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We consider two BERT-based methods for tackling HDL:
a BERT + MLP method
that added an MLP classifier on top of a pre-trained BERT model {{cite:09e6087a6907ef724bb5dc385c68110a860a8c5d}} for each distributional label;
a Hierarchical Distributional Learning Network (HDLN)
which was an adaption from HMCN-F network {{cite:1adb24e341e8d37e2f2a8dc621b9ea4691b962f0}}. For baseline models, we use bidirectional LSTM {{cite:760fb0f985cc961e309fde27f2208a63dd8f4cb1}} with an MLP classifier on top of it to learn each distributional label.
| m | 5025664ebe673c438454cbfcca4cc363 |
In addition to the standard linear regression model discussed in Section REF , the proposed framework can be applied to a range of generalized tensor regression problems. Recall that the classical generalized linear model focuses on an exponential family, where the response {{formula:63dd5d33-d05a-4674-a82b-16bb968128ed}} satisfies the following density or probability mass function {{cite:1e6bd3501d97a88c663828bbc81a65e6659666e5}},
{{formula:d7445ef9-9d21-44ed-a67a-248ba9e8f989}}
| d | 8bef59e8535ec4ec0dd9d49d1f41fe4a |
Let us now we verify if and when the proposal is implementable in a state-of-the-art optomechanical setup and a nanomechanical resonator can be prepared with high fidelity, at least for a long-lived transient, in the macroscopic superposition state {{formula:fab8d307-be93-46b6-886e-940b357dbf60}} . We consider parameter values achievable in state-of-the-art MIM setups {{cite:2ebd61ffd0497a932ccb7924ff707d0c12f1de5e}}, {{cite:cd6fe0aa2c519b0c7f5b4963f766bb3631e0bef3}}, {{cite:3ffcfc9ca20a7d559a30ead99353e535c923dedc}}, {{cite:47cd0c2a048eae5201efd523b1a98d0a0d571a3f}}, {{cite:19ff533ba9ef75f1761477e890efe226c5ca965a}}, {{cite:71087ee445ed057e6f6b53ddcdd5fdf4f625409e}}, {{cite:1180bdf0a6e8a4e22be8b5c23e0523d4982b5b07}}, {{cite:c1ee2ffa6f46c50a57362d2e1e89d0d32cd3ca63}}. For the mechanical resonator we take {{formula:1d848e53-22f4-4c0f-b5c6-5f62a4b4bc9d}} MHz, {{formula:b34f2d2b-1e7e-4c29-b9a4-4efbcd8f3572}} Hz (implying {{formula:a72db572-90f2-47fc-a672-26ee5a78ac86}} ), {{formula:f918d93f-27af-4abe-be55-a2b0d48126e4}} ng and we can take {{formula:7dac525f-5b9d-44a8-8081-ab9f1e3e6fc2}} GHz/nm{{formula:887462c1-00ff-4638-b3ed-4c00492d2ff2}} {{cite:71087ee445ed057e6f6b53ddcdd5fdf4f625409e}}, yielding {{formula:9b584ba5-554a-4438-a23b-690693bba41b}} Hz. We then take a laser with frequency {{formula:e0ddcf33-cc2b-4244-9d0d-e3b26f80c436}} Hz (corresponding to a wavelength {{formula:fcf4abca-8bb2-440c-909f-a503e5115539}} nm) and input power {{formula:e23b69f0-b6ab-4e74-aae6-450c2099ea10}} mW. We also choose a cavity with total decay rate {{formula:8c576b53-81af-49c3-911d-da44c7a1b991}} Hz and with decay rate through the input mirror {{formula:b23a7118-2526-47d2-a681-ecab4e175dd0}} , yielding {{formula:5d86231e-4f2d-4841-9c7f-c29b6c5dafa9}} Hz. The corresponding value of the intracavity amplitude from Eq. (REF ) is {{formula:13b3c8be-fe1e-4f96-9d49-6c35c3534e57}} . As a consequence {{formula:4e776db6-efd0-4683-9cc3-e86eece635fc}} Hz, which therefore agrees with the assumptions made. Moreover we have an effective decay rate {{formula:04d981f1-9095-4583-9a0e-3a5ec1a11a04}} kHz which is reasonably larger than the thermal decay rate {{formula:ecbef8ec-c7a4-4346-a4a8-68e90c52e238}} as long as {{formula:8dd27787-11c4-4d67-8759-08b68ea12251}} . Even though nontrivial, this latter condition is achievable in current optomechanical experiments because cryogenic environments at temperatures {{formula:1eaa214e-50a1-4f5b-8e6e-6f9e153caee2}} mK are feasible and, with the chosen value {{formula:393a758f-cbe9-4f36-b5f5-c718c0145adb}} MHz, this corresponds just to {{formula:c15f61af-1434-4eb3-a509-86425154c5a6}} .
| r | 61065fb5702f249a9c30bf7d4bdd799b |
LwPosr is compared to existing methods (with both lightweight and heavier techniques) for HPE on open-source benchmark datasets. Table REF and REF illustrate the comparison of the number of parameters and MAE for the compared frameworks. They are as follows. (1) 3DDFA {{cite:245c3adb32f6d7e6720bbde889a4ed83f43d11d6}} uses a cascaded CNN network which tends to fit 3D model to a single image. It is described to perform well on occlusions. (2) KEPLER {{cite:1b8bc805752ac3ee43e50086867cf48375e61abd}} uses Heatmap-CNN to understand the local and global features to detect keypoints for face alignment and HPE is a by-product task. (3) Dlib {{cite:22a203200da3537b2a419559ad290ac94713e9de}} is a standard well used library for faces for applications of HPE, face detection, keypoints prediction. (4) FAN {{cite:36e9ae262f7ae139cd04b2d2e2bb4c64852df6ea}} utilizes landmark localization network combined with residual block forming a multi-stage network with multi-scale features. (5) Hopenet {{cite:6801f4117ac1f76b8e8443b0e5a58895026355fd}} is ResNet based fine-grained structure using classification and regression loss. (6) Shao {{cite:1636d9b3584279b971dc31d6212c9a8798a1dae2}} works on the adjustment of margins of detected bounding box for faces using a CNN architecture. (7) SSR-Net-MD {{cite:0c16491bdf6d9e9edf41538a71af1a0728abf11c}} uses soft stage-wise regression. (8) FSA-Caps-Fusion {{cite:0c026522c280dfd4dbbc3f83d5fd4af93af4fa81}} learns feature aggregation for fine-grained regression. (9) TriNet {{cite:74b6a74e1d860eff97374e42852935fd6dadd471}} uses ResNet along with feaure agregagtion as used in {{cite:0c026522c280dfd4dbbc3f83d5fd4af93af4fa81}} for three different streams. It is a memory intensive network. (10) WHENet {{cite:35f59959c9b956ab94ce2518567da625dca0aee3}} is also one of the low memory networks (having {{formula:8392409a-1537-4875-88aa-27666d15c6ba}} number of parameters) which uses efficientNet (lightweight backbone) and uses multi loss (classification and regression loss). (11) VGG16 {{cite:148c4324157a3878c82447094a98055364ff31c4}} and VGG16+RNN {{cite:148c4324157a3878c82447094a98055364ff31c4}} are highly memory expensive models with CNN and CNN with RNN respectively, using Bayesian filters analysis. (12) DeepHeadPose {{cite:a92c0abbed656385b09a3a9fb9a7497ae597ae9c}} uses depth images (low resolution) and uses regression and classification for each angle prediction. (13) Martin {{cite:dea10678071b8552f02e7eeeb8eb45dcaf5c76de}} too uses depth images and performs registration to a 3D head model.
| r | af2b2da21841dcd6ba0e48e01b8f1083 |
We evaluate the quality of the representations learned using few-shot linear transfer.
Given training examples from the new dataset {{formula:6fdb4883-f891-4491-91ef-24daa1b1ff83}} , we use the pre-trained model {{formula:9c419333-1bed-4c4a-baf6-7bcf9561ecf0}} to extract a fixed representation {{formula:084fd6f6-8d4f-40b6-bfbb-fa0f341fdcd3}} of each image. We fit a linear regression model mapping {{formula:be89a9a1-40c6-46c7-8608-6f739611e5aa}} to the one-hot encoding of the target labels {{formula:75d680c6-278d-4346-902d-629619a14d57}} , following {{cite:ae7afe55e38718b89ed44feed89af3bc4da0bb0d}} (see {{cite:6cd17b7e956ab6c3d60e6af9ce8ee7cb355bf8e5}} for background).
| r | 8d79cc43c482f227b1137928f5b00c3c |
The fully conservation form has another advantage, adaptation
to higher order scheme. Various standard higher order schemes
are available, when differential
equations are written in the fully conservation form.
see e.g. {{cite:db11378ab9c4afabe1354503b05c9c05bb74b2db}} for the methods to achieve higher order
accuracy. Remember that the source terms and numerical fluxes
have been evaluated separately. Thus the source term can be another
source of numerical oscillation when it is evaluated to be of higher
order accuracy in space.
| d | acae2207b98027ede7a0e5b2531a3226 |
Consensus maximization realizes robust estimation by seeking the solution model that enables the largest number of measurements to have residual errors below the preset noise bound of inliers. RANSAC {{cite:cd7c848c6c9678084164ae2a4aaec42db50f0a36}} is the most common consensus maximizer which repetitively takes random small measurement subsets to make minimal estimates for the solution and finds the best estimate that corresponds to the largest consensus set of the measurements. Additional techniques like local optimization {{cite:602b7f68c52fecbd843373f15f43e40cf342379c}} or measurement ranking {{cite:142f61670783e3cc594847031e61f07b036a8f6b}} are also applied to improve RANSAC. But RANSAC solvers' exponential runtime with the growth of the outlier ratio and problem dimension makes them too time-consuming for use in some practical situations. Branch-and-Bound {{cite:3e8eef4fb2b377761a355371d51a125d61d45b1f}} is another consensus maximization paradigm that can return globally optimal results, but BnB is also plagued by the worst-case exponential time w.r.t. the problem size. In addition, ADAPT {{cite:e48fdc37a120578e3106fd5c6df97b822d795456}} can reject outliers by alternating between non-minimal estimation and measurement trimming with a gradually decreasing residual threshold. But its downside is: ADAPT often requires at least dozens of iterations for convergence, but given the slowness of some non-minimal solvers, time-efficiency could be tremendously compromised.
| m | bc19ba0f21fe141ddde80e6dfd636d19 |
In Fig. REF we show {{formula:3e576d21-d37b-4fc4-80f5-0ec7d9239edb}} as a function of {{formula:b6dfa90f-2d12-439a-b1ea-fdd16875bfbb}} (in fm). Here {{formula:88cb43be-3b21-40a6-8495-f6c1753691c8}} is the
value of {{formula:7b8d3030-deb0-4623-987b-437366de5c35}} in Eq. (REF ) in which we switch from the lattice correlator {{formula:b7642efa-ad3f-4ac4-b313-1d5b4407f040}} to the upper bound
(blue points) or lower bound (orange points) replacing {{formula:9a7cbed3-8aa0-484d-b7bb-0198d97c4e09}} from {{formula:dac4922f-c4e6-45f6-bc01-f51f60f7220a}} to {{formula:5274a694-ee01-4e91-a328-3a2ffb615d09}} by the upper or lower
bound, following the
bounding method of Ref. {{cite:8935f38d25480fe73d7c0281f1c519300a4d8284}}, cf. Sec. REF . The shaded bar indicates the {{formula:62cb3725-b6de-482b-853c-f5d157072fbb}} region from which we obtain
the values for {{formula:3af3e3e8-affa-47aa-bccf-750be149f8de}} shown in Table REF ; we did not use the bounding
method for the two window quantities also shown in the table as they depend much less on the long-time
tail of {{formula:84a1643f-4866-44f9-949e-1e9cdf66c8ab}} .
Errors are statistical only.
The lattice spacing is set using {{formula:5ecf820a-f2a8-4ecd-8237-d88d00726b48}} fm {{cite:71792326a179a72420193aeb83ec3a433e0014d0}}.Even though {{formula:16a2a7d9-a32e-410c-b9b0-7bbb446d0657}} is a dimensionless quantity, one needs to set the scale of the hadronic physics relative to the muon mass. As expected, the statistical errors for the longer-distance window W2 fall between those for {{formula:e9ac35fb-4641-44df-aa5d-3aea2c20fa04}} and those for the
shorter-distance window W1. There is a strong dependence on the lattice spacing, and, for {{formula:92de9b03-8552-4392-b479-ebd20e387273}} , a clear dependence on volume, shown by the difference of the value for the last two ensembles in the table, which differ only by volume. The volume dependence of the {{formula:227328cd-6e16-419b-81cf-c0a738d5b5b1}} fm ensembles is not visible in the two window
quantities. Here one should keep in mind that taste-breaking effects are large for {{formula:b940de5c-95e6-4b2c-bca8-692d86c26280}} fm, and FV effects would be much larger were they not “masked” by the taste splittings. All these systematic effects will be discussed in the following sections.
| r | 0f88318ff70b45f5b677576e3c798226 |
In another work {{cite:5b37c1543e43f1f2ccf6c6a9d08b2a15589649b9}}, VAE, GAN and other means are combined and attention mechanism is introduced for the first time into the anomaly detection field. The framework encourages attention map to cover the entire normal region, while suppressing attention maps corresponding to the anomaly classes in the training images. Two modes of unsupervised and weakly supervised are provided. 1.Unsupervised mode: GAN is used as the overall architecture, VAE is used as the codec and attention map is generated by Grad-CAM. Loss function consists of three parts: VAE, adversarial loss, and attention part. 2.Weakly supervised mode: Compared with mode 1, classifiers are added to distinguish normal and abnormal samples. Loss function consists of four parts: VAE, adversarial loss, complementary guided attention loss, and classification loss.
| m | 648829d0c2ba964d0f27fb05056f30dc |
Reinforcement learning (RL) is one of the main techniques to solve sequential decision making problems.
When combined with deep neural networks, RL has achieved impressive performance in many applications, including robotics {{cite:f06ef90a4313bd93480aee1127b5cdc0959d67b1}}, game playing {{cite:bd737a4fb82bdf6ac6c906bd15f4e7bce98700f3}}, recommender systems {{cite:cf20982a12530b025ea96645d39cee3cccc86f95}}, etc.
As RL fundamentally solves decision making problems via trial and error, a major drawback of RL is the huge amount of interactions required to learn good decision policies, which can lead to prohibitive cost and slow convergence.
| i | e8e2c3a00be5f3c1d98c39012ff9d3f0 |
Note that the high {{formula:737af603-40c9-4c22-8f93-ff90c35a45ef}} values deduced in Model A1 may not be consistent with the fact that the two HBLs show almost no superluminal motion in the Very Long Baseline Array (VLBA) scale {{cite:1530bc933e9585f13e261d29b5f01cac73d91d8d}}, {{cite:87de0860e4d2de089e6ecabe622d05bd92d97e53}}. However, the high {{formula:b7f259bf-a108-413c-9098-eb9a30edaf36}} -values are required to account for the observed rapid {{formula:edbfe98b-5956-4620-bc53-d712917c8a95}} ray variability presented in previous studies {{cite:7ba3fa27c224c25a56fe00f0798a5dd8dd2020ad}}, {{cite:6a67cd2509976ccf2de23dcd10da8c85162d1062}}.
This discrepancy indicates that the jet may either undergo severe deceleration {{cite:c4192a0067c2ef95f22020797e900e84c5288f26}} or be structured radially as a two velocity flow {{cite:98d305d720e270019e131b7b3f8f790043a8d91b}}.
Recently, by considering that the apparent motion of individual components result from some pattern motion,
such as a shock wave or a plasma instability propagating in the jet,
{{cite:5d81bf1f7311060f4f6647d9a0e389f482ee6c76}} argued that the true flow velocity in the jet may be higher than the one estimated from the observed apparent motions.
Interestingly, using 13 years of observations with the Swift-XRT, {{cite:f0a1a8384a960a10825e5800ab2b15dc1e13e120}} confirmed that the variability pattern in Mrk 421 is consistent with a perturbation passing through a recollimation shock suggested by {{cite:3209133e665d1fdc22f04780eb60598de813f481}}.
They found that the deduced Lorentz and Doppler factors of the flow are relatively high, and are within the range {{formula:bbf9f2f7-c6c1-43f1-b415-25e22335061e}} and {{formula:107d9af0-9b23-4daa-9590-b66990b89b27}} , respectively.
Thus, it seems that the shock acceleration may be in favor.
| r | 05ccd75f5ac904d452a71432be8b90ca |
Curriculum learning (CL) for deep learning was introduced and popularized by {{cite:ad15dfd6a026089d99dc05287ca8b1cdd9160f7a}}, but it has a long history, reaching all the way back to {{cite:4295a556bf167277dba345bc688de49e9b5dc14f}}. It is inspired by the way humans learn and proposes that we apply the same starting small concept to machine learning models. Hypothetically, employing the right curriculum has the potential to speed up convergence and lead to a more accurate model {{cite:ad15dfd6a026089d99dc05287ca8b1cdd9160f7a}}.
| i | bd0c93aa248377356d7d0c8f4ea04085 |
subparagraph51.5ex plus1ex minus.2ex-1emSMR liveness proofs.
PBFT {{cite:6bb39e1f7bb86d3e60cfe117afed61e9fc5889ce}}, {{cite:98b1c9845ce57e20c9e67bf2e3cf4ab16ed0dbe7}}, {{cite:f9f4345c33e47f589f77f957c72c10887f29058d}} is a seminal protocol whose design
choices have been widely
adopted {{cite:7e2b107fad595a04bba12c4c1c61f45f32194160}}, {{cite:5f7dbdf42ba4486ec2c37be1fe10bd087dcfeb76}}, {{cite:8fe138cdb140449c9313737ed24e9dea86122c90}}, {{cite:104f55426c9faa5b62de454ddc826a0ec41f6627}}, {{cite:7a412cb9e00268d29c33e81f6b960adfd042a4fe}}. To the best of our
knowledge, our proof in § is the first one to formally
establish its liveness. An informal argument given
in {{cite:f9f4345c33e47f589f77f957c72c10887f29058d}} mainly justifies
liveness assuming all correct processes enter a view with a correct leader and
stay in that view for sufficiently long. It does not rigorously justify why such
a view will be eventually reached, and in particular, how this is ensured by the
interplay between SMR-level timeout management and view synchronization
(§). Liveness mechanisms were also omitted from the formal
specification of PBFT by an I/O-automaton {{cite:f9f4345c33e47f589f77f957c72c10887f29058d}}, {{cite:98b1c9845ce57e20c9e67bf2e3cf4ab16ed0dbe7}}.
| d | 040469b0e52c5922c9f3d57ba988e1c4 |
Tensor decomposition: We use {{formula:19723805-8066-4e36-807e-986274575f5b}} to denote the Fourier transform of a single EEG epoch with {{formula:4e2f263a-37d9-4a81-9c72-0e9a014b4d1c}} sensors at {{formula:d6345fed-d363-445d-8471-e770cb263bb4}} frequencies. Then, a multi-subject dataset including a total of {{formula:44818c66-4769-4b2a-92bf-e59ffddc0392}} epochs is represented by a third-order tensor {{formula:5e2edde0-8ab9-4299-84e5-f8eef2c37509}} . Next, we apply the Canonical Polyadic Decomposition (CPD) {{cite:d728dc4f21aae04ac58aaf745d4c6dcdd517870c}} with rank {{formula:6c6daead-c676-4481-b0c7-3de3a14f0010}} to decompose the population-level tensor {{formula:b6f1a086-e99c-4bc5-b489-9acfe6fa3325}} as a sum of {{formula:624ea78d-cd3e-4613-90cc-dd4468ce1aef}} rank-1 tensors {{formula:5c72d98f-7d20-4318-b077-e0f82030dfdc}} for {{formula:38ca2ddc-6669-4294-bcd9-1fe282c340a5}} .
{{formula:b66da355-5440-4e0b-b8f4-3d7659a5d429}}
| m | 485605436c5d2371f6baee91b32a863b |
The results presented in this work provide tangible evidence that state-of-the-art classical machine learning models have the capacity to learn accurate representations of entire families of quantum states. Using trainable embeddings to condition generative models on classical parameters of the quantum system of interest, we have shown that the resulting generative models can be used to generate artificial measurement samples corresponding to states which were not present in the training set, and thereby predict properties like local observables, entanglement entropies, and phase diagrams. We have demonstrated our method on ground states of the two-dimensional anti-ferromagnetic Heisenberg model and Rydberg atom systems and shown remarkable improvements over related techniques based on shadow tomography and kernel methods.
Throughout our numerical simulations, we have used the transformer architecture as our generative model, since it has shown promising success in sequence modeling. However, the complexity of transformers scales quadratically with the length of the input sequence, which potentially becomes problematic when the goal is to model long sequences with thousands of qubits. This poses exciting future research avenues where one could potentially explore other models like long-range transformers {{cite:dfc031ba14079ae412208129d21ccdd6ae36941c}} or other ML models which are designed to model long-range dependencies such as state-space models {{cite:4b551f70e0051a68d42c25c09a7b616f7c3f969c}}, {{cite:63318ae287153508ac6a3147c7a1be7149f3368b}}.
Furthermore, in this work, we have only explored our proposed method on numerically simulated quantum systems of intermediate scales (up to 45 qubits). It would be interesting to investigate the proposed method on larger quantum systems (e.g., Rydberg-atom quantum simulators of more than 200 atoms {{cite:a9dcfa7ca2e95c105fa086576b3eea7032ab8f37}}), which would also expose our methods to various sources of imperfections like quantum noise and errors.
| d | c4aba851280f803acaafd77b570dfc81 |
The use of string-localized quantum fields in the interaction gives us
occasion to comment on the fact (underlying causal
perturbation theory also in the point-localized case): Interaction
does not need a free Lagrangian.
This is advantageous, because “canonical quantization” based on free
Lagrangians is beset with difficulties.
The zero-component of the Maxwell four-potential has no canonically
conjugate momentum: one needs a “gauge-fixing term” to
cure this problem, and one needs another cure (the Gupta-Bleuler
condition) to make the first cure ineffective for the dynamics. Why is the
classically purely auxiliary four-potential treated as
fundamental in the first place, and not the observable Maxwell
field tensor? For massive tensor fields of higher spin, “free
Lagrangians” need a host of auxiliary fields to implement constraints {{cite:3b2bf9f7ca9dc4be75773a6e4f2fe241fc80e6fa}}. For
spinor fields, anti-commutation relations have no a
priori “canonical” justification: they are needed to reconcile covariance with
Hilbert space positivity after the quantization has been performed at
the one-particle level, and Dirac's theory to deal with first-class
constraints is needed to save the idea of canonical quantization with
a free Lagrangian that is linear in the momenta.
| d | 8b4d7392f935a50fc42072aa258d9689 |
Ensemble methods {{cite:a1869bde66b043b31a5542cd374496f482fe57b2}}, {{cite:55be31ea521c804982c8d1af1495227427b2ef91}}, {{cite:180772f9a8775c497e44e40a4bc195e5b71c3bba}} are supervised learning algorithm which commonly combine multiple hypotheses to form a better one. There are two families of ensemble methods,
averaging methods and boosting methods. In averaging methods, several estimators will be built to average their predictions. It is a kind of vote, namely, on average. The combined estimator is usually better than any of the fundamental estimators since its variance is reduced (e.g., Bagging methods and Forests of randomized trees). By contrast, in boosting methods, fundamental estimators are built sequentially and each one tries to reduce the bias of the combined estimator. The idea behind it is to combine several weak models to generate a more powerful ensemble model (e.g., AdaBoost and Gradient Tree Boosting).
| m | 885efb3b848254f31c12cd9edc376e6b |
The Nash equilibrium is a strategy profile in which no player can do better by unilaterally changing their strategy to another strategy {{cite:b6f8f0007101d0048ce2639eb8f1ef02b7da7187}}. An evolutionarily stable strategy (ESS) is akin to the Nash equilibrium which is “evolutionarily" stable, i.e., once it is fixed in a population, natural selection alone is sufficient to prevent mutant strategies from invading successfully {{cite:3fe805fc444c2b9a640eb07c395dcbc035c2f644}}, {{cite:51bb0a27aa1950b3d96d117250b3a6db08095879}}. Therefore, the ESS is effective against any mutant strategy when it is initially rare and successful when it is eventually abundant.
| i | 78d3f36765048d1fe2161d8fcd65c121 |
A ridge is a multidimensional function {{formula:aca85815-d0fe-42fd-96d2-4bde919764d2}} from {{formula:95653f47-5975-47ce-a9db-3ae0e6ce0782}} that is characterized by a 1D profile {{formula:53eabc91-c56d-4230-882d-f38a1f636fbd}} and a weight vector {{formula:05a5de94-aaa3-4de3-a947-cd0329bb763d}} {{cite:96d2b3068533703c0f2f5482c43acdbcd8bc18dc}}. Ridges are ubiquitous in mathematics and engineering. Most significantly, the elementary unit (neuron) in a neural network is a function of the form {{formula:106a7097-08d5-4631-a30b-e89e4f4a2876}} , which is a ridge with a shifted profile {{formula:0c9bb652-9cd7-4107-8138-faaf71a12bbd}} , where {{formula:304f51e1-62f9-4581-9a2c-84bfa54ba30f}} is the activation function and where {{formula:eecd6834-6419-4797-9431-86849e958907}} (bias) and {{formula:aaffdb7e-abd1-4957-9f68-ab28ba38163a}} (linear weights) are the trainable parameters of the {{formula:d43e2fe8-f741-4eeb-9ad8-e51e8a3eff7f}} th neuron {{cite:b2c68f931e5deed5ef23025caaef75a768c7905b}}. Variants of the universal-approximation theorem ensure that any continuous function can be approximated as closely as desired by a weighted sum of ridges with a fixed activation under mild conditions on {{formula:a2bfdef3-ea88-4490-a99a-effa88cd22e1}} {{cite:dacb49f85adbb3b6761ab4624b4008dedb364c9b}}, {{cite:4ce9b8e2746b4f8b7ecfea23aa0ff07ce9e35ebe}}, {{cite:83cebca26d2ec28dd5525b9138bcb589dfe498f2}}.
| i | 0bcf6a5ce673a102447b228a33ef12b5 |
Remark.
Recall that inner functions {{formula:3ddcf6f5-63f3-422e-83dc-03f0ec7bfe01}} (i.e., holomorphic maps of the
unit disk {{formula:944d9871-96a9-401e-82df-6b1c09af5e79}} to itself that also send the circle {{formula:c19c38c5-08e5-4fe1-9858-b0b12fda94e2}} to itself) are a classical topic of function theory of complex
variable, see, e.g. {{cite:e7dc55611b62053dda5b67bdb60ac3dd63c2b3e9}}. Inner functions {{formula:e8ca6231-2757-4327-9a9a-6c11248a5d35}} arose in the context of works
of M.S.Livshits 1946-1954 on spectral theory of operators closed to unitary operators, see {{cite:1190ea674934a38ebc434d887b2bfe6ffb6a9bbc}},
{{cite:1d75210b78e524879bf6d0274654eee2d5cc735e}}, see also {{cite:e3f503ed4acfbfc1df1a3c667d1ec289d2ce74cb}}. V.P.Potapov {{cite:7516935535d525339f0c4d3e94e0f798401fbcb1}} obtained a multiplicative
representation of such functions, see also {{cite:5363fee3c45a482cbe932a7aec87fb597eb9b79b}}. Inner functions {{formula:63d11b4a-4bcf-4e55-bce0-8838a7e81636}}
arose in {{cite:1c5d415fd3905c05bbe61309fe342220aca6d99a}}–{{cite:d2d450b13559e6c89a6460264f8ea38fb6e4a725}} in representation theory of infinite-dimensional
classical groups.
{{formula:da6f6c97-b687-4c2f-b860-f7c5648afabe}}
| r | d6a05e452cd95afc196ee7dac7d4d947 |
Quality assessment. Solving Problem REF
yields a SR reconstructed image {{formula:8eb57e10-cace-4b81-9dc9-045b49cdf965}} which quality can be compared against the reference {{formula:db6e15c3-03a4-4c5c-a4e3-4616b0654ec2}} using various metrics. We use two common metrics for SRR assessment {{cite:7a53b6b5aabdd4803418d05f5e0eb2ee37d489c1}}, {{cite:1d967993c4a273e6903073e206cca13c04ea80e3}}, {{cite:ab0649ecd4f5442b66322e7a9a9c728ff34cc344}}, namely the peak signal-to-noise ratio (PSNR) and the structural similarity index (SSIM) {{cite:1457d1b79d8d22341daf556f3d44be8f8ac70d55}}.
The best regularization parameter {{formula:15169459-0455-405a-a4c0-926ba9ee7bff}} is identified as the one maximizing a given performance metric.
| m | 3d162a1650b6a1a146f254bc9191c5e5 |
Considering above issues, a more promising way is to align instance features according to their ground truth or pseudo labels. It means the detected objects with higher confidence in target domain should be paid more attention on aligning the instance features regarding to their categories. For example in Figure REF (b), the target objects predicted as class-2 (denoted as brown hollow circles) should be aligned to the class-2 objects in source domain (denoted as brown solid circles).
Here, we treat it as class-level domain alignment.
To achieve class-level alignment in all classes, a group of domain classifiers can be established as a domain classifier bank in which each classifier takes the charge of aligning features of a specific class.
In this way, the closest pairs of instances between the source and target domains refer to those objects sharing the same class from the perspective of the detector.
Note that, predicted results of domain classifiers also reveal the effects of feature alignment, i.e., the more extent of alignment, the more confused prediction will be made by the domain classifiers, as addressed in {{cite:f3b454d8f091b71b0ba49e4be678bebcef2644fb}}. Thereby, for those well-aligned features, their pseudo labels could be added more weight when training the detector on unlabeled data from the target domain.
Then the detection performance can be further enhanced.
| i | 0d5ebdca6362601ce06dee075140456d |
The kinematics of the warm and cold gas phases lead us to conclude that the AGN in the system might have recently experienced an energetic outburst. This AGN outburst temporarily led to the condensation of the uplifted gas, which is now probably cycling back down towards the AGN, promoting an elevated star formation rate of {{formula:8570f284-9fed-41ff-b4cb-a251f1c47dd7}} . The observed distribution of dust in the system {{cite:69c6f11246358b820232ff2c852263b0638d316f}} points to an uplift mechanism, with dust emission most prominent in the core and at the furthest extremity of the tail. The observed distribution of the gas phase metallicity can also hint to such an uplift mechanism. We observe the lowest (O/H) values of {{formula:1a408c2e-765b-4150-a589-f6db50d737f8}} 7.9 in the most central regions of the systems, while in the {{formula:f85cfb3c-be80-449e-87ce-5a2f32414568}} tail, the metallicity is slightly higher. This might mean that the metal enriched gas has been expelled outwards from the centre due to AGN outflows.
| d | a464f1b640ce8ce9ded39052fbeb9ca4 |
This basic argument has been appreciated for some time; indeed, its essential features
were outlined by Penrose {{cite:db26e6c3999095daf3603898ac0eec536c9ecfee}} even before inflation was invented.
Nevertheless, it has failed to make an important impact on most discussions of
inflationary cosmology. Attitudes toward this line of inquiry fall roughly into three
camps: a small camp who believe that the implications of Liouville's theorem represent
a significant challenge to inflation's purported ability to address fine-tuning
problems {{cite:29da27ce7c545e7e069aed5c5a7154c7aa2c1fe9}}, {{cite:2b40864d68a6aa8461022853e2bf2cb2295eb720}}, {{cite:3c4d879f210404378d0fa6605507c4e25facfe30}}, {{cite:b91fc1bf716a232d2a2fc3353427b6a235a3914c}}, {{cite:d56b78421f4ca3512149339ed2a641196a935bc4}};
an even smaller camp who explicitly argue that the allowed space of initial conditions is
much smaller than the space of later conditions, in apparent conflict with
the principles of unitary
evolution {{cite:5afb8ca71f7a59af51720cd74b63e3963dd8bbbc}}, {{cite:e13719dc100af5c368fea2075bcd18a954c7d292}}; and a very large camp who choose to
ignore the issue or keep their opinions to themselves.
| d | cefefc439f43105412dd01d390bde995 |
Table REF presents the best result from our model (doc-reranker) in comparison with prior work on the NIST Chinese–English translation task. The first three rows are numbers reported in prior work. {{cite:b2842899d54d0776d6559e347f27a533b80a7021}} incorporate document context by introducing a hierarchical RNN to an LSTM sequence-to-sequence model. {{cite:db568d760140160d6ac24835c526467f3988244f}} use a cache to store previously translated words across sentences, which they then use in sequence-to-sequence models. {{cite:443f4544f07ad28a776f352cd1c2e66a6eb33aa0}} extend the transformer model with an extra context encoder to capture information from previous source sentences. Apart from prior work, we also compare our doc-reranker with four baselines: the transformer {{cite:7897e78d8960c1c5bed1e0b967ceafbb68d95487}}, document transformer {{cite:443f4544f07ad28a776f352cd1c2e66a6eb33aa0}}, the sentence-level reranker (sent-reranker), and the document transformer with backtranslation.
| r | f40be2b3267c36817d75c9a56f5e5a5a |
We compare our approach with state-of-the-art weakly-supervised methods{{cite:d9eac72dcb9f28e12f70c8d9f1edfcce361321e7}}, {{cite:a97062ffe958aa286153e20b1a1e22a9cfc4cbe0}}, {{cite:b81881995569963032d06d1fdba7dc28556ecdae}}, {{cite:1e92703ffbb0fb5da8b87971959f86102df999be}}, {{cite:d1a12a15c86f7e008c1e06c098a66545e3e15e52}}, {{cite:01ada79added8d008b2020fab0b9a281e3b14cf3}}, {{cite:e03d2e0c0ac2e838795c3976e4eddb3417ba6cfb}}, {{cite:bfb03e413ca603f52d2da51dd61783b27f520efc}}, {{cite:d54f857a0793b138e4a85886a3b79dc6e58d4227}}, {{cite:391801724762a3afab6cac9d04ca7c70e74ffe6e}}, {{cite:1f800232bcfcf62de61f7640b9feaff584e1901f}} on three benchmark datasets. The comparison results are summarized in Table REF . Our approach achieves state-of-the-art on CUB-200-2011, with the Resnet50 backbone, our model can surpass all other methods even equipped with more advanced backbones by large margins. Our approach gets the best result on FGVC-Aircraft compared with other methods under the same backbone. For the Stanford Cars dataset, our methods implemented on the Resnet50 and Resnet101 achieve the best result like API-Net{{cite:bfb03e413ca603f52d2da51dd61783b27f520efc}}. However, API-Net{{cite:bfb03e413ca603f52d2da51dd61783b27f520efc}} spots discriminative regions by comparing image pairs,
it needs to consider different pairwise image combinations within a mini-batch
and requires large computing resources.
{{table:99b9a684-2f04-44b9-8d1c-8b298cbcf71a}}{{table:91542956-ae95-497f-abe4-5d6f3afb8b7e}}{{table:60a087b7-a499-4770-a0c1-d8541d417165}}{{figure:a075b0fc-8e02-43b1-ba5e-5777a0c1221e}} | m | 5c3d00893392d3bc77f891185b5f4594 |
Lemma 2.1 (See {{cite:0e8c98a2e024ed4f75f4a200d85b3bdbdea08285}}, Theorem 11.31, Künneth Formula) Two finite dimensional Lie algebras {{formula:f29283b5-2f92-49e4-aaeb-f3e2b7abf58f}} and {{formula:735840ba-dd0c-427e-9e61-c74b54329884}} satisfy the condition
{{formula:ae59d308-ff11-44f0-9f0e-8cfbe789a53d}}
| r | 5acffad5b1c9fd808dac2684198efcdd |
An aspect of the implementation of CQ for boundary integral equations that is rarely mentioned, is the spatial quadrature required to compute the integral operators. The reason for this is that unlike in space-time Galerkin methods, where quadrature needs to carefully deal with the sharp space-time cone {{cite:8fcb9446baacc67d888f4574d62fd3d69baf4c4d}}, the spatial quadrature in CQ schemes is usually straightforward. The reason for this is that the CQ smooths out the space-time cone and the quadrature required is the same as needed for steady state problems, where quadrature techniques are well-developed; see {{cite:9b6de2fb7071f8fcf577677a7727809bfdcc4459}}. This is however not the case if the frequencies
{{formula:4c4b8989-afb9-4cb8-86b5-7c3f05e2429f}}
| m | b5da9e93baaa9e76b2a7cc69e9266e89 |
In the coming years we will be flooded by data offering new windows on particle physics at high energy scales.
Telescopes such as CTA {{cite:fb6edaa5eafb3df085939a68e9126543aa05fb49}} and LHAASO {{cite:58944a45c5c60a769ddd495715a941abbc540d27}} will collect, for the first time, {{formula:a1288f74-f268-4491-aaaa-4cd7cc6a93d1}} rays at and above 100 TeV, and KM3NeT {{cite:70db6fe01a4bc046a0e2b302a358b622ca23eb1c}} will explore a similar energy range in upward going neutrinos from the Galactic Centre. Underground experiments for Dark Matter (DM) direct detection, such LZ {{cite:719370ab332a21d3bbdfffc3de36b1886342deaa}} and DARWIN {{cite:8076301ac249e91093e91202646df4e406e54f53}}, will test new parameter regions of heavy DM mass.
Further in the future, interferometers such as LISA {{cite:fa2a4bd963543075ae4f6af36f9b654c303b1819}}, DECIGO {{cite:4e088da916ad2b356c748de8ad6c68e5dd93ffab}}, and the Einstein Telescope {{cite:41e0cba73ba9b4ae215f101b1510438486b535d6}} will be sensitive to gravitational waves (GWs) generated at (currently unexplored) high temperatures in the early universe, thus offering yet another beacon on physics at high energies.
These prospects are particularly exciting as they could unveil some of the current mysteries of Nature at a fundamental level. It appears unavoidable that some physics beyond the Standard Model (BSM) lives at high energy scales, given the success of the Standard Model (SM) in explaining physics below a TeV.
| i | d9f1c03424a4e30840b4e63a16955e2b |
Extensive experiments on the large ImageNet dataset demonstrate the efficacy of our LBC.
For instance, our LBC achieves 77.2% in the top-1 accuracy for training a 2:4 sparse ResNet-50 on ImageNet, which takes the leading position in comparison with existing N:M sparsity methods {{cite:2e3f7fb15689753479ad39489ee0bb48f43d6e3e}}, {{cite:1cf33438040f07c7e6a9f654a88462c1af6ce465}}.
It is also worth mentioning that our LBC even surpasses some state-of-the-art unstructured sparsity methods that fail to achieve speedups.
For example, under an extremely high sparsity rate of 1:16, our LBC still achieves a top-1 accuracy of 71.8%, surpassing the recent competitor STR {{cite:d27b2ad4b4bac8d3c8e550ffd4d5c1376ac504c1}} by 1.2%.
| i | 308d4375817dc7f0d4a55e3cd64259c9 |
Actually, the AWB can improve performance with different {{formula:434d92a2-e1a0-463b-97a6-43b6646c4cd3}} values stably. Similar with MMT {{cite:a278b599308be50097a1be65ce627fe8bebbae67}}, we have tried three different {{formula:44708bc9-e006-4462-a641-2ede3e6d3ef0}} , i.e. 500, 700, and 900, for Duke-to-Market and Market-to-Duke tasks, respectively. The experiment results are shown in Table REF . No matter which strategy (Pre-A (I-CBAM) or Post-A (Non-local)) is chosen, the performance is improved significantly when compared with MMT
{{cite:a278b599308be50097a1be65ce627fe8bebbae67}}. These experiment results prove the generality of the proposed method.
| d | 8ebf5c76b214d00a63e7e225ae5e3a1f |
Timely updates are crucial in a large number of applications such as vehicular networks, wireless sensor networks, and UAV navigations. To achieve timely updates, we require the destination of the network to receive the freshest information from the remote source as quickly as possible. Age of information, or simply age, measures the data freshness and has been widely explored in recent years (e.g., {{cite:eefa74e78a6f74df99684477c1603cc311366195}}, {{cite:f2e32bb6eedfca74c19302ec7062c8f0eabc9754}}, {{cite:aa1b041b1f38b8e9daeff39167ca867828e4d93e}}, {{cite:1e1a6ad719234ea99e5c1b429e44dada61fea5ab}}, {{cite:74cb07e8d81bf114441d193dac3237948ca29e14}}, {{cite:7d2ad20552676d31d4e304e51ff2c42fc9c4111c}}, {{cite:d6c17b41d57f3c38c0d81f801860b60339a085d3}}, {{cite:f5093c9bc9ef5df10e394c68875f24dd09c86b50}}, {{cite:60210ca1bb25813e20bbf36dc5a53b1409376a85}}, {{cite:61a10f7bb37aedee9121c9897d48c4faf0267b3c}}, {{cite:6a093707608476fb7fcf3b398603f4644209b802}}, {{cite:8aadb657507b76f00cfbb7fa515a5742d2791109}}, {{cite:75ebbdb60a658647f3135f0f7fcc5e4eef7ca4fa}}, {{cite:74dca68065a681d625d52b3c4fb058467e989f48}}, {{cite:b31dbcc06e6b1b77ebd63ba9675944c51563d0c5}}, {{cite:e6a1646b1a563efa74891e1023ddad8411f77454}}, {{cite:b42119616aa0c6ad49c503465b4cd9ccc3edca94}}, {{cite:5fd61028ac306c5e52a21a60b693872767047c57}}, {{cite:08287deb3f3a8b9f276fefea2b7602f3d244ec21}}, {{cite:910569f359e1d667e5b4e8a5717b329e54fe18de}}, {{cite:ea70ed8e296d166d7427fa6211f7b6e1c2710ecb}}). Age of information with the function of current time {{formula:232120a2-fe0d-4b7c-9fc9-9245cea9f5f8}} is defined as {{formula:2446b8bb-2bf5-4062-95ad-76d32f961776}} , where {{formula:970e5789-0e14-491e-88c7-59a44e1d1f82}} is the generation time of the freshest information data. In several different queuing systems, the Last-Generated, First-Served (LGFS) policy is shown to achieve age-optimality {{cite:5fd61028ac306c5e52a21a60b693872767047c57}}, {{cite:08287deb3f3a8b9f276fefea2b7602f3d244ec21}}, {{cite:910569f359e1d667e5b4e8a5717b329e54fe18de}}. Scheduling policies in various wireless networks are studied to minimize age {{cite:6a093707608476fb7fcf3b398603f4644209b802}}, {{cite:8aadb657507b76f00cfbb7fa515a5742d2791109}}, {{cite:75ebbdb60a658647f3135f0f7fcc5e4eef7ca4fa}}, {{cite:e6a1646b1a563efa74891e1023ddad8411f77454}}, {{cite:b42119616aa0c6ad49c503465b4cd9ccc3edca94}}.
A literature review of the recent studies in age of information is provided in {{cite:aa1b041b1f38b8e9daeff39167ca867828e4d93e}}.
| i | 4282e6cefa17b35616400bd28bad9c43 |
For a fair comparison, we re-implement baseline models of cRT and LWS {{cite:8812a46aa4ef7194213184f82b2bdfd1ee5390c0}} with our hyper-parameters. As shown in Table REF , smaller batch size and learning rate benefits long-tailed recognition ({{formula:79190271-143e-41c3-b21e-74b6c45a4db3}} v.s. {{formula:23175224-ccdc-46eb-92b4-55471f326203}} ), and we can get further improvements with {{formula:0cfc40b5-24ff-4813-8339-0f52493f1f41}} scheduler especially for LWS ({{formula:29d402e6-3e22-4c91-abb4-8cc202f920e7}} ). Compared with these strong baselines, our method brings consistent performance improvement on every split by a large margin, with {{formula:9132d093-dafa-445d-a9c2-5cf377d8a685}} and {{formula:ea5f69e0-4097-455d-a0f0-1b0d67edd778}} improvements for {{formula:131569a3-1f0f-409e-b16f-21d97cdf0933}} and {{formula:2d5c1522-2891-447e-8383-1c1d45630ca5}} training scheduler. We arrive at {{formula:4b113e5c-50ff-43eb-8f06-9d33c0a4e871}} for overall performance, which sets a new state-of-the-art performance on the ImageNet-LT dataset.
{{table:53c35290-530c-43a6-9f79-3e6663b9f8fe}} | r | ba0aab04e0173a8468507780fbdcf633 |
where {{formula:118e66fc-07af-4579-a0b1-22c7ef1242b5}} is the conditional feature embedding, in our case, the raw image embedding, {{formula:a18d5be5-b049-4b17-8883-ae1c3ee12a13}} is the segmentation map feature embedding of the current step. The two components are added and sent to a UNet decoder {{formula:2d049556-1e44-4daf-be0d-f8a5f18d5204}} for the reconstruction. The step index {{formula:ffddbe18-9a33-42fb-aee7-f605eed5033c}} is integrated with the added embedding and decoder features. In each of these, it is embedded using a shared learned look-up table, following {{cite:502711b29d050d72a85b077e21bef52761f1c466}}.
{{figure:bb9ad42c-9cea-4031-9154-2f0b467a8921}} | m | 26302481aa7fd6b0edde198de717d9a4 |
Regression-based methods usually adopt MSE loss as their loss function. However, only use the MSE loss function will cause some problems, such as blur effect, neglecting the local consistency, and losing position information. Therefore, designing an appropriate loss function is also an essential researching direction in the training stage, which can promote the object counting ability. BL {{cite:9d53237db29ebdaad35bc43ba9be564d6e6463e3}} regards the density map as a probability map, computing the probability of each pixel. SPANet {{cite:6370ee382d47b5d901f295af391ab1ae6b72dff9}} proposes Maximum Excess over Pixels (MEP) loss by finding the pixel-level subregion with the highest discrepancy with ground truth.
| m | 56961772c745d5044f0a7fe9498f7917 |
The purpose of this analysis is to improve the precision of the calculation of the Higgs invisible decay width so that it can be used to constrain the parameters from the dark sector.
The current observed limit on the branching ratio of the 125 GeV Higgs decay into invisible particles is given by {{cite:e6e5080a2306079e36ee92ba5a0e18baeba361d7}}
{{formula:adcc5155-d0c5-411c-ad80-b13db9e664a9}}
| r | ba52fce125fdd8d15b058f847d40a047 |
The integrated and differential cross-sections have been calculated using MadGraph {{cite:3d52ae2e90342323b827b8427d8e5e02050f7f59}} by adopting a generic LHC parameter card.
Furthermore, we have used MadAnalysis {{cite:421b7f09a193331e7d7484d4d35e161d88dc57dc}} for constructing our selection, which involve basic cuts for leptons {{formula:e76dee65-9ebe-4adb-9267-e845883b0e6f}} and jets
{{formula:4c4bf6b5-f543-4b89-97e6-9c420ff42eec}}The latter being produced from QCD Initial State Radiation (ISR) and clustered with the Cambridge/Aachen algorithm with a 0.4 cone size {{cite:ee54b1aba70573d2714eab2893a81c1f47d3ce1e}}, {{cite:e96dd228c701970aa07c047a958fcc2c15203bf3}}.: in pseudorapidity {{formula:8d34b3ba-72ae-4595-944b-4812ee903acf}} , transverse momentum {{formula:1fa716eb-abf2-4afc-bd75-4332272b1beb}} GeV as well as separation {{formula:580f1ac1-c94d-4bea-b58c-37e8273dce94}} . Finally, event rates have been computed considering 100 fb{{formula:a454dab9-0d59-45b3-9cc6-e4b9b8f6bf3f}} of luminosity for the LHC machine.
| r | 0d66537fe0bcc953e75717cbc7c678e6 |
High Resolution Architecture
Unlike previous models, {{cite:e8a4f0ecdac175d10c59af272087d7960b1f9d08}} proposes a representative network, HRNetLink of HRNet Project: https://github.com/leoxiaobin/deep-high-resolution-net.pytorch (Fig. REF d), which is able to maintain high resolution representations through the whole process, achieving state-of-the-art results on multiple vision tasks.
This work demonstrates the superiority of high-resolution representations for human pose estimation and inspires a wide spectrum of later researches {{cite:a12cbb75506cdf67a1eeff7da9f0399c75f48e3d}}, {{cite:6a8f5eea02724baadcd5fabcb33d06b17b5eb304}}, {{cite:c1fabfcd606d8d85836fd8b4b8ac52aef0a1f09e}}.
{{cite:a12cbb75506cdf67a1eeff7da9f0399c75f48e3d}} takes HRNet as the backbone network, and further incorporates the gating mechanism as well as feature attention module to select and fuse discriminative and attention-aware features.
| m | d21b958827bbc249c5857cbfd6ac3ee9 |
The interaction of photon with the hadronic matter is one of the main aspects
of the hadronic physics and it is an important tool to learn about
QCD {{cite:9e8f2c8539786b94e082cc19bfb65149819758a0}}. Some applications involve the hadronic contribution
to the gyromagnetic ratio of the muon {{cite:70c1493d850aa9bf5fa5e71dc7a9dcb0442ba9b5}}, the study of
the intrinsic structure of the nucleon {{cite:fece02556797743c89fbd38f49d2a888b05fc21f}}, in-medium
modifications of hadrons {{cite:4495dd36cd60b4bea25171c40839dd819c9077bc}}. At energies below 1 GeV, the
neutral vector mesons play an important role in this interaction,
being well described by the vector meson dominance model (VMD).
Such a model proposes that all interactions between photons and
hadrons, in this energy range, are mediated by the neutral vector mesons.
| i | 9f8937b1ac44689b32fd79f6ff891781 |
In fig:ood we showcase our ability to edit out-of-domain videos. Both the encoder and PTI can seamlessly adapt to animated faces. Furthermore, the alignment of fine-tuned StyleGAN models ensures we can re-use the same editing directions, as previously demonstrated by {{cite:12fe0e81346687cdee27be068d0cfee1049c4dc9}}, {{cite:e17b6d4aa236ea5b9e205d28f9cfbc98dd898587}} and {{cite:10d66954e9d831b5e8a6c0c9bd7caad02dcbe589}}.
| r | f96dd22dfa1653f74688afd085f81cdd |
In the field of Computer Science, search trees, such as the Binary Search tree {{cite:08c0b909ef38cb3996047d85c485a1f3280e1523}}, are based on the idea of divide and conquer method.
They are often used to solve extrema in uni-modal arrays or find specific values in sorted arrays.
| m | de09c67c45f91d03d76fbcf234eaab8c |
Historically, the solution function (and optimal value function) has been an important basis for local sensitivity/stability and parametric analysis in optimization theory {{cite:006fb233539ded22c6a78d45ae4dff391e3dbb72}}, {{cite:a7b2b2f54f4ee8c2a50639e938e21465cc3c68a7}}; see {{cite:c427deb7f73a8248fb5f652a00e96c0e81e8f9f8}} for renewed interests. However, to the best of the authors' knowledge, a mathematical theory characterizing the global properties of solution functions is still missing. Two of the basic questions are:
| i | 687ef1393f1ab5abd67db7371943a20f |
Learning and recognition of spatiotemporal patterns—in contrast to static spatial patterns, or even sequences of such—is a central conceptual problem to neuromorphic and event-based processing {{cite:3b4f52cc3d7db7b8208b8492389ff341d1e2594c}},
and has been addressed, for instance, with snn that incorporate neural signal-propagation delays
{{cite:3b4f52cc3d7db7b8208b8492389ff341d1e2594c}}, {{cite:00078c5833876b872106d7c616e4bf3d60b84d5c}}, {{cite:9be19a1d9e2984f19a2f21ef1cb3132860ca9c4e}}, {{cite:3259356e2904042f8a123c778e694414fc10f922}}, {{cite:d6b66467cf5cd4b67d1c99ce841223cacdee6c2d}}.
Some current approaches to spatiotemporal pattern recognition with inhomogeneous neuromorphic hardware use neural processing frameworks that actually rely on variability in the processing elements {{cite:9be19a1d9e2984f19a2f21ef1cb3132860ca9c4e}}, {{cite:dfe9e5f7eea2140ad401cea1da4c6f3d68907f9d}}, {{cite:de70a18b3d3b7fca659e69459bf187e4699604c8}}, {{cite:dfe3470457c7d0599f4b4dbffcea38011fa1fbc7}}, {{cite:38af2c31c3768f886a107b2893a184feee5b2f70}}, {{cite:e64533e352fbfd6535a051a39c3b8fa79f9be64d}}, {{cite:178d54fbd4218185643d1f0fa3af3d6d182c48f4}}—such as reservoir computing, liquid state machines, and ensemble learning.
Another relevant concept is that of the stde {{cite:33108fa3e5c110951ccb57af688f6a87a30fa217}},
which provides a general neurocomputational primitive for temporal encoding but requires specialized hardware for its implementation.
| i | 9cabca96bdfe8979f1c1e372597298bd |
Note on social impact. As already mentioned, deep learning systems for video manipulation like ours can have a very positive impact. However, at the same time, this type of technology has the risk of being misused to produce harmful manipulated videos of individuals ( celebrities or politicians) without their consent. This raises concerns related to the creation and distribution of fake news and other negative social impact {{cite:4b66f120bbc127074030c2c7b2b3c7603b775d5d}}, {{cite:9103207480e3e912085e308f736a929984e527a0}}, {{cite:bb06a1aa36f432ce8ca04d42faf46af3b84daebe}}, {{cite:92d7e078bb511ebc09747ffc2179248f4cffa08c}}. We believe that scientists working in the relevant fields need to seriously take into account these risks and ethical issues. Some of the countermeasures include contributing in raising public awareness about the capabilities of current technology and developing systems that detect deepfake videos {{cite:474f2ed83fb711403993a06872e72fa18c16b6ab}}, {{cite:9ece3126ea4b911010c5bd4ecfbdca07493d7114}}, {{cite:a38898a84dcdd81f3025bad8edfa725d3ccbe602}}.
| d | 2bbfbe3e7aeaa51aadfe9c6db8a0b188 |
in which {{formula:e0a99fc4-4102-4d74-b6bf-0918578ad408}} are i.i.d. random variables and the weights {{formula:ee80d708-1f4b-4541-a24d-db0da4aeb82a}} correspond to either the eigenvalues or the singular values of a random symmetric matrix. Specifically, we take eigenvalues and singular values corresponding to the Erdős-Rényi-Gilbert random graph model. A random graph in this model, which was developed independently by Erdős-Rényi {{cite:2d11fe28a03badd741e5d95dba322a8df1b64fa1}}, {{cite:8591a0fdd6450decaa52c40e58b129f6f910e9a9}} and Gilbert {{cite:04c34ecc4ba1e9e36fd737b870348fbac7ef94c0}}, is constructed by attaching edges among a set of labeled vertices independently with probability {{formula:ed1f5991-8594-4bff-af28-7aef18588c70}} . The random variables {{formula:bc9a5c62-1c97-4458-a55d-938362a43d8d}} in this case are neither independent nor indentically distributed, and there is no general method available to handle this situation. However, adjacency matrices of Erdős-Rényi-Gilbert graphs have bounded entries which, modulo the constraints imposed by symmetry, are independent. This simple fact, together, with the almost sure convergence of their empirical spectral distributions to the semicircular law, allow us to establish central limit-type theorems for the sequences {{formula:0b0df3fd-7494-4113-b888-585c72bab77e}} .
| i | c2f6f197846943224fb63d1ac76e57c1 |
While the effects of EOS on the crust-core (liquid-gas) transition density and pressure have been extensively studied, see, e.g., reviews in Ref. {{cite:2cea4aeccafe65b1388f953ff5c3f1bb403d5d70}}, {{cite:e77843b83bca2f1e541572707771c669ffa441d8}}, {{cite:66fc49dc05bd87eab7d55cf1bfcd277a9c1c55a0}}, {{cite:6597394d95e1212488391770826cba59821beb1c}}, little is known about the hadron-quark transition density. In fact, determining the latter and the associated phase structures of dense matter has been a long standing goal of both nuclear physics and astrophysics. It is well known that QCD is still facing fundamental difficulties at finite baryon densities to predict accurately the hadron-quark transition density. Often in models considering a first-order hadron-quark phase transition in heavy-ion reactions and/or neutron stars, the transition density {{formula:5a2d9263-218b-4bde-b3b9-33d10f17d3a7}} is normally used as a free model parameter, see, e.g., Refs. {{cite:521e3c697fde20fa7d696ab32fb7d1bb76210d61}}, {{cite:bceed015c093e3af7caf39a3df84742cccc8a649}}, that may be inferred from observational data. Sometimes parameterized {{formula:8fed3f68-1ed3-4dc2-a082-deb948e38f42}} functions are used as inputs in constructing the EOSs to be tested against experimental data. Alternatively, the {{formula:3e99604f-a560-40e3-844a-8c5e00eddfc3}} may be obtained by examining the high-density behavior of {{formula:b0021be6-ac81-413a-a0aa-19e9e3decf17}} and its possible vanishing point in the hadronic phase.
| i | a9f04fe3c380c8f01d033ee6dc2d1eeb |
We test the efficacy of the proposed method in generating text in two different corpora, which pertain to different genres of text. The corpora we used are the Cornell Movie Dialog corpus {{cite:f892aada4ca7eb4ff352c91b2852fa6b03c3db1c}} and the Yelp Restaurant Review dataset. The Cornell Movie-Dialog corpus {{cite:f892aada4ca7eb4ff352c91b2852fa6b03c3db1c}} contains a large metadata-rich collection of fictional conversations extracted from raw movie scripts. There are 220,579 conversational exchanges between 10,292 pairs of movie characters involving 9,035 characters. There are 304,713 utterances in total. The Yelp review dataset contains 5.9M reviews. Along with the reviews, this dataset contains nine additional features, including usefulness score, which we use as external rewards. We perform the standard pre-processing steps on both the Cornell and Yelp dataset, including lowercasing all conversations, expanding contractions, compress duplicate end punctuation to one symbol and removing HTML entities.
| r | 2a01a4e986b5d5bb4ec141bcd6afe469 |
The overall architecture of the proposed method is shown in Fig. REF . The proposed method includes a keypoints extraction module using a CNN-based autoencoder with additional loss functions to capture the keypoints. The rl module is a model-free, actor-critic style method {{cite:30fa1d0b30764e1d5c12d9ef4de74c6b964cada2}} that maps the keypoints and robot states to the motion command and Q-value. The two-stage training is conducted entirely in simulation by using the simulation ground truth to self-supervise the training. The first stage trains an autoencoder for keypoints detection, while the second stage trains the rl module for control policy. The trained policy could be directly used in real-world experiment.
| m | f9fb7cea2be7a50c61e7ce65f988c692 |
(the Galerkin method) For fixed {{formula:87f85bab-5b13-48f3-848f-bf5164d98c08}} and for every {{formula:fa3879c0-7e80-4036-b716-94c52870a573}} the {{formula:452ef3ef-8cff-44af-9996-5b970c23aa2d}} -th step in the Galerkin method has a solution {{formula:b07dfff7-e668-4616-96f1-cf103f6dbeeb}} . Then every subsequence {{formula:6d09305c-9662-4e44-9899-ddaaeab921b5}} which converges weakly converges also strongly to solution {{formula:60722691-93b1-46b3-8f83-f37174e9b814}} of the problem (REF ). If equation (REF ) has the only one solution then whole sequence {{formula:fe829d47-43f9-44ae-8f93-0c93448ba48e}} converges strongly to solution {{formula:5b7d71a1-3bbc-4dff-b414-9155be16fb80}} .
Let us observe that the space {{formula:cda25c32-458d-401d-bcea-79c22cf967bd}} is a real separable and reflexive Banach space with dim {{formula:d33f6898-02d9-46b5-916d-548bf22152ea}} (see {{cite:fe0310ad12e95eed65419abc3aa531163a6b2052}} Theorem 8.1.6, p. 249). From Lemma REF we know that the operator {{formula:184ebcab-879c-4673-8ab9-5e593d64985b}} is well defined, bounded, pseudomonotone and coercive. Moreover from Theorem REF we know that the operator {{formula:c00eb57e-2077-40e3-a081-3a9755528506}} satisfies S+ property. So the thesis is a direct application of the Brezis theorem (see {{cite:a5b1962321b424c913901b5b7fbd69db9cfad591}} Theorem 27.A, p. 589)
Appendix
Let {{formula:2e625535-b8bf-46ed-b3e8-efbced227621}} be a normed space.
Definition 7.1
We define
{{formula:f4394e05-facb-4027-90fe-f4a8e0a2e411}}
{{formula:8e9eb9c1-f0ca-4fe2-966b-8fa001619d38}}
Definition 7.2
By {{formula:892f97ad-df5d-4011-99fc-4cea7a59f0c8}} we denote the space of Lebesgue measurable functions.
Definition 7.3
Let {{formula:41992e2e-6c39-4dee-bd78-5c6dadd9a1bf}} be {{formula:dd3398b1-482b-4ae9-aece-1fe6cafa938e}} -finite measure space and {{formula:dbf7fe13-eb0d-435b-a132-4711a808b8ce}} is a separable Banach space. For multifunction {{formula:11405b79-eba4-4cac-bbb9-40076acd5d83}} we define
{{formula:f144716f-fd52-49f4-aff4-c6d1051fe080}}
and for {{formula:15ebeb6b-3b37-493a-90d4-f6902d4747e5}} we define
{{formula:dc1c03ef-d07c-4de9-b05a-d548174de7ce}}
Definition 7.4
The first multivalued term in (REF ) is interpreted as
{{formula:9404f96d-69a9-49f7-ad0e-fb66631bc907}}
Definition 7.5
By solution of problem (REF ) we understand {{formula:2880b02c-f840-4c2d-8a6f-f2faaf97c428}} such that there exist {{formula:1087c10f-ec3f-46e4-907c-d0a4c991c0c0}} and {{formula:266455ca-6272-4b29-9fc1-4ca02c9a2947}} such that
{{formula:e669a587-b572-4259-a758-2a256dd18569}}
Let {{formula:3b284440-be00-4b77-bd46-df42276e0132}} be a normed space and {{formula:b25a7010-ad6f-4309-8c0a-24afc65968b1}} be a multifunction. For a definition of a graph of multifinction {{formula:d9f73c6d-a546-4ba7-888c-03177cabc045}} , see definition 1.2.2 in {{cite:05ad60b98eacd04b911152174c5ec42916c3a2b5}}. For a definition of upper and lower semicontinuity of multifunction {{formula:9e403a1b-863b-4129-b340-766c35be3f77}} , see definition 1.2.1 a) and b) in {{cite:05ad60b98eacd04b911152174c5ec42916c3a2b5}}. For a definition of graph measurability of multifunction {{formula:5c4bcc8f-8bff-43c8-be53-fe87fbb4b46a}} , see definition 1.2.6 b) in {{cite:05ad60b98eacd04b911152174c5ec42916c3a2b5}}.
Let {{formula:72012c77-167d-40df-b43c-c4e6582990de}} be an operator. For a definition of bounded operator, see. For a definition of coercive operator, see definition 2.5 in {{cite:32a4a09266606942b7a133902a6e632078fb277d}}. For a definition of pseudomonotone operator, see definition 2.1 iv) in {{cite:32a4a09266606942b7a133902a6e632078fb277d}}.
Let {{formula:45117abf-40b4-422f-a6c9-99a06fc3f151}} be a multivalued operator. For a definition of strictly monotone operator {{formula:82828859-2954-48df-b30b-1cb7d42896d8}} , see definition 1.4.3 b) in {{cite:05ad60b98eacd04b911152174c5ec42916c3a2b5}}. For a definition of generalized pseudomonotone operator {{formula:caa28e4b-15fd-44f1-943a-94b7009116f6}} , see definition 1.4.8 b) in {{cite:05ad60b98eacd04b911152174c5ec42916c3a2b5}}. For a definition of domain of operator {{formula:b041c366-67d6-4d7c-9e22-e8e7f88e1ef0}} , see section 1.4.2 in {{cite:05ad60b98eacd04b911152174c5ec42916c3a2b5}}.
Let function {{formula:c5aacc5c-0051-4eda-96c6-c8e4c0653877}} be proper and convex. For a definition of subdifferential of function {{formula:0591d3fe-48a1-4f73-ac54-5755e954f2c8}} at point {{formula:25bd9de1-a0ed-4c20-8325-c5cf4db4fda2}} , see definition 1.3.3 in {{cite:05ad60b98eacd04b911152174c5ec42916c3a2b5}}.
| m | ddec73dcb0eb2c804c389c273e9555ff |
Finally, we discuss the results in Fig. . These
explore the scenario with split
{{formula:e1f19ae6-f794-48e8-990f-2e902f095b72}} and {{formula:3871e351-82fc-484c-b341-42b8f9bfec31}} values, such that {{formula:7e555488-97a6-4ca7-a614-d77e482da946}} . We
have set {{formula:6520cf15-23bd-41c1-9c92-52bd4ea637b9}} in this figure and
present three cases in which we find
agreement with a possible new world average {{formula:46c26b49-6c4b-4af8-93ec-c008ef4f4323}} at the
{{formula:8c37f2fc-1c9b-42ed-aa4e-587e24b068ab}} level.Analyses in the 2HDM taking into account the recent CDF measurement of
{{formula:ca3d434a-cb36-41f9-b747-258a0acd0349}} can be found, e.g., in Refs. {{cite:50c93a86cbff85ebd436ee18720b0d8c7d9682c1}}, {{cite:fa7872663b5a76daf8c9b433dc77bb0e04e25190}}, {{cite:6b11b2836d988b008d07e6991f4f51ea855547a7}}.
The disallowed areas by {{formula:0899e8ce-7a86-4425-8abb-08b9bf31583c}} are shown in these
plots by the striped regions, which by construction are identical
in all four Yukawa types. In the first row we set
{{formula:563f552f-4257-4e00-8ab5-4f3778ceea11}} and {{formula:e7074d39-c8b2-4a79-ae81-1ef7a73813d9}} , in the second row {{formula:e8e4fee0-c46b-475d-bf08-5e6c7bcdf8e3}}
and {{formula:e9c87285-7c67-4292-a4bf-eb8d7af6428d}} , and in the third row
{{formula:1320c096-ed70-409d-b897-92a29bed22a0}} and {{formula:d0d4d115-4704-467c-a406-00627e89f198}} . We see in the first
row that {{formula:1f784b8c-ab70-4253-b127-d8255a1ea821}} yields no
additional constraints, i.e. no striped region appears.
In fact, the specified horizontal contour lines with the
predicted {{formula:a7369a41-cf64-452f-8124-090216fa65bc}} in the 2HDM are all compatible with {{formula:d8134f9b-c5d8-4986-9c8b-787aca6038f7}}
within {{formula:6e9aa304-e4db-4326-a302-2d576ced2f84}} . Therefore, the conclusions on the {{formula:a1ff51dc-3876-425c-8f9e-064b03955bfc}}
constraints are very similar to the fully degenerate case of
Fig. . Other choices for {{formula:94144144-a0d7-40db-9686-8e4ae25e3eee}} in the interval
{{formula:4ca23fcc-3cb2-493d-8ee8-3afce92e1f9d}} GeV with {{formula:de13a692-f044-45a9-af4c-912e6507b671}} yield
a similar result for the regions allowed by the “other constraints".
{{formula:241cffbd-7263-49d3-9ac2-4aa91c859a2f}} values outside this interval do not exhibit
allowed regions by {{formula:24e5f1bd-57c7-46d7-83fc-c8a0a15d8bf6}} and
result in a fully striped plots.
In the second row we have chosen {{formula:bfff2ef8-c424-4599-a380-749cb515c96a}} and
{{formula:9aa30694-a4fd-4c56-babb-16cfd1ef528e}} . In this case the parameter space allowed by
{{formula:104af4eb-5f7e-40f5-974c-4de3cb4c9e8d}} is a horizontal band from {{formula:2295b1d8-f3f3-4bec-b624-97ae26e59b7d}} to
{{formula:eadc8ed2-f454-44c3-808b-c5e81bb87b12}} .
Since this band contains
almost all the region allowed
by all the other constraints,
the conclusions on the final constraints on {{formula:fb1165e1-0cd2-4dfc-b432-8d6e7c5cb95d}} are
very similar to results found in the second row of
Fig. .
In the third row we set {{formula:f1453772-1e9a-4ee9-b429-9bbda696d426}} and {{formula:a2886c5d-2de3-44b0-9acb-99f9fb890a8c}} .
This results in a diagonal band allowed by {{formula:2c018fec-05bc-47d3-a997-3f373f5f20f9}} , going from
low values of {{formula:9495e065-a2bc-4ddc-8b4f-bcdf81daf6df}} , {{formula:8f963d91-7ca9-409f-99ce-780a4baf5996}} to large values of these parameters.
The intersection between this diagonal band
and the “reduced white area" provides the joint allowed region. The projection of
this final allowed region on to the upper axis and the intercept with
the red region provides the wanted constraints on {{formula:7926c1fa-6809-4fb6-b4ad-a144eb3fa008}} . This gives
the following disallowed intervals:
{{formula:b6ab782d-ccb8-4d1f-b4c0-b9014a92a2a8}} GeV in type I and IV and {{formula:605791c5-2f2a-4b12-846d-627e61d28b4f}} GeV in type II
and III for {{formula:9934aa34-4562-4f4c-b9b8-090875af9fa5}} and {{formula:15bcb1b8-7303-4c9b-84fd-c43f63fef81b}} ;
{{formula:e5548f0e-d0ba-4abb-b68f-01433ba17d2c}} GeV in type I and IV and {{formula:fb06fecb-f504-47b4-b677-93495a92faed}} GeV in type II
and III for {{formula:56e13e5a-74cd-4609-9870-89e2df885527}} and {{formula:5ea75c1d-c8f3-4827-aeee-927e01558f6b}} ; and
{{formula:24f1b2b9-1328-4bbd-aec1-7be7f975bf9d}} GeV in type I, {{formula:34f46599-936b-4f85-8d8f-44545492a47a}} GeV in type II and IV
and {{formula:725ee22e-1244-453b-93c1-6c8614cb5d16}} GeV in type III for {{formula:e0a0dd7f-c788-47bb-9d33-a64fe9f1c55b}} and {{formula:eda932b7-76a0-44c5-b3d4-2eb3b3e37e06}} .
| r | d098255ff07465aa155e3292d465d0b1 |
LGS can be created either by Rayleigh backscattering in the lower atmosphere or by fluorescent excitation of sodium in the upper mesosphere and lower thermosphere {{cite:dce5bf38ee6f0f7a544302f7a195a2924a67081b}}, {{cite:003c9e9ea90f8c07d263e3adfa699500c8082c3f}}. For extremely-large telescopes, sodium LGS are better suited, as their higher-altitude reduces errors arising from the cone effect {{cite:b591ddd32b822268b75de94bb2b946b3c57cd4f1}}. ELTs will employ multiple LGS and tomographic reconstruction techniques to map the distribution of turbulence in real time. In particular, lasers tuned to the Sodium D{{formula:ade73566-f022-4bf3-a53c-0470938ca347}} -line are used to excite transitions in the hyperfine structure of neutral sodium in the Earth's mesosphere. Since the excited atoms tend to migrate to the ground state of the D{{formula:ca75b486-6a49-40dd-9266-0c3c3d428f7c}} -line, re-pumping by tuning a fraction of the laser light to the D{{formula:7d2f0b3a-021f-406d-a21a-b98db169fdd4}} -line enhances the return flux for CW laser or long-pulsed laser excitation {{cite:028dcd93b330711c541d3c7c089634b0ae852583}}, {{cite:ee6b7d3a2be47fae4e30274898a7f24d0e0ee594}}. The column of luminous sodium in the mesosphere appears star-like when viewed from directly behind the laser beam propagation axis, but when viewed with an offset, the finite vertical extent of the sodium layer causes the LGS to appear elongated {{cite:e0bae056032df04dcf1d9a3b039875075a42ec91}}. The intensity distribution within the LGS image reflects the vertical structure of the sodium region.
| i | 0998e6384478f59c1a0433a10c08f3de |
For completeness, comparison is also provided with DNW {{cite:9495fed7e3a485e0651e7f1d1b7a9d1970fa6b07}}, RIGL {{cite:cb8e95c51cda9d9f4bb1db24d7362cc2d544bcf0}} and GraNet {{cite:c174d24b931c2b3910d6f3fe496b408ec71db031}} (see Section 2 for the presentation of those methods), implemented as recommended by their respective authors.
{{figure:62143195-3841-4362-9185-91d36c63e697}} | m | 7668d411341825f2baca266337b0e6ae |
where {{formula:3ffb3e06-9aaa-4e1a-a056-e10e541325e0}} is a differentiable function and {{formula:4db358f6-3824-44fe-a4f5-35c2f7934089}} is a 1-form {{cite:1c44cb932db283cf7e513233bc68173240b7347e}}, {{cite:e7618fdc16fb91ab6e687ff9727afdc3b2d25971}}.
The 1-form {{formula:981fde0c-7340-4b9a-ad45-b162ceddebab}} is called the generating form and
the function {{formula:648f30c5-393b-436d-a801-2137bfef9782}} is called the conformal scalar of {{formula:85a7274c-146a-4ba5-8ede-22f6a0359b95}} {{cite:766fe2224dd754f0cb998151a42ec3baf487fa87}}.
| r | 6d0b0620843485118a64bf6f56de9081 |
We report results on HMDB51 of our model compared to previous models in Table REF . We observe that our model outperforms by a large margin several state-of-the-art methods which, as our model are based on RGB frames only as input, namely {{cite:119f43342be4793b07596ade300e6834483aed13}} and the spatial model of {{cite:285044620b2074a69658f85f543ad8a5e73d535e}}. The two-stream model, based on convolutional neural networks proposed by {{cite:285044620b2074a69658f85f543ad8a5e73d535e}}, also includes optical flow explicitly and used as input to the system as an addition to the RGB frames. Their model achieves an accuracy performance, which is only slightly higher than the one of our model, that only has RGB frames as input.
| r | a4a5865ed5ce7a9715fbd6a11d4ce16c |
A direct extension of our work would be to use complex distributions such as mixture density networks {{cite:1fe3febae357729381a418192f0b8c7769739e51}} for modelling output distributions. There are many exciting future directions, such as unsupervised learning to form deeper representation for the clusters of features {{cite:da001d960b74cc43689902e38525a47e30f7ddfd}}, using uncertainty attention {{cite:187a267f2dc2b1211d214bd00acb48c697617b7d}}, {{cite:4045c66441f775299d471e0a4156a926d71b9320}} to aid in training of the ensemble classifiers, exploring adaptive defer systems {{cite:432762dd0b90a2da240400406999aca4da22cfe1}} along with partial deferring based on clusters for better calibration of uncertainties coupled with human experts, and considering uncertainty of human feedback {{cite:205d1856bc1093442202bc111243d516605b23a0}}.
| d | 3c808f2c38f3bbb44e797f92fe612032 |
The focus of the present work is the use of CV teleportation channels for the teleportation of coherent states, and the use of non-Gaussian operations to enhance the communication outcomes. However, it is perhaps worth briefly discussing the flexibility of our system in regard to the transfer of other quantum states in the uplink, and the use of additional quantum operations. It will also be worth discussing differences and advantages of our system relative to DV-only systems - after all the only currently-deployed qiantum satellite system is one solely based on DV states {{cite:eb5cd9e9c068b4fa6d0d27587021f6f5273083cc}}.
| d | 7a3665caa94a45d7f15c6799b1c210d7 |
The space of possible {{formula:270b0189-0ac0-4548-b044-14cc8388c817}} configurations with {{formula:3716eaed-098d-4370-a13f-a1c77d8114f4}} is infinite dimensionalIn the presence of strong gravitational effects, such {{formula:04a47df8-bfe3-4cfe-b255-d6d611c668ac}} configurations in AdS or Minkowski false vacua might not exist. When that happens, there is nowhere to tunnel to and gravity stabilizes the false vacuum {{cite:bae82156380d4e9c4c52f9b8937b8a4a82179b26}}. (For a recent simple description, see {{cite:a13725133bd6d92b709cdfae4066e3f26a93045e}}) and in principle nothing prevents the false vacuum from decaying into any one of these configurations. A complete calculation of the decay rate should sum over all possible final states of the decay process. When there exists a (4d Euclidean) Coleman bounce, its
{{formula:3a359787-8d52-4db4-8ae5-780564e5dcc9}} slice gives a (spherically symmetric) bubble, {{formula:17094a32-e5fe-431b-bd11-542e63c166fa}} , singled out among all {{formula:d023a9e7-35fc-4f2a-bc76-ac5f653500e7}} configurations by the fact that it has the minimum Euclidean actionThe bounce is a saddle point of the Euclidean action but is a minimum when only {{formula:681ab6c5-54fe-4d44-b369-90bcdc5326dc}} configurations are considered {{cite:74e9f6e4973cfb5cda05ba75a13ada31c588cf81}}. (See also {{cite:924117bfd3e51112cc83bf7d72ad3f510d806017}} for an excellent introduction to these topics.) and is therefore the most likely outcome of the decay process and the one that dominates in the sum over final states.
| d | 781a8f59d39955761af1093bf53638da |
More recently, surging interest in contrastive learners was sparked by the renewed understanding that connects to mutual information estimation {{cite:c46fdd5eb56f8da3822cf0acea6921217d9898a4}}, {{cite:660533ed5272a3a255aadd6ef7eb16854c234e66}}. Fueled by the discovery of efficient algorithms and strong performance {{cite:db8bf9c043de20809d0371458bdac0980de9c557}}, extensive research has been devoted to this active topic {{cite:614260fc7ddd9dafe9ae6272a32e4bfaaeb43eac}}. These efforts range from theoretical investigations such as generalization error analyses {{cite:4b0089a04819960e04ec913402fae6e1419c8708}} and asymptotic characterizations {{cite:9508381fe5e51a1f92cd8d47c7959b8ff81675ff}}, to more practical aspects including hard-negative reinforcement {{cite:7c0cc6191ec9024000252d08db713afd971766c1}}, {{cite:f4b86772f9baa7a26f2d3b4c5abb34368a2eb9e1}}, and sampling bias adjustment {{cite:d214cbee978eecfdfcd098a7bdee3b0fbd9d1a74}}. Along with various subject matter improvements {{cite:e1e8c6abcb482373a06b7f3c0250a588b690e49b}}, {{cite:8a6d58e7eb12200c053107a138a772510d9a1aa6}}, {{cite:dbaa2089643bbc5d2e3aa0f7377896a5c7f1a597}}, {{cite:efc67348100b7d336d649b04eaae32243a89c2fb}}, {{cite:f0186c92e7ed9d23be258d86bf5dcb79cb6a5e65}}, {{cite:ffcb69d64219248a133e4f9c412cd19eeedaf2b1}}, contrastive learners now provide comprehensive solutions for self-supervised learning.
| i | 5fefa8c887e9c69a2f6a02e5f7a381a9 |
We compare with the other three prioritized experience replay methods to indicate the advantage of our policy-adaptation mechanism for model learning.
The first one is Prioritized Experience Replay (PER) {{cite:9b292907755556e1dc11ecfc9bddd87693b09f9a}}, which weighs the samples according to their TD-error.
The second method is RECALL {{cite:30fd2cb2399263f3f154a04e0da3db010aa25a89}}, which chooses the top {{formula:142a34ce-ee43-419c-9567-d45154994413}} highest value sample.
They use this to recall the samples that can induce the high-value samples and train the policy.
We implement this by choosing the top {{formula:9eabc0e5-241a-4a4f-8292-af9c72213167}} highest {{formula:577da3ba-bbf9-47ae-a1ec-4e858fb55530}} value samples to train the model and as model rollout initial states.
The third method is Model-augmented Prioritized Experience Replay (MaPER) {{cite:299ae59b4df02b6012b8e64096959a43f8da1d4c}}, which is an extension of PER using both TD-error and model prediction error to weight the samples for model learning.
| m | 39422759852fe93eadf7645d237a514f |
We use the peak positions {{formula:41a58f77-1d4e-439b-ad01-25889efa445b}} and total width {{formula:c4e04b9a-b4cd-4a3f-b164-412595a6bc63}} of the resonances as given in Ref. {{cite:1d7f9189a31c75e531203973587484dba01c1db8}} and collected above in Table REF .
{{figure:73c1b15a-c88c-461f-8650-c0161d3512d8}}{{table:24a3245b-7861-4035-b20f-bbaf1dbc7525}}{{figure:b928049c-3216-4918-8f58-f509f9e03980}} | r | 23ea1776d0fa479885db4587a5c89009 |
By reducing the problem of certified segmentation to only non-fluctuating components,
we significantly reduce the difficulty and achieve strong results on challenging datasets.
However, a drawback of the method is the newly introduced hyperparameter {{formula:5934d1e8-e97b-4e32-8c30-a83edbadf883}} . In practice a
suitable value can be determined by the desired radius or the empirical
performance of the base classifier.
High values of {{formula:61d5c685-7646-4ad3-b088-603d11b4a271}} will permit a higher certification radius, but also lead to more abstentions and require more samples {{formula:c60020c6-ec48-4281-a18b-d0d47893f82e}} for both certification and inference (both done via SegCertify).
Further, as is common with adversarial defenses is a loss of performance compared to a non-robust model.
However we expect further improvements in accuracy by the application of specialized training procedures
{{cite:be4cac99babfe7c1ead9b59fd9bfd5a42aa55ca1}}, {{cite:07df202436380a8789a77d298137a7b55c6c51c9}}, {{cite:cca5f6e6438f3504d59514543018a572385614e0}}, which we briefly
investigate in
sec:additional-results-semantic.
| d | 7b16ec5bb4ef8f339f9628de1e0b18f2 |
The proposed method showed promising performance to segment the anatomical structures such as the myocardium and the left ventricular cavity from DE-MRI. To extend this approach, shape prior based deep learning methods could help constrain the segmentation of the anatomical structures {{cite:5604983db5f86423420a33b4d2a1707964938e9d}}, {{cite:c5d2e82cce0e94465cb87ea5a58c2b79ecac98b9}}, {{cite:5f3bc0c8e0c31f7b4e78b2fdd7b60ba1c2a3e8b4}}. Post processing methods using convolutional auto-encoders {{cite:3e0dad62c5bc90f4cff8449595b0bc8bd2b0e25f}}, {{cite:0eceea6c51b9d8b0fc6546c8d3920e6a261765ee}} could also constrain the segmentation process by guaranteeing the correct shape of the anatomical structures. Moreover, the clinical information could be used to constrain the segmentation process of the pathological areas.
{{figure:731be9a4-d993-4d1c-b61b-293df2436962}} | r | 3a050f340f0ad311d923c0c179974ce9 |
Since the projection map {{formula:77986738-e93b-48af-9909-fb185f29cda9}} is finite, the dimension of {{formula:8410fd96-f5fe-4634-951c-ea6eb203036a}} is {{formula:2ac3d930-333a-4622-97cd-655d0841598e}} , i.e. it is codimension two in {{formula:9e70c551-a77a-47a3-a841-9e7ed2a6a6c9}} .
The projection map is also flat.
Since {{formula:e28d5f85-9998-4147-bc13-9ed2bf7a0e98}} admits a finite, flat map to a smooth variety, {{formula:8522ba95-bc46-42b9-8e4c-429d50e6a316}} is Cohen-Macaulay {{cite:ffbb5c3393fec663849993863219a83fbd090609}}.
Since {{formula:4584d51c-b4df-49e4-80e7-cc9ae3516eba}} is a codimension two Cohen-Macaulay subscheme of the smooth variety {{formula:b1818497-40d4-4e68-a8e8-93cabedb26fa}} , the local ring {{formula:825c5d31-8db7-4e33-ae95-29d398cf1c93}} is a Cohen-Macaulay module over the regular ring {{formula:7418ca59-49f3-4112-a3eb-2c934f2f2510}} for any {{formula:1bcd74d4-50bd-4643-bdfe-94cca47ff1e9}} .
As a result, {{formula:5ebb58c0-3bac-4ae5-aaef-24491840f165}} has a minimal free resolution
0 [r] b2 [r, "M"] R b1 R [r] R [r] OZ[n,n+1], [r] 0
whose length is two by the Auslander-Buchsbaum formula, i.e. {{formula:5dc55b4c-df2f-4dce-9c07-28015f2be8ab}} has local projective dimension two over {{formula:d13179bb-227f-44c8-a77f-a9d6e25ea43a}} .
| r | f77a60a2be3e4c9696260944235b07f1 |
In this paper we have tried to connect the lading soft theorems to symmetries in the approach suggested by {{cite:603980f04359fa7383652208435ab380c44108d0}}, {{cite:162413971c3520916b7ea3e54e03acbd5880443c}}, {{cite:a06b529597cd242ee13d1f132fb11520e0b41c2c}}, {{cite:34df5003c27e67fafd7c841b29c35742fabe3905}}. This does This seems to raise more questions than it answers. Let us list some of the pressing questions :
| d | 9c4a593cbaa80fe9cdcda7a041b997e9 |
PITF: Pairwise Interaction Tensor Factorization {{cite:f1dd5e19e9b696106bf21947fe03bc43b9b424db}}. It makes prediction for a triplet based on
{{formula:a01759f1-3369-44ba-a3a5-794c9b17f703}}
| m | eb611f5134ca3d1ddf59e903acade6c7 |
Fig. 2(c) shows a color plot of the spectra recorded in the saturated state with {{formula:5d5e7a5b-1658-485d-abeb-7910401c9eb1}} mT for different transferred wave vector, thus providing a direct picture of the spin-wave dispersions, up to a wave-vector of about {{formula:1c18f4e0-fa10-492c-967d-e66346f30e06}} rad/{{formula:79e76ad8-08e8-44d9-810e-e8ca7a2f13f1}} m. One recognizes clearly three spin-wave branches. The two highest ones with nearly constant frequency can be assigned to perpendicular standing spin waves with an increasing number of nodal planes across film thickness {{cite:00bb8e07276fc4bd196fe9f004ab7fd7eaf3039d}}. On the other hand, the lowest frequency branch clearly shows a negative group velocity (frequency decreases as wave-vector increases) for wave vector above a few rad/µm, which fits very well with the dispersion relation calculated for the stripe precursor mode (red line). This negative velocity can appear surprising at first glance since spin-waves in the Damon-Eshbach configuration normally have positive group velocity {{cite:e4b7556d70616d8c630170cedf5123d9a03450b6}}. However, it was already observed in the presence of a perpendicular magnetic anisotropy {{cite:b55d659a3ba30fd20248a2ac34a65f77ac4bd4b7}} and it finds a natural explanation here: The perpendicular magnetic anisotropy favors the out-of plane component of the magnetization precession with respect to the in-plane one, which allows for a certain degree of dipolar field cancellation at sufficiently short length-scale. Decreasing the field to {{formula:0c5215e1-83fc-44d6-980c-b16267b132c1}} mT, i.e. about {{formula:fe8778b6-37bb-4433-a272-2ef820123a9c}} mT above stripe nucleation, leads to a clear frequency decrease [Fig. 2(d)], which can be extrapolated to a perfect softening at ({{formula:3e2424bb-5225-4283-a0af-f56d2add9aaf}} ).
Let us now examine the spin-wave dispersion below nucleation. Symbols in Fig. 3(a) show the positions of the Brillouin light scattering peaks measured at {{formula:42f9c3e5-210e-4168-9795-814bf5392a9b}} mT (see raw data in Fig. S5 in the Supplementary Information {{cite:00bb8e07276fc4bd196fe9f004ab7fd7eaf3039d}}). We distinguish clearly two branches. The frequency of the bottom one decreases rapidly as a function of wavenumber down to an extrapolate {{formula:f38c7cb8-96f1-4b7b-8522-d7554d79e72f}} at {{formula:d383ef1a-2efe-4ef6-83f8-4a1bece6f269}} . The frequency of the top one decreases much slower and extrapolates to a value of about {{formula:5f9dace1-e024-4770-b497-977153e89052}} GHz at {{formula:801b957e-1665-4f8a-986c-c72b36f8772e}} . To help interpret these observations, we have performed mumax3 finite difference micromagnetic simulations {{cite:cb1ba346a8e5550eedca0fcd9f277ea601365a44}} of spin-wave propagation. Fig. 3(a)-(c) show color plots of the amplitude spectral density obtained upon Fourier transforming the spatio-temporal evolution of the surface magnetization following a localized pulse excitation (see {{cite:00bb8e07276fc4bd196fe9f004ab7fd7eaf3039d}}) for field values of 7, 10 and {{formula:a88d83e6-6472-409b-8119-805a1f9001e0}} mT, respectively. Right below nucleation [Fig. 3(c)], one distinguishes a secondary branch with a non-zero minimum frequency emerging from the characteristic {{formula:48c3d433-b7c1-43d1-bf56-905c6b2c3f44}} cusp. Upon reducing further the field, the minimum frequency of this secondary branch gradually increases, while the main branch remains soft [Fig. 3(b)]. These two branches account very well for the measured inelastic peaks positions [Fig. 3(a)]. This phenomenology can be understood as the mesoscopic counterpart of the one occurring at the microscopic level for charge density waves {{cite:48d99c4422c42a80751a2b60a0f1a578b2a345af}} and incommensurate displacive phases {{cite:29d59692671f56f45bbdfe04f7cffe746e44b01a}} whose nucleation is also described by the softening of a dynamic mode which splits into amplitude and phase modes upon symmetry breaking. Fig. 3(d,e) show maps of the out-of-plane component of the dynamic magnetization {{formula:a547191b-b484-478e-9af6-4be77a722fe0}} at {{formula:7d5241a8-341c-43ae-9f1b-244864285925}} for these two branches, together with the distribution of the transverse static magnetization, sketched as a vector plot. One clearly recognizes two similar patterns phase-shifted by {{formula:7f688347-f001-43dc-b173-688608a9d42b}} . For the zero frequency mode, the antinodes of the dynamic magnetization are aligned with the nodes of the static distribution [Fig. 3(d)]. In contrast, for the non-zero frequency mode, dynamic and static antinodes are aligned with each other [Fig. 3(e)]. The evolution with respect to the spectrum above saturation is explained as follows: The phase transition being second order, the overall spin wave spectrum changes smoothly upon stripe nucleation. The soft spin waves actually adapt in the form of intensity modulations in phase or in quadrature with respect to the nucleated texture.
{{figure:6b47070c-7555-4cf7-a36a-59e1a56cc968}} | r | dc6486c26696557efb72b64a3aceafc5 |
In {{cite:c1db8e62212905edc08ecd754500f315c9672a64}}, it is suggested that the optically thin double-peaked line profiles of the {{formula:55883aaa-aad5-4fc0-a533-e1d6a05381ea}} = 1,0 {{formula:8a24f460-fc71-4884-99b7-3c0b272c2741}} 1,1 line of N{{formula:434f799a-956b-46fd-9a6c-9e29892d87b0}} H{{formula:79db6721-656d-4bce-88db-a953b290857c}} (1-0) and HC{{formula:e3e20841-bd5e-4dcb-84f6-792ddc63b280}} O{{formula:b3851de3-8ddb-4339-9add-a1cfffca627a}} (1-0) towards L1544 arises from the depletion of these molecules towards the centre of the core. To mimic this depletion the fractional abundance of N{{formula:f3fdf921-d07b-44ae-9f01-2346879f7796}} H{{formula:18ba34ab-e6e3-4bd5-8ec3-c2ba4754bc59}} and HC{{formula:cb435fec-2091-400f-8964-ffd93205f449}} O{{formula:70c6ce97-c93f-41e8-8948-3733d842d9ce}} was set to 0 between the centre and 2000 au and 1400 au, respectively. The size of these gaps in the fractional abundance profiles are related to the radius from the centre of the core at which these molecules present significant depletion. This artificial depletion reproduced the {{formula:3babd550-b958-4892-9c36-d9855796e1f7}} = 1,0 {{formula:0bced26c-94d0-4d3d-8c29-c83f76ba50e7}} 1,1 line of N{{formula:0d9c187e-dd65-4fda-ad0b-6817566d2b26}} H{{formula:a67a2eb3-1d95-4fd9-a4c4-0e08cf505a65}} (1-0) and HC{{formula:0b1c2127-76c9-411d-9529-8880171c5b34}} O{{formula:7d24336e-5e12-475b-af2d-41612780bb9e}} (1-0) line profiles. To test whether an enhanced depletion of HC{{formula:01efdae2-0138-40dc-9f91-0533156cb922}} O{{formula:0369d903-537a-4720-a0bb-6f4a5c73f591}} towards the core centre would reproduce the observations, we created a "hole" in the fractional abundance profile similarly to {{cite:c1db8e62212905edc08ecd754500f315c9672a64}} (more information in Appendix REF ), but the central depletion of HC{{formula:4b0cf5bc-5d78-4765-9b49-253e2aecbce7}} O{{formula:eb5798d6-be65-45fc-b450-01a157b2fbbf}} does not reproduce the observed line profile (e.g. Figure REF ). This was expected as the chemical model already naturally predicts the depletion of HCO{{formula:aa17c26b-8e19-4f20-81f2-456aa2ba7d1f}} towards the central part of the core.
| d | f8e4551e776441c48afca2109597e55f |
To overcome this deficiency of previous GNNs, recent work has proposed implicit graph neural networks {{cite:c6e1ff18d1105eba5962eac7189a76f6fb684b18}}, {{cite:03d70bd7d95d1399cf79603df3aee8e04f151298}}, {{cite:68d61ea465f8fd39a40d00594ec90ce6b15c3752}} to effectively capture long-range dependencies.
These implicit graph neural networks generally define a fixed-point equation as an implicit layer for aggregation and generate the equilibrium {{formula:bf26da96-d0e3-43ff-8c7d-6ed7e7995941}} as the node representations.
To get the equilibrium, they either use an iterative solver to solve the equation or directly obtain a closed-form solution with guaranteed convergence. Meanwhile, they utilize implicit differentiation to achieve {{formula:168f76cf-f397-4b8c-91b0-0cd8d7f57e8a}} memory complexity when computing the gradients during the iterations.
As mentioned in {{cite:c6e1ff18d1105eba5962eac7189a76f6fb684b18}}, {{cite:03d70bd7d95d1399cf79603df3aee8e04f151298}}, these models can be treated as a graph neural network with infinite layers which has the same transformation and shared weights in each layer.
This makes them able to effectively capture long-range dependencies without excessive memory requirements as compared with previous GNNs.
| i | ac4ab3a9eb9a6711d0ce96c7558f8e3c |
Active mapping refers to the process of actively perceiving environments by adapting self motions of the robot based on specific criteria {{cite:e527d5d371ee9f6ac2f40d029b5bc234c505ac36}}. Active mapping has wide applications in mobile robots, e.g., unknown environment exploration and target searching {{cite:fe4003732235f18e0d7ee1ae93e8ecea5ce6647e}}. In recent years, with the growing requirements on robotic manipulation in unknown or cluttered environments, active mapping also receives much attention in the manipulation community {{cite:ea04132dcc344c6b92f017c528013781fe28966d}}, {{cite:ed54d498185049bb7732c52ae2e2f043f74d89b1}}, {{cite:5c463e379319b042546aaa51d1788cfde72b1cb6}}, {{cite:28bd80353ecf1e6b7e21134c8a01dd3a717b4cdb}}.
| i | 10081f78510c76c5704adebd9f471edf |
We provide the results of proposed framework implemented based on non-contrastive methods. Specifically, we leverage SimSiam {{cite:825f32cd2046a8eae362258f31ce11c720f339e0}} and VICReg {{cite:8184a725d5a5874798ae6ef44badbe90cac46666}} as baselines. Table REF shows that the generalization performance of both baselines can be improved with the proposed debiasing framework.
{{table:9b109e74-c636-4c91-89e7-3ab913d8e0a4}}{{table:2542afd0-4a76-4a67-9496-6400894b831d}} | m | a689aff7ed2f9c9415e05451298e3ee9 |
In Section 3 we review the Hamilton-Jacobi formalism following to a large extend refs. {{cite:669cce7895ca1f3f055b775992fd582c5d48e5be}}, {{cite:db491edbce94b4077631e087d405f58a57660de7}}. Parts of the derivation are given in Appendix A.
The corresponding flow equations and Hamiltonian constraints are derived. In Section 4 we show that, within the expansion up to second order in derivatives, all Hamiltonian constraints up to one can be satisfied by an arbitrary 4d scalar QFT thanks to the consistency condition following from the local Wilsonian cutoff. A summary and outlook is given in Section 5.
| i | fda5f05fc860a317fb213e79eafbc950 |
While these approaches are effective in many scenarios, their use comes with a considerable cost.
For example, for the FeMoCo molecule, a widely-used benchmark in quantum computational chemistry, the best estimate of QPE runtime for determining its ground state energy is just under 4 days {{cite:af9cf56cec56e49ffcdf7482b501bfcfd64a5cc0}} on a fault-tolerant quantum computer with millions of physical qubits. On the other hand, VQE has the possibility of allowing for quantum computational chemistry with fewer, noisier qubits, but the number of measurements needed to estimate energies is often significant, making scaling of the algorithm to large molecules a challenge {{cite:cb985f7982b0c9b1676e9c3461f0edf09f59cf62}}, {{cite:c56702a73013f97e94733b52788de519108ec1a9}}, {{cite:5a13308fa09b6e24b90259876ea6849ab6e0538e}}, {{cite:a40cbec1889e0ee1799b2efbd8c9d4819bc75b60}}.
| i | 8b73560dd76f90acc3804b9c32be471d |
where {{formula:c2c00114-bff4-4987-979a-08c7586c5dc2}} stands for the {{formula:faf25964-1955-4bd2-857d-1fba92571772}} entry of {{formula:ff512b25-d44d-44f1-83c3-3468f1930a23}} . Since white-box source model {{formula:18438c81-3eba-4b32-9a3a-a194d9566a7d}} is required in (REF ), we term it as white-box unsupervised domain adaptation (WBUDA) to distinguish it from our investigated one in follow paragraphs.
In WBUDA, the target model is typically achieved by fine-tuning the white-box source model {{formula:c8034101-b9f4-4d35-b6fa-f82761e43752}} on unlabeled target data {{formula:23fe130f-eac5-47b3-814b-74a758490c96}} using proper objectives, e.g., the pseudo labeling and information maximization losses in {{cite:7dfe2c137340338212c9606b976f0f76a5ae1cfa}}.
{{figure:38e1d28f-487b-4558-b9a8-0ea9cc7616ed}} | m | ab12a12059e72b77926a5955c386be71 |
Entanglement wedge reconstruction. Harlow has proved that the validity of the quantum Ryu-Takayanagi formula is equivalent to the achievability of the task of entanglement wedge reconstruction with respect to the RT surface {{cite:393873fe32bf4f34282a52ddb965bf6051a7274c}}. Harlow's structural theorem is stated for the whole code subspace, but one can generalize this task of EWR to a state-dependent task {{cite:87d7945de5dc02b4af28b57193ff4300a43753bc}}, {{cite:1d65ce83af896d9500efcd54dbf27dfcc3209c2d}}, where the boundary operator is only required to have the same action as the bulk operator on the particular state. This is referred as state-specific EWR in AP. In the Schroedinger picture, AP argued that the state-specific EWR should be understood as one-shot state merging and it's characterized by the conditional max-entropy, which matches well with the conditions in the refined QES prescription. It's therefore promising that an analogue of Harlow's theorem can be established formally connecting state-specific EWR and the refined QES prescrition at least for the max-EW and the complement of min-EW. Regarding the indefinite regime and the corresponding “no man's land” region ({{formula:2c156003-e26b-44ca-a575-cc01e22b8baf}} ), it's important to note that the state-specific EWR could still be achievable in this region because accessing side information from the “no man's land” could assist the state transfer (or operator reconstruction) in the {{formula:099ed41d-00d2-42d7-bb0b-2cef5eef2596}} , provided this side information is sufficiently “quantum”, i.e. has sufficient entanglement with {{formula:f2a96726-6637-4d33-bd79-e32ee5bc41aa}} . It's less clear how Harlow's theorem can be extended to this regime. One potential direction is to consider a different setup that does not involve infinite replicas we considered in this work. The tensor network model and the error correction picture for holography suggest that we can think of the EWR as pushing a bulk operator through layers of the tensors to the boundary. In the Schrodinger picture, this corresponds to generate a bulk state supported over many bulk legs with an input state from the boundary. The conditional min/max-entropies of the bulk state generated as so can be estimated using a novel technique in entropy-calculus called the entropy accumulation theorem (EAT){{cite:269614b2a0d6b6891329c0525ff41f9dbb63d726}}, {{cite:554e727768f2efb98df2618348238726055081ea}}, which is a generalisation of the AEP. The EAT claims that even though in situations one does not have the i.i.d product structure as in the AEP replica trick, the sequential structure still guarantees that the output min/max-entropies can be estimated as the accumulation of von Neumann entropies on each site. We believe the EAT can help generalize Harlow's theorem beyond the conventional i.i.d. regime to probe the no man's land.
| d | 6b0d66ef1495de17723cb56fd6876c2c |
Dataset
We first use Scan {{cite:84ca670ebf2d9549151a53bf9d562a65eecbb8a7}} as a diagnostic dataset to test the performance of subtree substitution in compositional semantic parsing. Scan is a synthetic dataset, which consists of simple English commands paired with sequences of discrete actions. We use the program version of {{cite:ca9880eed3ab255bfc1796d0c34ef547bfc3a46a}}. For instance, “run right after jump” corresponds to the program “i_after ( i_run ( i_right ) , i_jump )”. Also, semi-automatically annotated span trees from {{cite:ca9880eed3ab255bfc1796d0c34ef547bfc3a46a}} are used for subtree substitution. To test compositional semantic parsing, we use the Primitive right (Right) and Primitive around right (AroundRight) compositional splits from {{cite:316947067312851e67f7530e9527c51847730b56}}, where templates of the form Primitive right and Primitive around right (respectively) appear only in the test set. In these templates, Primitive stands for jump, walk, run, or look. For simplicity, func(·) is defined only on i_right and i_left, where func(i_right) = func(i_left) = direction. That is, all “i_right” and “i_left” appear as leaf nodes in span trees and they are exchangeable.
| r | aeefddd88cd5f2dfe8bf5f2156a2cc6c |
For the WB experiments, we use HGCN (CEM+GHCM+HM) as the reference and introduce the improvements of each module step by step for comparison ({{formula:b3b6cbf7-2b64-4197-a7d1-e0c235b6b36d}} , {{formula:ae85d138-a72f-4f78-b2cd-1a78078ea947}} , {{formula:c7e45cf6-3d04-447d-bf19-08b8ba6e4595}} , {{formula:8d460f6c-1830-4fca-9b5a-3a402848c202}} denotes the updated version). The 32 ms hanning window with {{formula:20139469-9e10-47a9-825a-5bddab0a3f55}} overlap and 512-point STFT is used. The kernel size is {{formula:a24173bd-713e-4439-b873-dba3bb2a0fc9}} . The channel number and stride of encoder and decoder are {{formula:849fbcf8-1de7-4054-bcc9-c3a11deaeaec}} and {{formula:84ec10e3-a358-41fc-9170-d93c9f7801cb}} . For HGCN, a 512-units FC after 3-layer 128-units LSTM is adopted. The channel number and stride of GHCM are {{formula:83f83a3c-686c-4b11-98f5-30c7bfece322}} and {{formula:61102507-7310-4a5f-b662-30a1d232f7af}} and the out channel of last decoder is 22 ({{formula:d27a2721-2ff1-4385-9f43-2d9eb0c7c29e}} ). Since the {{formula:efea21d9-e557-4049-8ee4-abee8e55742f}} and the DPRNN are residual, the hidden dimension is the same as the input. The optimizer is Adam {{cite:bab41a2654bb17628d2d18ebd440d125211266a5}}. And the initial learning rate is {{formula:c91a5c04-28fb-4d46-8cc8-3798317e2292}} , which decays {{formula:90a81130-243d-431f-8d39-2eb491c85810}} when the valid loss plateaus for 5 epochs, and training is stopped if loss plateaus for 20 epochs.
| m | d2988b000b4e03b0afb0273af0396632 |
A substantially more challenging extension of our methodology is to targeted pair statistics derived from
general statistically inhomogeneous system in which there is a preferred origin in the system, e.g. liquid-gas interfaces, which requires a
position-dependent one-body potential {{formula:a6d8e3fe-f69f-4c1e-a5f7-3260c4996386}} and a pair potential that depends on absolute positions {{formula:fda018f3-4e1c-4f3d-a313-3193925b464f}} .
To treat such systems, one
could apply the inhomogeneous Ornstein-Zernike equations {{cite:6eec3fb37134a4e252e23acdf43722115dc4c130}} and the associated closures, such as the
Lovett–Mou–Buff–Wertheim equation {{cite:2fa06aa9a9b236cc6f82cb3bc166bbcfabd7faf6}}, to obtain an initial
guess for the functional forms of both {{formula:27e84e91-6adf-440a-9f62-1adfaf60a26c}} and {{formula:ca4179e9-7335-49be-a883-7d79594caa74}} {{cite:546be4060e27322beb4004614a245c777ae7e127}}.
However, it will be significantly more nontrivial to find appropriate pointwise
functional forms for the basis functions and to perform the corresponding optimizations
for inhomogeneous systems, and so represents an outstanding subject for future research.
| d | 4a720dd9550942b19277d9ddbea5e48d |
In view of Theorem REF , we only need to prove the necessary part. Suppose that {{formula:bac10798-2263-41a0-821a-7e23b4f50ea4}} in {{formula:d562cdb9-01c9-44e7-881c-39b06b4c22db}} By {{cite:f4a01e2e141201f90a4c0bcbe79ed9dce37305b2}}, we know that {{formula:2f0637f7-fdfc-4ad4-829a-dbe680442f91}} can be embedded (isometrically) as a subspace of {{formula:92617ebd-e8ec-4ac1-bd79-57f559f52d85}} via the embedding {{formula:d5973caf-82bd-44a6-830b-ee5e37e8137d}} , where {{formula:e77e6c8b-c444-4915-90f6-924711d7dbae}} represents the map {{formula:1f903b1d-5657-4c87-b641-fcfc82fefaa9}} for all {{formula:bd9a93ec-00c9-45fa-a3cc-1aac482100bd}} ;
here {{formula:028134dc-c26f-496a-8d78-2fb6bfa35021}} are closed unit balls in {{formula:5af64b52-bf7c-4f26-8fb7-94064ffa19fc}} and {{formula:aa93641c-f910-4675-aac6-0be284be5cc6}} respectively equipped with the weak{{formula:1960f484-66b7-4e3c-91c9-3024ff10bbb6}} -topology. Note that, by Banach Alaoglu's Theorem, {{formula:194a4bb4-74ef-49e7-bad0-4ec26e72219f}} is compact, {{formula:430be8ba-f435-4c86-939b-1cf26b1546b0}} and {{formula:db4710f1-ea36-4426-a091-d58db14035b8}} being compact.
Thus, {{formula:ec31f499-3b38-4521-b077-aca679d82c01}} in {{formula:3f61b337-7bc0-43b4-bb16-8baf81eb48e2}} is equivalent to saying that {{formula:06ac5723-f98d-47ee-814b-85677cbd3705}} in {{formula:7fb9b803-dd11-4008-8c84-2d23547c2ca9}}
We claim that either {{formula:a5f25d06-a60b-461b-a954-ce3227c27203}} in {{formula:2e8653ec-39a9-4113-8d56-0fb493b2dcd6}} or {{formula:4356e783-930f-4f64-9515-79b7c28b0133}} in {{formula:cfaa22f5-1b66-4ee4-9ed5-f9a2210c3930}} . Let, if possible, neither {{formula:9d94baef-9c1d-42b5-93ac-c981604f0d0e}} nor {{formula:9d8d3b3b-a5a2-4f49-be05-3412ff949eaf}} Then, by Theorem REF , either {{formula:14986374-ddb8-4209-bb49-191c3fb82940}} or {{formula:0b37c1e3-e4b6-49f7-9786-6f566570063e}} , and similarly, either {{formula:46efa0a1-1eb4-4fbe-bea3-254d5265ee08}} or {{formula:378d42ae-ca54-41fa-bd08-74693e19f888}} Let us discuss the case when {{formula:31a90187-6d17-42ba-a693-a1960a1a4506}} and {{formula:1ad56f08-5d0e-43ca-8c59-3cbbfc5a94f2}} for all {{formula:dcf6ba62-953b-43b1-9eca-07c2d852fcd1}} . Then, we have {{formula:c194cb31-de6a-485c-8f7f-6e16ff319fd7}} and {{formula:78c1b953-2dc5-4b5f-82de-e2bdbe83faaf}} for all {{formula:9b846337-06c5-43f2-b3a1-5a022ebdf643}} . This gives {{formula:04c95d48-2ba1-45e3-8ce5-c92c9cc744b9}} which contradicts the hypothesis {{formula:7a5625b0-6af3-4eef-b521-bc80f8c747e4}} So this case is not possible. Similarly, we will get contradiction in rest of the three cases.
Now, assume that {{formula:8ae1faa6-87fb-41b5-893f-b12aab89df02}} Therefore for any scalar {{formula:2051c805-d6a0-4e24-9d46-c12d5a72c7fb}} we have {{formula:bad38b15-278b-4187-976f-79c6cdde4a0b}} which, using a consequence of Hahn Banach Theorem, gives that {{formula:5af07432-f39b-46e4-b479-791c597cf45c}} and thus {{formula:8dbdc8b7-490b-4a48-b106-b3575bdff1a5}} . Similarly {{formula:aa7b3a0f-7d41-444c-ac31-f2f257eecd3f}} would imply that {{formula:fd38f84c-7485-4d82-961d-aadaccb19b52}} .
| r | 0d40e1c90069cef9a9b4c3df2f54ba17 |
Remark 3.9 Thanks to {{cite:786acbe3275183ec01a6b8bacf73aa68b28b7827}}, the RCQ is equivalent to the following condition
{{formula:c27d1bba-4683-4767-8143-50f09b1f8f4a}}
| r | 985b4460b59f0e59867236cb91496f30 |
To compare the performance improvements of our proposed domain adaptation model, we implemented 7 stste-of-art algorithms: 1) DANN (Domain-Adversarial Training of Neural Networks) {{cite:3423a0c4822468177e27283303580607d9ce622d}}; 2) CORAL {{cite:516a5f4c2a6812e47b2c67086d5d8cc6114dc34d}}; 3) ADR (Adversarial Dropout Regularization) {{cite:e550cf8218e2ac6cdb07476d6d1bff9dae3591bf}}; 4) VADA: A Virtual Adversarial Domain Adaptation (VADA) {{cite:8eea440fe56bfe2e2e6414385567f3a96c1e2a9f}}; 5) DIRT-T: Decision-boundary Iterative Refinement Training with a Teacher {{cite:e187d0ac1b0a862f4057ae89181615026f898a66}}; 6) ADA: Associative Domain Adaptation {{cite:94e1c8a73a3a033449dbc6875096d95de160cf31}}; and 7) SEVDA: Self-ensembling for visual domain adaptation {{cite:692283bec4a08a8979d8eea7ce21647f0fbe9e36}} models.
| m | 3eba95239f2705c45f74570635094420 |
Action Completeness Modeling. The methods of CMCS {{cite:7d2ff430260546ff60991ac725ad659055e46eae}}, Hide-and-Seek {{cite:df319b5cfbb3f3dc220dfecd2782f4d7bb1ef0a0}}, and Step-by-step {{cite:ddbca856deeede510dc41b366165974b32cb7dce}} target the action completeness and CMCS {{cite:7d2ff430260546ff60991ac725ad659055e46eae}} achieves a superior performance. This is because Hide-and-Seek {{cite:df319b5cfbb3f3dc220dfecd2782f4d7bb1ef0a0}} and Step-by-step {{cite:ddbca856deeede510dc41b366165974b32cb7dce}} do not guarantee the discovery of new parts by randomly hiding or removing different video regions. In contrary, CMCS {{cite:7d2ff430260546ff60991ac725ad659055e46eae}} employs a diversity loss to enforce the model to discover complementary action parts.
| m | 97a3e13bd1784261cafc08809d982f87 |
Topological entropy can be defined equivalently by using {{formula:9f720eb6-56d5-4f32-a3fc-5370b0df3240}} -spanning sets or open covers of {{formula:d8e5e37c-0969-4b6d-9957-a9aa61bf7d0c}} .
See Chapter 7 in {{cite:ec92e5b6a2e53c2465f277282f0aff7f1d692105}} or Chapter 3 in {{cite:016fa0ed57621d355fa936651ec834f26c109a4e}} for comprehensive discussions on topological entropy.
| r | 3057db17ab602ff8d35c37a49dfd7bce |
The second term of (REF ) is {{formula:14ca8547-073e-426b-9acb-3596aed4b2a5}} . It is the perceptual loss to measure perceptual difference between {{formula:d37e362c-b082-462c-83a5-fc76ec063305}} and {{formula:cc808ee2-67b8-4d9c-ae41-13b2235ec7f2}} , which can preserve details of the predictions and make interpolated frames sharper {{cite:e165267a0a88f248612e48fa8d356f21ba2e365b}}. The loss function of {{formula:ee6f508b-fc90-4848-87aa-dbb8ec84af39}} is defined as follows:
{{formula:c5756d9a-db5e-40b1-a55e-e45e1a9ea4cb}}
| m | 80aa8629aad5d823f46d7c1642184d0e |
The {{formula:3e923319-4a61-47eb-ba06-58006051eaeb}} calculations discussed in this paper are of rather complicated dynamical ones, however the production representation has been shown to be useful in providing us a simple and pictorial way of understanding the essence of the {{formula:8eac4caa-3166-4896-96e1-188930708853}} calculations: in the language of this work, the evidence on the existence of {{formula:ac97207d-e1d0-4894-a874-a61b85fb578c}} seems to be partly from the peculiar singularity structure of the background integral defined in Eqs. (REF ).
It reads that if {{formula:6582a3d5-eae8-4669-b15a-16519ac0362e}} does not vanish (or does not vanish fast enough), then an {{formula:8ed76d93-bfdd-4504-8e51-efed31ab9763}} -wave subthreshold resonance exist, in the most attractive channels.Similar observations are obtained, from a different point of view. {{cite:b6ee2b27b1a74b4063c77e5b8526c7bc661b9a40}}. This may even be a rather universal phenomenon, if the background contributions are universally negative, as suggested by quantum scattering theory {{cite:bef4899703e6ed638db8a562d9c20636f59856a0}} and repeatedly verified by calculations in quantum field theories. {{cite:9216d420278c60f4425366401898ed5ecea36916}} {{cite:96639535c4128e09d07d8b3b923c73bb23ce297a}}{{cite:9512cd7159bc227f91342c84d4beab2382124e9a}}
| d | 82c23f6d197cd9c1b480cf0aaadf5055 |
The Sinkhorn algorithm is the benchmark approach to fast computation of the entropic regularization of optimal transportation {{cite:d7f3dff898294b4161fe527f0c38851d4fefb05e}}. Ultimately, one is faced with the following numerical problem: Given two probability vectors {{formula:cd529dea-3f95-4049-8e91-11610d5c61b3}} , {{formula:5a36da00-ed69-4c5a-a14f-65c84514ab38}} and a matrix {{formula:fa8ddac2-ae06-41f6-b0fc-78777c5c2180}} , the goal is to find a pair of vectors {{formula:07ea6250-f1ae-4bc5-90bf-feaac9e13f47}} such that
{{formula:1b7b01b5-4234-416d-ac99-cdd3b719b451}}
| i | 685d201c0c1a615c8c245b99c26215ac |
Here, the smooth part {{formula:93817b34-0eef-4106-a8a1-9a81e432d333}} of the objective functional is linearized around {{formula:7d6bae2a-c655-4810-ac94-7a1210ba5deb}} while the nonsmooth part {{formula:b14236a3-2ae1-40e2-bd21-20f15dfa6080}} remains unchanged. Variants of this method have been applied to great success in applications such as super-resolution, {{cite:ccf52fd4ac417947fbcc6c1e1b89c636ecdbf2f3}}, acoustic inversion, {{cite:2ad845dda30381c25b12d952e4c9de1b61cddca6}}, and dynamic transport regularization, {{cite:5d20150c93fefa909ff6488b03a676ff630636dc}}, which all go beyond the setting of (REF ).
Of course, if {{formula:ca23089b-bd08-4407-a2f4-be28e2b14e86}} , the convex indicator function of {{formula:2c65459c-31dc-4643-9dd6-6febca35cffc}} , (REF ) reduces to (REF ) and the original conditional gradient method is recovered. Sublinear rates of convergence for the GCG method have already been proven for a variety of stepsize choices. Without any pretense of completeness we refer to {{cite:29b01c46d79afc17cf37d928566447dfbd030902}}, {{cite:8de2a941f8b4157e06d362801347ab21bac9b96e}}, {{cite:bc5236ab0023e1effa37c1c0e675c4f1f4d56396}}, {{cite:d922dfc4c3f785185783ccb6d4092a188d9bdb76}} as well as {{cite:9841c2711e50266c2b8d7fd3ba0d669339b2f360}}.
Nevertheless literature on improved convergence results for {{formula:4cbe80a4-46e6-45f5-8260-da7c1e0d9a15}} is scarce. We point to {{cite:14ed245bf599c2b80fefba322ac83aff62d82a00}}, {{cite:ccf52fd4ac417947fbcc6c1e1b89c636ecdbf2f3}}, {{cite:5dae51a3dae7875e34743e20284b4c4e1dd39c6b}}, {{cite:05ad88bddb7bd9335914d0499382cc6b8e5baeb7}} for examples of accelerated GCG methods, i.e. (REF ) with additional speed-up steps, which achieve linear, or even finite-step, convergence in particular settings. Faster convergence results without augmentations to (REF ), however, seem not to be available.
| i | 85dd60cf79b00b87d1b6aedd9f9aa865 |
However, graph structures cannot be handled succinctly in purely functional languages.
Although such structures can be handled with references,
this style implies imperative programming with destructive assignments,
which makes it hard to read and write programs and also makes verification more difficult.
In addition, classic type systems can only verify the types of the referenced data
and cannot verify the shape of the data structure.
Therefore, we aim to incorporate Graph Transformation {{cite:18d56775c84538a4dac6580d8563d5f652fad2d8}} to a functional language
and to develop a new type system for that.
Our approach is in contrast with the analysis of pointer manipulation
programs using
separation logic {{cite:8585086de6fc5ae864109308724098af2cff5b71}}, shape analysis, etc.
in that (i) we consider graph structures formed by
higher-level languages that abstract pointers and heaps away and
guarantee low-level invariants such as the absence of dangling pointers and
that (ii) we pursue what properties can be established automatically
using a rather simple typing framework.
| i | 2c5a89c585413f5f02c55b9a8e9a9138 |
Due to the effectiveness of this approach, transfer learning has become a central element in the machine learning toolbox. For instance, using pretrained feature maps is common practice in a variety of applications, including fine-grained classification {{cite:e2d4e66c529e226b2a591e250539ba7554d076d9}}, {{cite:44ac9faf2e8766264b31c013bc454d481ccc4211}}, {{cite:781011419326238f1ca465ff76ee470610817cb9}}, object detection, {{cite:79fae855c29e6f11a354700eb87fd1baadb28654}}, {{cite:97d040656d4d450f9e39f5db2caf7ebc1c3e14aa}}, {{cite:c0768debc7c747452afcba9abbea7b5992a7bf56}}, semantic segmentation {{cite:be8407bdbe507c530637f56d30f208eb50923220}}, {{cite:535ddc64ba51f5fce7be51dfe674346c81a63017}}, or medical imaging {{cite:8808addbdb6c859d41a6eb4f9ef60f5b8fe48d2a}}.
In fact, due to the cumulative success of transfer learning, large pretrained models that can be effectively adapted to a wide variety of tasks {{cite:33cf01fb7cc16f7b25b0de68f972ded885ffe5c2}}, {{cite:611ae88f3e960270bc186ff8a4a6b8a1ed4c0139}} have recently been characterized as foundation models {{cite:8b92a691273a14f26e51fdaf0da109a02472b9a3}}, emphasizing their central role in solving various learning tasks.
| i | 02f6b875fc78473cfa9c6dbd5cfc4e10 |
This slow adoption can be attributed to a combination of practical {{cite:70b399e61f46a997424ad91ee4678a5f16ee0e0a}}, {{cite:cb1b32feda60269dd704f522c57d01338ed59acb}}, social {{cite:c2c571035431833a07aff1ec5f823e060d48c4a6}}, {{cite:a322124eac522e2a243dbcfcf305b2521f17f1d8}}, {{cite:c1fd6b61c83fc4b51e68ba6ab3e62ad103cf9190}} and ethical reasons {{cite:23842b6cf7465ebbdf7c0d00ad98c9c67b788f7e}}, {{cite:d06e2fd3a478efc48463c54037f066160f880779}}, {{cite:bfbf95234e2e20e68fa9f04346e8d31bee87ed0e}}, {{cite:9abf6f3348765021136e255d418ccaaba4a1e47c}}, {{cite:3ac8da407b7d75d58e5e6c050c4f4e5f2335b064}}.
Some of these fall out of the scope of Machine Learning (ML), as they mostly involve legal accountability (e.g. who is to blame if a self-driving car crashes?), adverse side-effects (e.g. jobs becoming redundant) or philosophical questions on machine morality.
| i | f61962807d9499189576dd8b61ea8bc9 |
Our investigation adds a concrete case study to the discussion on how abstraction may be learned without explicit supervision. While images containing, say, five objects may look very different from each other, our model discovers a common property, i.e. the number of items, which is not immediately available from the brightness distribution. The mechanism driving such abstraction may be interpreted as an implicit contrastive learning signal {{cite:22f208625e609925654a157b024aa3930e90a136}}, where the shake action identifies pairs of images that ought to be considered as similar, while the put and take actions signal pairs of images that ought to be considered dissimilar, hence the clustering. However, there is a crucial difference between our model and traditional contrastive learning. In contrastive learning it is the designer who hand-crafts the similarity and dissimilarity training signals in order to achieve an intended learning goal. I.e. the abstraction is directly built into, not discovered by, the network. By contrast, in our model it is the network itself that associates a meaning of `close' and `far' to the P,T,S actions, and ultimately discovers the abstraction. This abstraction is surprisingly strong – while the primary supervised task, action classification, does not generalize beyond the training limit of three objects, the abstractions of number and quantity extend far beyond it.
| d | 847c7eb20455f0815fd0f8080ba7b95b |
we can easily train MaAST with any proven RL algorithm to achieve performance boosts from more efficient, large-scale training.
Further, while recent works have shown the success of using hierarchical DRL policies paired with analytical planners such as A{{formula:75c3cb7a-9a9b-4b60-8b85-824c6dcc0182}} in exploration and navigation {{cite:9167f4a3759b812767d4ece469524f5219d4c47a}}, {{cite:63d15ae1567d8773ee060fea0660675cc78eb47d}}, we restrict our focus on learning and improving end-to-end RL policies with simpler modules.
Our proposed approach (incorporating important semantic scene information into the map) can be incorporated with {{cite:9167f4a3759b812767d4ece469524f5219d4c47a}} as we did with {{cite:e66385b7ab9e1530164dd987daa4699589dfded8}}. We leave it as a future work.
As our main objective is to show MaAST's effectiveness under budget constrained situations, we evaluate all the methods under a fixed training budget
of 14 million steps of experience, as this was the point at which a Depth agent has been shown to exceed performance of SLAM {{cite:efe4aa36e93d8875d60c849428f95d874812b275}}.
Analysis of Results
In tab:baselines, we demonstrate that the proposed approach (MaAST) significantly outperforms other methods and baselines, under a much reduced computational load. Agents equipped with no visual sensors (i.e., blind) are expected to show poor performance. Surprisingly, a blind agent {{cite:efe4aa36e93d8875d60c849428f95d874812b275}} trained by PPO is already able to achieve a modest success (35%) with 75 million steps of training experience. However, agents equipped with visual sensors show large performance improvement with reduced experience.
Among agents equipped with visual sensors, MaAST shows significant improvement over other agents. The improvement is {{formula:5b9cd25c-c8bc-48c2-b2a3-808eaeb3bf39}} absolute ({{formula:ae3acf4b-3b41-438b-a267-8b6989e5e868}} relative) in SPL as compared to RGB-D alone and {{formula:c81021c3-1bb1-4992-9cc5-2dac108316ff}} absolute ({{formula:43dd77f6-c5d3-4c2a-9554-ca8f12d04c39}} relative) as compared to RGBD+OCC. In terms of success rate, the performance increase is comparatively less ({{formula:67bcfeb6-a407-40d6-b4fd-b2c9c0c39b47}} relative over RGB-D and {{formula:7bc560f7-ca2c-4bad-a736-6deef12cfd2c}} relative over RGBD+OCC). This shows that even though most of the methods succeed at nearly the same rate, MaAST's policy demonstrates superior efficacy in producing shorter paths to the target, due to our attention mechanism's ability to focus on more relevant parts of the map, such as potential collisions or new areas to explore.
With respect to the statistical significance of our results, we evaluated the performance of MaAST averaged over 5 random seeds and obtained SPL of {{formula:8cc22d54-ccf2-4323-a44d-c8800072a9d9}} , making the performance gain over other compared methods roughly an order of magnitude greater than the standard deviation of MaAST's performance. Furthermore, we note that MaAST is able to achieve significant improvements over SLAM in only 14 million training steps, which could not be achieved by RGB-D alone in prior work, even with five times more experience {{cite:efe4aa36e93d8875d60c849428f95d874812b275}}.
Ablation Study
To investigate the impact of different components of our proposed MaAST, we perform an ablation study comparing several baselines in tab:ablation. All the methods in tab:ablation are trained with both goal and exploration rewards except RGB-D which is trained with only goal rewards.
Exploration Rewards. We can compare {{formula:e095feba-fa29-4b62-9a57-7af212b43c93}} and {{formula:c59d16bb-f5d2-480b-b234-84733cca17de}} baselines in tab:ablation to evaluate the impact of the addition of exploration reward.
{{formula:19adb5cc-f290-4ffb-856d-19d7b1eaf70e}} agent performs reasonably well with a {{formula:9dabf8cb-c0e7-4710-b936-71c9c261fa00}} success rate. However, as seen in the SPL of RGB-D ({{formula:ee6b4d50-c027-4e5c-a56b-83ce0b7ededf}} ), the agent takes much longer paths as compared to the ground-truth shortest distance, thus rendering this policy inefficient in terms of path length.
We hypothesize this drop is due to the agent being not able to make efficient use of the implicit semantic cues in the scene.
To encourage the agent to move more efficiently,
we follow a similar procedure as above to train a policy that utilizes RGB-D along with additional exploration reward: RGBD+EXP.
However, the agent has no explicit access to the progressively growing, egocentric occupancy map.
The method achieves a {{formula:0ebb4c50-d315-411b-9203-3dc61c975ec4}} increase in SPL ({{formula:83dfad41-22d7-404d-bf6c-f152d19bbc28}} ); thus, the addition of exploration reward not only helps the agent reach its goals more often but also takes more efficient paths to do so.
{{table:ceca7664-d3ad-41eb-9f43-541f9bc57781}}Egocentric Semantic Map. It is evident from tab:ablation that our use of egocentric semantic map leads to an overall improvement in performance. To analyze the impact, we can compare several variants of MaAST (i.e., RGBD+OCC+ATT vs. MaAST, and RGBD+EXP vs. RGBD+SEM). We observe that MaAST achieves ({{formula:0b24c2a0-b07e-4061-a289-17ec724610bb}} absolute, {{formula:2bcc26b1-7f3c-480f-b169-218f06fc0bde}} relative) improvement in SPL and ({{formula:ab8e5cba-f5d3-4ddf-84c7-5f2241c03a6a}} absolute, {{formula:a3c015c0-a285-4d51-a2cc-2b9b54f11135}} relative) improvement in success rate using egocentric semantic map compared to RGBD+OCC+ATT (which uses egocentric occupancy map). However, comparing RGBD+SEM to RGB-D, we find that use of semantic map helps RGBD+SEM to achieve {{formula:376f2f15-aa0d-4ac2-9cbf-441042b8e7af}} improvement in SPL, but there is a drop in performance in terms of success rate ({{formula:7ac92f09-c8d6-43f8-9ace-bfdc91a20774}} ). We suspect this is because the information encoded in the egocentric semantic map is rich, however, the agent is unable to adequately decode and focus on relevant parts of the map (which inspires our use of the Transformer-based map attention mechanism).
Real vs. Predicted Semantics. To better measure the robustness of our method to sensor noise, we conducted an experiment utilizing predicted semantic segmentation, following the map construction method of {{cite:bb117746c11561db04ae23d0eb993b14f023d6f9}}; i.e., segment the RGB observation with Mask R-CNN trained on MSCOCO and project those classes using Depth.
This yields a sparser map now with 80 semantic classes rather than 40 from Matterport3D, and now only filled with confident predictions from the semantic segmentation model rather than dense labels for each pixel.
Due to computational constraints, we train this model for 7.7 million steps of experience, at which point it achieves 34.8% SPL outperforming our RGB-D results with about half as much experience.
This demonstrates the robustness of MaAST to even noisy semantic observations and its ability to adapt them to efficient navigation.
Egocentric Map Transformer. Our novel attention (ATT) mechanism based on multi-layer egocentric map Transformer leads to significant improvement in performance (tab:ablation).
We observe that MaAST achieves large performance improvement in SPL, compared to RGBD+EXP (+9%) and RGBD+SEM (+6%), due to the effective use of semantic cues. However, despite having access to the semantic map, RGBD+SEM fails to achieve consistent performance improvement over RGBD+EXP. This phenomenon supports our hypothesis that egocentric map transformer helps agents attend to most relevant regions of the map for efficient navigation.
We also use the proposed egocentric map Transformer (sec:attention) with the occupancy map (RGBD+OCC+ATT). However, this
does not result in a noticeable change in performance. We believe this is because of the information encoded in the egocentric occupancy map is significantly less rich and less diverse compared to the semantic map. Rather than encoding each map cell to about 40 semantic classes in the egocentric semantic map, each occupancy map cell encodes either unexplored, traversable, and non-traversable.
Qualitative Results
In fig:examples, we provide some visualizations of the paths toward the goal followed by the various methods in three different episodes from the Matterport3D validation set.
In the top row (qual11,qual12,qual13), we compare MaAST with RGBD+EXP,
and RGBD+SEM.
In the bottom row (qual21,qual22,qual23), we compare against our two baselines from prior work, RGB-D and RGBD+OCC.
All methods have their path colored with a gradient to capture the number of steps taken by the agent, all scaled between 0 and 500 steps.
For example, in qual22, RGB-D agent moves quickly towards the goal at first; however, it becomes stuck behind a chair.
When it moves away, its path is much more darkly colored, to indicate the amount of time taken to recover from the obstacle.
{{figure:385a3aab-0db7-421f-98b0-c3ec5c3f463b}}In the first episode (qual11,qual21),
all the agents reach the goal, but the RGB-D and RGBD+EXP take very long paths to do so.
It is clear
that RGBD+EXP tends to very aggressively follow the available traversable space, which leads to inefficient paths (qual12) or missing the goal entirely (qual13).
qual12,qual13,qual21,qual22 all help to demonstrate the efficiency gains of the MaAST attention mechanism.
Even in cases where several of the methods follow similar paths to the goal, MaAST is more quickly able to find obscured free space (such as around the obstacle in the center of the room in qual12) to move more efficiently towards the goal.
The final episode (qual13,qual23) represents a failure case for all the methods.
MaAST and RGBD+SEM reach close to the goal; however the episodes are registered as failures, as neither are within the 0.2 success radius.
On the other hand, RGBD+EXP completely misses the goal, heading off the visualized map into the next room, while both RGB-D and RGBD+OCC get stuck on the furniture and terminate.
In our analysis, we find that for this particular Matterport3D house model, there appears to be holes in the 3D model towards and around the goal, which provide confusing features to the policy network; e.g., all of the furniture at the bottom is fused together.
However, one of the strengths of leveraging semantics in our models seems to be avoiding areas that either present narrow spaces with high collision potential or low-lying objects below the agent's field of view.
This is a instance when we observe the agent utilizing semantics of the environment (i.e., “furniture is difficult to navigate through”) beyond just which areas are free and which are not.
Conclusion
In this paper, we introduced principled techniques for improved performance on visual navigation tasks with autonomous agents, by leveraging rich semantic features while simultaneously operating under a computational budget.
Our proposed MaAST, incorporates a novel attention mechanism based on multi-layer Transformers, which encourages agents to focus on the most relevant areas of the egocentric semantic map for navigation.
Through systematic experimentation with quantitative and qualitative analysis, we demonstrate the superior performance of our proposed approach as compared with several baselines. We show that MaAST provides significant performance gains (a {{formula:fb11295d-e482-463c-bcbb-41908b0aab4c}} gain in path efficiency over purely visual methods), while also outperforming classical geometry-based methods with decreased training budget (time, computational requirements, and cost).
| m | d3525e430a9daf04285cad7c40fded7b |
Second, we use the Holme-Kim network model {{cite:3aa0d26d6f1dc0c75978861db79a249717c12bfd}}, which is a modification of the BA model for high clustering (i.e., a large number of triangles). We construct networks with average degree {{formula:b8a80f69-a847-4b49-9f6d-24059bbd7b00}} by setting the number of edges that each new node brings in to five. We set the probability of constructing a triangle for the each new edge to {{formula:38a622bf-fe12-4a5c-97f4-071cdce63395}} .
Third, we use the largest connected component (LCC) of a coauthorship network of researchers in network science, which has {{formula:e3ad1dcc-d8b9-4d55-9696-7e09f8945d10}} nodes and 914 undirected edges {{cite:f1f3a1d8f1a461d9866f7c1ab0eb7a6716f8be53}}. Each node in this network represents a researcher publishing a paper in network science up to year 2006. An edge exists between two nodes if the two researchers coauthored at least one paper.
Finally, we use the LCC of the hamsterster social network, which has {{formula:d2e06d38-5aa3-4dcb-84f9-989f9f13866c}} nodes and 12476 undirected edges {{cite:94f20d1f4f210cc3ccaa659d0180d0d19175f6b4}}. A node in this network represents a user of hamsterster.com. Two users are adjacent if they have a friendship relation on the website.
| m | fb418fa79661791f7f99ebb827bdb0f5 |
We compare our method and utilize several of the popular models in our experiments : linear model fasttext {{cite:82940a70cb2de9f4fcaa4c414b65737120a7e603}}, we use CNN architecture inspired by {{cite:df3f58877fc65e0e250956f4dfa921776ad41b3e}} and train it using numerous teacher {{cite:e136b074762bc400cc8e3b42dbccb2f279f1c3ae}}, {{cite:20e36a53e45997f21944b5143df32d34262a83b2}} which are state of the art for text classification.
We compare the model with character level CNN {{cite:b2bb283bbd54edd256b867af066d13dfc2a23c82}} referred to as c-CNN and very Deep CNN network {{cite:9b921a7678c06e6f242e613f561f5c0c63ddfd8c}}.
We also benchmark it against {{cite:848aab3dba952019b6a0be9c093a706a71730018}} which proposes dense connection between convolutional layer and multi-scale feature attention for text classification.
They also experiment with depth of the network an found that shallow networks perform comparable to the deep models with only a slight drop in performance.
Shallowness of the model is advantageous for deployment to low - resource devices.
Our proposed training regime improves the performance of shallow CNN and performs comparable to other popular networks of the type.
| r | d1548a610ab1b6b0a0971d706f418a71 |
Unlike previous NeRF-SLAMs {{cite:4d486233bd599c3387d87f12210426aab559b8c4}}, {{cite:8ef98c09984557f2d7302ea34b4d1c5fdb9ac74f}} which require depth information to perceive geometry better, we develop Orbeez-SLAM that leverages VO for accurate pose estimations to generate a dense map with a monocular camera. Besides, it achieves pre-training-free adaptation and real-time inference. Next, the system overview is depicted in Sec. REF and the optimization objectives are described in Sec. REF . At last, ray-casting triangulation is introduced in Sec. REF .
| m | b23ef9de5aa37378746af8b48d5ff135 |
In further work, we aim to extend the SVD analysis ideas of section REF , e.g., in conjunction with {{formula:8520f250-e773-43d6-befa-2210c2c545a7}} -factor analysis {{cite:4f7590275b74092ebf092996c56677f9b1140124}}, {{cite:69bfaac0f3a533a4823ed4d38f4eb217269034c9}}, to determine optimal sub-sampling schemes for different imaging applications (e.g., in vivo medical MRI).
| d | 9037c441a150d0ad6f563495fa8c6bf2 |
does not deal with data in events.
From a broader perspective, we finally observe that while
we deal with a set of specific problems, the work paves the way for ASP to
become a general effective approach to Declarative PM.
The Framework
An activity (signature) is an expression of the
form {{formula:89da2967-8e68-420f-b7cc-99a6ffffa5c7}} , where
{{formula:f4c36469-4e6f-4833-8efd-f51be9884886}} is the activity name and each {{formula:aad6dba4-e371-4190-96d0-ed9762332c73}} is an attribute name.
We call {{formula:112bfc39-84b7-41a9-a326-01442fc95ac1}} the arity of {{formula:05739473-39ea-4b2e-b786-0415fd493e97}} .
The attribute names of an activity are all distinct, but different
activities may contain attributes with matching names.
We assume a finite set {{formula:3f14c22e-b355-47af-b510-ed8266563eae}} of activities, all with distinct
names; thus, activities can be identified by their name, instead of by
the whole tuple.
Every attribute (name) {{formula:63d22106-c6dd-47e4-9b4c-791f44edf6a3}} of an activity {{formula:ab140397-221b-44db-984a-14e0709d44a4}} is associated with a
type {{formula:7dbb533f-979d-4863-8a48-69f92f76d2a3}} , i.e., the set of values that can be assigned to
{{formula:e9c80239-5a65-4acf-a42f-5deaa85079e8}} when the activity is executed.
For simplicity, we assume that all domains are equipped with the
standard relations {{formula:53fcfa68-b9ee-460d-b69f-26338b4fa00d}} . All results can be immediately adapted
if some relations are absent in some domain.
An event is the execution of an activity (at some time) and is
formally captured by an expression of the form
{{formula:60614ee0-26a0-4211-888b-9effc568adf1}} , where
{{formula:8649da6b-a075-481b-bd1b-d4668504679e}} is an activity name and {{formula:41cd681b-9743-48a0-98bf-f279da7dca7f}} .
The properties of interest in this work concern (log) traces,
formally defined as
finite sequences of events {{formula:01436c59-36b0-46b0-9353-e4117dce1713}} , with
{{formula:dc6c4b05-59dc-4152-9f94-d00b212729af}} .
Traces model process executions, i.e., the sequences of activities performed
by a process instance. A finite collection of executions into a set {{formula:418edb25-80a7-4919-b448-c522399a7b2a}} of
traces is called an event log.
l-ltl{{formula:9590f56b-939f-4fec-abbb-c6d4c82ad32d}}
We adopt a declarative approach to
process modeling, meaning that processes are specified through
a set of constraints over their executions, i.e., over the traces they produce.
The formal language we use to express properties of traces is a
variant of the Linear-time Logic over finite traces, ltl{{formula:ab7fb40f-5d7f-42cc-82f5-f4f24d19fe80}} {{cite:080e0ef981626a0dce840b7e3ee3f3420f0880de}}, adapted
to deal with the data attributes of activities. We call such variant
Linear-time Logic with local conditions over finite traces,
or local ltl{{formula:a3a393e8-64fd-4194-b293-39eecbfc0d3d}} for short, and denote it as l-ltl{{formula:92a5c65b-80c8-4287-9dbe-f602705731dc}} .
Given a finite set of activities {{formula:21025ff3-d8ac-413c-bfd7-1d926a6e0d1d}} , the formulas {{formula:d92c68ba-a60a-47b7-b43c-23456669425f}} of
l-ltl{{formula:c2adbd00-ea78-4e1a-bcda-60d4b63e4ee3}} over {{formula:452ebf2d-256a-4125-a565-6775375b09c0}} are inductively defined as follows:
{{formula:c40001c6-4139-489a-9353-00a15d383fdb}}
where: {{formula:8bcc00c8-549c-45d1-89cc-685a0fd2a1a4}} and {{formula:20624d87-6f17-40c3-bc81-5542e2f2ac4e}} are attribute names from some activity in
{{formula:49b5e687-787a-47ab-98b7-9e7a009c0b83}} , {{formula:d7520854-fee2-4110-adcf-9d38022f16db}} , for some {{formula:cf80c65c-663a-42f0-9278-7b8922ca08f0}} , {{formula:9f699b5c-7a3c-4f0a-a7f3-6b3f41a816f3}} is an operator from
{{formula:84b8faa5-6a2c-4b4e-981f-3d82092dc3e0}} , and {{formula:13ddb92c-40c8-4f06-84d6-e03cd4545fc0}} is an activity name from {{formula:57c98a23-3477-48ca-bc56-d05d3ca24252}} .
Formulas of the form {{formula:18dd49c6-0c28-4009-8484-6452c798fb5b}} , {{formula:7621090a-b4f2-47b0-8636-ba3f2bcd38aa}} , {{formula:a0c23551-9a54-48c4-963b-4a9eb1608264}} , and {{formula:fb4cee76-5610-43e6-9c35-5a9e2bd9c15e}} are called
atomic; formulas not containing the operators {{formula:47abd5e7-67a5-4b71-acd3-a59934bc9ada}} and {{formula:9a37f323-ac18-40bd-b494-84ab0b961bae}} are
called event formulas.
The logic is interpreted over positions of finite traces.
Formula {{formula:a173e016-dc4e-4820-b13a-5a1a0c0f7cc3}} holds at every position;
{{formula:bb78a683-72f0-4e21-9210-a3c64cc3a6c8}} checks whether activity {{formula:f1ee68b5-bf19-457f-a25e-b5de3881a5f9}} occurs in the trace
at the given position;
{{formula:ba2b4bf9-73fa-419d-92c9-5f1452658be6}} (resp. {{formula:29d394db-3d6d-49c4-8482-025ed8a63f9d}} ) compares the value assigned to
attribute {{formula:9081f285-6223-4d69-815a-07f5922319ed}} with that of attribute {{formula:3746eb86-0ff5-4616-9a1f-65881eb387f9}}
(resp. with that of value {{formula:9686afd9-c180-44a9-92dd-35d7c97337e3}} ), at the given position;
boolean operators combine formulas as usual;
the next operator {{formula:323743e5-7f25-4540-b062-04a3f85ffe60}} checks whether
{{formula:c0e935ce-dfaa-4fed-8e40-5e39dc947e28}} holds in the suffix starting at the next position;
finally, the {{formula:431d2e67-7a98-4370-a4e1-cb1fe8f328dd}} operator {{formula:6232af62-d60f-4f5d-810c-375e260c435c}}
checks whether {{formula:941fc562-a0cf-4452-bc37-4c740014788b}} is
satisfied at some position {{formula:c7df6525-024e-4e7d-9ac8-8989eb8023e3}} , and whether {{formula:20d32fc5-68b7-46a1-8389-5e18479511f8}} holds
in all positions that precede {{formula:0a824c89-5023-418a-b6f9-addd83b689ea}} , up to the given position.
Formally, we define by induction when a
trace {{formula:48a1c2a5-163d-4912-a8d1-04e3678053c7}}
satisfies an l-ltl{{formula:e12cb861-499a-461e-8e2e-9dfdbea51ec9}} formula {{formula:3ed8866d-c837-467d-b033-cf8d83b4c119}} at position {{formula:db42ccae-5154-4d13-82a2-6dc15075b6cc}} , written
{{formula:d70d34b4-c979-447f-876c-9f64474c9179}} , as follows:
{{formula:598a8637-98c1-4089-847d-f802dace62b2}} ;
{{formula:7a379b0e-94e2-4466-bd94-56cd1dd9d490}} iff {{formula:bcf68490-5fd5-47ac-8985-4677bb5a87e3}} ;
{{formula:4da96ae8-6eea-42ea-b13a-fce72cabce43}} iff
for {{formula:a6b3423d-ad12-4e2e-8ef2-7cfda37a198e}}
and {{formula:f1009bea-213d-43e6-bd63-0d07f7bba99f}} the signature of {{formula:c715adc7-5636-4427-af82-f15548663e25}} ,
it is the case that, for some {{formula:fc7abd48-3a7f-4146-9bac-fe24a8b5ac2d}} and {{formula:76795756-a816-4f18-aaff-39d82c39197c}} , {{formula:1daeb054-9376-4f2a-9b1e-4d72c1099dc5}} , {{formula:174de2d8-b81f-436f-9f1b-8edab6ed3565}} ,
and {{formula:62a826a2-eff8-4d5f-a989-737f9f5fb998}} ; Notice that this requires compatibility
between the domains {{formula:d9f8157d-4442-400c-a3da-94841049862d}} and {{formula:c85a932b-2dc9-474d-ac3b-b585e4fc7b37}} wrt
relation {{formula:af96121e-1ee2-4d46-94e4-4d7c0e5806fc}} .
{{formula:de1a01da-e2db-455f-bd00-ed39a3364f48}} iff
for {{formula:901c34b8-b3e5-48ec-9c57-8fc5e0bf6198}}
and {{formula:5ca8cfe5-c2b6-437a-987d-3bb46746d470}} the signature of {{formula:fbea4afe-1691-49c1-9c71-323f8bfc34bc}} ,
it is the case that, for some {{formula:21884efb-0bce-4a66-bad6-c1226ceae3e8}} , {{formula:9a4d1a9c-8f16-430c-8c53-30d8ac1e8dfe}} and {{formula:f6d4ce80-8b1a-4bfb-82af-7045a46a2fe2}} ;
{{formula:7428e927-c754-47dd-a398-31a7bbdae03b}} iff {{formula:af279e23-798d-435c-90a8-789ef6eee988}} and {{formula:d7221c27-5946-44be-bb4e-dea7478ab447}} ;
{{formula:c88bf304-2cf9-4f7e-bb2e-9b587a36ff80}} iff {{formula:c0fa50d5-afc7-4835-acd5-c4296420a1be}} ;
{{formula:2bef61f3-486d-4c71-9003-ea6997382518}} iff {{formula:d0b8c24c-73d6-4536-be17-36fe9b05a605}} and {{formula:5065def8-680b-404a-83e1-ca20cb41f24e}} ;
{{formula:f3bf308b-fc93-45b5-9c86-d457e2313803}} iff there exists {{formula:78697f23-c6c2-4a71-8735-15fed3fc62af}}
s.t. {{formula:79dd15d2-d15e-4853-82a4-b31b3200b9c9}} and for every {{formula:d68177fc-4d6e-4a6d-977d-189702c479b0}} ,
it is the case that {{formula:8ae4c6f4-ffd5-45e6-88d3-eac5685dc481}} .
Notice that while, in general, the satisfaction of an l-ltl{{formula:06f3b6e9-77b6-461e-af98-aa62e80f2da4}} formula {{formula:de127cac-fef2-448e-ae24-143309330d15}}
at some position {{formula:f5201b17-9533-4232-addb-c96f2b43dfd8}} of {{formula:0cc4a339-10e7-48ac-9e38-ae2a8d2cde62}} depends on the whole trace, and precisely on the
suffix of {{formula:1a44de34-ff65-47a4-b385-6130b3512df1}} starting at position {{formula:9f487439-9d6f-4c68-b2fa-1f3c8d26f337}} , event formulas depend only on the event at {{formula:e176faef-f077-4920-9ff2-94d6aa8c1452}} .
As in standard ltl{{formula:a0e08e9d-6d66-469e-88bb-c5db1b6dc426}} , {{formula:182f362d-1012-48b4-b113-388cce607211}} denotes the strong next
operator (which requires the existence of a next event where the inner formula
is evaluated), while {{formula:ee2bd368-0cbc-4284-8d04-92c25de0b311}} denotes the strong until operator (which
requires the right-hand formula to eventually hold, forcing the left-hand
formula to hold in all intermediate events).
The following are standard abbreviations:
{{formula:c86f600f-fe57-4ca3-a9d2-52c097b0d934}} ;
{{formula:5aa14aff-f9b5-4c06-a5e9-86ef1461ba9d}} ;
{{formula:e922c4f0-e33a-4ca7-b17c-a212b1c286b7}} (eventually {{formula:fa506f9d-6d39-4678-9a40-7dff2af6ccc7}} );
and {{formula:2205d422-d1ec-4fda-9d91-a692c14d32c2}} (globally, or always, {{formula:3891798b-aae3-4d5f-bd9c-6a7cb1de9b9a}} ).
Through l-ltl{{formula:6d231fb1-5911-4b54-aff9-a1ead34a7698}} one can express properties of process traces that involve not
only the process control-flow but also the manipulated data.
Example 1
The l-ltl{{formula:0bd02d43-20b4-4921-bcbd-42412003797b}} formula
{{formula:c5368326-0290-41fb-a4a7-303fe18d3026}} ,
a so-called Response constraint,
says that whenever activity {{formula:c1a31832-7d6b-4b28-9627-2921cefb1cc8}} occurs, it must be eventually followed by
activity {{formula:f628804f-a7bd-42a5-a7b3-1248ac238548}} .
A possible data-aware variant of {{formula:16b9ce97-d935-429c-8e8e-206c3179e15e}} is the formula
{{formula:63717511-a212-4191-8436-466d5fd00767}} ,
which says that whenever activity {{formula:d3458d52-54cd-4f82-8e51-7e819dd1d7e4}} occurs with attribute
{{formula:3dcb9411-9dff-49a6-baa3-1bc4cd7fc9e6}} less than 5, it must be followed by activity {{formula:a764a7e1-075a-472c-8d43-6562b0f11fdf}} .
Formulas of ltl{{formula:1d3ddb8b-1578-4b77-b077-2a43629068ad}} , thus l-ltl{{formula:453dbfd4-441e-486e-a1ee-d05eb7b91be1}} , have the useful property of being
fully characterized by finite-state, possibly nondeterministic,
automata.
Specifically, for every
l-ltl{{formula:6e20aca6-34f4-46bc-b2c4-32936d198164}} formula {{formula:5f453589-ac71-4506-9840-f7252e0528c5}} there exists a finite-state automaton (FSA)
{{formula:a749ea8c-c7ea-4bea-843f-b5729e27293b}} that accepts all and only the traces that satisfy
{{formula:91ab54af-6f54-4dca-81de-2c92c3769811}} {{cite:080e0ef981626a0dce840b7e3ee3f3420f0880de}}. Such automata are standard FSA with transitions labelled by
event formulas. For a fixed set of activities {{formula:f6438f8f-d4eb-4077-8680-d306e9ca44f4}} , let {{formula:55ed37f7-396f-41a5-ab0b-631ff55a7899}}
be the set of event formulas over {{formula:aefeb1be-7423-4cc6-8676-9512432b8d6a}} . An FSA over a set of activities {{formula:1009f52f-9ddc-4c6e-bff5-bd54fbec2c72}}
is a tuple {{formula:e1a6cbb5-326e-4237-b4fe-31bec0e11e13}} , where:
{{formula:452b2276-f3aa-43c2-8d94-bc193a8bb65e}} is a finite set of states;
{{formula:66d79141-5694-4197-a08d-b0f5e8788e23}} is the automaton initial state;
{{formula:6f21e2a0-fed6-4240-917c-ead331dd4f30}} is the automaton
transition relation;
{{formula:e7096cec-ac6e-4dd3-a59e-b922ff72160f}} is the set of automaton final states.
Without loss of generality, we assume that formulas labeling transitions are conjunctions
of literals. It is immediate to show that every FSA can be rewritten in this way.
A run of an FSA {{formula:c778374a-6d75-4592-ac7a-cf94a06c5950}} on a trace {{formula:5a91d8ae-ff25-40e0-8936-bfb89e4766cb}} (over {{formula:cca2ac0c-f0f3-4c3d-a5df-9ea4c558359e}} ) is
a sequence of states {{formula:12f63490-aed3-497c-aa88-d45fcc099842}} s.t. for all {{formula:878abef8-f862-4164-9b2b-71ac6b72aa85}} there
exists a transition {{formula:0db487b0-e83b-43d3-8ede-11421bf744a7}}
s.t. {{formula:bf3b4d2e-4861-4c19-b988-159dda4331e7}} .
A trace {{formula:203d66e2-b7c8-48e2-baff-769a36c851cb}} over {{formula:462ec824-a501-4d02-bbc5-ca7d171eaada}} is accepted by {{formula:3eb50198-bef9-459f-8e7a-9581ffa066d4}} iff it induces a
run of {{formula:9af91b4c-0dfa-46e3-a953-0808e6484094}} that ends in a final state.
Notice that satisfaction of {{formula:494842bd-5431-4108-bc7d-54f13c43cfc6}} ,
this being an event formula, can be established by looking at each event
{{formula:cc9e4702-31d4-4863-82a2-29948ef832e4}} at a time, while disregarding the rest of the trace;
thus, in order to construct the induced run {{formula:729c3833-8cc9-4988-b6dc-9d8622cfca95}} , one can proceed in an
online fashion, as the next event arrives,
by simply triggering, at every step, a transition outgoing from {{formula:130a6adf-c656-42ee-bd5c-d18795a67ecc}}
whose label is satisfied by the event.
Example 2
Consider again the formulas
{{formula:32d7649f-93be-4309-983c-a50bb259ce24}} and {{formula:143f3f33-13b6-4996-bfac-c829e3a23fa9}} shown above,
and the (paramtric) automaton depicted in Fig REF .
{{figure:6094ff5e-ba8c-412a-9125-33d2cbd77131}}It is easy to see that for
{{formula:01ec0920-e981-4d39-8406-0ecbf546ed8a}} ,
{{formula:46511d2f-03e5-43e1-b32c-e34453448150}} ,
{{formula:bd51c861-9b94-4ffe-abcc-1c6b1db8b587}} ,
{{formula:5431c861-6f9f-4494-ac9d-c183505e2040}} ,
the resulting automaton accepts all and only the traces that satisfy {{formula:8fb82a9a-d4ce-4e0d-870f-cd29cc5c2c09}} ,
as well as that for
{{formula:67772f26-7f24-4dc9-90c2-d843e431b17a}} ,
{{formula:45c9861d-c7af-4fa5-ae8a-20b0fc077ef8}} ,
{{formula:ac21b8b9-3379-4041-96c0-24e770652944}} ,
{{formula:bff5b0aa-ec8e-4d01-bed6-824049f35027}} ,
the obtained automaton accepts all and only the traces that satisfy {{formula:30192170-e28a-4569-b24f-b1032f631e39}} .
The details about the construction of {{formula:bf837404-837b-4a78-b1fb-588be3f5594f}} from {{formula:55086560-86b8-4248-bb10-2b1f5114c830}} are not
in the scope of this work, and we refer the interested reader
to {{cite:080e0ef981626a0dce840b7e3ee3f3420f0880de}} for more information;
we rely on the results therein.
We observe that while the automaton construction
is time-exponential in the worst-case, wrt the size of the input formula
{{formula:b1524e9d-1819-484a-be6d-4dbee2cb7dff}} , tools exist, such as Lydiagithub.com/whitemech/lydia/releases/tag/v0.1.1 {{cite:05295be75ce94767088232b9d5b780d76778c0b3}},
which exhibit efficient
performance in practice; this, combined with the fact that the specifications of
practical interest are typically small, makes the approaches based on automata
construction usually feasible in practice.
We can now formalize the problems addressed in this paper.
Event Log Generation.
Given a set {{formula:d7a343de-df3b-44de-bfce-58d830513e1b}} of l-ltl{{formula:115eaa7f-2396-4924-910a-c0778d301192}} formulas over a
set of activities {{formula:43cb14d9-0b27-4d6d-aa27-2293dd882ce8}} and a positive integer {{formula:5955ec7a-c695-4a51-85d4-06f715cfe8a6}} , return
a trace {{formula:493bc3a8-b038-431a-a4c0-cdd83f085198}} over {{formula:fdf6a83b-3f8a-49d5-8109-1d78002349e8}} of length {{formula:b24b00cf-2e39-40c5-9dbf-9cd7305c2c00}} s.t., for every formula
{{formula:d6d9102d-f98b-4ab2-8660-a77003913878}} , it is the case that {{formula:5020a801-6baf-4860-9250-7be400d9292e}} .
In words, the problem amounts to producing a trace of length {{formula:8c372fa0-71cf-4e9c-bd34-6972aed6d845}}
over {{formula:608dfc2b-19cc-42ce-b401-1714e47f609f}} that satisfies all the input constraints in {{formula:2b0794b3-a619-4833-9159-8a2106de304d}} .
A more general version of the problem requires to
generate a log {{formula:fc7d68a4-3751-49dc-8919-c5cf097dac91}} of {{formula:756441ca-a34a-4cb0-97c2-7457a93cbedf}} traces of fixed length {{formula:a716cd2b-cfc8-4ac4-b85a-350d3abc825c}}
satisfying the constraints. For simplicity, we consider
the first formulation.
Query Checking.
Query Checking takes as input formulas from the extension of l-ltl{{formula:b95a6080-6794-4101-84a0-89d56b1eb37a}} with activity variables, defined as follows:
{{formula:c9d02ee1-6b9b-4bf8-8318-706fc31aec4c}}
where symbols starting with “?” are activity variables and
the other symbols are as in l-ltl{{formula:3caf969c-0ea7-4a28-b72c-065f391be6bb}} (given {{formula:1a869b74-3fc0-43c2-bd8d-9b439a34b6ff}} ).
Given an l-ltl{{formula:3f90246a-ab82-4563-9894-cfffe428492b}} formula with activity variables, by assigning an activity
(from {{formula:d77a0bf0-3279-4d7a-adf8-2e55e4df4652}} ) to every variable, we obtain a “regular” l-ltl{{formula:5ca32a88-8663-4d0f-bde3-0d600748cc7d}} formula.
Formally, for an l-ltl{{formula:f1d4abb8-abd1-41fc-9061-4c98a56319da}} formula {{formula:d5ea9309-2596-4f76-91c9-721734ee8dc5}} (over {{formula:ada0c5be-6322-4a66-8ff4-f300fa3502ea}} ), containing a (possibly
empty) set of activity variables {{formula:42c74bee-cb19-4a67-b0a0-dbd5c73685ee}} , an assignment to
{{formula:6b46963d-d444-4386-82fe-901e2b010332}} is a total function {{formula:2cb2f22a-b9de-4d0c-ab27-fdcfd2ab90a3}} .
Given {{formula:ba7a5cae-5971-48c1-8bdc-d472126eec5b}} and an assignment {{formula:cbb81aa9-4b4a-4d8f-b7e1-47239f0856fc}} to its activity variables,
{{formula:446f64a1-1ad3-4fe6-b237-375ce2abc9e7}} denotes the (regular) l-ltl{{formula:186ba563-8b75-4a2e-bfe3-549f6500afd9}} formula obtained by replacing, in
{{formula:c3e81f3b-e9c7-4511-9e2a-72aae83ca495}} , every variable symbol {{formula:671b4d50-a71e-4c0d-b87b-f87ff83dc00c}} with an activity name from {{formula:9ba86269-8d08-4205-9f02-7f96dd2461c6}} .
Observe that if {{formula:97dc9ad8-270a-46a6-9820-6b5a3e1f35a0}} there exists only one assignment
{{formula:c7e50537-0297-4d45-9012-d60a0d7bd269}} and {{formula:6cdfd1d8-cdac-4056-84a7-6dcab127db0f}} .
Given a trace {{formula:6192e3a1-526b-4d7f-9f1a-1b02a4c551f4}} , since {{formula:e4186bf7-77f9-4964-aaf6-f5dfb49f46be}} is a regular l-ltl{{formula:970d6e6d-f287-47af-8a16-79b811b51c88}} formula, we can check whether {{formula:f13f2f34-d8f4-4101-8733-b06a62d2d4dc}} .
An instance of Query Checking consists in a log {{formula:ecff113b-8fd7-4fa2-91de-611ce1f756d4}} and an l-ltl{{formula:8d4b23fb-064d-4c05-a9ee-2ada2a730894}} formula
{{formula:c1c3baaf-a15a-4a6b-bb91-09bc538162a2}} with activity variables {{formula:2fc4ac07-a793-4ec5-8fbf-6ad1649285eb}} ;
a solution is a set {{formula:fa1570c6-d772-4d78-87af-05d99a4b8671}} of assignments to {{formula:e67fbb56-8d34-40a7-8339-5cfb7c6b769f}} s.t. for every
assignment {{formula:80a30631-a812-4648-a2fe-3e37c8569132}} and every trace {{formula:0efb3f85-f828-4afe-8fd3-24f770a29ac2}} , it holds that
{{formula:fa1c5467-5107-43ba-bcdf-3e6d6d1741b0}} .
In words, query checking requires to find a set {{formula:237b305d-d523-4abd-b4b2-ffeda04b2c67}} of assignments {{formula:d909deed-efcd-45f9-8bf7-cd851c057f74}} ,
each transforming the input formula {{formula:87b03b5c-58dc-4977-bb09-ca3cafcaac2c}} into an l-ltl{{formula:8e959293-bc86-49fd-b436-f7b6f61c8dd4}} formula {{formula:edfe82fa-2934-4851-93b4-5b2e74436bfb}} satisfied by all the traces of the input log {{formula:4f03b34a-3420-4784-b3ef-8341a9b35980}} .
Observe that {{formula:3acff2a7-6ed1-4242-abe3-8a6aa8ce1bc1}} variables can only span over activities.
Conformance Checking.
Given a trace {{formula:56d9ed3a-adc4-4150-bf2b-13468fed9fab}} and a set {{formula:56dca48a-d0c7-4361-b2cf-c1630993857a}} of l-ltl{{formula:f64f38f6-f3d0-4acf-a491-722a5ed650b4}} formulas, both over the same
set of activities {{formula:f828e558-955d-4f7e-a447-074994f847d9}} , check whether, for all formulas {{formula:097578a8-6912-4fda-9e66-2e546dd5bf17}} ,
{{formula:40963af1-cdad-4915-98b5-a43d6ea0e571}} .
The problem can also be defined in a more general form, where {{formula:35eca509-df72-45af-8309-1b73e8b002d6}} is
replaced by a log {{formula:4a77f931-d45a-45bd-b96d-f2c741b692d8}} of traces over {{formula:4950f727-ab9d-4f55-b5d7-97a4f9563364}} and the task requires to check
whether for all the traces {{formula:3d42a873-804b-4c5c-a48e-e414348ca669}} of {{formula:5d736ce1-0d73-4c7f-ade9-52cdf13b79fc}} and all {{formula:f3ab0c86-1751-4946-9c5a-f580d7749d93}} ,
it holds that {{formula:46e3fe6b-dc70-40dc-a0b2-3308fb80daec}} .
Answer Set Programming (ASP)
An ASP program consists in a set of rules which
define predicates and impose relationships among them. The
task of an ASP solver is that of finding a finite model of the
program, i.e., an interpretation of the predicates that satisfies the
program rules.
ASP rules are written in a fragment of (function-free) First-order Logic (FOL)
extended with a special negation-as-failure (NAF) operator
(in addition to classical negation) which allows for distinguishing facts that
are false from facts that are unknown. The presence of this operator,
combined with the classical FOL negation, has a huge impact on the programs one
can write and the way models are found. Here, we do not discuss these details,
referring the interested reader to {{cite:a9ce6e6011a29e8ea0a811ab2bb094c0628243e9}}, {{cite:aecf94ad6d21681c74f06b358a70c7632b0f83fc}}.
For our purposes, it will be sufficient restricting to the class of
rules with the NAF operator as the only available negation operator
(that is, disallowing classical negation).
Syntax
The basic constructs of ASP programs are:
constants, identified by strings starting with a lower-case letter;
variables, identified by strings starting with an upper-case letter;
terms, i.e., constants or variables;
atoms, i.e., expressions of the form
{{formula:119f1248-b11c-4edf-b311-b8aac86c22cd}} , where {{formula:2786de50-f829-4bb4-8b9c-d910da575d19}} is a predicate, identified by a string,
and each {{formula:f4c3ef6a-1673-41a1-bf43-6ebd936087f4}} is a term.
A predicate {{formula:5a3d71be-0480-4912-867a-a43d2f95d24e}} is said to have arity {{formula:62433762-1d47-4302-86eb-9f46f08b4dbb}} if it occurs
in an expression of the form {{formula:3fb6fee9-7ada-4838-b0e5-2794a0cdf7d9}} .
An atom containing only constant terms is said to be ground.
ASP rules are obtained by combining the basic elements through boolean
operators and the NAF operator.
In this work, we use rules of the following form:
{{formula:fe72639e-cfa8-4b05-bcc4-936db3a26309}}
where {{formula:6d7b3d9f-51d8-4e71-8d1c-136a1ae3f68f}} and each {{formula:2a3a2268-9d3c-40e8-8e9c-86de1617d63b}} are atoms {{formula:40153623-b50f-49c6-97f6-cb035b1413b4}} , {{formula:82361484-d898-4c86-9d68-fc395c1f1cb2}}
denotes the NAF operator, and
every variable occurring in the rule also occurs in some
atom {{formula:4db95928-baba-4f15-b679-3741afee6dfd}} .
The left-hand side is called the rule's head
and is optional. When the head is absent, the rule is called an
integrity constraint. The right-hand side is called the
body and can be left empty, in which case the {{formula:b8a9775c-9e85-42d5-b611-0952b85df107}} symbol is
omitted and the rule is called a fact.
Semantics
Intuitively, a model of an ASP program {{formula:b4805879-ca0f-4aad-818b-d4332c3b29ff}} is a set of
ground atoms that satisfies all program rules.
In general, many models exist. Among these, only those that are
minimal wrt set inclusion and that contain a ground atom only
“if needed”, i.e., if it occurs as the head of a ground
rule, are taken as solutions, called the answer sets
of {{formula:33e9cf2a-2fb7-46aa-a3a8-6cd4b76527f0}} in the ASP terminology.
The task of an ASP solver is to compute such sets.
Given an ASP program {{formula:81d59704-b618-47a3-a981-d940b5a03570}} and a
rule {{formula:3be31a1e-37d2-4ca6-ab7d-860025f16ce6}} , the set of {{formula:30472fa1-3e3b-44e1-a1ca-85f20e9ca352}}
ground instantiations is the set {{formula:054838a3-4c19-47c4-aa58-f5db7ee99c64}}
of rules obtained by replacing
all the variables in {{formula:7f99e841-1f25-4310-a1d0-c8cea86792de}} with all the constants mentioned in {{formula:f5ec0524-e00d-4a8b-b94b-9347160b6355}}
(the so-called Herbrand universe of {{formula:bdcbc859-b210-424a-8531-efc8e0908689}} ), in all possible
ways, so that all rules in {{formula:2113b318-68a5-4e17-9333-af11313eb18b}} contain only ground atoms.
Then, the ground instantiation {{formula:6473c930-7e23-4755-af42-f5a851828905}} of a
program {{formula:7e1198bf-9e3c-48c2-9c6b-80358e2eaa96}} is the union of all the ground instantiations of its
rules, i.e., {{formula:76d45119-c2ce-4e30-a98c-863e269da4c4}} .
An interpretation {{formula:fc5681f0-c04b-4bb1-9915-98355463004e}} of a program {{formula:e4e0bcfe-7715-4695-b243-039f131b0f0f}} is a set of ground atoms
{{formula:808d5f91-291a-4e05-81ea-fc22f749992c}} , where {{formula:b7481e6e-db87-4e75-a59a-56567da3db02}} is a predicate of arity {{formula:c0e4ae8f-dea4-4644-bb75-bf8190dd9f33}} occurring in
{{formula:6ad9a432-77e3-42cb-9426-02bbe2e19c05}} and {{formula:928d41fc-3b2b-4606-94cc-7d00e0081ee5}} are constants from the
Herbrand universe of {{formula:9a48288d-3b80-439e-b183-cb77d1e6bddc}} .
Given a positive (i.e., without occurrences of {{formula:0f3e1033-9fcf-458c-b94b-8a012d66b3ba}} ) program {{formula:e0ea6aa8-a72d-49a0-9d1b-602f3674a191}} ,
an interpretation {{formula:24336436-28ef-4d45-9820-3215f01724e9}} is a model of {{formula:f33a2c70-6f88-4919-b7d9-9089e8a57aba}} if,
for every ground rule, {{formula:176b228f-6e5b-4a2c-b7c1-44c734f65609}} in {{formula:0c791eb7-1947-43b6-bb71-7dada85b5399}} ,
whenever {{formula:bad400bd-19b8-418d-96e2-aa242517d187}} for {{formula:2e9a715e-8650-4170-9c2f-27f97769f5f9}} , it holds that {{formula:66182035-cd9f-4192-9e97-5f70ca7a4afa}} .
An answer set of {{formula:6ed2e6b2-4e61-412a-aba4-4b6fd379f13b}} is a model {{formula:6b8096ee-1ec3-46b0-a2a9-d1b5fe707b90}} that is minimal wrt set inclusion.
The semantics of general programs is obtained as a reduction to
positive programs. Namely, the reduct of a ground program
{{formula:10f8be46-1061-4b72-af26-9f2687c0f3b1}} wrt an interpretation {{formula:da46cf7a-8a86-443f-a2d4-22eff07dba09}} is the positive ground program
{{formula:682c81ff-5cd8-4bd3-bff7-4b005cdc0c2b}} obtained by:
deleting all the rules
{{formula:12ee22a7-ab73-4c35-ace8-6166449516f5}}
of {{formula:6a1e71e7-5524-40c9-b792-4ad15a9bd83b}} s.t. {{formula:f75494e8-47f4-4865-8fad-e0ed5e2096b7}} for some {{formula:aaf053dc-738f-4fda-ac7f-8de221d7a8a0}} ;
replacing all the remaining rules
{{formula:f10eb576-cb7d-482c-9247-a0c9b17d2f29}}
with
{{formula:c6c61a89-1c01-4a23-a2f1-98ce0979044d}} .
Intuitively, the first transformation removes a rule, as already satisfied by {{formula:a89a4d39-34e3-4889-bfe0-640d4512e2a5}} ;
the second transformation removes the so-called negative body of the
rule, because it is satisfied. As it can be easily seen, the resulting program
{{formula:88f80548-44ff-4ad5-a260-0c0ac5321d20}} does not mention the {{formula:c7004f8d-da14-428c-b598-ee2d9bcf8ed3}} operator.
The interpretation {{formula:f0656f64-6b54-4c59-9260-ff11683a083b}} is an answer set of {{formula:7cf77328-1223-466e-9dbe-1c6fd758d314}} if it is an answer set
of {{formula:b09bc6af-7e5a-4c58-902e-44eed83e3258}} .
In this work, we do not discuss the algorithms to compute the answer sets of a
program, but focus on how the problems of our interest can be encoded in ASP
and then solved by an ASP solver, in such a way that the returned Answer Sets
represent the solution to our problems.
This is the focus of the next section.
For the experiments, we use the state-of-the-art solver
Clingo.
ASP for Declarative Process Mining
We encode Log Generation, Conformance Checking, and Query Checking
into ASP programs. For every l-ltl{{formula:d9a0ada2-9fcd-402c-a65f-c510f1f2cc75}} formula {{formula:4f33fd4c-d30a-4497-af50-92c99d33d93f}} we deal with, we assume
available the corresponding automaton {{formula:201b65bd-3374-407e-a4e0-a85167a19a70}} .
The three programs share some common parts, such as the automata and the traces,
which are modeled through suitable predicates and ASP rules.
Each encoding re-uses some of these parts, possibly customized, together
with additional fragments used to model problem-specific features.
Activities are captured by the unary predicate
{{formula:de540eac-853e-49e5-8fee-649715034681}} , where {{formula:8807783f-bebd-475c-98e5-36848a51f43f}} is the activity name.
In the presence of data, activity signatures are
modeled by the binary predicate {{formula:fad21f0b-edc1-4807-ac78-ad96c7f4b88b}} , where {{formula:09af2252-ade5-487e-a48f-3bdfb5c155e7}} is the
activity name and {{formula:be0739fb-3bbb-4204-8d40-55ef80550c25}} is the attribute name.
Attributes may be typed by stating the set of values they can take,
through predicate {{formula:0c749763-5abe-4c1c-bb1e-bbaeac0daf4a}} , where {{formula:28655f3f-20f3-4054-9aff-a77c858927d9}} is the attribute name and
{{formula:0586b0c0-b016-45d8-8061-5cb0338373be}} one of its possible values.
A trace is modeled by the binary predicate {{formula:ae487be2-e72c-44cd-b874-9301ab7cfec5}} , where
{{formula:a43c31d7-b36d-49fc-819a-136b8e9f0dc1}} is the activity and {{formula:6db88688-3d1b-47f5-9be2-fe312e61507a}} the time point where it occurs. Time points
come from predicate {{formula:109a423a-1c42-4884-9b02-65aceb7b5626}} , which contains the values {{formula:0d59f520-456b-4798-affe-8b4e24c685c3}} ,
for {{formula:09ff638a-5e09-4000-a5e5-f4d8ca581cd6}} the trace length. The trace is defined on time points from 0
to {{formula:95f1848f-8844-4945-969f-eac377e44a65}} .
In the presence of data, activity attributes are
paired with values through predicate {{formula:8381a7d8-07ee-4afc-b9e8-b11897a6a74e}} ,
where {{formula:705b258f-9ec8-48e8-bac2-5acb4544f1d7}} is the attribute name, {{formula:0abdce45-bd6f-4d45-a9d2-0b66624c2b4e}} the assigned
value, and {{formula:520ded54-d4ca-44bd-abc1-3cd647bb6204}} the time point . Notice that the association is based on the time point (exactly one
activity is performed at one time point).
Simple integrity constraints are
used to ensure that the mentioned attributes belong in fact to the
activity and that the sassigned value comes from the corresponding type.
Automata are encoded with predicates
{{formula:c38c0291-e3e4-4a41-888f-eb0997736946}} , {{formula:d6d85237-7cb3-4cb4-945b-37084ad63c3e}} , {{formula:1a450dc5-af91-4395-a1ed-f0a494ad4f2d}} ,
and {{formula:4dd8cf6c-7708-4f83-8e97-62c124c7b416}} . The first and the second one model the initial
state and the accepting states of the automaton, the third one models
the existence of a transition from {{formula:ad8bbd55-2693-414c-a560-7905d4c35714}} to {{formula:51077516-b028-48b0-a100-f95d7e84936d}} under the event formula
represented by integer {{formula:f2c15510-dcc0-4d37-9be6-151c66102144}} , and the last one models
satisfaction of (event) formula {{formula:e6bc5066-9248-45b5-a968-73d802252360}} at time point {{formula:9e08c38c-19b2-4fc8-a6ea-6697bd2dbc4e}} .
In the presence of multiple l-ltl{{formula:e6a3b4d3-7a1a-4a62-b890-38768d303b6c}} formulas,
each automaton is identified by a unique integer value and an additional
parameter is added to the above predicates to refer to the various automata.
Example 3
The ASP encoding of the automaton for the ltl{{formula:a8f326e1-860c-4330-b39c-2d9a5d27c92e}} formula {{formula:c1a6c2e6-a004-4200-be79-1125978dce2b}} ,
shown in Fig. REF ,
for
{{formula:f1d4528e-ef45-423e-aa1a-3c2ea4cd65eb}} ,
{{formula:6fb18f05-715e-4201-a202-3dfb737f5672}} ,
{{formula:214c5f6f-ca7f-4c54-b3b6-f2c0cb6baa92}} ,
{{formula:52143a63-beb7-46ad-bda1-46cd5ee7a482}} ,
is as follows:
{{formula:c72e28ad-72a5-4ba7-b5f2-5572a8e4ab29}}
where {{formula:fa4adba6-5297-4318-8c60-00473c51121c}} and {{formula:48e92389-3425-4c4e-911b-c5cce84e8427}} are activities
and each formula {{formula:eb14831f-246a-40c7-a702-eb7db0c6d1e6}} ({{formula:6e92dca7-97d7-496a-ac43-4fa5fd27d827}} )
is identified by index {{formula:e492e4a3-6aad-4bfb-a97d-c8ab6a44fb9a}} in the encoding.
In a data-aware setting, conditions on data can be simply added to the
rules for {{formula:aa020ff3-a889-4283-8470-9c6bbb1b9662}} . For example the following rule:
{{formula:d6fcfc86-add9-466d-a0ba-bd0dc2d859c7}}
expresses the fact that the event formula {{formula:eff6dea9-7053-489d-9427-7f8dd6d005b1}} holds at time {{formula:092f39be-73ab-4076-ae9a-e7b912fd55d9}} if
activity {{formula:177c880d-b86a-4e69-a09c-018d966978ec}} occurs at time {{formula:19dcfd5e-5cea-4e86-b63e-84e74ecb4496}} in the trace, with a value less than 5
assigned to its attribute {{formula:adc25f05-1c16-496d-b587-599b9095efeb}} .
To capture satisfaction of an l-ltl{{formula:f32c3e0e-8c50-49ab-90d8-47d1f9050ccd}} formula {{formula:e0432713-64ba-4f79-9f8e-795a0acf9e4c}} by a trace {{formula:8443b34e-d06a-448e-ba64-d1f284fd8472}} ,
we model the execution of the automaton {{formula:3e843171-e17a-4d0a-8671-598f08d439a5}} on {{formula:dee3006d-3b35-4f0e-ab89-285573a65fa0}} .
To this end, we introduce predicate {{formula:cd2beee4-3673-4fba-bfce-4dd1d2e6ce45}} , which expresses
the fact that automaton (with index) {{formula:b1d90b4f-ac64-4d56-afca-36e694ece424}} is in state {{formula:21e4cb1e-0a85-4416-915a-df9c1da3dc61}} at time {{formula:e9c89564-210b-4269-94f4-0ce7f0b2676b}} .
Since the automaton is nondeterministic in general,
it can be in many states at time point {{formula:757cd081-adf3-4889-957b-7cbc6a7314a5}} (except for the initial one).
The rules defining {{formula:85a34a1c-6291-444c-bee1-0288c848e85b}} are the following:
{{formula:cdece4c6-0266-4a58-8d9b-eeef4d579ba3}}
The first one says that at time point 0 every automaton {{formula:f207afea-d473-46a7-bd9d-266f5c678ca3}} is in its
respective initial state. The second one says that the current state of
automaton {{formula:fbab1ce6-ed26-4733-9650-e7c272e3a793}} at time point {{formula:7d00dbc4-246d-402b-884b-8369a624396b}} is {{formula:56205f29-7866-4b7c-802a-c49f44934b68}} whenever the automaton is in state
{{formula:7b24943c-17e7-4f11-b46f-ec69b9970232}} at previous time point {{formula:9da4c7f8-851e-4033-a0e4-205b932f2b0c}} , the automaton contains a transition from {{formula:6f495199-801c-40c1-a557-d3e749ae456e}}
to {{formula:94c3c058-2870-4c95-9b6b-7735f8864d95}} under some event formula with index {{formula:d1a90c61-05ce-455f-997a-d152d9d58b93}} and the formula holds at
time {{formula:9c75d034-0ba2-4511-ba49-8a9f2b39618e}} in the trace.
Finally, the fact that a trace is accepted by all automata, i.e., that the trace
satisfies the corresponding formulas, is stated by requiring that,
for each automaton, at least one of the final states be accepting
({{formula:a9b110db-2427-4110-8c47-e06ffee7a866}} denotes the length {{formula:f5a33b83-1932-4bbc-8b34-314b9a0df3cb}} of the trace):
{{formula:dcaf0935-1224-48f1-8898-e777178c7a2c}}
Next, we use these fragments to describe the ASP encodings for the problems
of interest.
For lack of space, we discuss only the main rules.
Event Log Generation
The encoding schema of Event Log Generation is as follows:
Activities, attributes, attribute types, and trace length are
provided as input and formalized as discussed above.
For each input l-ltl{{formula:4d9d8326-0820-4e67-b487-c0c53c89a503}} constraint {{formula:3773c000-d592-482b-b6c0-ea959a388539}} , the corresponding automaton
{{formula:f8f6adf1-b4af-4b70-99bc-fbc9ca232ce6}} is generated and modeled as discussed, using a unique integer
value to identify it.
Suitable integrity constraints are defined to ensure that:
each time point in the trace has exactly one activity;
every attribute is assigned exactly one value; and
the attributes assigned at a given time point actually belong
to the activity occurring at that time point.
Finally, predicate {{formula:bc81b6c5-970b-44de-a730-f26a5ff7e362}} is defined as above and
it is required that every automaton ends up in at least one final
state at the last time point.
Predicates {{formula:a378e9a2-3bc0-466b-b255-6b820490f226}} and {{formula:23403bc2-dd2f-4acc-bf63-f40a6a8db536}} contain the solution, i.e.,
they model a sequence of activities whose attributes have an assigned value,
which satisfies all the input constraints.
Query Checking
The ASP specification of query checking is analogous to that of
Log Generation except for the following.
Firstly, the problem takes as input a set of fully specified traces.
This is dealt with in a simple way, by adding a parameter to predicate
{{formula:9f8a0b33-9c3b-4c11-a251-3ab5144d31ef}} representing the (unique) identifier of the trace and,
consequently, by adding such parameter to all the predicates that depend on
{{formula:c1c4531b-c0ad-4a10-bfe6-1d8d87e56a75}} (e.g., {{formula:bb219b0a-4c23-4b00-b6d5-37ab6d299a58}} , {{formula:5eb1ed34-3224-44b4-95ab-1302f174e51b}} , {{formula:8d4d6a66-6770-4df8-b3a4-36932539504b}} ).
Secondly, the input l-ltl{{formula:dd7ba8d6-404b-4633-bd52-1ea3e09a50d6}} formulas contain activity variables.
To deal with them,
additional predicates {{formula:fa3af96e-7ba7-4db0-9908-f4a52c124212}} and {{formula:edb3f7a9-0486-4efd-9006-e518ef4386b8}} are introduced
to account for, respectively, variables {{formula:a3836c7a-8af5-4c30-a660-dd3d37135f28}} and assignments of value
{{formula:0e622baf-15f1-46d5-a657-f946c5c161d6}} to variable {{formula:94541db1-18ed-4ec9-b258-461ebf26631d}} .
Besides this, the automata {{formula:d0031fa3-d681-427c-9011-4114964dc57c}} associated with the formulas
are obtained by treating activity variables as if they were
activity symbols (without affecting the construction, which does not consider
the semantics of such objects), thus obtaining automata whose transitions
are labelled by event formulas, possibly containing activity variables
instead of activity symbols. Such formulas become regular event formulas
once values are assigned to variables and can thus be evaluated on the
(events of the) input trace. Formally, this requires a slightly different
definition of predicate {{formula:ebf1f7ff-c61b-4aea-be95-5aa30c736658}} , which must now
take {{formula:34ba5898-6d68-459d-8e8a-ca596297eb9f}} into account.
To see how this is done, consider the formula
{{formula:dbd90a77-30d5-494c-b6f1-8e4b85a863b1}}
The corresponding automaton is the same as that of Fig. REF , where
{{formula:d90abc24-4676-4cf9-93bd-ccaa9f527157}} ,
{{formula:a8665cad-7876-4a04-8505-3f153ef8d059}} ,
{{formula:4552b093-c41f-4b15-bc99-fa450e1d902f}} , and
{{formula:02ae2900-58bf-4aaa-b390-7fc249590203}} .
For formula {{formula:d47335ac-a6c4-427a-94a7-27f4d4807622}} , we have the following definition of predicate {{formula:db7698cb-0e79-43e9-b49f-5894bb6868dd}} :
{{formula:011d94c4-30a2-49c8-b7e9-465c581e6014}}
The parameter {{formula:72687b1d-c182-445e-b78b-8878c8102235}} stands for the trace identifier, as discussed above.
The above rule generalizes the corresponding one in Log Generation in the
presence of activity variable {{formula:f1c4aab2-7098-4701-99e4-0906342cdb72}} . As it can be seen, in order to
evaluate formula {{formula:aaa45cfc-a173-4ead-bf07-a36e5f2b4ace}} (second parameter in {{formula:a4659a23-6d37-4224-9e4e-af06505a276c}} ) of automaton
1 (first parameter), such variable (modeled as {{formula:6f23bbf5-da16-4381-8c77-683154443e25}} )
must be instantiated first, through
predicate {{formula:fa971996-983b-464d-beb1-b19deddac4dd}} .
Observe that once all variables are assigned a value,
the whole formula {{formula:f53f09bd-d1a2-4c4f-91d0-9162e7650b75}} becomes variable-free,
and the corresponding automaton is a regular automaton.
The returned extensions of {{formula:dd48149e-e882-4c2b-84db-3d32e52a7517}} and {{formula:4d17fc4d-b111-454a-a9aa-5e642d9d518c}}
represent, together, the problem solution.
Conformance Checking
Conformance Checking can be seen as a special case
of Query Checking with a single input trace and where all input formulas are
variable-free.
In this case, the problem amounts to simply checking whether the whole
specification is consistent, which is the case if and only if the input
trace, together with the assignments to the respective activity attributes,
satisfy the input formulas.
We close the section by observing how these problems provide a clear
example of how the declarative approach allows for specification reuse.
All the specifications, indeed, share the main rules
(for trace, automaton, etc.) and are easily obtained as slight variants of each
other, possibly varying the (guessed) predicates representing the solution.
Experiments
In this section, we provide both a comparison with state-of-the-art tools for Log Generation and Conformance Checking, based on multi-perspective declarative models, and an estimate of scalability for our query checking tool, for which, instead,
no competitors exist.
The state-of-the art tool used for Log Generation is the one presented in {{cite:aab4793588ca3f35d55817e3f3bb89040d43f111}},
which is based on Alloyhttps://alloytools.org/ and tailored for MP-Declare;
our results show that our ASP implementation for Log Generation scales much better than that and,
at the same time, supports a more expressive data-aware rule language.
As to Conformance Checking, we considered the state-of-the-art tool Declare Analyzer {{cite:15eb00dbcbae09f49ebce0418a761b62cbb51e07}};
we obtained comparable execution times but Declare Analyzer is specifically
tailored for Declare and optimized to check conformance wrt Declare rules only, while our tool is more general in this respect.
The experiments have been carried out on a standard laptop Dell XPS 15 with an intel i7 processor and 16GB of RAM.
All execution times have been averaged over 3 runs.
Source code, declarative models and event logs used in the experiments
are available at https://github.com/fracchiariello/process-mining-ASP.
Log Generation
{{table:128d42b2-5850-40b3-b1f6-a87c6b483958}}{{table:b4e6d9c0-231b-4f92-b787-8d965f475f34}}For testing the Log Generation tools, we have used 8 synthetic models and 8 models derived from real life logs. The experiments with synthetic models allowed us to test scalability of the tools in a controlled environment and over models with specific characteristics. The experiments with real models have been used to test the tools in real environments. For the experiments with synthetic models, we built 8 reference models containing 3, 5, 7, and 10 constraints with and without data conditions. Each model was obtained from the previous one by adding new constraints and preserving those already present.
Times are in ms.
The first and second blocks of Table REF show the execution times for the ASP-based log generator,
respectively with and without data conditions;
the third and fourth blocks show the results obtained with the Alloy log generator,
with and without data.
Times refer to the generation of logs with 10000 traces (of length from 10 to 30).
Consistent results are obtained also on additional experiments
for logs of size between 100 and 5000, not reported here for space reasons.
The results obtained with models containing data conditions show that the ASP-based tool scales very well, requiring less than 2 sec in the worst case. This occurs when a model with 10 constraints is used to generate 10000 traces of length 30.
As expected, the execution time increases linearly when the length of the traces in the generated logs increases.
The number of constraints in the declarative model also affects the tool performance but with a lower impact.
Without data conditions the results are similar but, as expected, the execution time is lower and increases less quickly when the complexity of the model and of the generated log increases. In the worst case (a model with 10 constraints used to generate 10000 traces of length 30), the execution time is lower than 1 sec.
The results obtained with the Alloy-based tool show similar trends but with execution times almost 60 times
higher than those obtained with the ASP-based tool.
The real life logs used in the experiments are taken from the collection available at https://data.4tu.nl/.
We used the declarative process model discovery tool presented in {{cite:fb9cf5b3ef8f020be35921dd6cedb6012c539278}} to extract a
process model using the default settings. The models in the real cases are much more complex and include a number of
constraints between 10 and 49 for a minimum support of 80.
The execution times needed for the Log Generation task with the ASP-based log generator and with the Alloy-based tool are shown,
respectively, in the first and second block of Table REF .
An asterisk indicates that for the specific model it was not possible to generate 10000 unique traces.
The complexity of real life models makes even more evident the significant advantage of using the ASP-based tool with
respect to the Alloy-based one.
In particular, in the worst case, the ASP-based tool requires around 9 sec (to generate 10000 traces of length 30 for log PL) while the Alloy-based generator almost 4 mins.
Conformance Checking
{{table:dd64e37a-495c-430f-a971-39658da9637d}}{{table:28a486dc-c70c-4a26-9db7-0c38e97781d5}}Also for Conformance Checking we used synthetic and real life datasets.
The former include the same declarative models as those used for Log Generation,
plus synthetic logs of 1000 traces of lengths from 10 to 30.
Table REF shows the execution times for the ASP-based tool, with and without data conditions,
and for the Declare Analyzer tool for synthetic datasets (times in ms).
The results show that in all cases the execution times increase when the model becomes larger and the
traces in the log become longer.
The execution times obtained with the ASP-based tool and the Declare Analyzer are comparable for data-aware constraints,
while, model constraints do not contain data conditions,
the Declare Analyzer is around 5 times faster.
This might be due
to the use of the #max aggregate to compute
a trace's length, which yields performance degradations.
A possible solution could be computing the trace length in advance
and then provide it in the ASP encoding as a fact.
In the real life experiments, we tested the Conformance Checking tools using models obtained with the discovery tool by
varying the minimum support between 60 and 90. The minimum support indicates the minimum percentage of traces in which a constraint should be fulfilled to be added to the discovered model. Clearly, a higher minimum support implies that the discovered models contain less constraints. As expected (see Table REF ), the execution times decrease when the minimum support used to discover the reference models increases in size.
Also in this case, the Declare Analyzer (second block in Table REF ) is faster.
However, the ASP-based tool also scales well (first block in Table REF ) requiring in the worst case around 1min.
Query Checking
{{table:da161587-43a7-4e1a-9f2a-0c07c38b758e}}Since for Query Checking no competitor exists
in the PM literature, we ran a set of controlled experiments to check how
execution times vary under different conditions.
We used the same synthetic logs used for Conformance Checking and
tested 8 queries corresponding to 8 standard Declare templates, with and
without data conditions. The results are shown in Table REF
(with and without data in the first and second block respectively).
The execution times are comparable for different types of queries and the
presence of data does not affect performance. In addition, as expected,
the execution times increase when the traces in the log become longer.
Conclusions
We have devised an ASP-based approach
to solve three classical problems from Declarative PM, namely
Log Generation, Query Checking and Conformance Checking, in a data-aware
setting.
Our results include correct ASP-encoding schemata
and an experimental evaluation against other approaches.
The experimental results show that, for Log Generation,
our approach drastically outperforms the state-of-the-art tool from PM.
Time performance are slightly worse wrt to the existing ad-hoc Conformance
Checker Declare Analyzer, which is optimized for Declare.
As to Query Checking, our approach provides the first solution in a data-aware
setting, a problem still open so far.
We believe that, by showing how the selected problems can be encoded and solved
in ASP, we are not only offering a solution technique but, more
in general, we are putting forward ASP an effective modeling paradigm for
Declarative PM in a data-aware setting.
For future work, we plan to extend the
approach to deal with actual, non-integer, timestamps in events and to
go beyond local ltl{{formula:1dd9aa1e-076e-43e1-a88d-45fb0d391866}} by investigating the
introduction of across-state quantification to relate the
values assigned to attributes at a given time point to those assigned at
a different time point.
Acknowledgments
Work partly supported by the ERC Advanced Grant WhiteMech (No. 834228),
the EU ICT-48 2020 project TAILOR (No. 952215), the Sapienza Project DRAPE, and the UNIBZ project CAT.
| i | d9bcd1fb5985d4032dbfdbcc955b2332 |
System identification {{cite:f85c4c1cf1793c8aebf057d6c7a901315474aecf}} is a field which deals with creating mathematical models of dynamical systems through statistical and machine learning approaches.
| m | a58eb1728003f7e30bb38ef3e54f5049 |
In this paper we have systematically studied statistical matching and subclassification with a many-leveled and continuous treatment dose. We propose two optimality criteria for subclassification, each based on a natural subclass homogeneity measure. We characterize the relationship between these two criteria and leverage this relationship to develop an efficient polynomial-time algorithm that finds a subclassification that is guaranteed to be optimal with respect to one criterion and near-optimal with respect to the other criterion. Our extensive simulations suggest that non-bipartite matching combined with regression adjustment helps remove bias in parametric causal inference; thus, we would recommend routinely using non-bipartite matching as a pre-processing step, as advocated by many researchers ({{cite:8e8f1b8e3b022bb619cfdb17ea39bf8af1bbb67d}}, {{cite:c36dfeea52a6715f07ef4933566dcd8f7c79f3a5}}, {{cite:9322ab79c4801ab64a327367787367d3e33db93b}}, {{cite:92333b0e99ff2b8f98427aeed40ae7868c8fbd54}}) in a binary treatment setting. Moreover, we found non-bipartite full match is advantageous over non-bipartite pair match in separating the treatment/encouragement doses and maintaining good subclass homogeneity and overall balance; therefore, the new design may be particularly useful in instrumental variable studies where separation of the IVs (or encouragement doses) would render outcome analysis much more efficient ({{cite:d416d4024bb8af5fa76dc3216304476f54e67653}}).
| d | 244619a0098807c805edba6b46f0488d |
Table REF shows that Info-StyleGAN and its variant with smaller network size, termed as Info-StyleGAN{{formula:ea0d16d4-1747-48a3-bb62-4f7a514692cb}} , consistently outperform state-of-the-art VAE-based methods by a large margin on both dSprites and Isaac3D. Meanwhile, Info-StyleGAN achieves competitive or even better disentanglement performance than the strong GAN baseline.
Although unsupervised disentanglement learning is impossible without supervision or inductive bias {{cite:4ff933e832a349a86dcaf32a0c917ecce71d0c09}}, this result reveals that the network structural improvement of StyleGAN provides a stronger prior for disentanglement learning compared to different explicit loss regularizations in disentangled VAEs or InfoGAN-CR. Besides, we observe that previous methods have much higher FID scores
on (downscaled) Isaac3D, along with their poor generated samples in Appendix REF .
We have also increased the capacity of VAEs but the improvement of image quality still cannot close the gap with Info-StyleGAN, as shown in Appendix REF .
These results show that previous disentanglement methods have difficulties on more diverse and complex data, such as Isaac3D, while StyleGAN does not.
| r | 370459d45a3b3cfb29454d3dc6486421 |
Compared to Step 3 of Algorithm REF , these methods rely on eigendecomposition of matrices distinct from {{formula:661ae6a9-8bdc-4b86-ab14-59d958a2c0a4}} . Specifically, in the standard kPCA implementation (Section 12.3 of {{cite:c8c8611d372c46ccc9a26683bfe35d3203307ab8}}), the eigendecomposition is applied to the centred kernel matrix
{{formula:3cc710e2-a19f-47c9-90be-d9529cd32307}}
| m | 2915ef4e71da1c601ea9976d1c93810c |
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