context stringlengths 250 7.19k | A stringlengths 250 4.62k | B stringlengths 250 8.2k | C stringlengths 250 3.89k | D stringlengths 250 4.12k | label stringclasses 4
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Rnm(x)=∑s=0(n−m)/2(−1)s(n−m2s)(D2+n−s−1n−m2)xn−2s.superscriptsubscript𝑅𝑛𝑚𝑥superscriptsubscript𝑠0𝑛𝑚2superscript1𝑠binomial𝑛𝑚2𝑠binomial𝐷2𝑛𝑠1𝑛𝑚2superscript𝑥𝑛2𝑠\displaystyle R_{n}^{m}(x)=\sum_{s=0}^{(n-m)/2}(-1)^{s}\binom{\frac{n-m}{2}}{s%
}\binom{\frac{D}{2}+n-s-1}{\frac{n-m}{2}}x^{n-2s}.italic_R st... | to the weight such that a Gauss-Legendre integration for moments xD+m−1superscript𝑥𝐷𝑚1x^{D+m-1}italic_x start_POSTSUPERSCRIPT italic_D + italic_m - 1 end_POSTSUPERSCRIPT
is engaged and the wiggly remainder of Rnmsuperscriptsubscript𝑅𝑛𝑚R_{n}^{m}italic_R start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT start_POSTSUPE... | The Newton’s Method of third order convergence is implemented for
Zernike Polynomials Rnmsuperscriptsubscript𝑅𝑛𝑚R_{n}^{m}italic_R start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_m end_POSTSUPERSCRIPT by computation of the ratios | Following the original notation, we will not put the upper (azimuth) index m𝑚mitalic_m in Rnmsuperscriptsubscript𝑅𝑛𝑚R_{n}^{m}italic_R start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_m end_POSTSUPERSCRIPT—which
is not a power—into parentheses. | to not exist because Rnmsuperscriptsubscript𝑅𝑛𝑚R_{n}^{m}italic_R start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_m end_POSTSUPERSCRIPT changes sign over the integration interval.
(i) (14) suggests to split Rnmsuperscriptsubscript𝑅𝑛𝑚R_{n}^{m}italic_R start_POSTSUBSCRIPT italic_n end_POS... | C |
0&I_{d-4}\end{array}\right)\text{for $d$ even or }x=I_{d}\text{ for $d$ odd}.italic_x = ( start_ARRAY start_ROW start_CELL italic_x start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT end_CELL start_CELL 0 end_CELL end_ROW start_ROW start_CELL 0 end_CELL start_CELL italic_I start_POSTSUBSCRIPT italic_d - 4 end_POSTSUBSCRIPT end_CE... | Note that a small variation of these standard generators for SL(d,q)SL𝑑𝑞\textnormal{SL}(d,q)SL ( italic_d , italic_q ) are used in Magma [14] as well
as in algorithms to verify presentations of classical groups, see [12], where only the generator v𝑣vitalic_v is slightly different in the two scenarios when d𝑑ditali... | The lower-unitriangular matrices u1subscript𝑢1u_{1}italic_u start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT and u2subscript𝑢2u_{2}italic_u start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT are returned as words in the Leedham-Green–O’Brien standard generators [11] for SL(d,q)SL𝑑𝑞\textnormal{SL}(d,q)SL ( italic_d , italic_q ) define... | Finally, we construct a second MSLP, described in Section 3.5, that writes a diagonal matrix h∈SL(d,q)ℎSL𝑑𝑞h\in\textnormal{SL}(d,q)italic_h ∈ SL ( italic_d , italic_q ) as a word in the standard generators of SL(d,q)SL𝑑𝑞\textnormal{SL}(d,q)SL ( italic_d , italic_q ) (when evaluated with these generators as input)... | Our aim is to determine the length and memory quota for an MSLP for the Bruhat decomposition of an arbitrary matrix g∈SL(d,q)𝑔SL𝑑𝑞g\in\textnormal{SL}(d,q)italic_g ∈ SL ( italic_d , italic_q ) via the above method, with the matrices u1subscript𝑢1u_{1}italic_u start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT, u2subscript𝑢2u... | A |
It is hard to approximate such problem in its full generality using numerical methods, in particular because of the low regularity of the solution and its multiscale behavior. Most convergent proofs either assume extra regularity or special properties of the coefficients [AHPV, MR3050916, MR2306414, MR1286212, babuos85... |
As in many multiscale methods previously considered, our starting point is the decomposition of the solution space into fine and coarse spaces that are adapted to the problem of interest. The exact definition of some basis functions requires solving global problems, but, based on decaying properties, only local comput... | mixed finite elements. We note the proposal in [CHUNG2018298] of generalized multiscale finite element methods based on eigenvalue problems inside the macro elements, with basis functions with support weakly dependent of the log of the contrast. Here, we propose eigenvalue problems based on edges of macro element remov... | The remainder of the this paper is organized as follows. Section 2 describes a suitable primal hybrid formulation for the problem (1), which is followed in Section 3 by its a discrete formulation. A discrete space decomposition is introduced to transform the discrete saddle-point problem into a sequence of elliptic dis... | Of course, the numerical scheme and the estimates developed in Section 3.1 hold. However, several simplifications are possible when the coefficients have low-contrast, leading to sharper estimates. We remark that in this case, our method is similar to that of [MR3591945], with some differences. First we consider that T... | A |
We think Alg-A is better in almost every aspect. This is because it is essentially simpler.
Among other merits, Alg-A is much faster, because it has a smaller constant behind the asymptotic complexity O(n)𝑂𝑛O(n)italic_O ( italic_n ) than the others: | Comparing the description of the main part of Alg-A (the 7 lines in Algorithm 1) with that of Alg-CM (pages 9–10 of [8]),
Alg-A is conceptually simpler. Alg-CM is claimed “involved” by its authors as it contains complicated subroutines for handling many subcases. |
Our experiment shows that the running time of Alg-A is roughly one eighth of the running time of Alg-K, or one tenth of the running time of Alg-CM. (Moreover, the number of iterations required by Alg-CM and Alg-K is roughly 4.67 times that of Alg-A.) |
Alg-A has simpler primitives because (1) the candidate triangles considered in it have all corners lying on P𝑃Pitalic_P’s vertices and (2) searching the next candidate from a given one is much easier – the code length for this is 1:7 in Alg-A and in Alg-CM. | Alg-A computes at most n𝑛nitalic_n candidate triangles (proof is trivial and omitted) whereas Alg-CM computes at most 5n5𝑛5n5 italic_n triangles (proved in [8]) and so as Alg-K.
(by experiment, Alg-CM and Alg-K have to compute roughly 4.66n4.66𝑛4.66n4.66 italic_n candidate triangles.) | D |
𝖫(x(i),y(i))=1{y(i)=yrumor}log(y~rumor(i))+1{y(i)=ynews}log(y~news(i))𝖫superscript𝑥𝑖superscript𝑦𝑖1superscript𝑦𝑖subscript𝑦𝑟𝑢𝑚𝑜𝑟𝑙𝑜𝑔superscriptsubscript~𝑦𝑟𝑢𝑚𝑜𝑟𝑖1superscript𝑦𝑖subscript𝑦𝑛𝑒𝑤𝑠𝑙𝑜𝑔superscriptsubscript~𝑦𝑛𝑒𝑤𝑠𝑖\mathsf{L}(x^{(i)},y^{(i)})=1\{y^{(i)}=y... | In the lower part of the pipeline, we extract features from tweets and combine them with the creditscore to construct the feature vector in a time series structure called Dynamic Series Time Model. These feature vectors are used to train the classifier for rumor vs. (non-rumor) news classification.
| Based on the credibility model we develop a novel and effective cascaded model for rumor classification. The model uses time-series structure of features to capture their temporal dynamics. Our model clearly
outperforms strong baselines, especially for the targeted early stage of the diffusion. It already |
Most relevant for our work is the work presented in [20], where a time series model to capture the time-based variation of social-content features is used. We build upon the idea of their Series-Time Structure, when building our approach for early rumor detection with our extended dataset, and we provide a deep analys... |
As observed in [19, 20], rumor features are very prone to change during an event’s development. In order to capture these temporal variabilities, we build upon the Dynamic Series-Time Structure (DSTS) model (time series for short) for feature vector representation proposed in [20]. We base our credibility feature on t... | D |
\prime}\left(u\right)=0roman_lim start_POSTSUBSCRIPT italic_u → ∞ end_POSTSUBSCRIPT roman_ℓ ( italic_u ) = roman_lim start_POSTSUBSCRIPT italic_u → ∞ end_POSTSUBSCRIPT roman_ℓ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT ( italic_u ) = 0), a β𝛽\betaitalic_β-smooth function, i.e. its derivative is β𝛽\betaitalic_β-Lipsh... | The follow-up paper (Gunasekar et al., 2018) studied this same problem with exponential loss instead of squared loss. Under additional assumptions on the asymptotic convergence of update directions and gradient directions, they were able to relate the direction of gradient descent iterates on the factorized parameteriz... | decreasing loss, as well as for multi-class classification with cross-entropy loss. Notably, even though the logistic loss and the exp-loss behave very different on non-separable problems, they exhibit the same behaviour for separable problems. This implies that the non-tail
part does not affect the bias. The bias is a... | Assumption 1 includes many common loss functions, including the logistic, exp-loss222The exp-loss does not have a global β𝛽\betaitalic_β smoothness parameter. However, if we initialize with η<1/ℒ(𝐰(0))𝜂1ℒ𝐰0\eta<1/\mathcal{L}(\mathbf{w}(0))italic_η < 1 / caligraphic_L ( bold_w ( 0 ) ) then it is straightforward to... | loss function (Assumption 1) with an exponential
tail (Assumption 3), any stepsize η<2β−1σmax−2(𝐗 )𝜂2superscript𝛽1superscriptsubscript𝜎2𝐗 \eta<2\beta^{-1}\sigma_{\max}^{-2}\left(\text{$\mathbf{X}$ }\right)italic_η < 2 italic_β start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT italic_σ start_POSTSUBSCRIPT roman_max ... | C |
Twitter Features refer to basic Twitter features, such as hashtags, mentions, retweets. In addition, we derive three more URL-based features. The first is the WOT–trustworthy-based– score which is crawled from the APIs of WOT.com555https://www.mywot.com/en/api. The second is domain categories which we have collected fr... | To construct the training dataset, we collected rumor stories from the rumor tracking websites snopes.com and urbanlegends.about.com. In more detail, we crawled 4300 stories from these websites. From the
story descriptions we manually constructed queries to retrieve the relevant tweets for the 270 rumors with highest i... | As we can see in Figure 9 the best result on average over 48 hours is the BestSet. Second one is All features. Except those two, the best group feature is Text features. One reason is the text feature set has the largest group of feature with totally 16 features. But if look into each feature in text feature group, we ... | User Features. Apart from the features already exploited in related work (e.g., VerifiedUser, NumOfFriends, NumOfTweets, ReputationScore), we add two new features captured from Twitter interface: (1) how many photos have been posted by a user (UserNumPhoto), and (2) whether the user lives in a large city. We use the li... | The performance of user features is similar with the Twitter features, they are both quite stable from the first hour to the last hour. As shown in Table 9, the best feature over 48 hours of the user feature group is UserTweetsPerDays and it is the best feature overall in the first 4 hours, but its rank decreases with ... | C |
We further investigate the identification of event time, that is learned on top of the event-type classification. For the gold labels, we gather from the studied times with regards to the event times that is previously mentioned. We compare the result of the cascaded model with non-cascaded logistic regression. The res... | We further investigate the identification of event time, that is learned on top of the event-type classification. For the gold labels, we gather from the studied times with regards to the event times that is previously mentioned. We compare the result of the cascaded model with non-cascaded logistic regression. The res... | Learning a single model for ranking event entity aspects is not effective due to the dynamic nature of a real-world event driven by a great variety of multiple factors. We address two major factors that are assumed to have the most influence on the dynamics of events at aspect-level, i.e., time and event type. Thus, we... | RQ3. We demonstrate the results of single models and our ensemble model in Table 4. As also witnessed in RQ2, SVMall𝑆𝑉subscript𝑀𝑎𝑙𝑙SVM_{all}italic_S italic_V italic_M start_POSTSUBSCRIPT italic_a italic_l italic_l end_POSTSUBSCRIPT, will all features, gives a rather stable performance for both NDCG and Recall... | For this part, we first focus on evaluating the performance of single L2R models that are learned from the pre-selected time (before, during and after) and types (Breaking and Anticipate) set of entity-bearing queries. This allows us to evaluate the feature performance i.e., salience and timeliness, with time and type ... | D |
RL [Sutton and Barto, 1998] has been successfully applied to a variety of domains,
from Monte Carlo tree search [Bai et al., 2013] and hyperparameter tuning for complex optimization in science, engineering and machine learning problems [Kandasamy et al., 2018; Urteaga et al., 2023], | SMC weights are updated based on the likelihood of the observed rewards:
wt,a(m)∝pa(yt|xt,θt,a(m))proportional-tosuperscriptsubscript𝑤𝑡𝑎𝑚subscript𝑝𝑎conditionalsubscript𝑦𝑡subscript𝑥𝑡superscriptsubscript𝜃𝑡𝑎𝑚w_{t,a}^{(m)}\propto p_{a}(y_{t}|x_{t},\theta_{t,a}^{(m)})italic_w start_POSTSUBSCRIPT italic_t , it... | The techniques used in these success stories are grounded on statistical advances on sequential decision processes and multi-armed bandits.
The MAB crystallizes the fundamental trade-off between exploration and exploitation in sequential decision making. | the fundamental operation in the proposed SMC-based MAB Algorithm 1
is to sequentially update the random measure pM(θt,a|ℋ1:t)subscript𝑝𝑀conditionalsubscript𝜃𝑡𝑎subscriptℋ:1𝑡p_{M}(\theta_{t,a}|\mathcal{H}_{1:t})italic_p start_POSTSUBSCRIPT italic_M end_POSTSUBSCRIPT ( italic_θ start_POSTSUBSCRIPT italic_t , itali... | we propagate forward the sequential random measure pM(θt,a|ℋ1:t)subscript𝑝𝑀conditionalsubscript𝜃𝑡𝑎subscriptℋ:1𝑡p_{M}(\theta_{t,a}|\mathcal{H}_{1:t})italic_p start_POSTSUBSCRIPT italic_M end_POSTSUBSCRIPT ( italic_θ start_POSTSUBSCRIPT italic_t , italic_a end_POSTSUBSCRIPT | caligraphic_H start_POSTSUBSCRIPT 1 : ... | B |
In order to have a broad overview of different patients’ patterns over the one month period, we first show the figures illustrating measurements aggregated by days-in-week.
For consistency, we only consider the data recorded from 01/03/17 to 31/03/17 where the observations are most stable. | Median number of blood glucose measurements per day varies between 2 and 7. Similarly, insulin is used on average between 3 and 6 times per day.
In terms of physical activity, we measure the 10 minute intervals with at least 10 steps tracked by the google fit app. | The insulin intakes tend to be more in the evening, when basal insulin is used by most of the patients. The only difference happens to patient 10 and 12 whose intakes are earlier at day.
Further, patient 12 takse approx. 3 times the average insulin dose of others in the morning. | Patient 17 has more rapid insulin applications than glucose measurements in the morning and particularly in the late evening.
For patient 15, rapid insulin again slightly exceeds the number of glucose measurements in the morning. Curiously, the number of glucose measurements match the number carbohydrate entries – it i... | These are also the patients who log glucose most often, 5 to 7 times per day on average compared to 2-4 times for the other patients.
For patients with 3-4 measurements per day (patients 8, 10, 11, 14, and 17) at least a part of the glucose measuremtents after the meals is within this range, while patient 12 has only t... | B |
The spatial allocation of attention when viewing natural images is commonly represented in the form of topographic saliency maps that depict which parts of a scene attract fixations reliably. Identifying the underlying properties of these regions would allow us to predict human fixation patterns and gain a deeper under... | Early approaches towards computational models of visual attention were defined in terms of different theoretical frameworks, including Bayesian Zhang et al. (2008) and graph-based formulations Harel et al. (2006). The former was based on the notion of self-information derived from a probability distribution over linear... |
With the advent of deep neural network solutions for visual tasks such as image classification Krizhevsky et al. (2012), saliency modeling has also undergone a paradigm shift from manual feature engineering towards automatic representation learning. In this work, we leveraged the capability of convolutional neural net... |
Figure 1: A visualization of four natural images with the corresponding empirical fixation maps, our model predictions, and estimated maps based on the work by Itti et al. (1998). The network proposed in this study was not trained on the stimuli shown here and thus exhibits its generalization ability to unseen instanc... |
With the large-scale acquisition of eye tracking measurements under natural viewing conditions, data-driven machine learning techniques became more practicable. Judd et al. (2009) introduced a model based on support vector machines to estimate fixation densities from a set of low-, mid-, and high-level visual features... | B |
loc(Zi)=|Zi|+14=2i−2locsubscript𝑍𝑖subscript𝑍𝑖14superscript2𝑖2\operatorname{\textsf{loc}}(Z_{i})=\frac{|Z_{i}|+1}{4}=2^{i-2}loc ( italic_Z start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ) = divide start_ARG | italic_Z start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT | + 1 end_ARG start_ARG 4 end_ARG = 2 start_POSTS... | It is easy to see that 1111-locality implies some sort of palindromic structure of a word. For example, palindromes like the English words radar, refer and rotator are obviously 1111-local, while the palindrome 𝚊𝚋𝚊𝚋𝚊𝚋𝚊𝚊𝚋𝚊𝚋𝚊𝚋𝚊\mathtt{a}\mathtt{b}\mathtt{a}\mathtt{b}\mathtt{a}\mathtt{b}\mathtt{a}typewriter_... |
Observation 2.1 justifies that in the following, we are only concerned with condensed words (and therefore words with at most 2loc(α)2loc𝛼2\operatorname{\textsf{loc}}(\alpha)2 loc ( italic_α ) occurrences per symbol and total length of at most |X|2loc(α)𝑋2loc𝛼|X|2\operatorname{\textsf{loc}}(\alpha)| italic_X |... |
Notice that both Zimin words and 1111-local words have an obvious palindromic structure. However, in the Zimin words, the letters occur multiple times, but not in large blocks, while in 1111-local words there are at most 2222 blocks of each letter. With respect to palindromes, we can show the following general result ... | Regarding the locality of Zisubscript𝑍𝑖Z_{i}italic_Z start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT, note that marking x2subscript𝑥2x_{2}italic_x start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT leads to 2i−2superscript2𝑖22^{i-2}2 start_POSTSUPERSCRIPT italic_i - 2 end_POSTSUPERSCRIPT marked blocks; further, marking x1subsc... | C |
Hengling et al.[244] argue that substantial investments will be required to create high quality annotated databases which are essential for the success of supervised deep learning methods.
In[238] the authors argue that the continued success of this field depends on sustained technological advancements in information t... | Lee et al.[250] conclude that international cooperation is required for constructing a high quality multimodal big dataset for stroke imaging.
Another solution to better exploit big medical data in cardiology is to apply unsupervised learning methods, which do not require annotations. | It is evident from the literature that most deep learning methods (mostly CNNs and SDAEs) in this area consist of three parts: filtering for denoising, R-peak detection for beat segmentation and the neural network for feature extraction.
Another popular set of methods is the conversion of ECGs to images, to utilize the... | Loh et al.[251] argue that deep learning and mobile technologies would expedite the proliferation of healthcare services to those in impoverished regions which in turn leads to further decline of disease rates.
Mayer et al.[237] state that big data promises to change cardiology through an increase in the data gathered ... | Deep learning requires large training datasets to achieve high quality results[3].
This is especially difficult with medical data, considering that the labeling procedure of medical data is costly because it requires manual labor from medical experts. | A |
Reinforcement learning is formalized in Markov decision processes (MDP). An MDP is defined as a tuple (𝒮,𝒜,P,r,γ)𝒮𝒜𝑃𝑟𝛾(\mathcal{S},{\mathcal{A}},P,r,\gamma)( caligraphic_S , caligraphic_A , italic_P , italic_r , italic_γ ), where 𝒮𝒮\mathcal{S}caligraphic_S is a state space, 𝒜𝒜{\mathcal{A}}caligraphic_A is a... | In Atari 2600 games our goal is to find a policy which maximizes the value function from the beginning of the game.
Crucially, apart from an Atari 2600 emulator environment env𝑒𝑛𝑣envitalic_e italic_n italic_v we will use a neural network simulated environment env′𝑒𝑛superscript𝑣′env^{\prime}italic_e italic_n i... | We will now describe the details of SimPLe, outlined in Algorithm 1. In step 6 we use the proximal policy optimization (PPO) algorithm (Schulman et al., 2017) with γ=0.95𝛾0.95\gamma=0.95italic_γ = 0.95. The algorithm generates rollouts in the simulated environment env′𝑒𝑛superscript𝑣′env^{\prime}italic_e italic_n ... | In this work we refer to MDPs as environments and assume that environments do not provide direct access to the state (i.e., the RAM of Atari 2600 emulator). Instead we use visual observations, typically 210×160210160210\times 160210 × 160 RGB images. A single image does not determine the state.
In order to reduce envir... |
The primary evaluation in our experiments studies the sample efficiency of SimPLe, in comparison with state-of-the-art model-free deep RL methods in the literature. To that end, we compare with Rainbow (Hessel et al., 2018; Castro et al., 2018), which represents the state-of-the-art Q-learning method for Atari games, ... | C |
A high level overview of these combined methods is shown in Fig. 1.
Although we choose the EEG epileptic seizure recognition dataset from University of California, Irvine (UCI) [13] for EEG classification, the implications of this study could be generalized in any kind of signal classification problem. | The two layer module consists of two 1D convolutional layers (kernel sizes of 3333 with 8888 and 16161616 channels) with the first layer followed by a ReLU activation function and a 1D max pooling operation (kernel size of 2222).
The feature maps of the last convolutional layer for both modules are then concatenated al... | For the CNN modules with one and two layers, xisubscript𝑥𝑖x_{i}italic_x start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT is converted to an image using learnable parameters instead of some static procedure.
The one layer module consists of one 1D convolutional layer (kernel sizes of 3333 with 8888 channels). | Architectures of all bdsubscript𝑏𝑑b_{d}italic_b start_POSTSUBSCRIPT italic_d end_POSTSUBSCRIPT remained the same, except for the number of the output nodes of the last linear layer which was set to five to correspond to the number of classes of D𝐷Ditalic_D.
An example of the respective outputs of some of the m𝑚mita... | Here we also refer to CNN as a neural network consisting of alternating convolutional layers each one followed by a Rectified Linear Unit (ReLU) and a max pooling layer and a fully connected layer at the end while the term ‘layer’ denotes the number of convolutional layers.
| D |
As depicted in Fig. 10, for the step negotiation operation with a height of hℎhitalic_h, both ERw<ECwsubscript𝐸𝑅𝑤subscript𝐸𝐶𝑤E_{Rw}<E_{Cw}italic_E start_POSTSUBSCRIPT italic_R italic_w end_POSTSUBSCRIPT < italic_E start_POSTSUBSCRIPT italic_C italic_w end_POSTSUBSCRIPT and ERr<ECrsubscript𝐸𝑅𝑟subscript𝐸𝐶... | Similarly, when the robot encountered a step with a height of 3h (as shown in Fig. 12), the mode transition was activated when the energy consumption of the rear track negotiation in rolling mode surpassed the threshold value derived from the previously assessed energy results of the rear body climbing gait. The result... |
Figure 10: The Cricket robot tackles a step of height h using rolling locomotion mode, negating the need for a transition to the walking mode. The total energy consumed throughout the entire step negotiation process in rolling locomotion stayed below the preset threshold value. This threshold value was established bas... | Figure 11: The Cricket robot tackles a step of height 2h, beginning in rolling locomotion mode and transitioning to walking locomotion mode using the rear body climbing gait. The red line in the plot shows that the robot tackled the step in rolling locomotion mode until the online accumulated energy consumption of the ... |
To assess the efficacy of the suggested autonomous locomotion mode transition strategy, simulation experiments featuring step heights of h, 2h, and 3h were conducted. These simulations involved continuous tracking of energy consumption for both total body negotiation (ERwsubscript𝐸𝑅𝑤E_{Rw}italic_E start_POSTSUBSCR... | A |
It should be fairly clear that such assumptions are very unrealistic or undesirable. Advice bits, as all information, are prone to transmission errors. In addition, the known advice models often allow
information that one may arguably consider unrealistic, e.g., an encoding of some part of the offline optimal solution.... |
All the above results pertain to deterministic online algorithms. In Section 6, we study the power of randomization in online computation with untrusted advice. First, we show that the randomized algorithm of Purohit et al. [29] for the ski rental problem Pareto-dominates any deterministic algorithm, even when the lat... | As argued in detail in [9], there are compelling reasons to study the advice complexity of online computation.
Lower bounds establish strict limitations on the power of any online algorithm; there are strong connections between randomized online algorithms and online algorithms with advice (see, e.g., [27]); online alg... | We introduced a new model in the study of online algorithms with advice, in which the online algorithm can leverage information about the request sequence that is not necessarily foolproof. Motivated by advances in learning-online algorithms, we studied tradeoffs between the trusted and untrusted competitive ratio, as ... | The above observations were recently made in the context of online algorithms with machine-learned predictions.
Lykouris and Vassilvitskii [24] and Purohit et al. [29] show how to use predictors to design and analyze algorithms with two properties: (i) if the predictor is good, then the online algorithm should perform ... | D |
This scenario, known as “early risk detection” have gained increasing interest in recent years with potential applications in rumor detection [Ma et al., 2015, 2016, Kwon et al., 2017], sexual predator detection and aggressive text identification [Escalante et al., 2017], depression detection [Losada et al., 2017, Losa... | Finally, [Loyola et al., 2018] considers the decision of “when to classify” as a problem to be learned on its own and trains two SVMs, one to make category predictions and the other to decide when to stop reading the stream.
Nonetheless, the use of these two SVMs, again, hides the reasons behind both, the classificatio... | It is true that more elaborated methods that simultaneously learn the classification model and the policy to stop reading could have been used, such as in [Dulac-Arnold et al., 2011, Yu et al., 2017].
However, for the moment it is clear that this very simple approach is effective enough to outperform the remainder meth... | Although the use of MDP is very appealing from a theoretical point of view, and we will consider it for future work, the model they proposed would not be suitable for risk tasks. The use of SVMs along with Φ(s)Φ𝑠\Phi(s)roman_Φ ( italic_s ) implies that the model is a black box, not only hiding the reasons for classif... | As far as we know, the approach presented in [Dulac-Arnold et al., 2011] is the first to address a (sequential) text classification task as a Markov decision process (MDP) with virtually three possible actions: read (the next sentence), classify333In practice, this action is a collection of actions, one for each catego... | D |
\frac{1}{2},k})bold_w start_POSTSUBSCRIPT italic_t + 1 end_POSTSUBSCRIPT = bold_w start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT - italic_η divide start_ARG 1 end_ARG start_ARG italic_K end_ARG ∑ start_POSTSUBSCRIPT italic_k ∈ [ italic_K ] end_POSTSUBSCRIPT caligraphic_C ( bold_e start_POSTSUBSCRIPT italic_t + divide s... | DEF-A achieves its best performance when λ=0.3𝜆0.3\lambda=0.3italic_λ = 0.3. In comparison, GMC+ outperforms DEF-A across different λ𝜆\lambdaitalic_λ values and shows a preference for a larger λ𝜆\lambdaitalic_λ (e.g., 0.5).
In the following experiments, we set λ𝜆\lambdaitalic_λ as 0.3 for DEF-A and 0.5 for GMC+. λ=... | Since RBGS introduces a larger compressed error compared with top-s𝑠sitalic_s when selecting the same number of components of the original vector to communicate, vanilla error feedback methods usually fail to converge when using RBGS as the sparsification compressor.
To address this convergence issue, | Due to the larger compressed error introduced by RBGS compared with top-s𝑠sitalic_s when selecting the same number of components of the original vector to communicate, vanilla error feedback methods usually fail to converge. Xu and Huang (2022) propose DEF-A to solve the convergence problem by using detached error fee... | Note that the convergence guarantee of DEF-A and its momentum variant for non-convex problems is lacking in (Xu and Huang, 2022). We provide the convergence analysis for GMC+, which can be seen as a global momentum variant of DEF-A. We eliminate the assumption of ring-allreduce compatibility from (Xu and Huang, 2022) a... | C |
An advantage of SANs compared to Sparse Autoencoders [37] is that the constrain of activation proximity can be applied individually in each example instead of requiring the computation of forward-pass of all examples.
Additionally, SANs create exact zeros instead near-zeros, which reduces co-adaptation between instance... | Olshausen et al. [43] presented an objective function that considers subjective measures of sparseness of the activation maps, however in this work we use the direct measure of compression ratio.
Previous work by [44] have used a weighted combination of the number of neurons, percentage root-mean-squared difference and... |
Regarding the φ𝜑\varphiitalic_φ metric and considering Eq. 17 our target is to estimate an as accurate as possible representation of 𝒙𝒙\bm{x}bold_italic_x through 𝜶(i)superscript𝜶𝑖\bm{\alpha}^{(i)}bold_italic_α start_POSTSUPERSCRIPT ( italic_i ) end_POSTSUPERSCRIPT and 𝒘(i)superscript𝒘𝑖\bm{w}^{(i)}bold_italic... | Previous work by Blier et al. [31] demonstrated the ability of DNNs to losslessly compress the input data and the weights, but without considering the number of non-zero activations.
In this work we relax the lossless requirement and also consider neural networks purely as function approximators instead of probabilist ... | φ𝜑\varphiitalic_φ could be seen as an alternative formalization of Occam’s razor [38] to Solomonov’s theory of inductive inference [39] but with a deterministic interpretation instead of a probabilistic one.
The cost of the description of the data could be seen as proportional to the number of weights and the number o... | D |
In this section, how the key parameters in the UAV ad-hoc network affect the performance of PBLLA and SPBLLA will be studied. In the simulation, besides the quantity of UAVs and channel, other parameters are fixed as constant values. We set up the post-disaster area as D=4000km2𝐷4000𝑘superscript𝑚2D=4000km^{2}itali... | As the dynamic degree index τ𝜏\tauitalic_τ decreases from 0.030.030.030.03 to 0.010.010.010.01, the goal function’s values are increasing, which illustrates that lower values of τ𝜏\tauitalic_τ approach to maximizer of the global utility function. When τ=0.03𝜏0.03\tau=0.03italic_τ = 0.03, the value of U𝑈Uitalic_U do... |
Let denote τ𝜏\tauitalic_τ as the dynamic degree of the scenarios. The harsher environment the networks suffers, the higher τ𝜏\tauitalic_τ it is. In the highly dynamic scenarios, we suppose that τ≥0.01𝜏0.01\tau\geq 0.01italic_τ ≥ 0.01. With proper τ𝜏\tauitalic_τ, PBLLA asymptotically converges and leads the UAV ad-... |
The essence of PBLLA is selecting an alternative UAV randomly in one iteration and improving its utility by altering power and altitude with a certain probability, which is determined by the utilities of two strategies and τ𝜏\tauitalic_τ. UAV prefers to select the power and altitude which provide higher utility. Neve... |
In this part, we investigate the influence of environment dynamic on the network states. With different scenarios’ dynamic degree τ∈(0,∞)𝜏0\tau\in(0,\infty)italic_τ ∈ ( 0 , ∞ ), PBLLA and SPBLLA will converge to the maximizer of goal function with different altering strategy probability. Fig. 6 presents the influence... | D |
∇^¯U¯¯^∇¯𝑈\displaystyle\overline{\widehat{\nabla}}\,\,\overline{U}over¯ start_ARG over^ start_ARG ∇ end_ARG end_ARG over¯ start_ARG italic_U end_ARG
=(Dr^¯∗U¯)𝐫^+(Dz^¯∗U¯)𝐳^absent¯^𝐷𝑟¯𝑈^𝐫¯^𝐷𝑧¯𝑈^𝐳\displaystyle=\left(\overline{\widehat{Dr}}*\overline{U}\right)\hat{\mathbf{r}% | }}+\left(\overline{\overline{Dz}}*\overline{U}\right)\hat{\mathbf{z}}= ( over¯ start_ARG over¯ start_ARG italic_D italic_r end_ARG end_ARG ∗ over¯ start_ARG italic_U end_ARG ) over^ start_ARG bold_r end_ARG + ( over¯ start_ARG over¯ start_ARG italic_D italic_z end_ARG end_ARG ∗ over¯ start_ARG italic_U end_ARG ) over^ ... | }+\left(\overline{\widehat{Dz}}*\overline{U}\right)\hat{\mathbf{z}}= ( over¯ start_ARG over^ start_ARG italic_D italic_r end_ARG end_ARG ∗ over¯ start_ARG italic_U end_ARG ) over^ start_ARG bold_r end_ARG + ( over¯ start_ARG over^ start_ARG italic_D italic_z end_ARG end_ARG ∗ over¯ start_ARG italic_U end_ARG ) over^ st... | \widehat{Dz}}*\overline{U}\right)\,/\,\widehat{r}\right)\right)over¯ start_ARG over¯ start_ARG roman_Δ start_POSTSUPERSCRIPT start_FLOATSUPERSCRIPT ∗ end_FLOATSUPERSCRIPT end_POSTSUPERSCRIPT end_ARG end_ARG over¯ start_ARG italic_U end_ARG = over¯ start_ARG italic_r end_ARG start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT (... | \widehat{Dz}}*\overline{U}\right)\right)\right)\right)\,/\,\overline{r}over¯ start_ARG over¯ start_ARG roman_Δ end_ARG end_ARG over¯ start_ARG italic_U end_ARG = over^ start_ARG over¯ start_ARG ∇ end_ARG end_ARG ⋅ over¯ start_ARG over^ start_ARG ∇ end_ARG end_ARG over¯ start_ARG italic_U end_ARG = ( ( over^ start_ARG o... | B |
Let r𝑟ritalic_r be the relation on 𝒞Rsubscript𝒞𝑅\mathcal{C}_{R}caligraphic_C start_POSTSUBSCRIPT italic_R end_POSTSUBSCRIPT given to the left of Figure 12.
Its abstract lattice ℒrsubscriptℒ𝑟\mathcal{L}_{r}caligraphic_L start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT is represented to the right. | First, remark that both A→B𝐴→𝐵A\operatorname{\rightarrow}Bitalic_A → italic_B and B→A𝐵→𝐴B\operatorname{\rightarrow}Aitalic_B → italic_A are possible.
Indeed, if we set g=⟨b,a⟩𝑔𝑏𝑎g=\langle b,a\rangleitalic_g = ⟨ italic_b , italic_a ⟩ or g=⟨a,1⟩𝑔𝑎1g=\langle a,1\rangleitalic_g = ⟨ italic_a , 1 ⟩, then r⊧gA→... | If no confusion is possible, the subscript R𝑅Ritalic_R will be omitted, i.e., we will use
≤,∧,∨\leq,\operatorname{\land},\operatorname{\lor}≤ , ∧ , ∨ instead of ≤R,∧R,∨Rsubscript𝑅subscript𝑅subscript𝑅\leq_{R},\operatorname{\land}_{R},\operatorname{\lor}_{R}≤ start_POSTSUBSCRIPT italic_R end_POSTSUBSCRIPT , ∧ start_P... | The tuples t1subscript𝑡1t_{1}italic_t start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT, t4subscript𝑡4t_{4}italic_t start_POSTSUBSCRIPT 4 end_POSTSUBSCRIPT represent a counter-example to BC→A𝐵𝐶→𝐴BC\operatorname{\rightarrow}Aitalic_B italic_C → italic_A for g1subscript𝑔1g_{1}italic_g start_POSTSUBSCRIPT 1 end_POSTSUBSCRI... | For convenience we give in Table 7 the list of all possible realities
along with the abstract tuples which will be interpreted as counter-examples to A→B𝐴→𝐵A\operatorname{\rightarrow}Bitalic_A → italic_B or B→A𝐵→𝐴B\operatorname{\rightarrow}Aitalic_B → italic_A. | D |
To that end, we ran Dropout-DQN and DQN on one of the classic control environments to express the effect of Dropout on Variance and the learned policies quality. For the Overestimation phenomena, we ran Dropout-DQN and DQN on a Gridworld environment to express the effect of Dropout because in such environment the optim... |
To evaluate the Dropout-DQN, we employ the standard reinforcement learning (RL) methodology, where the performance of the agent is assessed at the conclusion of the training epochs. Thus we ran ten consecutive learning trails and averaged them. We have evaluated Dropout-DQN algorithm on CARTPOLE problem from the Class... |
Reinforcement Learning (RL) is a learning paradigm that solves the problem of learning through interaction with environments, this is a totally different approach from the other learning paradigms that have been studied in the field of Machine Learning namely the supervised learning and the unsupervised learning. Rein... |
The sources of DQN variance are Approximation Gradient Error(AGE)[23] and Target Approximation Error(TAE)[24]. In Approximation Gradient Error, the error in gradient direction estimation of the cost function leads to inaccurate and extremely different predictions on the learning trajectory through different episodes b... | To that end, we ran Dropout-DQN and DQN on one of the classic control environments to express the effect of Dropout on Variance and the learned policies quality. For the Overestimation phenomena, we ran Dropout-DQN and DQN on a Gridworld environment to express the effect of Dropout because in such environment the optim... | A |
V-Net (Milletari et al., 2016) and FCN (Long et al., 2015). Sinha and Dolz (2019) proposed a multi-level attention based architecture for abdominal organ segmentation from MRI images. Qin et al. (2018) proposed a dilated convolution base block to preserve more detailed attention in 3D medical image segmentation. Simil... |
Several modified versions (e.g. deeper/shallower, adding extra attention blocks) of encoder-decoder networks have been applied to semantic segmentation (Amirul Islam et al., 2017; Fu et al., 2019b; Lin et al., 2017a; Peng et al., 2017; Pohlen et al., 2017; Wojna et al., 2017; Zhang et al., 2018d). Recently in 2018, De... |
The standard CE loss function and its weighted versions, as discussed in Section 4, have been applied to numerous medical image segmentation problems (Isensee et al., 2019; Li et al., 2019b; Lian et al., 2018; Ni et al., 2019; Nie et al., 2018; Oktay et al., 2018; Schlemper et al., 2019). However, Milletari et al. (20... |
Khosravan et al. (2019) proposed an adversarial training framework for pancreas segmentation from CT scans. Son et al. (2017) applied GANs for retinal image segmentation. Xue et al. (2018) used a fully convolutional network as a segmenter in the generative adversarial framework to segment brain tumors from MRI images.... | V-Net (Milletari et al., 2016) and FCN (Long et al., 2015). Sinha and Dolz (2019) proposed a multi-level attention based architecture for abdominal organ segmentation from MRI images. Qin et al. (2018) proposed a dilated convolution base block to preserve more detailed attention in 3D medical image segmentation. Simil... | C |
The red line indicates the number of edges that remain in 𝐀¯¯𝐀\bar{{\mathbf{A}}}over¯ start_ARG bold_A end_ARG after sparsification.
It is possible to see that for small increments of ϵitalic-ϵ\epsilonitalic_ϵ the spectral distance increases linearly, while the number of edges in the graph drops exponentially. | The GNN is then trained to fit its node representations to these pre-determined structures.
Pre-computing graph coarsening not only makes the training much faster by avoiding to perform graph reduction at every forward pass, but it also provides a strong inductive bias that prevents degenerate solutions, such as entire... | The reason can be once again attributed to the low information content of the individual node features and in the sparsity of the graph signal (most node features are 0), which makes it difficult for the feature-based pooling methods to infer global properties of the graph by looking at local sub-structures.
| We notice that the coarsened graphs are pre-computed before training the GNN.
Therefore, the computational time of graph coarsening is much lower compared to training the GNN for several epochs, since each MP operation in the GNN has a cost 𝒪(N2)𝒪superscript𝑁2\mathcal{O}(N^{2})caligraphic_O ( italic_N start_POSTSUP... |
The proposed spectral algorithm is not designed to handle very dense graphs; an intuitive explanation is that 𝐯maxssubscriptsuperscript𝐯𝑠max{\mathbf{v}}^{s}_{\text{max}}bold_v start_POSTSUPERSCRIPT italic_s end_POSTSUPERSCRIPT start_POSTSUBSCRIPT max end_POSTSUBSCRIPT can be interpreted as the graph signal with the... | A |
Fernández-Delgado et al. (2014) conduct extensive experiments comparing 179 classifiers on 121 UCI datasets (Dua & Graff, 2017). The authors show that random forests perform best, followed by support vector machines with a radial basis function kernel. Therefore, random forests are often considered as a reference for n... | Random forests are trained with 500500500500 decision trees, which are commonly used in practice (Fernández-Delgado et al., 2014; Olson et al., 2018).
The decision trees are constructed up to a maximum depth of ten. For splitting, the Gini Impurity is used and N𝑁\sqrt{N}square-root start_ARG italic_N end_ARG features ... | The generalization performance has been widely studied. Zhang et al. (2017) demonstrate that deep neural networks are capable of fitting random labels and memorizing the training data. Bornschein et al. (2020) analyze the performance across different dataset sizes.
Olson et al. (2018) evaluate the performance of modern... | Mapping random forests into neural networks is already used in many applications such as network initialization (Humbird et al., 2019), camera localization (Massiceti et al., 2017), object detection (Reinders et al., 2018, 2019), or semantic segmentation (Richmond et al., 2016).
State-of-the-art methods (Massiceti et a... | Neural networks have become very popular in many areas, such as computer vision (Krizhevsky et al., 2012; Reinders et al., 2022; Ren et al., 2015; Simonyan & Zisserman, 2015; Zhao et al., 2017; Qiao et al., 2021; Rudolph et al., 2022; Sun et al., 2021), speech recognition (Graves et al., 2013; Park et al., 2019; Sun et... | B |
Coupled with powerful function approximators such as neural networks, policy optimization plays a key role in the tremendous empirical successes of deep reinforcement learning (Silver et al., 2016, 2017; Duan et al., 2016; OpenAI, 2019; Wang et al., 2018). In sharp contrast, the theoretical understandings of policy opt... | for any function f:𝒮→ℝ:𝑓→𝒮ℝf:{\mathcal{S}}\rightarrow\mathbb{R}italic_f : caligraphic_S → blackboard_R. By allowing the reward function to be adversarially chosen in each episode, our setting generalizes the stationary setting commonly adopted by the existing work on value-based reinforcement learning (Jaksch et al.... | Our work is based on the aforementioned line of recent work (Fazel et al., 2018; Yang et al., 2019a; Abbasi-Yadkori et al., 2019a, b; Bhandari and Russo, 2019; Liu et al., 2019; Agarwal et al., 2019; Wang et al., 2019) on the computational efficiency of policy optimization, which covers PG, NPG, TRPO, PPO, and AC. In p... |
A line of recent work (Fazel et al., 2018; Yang et al., 2019a; Abbasi-Yadkori et al., 2019a, b; Bhandari and Russo, 2019; Liu et al., 2019; Agarwal et al., 2019; Wang et al., 2019) answers the computational question affirmatively by proving that a wide variety of policy optimization algorithms, such as policy gradient... |
Broadly speaking, our work is related to a vast body of work on value-based reinforcement learning in tabular (Jaksch et al., 2010; Osband et al., 2014; Osband and Van Roy, 2016; Azar et al., 2017; Dann et al., 2017; Strehl et al., 2006; Jin et al., 2018) and linear settings (Yang and Wang, 2019b, a; Jin et al., 2019;... | C |
Compared to ResNets, DenseNets achieve similar performance, allow for even deeper architectures, and they are more parameter and computation efficient.
However, the DenseNet architecture is highly non-uniform which complicates the hardware mapping and ultimately slows down training. | By using depthwise-separable convolutions, the number of trainable parameters as well as the number of multiply-accumulate operations (MACs) can be substantially reduced.
It is empirically shown that this has little to no negative impact on prediction quality. | The challenge is to reduce the number of bits as much as possible while at the same time keeping the prediction accuracy close to that of a well-tuned full-precision DNN.
Subsequently, we provide a literature overview of approaches that train reduced-precision DNNs, and, in a broader view, we also consider methods that... | In this regard, resource-efficient neural networks for embedded systems are concerned with the trade-off between prediction quality and resource efficiency (i.e., representational efficiency and computational efficiency). This is highlighted in Figure 1.
Note that this requires observing overall constraints such as pre... | Section 5.1 explored the impact of several network quantization approaches and structured pruning on the prediction quality.
In this section. we use the well-performing LQ-Net approach for quantization and PSP (for channel pruning) to measure the inference throughput of the quantized and pruned models separately on an ... | A |
(iλ,λ′)∗(ω0)=ω1+ω2subscriptsubscript𝑖𝜆superscript𝜆′subscript𝜔0subscript𝜔1subscript𝜔2(i_{\lambda,\lambda^{\prime}})_{*}(\omega_{0})=\omega_{1}+\omega_{2}( italic_i start_POSTSUBSCRIPT italic_λ , italic_λ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT end_POSTSUBSCRIPT ) start_POSTSUBSCRIPT ∗ end_POSTSUBSCRIPT ( ita... | ω1 is the degree-1 homology class induced bysubscript𝜔1 is the degree-1 homology class induced by\displaystyle\omega_{1}\text{ is the degree-1 homology class induced by }italic_ω start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT is the degree-1 homology class induced by
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ω0 is the degree-1 homology class induced bysubscript𝜔0 is the degree-1 homology class induced by\displaystyle\omega_{0}\text{ is the degree-1 homology class induced by }italic_ω start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT is the degree-1 homology class induced by |
ω2 is the degree-1 homology class induced bysubscript𝜔2 is the degree-1 homology class induced by\displaystyle\omega_{2}\text{ is the degree-1 homology class induced by }italic_ω start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT is the degree-1 homology class induced by | and seeks the infimal r>0𝑟0r>0italic_r > 0 such that the map induced by ιrsubscript𝜄𝑟\iota_{r}italic_ι start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT at n𝑛nitalic_n-th homology level annihilates the fundamental class [M]delimited-[]𝑀[M][ italic_M ] of M𝑀Mitalic_M. This infimal value defines FillRad(M)FillRad𝑀\m... | B |
As described in Subsection 6.1, we complemented the data from the tasks themselves by using the ICE-T methodology and questionnaire to gather and compare structured user feedback from both groups. The scores obtained from all participants, for all ICE-T components, can be seen in Table II. Larger is better, with green ... | The observed conclusions are confirmed when we compare the component-wise CIs for both groups—since none of them overlap—and the results of all component-wise Mann-Whitney U tests, with all U’s well below the critical value of 47, showing that t-viSNE had significantly larger scores in all four ICE-T components. These ... |
A quick visual inspection of the two tables already hints at t-viSNE having superior scores than GEP in all components, with all cells being green-colored (as opposed to GEP’s table, which contains many red-colored cells). Indeed, the smallest score for t-viSNE was 4.75, while GEP got many scores under 4 (or even unde... | In this paper, we introduced t-viSNE, an interactive tool for the visual investigation of t-SNE projections. By partly opening the black box of the t-SNE algorithm, we managed to give power to users allowing them to test the quality of the projections and understand the rationale behind the choices of the algorithm whe... | On the other hand, t-viSNE obtained consistently higher scores for Tool Supportiveness, with a higher average in all the proposed tasks. The bulk of the distributions of the supportiveness scores from the two groups overlap little, mostly near outliers (the “N/A” option was chosen three times, all in the GEP group).
Wh... | B |
More in detail, in these algorithms we have a population with individuals that have the ability to breed and produce new offspring. Therefore, from the parents, we get children, which introduces some variety with respect to their parents. These characteristics allow them to adapt to the environment which, translated t... |
Figure 2 depicts the classification we have reached, indicating, for the 518 reviewed algorithms, the number and ratio of proposals classified in each category and subcategory. It can be observed that the largest group of all is Swarm Intelligence category (more than a half of the proposed, 53%), inspired in the Swarm... | We have reviewed 518 nature- and bio-inspired algorithms and grouped them into two taxonomies. The first taxonomy has considered the source of inspiration, while the second has discriminated algorithms based on their behavior in generating new candidate solutions. We have provided clear descriptions, examples, and an e... | Table 2 compiles all reviewed algorithms that fall within this category. As could have been a priori expected, well-known classical Evolutionary Computation algorithms can be observed in this list, such as Genetic Algorithm (GA), Evolution Strategies (ES), and Differential Evolution (DE). However, other algorithms base... | The second and third most influential algorithms are GA, a very classic algorithm, and DE, a well-known algorithm whose natural inspiration resides only in the evolution of a population. Both have been used by around 5% of all reviewed nature-inspired algorithms, and they are the most representative approach in the Evo... | C |
where φ(⋅)𝜑⋅\varphi(\cdot)italic_φ ( ⋅ ) is certain activation function, A^=D~−12A~D~−12^𝐴superscript~𝐷12~𝐴superscript~𝐷12\hat{A}=\widetilde{D}^{-\frac{1}{2}}\widetilde{A}\widetilde{D}^{-\frac{1}{2}}over^ start_ARG italic_A end_ARG = over~ start_ARG italic_D end_ARG start_POSTSUPERSCRIPT - divide start_ARG 1 e... |
Figure 1: Framework of AdaGAE. k0subscript𝑘0k_{0}italic_k start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT is the initial sparsity. First, we construct a sparse graph via the generative model defined in Eq. (7). The learned graph is employed to apply the GAE designed for the weighted graphs. After training the GAE, we update ... | (1) Via extending the generative graph models into general type data, GAE is naturally employed as the basic representation learning model and weighted graphs can be further applied to GAE as well. The connectivity distributions given by the generative perspective also inspires us to devise a novel architecture for dec... | Network embedding is a fundamental task for graph type data such as recommendation systems, social networks, etc.
The goal is to map nodes of a given graph into latent features (namely embedding) such that the learned embedding can be utilized on node classification, node clustering, and link prediction. | To apply graph convolution on unsupervised learning, GAE is proposed [20].
GAE firstly transforms each node into latent representation (i.e., embedding) via GCN, and then aims to reconstruct some part of the input. GAEs proposed in [20, 29, 22] intend to reconstruct the adjacency via decoder while GAEs developed in [21... | D |
Closely related to volunteers is the vantage points measurements with faulty or misconfigured servers. (Mauch, 2013) noticed that some DNS resolvers do not change the source IP addresses of the DNS requests that they forward to upstream resolvers and return the DNS responses using the IP addresses of the upstream reso... |
∙∙\bullet∙ Limited representativeness. Volunteer or crowd-sourcing studies, such as the Spoofer Project (Lone et al., 2018), are inherently limited due to bias introduced by the participants. These measurements are performed using a limited number of vantage points, which are set up in specific networks, and hence are... | Vantage Points. Measurement of networks which do not perform egress filtering of packets with spoofed IP addresses was first presented by the Spoofer Project in 2005 (Beverly and Bauer, 2005). The idea behind the Spoofer Project is to craft packets with spoofed IP addresses and check receipt thereof on the vantage poin... | Since the Open Resolver and the Spoofer Projects are the only two infrastructures providing vantage points for measuring spoofing - their importance is immense as they facilitated many research works analysing the spoofability of networks based on the datasets collected by these infrastructures. Nevertheless, the studi... | How widespread is the ability to spoof? There are significant research and operational efforts to understand the extent and the scope of (ingress and egress)-filtering enforcement and to characterise the networks which do not filter spoofed packets; we discuss these in Related Work, Section 2. Although the existing stu... | C |
For each batch T𝑇Titalic_T from 3 through 10, the batches 1,2,…,T−112…𝑇11,2,\ldots,T-11 , 2 , … , italic_T - 1 were used to train skill NN and context+skill NN models for 30 random initializations of the starting weights. The accuracy was measured classifying examples from batch T𝑇Titalic_T (Fig. 3A, Table 1, Skill... | An alternative approach is to emulate adaptation in natural sensor systems. The system expects and automatically adapts to sensor drift, and is thus able to maintain its accuracy for a long time. In this manner, the lifetime of sensor systems can be extended without recalibration.
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Second, skill NN and context+skill NN models were compared. The context-based network extracts features from preceding batches in sequence in order to model how the sensors drift over time. When added to the feedforward NN representation, such contextual information resulted in improved ability to compensate for senso... | While natural systems cope with changing environments and embodiments well, they form a serious challenge for artificial systems. For instance, to stay reliable over time, gas sensing systems must be continuously recalibrated to stay accurate in a changing physical environment. Drawing motivation from nature, this pape... |
The purpose of this study was to demonstrate that explicit representation of context can allow a classification system to adapt to sensor drift. Several gas classifier models were placed in a setting with progressive sensor drift and were evaluated on samples from future contexts. This task reflects the practical goal... | D |
For the second change, we need to take another look at how we place the separators tisubscript𝑡𝑖t_{i}italic_t start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT.
We previously placed these separators in every second nonempty drum σi:=[iδ,(i+1)δ]×Balld−1(δ/2)assignsubscript𝜎𝑖𝑖𝛿𝑖1𝛿superscriptBall𝑑1𝛿2\sigma_{i}:=... | We generalize the case of integer x𝑥xitalic_x-coordinates to the case where the drum [x,x+1]×Balld−1(δ/2)𝑥𝑥1superscriptBall𝑑1𝛿2[x,x+1]\times\mathrm{Ball}^{d-1}(\delta/2)[ italic_x , italic_x + 1 ] × roman_Ball start_POSTSUPERSCRIPT italic_d - 1 end_POSTSUPERSCRIPT ( italic_δ / 2 ) contains O(1)𝑂1O(1)italic_O ( ... | It would be interesting to see whether a direct proof can be given for this fundamental result.
We note that the proof of Theorem 2.1 can easily be adapted to point sets of which the x𝑥xitalic_x-coordinates of the points need not be integer, as long as the difference between x𝑥xitalic_x-coordinates of any two consecu... | Finally, we will show that the requirements for Lemma 5.7 hold, where we take 𝒜𝒜\mathcal{A}caligraphic_A to be the algorithm described above.
The only nontrivial requirement is that T𝒜(Pλ)⩽T𝒜(P)subscript𝑇𝒜subscript𝑃𝜆subscript𝑇𝒜𝑃T_{\mathcal{A}}(P_{\lambda})\leqslant T_{\mathcal{A}}(P)italic_T start_POSTSUBS... | However, in order for our algorithm to meet the requirements of Lemma 5.7, we would like to avoid having a point enter a drum after the x𝑥xitalic_x-coordinates are multiplied by some factor λ>1𝜆1\lambda>1italic_λ > 1.
Furthermore, since the proof of Lemma 4.3 requires every drum to be at least δ𝛿\deltaitalic_δ wide,... | D |
While we define the congruence over Q∗superscript𝑄Q^{*}italic_Q start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT, we are only interested in the generated semigroup and let Σ(𝒜)=Q+/=𝒜\Sigma(\mathcal{A})=Q^{+}/{=_{\mathcal{A}}}roman_Σ ( caligraphic_A ) = italic_Q start_POSTSUPERSCRIPT + end_POSTSUPERSCRIPT / = start_POSTS... | from one to the other, then their free product S⋆T⋆𝑆𝑇S\star Titalic_S ⋆ italic_T is an automaton semigroup (8). This is again a strict generalization of [19, Theorem 3.0.1] (even if we only consider complete automata).
Third, we show this result in the more general setting of self-similar semigroups111Note that the c... | A semigroup arising in this way is called self-similar. Furthermore, if the generating automaton is finite, it is an automaton semigroup.
If the generating automaton is additionally complete, we speak of a completely self-similar semigroup or of a complete automaton semigroup. | Let S𝑆Sitalic_S be a (completely) self-similar semigroup and let T𝑇Titalic_T be a finite or free semigroup. Then S⋆T⋆𝑆𝑇S\star Titalic_S ⋆ italic_T is (completely) self-similar. If furthermore S𝑆Sitalic_S is a (complete) automaton semigroup, then so is S⋆T⋆𝑆𝑇S\star Titalic_S ⋆ italic_T.
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Let S𝑆Sitalic_S be a (completely) self-similar semigroup. Then S⋆t+⋆𝑆superscript𝑡S\star t^{+}italic_S ⋆ italic_t start_POSTSUPERSCRIPT + end_POSTSUPERSCRIPT is (completely) self-similar. Furthermore, if S𝑆Sitalic_S is a (complete) automaton semigroup, then so is S⋆t+⋆𝑆superscript𝑡S\star t^{+}italic_S ⋆ italic_t ... | B |
Some recent approaches employ a question-only branch as a control model to discover the questions most affected by linguistic correlations. The question-only model is either used to perform adversarial regularization Grand and Belinkov (2019); Ramakrishnan et al. (2018) or to re-scale the loss based on the difficulty o... |
The VQA-CP dataset Agrawal et al. (2018) showcases this phenomenon by incorporating different question type/answer distributions in the train and test sets. Since the linguistic priors in the train and test sets differ, models that exploit these priors fail on the test set. To tackle this issue, recent works have ende... | To reduce the reliance on linguistic priors, visual sensitivity enhancement methods attempt to train the model to be more sensitive to relevant visual regions when answering questions. Following Wu and Mooney (2019), we define the sensitivity of an answer a𝑎aitalic_a with respect to a visual region visubscript𝑣𝑖v_{i... |
Both Human Importance Aware Network Tuning (HINT) Selvaraju et al. (2019) and Self Critical Reasoning (SCR) Wu and Mooney (2019), train the network to be more sensitive towards salient image regions by improving the alignment between visual cues and gradient-based sensitivity scores. HINT proposes a ranking loss betwe... |
HINT uses a ranking loss, which penalizes the model if the pair-wise rankings of the sensitivities of visual regions towards ground truth answers agtsubscript𝑎𝑔𝑡a_{gt}italic_a start_POSTSUBSCRIPT italic_g italic_t end_POSTSUBSCRIPT are different from the ranks computed from the human-based attention maps. | C |
For the URL model, the words in the URL path were extracted and the tf-idf of each term was recorded to create the features (Baykan et al., 2009). As privacy policy URLs tend to be shorter and have fewer path segments than typical URLs, length and the number of path segments were added as features. Since the classes w... |
In order to address the requirement of a language model for the privacy domain, we created PrivBERT. BERT is a contextualized word representation model that is pretrained using bidirectional transformers (Devlin et al., 2019). It was pretrained on the masked language modelling and the next sentence prediction tasks an... | To train the RoBERTa model on the privacy policy classification task, we used the sequence classification head of the pretrained language model from HuggingFace (Wolf et al., 2019). We used the pretrained RoBERTa tokenizer to tokenize text extracted from the documents. Since Roberta accepts a maximum of 512 tokens as i... |
We use the byte pair encoding tokenization technique utilized in RoBERTa and retain its cased vocabulary. We did not create a new vocabulary since the two vocabularies are not significantly different and any out-of-vocabulary words can be represented and tuned for the privacy domain using the byte pair encoding vocabu... | Table 2 shows the results for the data practice classification task comparing the performance between RoBERTa, PrivBERT and Polisis (Harkous et al., 2018), a CNN based classification model. We report reproduced results for Polisis since the original paper takes into account both the presence and absence of a label whil... | B |
T4: Compare the results of two stages and receive feedback to guide interaction. To assist the knowledge generation, a comparison between the currently active stack against previously stored versions is important. In general, this includes monitoring the historical process of the stacking ensemble, facilitating intera... | The use of visualization for ensemble learning could possibly introduce further biases to the already blurry situation based on the different ML models involved. Thus, the thorough selection of both interaction techniques and visual representations that highlight and potentially overcome any cognitive biases is a major... | T5: Inspect the same view with alternative techniques and visualizations. To eventually avoid the appearance of cognitive biases, alternative interaction methods and visual representations of the same data from another perspective should be offered to the user (G5).
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G5: Reveal and reduce cognitive biases. Visualizations should be carefully chosen in order to reduce cognitive biases. Cognitive bias is, in simple terms, a human judgment that drifts away from the actual information that should be conveyed by a visualization, i.e., it “involves a deviation from reality that is predic... | Interpretability and explainability is another challenge (mentioned by E3) in complicated ensemble methods, which is not necessarily always a problem depending on the data and the tasks. However, the utilization of user-selected weights for multiple validation metrics is one way towards interpreting and trusting the re... | B |
We thus have 3333 cases, depending on the value of the tuple
(p(v,[010]),p(v,[323]),p(v,[313]),p(v,[003]))𝑝𝑣delimited-[]010𝑝𝑣delimited-[]323𝑝𝑣delimited-[]313𝑝𝑣delimited-[]003(p(v,[010]),p(v,[323]),p(v,[313]),p(v,[003]))( italic_p ( italic_v , [ 010 ] ) , italic_p ( italic_v , [ 323 ] ) , italic_p ( italic_v... | {0¯,1¯,2¯,3¯,[013],[010],[323],[313],[112],[003],[113]}.¯0¯1¯2¯3delimited-[]013delimited-[]010delimited-[]323delimited-[]313delimited-[]112delimited-[]003delimited-[]113\{\overline{0},\overline{1},\overline{2},\overline{3},[013],[010],[323],[313],%
[112],[003],[113]\}.{ over¯ start_ARG 0 end_ARG , over¯ start_ARG 1 end... | By using the pairwise adjacency of (v,[112])𝑣delimited-[]112(v,[112])( italic_v , [ 112 ] ), (v,[003])𝑣delimited-[]003(v,[003])( italic_v , [ 003 ] ), and
(v,[113])𝑣delimited-[]113(v,[113])( italic_v , [ 113 ] ), we can confirm that in the 3333 cases, these | Then, by using the adjacency of (v,[013])𝑣delimited-[]013(v,[013])( italic_v , [ 013 ] ) with each of
(v,[010])𝑣delimited-[]010(v,[010])( italic_v , [ 010 ] ), (v,[323])𝑣delimited-[]323(v,[323])( italic_v , [ 323 ] ), and (v,[112])𝑣delimited-[]112(v,[112])( italic_v , [ 112 ] ), we can confirm that | p(v,[013])=p(v,[313])=p(v,[113])=1𝑝𝑣delimited-[]013𝑝𝑣delimited-[]313𝑝𝑣delimited-[]1131p(v,[013])=p(v,[313])=p(v,[113])=1italic_p ( italic_v , [ 013 ] ) = italic_p ( italic_v , [ 313 ] ) = italic_p ( italic_v , [ 113 ] ) = 1.
Similarly, when f=[112]𝑓delimited-[]112f=[112]italic_f = [ 112 ], | B |
We use Transformer [Vaswani et al., 2017] as the base model in dialogue generation experiment.
In Persona, we use pre-trained Glove embedding [Pennington et al., 2014]. In Weibo, we use Gensim [Rehurek and Sojka, 2010]. We follow the other hyperparameter settings in [Madotto et al., 2019]. | We use Transformer [Vaswani et al., 2017] as the base model in dialogue generation experiment.
In Persona, we use pre-trained Glove embedding [Pennington et al., 2014]. In Weibo, we use Gensim [Rehurek and Sojka, 2010]. We follow the other hyperparameter settings in [Madotto et al., 2019]. | In text classification experiment, we use accuracy (Acc) to evaluate the classification performance.
In dialogue generation experiment, we evaluate the performance of MAML in terms of quality and personality. We use PPL and BLEU [Papineni et al., 2002] to measure the similarity between the reference and the generated r... |
To answer RQ1, we compare the changing trend of the general language model and the task-specific adaptation ability during the training of MAML to find whether there is a trade-off problem. (Figure 1) We select the trained parameter initialization at different MAML training epochs and evaluate them directly on the met... |
To answer RQ2, we find the fine-tuning epochs for each task in Persona where its BLEU and C Score reaches the best respectively to find the impact of data quantity and the task profile (persona description) on fine-tuning. (Table 1) We cluster the tasks with similar best fine-tuning epoch number and calculate the aver... | B |
A conceptual frame structure is designed which contains two types of time slots. One is the exchanging slot (e-slot) and the other is the tracking slot (t-slot). Let us first focus on the e-slot. It is assumed that UAVs exchange MSI every T𝑇Titalic_T t-slots, i.e., in an e-slot, to save resource for payload transmissi... |
Moreover, the data block of MSI is set as BMSI=nMSI×T×BMSIsubscript𝐵MSIsubscript𝑛MSI𝑇subscript𝐵MSIB_{\text{MSI}}=n_{\text{MSI}}\times T\times B_{\text{MSI}}italic_B start_POSTSUBSCRIPT MSI end_POSTSUBSCRIPT = italic_n start_POSTSUBSCRIPT MSI end_POSTSUBSCRIPT × italic_T × italic_B start_POSTSUBSCRIPT MSI end_POSTS... | The GP-based MSI prediction is proposed to solve the problem in [31].
Specifically, the r-UAV/t-UAV’s historical MSI is first exchanged with the t-UAV/r-UAV over a lower-frequency band and then the t-UAV will predict the future MSI of the r-UAV based on the historical MSI by using the GP-based MSI prediction model. | The tracking error of beam angles has a negative influence on the beam gain obtained by CCA. The proposed tracking error bounding algorithm uses the position/attitiude prediction error of the GP-based MSI prediction to obtain the beam angle tracking error, wherein the geometry relationship between UAVs and the Monte-Ca... | A conceptual frame structure is designed which contains two types of time slots. One is the exchanging slot (e-slot) and the other is the tracking slot (t-slot). Let us first focus on the e-slot. It is assumed that UAVs exchange MSI every T𝑇Titalic_T t-slots, i.e., in an e-slot, to save resource for payload transmissi... | C |
There are other logics, incomparable
in expressiveness with 𝖥𝖮Pres2subscriptsuperscript𝖥𝖮2Pres\mathsf{FO}^{2}_{\textup{Pres}}sansserif_FO start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT Pres end_POSTSUBSCRIPT, where periodicity of the spectrum has been proven [17]. The | The paper [4] shows decidability for a logic with incomparable expressiveness: the quantification allows a more powerful
quantitative comparison, but must be guarded – restricting the counts only of sets of elements that are adjacent to a given element. | Related one-variable fragments in which we have only a
unary relational vocabulary and the main quantification is ∃Sxϕ(x)superscript𝑆𝑥italic-ϕ𝑥\exists^{S}x~{}\phi(x)∃ start_POSTSUPERSCRIPT italic_S end_POSTSUPERSCRIPT italic_x italic_ϕ ( italic_x ) are known to be decidable (see, e.g. [2]), and their decidability ... | In addition, to make the main line of argument clearer, we consider only the finite graph case in the body of the paper,
which already implies decidability of the finite satisfiability of 𝖥𝖮Pres2subscriptsuperscript𝖥𝖮2Pres\mathsf{FO}^{2}_{\textup{Pres}}sansserif_FO start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT start_... | There are other logics, incomparable
in expressiveness with 𝖥𝖮Pres2subscriptsuperscript𝖥𝖮2Pres\mathsf{FO}^{2}_{\textup{Pres}}sansserif_FO start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT Pres end_POSTSUBSCRIPT, where periodicity of the spectrum has been proven [17]. The | A |
The key to our analysis is a mean-field perspective, which allows us to associate the evolution of a finite-dimensional parameter with its limiting counterpart over an infinite-dimensional Wasserstein space (Villani, 2003, 2008; Ambrosio et al., 2008; Ambrosio and Gigli, 2013). Specifically, by exploiting the permutati... | Meanwhile, our analysis is related to the recent breakthrough in the mean-field analysis of stochastic gradient descent (SGD) for the supervised learning of an overparameterized two-layer neural network (Chizat and Bach, 2018b; Mei et al., 2018, 2019; Javanmard et al., 2019; Wei et al., 2019; Fang et al., 2019a, b; Che... |
In this paper, we study temporal-difference (TD) (Sutton, 1988) and Q-learning (Watkins and Dayan, 1992), two of the most prominent algorithms in deep reinforcement learning, which are further connected to policy gradient (Williams, 1992) through its equivalence to soft Q-learning (O’Donoghue et al., 2016; Schulman et... | Szepesvári, 2018; Dalal et al., 2018; Srikant and Ying, 2019) settings. See Dann et al. (2014) for a detailed survey. Also, when the value function approximator is linear, Melo et al. (2008); Zou et al. (2019); Chen et al. (2019b) study the convergence of Q-learning. When the value function approximator is nonlinear, T... |
Related Work. When the value function approximator is linear, the convergence of TD is extensively studied in both continuous-time (Jaakkola et al., 1994; Tsitsiklis and Van Roy, 1997; Borkar and Meyn, 2000; Kushner and Yin, 2003; Borkar, 2009) and discrete-time (Bhandari et al., 2018; Lakshminarayanan and | D |
Directly replacing residual connections with LSTM units will introduce a large amount of additional parameters and computation. Given that the task of computing the LSTM hidden state is similar to the feed-forward sub-layer in the original Transformer layers, we propose to replace the feed-forward sub-layer with the ne... | We also study the merging operations, concatenation, element-wise addition, and the use of 2 depth-wise LSTM sub-layers, to combine the masked self-attention sub-layer output and the cross-attention sub-layer output in decoder layers. Results are shown in Table 4.
| Specifically, the decoder layer with depth-wise LSTM first computes the masked self-attention sub-layer and the cross-attention sub-layer as in the original decoder layer, then it merges the outputs of these two sub-layers and feeds the merged representation into the depth-wise LSTM unit which also takes the cell and t... |
Different from encoder layers, decoder layers involve two multi-head attention sub-layers: a masked self-attention sub-layer to attend the decoding history and a cross-attention sub-layer to attend information from the source side. Given that the depth-wise LSTM unit only takes one input, we introduce a merging layer ... | The encoder layer with the depth-wise LSTM unit, as shown in Figure 2, first performs the self-attention computation, then the depth-wise LSTM unit takes the self-attention results and the output and the cell state of the previous layer to compute the output and the cell state of the current layer.
| D |
Assume that ℒX′subscriptsuperscriptℒ′𝑋\mathcal{L}^{\prime}_{X}caligraphic_L start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_X end_POSTSUBSCRIPT defines a diagram base of X𝑋Xitalic_X.
Consider a definable open set U∩Y∈ℒY𝑈𝑌subscriptℒ𝑌U\cap Y\in\mathcal{L}_{Y}italic_U ∩ italic_Y ∈ caligraphic_L... | particular, U∩Y∈ℒY𝑈𝑌subscriptℒ𝑌U\cap Y\in\mathcal{L}_{Y}italic_U ∩ italic_Y ∈ caligraphic_L start_POSTSUBSCRIPT italic_Y end_POSTSUBSCRIPT is a definable open set of
Y𝑌Yitalic_Y. By restriction, U∩X∈ℒX𝑈𝑋subscriptℒ𝑋U\cap X\in\mathcal{L}_{X}italic_U ∩ italic_X ∈ caligraphic_L start_POSTSUBSCRIPT italic_X end_POSTS... | where U∈ℒ𝑈ℒU\in\mathcal{L}italic_U ∈ caligraphic_L. Remark that U∩X∈ℒX𝑈𝑋subscriptℒ𝑋U\cap X\in\mathcal{L}_{X}italic_U ∩ italic_X ∈ caligraphic_L start_POSTSUBSCRIPT italic_X end_POSTSUBSCRIPT
is a definable open set in X𝑋Xitalic_X, hence there exists a family | ℒℒ\mathcal{L}caligraphic_L of ℘(Z)Weierstrass-p𝑍\wp(Z)℘ ( italic_Z ), we write ℒX≜{U∩X∣U∈ℒ}≜subscriptℒ𝑋conditional-set𝑈𝑋𝑈ℒ\mathcal{L}_{X}\triangleq\{U\cap X\mid U\in\mathcal{L}\}caligraphic_L start_POSTSUBSCRIPT italic_X end_POSTSUBSCRIPT ≜ { italic_U ∩ italic_X ∣ italic_U ∈ caligraphic_L } for the lattice induce... | Assume that ℒX′subscriptsuperscriptℒ′𝑋\mathcal{L}^{\prime}_{X}caligraphic_L start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_X end_POSTSUBSCRIPT defines a diagram base of X𝑋Xitalic_X.
Consider a definable open set U∩Y∈ℒY𝑈𝑌subscriptℒ𝑌U\cap Y\in\mathcal{L}_{Y}italic_U ∩ italic_Y ∈ caligraphic_L... | B |
The first limitation is that the principal point needs to be at the center of the image. Observing that the principal point is slightly disturbed around the center of the image, we mainly consider the estimation of distortion coefficients using the proposed ordinal distortion in our work. Nevertheless, our method can b... | In this section, we first state the details of the synthetic distorted image dataset and the training process of our learning model. Subsequently, we analyze the learning representation for distortion estimation. To demonstrate the effectiveness of each module in our framework, we conduct an ablation study to show the ... | The second limitation is that the distortion needs to be radially symmetric. This problem may be addressed by the grid optimization technique in computer graphics, and we can teach the network to learn an asymmetric grid to warp each pixel of the distorted image. Based on the above limitations and the presented solutio... | To demonstrate a quantitative comparison with the state-of-the-art approaches, we evaluate the rectified images based on the PSNR (peak signal-to-noise ratio), SSIM (structural similarity index), and the proposed MDLD (mean distortion level deviation). All the comparison methods are used to conduct the distortion recti... |
In contrast to the long history of traditional distortion rectification, learning methods began to study distortion rectification in the last few years. Rong et al. [8] quantized the values of the distortion parameter to 401 categories based on the one-parameter camera model [22] and then trained a network to classify... | B |
The momentum coefficient is set as 0.9 and the weight decay is set as 0.001. The initial learning rate is selected from {0.001,0.01,0.1}0.0010.010.1\{0.001,0.01,0.1\}{ 0.001 , 0.01 , 0.1 } according to the performance on the validation set. We do not adopt any learning rate decay or warm-up strategies.
The model is tra... | Hence, with the same number of gradient computations, SNGM can adopt a larger batch size than MSGD to converge to the ϵitalic-ϵ\epsilonitalic_ϵ-stationary point.
Empirical results on deep learning further verify that SNGM can achieve better test accuracy than MSGD and other state-of-the-art large-batch training methods... | Figure 2 shows the learning curves of the five methods. We can observe that in the small-batch training, SNGM and other large-batch training methods achieve similar performance in terms of training loss and test accuracy as MSGD.
In large-batch training, SNGM achieves better training loss and test accuracy than the fou... | Table 6 shows the test perplexity of the three methods with different batch sizes. We can observe that for small batch size, SNGM achieves test perplexity comparable to that of MSGD, and for large batch size, SNGM is better than MSGD. Similar to the results of image classification, SNGM outperforms LARS for different b... | showed that existing SGD methods with a large batch size will lead to a drop in the generalization accuracy of deep learning models. Figure 1
shows a comparison of training loss and test accuracy between MSGD with a small batch size and MSGD with a large batch size. We can find that large-batch training indeed | A |
5555-approximation for homogeneous 2S-MuSup-Poly, with |𝒮|≤2m𝒮superscript2𝑚|\mathcal{S}|\leq 2^{m}| caligraphic_S | ≤ 2 start_POSTSUPERSCRIPT italic_m end_POSTSUPERSCRIPT and runtime poly(n,m,Λ)poly𝑛𝑚Λ\operatorname*{poly}(n,m,\Lambda)roman_poly ( italic_n , italic_m , roman_Λ ).
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We follow up with 3333-approximations for the homogeneous robust outlier MatSup and MuSup problems, which are slight variations on algorithms of [6] (specifically, our approach in Section 4.1 is a variation on their solve-or-cut methods). In Section 5, we describe a 9-approximation algorithm for an inhomogeneous MatSu... | The other three results are based on a reduction to a single-stage, deterministic robust outliers problem described in Section 4; namely, convert any ρ𝜌\rhoitalic_ρ-approximation algorithm for the robust outlier problem into a (ρ+2)𝜌2(\rho+2)( italic_ρ + 2 )-approximation algorithm for the corresponding two-stage sto... | If we have a ρ𝜌\rhoitalic_ρ-approximation algorithm for AlgRW for given 𝒞,ℱ,ℳ,R𝒞ℱℳ𝑅\mathcal{C},\mathcal{F},\mathcal{M},Rcaligraphic_C , caligraphic_F , caligraphic_M , italic_R, then we can get an efficiently-generalizable (ρ+2)𝜌2(\rho+2)( italic_ρ + 2 )-approximation algorithm for the corresponding problem 𝒫𝒫\m... | We now describe a generic method of transforming a given 𝒫𝒫\mathcal{P}caligraphic_P-Poly problem into a single-stage deterministic robust outlier problem. This will give us a 5-approximation algorithm for homogeneous 2S-MuSup and 2S-MatSup instances nearly for free; in the next section, we also use it obtain our 11-a... | B |
In real networked systems, the information exchange among nodes is often affected by communication noises, and the structure of the network often changes randomly due to packet dropouts, link/node failures and recreations, which are studied in [8]-[10].
| However, a variety of random factors may co-exist in practical environment.
In distributed statistical machine learning algorithms, the (sub)gradients of local loss functions cannot be obtained accurately, the graphs may change randomly and the communication links may be noisy. There are many excellent results on the d... |
Motivated by distributed statistical learning over uncertain communication networks, we study the distributed stochastic convex optimization by networked local optimizers to cooperatively minimize a sum of local convex cost functions. The network is modeled by a sequence of time-varying random digraphs which may be sp... | Besides, the network graphs may change randomly with spatial and temporal dependency (i.e. Both the weights of different edges in the network graphs at the same time instant and the network graphs at different time instants may be mutually dependent.) rather than i.i.d. graph sequences as in [12]-[15],
and additive and... | such as the economic dispatch in power grids ([1]) and the traffic flow control in intelligent transportation networks ([2]), et al. Considering the various uncertainties in practical network environments, distributed stochastic optimization algorithms have been widely studied. The (sub)gradients of local cost function... | A |
In recent years, local differential privacy [12, 4] has attracted increasing attention because it is particularly useful in distributed environments where users submit their sensitive information to untrusted curator. Randomized response [10] is widely applied in local differential privacy to collect users’ statistics... | The advantages of MuCo are summarized as follows. First, MuCo can maintain the distributions of original QI values as much as possible. For instance, the sum of each column in Figure 3 is shown by the blue polyline in Figure 2, and the blue polyline almost coincides with the red polyline representing the distribution i... | Differential privacy [6, 38], which is proposed for query-response systems, prevents the adversary from inferring the presence or absence of any individual in the database by adding random noise (e.g., Laplace Mechanism [7] and Exponential Mechanism [24]) to aggregated results. However, differential privacy also faces ... |
In recent years, local differential privacy [12, 4] has attracted increasing attention because it is particularly useful in distributed environments where users submit their sensitive information to untrusted curator. Randomized response [10] is widely applied in local differential privacy to collect users’ statistics... | Note that, the application scenarios of differential privacy and the models of k𝑘kitalic_k-anonymity family are different. Differential privacy adds random noise to the answers of the queries issued by recipients rather than publishing microdata. While the approaches of k𝑘kitalic_k-anonymity family sanitize the origi... | D |
HTC is known as a competitive method for COCO and OpenImage. By enlarging the RoI size of both box and mask branches to 12 and 32 respectively for all three stages, we gain roughly 4 mAP improvement against the default settings in original paper. Mask scoring head Huang et al. (2019) adopted on the third stage gains an... |
Due to limited mask representation of HTC, we move on to SOLOv2, which utilizes much larger mask to segment objects. It builds an efficient yet simple instance segmentation framework, outperforming other segmentation methods like TensorMask Chen et al. (2019c), CondInst Tian et al. (2020) and BlendMask Chen et al. (20... | Bells and Whistles. MaskRCNN-ResNet50 is used as baseline and it achieves 53.2 mAP. For PointRend, we follow the same setting as Kirillov et al. (2020) except for extracting both coarse and fine-grained features from the P2-P5 levels of FPN, rather than only P2 described in the paper. Surprisingly, PointRend yields 62.... | Deep learning has achieved great success in recent years Fan et al. (2019); Zhu et al. (2019); Luo et al. (2021, 2023); Chen et al. (2021). Recently, many modern instance segmentation approaches demonstrate outstanding performance on COCO and LVIS, such as HTC Chen et al. (2019a), SOLOv2 Wang et al. (2020), and PointRe... | HTC is known as a competitive method for COCO and OpenImage. By enlarging the RoI size of both box and mask branches to 12 and 32 respectively for all three stages, we gain roughly 4 mAP improvement against the default settings in original paper. Mask scoring head Huang et al. (2019) adopted on the third stage gains an... | A |
For the significance of this conjecture we refer to the original paper [FK], and to Kalai’s blog [K] (embedded in Tao’s blog) which reports on all significant results concerning the conjecture. [KKLMS] establishes a weaker version of the conjecture. Its introduction is also a good source of information on the problem.
| For the significance of this conjecture we refer to the original paper [FK], and to Kalai’s blog [K] (embedded in Tao’s blog) which reports on all significant results concerning the conjecture. [KKLMS] establishes a weaker version of the conjecture. Its introduction is also a good source of information on the problem.
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In version 1 of this note, which can still be found on the ArXiv, we showed that the analogous version of the conjecture for complex functions on {−1,1}nsuperscript11𝑛\{-1,1\}^{n}{ - 1 , 1 } start_POSTSUPERSCRIPT italic_n end_POSTSUPERSCRIPT which have modulus 1111 fails. This solves a question raised by Gady Kozma s... |
Here we give an embarrassingly simple presentation of an example of such a function (although it can be shown to be a version of the example in the previous version of this note). As was written in the previous version, an anonymous referee of version 1 wrote that the theorem was known to experts but not published. Ma... | We denote by εi:{−1,1}n→{−1,1}:subscript𝜀𝑖→superscript11𝑛11\varepsilon_{i}:\{-1,1\}^{n}\to\{-1,1\}italic_ε start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT : { - 1 , 1 } start_POSTSUPERSCRIPT italic_n end_POSTSUPERSCRIPT → { - 1 , 1 } the projection onto the i𝑖iitalic_i-s coordinate: εi(δ1,…,δn)=δisubscript𝜀𝑖subsc... | B |
The proof idea is similar to that of Theorem 1. The only difference is that within each piecewise-stationary segment, we use the hard instance constructed by Zhou et al. (2021); Hu et al. (2022) for inhomogenous linear MDPs. Optimizing the length of each piecewise-stationary segment N𝑁Nitalic_N and the variation magni... |
In this section, we describe our proposed algorithm LSVI-UCB-Restart, and discuss how to tune the hyper-parameters for cases when local variation is known or unknown. For both cases, we present their respective regret bounds. Detailed proofs are deferred to Appendix B. Note that our algorithms are all designed for inh... |
The rest of the paper is organized as follows. Section 2 presents our problem definition. Section 3 establishes the minimax regret lower bound for nonstationary linear MDPs. Section 4 and Section 5 present our algorithms LSVI-UCB-Restart, Ada-LSVI-UCB-Restart and their dynamic regret bounds. Section 6 shows our experi... | In this section, we derive minimax regret lower bounds for nonstationary linear MDPs in both inhomogeneous and homogeneous settings, which quantify the fundamental difficulty when measured by the dynamic regret in nonstationary linear MDPs. More specifically, we consider inhomogeneous setting in this paper, where the t... |
In this paper, we studied nonstationary RL with time-varying reward and transition functions. We focused on the class of nonstationary linear MDPs such that linear function approximation is sufficient to realize any value function. We first incorporated the epoch start strategy into LSVI-UCB algorithm (Jin et al., 202... | A |
While fake news is not a new phenomenon, the 2016 US presidential election brought the issue to immediate global attention with the discovery that fake news campaigns on social media had been made to influence the election (Allcott and Gentzkow, 2017). The creation and dissemination of fake news is motivated by politic... | While fake news is not a new phenomenon, the 2016 US presidential election brought the issue to immediate global attention with the discovery that fake news campaigns on social media had been made to influence the election (Allcott and Gentzkow, 2017). The creation and dissemination of fake news is motivated by politic... | Fake news is news articles that are “either wholly false or containing deliberately misleading elements incorporated within its content or context” (Bakir and McStay, 2018). The presence of fake news has become more prolific on the Internet due to the ease of production and dissemination of information online (Shu et a... | Singapore is a city-state with an open economy and diverse population that shapes it to be an attractive and vulnerable target for fake news campaigns (Lim, 2019). As a measure against fake news, the Protection from Online Falsehoods and Manipulation Act (POFMA) was passed on May 8, 2019, to empower the Singapore Gover... | Many studies worldwide have observed the proliferation of fake news on social media and instant messaging apps, with social media being the more commonly studied medium. In Singapore, however, mitigation efforts on fake news in instant messaging apps may be more important. Most respondents encountered fake news on inst... | B |
In this work, we propose Decentralized Attention Network for knowledge graph embedding and introduce self-distillation to enhance its ability to generate desired embeddings for both known and unknown entities. We provide theoretical justification for the effectiveness of our proposed learning paradigm and conduct compr... | In this work, we propose Decentralized Attention Network for knowledge graph embedding and introduce self-distillation to enhance its ability to generate desired embeddings for both known and unknown entities. We provide theoretical justification for the effectiveness of our proposed learning paradigm and conduct compr... |
The performance of decentRL at the input layer notably lags behind that of other layers and AliNet. As discussed in previous sections, decentRL does not use the embedding of the central entity as input when generating its output embedding. However, this input embedding can still accumulate knowledge by participating i... | The existing methods for KG embedding and word embedding exhibit even more similarities. As shown in Figure 1, the KG comprises three triplets conveying similar information to the example sentence. Triplet-based KG embedding models like TransE [11] transform the embedding of each subject entity and its relation into a ... |
This work is funded by National Natural Science Foundation of China (NSFCU23B2055/NSFCU19B2027/NSFC91846204), Zhejiang Provincial Natural Science Foundation of China (No.LGG22F030011), and Fundamental Research Funds for the Central Universities (226-2023-00138). | D |
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