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While the previous works enhance our understanding in competitive interactions, i.e., interactions in which gains can only come at the expense of others, MARL in cooperative settings remains largely under-explored and constitutes one of the current frontiers in AI research {{cite:73ef338b33171f76da1ca439b30e926628aff72e}}, {{cite:9ef7a7ef1405eb1e1ed269ccd945064cae606866}}. Based on the above, our work is motivated by the following natural question:
| r | a412da52b50b3610f0ec9d27690d2136 |
OTOCs demonstrate several interesting physical features in the integrable and nonintegrable systems. For example, magnetization OTOCs ({{formula:eeed0fd9-2d30-4248-b6a8-d22bef815c83}} Magnetization) point to dynamical phase transitions{{cite:a9e869d3ee72f72bc00a9fd5268e56931d65fce9}}. Disorder slows the growth of {{formula:3b11cd97-15e8-4b84-9b24-46c3830a556f}} in time, and therefore, scrambling can be used to identify the many-body localization phase{{cite:6ebb8906cba599bef6f5e6c8d90a526dae9556d4}}. Scrambling itself is nothing other than the zero velocity Lieb Robinson bound{{cite:2d58fbfa858cbd66560da0538320b40f1eefc413}}.
{{formula:089d8ee8-a370-446f-b144-06a2f78e5bb9}}
| i | b84ca6bad41fb1a00ea7b4b42492778e |
[itemindent=-10pt]
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EIL {{cite:3642ef8b14d4c7ab41ddd03d3cd2ee0ed4fe10b7}}: It introduces a novel adversarial erasing technique jointly exploring highly response class-specific areas and less discriminative regions to obtain a complete object region.
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SPA {{cite:35ce4ff2272827d7147b69fafec5b06b818c41b7}}: It explores how to extract object structure information during training and proposes a structure-preserving activation method that leverages the structure information incorporated in the convolutional features for WSOL.
-
TS-CAM {{cite:299c25d5b65cc9777b151554589d828c36611d01}}: It proposes a token semantic coupled attention map to take full advantage of the self-attention mechanism in visual transformer for long-range
dependency extraction.
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BAS {{cite:362f48fbdc6bd88322bdd49ab96589e343b3a08f}}: The model promotes the foreground map generation by introducing an activation mapping constraint module that mainly facilitates the learning of predicted maps by suppressing background activation, leading to more fine-grained prediction results.
| m | 6379812972aeef1a26c62c4962d21760 |
When estimating {{formula:353deef4-c211-4ce2-be3c-03e2c0b79295}} in Section , we employ a regular lasso regularizer to encourage element-wise sparsity, as commonly done in the covariate-adjusted Gaussian graphical model literature {{cite:2f0126893a9bc6e94791cf1afdb9efc40617b695}}, {{cite:f6fb4a766f5a85dc0a100d2b42a626eb7188b533}}, {{cite:47af3dfcefa0c66395ced3680327ab059da6e02f}}, {{cite:c16cbcda717136d2808e7538e0ebcd1d0e4b4b75}}. When {{formula:af15f9c9-2fe2-4946-9256-263d2ba47ef1}} is large (e.g., a large number of SNPs), it may be desirable to pose a sparse group lasso penalty on {{formula:fddac9e9-3000-4c56-97eb-0524122630ff}} to encourage effective covariates and their effects on the means of nodes to be simultaneously sparse. In this case, {{formula:627cd5cb-f385-4522-91d7-2e1874a456c5}} can be estimated similarly as in Section , while the estimation of {{formula:6299487c-e627-445b-bacb-e9d9cc29bec2}} 's remains intact. When establishing the properties of {{formula:785800e4-0714-47c4-b201-9faf525512cd}} , we need to extend our current analysis of the sparse group lasso estimator to allow heteroskedastic Gaussian errors. We envision that it can be done by using a similar technique as in {{cite:7f0f528af3327ce27700fdd38b064b376246f98f}}.
| d | a2a8a9128c1c3f3c7e883348cc4ce3ac |
We compare GRASSY to three state-of-the art frameworks for molecular graph generation: GraphAF {{cite:184f2c341612b4cf734c1a0dac47c2841fc4a5ca}}, MolGAN {{cite:2fc717eb2fec9647056decf41221c21f816be74d}} and GSAE {{cite:de0a2431adffc6fdc271a30a96c59148764cb316}}. For GraphAF, we trained the TorchDrug implementation using a custom dataloader but without any architectural modifications. For MolGAN, we set the hyperparameter {{formula:f79832a5-f149-42af-b5d0-d6371d6ebd00}} to 0 (full RL version). We also compared with experimented with ablations of the GRASSY architecture, turning off and on the regression penalty (with or without REG), as well as toggling variational vs vanilla autoencoder training (GRASSY-VAE vs. GRASSY-AE).
| r | badbde0abcbb6543f940a7e458fdf812 |
Although self-supervised learning can outperform supervised learning on the ImageNet size dataset (1.3 million images/1k classes), supervised learning is still a better pre-training method on JFT size dataset (300 million images/18k classes). The gap may be compensated by training with more unlabeled data for self-supervised learning. However, self-training can also expand one or multiple supervised models by generating pseudo labels on unlabeled data. Overall, both self-supervised and self-training are able to scale, but at the moment self-training presents better performance in learning general features. A promising direction is to combine self-supervised and self-training for representation learning {{cite:8590702b775a3404d4aaad70c0c41d5666a156a6}}, {{cite:b2173d82a43973eee676c863f585a0212e66ed6f}}, {{cite:fce4c22b628297506e80f36f6d53338e59b83acb}}.
| m | f355cf1c203ac2970865f977eaef2fde |
Our experiment realized Wu and Yang's gedanken experiment {{cite:89f72c983996dd130768be7cb9530e265f94ceb2}} to apply the generalized Aharonov-Bohm effect to the {{formula:04424b7b-e602-43d8-8957-c87d277a58a4}} isospin doublet of neutron and a proton, as an isospin gauge field detector. Such experiments remain impractical for probing the standard model's combined {{formula:ebde9598-7522-4c59-a88c-6ba057b07a83}} gauge symmetry, but further progress in quantum analogues such as ours can shed light on the operation of such experiments. An exciting next step in this direction would be creating a monopole source of a {{formula:4610bc3c-af8e-4284-9f4c-440b11733d00}} gauge field (requiring a three-fold degenerate manifold), in analog to the Dirac monopole's {{formula:4b12b399-553b-4566-b46a-3f67baa1a93e}} gauge field (for a single non-degenerate state) and the Yang monopole's {{formula:3c1509de-3bad-483b-b6a4-bd5ae64ee920}} gauge field (the two-fold degenerate manifold discussed here).
| d | 1db6534fd7f7875440c5712aff8ddef8 |
a{{formula:49bf4f42-95e6-4e2f-be00-5418d5eeefd9}} Let {{formula:c992de74-95e4-4325-ac13-1c72721f0d0b}} be the ball which {{formula:20708d21-128c-4fa8-9a88-7552570754ac}} is supported, we put {{formula:922aedb8-4410-4253-b33f-b633b949f70e}} with {{formula:ec4ac8af-fbf3-4969-8813-e4c41ab5a96e}} . We decompose {{formula:57b42bed-e2de-4542-bc54-0bb5e1b54ce2}} , where {{formula:61b58c73-0af4-41a5-96bb-0dfc5b5f3b49}} and write
{{formula:4bfdc5ff-de86-4301-a64d-089c866f1819}}
{{formula:88813e4b-b934-4335-9b49-78f63d006633}}
We first estimate {{formula:0049611f-9af7-4a8d-8396-43eb278c547d}} ,
{{formula:22d93b15-c1c3-4334-8855-13d608f9b165}}
for {{formula:a62ea2e4-c756-4e6e-ae0f-84b1130fa679}} , we write {{formula:4f8ca6c9-2dc9-40fd-9a51-aea08c19be64}} , Lemma 14 gives
{{formula:7cb3f973-3ccc-4bb8-9ac6-b701ebe2e086}}
{{formula:bb0b3015-13c4-4525-94d4-1b9b8e6807e6}}
taking {{formula:4451ee86-5992-462e-92a6-173d335578ae}} , we get
{{formula:b646fd17-0340-4cb3-b08b-0ca3b9494c08}}
Now we estimate {{formula:c45360e8-e7d1-4728-87b6-7fbd93d9e23e}} , by Hölder's inequality and since {{formula:6ef5f103-eeda-4ad8-acab-239d56668524}} is a {{formula:89c9e7b6-523d-4b06-93d7-5625b66087bb}} atom we get that
{{formula:a362e30a-7ad2-49cf-b420-08d9829a0c52}}
{{formula:efa7249a-4127-4226-b14d-5b6cde987881}}
{{formula:106c07a6-fb24-4954-a1d8-53c6ea4a8cfc}}
the condition {{formula:1cc97e14-fe1d-4c33-98da-1371ec45ebe8}} implies {{formula:9f9fafd8-4cc4-42ae-af4d-d1894b9f64d5}} , then from Hölder's inequality we obtain
{{formula:12743643-1a86-4742-aced-c4d70b1a9f6f}}
so
{{formula:5582ce92-ca68-40cb-bb7c-fbff10f8734c}}
{{formula:f827ae29-a0f3-4ed3-8004-9785f7feca4c}}
Since {{formula:41221fc4-9ac0-4065-bfe4-bf0030a82e08}} for each {{formula:94a431c9-1159-488b-963c-9d69ff79cba8}} (see Remark 9) and the weights in {{formula:af23478d-f334-4f6b-bf59-b8ad16731a2a}} are doubling measures (see Remark 7.7 in {{cite:e7dde1901e2ff4a6cd4fb8437c7ecc9ad8014f0d}}), it follows that
{{formula:bda17149-a5b4-4e77-a6fb-953b9a1bb3f5}}
To estimate {{formula:10016fc0-0121-45c1-a9f0-8c7939ba181a}} , we start with a pointwise estimate. Let {{formula:dbe80938-3280-4e1e-adcd-1830474584c0}} .
We denote {{formula:c1a65a3b-0db0-49b9-b0b7-dba5ca92b303}} In view of the moment condition of {{formula:952898b0-592d-48c5-9783-3bb98b4ee67a}} we have
{{formula:cffc20cf-91e4-4f3a-83af-167092868b7b}}
where {{formula:022736e6-a834-4700-8047-ca389bad0f0b}} is the degree {{formula:87509503-a9be-46d4-b25a-d8512bbbe13a}} Taylor polynomial of the function {{formula:631a2e2b-f5e0-43b9-b04c-57180501cc81}} expanded around {{formula:afe4abeb-94a9-452f-bf27-c5638536a784}} . By the standard estimate of the
remainder term of the Taylor expansion, there exists {{formula:912217ae-6dd7-4d24-8ccb-b226a1d9cf04}} between {{formula:6d117c4e-3e57-4b6b-99f7-7ffa1d8a04d3}} and
{{formula:377900da-8e48-456b-9a3d-e8a41358f9f3}} such that
{{formula:bea58284-aea2-4734-8550-fb52c58de3ad}}
{{formula:57e47706-8e71-43ad-aef1-c5e00f1f69f1}}
Now, we decompose {{formula:1beab34a-7ec5-4bed-836b-d1b666e8a449}} where
{{formula:b0c351dd-e771-4c07-8b25-4281c126602a}}
If {{formula:67c3cebb-4a0e-48df-ab3f-7debaf6fc589}} then {{formula:0b498ce5-cf88-403e-82d7-53ff070ab00e}} , since {{formula:fb971cf4-36c2-460c-ba5a-65e5774ed356}} it follows that {{formula:3ae55c36-476d-4ba4-8d20-5a41e3c9a24c}} so
{{formula:fbf7a422-f8ad-4d3b-98c0-a43493255095}}
If {{formula:d178fad5-486c-4003-9afc-739798a184b5}} , then {{formula:35aca04a-f2b6-4e0f-b58a-1f3aad2ec787}} for some {{formula:2238c0fd-acbc-4000-8b3e-850dd5251d8c}} and since {{formula:a9c181a2-3da3-4eec-a088-20706c3fdd8f}} we obtain
{{formula:97f84b50-aa9c-4b22-93bd-f7bec0af9f33}}
{{formula:20bc58f6-8afd-4fa4-9d13-5facdb9cb119}}
this inequality allow us to conclude that
{{formula:0076d224-a962-4d20-a070-fb8c2172f4a7}}
since {{formula:5ce34563-9450-4a39-8c17-258d3b5600cd}} , we have
{{formula:98e4096b-ae92-4b88-af37-cf08e9c95d29}}
{{formula:32cae310-83c1-41da-8bfa-2a9ed8d8fbe5}}
This pointwise estimate gives
{{formula:d89f2da7-01c8-44ff-976a-957172344d16}}
{{formula:f8ce4316-c6da-42d4-900f-400b45bf40c2}}
Since {{formula:13a17464-5296-424a-b89c-eb84f4fe951f}} , we have {{formula:b6df4b37-6bc4-4275-a119-6175a5d830d0}} . We write {{formula:f95280f8-80b2-4c93-941f-9af32f6a0b0a}} and let {{formula:2714caab-f4ec-49cb-ba9f-5c550fb7af2d}} , so {{formula:5ef8d9fe-3f18-46f9-b39d-ba302b8438e1}} and {{formula:9bafbbc8-c565-4a4c-8dba-775ee08e7722}} . From Theorem 3 in {{cite:dc0a16aa44eef4234c791f8557bafa958c89c5fa}}, we obtain
{{formula:9c2868ae-8593-46f9-9b6c-623e8e1835b6}}
{{formula:1c68617d-0be0-4ca8-8ba0-df55294d2de3}}
where Hölder's inequality gives the last inequality.
b{{formula:65864d1b-479c-45a3-b267-e1e5ea2e7eb8}} As in a{{formula:45919d4c-76d4-4847-bd5c-a764d223793f}} we decompose {{formula:1e0da00b-9f9c-47b1-83c8-2aaf100d5420}} , where {{formula:8a499651-a696-4979-8e38-d437ce9f56b4}} , but now we write
{{formula:404b4557-7002-4b05-8710-13c087ae2d5b}}
{{formula:c679a530-a549-46d9-b6bd-c29e4078e51c}}
A similar computation to done in a{{formula:84a4fa53-6b8e-4cd5-a18c-ea762bf01101}} allows us to obtain
{{formula:9ae957dd-7161-4a31-97f9-d1661b722f3d}}
To estimate the last integral we use that {{formula:39735da1-f1f6-4314-a1fa-d82d8275a7f2}} is an {{formula:0c6718f1-bc97-4226-bcc6-8f505b5cd47d}} atom and {{formula:12074cf5-5eb8-4f77-8864-90a875681bd4}} , so
{{formula:e4b4e3a5-cfbe-4d06-9df7-0951c89b7888}}
{{formula:26fadaae-7195-4d11-880a-13fdb43ad710}}
Therefore
{{formula:569fbd27-a407-4b11-95b8-842faf4cdedf}}
To estimate {{formula:0d720b1d-2b81-433a-b29f-3bafda5ce316}} , following a similar argument to that used in a{{formula:287a4320-e618-405a-8c2f-6eb488bf427c}}, we get
{{formula:bd5614e7-9377-4e2a-90e5-e609238ddb00}}
where {{formula:555f46bf-cc06-4143-8246-6855db1794dc}} , so {{formula:debf4f77-594d-4985-a489-ff3b832272b5}} . Finally, since {{formula:db13650f-9a6e-4c20-93ad-2932885b86e3}} for each {{formula:d3d4e78e-e7b8-42f4-b8aa-1c0cb148e162}} , from Theorem 9 in {{cite:725fcddab56abb9b78bc0473faf2e8e8a0d17fcf}}, it follows that
{{formula:4739a2bb-3b15-4d15-b6be-001ed75075c6}}
The proof is therefore concluded.
| r | 506c85180a3b8786a39870d2554810be |
Backbone. We used ResNet {{cite:637d4c6d7dbcfb6eed407862df099c457b950603}} as our image encoder to obtain 1024D features from {{formula:dc149b85-7932-4f52-b955-5bd8a2d321cb}} images.
In addition, all relu layers in ResNet were replaced with leakly-relu layers.
| m | 747f18bc5e2e6c270d514188dc3db016 |
In CPT, the distributional character of quantum fields is taken into account. As a consequence, the {{formula:07f273d3-728b-4e5d-9706-f19272b3dc5c}} -operator is a functional of the switching function {{formula:bde89d3f-a35c-497f-9666-00af6f41f8a5}} {{cite:8c8f592cf71bf90e19e78649cdda59c345e44a75}} that multiply the coupling constant of the interaction, isolating the problem of infrared divergences; it is through the adiabatic limit {{formula:e2322ff3-0783-40e1-bacd-9a2aacb1193f}} that the real interaction is recovered. CPT is constructed over the axioms of translation invariance and causality, complemented with additional conditions as other symmetries and unitarity only at a later stage for the normalization of the solution. The scattering operator corresponding to an interaction regulated by {{formula:930f9ee6-449b-406b-a0cc-9715f72f6152}} is written as a formal series:
{{formula:de07cd97-2b9e-438b-b68c-684e7f397ef4}}
| i | 77adedc47288f69fe9ef74d3a329037c |
The performance gains from using a pretrained language model instead of training a transformer from scratch are underlined by the performance difference of these two models in our experiments. The model trained from scratch showed AUROC lower by by 0.079 compared to the pretrained one. There are known challenges in training full-sized transformer models from scratch {{cite:f10a4e303c6e1cb057f268bdfd9af6654ddde53d}}, {{cite:dc07c4e06741247db7d65d871351cd007cf108f1}}, {{cite:89ebecd8afc2ef163542badc57a8211790983695}}, {{cite:68e15a947cbd12ab45649f732e4a2f76678bd367}}. Our experiments show that the feature representations learned by language modelling in transformers are not only useful, but needed when using these neural network architectures in out-of-domain tasks.
| d | dbb336b8379153455e107e5d7b754a8b |
The second type of architectures includes the schemes developed for the cat-basis encoding {{cite:28b1119366b0c1fd5357dedbaaca95fd938316bd}}, {{cite:ecb4b518a5280bbd1a3f13d3a3a0519f96d41143}}, the GKP encoding {{cite:a7fe2b220b82d0abaf6a791443b4c7a687fe9c40}}, {{cite:2771bd29f18ff3e217daca536d7dd605f4616567}}, and the dual-rail encoding {{cite:072d954b66541c619e4910e74cf788eca284709c}}.
These approaches must contend with the non-deterministic generation of individual qubit states, particularly in the former two cases where the states have a complicated structure.
The latter case has the added challenge of non-deterministic entangling or “fusion” gates, which are required to grow a cluster state.
Each gate is eventually implemented by consuming probabilistically generated photons, which imposes formidable multiplexing requirements for cluster state generation—unlike schemes for generating CV cluster states.
| i | a0e06bb2460c3d47f79bd6b1455d936b |
Decoding and Vocoding:
Each content vector is summed with the style vector {{formula:bc1d3d01-0e78-4a02-81b2-f97aaa55a82c}} .
The resulting sequence is then passed into a Tacotron 2 decoder network {{formula:36c5ed12-c0e3-4bab-9aa9-aab1180efca6}} to produce an output mel-spectrogram {{cite:9ffd77bac647061580c96c098bfb919f6b02084b}}.
We opted to use a Tacotron 2 decoder due to its high reconstruction quality and relatively fast inference speed.
We use the same architecture for {{formula:f576f078-4929-43d0-a320-03fb6e912454}} as in {{cite:9ffd77bac647061580c96c098bfb919f6b02084b}}, with a location sensitive attention followed by a 2-layer LSTM and several convolution layers to produce the final spectrogram, and a separate linear head to predict the output duration.
During training (Fig. REF ), the loss is formulated the same as for the original Tacotron 2: an {{formula:f3b3af1a-d2cf-41eb-bf2a-daf0a73940b2}} loss between the predicted spectrogram and the spectrogram of the source utterance
with an additional binary cross entropy loss associated with the length of the output spectrogram {{cite:9ffd77bac647061580c96c098bfb919f6b02084b}}.
During inference (Fig. REF ), the output spectrogram is converted to the time-domain using the HiFi-GAN vocoder {{cite:4706b15a8bb9142a060f6f48f690aaaa336fa210}}.
We use the pretrained HiFi-GAN model from {{cite:4706b15a8bb9142a060f6f48f690aaaa336fa210}}, due to its high out-of-the-box performance and fast inference speed.
| m | 90ecfa8479ee7a0fcb6324e49c3f19ae |
Assuming that {{formula:0eb37fc6-18a5-43d8-8991-b4edc2b5460c}} and {{formula:39818320-e26e-4247-a7e4-6199f9d5333e}} are accessible, Golatkar et al. {{cite:86fa0f90084d596da093aeb7ff04dadfc0ebb756}} propose a robust scrubbing procedure modifying model {{formula:187173d3-47b5-43d4-b05f-ee6ce403a742}} , to brings it closer to a golden standard model {{formula:f42d8727-a824-4448-86c1-af2e9f6dc400}} . They use FIM to approximate the hessian of the loss on {{formula:6c11c6da-bce6-4348-ba4a-72e5186a2f33}} , where higher values in FIM denote higher correlation between corresponding model weights and {{formula:bd733ba2-fa65-4035-aa84-a2eb98444c54}} . With the FIM, they introduce different noise strength to model weights to remove information not highly informative to {{formula:5da07c07-b64f-4073-94ff-5b9bf6a92a95}} , and thus forget information corresponding to {{formula:005348a4-aa8e-48a7-9cc3-2aeb0682a3e6}} . The scrubbing function is defined as:
{{formula:19cf3ddd-e0e1-4455-b0fe-e8495879beca}}
| m | ba4ad20d5e2b6cca1d1a18a8702b4c8f |
Based on external datasets, previous work maximizes the error reduction by modeling interactions among various types of signals such as uncertainty estimation, input features, and the state of the sampling process {{cite:2a4b31d9472c927e69b66ad40c4d1eef1a839542}}, {{cite:90a7f8bea825b0070dc2e87bd4a756dc44ec60a8}}, {{cite:ee70a0a4b119bd84d7e8f0600e70bbfabde7c9e7}}, {{cite:1cbfe2d85eb4b3f08a12b4bbdaad08c6af7d9825}}.
In order to not rely on a large external dataset, we first cluster samples into multiple groups,
and assume that the validation error of the samples in each group only depends on the number of annotated samples in the same group. Then, estimating the error reduction is decomposed into simple one-dimensional regression problems which can be done by observing only a few pairs of validation errors and its corresponding number of samples.
| m | 0b2dbe91ddeafc2c72e7591c90f78346 |
To complement our analysis of the poles and the channel couplings we present our predictions
for the compositeness of the dynamically generated states, see Eq. (REF ), for both
the {{formula:20719318-8ff6-4937-a70f-852802cbc8fd}} and {{formula:86186f08-1b92-46cc-8783-73a3e793b673}} limits. Our results are shown in Tables REF and
REF . For the {{formula:1baf99d4-9b2a-4b4f-b716-855bf606925b}} case, the reader can easily check that the simple rules
{{formula:1c4fc2aa-fe74-456a-9956-cb8e92a09d3a}} and {{formula:adb937d3-c10c-4dca-8d63-4a106e89c9b8}}
apply for the singlet state, and {{formula:eafb3e2f-d2b3-403a-9e96-884426acb1ba}} for both
singlet and octet states, compare Eqs. (REF ), (REF ) and (REF ). Turning
to the {{formula:57a08f5a-9600-409c-80f6-8d3461aa3185}} case, it is seen that the aforementioned ratios deviate strongly from these SU(3)
predictions. While we refrain here from joining the debate on the (probabilistic) interpretation
of the {{formula:c9eaa6fb-a42c-4bf2-bbb7-6aec9b8f9e5f}} values (see e.g. {{cite:f7b55d6bb89a5b576decb4e6df56d24544c4ab61}}, {{cite:f082edf9775b92549059fd76ae641e659d65e015}}, {{cite:b707d284e0082c57104386511d16dd37c9a6193e}}, {{cite:a342d96cc92278d4447268935637ff5f2e5c6eef}}), we just point out
that the state related to the {{formula:4bc96c4c-9789-42a7-b3cf-739da85740ef}} pole {{formula:737c6145-eb5c-45a8-9e3d-cbf968948113}} is apparently dominated
by a {{formula:2d744531-9649-4672-9aa7-300de1a4890b}} molecular component ({{formula:99017f98-02a3-4610-84fb-ed9247acae11}} ), whereas the state
related to {{formula:7e130090-0aaa-42e7-8a7c-413e5a3fefa9}} is dominated by a {{formula:512f3a73-509a-4e62-9890-4f66d7657e51}} component ({{formula:707ccad1-4346-4b71-931f-30070317c4fd}} ).
The higher-lying channels seem to play only a minor role in the composition of these states,
but take a somewhat bigger part in the formation of the states related to {{formula:e0413628-d565-40ea-bfc4-1ba5ed70abee}} and {{formula:c440c26a-9866-421c-87d3-c063832c8217}} .
These findings are in good qualitative agreement with earlier studies, compare e.g. Table 1
in {{cite:f7b55d6bb89a5b576decb4e6df56d24544c4ab61}}, Table 1 in {{cite:dfe9582fd042898242ce6356c89bf2e31ab00ec6}} and Table 4 in {{cite:7811457ee487532a890c8ea2f7eca4ebf22531ce}}.
{{table:081a0ac6-c5b3-4dcb-91bf-69a7df586190}}{{table:88645078-7e18-44da-8c19-bbd9b5618903}} | r | 7cd51356610dd553d1d8afc34a0d66d5 |
We compare with methods based on estimation of the transition matrix (Forward {{cite:77826cf3aeb8d9265c8dc8d246412cab2c54d801}}), design of loss functions
(GCE {{cite:bb9105ec0107ea9f59e2e877e7269a2fdaced1d2}} and SL {{cite:d101256f4b56d38dcc0babe9f459f8bcb41570f3}}), training two networks (Co-teaching {{cite:217bb4c9c25771a255ea9102200bbc9587c6dd71}} and DivideMix {{cite:6ef4333c0401ab9d95ba8cd30847182d9c7a3b6d}}), and label noise correction (ELR {{cite:2ded154f8ad959c68fe552b050f25e467ca4bb68}} and CORES{{formula:8aec9c68-2caa-41eb-a51a-b4ee632c154c}} {{cite:a044d24e71e8fce62549583ab1878c8b3208d477}}).
| r | b7b3232e9e5a0b2ce3273d697befce2b |
In this work, we analyze different sources of fairness risks, in terms of commonly-used group fairness metrics, when we train a model from imputed data.
Extension of our analysis to multiple imputation (e.g., MICE {{cite:1eaa104e956dd0f59f23fd6f22d02e9d7ca447f4}}) and to other fairness metrics (e.g., individual fairness {{cite:f7d8568ca6e399c6524fb27a93b1b1d4e2d16c01}}, preference-based fairnes {{cite:68ea62ead75c4e6f237ca2f6894d6e8a2acc51b6}}, or rationality {{cite:d3f3b566051f93bb9bf8967857e5a0c8fe5dc89a}}) would be an interesting future direction.
We then introduce our solution to training a fair model with missing values, that utilizes decision trees. While tree-based algorithms are a preferred choice in many settings for their interpretability and ability to accommodate mixed data types (categorical and real-valued), we hope our work can inspire the development of fair handling of missing values in other supervised models, such as neural networks.
Finally, the general question of how to design a fair imputation procedure is a widely open research problem.
| d | 95eeca2d91d5f145d3af83303609f7e5 |
On the gym domain, we notice that the performance of PessORL and CQL on datasets containing expert trajectories is not satisfying, often not as good as BC. We believe it is because of overly conservative value estimation.
In fact, it is widely believed that conservative methods suffer from underestimation {{cite:09840c24883e0bec1aceef0d2e1f292855e2cb1b}}. The conservative objective function in Eqn. REF sometimes assign values that are too low to OOD states and actions. Besides, the uncertainty estimation method cannot be guaranteed to be precise on high-dimensional spaces.
It is actually a possible future work direction to solve the underestimation and uncertainty estimation problems in conservative methods.
| d | baac800a8d0403ee339ff0ac88ddcb2b |
Data Processing and Training. We follow {{cite:925ba848835e62584c2d930d9dcf9b1c5079665e}} and extract 64-dimensional log mel-spectrograms with a window size of 25 ms, and perform normalization by mean and variance of each frequency bin for each utterance. In the unsupervised setting, we adopt SynergyNet {{cite:5830bf81665704df0dd8859145dddefaa4323893}} as the expert. Face images from the generator are 64{{formula:bb7b0aae-d400-4e0c-ba40-c8a7aba4e532}} 64, and we bilinearly upsample them to 120 {{formula:8134e187-1659-44e4-8650-319c346e7416}} 120 to fit the input size of the expert for 3D face reconstruction from images.
Our framework is implemented in PyTorch {{cite:01db483fe088cd3e19f56ad3c3487250ac56c998}}. We use Adam optimizer {{cite:ca033dd0d1218df05118e5cee8acb167304dd448}} and set the learning rate to 2{{formula:91d8ec50-108d-4410-9b23-05e85154f8fa}} 10{{formula:a85c2e28-563f-4122-a475-6e1ab11d1fbb}} , batch size to 64, and a total number of training steps to 50,000, which consumes about 16 hours to train on a machine with a GeForce RTX 2080 GPU.
| r | 615eb3a815ef936097ac64d9bb5ea99a |
The possibility to move down along the spin temperature scale depends on the interactions in which nuclear spins are involved. These include, in addition to the Zeeman interaction with the external field, the dipole-dipole interaction between magnetic moments of nuclei, and their indirect coupling via electron states {{cite:aec2f9ab72054cfdbbec728c7e36699ec6c2207f}}. All the interactions except the Zeeman one are usually lumped together under the name of spin-spin interactions, which form the spin-spin energy reservoir. In addition, if nuclei have spins larger than {{formula:0cc2b334-91d8-4417-9e10-1d589a87db4c}} , as it is the case in III-V semiconductors, they experience quadrupole coupling with electric field gradients induced by strain {{cite:aec2f9ab72054cfdbbec728c7e36699ec6c2207f}}, {{cite:f50fb018b94ffe4345e6dfcc9b9e6ac49810e419}}, {{cite:e4c454a01d566582b33b79b013b983793895d20a}}. In case of strong quadrupole splitting (e.g. in self-assembled quantum dots) it may prevent establishing of the thermodynamic equilibrium in the nuclear spin system {{cite:7dbee21b5bfa8d1167adac09388df1c9436e3156}}. However, if the quadrupole and spin-spin interaction energies per nucleus are comparable, a quadrupole and spin-spin energy reservoirs are effectively coupled, and the nuclear spin system can be characterized by a unified spin temperature {{cite:71e89ce8d073567cef3822bd6fc8b3c12dedcedc}}. The nuclear magnetic ordering is expected to develop when the coupled energy reservoirs are cooled down below a certain critical spin temperature. For this reason, understanding the properties of the spin-spin and quadrupole (SS&Q) reservoir under cooling is crucial for realization of nuclear magnetic ordering in a specific structure.
| i | 063a79dfe7dffd76f5a979a0d2e8373c |
ANCE-PRF also outperforms several strong dense retrieval baselines and produces the most accurate rankings on almost all datasets.
While Luan et al. {{cite:2e58a348a1691bbe3d0ac55fa84b89f5abee7119}} discuss the theoretical benefits of higher dimensional dense retrieval as in ME-BERT, our empirical results show that a well-informed query encoder can achieve comparable results, while avoiding the computational and spatial overhead caused by using multiple vectors per document.
{{figure:bfe0e1c6-34a7-44e3-ba84-cab26d4f6aff}}{{figure:d10f0921-3c30-4bf8-83d8-dfd230d28a29}} | r | 6f9110943919b244870646ebfbff6e06 |
In this work, we considered the case of nonlinear models in the overparameterized case.
However, typical applications of MAML (and meta-learning in general) implement relatively small models due to the heavy computational load of running bi-level optimization, including both outer and inner loop.
Our theory also assumes a limited number of tasks where data is independently drawn in each task, while some applications use a large number of tasks with correlated draws (for example, images may be shared across tasks in few-shot image classification, see {{cite:eb1a8ed5e6932cf7d2f24aad36f4af1c2e4069a6}}).
Our theory is valid at the exact optimum of the outer loop, which is equivalent to training the outer loop to convergence, therefore overfitting may occur in the outer loop of our model.
Another limitation of our theory is represented by the assumptions on the input covariance, which has no correlations in Theorems REF , REF , and is subject to some technical assumptions in Theorem REF .
| d | 91a69321fb9552f5e666bde1af453ccf |
The theory for the zebrafish regulatory function could be refined using the experimentally measured relative affinities of the binding sites at the her1 and her7 promoters {{cite:ecda026c730f2a990eb4d9737a97143b935e829e}}.
Apart from the effects reported here, the number of binding sites may have additional roles.
For example, it could serve as a buffer for fluctuations in gene expression {{cite:187f5d223c0e522d5934e4b57f6f41e21f38e721}}, {{cite:6cfc11afc5214e8a2467c3aa29ffe88af192a4fc}}, {{cite:3161083d0d5e73adaa04494db8c2a020a704aaca}}, {{cite:24546f60858bc653618e4bfd2970006f86df946c}}, {{cite:82ce40f71c50909cd03a102e93a0b530b69c7e6d}}, {{cite:57408c3e2c461e32d2fe9df4cb2cae853a961da0}}, augmenting the precision of genetic oscillations.
This will be the topic of future work.
| d | 806d027d77646e8dd5fcaa77a81baffe |
The most related work to our model is ViT {{cite:6825c010e88823b3c01f0ad8e7041d007e0cba90}}.
Here, we discuss the relationship and differences between them.
First, both PVT and ViT are pure Transformer models without convolutions. The primary difference between them is the pyramid structure.
Similar to the traditional Transformer {{cite:5aee1896f9b538ea60256808aff5a958edc4e8e6}}, the length of ViT's output sequence is the same as the input, which means that the output of ViT is single-scale (see Figure REF (b)).
Moreover, due to the limited resource, the input of ViT is coarse-grained (e.g., the patch size is 16 or 32 pixels), and thus its output resolution is relatively low (e.g., 16-stride or 32-stride).
As a result, it is difficult to directly apply ViT to dense prediction tasks that require high-resolution or multi-scale feature maps.
| d | c6bdc66630e0387615a5b20f622028dc |
We review and implement seven different attenuation
models describing visco-acoustic wave propagation.
Each model encompasses a different
effect of wave dissipation and dispersion.
We carry out inversion with attenuation model uncertainty,
that is, we use a different attenuation model to generate the synthetic data (simulating measurement data) and
to carry out the numerical reconstruction procedure.
Despite the resulting changes in the forward PDE models, we
show that FWI is a robust approach that does not suffer from
inconsistency in the attenuation model.
We start with experiments where we impose
absorbing boundary conditions to constrain the
numerical domain, hence mimicking a free-space
wave propagation.
We then investigate the consideration
of wall boundary on the sides of the domain.
The resulting multiple reflections are shown to
strongly influence the accuracy of the reconstructions.
To overcome the difficulty, we use complex frequencies.
This approach is also referred to as the Laplace-Fourier
domain method, {{cite:f010b7c2278c5a6d030b82bf6d849a3aca439313}}, {{cite:9c12f138b9b68275912d45d086e91de4722d634e}} and it is shown to improve
the convexity of the misfit function for inversion
in {{cite:573acfc9eb6f871723b0e43a969c3d65a1276338}}, {{cite:feaab54dbb94075ffdfc46b538607fcb25fe9b7c}}.
In our work, we show that this transformation can alleviate the
difficulty that occur from the multiple reflections coming
from wall boundaries, by enhancing wave first arrivals, {{cite:bbf0e2d2cb588093ea5e5aa2dc526f4e3535f874}}.
In the context of multi-parameter inversion, we investigate
the choice of parametrization, that is, the choice of model
parameters with respect to whom the gradient is computed,
{{cite:7c9119f7767dbf03d477181b674e4be454fe18fd}}, {{cite:7ca47abc54cb1942dc5ce3227d13c9c79b84bde4}}, {{cite:feaab54dbb94075ffdfc46b538607fcb25fe9b7c}}.
In particular, the density and attenuation properties
are known to be hard to reconstruct, {{cite:0c591e2b45fb45d94101a57c6f05e580794015c2}}, {{cite:d54c0334d09a76d52ebb64518bb369a696a84c3f}},
and possibly require a specific misfit function, {{cite:be3859a8f768d1c672fa7999a606fd473bb424ab}}.
We perform experiments in three dimensions to explore
the feasibility of our methodology and detail the
computational cost.
| i | ba9fad1448c84091d9544f0bda1533d5 |
As an alternative to the proposed framework, label space dependencies could be exploited also through adversarial loss (AL) objective functions. Such approaches have been used successfully in natural image super-resolution (SR) {{cite:a4e96c66ac5ba0800a9c0ee2656a720e88faf8b4}} and segmentation {{cite:b0a17a82c13a6b4e93692cad49b2a37e01d8c6df}} tasks. In SR application, AL enables the SR network to hallucinate fine texture detail, and the synthesized HR images appear qualitatively more realistic. However, at the same time the PSNR and SSIM scores are usually worse. For this reason, the authors of {{cite:a4e96c66ac5ba0800a9c0ee2656a720e88faf8b4}} have pointed out that adversarial training may not be suitable for medical applications, where the accuracy and fidelity of the visual content more important than the qualitative appearance of the HR images. Moreover, we believe that adversarial training comes at the expense of less interpretability of the regularisation term and unstable model training behaviour, which still remains an open research problem.
| d | ba156cceee6280b3850cfff8e23906c1 |
Finally, by re-plotting the data as {{formula:77e11bc2-0c23-4093-9e4a-3b09d6b87836}} against strain in Figure REF (c), we can compare the experimental results to predictions from two-dimensional weak-coupling calculations, taken from Ref. {{cite:dc514fd264c31e89f2dabf7b348ef81d575b20b9}}, for even- ({{formula:930d1225-efb0-4d35-8a69-26374616da09}} ) and odd-parity ({{formula:ff42d2c1-8d3f-44dc-b015-6a462f3b234d}} or {{formula:8cecdfcf-2949-43d5-b02b-24a9e9598404}} ) order parameters.
As noted above, the increase in {{formula:c5f78e8e-4099-4dd8-871c-7d7ef2c44c7a}} indicates a non-zero gap in the vicinity of the Lifshitz transition, which is only possible for even-parity order.
It is notable that the observed {{formula:6a652d24-67a4-4ae7-b735-07aa9590edf2}} peaks close to the VHS much more sharply than in the calculation.
At the Van Hove singularity, {{formula:dd2c24cb-e98d-4e36-b9f6-3ec4770f6f01}} is enhanced by a factor of {{formula:54172564-5539-44b6-b535-13964226a80b}} , in good agreement with Ref. {{cite:dc514fd264c31e89f2dabf7b348ef81d575b20b9}}.
The much larger enhancement of {{formula:a6872aa7-5d0d-41ea-8258-784f4429ce23}} over the calculations might be explained by strengthened many-body effects as pointed out in Ref. {{cite:dc514fd264c31e89f2dabf7b348ef81d575b20b9}} and discussed in {{cite:793d3db214f60100e899a7a6d87de4a47d5fb712}}.
Independent of the microscopic details, the experimental results presented here strongly support Sr2RuO4 being an even-parity superconductor at all strains between zero strain at the Van Hove strain, in agreement with conclusions drawn on the basis of studies of the NMR Knight shift {{cite:0673bdcfb8630f49728a69d026d4f672a406381c}}.
| r | 881f5c20dc6de69372d6ddf92b8b74c2 |
In this brief section we check some of the robust formulations proposed in this paper.
It is rather straightforward to extend the Nyström discretization based on global trigonometric interpolation and Kussmaul-Martensen singularity splittings for the four Helmholtz BIOs {{cite:47d8feaa3d57038559f60bb388f7d5e3fa34ad41}} to Nyström discretizations of the BIOs introduced in Sections REF and REF . These extensions were described already in our previous contribution {{cite:f4e4be5a8efbea7c265cdabbd402f295f94a941d}}. In addition, the Fourier multipliers required by the various regularizing operators considered in this paper are easy to discretize using global trigonometric interpolation. We present in this section numerical results concerning the iterative behavior of solvers based on the Nyström discretization of CFIE and CFIER Helmholtz decomposition formulations using GMRES {{cite:8cf6a9e39c422eef9deb2e294b3d80adbf047da5}} iterative solvers. Specifically, we report numbers of GMRES iterations required by various formulations to reach GMRES residuals of {{formula:ab1ae208-bb79-4dc1-8019-073cdb33bdbc}} for discretizations sizes that give rise to results accurate to at least four digits in the far field (which was estimated using reference solutions produced with the high-order Nyström solvers based on Navier Green functions {{cite:30cb6cd436984dcff7a46bd6a8951956d228cb1d}}).
| r | d8d8c304066ca6d1e8f340aa65888130 |
[nosep, leftmargin=*]
BERT {{cite:ddb054a9366ded1f42096e36e7e3d65b42341be5}} is a text-only auto-encoding pre-trained language model using the large-scale mask language modeling. We fine-tune the pre-trained BERT-base model with the few-shot training samples on each datasets.
RoBERTa {{cite:adb68ff9d4cdbdda5fe101c987a29adce8f1ae6c}} extends the capacity of BERT and achieves better performance in multiple natural language understanding tasks. We also conduct the fine-tuning with few-shot training samples.
LayoutLM {{cite:39a72fec10c5f5df32d14fb2fc6f5563750b1703}} is a multi-modal language model which includes the layout and text information. It is built upon BERT and adds the extra spatial embeddings into the BERT embedding layer. Following LayoutLM, LayoutLMv2 {{cite:275e71b26924bb034d29b87f87c07ed4068533d4}} leverages extra computer vision features and improves the performance, which are strong signals but absent in our settings. For a fair comparison, we do not include LayoutLMv2 in our comparative experiments.
LayoutReader {{cite:e7180bc345574c7dd3273ac7c361fb7b997887a2}} is a layout-aware sequence-to-sequence model for reading order detection. We append a linear layer upon the hidden states to conduct sequence labeling.
| m | 8671320abc02fd5272833df9fee3f5e1 |
Let {{formula:0f228efc-daa1-4957-ab1d-f25e2cf425e3}} denote a stochastic signal fluctuating in time governed by a particular dynamics. The persistence is then the probability {{formula:145d32f8-494d-4dd4-a544-1a637d9154ee}} that the quantity {{formula:bd90aff3-27f9-4c7d-ad3a-7af752178c9d}} does not change sign up to the time {{formula:361d1d14-813c-48c4-99ff-f959b11b4b69}} {{cite:f7ef81e282c662fedc44acd5127988192c423aaa}}, {{cite:85447cad6a97cd04dc8d54b3d5516d8165858395}}, where the overbar denotes the time average. Despite its simple description, only for some specific systems, such as those exhibiting fractional Brownian motions, the persistence probability density functions (PDFs) could be analytically shown to decay as a power-law, {{formula:00e84f16-7ed8-4939-8f3d-ee33c22b7537}} {{cite:f7ef81e282c662fedc44acd5127988192c423aaa}}, {{cite:296fe89a57fa3d3e57c9b0bfef14ff3dbf448b5e}}, {{cite:2f8873e707e2bc69706bb99e91d630299c324177}}, {{cite:803998dd8ed6221c3005f6a0e5b788f1bf5623b8}}. Here {{formula:22ac111f-880d-4b23-b5df-2bf968e54843}} is the Hurst exponent ({{formula:d95388a2-ea29-4f16-95b5-315bdeaae4e8}} ), whose value when {{formula:ccb00d0d-cf46-4021-bbb7-f4da745d4cce}} indicates simple Brownian motion. The power law form of {{formula:2cf0d75a-1d60-4d9e-89d5-5d68cef0c38d}} dictates that as the {{formula:659737f4-8bbe-4cc0-a3aa-eecaeb320719}} values get larger the persistence PDFs decrease more slowly, which seems consistent with the general notion that a stochastic signal displays anti-persistent or persistent behaviour depending on whether {{formula:a79750a6-0d24-485c-9e55-f1391052e21a}} or {{formula:37549d7a-4652-4de8-9d4a-63adcd6c3b0c}} {{cite:09a4431e694497a51e45b3f7a12e1444e1bb7b0a}}. However, for other complex systems, no theoretical solutions exist for the persistence PDFs and these need to be computed empirically from the experimental data at hand {{cite:81af29301253667ac817204543cb773e13aba989}}. Notwithstanding the theoretical challenges, the concept of persistence has many practical applications, such as in the field of biology where one can ask how long does it take for an epidemic to spread {{cite:7a4d38eb95a9537ae716ce599cfdfb233600370a}}, or in financial markets to assess when does a preferred stock will cross a threshold price {{cite:2c570cf4686ec2271cfdb29908b79d2f5a862c32}}, or in the field of geophysics to predict when will the next earthquake have a dangerously high magnitude {{cite:34b35444335c4663cffb6dcedc8fbc2fd9260991}}. Note that, depending on the context, the persistence could also be referred to as distributions of the first-passage time, or survival probability distributions, or return-time distributions, or the distributions of the inter-arrival times between the successive zero-crossings {{cite:5face9f2aa48f9881f59a42c97743eb6fdae1213}}.
| i | cefc2ce94631322fc95b10bd1a859d49 |
Despite the substantial progress, there are still numerous problems unsolved in this emerging direction {{cite:0475b83b4238b6d2c5c73365c199eae34bebd3e6}}. Among these problems, a critical one is about information evolution, a phenomenon referring to the dynamic variation of information content during its diffusion. Although information evolution is widespread in various complex systems, much unknown remains about its underlying mechanism. While some obstacles arise from the inapplicability of existing information diffusion models (e.g., percolation) that treat information as an entirety rather than a compound of contents {{cite:ef173e0a9b76a541da9dc8e0366af0a7e29f0232}}, {{cite:e28b30e59ea654fccb8eedfe14e2744f488d6b01}}, {{cite:5045da72787915a19cb3d32ac68a0517d43f0d2f}}, {{cite:1ea2e8391607492bad2a3a8dc00b7c474882ed31}}, {{cite:0c558e9a44faaac3ef7336c3bb10d1f11d77dcda}}, {{cite:f7a7aa25d8337b3b1555e266b17ac2b54c457c08}}, {{cite:2dc75825ee292533b8341aa010f540d15bbc169e}}, {{cite:d66162a89ba4d2135e385233e24644607dcaba7a}}, {{cite:4a1a39a7694dfd95338d577ec3a47addbbb1bd9b}}, {{cite:a52f29e56682f160574d0853f1418efd358bb5c9}}, more essential problems lie in a seeming paradox of information evolution: some regular global patterns of information evolution can naturally emerge from and robustly coexist with the random distortion of information during local individual-individual diffusion (e.g., the random distortion studied by Shannon {{cite:b4ec6002063606b6575c98f70fbb3e4ad35e717c}}), irrespective of whether individuals tend to create such regularity or not. It is elusive how local random distortions ultimately lead to global regularity rather than accumulate to utter disorder, especially when individuals' tendency or strategy is absent. Such spontaneous global regularities, frequently observed when information diffuses in real complex networks (e.g., the hierarchical representation of visual information in the brain {{cite:c65db6779b91f2437b4300bcc33426aef81f3047}}, {{cite:4a39d68490db31a1eb4bed264ce460ef76874740}}), may originate from specific undiscovered laws governing information evolution.
| i | 6e57228243d62551155aa068bc816ba5 |
In Fig. REF , we compare the NMSE of different channel estimation techniques. Considering {{formula:f1e27642-0ed5-4e7d-958f-db9b1106f124}} , we take {{formula:57d78a4e-2c3b-4fde-8890-feed08c3286f}} as per Lemma REF . Observe the significant difference between the NMSE values for the sparse signal recovery-based techniques and `QAM-pilot'. The proposed method and `MSP' are better than `QAM-pilot' in terms of NMSE since they are based on estimation of {{formula:73afe8f3-2955-455e-8621-2430a4d1628b}} as a vector.
Moreover, the proposed method gives slightly better NMSE than `MSP'. This improvement may be attributed to the CSC model acting independently to each delay tap and the sequential initial estimate method giving equal preference to all users. For `QAM-pilot' of {{cite:32f08de1fea0b0857f9a45a1735a29c7a4a78b50}}, an error floor occurs at higher SNR{{formula:de28942e-abc6-4662-880c-5fa83cde3ad4}} . The error floor issue arises as this method detects a path by thresholding the components scalar-wise and then evaluating the corresponding channel coefficient rather than estimating {{formula:8a692431-9da3-4a0d-b73b-c981b80d0b8d}} as a vector. The CRLB derived in Section REF is also shown in Fig. REF .
| m | 99caf5c67b55974b5ff22cb40c412b76 |
The modelling of reactive behaviors is a challenging problem that has attracted increasing attention recently. Many uncontrolled agents encountered by autonomous agents exhibit highly nondeterministic and multimodal behaviors. For instance, a human driver may choose totally different behaviors under the same situation at different times (swerve left or right, yield or not yield). Therefore, accurately modeling these nondeterministic behaviors is almost impossible. Stochastic models, naturally, have been proposed to model the nondeterministic reactive behavior, such as Markovian models {{cite:28c0f590a7ea580e1a86c6a5c8f893a3a6abd877}}, {{cite:622901f5264a5ba703be57c8f7dc10dabad93861}}, {{cite:a2f8b8be275e4d97c5696b609748ad978386e3cb}}, and generative models {{cite:72304a9278c8f27fd5fffc47c55fa3dce514e8a9}}, {{cite:0add56b121fbc1883bd048701467f8642fad75bb}}. Another class of approaches is the set-based method that models the set of possible behaviors, including the GAN-based prediction {{cite:5ef96e513749d119e74645ba97d7ba195aa59517}}, and classifier-based approaches {{cite:9c83e77f1836ad31b2a13c645356958987ad987a}}, {{cite:591eeb68886f1d8ccc47419b2b6c520cc8314fdc}}, {{cite:f2a980a71668da5e937da2283db015b894673eb6}}, {{cite:509db9d42a2c11ac1931bf38e55ee2a614bd07d9}}.
| i | c9c86ac18ba3c11fc1be12871e13cb74 |
Another area of focus could be to extend the financial pre-training corpus beyond Reuters News to include other news sources, as well as additional sources of financial text such as SEC company filings and transcripts of earnings calls. Reuters News has specific style guidelineshttp://handbook.reuters.com (accessed 2020-06-39), so we may be sacrificing stylistic diversity by using only a single source. The rich metadata provided in RNA does however allow us to filter the contents to ensure high quality and relevance, and this information is much more limited elsewhere. A closer inspection of the underlying mechanisms that contribute to the performance gains of domain-specific models may also yield useful insight. A more in-depth analysis of the self-attention head patterns could reveal whether certain linguistic features are more or less prevalent in the financial domain {{cite:e495a662f6b5b39ba300973199065daedbbaa2f7}}, {{cite:f757d3012ad75b06cd16f24067284f5ef2014498}}, while extensions to the underlying transformer architecture may enable the processing of much longer financial texts (such as SEC company filings) than is currently possible {{cite:7a069bf1755697470e878ba42773b96f318458c4}}. There are also more advanced methods for data augmentation available, such as the unsupervised data augmentation {{cite:f7e5a386dc12b203dde0a2d167de8a70d50c3fcc}}, which uses weighted supervised cross entropy and unsupervised consistency training loss, and combines well with BERT fine-tuning. Other loss functions such as cosine loss are also reported to benefit deep learning on small datasets {{cite:4e4a4a1b787182213a63c1eea230feafaa3dad02}}. Although we have tested our model here on ESG and UN SDGs classification problems, we intend to extend this validation to a much broader range of financial NLP and NLU tasks. Examples include analysis of financial sentiment, named entity recognition (NER), relation extraction and question answering. We also intend to adapt the approaches described here to some of the many BERT variants that have emerged recently {{cite:c9659d22c7996d2de9a1e9272c105fec95f3cdbc}}. We aim to address these challenges in future work.
| d | add54507c6a864b26e39b7ca134be73d |
The new measures of coverage we develop here—tailored to partially
supervised data that may be easier to collect in many engineering and
measurement-centric scientific scenarios—help to bridge a gap between
typical conformal predictive inference methods, which require expensive
supervised data, and problems with partial supervision, whose typical focus
is on prediction but not uncertainty quantification. Our hope is that this
work opens several avenues for future work. The new
definition () a 0-1 loss-based
approach, in the sense that the confidence set {{formula:303da7ed-04bc-49b6-9dcd-68f3a33e856a}} either covers
the weakly supervised set or fails. A natural initial extension is thus
similarly to what {{cite:2d1c00e55463dfd2da561fe12245c6facc4abf1a}} propose in the strongly supervised
case, recognizing that many structured prediction problems (e.g.,
segmentation tasks or multilabel problems) benefit from more subtle
and granular loss functions. In the same vein, we present a few
efficient choices of scoring mechanisms for structured prediction, which
highlight the practicality and potential
application of our general methodology; it seems quite
plausible that more sophisticated scoring models could yield substantial
improvements.
| d | 1af887b5b329a5c8c95b1ef99dacc862 |
Applying the Rice formula (see {{cite:8b14b945a3ec440bcfb8f869b97db33e4af619ee}}),
{{formula:a8a6af45-3a4a-434d-a976-92fc2b578c13}}
| r | 9b6c0fd523aeb42c41335ff56815ede9 |
The one-dimensional Goldstein-Taylor (GT) model {{cite:8ea42459bfa3286a210ab0fb5e96541766f0d739}}, {{cite:040cb31ba82d532b9fc496bea0e9fb406c86d0df}} with random inputs is given by
{{formula:1bacd80a-3478-4e06-91fa-3c36d9510a2d}}
| m | 1cf8d9ba80e56aa496de1af5eff37c75 |
To achieve this objective, inspired by the small-loss trick used in noisy label learning {{cite:f2051bf1f87a39938f25443d8613830302fb5545}}, {{cite:b1352fc2eeac9f7ad4558b39f66efc3d76fdd89d}}, {{cite:694d5bd5f613d44921e00017fd87b5146664c90d}}, we split the target data {{formula:0c8caa0a-4f1f-43dc-81c8-a0fa9cea51f0}} into a cleaner part {{formula:3957955f-1a75-45fe-9f0d-a9597ceee794}} with smaller loss and a noisier part {{formula:13989252-d0c6-46c9-a5e4-bd03f1f5a9e6}} with greater loss with respect to the pre-generated label. To avoid the aforementioned model collapse problem, we further develop it into a label-wise dataset splitting method, which ensures no empty classes in the cleaner part {{formula:8d953b62-8e28-4d39-b3c4-f96a830ce4d9}} . After that, we sample images from {{formula:0ebf64a3-5d73-4be3-92fa-d9d532be4984}} and {{formula:f9923f26-4a02-4599-b1a5-3476031feeb4}} uniformly to train the network with pre-generated label and self-generated label, respectively. As the training goes, the loss with respect to the fixed pre-generated label will get smaller in true-labeled samples and get larger in false-labeled samples. To fully exploit this positive feedback, the dataset splitting operation and network training operation are alternated epoch by epoch so as to progressively boost the performance.
| i | 3f0f7a6905a7b67a8cc03b26be389ee2 |
We constrain ourselves to the case of linear processing on both the transmitter and the receiver. For the case when each user has only one receiving antenna, the optimal linear schemes for MMSE were derived in the papers {{cite:cb0cafc0f621a48df8162cef4f04e1b7cc08eaaf}}, {{cite:365d02accfe8c11e257a29a57d616bdb6acda58b}}. In this paper, we investigate a more complex case with several antennas per user. There are well-known methods of of block diagonalization (BD) {{cite:fc219738364c8f92e13fb5de77cdd8182095626a}} and sequential MMSE (S-MMSE) {{cite:225b6a5066d714852d25de9e421d656589b32d44}}. Both have relatively low complexity but do not reach the minimum amount-MSE. Hence, we proceed to obtain a set of necessary conditions for the MMSE solution, which was presented in a similar form in {{cite:9f3e4cac1f66a32a467ed9c960b6badb23209a27}}. The necessary conditions can be used to obtain an iterative approximation of the MMSE solution, an idea also used in {{cite:2d5a8691986d8906febd04f342723a7a2b4cd98f}}. However, the non-convexity of the objective function implies that this scheme ("direct optimization") does not always converge to a true MMSE solution. This problem can be partially solved by choosing a good initial assumption for the numerical algorithm. In {{cite:090a1c6f88486748be3e67fc9ce3bfa2a46c8914}}, {{cite:85d0c2af78a3e24ee28a44febb5654a5fdf33ec4}}, {{cite:531a5406fb8f11bddd2162c48842cc1a76491fad}}, the duality between the problem under consideration and the equivalent uplink channel is used to obtain an iterative algorithm that determines the true MMSE solution in each case.
| i | bfbb7a0b42d491f3527998005357591d |
Results.
Table REF presents the results. Our method achieves an average mAP ({{formula:b69e602e-7b62-4c77-9cb2-c45f14c4ddb7}} :{{formula:5337fc15-4e44-4217-aa4e-78e3c5d2f2f3}} :{{formula:4fcfe1a2-5f3b-4c51-8569-844c8efdc14b}} ) of 23.4% and 21.9% for verb and noun, respectively. Our results again largely outperform the strong baselines of BMN {{cite:b52c75290d9accd25dc89828f102398cdbc105b7}} and G-TAD {{cite:28406126acbb1722ec9e5e06437981efd424f1ac}} by over 13.5% in absolute percentage points. An interesting observation is that the gaps between our results and BMN / G-TAD are much larger on EPIC-Kitchens 100. BMN / G-TAD has an average mAP of 33.9% / 34.1% on ActivityNet-1.3, respectively. That is within 1.5% average mAP as our method. We conjecture that the difference might be attributed to the characteristics of the datasets. These results further confirm the effectiveness of our method.
{{table:25f927fb-49de-4a62-aa8d-eaa8ec69c2f7}} | r | 853dbbb2ba5124e97e041e1199b54fa4 |
The objective function in (REF ) is the sum of a smooth term, the squared norm, and a convex nonsmooth one {{formula:574a44d6-8fe3-4208-ad71-11f4c40a118c}} .
Problems such as (REF ) are called structured composite convex minimization problems, and can be often solved efficiently by proximal-gradient methods {{cite:2c3023520c835c2d96ad89192e85ea8a943f479b}}, a class of first order methods splitting the contribution of the smooth and the nonsmooth part. At every iteration, the smooth part is activated through a gradient step, while for the nondifferentiable one the computation of the proximity operator is required.
In order to implement a proximal gradient algorithm to solve problem (REF ) we would need the computation of the proximity operator of {{formula:7f7d7fd2-7d99-4388-8313-8b1a338265b9}} , which is not available in closed form and may be computationally expensive. Therefore, we consider the dual problem (see for example {{cite:6dd839ab2c4abd5d2f4081e014d3abc5fce8b929}}) associated to (REF ) (which is equivalent to (REF )) which is given by
{{formula:0ceb1c1f-668b-4740-ac1b-6fb165940c95}}
| m | 5fd48dcaea99f25605af2727794a830a |
Our attention-based model showed significant improvements over the baseline models, but still has some room to improve.
For example, in Section REF , the BERT baseline model did not perform significantly better than other simpler baseline models that used sentence length or co-occurrence information.
We also observed that prediction results may be somewhat less accurate for lower- and higher-end informative scores (Appendix REF ).
Although we did not identify any systematic characteristics of these less accurate prediction cases, the results might indicate the pre-trained NLP model's limited vocabulary size or difficulty in processing grammatically complex or incorrect sentences.
Example-based analysis, such as word-level permutation, to investigate which context words most impact prediction results {{cite:f58801d00b1ea8ded50f123345a0c3289acd6f9a}}, can help to systematically identify these difficult cases.
Applying more sophisticated methods for processing attention weights from multiple layers {{cite:6ce236d4f810464ddddca3b202002b3ac99d1ca3}} may provide more accurate results.
{{cite:c2bd044fc5d867d309a37dcecc53a53f88f53f8f}} points out that the performance of pre-trained models on predicting cloze responses can be affected by specific contextual terms in a sentence. Our future work could evaluate our prediction model with diverse sentences for a more thorough comparison.
More thorough hyperparameter optimization process would improve the models' performance too.
| d | 0fde48f88fa911247baa3e065dfc79f2 |
Evaluation setup. Prior works {{cite:d561629b248ac4d6849aa5b9a45a546f5655fcf3}}, {{cite:72049d57f45c6a63a7b652277bc9229026e0845c}} show that Conv-TasNet, originally proposed for speech separation, can also be used for target sound extraction. Further, ReSepformer proposes an efficient transformer architecture for speech separation that allows a streaming inference. Here, we compare the performance of our architecture with the causal or streaming implementations of Conv-TasNet and ReSepformer as described in the original papers {{cite:bd97fea332aa3b78d96c8162e6b12cded3590278}}, {{cite:5e117238f025f150929ee8a6a4643def11b16dda}} for the target sound extraction task.
| r | 7b0ff1215a07c6650ba06e229faf3168 |
The objective of this paper is a class-agnostic counting network – one that is able to flexibly count object instances in an
image by, for example, simply specifying an exemplar patch of interest as illustrated in Figure . To
achieve this, we build on a property of images that has been largely ignored explicitly in previous counting
approaches – that
of image self-similarity.
At a simplistic level,
an image is deemed self-similar if patches repeat to some approximation – for example
if patches can be represented by other patches in the same image.
Self-similarity has underpinned applications for many vision tasks,
ranging from texture synthesis {{cite:ea9d1e8baa335dd3344a72066fa9a836db23db22}}, to
image denoising {{cite:40917e6a06058cc7a76e0c53e45b2242fb4d8225}}, to
super-resolution {{cite:850fc199d5b0a6b340b6284770c6fbf985ccebdc}}.
| i | d041398ccdc3d27dc12af292de4a1450 |
Remark 5.2 (Error metrics)
Theorems REF and REF provide rates of convergence for the distance of the iterates {{formula:27b359b6-afe0-4ea2-9d54-712556842a93}} to the minimal norm solution, as well as the angle gap and the margin gap of the normalized iterates {{formula:efed4ac8-7c64-4b36-9e86-8807afce0ed0}} to the max-margin solution {{formula:5713f42e-d183-47d0-9d5e-dfdef1bf72e3}} , for Algorithms and (respectively). As mentioned in Section , since the original max-margin problem (REF ) is a direction problem {{cite:9bea2bba7893e9b8c7a6bdb0b8690d4a531e2310}}, {{cite:fa8a36bdd542f23a7d17a1bdbafc15dafadf62ed}}, the margin and the angle gap are relevant quantities to measure the performance of the proposed methods, see {{cite:04904a4a1b3f154e5ed87dee9c7fb0b608c6d632}}, {{cite:5b74f4889d24ee205a9a531605a87340041e531e}}, {{cite:2f98d80ce309a97af0e993c259b3e49aa60066cc}}, {{cite:192c81429b825bd66a14f96fe604e5f440ac8f1d}}, {{cite:2366a6b65e7d9757814096f73702ff3e6a40a0bc}}, {{cite:2ba7ecca7c85200af9f00baf30414a923840ec76}}.
| r | 4117b76e3d9653986ddc222824eba267 |
Magnetic fields also influence other interesting observables such as the entanglement entropy and the butterfly velocity that can be studied using holography. In {{cite:44c3b5086e858bf586d3000f96af27f4b0efa675}} these observables were proposed as tools to disentangle the effect of pressure anisotropy and magnetic fields in heavy ion collisions. Finally, the techniques we discussed in this review have interesting applications in condensed matter {{cite:a487cea4d38f2795e4058a8bd2448472e3a88038}}, {{cite:3b57f544ba61bcd8e78ae9acbef0dbb85275f38a}} where magnetic fields provide crucial probes, for example, of quantum phase transitions.
| d | 40bdac59bcbaa523a4899b59d307b42d |
Further, our approach adopted the three methods from Aghabozorgi, Shirkhorshidi, and Wah {{cite:1ee870c779f1e035951857ae5972bac6c29acd21}}: the shape-based method (raw-data-based method), feature-based method, and model-based method. The shape-based method matches the shapes of the two-time series by a non-linear stretching and contraction of the time axes. Then, conventional clustering methods are applied by modifying distance/similarity measures for time series data. The shape-based method converts the raw time series into a feature vector for a lower dimension. After that, conventional clustering methods are applied to the extracted feature vectors. The model-based method transforms the raw time series into model parameters. Finally, a suitable model distance and a clustering algorithm are applied to the extracted model parameters.
| d | 8b020d2ab79a7fc5408c2c9fd507abe3 |
We solve Problem REF by using new compressed cover trees on both sets {{formula:d5c85f1f-8407-4431-b034-2527ac704946}} .
{{cite:a2029b60f4ee67a5462c9428f0b8ad97a7e3549b}} introduced a first version of a cover tree, which implicitly repeats every data point at infinitely many levels, see a comparison of two trees on the same {{formula:74e33dfd-bbc6-4281-87b2-5739d9bbe7bb}} in
Fig. REF .
The new tree {{formula:a1d575f1-6e1c-47f8-be34-553471bc64a3}} in the right hand side of Fig. REF has nodes at levels {{formula:dd696899-c5f2-4421-9508-95852bb64832}} , so its height is {{formula:6352fb9e-a583-426b-8afa-2ce6b7004189}} .
| r | 2f2f20a29098fdade0e9a67c555c6c5e |
For over a century experimental efforts have probed Einstein's theory of General Relativity (GR) finding agreement with all its theoretical predictions {{cite:3cda5e983181e8974593e9255a8d7ef438321cae}}, {{cite:1f84aad14839e6e9c43af7795f77bbd533164574}}. Even though its original formulation was based only on Einstein's Equivalence Principle (EEP) and general covariance, the Strong Equivalence Principle (SEP), which requires gravitational self-interactions of massive bodies like stars and planets also obey the tenets of EEP, was an unstated requirement. Lunar laser ranging and observations of pulsars in multiple stellar systems have tested SEP as well {{cite:85e7b10c86c103fc52a08787e087d30df08aaf8e}}, {{cite:e6ec399cb1114692c739925a5cf6dd1d9a1e3530}}. Recent analysis of a SPARC sample of galaxies by Chae et al. {{cite:92a1f31b5e285cfce78ade8df3adec8bc4d2524a}} however has cast doubts on the validity of the SEP. If confirmed this is the first indication that we need to modify GR. Similarly, the Standard Model of Particle Physics (SM) is a non-abelian gauge theory with the symmetry group U(1){{formula:92a4ba35-3bc4-4a26-b486-545fe634ffd2}} SU(2){{formula:7a8851ad-c964-4310-a301-b9ffc461d462}} SU(3), which has also been eminently successful in accommodating an extensive set of experimental findings probing its validity. However, the model, while explaining elegantly the phenomena related to strong, electromagnetic, and weak interactions, is not able to provide as yet an acceptable candidate particle that can serve as dark matter. Nor is it able to include a quantized version of gravitation within its framework. There have been several attempts at extension of SM, which predict the existence of new forces {{cite:d6cfc08316fb07150edc22ed068504c008a6e4f5}}, {{cite:981f5443daa96c1b92c2605b21d506bccbfe7c42}}, {{cite:2f8328210a79b4025e8c7c7d5001062613e7cc89}} that will appear as a signal in apparent violation of EEP in our experiment . Our torsion balance is designed specifically to search for such forces and characterize them.
| i | 78c7a7dc9f8e1bcdf43c21caaecd9a6a |
Although this might has an analytic solution for a low dimensional cases, for a high denominational problem it is intractable analytically and we have to use numerical methods to evaluate the integral value. Here, we use the sequential Monte Carlo (SMC) algorithm to sample the posterior. The evidence is a crucial quantity for model selection in Bayesian framework and in comparison between two models.
In this paper, we use the Jeffreys’ scale {{cite:37483f8708d23db8180381378751eeacf7d33905}} to measure the significant difference between two different models. Considering two models {{formula:85d0ef57-3fc1-4bb3-99db-fe033ce37356}} and {{formula:8963638b-d801-4d03-9b73-6ad32213da6f}} the Jeffreys scale with respect of {{formula:19364f1b-1f8e-4b04-a50d-edcfcde3418a}} is as following{{cite:099e42b81865d156c16be9020ef5b506745d394d}}:
| r | 6d44be5a02e74d515e3202f1a988d0d9 |
On the other hand, {{formula:7b488e93-d9ca-48e0-8a58-8d9942dfa866}} -ray emitted in the dissipation region might be absorbed due to the internal {{formula:74a0fb80-39e3-43e3-a3cb-dad95a57ebc9}} absorption. For {{formula:612d0914-43fc-4303-8f76-512d8c3f08fe}} satellite, its detection energy range is from 50 MeV to 1 TeV {{cite:15b58ecaccff832250eaf834187cab21e33e8286}}, therefore the {{formula:d94bd595-d2c4-44f8-99ad-3ec52360295a}} absorption optical depth at 50 MeV {{formula:8fdd86f2-f5fa-44eb-8c90-600f63227544}} should be {{formula:f5dee721-f235-47e5-8610-ef956ba2c05c}} . For each FSRQ in our sample, the soft photon's energies in observer's frame that annihilate {{formula:e6564d42-ef11-4bc5-a401-aaf9268e61e3}} -ray at 50 MeV are estimated with {{cite:455072c2e26f0c830a8b5fd489ec809dc623fe54}}
{{formula:ffbab52f-eb05-44e7-92bb-bc544a19c3e2}}
| d | 3f4fe9467ad5a9a3f11d0e8b4e62a9fd |
Middlebury {{cite:c6cf8e7d4924e453017552f2da2f5a0b00caa948}}, {{cite:090ebad459d26ed734140cb53ca7b518d4c1d90a}}, {{cite:44d95703f94c7cc2f54a9afc9f5f8caf481656c5}}, {{cite:b2ed31f1ef2bc5801ed42d5ee64ae5802630482d}}, {{cite:960d7e357ff0d987cf6e747266e5cba19293ab63}} We use all 50 RGB-D images available from the Middlebury 2005-2014 datasets. We split the data randomly into 40 images for training, 5 for validation and 5 for testing. A challenging aspect of this dataset is that it contains missing values in the depth ground truth. For generating the source, we therefore only take into account valid pixels during downsampling. Furthermore, we generate a pixel validity mask for both the target and source, so we can ignore the invalid pixels during training and testing.
| r | 41fc3e58cff7046402342b7d1ff61161 |
where {{formula:8f09bb49-44a0-4de7-a791-dc383e9e9244}} are tensors and {{formula:21fdf848-cbac-4bae-b15f-68a66faad1fc}} denotes the Einstein productwith order {{formula:dcb6d197-095f-48cc-89cb-3e77bf4685b1}} {{cite:eb8742b6556a8ee9ccfbeceb37b338fd184cb658}}. Basically, there are two main approaches to solve the unknown tensor {{formula:ddd4e5a2-af35-43a4-8988-25b3fa00d0a6}} . The first approach is to solve the Eq. (REF ) iteratively. Three primary iterative algorithms are Jacobi method, Gauss-Seidel method, and Successive Over-Relaxation (SOR) method {{cite:740c16205a1c689ed920f9e0cbb101c2f8da6835}}. Nonetheless, in order to make these iterative algorithms converge, one has to provide some constraints during the tensor update at each iteration. For example, the updated tensor is required to be positive-definite and/or diagonally dominant {{cite:5382b0364af1100838a1e681eeb08e30d9be3b1e}}, {{cite:576eb0b84c0ef1c5682d5356f0107c5ad1878c00}}, {{cite:b8e0e3762f35f533e7d5c4c861af030ef95c121a}}, {{cite:85fcd0c06843837fbd41798fd7956ef007eaa7e7}}. When the tensor {{formula:d3ac951e-9511-4c66-977f-7c4b4f7e4deb}} is a special type of tensor, namely {{formula:2a97149d-7bf5-42db-9c85-3e65ddfc1443}} -tensors, the Eq. (REF ) becomes a {{formula:556bf57f-a92c-41a5-8c65-96f257704abe}} -equation. Ding and Wei {{cite:eb79c5fcd39de3b1a1f24dc4b47c0d4b0a9e9dd5}} prove that a nonsingular {{formula:0b2c3251-43b2-4b0b-827b-44676811caf8}} -equation with a positive {{formula:7ab9d608-5b3f-4a63-abdf-ab78c14cba5d}} always has a unique positive solution. Several iterative algorithms are proposed to solve multilinear nonsingular {{formula:7d82fe95-ee56-46d3-b60d-9e8bab753059}} -equations by generalizing the classical iterative methods and the Newton method for linear systems. Furthermore, they also apply the {{formula:fc356436-4c7d-4fa8-8210-2e1708174508}} -equations to solve nonlinear differential equations. In {{cite:41ea842eae684639cfc5560d3a2cf3057e95ef51}}, the authors solve these multilinear system of equations, especially focusing on symmetric {{formula:173b35a0-c873-4bd3-89f2-f3a761722b4b}} -equations, by proposeing the rank-1 approximation of the tensor {{formula:35f8e633-48b0-40c9-acf1-8d6f98f647d6}} and apply iterative tensor method to solve symmetric {{formula:c321b765-278d-440a-9c7f-fec382f8228c}} -equations. Their numerical examples demonstrate that the tensor methods could be more efficient than the Newton method for some {{formula:dd1b6437-68a3-4179-bae7-035a2ef9efc5}} -equations.
| i | cf5a5d8c3e510ed8f547d062a8ca19df |
The time- and temperature-dependent expansion coefficients {{formula:268ee487-221e-4c07-9126-092ece456b73}} correspond to an {{formula:230c1f25-b866-405b-83de-922ea3784d05}} complex array which requires storage space and computational effort that grows exponentially with {{formula:40fd9060-bf5b-4bf5-9e7a-ac3eb1856859}} . Thus, we avoid the curse of dimensionality by implementing the TFD wavepacket in the tensor-train (TT) format.{{cite:5698cd08a17e5e4fb9c8afcf245f6b9321c62412}}, {{cite:ea978892475b7de2d3b65ad53dc3afd454999ccc}}, {{cite:5d579db60db8488599a9d80ba84ad792f206e06e}}, {{cite:3a405a684b59efdd8ad649e831c6535fec2a6faa}}, {{cite:1776cceac981868e4e9b34d234d707fcec2cc381}}, {{cite:ef0795089e2b826ca3cce3824fe8a9d531c56546}}, {{cite:f7010a564450713c2249ffc2b5d238d92a0dd8f8}}, {{cite:584dcb8fddcc830a4307a6028717d7e117a39ab0}}
| m | 37935079154f3582ce1b6bc2ba7d34d8 |
Caranti and Vaughan-Lee classified algebras of type 2 over a field of odd characteristic in {{cite:6b49a04fa9cc4e6ac23138a606ce94ebbf784cce}}.
They showed that all algebras of type 2 which are not graded subalgebras of algebras of type 1 in the way described above are soluble,
and belong to an explicitly described family (with an additional family appearing in characteristic 3).
They anticipated that the case of characteristic two would be considerably complicated,
but then a classification in that case, which they achieved in {{cite:0df09ee9bae63140382f70b88cca02a01f15c04f}}, actually turned out to be simpler to state.
It is the special case {{formula:c3165cc0-3501-4a9e-b6b8-0310a733452a}} of Theorem REF below.
| i | 87f0cc9d17b66f8a5f14bade3af83dff |
Model Training. The model is trained to predict {{formula:9989780a-2ea9-4dc5-8a6c-8284fa05842c}} from {{formula:1f4ee0b8-3e7f-4b63-9463-1e6a3bed3f02}} , for an unknown but fixed value of {{formula:0d425174-244a-4f9d-8596-6abb6151322e}} . We use sequence-to-sequence transformers {{cite:5225ab85e7f898e8d805563635db34d86c4d0984}} with one layer in the encoder and decoder, 512 dimensions and 8 attention heads. We minimize a cross-entropy loss, and use the Adam optimizer {{cite:b19455b476244f259191e54e96456e91d71e182d}} with a learning rate of {{formula:dbf87a29-c80c-4d6d-a4b9-5e092b29a6ed}} .
At epoch end (300000 examples), model accuracy is evaluated over a test set of 10000 examples. We train until test accuracy is {{formula:435b6249-5e30-4b68-aad6-6edf7a976803}} or loss plateaus for 60 epochs.
{{figure:353fc5b9-def3-4607-80d8-58addce72da0}}{{figure:cb9a79bd-7fc6-42f1-b1b8-472abbd1d29a}} | m | 54fb102679222ea58e965688844ac621 |
Fourier phase gradient (PGS):
The most
common template-matching method used to date (and the default
method used in the psrchive software package) is the
so-called PGS method described in detail by
{{cite:69accb7daf42b860bea95fc03923c161fe43f533}}. Based on the Fourier shift theorem, it matches the
template to the observation by fitting for a slope in the Fourier
space. A clear advantage of this approach is that the phase resolution does not impose a fundamental limit on the achievable measurement precision and as such can
result in significantly more precise measurements than time-domain
cross-correlation methods {{cite:69accb7daf42b860bea95fc03923c161fe43f533}}. The main disadvantage of this method is that
in the low-S/N regime it underestimates the TOA uncertainty since
the TOA distribution no longer follows a Gaussian
distribution {{cite:c2a44a357330ae055bd7710eb869ad039989829e}}.
Fourier domain with Markov-chain Monte Carlo (FDM):
One proposed solution to the underestimation of low-S/N TOA
uncertainties is to probe the likelihood–phase shift dependence
with a one-dimensional Markov-chain Monte Carlo, from which the
TOA variance can be derived. This results in TOA values that are
identical to those of the PGS method, but TOA uncertainties
that are more realistic (i.e. larger), particularly for low-S/N
observations.
Gaussian interpolation shift (GIS):
This algorithm
carries out a standard cross-correlation of the template and
observation in the time domain; and determines the phase offset by
fitting a Gaussian to the cross-correlation function, whereby the
centroid of the resulting Gaussian is defined as the TOA; the offset
required to double the {{formula:d842aa47-2bd0-45fd-b91f-f2f74e2ddff0}} of the template-observation
comparison is defined as the TOA uncertainty {{cite:2e3c90692aa4124a71bdf529b3439e1e2b57c899}}. As
mentioned above, this time-domain method has limited precision, but
it was proposed as a more robust TOA determination method in the
low-S/N regime.
The application of a Gaussian in
determining the peak position of the cross-correlation function
should result in timing precision exceeding 10% of a phase bin,
although this likely depends on the exact pulse shape.
| m | 887595b165aa455ab115e8fdab86dfc4 |
for some {{formula:e1892304-ed4c-464d-84dc-15924babf235}} and {{formula:48be0b8a-9bee-43b7-80dd-c5f650feea4a}} .
It follows that {{formula:1f764db4-c20c-481f-bb58-5a52f044ab8c}} , where {{formula:10f242a8-d54e-4931-bd80-65196bbe1315}} .
We now recall a classical result for linear stationary iterative methods of first degree which will later be useful.
The following is based on {{cite:3517b1ca8fc2a7148123dcf5e0b08d95b21f827e}} and {{cite:4f6f730d346904513770627c4bdbd9ff1ce0ea0b}}.
| m | 8b1a719688dfbaea05dc64e73bf4ad0f |
We show that ML classifiers (Logistic regression and LSTM), when used by themselves directly on time-series measurements are dumb to the temporal/ causal-structure in the data. This fact has also been discussed in existing literature {{cite:b2cea9c2c8e449442a7118d06b2dd9855945271b}}, {{cite:a59ba8e1ea29e6da08fca1f343cd2e0009ce4d19}}. When time-series values were directly passed to the classifiers, LR and LSTM, they failed to learn any causal-structure characteristics from the data. Even though LSTM has been developed for the classification of sequential data, it seemed to be learning some statistical features from the data, giving high classification accuracy when the testing set followed the same distribution as the training set and failing when there was a distribution shift in the non-causal time series structure.
| d | 5968e09b4a060b3abd66cc47944ddc58 |
There also exist some hallucination issues. Retrieved knowledge can alleviate this problem {{cite:bcef1a866c155096b3f25bd86baf69ebe8c552eb}}. A pre-trained reader can also get advantages if the pre-trained LM itself also performs well for open-domain QA, as shown in T5 and FiD in open-domain question answering {{cite:742e7a36d288494b2278d1fffda0c1d8e14b37fc}}, {{cite:1265eb0e4b94c58920b35633cf50857fa4b96651}}.
| d | 04e3478e6f2e26612850b577025d3482 |
The idea of using particle filters to sample general distributions,
including those arising in Bayesian inversion, maybe be found in
{{cite:ed8cf583cf3aaeb24d758f25babc1d3acf7f391d}}; a recent application to a Bayesian
inverse problem, which demonstrated the potential of the
methodology in that context, is {{cite:233ec36188266ea46f021c3a1a4ead00023e37d7}}.
A simple proof of convergence of the method may be found in
{{cite:cf31aaa58e795e25b98a0554e7bad1745f8e6379}}; it is based on the proof described in
{{cite:1426a5d4216e41c422c444103364375fe25098f4}} for the standard bootstrap particle filter.
| d | b29e446d27727755107114e05f54681a |
We have illustrated the concept of Domain-Aware Zero-Shot Learning (DAZSL) and Generalized Domain-Aware Zero-Shot Learning (GDAZSL) setting in the main text and Section. REF in this supplementary. Here we provide more details. We first present the statistics of benchmark DomainNet {{cite:f585524dbd8503755998519a642071da89982350}}. Then we provide more statistical results.
{{table:0449647e-9144-440e-9b8a-26671c3344b1}} | r | 67667af9b4293af7e31dada87e8ba703 |
The main accepted galaxy formation paradigm predicts that galaxies grow hierarchically through mergers with other galaxies (e.g., {{cite:1d0c8248bd30772760dcf14c315ec54af7eefb81}}, {{cite:2a3b7480eac7311f7b0bf146929b7147f95d61c7}}), and thus the accretion of diffuse gas and dark matter occur especially into the halo. There are different types of mergers, but broadly we can distinguish major mergers from minor mergers, depending on the mass ratio of the two objects. In the first case, the masses of the two colliding galaxies are comparable, while in the second case a galaxy of lower mass is accreted into a more massive galaxy. Obviously, when a galaxy is observed, evidence of substructures and deviations from symmetry are indicative of past or/and ongoing mergers. Clues can be detected within galaxies themselves in different forms, such as streams, bridges, density waves, overdensities of stars, substructure in galaxy's gas, different globular cluster populations as well as changes in kinematics. Proofs of merging events are found both in the Galaxy {{cite:8b332fd7d6be7a9abeac7113aa81f2ea96182f15}}, {{cite:e12a602c498a6194d32e980e0c0b004b60b5a8c2}}, {{cite:6882728f06d36fcfc034cacf4d5193d3005ca2d1}} and in external galaxies (i.e., {{cite:689756b58e9712730a5cfc17847132d828c0a55d}}, {{cite:8d21fd2eab5eaf26e8c737a7c9fd2b9c7c83492e}}, {{cite:7576b3da1b2df104e6ddbbe6987f9fdac9b1f95d}}), like e.g. the Andromeda galaxy (M31, {{cite:7204402aefed69c44e77fdbdd143592fc1fc7a14}}). Therefore, the history of our Milky Way is a history of accretion. At least seven past accretion events can be singled out: Kraken {{cite:8885aaf0031790dc337de2ff2deb24c8cd73795e}}, {{cite:e19891a68d0c2db9d1187a1cc6dac5bb6464a81a}}, Sequoia, {{cite:8d957e2ebf75bdbbaf9ea5c43f41521763bcaa64}} Sagittarius {{cite:70339a07c4a7762e05fafa037cf8b8ab90059c6b}}, Helmi stream {{cite:36867c85d4ca5cc56687a4d73eb6ffe230296921}} and Gaia-Enceladus {{cite:d401342481adf50f17cfa42267208521f5d4f2ea}}, and both Large and Small Magellanic Clouds (LMC and SMC) will infall towards the MW, we know that the Magellanic system is likely on its first passage about the Milky Way {{cite:863061445b768a2ebf0ce52e235da3c52ecc7dba}}, {{cite:4495a50372e70c612d16a057b42cb7dadc63dce6}}, {{cite:daac07ffe2100fa38f17f1c1705bce827db7e8ac}}.
| i | d92577ae0402de69ffd5baef35053be4 |
Roughly speaking, the main problem with the continual learning setting is that areas in the parameter space that guarantee each task's performance can have arbitrary shape, see Fig. REF . Thus, our primary goal is to detect weight in the intersection of such regions.
Even simple linear models together with an intuitively appealing upper bound on the prediction error as optimality criterion are NP-HARD (see {{cite:b54179ca34d2e9c642d3653521f20848995d71d7}}[Example 1]).
| r | 561b26603104cde335f7e666e6aa5fb5 |
To pursue more efficient VSR networks, we propose Residual Sparsity Connection Learning (RSCL), a structured pruning scheme. Specifically, network pruning has three stages, including pretraining, pruning, and finetuning. In the pretraining stage, we train a powerful VSR network. Since current VSR networks do not use BatchNorm {{cite:4787007ddb4b36182d8e955fc461157c424fd032}}, we introduce a scaling factor to tune the sparsity of each channel and filter. In the pruning stage, we select the unimportant filters according to the pruning criterion and apply sparsity-inducing regularization on corresponding scaling factors. In addition, for the residual block extensively used in VSR, we propose a Residual Sparsity Connection (RSC) scheme to increase the pruning space. Moreover, for the upsampling networks in VSR, we specially develop a pruning scheme for the pixel-shuffle operation to guarantee the accuracy of channel-space conversion after pruning. The error of the hidden state will be amplified with the propagation steps increasing in the recurrent unit after pruning. Therefore, in the finetuning stage, we further introduce Temporal Finetuning (TF) to reduce the error of temporal information propagation.
{{figure:c958a628-47bb-4042-94af-5e0b50e90948}} | m | 60892bea8c464dbef6eb7c13c5e7ef74 |
Beyond the results presented in this paper, there are few directions that need further investigation. First, while the current UQDeepONet method is mostly based on the original DeepONet architecture of Lu et al. {{cite:95877758ab3fe912f63f6249267ddabd71e9ee1e}}, it would be interesting to extend it to include the modifications recently proposed in {{cite:846ddbc446b88ec279764400d2a2ab3859a27373}}, {{cite:06dd1b8dc099c025d32eaa9c0e888413d8b20406}} that have been empirically demonstrated to yield better performance. Second, randomized priors are not a concept is only applicable to the DeepONet model, but could be also enable scalable uncertainty quantification for other operator learning frameworks, such as the Fourier Neural Operator {{cite:b05102faaeba97e6cf64ce397ac32a93b06f2dc3}} or the attention-based architecture LOCA {{cite:caad6ace3f048335152a628bfcdd177648dec732}}. Third, several advanced tools for efficient optimization and stabilization of the training dynamics, such as the Neural Tangent Kernel approach {{cite:1b78e6baee1106668d2e38180893692bceb903fe}}, {{cite:06dd1b8dc099c025d32eaa9c0e888413d8b20406}} and hierarchical incremental gradient descent {{cite:2303475ce25b87c63f3ca30d0887027d3809ec93}}, could be considered for achieving better predictive accuracy and further accelerate the training process of multiple neural networks. One current limitation that warrants attention in future work is the limited ability of DeepONet and other operator learning techniques to receive input functions whose domain is very high-dimensional. To this end, dimension reduction or low-rank approximation techniques can be employed to reduce computational complexity. Finally, while uncertainty quantification is predominately used for providing prediction error bars and confidence intervals, it also plays a prominent role in decision making and the judicious acquisition of new data. To this end, the question of how to acquire informative data for operator learning tasks is currently under-explored and calls for further investigation in the future.
| d | 82aa37687299ece5ec634f53fa84f376 |
These results suggest that the pre-trained ALBERT generates a relatively stable trajectory, with higher dimensionality in a certain short-term range.
Moreover, the gradual changes in the benchmark scores around {{formula:fb5a180d-7270-4704-b54f-f4f9fbafc044}} indicate that NLP functionality is not implemented by the designated composite function {{formula:aaebfa41-812d-4fb6-bc65-84fe62602415}} ; instead, it is formed by a single mapping {{formula:de8e0dca-938f-4000-95ef-56074f6e37ba}} , and essential structures required in NLP tasks are maintained in its transients for a certain period.
This property allows the transients to design the output dynamics according to the meaning of input sentences, which was demonstrated in the handwriting task.
Ref. {{cite:91bc476b4cb9e80801f52e3eb1c17277ec77d797}} also reported that optimal performance was not always obtained in the predetermined number of layers (e.g., {{formula:08f045f0-4fff-43f1-9a1a-18001d4e3766}} for ALBERT-large model), which is also compatible with our results.
Since the NLP performances were especially high when using short-term transients of {{formula:daa8a103-6876-4e70-973d-a6ef2c60a9a3}} , it is assumed that the discrimination ability of ALBERT for NLP tasks is enhanced by diverse trajectory patterns induced by pre-training.
| d | ee8b8f448e474159a0936734237df4df |
(1)
Branching ratio for the {{formula:fd577d77-f570-4e17-85c9-44dcbae46983}} {{formula:d6deef93-498b-44b2-8e5a-0e52bdfc4e13}} {{formula:25274ef9-d067-483e-a01e-4be0032b2f74}}
decay can reach up to {{formula:6edc6c07-a745-4ff0-8363-462b939e8a56}} with the pQCD approach,
which might be promisingly measurable at the running LHC and
forthcoming SuperKEKB.
For example, the {{formula:ed87171b-c3f4-4803-99bf-589f183341dc}} production cross section in
p-Pb collision is about a few {{formula:a0f86243-c80f-438b-9560-32c162be156b}} at the LHCb {{cite:916beccfaedabbe00241e8df5ee3e8edca37adc1}}
and ALICE {{cite:6cea18430965dc1dfa84a254378de9fb083f91a0}} detectors. So, more than {{formula:fb0fc298-276c-4048-9949-deb08282c933}} {{formula:80e03c44-f886-4282-b6b6-98f1b47a4825}}
data samples could be in principle available per {{formula:ce38cfeb-d65d-4966-8501-399bc65d3422}} data
collected by the LHCb and ALICE detectors, corresponding to a few thousands
of the {{formula:52fbdede-9be5-42f1-a932-c878a55de215}} {{formula:8fae4a87-908c-4080-a429-7c2e3f8b5860}} {{formula:3412d63e-a2f8-4029-8836-5dc00c5b13ab}} events.
| r | dc1bd966486a788c6b2b74de788c49dc |
To avoid ambiguity, we start by presenting the problem of our interest, i.e. robust SSL, and common fine-tuning methods for evaluating the learned robust representation. Then, we briefly summarize how prior attempts {{cite:f1999b915c2bd69d16ada3bece7a3a8d9a827585}}, {{cite:8b02b7b27a34263598a36d36b91350bc60e356e1}}, {{cite:96ba1f896b181aa5b279b0decb30c99b3a08abb8}}, {{cite:f86aa6aafeb56ab84850bbc21d6bb0d6ea44e778}}, {{cite:1a8718882031035b08581f980204b7be8ab5a135}} solve this problem in a single-stage framework. Compared with standard supervised training, either SSL or AT makes the optimization more complex, while simultaneously realizing SSL and AT clearly makes the problem complexity to an even higher level thus is difficult to solve. Inspired by the philosophy of the divide-and-conquer algorithm, we divide the complex robust SSL problem into two sub-problems: non-robust SSL and pseudo-supervised AT, and sequentially conquer them. We identify multiple important details that need to be configured differently for AT at stage 2 from standard SSL at stage 1.
| m | 72b2aa880aebf83afa2e34059a2b9d4d |
The initial literature search has been conducted in 2020 and was updated in 2022. The retrieved body of literature roughly covers a time span from 1995 to 2022. The distribution is heavily skewed towards recent publications across all hermeneutic circles. This underlines the radical change *tr has undergone, rendering publications earlier than 2013 mostly irrelevant for the current progress in the field. This is due to two reasons: First, in that year a paradigm shift in the field of *tr has led to the replacement of virtually all previous methods with superior artificial-neural-network-based approaches {{cite:f2a93c5a09487912faa9313eed1c8b5efc879a0c}}. Second, this paradigm shift has (re-)ignited interest in the research field, resulting in a substantial increase in publications. In consequence, we only include *tr methods from 2013 or later in our review.
| m | fb87e219444ad0585348564cec31052a |
The proof can be carried out along the same lines as the proof of Theorem 3 in {{cite:a6fad59ead1a13ea4c2c6551dda40c434cd3cd6b}} by noting that their equation (A.2) reads in our case (this is a consequence of Lemma REF )
{{formula:a9c7cb50-837a-48ed-b8f7-1f361ae09a6d}}
| r | 6b56dedb69d4fde7349ec71d27d0268b |
We will also unfortunately not have time to explore Bayesian model
selection. This allows one to quantify the degree to which the the
data prefer one model over the other using a quantity called the Bayes
factor. These have not yet been widely used in particle physics but
should be kept in mind as providing important complementary
information to the corresponding outputs of frequentist hypothesis
testing such as {{formula:9de597fa-9c8c-4391-b9f1-8f84f6a7c7fc}} -values. A brief description of Bayes factors can
be found in Ref. {{cite:b7f42fa66abb764b9a102967d07c40d59dbc951a}} and a more in-depth treatment is given in
Ref. {{cite:af5919ef80c8bf73d2890a77df503763f1f7e6c1}}.
| m | 3039f08208c90b5c49f302a2ae908feb |
For practitioners, this model offers a great flexibility with a closed-form density that is relatively easy to work with.
Only a few statistical models proposed in extremes literature possess a density describing the bulk and both tails {{cite:baf7e00f5505c215dcf12ab1f332fa689ca07dd4}}, {{cite:5257beebd4ff3ebea5d38b2c209cff0b5220f9d0}}, {{cite:ecf6aa45df3b7522ffa25ce350dc8f6f4fbfc13c}}, {{cite:d1492f6d83c53cafcedbb940573d3355f727cb4c}}. Extreme value analysis is still traditionally performed with block-maxima or peak-over-threshold techniques, which limits analysis to a tail at a time and avoids an all-encompassing model that describes the entire distribution {{cite:d8cf7474e4d5a3356f9d9d1e98db570eec30bd96}}.
The proposed framework also allows parameters in the BATs distribution to change over time, both seasonally and long-term. A stratified block bootstrap procedure was conducted for uncertainty quantification.
| d | 0e33d1b22b11402daa9233703befb36f |
Notice that, in the in-in formulation, there are two types of interaction vertices with time-ordering and anti-time ordering and the corresponding propagators connecting them in the dS bulk.
This is related to consider both signs for analytic continuation instead of our prescription (), see {{cite:55b43ac6af335e6de718467231fa45e9994bddf0}}, {{cite:6e0dc797f8ca974153681d581aa962810b160310}}.
Moreover, as in the case of AdS computations, bulk 4-pt. dS correlators can reduce to the evaluation of the product of two 3-pt. functions by applying a formula analogous to (), see, e.g., {{cite:55b43ac6af335e6de718467231fa45e9994bddf0}}, {{cite:6e0dc797f8ca974153681d581aa962810b160310}}.
However in such computations, further integrals over spectral parameter {{formula:ac6b5e02-514a-4ca7-8947-60a8cede3354}} are needed to make full comparisons with CFT correlators, which are usually very difficult.
| d | bb27e06d6f5c0cc1a661bfd49436decd |
We build on the characterizations of {{formula:80aefd96-fcea-4260-9191-6a8cedbbdbcd}} and {{formula:f546c3e4-913c-47f9-9c2a-c4864a9cfd4a}} given by Hylandand Wadsworth {{cite:092377c34a2aa34db67b1b43511a38e413113c59}}, {{cite:bebebf858f09628fcdf13132caa8c0ff9ec1731e}}, {{cite:e78f8fbb10a3eadab2513cf6e3704c3ed38a0763}} and subsequently improved by Lévy {{cite:5a7096f0b161b5ee0ad18b843635efa830a94b50}}.
In Section we give a uniform presentation of these preliminary results using the formulation given in {{cite:2420e4aa122b1bc001e6df6509095aa28466a386}} for {{formula:bd995c39-7bb1-4cff-a654-f83594cdc144}} , that exploits the notion of Böhm-like trees, namely labelled trees that “look like” Böhm trees but might not be {{formula:ec97dd3c-4173-459e-bd7c-215c13363f53}} -definable.
Böhm-like trees were introduced in {{cite:2420e4aa122b1bc001e6df6509095aa28466a386}} since at the time researchers were less familiar with the notion of coinduction, but they actually correspond to infinitary terms coinductively generated by the grammar of {{formula:ec5b8ebd-c71a-4da9-9a2e-bd35910242eb}} -normal forms possibly containing the constant {{formula:4b3bcd67-28dd-4324-bc94-25c16d59eb32}} .
It is worth mentioning that such characterizations of {{formula:8b34389d-fe58-4956-aa4e-5764ccf7f833}} and {{formula:7166f3a5-2319-4dcf-b810-f0507ac7046e}} have been recently rewritten by Severi and de Vries using the modern approach of infinitary rewriting {{cite:1b34036f9bb92ce4376edd70e923b0da5e06773f}}, {{cite:2692532a31dd24c2359df3070ae5573e85676229}}, and that we could have used their formulation instead.
| d | 913fb6a6f30a0c4f9c17ad27df6fbb2c |
Here, {{formula:41c54c24-4ede-437f-a7e5-d1888d819ac0}} is a matrix-wise indicator function that returns 1 for elements of {{formula:5280e882-632a-4ee0-b308-71b5be2d0d34}} that are less than 0 and {{formula:68e179de-5313-4e0a-8ef2-40b0117c900b}} returns 1 for elements of {{formula:e42846f4-7f62-412c-a7a4-57f5a10cfd21}} greater than or equal to 0. {{formula:d6b5ec18-59f6-4d67-83a0-c2549375c709}} is the Hadamard product. For readability, we refer to this operation as {{formula:84a440ae-5283-4d2d-aaaf-38adb2809f1a}} .
Inspired by {{cite:733a8b836c5c48ad71eb3da86b5554ff4e7a29ca}},
We add a small amount of Gaussian noise {{formula:028c8b90-e3a8-4db5-8a69-8f1b84b65482}} to avoid overfitting {{formula:dee9988d-4d3f-4816-9701-040618c76cf6}} to extremely specific values.
Using Equation REF , the final values of {{formula:913cb68e-b1e0-4433-929e-110dc00b5f7f}} , the perturbed version of {{formula:dc0a17da-7cd0-4c26-a67c-848b3ad58cf2}} , are thus interpolations between the original time steps of {{formula:adaab778-bca2-4711-b1ce-cffd3e67ee00}} and the replacement series {{formula:4d11e769-34cb-4aa3-b352-b14d639cf077}} or {{formula:d2f3d21c-eb57-42d9-b98f-ae6225c8fc8d}} where {{formula:8455762c-843e-444d-8f0f-8e50ad39b873}} is the {{formula:aaac8e16-3486-40db-9dce-20e28da8c7bc}} -th class in {{formula:0d85c20b-5102-4323-97ad-04506cd61324}} according to the scale of the corresponding value in {{formula:14759f28-2c6e-4ff7-b1ea-0b40cff2ba73}} . The conditional interval specific operations on {{formula:1becaaa6-659a-46f7-8935-59ced63f0953}} are necessary to derive evidence both for and against class {{formula:d38c2834-b73a-4a42-b469-52094aa01507}} .
| m | 2b1620da2f9c508753e324a6efb5b3a1 |
Driven by the promises of learning to learn, meta-learning has shown that automatically learning neural optimizers from data is possible, achieving results close to the state-of-the-art for the task of training neural networks {{cite:0950f36a210cbd90b50748ef61d7376a43e072c7}} or solving inverse problems {{cite:66f92a542a764108fe4882f3ea63ec94c6495496}} when the gradient of the objective function is available. Meanwhile, {{cite:f9ee46add622c9350829a1c31b3622c0b61eb86c}} have shown that meta-learning is also capable of learning neural optimizers that rely at each step on the value of the objective function only, without requiring access to its gradient.
| i | b387282415ab0822fa1fab3f32cc8568 |
To quantify attribution changes before and after feedback, attributions overlapping with irrelevant features were computed using four methods (see tab:attroverlap): Saliency {{cite:8343d77b044287e24fb2bac4a440ecfd251b42be}}, *deeplift {{cite:86bc8ea08eecd18c80dfbc8cdfbd800f1a0169dd}}, *gradcam and Occlusion {{cite:50050044c3a1ad80d49e7ad2878d2513e3347a78}}. Consider an attribution mask {{formula:46d43fc0-1d74-4295-9dde-e082d49d6233}} ({{formula:ede40660-ca8a-42ef-b56c-94463b3e143b}} is the number of channels that depends on the method and the model) of sample {{formula:a8df7571-04ba-4a15-9391-3867cd4a8de1}} for one of the attribution methods. {{formula:1ed23698-e8f0-4bbb-a37e-05c2ea8f3e6e}} is the number of samples in the test dataset with annotated explanation (not used in the fine-tuning process). The attribution overlap in tab:attroverlap is computed as
{{formula:cba1d6ac-495a-4a9b-a13e-272d91297f0d}}
| r | d7b22a2ad3e342e05156684a418cca06 |
where {{formula:be0210ca-0c31-498e-8eba-2d46d36488bb}} is an operating loss, {{formula:50f79b17-b920-4213-9177-b7c546ae6c22}} is a candidate probability function with {{formula:b26b71dd-7ee3-4c46-ad90-dd11c65a3bb3}} being the candidate probability of the {{formula:f808943a-7052-456d-8da7-921f4faffa31}} -th pixel, {{formula:09849de0-ff5e-4d56-9a05-ebc17e41fa82}} is a class of candidate probability functions, {{formula:828dc2c6-a7e3-48d0-a09c-da3d8a7f7ad9}} is a regularization term, {{formula:b11161a4-3893-4870-b232-7d561f90556c}} is a tuning parameter to balance the overfitting and underfitting, and {{formula:58eac9e0-27f3-4119-a0b5-a6392a96be28}} is an indicator function.
For ease of presentation, {{formula:df1b2c99-766a-48ef-9af5-613d889bcc1e}} is specified as a probability function and a predicted segmentation is produced by thresholding at 0.5, yet it can be equally extended to a general decision function.
For example, we may formulate {{formula:dd34ed4f-4456-4d58-b9ed-dd1dfc57a4d9}} as a decision function with range in {{formula:1237ed0c-d034-4da3-8e3f-e5bbdf89a8f3}} , and the prediction is produced by thresholding at 0, analogous to SVMs in classification {{cite:fd8071ce60119f339a4358341d96c17292d30d5d}}.
Next, under the framework (REF ), two different types of operating loss functions are considered, namely the classification-based losses and the Dice-approximating losses.
| m | f73985f20af28923a3508617fb4f29c6 |
Connectionism takes a different, brain-inspired, approach to Artificial Intelligence that stands in contrast to symbolic AI and its focus on the conscious mind {{cite:786823c8e647dbb1d4107644e0b07d621b4e034c}}, {{cite:3ad8fde58d9213d1b77aa90193dac14b4c53966e}}.
Rather than relying on hand-crafted symbols and rules, connectionist approaches such as neural networks focus on learning suitable distributed representations directly from low-level sensory data.
In this way, neural networks have resolved many of the problems that haunted symbolic AI, including their brittleness when confronted with inconsistencies or noise, and the prohibitive amount of human engineering and interpretation that would be required to apply these techniques on low-level perceptual tasks.
Importantly, the distributed representations learned by neural networks are directly grounded in their input data, unlike symbols whose connection to real-world concepts is entirely subject to human interpretation (see symbol grounding problem; {{cite:05adff8f386cfbd039ff7154ed85ac6ec60e78f6}}).
Modern neural networks have proven highly successful and superior to symbolic approaches in perceptual domains, such as in visual object recognition {{cite:e81a2bf1f41aacc3437e3878b1b0f34309488f4c}}, {{cite:cd6e132754931ec7f387ad770db789730f8c22cd}}, {{cite:3a3c42a0418182e4c74734733aa5bcb5d7eb6cf7}} or speech recognition {{cite:c6b1a1c04e964582058764f67fb196e7afc60643}}, {{cite:0ada096ba3630456ba38f2b91d3a5cf8b014c30a}}, and even in some inherently symbolic domains such as language modeling {{cite:a2c4fa23636277ce62c008eeac2ff1eacaa28c2e}}, {{cite:726ddd873de1ecb4edf4f827285b98270c68be71}}, {{cite:7f6d534f80c5e3d6858231ad549c874e66183309}}, translation {{cite:28a1c43dd552a3bf714e2838b49c2b8067e561b6}}, board games {{cite:748347e0caad620c9d3181e0b7fecd4713766c0a}}, and symbolic integration {{cite:e8640890b624e2b36dae98909cb6ced580af6d51}}.
| m | 874601a5a88d6847ec4c87b44668bde9 |
Let {{formula:aa3ecc93-5460-4527-9b6e-dd4cca9bd1fe}} Then {{formula:5cca571f-4468-4121-b0c1-3f50afda0574}} since {{formula:42b251cd-607c-41e8-b2aa-daaecf032dd9}} is dense in {{formula:44028d6e-f8ee-4ab2-983d-6f0258d31c8a}} (from its atomic decomposition). Define the functional {{formula:d53b692d-756c-433e-a81b-8464f7bb39a1}} by
{{formula:dfc622f2-bb2b-4c46-8fe8-6dc912b66611}}
We will show that (REF ) is a bounded linear functional on {{formula:d487ca5b-2314-46c5-b8b4-ddcfb03d5bb6}}
Linearity follows since the expectation operator is linear. Also as {{formula:e106a195-b475-400d-96e6-c8a561219660}} is dense in {{formula:bf3a44db-eb81-487e-b9f1-807916c5ed93}} , we have that {{formula:d26aea6d-a429-4eb6-9c9d-2e89d4e32acf}} is well defined.
As {{formula:6a329d1a-df55-4fe4-9641-6eb61a3111a8}} in {{formula:9bcb3f72-2fa5-4a1d-87d4-a713aa4df3ea}} norm (as {{formula:664f94ca-389c-49c5-ab20-f70602790b35}} ), we have that
{{formula:8bf59259-23c4-491c-9279-787898b835dd}}
Now for {{formula:a49a32ca-54e8-419f-a30a-bc3dce7214af}} we know from Davis' decomposition (Corollary REF ) that {{formula:9da88af0-833c-4e26-a31e-f656171f8b0f}} where {{formula:f0f24aa5-00de-46c0-8cff-207e727f40c0}} and {{formula:e635c760-3e8c-46b4-af66-003cb76155fc}} are martingales such that
{{formula:1d1fdd5d-4bf4-4cb0-bda6-c36a13246086}}
and
{{formula:101c15b6-04f9-4639-a410-44d14a03ed55}}
Hence we have by linearity of {{formula:b436fb0f-da5a-43d5-a72d-a0d2925d6e25}} that
{{formula:bbfc1b94-6c7c-45d8-a0db-585e6b3f55ff}}
From (REF ) we have that {{formula:9a781726-1566-475b-9ed5-0b1a503f9d7e}} since {{formula:c34c6f18-a437-42e3-a65e-bc8c666b1b03}} Hence since {{formula:72096cd0-0319-45c3-a3d7-63dbd395d875}} it follows from Theorem REF for {{formula:d3918b61-7537-4664-a490-57aeb78d1fed}} that
{{formula:e71a6cdf-17cc-449e-90c1-f553976d265c}}
Similarly, since {{formula:4788b572-b1de-433c-8566-b69f6d6fd60b}} and {{formula:5d370869-37e1-4c7a-a9f5-c1549803a861}} we have by Theorem 4.13 that
{{formula:e6238e7d-2887-4937-8a9f-1074d0e9b14f}}
Therefore (REF ) becomes
{{formula:88b0dd5f-5d6c-40d9-b932-af1176b97808}}
and thus
{{formula:16c984f9-b83a-4b63-b6f5-3a2dc635643a}}
It then follows from (REF ) and (REF ) that
{{formula:166f54e0-b47e-4a69-8f11-c9549367e7ea}}
In other words,
{{formula:84b8ef52-ef38-415b-93ee-256f721dfe82}}
Thus the functional {{formula:3a9dfe93-ae7a-4d65-875d-03e8f5a5e43e}} is continuous linear functional on {{formula:ef420f12-02c1-4af4-9174-07247c7d4150}}
Conversely, assume that {{formula:058af116-cb75-4922-b833-f6919cd39c23}} is an arbitrary continuous linear on {{formula:97beeb4d-3978-44e7-806b-183cc2c41427}} Then as {{formula:56d02caa-6e00-4158-b6ba-4d5f777e8052}} embeds continuously in {{formula:ef3cbc81-8936-46b9-8426-d9e2aca0488c}} we have by Hahn-Banach theorem that {{formula:089fe364-f933-4e45-a157-ed44755b579b}} can be extended to a continuous linear functional {{formula:e7b0063a-d548-462f-b300-2e3b11550022}} on {{formula:56111a86-c5e4-4283-ba2c-9b5104698259}} having the same operator norm as {{formula:4702d516-d2ae-4d4a-8217-568a5f597255}} It follows from {{cite:534428b852494c871cdb156b64110f4bf6fec525}} that there exists some {{formula:d95f71d5-c085-430a-9d72-361ae6d68c5f}} such that
{{formula:9f7b09ed-529a-45f9-86bd-c6a6ebe8f214}}
In particular
{{formula:bfdcdde2-2498-44ef-94ce-b6eb9b7b1816}}
We observe that since
{{formula:d4810e27-966a-4dc6-97b1-60aa2ff392c1}}
we have that
{{formula:abb539ed-a9fc-4484-bcbd-d0008842d263}}
Thus {{formula:032f1a62-dbb3-4918-bfe9-14941199f6a1}} Therefore {{formula:10387260-10bc-4e2c-92fa-45f177060053}} is also a continuous linear functional on {{formula:e464f8a4-4768-41c9-9ca4-35dddc6cd60a}} It follows from Theorem REF that
{{formula:45f72b32-cfd5-411c-830f-a9e1b99dcc51}}
We also recall that from Theorem REF , we have {{formula:493fa611-2f2c-4f85-8ee5-1ec6c3c126ad}} Therefore {{formula:08cab752-3fc0-4c3d-a752-00d945b3846b}} is also a continuous linear functional on {{formula:f7616e1a-eff0-4610-b8c6-25cd612a6e6d}} Hence by Theorem REF , for {{formula:bcb6dffa-2427-48d7-bfad-31c2a7a0f6da}} ,
{{formula:1abb7394-7f59-4bf6-8461-9a7b800c672f}}
From (REF ) and (REF ), we obtain that
{{formula:da0a6226-08f1-4f1e-9967-48d755b36a4b}}
and the proof is complete.
| d | 70fdfbb857dee05b92407425b276e61b |
The following theorem is a bit modified version of Theorem I, p.64. of Cassels {{cite:56f818d89e67f27eafbcad1f1b07c2190c4a7cbb}} and it plays a crucial role in this paper.
| r | bec5374537e203127850506b1d36ecc3 |
However, the rehearsal strategy relies on stored data, which is undesirable for several reasons. First, data storage is not always possible in practice due to safety or privacy concerns. Second, the approach is difficult to scale up to address problems involving many tasks. Finally, the rehearsal method is questionable in terms of the neuroscience perspective because the brain does not directly store data, such as all pixels of an image. As an alternative, generative replay (GR) has been proposed to rehearse past data without having access to them. In contrast to restoring the exact samples in old tasks, this approach uses a separate generative model to generate a pseudosample of old tasks, as shown in Figure REF (b). Deep generative replay (DGR) {{cite:6cb4dc1160f69efa2d14d4dbcd7420958029fd9b}} introduces generative adversarial networks (GANs) {{cite:708ae1d381400e1ea58ea552ae6029b3363a5e70}} to mimic past data. The generated pseudodata and their responses pertaining to the past model are paired to represent old tasks, and the data are interleaved with new data to update the model. DGR achieves promising continual learning results; however, the generator must be repeatedly trained using a mix of samples synthesized for previous categories and real samples of new classes. Therefore, certain researchers attempted to reduce the computational overhead for the replayed data based on DGR. For example, the deep generative memory (DGM) {{cite:0b3284e3828340ccf6d49ea2b42638b6f5d8f838}} approach eliminates the reuse of previous knowledge by introducing learnable connection plasticity for the generator. The approach designs task-specific binary sparse masks for the learnable units of the generator weights. The gradients of weights in each layer of the generator are multiplied by the reverse of the cumulated mask to prevent the overwriting of previous knowledge. Rather than replaying the real samples, BIR {{cite:e132d6768f14adbdbf3fa51da42dfbed9dfbe53a}} replays the internal or hidden representations of past tasks. The replayed representation is generated by the context modulated feedback connection of the network. GRFC {{cite:77a1ea17a967f07b1bca02c5a4c47f4fcb878469}} reduces the computational cost by integrating the generative model with the main model through generative feedback connections. In addition, because combining DGR with a distillation strategy can enhance the performance, the approach labels the input data of the current task by using the model trained for the previous tasks as soft targets and uses the resulting input-target pairs as the pseudodata. DGM, BIR and GRFC are more scalable than DGR in the case of complicated problems involving many tasks or complex inputs. It has been highlighted that reliable data help retain the corresponding past information, and thus, certain researchers focused on enhancing the quality of the replayed data. For example, MeRGAN {{cite:408023cfae36c129a994498208cef36238478c8f}} uses a conditional GAN, in which the category is used as an input to guide the replay process, thereby avoiding less biased sampling for past categories and generating more reliable past data. CloGAN {{cite:099fed1020b6782475017052e7d683bc8e68f2e2}} uses an auxiliary classifier to filter a portion of distorted replays to block inferior images from entering the training loop.
| m | f7a510ac5a0257b221a2d55df1cfa143 |
While assumptions like additivity and linearity could, in fact, be
successfully overcome in the algorithmic modelling culture, other classical
assumptions inherent in the parametric modelling culture did not likewise
magically disappear. It was earlier demonstrated
{{cite:9260c1083dd19818cacf6d9c852c83861bde1fba}}, {{cite:0744f0fc907ab8f97e2d3831592fdb660fe699a3}} that random forests rely on
homogeneous residual variances and, consequently, quantile regression
forests {{cite:d9bf898023cabdb71bbc9b16acd89976c9748c39}} are unable to adapt to patterns where only
the variance depends on certain explanatory variables. Here, we used a
similar line of argumentation to demonstrate that survival forests, or at
least prominent implementations that rely on trees based on log-rank split
statistics for cut-point estimation, inherit the assumption of proportional
hazards from the corresponding Cox model that defines the associated
log-rank score statistics.
| d | 67896fafe606dd727818cfffb682fb4a |
In first place, we reproduced the old results obtained with MSTW2008NLO PDFs {{cite:5499ad04134cb694f3b08aca8ac9f8d6d4959cc0}} and DSS2007 fragmentations {{cite:2430c3ac9cde38b96b00a8b9b3be76034fcbc353}}, but using the new Monte Carlo implementation within the LHAPDF framework. Then, we explored the effects introduced by switching to novel versions of the PDFs and FFs. In particular, we considered three configurations:
| r | 3c1b6f5ff949a5df6f7cac5cf3d7b8a4 |
One way to do so is through a process called weakly supervised learning (or weak supervision for short) {{cite:ea52a658bfed82c5dcd5b578ef4e40e6e3edd478}}. In this process, we ask domain experts to define labelling functions: rules that they think are indicative of a given class, such as “IF {{formula:1dd8429b-f5d0-488f-8e63-fa5df02f3395}} THEN {{formula:b8c0487c-637b-47db-b8d6-e8fd34a9ff22}} ” (Figure 1A). These labelling functions are applied to the data, resulting in a set of weak labels {{formula:510f931e-a5b2-48b9-b236-5bbb0f48f96c}} , which are then combined using a generative model, resulting in the probabilistic labels {{formula:7b49bc85-7cb2-4eb9-9e9c-6ee757bab7ec}} for all data points (Figure 1B). Finally, the probabilistic labels are used as a proxy to train a discriminative model that predicts {{formula:59103f44-2e66-46ea-8101-58e5dedefac7}} from the feature matrix {{formula:12f4cfa3-073a-4d02-bfb3-2897f76a047b}} (Figure 1D). In short, weak supervision allows one to train a supervised model using expert-defined rules.
| i | 4223978e83caa3d79d2313172689ad0b |
The results show that the 8/24 {{formula:79bf5ab9-5aa6-425b-b9b2-71d1cf019515}} m ratio decreases in many regions with high SSFR, in agreement with previous findings from {{cite:1e23d4fe0c39525cab68b7d66404ae5e5da2234a}}, {{cite:b5e25922f5623f9864b7f4c84eb59f9b05866e0b}}, {{cite:576a7b2183cdac720c3fa97f9dbfa8ebcd08d562}}, {{cite:6c1b11050b2c67dc471cfda2c1ceeb9cc9ea87b5}}, {{cite:fdf893f5cf8b5bfadbab2500bb3e03c25935b513}}, {{cite:4dfa0c3845b696e645ccd2fc3e9321d3bce9340b}}, {{cite:8adfb3d3b05ddd14be34b9db8b2be0b0b7b76668}}, {{cite:7da14b1b999756d406996d261d68b6945dea38e1}}, {{cite:ae9071588b005130a05096345a79dc8c66e56b44}}, and {{cite:860ed0fd467abdc7ee45a2c59cdd337233cab164}}. Even though our analysis is mainly focused on the 7.7 {{formula:be5dfdc6-85b2-4052-a452-8ba039c08c83}} m PAH feature that falls within IRAC channel 4, the results from {{cite:4dfa0c3845b696e645ccd2fc3e9321d3bce9340b}}, {{cite:8adfb3d3b05ddd14be34b9db8b2be0b0b7b76668}}, and {{cite:ae9071588b005130a05096345a79dc8c66e56b44}} suggest that other PAH emission features may also decrease relative to hot dust emission within star forming regions.
| d | d3820cbf885588353fc93e3f06767a02 |
Early SSL approaches—e.g. Scudder's {{cite:fe33beb248c94a313a1e672adec86e8a67527576}} untaught pattern recognition machine—simply replaced unknown labels by predictions made by some estimate of the predictive model and used the obtained pseudo-labels to refine their initial estimate. Other more complex branches of SSL have been explored since, notably using generative models (from {{cite:630256c1d55d3d3234522ec78e47676f7fdbb49f}}, to {{cite:cd82da62cb608c5ac94809c639660d2d549aedde}}) or graphs (notably following {{cite:4b8610d082fecfa158d390b9057d49fac2d64a07}}).
| i | edc1e9870ea9aebcdcff1a6a63189d7c |
[leftmargin=0.4cm,rightmargin=0cm]
In this work, we exploit local and glocal clues together since use of both local and global visual features play a critical role to disentangle the weaknesses of each feature with other's superiority. More precisely, local features tend to attain better performance under severe scale, rotation and translation changes {{cite:426e8fd94e926433275baccb53d7de15ad0b3dd7}}, {{cite:cd4f630a8599682d087eea33043d66d7d9b668ea}}, {{cite:f8fe2068c9e6390bd72e235109de3183fb0fe98f}}. In similar, global descriptors can yield superior results on semantic tasks by the fact that they mostly rely on the part-based visual representations {{cite:bebe44232e1157bb3c61720c2132153f0bc8d9e2}}, {{cite:b8d52a8d9ddc1d22e4866bc140bdc1991835402a}}, {{cite:aed8754fccf8105cadd706b7cf2cca2ee15b8bce}}, {{cite:3c8cff6e460bcdf69496650f46873acb22359baa}}. For this purpose, we lately fuse the confidence scores of local and global descriptors computed for the same scenes with a novel fusion technique. This scheme is inspired by the notion of query expansion {{cite:f5aedafab2dc921dc62334b48bfce093bd81d613}}. In short, the features (either local or global features) tend to reflect a similar error characteristic for the queries after some ranked points. To this end, the proposed method is able to normalize the confidence scores of both local and global features and fuse in the final ranked list by adaptively selecting a settling point for each individual query.
{{figure:98b75173-aab9-40f1-885e-07b05a0d0fd0}}
In particular, utilization of local and global descriptors for retrieval scenario can contradict with the low cost computation constraint. Hence, we introduce critical improvements to the commonly used indexing and global pooling techniques, namely, Product Quantization (PQ) {{cite:8133cca1f45102c73961133f31b05d11e1b10fa0}} and Compressed Fisher Vector (CFV) {{cite:48d0035e9f2f91e5aa6a8f437682bf79c15fb403}}, to balance the workload and to promote modest visual description. In short, we propose a non-parametric score function to compute the probabilistic similarity scores between local features of query and reference data in an asymmetric PQ space. Ultimately, this function enables us to assess the quality of matches by the probabilistic scores than Euclidean distances. Furthermore, we replace hand-crafted features {{cite:426e8fd94e926433275baccb53d7de15ad0b3dd7}}, {{cite:cd4f630a8599682d087eea33043d66d7d9b668ea}} and sparse keypoints {{cite:426e8fd94e926433275baccb53d7de15ad0b3dd7}}, {{cite:f8fe2068c9e6390bd72e235109de3183fb0fe98f}} with densely sampled mid-level convolutional features. Note that this step still has the low computation workload, since deep features are densely estimated. In addition, semantic content can be depicted more precisely with deep features {{cite:aed8754fccf8105cadd706b7cf2cca2ee15b8bce}}, {{cite:5ee0628e5e31db2d5b8d929315cf18bdcc90fe49}} which differs from the local feature content (relevent to the goal of our work). Last but not least, we apply an approximate binary nearest neighboring search (NN) to make querying up to 6x faster for CFV with a minor decrease in the accuracy.
To this end, the proposed method enables fast query and low computational workloads for large-scale datasets while outperforming the baselines by a large margin.
Lastly, the ground truth annotations for Stanford I2V dataset are updated by the retrieval results of the proposed method, thus more reliable performance evaluation becomes possible for the future works.
| i | 3130b59f34ea7f09f0b42df2fca5ace8 |
In Figure REF we show the quantum average power as a function of time, for a fixed external constant bias {{formula:f010ac2c-3cd6-447f-801b-ab2eec099123}} . Different curves are obtained considering different approximation schemes.
The choosen initial conditions and the finite external bias are responsible of a finite value of {{formula:ec6c061d-120f-4ec0-ac1d-33545f02febb}} .
For long times, the quantum average power vanishes, in all approaches, when the whole system reaches equilibrium, as one would expect for the case of constant bias.
This feature is clearly visible in Figure REF in all curves for sufficient long time.
On the contrary, the transient dynamic evolution towards equilibrium shows different features for the three approaches considered here.
In particular, the master equation approach in the full secular approximation {{formula:ccaea5ac-4e5e-46eb-824e-557666f08a08}} (dotted line) is able to capture only the exponential decay towards equilibrium.
The quantum average power {{formula:a9644721-a3d5-48dd-8944-c64c1e683b56}} shows an oscillating behaviour if one consider the path integral approach {{formula:ba3a86e7-b07e-4a1b-982e-17ae29c34439}} (solid line) or the Born-Markov scheme {{formula:6dc89ebc-fd8f-4768-b918-ad9f3d2919b1}} (dashed line).
In passing we note that these different behaviours (relaxation decay or oscillations) are analogous to the ones obtained in similar approaches for the population dynamics of the dissipative TSS {{cite:1f85a0bb4beb2b754324e5f30a34b0a9fada4717}}, {{cite:355ea23920061fbdbbc745fc8ccd78083877fbf7}}, {{cite:933d7a5ed8938c51aa68304ec5e4b769a3bd7e2a}}
{{figure:81965698-e514-40db-b346-d558473993ae}} | r | 4e261731d62f1a5f4f13610ca87431ce |
The fact that the dynamical behaviors portrayed by neurons are remarkably complex, demands the requirement of statistical tools to study and quantify their complexity. Measures like spatial average density, and entropy are effective tools to study the complexity in the dynamics of neurons. Banerjee and Petrovskii {{cite:88d4c97f008a06906b355266543884cfd80e0e68}} applied the spatial average density approach to show that the spatial irregularity in an ecological model is indeed chaotic. Similar approach is considered in the reference {{cite:cc1c115678e2d75e2593486c0cf013926cdbf19f}}. Entropy is an ubiquitous concept first introduced by C. E. Shannon in his revolutionary work {{cite:47d291743833e2328b4e94b6cfc005f36dc8ed45}}. Since then, it has had a widespread application in various domains of research, including neuroscience {{cite:3eea207814ac4d0d0b357666fe852f3fc3ac076e}}, {{cite:432f2d1a5e815d01f23a3e4dee2ead7d5c3ef299}}. In another study {{cite:c1864215e1dbe7c8bfac80018169e8d10e982503}} authors report the study of applying entropy to EEG data from patients and report that Alzheimer’s disease could result in complexity loss. More relevant paper {{cite:50edf9b3ecc411c245ac107069bef8e90472461a}} related to this topic can also be found. Other applications of entropy in neuroscience include study of topological connectivity in neuronal networks {{cite:491e03bbd48ab8c01ed87c88ef5c813fabb984b8}}, {{cite:9548ee575d783c103dba600f205c84375a6b9e43}}, {{cite:0769a7c521869046a9569cab5b0bc6b5d2cc3863}}, and estimation of the upper limit on the information content in the action potential of neurons {{cite:62cad79d0e3cce54a3c9bc2ebdfeaf671b79a782}}. Motivated by these, we utilize the tool of sample entropy {{cite:fb3bca8242f09279b676d8e4a9a082724fed01c3}} to analyze time-series data of the spatially averaged action potential generated from our model and study the complexity of the dynamics.
| i | dce1382410e4a864d44aec04d3faf173 |
Thus {{formula:8ce4ea28-8500-4ccd-a99d-943ebc1c85ab}} in our sample is not significantly correlated with {{formula:7b7256dd-612c-4df3-8efb-02bd47a358fe}} , but it is with {{formula:5ecc2809-b27e-405b-8705-4f4a780b2508}} at {{formula:e8b47cfd-9192-4090-b849-0f82f60fce96}} 99% significance. This indicates that changes in the covering factor are driven more by changes in the Eddington ratio, rather than by changes in the bolometric luminosity. This adds to a growing body of evidence that there are large-scale changes in the SED with {{formula:628c3c84-2b39-4845-b38e-7e3c91daf777}} {{cite:90ec0d496efe26266cd40e3fca41ef7fec7dc059}}, {{cite:c5bde3b297fe176bac2e332416eb8aa6965eb783}}, {{cite:14128606a556d49f8346abd79bf8864935e3a220}}.
Therefore we find that the most basic of the unification models in which it is proposed that the observed AGN properties only depend on inclination are too simple, and there are changes in the shape of the SED which depend on {{formula:65a9e17c-c084-4112-9706-5db269b71447}} , as well as M{{formula:82c2c4df-d6c7-4f44-8ab3-b868ac26fbe6}} which sets the overall luminosity scale. However, the anti-correlation of the dust covering fraction with {{formula:84da6ecc-d244-4a66-9772-8fa21c782526}} rather than {{formula:50a4f798-2a30-480b-bd43-efa9076156b9}} indicates a change in the larger scale geometry of the AGN rather than just the expected response of the dust to increasing illumination. Such a large-scale change may also be required to produce the observed anti-correlation of the forbidden series of the narrow emission lines with {{formula:f01888a5-fbee-4619-a737-36bf8dc55026}} , as Narrow Line Seyfert 1s and other high {{formula:777e27e4-4f72-48ea-b4bd-92c0da2fb906}} AGN are known to have weak [OIII] {{cite:831ad383fa73f3b9aa3ddf9ca2aec8e77c4d6d3b}}, {{cite:42471445edf67a76e0dda759979da744222cc581}}. Furthermore, {{cite:e64cbee6e6f6362ac44d602a7cb5a2076f3a189e}} speculate that this is due to the very inner regions of the accretion flow being progressively shielded by a wind, with increasing {{formula:74c50826-a7ca-405b-a1e5-4baf5621109d}} . Thereby even if there is copious dust present, the irradiated fraction decreases as the ionising radiation becomes more collimated, and hence the reprocessed fraction drops. {{cite:5c9bd3cf55cafd586432d67485cea6061215af56}} have discussed the fact that efficient coupling of dust to gas boosts the effect of radiation pressure feedback. The result is that absorbed AGN are mostly found at low Eddington ratios. Here, we are seeing a decrease of the (illuminated) dust fraction in type 1 AGN. The effect could be related to that noted by {{cite:5c9bd3cf55cafd586432d67485cea6061215af56}} in absorbed AGN, with the feedback in our sample occurring out of our direct line of sight.
Conversely, if the bulk of the MIR is emitted by dust located in the polar directions, then this result relates to the relative efficiency of illuminated dust emission in the line of sight.
{{table:6f079717-f430-497f-83ab-e87b9359935c}} | d | d8950aa38c5d5ecbdc40f37b1290587d |
The original paper of Kalman, which is arguably the first systematic
presentation of a methodology to combine models with data,
is {{cite:6582d7a2e78331fdf29520b85fb82a4fe814f39a}}. The continuous time analogue of
that work may be found in {{cite:b3a78a4340b0f3169ad1667edcd311226af5914d}}.
The book {{cite:ba3bbfa539944477dbb0335786066fbf8b2aa130}} overviews the subject in the
context of time-series analysis and economics.
The proof of Corollary REF may be found in {{cite:847cf9a1b03f11b523de2967fd35d7c461d4ac63}}.
The paper {{cite:35ba88a047ec2aa7f987e3c183ef87fa09326431}} contains an application of the
optimality property of the Kalman filter (which applies beyond
the linear Gaussian setting to the mean of the filtering distribution
in quite general settings).
| d | c5753d037043b67a05244d45675d5e97 |
Subgraphs can naturally be more informative than paths
in capturing the structural information {{cite:9d294d6d03674cce2dae35d55c934e007a41301d}}.
Their effectiveness has been empirically
verified in, e.g.,
graph-based recommendation {{cite:e6113a3669360e634e8b69478caa06b39b978015}}
and node representation learning {{cite:3d151b5abbf6f29aabc23f5b9330e4edbe42ff1a}}.
With the success of
graph neural network (GNN) {{cite:f10321f989e815eb5c96b71aacb5d97f7b16c9cf}}, {{cite:bca22700aa97476a4c2fb04af7ef3f961a141bfa}}, {{cite:00ad7dd26983745a3dcb1b45e77967cae9a8076b}}
in modeling graph-structured data,
GNN has been introduced to capture the subgraph structures in KG.
R-GCN {{cite:422468316a9117b1cbb61db6f425bddab571b955}} and
CompGCN {{cite:b03fb51dd216315e574c2f5d57be47bd5c836237}} propose
to update the representations of entities by aggregating all
the 1-hop neighbors on KG in each layer.
However,
it cannot distinguish the structural dependency of different neighbors
and cannot be interpretable.
DPMPN {{cite:c953a870bca8ebb024808c60000eab396aa7e273}} learns to reduce the size of subgraph
for reasoning on large-scale KGs
by preserving the most probable entities for a given query
rather than learning the specific local structures.
Recently,
GraIL {{cite:3ce0a45ea521da93b92bcd50565493d8321543eb}}
proposes to predict relation from the local enclosing subgraph structure
and shows the inductive ability of subgraph.
However,
it suffers from both effectiveness and efficiency problems
due to the limitation of the enclosing subgraph.
| i | 15d6827794152c0c70eb92acdc74d878 |
Complex systems have undergone intense, interdisciplinary study in recent decades, with network science {{cite:cf11ba1e4e187e19061489b646d80856f46b2c76}}, {{cite:5a0334a79a90e575b8c80cea9a37501964830182}} having emerged as a viable framework for understanding complexity. While early studies in network science tended to be limited to lower-order structures like dyadic links or edges {{cite:f9bcfd9fb8598ba54739d873c256f4f853275933}}, {{cite:2e6796e4d781c3caf6dff92c7744991fd90c520b}}, {{cite:79aec5daf8fb8261a9217b76c65a0abee51fc2ae}}, {{cite:f99bb067327f704a52af72a0b1aeeb4d49794a0b}} (and later, triangles), a recent and growing body of research has revealed that deep insights can be gained from the systematic study of non-simple networks, multi-layer networks {{cite:d5ef88b8d689cb60ce6f8f59d16f20913982f0cc}} and `higher-order' structures {{cite:639a41b233dad4ca9ed09f2bf05350ee690b390a}} in simple networks.
{{figure:9e7e65f0-d302-40c6-ab59-6ab15c7f1359}} | i | cd37dee551cf32af419da091940c7d87 |
The formation and evolution of voids is well-understood in the
framework of gravitational instability {{cite:50dd4a844fd3e88f22f553edaedecc91862e7b90}}, {{cite:cdb94ac08a0ff3848fb73d1500372dc56759832f}}.
However, when one compares void properties of observations and simulations based on
{{formula:3986d5f7-78a5-4d7d-be94-2e79b41114dc}} CDM, certain problems still remain to be better understood.
By definition, voids are devoid of galaxies
or contain only a negligible number of faint galaxies. The
perplexing issue is that we do not see a large population of
low-mass galaxies populating voids ({{cite:1ded46307e43a53e58702e618dba3f2a3a84cb6a}}; {{cite:9292f1f8b1054849036aecc6878f40a3db81e4f5}}),
and furthermore, the void galaxies that we do see are basically
representative of the general population {{cite:502613e00a3a3e8f42ca1724ad231296decab763}}.
| i | 47ac05c3f721d69f9f8b8ba2406a4c5a |
Sign-concordant feedback was also crucial to performance, consistent with the idea that “vanilla” feedback alignment does not scale to deep networks {{cite:39fe71b3c2201e2f81abaf3b0093b2d142551596}}, {{cite:00f636671b556f96f135e05ca2ea9039caff3864}}. An attractive possibility is that the segregation of biological neurons into excitatory and inhibitory subtypes permits cell-type-specific wiring that promotes sign-concordant feedback. However, the adverse effects of enforcing fixed E/I connections (Figure REF ) represent a significant obstacle to biological realism. Our experiments show not only that unconstrained neurons continue to switch between excitatory and inhibitory modes throughout learning, but also that the freedom to do so is directly connected with improved task performance. Developing further understanding of this phenomenon is important for understanding not only the brain, but also the learning process in deep networks.
| d | 93d7d056a5c8ebb66e1607e815982d3c |
where {{formula:cb762a32-ae3e-49b2-8569-a7836510acf3}} is the transverse momentum of hadrons, {{formula:5e26bacf-2ecd-4c7d-ae3f-e0b015da7972}} is the number of constituent quarks {{cite:2b07e272abb673b98f2b58364e669e316202ade7}}. The {{formula:3b3494b5-5a7f-425f-b2ac-6ed46a149c61}} and {{formula:d21bdc8d-3254-42e2-bd78-f95d027be90f}} are the {{formula:b2656f1d-a7af-4cc7-a831-3f11c07469ad}} of hadrons and quarks, respectively.
We have plotted the {{formula:85cd7917-9b6e-469e-a2b6-185d75d06961}} scaled {{formula:d4b9b8a0-46d0-47b4-9990-68a775ada9a4}} of hadrons as a function of {{formula:6a4a58df-561d-4eaa-b329-9c659f1cf055}} for different identified hadrons in Au+Au collisions at {{formula:2cc49cd7-81f0-48bf-90f5-06ef2e216793}} = 19.6, 39 and 200 GeV measured by the STAR experiment. Under the assumption of hadronization via quarks coalescence, these {{formula:df2e3513-6bb1-447d-bf30-a92c6eab92f5}} scaled {{formula:0c225d6b-5bff-4335-8658-a8059119382c}} of hadrons as a function of {{formula:8b7bca46-a00c-4121-8f23-5e976495bcce}} are equivalent to {{formula:118522ed-3d40-44ed-8a96-9a979071450e}} of quarks, e.g. {{formula:043ebc47-b25e-47da-9305-832fead2da8a}} scaled {{formula:48fa0ea2-3d5f-4acb-ab95-6dc796fec032}} of {{formula:58740c4d-9742-4eea-a545-6187429415ac}} meson will give {{formula:17573204-d28b-4a95-8342-d7c2e9cf6343}} of strange quarks (assuming quarks and anti-quarks have the same {{formula:88b2cc74-69ac-4038-b8fb-718a8d4ef150}} ).
{{figure:e3e593ce-ebdc-4f4a-b405-980413d9748e}} | r | 050b0752cbd86fd2856183ac6a3bec97 |
Let us start with the calculation of {{formula:bb738933-d0a1-410b-b591-1496811be82b}} -particle (where {{formula:56e5fd2a-0b34-4ba0-bd9b-65af10e91d53}} ) azimuthal
correlations {{cite:a94af29142c35139789c04343a492c954538ebb6}}, {{cite:a716f05413b1f18068979cdfce349255dfc0e139}}, {{cite:8dd0cac5adeadb3133a14ebec9d7ef29d0276237}}
{{formula:167fc5aa-cd98-49f2-80ce-41c4ed60a9d4}}
| m | 3ff5abcd442ec4594ae7773c0974d9db |
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