context stringlengths 250 4.63k | A stringlengths 250 4.99k | B stringlengths 250 4.17k | C stringlengths 250 5.14k | D stringlengths 250 8.2k | label stringclasses 4
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x2(x2−1)d2dx2Rnm(x)=[nx2(n+D)−m(D−2+m)]Rnm(x)+x[D−1−(D+1)x2]ddxRnm(x).superscript𝑥2superscript𝑥21superscript𝑑2𝑑superscript𝑥2superscriptsubscript𝑅𝑛𝑚𝑥delimited-[]𝑛superscript𝑥2𝑛𝐷𝑚𝐷2𝑚superscriptsubscript𝑅𝑛𝑚𝑥𝑥delimited-[]𝐷1𝐷1superscript𝑥2𝑑𝑑𝑥superscriptsubscript𝑅𝑛𝑚𝑥x^{2}(x^{2}-... | ^{2}-m^{2}\right]x^{2}\\
+D^{2}+D(m-1)-2m+m^{2}\Big{\}}\frac{d}{dx}R_{n}^{m}(x).start_ROW start_CELL italic_x start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT ( italic_x start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT - 1 ) start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT divide start_ARG italic_d start_POSTSUPERSCRIPT 3 end_POSTSUP... | +x\left[D-1-(D+1)x^{2}\right]\frac{d}{dx}R_{n}^{m}(x).start_ROW start_CELL italic_x start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ( italic_x start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT - 1 ) divide start_ARG italic_d start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT end_ARG start_ARG italic_d italic_x start_POSTSUPERSCRIPT 2 e... | }\left[\left(n(n+D)-\frac{m(D-2+m)}{x^{2}}\right)\frac{R_{n}^{m}(x)}{{R_{n}^{m%
}}^{\prime}(x)}+\frac{D-1-(D+1)x^{2}}{x}\right].divide start_ARG italic_R start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_m end_POSTSUPERSCRIPT start_POSTSUPERSCRIPT ′ ′ end_POSTSUPERSCRIPT ( italic_x ) end_ARG s... | {n,n^{\prime}}.∫ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 1 end_POSTSUPERSCRIPT italic_x start_POSTSUPERSCRIPT italic_D - 1 end_POSTSUPERSCRIPT italic_R start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_m end_POSTSUPERSCRIPT ( italic_x ) italic_R start_POSTSUBSCRIPT italic... | B |
The sets T2subscript𝑇2T_{2}italic_T start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT and T3subscript𝑇3T_{3}italic_T start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT are computed as described above in preparation for the first column clearing stage, but are subsequently computed via the recursion (3) (with increased memory quota relati... | To aid the exposition and analysis, Algorithm 3 refers to several subroutines, namely Algorithms 4–7. In an implementation the code for the Algorithms 4–7 would be inserted into Algorithm 3 in the lines where they are called. We present them as subroutines here to improve the readability of Algorithm 3. However, we ass... | The case where d𝑑ditalic_d is even is very similar, but requires a few changes that would complicate the pseudocode.
So, for the clarity of our exposition, we analyse the case d𝑑ditalic_d odd here and then explain the differences for the case d𝑑ditalic_d even in the next subsection. |
Although the described modifications are not complicated in and of themselves, they would introduce noticeable complications into our pseudocode and hence we have chosen to separate the d𝑑ditalic_d even case for the sake of clearer exposition, opting to simply point out and explain the changes instead of writing them... | Let us now explain the changes required when d𝑑ditalic_d is even.
The main issue is that the formula (3) used to compute the sets of transvections Tisubscript𝑇𝑖T_{i}italic_T start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT recursively throughout our implementation of the algorithm described by Taylor looks two steps b... | C |
It then follows from Lemma 1 that 1≤αiF≤α1superscriptsubscript𝛼𝑖𝐹𝛼1\leq\alpha_{i}^{F}\leq\alpha1 ≤ italic_α start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_F end_POSTSUPERSCRIPT ≤ italic_α for all the local eigenvalues. Thus, Λ~h△=Λ~hfsuperscriptsubscript~Λℎ△superscriptsubscript~Λℎ𝑓\ti... | 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... | 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... |
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... |
The key to approximate (25) is the exponential decay of Pw𝑃𝑤Pwitalic_P italic_w, as long as w∈H1(𝒯H)𝑤superscript𝐻1subscript𝒯𝐻w\in{H^{1}({\mathcal{T}_{H}})}italic_w ∈ italic_H start_POSTSUPERSCRIPT 1 end_POSTSUPERSCRIPT ( caligraphic_T start_POSTSUBSCRIPT italic_H end_POSTSUBSCRIPT ) has local support. That al... | A |
Moreover, Alg-A is more stable than the alternatives.
During the iterations of Alg-CM, the coordinates of three corners and two midpoints of a P-stable triangle (see Figure 37) are maintained. These coordinates are computed somehow and their true values can differ from their values stored in the computer. Alg-CM uses a... | 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.) |
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. | 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. | D |
. As shown in Table 5, CreditScore is the best feature in overall. In Figure 4 we show the result of models learned with the full feature set with and without CreditScore. Overall, adding CreditScore improves the performance, especially for the first 8-10 hours. The performance of all-but-CreditScore jiggles a bit afte... |
We observe that at certain points in time, the volume of rumor-related tweets (for sub-events) in the event stream surges. This can lead to false positives for techniques that model events as the aggregation of all tweet contents; that is undesired at critical moments. We trade-off this by debunking at single tweet le... | at an early stage. Our fully automatic, cascading rumor detection method follows
the idea on focusing on early rumor signals on text contents; which is the most reliable source before the rumors widely spread. Specifically, we learn a more complex representation of single tweets using Convolutional Neural Networks, tha... | . We showcase here a study of the Munich shooting. We first show the event timeline at an early stage. Next we discuss some examples of misclassifications by our “weak” classifier and show some analysis on the strength of some highlighted features. The rough event timeline looks as follows.
|
In this work, we propose an effective cascaded rumor detection approach using deep neural networks at tweet level in the first stage and wisdom of the “machines”, together with a variety of other features in the second stage, in order to enhance rumor detection performance in the early phase of an event. The proposed ... | C |
\left(\sqrt{\frac{\log\log t}{\log t}}\right)∥ divide start_ARG bold_w ( italic_t ) end_ARG start_ARG ∥ bold_w ( italic_t ) ∥ end_ARG - divide start_ARG over^ start_ARG bold_w end_ARG end_ARG start_ARG ∥ over^ start_ARG bold_w end_ARG ∥ end_ARG ∥ = italic_O ( square-root start_ARG divide start_ARG roman_log roman_log i... |
where the residual 𝝆k(t)subscript𝝆𝑘𝑡\boldsymbol{\rho}_{k}(t)bold_italic_ρ start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT ( italic_t ) is bounded and 𝐰^ksubscript^𝐰𝑘\hat{\mathbf{w}}_{k}over^ start_ARG bold_w end_ARG start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT is the solution of the K-class SVM: | 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... | In some non-degenerate cases, we can further characterize the asymptotic behavior of 𝝆(t)𝝆𝑡\boldsymbol{\rho}\left(t\right)bold_italic_ρ ( italic_t ). To do so, we need to refer to the KKT conditions (eq. 6)
of the SVM problem (eq. 4) and the associated | where 𝝆(t)𝝆𝑡\boldsymbol{\rho}\left(t\right)bold_italic_ρ ( italic_t ) has a bounded norm for almost all datasets, while in zero measure case 𝝆(t)𝝆𝑡\boldsymbol{\rho}\left(t\right)bold_italic_ρ ( italic_t ) contains additional O(loglog(t))𝑂𝑡O(\log\log(t))italic_O ( roman_log roman_log ( italic_t ) ) componen... | C |
We use Levenberg-Marquardt algorithm to learn the parameters of the SIS and SEIZ. In each time interval from t0subscript𝑡0t_{0}italic_t start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT to tnsubscript𝑡𝑛t_{n}italic_t start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT, we fit the sequenced tweets’ volume from the beginning time t0s... |
But the SpikeM can’t fit to the events with multi-pikes. For that, the term external shock S(n)𝑆𝑛S(n)italic_S ( italic_n ) should not occur once but more. So (kwon2013prominent, ) extend the SpikeM by adding a periodic interaction function for the term external shock S(n)𝑆𝑛S(n)italic_S ( italic_n ). Same approac... | 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 ... | But if we fit the models of the first few hours with limited data, the result of learning parameters is not so accurate. We show the performance of fitting these two model with only the first 10 hours tweets’ volume in Figure 4. As we can see except for the first one, the fitting results of other three are not good eno... | . As shown in Table 11, CreditScore is the best feature in general. Figure 10 shows the result of models learned with the full feature set with and without CreditScore. Overall, adding CreditScore improves the performance, significantly for the first 8-10 hours. The performance of all-but-CreditScore jiggles a bit afte... | C |
Results. The baseline and the best results of our 1stsuperscript1𝑠𝑡1^{st}1 start_POSTSUPERSCRIPT italic_s italic_t end_POSTSUPERSCRIPT stage event-type classification is shown in Table 3-top. The accuracy for basic majority vote is high for imbalanced classes, yet it is lower at weighted F1. Our learned model achie... | 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 ... | 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... | 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... | Multi-Criteria Learning. Our task is to minimize the global relevance loss function, which evaluates the overall training error, instead of assuming the independent loss function, that does not consider the correlation and overlap between models. We adapted the L2R RankSVM [12]. The goal of RankSVM is learning a linear... | C |
The special case of piecewise-stationary, or abruptly changing environments, has attracted a lot of interest in general [Yu and Mannor, 2009; Luo et al., 2018],
and for UCB [Garivier and Moulines, 2011] and Thompson sampling [Mellor and Shapiro, 2013] algorithms, in particular. | The special case of piecewise-stationary, or abruptly changing environments, has attracted a lot of interest in general [Yu and Mannor, 2009; Luo et al., 2018],
and for UCB [Garivier and Moulines, 2011] and Thompson sampling [Mellor and Shapiro, 2013] algorithms, in particular. | with Bernoulli and contextual linear Gaussian reward functions [Kaufmann et al., 2012; Garivier and Cappé, 2011; Korda et al., 2013; Agrawal and Goyal, 2013b],
as well as for context-dependent binary rewards modeled with the logistic reward function Chapelle and Li [2011]; Scott [2015] —Appendix A.3. | 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], | The use of SMC in the context of bandit problems was previously considered for probit [Cherkassky and Bornn, 2013] and softmax [Urteaga and Wiggins, 2018c] reward models,
and to update latent feature posteriors in a probabilistic matrix factorization model [Kawale et al., 2015]. | D |
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... | 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... | For time delays between carb entries and the next glucose measurements we distinguish cases where glucose was measured at most 30 minutes before logging the meal, to account for cases where multiple measurements are made for one meal – in such cases it might not make sense to predict the glucose directly after the meal... | For example, the correlation between blood glucose and carbohydrate for patient 14 was higest (0.47) at no lagging time step (ref. 23(c)).
Whereas for the correlation between blood glucose and insulin was highest (0.28) with the lagging time = 4 (ref. 24(d)). | 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 |
Table 3: The number of trainable parameters for all deep learning models listed in Table 1 that are competing in the MIT300 saliency benchmark. Entries of prior work are sorted according to increasing network complexity and the superscript ††{}^{\dagger}start_FLOATSUPERSCRIPT † end_FLOATSUPERSCRIPT represents pre-trai... | Table 6: A summary of the quantitative results for the models with ⊕direct-sum\oplus⊕ and without ⊖symmetric-difference\ominus⊖ an ASPP module. The evaluation was carried out on five eye tracking datasets respectively. Each network was independently trained 10 times resulting in a distribution of values characterized b... |
We further evaluated the model complexity of all relevant deep learning approaches listed in Table 1. The number of trainable parameters was computed based on either the official code repository or a replication of the described architectures. In case a reimplementation was not possible, we faithfully estimated a lowe... | Table 4: The results after evaluating our model with respect to its computational efficiency. We tested five versions trained on different eye tracking datasets, each receiving input images of their preferred sizes in pixels (px). After running each network on 10,000 test set instances from the ImageNet database for 10... |
The images presented during the acquisition of saliency maps in all aforementioned datasets are largely based on natural scenes. Stimuli of CAT2000 additionally fall into predefined categories such as Action, Fractal, Object, or Social. Together with the corresponding fixation patterns, they constituted the input and ... | C |
Since a marking sequence is just a linear arrangement of the symbols of the input word, computing marking sequences seems to be well tailored to greedy algorithms: until all symbols are marked, we choose an unmarked symbol according to some greedy strategy and mark it. Unfortunately, we can formally show that many nat... |
We call a marking sequence σ𝜎\sigmaitalic_σ for a word α𝛼\alphaitalic_α block-extending, if every symbol that is marked except the first one has at least one block-extending occurrence. This definition leads to the general combinatorial question of whether every word has an optimal marking sequence that is block-ext... | This proposition points out that even simple words can have only optimal marking sequences that are not block-extending. In terms of greedy strategies however, Proposition 5.4 only shows a lower bound of roughly 2222 for the approximation ratio of any greedy algorithm that employs some block-extending greedy strategy (... | These strategies are – except for LeftRightLeftRight\operatorname{\textsf{LeftRight}}LRstrategy – nondeterministic, since there are in general several valid choices of the next symbol to mark. However, we will show poor performances for these strategies independent of the nondeterministic choices (i. e., the approximat... |
Our strongest positive result about the approximation of the locality number will be derived from the reduction mentioned above (see Section 5.2). However, we shall first investigate in Section 5.1 the approximation performance of several obvious greedy strategies to compute the locality number (with “greedy strategie... | C |
There are also cardiology applications that used CRFs with deep learning as a segmentation refinement step in fundus photography[171, 174], and in LV/RV[143].
Multimodal deep learning[271] can also be used to improve diagnostic outcomes e.g. the possibility of combining fMRI and ECG data. | The proposed framework uses FNN and GRU for handling non-temporal and temporal features respectively, thus learning their shared latent representations for prediction.
The results show that deep learning methods consistently outperform the super learner in the majority of the prediction tasks of the MIMIC (predictions ... | There are also cardiology applications that used CRFs with deep learning as a segmentation refinement step in fundus photography[171, 174], and in LV/RV[143].
Multimodal deep learning[271] can also be used to improve diagnostic outcomes e.g. the possibility of combining fMRI and ECG data. | According to the literature, RNNs are widely used in cardiology structured data because they are capable in finding optimal temporal features better than other deep/machine learning methods.
On the other hand, applications in this area are relatively few and this is mainly because there is a small number of public data... | Dedicated databases must be created in order to increase research in this area since according to the current review there are only three cardiology databases with multimodal data.
In addition to the previous databases MIMIC-III has also been used for multimodal deep learning by [68] for predicting in-hospital, short/l... | D |
Figure 3: Comparison with Rainbow and PPO. Each bar illustrates the number of interactions with environment required by Rainbow (left) or PPO (right) to achieve the same score as our method (SimPLe). The red line indicates the 100100100100K interactions threshold which is used by the our method. |
Figure 3: Comparison with Rainbow and PPO. Each bar illustrates the number of interactions with environment required by Rainbow (left) or PPO (right) to achieve the same score as our method (SimPLe). The red line indicates the 100100100100K interactions threshold which is used by the our method. |
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, ... | In our empirical evaluation, we find that SimPLe is significantly more sample-efficient than a highly tuned version of the state-of-the-art Rainbow algorithm (Hessel et al., 2018) on almost all games. In particular, in low data regime of 100100100100k samples, on more than half of the games, our method achieves a score... | We evaluate our method on 26262626 games selected on the basis of being solvable with existing state-of-the-art model-free deep RL algorithms222Specifically, for the final evaluation we selected games which achieved non-random results using our method or the Rainbow algorithm using 100100100100K interactions., which in... | B |
We used Adam [20] as the optimizer with learning rate lr=0.001𝑙𝑟0.001lr=0.001italic_l italic_r = 0.001, betas b1=0.9subscript𝑏10.9b_{1}=0.9italic_b start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT = 0.9, b2=0.999subscript𝑏20.999b_{2}=0.999italic_b start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT = 0.999, epsilon ϵ=10−8italic-ϵsupe... | 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... | As shown in Table. I the one layer CNN DenseNet201 achieved the best accuracy of 85.3%percent85.385.3\%85.3 % with training time 70 seconds/epoch on average.
In overall the one layer CNN S2I achieved best accuracies for eleven out of fifteen ‘base models’. | The names of the classes are depicted at the right along with the predictions for this example signal.
The image between m𝑚mitalic_m and bdsubscript𝑏𝑑b_{d}italic_b start_POSTSUBSCRIPT italic_d end_POSTSUBSCRIPT depicts the output of the one layer CNN Signal2Image module, while the ‘signal as image’ and spectrogram h... | C |
Hybrid robots typically transition between locomotion modes either by “supervised autonomy” [11], where human operators make the switch decisions, or the autonomous locomotion mode transition approach, where robots autonomously swap the modes predicated on pre-set criteria [8]. However, the execution of supervised con... |
Hybrid robots typically transition between locomotion modes either by “supervised autonomy” [11], where human operators make the switch decisions, or the autonomous locomotion mode transition approach, where robots autonomously swap the modes predicated on pre-set criteria [8]. However, the execution of supervised con... | A major obstacle in achieving seamless autonomous locomotion transition lies in the need for an efficient sensing methodology that can promptly and reliably evaluate the interaction between the robot and the terrain, referred to as terramechanics. These methods generally involve performing comprehensive on-site measure... | The Cricket robot, as referenced in [20], forms the basis of this study, being a fully autonomous track-legged quadruped robot. Its design specificity lies in embodying fully autonomous behaviors, and its locomotion system showcases a unique combination of four rotational joints in each leg, which can be seen in Fig. 3... | There are two primary technical challenges in the wheel/track-legged robotics area [2]. First, there’s a need to ensure accurate motion control within both rolling and walking locomotion modes [5] and effectively handle the transitions between them [6]. Second, it’s essential to develop decision-making frameworks that ... | B |
For paid exchanges at the beginning of the phase, Tog incurs a cost that is less than m2superscript𝑚2m^{2}italic_m start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT. Before serving the last request σℓsubscript𝜎ℓ\sigma_{\ell}italic_σ start_POSTSUBSCRIPT roman_ℓ end_POSTSUBSCRIPT of the phase, the access cost of Tog is less ... |
The worst-case ratio between the costs of Tog and Mtf2 is maximized when the last phase is an ignoring phase. In this case, we have k𝑘kitalic_k trusting phases and k𝑘kitalic_k ignoring phases. The total cost of Mtf2 is at least km3+k(βm3/2−m2)=km3(1+β/2−1/m)𝑘superscript𝑚3𝑘𝛽superscript𝑚32superscript𝑚2𝑘sup... |
For a trusting phase, the cost of Tog is in the range (m3,m3(1+1/m+1/m2))superscript𝑚3superscript𝑚311𝑚1superscript𝑚2(m^{3},m^{3}(1+1/m+1/m^{2}))( italic_m start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT , italic_m start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT ( 1 + 1 / italic_m + 1 / italic_m start_POSTSUPERSCRIPT 2 en... | Similar arguments apply for an ignoring phase with the exception that the threshold is β⋅m2⋅𝛽superscript𝑚2\beta\cdot m^{2}italic_β ⋅ italic_m start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT and there are no paid exchanges performed by Tog. So, we can observe the following.
|
In an ignoring phase, the cost of Tog for the phase is in the range (βm3,βm3(1+1/m2))𝛽superscript𝑚3𝛽superscript𝑚311superscript𝑚2(\beta m^{3},\beta m^{3}(1+1/m^{2}))( italic_β italic_m start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT , italic_β italic_m start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT ( 1 + 1 / italic_m ... | C |
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... | 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... | 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... | B |
We can find that DGC (Lin et al., 2018) is mainly based on the local momentum while GMC is based on the global momentum. Hence, each worker in DGC cannot capture the global information from its local momentum, while that in GMC can capture the global information from the global momentum even if sparse communication is ... |
We find that due to the momentum factor masking (mfm) in DGC (Lin et al., 2018), DGC (w/ mfm) will degenerate to DSGD rather than DMSGD if sparse communication is not adopted, while GMC will degenerate to DMSGD if sparse communication is not adopted. | We can find that both local momentum and global momentum implementations of DMSGD are equivalent to the serial MSGD if no sparse communication is adopted. However, when it comes to adopting sparse communication, things become different. In the later sections, we will demonstrate that global momentum is better than loca... | We can find that DGC (Lin et al., 2018) is mainly based on the local momentum while GMC is based on the global momentum. Hence, each worker in DGC cannot capture the global information from its local momentum, while that in GMC can capture the global information from the global momentum even if sparse communication is ... | process. As for global momentum, the momentum term −(𝐰t−𝐰t−1)/ηsubscript𝐰𝑡subscript𝐰𝑡1𝜂-({\bf w}_{t}-{\bf w}_{t-1})/\eta- ( bold_w start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT - bold_w start_POSTSUBSCRIPT italic_t - 1 end_POSTSUBSCRIPT ) / italic_η contains global information from all the workers. Since we are... | A |
SANs combined with the φ𝜑\varphiitalic_φ metric compress the description of the data in a way a minimum description language framework would, by encoding them into 𝒘(i)superscript𝒘𝑖\bm{w}^{(i)}bold_italic_w start_POSTSUPERSCRIPT ( italic_i ) end_POSTSUPERSCRIPT and 𝜶(i)superscript𝜶𝑖\bm{\alpha}^{(i)}bold_italic_α... | It is interesting to note that in some cases SANs reconstructions, such as for the Extrema-Pool indices, performed even better than the original data.
This suggests the overwhelming presence of redundant information that resides in the raw pixels of the original data and further indicates that SANs extract the most rep... | During supervised learning the weights of the kernels are frozen and a one layer fully connected network (FNN) is stacked on top of the reconstruction output of the SANs.
The FNN is trained for an additional 5555 epochs with the same batch size and model selection procedure as with SANs and categorical cross-entropy as... | 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... | From the point of view of Sparse Dictionary Learning, SANs kernels could be seen as the atoms of a learned dictionary specializing in interpretable pattern matching (e.g. for Electrocardiogram (ECG) input the kernels of SANs are ECG beats) and the sparse activation map as the representation.
The fact that SANs are wide... | D |
With the rapid commercialization of UAVs, a lot of research has emerged in this field [16]. To efficiently deploy UAVs, studies have been made to find out UAV distribution on network graph [9] and a graphical model has been proposed for channels reuse [17]. The resource allocation of channel and time is also a hot are... |
Typical wireless protocol 802.11b/g only provides limited channels for users, which is far more than enough for high-quality communication services [18]. To reduce the load in central system, making use of distributed available resources in networks turns out to be an ideal solution. Underlay Device-to-Device (D2D) co... |
Catastrophic natural and man-made disasters, such as earthquakes, typhoons, and wars, usually involve great loss of life and/or properties, historical interests in vast areas. Though sometimes unavoidable, the loss of life and property can be effectively reduced if proper disaster management has been implemented. Sinc... | To investigate UAV networks, novel network models should jointly consider power control and altitude for practicability. Energy consumption, SNR and coverage size are key points to decide the performance of a UAV network [6]. Respectively, power control determines the signal to energy consumption and noise ratio (SNR) ... | To support the communication mission, all UAVs are required to cooperate and support the user communication in need. UAVs work above post-disaster area D𝐷Ditalic_D. If a user (User1subscriptUser1{\rm User}_{1}roman_User start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT) needs to communicate with another user (User2subscriptUser... | A |
}_{\perp\alpha}\,\,\left(\overline{\widehat{\nabla}}\,\,\overline{T}_{\alpha}%
\right)\right\}= - { ( over^ start_ARG italic_κ end_ARG start_POSTSUBSCRIPT ∥ italic_α end_POSTSUBSCRIPT - over^ start_ARG italic_κ end_ARG start_POSTSUBSCRIPT ⟂ italic_α end_POSTSUBSCRIPT ) ( over^ start_ARG bold_B end_ARG start_POSTSUBSCRI... | [m-3] is a typical representative number density, and the
thermal diffusion coefficients χ∥α,χ⟂α\chi_{\parallel\alpha},\,\chi_{\perp\alpha}italic_χ start_POSTSUBSCRIPT ∥ italic_α end_POSTSUBSCRIPT , italic_χ start_POSTSUBSCRIPT ⟂ italic_α end_POSTSUBSCRIPT | =−((κ∥α−κ⟂α)∇∥Tα+κ⟂α∇Tα)\displaystyle=-\left(\left(\kappa_{\parallel\alpha}-\kappa_{\perp\alpha}\right%
)\nabla_{\parallel}T_{\alpha}+\kappa_{\perp\alpha}\nabla T_{\alpha}\right)= - ( ( italic_κ start_POSTSUBSCRIPT ∥ italic_α end_POSTSUBSCRIPT - italic_κ start_POSTSUBSCRIPT ⟂ italic_α end_POSTSUBSCRIPT ) ∇ start_POST... | \kappa{}_{\perp\alpha}\nabla_{\perp}T_{\alpha}\right)= - ( italic_κ start_POSTSUBSCRIPT ∥ italic_α end_POSTSUBSCRIPT ∇ start_POSTSUBSCRIPT ∥ end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT italic_α end_POSTSUBSCRIPT + italic_κ start_FLOATSUBSCRIPT ⟂ italic_α end_FLOATSUBSCRIPT ∇ start_POSTSUBSCRIPT ⟂ end_POSTSUBSCRIPT i... | of the order κ∥α=n0χ∥α\kappa_{\parallel\alpha}=n_{0}\chi_{\parallel\alpha}italic_κ start_POSTSUBSCRIPT ∥ italic_α end_POSTSUBSCRIPT = italic_n start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT italic_χ start_POSTSUBSCRIPT ∥ italic_α end_POSTSUBSCRIPT
and κ⟂α=n0χ⟂αsubscript𝜅perpendicular-toabsent𝛼subscript𝑛0subscript𝜒perpen... | D |
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. | 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. | 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... | 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... | 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→... | A |
Figure 6 shows the loss metrics of the three algorithms in CARTPOLE environment, this implies that using Dropout-DQN methods introduce more accurate gradient estimation of policies through iterations of different learning trails than DQN. The rate of convergence of one of Dropout-DQN methods has done more iterations t... | In this paper, we introduce and conduct an empirical analysis of an alternative approach to mitigate variance and overestimation phenomena using Dropout techniques. Our main contribution is an extension to the DQN algorithm that incorporates Dropout methods to stabilize training and enhance performance. The effectivene... | In this study, we proposed and experimentally analyzed the benefits of incorporating the Dropout technique into the DQN algorithm to stabilize training, enhance performance, and reduce variance. Our findings indicate that the Dropout-DQN method is effective in decreasing both variance and overestimation. However, our e... | 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... |
The results in Figure 3 show that using DQN with different Dropout methods result in better-preforming policies and less variability as the reduced standard deviation between the variants indicate to. In table 1, Wilcoxon Sign-Ranked test was used to analyze the effect of Variance before applying Dropout (DQN) and aft... | B |
The scarcity of richly annotated medical images is limiting supervised deep learning-based solutions to medical image analysis tasks (Perone and Cohen-Adad, 2019), such as localizing discriminatory radiomic disease signatures. Therefore, it is desirable to leverage unsupervised and weakly supervised models. | Chartsias et al. (2017) used a conditional GAN to generate cardiac MR images from CT images. They showed that utilizing the synthetic data increased the segmentation accuracy and that using only the synthetic data led to only a marginal decrease in the segmentation accuracy. Similarly, Zhang et al. (2018c) proposed a G... | Kervadec et al. (2019b) introduced a differentiable term in the loss function for datasets with weakly supervised labels, which reduced the computational demand for training while also achieving almost similar performance to full supervision for segmentation of cardiac images. Afshari et al. (2019) used a fully convol... | Guo et al. (2018) provided a review of deep learning based semantic segmentation of images, and divided the literature into three categories: region-based, fully convolutional network (FCN)-based, and weakly supervised segmentation methods. Hu et al. (2018b) summarized the most commonly used RGB-D datasets for semantic... | Vorontsov et al. (2019), using a dataset defined in Cohen et al. (2018), proposed an image-to-image based framework to transform an input image with object of interest (presence domain) like a tumor to an image without the tumor (absence domain) i.e. translate diseased image to healthy; next, their model learns to add ... | B |
In the supplementary material we report numerical differences in the size of the cut obtained on random graphs when using 𝐯maxsubscript𝐯max{\mathbf{v}}_{\text{max}}bold_v start_POSTSUBSCRIPT max end_POSTSUBSCRIPT or 𝐯maxssubscriptsuperscript𝐯𝑠max{\mathbf{v}}^{s}_{\text{max}}bold_v start_POSTSUPERSCRIPT italic_s en... | Since computing the optimal MAXCUT solution is NP-hard, it is generally not possible to evaluate the quality of the cut found by the proposed spectral method (Sect. III-A) in terms of discrepancy from the MAXCUT.
Therefore, to assess the quality of a solution we consider the following bounds | The results show that on the two regular graphs, which are bipartite, the cut obtained with the spectral algorithm coincides with the MAXCUT upper bound and, therefore, also with the optimal solution.
For every other graph, the cut yielded by the spectral algorithm is always larger than the random cut. | The results show that on the two regular graphs, which are bipartite, the cut obtained with the spectral algorithm coincides with the MAXCUT upper bound and, therefore, also with the optimal solution.
For every other graph, the cut yielded by the spectral algorithm is always larger than the random cut. | The examples encompass the two extreme cases where the MAXCUT solution is known: a bipartite graph where MAXCUT is 1 and the complete graph where MAXCUT is 0.5.
In every example, when λmaxssubscriptsuperscript𝜆𝑠max\lambda^{s}_{\text{max}}italic_λ start_POSTSUPERSCRIPT italic_s end_POSTSUPERSCRIPT start_POSTSUBSCRIPT ... | A |
The results are shown in Figure 3 exemplarily for the Car, Covertype, and Wisconsin Breast Cancer (Original) dataset. The other datasets show similar characteristics. The overall evaluation on all datasets is presented in the next section.
The number of training examples per class is shown in parentheses and increases ... | Sethi (1990) presents a mapping of decision trees to two-hidden-layer neural networks.
In the first hidden layer, the number of neurons equals the number of split nodes in the decision tree. Each of these neurons implements the decision function of the split nodes and determines the routing to the left or right child n... | For each setting, the test accuracy of the random forest is indicated by a red dashed line.
The average test accuracy and standard deviation depending on the network architecture, i.e., the number of neurons in the first and second hidden layer, are plotted for different architectures. | First, we analyze the performance of state-of-the-art methods for mapping random forests into neural networks and neural random forest imitation. The results are shown in Figure 4 for different numbers of training examples per class.
For each method, the average number of parameters of the generated networks across all... | NRFI with and without the original data is shown for different network architectures. The smallest architecture has 2222 neurons in both hidden layers and the largest 128128128128. For NRFI (gen-ori), we can see that a network with 16161616 neurons in both hidden layers (NN-16-16) is already sufficient to learn the dec... | 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.... |
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;... | 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... | D |
A variant of the VGG architecture is used on the CIFAR-10 task for evaluation because FINN does not support residual connections yet, and the configuration of the FINN framework is adjusted so that highest throughput is targeted with respect to the available resources of the device (BRAM, LUTs, etc).
| The WRN model on the CIFAR-10 task is used again as a baseline, with a depth of 28 layers, varying widths of the model, and weights/activations quantized to different bit widths.
Figure 5 reports test accuracies and throughput for different WRN variants and compression methods. | Quantized DNNs with 1-bit weights and activations are the worst performing models, which is due to the severe implications of extreme quantization on prediction performance.
As can be seen, however, the overall performance of the quantized models increases considerably when the bit width of activations is increased to ... | As expected, the test accuracy increases gradually with high bit widths while the throughput decreases accordingly.
Following the Pareto front starting from the bottom right indicates that the best performing models use a combination of 1 bit for the weights and a gradual increase of activations up to 3 bits. | Afterwards the models perform best if the weights are scaled to 2 bits and the activation bit width is further increased to 4 bits.
This supports the observation of the previous sections, showing that model accuracy is sensitive to activation quantization rather than weight quantization. | C |
Let M𝑀Mitalic_M be an n𝑛nitalic_n-dimensional metric manifold. Then, note that we have FillRadn(M,G,[M])=FillRad(M)subscriptFillRad𝑛𝑀𝐺delimited-[]𝑀FillRad𝑀\mathrm{FillRad}_{n}(M,G,[M])=\mathrm{FillRad}(M)roman_FillRad start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT ( italic_M , italic_G , [ italic_M ] ) = roma... | A priori, one can define the generalized filling radius for any metric space X𝑋Xitalic_X. However, we believe that the context of ANR metric spaces is the right level of generalization for our purposes because of the following proposition analogous to Proposition 1.
| Let (X,E)𝑋𝐸(X,E)( italic_X , italic_E ) be a metric pair where X𝑋Xitalic_X is a compact ANR metric space. For any integer k≥1𝑘1k\geq 1italic_k ≥ 1, any abelian group G𝐺Gitalic_G, and any ω∈Hk(X;G)𝜔subscriptH𝑘𝑋𝐺\omega\in\mathrm{H}_{k}(X;G)italic_ω ∈ roman_H start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT ( ital... |
The goal of this section is to provide some partial results regarding the structure of barc∗VR(⋅)subscriptsuperscriptbarcVR∗⋅\mathrm{barc}^{\mathrm{VR}}_{\ast}(\cdot)roman_barc start_POSTSUPERSCRIPT roman_VR end_POSTSUPERSCRIPT start_POSTSUBSCRIPT ∗ end_POSTSUBSCRIPT ( ⋅ ) for non-smooth spaces; see Figure 12. In ord... |
In this section, we recall the notions of spread and filling radius, as well as their relationship. In particular, we prove a number of statements about the filling radius of a closed connected manifold. Moreover, we consider a generalization of the filling radius and also define a strong notion of filling radius whic... | A |
Overall Accuracy
We start by executing a grid search and, after a few seconds, we are presented with 25 representative projections. As we notice that the projections lack high values in continuity, we choose to sort the projections based on this quality metric for further investigation. Next, as the projections are q... | C1: Remaining Cost
Looking at the main view (Figure 7(c), \raisebox{-.9pt} {1}⃝), we detect an area on the top of cluster C1 with slightly increased size for a few points (in comparison to the other points in the same cluster), which means there are high values of remaining cost in this small area. | C3: Densities
The next step in our analysis is to confirm if the layout of the points accurately represents the original N-D densities of the clusters. By inspecting the distribution of colors over the points in the main view (Figure 7(c)), we can see that each cluster has a different density profile: C1 presents the... |
Figure 7: Use case based on the Pima Indian Diabetes data set. Although there are three separate clusters C1–C3, the class labels are mostly mixed (a), and the Shepard Heatmap (b) indicates that smaller N-D distances are spread out in 2-D. Some insights about the clusters (c): C1 has a small area with high remaining c... | The second option of the Visual Mapping panel, the Remaining Cost, indicates (in the points’ sizes, by default) the final value of KLD(Pi∥Qi)𝐾𝐿𝐷conditionalsubscript𝑃𝑖subscript𝑄𝑖KLD(P_{i}\|Q_{i})italic_K italic_L italic_D ( italic_P start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ∥ italic_Q start_POSTSUBSCRIPT ... | A |
Taking into account all the reviewed papers, we group the proposals therein in a hierarchy of categories. In the hierarchy, not all proposals of a category must fit in one of its subcategories. In our classification, categories lying at the same level are disjoint sets, which means that each proposed algorithm can be ... |
It has not been until relatively recent times that the community has embraced the need for arranging the myriad of existing bio-inspired algorithms and classifying them under principled, coherent criteria. In 2013, [74] presented a classification of meta-heuristic algorithms as per their biological inspiration that di... |
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... | Methodologically, a classification of all nature- and bio-inspired algorithms that can be found in the literature can become complicated, considering the different sources of inspiration as biological, physical, human-being, … In some papers, authors suggest a possible categorization of more well-established groups, bu... |
The above statement is quantitatively supported by Figure 1, which depicts the increasing number of papers/book chapters published in the last years with bio-inspired optimization and nature-inspired optimization in their title, abstract and/or keywords. We have considered both bio-inspired and nature-inspired optimiz... | C |
To study the impact of different parts of the loss in Eq. (12), the performance with different λ𝜆\lambdaitalic_λ is reported in Figure 4.
From it, we find that the second term (corresponding to problem (7)) plays an important role especially on UMIST. If λ𝜆\lambdaitalic_λ is set as a large value, we may get the trivi... | (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... | To illustrate the process of AdaGAE, Figure 2 shows the learned embedding on USPS at the i𝑖iitalic_i-th epoch. An epoch means a complete training of GAE and an update of the graph. The maximum number of epochs, T𝑇Titalic_T, is set as 10. In other words, the graph is updated 10 times. Clearly, the embedding becomes mo... | It should be emphasized that a large k0subscript𝑘0k_{0}italic_k start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT frequently leads to capture the wrong information.
After the transformation of GAE, the nearest neighbors are more likely to belong with the same cluster |
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 ... | C |
Although the agents provide the optimal setup for testing filtering, with control over the packets that can be crafted and sent from both sides, as we explain in Related Work Section 2, this approach is limited only to networks that deploy agents on their networks. In contrast, SMap provides better coverage since it i... |
SMap (The Spoofing Mapper). In this work we present the first Internet-wide scanner for networks that filter spoofed inbound packets, we call the Spoofing Mapper (SMap). We apply SMap for scanning ingress-filtering in more than 90% of the Autonomous Systems (ASes) in the Internet. The measurements with SMap show that ... | 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... |
These findings show that SMap offers benefits over the existing methods, providing better coverage of the ASes in the Internet and not requiring agents or conditions for obtaining traceroute loops, hence improving visibility of networks not enforcing ingress filtering. | Agents Active Measurements. Agents with active probes found 608 ASes that were found not to be enforcing ingress filtering using the agents approach of the Spoofer Project (these include duplicates with the traceroute loops measurements). Those contain some of the duplicates from traceroute measurements: together both ... | C |
This paper also presents the NN ensemble created in the same way as with SVMs. In the NN ensemble, T−1𝑇1T-1italic_T - 1 skill networks are trained using one batch each for training. Each model is assigned a weight βisubscript𝛽𝑖\beta_{i}italic_β start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT equal to its accuracy on... |
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... | The context+skill NN model builds on the skill NN model by adding a recurrent processing pathway (Fig. 2D). Before classifying an unlabeled sample, the recurrent pathway processes a sequence of labeled samples from the preceding batches to generate a context representation, which is fed into the skill processing layer.... | Figure 2: Neural network architectures. (A.) The batches used for training and testing illustrate the training procedure. The first T−1𝑇1T-1italic_T - 1 batches are used for training, while the next unseen batch T𝑇Titalic_T is used for evaluation. When training the context network, subsequences of the training data a... | This paper builds upon previous work with this dataset [7], which used support vector machine (SVM) ensembles. First, their approach is extended to a modern version of feedforward artificial neural networks (NNs) [8]. Context-based learning is then introduced to utilize sequential structure across batches of data. The ... | B |
$P_{0}\cup\dots\cup P_{i-1}\cup B$ realizing the matching $M$}\end{cases}italic_A start_POSTSUPERSCRIPT ( 1 ) end_POSTSUPERSCRIPT [ italic_i , italic_B ] := { start_ROW start_CELL A representative set containing pairs ( italic_M , italic_x ) , where italic_M is a perfect matching on italic_B ∈ caligraphic_B start_POSTS... | A(2)[i,B]:={A representative set containing pairs (M,x), where M is a perfect matching on B∈ℬi(2) and x is a real number equal to the minimum total length of a path cover of P0∪⋯∪Pi−1∪B realizing the matching M.assignsuperscript𝐴2𝑖𝐵casesA representative set containing pairs (M,x), where M is a perfect matching on B... |
A[i,B]:={A representative set containing pairs (M,x), where M is a perfect matching on B∈ℬi and x is a real number equal to the minimum total length of a path cover of P0∪⋯∪Pi−1∪B realizing the matching M.assign𝐴𝑖𝐵casesA representative set containing pairs (M,x), where M is a perfect matching on B∈ℬi and x is a re... |
A[i,B]:={A representative set containing pairs (M,x), where M is a perfect matching on B and x is a real number equal to the minimum total length of a path cover of P0∪⋯∪Pi−1∪B realizing the matching M.assign𝐴𝑖𝐵casesA representative set containing pairs (M,x), where M is a perfect matching on B and x is a real num... | A(1)[i,B]:={A representative set containing pairs (M,x), where M is a perfect matching on B∈ℬi(1) and x is a real number equal to the minimum total length of a path cover of P0∪⋯∪Pi−1∪B realizing the matching Massignsuperscript𝐴1𝑖𝐵casesA representative set containing pairs (M,x), where M is a perfect matching on B∈... | A |
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... | 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.
| 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. | 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... |
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 |
As shown in Table 1, we present results when this loss is used on: a) Fixed subset covering 1%percent11\%1 % of the dataset, b) Varying subset covering 1%percent11\%1 % of the dataset, where a new random subset is sampled every epoch and c) 100%percent100100\%100 % of the dataset. Confirming our hypothesis, all varian... | Here, we study these methods. We find that their improved accuracy does not actually emerge from proper visual grounding, but from regularization effects, where the model forgets the linguistic priors in the train set, thereby performing better on the test set. To support these claims, we first show that it is possible... |
Based on these observations, we hypothesize that controlled degradation on the train set allows models to forget the training priors to improve test accuracy. To test this hypothesis, we introduce a simple regularization scheme that zeros out the ground truth answers, thereby always penalizing the model, whether the p... | It is also interesting to note that the drop in training accuracy is lower with this regularization scheme as compared to the state-of-the-art methods. Of course, if any model was actually visually grounded, then we would expect it to improve performances on both train and test sets. We do not observe such behavior in ... | While our results indicate that current visual grounding based bias mitigation approaches do not suffice, we believe this is still a good research direction. However, future methods must seek to verify that performance gains are not stemming from spurious sources by using an experimental setup similar to that presented... | C |
URL Cross Verification. Legal jurisdictions around the world require organisations to make their privacy policies readily available to their users. As a result, most organisations include a link to their privacy policy in the footer of their website landing page. In order to focus PrivaSeer Corpus on privacy policies ... |
To satisfy the need for a much larger corpus of privacy policies, we introduce the PrivaSeer Corpus of 1,005,380 English language website privacy policies. The number of unique websites represented in PrivaSeer is about ten times larger than the next largest public collection of web privacy policies Amos et al. (2020)... |
We created the PrivaSeer Corpus which is the first large scale corpus of contemporary website privacy policies and consists of just over 1 million documents. We designed a novel pipeline to build the corpus, which included web crawling, language detection, document classification, duplicate removal, document cross ver... | Duplicate and Near-Duplicate Detection. Examination of the corpus revealed that it contained many duplicate and near-duplicate documents. We removed exact duplicates by hashing all the raw documents and discarding multiple copies of exact hashes. Through manual inspection, we found that a number of privacy policies fro... |
To remove near-duplicates from within the same domain we used Simhashing (Charikar, 2002). Simhashing is a hashing technique in which similar inputs produce similar hashes. After creating shingles (Broder et al., 1997) of size three, we created 64 bit document Simhashes and measured document similarity by calculating ... | C |
G2: Support exploration. VA systems enable users to reach crucial findings and to take actions according to them. This iterative process requires a human-in-the-loop who can thus explore the data and the model through the interactive visualization [1]. | Predictions’ Space.
The goal of the predictions’ space visualization (StackGenVis: Alignment of Data, Algorithms, and Models for Stacking Ensemble Learning Using Performance Metrics(f)) is to show an overview of the performance of all models of the current stack for different instances. | and (v) we track the history of the previously stored stacking ensembles in StackGenVis: Alignment of Data, Algorithms, and Models for Stacking Ensemble Learning Using Performance Metrics(b) and compare their performances against the active stacking ensemble—the one not yet stored in the history—in StackGenVis: Alignme... | As the solution space for ensemble learning is more confusing compared to single ML techniques, keeping track of the history of events and providing provenance for exploring and backtracking of alternative paths is necessary to reach this goal.
Furthermore, provenance in VA for ensemble learning increases the interpret... | There is a large solution space of different learning methods and concrete models which can be combined in a stack. Hence, the identification and selection of particular algorithms and instantiations over the time of exploration is crucial for the the user. One way to manage this is to keep track of the history of each... | C |
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... | 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 ], | {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 | D |
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... | The finding suggests that parameter initialization at the late training stage has strong general language generation ability, but performs comparative poorly in task-specific adaptation.
Although in the early training stage, the performance improves benefiting from the pre-trained general language model, if the languag... |
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... | In this paper, we take an empirical approach to systematically investigating these impacting factors and finding when MAML works the best. We conduct extensive experiments over 4 datasets. We first study the effects of data quantity and distribution on the training strategy:
RQ1. Since the parameter initialization lear... | 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... | A |
The specialized codebook design of the DRE-covered CCA for multi-UAV mobile mmWave communications. Under the guidance of the proposed framework, a novel hierarchical codebook is designed to encompass both the subarray patterns and beam patterns. The newly proposed CA codebook can fully exploit the potentials of the DR... | The CCA codebook based SPAS algorithm is proposed in the previous section to solve the joint CCA subarray partition and AWV selection problem. In this section, the TE-aware beam tracking problem is addressed based on the CCA codebook based SPAS algorithm.
Tracking the AOAs and AODs is essential for beam tracking, which... |
The CCA codebook-based multi-UAV beam tracking scheme with TE awareness. Based on the designed codebook, by exploiting the Gaussian process (GP) tool, both the position and attitude of UAVs can be fast tracked for fast multiuser beam tracking along with dynamic TE estimation. Moreover, the estimated TE is leveraged to... | 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... |
Note that there exist some mobile mmWave beam tracking schemes exploiting the position or motion state information (MSI) based on conventional ULA/UPA recently. For example, the beam tracking is achieved by directly predicting the AOD/AOA through the improved Kalman filtering [26], however, the work of [26] only targe... | B |
The case of 1111-color is characterized by a Presburger formula that just expresses the equality of the number of edges calculated from
either side of the bipartite graph. The non-trivial direction of correctness is shown via distributing edges and then merging. | After the merging the total degree of each vertex increases by tδ(A0,B0)2𝑡𝛿superscriptsubscript𝐴0subscript𝐵02t\delta(A_{0},B_{0})^{2}italic_t italic_δ ( italic_A start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_B start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ) start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT.
We perform the... | The case of 1111-color is characterized by a Presburger formula that just expresses the equality of the number of edges calculated from
either side of the bipartite graph. The non-trivial direction of correctness is shown via distributing edges and then merging. | To conclude this section, we stress that although the 1111-color case contains many of the key ideas, the multi-color case requires a finer
analysis to deal with the “big enough” case, and also may benefit from a reduction that allows one to restrict | The case of fixed degree and multiple colors is done via an induction, using merging and then swapping to eliminate parallel edges.
The case of unfixed degree is handled using a case analysis depending on whether sizes are “big enough”, but the approach is different from | D |
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 | 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... | 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... | To address such an issue of divergence, nonlinear gradient TD (Bhatnagar et al., 2009) explicitly linearizes the value function approximator locally at each iteration, that is, using its gradient with respect to the parameter as an evolving feature representation. Although nonlinear gradient TD converges, it is unclear... |
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... | B |
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.
| 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.
|
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 ... |
Another way to take care of the outputs of these two sub-layers in the decoder layer is to replace their residual connections with two depth-wise LSTM sub-layers, as shown in Figure 3 (b). This leads to better performance (as shown in Table 4), but at the costs of more parameters and decoder depth in terms of sub-laye... | 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... | B |
which strictly contains V1×V2subscript𝑉1subscript𝑉2V_{1}\times V_{2}italic_V start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT × italic_V start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT,
but is still included in f−1(U)superscript𝑓1𝑈f^{-1}(U)italic_f start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT ( italic_U ) which is in contradictio... | compact in X1×X2subscript𝑋1subscript𝑋2X_{1}\times X_{2}italic_X start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT × italic_X start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT.
We are going to prove that f−1(U)superscript𝑓1𝑈f^{-1}(U)italic_f start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT ( italic_U ) is actually | First of all,
because f−1(U)superscript𝑓1𝑈f^{-1}(U)italic_f start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT ( italic_U ) is open in (X1,τ1)×(X2,τ2)subscript𝑋1subscriptτ1subscript𝑋2subscriptτ2(X_{1},\uptau_{1})\times(X_{2},\uptau_{2})( italic_X start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT , roman_τ start_POSTSUBSCRIPT 1 e... | ≡\equiv≡-saturated sets in X1×X2subscript𝑋1subscript𝑋2X_{1}\times X_{2}italic_X start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT × italic_X start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT.
Hence, writing f−1(U)superscript𝑓1𝑈f^{-1}(U)italic_f start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT ( italic_U ) as the finite union of maximal | compact open set of X1×X2subscript𝑋1subscript𝑋2X_{1}\times X_{2}italic_X start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT × italic_X start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT is a finite union of sets of
the form K×X2𝐾subscript𝑋2K\times X_{2}italic_K × italic_X start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT and X1×Ksubscript𝑋1𝐾X_{... | C |
(2) For each backbone network, the layer depths of VGG16, InceptionV3, and ResNet50 are 23, 159, and 168, respectively. These architectures represent the different extraction abilities of image features. As illustrated in Fig. 6, the distortion parameter estimation achieves the lowest error (0.15) using InceptionV3 as... | (3) From the loss curves in Fig. 7, the ordinal distortion estimation achieves the fastest convergence and best performance on the validation dataset. It is also worth to note that the ordinal distortion estimation already performs well on the validation at the first twenty epochs, which verifies that this learning rep... | Figure 7: Analysis of two learning representation in terms of the training and validation loss curves. We show the learning performance of the distortion parameter estimation without (top) and with (middle) the normalization of magnitude, and the ordinal distortion estimation (bottom). Our proposed ordinal distortion e... | (1) Overall, the ordinal distortion estimation significantly outperforms the distortion parameter estimation in both convergence and accuracy, even if the amount of training data is 20% of that used to train the learning model. Note that we only use 1/4 distorted image to predict the ordinal distortion. As we pointed o... |
To exhibit the performance fairly, we employ three common network architectures VGG16, ResNet50, and InceptionV3 as the backbone networks of the learning model. The proposed MDLD metric is used to express the distortion estimation error due to its unique and fair measurement for distortion distribution. To be specific... | A |
Furthermore, researchers in [19] argued that the extrapolation technique is suitable for large-batch training and proposed EXTRAP-SGD.
However, experimental implementations of these methods still require additional training tricks, such as warm-up, which may make the results inconsistent with the theory. | We compare SNGM with four baselines: MSGD, ADAM [14], LARS [34] and LAMB [34]. LAMB is a layer-wise adaptive large-batch optimization method based on ADAM, while LARS is based on MSGD.
The experiments are implemented based on the DeepCTR 888https://github.com/shenweichen/DeepCTR-Torch framework. | SGD and its variants are iterative methods. In the t𝑡titalic_t-th iteration, these methods randomly
choose a subset (also called a mini-batch) ℐt⊂{1,2,…,n}subscriptℐ𝑡12…𝑛{\mathcal{I}}_{t}\subset\{1,2,\ldots,n\}caligraphic_I start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT ⊂ { 1 , 2 , … , italic_n } and compute the | In this paper, we first review the convergence property of MSGD, one of the most widely used variants of SGD, and analyze the failure of MSGD in large-batch training from an optimization perspective. Then, we propose a novel method, called
stochastic normalized gradient descent with momentum (SNGM), for large-batch tra... | If we avoid these tricks, these methods may suffer from severe performance degradation.
For LARS and its variants, the proposal of the layer-wise update strategy is primarily based on empirical observations. Its reasonability and necessity remain doubtful from an optimization perspective. | D |
In Two-Stage Stochastic Multi-knapsack Supplier or 2S-MuSup for short, there are L𝐿Litalic_L additional knapsack constraints on FIsubscript𝐹𝐼F_{I}italic_F start_POSTSUBSCRIPT italic_I end_POSTSUBSCRIPT. Specifically, we are given budgets Wℓ≥0subscript𝑊ℓ0W_{\ell}\geq 0italic_W start_POSTSUBSCRIPT roman_ℓ end_POSTSUB... |
We define a strategy s𝑠sitalic_s to be a (|𝒟|+1)𝒟1(|\mathcal{D}|+1)( | caligraphic_D | + 1 )-tuple of facility sets (FIs,FAs)subscriptsuperscript𝐹𝑠𝐼subscriptsuperscript𝐹𝑠𝐴(F^{s}_{I},F^{s}_{A})( italic_F start_POSTSUPERSCRIPT italic_s end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_I end_POSTSUBSCRIPT , italic_... | Clustering is a fundamental task in unsupervised and self-supervised learning. The stochastic setting models situations in which decisions must be made in the presence of uncertainty and are of particular interest in learning and data science. The black-box model is motivated by data-driven applications where specific ... | The most general way to represent the scenario distribution 𝒟𝒟\mathcal{D}caligraphic_D is the black-box model [24, 12, 22, 19, 25], where we have access to an oracle to sample scenarios A𝐴Aitalic_A according to 𝒟𝒟\mathcal{D}caligraphic_D. We also consider the polynomial-scenarios model [23, 15, 21, 10], where the ... | Our main goal is to develop algorithms for the black-box setting. As usual in two-stage stochastic problems, this has three steps. First, we develop algorithms for the simpler polynomial-scenarios model. Second, we sample a small number of scenarios from the black-box oracle and use our polynomial-scenarios algorithms ... | C |
I. The local cost functions in this paper are not required to be differentiable and the subgradients only satisfy the linear growth condition.
The inner product of the subgradients and the error between local optimizers’ states and the global optimal solution inevitably exists in the recursive inequality of the conditi... | (Lemma 3.1).
To this end, we estimate the upper bound of the mean square increasing rate of the local optimizers’ states at first (Lemma 3.2). Then we substitute this upper bound into the Lyapunov function difference inequality of the consensus error, and obtain the estimated convergence rate of mean square consensus (... |
III. The co-existence of random graphs, subgradient measurement noises, additive and multiplicative communication noises are considered. Compared with the case with only a single random factor, the coupling terms of different random factors inevitably affect the mean square difference between optimizers’ states and an... | As a result, the existing methods are no longer applicable. In fact, the inner product of the subgradients and the error between local optimizers’ states and the global optimal solution inevitably exists in the recursive inequality of the conditional mean square error, which leads the nonegative supermartingale converg... | I. The local cost functions in this paper are not required to be differentiable and the subgradients only satisfy the linear growth condition.
The inner product of the subgradients and the error between local optimizers’ states and the global optimal solution inevitably exists in the recursive inequality of the conditi... | A |
Although the generalization for k𝑘kitalic_k-anonymity provides enough protection for identities, it is vulnerable to the attribute disclosure [23]. For instance, in Figure 1(b), the sensitive values in the third equivalence group are both “pneumonia”. Therefore, an adversary can infer the disease value of Dave by mat... | 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... | However, despite protecting against both identity disclosure and attribute disclosure, the information loss of generalized table cannot be ignored. On the one hand, the generalized values are determined by only the maximum and the minimum QI values in equivalence groups, causing that the equivalence groups only preserv... | Specifically, there are three main steps in the proposed approach. First, MuCo partitions the tuples into groups and assigns similar records into the same group as far as possible. Second, the random output tables, which control the distribution of random output values within each group, are calculated to make similar ... |
For instance, suppose that we add another QI attribute of gender as shown in Figure 4, the mutual cover strategy first divides the records into groups in which the records in the same group cover for each other by perturbing their QI values. Then, the mutual cover strategy calculates a random output table on each QI a... | B |
We implement PointRend using MMDetection Chen et al. (2019b) and adopt the modifications and tricks mentioned in Section 3.3. Both X101-64x4d and Res2Net101 Gao et al. (2019) are used as our backbones, pretrained on ImageNet only. SGD with momentum 0.9 and weight decay 1e-4 is adopted. The initial learning rate is set... | Table 3: PointRend’s performance on testing set (trackB). “EnrichFeat” means enhance the feature representation of coarse mask head and point head by increasing the number of fully-connected layers or its hidden sizes. “BFP” means Balanced Feature Pyramid. Note that BFP and EnrichFeat gain little improvements, we guess... | As shown in Table 3, all PointRend models achieve promising performance. Even without ensemble, our PointRend baseline, which yields 77.38 mAP, has already achieved 1st place on the test leaderboard. Note that several attempts, like BFP Pang et al. (2019) and EnrichFeat, give no improvements against PointRend baseline,... | 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... | 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.... | B |
(0log0:=0assign0000\log 0:=00 roman_log 0 := 0). The base of the log\logroman_log does not really matter here. For concreteness we take the log\logroman_log to base 2222. Note that if f𝑓fitalic_f has L2subscript𝐿2L_{2}italic_L start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT norm 1111 then the sequence {|f^(A)|2}A⊆[n]subsc... |
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... |
where for A⊆[n]𝐴delimited-[]𝑛A\subseteq[n]italic_A ⊆ [ italic_n ], |A|𝐴|A|| italic_A | denotes the cardinality of A𝐴Aitalic_A. This object, especially for boolean functions, is a deeply studied one and quite influential (but this is not the reason for the name…) in several directions. We refer to [O] for some info... |
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... | 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.
| D |
For any algorithm, the dynamic regret is at least Ω(B1/3d5/6HT2/3)Ωsuperscript𝐵13superscript𝑑56𝐻superscript𝑇23\Omega(B^{1/3}d^{5/6}HT^{2/3})roman_Ω ( italic_B start_POSTSUPERSCRIPT 1 / 3 end_POSTSUPERSCRIPT italic_d start_POSTSUPERSCRIPT 5 / 6 end_POSTSUPERSCRIPT italic_H italic_T start_POSTSUPERSCRIPT 2 / 3 en... | The last relevant line of work is on dynamic regret analysis of nonstationary MDPs mostly without function approximation (Auer et al., 2010; Ortner et al., 2020; Cheung et al., 2019; Fei et al., 2020; Cheung et al., 2020). The work of Auer et al. (2010) considers the setting in which the MDP is piecewise-stationary and... | 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... | Motivated by empirical success of deep RL, there is a recent line of work analyzing the theoretical performance of RL algorithms with function approximation (Yang & Wang, 2019; Cai et al., 2020; Jin et al., 2020; Modi et al., 2020; Ayoub et al., 2020; Wang et al., 2020; Zhou et al., 2021; Wei et al., 2021; Neu & Olkhov... | We consider the setting of episodic RL with nonstationary reward and transition functions. To measure the performance of an algorithm, we use the notion of dynamic regret, the performance difference between an algorithm and the set of policies optimal for individual episodes in hindsight. For nonstationary RL, dynamic ... | B |
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