} for a given mean and a given covariance matrix. Thus, we can find some constants {{formula:9f65627b-45e4-4fab-9612-247e93515978}} such that
{{formula:1fb1c165-b4d4-47e4-bd60-22bdf07e541d}}
This implies that
{{formula:2c6a245d-a691-4195-bff6-f86deea46eb1}}
Since we randomly generate {{formula:45842198-c77e-4da9-a390-979c9ae7eace}} samples from the posterior distribution of {{formula:d7de2c6e-749c-4ee7-a5ee-4e6f85a6f8d0}} and select the argmin that minimizes {{formula:a11892c5-37de-4b9d-b554-ab97bae8ab11}} , with some calculations, we have that
{{formula:f643fd2f-a2f9-4299-b40c-b34f24cc71f2}}
By letting {{formula:674c7572-9482-4232-8c55-dab9728117a7}} , we can get that
{{formula:9a26c781-a633-4503-bd8b-ee0ca25c64d5}}
for any {{formula:a6e76c22-6dd4-4ec1-ac95-e108f8bf3e66}} .
From Proposition REF , we know that
{{formula:b5763651-feb7-4bfc-8523-d6ccc33ce54b}}
Combining it with equation REF , we prove that for any {{formula:7b265abe-36a1-4b90-b798-3b843f60ef6c}} ,
{{formula:9657bade-c11f-4c1d-b3fc-c5c884e6d3ae}}
where {{formula:e6f88737-2505-4563-8963-f0e0e3b01e73}} . Since {{formula:a92ce3db-eaed-4493-86be-469bc2cc6509}} can be chosen arbitrarily small, we have that
{{formula:4a3d0bda-d26f-4247-8c54-efa174fb1791}}
With Corollary 7 of {{cite:d97c70879c7a93c787ee5f524f8f64ee7ba3fc24}}, we have ,
{{formula:ffb98f44-c670-412a-9e8a-5006655ad6b0}}
Proof of Theorem REF
In Algorithm REF , we employ dynamic programming, and construct the pseudo-reward {{formula:f73fe80c-00a9-48ba-bf75-f43486d0316e}} for each instance at the each {{formula:175bf3f8-ff61-4bbd-8865-b2ab978d05e6}} -stage with {{formula:65032263-8220-4cf1-8b7c-f3f9b58c2bf4}} . Define the event
{{formula:e37c7b51-c8a6-419f-a668-d57a27cb5c31}}
for {{formula:e3fdd7f8-4e03-4f39-a5e8-8266f1f2f400}} . We also introduce the notation of the joint event as {{formula:4362c22c-b8d0-4395-8c0a-6bb5daa5a5af}} .
With Proposition REF , we can show that {{formula:087a12a7-51e5-4b00-a78b-dfd3bd87d1a9}} as both {{formula:b7110801-5a06-4f4c-8829-2f9b4de636f1}} and {{formula:226ffe1b-3ace-41af-a44f-d7a9c40db7e2}} goes towards infinity for any {{formula:de34fb56-69a7-4668-9eca-3e27bc0808f2}} . Then with the Bonferroni correction, we have that {{formula:cf52daf5-4ec5-4edb-881f-073623f71f50}} when {{formula:6328a017-6c32-4dc7-b1a1-6867be7a6df1}} and {{formula:e74cd7b2-b280-433c-8025-7c56b03e1c61}} goes towards infinity. We use {{formula:acea18e8-1aa6-444c-a810-a60ad0fa5e1f}} to denote the average regret given the initial state {{formula:94591540-c57a-46d0-b340-d9ca71821eeb}} .Then we decompose decompose the average regret into the following three components
{{formula:a24b1c86-5c5d-45a8-add0-e69eb23ed9b1}}
where {{formula:fbe7730f-21d5-4a07-8852-db0c365b1993}} is the model evaluation error.
In the following, we start with the last stage {{formula:c2b18835-f6af-4417-bb90-8a0233b818ed}} for backward induction. We first point out that since {{formula:9019c0df-8d6f-481f-a98d-04c1f14ae156}} is greedy w.r.t {{formula:91510429-2502-4d2a-8601-780e8bd1c3b1}} , the optimization error (iii) is nonpositive. So it can be directly removed from the bound. Next, we consider the spurious error (i). Under event {{formula:cf0761a0-a980-42da-8367-2c0b7badb003}} , we have that
{{formula:02b61fe7-c7ad-4c6e-ae31-d452544dcac7}}
Thus, we get
{{formula:c7d5240a-d4fb-4ea6-bbc5-a86561e4a37c}}
Then we repeat the same produce for {{formula:e66efad5-bf3d-4d98-83ca-ed9f3fa983cb}} , and under each event {{formula:0c10b620-4162-4ffa-b5a2-871f186fcb5a}} , we get
{{formula:4468766d-ac9a-4a3f-a676-52f95d7c0dfd}}
Combining the inequalities above, we have that under the event {{formula:a3602c39-b3af-4c3a-9172-8fe69af3dce7}} ,
{{formula:b026a22b-d02a-4521-8a67-431f9b13ea7b}}
which implies that
{{formula:bd5c6bad-5799-432e-a088-45fd15c7d18a}}
By taking the integral over the randomness of {{formula:936ab171-6a0f-4c56-a03b-ef552c77de8a}} on the both sides, as {{formula:145397ce-773e-48e0-8326-603a9c3cfac4}} , with probability at least {{formula:7dd82e2a-9f08-49f6-adb1-1f5e75d145fb}} , we can upper bound the average regret by
{{formula:ecfbfb58-1fae-456f-b32b-7a599e331511}}
When we consider the specific case of BLBM, we have that
{{formula:0a471de5-425a-4633-bc78-9eff8ab1efca}}
where (II) is 0 if we can directly solve optimization REF without Monte Carlo
sampling. With the Corollary 7 of {{cite:d97c70879c7a93c787ee5f524f8f64ee7ba3fc24}} and the Lipschitz continuous condition for {{formula:58449ce7-a548-48ec-8e22-9fce87f8080c}} , we have
{{formula:d500a3d5-4780-4a57-8393-c519aa2513ce}}
where {{formula:c2116d41-a02b-467c-9814-0b3fad311309}} is the {{formula:2b9fe61e-0c9c-4824-b1f7-5a3da6c04654}} percentile of the standard normal distribution and
{{formula:1331081a-b1cb-429a-bcd2-6ae9ef3257a4}}
.
Hence, we have
{{formula:afb4ce20-b707-44e9-ba1d-6542a3d9feeb}}
for some constant {{formula:42ae794a-7c9e-4c2d-8be8-c446aab5467e}} .
Data Generating Process for Simulations
One-Stage Contextual Bandits
Linear Signal:
{{formula:414932c0-2bfe-4044-949c-f75909ca19d5}}
where {{formula:e928d9ab-e33d-4069-9eca-90dd5785e2f5}} . We draw {{formula:a2e9bad6-39e6-4a53-ba57-619e6efa2f8f}} with {{formula:bd93ae57-5674-4a1c-ae25-b09d6dede5ca}} for {{formula:4baf8daf-21c7-45dd-a2ae-6999031847a7}} . For each state {{formula:55065494-125d-4c4f-8025-2674725f04c4}} , we denote {{formula:d40ac92c-55a7-450c-afe6-40905c148127}} and generate {{formula:675e28d7-a75e-4980-9053-8bc0e8f8be23}} with the probability {{formula:fe4c793a-acb1-467d-be4d-deed6cd7a5e0}} , where {{formula:d132bc79-8e31-4306-8fb3-10f07373ef55}} is taken w.r.t the randomness of the reward function.
Nonlinear Signal:
We define two transformation functions for the second stage
{{formula:068599ed-2f95-4bef-8a1a-2817e6445e2d}}
{{formula:2425d223-1318-446d-bb48-a56077c03ee5}}
where {{formula:7c4c1a38-f8dd-4a23-9765-a7a277dc6764}} . We draw {{formula:b41491cc-1815-4847-a293-93e1a90137ac}} with {{formula:3ffa13f3-da98-4f83-a363-4fb299b1f662}} for {{formula:692940e7-479b-4636-8e0a-7d784c901afb}} . For the action generations, we use the exact same way of linear signal.
Two-Stages Contextual Bandits
Linear Signal: We define two transformation functions for the second stage
{{formula:0ff1aff4-3445-40ad-b8ab-fd1f8fa217d2}}
We first randomly generate the coefficient matrix {{formula:0dd40a12-7ec0-40b9-8e49-1fa86336769a}} with each entry independently drawn from {{formula:a164a620-76e9-4c91-aa0c-f816a229354b}} . Then we define {{formula:0829b5bc-d69d-4964-98cd-6291bd3cdb47}} , where the sum calculation is elementwise. We fix {{formula:49c2b30e-14f4-454c-a08d-ed8ef4cab27d}} and {{formula:8b7e87cd-930d-4d63-891b-56aa3f5280ca}} . For each replication, we draw the state at the first stage {{formula:6dcca4e8-7828-4dfe-b0c3-1af8e8d2b414}} with {{formula:aceaa268-4c8d-4ce0-a1d1-fdea079ff930}} for {{formula:b090c99d-16cd-4007-ba87-06274b51191b}} . Suppose that the action of the first stage is chosen as {{formula:f8d57d04-ee25-4efc-b7d7-6bcc5a3f59e4}} , then we can generate the state at the second stage as
{{formula:13e11290-931c-4aa5-a0ad-67a3c66dab1d}}
where {{formula:03771358-472a-46f6-be89-1328d66b4892}} and {{formula:fc5475f1-c515-49cf-9cd4-22149b066b45}} for {{formula:c2eb1849-d916-47e6-a825-ad6f61257316}} . Assume that we get {{formula:195e0051-30ed-4527-bc49-e876578938a1}} as the action of the second stage. We can generate reward as
{{formula:d8339c84-ddbb-4f79-aee1-a4eaa4867342}}
Note that we haven't mentioned how to generate the actions at each stage yet. For the action of the first stage, we introduce the notation
{{formula:dbe74da1-426f-47c4-bab8-28969d6ffb5c}}
where {{formula:3dff0bd2-eb5b-4d16-baf4-6b74c23effa9}} is taken over the randomness of the noise of reward function and of the generation of state {{formula:5d424f63-56f4-47ad-9631-e71ce1b07980}} and {{formula:3a2171e5-0364-4227-bee4-03697a6e1722}} is only taken over the randomness of the generation of state {{formula:fe8dbd55-7ac4-4e26-ac4b-df2a5150126a}} . We generate {{formula:3d5a5cff-7041-4875-91af-ab958ef68002}} with the probability distribution of {{formula:b541e2f9-d58b-42d3-8bce-f8d1a0fc1e4d}} , where {{formula:a3c8b316-6e50-4c61-938e-3ba183ea8a7e}} is a fixed greedy parameter.
Then for the second stage's action, we define
{{formula:37de284d-0e85-433a-9ce4-b37e2b4834f2}}
where {{formula:ec8f586a-699e-434e-bb3f-ecbbaf2191d5}} is taken w.r.t. the randomness of the reward function. Then similarly we generate {{formula:252276f6-416a-4e4a-8cda-7c7ea55c4e71}} with the probability distribution of {{formula:b4313cb6-a92d-4666-b615-58981d675048}} .
Nonlinear Signal: We define two transformation functions for the second stage
{{formula:a968cdbc-21ba-4486-9d5f-c203e8b203ec}}
We first randomly generate the coefficient matrix {{formula:e619db35-04aa-407a-b613-941a2c35dde6}} with each entry independently drawn from {{formula:60f46254-319d-4205-b2b8-1b4218cfe35b}} . Then we define {{formula:0fab48c2-49a6-42df-a2e3-4bc876284e2c}} , where the sum calculation is elementwise. We fix {{formula:1cb69097-4db6-4274-b272-557351f29367}} and {{formula:4249ff30-d0f3-4583-b46a-ddf617223da1}} . For each replication, we next draw the stage at the first stage {{formula:574b00fc-cc9a-46b3-a03a-ed0957171b8d}} with {{formula:1c80ea97-311e-4d42-984f-0c87c0e9fb97}} for {{formula:4e9d3220-faa4-4a34-adea-76fd49b1b7d6}} . Suppose that the action of first stage is {{formula:1efbb1aa-349c-423b-bf07-14aa0738c6d2}} , then we can generate the state at the second stage as
{{formula:495a7717-4096-499e-ad31-0f9112ed3340}}
where {{formula:cdbc8e5e-03c8-435c-943d-5be6f71f2e94}} and {{formula:494b39cd-5993-4311-a9ba-6c3fa34d7de0}} for {{formula:12f7fe86-b534-4ef8-b2d9-08df15340a3a}} . Assume that we get {{formula:1fcb0bed-28d6-4c7e-8a82-5e719c4f86db}} as the action of the second stage. We can generate reward as
{{formula:2f9ca55d-e843-4d5d-a0a9-79e21aa1ceea}}
where {{formula:2f6afb26-03dc-4fd3-9f00-afb2f735447e}} is calculated in elementwise. For the action generations, we use the exact same way of linear signal.
Model Settings and Computing Resources
For BLBM, we use RBFSampler function in sklearn package to generate basis with random Fourier features and use its default settings. For BNN, we use a two-layer neural network with 16 hidden units at each layer and ReLU activation functions. SGD is used for optimization with learning rate {{formula:0113c01b-844d-490f-a521-fce8601e96cb}} . The number of training epochs is set as 500, the batch size is 100, and the number of Monte Carlo sample is 5 for Monte Carlo gradient descent. The number of samples collected from the posterior distribution {{formula:3dc07e07-2745-4cd7-9e3e-d121f31d6616}} is set as 10000. We use savio_htc cluster for computations. For BLBM, it takes around 1.5s to run for one replicate of each setting on one CPU under single stage while around 25s in average under two stages. For BNN, it takes around 3 min under single stage and 20 min around two stages for one replicate of each scenario on one CPU. We use multiple CPUs for parallelization.
{{figure:ca804b7d-078c-4d94-96d9-237937a8ed83}}
Additional Experimental Results
We also conduct sensitivity analysis for BNN to explore how the number of Monte Carlo samples {{formula:0b16439f-632a-4d86-bafd-3b3187b6bf80}} and smaller sample size {{formula:dc881043-926c-4daf-a903-3b3095b94896}} affect the performance of our proposed method. Specifically, we focus on the single-stage contextual bandit settings of Section . We vary the the number of Monte Carlo samples {{formula:05b8265e-6a97-4829-b34e-27ba47c69a3d}} in the range of {{formula:80a8251e-2228-4978-8cfa-64adc68940e5}} and also include a smaller sample size {{formula:007d0416-c5d9-4abd-812f-6b38abea2425}} . The result is presented in Figure REF . We can observe that the performance of both PBL and the standard Q-learning method without pessimism is insensitive to the choice of {{formula:bc61b207-b201-49f9-8520-4641b0eb8daf}} and it gets relatively larger regret and higher variance when sample size {{formula:66f1c8bd-f48d-4433-a8aa-72064b890e69}} decreases.
{{figure:48f5a29f-ca9c-460b-883f-7de4bea383df}} | d | 1fb154f66e28686c678b1bb9e055eb6a |
The recent strategies of ameliorating CNN efficiency mostly focus on compressing models and accelerating inference without significantly sacrificing their accuracy performance. Among adopted methods, progressive pruning appears to be an outstanding one where a deep neural net is trained, then pruned, and then fine tuned to restore performance ({{cite:f8e7a5c63d0fa4edee8f3d8299cd8b414c37a2d3}}).
| m | 5cdf93f4be08cdb66e29f47be6662b7d |
In the remainder of this chapter, we categorize meta-learning techniques based on the type of meta-data they leverage, from the most general to the most task-specific. First, in Section , we discuss how to learn purely from model evaluations. These techniques can be used to recommend generally useful configurations and configuration search spaces, as well as transfer knowledge from empirically similar tasks. In Section , we discuss how we can characterize tasks to more explicitly express task similarity and build meta-models that learn the relationships between data characteristics and learning performance. Finally, Section covers how we can transfer trained model parameters between tasks that are inherently similar, e.g. sharing the same input features, which enables transfer learning {{cite:0e11098864302078a87c5b3e441f176dd975bd2e}} and few-shot learning {{cite:edbbe753c5ca1c9629db42e57c7d1030c881e800}}.
| i | c1849cf3888c1102fe8f3fa5f9c9855e |
CE is crucial for a number of downstream applications, including, e.g., language understanding, ontology population, semantic search, and question answering; it is also the key to entity linking {{cite:b7fdd573b7813a877a7e0fd93fc252d3b68bbb04}}. In generic open domain subject-neutral discourse across different (potentially unrelated) subjects, indexing the longest possible nominal chunks and their head words located in sequences of tokens between specified “break words" {{cite:fa3e0ea187bef5117e0e9742eada80e17de8ffd0}} and special dictionary lookups such as DBpedia Spotlight {{cite:06302e35c40f4024f30848edb24dc94f07f53028}} and WAT {{cite:158551d028c7142beb10cfd586bfba0fdd8af44e}} are very common techniques. They generally reach outstanding precision, but low recall due to constant evolvement of the language vocabulary. Advanced deep learning models that already dominate CE in specialized closed domain discourse on one or a limited range of related subjects, e.g., biomedical discourse
{{cite:e73eabce52eb092c71c569cfbea002263aca4c5c}}, {{cite:3b24f2e0ba5588f732636db013f377a5cdf82154}}, and that are also standard in keyphrase extraction {{cite:a079bbe9838320b7068f8cfe8cc9da4eb983cc08}}, {{cite:d8e2475438818f023560097d2d537a0feb58e3cf}} are an alternative. However, such models need a tremendous amount of labeled data for training.
| i | 0c90770d17dcdd177dfdd052eb5ba7c9 |
In the literature, the simple Gradient {{cite:d36d5d9056f9b2783ad7bfdd9986aa6fabda3cb3}} method often yields noisy saliency maps {{cite:e22c9f627fd54d0f12e7bda73ce2ce657141f658}}, {{cite:eb208579d820ae88903ca5e3d5e8eb5c87985c14}}, {{cite:8a39e84c5f9422470010b7a9e7b6e03e297c4b2e}} on vanilla CNNs and is thus regarded as one of the worst AM methods.
However, interestingly, when averaging its performance over all 10 CNNs (both vanilla and robust), the simple Gradient method outperforms the more complicated methods LIME, IG, SHAP, and MP in terms of both WSL (Fig. REF ) and runtime.
| m | bb6ca8f27b15c4d7efc12bf1269b74b7 |
These issues motivated recent efforts in the nonlinear filtering literature to develop numerical algorithms
based on a controlled system of interacting particles to approximate the posterior
distribution {{cite:1626dea15345bd1e822e18b814e4ec3d8c6498cd}}, {{cite:e2cf31824e3f7643f2b63b07b48304bf0f7de8bb}}, {{cite:e8fb9178b60eddad848ebcbe34a6a0c9fa1c94ec}}, {{cite:443733beadbcf1912f2aba3ff740823fcfbc31fa}}, {{cite:699ee4cb615e3fa359b0ae4dce06bdcd320d37b4}}, {{cite:90841839da4ca1f3eb5520388864ae08b8d52c2a}}, {{cite:60b92c256e6764c97bd918b97254f0ed12685e17}}, {{cite:862c754880e03cb13436041af9f99069e47d7fa8}}. A prominent idea is to view the problem of transforming samples from the prior to
the posterior from the lens of optimal transportation theory
{{cite:576da6811b80ec59ad45ed3979a164b70b0ab613}}, {{cite:21dd8026552442d365103c027be939ae5e34835d}}, {{cite:a1f4867842ea2cc1b27e5c8732781a67ee940a40}}, {{cite:13190b383e6ecfaf667087023ffd15cce70b32d2}}, {{cite:72edf93602702d7327e09143053ec986a8b045a2}}, {{cite:06c1b3c4ff63cf656801363618888b9427f62b06}}, which has
also become popular in the Bayesian inference literature {{cite:a07ec64f6715c40e5442c856ba4268f94e47afc7}}, {{cite:deb11361e8f888db52159c719628ec054431312a}}, {{cite:80633356d5fb4b81a2567f82b4456e5e9b190bea}}, {{cite:d83ce4b012fc5187e84a6a8977e893e269403243}}, {{cite:beb6fca0d30ba8cbdaa0787aff2804a3a07ca02b}}, {{cite:a1e3cb74b4813b7e5175991bd06274fb1b4563a3}}, {{cite:0af20ec538fb00e0881312eb7d4a4ab239e683b8}}.
Broadly speaking, the aim of the above methods is to find a transport map (be it stochastic or deterministic)
that transforms the prior distribution to the posterior distribution while minimizing a certain cost.
| i | be80e185f6be82fc7f01fb70df1a9906 |
Combining aforementioned observations, we concluded that the utilization of deeper layers are a suitable estimation of EMC. It can be easily calculated, which makes it extremely useful in practice. Finally, we also provide the empirical proof that performing rolling back on final layers does in fact allow models to revert overfit behaviour. This agrees with the results of {{cite:0887fd560f8036d97d4d94316cca751881224155}}, {{cite:d5d903565cc309403ad172017cc7a7d93ae708a4}}. While experiment results are promising, there are still several questions that are yet to be addressed.
| d | 50362e13bef9de8a70bc0368d5fadbd4 |
Algorithmic information theory has been used in causal modeling(see e.g. {{cite:3283b6b083a09fc8ea4165ff434a23ee621ffdef}}).It is also worth to mention that, broadly speaking, the information accounts of causality can also facilitate interpretation of existing widely used causal propositions. For example, regarding back-door/front-door criteria, the goal of which can be consistently considered as whether the observational information of a set of variables is enough or not to answer causal-effect estimation question, instead of conventional understanding such as controlling variables. Moreover, in general sense of information accounts, Pearl points out that questions in one layer of the causal hierarchy can only be answered when corresponding layer information are available{{cite:47ea28516cd424e801ab76ead8f224fc12d7a435}}, {{cite:65b75f8978801918cbc10e54ad16ec9841b63baf}}, and Scholköpf believes causal science will enable us act and decision with information from Lorenzian imagined space {{cite:3283b6b083a09fc8ea4165ff434a23ee621ffdef}}. The recently proposed Mini-Turing test for AI — How can machines represent causal knowledge in a way that would enable them to access the necessary information swiftly, answer questions correctly, and do it with ease, as a human can? {{cite:aa24f163d1d440f5142e0187712c034f6cc32bc2}}. In summary, to build true intelligent machines, climb the ladder of data, information, knowledge and wisdom, we might need to incorporate the information accounts of causality into causal tasks.
| d | ebd2a4445e0b532db8ffe4aca98f2e55 |
Some important aspects concerning the inversion formula remain to be clarified. Firstly, we did not place an upper bound on {{formula:622a0b70-fe7e-4878-959b-eafc2eeef833}} . Theories whose correlators are not polynomially bounded in the asymptotic region mentioned earlier may not display Regge trajectories. It would be very interesting to prove an upper bound, or to find a counter-example. A bound cannot be proven in the same way as in {{cite:031c9dc64a5acd667d331449b0c9dc0ebeadfee6}}, because the bulk channel OPE is not positive, a fact that is also tied to the appearance of the discontinuity in the formula, which has no definite sign, unlike the double discontinuity of the Caron-Huot formula.
| d | d990ef8793910e426a9aab942da1f4f0 |
Many systematic studies of dark clouds and low-mass protostellar cores have shown the HNC/HCN ratio to be close to unity {{cite:cccf913c192e438348e62745a71b13d31a58e42e}}, {{cite:f86af0845a2a186fc37ab3ca6026d1f2a7342041}}, {{cite:dc9c2aa928006192d58d68547c745995d9f58d62}}. No difference is observed between the values measured in prestellar and protostellar cores, implying that the evaporation of HCN and HNC from dust grains does not contribute significantly to the observed emission in the cold envelope. On the contrary, towards the high-mass star forming region OMC-1 in Orion, the HNC/HCN ratio displays strong variations with especially low values {{formula:174277f0-0bad-422d-88e1-74b4cb84dde9}} towards the hot core regions while it is of the order of 0.2 in adjacent ridge positions. While the abundance of HCN is similar to that of dark cloud cores, the HNC abundance is 2 orders of magnitude lower in the high-temperature gas of the hot core {{cite:be3cb1395513b96b0f14a6c431a223630c7fa919}}. A somewhat similar behaviour is observed towards IRAS16293{{formula:48abc569-199c-448a-910f-130614d07493}} 2422 when looking at the high-excitation lines of HCN and HNC {{cite:cb1c212949d10af05c09cca4048e48e194fda3b2}}.
Recently, {{cite:42008d3d659ad914b97b61a72e0e7875b2738a8a}} demonstrated the high sensitivity of the HCN/HNC {{formula:f82e7283-8246-401b-9600-df8a3f4fda21}} =1–0 line intensity ratio to the gas kinetic temperature.
| i | 673f2ffe9d10d0aeefcd5775990646cf |
Table IV shows the result of our model for sentiment classification against other models. We compare our model performance with the approaches of {{cite:03088432ee2d626baa295f073720ac5040dea03c}}{{cite:6e7258e597f48c433d5867bf974962ffd02978f0}} on STS Corpus. {{cite:03088432ee2d626baa295f073720ac5040dea03c}} reported the results of Maximum Entropy (MaxEnt), NB, SVM on STS Corpus having good performance in previous time. The model of {{cite:6e7258e597f48c433d5867bf974962ffd02978f0}} is a state-of-the-art so far by using a CharSCNN. As can be seen, 86.63 is the best prediction accuracy of our model so far for the STS Corpus.
| r | 931dbc2412fcd5d88d01b71a9e6bd831 |
where Please see Appendix: for a derivation using the loop number density obtained from the Velocity-dependent One-Scale (VOS) model{{cite:51943941f842ce865dbc85492edcd7dcf2b9e03a}}, {{cite:63aa375b6537091ba981c08347e12a77ab318006}}, {{cite:4f5ace063d6308507e708bba3b8283b6553cf559}}.
{{formula:271a8004-ca2b-438c-ab53-1eca2389fb70}}
| d | 2881bdc949d2bef02a8852dbbc3cde5d |
The above corollary can be viewed as an extension of Theorem 1
in {{cite:7b2bced6bf3daa51cf9115df21d3e99f9addf06e}},
which established that {{formula:46c5a5ef-1fef-49cd-a2b4-53acb1628203}}
when {{formula:02eeea77-0b0a-401b-bb30-9a3d9629ce5d}} is equally spaced
over a bounded interval {{formula:2681c7ad-ca45-456c-98d6-c64ff8df6d4a}} with {{formula:0247ae81-4b0c-46e5-9013-c6d56961cb70}} .
In particular,
we can see from (REF ) that
{{formula:05cad66d-6e2b-4208-b3a1-aedd2993c7ea}} when {{formula:fa0582ea-7799-4819-8bf7-339274aa3047}} or {{formula:2fb3d048-75f9-4b14-87f8-5873488ccbaf}} .
In other words, when {{formula:1ada119b-a13c-48c9-b829-d9113b200c88}} , we have {{formula:44fa99ea-70d5-4014-84b7-4f48158bf090}}
for all {{formula:49c35801-7355-408f-b935-f3362a66155b}} ; and when {{formula:44ff8e47-3ef7-4951-bd16-4625a1bf3384}} , we have
{{formula:1b563d0a-121e-4968-bc1c-df7794b235ee}} when {{formula:af6baf3a-d681-47e0-b7db-412a868ed783}} is large enough.
This suggests that
the precision at the selected grid points for
the Newton method is often of order {{formula:ca3d96aa-4973-426f-a8f5-9157e2b48e2f}} . This rate is comparable to
that derived in {{cite:7b2bced6bf3daa51cf9115df21d3e99f9addf06e}} and
that of the second-order Runge-Kutta method {{cite:2e82f080de6a7c3eeab2224ef074c6923365b40c}}
if a constant step size scheme is taken {{formula:69224d67-7687-4d9f-85b1-0aed7826bf62}} .
| m | 59a44a2450796afd839ebb1b97627b4a |
Towards this end, we proposed an explainable machine learning model to predict driver fatigue using XGBoost (eXtreme Gradient Boosting) {{cite:b3da41c4a689f04128944a40963640699e42fd21}} and SHAP (SHapley Additive exPlanations) {{cite:7dac22b7367ac263ee9b09a5ffd3ce217119d8f8}}, {{cite:643d1cc83bf773518904fe37f733b3a49abea270}} in automated driving. First, XGBoost is a highly effective and efficient algorithm based on tree boosting and it is one of the most successful machine learning algorithms in various areas, including driver fatigue prediction {{cite:ea03b913373810d18f1c01533b4c905c9b4cecad}}. In order to understand the hidden patterns captured by the XGBoost model, SHAP {{cite:7dac22b7367ac263ee9b09a5ffd3ce217119d8f8}}, {{cite:643d1cc83bf773518904fe37f733b3a49abea270}} was used to explain the XGBoost model by examining the main effects of the most important measures globally and explaining individual prediction instances locally.
SHAP uses the Shapley value from cooperative game theory {{cite:9867f937a33b08815664a1b19488c1ee70e8720e}} to calculate individual contributions of the features in the prediction model and satisfies many desirable properties in explaining machine learning models, including local accuracy, missingness, and consistency {{cite:643d1cc83bf773518904fe37f733b3a49abea270}}. However, it is challenging to compute the exact Shapley values for features of machine learning models, especially deep learning models. {{cite:c735ffa0e9d4e7a5636a75b4258efc22f7ff2e0a}} proposed the SHAP algorithm to reduce the complexity of calculating Shapley value in algorithms based on tree ensembles from {{formula:c88e6086-b167-4f51-8366-4b7d8d5b62ee}} to {{formula:9554bd17-bea8-4824-9b58-9c9422bd7fa1}} , where {{formula:001a9242-7680-42fa-b4bf-6cfc4b8f2cc0}} is the number of trees, {{formula:3ceab279-5e5b-4f6d-a789-77d09919ea8c}} is the largest number of leaves in the trees, {{formula:b0879b37-b8ca-43ee-ab95-d75a5eda8e3d}} is the number of the features, and {{formula:1bc52247-4464-4b3b-9f5d-b95a8841e021}} is the maximum depth of the trees. Hence, XGBoost and SHAP were used in this paper to predict driver fatigue and uncover the hidden patterns in the machine learning model.
| i | a948048d03c8390d4d2dca628db2898b |
models accuracies drop on {{formula:0437e914-d41a-49d5-9ba2-d2f3a24590ec}} and {{formula:fe771985-0da5-4a40-85a9-997880981409}} , suggesting that all three results together should be used to characterize the model, and not any single one of them.
All our models are significantly worse than the human performance ({{formula:bd4a88ce-03f3-4125-827f-7e993f6cc22b}} ,
{{formula:6ad1edd6-bc9e-41ae-984d-5e784fbc876d}} and {{formula:2ecc8934-6b07-4059-8ff6-dc7f90ff8efc}} for {{formula:95af15bb-8707-458a-8a53-259670c10798}} , {{formula:a2f3ddd2-0941-4974-8459-362f7f1593ad}} and {{formula:29ca47ad-d914-4c5e-a6ef-1b02e16946f1}} respectively).
With a difference of {{formula:0252c828-a4cd-45e3-8e4a-bbb3767d123e}} between our best model and the human performance, these results indicate that InfoTabS is a challenging dataset.
Related Work
NLI Datasets
Natural language inference/textual entailment is a
well studied text understanding task, and has several datasets of various
sizes. The annual PASCAL RTE challenges {{cite:4ed6f847360e28f89018079397cf2dfe0f1b68b2}} were
associated with several thousands of human-annotated entailment pairs. The SNLI
dataset {{cite:867966089a1fbe3762b84b69bf42dab3ba6dc533}} is the first large scale entailment dataset that
uses image captions as premises, while the MultiNLI {{cite:bc2a557dbc99e0abd66da900d7af7291a50e8586}} uses
premises from multiple domains.
The QNLI and WNLI datasets provide a new perspective by converting the SQuAD
question answering data {{cite:6e09520f151164b965c4dbdbffbe866d843b7d7e}} and Winograd Schema
Challenge data {{cite:8598b1f078ed9c2820f25c473c58b8dc5a22d985}} respectively into inference
tasks. More recently, SciTail {{cite:a8eaac572e88af1c92b81b8a60bd7e685d7fe9bb}} and Adversarial
NLI {{cite:20095401d429dc3068861be3e09add38d8df6164}} have focused on building adversarial datasets; the
former uses information retrieval to select adversarial premises, while the
latter uses iterative annotation cycles to confuse models.
Reasoning
Recently, challenging new datasets have emerged that emphasize complex reasoning. {{cite:a3e8d490c369c7de85345402f7cea13894fdfc3d}} pose the task of determining the most plausible inferences based on observation (abductive reasoning). Across NLP, a lot of work has been published around different kinds of reasonings. To name a few, common sense {{cite:8adbe8ae95ed3cb55e3c19a352af87df5c2aad68}}, temporal {{cite:0f5057e03e72f255ecbe53eeff5163b67d543562}}, numerical {{cite:b7bf8c723f1d2c6d509b8ac765e148dc643b1c09}}, {{cite:515fa830022a5df383ccfd3bda7ba2948eaf2974}} and multi-hop {{cite:da11f5820b3c1b48235c2f51e907a3f3c38c632a}} reasoning have all garnered immense research interest.
Tables and Semi-structured data
Tasks based on semi-structured data in the form of tables, graphs and databases (with entries as text) contain complex reasoning {{cite:b22bf4f02b97c40431f4754826a227542461777c}}, {{cite:998e7135fde19ed6bcb116ef7541fbc6e740811e}}. Previous work has touched upon semantic parsing and question answering {{cite:b2e6ff4d00c18ee61b2a73e217ae40cd656b491c}}, {{cite:d45f0d7dc3ca917ffebb7959e4d2f4eafd2878eb}}, which typically work with tables with many entries that resemble database records.
Our work is most closely related to TabFact {{cite:998e7135fde19ed6bcb116ef7541fbc6e740811e}}, which considers database-style tables as premises with human-annotated hypotheses to form an inference task. While there are similarities in the task formulation scheme, our work presents an orthogonal perspective:
[(i)]
The Wikipedia tables premises of TabFact are homogeneous, i.e., each column in a table has structural redundancy and all entries have the same type. One can look at multiple entries of a column to infer extra information, e.g., all entries of a column are about locations. On the contrary, the premises in our dataset are heterogeneous.
TabFact only considers entailment and contradiction; we argue that inference is non-binary with a third “undetermined” class (neutrals).
Compared to our multi-faceted reasonings, the reasonings of the hypotheses in TabFact are limited and mostly numerical or comparatives.
The {{formula:96714356-427d-4cbb-827c-9bbb985ee737}} and {{formula:b705cc9a-7c3b-424a-9422-a8a1946afcb2}} sets help us check for annotation and domain-specific artifacts.
Artifacts
Recently, pre-trained transformer-based models {{cite:61278f11f9ff2b06c20e19b2425f8c35e9292ea4}}, {{cite:6beb611d0d68f8e4710690d0e61158be1390e196}}, {{cite:2d854abdad3885ac40bf4ecfdc97d94e9b5daa94}} have seemingly outperformed human performance on several NLI tasks {{cite:b24feda71a6b7771fca40ee2cc823f0a396e9bc3}}, {{cite:7c1c75cb9c5f9f5737409e62dc47f455e3c7e0a0}}. However, it has been shown by {{cite:c26a93c7c69242c0ddff48efcf257ed8bcb44a59}}, {{cite:b2abf6f308896f20f9e309e283273c990b413f08}}, {{cite:a5e1b21c5aed58f4e926cabdf13936d0196fdca9}}, {{cite:a57843a0886fecd7051b651305e4a78fd2633cbb}}, {{cite:fd894b63647087065f089dbaae083bd9760bcd31}}, {{cite:baad1d0d3a8f5c6d45d7634a51f28bf2a90b8fa3}} that these models exploit spurious patterns (artifacts) in the data to obtain good performance. It is imperative to produce datasets that allow for controlled study of artifacts. A popular strategy today is to use adversarial annotation {{cite:1f970e4687f414ed8dcc04d3e2b061f8debaafeb}}, {{cite:20095401d429dc3068861be3e09add38d8df6164}} and rewriting of the input {{cite:998e7135fde19ed6bcb116ef7541fbc6e740811e}}. We argue that we can systematically construct test sets that can help study artifacts along specific dimensions.
Conclusion
We presented a new high quality natural language inference dataset,
InfoTabS, with heterogeneous semi-structured premises and natural language
hypotheses. Our analysis showed that our data encompasses several different
kinds of inferences. InfoTabS has multiple test sets that
are designed to pose difficulties to models that only learn superficial
correlations between inputs and the labels, rather than reasoning about the
information.
Via extensive experiments, we showed that derivatives of several popular classes
of models find this new inference task challenging. We expect that the dataset
can serve as a testbed for developing new kinds of models and representations
that can handle semi-structured information as first class citizens.
Acknowledgements
We thank members of the Utah NLP group for their valuable insights and
suggestions at various stages of the project; and reviewers their helpful comments. We acknowledge the support
of the support of NSF Grants No. 1822877 and 1801446, and a generous gift from
Google.
Examples of Data
Figure REF shows two additional examples of table premises
and their corresponding hypotheses available in the development set of
InfoTabS.
{{figure:0da76f98-602a-4a2a-b29a-528e8ea9ec4c}}{{figure:ab4787ef-0018-4cba-ba8d-ee12f693a987}}
Reasoning for InfoTabS
Our inventory of reasoning types is based on GLUE diagnostics {{cite:b24feda71a6b7771fca40ee2cc823f0a396e9bc3}}, but is specialized to the problem of reasoning about tables. Consequently, some categories from GLUE diagnostics may not be represented here, or may be merged into one category.
We assume that the table is correct and complete. The former is always true for textual entailment, where we assume that the premise is correct. The latter need not be generally true. However, in our analysis, we assume that the table lists all the relevant information for a field. For example, in a table for a music group as in Figure REF , if there is a row called Labels, we will assume that the labels listed in that row are the only labels associated with the group.
Note that a single premise-hypothesis pair may be associated with multiple types of reasoning. If the same reasoning type is employed multiple times in the same pair, we only mark it once.
Simple lookup
This is the simple case where there is no reasoning, and the hypothesis is formed by literally restating information in the table. For example, using the table in Figure REF , Femme aux Bras Croisés is privately held. is a simple lookup.
Multi-row reasoning
Multiple rows in the table are needed to make an inference. This has the strong requirement that without multiple rows, there is no way to arrive at the conclusion.
Exclude instances where multiple rows are used only to identify the type of the entity, which is then used to make an inference. The test for multi-row reasoning is: If a row is removed from the table, then the label for the hypothesis may change.
Entity type
Involves ascertaining the type of an entity in question (perhaps using multiple rows from the table), and then using this information to make an inference about the entity.
This is separate from multi-row reasoning even if discovering the entity type might require reading multiple rows in the table.
The difference is a practical one: we want to identify how many inferences in the data require multiple rows (both keys and values) separately from the ones that just use information about the entity type.
We need to be able to identify an entity and its type separately to decide on this category. In addition, while multi-row reasoning, by definition, needs multiple rows, entity type may be determined by looking at one row. For instance, looking at Figure REF , one can infer that the entity type is a painting by only looking at the row with key value Medium. Lastly, ascertaining the entity type may require knowledge, but if so, then we will not explicitly mark the instance as Knowledge & Common Sense.
For example, knowing that SNL is a TV show will be entity type and not Knowledge & Common Sense.
Lexical reasoning
Any inference that can be made using words, independent of the context of the words falls. For example, knowing that dogs are animals, and alive contradicts dead would fall into the category of lexical reasoning. This type of reasoning includes substituting words with their synonyms, hypernyms, hyponyms and antonyms. It also includes cases where a semantically equivalent or contradicting word (perhaps belonging to a different root word) is used in the hypothesis., e.g., replacing understand with miscomprehend.
Lexical reasoning also includes reasoning about monotonicity of phrases.
Negation
Any explicit negation, including morphological negation (e.g., the word affected being mapped to unaffected).
Negation changes the morphology without changing the root word, e.g., we have to add an explicit not.
This category includes double negations, which we believe is rare in our data. For example, the introduction of the phrase not impossible would count as a double negation.
If the word understand in the premise is replaced with not comprehend, we are changing the root word (understand to comprehend) and introducing a negation. So this change will be marked as both Lexical reasoning and Negation.
{{figure:6f3b9004-7567-4885-a0d3-4a0ebd2abe27}}
Knowledge {{formula:180e1e39-7025-4a39-9961-3b61dfdf3519}} Common Sense
This category is related to the World Knowledge and Common Sense categories from GLUE. To quote the description from GLUE: “...the entailment rests not only on correct disambiguation of the sentences, but also application of extra knowledge, whether it is concrete knowledge about world affairs or more common-sense knowledge about word meanings or social or physical dynamics.”
While GLUE differentiates between world knowledge and common sense, we found that this distinction is not always clear when reasoning about tables. So we do not make the distinction.
Named Entities
This category is identical to the Named Entities category from GLUE. It includes an understanding of the compositional aspect of names (for example, knowing that the University of Hogwarts is the same as Hogwarts). Acronyms and their expansions fall into this category (e.g., the equivalence of New York Stock Exchange as NYSE).
Numerical reasoning
Any form of reasoning that involves understanding numbers, counting, ranking, intervals and units falls under this group. This category also includes numerical comparisons and the use of mathematical operators to arrive at the hypothesis.
Temporal reasoning
Any inferences that involves reasoning about time fall into this category. There may be an overlap between other categories and this one. Any numerical reasoning about temporal quantities and the use of knowledge about time should be included here. Examples of temporal reasoning:
9 AM is in the morning. (Since this is knowledge about time, we will only tag this as Temporal.)
1950 is the 20th century.
1950 to 1962 is twelve years.
Steven Spielberg was born in the winter of 1946. (If the table has the date—18th December, 1946—and the location of birth—Ohio, this sentence will have both knowledge & Common Sense and temporal reasoning. This is because one should be able to tell that the birth location is in the northern hemisphere (knowledge) and December is part of the Winter in the northern hemisphere (temporal reasoning)).
Coreference
This category includes cases where expressions refer to the same entity. However, we do not include the standard gamut of coreference phenomena in this category because the premise is not textual. We specifically include the following phenomena in this category:
Pronoun coreference, where the pronoun in a hypothesis refers to a noun phrase either in the hypothesis or the table. E.g., Chris Jericho lives in a different state than he was born in.
A noun phrase (not a named entity) in the hypothesis refers to a name of an entity in the table. For example, the table may say that Bob has three children, including John and the hypothesis says that Bob has a son. Here the phrase a son refers to the name John.
If there is a pronoun involved, we should not treat it as entity type or knowledge even though knowledge may be needed to know that, say, Theresa May is a woman and so we should use the pronoun she.
To avoid annotator confusion, when two names refer to each other, we label it only as the Named Entities category. For example, if the table talks about William Henry Gates III and the hypothesis describes Bill Gates, even though the two phrases do refer to each other, we will label this as Named Entities.
Quantification
Any reasoning that involves introducing a quantifier such as every, most, many, some, none, at least, at most, etc. in the hypothesis. This category also includes cases where prefixes such as multi- (e.g., multi-ethnic) are used to summarize multiple elements in the table.
To avoid annotator confusion, we decide that the mere use of quantifiers like most and many is quantification. However, if the quantifier is added after comparing two numerical values in the table, the sentence is labeled to have numerical reasoning as well.
Subjective/Out of table
Subjective inferences refer to any inferences that involve either value judgment about a proposition or a qualitative analysis of a numerical quantity. Out of table inferences involve hypotheses that use extra knowledge that is neither a well known universal fact nor common sense. Such hypotheses may be written as factive or implicative constructions. Below are some examples of this category:
Based on a table about Chennai: Chennai is a very good city.
If the table says that John's height is 6 feet, then the hypothesis that John is a tall person. may be subjective. However, if John's height is 8 feet tall, then the statement that John is tall. is no longer subjective, but common sense.
If the table only says that John lived in Madrid and Brussels, and the hypothesis is John lived longer in Madrid than Brussels. This inference involves information that is neither well known nor common sense.
Based on the table of the movie Jaws, the hypothesis It is known that Spielberg directed Jaws falls in this category. The table may contain the information that Spielberg was the director, but this may or may not be well known. The latter information is out of the table.
Syntactic Alternations
This refers to a catch-all category of syntactic changes to phrases. This includes changing the preposition in a PP, active-passive alternations, dative alternations, etc. We expect that this category is rare because the premise is not text. However, since there are some textual elements in the tables, the hypothesis could paraphrase them.
This category is different from reasoning about named entities. If a syntactic alternation is applied to a named entity (e.g., The Baltimore City Police being written as The Police of Baltimore City), we will label it as a Named Entity if, and only if, we consider both phrases as named entities. Otherwise, it is just a syntactic alternation. Below are some examples of this category:
New Orleans police officer being written as police officer of New Orleans.
Shakespeare's sonnet being written as sonnet of Shakespeare.
Ellipsis
This category is similar in spirit to the category Ellipsis/Implicits in GLUE: “An argument of a verb or another predicate is elided in the text, with the reader filling in the gap.” Since in our case, the only well-formed text is in the hypothesis, we expect such gaps only in the hypothesis. (Compared to GLUE, where the description makes it clear that the gaps are in the premises and the hypotheses are constructed by filling in the gaps with either correct or incorrect referents.). For example, in a table about Norway that lists the per capita income as {{formula:2941179e-606c-400f-b8b1-1420164dd105}} 74K, the hypothesis that The per capita income is {{formula:dd9b2b48-630d-4c36-bc58-12e32fa35c44}} 74K. elides the fact that this is about citizens of Norway, and not in general.
InfoTabS Worker Analysis
Figure REF shows the number of examples annotated by frequent top-{{formula:b4af314e-07e8-4831-b92d-d76c32d7ee52}} workers. We can see that the top 40 annotators annotated about 90{{formula:d187f3c2-5350-4ee7-b2b7-cf42be011cf9}} of the data. This observation is concordant with other crowd-sourced data annotation projects such as SNLI and MultiNLI {{cite:a5e1b21c5aed58f4e926cabdf13936d0196fdca9}}.
{{figure:96a011a9-6e61-42fa-8209-505b6eb04044}}
InfoTabS Dataset Statistics
In this section, we provide some essential statistics that will help in a better understanding of the dataset.
Table REF shows a split-wise analysis of premises and annotators. The table shows that there is a huge overlap between the train set and the other splits except {{formula:181dfc5d-7b1a-4d74-bdbd-83f7a5f8cf76}} . This is expected since {{formula:8a19c76d-a887-4dc8-aaaa-5ba8c1c3cafd}} is from a different domain. Also, we observe that tables in {{formula:37e50b82-a1ab-44d1-acf0-605a08bc8f4b}} are longer. In the case of annotators, we see that most of our dataset across all splits was annotated by the same set of annotators.
{{table:a80f8b41-e76d-4a1b-bc30-79c2fb32fe51}}Table REF presents information on the generated hypotheses. The table lists the average number of words in the hypotheses. This is important because a dissimilar mean value of words would induce the possibility of length bias, i.e., the length of the sentences would be a strong indicator for classification.
{{table:2b767c5a-f4e6-4eab-a8a1-374a53448cf7}}Table REF shows the overlap between hypotheses and premise tables across various splits. Stop words like a, the, it, of, etc. are removed. We observe that the overlap is almost similar across labels.
{{table:8d958b53-a651-4673-b5e5-5c5586393949}}Table REF and REF show the distribution of table categories in each split. We accumulate all the categories occurring for less than 3% for every split into the “Other” category.
{{table:ec25ff1c-7d6b-4f1f-80a3-40a805a2c4b6}}{{table:71b8aaaa-dce4-40ca-ae06-fa52410756db}}
F1 Score Analysis
The F1 scores per label for two model baselines are in Table REF . We observe that neutral is easier than entailment and contradiction for both baseline, which is expected as neutrals are mostly associated with subjective/out-of-table reasonings which makes them syntactically different and easier to predict correctly. Despite this, we found that in all evaluations in (§) (except for {{formula:02f51a3a-09ce-4c39-8725-a5d00603f3ea}} test set), our models found neutrals almost as hard as the other two labels, with only an {{formula:2f12aa11-c471-4dba-92d5-91c83b61abab}} gap between the F-scores of the neutral label and the next best label. For {{formula:1ca2346d-823c-43d8-bac2-002e63f10906}} test set neutral are much easier than entailment and contradiction. This is expected as entailment and contradiction in {{formula:d18979b8-aaea-47c8-afea-d7b5195459e2}} were adversarially flipped; hence, these predictions become remarkably harder compared to neutrals. Furthermore, {{formula:d3167380-2353-400d-b1ba-3ed12cb1200b}} is the hardest data split, followed by {{formula:4f15d7bf-19eb-4d14-9448-74dc764dec49}} and {{formula:bddd7dcb-13c8-4384-9f94-101b65418bd9}} .
{{table:9ee3b076-a1ab-41cf-8139-08dc5395c7af}}
Statistics of InfoTabS Verification
Table REF shows the detailed agreement statistics of verification for the development and the three test splits. For every premise-hypothesis pair, we asked five annotators to verify the label. The table details the verification agreement among the annotators, and also reports how many of these majority labels match the gold label (i.e., the label intended by the author of the hypothesis). We also report individual annotator label agreement by matching the annotator's label with the gold label and majority label for an example. Finally, the table reports the Fleiss Kappa (across all five annotation labels) and the Cohen Kappa (between majority and gold label) for the development and the three test splits.
We see that, on average, about 84.8{{formula:6fd1aecd-0a87-46b2-93e0-dac33f628c40}} of individual labels match with the majority label across all verified splits. Also, an average of 75.15{{formula:5ca02f45-b8ad-4d8f-9f01-734df850c4f0}} individual annotations also match the gold label across all verified splits.
From Table REF , we can calculate the percentage of examples with at least 3, 4, and 5 label agreements across 5 verifiers for all splits. For all splits, we have very high inter-annotator agreement of {{formula:b4565fd1-dcea-43d6-801f-fa2829a17e3a}} 95.85{{formula:cedad2fc-b64f-4d0d-a107-e3194ddba9de}} for at-least 3, {{formula:8ebc32e6-8369-41d7-91d5-4b18ce505146}} 74.50{{formula:c765340c-cc4c-4506-a21c-e0e286286336}} for at-least 4 and 43.91{{formula:8c3b23fd-4463-4c77-ac83-b1ccb7ad82d4}} for at-least 5 annotators. The number of these agreements match with the gold label are: {{formula:ee5e6b20-897d-4a44-813b-aa9589d72f9b}} 81.76{{formula:c1b07bd7-0d2e-4de3-bbce-ea0a8bb69372}} for at-least 3, {{formula:f8cb7181-e099-47d9-bfb8-e75191bf938e}} 67.09{{formula:7536fdda-8028-4e45-b33d-81039e0f07a0}} for at-least 4 and 40.85{{formula:102cac44-cc36-4edf-888b-b75e86faeb98}} for at-least 5 for all splits.
{{table:d62ac778-7dcd-4320-bf8f-04311353635b}} | d | a70f9f9f68f2c5e29b7b398a8bb19653 |
Y. Lin et al. suggest a novel multi-task framework called Seg4Reg to generate precise spinal curvature estimation. This new approach proposes an automated method for the prediction of Cobb angles from X-ray scans. Its process contains two deep neural networks respectively concentrating on segmentation and regression ( see Fig.REF ). In detail, the segmentation network first outputs the segmentation masks, and then based on these masks, the regression model directly predicts the Cobb angles. The architecture of segmentation model is similar to Pyramid scene parsing network (PSPNet) {{cite:e8cff6739a33df07f0af2a9f6602b2c42b59a437}} while the regression part makes use of traditional classification networks such as ResNet {{cite:b3e06c658d1901a473e61370e9ade0bd39f0f9f7}} or DenseNet. Besides, the domain shift issue which appeared between training and testing sets is mitigated by adding a domain adaptation module into the network structures.
{{figure:d7de5cad-6acb-491c-96db-65543793c5cc}} | m | cbb76fd25994e32b6543a0d75817d0d7 |
[leftmargin=]
Temperature {{cite:b3a27fc9b31e48384898b518f1c16fb4cdef1869}}: control the randomness of predictions by dividing the logits by t before applying softmax
Top-k {{cite:143a0e3c2941c9519d1d5224088235d36460896d}}: filter the k most likely next words and redistribute the probability mass
Top-p {{cite:f19986c889807f3d79e2d4cebf89ae927d438856}}: choose from the smallest possible set of words whose cumulative probability exceeds the probability p
| m | 35312f42a371c60d30b11e70913653b1 |
In addition, spacecraft such as Solar Orbiter may also be able to reveal this newly identified sub-inertial range in magnetic energy spectra through remote sensing observations. Recently, Extreme Ultraviolet Imager (EUI) onboard Solar Orbiter observed transient small-scale brightenings prevalent in the corona of the quiet Sun termed `campfires' {{cite:d124f6b020a5860fd4258f8181cda09ae422eec4}}. It has been proposed that the majority of campfire events observed by EUI are driven by magnetic reconnection, which may play an important role in the coronal heating of the quiet Sun {{cite:e64a1d6f5ca07456570ec4ea0f0a6c4816d0e0cb}}, {{cite:3468a74e6f49a0dcf5a906295a8857b276de647e}}. Our 3D simulation results in the large-{{formula:c2e03f54-7d8b-44d6-acb6-6f77bb38bc2e}} regime suggest that magnetic reconnection is a ubiquitous process in the turbulent solar corona where the {{formula:a8c2e080-0908-4ba3-91e6-6a67f440c15a}} is even larger and thus the current sheets can thin down to much smaller scales and form the fractal structures within which copious formation of plasmoids occurs. Hence, there should be many more reconnection sites than observed, which can be revealed by (future) high-resolution extreme ultraviolet images.
| d | 690f772cfef0a768c02b240c72e588c1 |
We employ a deep neural network for the experiments in morphological inflection.
This consists of an attentional sequence-to-sequence model, as described in {{cite:1974c20171e41ca0fa3da4c3f2f8201fcb76bce9}}.Available at https://github.com/bjerva/sigmorphon2017.In the SIGMORPHON shared task, this team placed as the 4th best {{cite:549926f88a2dd5173438ca3c13affc6d89ff457f}}.
The system takes embedded character representations as input to a Bi-LSTM encoder.
The output of the encoder is passed through an attention mechanism, to an LSTM decoder which also takes the target form's morphological tags as features.
All layers in the network has 128 hidden units.
Optimisation is done using Adam {{cite:e70e0c0e233c3f0ce6de1bda5965d79a43abd791}} with default parameters.
Whereas {{cite:1974c20171e41ca0fa3da4c3f2f8201fcb76bce9}} explore learning a single model per language, in this chapter we experiment with learning joint models across languages.
Additionally, we do not use an ensemble for the results presented in this chapter.
The system architecture is visualised in Figure REF
{{figure:14f9ca9a-76e5-418d-a8b3-57036958762b}} | m | 279147536af8c20b178d3ad091238d49 |
A general GNN framework mainly consists of two key steps: neighborhood aggregation and feature transformation. In neighborhood aggregation, a given node first aggregates (such as sum, mean and pooling) its neighbors, followed by a linear mapping or a multi-layer perceptrons (MLPs) in the feature transformation step to get the node's new representation {{cite:1e3f11e6f19441c7857f783ba979aa75cd1e8e72}}.
| i | 80e7c77fea8fe211cc49e9bd1061849e |
Our approach is to present briefly the single-record SSI data equation and approach in Section before posing the multi-record formulation in Section , drawing on their similarity. This multiple-segment algorithm is an extension of that from {{cite:1025de44370e6c1bb4b6f987d4bb6225859db3c2}}, {{cite:de486d5a939bc89c3fd62e09e8e3655c10261b5c}} associated with radio channel equalization. The algorithm was presented in the form of this paper in {{cite:3f0ae807a69280c432a9d64c8a062a67f8e6e353}} using the instrumental variable variant, but without the current theory. Theorem REF is presented in Section providing a testable sufficient identifiability condition on the data in this noise-free, exact-modeling environment. These results are a natural extension of those of Willems and Markovsky {{cite:8e1c995f39c6d81399c09d60e4587208f249fd2e}}, {{cite:72dd5749a573d82ba224cdf60dcb9386eeae006f}} and an improvement of the test of {{cite:3f0ae807a69280c432a9d64c8a062a67f8e6e353}}, which did not present a proof. A simple computational example is given in this section to fix ideas. Then in Section , multiple archival gas turbine data sets are used to construct an informative experiment from which a model can be calculated. These data sets are not contiguous. Nor is any one data set completely informative by itself.
| i | 1d1a43531f7c699362c8ed76638061e7 |
By Table REF , the tangential circle packing is a special case of Thurston's circle packing and
Thurston's circle packing is a special case of inversive distance circle packing.
For simplicity, we unify all these three types of circle packings as inversive distance circle packing in the following.
By Table REF again, the discrete conformal structure in Definition REF contains
inversive distance circle packing and vertex scaling as special cases.
Furthermore, the discrete conformal structure in Definition REF
contains the mixed type of discrete conformal structures with
{{formula:93a0dabd-3e29-423f-abde-284985d7ac0e}} for some vertices {{formula:0c47b172-811b-4afb-93e1-230ebc6c465b}} and {{formula:d4b2ace9-d0d3-49e8-b16f-1248092d092a}} for the other vertices {{formula:cbf417a9-b1f6-4e40-ac2b-e5d19b4914a8}} .
There have been lots of research activities on special types of discrete conformal structures on polyhedral manifolds.
For inversive distance circle packings on surfaces, please refer to {{cite:86e9ab0575b9fb04598cffff69405ee990099260}}, {{cite:f4e5e2d7a0ad62bf233a3c956cf757a07ff240b2}}, {{cite:83a44d710adc784c90c9785a199132fac5122138}}, {{cite:b42c5382f6a4842961d2417250db41c6005e552b}}, {{cite:8b6bdde34a40950145561c675b60826d09aaa9be}}, {{cite:d45c92f07b291a22e84d1945efd4545766e639da}}, {{cite:5b871474d614bbe439b8a8b2546d9f17b1fc91f1}}, {{cite:9ee302dcf85f3d5a0a76351099fdaa570dafe850}}, {{cite:91de589a73eae0a5bcf35e84961e3ab5b15e9763}}, {{cite:34eaa79b1d9b9b365e234c46a48051096519ee01}}, {{cite:b2449ffb5b6d1413eb5f5368b2969e858d669e49}}, {{cite:88331b3be4169bb1e11cfa0a999a8e113fc8baeb}}, {{cite:cf31a4c81751632c40712b7d27c1bd6f972bb20c}}, {{cite:a4db9781592a88163843d8ef68e3f50d6ee1252e}}, {{cite:ece05bcf5008646cedd32f4bc5ea44630f74cd76}}, {{cite:37bedebe4ee4659a12fdc0e51039c65d0fcc96c9}}, {{cite:cecf3c1524717a7e83e65244d2f759331ce839fa}}, {{cite:4c235ed4d5c776cda9f70080aefe445dff8c4c24}}, {{cite:7eccbdc36bb21511d923c8104a5873efb14bc2e4}}, {{cite:eb5a323bfd81ca365836f95be044a67ff9c96963}}, {{cite:83cad685114e8d54eaf8286d31e9c644b72a1524}}, {{cite:e2ae42982fe49195f3e983045dc572490856ab53}}, {{cite:af49ff323c86ce649cb93dc86252fa6e1d2b025c}}, {{cite:41e1e87da3390d1389a30a7bc5c74bb1d06bd86a}}, {{cite:9642602a8c9f1ead5a90b68d4ddc58b7bbf5ce53}}, {{cite:a6eab25d9636cd4506112c10737dbbb620f80eb7}}, {{cite:4465ea35069afda38503bf5f7b83d35f69e70ad4}}, {{cite:5b27818df67809515980f342777676443da488a2}}, {{cite:b68c50f65610052788cb57d2a00bc9725622e985}}, {{cite:9e49b33e1e3402f6229aa58c2741f838502483c7}}, {{cite:059d38ba26afae6fad088a05565ef60ca9639184}}, {{cite:ddd49cc1deba8d440cd96dbc371cf49a436e0005}}, {{cite:370efe0693d585bf51e480854744931842e395d1}}, {{cite:bc10bf84d39387d513bea06426b364aa30d23890}}, {{cite:4d2bff4452ab957553c2356305c7e7d3b27f907d}}, {{cite:ae608e14e86fc623cb63766c0222953b6f21349f}}, {{cite:b73c6864a963efe007deb96ec896cce743d727e4}}, {{cite:7413030cf1f5ed8530c81de7ff06c8d10382fd96}}, {{cite:234a2eeadc310eefb1d97d8fb25fcd02eab5f795}}, {{cite:e674fd67a8ad562e82df31083d97be37e97e27b5}}, {{cite:a5011fd2a0a45052e5cd6d669cc005ad2cb8a968}}, {{cite:b225f78b78afa66f444bf2463a49a8bd9453e1ca}}, {{cite:1d164b76107d0a0b5e321cb1708090599a7b7976}}, {{cite:663b0db2aa16a6b363624a9cb3968a724ca3b00e}} and others.
For vertex scaling on surfaces, please refer to {{cite:87b2ec211cc44234ef8c4ed3e5ff73e23015c8ea}}, {{cite:859eb8c7eb1fd09a8218913bb0f3fb3a34f8df69}}, {{cite:08dce4934d21673d880ade230406018f7d9be0d6}}, {{cite:b9779f6763e188de1463ed378ee9e1355fe6101a}}, {{cite:8d090798c5ffe4d166c1d05130cc9c532726f4ce}}, {{cite:72c4257befb6dd9ab63b01944f5a8c51dd2f75d5}}, {{cite:406ebb7fc34c1d311a0fc14c699651586a0e7538}}, {{cite:3123c0280cc5159f1a4725d81755826c8148e6a8}}, {{cite:1191fca8f872b447fcc0c5edb54df993f21f76a4}}, {{cite:8f962a8abaa0e825b434fb8612bfe7ff36ff18ad}}, {{cite:7bca49df9db1cddd60f9979338e0976cda59cad9}}, {{cite:eb303c5f44b4f444a636bb1b03997ff21acf6a52}}, {{cite:c5d88876d47fcb3a9f6e35a3d1c82c0f859865fa}}, {{cite:7747e419ddd959a35a6bba9bd092c51d3495179f}}, {{cite:8461c772ff2ea6d18500b837177b420775d438d5}}, {{cite:b9516c90a96fc5a89570588beb2f83a2ee92f963}}, {{cite:a1beeb46c41c058a17caa175afacc229f238bc94}}, {{cite:4783f168316c318e12458cb5e5c96eac86ff83a5}} and others.
There are also some research activities on tangential sphere packing and Thurston's sphere packings on 3-dimensional manifolds, please
refer to {{cite:76afebf0f180a7abfd799b17411a77ffd5398832}}, {{cite:eef33265a6cabd74b3d205222dd6237eea6d82a5}}, {{cite:e890390196716bf0a13334734878bb11a3b94686}}, {{cite:0d57a4fe35d3a6f0887b7327d524316c14d8be34}}, {{cite:37b5eaa6164dbdc0505f021d4f1986fb8a9553d6}}, {{cite:26d92291ee99d68ea805ca6c810f4c2259c869de}}, {{cite:e2ae42982fe49195f3e983045dc572490856ab53}}, {{cite:af49ff323c86ce649cb93dc86252fa6e1d2b025c}}, {{cite:0a0183c750f858c0d7b51e4823bc8b6463bdae9e}}, {{cite:c1727f131fc1e3032359b9c35cf64292ca27f82e}}, {{cite:67336614a45b45f6fcafc46373ebda391fdee9e4}}, {{cite:7413030cf1f5ed8530c81de7ff06c8d10382fd96}}, {{cite:b05b247bade2c45e9d36e18d3c2421ef5c326d4a}} and others.
In the following, when we mention the discrete conformal structure on polyhedral surfaces, it is
referred to the generic discrete conformal structure in Definition REF
unless otherwise declared.
| r | 77fa499a7e746dfcff5f2191c50eb2a3 |
NGC 5322 is the foremost member of a galaxy group with velocity dispersion of 169 km s{{formula:3bde80d3-0b47-4322-9f0c-75f0f1de379f}} with 21 members {{cite:3e896896b346dcdc672ab2779ca4b2f579f4cb9e}}.
In a study of several galaxy groups using XMM-Newton, {{cite:16e8b2ee7e5994e40c3fd641967ef68c09756faf}} found that NGC 5322 is a X-ray faint (log L{{formula:eb123bd9-867c-47ea-b901-c4f611bd3fc9}} erg s{{formula:4262506b-4b82-4226-9aa1-fcd6977fe3b1}} ; {{cite:84e8a3ff608bc6c3264be4a85874a22934222a4e}}) group with exceptionally low thermal pressure in the X-ray emitting gas in the inner region. As the X-ray emission was detected only in close proximity of the central BH, it was suggested to be coming from the ISM within the galaxy and not with any in-falling matter on cluster-wide scales associated with cosmological structure formation. Therefore, the IGM surrounding NGC 5322 is likely to be of very low density. It is also worth to mention here that we found NGC 5322 to be well located in the fundamental plane of BH activity, described by a relation in {{cite:7b0e5879f36da303668802a8aa216203df0f8ea6}} between X-ray luminosity, BH mass, and 5 GHz radio luminosity, within its scatter, using X-ray luminosity (log L{{formula:ca75406b-d89e-45a2-9f06-8fe26b8d7a4d}} /erg s{{formula:b258313c-7aed-48e7-9f5a-8f7f6f28ed5c}} ={{formula:5795c3b2-c227-488a-87ae-a72b4f0c1939}} ; {{cite:84e8a3ff608bc6c3264be4a85874a22934222a4e}}), BH mass (log M{{formula:422d8828-1010-4f9e-ae00-2732415620b3}} /M{{formula:9c55e4d1-fbd0-4fa1-8888-84b88c9ef904}} ={{formula:0425d965-c007-46aa-9b30-b80e736121ca}} ; {{cite:a664d52309fa10495d8f1c9cd7b113457daf985e}}), and 5 GHz luminosity (log L{{formula:41884ced-2045-44f3-b6e4-68385900970d}} /erg s{{formula:0aeb1ecd-0ef7-4ef1-9977-5afca52470cb}} ={{formula:235f648d-0b8d-4330-a0a7-dfafd5125877}} ) using the 4.8 GHz flux as {{formula:7c5f1a5f-2a0f-4b1d-9087-6190be98b261}} mJy from {{cite:b2862ce7cd9e20f964020235cba403b762e0cf18}} for NGC 5322. Therefore, the BH activities in NGC 5322 appear similar to other radio galaxies in terms of central engine properties and the jet power.
| d | 7737b98b8b5b8a15807ca7f8172ca80c |
Moving object segmentation (MOS) is a fundamental task for autonomous vehicles as it separates the actually moving objects such as driving cars and pedestrians from static or non-moving objects such as buildings, parked cars, etc. This is an important processing step needed in many applications, such as predicting the future state of the surroundings {{cite:4ee65bb56f4447dfcb5762f98ec030737fee1204}}, collision avoidance {{cite:b392069cd261447b76161afa3b61a2a327826ea2}}, or robot path planning {{cite:e2c604da823cc2a658dfb299cacc97b558f6a715}}. This knowledge can also improve and robustify pose estimation, sensor data registration, and simultaneous localization and mapping (SLAM) {{cite:fe5cc0a5dde2f8a05c14e2bbd005fcadafebd34c}}. Thus, accurate and reliable MOS available at frame-rate is relevant for most autonomous mobile systems.
{{figure:640f9b24-00e9-42be-bfd3-960cca963c9d}} | i | 837d475487a7316e0b36e43730d071d7 |
In the following we describe in more detail how the {{formula:8790779b-f5c0-44d3-b6a2-a1a00b803781}} SCF calculations and the linear-response TDDFT calculations are carried out. For all molecules, calculations were carried out for the relaxed structure obtained using the SCAN functional with the default tight basis sets in the FHI-AIMS computer programme {{cite:8c9119dcf8294a7d020864f15c51cb6234faee32}}, {{cite:c443c51b86f5d3425f547f08165e5db724d2c875}}.
| m | d32396f156315a82415cc1c78c30edfc |
Numerical simulations of the collapse of a rotating, self-gravitating,
isolated cloud cores, began to be performed many years
ago; see {{cite:d57ca0b63d865db988aa9ca23e40e8b3f0337106}}, {{cite:e8f1695f717d6e1ef30df7a7283cbab0a68b4c24}}. One of the
classic models of binary formation is based on the
collapse of a rotating spherical core of 1 M{{formula:0158716e-0a31-4a0c-88e8-97830008dde8}} , in which an
azimuthal symmetric mass perturbation was initially
implemented such that a binary system was formed by prompt
fragmentation; see the so-called "standard isothermal test case" calculated by
{{cite:87afb79131754170b134fcd231f845d4d95837d8}}, {{cite:acd4539308ed904979c5f4404509948f41fa552f}}, {{cite:0641728010f8ff8d973a0970cfb56b443e7249d9}},
{{cite:74b268ac3a8217413b287a00cac319a2098e36b8}}, {{cite:fb46c0802b58489be034b65b0f899facc434de87}}, and {{cite:05b6d3bdb0cd06238dbb392506a37b7965e25451}}, among
others.
| i | 19a8d96bae546b8bdd9b481ca8ed8355 |
This inducing-point approach is initially proposed in the deterministic training conditional (DTC) approximation {{cite:04d81d5ce5d7aac5b92791179a46bdd9ee48cc5c}}, and then it has been fully studied in several works. {{cite:0701af71a6d645be5d1fe1a257084711911727b0}} provides a unifying view for the approximation of GP regressions. This framework includes the DTC, the fully independent training conditional (FITC) approximation {{cite:59f862713f080169951f46b167c88f5a02e33206}}, and the partial independent training conditional (PITC) approximation. All above methods modify the joint prior using a conditional independent assumption between training and test data given inducing variables. Alternatively, {{cite:88a66110b3c2e15ece9b955f0c69e7c1117cf450}}, {{cite:4a11c1e81c5e3b31b2299ff9cd06103a75a2773a}} leverage the inducing-point approach into the computing of the evidence lower bound of the log marginal likelihood. They retain exact priors but approximate the posteriors via variational inference. On the other hand, the estimation of inducing inputs has been generalized into an augmented feature space in {{cite:3669b5d7f517d7b666250e18cf0681d50512d65b}}. In particular, SGPs are extended in the spectral domain with and without variational inference {{cite:132768dc42dd88cc05c37cdcccc08da11988670c}}, {{cite:6291714dd46c9d423ad1e5cafe5c429e627e912b}}. Moreover, some works direct speed up the computation of GP regressions through fast matrix-vector multiplication and pre-conditional conjugate gradients {{cite:c8bc80625c05fba88303b79bab31f9dd0b269d4a}}, and through structured kernel interpolation {{cite:2ebc6f290efe438a6b73d13f7d2a562682c24ec4}}.
| i | 32632b861e36c0dd3f863ec51fa83528 |
For fairness, we compare DirectCopy to the gradient-based baseline which uses the same-sized linear predictor as ours. At 100-epoch, this baseline achieves 68.6 top-1 accuracy, which is already significantly higher than BYOL with two-layer predictors reported in the literature (e.g., {{cite:ec283fd3abd2cfc154a0a9182efe4c1d0ee69bc2}} reports 66.5 top-1 under 100-epoch training). DirectCopy using normalized {{formula:157ccec5-6918-4155-986f-3b1975d3d6d4}} accumulated with EMA {{formula:0cca7a56-9a6d-4e1c-8859-048743b0d2f3}} on the correlation matrix, regularization parameter {{formula:92d4ed5c-bd0b-44dd-baea-29372bf50382}} achieves 68.8 under the same setting, better than this strong baseline. In contrast, DirectPred {{cite:52417d6a9eaa59a773411aba3770b70c0ae03b6c}} achieves 68.5, slightly lower than the linear baseline.
| r | 263f6be8406634b4f3d231bb311c877c |
One challenge of leveraging interpretable machine learning techniques is that current interpretable models are usually developed for supervised learning models {{cite:e36e9589dea82a9fa15eeda3ee7854776580fb33}}. For the counterfactual explanation approach, a classifier is usually trained to distinguish the original samples from the counterfactual samples. However, in the anomaly detection scenario, due to limited anomalous samples, it is hard to train a supervised classification model, and most anomaly detection approaches are unsupervised or one-class classification models {{cite:ba2b6f371fd660fa26ed100f792c996901bca343}}, {{cite:35438157ad5e1e1fa8fb781334cb6ed7196af148}}, {{cite:e92ba002e83f49fb628d486d72ab9919e0431bce}}. To tackle this challenge, we propose a framework only using the normal samples, where the counterfactuals are generated based on the distances to normal samples. In particular, we can divide an anomalous sequence into two parts, a subsequence with normal entries and a subsequence with anomalous entries. We consider the subsequence with normal entries as the counterfactual sample of the original anomalous sequence by imagining that the anomalous entries had not occurred.
Inspired by the deep support vector data description (Deep SVDD) {{cite:35438157ad5e1e1fa8fb781334cb6ed7196af148}}, where the basic assumption is that the normal samples enclose to the center of a hypersphere, we aim at identifying the subsequence with anomalous entries having a large distance to the center while the counterfactual is close to the center.
| i | d3bbe87d86dd1d32cba0568a5127db98 |
Repeated data induces a strong double-descent phenomenon {{cite:a7b3b88b0d450ef6c9f275aaf7de6d0ea6339db5}}, {{cite:e20c953d1872c5b7b6a64646714480a99acee48d}}, {{cite:6a36be747a301e4dbe1b73c1e9f216a09753d2f1}}, in which data repeated a few times does not cause much damage to language model performance, data repeated very many times also does not cause much damage, but there is a peak in the middle where damage is surprisingly large. For instance, when we train an 800M parameter transformer with 10% of training tokens drawn from the repeated subset (yellow curve in Figure REF ) we find the loss can be nearly as high as for the 340M parameter transformer (light green curve). We see an epoch-wise {{cite:6a36be747a301e4dbe1b73c1e9f216a09753d2f1}} double descent learning curve in Figure REF is driving this performance degradation. We suspect there is a range in the middle where the data can be memorized and doing so consumes a large fraction of the model's capacity, and this may be where the peak of degradation occurs. Figure REF on the right shows that the peak performance hit coincides with where the train loss on the repeated data approaches zero, similar to previously observed double-descent phenomena. This also provides a practical diagnostic for when repeated data is likely to be harming the model.
Repeated data can cause a divergence from power-law scaling. For the blue curve in Figure REF right (122 repeated epochs), we see only a moderate impact to performance (line on log-log graph) until the model is scaled up to 100M parameters, after which we see a large divergence from power law scaling of cross entropy loss. Extrapolating the region of large degradation in Figure REF predicts meaningful degradation of repeating data only 2 times for large (GPT-3 size) models, though the region would be shifted if the models were trained to the compute optimal frontier {{cite:5259ac9e4401f49a43f6e9ef237ca06f0074ece7}}.
Repeated data causes a disproportionately large performance hit to copying, a mechanism for in-context learning. We constructed a simple copying eval, the loss on the first paragraph of Harry Potter copied 11 times. We observe that using 3% repeated data at the worst number of repeated epochs caused up to a 3x reduction in effective model size (performance equal to model with 3x fewer parameters) on this task whereas it only caused at most a 15% reduction in effective model size on test loss.
The disproportionate performance hit to copying coincides with a disproportionate degradation of induction heads. In line with {{cite:d0e4d34e8848975e23abc1f7da527b4438de3e40}} we evaluated the models on their prefix matching score, repeated sequences of random tokens and observed the degree to which attention heads attend to earlier tokens that are preceded by a token that matches the present token. We observe that using 3% repeated data at the worst number of repeated epochs caused on average a 32% reduction in effective model size on this task whereas it only caused at most a 15% reduction in effective model size on test loss.
Repeated text data causes a small but still disproportionate performance drop out of distribution, as measured by cross entropy loss on Python code. Unlike our the Harry Potter copying and prefix matching evals we mostly see the performance drop with higher levels of repetition, 50-90%.
One and two-layer attention only models trained on repeated data are worse at exactly copying and fuzzily copying (for instance correctly predicting Dursleys given that Dursley has appeared previously) proper names on inspection. When we inspect per tokens losses of smaller models we can see this degradation in a simple, understandable form of copying in a paragraph of text.
Training on repeated Python code creates a similar behavior. When training on Python we also observe a double descent phenomenon and a predictable poor performance region in terms of model size and repeated epochs, though the shape of both curves are somewhat different.
Pre-training on repeated data damages models. Pre-training with repeated data leads to worse performance than both training from scratch and fine-tuning from a control model pre-trained on the original text dataset. During fine-tuning, the repeated data model forgets the repeated dataset, so we consider the model pre-trained with repeated data to be strictly worse than the model fine-tuned from the unique dataset.
| r | c436ddd81a31e5c642ec5ac77f5768d4 |
Data Set Description.
We used Pushshift {{cite:7ce7c43ab1a6673061e2cb3b005b5f6eaec02775}} to extract Reddit data. In particular, we extracted all submissions that contained the word “Cuba” from 07/07/2021 to 07/17/2021, covering a few days before the protests started on July 11th and the first week of the protests, allowing us to capture any useful signals on social media prior to the start of protests and the early narratives that emerged just after they started. We retrieved 4810 submissions. We focused on the top five communities according to their number of posts (see Table REF ). We stopped at five because the sixth community (r/FreeKarma4U) was a karma farming group {{cite:f3bc3966982ff084430182dc5ebd4433eea84b5c}} unrelated to the protests that did not have a cohesive ideology or group identity and the number of posts rapidly declined in all subsequent communities. We manually analyzed all the submissions to ensure that they were relevant to the protests, finding that roughly 95% out of 550 were relevant.
{{table:99b0aff2-6cb1-4f7f-85e9-a8b30ab3b152}} | m | db91adca9af87267bb073b6bf6d98df9 |
The proposed architecture is described in fig:architecture which is based on TransTrack {{cite:a6f9854cde37893d27769568d3d9ba0d0dcfe341}} with several improvements to reduce the computational complexity and model size. On a high-level, we generate a set of bounding boxes per objects of interests in each frame. These boxes are predicted through object and track queries learned during the training process. Following the JDT paradigm of TransTrack {{cite:a6f9854cde37893d27769568d3d9ba0d0dcfe341}}, these two sets of bounding boxes are called detection and tracking bounding boxes. At the final stage, these are associated with each other through Hungarian algorithm {{cite:35af23c783d68447946ca3067d06b69ee12c406f}} to generate final set of bounding boxes.
| m | 55d50e5437cbe6b33fc81f7b73694c4e |
In recent years, on-policy methods have also considered non-parametric target policies obtained by solving policy optimization problems similar to those used in TRPO and PPO. These target policies are then projected back onto the space of parameterized policies. {{cite:ea9df1c2b649078299e965bed3a7953a123d3b04}} considered a variety of non-parametric target policies, while {{cite:b6b9eeeda6f78a73bcbfcbcf56111c1dd3127e50}} focused on the target policy induced by a reverse Kullback-Leibler (KL) divergence constraint in their algorithm VMPO. Note that VMPO is motivated by applying the expectation-maximization framework from {{cite:c0b602553b17cc278ce8479fdb35b7ff2a9cdd5e}} to the on-policy setting, but its practical trust region implementation can also be interpreted from a policy improvement perspective. In addition to generalized versions of TRPO and PPO, we also propose a generalized version of VMPO as a representative instance of policy improvement algorithms based on non-parametric target policies.
| m | a4d6b1311a274a2c52721460f36bfa2a |
The GA is now amongst several other very large LSS discoveries with sizes
that exceed the theoretical upper-limit scale of homogeneity of
{{cite:692c7fa1370256dcce0e8af9cb01943537b40d43}}. In Table REF , we listed some of the very
large LSSs, and also some of the reported CMB anomalies. In standard
cosmology we expect to find evidence for a homogeneous and isotropic
universe. However, the accumulated set of LSS and CMB anomalies now seems
sufficient to constitute a prima facie challenge to the assumption of the
Cosmological Principle (CP). A single anomaly, such as the GA on its own,
could be expected in the standard cosmological model. For example,
{{cite:4059acf1ca28ac67f72a9f2aa93a2adc470ff07a}} find that the Huge-LQG {{cite:c2d7706d73d0f24f397f18ad2397caeca060543f}}, a structure
comparable in size to the GA, is, by itself (there are others), compatible
with the standard cosmological model. However, {{cite:4059acf1ca28ac67f72a9f2aa93a2adc470ff07a}} state
that this is on the condition that only one structure as large as the
Huge-LQG is found in a field {{formula:6ba46057-b612-4f17-949b-f9c57efaf412}} times the sample survey, in this case,
the DR7QSO quasar database for {{formula:d3cc4f56-3440-4fef-b468-b3919e3ef2c0}} . Note that the GA is
found in the combined footprint from DR7QSO and DR12Q (the combined footprint
being almost the same area as the individual footprints), in a narrow
redshift interval, so its challenge to the CP seems likely to be
exacerbated. Of course, the GA is now the fourth largest LSS, so there are,
at minimum, four LSSs comparable to the size of the Huge-LQG, plus several
other LSSs exceeding the scale of homogeneity. We suggest that there is a
need to explore other avenues within cosmology that could explain multiple,
very large LSSs.
| d | 177c7e62c4c7a60ab05396b3233ee0c1 |
Is there any advantage of one approach over the other?
Our experiments show that for a deep network of the same size, invariant representation learning can be just as effective (Tab. REF ).
However, invariant learning is conceptually simpler and scales better than equivariance approaches, as the latter maintains high-resolution feature maps across the hierarchy.
Using a deeper network (e.g., ResNet50 vs. ResNet18) gives consistent improvements, outperforming DVE {{cite:a008130a4014cdfbd3efb89ebaacab41ef6167e2}} on four out of five datasets, as shown in Tab. REF .
A drawback of our approach is that the hypercolumn representation is not directly interpretable or compact, which results in lower performance in the extreme few-shot case.
However, as seen in Fig. REF a, the advantage disappears with as few as 50 training examples on the AFLW benchmark. This problem can be effectively alleviated by learning a compact representation using equivariant learning which further reduces the number of required training examples to 20.
Invariant learning is also more data-efficient and can achieve the same performance with half the unlabeled examples, as seen in Fig. REF c.
| d | cb0be73b9d0a03e846c9796d6b47364f |
Attention Mechanisms.
To address this problem, we add attention mechanisms (AM) into our network.
AM was first applied to NLP problem, and then it has achieved great success in CNNs recently, which can help networks to focus on key objects and take advantage of contextual information {{cite:ef63b246db367f1398a10030f22fed1ca62d3fd7}}.
From this perspective, our work is most closely related to {{cite:8132e8e1029ae81386e1e27f7eec4b90492eb67e}}, which propose an Attention-Based Context Aggregation Network (ACAN) which utilizes the deep residual architecture, dilated layer and self-attention to estimate depth.
It should be pointed that we keep the traditional encoder-decoder architecture with skip connections and attention module, and our AM is lightweight.
Therefore, our model is more applicable to resource-constrained applications.
In addition, {{cite:8132e8e1029ae81386e1e27f7eec4b90492eb67e}} adopt the sum of attention loss and ordinal loss added in a certain proportion as loss function,
but we utilize Structural Similarity Index Measure (SSIM) and gradients between adjacent pixel blocks to propose a new loss function.
| m | c82851b67f7744c333d547dcc6a0fefd |
As shown in Table REF , PNODE outperforms all of our baselines by atleast 27%, 48%, 70% and 5% on clean, FGSM, PGD and SMIA attacks respectively for BCV in-domain Liver setting. While PNODE provides a better defense against the adversarial attacks, it also outperforms the baselines for clean samples. This indicates that PNODE also learns a better representation space of unperturbed support and query samples which is attributed to the continuous dynamics of the Neural-ODE. With small perturbations, the integral curves with respect to the perturbed samples are sandwiched between the curves that correspond to the neighbouring samples ensuring that outputs of the perturbed samples do not change drastically. This is not the case with traditional CNNs, as there are no such intrinsic constraints {{cite:f7301f5fb196941363d64300f735983e448fab88}}.
To further show the Neural-ODE’s role in robustness, we conduct a set of ablation studies. Upon removing the Neural-ODE block from PNODE, maintaining the remaining architecture and training procedure, we observed 0.41, 0.36, 0.36 and 0.31 units of drop in performance for clean, FGSM, PGD and SMIA, respectively. Further, using SAT made this model more robust, but PNODE outperformed it by 0.28, 0.19, 0.20 and 0.31 units, respectively. An interesting observation is that the baseline results tend to perform well for some attacks, while fail for others. For example, SENet {{cite:399cbe7e0295f9d80f92d33943eaa497e5d9ff88}} does very well on PGD {{cite:cbcff34c5ab3e7e9f9f40c31f0c44abd6909eeae}} attack with a dice of 0.21, but performs very poorly on SMIA {{cite:0697b8ea5513a5751abac81f0eebe22d530d7a47}}. PNODE, on the other hand performs consistently across the different attacks. As can be seen in Fig.REF , PNODE also performs well on a wider range of attack intensities. Some other experimental analyses in the cross-domain setting can be seen in Fig.REF , which follow similar patterns with consistently better performance of PNODE. We also perform experiments on the 3-shot setting in Table REF . While there is a consistent drop between in-domain and cross-domain performance of all models, the drops corresponding to PNODE are relatively smaller. Thus, similar to distribution shifts between clean and perturbed samples, PNODE is also robust to cross-domain distribution shifts. We visualise
{{figure:b83b43b8-88c9-46dc-b601-4b1db6c5eef1}}{{figure:b965879c-4859-4888-b518-1a3c659d7244}} | r | 5e8456b84a0c969a11cbaa37b7006cf2 |
The enhanced impact flux by ejected particles may persist on short time scales. Particles most likely to impact Gault have intersection speeds below 0.2 km s{{formula:683a24e1-f2a9-46c5-8d1a-17d6257e7959}} , regardless of when they are ejected. This encounter speed of a single particle may not be high enough to induce mass movement on the surface. Given the momentum conservation law, when a dust particle having 1 mm diameter with a bulk density of 2.5 g cm{{formula:46ac5c34-8c4e-4814-a74a-b72e571aed04}} hits a particle on Gault having 1 cm diameter with the same bulk density, the resulting speed of the 1 cm diameter particle may be 20 cm s{{formula:c04f4cff-7584-491d-93cc-a65ba582af44}} . Similarly, a 5 cm diameter particle may have a speed of 0.15 cm s{{formula:8d0453cf-197b-472b-9f00-c66ac928b2be}} by such an event. However, if clouds composed of numerous particles bombard Gault, a small amount of dust or boulders on the surface may be mobilized. This could result in a cascade effect inducing greater mass movement that may cause mass shedding. Such enhanced mobilization is observed on asteroids Ryugu and Bennu {{cite:b3eec1fc280003703041fa86338fd6b88546e6b9}}, {{cite:9123270734f950b7661ccc5847e084598c1cdc2f}}, as well as by experimental tests {{cite:74a0585e792422c2787fccdc91f1dd33ea85b29e}}. If this is the case, active asteroids with frequent activities may be exposed to interplanetary dust particles and micrometeoroid streams originating from themselves (typically called sesquinary events {{cite:59a21de22e2f0a1c6197fee87b7b20a2ba718ed5}}). However, given our limited assessment, we cannot constrain how such returned small particles can influence Gault’s surface condition. Larger boulders should also be ejected from Gault. They are less influenced by SRP and PRD and would exhibit motion similar to the simulated {{formula:e1dea10a-8bb2-4c9e-9ff3-f58667ebabf0}} case, but could eventually come back after longer times than considered here ({{formula:a6d99474-95bb-4163-8499-00c48f9504c7}} yrs). Because these larger boulders are less infulenced by SRP and PRD, they will not experience the same accelerations due to perturbations and would likely have encounter speeds much lower than that of the small particles discussed above. How such encounters influence Gault's surface condition is unknown. Finally, this may not be the case for much longer time frames when both Gault and ejected particles dynamically evolve due to complex gravitational interactions with larger bodies and non-gravitational effects.
| d | 1928a52925d24c4b8e6a8e8018d03029 |
As we mentioned before, a larger batch size in architecture searching phrase is prone to produce a better result. Our method achieves 2.81% test error on CIFAR10 with the same batch size as DARTS and GDAS (B=64). We obtain 2.61% with same batch size as P-DARTS {{cite:6d8f79821cd1534f7b917cdd402dd805f6749884}} (B=96). Our algorithm reaches 2.40% with batch size 160 and outperform PC-DARTS (B=256).
| r | 1b7f4a4a031b9c52be7cf5227cfe0eeb |
{{formula:c646e9e9-05d7-4063-92f3-3c517f44b6b7}} //Assign rank using non-dominated sorting {{cite:8a87a5733554b3308bca59ba83f0c122f490e1a0}}.
| m | d6bc7a4a1ed79902dbb914fb1d91e577 |
When analysing a complex probability distribution or facing an unsolvable integration
problem, as in most of Bayesian inference, Monte Carlo methods on a large
variety of solutions, mostly based on the ability to simulate a sequence of random
variables and subsequently call for the law of large numbers. Techniques based on
the simulation of Markov chains are a special case of these methods, in which the
current simulation value (and its probability) are used to switch to a different simulation
value (hence the Markovian nature of such techniques). While the working
principle of MCMC methods was proposed almost as early as the original Monte
Carlo algorithms, the variety and efficiency of these methods has grown significantly
since {{cite:709c5da6e6964947265ec78bd2a309faf2b88696}} (re)introduced them to the statistical community
and in particular to its Bayesian component {{cite:41d4008093a6d3f13d4d73e5c52f8e3c6af7e9bf}}.
| i | 895241eac40dab512b8c051f678f646d |
In comparison, our results in the same order are 2.8 %, 2.8%, 3.3%, 1.2%, 5.9%, 4.5%.
We note that these results are in the same ballpark as those of {{cite:8d3821a0d27b01fb2f300010d323b750f77a39c6}},
although there are differences due to the detailed assumptions of each setting.
| r | 87ba436956ef6dc42f36ba672d55d023 |
The effects of rotation and enhanced diffusion were studied by {{cite:4862d49a0444c69341c18527ca44dcd05e4389f0}}, where the value of
multiplier ({{formula:27b012f8-52e6-4226-9942-7fc62869bf0b}} ) was larger than or equal to {{formula:af671ad1-22ee-4d7a-8463-6d9cf07480c3}} and OPAL opacity tables constructed in accordance
with AGSS09 mixtures were used. The flux of {{formula:67b9aa88-72be-4c8a-b93d-ffe4b980c55e}} Be neutrino and the total fluxes of {{formula:c32e2535-6263-412f-bc00-8c7bcb97e60d}} N, {{formula:18615e02-963a-41e7-be73-24b10dafe788}} O,
and {{formula:82cc6e3e-06ce-4f6a-aabc-8ca1062e612a}} F neutrinos predicted by the best model of {{cite:4862d49a0444c69341c18527ca44dcd05e4389f0}} are larger than those detected
by {{cite:ef17ca3b87627212c18ee7308d04f6e2a39dbda0}}, {{cite:b7433a2b744a4aed226867657e2798ce1d12b02b}}. The {{formula:766691f8-1173-426a-8630-9dbe4e7d8df9}} Be neutrino flux is also higher than that determined by {{cite:f37a14c3f9718a7c5a98ee9be5e1af7941e9cff3}}.
Different from the earlier models of {{cite:4862d49a0444c69341c18527ca44dcd05e4389f0}}, Copal11r and Copal11ri, in which the value of
multiplier is {{formula:dfcd6fc4-319a-4c29-a12d-675e652b1ff3}} and opacity tables are reconstructed in accordance with {{cite:72c4b9842bc17bc20e80068616a3d68c61f3ee83}} mixtures,
are in good agreement with the detected neutrino fluxes at the level of {{formula:130a26c9-f7aa-4246-b957-59481b1aa55b}} .
| d | 46286dc9e000321e45b58e8fc74b90b0 |
More importantly, we propose hydrodynamic entropy to quantify disorder in Euler turbulence. We observe that the hydrodynamic entropy of 3D Euler turbulence increases monotonically with time, whereas it decreases for 2D Euler turbulence. Thus, 2D Euler turbulence is a unique isolated system that exhibits evolution form disorder to order. This feature arises due to the inverse energy cascade, which is a property of 2D hydrodynamics {{cite:60ee0afc47f480317d8cdcb84a11751eee1a56dd}}, {{cite:5946ea51f5b310d8816e50f7813bd8277ceb1074}}, {{cite:49a88b6437db91b60ddfbb3b78a95fd78c9cb480}}, {{cite:512e6c893af6ec8e0ded27f99912cd38aad08b8d}}. Hence, the emergence of hydrodynamic order in 2D Euler turbulence has a dynamic origin. Note that the thermodynamic entropy of Euler turbulence remains constant throughout its evolution. Therefore, the decrease in hydrodynamic entropy with time does not violate second law of thermodynamics.
| d | 16f19653c2fbf9e6fe3f02c0b5186824 |
For VAEs, neither data for the “zero-shot” category nor for the other categories are (to the knowlege of the authors) available for the standard benchmarks we used. A reason may be that (like for the BDGAN) very intricate DNNs as well as sophisticated sampling and training methods are required to be competitive. Experiments with standard VAE setups that we conducted did, e.g. for denoising, not result in PSNR values close to those reported in Figures REF and REF . Another possible reason for the absence of competitive values for VAEs may, however, be related to the variational approximation used for VAEs.
VAEs for continuous data usually use Gaussian as variational distributions {{cite:40c3bde930e58750e93c036c421ecac7dd5165e9}}, {{cite:2872b0a4d3cc22018353d6d47367981e6cbecbe0}} that are in addition fully factored (i.e., mean field). The parameters of the VAE decoder may thus suffer from similar biasing effects as they were described for mean field approaches as used, e.g., by MTMKL {{cite:609b79dc558aaff01d51f477f2d66ee4fb88ac71}} for the SSSC model. That standard VAEs do show such biases has recently been pointed out, e.g., by {{cite:fc877219a6ba33875daf9dc269d69ff7c337c63c}}.
| d | a9766e1f202a344829538bdc2a0315c6 |
We envisage that the approaches developed here could be useful for a variety of other problems. The thinning algorithm by Lewis {{cite:fc44abd09daab954e0790185f1d4ffe267b36033}} is somewhat undervalued in our opinion and can be modified for systems beyond those involving single-species Poisson processes for which it was originally conceived. We have here shown how the algorithm can be used for systems in which the reaction rates at a given point vary in time due to a dependence on the state of the system at an earlier time. We also anticipate that the analytical methods we used could be applied in other systems. Fluctuations in subdiffusive systems or gene regulatory circuits are often treated using a Gaussian approximation {{cite:e220789c27594b75ef61d7181760eb317afbfb15}}, {{cite:a2c2ab0e264bda29de4bd4c8bc5e582d5b3004e6}}, {{cite:87299946aa1e9b0ae1172e6069115abb04a47285}}. One future avenue might be to try to eliminate the equivalent of the ageing variable in those systems along the lines of what we have done in Sec. REF . One could then try to characterise the stationary distribution of these models based on a reduced Markovian birth-death process. As a further line of future work, our method for studying the approach to consensus could also be re-purposed for the approach to absorbing states in more general non-Markovian models. The approach to fade-out in models of an epidemic could be an example.
| d | 9c484cebd1b66a442860b6a1bfc811c1 |
Inspired by Proposition REF , we aim to estimate the cost function in (REF ) and then minimize it over the shrinkage factors. This may be achieved using different strategies, e.g., {{cite:006b772170218c030888d1d2e2b326004d59739e}}. In this paper, we apply the LOOCV strategy {{cite:cfb76cd32e799f71fb2898277152550c664d6ea3}} to estimate {{formula:1c5a0718-9d74-435f-89a7-5060f26f1f15}} and {{formula:7a10cebb-7b56-40f1-b686-288b5c988acc}} and minimize them to determine the shrinkage factors. With the standard LOOCV, the samples {{formula:056b96ad-5468-463b-b714-990950644e7d}} are repeatedly split into two sets. For the {{formula:797b73d8-56e0-4203-b66a-88ee678cb433}} th split, the samples in the training set {{formula:b393fdc1-dc8d-4ff1-97b2-966e08be8bf1}} (with the {{formula:9618c11b-b2a1-43eb-ac51-401bf9913def}} th sample {{formula:bc200a21-cd02-49f3-9fe8-a503614ed1ce}} omitted from {{formula:ec14ba72-36f4-4102-a91e-518849a7c47a}} ) are used for producing shrinkage CM estimates {{formula:fa6cf254-2681-4b84-bcad-d55c3eb665ad}} and the remaining sample {{formula:d75400c9-49eb-4879-946b-815fe7c18cd7}} is used for constructing {{formula:0e1af258-c5bc-4990-9048-43a2bc2920f6}} to estimate {{formula:879bb175-6243-4318-bc4a-f7fbec59144f}} and {{formula:41e21230-b397-4201-8823-6132404e41b0}} .
The standard LOOCV process requires the iterative estimator to be applied for {{formula:36294c33-e088-47b9-864b-6ad1f303dc09}} times for each pair of candidate shrinkage factors {{formula:e3ef7060-afdb-4b8e-8907-34e7a451db7b}} , which can lead to significant complexity, especially when grid search of {{formula:f0635248-c666-4b18-b52c-06758a351dea}} is conducted. In order to address this complexity challenge, we propose an alternative solution by using proxy estimators so that closed-form expressions can be found for the optimized shrinkage factors.
| m | 668f41ecf0eec36560c77dd7dc55b25d |
To remove Martian dust storms with deep learning, the first key step is to synthesize dusty images from clean ones to supervise the learning process. In particular, the data synthesis process must be fully controllable without changing any other image content except adding dust storms, which prevent us from using unsupervised techniques such as Cycle-Consistent Adversarial Networks {{cite:759488a4e7fb1d0c3208c97d7369a5cc81b887b4}}. Therefore, we refer to Eq. REF and synthesize dusty images with random parameters.
{{figure:9a2860cc-a6fc-4569-a3c0-e91501c530ae}} | m | 30e6b087c978f0103d7e12337e742b93 |
The {{formula:21252b42-8ccd-4b67-b3c9-d4212f5e7be3}} Minkowski problem. The {{formula:21eb03cc-1178-47b5-8ed0-770c654f2dc6}} Minkowski problem is one of the central problems in contemporary convex geometric analysis. The classical Minkowski problem states that: given a finite Borel measure {{formula:20ca1f9e-9974-4636-a455-30d1b497ae52}} on {{formula:6fad1a85-8237-4e99-81e1-e4c98a98dc69}} , what are the necessary and sufficient conditions so that {{formula:54bdf8a9-6dd0-4f3c-a717-1a56d1f7cd25}} is the surface area measure of a convex body {{formula:6bf8b78f-ec3f-4fa1-91d9-dda86fdc8c5c}} ? Minkowski {{cite:7aa0e866fbe08548d21d7c54299d07a7e4a14f74}} solved this question when the given measure is either discrete or has a continuous density. Later, Aleksandrov {{cite:ffc56cd3b30c9f03c1f130d7a008e8a5c152d630}}, {{cite:57cca45036ec2e9e65af14f40c89b3923add5a0b}}, Fenchel and Jessen {{cite:a86fc7b058b9f59821935a49dac18b801b1743bc}} solved the problem for general measure. It showed that if {{formula:13b9ca53-220b-4788-8d8c-21a902a21782}} is not concentrated on any closed hemispherical surface, then {{formula:b465e43d-ad74-4a72-98c1-b77c14b32bbc}} is the surface area measure of {{formula:b8db158e-75c2-4ce2-8b48-49fb519b0b48}} when and only when its centroid is at the origin. The {{formula:4ddf535c-f7ea-48c1-83d0-5d8b72f46b62}} Minkowski problem is an extension of the classical Minkowski problem and has achieved great developments. The {{formula:7511d431-5999-4d2b-b6dd-0e6f23453512}} Minkowski problem in the plane is solved by Stancu {{cite:1a6cfb5037dd55c80553834bc6a689c5d0bba4ab}}, {{cite:19da9e5d093ec04fab9fb51012c9cc7937734602}}, Umanskiy {{cite:0c16cf8ecdaebc30e1d7994884dc4a915f22bc87}}, Chen {{cite:341b5a8eb9345eb3d449ca9119db6d5387cac2e2}}, and Jiang {{cite:6efadfb379453c27c0d0f1e5f0996f6ed267686b}}. The solution of {{formula:87191dfe-320f-4dcd-bd39-a4de4febfe0f}} Minkowski problem is homothetic solutions of Gauss curvature flow, see {{cite:e1a007781bac226ebfb6f0813fa2614beeceadfe}}, {{cite:a617bbaa0b7daee69bd271da884ed2258145d3fe}}, {{cite:cee9d301364c33e0b295408653f42ab830e9008c}}, {{cite:5fba072531ac693e9fe2bdbc77d5b1934a5719e0}}, {{cite:920d452f8d728cdfaca89e563d84c42cbab2d0cd}}. When {{formula:2c97292c-ec5f-47cd-8e35-cb30fbbfcc0d}} is Lebesgue measure on unit circle {{formula:2a5daa67-c8d5-4427-8b19-dd0a2cd57a92}} , then the solution of {{formula:c863b1dc-fb24-4830-a7ec-51cf60d075f2}} Minkowski problem in {{formula:a5cab766-00b8-4950-8f9c-4fc8605066e0}} is homothetic solutions of misdirected curve flow, see Andrews {{cite:a617bbaa0b7daee69bd271da884ed2258145d3fe}}. Obviously, the {{formula:aada27e7-bd45-4b2f-bef5-0c3f0f564832}} Minkouski problem is the classical Minkowski problem, while the {{formula:0fef37d7-bb5d-47aa-8c81-d7c111a24c22}} Minkowski problem is the logarithmic Minkowski problem.
| i | 2c850100edd3ed6802dc684bbe46f0c4 |
Simple Baselines: We construct simple baseline classifiers {{cite:0459be861e49e057e1ca42b1b4d65df18c8fa443}}: Logistic Regression (LR) and Support Vector Machines (SVM). The input to these models are constructed by aggregating the 300-dimensional word embeddings of words in each review.
CNN: A standard Convolutional Neural Network inspired by Kim, 2014 {{cite:a7da0201361e55284bceb9380029133f96628adb}} is constructed with the following architecture:
{{formula:895a36e9-464a-495b-b446-4e4c05967353}}
{{formula:6b4a4fa7-6986-44ee-90bd-fd07fbd9428a}} {{formula:9a03eee9-d72e-4a8d-90ee-8bfa99fefb43}} {{formula:e5f6f26d-9131-4b84-9917-7ffa908034f5}}
{{formula:57d52282-503f-468b-8ed3-a7d12cb6eda2}} .
This is combined with dropouts, relu activations, and ending with softmax activation producing labels for binary classification. State-of-the-art deep learning methods for existing social media mining approaches of crisis analytics {{cite:2bf0606a660a966922cad408df1ed6112f760922}}, {{cite:c1467c755236de25c1506d213bc656c96b6b164c}} use a similar architecture.
BiLSTM: This is the bottom-most layer in Figure REF with the activation {{formula:844ae889-dd36-4028-8567-bf85081e4b80}} passed through the following: {{formula:ed4bc3da-4bd7-44c0-bd41-62bf62b2aa27}} also including dropouts, relu activation, and ending with softmax.
AMN and HATN: AMN {{cite:3a101748800709cf030c99baf24eb2e050f2d684}} and HATN {{cite:301850b9079a66b8d4a63d8734cdafbff613158b}} are attention-based methods which use gradient reversal to perform domain adversarial training on the unlabeled data from source and target domains. HATN is an extension to AMN by adding the hierarchical component and jointly training pivot and non-pivot networks.
| r | aa5433498eebf0df4a85c4707689926a |
We note that the performance of all methods can be further improved using additional structural information as discussed in {{cite:a42c077eaf82344fd08115da7a82225081cffdf5}} and falsification techniques in training as in {{cite:928a532e63e8e45f79d50b0d3382c362d4e9d21b}}. We leave these improvements to future investigations.
{{figure:78386fab-ff12-4ce6-a7a2-5042499eb54c}} | m | adf0d2924ac53b3704b52e9ca4ef3f3f |
To the best of our knowledge, this work is the first of its type to comprehensively cover the most popular deep learning methods in NLP research today We intend to update this article with time as and when significant advances are proposed and used by the community.
The work by {{cite:8cbe5e281aa4efff214fcd82d4c04ba0684bd65d}} only presented the basic principles for applying neural networks to NLP in a tutorial manner. We believe this paper will give readers a more comprehensive idea of current practices in this domain.
{{figure:3b9bdfbf-a135-4f58-8db4-81eada0f877c}} | i | 132fe39cbbecdd3d2507951fc320a6a3 |
Segmentation CNN: The segmentation CNN ({{formula:4714c26b-c76c-4904-9162-6cf1355b57b8}} ) used is an encoder-decoder like architecture {{cite:c9dfbf22e567de6343b30138ab16a297128530fe}} with the encoder having layer definitions similar to that of VGG11 {{cite:af16b45dc77ff2a7934d06a60ab3609698886503}}. Concatenation of features across matched layers in the encoder and decoder is present in this architecture along with the passing of max pooling indices for up-sampling in the decoder. We additionally add batch normalization after each convolutional layer. The VGG11 like encoder is initialized with ImageNet pre-trained model weights.
| m | c700a195ee6d7e0faf24d1ee905ce785 |
First of all, the case {{formula:7dde837e-059a-4983-be66-647299f3707d}} is treated (together with the unlabelled case) in {{cite:00d34b4fb471a84c16855cf36e9767e3f0c7d58b}}. There it is shown that in the subexponential setting both {{formula:c1c3854f-5b1d-47be-86d8-6b95e78ecf4c}} and {{formula:8e3a7181-1b87-40d9-8fa1-c2eda428210b}} converge in distribution; hence, for a fixed number of components the labelled and unlabelled cases behave qualitatively the same. Also the global structure of the associated random variables {{formula:fac02e17-7f05-4ea3-970c-f23cf25f915b}} and {{formula:cd1147db-3475-4d16-adc0-5c463d0305ec}} is in both cases governed by the same condensation effect, see , .
However, the situation changes as {{formula:981bc142-6219-494e-ac90-e37cbcb572cb}} .
The works , {{cite:0f17e30e8ffa5bd74c3205987afd98c6450d8535}} treat this topic extensivelyIn particular we want to highlight {{cite:0f17e30e8ffa5bd74c3205987afd98c6450d8535}}.: under the condition that {{formula:f4dac2fb-80e1-4fdb-8d34-9e843e659ae1}} for {{formula:a45d821f-9a54-46e7-aaff-89e46a11cde9}} and {{formula:41e9a36f-1b0d-4d7e-93ce-9a4da2473c1a}} as {{formula:889c0fe4-b4c4-4cb1-98db-69bee9b16f17}} there emerges a “trichotomy" ({{formula:7133f0d8-f70c-4ffb-859f-ae8c37ea5202}} ) and in some cases a “dichotomy" ({{formula:ec5155cc-5122-47d5-a216-956e12128f5f}} ) depending on the asymptotic regime of {{formula:03f28ca3-8784-4c13-a26a-b9183feca702}} .
To illustrate the nature of these results, let us consider the class of labelled trees {{formula:10ff93b2-eaf3-42e4-ab64-33ee8c975148}} such that {{formula:818a46bd-8f38-466f-8b4c-d65519e89183}} is the class of labelled forests. The well-known formula by Cayley states that {{formula:4b0beb06-53fa-4b4d-b281-14bef5477b4d}} , so that {{formula:1a3e5dc3-e1ae-4b50-a176-c2f7518f5c19}} . Abbreviating by {{formula:3e9def68-1ef0-4c97-9c90-04b0e8b48f28}} the number of forests on {{formula:2ee4df55-e17b-42c8-affd-dd608928e0ec}} nodes and {{formula:96257265-0cd1-46c5-a72a-7cc411ba0e25}} trees, the following detailed result exposing two phase transitions is known. Let {{formula:017c2e41-1c48-4ada-b8b7-6ad9bc1b8f90}} , then
{{formula:e4c72b5c-8573-4658-b897-1c0463d39c25}}
| d | fc6cab3df81ad68765f1c3c6a300c922 |
In DynLab, each rigid body (object) is now semantically meaningful, so apart from the 4 baseline methods from subsec:exp:sapien, we additionally compare to the following two alternatives:
(5) InstSeg (Instance Segmentation): We take the state-of-the-art indoor semantic instance module PointGroup {{cite:ed6c27f2230016f5755be7d9902bfa0af80f4969}} trained on ScanNet dataset to segment for each input cloud.
(6) Geometric: We use the Ward-linkage {{cite:bd21332f0c56fc2b0c4d9857aa97999d4768b2d9}} to agglomeratively cluster the points in each scan.
In order to obtain consistent segmentation across multiple inputs, we associate the segmentations between two different scans using a Hungarian search over the object assignment matrix, whose element is the root mean squared error measuring the fitting quality between any combinations of the object associations.
{{table:69ff46e3-8dab-4b08-92ae-7868a6d17ca9}}{{figure:9d6f59a1-a41c-4eda-997e-50fd228bbea7}} | r | 38325c898dc2ae6db682bc80d2434093 |
In this paper we have focused on the simplest case of Schwarzschild-AdS black holes, but orbits should exist in more general situations as well. It would be interesting to generalize our analysis to other gravitational solutions, such as charged, rotating, extremal, and supersymmetric black holes. On the boundary, this corresponds to considering {{formula:ad1dd245-d200-4ef0-8508-e82cf6f9edd9}} , where now {{formula:63c79810-366a-490c-8394-28054b8433c2}} is a more general heavy operator with one of the aforementioned properties. It would be interesting to use the Bohr-Sommerfeld condition to compute the spectrum of anomalous dimensions in this more general case, as well as to reproduce these results using the light-cone bootstrap.
Quasi-normal modes of black holes in flat space were recently connected to four-dimensional supersymmetric gauge theories {{cite:5d943b8be463f2c37790bc45b72d416a6563d68f}}, see also {{cite:269ba59891d61f5de14e405e680e2c6b21eefd8c}}. In that work an exact Bohr-Sommerfeld quantization condition was formulated and solved using the Nekrasov partition function in a particular phase of the {{formula:ec0753f8-940a-4560-9e38-4b4d5cc00e6f}} -background {{cite:21b43b6e965daa9519728a077d043bb4b9367b87}}, {{cite:6eedfaf47a13a088c7369a4fecee001603b18de5}}, {{cite:71d4dede34aedc6b81b3e13aead9edb98cfcfe7b}}. This connection can be also generalized to the AdS black holes {{cite:b4dee67b24b87b64901ff8892373e04085affd98}}. It would be very interesting to explore this connection further in the context of the conformal bootstrap and see if it can be used to “solve” the thermal two-point function in the black hole background.
It would be interesting to develop a deeper understanding of the connection between the many-body scars and gravitational orbits. In particular, it would be very interesting to see if there are other condensed matter systems which exhibit a similar phenomenon of perturbative scars. As emphasized in {{cite:e091c67fe90529e21a5ae6e10b0dc4c0ca17db1a}}, the spatial curvature and the finite volume of the space on which the quantum system lives are necessary for the existence of stable orbits in the gravity dual. It would be also very interesting to understand the interplay between the lifetime of gravitational orbits and maximal chaos. In the context of holographic theories this is related to understanding the fate of gravitational orbits at finite 't Hooft coupling {{formula:d9f527cb-693d-4c5f-b8a9-2b1f956bc57b}} and understanding how stringy corrections affect the lifetime of the orbits.
We have observed that a finite lifetime of the gravitational orbits drastically changes the structure of the heavy-light OPE. Instead of a discrete sum over the double-twist operators we get a continuum spectrum with many narrow resonances. The width of these resonances is nonperturbative in spin {{formula:15f1dc75-c517-4125-982a-19acbd51342b}} . It would be interesting to explore nonperturbative in spin {{formula:fa73214e-0b48-4848-aa4a-29d298bdab5b}} effects using the Lorentzian inversion formula, which should correctly capture them {{cite:ef8d9986f3b10e25ca8e1a03cf0b864a07385bc7}}, {{cite:ec47830d1f25bd23be14dde0aefd1cf465e23c86}}. It would be also interesting to see if the heavy-light four-point function bootstrap together with the ETH could provide new insights into the finite temperature bootstrap {{cite:6d81b1dfde8aa8e057c3fe23e62b54ce72fbe927}}, {{cite:37b6af45e9310e049fb4015f4b7e697853dc939f}}, {{cite:80e2ee792038f0bc35f20274ce6e27b7a4a61bb3}}.
Existence of gravitational orbits around AdS black holes is a very robust feature of holographic theories. In particular, it would be interesting to analyze orbits when the geometry of the boundary is different from {{formula:67725bdb-793e-4200-99ea-6b4161b89b41}} . It is clear that the positive curvature of {{formula:825e9ad4-50b1-4931-8c66-902300a14178}} is important for having gravitational orbits, e.g. they are obviously absent for {{formula:0011520e-184e-471b-83ad-bf10bace5bcb}} or {{formula:81fbc237-593b-4d9c-8e39-a5ac46a16efb}} . Relatedly, it would be interesting to better understand the implication of the light-cone bootstrap for CFTs on general spatial manifolds {{formula:229c5b32-d740-4113-bfa3-24cf9eb113e7}} .
In this work we have focused on gravitational orbits in asymptotically AdS spaces. As Earthlings well know,This comment does not apply to flat-Earthers. stable orbits are characteristic to the gravitational dynamics in four dimensions in asymptotically flat and de Sitter spacetimes as well. It would be very interesting to understand how potentially very intricate structure of the orbits, e.g. the Milky way galaxy, is realized in the dual theories and if there are simple toy models that could correctly capture the gross features of the orbital dynamics (together with the maximal chaos).
An interesting aspect of the heavy-light bootstrap is the role of the horizon in the dual classical geometry. The presence of the horizon makes the spectrum of the normalizable solutions to the bulk wave equation continuous (and correspondingly the spectrum of the dual CFT). Instead having a horizon-less geometry, e.g. an AdS star {{cite:a5bd135533969de534932c733a78bede86515bb2}}, {{cite:accfa59f79360ac1cff678d11021c82c07aa7cd8}}, would produce a discrete spectrum in the heavy-light channel. Both geometries look identical close to the boundary (due to the no-hair theorem) and in a related manner they will acquire an identical contribution from the multi-trace stress energy tensor operators {{formula:becf61e7-51b0-4713-8882-580ee8342075}} as discussed, for example, in {{cite:9ad1c5f4c9fc117d218c39ab3034aee72748f242}}. The difference between the two geometries is captured in the light-light channel by the properties of the double-twist operators {{formula:81a8f4f9-f386-4d33-b046-88aef3ae9633}} as well as by the spectrum of the double-twist heavy-light operators {{formula:b058c564-5b7f-469a-8ba8-6e7abece0f32}} . When using the Lorentzian inversion formula {{cite:ef8d9986f3b10e25ca8e1a03cf0b864a07385bc7}}, {{cite:726b691ec9598815d50c780bd58887a036af344f}}, {{cite:07399f20c5f38c5626989d8b073a3b92a3153824}} the contribution of the double-twist operators {{formula:1d72bfb0-ea4d-422c-89a7-fffc3c42584a}} is suppressed by {{formula:155313d9-3263-4d01-b012-be7d19cfa5a7}} , but the contribution of the operators {{formula:0367d940-cd18-49b1-affa-a052c82b0b11}} is only suppressed by powers of {{formula:2ba0840a-f643-493a-83cc-4573e6c08837}} . Therefore, the difference between black holes and stars will be visible. It would be interesting to explore these effects in detail.
It would be very interesting to generalize our discussion to finite {{formula:007deb55-f357-4626-af94-5aa0b6d566fd}} . There are many places in which our discussion will have to be modified. One important effect is gravitational radiation, which contributes to the lifetime of the orbits at order {{formula:dac07c4e-ee5c-4eb6-aa66-4a0d90f0c500}} . More conceptually, the basic features of the black hole geometry, such as the black hole horizon or the black hole singularity {{cite:96acc8a448f808d9f9037cb08fb3c84bbe2794d3}}, {{cite:18dc23d13751975b9e20f80b4a4fc6124c18d61d}}, {{cite:2314425438f39ef68d3f72a20000bb38cb20830e}}, naturally appear on the second sheet of the conformal partial wave expansion {{formula:7dfd00dd-ddce-4773-8bd8-d4a21ae7436a}} . The notion of a second sheet of {{formula:b1d4e27d-29e1-4089-8b86-7a2038136dc6}} is a large {{formula:8ce12220-cb44-4c39-a615-4f1043dc9dcb}} effect, which is absent in a single CFT at finite {{formula:8fd0e7be-46eb-4917-8cd0-8f07390fb6d8}} with a discrete spectrum. Still, it should be possible to define the second sheet of {{formula:8d0ae227-892c-4301-bfd1-7450b21d27a4}} at finite {{formula:f6c17b6a-70a4-4e79-85cc-e5681f67a829}} upon a proper coarse-graining procedure. Naturally it should be related to the experience of a low-energy observer in the bulk with a finite energy resolution. For example, it is natural to smear {{formula:d6b8169b-3dac-4f73-8c41-0f8ca5b1d364}} over a finite region of the {{formula:02b4f3bb-1561-430f-a770-9845d9fea840}} -plane, which effectively creates a cut even at finite {{formula:db66c2e7-645c-41af-bbe0-82c565bbb648}} , see e.g. {{cite:00b6816d5ee2202509affc6bcc406ec766cdbe4b}}. Indeed, perturbative in {{formula:97bfb56a-f62a-439d-819a-c435ad05d44d}} computations effectively perform such an averaging in a region of size {{formula:c6a02c89-89e5-4ddf-9ef7-72f5175f0b26}} since they do not resolve the {{formula:a3e86d8d-167e-4f09-8269-28e83739e219}} discreteness of the spectrum. It would be also interesting to explore the effects of other notions of averaging in higher-dimensional CFTs that have been recently discussed in the literature, see e.g. {{cite:ca4251bb612535be2dd26fdd17b01784300f4453}}, {{cite:7f87f899b22bacfbfd2868b469ac7f0369e8d2bb}}, {{cite:d4986883796e320c9ff830977a2677bc990bf03d}}, {{cite:c5c6a20d389ca0a808dc218e672c8e67d24853b5}}, {{cite:0a14107279514e2fbac8f5babc7589531b683ecb}}.
| d | 04b13c9b68162cdd11bd3fdf3b1a24cb |
Linear Multi-Step (LMS). These methods rely on the approximations generated at the past {{formula:02193953-9a9f-41b2-b95e-e840966e89b2}} points, that is
{{formula:09c3333f-527b-4e40-8fc8-9c273b7a9ea9}} and the first-order derivatives at those points to obtain an approximation to {{formula:c769e2c4-39da-476d-9dae-a9e869994c6f}} . LMS methods are usually represented by the following formula,
{{formula:da79c5c7-d195-4dcc-a0e5-29f5ce536533}}
where the coefficients {{formula:0e356741-8dbf-40e4-8387-8b7775e7e56a}} are specific to each integration method and are chosen to make the first {{formula:b7c6205b-4407-407c-9e17-e805f5f2b6f0}} Taylor series terms in the operator {{formula:d0dc8e24-064a-43f0-9200-7e44c56ac322}} vanish {{cite:2f025054c982bac0277ae041e2dee078f0fa77d8}}. Notable example among these methods, are the backward Euler (BE), trapezoidal rule (TR) and the backward differentiation formulae (BDF).
Single-Step Multi-Stage (SSMS).
Those methods use the approximation at a single past time point, {{formula:95ea479f-cc7f-4501-b181-0554d5e6057c}} , along with approximations to off-step points (known as stages), at {{formula:39b9376c-dfac-4d88-bd96-96c3e09c85ae}} , where {{formula:847ac21c-1e74-4405-b241-074645910d81}} , {{formula:70fba581-2bc6-4d2f-bfc7-cc8657ae4346}} . The Runge-Kutta (RK) methods {{cite:86182465e94b160f7094d6648821a495e237b9c5}} are the best known example in this class of methods. An RK-method is typically represented by the Butcher tableau {{formula:cbd15ab3-a0bf-4a5a-917d-63014731444b}} , where {{formula:017e576f-5bbd-415b-b38b-631d9a69f284}} with {{formula:0237d24c-3161-409f-8277-dfe013ee686b}} the number of stages. The formulation of the RK for a system of ordinary differential equations {{formula:aa4cb2eb-dc2a-41fd-9825-e66602397d84}} takes the following form
{{formula:aad06afe-3d33-414c-8c08-a56f349ef500}}
where {{formula:5e5b5f25-d321-4018-90fc-2eb88117200a}} are called the stage value that approximate {{formula:0765b69b-fb6f-4ffb-97dd-e3c0f34d0070}} and {{formula:a80df954-8935-4797-ba2d-a296b3460674}} are the components of {{formula:7864aa1d-5e67-442a-ab8f-d7c64b9489c2}} and {{formula:1e3d33ce-dc68-4b14-abba-d38f1e5a2054}} , respectively.
General Linear Methods (GLM). The GLM are typically viewed as a hybrid between the LMS and SSMS methods, since it uses the past {{formula:1a649d79-82de-40f0-b9ea-abecc09a0b0f}} points along with {{formula:8fd59878-d3fd-4cd8-b90a-3500caf34878}} stages to advance
to the next step. The construction of a GLM method is usually represented by the block matrix
{{formula:e2203cd8-3139-493e-84ad-25ce51ebe6f9}}
where {{formula:324b9c20-c727-4543-aef4-eb94f0746f85}} , {{formula:9db1c29b-754b-41fd-9347-eed5ebe71829}} . The time stepping to {{formula:90974ccd-25a5-475f-8f6c-af7a38e7bc92}} is presented as
{{formula:f923e8f9-394f-4b2d-bc41-da1d6afb5f48}}
where {{formula:4b36a499-e2e2-44ca-9fe0-d51759207915}} , {{formula:17388d3b-5746-44c3-bd6f-cb02b01b0fee}} , {{formula:ec24b9d3-df88-4154-8b67-28ed9231cbec}} , {{formula:598be256-ce11-49f1-9936-dc182fc348c7}} are the components of {{formula:b1c88470-2858-4b41-9a8f-dbd2d7c6a615}} , {{formula:f9b72e60-149d-4a11-b07b-cc26e298d433}} , {{formula:d4ae5c44-b9b6-4773-a90a-9363b2469fca}} and {{formula:02c9e3b2-3df9-410c-b9e3-26d0d066e0ce}} , respectively.
| m | c7be8788a2bdc611892ae9f3b6bbefea |
Input to all the models are word vectorshttps://code.google.com/archive/p/word2vec/ {{cite:1c27f98fd19318daa937905307d55b92b3f0e2e7}}.
The evaluation on amazon reviews shows how well the single-task (ST) model perform when compared to the existing top-performing domain adaptation models on benchmark dataset. Table REF shows accuracy scores on the Amazon cross-domain sentiment analysis dataset. HATN uses unlabeled target data, gradient reversal, explicit pivot extraction, and joint training making it a computationally expensive method. As shown in the experimental evaluation, we use the same Amazon dataset and GoogleNews word vectors for our experiments. ST, being unsupervised with no need of unlabeled target data, performed competitively with an overall accuracy of 85.02%; thus establishing a strong fully unsupervised building block for us to build upon.
| r | 6178449829835f3e0f6f3a57eb0c490f |
In this paper, we present Mixer-TTS, a non-autoregressive model for text to mel-spectrogram synthesis. The model backbone is based on the MLP-Mixer {{cite:b42df816944fe7fc5fa5fe0b206d6ad774b153ce}} architecture from computer vision adapted for speech. The new backbone makes the model significantly smaller and faster than Transformer-based TTS models {{cite:f100a5cd11f331faf04de95a7f5d5a9ebaef232b}}, {{cite:a103468c22ed10a5ea6c76cfd76da058d9de9772}}.
Our model uses an explicit duration predictor, which is trained by the unsupervised alignment framework proposed in {{cite:2b2a59f023ff96945e61ff50d3451ac400ab9dc2}}. Mixer-TTS combines two methods to improve the prosody of generated speech. The basic version has an explicit pitch predictor similar to FastPitch {{cite:a103468c22ed10a5ea6c76cfd76da058d9de9772}}. The extended version adds token embeddings from an external pre-trained LM to improve speech prosody and pronunciation. Using token embeddings is significantly less expensive than inferring BERT outputs as in {{cite:244f022060090d7fea6b9a69c5b5e9840a4099b9}}. They notably improve speech quality with a very modest increase in the model size and inference speed.
| i | 632a457728ff76fb3a5b3d223fbac355 |
From Table REF we can find that the branching ratios of {{formula:0896ffa8-a4a8-4e19-acd8-92a91e7ec2c9}} decays fall in {{formula:4d3480bb-07ea-4f5c-919a-0429de9e944f}} order.
The experimental data for the branching ratios of the decays {{formula:7d5ee2af-b698-45b9-8963-6a5fbc185e51}} , which are given as
{{formula:c1bfa4e3-a14c-4ffb-9b10-cf73aee0e355}} and {{formula:5be4c76a-b0b2-448f-94cc-d8871444e827}} , respectively, are large and incompatible with all the present
theory predictions. Even for the two sided intervals {{formula:9fb02c98-58aa-475f-adbe-8f859382ca57}} and
{{formula:57ab192b-1ed3-4c89-adf6-f167c99cba1d}} , they almost can not contain the different theoretical results. While the branching ratios of the
charged {{formula:d8def6e9-0a5d-409b-8cfe-7d45c7e55e96}} decays can be explained by the theories for the large uncertainties of the intervals {{formula:53277b20-e969-4ed8-ad63-cf3cf8b80742}} . The large large differences between theories and experiments do not happen to the decays
{{formula:40ddb24a-b0ad-4b72-bb74-15d318819892}} , which are tree-dominated. If the decay
constants {{formula:137ac343-4961-4c13-ad05-7d36df5ede02}} and the form factors {{formula:7f366d8f-fe1e-443a-b766-625372dafcb4}} can be well determined, it is not difficult for us to
predict the branching ratios
of the decays {{formula:42a2926d-5d47-4673-bc70-fe49e6e159e2}} accurately, because the penguin contributions can be neglected and there are fewer uncertainties. For
the considered decays {{formula:5b85ca39-cebe-43de-a406-bfa0c823c3e0}} ,
the tree operators are suppressed by the CKM matrix elements {{formula:a26edf58-5cf2-439d-b33d-5aeba43e5434}} , and the penguin operators will play a significant role.
If the future data are really larger than the present predictions for here considered decays, the authors {{cite:87d0c8de2c3341c5a15847a9dc6891aae7d49858}} claimed that there
are two possible reasons: one
is because the larger corrections from the weak annihilation and the hard spectator contributions, the other is from the charming penguin contributions.
In our calculations, the hard spectator contributions which correspond to the non-factorization emission diagram ones are very small. Although the
factorizable
annihilation contributions are more important, they can not promote the branching ratios too much. So we consider that the charming penguins are
more likely to explain the large data. Unfortunately, the charming penguins are non-perturbative in nature and remain untouched by
many theory approaches.
While it is helpful to consider these decays by using the
soft-collinear-effective-theory (SECT) {{cite:a6b7ab31d3b3286e815a13e186ad8295ef0aad91}}, where the charming penguin contributions from loop diagrams are included. Certainly, these contributions
can also be incorporated in the final-state interactions {{cite:5546886029523c90c8e59100acf87ff085b47ad0}}. There exits the similar situation for the decays {{formula:79a98d99-9563-4cb8-918a-36d76b720262}}
{{cite:f52b34824861211aad915c8ce507b20df0382a18}}, where the PQCD predictions are larger than the data. The nonperturbative contributions, such as the final state interactions or the charming penguins,
are suggested to explain the data.
The penguin contributions from the factorization annihilation diagrams in the {{formula:c54168ec-a6a7-4c25-94b9-32f8e6ad161b}} modes are much larger than those in the {{formula:4ffa133e-5511-4082-ac41-44233fa927be}} modes.
So we can find that the branching ratios of {{formula:98aa5acd-2fc3-497b-b3cd-628eac914272}} decays are always larger than those of {{formula:45f2704f-425f-4a1b-a348-18ccefd199ed}} decays, which is shown in Table REF .
{{table:e48e092c-6f1c-4637-a766-b53a4fcca66b}} | r | 6863722a0862a0d52f6e25638c994f79 |
Many pruning techniques have been researched to trade-off model quality and computation efficiency {{cite:11c6dc2c5c0592d6bc489bd1b47aa62b54203233}}, {{cite:aec2e02b86a813a9e0047f7a8febc73521a04eae}}, {{cite:457f27f30bad5baac77b8f9ee5a23eac5219d10e}}, {{cite:618ab496b5531a92d29869cc69379a7d8b20e3b9}}, {{cite:366650d18109e52f1e1e035c1bcd576181f7632c}}, {{cite:6400d9c82c3eb5267cfa0376c0577ced34ae1d3c}}, {{cite:f3f6e5f317e94cfffd8b9c7ebfbf59ea986a0655}}. Irregular sparsity {{cite:aec2e02b86a813a9e0047f7a8febc73521a04eae}}, where each value in the weight matrices is individually determined to be zero or not by the pruning algorithm, usually results to better model quality.
However, it is less hardware friendly because of its irregular memory access patterns. Structured sparsity {{cite:11c6dc2c5c0592d6bc489bd1b47aa62b54203233}}, where a group of values in the weight matrices are determined to be zero or not as a unit, is more hardware efficient, but is less accurate at the same sparsity level as the irregular sparsity.
| i | 4cfba5501d5011400eb4b9af8381911c |
Our group importance method may be relevant in a wide range of applications beyond risk adjustment, although we caution researchers to first carefully consider the context before attempting to identify potentially marginalized groups. In some settings, identifying groups could actively cause harm, e.g., may involve collecting or amplifying stigmatizing information. In other cases, our tool may be useful in mitigating ongoing harms. Machine learning predictions for clinical outcomes have been found to be less accurate for groups defined by age, race, or other attributes, contributing to health disparities {{cite:f342110adb39b73227dcecedcde77fa87621d56d}}. Our new method could help ensure that algorithms deployed in such settings remedy inequities for currently unidentified marginalized groups. We recommend researchers create a social impact statement and follow an ethical pipeline for building algorithms when considering adapting our tool to any setting {{cite:21246d203350999e32515217fe3156e7565b9c54}}, {{cite:71dedbc6086cf2613401a6bb680a13622a01578e}}.
| d | 7abbef59967c17bdc678447f8a9c7dad |
RelGAN {{cite:a52c2c255406678303b408e5795e245a6299a3f0}}, DLOW {{cite:69ea880f9523768be48d79b1084615351a68bf53}}, BicycleGAN {{cite:7bfbd9f0a5bed4f37be7e771d3aaa0655e9469ed}} and AugCGAN {{cite:a75ab2eaeb94b1e93c9fee7dea845a320b5984d1}} seeks to study consistency on unseen transitions. However, the generalization ability of their model could be inferior to
our TEGAN in mainly two aspects. RelGAN and DLOW introduce unseen transitions via synchronized interpolation on the observed {{formula:20153638-1dc8-4f16-b15e-d341ff0c772e}} and its corresponding image pair, i.e., {{formula:1fc91b89-42bb-4a24-8f27-61ddfd6adaef}}. They can simply obtain {{formula:590ee22d-46d5-4039-bba3-fe0dff65dc90}} via interpolation, i.e., the simple linear case of {{formula:ddf52bc1-9375-4164-9862-8f75a855bf71}} in the transition encoding of TEGAN (Fig. REF ), making their manipulation inflexible. In addition, the interpolated images may not be realistic itself, thus leading to unreasonable transitions {{formula:6590a1bb-1a7f-407b-bbb2-5fc58c1e68c0}} that fails to capture the intrinsic relations among the data, e.g. relations between attribute annotations in face editing tasks {{cite:a52c2c255406678303b408e5795e245a6299a3f0}}. This can disorder the transition consistency defined on unseen transitions. BicycleGAN {{cite:7bfbd9f0a5bed4f37be7e771d3aaa0655e9469ed}} and AugCGAN {{cite:a75ab2eaeb94b1e93c9fee7dea845a320b5984d1}} flexibly manipulate {{formula:99ffb0d8-3213-4578-876f-c5c49db2bc6b}} by encoding {{formula:45c8a8fd-8856-4962-b9a4-4fec9bd4ffde}} , and enforce result consistency via attribute prediction. However, such regularization can only work on the explicitly sampled transitions.
| d | 294bd7ac3926f1d9393fd33f15ba7019 |
For the graphite structure, the experimental evidence obtained in the last years suggests
that high temperature superconductivity exists at certain interfaces or
interface regions within the usual Bernal structure
although the structure of the superconducting
regions remains unknown.
One can
further speculate that due to the high carrier concentration that
can be localized at those interfaces, they should be
predestined to play a role in triggering superconductivity.
Following a BCS approach in two dimensions (with anisotropy), for
example, a critical temperature {{formula:3341e890-a06b-4aee-946a-166953be2780}} K has been estimated
if the density of conduction electrons per graphene plane
increases to {{formula:5fbd9dbc-e2fe-483f-93c5-b229c80de536}} cm{{formula:4588ba43-f16f-4918-b23f-fdbc254b2d1e}} , a density that might be
induced by defects and/or hydrogen ad-atoms {{cite:4044e360daabb9b2c5a2135d4489c5b7fc9ad889}} at the
interfaces, or by Li deposition {{cite:2b31ddd908bd30138c0828161bb2127f29f10241}}. Further predictions
for superconductivity in graphene support the premise that {{formula:b4258760-1158-4747-a6ca-0e7cc29cdd26}} cm{{formula:75d29449-d598-4e04-b1aa-f98c8d63ae44}} in order to reach {{formula:7bfd0227-e9eb-4e3c-a27b-b2936f3b4235}} K {{cite:d2956a935e8847fbe75ca49f26a0d15196876a4d}}, {{cite:85ce3d18969270f4c415a30c25f9fba32deeff37}}. On
the other hand, the possibility to have high temperature
superconductivity at the surface of or in the rhombohedral
graphite phase {{cite:72e84363f8c08719685a9e52204fe55015ff04d6}}, {{cite:2935fde7276ab3dbba2e5c5f4ceb7e079c74b8ae}} – a phase that sometimes is
found in graphite samples {{cite:10282d66cc779c1fae4e9331581d952b5d26bfa7}}, {{cite:6036754a1f483b3d02d34dbc477e36e5f3b6ca30}} – stimulates further
careful studies of these hidden interfaces. In the last years,
superconductivity has been found at the interfaces between oxide
insulators {{cite:5d2552c87d62cfdd0b5b260ef5ad5898232e7632}} as well as between metallic and insulating
copper oxides with {{formula:0cc2dcd0-09cf-4409-916e-3d927fbd9415}} K{{cite:3207f51dc1b4ec78111199824b03d0cdbf1ddcd5}}. Also,
interfaces in different Bi bicrystals
show superconductivity up to 21 K, although Bi
bulk is not a superconductor {{cite:726adb10f7a2dfe46992b1f2fd1514304a56c942}}, {{cite:618b9f19d55de9fad2b3c8c7de7442843d945333}}.
| d | c89046d254d38879591bbfa15bdbccc8 |
A classic reference on the Monte Carlo method
which includes discussion of several variance-reduction techniques is {{cite:bae6dd2e1f5f9071260f1be1008a9d752fad31f6}}. The
chapter notes {{cite:bcc677c433042359e6d1da58e85e1fba4c0360be}} give a comparison of Monte Carlo and Importance Sampling with examples. The paper {{cite:afc2f664fd0addf5e4a06654cbe2dc250f90b99a}} further explores advanced Importance Sampling via adaptive algorithms.
When {{formula:913a3d8e-258c-4190-bae7-e41da790913c}} is large enough, {{formula:3e6415de-04d1-4e67-a638-458727c4e92d}} arising from a Monte Carlo simulation should be close to {{formula:c1cfcad5-949d-47eb-ac78-8b78c9973da9}} {{cite:3b343268d5bd15a13792c26a318200ebad188a77}}.
In practice, all probabilities, integrals and summations can be approximated by the Monte Carlo method {{cite:558df8a4fff56986c8a8b8e380b69c2a66457b21}}.
A review of importance sampling, from the perspective of filtering
and sequential importance resampling, may be found in
{{cite:461909c94e92bc858f5fff99191a27783b66b042}}; the proofs in this chapter closely follow the presentation in that paper. Necessary sample size results for importance sampling in terms of several divergences between target and proposal were established in {{cite:32d08dc7f5c87746a3e9ee0cdbd00369cd0847a7}}.
The subject of multi level Monte Carlo (MLMC) has made the use of
Monte Carlo methods practical in new areas of application;
see {{cite:dd4f879edb807ca40085ebfa1a0a9d9cf785d2ae}} for an overview. The methodology applies
when approximating expectations over infinite dimensional spaces,
and distributes the computational budget over different levels of
approximation, with the goal of optimizing the cost per unit
error, noting that the latter balances sampling and approximation based
sources.
| d | 5b486a8263cec7744c85925977846d91 |
In this study, we focused on estimating HTE using an ML method with an interpretable model to capture the relationship between the characteristics of the individual and the effect of treatment. However, the models of most previous ML methods are black boxes, making the relationship between the characteristics of the individual and the treatment effect challenging to interpret. To overcome this weakness, we focus on the rule ensemble method, RuleFit {{cite:9faef635c80f298d16f7a841a122ebbe9930d70e}}. This method provides an interpretable rule-based ensemble model and has shown a prediction accuracy similar to the random forest and gradient boosting tree algorithms. In addition, we focus on the “pollination” procedure {{cite:cd83cd2aa7d4746a0ccd04ac88a5cd2e02600068}} for easy use of existing supervised methods. Therefore, we propose an ML method for HTE estimation by RuleFit using the “pollination” procedure. To demonstrate the usefulness of the proposed method, we provide a numerical simulation to demonstrate its prediction accuracy. Furthermore, we apply it to real clinical data to demonstrate the interpretability of the proposed method.
| i | 73c9f04a264e5276ee79ad4e8259471c |
In order to scale learning for combinatorial problems, we ask: how much can we learn from unlabelled combinatorial instances?
In this work, we consider a contrastive learning approach, which begins by creating multiple “views” of every unlabelled instance, a process called augmentation. An encoder is trained to maximize the similarity between the representations of augmentations that come from the same instance, while minimizing the similarity between those of distinct ones {{cite:ea8487d89887e9dab7b8bdd2f02359d8bcdbb2d7}}. This has been successful in computer vision: contrastive representations can be used with linear predictors to achieve competitive accuracies on ImageNet using a fraction of the labelled instances {{cite:ea8487d89887e9dab7b8bdd2f02359d8bcdbb2d7}}, {{cite:31007b41a83d9811a6b4ef49bed2d47979b2c7bf}}, {{cite:1fd737580a0f2505e996aefe60ec4e6aab5b6ea0}}.
| i | a49c4f712d33378b4ff1c0bec0397134 |
P r o o f.
We follow the standard argument of Ruzsa see, e.g., {{cite:7035595a26594818cf5a8e367a18f02a16cd11de}}. In other words, we need to estimate the size of {{formula:642b0376-3455-49bb-9feb-3c68e4c3812e}} .
In terms of {{formula:33872e5a-fef6-4455-a9de-c7a421eaf5a3}} it gives us
(consult the proof of Lemma REF )
{{formula:ba5976b2-102e-417f-b98f-406b657cf752}}
| r | 713bbd30689a525150125e5f6d927f59 |
This paper addresses problems that have a long history, going back to seminal contributions by Kondrat'ev {{cite:87e966cbc6ff607c45c1a29de544434ed7f3ebe7}}, who investigated Fredholm solvability of classical boundary value problems in domains with isolated conical singularities on the boundary, and Cheeger {{cite:30a55df4ef1568f7319d296503e83d14ac0ebb6c}}, {{cite:b80b15a21d31518a5bb2e82dd9f868b0a7e5fb42}} who initiated geometric and global analysis on singular manifolds. Both contributions seeded independent developments (e.g. {{cite:1afa76f827630106c841bddd735d8d4627f0a209}}, {{cite:75033a102e80d9a2eb9c41b10eb9bee26c91f7e9}}, {{cite:c9d7374d07d05e105993051088bfcc7dfab57da8}} are rooted in Kondrat'ev's theory, {{cite:f19d4aef5e0c85fc5b37e9c8e1187e1fedb4bfb3}}, {{cite:af920d966f887f184298c32b323992c111ca266f}}, {{cite:d561bcd4dbcd8f1d3bd84019880f40fd49f243ee}} draw their inspiration from Cheeger's works), which have increasingly been merging since the 1990s {{cite:903c7774952d4a1f1f461ef5fd913c0c7705ca5a}}, {{cite:d8d1d104e32626a955a4611097ce358fa51ccfed}}, {{cite:1985f023bbdbdd28424169ed46edc8b5e5f18375}}, {{cite:2f1ca1ce7380838d993fe46b9307cbc277ac9d4c}}, {{cite:af68777adb65c4919e627e69fe5b7a29d1c80d60}}, {{cite:73aa782545f06693ff3516ca1e66d6b27033988d}}, {{cite:d9dfead4e570f630540387dc2e87b63fb88524f5}}, {{cite:49be6868770767689bd4248b187ecb8b57b29d8a}}, {{cite:23931a789a662e6d9d894bbde647683ec7c93788}}, {{cite:b699d23418ccab508f78e33fc9e64ebb5f69e9ca}}, {{cite:5fb2a59679e6c801d2d66932e8fb6c6b6da234ef}}, {{cite:363178127644991be0048d3819545ac14b02a227}}, {{cite:48353bb606b850f38736501c0221a266b3fe11ff}}, {{cite:da820eafb21530e6c081665f28942de0da82a814}}, {{cite:c11a67bcd3e3088a92f4f388c9c868bc3d1d0198}}, influenced by Melrose and Schulze. An analytic theory of solvability, regularity in Sobolev spaces with weights, and asymptotics for differential equations with unbounded operator coefficients with applications to partial differential equations in generalized cones and cylinders is developed in {{cite:98a221bc3dea473bc110d21447ea0507c9848dcf}}.
| i | 59f36ff4ef1a9e6b3476b80cd6820410 |
We take into account the randomness of the {{formula:fddd8a70-62c4-4581-954a-42900d889c12}} sites distribution in the KAM using a DMFT/CPA approach {{cite:b795eba1a217b475e9cb00711ab70f93b312c5c5}}, {{cite:b8044f0b461c23a952abdad20849523e457664d8}}.
First, the action related with the KAM Hamiltonian Eq. (REF ) is expressed as
{{formula:c0b6e29f-f5c9-48ae-8396-fa1b98079a87}}
| m | 648e68938c9ea52553f3eb78fda83fb0 |
In recent years, with the development of technology, the research on
networks has shifted away from the analysis of single small graphs and the
properties of individual vertices or edges within such graphs to
consideration of large-scale statistical properties of complex networks.
Newman {{cite:90ed16b7ebd70ab83f0c9c05244210757f97ca3d}} reviewed some latest works on the structure and
function of networked systems such as the Internet, the World Wide Web,
social networks and a variety of biological networks. Besides reviewing
empirical studies, the author also focused on a number of statistical
properties of networks including path lengths, degree distributions,
clustering and resilience. In this paper, we pay attention to another
aspect of networks, namely their multifractality. We aim to develop a tool
based on this property to characterize and classify real-world networks.
| r | c3fb30978e2866a51a5ef55caf4f523b |
At present, a quantifiable generalized metric for the visual quality assessment of images is an open problem in computer vision. However, in the previously proposed pose transfer algorithms {{cite:a697dd698a9655c9ec99a5778b7dd66a76ff7d1e}}, {{cite:c95cd184aec3c470f52c1740fe305f7f6af550ae}}, {{cite:03dba14767f326ac4e5bd8a0f567074e90d4b4db}}, {{cite:71a6cbc9db491fefd7349e4f97f30b109a67b5c6}}, the authors have estimated a few widely used evaluation metrics for quantifying visual quality. This includes the Structural Similarity Index Measure (SSIM) {{cite:30f8093b189aaa4c33f97370ab07629c8d87b8f5}}, Inception Score (IS) {{cite:56bf440d6edfa722d2259606ef612d926dd0cb96}}, Detection Score (DS) {{cite:77c861afcb58a9f16b494dfb9b3160e378ef2c96}} and PCKh {{cite:eabcdfff4ad2df7a48359904003d40438496a582}}. SSIM measures the perceived quality of the generated images by comparing them with the respective real images and considering image degradation as a perceived change in the structural information. IS uses Inception architecture {{cite:25199a00b4f1b656090830421f8da60692ed82c1}} as an image classifier to estimate the KL divergence {{cite:af0177216908b54021d6eda5f73d03fa874c6db0}} between the label distribution and the marginal distribution for a large set of images. DS uses an object detector to estimate the target class recognition confidence of the object detection model as a measure of the perceptual quality. PCKh aims to quantify the shape consistency between the generated and real person images by estimating the percentage of correctly aligned keypoints. We also evaluate the Learned Perceptual Image Patch Similarity (LPIPS) {{cite:e0dcd32cf96fda37dd40fcdd9613bb332e33e1ef}} metric, which is a more modern standard for assessing perceptual image quality.
| r | a6fc713d57786a9bbc10e752de2f223e |
A second example of a {{formula:f20365c7-c3fc-4cca-aeed-aed1a8cdea6a}} , identified in {{cite:e74e4ddea0450831d21ac16ef1dea2918acf31b8}}, is finding a “not-all-equal” assignment to a monotone 3-CNF formula given that a “1-in-3” assignment is promised to exist; i.e., given a 3-CNF formula with positive literals only and the promise that an assignment exists that satisfies exactly one literal in each clause, the task is to find an assignment that satisfies one or two literals in each clause.
This problem is solvable in polynomial time via a constant level of the Sherali-Adams linear programming relaxation {{cite:e74e4ddea0450831d21ac16ef1dea2918acf31b8}} but not via a reduction to finite-domain {{formula:80036443-b116-4ee6-99bf-9934d7a00c52}} s {{cite:cea2cfd3408d989f9158cfc4dc5951a7f16c3f0e}}.
| i | c92834b2fca035e553c619bafa38eb02 |
As shown in Table REF , MAFormer-S with only 23M parameters can achieve a top-1 accuracy of {{formula:11738b2f-4531-41f4-9446-76f7062b4d6c}} % on ImageNet-1k. Increasing the embedding dimension and network depth can further boost the performance. Table REF shows in details that MAFormer outperforms the previous state-of-the-art vision transformers. Specifically, MAFormer-L achieves 85.9{{formula:583bb5a5-4d62-490d-ad1a-de520aa3474f}} Top-1 accuracy with 22.6G FLOPs, surpassing CSWin-B {{cite:b1fa1a24e928922393eaa9882010333671145c29}} and LV-ViT-L {{cite:30ce052e7a335b73a47ff11dbe54d5474b21faa1}} by 1.7{{formula:4a791684-53bd-4c8e-aad1-77166278835c}} and 0.6{{formula:4ad3d014-de5a-4ffc-9d82-4fe4d99ba6f7}} respectively. MAFormer variants also outperform the prior art hybrid architectures {{cite:20e8dcbe033eb3d9965ae7e49be3d442f9ec6fba}}, {{cite:52f7e40a5c3ce993baf79c5fcb6bd60614628958}} and local window-attention-based transformers {{cite:b6f0423da2565ea4396c670b4f27582e5d637fb3}}, {{cite:882b9c26cf97aea3d29705f8a21a410b0293f7b3}}, {{cite:fc4831a676c569313ba3cec138a4dacd36b04bf1}} by large margins with a fair amount of computation.
{{table:a475d7cb-ec15-43af-80a5-5ad49877c22e}} | r | 8fa1999894e1d2abe9c5bc8299d8ca14 |
apostle uses
the same hydrodynamics and galaxy formations prescriptions as the eagle
project {{cite:fc3b083416ca02320cbdd1d54a32200d8c90f770}}, {{cite:b2c2aa60e78be7ca07eb6440022ff20f754c0fcf}}—specifically, the model labelled “Ref” by {{cite:fc3b083416ca02320cbdd1d54a32200d8c90f770}}. The hydrodynamics are solved using the pressure–entropy formulation of smoothed particle hydrodynamics {{cite:c2e1410a0dfb308d02d4de71b48c166439a52e5d}}, and the anarchy collection of numerical methods (for a brief description, see {{cite:fc3b083416ca02320cbdd1d54a32200d8c90f770}}) is used. The model includes prescriptions for radiative cooling {{cite:c267fddefadabfe97efdbab5a8ca902275760885}}, star formation {{cite:cb976eacd32690c88c750430e878db5b16490ace}}, {{cite:3027876cb94b593fe2340633d34943e9bf3b5470}}, stellar and chemical enrichment {{cite:46596cb27f8515f91598ec2e86c5ef79fd38c851}}, stellar feedback {{cite:45f5363e2728983bb7ae6fc93abce250032f2afc}}, and cosmic reionization {{cite:2d1b01e66a05f294335db3b9ed035adf987ce81c}}, {{cite:46596cb27f8515f91598ec2e86c5ef79fd38c851}}. The model is calibrated to reproduce the galaxy mass–size relation and galaxy stellar mass function of {{formula:5e99fa98-c90d-42c9-917e-f16b2e871c99}} objects {{cite:b2c2aa60e78be7ca07eb6440022ff20f754c0fcf}}.
| m | 9529e6918eecb29715a8b5f0b875d450 |
Self attention-based models suffer from the complexity of {{formula:8d86fc9b-026d-4ba1-b15d-e536d40eb254}} , where {{formula:6c7aeff1-5ad9-496a-a9a0-3c982c10de1c}} is the sequence length, and {{formula:4ee5d5a1-2b38-4540-8e80-d55a0640f1f7}} is the dimension of hidden representation, making it hard to encode extremely long documents.
We investigated how to incorporate the pretrained BERT model and its variants with hierarchical fine-tuning architecture to tackle lengthy clinical document encoding.
Nevertheless, CNN-based models {{cite:ded6973a9da2b1b550f5c78153382d891a3830c3}}, {{cite:cf32207f779c1d803f967f61b0e52407faa0781e}}, {{cite:481dc6411cbe672074d6fa8e4969ebdb9cc961a3}} and RNN-based models {{cite:c0225107ae940c88730f02f0155ace00779f4c51}} perform considerably well with the relatively small model scale and remain a meaningful direction.
Recently, some improved transformer-based models such as Longformer {{cite:d84d31c6d77e913f28955ddf5b19283532f266b3}}, Linformer {{cite:b62dcd9622422559a639c9efc562086b94cfde26}} and Big Bird {{cite:e74caabec796d89cac507bd6c5ebbd380671c6cc}} aim to solve the problem of encoding long document and mitigating the quadratic complexity.
We leave these emerging models as future work.
| d | 7f95856583fe4eeb721620a13402c0b5 |
It can be shown {{cite:4f82440fef749d78cb101eacf2a71d6f0bd332fd}}, {{cite:79a3331720aff493825512b5a59d27bd5145d26a}}, {{cite:c5ae31f763d9f528e44f9e3978c8ce20240af256}} that the optimal control law/policy is the one that maximizes the Hamiltonian {{formula:9c4aca66-4fe5-4428-a01b-2122dd5a5422}} of the system, defined as:
{{formula:37a576fb-e383-4f93-b398-80f2e4be456c}}
| m | 177196ff94e2afea1a333765d2e4ecad |
Long Short-Term Memory (LSTM): As an effective model used for time series data, LSTM {{cite:89166609df7ec4f08d7f5e25821900993bdb4f4f}} has been widely utilized in stock prediction {{cite:02d0c1b354aa1f2c0dcdcd5144af5c9786da0ad3}}, {{cite:cf20f7a8b1292a08a3c240fd481b304b70f9528d}} that achieves great performance.
| m | 3b4ccbc50683c51b1bb3d1f5b33db9c1 |
We next investigate why contrastive approaches show superior transferability by analyzing the similarity between hidden representations, intra-class separation, and robustness to image corruption. We find that contrastive approaches learn more low-level and mid-level information that can be easily adapted to a different domain than the supervised cross-entropy models, which mostly learns high-level semantics in the penultimate layers. Zhao {{cite:83f4c1c8e9fb6d13dfce62cc1a584d6338c64f09}} hypothesized that one of the limiting factors of supervised cross-entropy models is the objective of minimizing intra-class variation. Our analysis also suggests that a model should have sufficient intra-class variation in the source domain to better transfer the learned representations to a different domain. Most standard supervised loss functions aim to increase inter-class distance and decrease intra-class variation, which might be harmful for transferability of features. We infer that contrastive approaches have larger within-class separation than the standard cross-entropy models, which could be one of the factors underlying their superior transferability. We also analyze the robustness and calibration of different models, and find that contrastive losses are more robust to different image corruptions and predict well-calibrated class probabilities that are more representative of true correctness likelihoods than cross-entropy models. Our key contributions in this work are as follows:
| i | 38d6de9873efb41f9b6033223f5afe58 |
Even among mathematicians it has been firmly believed that
the quantization must necessarily smear out the singularities
of the classical Einstein's general relativity {{cite:7a154b0d931dc69913fb1d58200a9190cab7b041}}.
In this sense,
before any return to the quantum Big Bang hypothesis
it was necessary to wait for
a renewal of its support in the
realistic LQG context {{cite:ef70dcf00d8511293eb6198fd3a8f41fcc266aaf}}.
Naturally, the problem is technically complicated.
In this sense also the present
methodical support of the latter hypothesis
is just schematic and incomplete. In its framework
we only had to leave
many important phenomenological requirements
aside.
Let us now mention some of them in the form of brief comments.
| d | 236d02884b244be1e75486042da492f6 |
which is {{formula:e6e0ba7d-4985-4df2-a808-525ada44b15d}} for the spectral index {{formula:48aedbca-83f4-48ef-9c67-dfbe970cbf20}} and {{formula:ce02018d-55dc-4b2c-9e02-bea1a27ab0bb}} for the rigidity cutoff. No far outliers are found and the small widening of the distribution for larger values of {{formula:929bd140-1153-428a-841e-3c54ccb590d6}} is due to the degeneracy of high rigidity values for larger spectral indices {{formula:829a6441-bbaa-426b-b119-4628daeb5a4e}} as revealed by the previous data analysis presented in {{cite:bf362e16338265d8192d7aec39ae8bd33d224f53}}.
{{figure:2370817e-1c7d-442d-a875-0241173e6b2d}} | r | 47d9209a34d35b76a2a6ea15291de285 |
We consider a BS with {{formula:2d72a7c4-6a93-4741-9c0e-07f1382583e1}} transmit antennas and an RIS with {{formula:9736bc4c-6d01-482c-b6f6-938f34484f9e}} elements for serving {{formula:ab92b5f2-5b2d-48d1-af32-5b34045a7aa4}} users. For the wideband THz communication, the transceivers work at 100 GHz frequency with {{formula:c9f89f1b-f1ce-4fee-8305-9394f4c4f489}} subcarriers {{cite:0090a7a08b4acf55302c5c0d6ce23898b6af0c48}}. The number of clusters are {{formula:fce49222-6453-4efd-b30a-57d023c3da94}} , where each cluster includes {{formula:b9ac0189-a8e5-4f10-831a-8155a40291b4}} , respectively. The delays of the clusters and the delay offsets for the rays follow a uniform distribution within {{formula:b99bc1fc-1d89-4f52-a616-730b8e411a72}} (ns) and {{formula:d0005b7c-c74f-4743-aa9c-3b1ebab3a5ba}} (ns), respectively. The complex gain also follows a complex Gaussian distribution {{formula:adc29e2b-adf8-4c8c-95f1-92859b8911ef}}{{cite:1f0706431e68ab6630bf893222918aceac321733}}. Besides, a fully digital zero-forcing (ZF) beamforming is employed to eliminate inter-user interference.
For evaluating the LSM training performance, root mean square error (RMSE) metric is invoked as {{formula:77d1d45a-3308-48c8-a449-efa4838d5f44}} , whereas for evaluating the variance of RIS reflection coefficients tracking through the LSM, we use mean absolute deviation and standard deviation metrics {{cite:69df9fb4fc390794605b434022a6e5287316ba83}}, respectively, given by
{{formula:47a86806-02b2-43d0-970c-c06175c2fbde}}
and
{{formula:0b0d08c0-2a16-49a2-85d5-94181dce002e}}
with {{formula:32a2557c-c295-4268-8bfc-44877ed9bc51}} and {{formula:846d05b5-9c12-4914-80a2-9d03a7047677}} denoting the number of predictions and the prediction average, respectively. We observe 100 time slots for tracking the RIS reflection coefficients with 1sec interval in an LSM equipped with 5 reservoir layers and trained by extreme learning (i.e., random weight assignment in reservoir layers). The training and validation steps use 70% and 30% of the total samples of the DeepMIMO dataset{{cite:1c72b68009d02c94f74fab3c12357ebfb5826bbd}} and we set {{formula:8ce96d94-2979-4a1a-a435-88e4f5efdb5c}} =15 for ensemble learning.
| r | a06e46322c9887663a058a200b476f9d |
It is important to note that each of the two states on the left and right side are exactly thermal and the thermality in each copy arises due to the entanglement with the other one. In the language of AdS/CFT correspondence {{cite:51b9e6b523cbdf8dba056f4d29bca95443f37ec2}}, thermofield double state is dual to the eternal black hole geometry which can be realized in Penrose diagram (see figure- REF) as a maximal analytic extension of the usual one sided black hole geometry {{cite:3d19f1774c1877f56a61b8de9432f6ddf8226215}}. Here the interior of the two black holes are connected through the wormhole geometry that indicates the entanglement between the two black holes.
Mutual information {{formula:3c4b0279-d897-4b97-a2af-f9a42deed112}} between two subsystems {{formula:3ed5a015-ac35-4ea7-8ef9-05a461877236}} and {{formula:c11ce361-8427-4653-aec4-559c1d6dc512}} is defined as,
{{formula:0899f6ff-27c2-41d6-b9ab-5aefcfc2a48f}}
| i | 15025e73c2370c57d8601e8b644a202d |
Since the derivation of the method does not depend on the details of the model, but only on that its equilibrium distribution is of maximum locational entropy with moment constraints, the maxent closure may be useful beyond spatial ecology where unclosed hierarchies for particle distribution functions are also commonly found, for instance in the statistical mechanics of fluids where the Kirkwood closure was first introduced {{cite:38eb05c5f23e5dfe9bf4399513f08f76cce6605c}}, or in problems where the organisms move in space {{cite:b6abdbd12114b2f3810bb066944a1caee07b3fba}}, {{cite:1a84b44519bbca0da2f1ee4ee66375aaf09a062c}}, {{cite:d9f19f30315ec406e762bd07d37babbfd46515b9}}, provided that the correlation functions in those models are stationary in both space and time. A limitation of the method is its poor ability to predict the transient. This is to be expected, since maximum entropy is a meaningful property of the equilibrium distribution only when detailed balance is satisfied {{cite:ff83bca79badeeb377776228c40d52009eab685e}}, {{cite:dd2f7d71acf4d6a995500763d7b92bb0ab096b0c}}, {{cite:cbaa8f6e7758bc1a9f5229eb2a220b46ef8d6e89}} and the transitions due to fecundity and dispersal events coincide with mortality.
Other areas of current and future work include the generalisation of the moment hierarchy and the maxent closure to an arbitrary order of truncation, extensions to marked spatial point processes for populations with both spatial and size structure.
| d | 76f118b63277c07088ed5a60d2d6f3ff |
Very recently this issue was generalized to Taub-NUT/Bolt-AdS spaces
in {{cite:c18b3df4438a6895bfa9768a68975d926b467df3}}, {{cite:e75f354133c30b1d83a6cb9fbae24bc639029788}} and to Kerr-Bolt-AdS
spaces in {{cite:0b767a612939da47e6521a1ed106d7ae78930706}}. Interestingly, they found the
thermodynamic volume in Taub-NUT-AdS metric can be negative. In the
context of enthalpy, the positive thermodynamic volume may be
understood as applying the work on the environment (universe) by the
system (the whole black hole) considering the process of forming the
black hole. In addition, the negative thermodynamic volume may be
understood in that the environment (universe) applies work to the
system (Taub-NUT-AdS black hole) in the process of the Taub-NUT-AdS
black hole formation {{cite:c18b3df4438a6895bfa9768a68975d926b467df3}}.
They also found that there is the first order phase transition from Taub-NUT-AdS to Taub-Bolt-AdS
through exploring the phase structure of a NUT solution and a Bolt solution {{cite:e75f354133c30b1d83a6cb9fbae24bc639029788}}.
| i | fb8446ad583904905443dbcd49329ac3 |
Proposition REF also gives a way to explicitly control both sampling and labelling bias:
i.e.,
operate on a subset of labels
(for computational efficiency),
but also
ensure good performance on rare labels
(to ensure “fairness” across classes).
Given a target set of label margins {{formula:19c54be7-13e1-4728-8cda-b3e7db71a98d}} (as in (REF ))
—
which can suitably
balance dominant versus rare class performance
—
one may use (REF )
to pick a suitable combination of {{formula:3eac78fc-0c75-478f-9b67-0357842eb364}} to achieve this balance. For example,
suppose we wish to approximate the logit-adjustment loss of {{cite:1d49e405c322483ef54b9f5824aeade9fefe925b}},
where {{formula:e4785dd4-1e07-4465-8404-f04cce78c61a}} .
Then,
for a given {{formula:ab936542-3cc9-4b9f-b522-0ca8eb24e3c7}} , we may set
{{formula:f024b02c-4f0f-4593-be2b-09c66e4660dc}}
| d | 2ac4313ee4dba730e9d26ffd1d11e40d |
The accelerating developments in machine learning and reinforcement learning have increased the interest of the control community in using data-driven techniques. Specifically in the area of control of distributed and multi-agent systems, very recent developments include algorithms for multi-agent reinforcement learning {{cite:f1d1c7795581857e303c1cf06ede4d70809ec048}}, {{cite:a502d2035261601ccc68f36ab3753c989f0eeaf4}}, {{cite:f45e2d2d7c062c7eedfbba512af0f9e2eb2683ed}}, reinforcement learning over networks/graphs {{cite:aaa1b2d0b559e1166ae1bf1f9c43f6a11eefe4e9}}, {{cite:31edc18832be92a76888bb068ca761cf56fe22a7}}, {{cite:5f3eb3b80939b36435377b933695a2cc06c44e0b}}, {{cite:c8f3ec6587ab249153439f5bb51e26d14e54a5cf}},
as well as the search for appropriate parameterizations for these problems {{cite:ea79d7e2440807cc9a1289aee534b2fca2b7120f}}. However when dealing with distributed learning at the edge, there is also the need for communication efficiency, especially if agents have high dimensional time-series data and operate over resource-limited communication networks.
| i | c14e021f8839a9710caf9e22cc2581f0 |
Autonomy will play an important role in future complex missions where multiple assets act independently{{cite:5346ef8cac3c1e29445524a7f5b97375607be5fe}}. Localization, or more generally state estimation, is one of the key components in establishing autonomy. Due to the absence of global positioning systems, dead-reckoning methods such as WO and VO are the major source of localization on Mars. The rover's remote sensing capability is strongly impacted by localization performance since the accumulated errors in rover positions impose challenges in targeted observations after a few drives.
Perception-aware planning is one of the effective methods to improve the performance of dead-reckoning-based localization {{cite:949f40a67f61dc381b60188d1656877dc12455bc}}, {{cite:ca13836c45ca30c28e5db4fe2342b5c63f385c78}}, {{cite:28cee382bd7c01edd52b15c72b9f03c65c0470eb}}, {{cite:3b26d5866e7b17e6b92fda1220beb7a2081aa9de}}, {{cite:72fe829e5e7a6a3eca41771055d3ee67829044bb}}. It aims at improving the perception results by actively choosing future measurement targets. For example, the works in {{cite:3b26d5866e7b17e6b92fda1220beb7a2081aa9de}}, {{cite:72fe829e5e7a6a3eca41771055d3ee67829044bb}} improved the performance of VO localization by actively choosing timing and camera direction to obtain an optimal image sequence using the predictive perception technique. This problem is typically approached by POMDP, or belief-space planning {{cite:97f116cc79b338c64ab987b0d2306d5541c842d1}}, {{cite:244f475e52f3a3346e6b0edae3bbe79ae078bcdd}}, {{cite:2121dfb1bc48807ea5a353cc5c93f8334b32b527}}, {{cite:f0bc73c80bdf063311a27a6c03368947ac283b7a}}, {{cite:5ae544981826a3dbb8e5f7524ae8a2c5c1bd0094}}, where the planner chooses optimal actions under motion and sensing uncertainty.
| i | d72c38e0bcf4fd1bdd42e2597ab34bfc |
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