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A final application of {{formula:e54bbb68-49e0-4657-bb35-92502b2e1c6b}} -graph calculus for Legendrian weaves develops the connection of symplectic topology to V. Fock and A. Goncharov's cluster varieties of framed local systems {{cite:383b54b26f3ee8a896892710cffdd39f9d9e654c}} (see also {{cite:5d0f6f3d2877584412c88a786052ca77d00f87ec}}, {{cite:f7be297c423bbb7c7c4ab9298e345759d75f921e}}), and should relate to the spectral networks of Gaiotto-Moore-Neitzke {{cite:3415fde9e57aa39215e180cc19167481d47b2569}}, {{cite:9c7f81a5e10a9ed97b578abfd51f97ba8aadbcf3}}, {{cite:56df939188a5ced3419c4108d9cd07939c4a5b0c}}. For that, consider {{formula:6c38dc30-9ad5-4eae-933f-9a5667d06eb3}} and {{formula:b7e7c3ee-4e4d-41b1-8bd2-ec08b3053a72}} an ideal {{formula:a69d1831-172d-4fce-b516-d025ccd665bd}} -triangulation of the smooth punctured surface {{formula:07c0a43b-6a35-4cbe-ad8a-dc641c8a3ade}} . In Section , we present a new construction that associates an {{formula:1ae7a89a-fea3-4883-b732-b7031d80c4ae}} -graph {{formula:de4b516c-46c1-478a-acb9-0740e90c5e95}} to an ideal {{formula:f9a4f1b5-41e8-45ca-9408-b57b353a4447}} -triangulation {{formula:9e6fa3eb-8c51-4667-ab22-cfb238943ff1}} . In particular, each ideal {{formula:e68289fc-ce81-41a1-91a6-012b002a2bb4}} -triangulation {{formula:19421958-3845-4a93-8b21-be59816ce7a8}} yields a Legendrian surface {{formula:4303e494-8c40-4589-a64d-f90ff8972471}} . In general, different {{formula:7325bd55-6bec-4f2f-82a7-311b6f492fde}} -triangulations lead to smoothly isotopic Legendrian surfaces which are not Legendrian isotopic, and they are distinguished by their flag moduli space {{formula:ff421d6a-71e4-4073-b52f-d281f4d276a7}} . This also relies on the connection between microlocal monodromies and cluster algebras.
{{figure:a07db43f-125b-465a-9873-532b5e7fd1ab}} | r | bd12b331b23dd178c075ab117f4c91ea |
In this work, the perceptual network {{formula:e1c356fa-6a5d-46ee-91cb-c4a9b6632608}} is a pretrained VGG16 net {{cite:25b36db187bbd4cff87e0f8337cf78a9b806a699}} and we empirically find that {{formula:009564ed-fa65-486c-ab13-34378157c274}} works well.
| m | f8557ed6f6d0d25b32ceb65f539fdb5e |
Stability. The RTI implies an obvious explanation for the need for IMP for stability: only when the network is stable enough to retrain to a similar region can we find lottery tickets. Our results in section confirm this by looking at the large-batch training on common vision tasks. This reinforces the hypothesis of {{cite:295034d90a64925642f968a310fb8d93fff6a90b}} that finding lottery tickets is possible only when resetting to a state that is stable to SGD noise.
| d | 4ae2223ccef5d52eae946716340b5d8e |
We also compare with several popular zero-shot KD methods, including
Meta-KD {{cite:d8bb79a804af9a7d79ef01d8cee3f2e221c7896d}}, ZSKD {{cite:726e88d9cf610dd477923e2f905808f11c5f5038}},
DAFL {{cite:d007ad1110db641161f2ae964c44140502600320}}, DFKD {{cite:6d32333f39b8216c251a2a38b83d67706e549a04}},
and ZSDB3KD {{cite:5e34477aeed7398c3299435c96a496fe45898b51}}.
| m | 66313040837010c7c6e6e58416d794da |
A thorough research framework is established in {{cite:b98b1061f30951b22b70d12ffedc06be5baaaaee}} pointing out principles concerning deep neural network theories. Tacit knowledge represented by user characteristics may be quantified with mastering level of these principles in {{cite:b98b1061f30951b22b70d12ffedc06be5baaaaee}}.
How to measure these user characteristics and what dimensions to focus on remain open problems for future research.
Ideally these user characteristics are exactly the set of all features related to user-specific modelling issues, which constructs a user-specific mapping from data to its optimized algorithmic model.
| d | e37f8dc5366dad73dd05f8335e803664 |
According to the experiment results, MACRL shows better performance across different benchmarks. Moreover, we show that the learned representations from MACRL can be tuned more easily and efficiently (e.g., better accuracy within less epochs). Furthermore, we visualize the attention from the pre-trained weights using the method described in {{cite:932302725df8acc7b9a64d356d0ea4eea2650d29}}. According to the results shown in Figure REF and Figure REF, we can see that MACRL has better interpretability than MAE and MoCo as MACRL focuses on the objects in the image, especially the key components. However, MAE and MoCo present scattered attention over the image and do not have a clear emphasis on the salient objects. Furthermore, the visualizations show that MAE and MoCo focus more on the background in the image rather than the foreground object. Instead, MACRL pays more attention to only the foreground objects. Additionally, we observed performance drops (e.g.,fine-tune, linear probe accuracy, and visualizations) for MAE and MoCo when they are applied on smaller scale datasets using lightweight network structure. Whereas, MACRL still maintains good performance given smaller-scale data and smaller model size.
| d | a70bf97a5b6899958d7fcae06e28b339 |
Golub and Van Loan {{cite:59189020d85cef97bcadbd23a9f3e69f88ada3fd}} took errors of {{formula:0d26f3ec-dd5b-4181-a1d1-41e5659abce2}} into consideration and established the total least squares for matrix linear equations. It is aimed to solve the following problem,
{{formula:788db429-e319-44bd-8630-876bd4b0700b}}
| m | 320957d14bb17014257ae2c903b4bafe |
The attempts to detect early warning signs for critical transitions
are based on the concept of a deteriorating environment as embodied
in a changing parameter {{cite:1d65f749a2dd0f4afdb317ed2530d97f378f8a46}}, which is a different kind
of transition than one which is driven instead by stochasticity in an
environment which is otherwise constant and exhibiting no directional
change. When trying to use historical data to understand critical
transitions we often do not know which category, changing environment
or simply chance, an observed large change falls into.
| d | cb24edf3721c1294f5f365e4e7bbcf08 |
The ability to continue operating in an environment where partial failures are to be expected is a core concern in distributed computing. Checkpoint and Rollback Recovery (CPR) is the most widely used fault tolerance strategy for DSP systems. It improves the overall reliability of streaming jobs executing within them as well as the integrity of results. This can be evidenced by its implementation in many of today's most popular streaming platforms such as Storm{{cite:e86df8f3ad227bcd152295e2264938a57a881c93}}, Spark{{cite:91e741e3aadf89c0fdd8f9abb45e7986fb6e66c9}}, and Flink{{cite:e91d3422e373bdd1dc7cb4d5aacf767c05e6e60b}}. This strategy involves creating a snapshot of the global state contained within the system and saving it. This is done so that, should a failure occur, the individual worker nodes can be instructed to stop, rollback to the latest save-point, and continue operating without the job failing{{cite:2eb5be26fd9d5cc7b44da91dd2bb28d0307b6ea2}}.
| i | 37937c7006de105b08c04d8bf9c2b0bf |
Corollary G.2 (TPM, from {{cite:0ab8b11e0f58eb7f6fd6d2998a7e126af2366202}})
Let {{formula:40dd34a2-6cef-4593-b4cf-d239c48e6247}} be a constant and {{formula:54509e67-4e79-493e-b577-9f9da802ed75}} and {{formula:a0f0de3f-769a-47c3-bef4-2a49d02fce22}} . Let {{formula:1e7e0f37-1580-4fca-b913-017883764e3a}} be two positive sequences updated as
| m | 5e49f978cbec8bf59f3e54d0f9abb815 |
Let's list three equation we are going to use {{cite:a0ddb352ac56ac2c14f7d39ae5ef5236cf949957}}, {{cite:ab73ac2a3cb4a5710087673f8725580c5e3394a9}}, {{cite:adbb027dfe02226bf74ce192819a0a77c7e5ad8d}}
{{formula:b89a720b-89fd-4f8f-bd9d-603d803575bc}}
| r | e45b0c4c003cc200b7ff7fc4c3ec16ae |
We used two methods to train our models on word embeddings, Fasttext and N-Grams {{cite:6ea61fe418cabd80b5abe77adc9d7c06023b845a}}. Fig. REF shows the working of modified N-Gram model used in this research. The n-gram model converts the document into tokens and stores these tokens in a dictionary based on the co-occurrences of words. That is the number of times a token {{formula:e7b08194-072e-4be2-bb4c-67dddd25885c}} appears next to a token {{formula:b2b41502-ecb8-4e95-b080-83fe709ab301}} is stored in a co-occurrence dictionary. Against each key there is a are multiple word vectors with the probability score of its occurrence. In fasttext a document is tokenized and passed through a network. The network learns weights which can be extracted as word embeddings. Fig. REF shows how words are propagated through the network to extract embeddings for Urdu. In next sections we will discuss in detail about the dataset, experimentation and results.
| m | fd302720d49443285a7ebb767414a702 |
In quenched QCD at high temperatures the spectral density of eigenstates
(of the staggered Dirac operator) shows a square root behaviour
{{cite:a143bd19b684d7dbeb10a905d036ffa6be96bb73}}, and the delocalization energy scale has been
empirically identified using the inverse participation ratio
(IPR) {{cite:c387d6f73fee877b9f5a041ffa0cc11acc082fc5}}. A clear correlation between the space-time
density of the localized eigenmodes and the local Polyakov loop has been
observed {{cite:b2ef734cbcda2afef43d7ed10b949befe4720d68}}. The modes close to the mobility edge
possess a multifractal structure {{cite:d8133cf3dae5b51b38e65c6bb9535a3c12185835}}, {{cite:31108e720e564ef27d6edcaa922097e72691bd57}}.
This has been shown for both full QCD as well as in models with orthogonal
and symplectic universality classes {{cite:69f51f86238a6994f770c62e7742b9bc243c3dcd}}. The critical exponent
of this transition occurring in the Dirac operator spectrum has been found
to agree with the critical exponent of the corresponding Anderson model
{{cite:149fc596d2916e8a7f7d9b173340410d264eaac4}}, {{cite:5e4e6c28af498713d848365016ed692e30a5bf4e}}. Fluctuations of the Polyakov loop
and regions of exceptional self-duality have been identified to act as source
for mode localization in the case of Möbius Domain-Wall fermions
{{cite:cf8196f6f48f1376cbacebc8640d586444c1a456}}.
| i | 1e685a7cde1c1629fb959a0771ea3ffb |
The first round (Round 0: Key Exchange) is similar to other protocols such as {{cite:a140589bde377e15b5ce236af049ac93ca7d29d4}} and {{cite:a002acfed4ca3ad4f8486fd354b5e5e527fdb0c8}},
and only involves standard PKI and symmetric key encryption primitives. This round does not need
to be executed each time a new secure
aggregate is computed, only when new nodes enter the system, which we, as previously mentioned, assume
is a rare occurance. Shared secrets can be exchanged in this step as an optimization but they can also be shared
as part of the aggregation in the following step.
| m | 136332d3adb109be5719ac0c936b4765 |
CIFAR-10 and CIFAR-100:
The MEST accuracy results are shown in Table REF . We include the results at sparsity ratios of 90%, 95%, and 98% with unstructured sparsity scheme.
Methods that use dynamic sparse training (DeepR, SET, and DSR) achieve slightly better results compared to fixed-mask sparse training.
Compared to MEST (vanilla), which uses a fixed mutation ratio along with the training process, our MEST+EM consistently achieves higher accuracy.
This proves the effectiveness and importance of our elastic mutation method in sparse training.
And our MEST+EM&S further improves the accuracy significantly, especially in extremely high sparsity ratio (e.g. 98%).
In terms of peack memory footprint, Lottery Ticket (LT), SNIP, and GraSP are equivalent to dense training.
Because the SNIP and GraSP require computing the forward and backward propagation of a dense model to find a desired sparse structure.
The LT method requires an iterative magnitude pruning process to find the “winning ticket” sparse structure first, it is also considered the same as the dense model in an end-to-end training scenario {{cite:e753fa01bf5c35b956128e29f1d479931a44a2bf}}, {{cite:e6bd0da1918ba587aa66497721e4ed86460be486}}, {{cite:fd86f3e9588d1e01be0361cb08626e47d4ee0a58}}.
The VGG-19 results are in Appendix .
| r | da57c33ee0489b8393fee710a418b2cb |
Settings To demonstrate that the proposed SLIM is able to disentangle the high level semantic attributes of featres at different scales, we conduct the style mixing experiment as done in the FastGAN paper {{cite:9420a8de32caf92929b3d0f7cc24239333518c0d}}, in which for a pair of style and content images, we extract channel weights from style images, and use them to modulate the features of content images, while retaining the spatial masks of the content images. The resulting effects as shown in Fig. REF is that the appearance and color scheme of the style image is propagated to the content image, and the spatial structure of the content image is unchanged.
| r | b4592dbd806f5bf7f338ce72ff1e9bf5 |
Every Banach space is a Banach space of type 1 and every Hilbert space a Banach space of type 2 {{cite:2de2df9dce6f97231faf89c1a591ceee6ef5c3c7}}. Moreover, {{formula:ffd65efb-5e2d-452e-9bf9-50abff28eb86}} spaces are Banach spaces of type {{formula:25265ae6-b07c-4147-9a38-b18186a5ca22}} for {{formula:1d158963-563f-44d9-8023-9a203ae508ce}} {{cite:2de2df9dce6f97231faf89c1a591ceee6ef5c3c7}}.
We will need the following results regarding Lebesgue spaces of functions with values in a Banach space of type {{formula:8fb930bb-eb79-44b4-b1c4-aceb58a437f6}} .
| m | 4ba4eb75742109052289d9f66c77fdec |
Understanding what happens to rocky planets and their atmospheres in the habitable zones (HZs) of
low mass stars is currently one of the greatest astronomical challenges. The nearest Earth-mass
planets in the HZ orbit M dwarfs, and these are prime targets for spectroscopic atmospheric
characterization in the next decade ({{cite:19e41343bd17a38a816ff1d48ef2b709f67fcc8e}}, {{cite:f6b519e11675133925544d879421ee305173887a}}).
M dwarfs are the most common type of star in the Galaxy, and {{formula:290fdbee-0c39-4381-a781-bc2312c4f5a4}} 25 % of them have planets
orbiting in their habitable zones {{cite:8f9e86ecebfb6bd446a269ad05f3fe17fea13c28}}.
Theoretical work shows that planets around M dwarfs could be habitable despite
their phase-locked orbits ({{cite:9830d754679dfa5b3e8baf53506719a3a682bdc2}}, {{cite:8ba9b2a40d4efced8695582221f334ab6b274504}}) and dynamic modeling
of transiting systems reveals that most systems permit stable orbits of Earth-mass planets
long enough for the development of life, i.e. {{formula:c7a72c1b-5891-45a9-8ee2-dc32a1b2e8c3}} 1.7 Gyr {{cite:1189e86732025552448d347da34c400d0683686f}}.
Ground-based surveys, such as MEarth {{cite:9f25259f03412702cd5fbfe28fd4e2b64e7e6dee}} and the
SPECULOOS project {{cite:d8b60639d3c5b427603162ae27f4def1240e4d6f}}, and space-based surveys like the Transiting Exoplanet
Survey Satellite (TESS; {{cite:a15f70797ffc8215a212d9bedefe1489f3080af5}})
are finding and confirming nearby transiting planets orbiting M dwarfs whose atmospheres
should be observable with JWST {{cite:7c863b3cdedf3fff1fea73f66b5564833efd50d6}}.
The best host stars for JWST atmospheric characterization will be nearby, slowly-rotating,
relatively inactive, mid-late M dwarfs with masses of 0.10-0.25 M{{formula:710d1073-c4f1-46e2-a5da-91b21b57a1bf}} {{cite:23f3910e60d250cbb00685a89258a78c0893571c}}.
| i | ccb5e9eb46a7d2fb9663aed4c1c700ff |
To numerically reproduce the optical response of our fabricated TiO{{formula:180bb667-37c1-4514-85dd-1bb9798afab6}} nanodisk arrays, we apply the first Born approximation,{{cite:e1feb7b5ebb601d1a6dba53769e8eade24730894}} i.e. the exciting light field for each scatterer is assumed to be the unperturbed incoming light field {{formula:2b41c133-4800-4a24-b061-5aab4a43b2af}} .
Throughout this work we consider plane wave irradiation through a transparent substrate of refractive index {{formula:ac08451b-34a6-46d9-bc0b-2244ed6d2334}} occupying the {{formula:6ee37714-dcb7-4bf5-a8f5-d481e162f3f8}} half space.
The {{formula:b9df3238-6662-4d8b-8d46-8b266a3e34fd}} half space is vacuum with {{formula:d1521644-c016-4b29-ae90-3ceba2645d63}} , see Figure REF for notation.
The plane wave with field amplitude {{formula:c6291dbd-0b75-43bf-b8f6-e9f13723ef4e}} is {{formula:afb8c63f-ec3a-44e0-88bb-efb721c042e6}} -polarized and normally incident onto an infinite array of identical scatterers covering the substrate, i.e. {{formula:e49b6d16-df35-4fac-b292-f4a6e52e87a4}} .
{{figure:44c8ce72-a55b-45e3-a7be-794b3691d0e6}} | m | 38a55acb194b7d256c68fb791d61d1df |
Defining a realistic augmentation function is an ill-posed problem, and to the best of our knowledge, has not been explored. We propose a heuristic, based on the observation that it might be possible to generate realistic augmented domains that show a small reduction in validation accuracy, when a small augmentation magnitude is used. More concretely, we define an augmentation policy similar to {{cite:bf888a4ec3b7651b7b44803e5b258cc44d72fdc9}}, which consists of a set of augmentation functions, each having a probability of application and a transformation magnitude. The magnitudes are the highest values such that the resulting validation accuracy drop is still within a heuristic limit.
| m | 4af0bbac59a5b483bf419e8febceaba6 |
Similar remarks may be made about the Ni-Na correlation, which has received considerable attention in the literature and is thought to be linked to the production of both elements in Type II SN nucleosynthesis {{cite:96b53e097938a1f0e493c82248cf567130f6e309}}, {{cite:7857791900db92e95f2df62b4605644e84f3e112}}, {{cite:0dc0a5172b1f2130cb4711f9a19840ee4f9eff49}}, {{cite:89cac96df421a018be4527e06e731326f9fb9743}}. The two abundance ratios, [Ni/Fe] and [Na/Fe], are also correlated in our dataset though PC2, but cannot here be separated in an unambiguous way from the general correlation of both elements with the {{formula:4ad196b7-9565-4054-ba51-faba355f593e}} -element abundances.
| d | 6bef1fe7c664b88c2967ed4b9f9257b3 |
To compare our analytical model of eq. (REF ) against the simulated data we let free nine parameters: four bias parameters {{formula:624dd1f2-27f9-4eb8-8a2e-ab4d90a05c4c}} , three counterterms {{formula:cd399881-72d1-4afb-92bf-72c60a4764a8}} ,
and two stochastic parameters {{formula:4d9d0908-13bd-4262-b30c-2dc7d1f23d02}} . Given that we subtracted the Poissonian shot noise {{formula:1e2949b5-8691-4b09-af79-8af8d35abde4}} from the monopole data, hence the parameter to fit is {{formula:eda8e354-d0ec-49dd-b083-6ce93cb6607e}} instead of {{formula:650d6eba-a6e8-4aeb-9045-25521aec9ee8}} .
Moreover, for our fittings we only use the diagonal elements of the covariance matrix, because the non-diagonal ones are dominated by statistical noise, even for different multipoles at the same {{formula:b05de307-f5fa-4a79-8f07-91160130595d}} -bin.
In order to sample the parameter space, we run Monte Carlo Markov Chains (MCMC) using the emcee sampler {{cite:6b11066a491f1236a5b4522a0657915d6dcd74dd}} and the GetDist Python package to present the posteriors {{cite:87347e477e69c4c18cc868aeeaec0278665b0758}}.
We choose uniform priors over sufficiently wide intervals because apriori all sensible values are equally likely. (Notice that some recent work, which also estimate cosmological parameters, choose Gaussian priors around expected values obtained through {{formula:7178e78b-7af4-461d-9895-a2bee88e7f3f}} -body simulations and co-evolution {{cite:d5d6a4e9260383415e1578e237ae4a28012e82f9}}, {{cite:02429aa323ac16708cbbd13febaa8a3cdab9c55c}}, {{cite:ffd68296750a2bbf0842b116f8d6f9d821d059d6}}.)
| r | f6d3d6b07bbb249884ac1740ad835647 |
Amorim and Veloso {{cite:5a567f4df061e392f3bd5ebae834942c6df3b729}} developed 19 features: number of grammatical errors, number of verbs,
number of pronouns, and others. These features fed a linear regression to score an essay.
Fonseca et al. {{cite:d9c581917e6361af92674db3f3434923e544d6b5}} created a pool of 681 features, as the number of discursive markers,
number of oralities, number of correct words, among others, and these features fed the gradient boosting
regressor to score an essay. To extract the Essay-BR corpus features, we used the same tools
reported by the authors, and to implement the regressors, we used the scikit-learn library {{cite:8b5317cb6541f0c0415a06666e38ce545e7076cb}}.
| r | 611a1ccd268e2f2280ea55f44f2890b2 |
The basic idea is to control timestepsizes to keep an error estimate at a given tolerance {{formula:f3000ed9-abd8-4e4d-8d6b-65a47515e3ac}} . We use a local error estimate obtained by an embedded technique {{cite:61ffbbbdc6861541681eeb5ab311b276f37c7d4f}}, i.e., for the SDIRK2 method we use the coefficients {{formula:acda56dd-67b2-4914-b352-f67803d2045b}} , see Table REF , to obtain {{formula:84725284-648f-4bf0-9b81-c8fe213c2e87}} , another solution of lower order. The local error estimate is {{formula:e6fb3e06-8693-47b5-bba9-ab7d1d381534}} .
| m | b3ad2f9733392d725ec6e70f664185c0 |
While the Bekenstein bound {{cite:302a5b7841a4e2533714abe11ab3404d72104a6a}}
is fulfilled, our results suggest that the GSL might be violated
not only when {{formula:8527f9bb-891e-4129-ab7c-e1d5a232d33d}} is of the order of {{formula:3a2f7a12-d6f1-4538-946a-6ae5b4ed685b}} but also when it is
larger since the temporal derivative of
the total entropy decreases with time. Also a Gedanken experiment
that compares the total entropy after and before removing a
intermediate box around the black hole shows violation of
the GSL. The latter is recovered when the bigger box
is much greater than the intermediate one.
| d | 6da1413e166519aad8f6605fb2501d78 |
In {{cite:a2756cd2cd9fadcd3acaa1afde9d08cf7455f440}}, Etingof, Schedler and Soloviev introduced the so-called retract relation, an equivalence relation on {{formula:10516eae-cc46-4145-a30c-3ed3c058901c}} which we denote by {{formula:3f388014-0f2d-492f-8fa6-6b5fcbeecec5}} . If {{formula:25b92dc5-5824-453d-b0e4-35e3487e4f6e}} is a solution, then {{formula:29bf3e5c-b64d-4ffb-8341-f3333b808ef5}} if and only if {{formula:278234d9-80ee-4c35-bfff-32da00356249}} , for all {{formula:ec49dd77-7b2f-47dc-8062-3dee67111765}} . In this way, we can define canonically another solution, having the quotient {{formula:8b10f94e-2b37-479a-a922-93695ef91617}} as underlying set, which is named retraction of {{formula:0a531838-4b5c-47f9-a579-334408547f7e}} and is indicated by {{formula:3eb23575-298c-4da2-b055-2ff60c035b16}} .
As one can expect, the retraction of a solution corresponds to the retraction of a cycle set. Tecnically, in {{cite:42886aff56b0aa6aa526461937fd9ab65c8836b3}} Rump defined the binary relation {{formula:92cbdd11-4886-459b-b21a-56df43e03aee}} on {{formula:b6977624-442d-4760-8dd7-e5a641d70d3a}} by {{formula:7ed6d67c-180d-4c6b-9290-033816de31d4}} for all {{formula:4b8110f9-a62f-4abe-a5f5-c9ba1529d748}} , and he showed that it is a congruence of {{formula:1839d6ba-ff99-4a20-86a2-cf7d6d411a43}} . Moreover, he proved that the quotient {{formula:5b98559e-dfab-4e92-96db-c62200979c5d}} , which we denote by {{formula:c4b6b536-828f-4e15-a6a8-7288d6ac457d}} , is a cycle set whenever {{formula:607e8782-5721-4f44-993e-7690fb2d155c}} is non-degenerate and he called it the retraction of {{formula:a8fb5432-15d1-497e-8715-339b43db5673}} . As the name suggests, if {{formula:4a54d9b8-c81c-4a7f-9d24-10bbd375a8df}} is the cycle set associated to a solution {{formula:6dbc665e-736f-4c2d-b328-611536662a81}} , then the retraction {{formula:fb64438a-f27d-4015-b9ae-80758767cc8a}} is the cycle set associated to {{formula:16287f50-6028-4954-8de2-15ed2b7f87b3}} . Besides, a cycle set {{formula:d619d0bf-dac2-46f4-ba6b-b757446d081f}} is said to be irretractable if {{formula:762925da-8df5-4528-87de-cf60737e0688}} , otherwise it is called retractable.
| r | 3340557277368acdaaf4cf1ff0eaee7a |
Neural machine translation (NMT) systems map text from one language into another via a neural network. Several approaches to NMT have been developed, commonly consisting of an encoder-decoder architecture and an attention mechanism {{cite:c87d6ee893728e7ccf53be7f7bac4407219344e8}}, {{cite:5a59e9902f6cda194a8d7d42bc9a9acd15a38db0}}, {{cite:cd5441b8d7a4e1e98120ba01712eb89cffe0f185}}. The encoder seeks to extract a representation for the source sequence that captures all relevant semantics in the sequence. The decoder then utilizes this representation to generate a sequence of words, which is the translation. Attention allows the decoder to weight individual tokens in the source sequence depending on their importance to the word being generated. The Transformer {{cite:b172c18f3521418f2798ab9f4fca29f319e54b6a}}, a more complex architecture which employs multi-headed self- and cross-attentionAmong other features, including positional encoding and layer normalization, leading to a new state-of-the-art, has led to an unprecedented wave of research in NMT.
| i | e81e3921dc64f7a736b4ca4b4c9d0d10 |
The complexity of Arrival is particularly interesting in the context of other games on graphs, such as Condon's simple stochastic games, mean-payoff games, and parity games {{cite:6c529c1a1edbeb5dbff40c18cea443d8de8cc9a0}}, {{cite:2b2f306c37a96e48980d396fe24e2db2fd1896ae}}, {{cite:eba29c3d1edaabde41491e3b5fb2d7f4ef1ba022}}, for which the two-player variants are known to be in {{formula:112c7e55-08fb-4ac0-9c78-b899a3035093}} , whereas the one-player variants have polynomial time algorithms. Arrival however is a zero-player game which has no known polynomial time algorithm and furthermore it was shown by Fearnley et al. {{cite:75db50d473e1c6a6a745b10649648325671e757c}} that a one-player generalisation of arrival is in fact -complete, in stark contrast to these two-player graph games.
| i | 13c5d0ea62eb097419e3834ff1743629 |
Existing approaches to meta-embedding rely on self-supervised learning such as autoencoding {{cite:403350c6688230d2e2c791e7db82ec90cacec453}} to find a lower-dimensional hidden representation of the set of source embedding (further discussed in § REF ).
This can be advantageous in cases where (1) pre-training is expensive, (2) pre-trained embeddings are available but not the algorithm or the training data used,
and (3) the available source embeddings vary in their dimensionalites.
However, for problems that rely on representations that are better aligned with human judgment (e.g., genuine similarity {{cite:a56e8ba943bccab13a320a92161691cb5b7b81b6}}), word embeddings and word meta-embeddings struggle to perform well when only given co-occurrence statistics.
How to best incorporate task-specific human judgements into the meta-embedding learning process remains a challenging and unsolved problem.
| i | 2c97a71361b7534dec5325a9742391d3 |
Besides the multiscale challenges, practical applications of the linear transport model usually contain uncertainties {{cite:7a16dab47099c91564cfe8acf7b5c60124e60222}}, {{cite:a2ddf73c0fbb48188912d4523f4945815d58a087}}, {{cite:a05e1b1c5a831d2b0b59c14799a956514dd7509c}}, {{cite:f3991d7c8da70301c7c3ab3e0d00c4b7d2012dcb}}. For example, the scattering cross-section in the collision operator is usually extracted from data, or in some cases we have only a rough estimate of the initial data. Such uncertainties could compromise the predictive capability of the underlying model. Efficient uncertainty quantification (UQ) for such problem becomes critical for improving the reliability of numerical predictions in
real-life applications, see example {{cite:07b6c5b396a78aac21fe480ee0016d779f0f7457}}, {{cite:20ba2dc788705fcab496970fbbeb692f2024fa73}}, {{cite:f4ead280db50ee5c9418dfdcb321ffe39a8310da}} for an overview of broader UQ problems for kinetic and related models.
Among many numerical methods in UQ, stochastic collocation (SC) method has shown its competitiveness in many practical applications due to its intrinsic simplicity and non-intrusive nature. There has been many work in this direction developed in recent years, see for examples {{cite:5905b1e49fc5fa25a83615efef9399aa72313612}}, {{cite:d7772ce2c152ae5b826703ec0e161bcd88421730}}, {{cite:36399032757b9ca4fde7376bab9c761d78a002c3}}, {{cite:d361b14c394154ef6c97d9edec7fcbd73cdd6480}}, {{cite:fc730dd5982ffa64dbf4c72e04b0537568718b03}}, {{cite:dc3bfd5b27b4dc3505b361f1675468e0568649e8}}, {{cite:8296a48c40b5627296ff614f4978f8f94a5e443a}} and the references therein. Despite the successful development of SC methods, the high cost of a single high-fidelity run together with the number of required high-fidelity simulation runs, can still render it computationally infeasible for large-scale applications with high-dimensional random parameter space.
| i | 785cac1e8326d0dec524e2f29ee4923d |
Furthermore, the semiconductor coupled dots or hetero-dimers has similarity with molecules in molecular electronics{{cite:e334cde3ce5d2f53a9b69341d0e3e32d1a1c03c3}}, {{cite:096e0ad260cf3ec140e1ce4b981bb090e6d7c916}}, where a single molecule with a donor part and an acceptor portion connected by
a bridge acts as a molecular rectifier as shown by Aviram and Ratner.{{cite:096e0ad260cf3ec140e1ce4b981bb090e6d7c916}} Molecular rectifiers made from organic molecules are generally unstable and device fabrication is difficult, while colloidal nanostructures are expected to have an advantage from device fabrication viewpoint. We recently showed this concept for a type-II CdS-ZnSe colloidal coupled dots, where band alignment at the interface plays a crucial role.{{cite:8302eb2b9c1573d496460f6389efaf1d6a1124d6}}
| i | 02653ba351c64e3114a0802cecf269f8 |
We examined the viability of reheating via the evaporation of Q-ball derived black holes in the event that they come to dominate the energy density after inflation and then decay to radiation at later times. We find that this reheats the Universe at a very low temperature {{formula:88bc50ba-319d-4471-8457-fc5b1526e288}} , which produces an insufficient value for the scalar spectral index of {{formula:becf2e4a-1ad3-4abf-99f0-3fb8838323a4}} , which is excluded by the {{formula:b3a45ab9-c301-4729-a8c3-7c852461b07c}} Planck bound of {{formula:baf413fa-cea7-42bc-a663-bc38bc76adab}} {{cite:174859f032d63ca45c9fcf7a42d934c59f9c78b2}}. An alternative scenario is where only a small fraction of the Q-balls produced collapse into black holes, and the remaining Q-balls rapidly decay to radiation, instantly reheating the Universe. This means that the Universe enters immediately into an era of radiation domination following inflation, and that the Q-ball black holes come to dominate the energy density at a later time. By this mechanism, reheating completes within a greater number of e-folds of expansion than the case of early Q-ball derived black hole matter domination. It can give a much large reheating temperature, up to {{formula:731ac91c-bf9b-4cca-b24d-213e52c777ea}} , and a scalar spectral index of {{formula:2ac0d362-1164-4dc6-99fe-20be72fc16ab}} which is within the {{formula:994c63a9-51b0-47ad-856d-5355fa113a3b}} Planck bounds of {{formula:1ca93346-3c4e-4fb2-bd8b-bd9e80500e83}} {{cite:174859f032d63ca45c9fcf7a42d934c59f9c78b2}}. This shows that although reheating purely via the evaporation of Q-ball derived black holes is not a viable reheating mechanism, the model can still reheat successfully if a only small fraction of the Q-balls produced collapse to black holes.
| d | d1c3b720b59d6569bc11b94d813924b8 |
Another issue to be considered
is
that the dependence of the frequency of the gap edge
on the directions of external fields is strong
for the clean case
in the surface resistance. {{cite:a7d072122a19228e02244d8f8677ece2cc37b9c2}}, {{cite:40d97cc1eb6737dfdd6827ad02dded176138fb5e}}
In our calculation,
there is no difference in the frequency of the gap edge
between the surface resistances for {{formula:30e11a82-987d-44ae-9251-075cd3280341}}
and {{formula:fda7d0f2-0c6f-4d18-a916-32105a409906}} , which correspond to
the term `sum' and `no vc' in Fig. 4(b), respectively.
This is because
the effect of
impurity scattering is integrated over the
Fermi surface and the self-energy does not
depend on the direction in the momentum space.
A possible reason for this discrepancy is
the smallness of {{formula:cf83983b-9c03-4d34-b766-8305c3867c78}} in experiments.
It is possible that
the interaction between electrons and acoustic phonons
predominates over the impurity scattering effect
in the extreme clean case.
In this case,
the damping rate is written as
{{formula:e17c36fb-fbb6-4c98-aa0f-05cd5c8a9aab}} {{cite:f6a307eb660932672bad5c478637a9f2d8d0e014}}
({{formula:229f3f4c-aa14-4749-8aa8-77c00ba9bb16}} is the contribution to {{formula:95e29ee4-6e2d-4d93-828c-3c5679e8c78a}} by acoustic phonons
and {{formula:7af735b4-a308-47fc-9255-301084d7c78c}} ).
This quantity depends on the direction of {{formula:cb1448a7-e932-4504-8cdf-47e579dc24ec}}
through {{formula:de015c06-a269-4284-a4ff-978ce07b593e}}
and makes the surface resistance dependent
on the direction of the external field.
| d | 57421cb3ae824ea8657ccacabdba0e83 |
Applying Lions' compactness theorem (see Ref. {{cite:703c268422f35821fbb00bdb822320fddf0574b3}}, p. 58) we deduce
that
{{formula:4d48bcf6-b6f9-4568-a337-5e89cf9bd169}}
| r | d55ff0e7e851e5481fa860e0668f2c74 |
As for the computation complexity, we performed FLOPs {{cite:b44aeaf2017b3ad1d9f8d6f54aedb2650d39aeb8}} analysis on the proposed method in four different situations. The results are shown in Table REF . As can be observed, the proposed model with ROI-Seg achieves the lowest computational cost in Frustum US, while it has higher cost when applying the segmentation on the whole volume (we failed to train the model due to out of memory). In contrast, its corresponding Cartesian US would leads to a higher computation cost, meanwhile, the proposed model cannot be loaded with a standard GPU memory.
| m | 7ff91aa88a11df4cca3ec4acb9e29bb0 |
In this section, we introduce the concept of a middle Roman dominating function to study the Roman domination number of the middle graph {{formula:f337eb45-5340-48a3-963d-41673063cfd2}} for a given graph {{formula:2b36e3ce-f309-4aba-be94-b3559f74a7f3}} .
A middle Roman dominating function (MRDF) on a graph {{formula:d3159c5e-1406-41ef-be04-8e3cfbc64c08}} is a function {{formula:c98ef14c-1e68-48c3-b72a-8cb1e40e7fa5}} satisfying
the following conditions:
(i) every element {{formula:6a233bcd-60cd-4556-917f-f58cbcdf87c7}} for which {{formula:0d71e5c9-8241-466e-9ea1-584796e8e5d3}} is incident to at least one element {{formula:70e4dbcd-6386-41bb-964b-af4232bd931f}} for which {{formula:40a4eefe-6e8e-4897-862c-fc8c27c9181f}} ,
(ii) every element {{formula:2e8c2c86-ebfe-4c27-9026-bdd3e1103dd0}} for which {{formula:4759ccd5-78c7-49d9-b165-d062a44f8430}} is adjacent or incident to at least one element {{formula:d8b32b3c-8bbc-426a-9e01-0716aa704cce}} for which {{formula:f65cb309-68ae-41d3-a970-c388716d7523}} .
A MRDF {{formula:4c2e9c2c-7e25-4160-9af0-2ef53ef0b7f3}} gives an ordered partition {{formula:22843093-bbf9-45ed-b52c-caff578e00e0}} (or {{formula:1d165cbd-bfc5-47db-b2bf-40d29f8df301}} to refer to {{formula:8a863e5d-b9b6-4560-95f1-d02f7b934f89}} ) of {{formula:e42af38c-17f4-403f-a913-327af25031b0}} , where {{formula:dc2b1f4b-71aa-4dd6-ba69-a0da66f83d67}} and {{formula:b50b02b0-d503-47a6-b51d-17e1b516bd3c}} .
The weight of a middle Roman dominating function {{formula:770333ff-4ecb-4e13-a127-8ed590584edb}} is {{formula:c89cfcbe-5f09-48e6-b1d0-c3dc697f84c8}} .
The middle Roman domination number {{formula:70103a5f-473a-4984-816c-21f969b1b660}} of {{formula:b177c78b-ec5c-4a5c-9673-c0134d8904c4}} is the minimum weight of a middle Roman dominating function of {{formula:47e4f8f3-8388-42fc-bf0c-c4535a35a18e}} .
A {{formula:c6e2410b-8e61-4a34-92d0-2bd766a99cef}} -function is a MRDF on {{formula:fef69b9b-05f4-456e-b564-537e33bc4233}} with weight {{formula:084ad588-03ff-44b6-ac2f-683d0986f918}} .
Similarly, we can define a perfect middle Roman dominating function (PMRDF) and related definitions.
For a subset {{formula:0a9d6702-c8e6-448a-8321-770a0bb73a89}} of {{formula:8ff27e77-33d9-49ee-bd91-d84a95430f08}} , the subgraph obtained from {{formula:a864835b-09fa-47a7-a4d3-2c47928fee11}} by deleting all vertices in {{formula:1dd91360-6b18-40ad-97f6-9045fb0851d9}} and all edges incident with {{formula:abd5c5e6-4f33-41a0-9660-d8dac3ddf671}} is denoted by {{formula:af586a37-8127-455b-a464-497c29cf9720}} .
For terminology and notation on graph theory not given here, the reader is referred to {{cite:c78aa37c68e857e11c216fcb7f34ae312d46828f}}.
We make use of the following result.
| r | b0160e84144e0d3ccfdf489c999a02d1 |
Gravitational torsion may be viewed as a twisting of spacetime, analogous to the curving of spacetime accomplished by curvature tensor. In this regard, Einstein-Cartan-Sciama-Kibble (ECSK) theory of gravity turns out to be convenient {{cite:7308b8a68861f667444fbd58d4d9800c0c2638d5}}, {{cite:3731e25864cda63fe3966fd20b2360be9310c7b7}}, {{cite:e3b9cac6762fc1757baa1c61de9d796c89a76567}}, {{cite:478122739c4c17a4187692d82bbfd5263e464bea}}, not the least because it has been thoroughly developed for over half a century. It is a minimal extension of general relativity that incorporates torsion. For a recent review, see, for example, {{cite:ab2d4ba9261eff5a3068c83a21a8810425a6259e}}. According to the ECSK theory, the spin of a fermion is a mechanism that twists spacetime. In this essay we argue that, in fact, a fermion would not exist without extreme twisting of spacetime. A fermion, in our view, is simply a twisted spacetime {{cite:8ac3adbe23aa1f83fc5f1d06d7951ab3ac80ad3e}}.
| i | 82406cf93a322114f26f5afe4368cfa2 |
In recent years, high-fidelity image synthesis has significantly improved by through the use of Generative Adversarial Networks (GANs) {{cite:93ee6f88019153721a301f79754cc9f22c1d7f1a}}. Whereas early work such as DCGAN {{cite:f1f7429b9083614993c648662edf40492ca3f2bb}} could generate images having a resolution up to 64x64 pixels, modern networks such as BigGAN {{cite:12fdc3c8653b1622a08b0bf9062b4e1ed76a8db3}} and StyleGAN {{cite:85350bdc8a30e82c93bd33f30a655826c0faf8da}}, {{cite:d078bcd7f0f69a129f7b84ace8247ab2331dbdc8}}, {{cite:098647bbd2fc25ea042959191f714d853fcc98c4}} allow the generation of photorealistic images with up to 512x512 and even 1024x1024 pixels. Although the quality of generative models has significantly improved, image generation still requires many computation resources. The high computational complexity makes it difficult to deploy state-of-the-art generative models to edge devices.
| i | a78c12d27107f7eb4654a9029a5f6cca |
In the subsequent large-scale experiments,
we list the performances of the comparisons in Tables REF and REF . The symbol “–" in Tables REF and REF means that Gurobi fails to solve the problem due to excessive memory requirement. In the implementation of the ADMM, we apply the Sherman-Morrison-Woodbury formula {{cite:4d2b3d27f0b97bde47422d329a1e2b6e2821f052}} if it is necessary, depending on the size of {{formula:95b3d25b-5942-4dc5-b1d0-6db319ddc1a8}} and {{formula:47fab492-34f3-480d-9963-3e9fa538982f}} . We solve the linear system either by the Cholesky factorization or by an iterative solver such as the preconditioned conjugate gradient (PCG) method. From the comparisons, we can see that the PPMM algorithm can obtain all the solutions with a desired accuracy efficiently. When the sample size {{formula:38215694-309c-45eb-8450-4ff6bc855f5d}} and the number of features {{formula:89fa9f97-bf20-4e90-95af-9853b05c3b8a}} are small, Gurobi can also solve the problem with high accuracy but with much more time. For high dimensional problems, Gurobi fails with too much memory consuming.
| r | c36dce611c5334eed1b5a7f50ba84497 |
where {{formula:c3b26e4a-4c77-4c90-b081-d6eebaca6092}} follows a Gaussian prior, {{formula:3ee5eab9-e2aa-4ec1-9b10-f567c37122a6}} and {{formula:816a0ec8-f8ba-4653-b3cb-5a4fbfcc9147}} are learnable
parameters. With a ConvGNN as the encoder and a simple
multi-layer perception as the decoder, GraphVAE outputs a generated graph with its adjacency matrix, node attributes and
edge attributes. Regularized Graph Variational Autoencoder, such as Ma et al. {{cite:8cf99b7a40df36d5793e0c8b5c6efadb78d17684}} impose validity constraints
on a graph variational autoencoder to regularize the output
distribution of the decoder. Cao et al. {{cite:b38bb97c02ae020148af7a981a8d8371dc5e0bb7}} integrates convGNNs. {{cite:2b0894fa71edbd23bdcbb6d059267d59a34b6874}}, {{cite:f6b758869d1132d561b7384eec369a666c9f8d6f}} and reinforcement learning objectives to generate graphs
with the desired properties.
| m | 7a394155398e8759f334704b5c9c0b28 |
Convolutional Neural Networks (CNNs) have made extraordinary progress in various computer vision tasks, with image classification as a most representative one.
The trained models generally perform well on the testing data which shares similar data distribution to that of the training data. However, in many practical scenarios, drastic performance degradation is
observed when applying such trained models to new domains with domain shift {{cite:de785d1ce84c6d2109101364236fbbfeab89a4e7}}, where the data distributions between the training and testing domains are different.
Fine-tuning
on labeled target data is a direct solution but is costly due to the requirement of target sample annotations.
In contrast, unsupervised domain adaptation (UDA) requires only the labeled source data and unlabeled target data to enhance the model's performance on the target domain, which has attracted increasing interests in both academia {{cite:c52cfa721f02a9701d346e013cb215587a367c85}}, {{cite:85c2c79fb4131590b92e2cbbd99361335e24123f}}, {{cite:1fa77abc20d5e11cb4cfb214996b7b94bacf1fea}}, {{cite:f6f50f5a450417e12a2648c384c0b6ca975dbe8a}} and industry {{cite:bbeabd4e4f4e2160557a626b47288852d357148e}}, {{cite:04553125fd8c0404d3fb1c08f14fedde943f61e0}}.
{{figure:4ea58d29-0c98-4615-a0a3-82ac1763c873}} | i | c14a9d00e9fea8e9e1d5b334736ff49c |
As we all knows, the memory effect of the environment is caused by the long time correlation between the system and the environment and the environment can be divided into Markovian and non-Markovian types according to the memory effects. Many methods for quantifying non-Markovian features have been proposed, such as Rivas-Huelga-Plenio (RHP) measure{{cite:96d9d52819c366900ce15e2f23f238c97517769e}}, Breuer-Laine-Piilo (BLP) measure{{cite:6e7a7953600dd73ec6aa61df53a3a3e069114281}} and Luo-Fu-Song (LFS) measure{{cite:1a1210671764cf713bb880bf095ed4b46be4bda7}}. Besides, Zhi He et al.{{cite:06b55bc4d40dccfb565210078e339a565c515c22}} has used the BLP measurement to calculate the non-Markovianity for single-channel open systems, and they obtain a very tight lower bound of non-Markovianity. Yu Liu et al.{{cite:4a081f3020b596397fde3d0d03da3db6b16e17b3}} has calculated the non-Markovianity in the dissipative cavity and used it to explain the dynamical behavior of quantum coherence.
| i | 12ff55e01ebb13016f5f8f3ab1b30def |
Baseline Plus. Inspired by several improved baseline methods {{cite:3ce2e2a83787fe9804967d4181ecedb7281c595f}}, {{cite:b104d89eee6fcd1d73ec81db4603c933d105ad9c}}, {{cite:31ea9c2d190f314daa64b71610693623e134c419}}, {{cite:fabc70aafe4ec35a27b56a1a10ef222bbc98b983}}, we propose our modified baseline for few-shot video classification, termed as Baseline Plus.
| m | f46ae3169bef90df8d08190ce019d64f |
We calculated spin susceptibility
and found the rapid linear increase at low temperatures
compared with
that of {{formula:f6de88cf-3153-45d8-9a2c-80947021bc76}} -(ET){{formula:696b87b2-18ec-4aaf-8eb9-3fc8958ffe02}} I{{formula:4ae9691f-a0d7-49fd-9be4-d8b0862130d2}} .{{cite:4eb301f241f47a86cd33f291b00dd12fe24cb767}}
Such a linear increase
is compatible with a measurement under ambient pressure
of the susceptibility in {{formula:4187fbf3-1b2b-410f-b114-2b24e6ad7739}} -(BETS){{formula:32cf7af5-4a37-40b8-be2c-b73ad8dc5347}} I{{formula:a9d8162e-0662-4708-ab9b-0b8ff72daf1b}} . {{cite:d60bba60985e12666924555bf133b7e612c2d34f}}, {{cite:48943b54d59b227d01eceea9516948ed16d83b8f}}
Although the rapid decrease of susceptibility is found
in {{formula:f450e307-cbfd-466a-856d-da34a1349e8e}} -(ET){{formula:c2936bfb-38ce-4917-93dc-246fb4847e03}} I{{formula:0af30098-76de-467f-874b-040284e417b5}} due to the effect of long range Coulomb interaction,
{{cite:d955a8f2dac7d1f8140c18d85ec47d40aa46f338}}
the linear behavior in {{formula:147dd6a3-cab3-4860-9d44-dfcd7a332ac0}} -(BETS){{formula:45a7ccea-3dba-4613-901c-c6d129f81623}} I{{formula:bcab3697-e289-47d1-a129-0bf7891f0a44}} {{cite:d60bba60985e12666924555bf133b7e612c2d34f}}
suggests that such a correlation effect is small
and the effect of SOC is dominant for the insulating behavior.
| d | fed48b30382902fe894fb6fe2301917d |
The miniImageNet dataset {{cite:05c362a4e620513612cf2d8bea3bc9a67031f49e}} is a standard benchmark for few-shot learning algorithms for recent works. It consists of 100 classes randomly sampled from the ImageNet; each class contains 600 downsampled images of size 84x84. We follow the widely-used splitting protocol proposed in {{cite:b9ca6b632e1ac2f9766385794ec1944fb2a817fe}}, which uses 64 classes for meta-training, 16 classes for meta-validation, and the remaining 20 classes for meta-testing.
| r | 7b0490b46557c4adf5e95c6657d8c34c |
was obtained in Ref. {{cite:a80b947ec7beeb864d828656b43c0ee1df0d19e6}} taking into account the KSFR relation. With this result Eq. (REF ) has a {{formula:d0f6470c-9906-48d2-bcd9-bab2c608582b}} -resonance pole at {{formula:91a36231-8083-44a4-a03b-0824db81a9d6}} GeV{{formula:fd90c706-3aa8-49ee-8f3b-47677f5749e4}} , which is very close indeed to its physical value {{formula:d7c5bde6-d45d-452f-9399-99553fa2b945}} GeV{{formula:47db6dfc-a64e-4caf-a9f3-7ddc98760403}} {{cite:173536cb2ff20d6e536ee52f50fb83b117d5e9ee}}. The pole position {{formula:9717793b-e7bc-4fbb-964e-cda4d9ddde81}} only depends logarithmically on the scale {{formula:10204364-c9ab-4c8d-8c7b-44e73f7dcbb1}} , so that for {{formula:3b061eb5-0aaf-4460-af27-712391a6a0c4}} {{cite:3cd6302c1c6e6e74e306e98509afca103d307413}}(another typical value for the chiral expansion scale, around {{formula:1ab5ca30-dbb6-4ced-9f11-4542f61508f9}} ) we find {{formula:caf0887d-f17e-4aec-a1b7-518f512eb44f}} GeV{{formula:d0058b79-e016-4136-9e6b-7c2d91f1c05e}} .
| d | a9a747e76571f5d82d516832447c8886 |
The form of {{formula:5849ba17-f282-45be-b757-cf7cc248d69a}} generalizes for other values of {{formula:7c6c6c72-5657-4cbe-ba77-6ccb850180a0}} and {{formula:779d5285-d159-4425-87a4-74503f3d978a}} . The structure of Toeplitz matrix {{formula:39d01352-3c7b-4dc6-933e-6ec70e03f942}} depends on how the vector convolution operation {{formula:72be2059-7a6a-464e-b91a-d9502625222a}} is defined, but its dimensionality is always {{formula:c5cf5169-8468-495b-abd0-80796c335415}} . In the case of the convolution function from the Numpy library {{cite:4460c632c2e9952a1076364f643c3618a8cbe748}} with the parameter "padding=same" , the aforementioned definition of {{formula:65e39cb3-628b-4e35-ad70-e1f573de2e47}} is the same.
| m | a85c7a1c51d080e05fe4cd3378bbfae3 |
One of the first theories of nonlocal elasticity is the strain-driven model introduced
by {{cite:cdb2a15d6ef68f9963b7a39c9108d87e18abbf15}} in the wake of seminal contributions by {{cite:660f156463f29b8e38ff38c06f9cfe8b3176879b}}, {{cite:e46dcde71bb636bf20d7660aa2b99c5695db769e}}, {{cite:19d071a1b99dae7ec40f3924ea92b0317b24d529}}.
According to the strain-driven model, the nonlocal
stress field is the convolution integral between elastic strain and an averaging kernel depending on a characteristic length.
Originally exploited by Eringen to deal with screw dislocations and surface waves, when applied to structural problems involving bounded domains, Eringen's strain-driven model
leads to ill-posed structural problems due to incompatibility
between nonlocal and equilibrium requirements {{cite:317fa87aaa60d5ff38b1da54e4da0b6a233436e7}}.
| i | 6aa9f14eac0c8d25995420215e6ba6a6 |
The classical AIC and MDL methods are based on information theory and these methods have originally been applied to one dimensional data. According to {{cite:c589802aa27f99482c626477cffa9c1dae8d8bfe}} the AIC criterion is given by
{{formula:727a3e8b-0aad-473b-b7dd-fded24616f88}}
| m | f0bf4160a8d6b5a7f1e64b770d42b6b4 |
Table REF contains the obtained results.
Our unaugmented model outperformed other published results, including BPL {{cite:e42ce868fd7c55cc46179e5929f14a2a41162746}} and Prototypical Networks {{cite:2a3fcc1069d0a9693e86d56f3ca089e6cf0a64a2}} and achieved perfect accuracy after applying Hungarian algorithm at test time, denoted by “full context” in the results. When training on the Minimal set, our model benefits from augmentation, and when full context is used, outperforms the previous state of the art, BPL. The model trained on points using data augmentation (three extra rotations per character) shows comparable accuracy to our image model, while the unaugmented results on points fall short of the corresponding image results. This is somewhat surprising, as one would assume that stroke trajectories contain the same amount of relevant information as the images. A likely reason for images performing better is the translation invariance induced by the convolutional network helping model to generalize better when compared to point-features prepared by simple MLPs.
| r | 8e7723a34cf9101f762a7ca3d1460f98 |
Besides, since the combined patch embeddings only contain part of the information in the whole image, pulling the partially combined patches closer to the target view that contains the whole image information is more challenging than pulling the original image pairs and implicitly increasing the asymmetric of the network structure, which have been demonstrated beneficial for increasing the richness of feature representations and improve the self-supervised learning performance {{cite:02a9c313e5f00a8594cd6fa3047dfeaaee032da2}}, {{cite:3039ae3d733233475f816ec90f5c08788785d306}}, {{cite:9f7cc988fdd1f8b4f81170766fe47de77b4667c8}}. Owing to these merits, Fast-MoCo can achieve high sample utilization efficiency with marginal extra computational cost and thus obtain promising performance with much less training time.
Experimental results in Section REF and REF below will validate these analysis.
| d | 80166d8c71e6f15313218cd42f910e1c |
There are a number of extensions of these results in the commutative setting esp. the so called hyper-Kloosterman sums {{cite:13d49e57dd63b0849b3f732538e5fb9c1f751bc6}}, {{cite:b807f065daccbd7474ad8b3115ec41043ad30128}}, {{cite:c77c523674dfde3a5647822f59ccb6f1c6bed097}}, {{cite:1cd83b15f88a3a13d9d17ed1b0366b6544af0aaa}}, and both these and the classical Kloosterman sums are ubiquitous in the theory of exponential sums {{cite:5d6357ded6fe5acdfdd3017e6010dcc8e3c04cc9}}. There is also a deep connection between Kloosterman sums and modular forms {{cite:ec1ad063cc0409e1f698fdaad3654de126ef6b9d}}, {{cite:50c58d7b3c78ac5fe2b9ddc1b190592dfb1d2abe}}, {{cite:86b522016a9efb358755a2c98cdfc88d6a57c55a}}, {{cite:94fede9a5dc4fc04fe15c20034b9e239439eff84}}, and the notion of Kloosterman sum is extended to other algebraic groups {{cite:35756a4ab56a858c0840bf57b9986a15a52ef8ea}}, esp. to {{formula:f3bdab9c-caaa-4f82-a137-0e455f77040c}} , {{cite:be72dcfdabe777cd6bb4680ef7052accbd359366}}, {{cite:0f053111dd67d0e59e9b7a99200547f629ed5ee4}} with many applications. The sums {{formula:93750e09-cb69-44a9-8690-ab1247570c5f}} considered here are less group theoretic in nature, or if one views them that way, they are tied to the standard representation of {{formula:64776092-0584-4ca6-9b31-89f642dd6274}} . While it is possible to highlight this approach it seems more advantageous to regard {{formula:3b4ebe81-fcc9-4600-a548-aab1d54faa20}} as a generalization of {{formula:81b368a1-36fb-42fc-92d6-24d58f3fe2d0}} to general rings, of which {{formula:85847e3f-2537-4ef3-8daa-655bcf16bba5}} matrices are of the simplest non-commutative examples. In particular the underlying additive structure will be exploited on several occasions. From this ring theoretic point of view we have again
{{formula:d490d11c-a950-4b3e-974b-f556eb12e4b8}}
| i | 71ebd95ffc370ec7043c82a93238ed43 |
Performance of different unlearning methods. Next, we test various unlearning schemes combined with GST. In this set of experiments, we sequentially unlearn one node from each of the selected {{formula:1d14dd03-19c1-4be8-b270-ca9313b923ff}} training graphs. We compare our Algorithm with the unstructured unlearning method {{cite:d15c81abf8d20e1d1a2daa3090b8efc045162052}} and complete retraining (Retrain). Note that in order to apply unstructured unlearning to the graph classification problem, we have to remove the entire training graph whenever we want to unlearn even one single node from it. The results are depicted in Figure REF . We can see that our unlearning scheme with GSTs has accuracy comparable to that of complete retraining but much lower time complexity. Also, note that a naive application of {{cite:d15c81abf8d20e1d1a2daa3090b8efc045162052}} (indexed “UU” for unstructured unlearning) results in complete retraining in almost all the cases (see Table REF ). In addition, the method requires removing the entire training graph instead of just one node as requested, thus the accuracy can drop significantly when unlearning many requests (Figure REF ).
{{figure:ae067c7d-b497-4f44-ad2e-0e7ba62ac760}}{{table:df888292-ab10-40dc-a24b-c3e749114f8b}} | r | 0e828a98746a66720df869890ba7a42c |
This is the first coreset construction with an optimal dependency on {{formula:921f849c-cea7-4c68-a12a-b4abf1d1a95c}} , at the cost of a quadratic dependency on {{formula:88192f72-f687-42dc-ae6f-a8d362767cd7}} . Previously, all upper bounds either had a dependency of at least {{formula:ad8498cf-f52c-43dd-9190-3be8abde5f42}} {{cite:a79eb5bcb5ef0a6a18801684cfa3f68d00da2627}}, {{cite:830d40ae72cf8bff741ef4df43875b73ec4c1c64}}, {{cite:654eb69d4573ac438d9759a47b9b1110242e6fed}} or a dependency on {{formula:bd5ea8f3-c8a4-4f6e-85ad-1eb90b9db3f5}} {{cite:2e8e22b89618808d794d74b117ba38bc2c264451}}, {{cite:63a739a9902bb1c2eed8ee4a078a3f733d4349ca}}.
| r | 39f1db29ee93957f38ffeb1383abfc02 |
where {{formula:980d1f46-f8e3-41e0-ae78-526d6d011d48}} denotes the subgradient of {{formula:9a6bc3c1-1069-487b-8033-9db8a1b8790d}} at point {{formula:3274432c-a5f4-4f83-a3f9-b440042843a8}} . It is worth pointing out that
{{formula:23521183-cb26-4aeb-95ed-58ecc3c7068f}} can be calculated from Proposition 4 of reference {{cite:80d19b5171fb3c83e967e1276c4f0009095fbec6}} and is given by
{{formula:74bc12b5-b0fd-4ca0-b0fc-e4e95c61d63f}}
| m | 47ff6ae7f9559b18eb938e6bd2d38f53 |
We compare IPE-LIIF with five baseline methods: bicubic interpolation, EDSR-baseline{{cite:40bcc072efd76c03e01ce106c085258e1186a388}}, RDN{{cite:074992fddeafbe47a0746bed5df768a09fec8df0}}, MetaSR{{cite:b179cb29d6e3e6e453db99544036d93697b2e443}} and LIIF{{cite:1924daeed416ac3f86ccb7b025d1f3934a43ca59}}. Note that EDSR-baseline and RDN train different models for different scales, thus cannot be applied to out-of-distribution scales. The remaining parametric methods are designed for arbitrary-scale image SR and their feature extraction modules are exchangeable. The feature extraction module used by the three models is indicated by the prefix of the name. All the parametric methods are trained on the DIV2K{{cite:897f14ca8f90eea30e1d709b95e635d5e053928b}} training set.
| r | 6d53505cc0825ff036b79b6584fa866f |
It is known that the irregular set associated to a uniquely ergodic dynamics is empty (cf. {{cite:26da4fb4879741be2ea1d561c602e912f3f992ad}}). Besides, some of the most interesting known examples of minimal non-uniquely ergodic homeomorphisms have zero topological entropy. Thus, in this setting, it is useful to describe the complexity of the irregular set using Baire category arguments instead of other measurements of chaos. The next consequence of Corollary REF benefits precisely from this strategy.
| r | 41309c17b39bc5160a24f3494c9c0101 |
This research makes a first attempt to design the coarse trajectory for the energy minimization in UAV-enabled wireless communications with latency constraints. The proposed approach can be extended to a fine trajectory, e.g., waypoints based on VBS placement and convex optimization (WVC) {{cite:d960ed2e756ec5c0bdaa49dde13c09393e86490e}} and fly-hover-communication (FHC) {{cite:c1122c43345c8db416c4edafc66966969e2e6c4b}}. However, it leads to new challenges since {{cite:d960ed2e756ec5c0bdaa49dde13c09393e86490e}} and {{cite:c1122c43345c8db416c4edafc66966969e2e6c4b}} do not take the latency constraints into consideration. Thus, FHC and WVC can not be directly applied to the problem investigated in this paper. Fortunately, the proposed algorithms in our work, i.e., exhaustive, heuristic, and DP in Section III-A, become initial feasible paths for the block coordinate descend (BCD) in combination with the successive convex approximation (SCA) method {{cite:a7adc35ed80b2a0e88c3b3aaded6a2818319b6d4}} that can be considered as a new method to obtain the fine trajectory, e.g., FHC and WVC. Moreover, a variable velocity can also be achieved by applying this new approach.
| d | 0c294c322244a400bbf16ec664f6adae |
is well defined under the energy-momentum conservation principle; see {{cite:3bf6e928f7676a3c578d4948bbb402846be82754}}, Lemma 3.15.3. Let's compute the numerator {{formula:ac386a64-c784-40cf-84c8-9250360bc4b6}} of {{formula:f6494460-1391-4543-b0bb-6caba156f5ce}} .
{{formula:f76c1e5d-390b-4e2f-add4-b8383d5e4e6a}}
| r | bfcb412f02766e9bba44ed318ea883bf |
These results can be found in many convex optimization books and papers, e.g. in {{cite:5a638c2e14a5f45aabe620d6fa90ad1f4056ae6c}}.
| r | 875f302bb21986b0258bd02e2351d220 |
To evaluate the generalized ADMM, we deploy the setup of Matlab codes from {{cite:e6f83ffd87565235f34ec4ceaa76b0b3f15bb385}}, {{cite:6682b70bcc1092bfc165aa9a6876d4b56bca71ab}}. We evaluate the performance in terms of numbers of iterations for convergence and we define {{formula:5a458b63-d0d6-43a0-b302-ee5253413c12}} which is the difference between solution in (REF ) and (REF ). The distributed algorithm will be stopped when the difference between the solution of consecutive iterations is less than {{formula:004747f4-87de-45ed-adaf-13387b58377a}} . We simulate for both logistic and Linear regression objective over the data set 29 in {{cite:6682b70bcc1092bfc165aa9a6876d4b56bca71ab}}. We use the projection algorithm to update the value of {{formula:4d3e1cd6-d0e6-4ce6-919d-6823094babca}} where we have {{formula:b655f097-ffa0-4d43-b288-a0bbd272ef1f}} . For the protection function, we use norm 2, i.e., {{formula:29c55c0c-02d2-4a5a-ac7b-3b88dcb0933b}} where we set {{formula:ca775a3e-a405-450d-9b4e-34b7dd7e9d45}} and {{formula:2fd6c1f5-c5d4-4f72-96dd-a2aad43c31e5}} .
| r | bbb65738c826c2a1d52f99bbc670f327 |
The analysis in {{cite:eff8752ba718f343513da980f91a904cf52728d0}} was dedicated to maps from smooth source spaces with values into locally finite Riemannian simplicial complexes, with striking applications in Geometric Group Theory. Korevaar-Schoen {{cite:73e2444c9dcae3fd5d62bd365d12b4919fca9c31}}, {{cite:afafb8eadf20b89a22983735d6a75afe88fdf99f}}, and independently Jost {{cite:55215d93e6725d1b95dd98149b0df3af07944ca7}}, {{cite:d6a6f6066cca9db57bf90055433eecb6d072450b}}, later developed a general theory of Sobolev and harmonic maps with values into metric spaces with non-positive curvature in the sense of Alexandrov. From the variational perspective, the curvature assumption on the target guarantees convexity of the energy functional.
| i | 7634fc8bff5cd7d1d48beb2af27d9009 |
We did not apply any post-processing on the prediction segmentation maps. However, connected component analysis (CCA) or conditional random field (CRF) are among the post-processing approaches that were used in the literature to remove the false positive detections {{cite:240402240012745fa2920ef64c3dda55d075dbab}}.
| d | 3361135c54f118d0c6c4c00b677a5102 |
Condensation of pions, kaons, and diquarks in QCD and QCD-like theories has also been studied using chiral perturbation
theory
({{formula:5f4695b1-46ce-42be-9f2e-571b8a2ef26d}} PT) {{cite:b14f168753101d2df1b86dc8122f4edd71a5d32a}}, {{cite:95c44b56d4e9e4eb098674023d75d4884c8a6d30}}, {{cite:0507c4cea2efe0fdb938545e4f4cf77153386159}}, {{cite:5f5f603a4bc5e965a22ce75b2107cd4aa40b8783}}, {{cite:ca1b1c744b33a5f8412dab8e220307eb842ac5d1}}, {{cite:26a67bb56d4e4e3dc6e46f44522c9180293f5381}}, {{cite:ecd1e667b2d4f2a714c0ddd81f8802700c758967}}, {{cite:2277bb2422fc0b086fc0bfba36ed187a07e3e06c}}, {{cite:3cb3ff015a96f2261748ffe0d118c9cf12a0e168}}.
{{formula:a046a307-9b26-4772-9405-84a0848c0a1d}} PT is an effective low-energy theory based
on the global symmetries and relevant
degrees of freedom of the the fundamental theory (QCD or QCD-like) {{cite:56bd9812374c6da509534a6286815109995d67c8}}, {{cite:ece9b3d2e43ac5c5e1a8f8de8b9cb98b9349acc9}}.
The second-order nature of the transition at low temperatures,
where {{formula:9522dc93-61cf-4849-af1b-71fc41a30961}} PT is valid, as well as the
critical chemical potential being equal to the mass of the
condensing particle (at {{formula:9ae34b85-c998-4c04-b968-7dbf716cbd56}} )
were confirmed. This has been shown
at order {{formula:d6fd6b3d-29d3-4df6-990f-505472ab0e26}} and {{formula:835742da-bde8-40d1-8782-0f482102e131}} in the low-energy expansion
of {{formula:fe59d389-b3ca-47bb-be6c-98fabda7872f}} PT and is expected to hold to all orders.
Finally, excellent agreement between lattice and {{formula:1ceb6cc5-8203-4d41-80a2-34a26139e857}}
result in chiral perturbation for the quark and pion condensates at {{formula:80709331-2da2-44f9-87e1-276dda2a4113}}
was found. A recent review of meson condensation can be found
in Ref. {{cite:5a1dc058b60c89d70c6404b9c6549574b3214a44}}.
| i | 9a6fd8bb8735861a460a1368e339cdf6 |
Finding first integrals is often a complicated task, and during the
past decades several algorithms to construct them have been
developed. One of the most effective methods to produce first integrals
of a given mechanical system is the so-called Lax pair representationOften {{formula:0c0bed1e-2c31-457b-a7e4-c4a82a854562}} pair in the
Russian literature.. The concept of Lax pair originates from the work
of P. D. Lax on the theory of PDEs {{cite:3e844ae866e54f8d37c301a7c41aeb9543e1d9c6}}, where
it was used to produce exact solutions through the so-called inverse
scattering method {{cite:202313c227d9b71222cd325eb3379b13311b0ecd}}, {{cite:61e444d69483339cdbb0f969ca8c4d49a386f030}}. In the finite dimensional setting,
the construction runs as follows {{cite:387ac5175b5e1e31b9a14f28e6b63c00121927ee}}, {{cite:745caa93cfb1bebd09e6c532f72524c37df95ee4}}:
assume there are {{formula:3eff74b0-2c0c-4e9d-b0bc-e447393c68bc}} matrices, {{formula:24a615ee-8e4b-4216-9ad5-b3f56572ac76}} and {{formula:f89e8168-f3e8-4564-8409-89a6b29a2ad5}} with {{formula:5558de43-9cef-490a-a6ec-f89c4b3912b8}} and such that the equation
{{formula:7397c119-ea2a-468e-88a4-8d4695967181}}
| i | 6cbd279166a6514e896e0db796ce8cc0 |
The results on the full Nordland dataset show that our proposed CNN+RNN model is capable of learning meaningful temporal relations from a single image sequence of a large driving dataset; while significantly outperforming classical sequence-based methods in runtime, accuracy, and computational requirements. We used a small two-layer CNN for exploring the end-to-end training behavior (from scratch) of DeepSeqSLAM but our preliminary results showed that the CNN component does not generalize well to drastic visual changes; which was expected since these models require a significant amount of data for effectively training and generalizing. We see this observation as future work to further investigate the advantages of jointly learning visual and positional information for AD applications. Finally, we call our method DeepSeqSLAM since it is our goal to build a full simultaneous localization and mapping (SLAM) system using this framework by incorporating a learning-based component for geometric mapping such as those in {{cite:c9e87f9a220475cd3210832241757049df01efdc}}, {{cite:7ee9cc39c7707e78ebc7e8c6e23d4a58f3bec3dc}}, {{cite:b39a27f4137f23cd80da6bddb445000fa9ac979c}}. Our first attempts to integrate these mapping systems into our framework were limited by different, expensive training requirements from these models, but we found that on the deployment stage our approach can be easily integrated with a mapping system and we are currently exploring this for future work.
| d | 0988dac274f0e902e4a5335065752361 |
Texture is ubiquitous and provides useful cues of material properties of objects and their identity. Visual representations based on orderless aggregations of local features (e.g. SIFT {{cite:25659a8bb30ea83dd77d232cc4ba38e0a0690da1}}, SURF {{cite:dd810ac431304666e40afb0d9ccb1652c0bac41d}}, HOG {{cite:0177cfcfb3a6dc6a8addcfe50f7b2ad058bace78}}, and LBP {{cite:541cd0686372625b45dd090ad218512c40853f7e}}) were originally developed as image texture descriptors. Before the `deep learning era', models such as the histograms of filter bank responses {{cite:d27479f15a6cdc66bdc87bed204db34ca8a8f1ad}}, {{cite:aa3431d6d4ba892e4338b1ec5a78b62c0c7ca2f3}}, Bag-of-visual-Words (BoW) {{cite:cac3f06a1715ff4362a9a6b421b7e3cbd6411c43}} and Fisher vector {{cite:4978275bcb4e3994180b2eb42426a099da0b5cdc}} have been successfully applied to texture recognition. The main idea of BoW is to represent an image by a histogram of feature words of a data-learned dictionary (the so-called codebook). The BoW model usually consists of the following five steps: i) creating local patches from the input images, ii) extracting local features from the patches and creating the `bag', iii) learning a dictionary of visual words, iv) quantizing features using dictionary and representing samples by histogram of words (encoding), and v) classification of features using SVM or decision tree. A block diagram of the traditional BoW is shown in Figure REF (top). In fact, convolutional neural networks (CNNs) can be viewed as BoW models too. The convolution layer of CNNs operates in a sliding window manner acting as a local feature extractor. The output feature maps preserve a relative spatial arrangement of input images. The resulting globally ordered features are then concatenated and fed into a fully connected (FC) layer which acts as a classifier. Despite massive achievement on a broad range of applications such as image classification, object detection, segmentation, and scene understanding, CNNs are typically not ideal for texture recognition due to the need for a spatially invariant representation describing the feature distributions instead of concatenation.
| i | 40bf3cc005dc5fb4947163f252a5ae47 |
To make NMT models better learn from and cope with lexical constraints, we propose to leverage attention modules {{cite:8fa86d6af9fba1f783d0ee332be4f1e3fddf6789}} to explicitly integrate vectorized lexical constraints. As illustrated in Figure REF , we use vectorized source constraints as additional keys and vectorized target constraints as additional values.
Intuitively, the additional keys are used to estimate the relevance between the current query and the source phrases while the additional values are used to integrate the information of the target phrases.
In this way, each revised attention is aware of the guidance to translate which source phrase into what target phrase.
| i | a63c5169a8199f5d1818e2993d4fae33 |
We further report the experimental results on CamVid {{cite:b208b8ea92fcaa4e111c591ca38ec54c8f16081a}} in Table REF , using DDRNet-39 backbone network {{cite:951fd7b524589149bd21dd72c3543ad1d8b5cc85}}. The results show that our method can achieve 70.2 FPS, achieving 18.8% gain over the base model. We increase the FPS with less than 2% drop in accuracy. That is, STMG provides a good trade-off comparable to state-of-the-art models on CamVid.
| r | 9b5733ebaac092b1ca7b9c47e4d46e1d |
Before evaluating CERT, we would like to evaluate our base model PyCodeGPT on HumanEval {{cite:6102d242d74bdf5f16324313920fe7f543f4359a}} compared to several advanced pre-trained models. As shown in Table REF , PyCodeGPT (110M) achieves competitive {{formula:c6e299df-88c6-4305-83fc-1ca9ae4880a5}} pass{{formula:3f16c173-7aa5-4d57-a48f-0fb76c1dbbeb}} . It largely exceeds other models with comparable parameters, e.g., AlphaCode (89M) {{cite:564d46cc4caec5ffa780e12c3e3f317bcfcfa904}}, CodeClippy (125M), and CodeParrot (110M), and also is better than the larger model GPT-Neo ({{formula:a0885b73-dd3a-4f7a-aad6-4ea83b2ded6b}} B).
| r | 7093ede9fa759bad9ae3556306e2708b |
it is clear that {{formula:2005e111-8391-4025-be01-49e16d09dd56}} and similarly for system B with equality if and only if all {{formula:f329ed63-2c45-46e1-af78-af8b3181364e}} are equal, where {{formula:6ff9b372-67ff-4cda-bec4-c153e76884e7}} are the eigenvalues of the density matrix {{formula:4a191127-6729-4c4a-8f76-6dc0139afe75}} . Due to the entanglement between A and B, we also have {{formula:ceebeb76-6188-40a7-817a-ed2c87dbf0f8}} . In the limit of large Hilbert spaces, entanglement entropy of subsystem A follows the Page curve {{cite:521d16400bfdf1f69a5e7326ea8ab0372a485a2a}}, {{cite:1ae869dcc3b19ef4e88705a9fd40b4d29e25c128}}
{{formula:a6b57894-11ce-4ab3-8ec7-ab1839580e56}}
| d | 4336df19439a0bba4b72374427db80dd |
We compare the performance of two architectures across all datasets. First, we utilize the U-Net architecture {{cite:3074e99fba318c3e7ef857ef8928f90bd2e1899e}}. Our U-Net implementation takes as input the adjoint of the measurements under the forward model {{formula:48209ce1-cdb4-43f2-bcc1-293ae5436d64}} , which is then passed through several CNN layers before obtaining a reconstructed image {{formula:fe1754f6-0562-4d2d-bc21-d4191d23ba90}} .
| m | ae239a4bb60f073948e50b8469b678cf |
BiLSTM-CNN-CRF
We used the PyTorch implementation of a BiLSTM-CNN-CRF model {{cite:775bdf6f8bddd1bc8bf7fd22ce9f5306c27ccc08}}.
The model combines the word embeddings with the character-level representations extracted using the CNN and feeds them into the BiLSTM module with the CRF output layer.
Word embeddings are usually pre-trained on large unlabelled corpora, but, in the present study, we used randomly initialized embeddings.
| m | bc90b155c55ff6648eafcf7929915abd |
We do not consider the gravitational lensing by a marginally unstable photon sphere for {{formula:7db812e7-d73a-4b87-900d-64f6e19c7441}} .
In this case, we cannot use Eqs. (REF ) and (REF ) since the deflection angles do not logarithmically divergence in the strong deflection limit.
We can use formulas in Ref. {{cite:b534726f39aefaa8ac07c7d07005ed8617d57f2a}} for the lensed images slightly outside of the marginally unstable photon sphere while
we cannot use them for images slightly inside of the marginally unstable photon sphere.
The later case is left as one of future works.
| d | fb5a7fd4d407b29e61c43df7caf7b526 |
We named our AI improviser A.L.Ex, the Artificial Language Experiment, an homage to Alex the Parrot, trained to communicate using a vocabulary of 150 words {{cite:8fab90e1281f2d1dd3068ecff32562360188edda}}.
The core of A.L.Ex consists of a text-based chatbot implemented as a word-level sequence-to-sequence recurrent neural network (4-layer LSTM encoder, similar decoder, and topic model inputs) with an output vocabulary of 50k words. The network was trained on cleaned and filtered subtitles from about 100k filmsSubtitles from 100k movies were collected from https://opensubtitles.org.
Dialogue turn-taking, candidate sentence selection, and sentiment analysis {{cite:2bb3939d325b4b5c7d6f53c6d3b50f0b2d37cb63}} on the input sentences are based on heuristics. The chatbot communicates with performers through out-of-the-box speech recognition and text-to-speech software. The chatbot runs on a local web server for modularity and allows for integration with physical embodiments (e.g. parallel control of a humanoid robotThe robot was manufactured by https://www.ez-robot.com.
The server also enables remote connection which can override the chatbot and give dialog control to a human operator. Further technological implementation details are provided by {{cite:8395536ea832ab7d3bd6fb9b56192c3addd97001}}.
| m | 4b0d163ae08165457fb6400e886b93be |
Table REF and REF show examples of incorrect predictions when a counterfeit key is embedded into the recurrent neural network (RNN) model during inference phase. For classification tasks (i.e. TREC-6 {{cite:afb789cb0662b3b6c08d05fb38af692e60609c77}}), Table REF shows that when a counterfeit key is used, the RNN model gets confused between similar classes, i.e. DESC and ENTY for TREC-6. Meanwhile, for machine translation task (i.e. WMT14 EN-FR {{cite:d9ac1bf7feac6fdbd18d1f19e74868c47baec742}}), Table REF demonstrates the translation results when a genuine key is used against a counterfeit key. It is observed that when a counterfeit key is used, the RNN model can still somehow translate accurately at the beginning of the sentence, but the translation quality quickly deteriorates toward the end of the sentence. This is in line with our idea and design of Gatekeeper where the information (hidden state) passed between timesteps would be disrupted with a counterfeit key and the output of RNN would deviate further from the ground truth the longer the timesteps are.
{{table:8c41ab21-8864-4990-81d4-8307255f92ea}} | r | 5f1258e8bef0154b2bc859292cba767a |
The emergent rule for graph growth is related to fractal properties of the graph. Structures present in the seed or formed early on in this process will determine the basic fractal structure. A growth algorithm similar to the iterated tensor products might satisfy this property.
The emergent rule for graph growth is contained in a mechanical structure that imparts new shape. We may imagine a “brewing vat” embedded in a larger universe. Note that such structures are known to exist in Conway's Game of Life {{cite:1dd3dbda6ca760d7aaa7b730fd512c390a4fa003}}.
The emergent rule is related to the way information is transmitted through the graph. Rather than having a graph which constantly grows in all directions, like in our iterated tensor products algorithm, we may imagine graph growth happening only at specific places at one time. In order to determine such growth locations, we could in principle utilize something like the GraphWave algorithm, in which we release a wavelet from a given node and see where it is most likely to land.
The emergent rule consists of the graph itself interpreted in some machine language. This begs the question of what complexity of the “external CPU" that interprets this graph we are willing to allow.
The look-ahead protocol is somewhat related to algorithms in reinforcement learning such as AlphaZero {{cite:05a828c322a08026c82573c23cda65360d31e421}}. Yet, we note the sample space here is much larger, which is likely to make learning more difficult.
{{figure:f4fe4e42-5b82-4830-adff-45a2f47ba0d1}}{{figure:cf7c2309-3b51-414c-a077-9cd2a3975b33}} | m | ce91aff71cd2677672c7ef07b63b62d0 |
Compared to the rich literature on the well-posedness of classical water waves, the research on the well-posedness of water waves problem with non-smooth boundaries (we call it “non-smooth water waves”) just started several years ago and there are a lot of open questions . In general, there are two kinds of non-smooth water waves problems: The first kind of problems has contact points (or contact lines) between the free surface and the bottom, i.e. {{formula:cd6dc7ab-a1c4-4339-8e45-3e9097ec1dad}} ; The other kind contains crests or cusps on the free surface, i.e. the surface is Lipschitz. We would like to mention that in the case with large crest angles, the famous Stokes waves can be dated back to papers by G. Stokes {{cite:56a91bf9a5c0f98700d2f45d6ed30cba339f3970}}, {{cite:ceb08aca8ad3308f626ba1a9634621af589797d0}} which obtained traveling-wave solutions with limit crest angle {{formula:4511ae1d-c720-4835-a881-cc5fe3a8bc70}} . Obviously, the main difference here compared to classical water waves lies in the corners on boundaries. As a result, the analysis involving the corners (i.e. domain singularities) becomes the key point in the non-smooth water waves.
| i | 1daf66fbfb117f9c6fc5c017fe79c499 |
The following definitions of a blr makes use of the introductions in {{cite:cc7c91e0f71c793470233738c00036244cd02d04}}.
In contrast to a deterministic perspective to learn the model weights of a linear regression model, a Bayesian approach gives additional insights through the posterior, especially when there is insufficient data {{cite:cc7c91e0f71c793470233738c00036244cd02d04}} as for tl.
It helps in measuring task similarity for model selection and allows assessing the quality of the model in terms of its uncertainty.
We can also utilize it for an adaptation by replacing the final layer of a neural network with a blr, train it with the target data, and make predictions and the target afterwards.
This approach allows combining models through bma, see Sec. REF .
Finally, we can utilize it to learn a belm.
The following equation details the posterior distribution of a (linear) model:
{{formula:ffdd8b9c-04ba-42a6-8e92-74bf36da0f07}}
| m | 56a5050a12b1c27d1d188b726624b598 |
Fig. REF shows the minimum on-line training overhead versus {{formula:927b490c-0aa4-4049-b49f-b4e0de0cca6f}} , with {{formula:b507352e-940a-4537-b7be-94cf979360b7}} and {{formula:be1c48b0-1dec-4bb6-9d19-754fc14c4734}} . On one hand, it is observed that both our proposed schemes are more efficient than the scheme in {{cite:2e13a9037001af6e7f5943b8bf4c8af2721e5f93}}. On the other hand, Scheme 1 generally outperforms the benchmark scheme in {{cite:529f41eb7b8a3b1902791b549a5876ebfc054be9}}, when {{formula:24904991-d740-43eb-9891-eb3fe1cf48ed}} and {{formula:af771ffc-0552-430d-9bb7-5319ead964ec}} due to the similar reason given for Fig. REF . Moreover, Scheme 1 is more efficient than Scheme 2 under this setup.
| r | 78e139cc69f66c68152716c6af8c98b2 |
A widely used technique to study the stability of the synchronous solution is based on the derivation of a Master Stability Function (MSF) {{cite:438ddcff193685b932990df5a7d9f87a2cc18d04}}. The technique consists in linearizing Eqs. (REF ) around {{formula:a6d49a2a-99e0-401c-bbaa-2565160cacb1}} , and then applying a proper transformation of variables that leads to a generic variational block of this type:
{{formula:393a5ae7-3988-4694-b69d-3a633bdd05ec}}
| m | f7b21d9571c5edf64f6806c458474d85 |
Split MNIST and Permuted MNIST: Subsequent classes in the MNIST {{cite:2f348876d5c71ce9c6052da1104b7a510256efcc}} dataset are paired together and presented as a task in Split MNIST, a well-known benchmark for continual learning. This results in 5 incremental tasks. In Permuted MNIST, each task is a unique spatial permutation of {{formula:40c6bcf9-c817-4d3b-8320-6971a8d9d68b}} images of MNIST. 10 such permutations are generated to create 10 tasks. We use 1000 images per task for training and the model is evaluated on the all test examples, following the protocol in {{cite:569964b30f139b89ad9ca7872b6a36987957a102}}.
| r | 06277e88dbc963558ab80a64d867e4fa |
In section REF , we outlined the most conceptually similar methods that conducted large-scale model pretraining with task-agnostic parallel sentence alignment as part of the training routine {{cite:6728b9c079e5b3ab9140bd3d1f0593928e7deab0}}, {{cite:0032534a03dded45256c6b11289ae71f16efd301}}, {{cite:7f00783d26e63b4c141566c616d5c5687a02785d}}, {{cite:7f9ae44486f65807240231d5559cfd49da42684c}}. Where ablation studies were provided, the average improvement attributed to contrastive alignment was {{formula:26249655-c944-4f84-a879-07a70921950a}} 0.2-0.3 points (though the tasks were slightly different). While we do not directly compare XeroAlign to contrastive alignment, it seems that task-specific alignment may be a more effective and efficient technique to improve zero-shot transfer, given the magnitude of our results. This leads us to conclude that the effectiveness of our method comes primarily from cross-lingual alignment of the task-specific vocabulary. Language is inherently ambiguous, the semantics of words and phrases shift somewhat from topic to topic, therefore, a cross-lingual alignment of sentence embeddings within the context of the target task should lead to better results. Our simplified, lightweight method only uses translated task utterances, a single encoder model and positive samples, the alignment of which is challenging enough without arbitrary negative samples. In fact, this is the main barrier for applying contrastive alignment in task-specific NLP scenarios, i.e. the lack of carefully constructed negative samples. For smaller datasets, random negative samples would mean that the task is either too easy to solve, resulting in no meaningful learning or the model would receive conflicting signals by training on false positive examples, leading to degenerate learning.
| d | c0658b195b9af6f20c18b68f07f05130 |
End-to-end text spotting results on the Total-Text dataset are reported in Table REF .
Compared with the previous fastest ABCNet {{cite:40c4b988bf4ea4e44b12ef709293e29fd25513ff}}, our method with shorter side being 640 pixels runs 1.3 times faster, while our end-to-end text spotting F-measure is 2.2 points higher (66.4% vs. 64.2%).
When adopting a larger input scale or jointly training strategy, the performance of our method can be further improved.
With low-resolution input (the shorter side being 512 pixels), the inference speed of our method reaches 29.2, at least 11 FPS faster than previous methods.
At the same time, its end-to-end text spotting F-measure is 64.9%, which is higher than most counterparts.
It is notable that PAN++ achieves the best end-to-end text spotting F-measure of 68.6%, which is much better than the second-best method (Qin et al. {{cite:7e8cf827bb4669ff40bb93ae2f4347ada46278ef}}) and our speed is 4 times faster (21.1 FPS vs. 4.8 FPS).
| r | a040f5f56bea4295d25e0d7aedee5158 |
In {{cite:7ec4a8176c66a7f4dffb42f0309784a7a0d3d8cb}}, the optical and thermal information was mined to recognize pedestrians. In {{cite:f4b5bdd10581fcbe48758c31106e76537be07bcc}}, a cross-view cross-scene multi-view counting method was proposed to improve the performance and generalization of the model. In {{cite:e0fd5f7391f1d7cf874d8b5bbd859bbe2f5f2b29}}, a generalized loss function based on an unbalanced optimal transport was introduced for crowd counting and localization. In {{cite:43e5bb7d3e9a52f6aa80ead8eb0b071621b472f5}}, a purely point-based framework with a new metric was designed for joint crowd counting and individual localization. In {{cite:e47dc79551931febf8cd3d85787a1a47ae8025a5}}, a spatial uncertainty-aware semi-supervised method with regularized surrogate task was proposed to reduce the annotation cost. In {{cite:bb9cae38ba59ed33ae3c15681aa7ce7bdbc6d46b}}, the domain-specific knowledge propagating model was constructed to unbiasedly learn the knowledge from multi-domain data at the same time. In {{cite:c9f8221970e8089e8b6316110be09df53fae9575}}, the temporal consistency was explored to estimate crowd flows and infer crowd densities. In {{cite:4ee86139c2e639ca279b8f4a85e29e638747c980}}, a locality-aware data partition method was proposed to tackle the severe under-estimation and over-estimation problems.
| m | 72f1a0d4a831ec9020a49a4ba3ac4d78 |
where {{formula:80034e81-7725-4cb2-8fc0-c9026260245c}} denotes a {{formula:ec160c6e-c876-47db-9495-b7c355f8c049}} -dimensional random vector taking values as in the rows of {{formula:0286193e-9493-47c1-957e-ac03bedf4c45}} . In this case the random compositions {{formula:ae7ee203-a4f2-4ad0-bcaa-9b85cb75d8e2}} are distributed according to Aitchison's celebrated logistic normal distribution {{cite:e66b2355aeb0dc14878446c54bb6d0adfd607f59}}. If we denote the density of the compositions themselves by {{formula:9e436e39-c676-4121-9c35-7202f6f8dd66}} , the Gaussian density {{formula:15f51a59-b998-4943-802e-e0f8ef0dd88b}} will be multiplied by an additional factor due to the resulting Jacobian:
{{formula:0e678992-0b05-4b12-9b33-ba077678e7bf}}
| i | d0a47e7f63cfdf719b368ee94c34b009 |
Fredholm integral operators canonically arise in numerous applications ranging from a classical fixed-point formulation of linear elliptic boundary value problems {{cite:3f8d8663b34557620df6068a18d3c166168730a3}} to Fréchet derivatives of recent models in theoretical ecology {{cite:063e4dfd2b4ec2e8053bb745784025420e21b8c9}}. Often their Green's function resp. kernel is positive. This is understood that such a matrix-valued function preserves an order relation induced by an order cone. For instance, dispersal kernels used in theoretical ecology preserve an order relation in order to capture predator-prey or symbiotic relationships between different species, or differential operators satisfy a maximum principle which transfers to positivity of their inverses via the Green's function. Moreover, for example {{cite:35196f4eed95ddd3c1cfb825e3c37eb12bbafcc8}} provides sufficient conditions that Hammerstein operators can be transformed into an order-preserving form.
| i | 7227a8abd8691c95dddf13235db49965 |
Based on the nature of problems, a ConvAI system is expected to solve three major research problems {{cite:0fea7d98567a468df900c615081f63b904fd14ca}}. Question Answering (QA) involves providing answers to user queries through conversation, using the knowledge drawn from various data sources like a snippet from a text, a collection of web documents, or an entire knowledge base. Task completion expects the conversational agent to accomplish task/s for the user, using the information acquired through conversation. Finally, Social Chat makes the agent emulate humans and converse seamlessly and appropriately with users, as in the Turing test {{cite:bc46bc710bb1dda54495685e72b55d9bc9b5740f}}. Each of these fields has its own set of challenges to tackle.
| i | 4718c1f0a1b41a2c226b0add2c661fd6 |
blackSo far, much attention has been devoted to the detection of binary mesoscale structures, i.e. communities and, to a far less extent, core-periphery structures: the efforts to solve these problems have led to a number of approaches that are briefly sketched below (see {{cite:a9caa62859934c2454ef4daa9f76a20962fe4dd1}}, {{cite:fb7ff63af73a720d51956f59b4b6db81c9991d90}} for a detailed review).
| i | ff283010e96c72186df2945d966aa2e6 |
We have shown that {{formula:d7f6e74a-e15f-4369-99f3-a47232ad7682}} scalar field perturbations of the nearly extremal black holes are governed by the effective potential which has a deep negative gap, and, that, nevertheless, time-domain profiles are decaying, which points to the stability of the scalar field.
When the effective de Sitter term vanishes ({{formula:3c924b81-438e-4b5d-b658-1d406da61cef}} ), the asymptotic tails of the massless scalar fields are not power-law, as it happens for the Schwarzschild case {{cite:3639234bb37bc7bba2163ffa1da8597c153789cd}}, {{cite:6f95b00a95beb3c1dba39da9217fb3c5358364f1}}, but the oscillatory ones with a power-law enveloping of oscillations, like it happens for massive fields in the background of asymptotically flat black holes {{cite:b81ce2fba665dd9357fad0d7b94e0f160d39adeb}}, {{cite:9a7e9424222eeea0e8fc54e01510c83746f64695}}.
When the effective de Sitter term is turned on, this oscillatory tail goes over into the exponential quasinormal ringing dominated by an essentially non-Schwarzschildian, longer-lived, frequency.
The asymptotic decay law at {{formula:307ab5c9-e84f-4128-85fb-2ffffe2b5719}} for the scalar field is, then, exponential, so that the whole evolution of the signal consists of the three stages: the first stage of quasinormal ringing at the Schwarzschild-like frequency, the second stage of quasinormal ringing at the long-lived non-Schwarzschild frequency and the exponential tail.
The asymptotic tails for electromagnetic field are exponential even when the effective cosmological term is tuned off ({{formula:4d824ca6-231b-4b76-828a-8a271d858fb9}} ).
| d | aee24e1a33db91fce12e8290746573a9 |
LASER+LSTM+T5: this method uses pre-trained LASER embeddings, which are passed as input to a LSTM model for category classification and then to a T5 model for summarization;
C-SKIP {{cite:5e96aac49213844236116bd86d679a5ab5357212}}: this is a centroid-based method using a FastText skipgram model trained on the CrisisLexT26 dataset {{cite:f12b312b613912aa585bc9642e75fa1180c44b72}}, improved by the use of T5 pre-trained model (originally, the method used a corpus extracted from Google News);
CX_DB8 {{cite:9d252ea6cc3439f0e9c2939aff7b614abb500b71}}: this is a queryable word-level unsupervised extractive summarizer, which is based on the text embedding framework Flair {{cite:f1a4b4d994e7d1a77009879c7455227a70cbf924}}.
We tested this with different pre-trained embeddings, including transformer-based such as BERT and XLNet; for this task and datasets, the best results were obtained with GLOVE embeddings;
NAFI {{cite:67e29fa06a74475146ccad226f998fe69d3b248c}}: this is an abstractive text summarization method developed specifically for crisis events;
CLiQS-CM (ours): we use a combination of LASER embeddings with tweet-related features and query similarities features that are passed to a LSTM model for the ranking step and then uses a T5 model for the summarization step;
CLiQS-D-CM (ours): this is the same as CLiQS-CM but retrieves diversified (see §REF ) top-k candidates in the ranking step.
| m | c2724127b4b3ca817b73e52e8db91d13 |
To show how general the proposed framework is, we propose to express the state-of-the-art approach proposed by Ustun et al. {{cite:e232155acd1a99c9fc868e828df738f3852a1387}} in the proposed formalism
highlighting the definition of the three involved functions.
In this approach, the user knowledge {{formula:8a8cc88d-dada-4935-8382-2f594798a106}} is denoted {{formula:41d74f04-4532-4b7f-b364-76a27e3df021}} and defined as the set of modifications that can be applied to instance {{formula:01bb4726-eaf1-4b1c-9250-a4076f2ac44b}} , it is integrated to generate an actionable counterfactual explanation. The latter is the solution to an optimization problem of the form:
{{formula:f4e5f2ba-a439-4b3c-8cdd-928735be8d56}}
| m | 9dbb330e676348354702d1982653bfc8 |
DL has become very popular for imaging inverse problems {{cite:30f3fca7715b8d6b38c667194addea39e5db22ab}}, {{cite:97493874f407c4340994d8ba5147c5924737d72a}}, {{cite:d20b61ccd53ceae9b08c91032684dd41933cea5c}}, {{cite:afeeabd6938edb435f83fe2540aa6131cb9d9795}} due to its excellent performance.
Traditional DL methods first bring the measurements {{formula:7e5926ce-fc91-4121-8719-fd9fce495ef2}} to the image domain and then use a deep CNN architecture, such as UNet {{cite:c950b0530d332142bad09b3e0ffeece93a3a4f1a}}, to map the resulting low-quality images {{formula:d941a2f3-ea31-4c49-88dd-e31cdfe70490}} to high-quality images {{formula:af6e7987-8432-4ead-ab70-5b940f5c0563}} .
Here, {{formula:10c494f8-4335-4ae5-af11-de7c1bd527ca}} denotes the total number of training examples.
Typically, these CNNs are trained by minimizing a loss function
{{formula:73770038-b533-4540-8582-ed336259a978}}
| m | 5f9713ca7ab9d20a53c3f3c7dc4ffbac |
Despite the growing application of GNNs to fMRI data, a major limitation is the requirement that the graph adjacency matrix is known prior to model training. It is therefore implicitly assumed that FCMs represent the ground-truth dependency structure of fMRI data. In reality, however, this is not the case, as FCMs are highly dependent on the choice of measure used to quantify statistical dependence {{cite:ccf13bd6b72fbeb4c051fc799c3687047143151e}} as well as on any pre-processing steps, such as thresholding or binarization, which are commonly used to simplify the matrix {{cite:bbeb6f6f3d0c7b01be515889f086ff08cb252632}}. As such, brain regions may appear functionally connected under one combination of pre-processing steps but disconnected under another {{cite:d78477faf54b1b11b91a43214906be0e73cf23f5}}. Moreover, to date the majority of GNN works use FCMs that capture only static FC {{cite:5fb7e5e3c966a193c4338ff65b92d6a68623b8a5}}, {{cite:59ffb55d5a28fb4380260f2f378134a2d318a1fe}}, despite growing neuroscientific evidence that FC dynamically changes over time {{cite:14ccb45e82a5b7bb594c50a83838f0367ee95017}}, {{cite:09a17e2ebcbb7e2a9a7d094fd2d55c17bc0bfcc0}}. This suggests important potential benefits in choosing a measure of dynamic FC {{cite:d78477faf54b1b11b91a43214906be0e73cf23f5}} in order to create time-varying dynamic adjacency matrices for GNN-based models applied to fMRI data. Thus, to ensure GNNs are able to learn useful representations of brain graphs, it is of high priority to establish the most appropriate way to construct prior FCMs from fMRI data.
| i | 9602aeb681da11938d4faa59cd41c925 |
We note that {{formula:1a96fbce-dcba-4913-a44b-45c3735c9278}} , {{formula:d38258bf-77b0-45c8-aaab-d301c30cfa80}} by the regularity assumptions of Definition REF . (See {{cite:367d00021325a5f0061db69111dafbbf59552d5d}}, for example.) Thus (REF ) is well-defined.
| r | b74d19539e9147c5abcf6fd0e193a753 |
In order to investigate the learned feature distributions quantitatively,
Figure REF provides Proxy {{formula:79a9ecce-382a-4c44-b592-ed7af8297edc}} -Distance (PAD) between the feature distributions from STA, ROS, and UADAL.
PAD is an empirical measure of distance between domain distributions {{cite:8867d57187a9b222730302bfcad071faaa74de27}} (Details in Appendix REF ), and a higher PAD means clear discrimination between two distributions. Thus, we calculate PAD between the target-known ({{formula:0e9f3dba-a5c5-4323-9441-3f478259cc54}} ) and the target-unknown ({{formula:68835a8e-6996-4710-85b3-bf2236c85cef}} ) feature distributions from the feature extractor, {{formula:6d61fdf2-6f20-48dc-92af-d2d05201b086}} . We found that PAD value from UADAL is much higher than STA and ROS. These results represent that UADAL explicitly segregates the unknown features from the known features in the target domain.
{{figure:a3ce7294-e45a-4f3b-8c84-c7223ac43ab7}} | r | d1efe1a3b2727be550ddbaed1c1cffe9 |
To train MIME, we built a new dataset called 3D-FRONT Human that extends the large-scale synthetic scene dataset 3D-FRONT {{cite:983504f9c1a7b93d62f90c0aa2049d1c317438dc}}.
Specifically, we automatically populate the 3D scenes with humans, i.e., non-contact humans (a sequence of walking motion and standing humans) as well as contact humans (sitting, touching, and lying humans).
To this end, we leverage motion sequences from AMASS {{cite:9e8e828d7541bbff5bfc0a90cf8e06f9ddc7cd4b}}, as well as static contact poses from RenderPeople {{cite:7725799255d4313673cedce51d0352bd5688c714}} scans.
| i | 450637a51d858d8db485aca8825aaaa0 |
where {{formula:a014fa9a-7f78-4a10-9bf1-f33296a15cbc}} and {{formula:f362cda2-b762-4344-a738-d4df405aef33}} refer to
the average path-length of high-{{formula:a4b58798-96ab-4293-9520-71127163a1b9}} particles in the in-plane
and out-of-plane directions. For every temperature profile, {{formula:763a2e8b-f93e-4428-b77d-ea957e657c0c}} and {{formula:3fc3520b-9674-4a80-a3fa-647a89d33c0f}} are calculated using the
Monte Carlo method to generate an initial hard parton position in the
XY plane according to the binary collision densities. The parton then
traverses the medium in the {{formula:5840d219-8915-453a-9e9b-88a994967dc4}} (or {{formula:1c8ad55d-d7d2-4c3e-866c-72e12cbccc8c}} ) direction,
until the temperature at parton's current position drops below critical
temperature {{formula:d736dadb-855f-4c32-9ef8-3a66def1fb47}} . We use {{formula:678ca311-54f1-4df8-a862-ec8bc8563936}} =160 MeV, which is within the uncertainty of
the lattice QCD critical temperature of {{formula:9e8afd6a-9f76-405b-bd56-0941d6c61333}} MeV {{cite:fde19cfa183b1688b057afe4a3749c6feb938c25}}. We then obtain
{{formula:a3d4c845-4129-4196-9c3a-759eb984dcf7}} and {{formula:115952cf-8fdd-4fca-b759-7d35e7ffc699}} by averaging
the in-plane and out-of-plane path lengths over many different partons.
| r | 0219dc0307470a6e49f171dd14a31f4e |
Body2Hands w/wo image{{cite:4bd7a2ae8f416101c56dad01b5ec3e13cfc2ddea}}: State-of-the-art 3D hand shape synthesis and estimation by a learned deep prior of body motion. Models are re-trained using the codes released by the authors, since the pre-trained model is not available.
Body2Hands*{{cite:4bd7a2ae8f416101c56dad01b5ec3e13cfc2ddea}}: The original Body2Hands model takes the output of MTC{{cite:96f0fb64a4bac56c2b727c9b714294d86e47d9bf}} as input and predicts the rotations of hands. However, in our experiments, MTC output is not provided. Thus we retrain a Body2Hands model of the same structure as the original version which takes 3D body joints and 2D hand key-points as input. We take the retrained version of Body2Hands as Body2Hands*.
ExPose{{cite:7281f41d78fa6a42ee5b414801c90a20bd23640d}}: State-of-the-art method for full body pose including hand gesture estimation, which directly regresses the body, face, and hand poses from RGB image.
FrankMocap{{cite:e3aadd53724a651d0d117f6f26c973048399f959}}: State-of-the-art method for full body pose including hand gesture estimation, which leverages multiple leading solutions for pose estimation of different human body parts.
Our CNN: The same model structure with Body2Hands{{cite:4bd7a2ae8f416101c56dad01b5ec3e13cfc2ddea}}, trained with the proposed objective functions, takes 3D arm joints and 2D hand key-points as input and predicts the rotations of both arms and hands.
Our AHMT: Same configuration as Our CNN, except that the network architecture is replaced by a temporal transformer.
Our PAHMT: Same configuration as Our CNN, except that the network architecture is replaced by our carefully designed Spatial-Temporal Parallel Arm-Hand Motion Transformer(PAHMT).
{{figure:d262ecb0-9b25-4ed7-9f06-abecbd9602ee}}{{figure:165658e2-952a-4b64-b47e-47daa45d915a}} | m | c1291d2dfde26c6aef7f867769465482 |
In this work we analyse the combination of differentially private training, model compression and adversarial training techniques against model poisoning attacks. We determined that for the strongest insider adversary, post-training quantization did not have a significant impact on the results of the attack. The opposite is true for BB attacks, where the federation enjoys an improvement in robustness of up to {{formula:1c38cf92-48cc-4b0e-8f52-a825b458b43c}} in certain contexts compared to an uncompressed setting. In general, we found DP-SGD to be detrimental in BB and in partially WB settings, which is primarily due to a significantly lower accuracy of the DP-trained models after training. The result we found particularly interesting relates to a higher susceptibility of DP-trained models (when used to generate the adversarial samples) to transferable adversarial samples, especially given a significantly higher robustness of DP-trained models at train time. In essence, these models can be either significantly more or significantly less vulnerable to adversarial samples, based on the nature of the attacker, therefore not allowing a concrete overall conclusion about the effectiveness of this method.
However, there also exist a number of factors that can potentially have an influence on the results of our evaluations that we have not explicitly covered. Firstly, similarly to {{cite:bf05c419b3affa552f814fc213046403523ed40b}}, we discovered that the accuracy of the trained model can have a significant impact on the results of the attack. This is due to the fact that the adversarial labels (i.e. those used by the train-time adversary) are inferred from model predictions and these depend on how well the model is able to distinguish between different classes, affecting the difficulty of image perturbation. This, in turn, makes it more challenging for us to disentangle how the individual factors that influence model accuracy can affect adversarial robustness. Secondly, in this work, we relied on the post-training quantization, as we find this approach to be the most practical (or low-effort and foolproof), as it only requires a few additional lines of code, a single calibration round and a replacement of a small number of operations during model initialisation. It is of note that other approaches can, arguably, be applicable when discussing robustness of collaboratively trained models, such as train-time quantization or quantization-aware training. However, these methods are significantly more difficult to set up, as they require a larger number of steps and adaptations of the training process, making them less practical. It is also of note that a shared or public validation dataset is required for the quantization procedure to be calibrated properly, without negatively affecting the utility of the joint model.
Finally, as these are the preliminary results of an ongoing work, there exists a number of contexts that we have not covered in this extended abstract. We are planning to expand our experimental base with other robustness-enhancement methods, such as adversarial regularisation, knowledge distillation {{cite:9d9afc42c3ccc4fcfa419bdca5ea3c402765f43c}} and feature squeezing {{cite:0ce05976570a88391c68169635b56e8496361ab6}}, all of which were previously shown to mitigate utility-oriented adversaries in CML. Additionally, we are aiming to produce a more context-agnostic study, including attacks on image segmentation and object detection tasks.
Appendix
Experimental setting
In this study we perform two collaborative classification tasks on CIFAR-10 and paediatric pneumonia prediction (PPPD) (adapted from {{cite:5377ab0340d581da797f648e05b313758f015430}}) datasets. We utilise ResNet-9 and ResNet-18 architectures. We employ ReLU as our activation function and replace the batch norm layers with group norm layers for compatibility with DP. For DP training we utilise the opacus library {{cite:c97212e3df34d7651b08a9fcd814809f34a2b5c1}} with three privacy regimes (representing different end on the privacy-utility spectrum): High privacy ({{formula:6d40cb73-339d-4375-b983-52111323790c}} ), medium ({{formula:f4232713-6bb2-4260-9cc1-70885c9a689d}} ) and low ({{formula:bd0fd1e7-16d7-4a63-9180-28dedd7104ee}} ). For PPPD {{formula:e83ddb68-2306-4e56-9e0b-6df209b631b5}} and for CIFAR-10 {{formula:e5406ca7-84e2-496b-ae3e-a3ea5c7c98df}} . We utilise three adversarial attacks methods, namely PGD {{cite:cb2ded6bdbfb54cc253180d06e05b6521ef3f63b}}, FGSM {{cite:b1ccecaca5d2ea8fb551837ad1b494de3b5100d3}} and FAB {{cite:8a80836d2f5ca8ff041d8753df7cc46ec861093d}}. When performing train time attacks and adversarial training, we experiment with different proportions of adversarially controlled data: The adversary can control {{formula:6e176a05-0f1f-423d-b3a5-0bb7d12f9b39}} , {{formula:530e22f2-5e4e-49bb-a2d9-ba77e279b77e}} , {{formula:1dd482c0-63b8-48fc-9772-ec0eb6891bf6}} or {{formula:a5bd6a4a-e84b-463b-ad3f-47384c887ef1}} of the training dataset. By default, each attack (if required) is ran for 10 steps, with a perturbation budget of {{formula:c8840436-01fa-4c95-9de3-933621afa46f}} and a step size (the limit of perturbation during a single step) of {{formula:a9d5f618-598c-4af4-9f08-6b45a11360b3}} . We deliberately chose a high perturbation budget (in comparison to the frequently used budget of {{formula:54d645c5-8a62-4aa9-a5f4-7b61e30467a3}} {{cite:8a80836d2f5ca8ff041d8753df7cc46ec861093d}}) to represent the worst-case scenarios, when the adversary has an ability to significantly affect the training process.
Performance of the original models
{{table:5cb03f25-3c5d-47ee-a664-e9fcbda80db2}}
Adversarial training results for different privacy regimes
{{figure:403a1c24-f534-4126-8e30-5dc5a3a3f27d}}{{figure:0caacc42-c273-4cbf-9935-ffba28aad2a9}}
Train-time attacks
{{figure:8ddb4c08-3e52-4f4b-8778-51762b59a7cd}}{{figure:aa478621-44fa-46df-8647-84bb453a2370}} | d | 16c7c60c53e94288e8d1991a386808f3 |
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