context stringlengths 250 7.19k | A stringlengths 250 4.12k | B stringlengths 250 8.2k | C stringlengths 250 5.47k | D stringlengths 250 3.94k | label stringclasses 4
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(−1)a(b−1−a)[ddxxmF(a,b;c;z)+xmddxF(a,b;c;z)];superscript1𝑎binomial𝑏1𝑎delimited-[]𝑑𝑑𝑥superscript𝑥𝑚𝐹𝑎𝑏𝑐𝑧superscript𝑥𝑚𝑑𝑑𝑥𝐹𝑎𝑏𝑐𝑧\displaystyle(-1)^{a}{b-1\choose-a}\Big{[}\frac{d}{dx}x^{m}F(a,b;c;z)+x^{m}%
\frac{d}{dx}F(a,b;c;z)\Big{]};( - 1 ) start_POSTSUPERSCRIPT italic_a end_POSTSUPERSCRI... | d2dx2F(a,b;c;z)superscript𝑑2𝑑superscript𝑥2𝐹𝑎𝑏𝑐𝑧\displaystyle\frac{d^{2}}{dx^{2}}F(a,b;c;z)divide start_ARG italic_d start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT end_ARG start_ARG italic_d italic_x start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT end_ARG italic_F ( italic_a , italic_b ; italic_c ; italic_z )
=\disp... | }\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... | d3dx3Rnm(x)superscript𝑑3𝑑superscript𝑥3superscriptsubscript𝑅𝑛𝑚𝑥\displaystyle\frac{d^{3}}{dx^{3}}R_{n}^{m}(x)divide start_ARG italic_d start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT end_ARG start_ARG italic_d italic_x start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT end_ARG italic_R start_POSTSUBSCRIPT italic_n end_POS... |
d2dx2Rnm(x)superscript𝑑2𝑑superscript𝑥2superscriptsubscript𝑅𝑛𝑚𝑥\displaystyle\frac{d^{2}}{dx^{2}}R_{n}^{m}(x)divide start_ARG italic_d start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT end_ARG start_ARG italic_d italic_x start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT end_ARG italic_R start_POSTSUBSCRIPT italic_n end_PO... | D |
Now let d𝑑ditalic_d be even. The same results for the transvections t21(ωℓ)subscript𝑡21superscript𝜔ℓt_{21}(\omega^{\ell})italic_t start_POSTSUBSCRIPT 21 end_POSTSUBSCRIPT ( italic_ω start_POSTSUPERSCRIPT roman_ℓ end_POSTSUPERSCRIPT ) and t12(ωℓ)subscript𝑡12superscript𝜔ℓt_{12}(\omega^{\ell})italic_t start_POSTSU... | 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)... |
The first step of the algorithm is the one-off computation of T2subscript𝑇2T_{2}italic_T start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT from the LGO standard generators of SL(d,q)SL𝑑𝑞\textnormal{SL}(d,q)SL ( italic_d , italic_q ). The length and memory requirement of an MSLP for this step is as follows. |
We now compute upper bounds for the length and memory quota of an MSLP for expressing an arbitrary diagonal matrix h∈SL(d,q)ℎSL𝑑𝑞h\in\textnormal{SL}(d,q)italic_h ∈ SL ( italic_d , italic_q ) as a word in the LGO generators, i.e. the computation phase of the algorithm. | 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... | C |
where Ω⊂ℝdΩsuperscriptℝ𝑑\Omega\subset\mathbb{R}^{d}roman_Ω ⊂ blackboard_R start_POSTSUPERSCRIPT italic_d end_POSTSUPERSCRIPT with d=2𝑑2d=2italic_d = 2 or 3333 for simplicity, and is an open bounded domain with polyhedral boundary ∂ΩΩ\partial\Omega∂ roman_Ω, the symmetric tensor 𝒜∈[L∞(Ω)]symd×d𝒜superscriptsubscrip... |
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... | One difficulty that hinders the development of efficient methods is the presence of high-contrast coefficients [MR3800035, MR2684351, MR2753343, MR3704855, MR3225627, MR2861254]. When LOD or VMS methods are considered, high-contrast coefficients might slow down the exponential decay of the solutions, making the method ... | 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... | In [MR2718268] is shown that the number of eigenvalues that are very large is related to the number of connected sub-regions on τ¯∪τ¯′¯𝜏superscript¯𝜏′\bar{\tau}\cup{\bar{\tau}}^{\prime}over¯ start_ARG italic_τ end_ARG ∪ over¯ start_ARG italic_τ end_ARG start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT with large coefficien... | C |
Moreover,
(iii) A back-stable edge (e.g. the one at ersubscript𝑒𝑟e_{r}italic_e start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT) remains back-stable when we change another edge (e.g. the one at essubscript𝑒𝑠e_{s}italic_e start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT or etsubscript𝑒𝑡e_{t}italic_e start_POSTSUBSCRIP... |
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.) | 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. | It is easy to compute one 3-stable triangle in O(n)𝑂𝑛O(n)italic_O ( italic_n ) time; we show how to do this in section 4111Alg-DS fails to find one 3-stable triangle and so we introduce the algorithm in section 4. This algorithm in section 4 is not the same as and does not originate from Alg-DS (see appendix A.2)..
... | Our algorithm given in section 4 (denoted by Alg-One) is different from Alg-DS.
First, step 1 of Alg-One sets the initial value of (r,s,t)𝑟𝑠𝑡(r,s,t)( italic_r , italic_s , italic_t ) differently from the initial value (1,2,3)123(1,2,3)( 1 , 2 , 3 ) used by Alg-DS. | D |
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 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... | The processing pipeline of our classification approach is shown in Figure 2. In the first step, relevant tweets for an event are gathered. Subsequently, in the upper part of the pipeline,
we predict tweet credibilty with our pre-trained credibility model and aggregate the prediction probabilities on single tweets (Cred... | 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.
|
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... | B |
In a follow-up work Nacson et al. (2018) provided partial answers to these questions. They proved that the exponential tail has the optimal convergence rate, for tails for which ℓ′(u)superscriptℓ′𝑢\ell^{\prime}(u)roman_ℓ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT ( italic_u ) is of the form exp(−uν)superscript𝑢𝜈... | The convergence of the direction of gradient descent updates to the maximum L2subscript𝐿2L_{2}italic_L start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT margin solution, however is very slow compared to the convergence of training loss, which explains why it is worthwhile
continuing to optimize long after we have zero training ... | 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... | Perhaps most similar to our study is the line of work on understanding AdaBoost in terms its implicit bias toward large L1subscript𝐿1L_{1}italic_L start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT-margin solutions, starting with the seminal work of Schapire et al. (1998). Since AdaBoost can be viewed as coordinate descent on th... | 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... | B |
The effective cascaded model that engages both low and high-level features for rumor classification is proposed in our other work (DBLP:journals/corr/abs-1709-04402, ). The model uses time-series structure of features to capture their temporal dynamics. In this paper, we make the following contributions with respect to... |
We investigate how the performance of different types of low and high-level features changes over time (during the spreading of rumors); improving the understanding of feature impact and model design for rumor detection at different points in time. |
In this work, we present a deep analysis on the feature variants over 48 hours for the rumor detection task. The results show that the low-level hidden representation of tweets feature is at least the second best features over time. We also derive explanations on the low performance of supposed-to-be-strong high-level... | 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 ... |
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... | A |
Evaluating methodology.
For RQ1, given an event entity e, at time t, we need to classify them into either Breaking or Anticipated class. We select a studied time for each event period randomly in the range of 5 days before and after the event time. In total, our training dataset for AOL consists of 1,740 instances of b... | 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... |
RQ2. Figure 4 shows the performance of the aspect ranking models for our event entities at specific times and types. The most right three models in each metric are the models proposed in this work. The overall results show that, the performances of these models, even better than the baselines (for at least one of the ... |
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... | 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... | C |
RT=𝔼{∑t=1TYt,at∗−Yt,At},subscript𝑅𝑇𝔼superscriptsubscript𝑡1𝑇subscript𝑌𝑡subscriptsuperscript𝑎𝑡subscript𝑌𝑡subscript𝐴𝑡R_{T}=\mathbb{E}\left\{\sum_{t=1}^{T}Y_{t,a^{*}_{t}}-Y_{t,A_{t}}\right\}\;,italic_R start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT = blackboard_E { ∑ start_POSTSUBSCRIPT italic_t = 1 end_POST... | 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], | one uses p(θt|ℋ1:t)𝑝conditionalsubscript𝜃𝑡subscriptℋ:1𝑡p(\theta_{t}|\mathcal{H}_{1:t})italic_p ( italic_θ start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT | caligraphic_H start_POSTSUBSCRIPT 1 : italic_t end_POSTSUBSCRIPT ) to compute the probability of an arm being optimal,
i.e., π(A|xt+1,ℋ1:t)=ℙ(A=at+1∗|xt+1,θt,... | Thompson sampling (TS) [Thompson, 1935] is an alternative MAB policy that has been popularized in practice, and studied theoretically by many.
TS is a probability matching algorithm that randomly selects an action to play according to the probability of it being optimal [Russo et al., 2018]. | the combination of Bayesian neural networks with approximate inference has also been investigated.
Variational methods, stochastic mini-batches, and Monte Carlo techniques have been studied for uncertainty estimation of reward posteriors of these models [Blundell et al., 2015; Kingma et al., 2015; Osband et al., 2016; ... | C |
Likewise, the daily number of measurements taken for carbohydrate intake, blood glucose level and insulin units vary across the patients.
The median number of carbohydrate log entries vary between 2 per day for patient 10 and 5 per day for patient 14. | 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... | 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. | Likewise, the daily number of measurements taken for carbohydrate intake, blood glucose level and insulin units vary across the patients.
The median number of carbohydrate log entries vary between 2 per day for patient 10 and 5 per day for patient 14. | B |
Table 2 demonstrates that we obtained state-of-the-art scores for the CAT2000 test dataset regarding the AUC-J, sAUC, and KLD evaluation metrics, and competitive results on the remaining measures. The cumulative rank (as computed above) suggests that our model outperformed all previous approaches, including the ones ba... | 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... | To quantify the contribution of multi-scale contextual information to the overall performance, we conducted a model ablation analysis. A baseline architecture without the ASPP module was constructed by replacing the five parallel convolutional layers with a single 3×3333\times 33 × 3 convolutional operation that result... |
Table 2: Quantitative results of our model for the CAT2000 test set in the context of prior work. The first line separates deep learning approaches with architectures pre-trained on image classification (the superscript ††{}^{\dagger}start_FLOATSUPERSCRIPT † end_FLOATSUPERSCRIPT represents models with a VGG16 backbone... |
Table 1: Quantitative results of our model for the MIT300 test set in the context of prior work. The first line separates deep learning approaches with architectures pre-trained on image classification (the superscript ††{}^{\dagger}start_FLOATSUPERSCRIPT † end_FLOATSUPERSCRIPT represents models with a VGG16 backbone)... | A |
For example, the path decomposition ({u,w,x},{u,v,x},{v,y,z})𝑢𝑤𝑥𝑢𝑣𝑥𝑣𝑦𝑧(\{u,w,x\},\{u,v,x\},\{v,y,z\})( { italic_u , italic_w , italic_x } , { italic_u , italic_v , italic_x } , { italic_v , italic_y , italic_z } ) for graph H𝐻Hitalic_H can be represented as a pd-marking scheme as illustrated in Figure 3 (for... | In the following, we obtain an approximation algorithm for the locality number by reducing it to the problem of computing the pathwidth of a graph. To this end, we first describe another way of how a word can be represented by a graph. Recall that the reduction to cutwidth from Section 4 also transforms words into grap... | The locality number is rather new and we shall discuss it in more detail. A word is k𝑘kitalic_k-local if there exists an order of its symbols such that, if we mark the symbols in the respective order (which is called a marking sequence), at each stage there are at most k𝑘kitalic_k contiguous blocks of marked symbols ... | Both the locality number of a word and the pathwidth of a graph is defined via markings. In order to avoid confusion, we therefore use different terminology to distinguish between these two concepts (see also the terminology defined in Section 2.2): The markings for words are called marking sequences, while the marking... |
We use Gαsubscript𝐺𝛼G_{\alpha}italic_G start_POSTSUBSCRIPT italic_α end_POSTSUBSCRIPT as a unique graph representation for words and whenever we talk about a path decomposition for α𝛼\alphaitalic_α, we actually refer to a path decomposition of Gαsubscript𝐺𝛼G_{\alpha}italic_G start_POSTSUBSCRIPT italic_α end_POSTS... | C |
In[128] the authors created a recurrent u-net that learns image representations from a stack of 2D slices and has the ability to leverage inter-slice spatial dependencies through internal memory units.
It combines anatomical detection and segmentation into a single end-to-end architecture, achieving comparable results ... | Tan et al.[135] parameterize all short axis slices and phases of the LV segmentation task in terms of the radial distances between the LV center-point and the endocardial and epicardial contours in polar space.
Then, they train a CNN regression on STA11 to infer these parameters and test the generalizability of the met... | Other papers combined deep learning methods with level set for LV segmentation.
Rupprecht et al.[129] trained a class-specific four layer CNN which predicts a vector pointing from the respective point on the evolving contour towards the closest point on the boundary of the object of interest. | These predictions formed a vector field which was then used for evolving the contour using the Sobolev active contour framework.
Anh et al.[130] created a non-rigid segmentation method based on the distance regularized level set method that was initialized and constrained by the results of a structured inference using ... | For this task they introduce marginal space deep learning which provides high run-time performance by learning classifiers in clustered, high-probability regions in spaces of gradually increasing dimensionality.
Given the object localization, they propose a combined deep learning active shape model to estimate the non-... | B |
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, ... |
While SimPLe is able to learn more quickly than model-free methods, it does have limitations. First, the final scores are on the whole lower than the best state-of-the-art model-free methods. This can be improved with better dynamics models and, while generally common with model-based RL algorithms, suggests an import... | The iterative process of training the model, training the policy, and collecting data is crucial for non-trivial tasks where random data collection is insufficient. In a game-by-game analysis, we quantified the number of games where the best results were obtained in later iterations of training. In some games, good pol... | Figure 1: Main loop of SimPLe. 1) the agent starts interacting with the real environment following the latest policy (initialized to random). 2) the collected observations will be used to train (update) the current world model. 3) the agent updates the policy by acting inside the world model. The new policy will be eva... | The results in these figures are generated by averaging 5555 runs for each game.
The model-based agent is better than a random policy for all the games except Bank Heist. Interestingly, we observed that the best of the 5555 runs was often significantly better. For 6666 of the games, it exceeds the average human score (... | D |
Zhang et al. [11] trained an ensemble of CNNs containing two to ten layers using STFT features extracted from EEG band frequencies for mental workload classification.
Giri et al. [12] extracted statistical and information measures from frequency domain to train an 1D CNN with two layers to identify ischemic stroke. | The spectrogram S2I results are in contrary with the expectation that the interpretable time-frequency representation would help in finding good features for classification.
We hypothesize that the spectrogram S2I was hindered by its lack of non-trainable parameters. | Figure 1: High level overview of a feed-forward pass of the combined methods.
xisubscript𝑥𝑖x_{i}italic_x start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT is the input, m𝑚mitalic_m is the Signal2Image module, bdsubscript𝑏𝑑b_{d}italic_b start_POSTSUBSCRIPT italic_d end_POSTSUBSCRIPT is the 1D or 2D architecture ‘base ... | 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... | For the purposes of this paper and for easier future reference we define the term Signal2Image module (S2I) as any module placed after the raw signal input and before a ‘base model’ which is usually an established architecture for imaging problems.
An important property of a S2I is whether it consists of trainable para... | D |
While the study of legged locomotion gaits has been a topic of research for several decades, the investigation of locomotion in wheel-legged robots is a relatively recent area of study [9]. Hybrid ground robots, equipped with highly articulated legs with more than three degrees-of-freedom, present unique challenges in... | The evaluation of energy consumption for the walking locomotion mode encompassed the entire step negotiation process, from the commencement of the negotiation until its completion. Fig. 8 reveals minimal discrepancies in energy consumption for the whole-body climbing gait, which can be attributed to the thoughtful desi... |
Fig. 7 illustrates the hierarchical control design for the autonomous locomotion mode transition. The decision-making process for this transition is accomplished in MATLAB, whereas the control of each separate locomotion mode is enacted in CoppeliaSim. The connection between MATLAB and the physical robot model in Copp... | The track tip positioning was the key parameter controlled during the creation of these climbing gaits. To assure seamless locomotion, trajectories for each joint of the robot were defined through a fifth-order polynomial along with their first and second derivatives. The trajectory design took into account six constra... | 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 ... | C |
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... |
Under the current models, the advice bits can encode any information about the input sequence; indeed, defining the “right” information to be conveyed to the algorithm plays an important role in obtaining better online algorithms. Clearly, the performance of the online algorithm can only improve with larger number of ... |
In future work, we would like to expand the model so as to incorporate, into the analysis, the concept of advice error. More specifically, given an advice string of size k𝑘kitalic_k, let η𝜂\etaitalic_η denote the number of erroneous bits (which may be not known to the algorithm). In this setting, the objective would... | 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.... | Notwithstanding such interesting attributes, the known advice model has certain drawbacks. The advice is always assumed to be some error-free information that may be used to encode some property often explicitly connected to the optimal solution. In many settings, one can argue that such information cannot be readily a... | D |
With the aim of avoiding cases of misclassification like in (d), we decided to implement the second classifier, SS3Δ, whose policy also takes into account the changes in both slopes.
As it can be seen from Algorithm 3 and as mentioned before, SS3Δ additionally classifies a subject as positive if the positive slope chan... | the accumulated negative confidence value starts being greater than the positive one, but as more chunks are read (specifically starting after reading the 3rd chunk), the positive value starts and stays growing until it exceeds the other one. In this case, this subject is classified as depressed after reading the 6th c... |
the subject is misclassified as positive since the positive accumulated exceeded the negative one. When we manually analyzed cases like these we often found out that the classifier was correctly accumulating positive evidence since the users were, in fact, apparently depressed. | This problem can be detected in this subject by seeing the blue dotted peek at around the 60th writing, indicating that “the positive slope changed around five times faster than the negative” there, and therefore misclassifying the subject as positive. However, note that this positive change was in fact really small (l... | In Figure 7 is shown again the subject 1914, this time including information about the changes in the slopes.
Note that this subject was previously misclassified as not depressed because the accumulated positive value never exceeded the negative one, but by adding this new extra policy, this time it is correctly classi... | D |
There are some other ways to combine momentum and error feedback. For example, we can put the momentum term on the server. However, these ways lead to worse performance than the way adopted in this paper. More discussions can be found in Appendix A.
| 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... | GMC combines error feedback and momentum to achieve sparse communication in distributed learning. But different from existing sparse communication methods like DGC which adopt local momentum, GMC adopts global momentum.
To the best of our knowledge, this is the first work to introduce global momentum into sparse commun... | However, the theory about the convergence of DGC is still lacking. Furthermore, although DGC combines momentum and error feedback, the momentum in DGC only accumulates stochastic gradients computed by each worker locally. Therefore, the momentum in DGC is a local momentum without global information.
| 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 ... | D |
φ¯¯𝜑\bar{\varphi}over¯ start_ARG italic_φ end_ARG is non-differentiable due to the presence of the ℓ0subscriptℓ0\ell_{0}roman_ℓ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT pseudo-norm in Eq. 3.
A way to overcome this is using ℒℒ\mathcal{L}caligraphic_L as the differentiable optimization function during training and φ¯¯𝜑\... | We set med=m(i)𝑚𝑒𝑑superscript𝑚𝑖med=m^{(i)}italic_m italic_e italic_d = italic_m start_POSTSUPERSCRIPT ( italic_i ) end_POSTSUPERSCRIPT for utilizing fair comparison between the sparse activation functions.
Specifically for Extrema activation function we introduce a ‘border tolerance’ parameter to allow neuron ac... | The Extrema-Pool indices activation function (defined at Algorithm 2) keeps only the index of the activation with the maximum absolute amplitude from each region outlined by a grid as granular as the kernel size m(i)superscript𝑚𝑖m^{(i)}italic_m start_POSTSUPERSCRIPT ( italic_i ) end_POSTSUPERSCRIPT and zeros out the ... | We then pass 𝒔(i)superscript𝒔𝑖\bm{s}^{(i)}bold_italic_s start_POSTSUPERSCRIPT ( italic_i ) end_POSTSUPERSCRIPT and a sparsity parameter d(i)superscript𝑑𝑖d^{(i)}italic_d start_POSTSUPERSCRIPT ( italic_i ) end_POSTSUPERSCRIPT in the sparse activation function ϕitalic-ϕ\phiitalic_ϕ resulting in the activation map 𝜶(... |
We choose values for d(i)superscript𝑑𝑖d^{(i)}italic_d start_POSTSUPERSCRIPT ( italic_i ) end_POSTSUPERSCRIPT for each activation function in such as way, to approximately have the same number of activations for fair comparison of the sparse activation functions. | D |
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... |
Compared with other algorithms, novel algorithm SPBLLA has more advantages in learning rate. Various algorithms have been employed in the UAV networks in search of the optimal channel selection [31][29], such as stochastic learning algorithm [30]. The most widely seen algorithm–LLA is an ideal method for NE approachin... |
The learning rate of the extant algorithm is also not desirable [13]. Recently, a new fast algorithm called binary log-linear learning algorithm (BLLA) has been proposed by [14]. However, in this algorithm, only one UAV is allowed to change strategy in one iteration based on current game state, and then another UAV ch... |
Since PBLLA only allows one single UAV to alter strategies in one iteration, such defect would cause computation time to grow exponentially in large-scale UAVs systems. In terms of large-scale UAVs ad-hoc networks with a number of UAVs denoted as M𝑀Mitalic_M, M2superscript𝑀2M^{2}italic_M start_POSTSUPERSCRIPT 2 end_... | Fig. 15 presents the learning rate of PBLLA and SPBLLA when τ=0.01𝜏0.01\tau=0.01italic_τ = 0.01. As m𝑚mitalic_m increases the learning rate of SPBLLA decreases, which has been shown in Fig. 15. However, when m𝑚mitalic_m is small, SPBLLA’s learning rate is about 3 times that of PBLLA showing the great advantage of sy... | C |
+[1μ0ω𝐁⋅∇f+1μ0f∇⋅(ω𝐁)]delimited-[]⋅1subscript𝜇0𝜔𝐁∇𝑓⋅1subscript𝜇0𝑓∇𝜔𝐁\displaystyle+\left[\frac{1}{\mu_{0}}\omega\mathbf{B}\cdot\nabla f+\frac{1}{%
\mu_{0}}f\nabla\cdot\bigg{(}\omega\mathbf{B}\bigg{)}\right]+ [ divide start_ARG 1 end_ARG start_ARG italic_μ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT end_ARG it... | with Poynting flux. Note that the terms +(𝐯⋅∇ψ)μ0r2∇ψ⋅𝐯∇𝜓subscript𝜇0superscript𝑟2∇𝜓+\frac{(\mathbf{v}\cdot\nabla\psi)}{\mu_{0}r^{2}}\nabla\psi+ divide start_ARG ( bold_v ⋅ ∇ italic_ψ ) end_ARG start_ARG italic_μ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT italic_r start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT end_ARG... | +[η(Δ∗ψ)2μ0r2+1μ0r2∇ψ⋅∇(ηΔ∗ψ)]delimited-[]𝜂superscriptsuperscriptΔ𝜓2subscript𝜇0superscript𝑟2⋅1subscript𝜇0superscript𝑟2∇𝜓∇𝜂superscriptΔ𝜓\displaystyle+\left[\frac{\eta(\Delta^{*}\psi)^{2}}{\mu_{0}r^{2}}+\frac{1}{\mu%
_{0}r^{2}}\nabla\psi\cdot\nabla(\eta\Delta^{*}\psi)\right]+ [ divide start_ARG italic_η (... | +[η(∇f)2μ0r2+fμ0∇⋅(ηr2∇f)]delimited-[]𝜂superscript∇𝑓2subscript𝜇0superscript𝑟2⋅𝑓subscript𝜇0∇𝜂superscript𝑟2∇𝑓\displaystyle+\left[\frac{\eta(\nabla f)^{2}}{\mu_{0}r^{2}}+\frac{f}{\mu_{0}}%
\nabla\cdot\bigg{(}\frac{\eta}{r^{2}}\nabla f\bigg{)}\right]+ [ divide start_ARG italic_η ( ∇ italic_f ) start_POSTSUPERS... | −[1μ0r2Δ∗ψ(𝐯⋅∇ψ)+1μ0r2∇ψ⋅∇(𝐯⋅∇ψ)]delimited-[]1subscript𝜇0superscript𝑟2superscriptΔ𝜓⋅𝐯∇𝜓⋅1subscript𝜇0superscript𝑟2∇𝜓∇⋅𝐯∇𝜓\displaystyle-\left[\frac{1}{\mu_{0}r^{2}}\Delta^{*}\psi(\mathbf{v}\cdot\nabla%
\psi)+\frac{1}{\mu_{0}r^{2}}\nabla\psi\cdot\nabla(\mathbf{v}\cdot\nabla\psi)\right]- [ divide start_AR... | 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→... | 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. | 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... | C |
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... | Q-learning is among the most widely used reinforcement learning (RL) algorithms[4]. It’s based on an incremental dynamic programming technique because of the step by step look-up table representation in which it determines the optimal policy[22]. The Q-learning algorithm employs a table to estimate the optimal action v... |
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 Gridworld problem (Figure 4) is a common RL benchmark. Its relatively small state space permits the Experience Replay (ER) buffer to store all possible state-action pairs. Moreover, this setup allows for the precise computation of the optimal action value function.
| where st+1subscript𝑠𝑡1s_{t+1}italic_s start_POSTSUBSCRIPT italic_t + 1 end_POSTSUBSCRIPT is the resulting state after applying action a in the state s, r is the immediate reward observed for action a at state s, γ𝛾\gammaitalic_γ is the discount factor, and α𝛼\alphaitalic_α is learning rate.
| C |
Weakly supervised segmentation using image-level labels versus a few images with segmentation annotations. Most new weakly supervised localization methods apply attention maps or region proposals in a multiple instance learning formulations. While attention maps can be noisy, leading to erroneously highlighted regions... |
We provide comprehensive coverage of research contributions in the field of semantic segmentation of natural and medical images. In terms of medical imaging modalities, we cover the literature pertaining to both 2D (RGB and grayscale) as well as volumetric medical images. | Deep learning has had a tremendous impact on various fields in science. The focus of the current study is on one of the most critical areas of computer vision: medical image analysis (or medical computer vision), particularly deep learning-based approaches for medical image segmentation. Segmentation is an important pr... |
Because of the large number of imaging modalities, the significant signal noise present in imaging modalities such as PET and ultrasound, and the limited amount of medical imaging data mainly because of high acquisition cost compounded by legal, ethical, and privacy issues, it is difficult to develop universal solutio... |
While most deep segmentation models for medical image analysis rely on only clinical images for their predictions, there is often multi-modal patient data in the form of other imaging modalities as well as patient metadata that can provide valuable information, which most deep segmentation models do not use. Therefore... | D |
Black line: the threshold from [28] indicating the value of λmaxs/2subscriptsuperscript𝜆𝑠max2\lambda^{s}_{\text{max}}/2italic_λ start_POSTSUPERSCRIPT italic_s end_POSTSUPERSCRIPT start_POSTSUBSCRIPT max end_POSTSUBSCRIPT / 2 below which one should switch to the random cut to obtain a solution ≥0.53absent0.53\geq 0.53... | Fig. 4 illustrates how the size of the cut γ(𝐳)𝛾𝐳\gamma({\mathbf{z}})italic_γ ( bold_z ) induced by the spectral partition 𝐳𝐳{\mathbf{z}}bold_z changes as more edges are added and the original structure of the graph is corrupted (blue line). The figure also reports the size of the random cut (orange line) and the... | We replicate for each graph type the experiment in Sect. IV-B, which illustrates how the size of the cut obtained with the proposed algorithm changes as we randomly add edges.
Fig. 11 reports in blue the size of the cut associated with the partition yielded by the spectral algorithm; in orange the size of the cut yield... | Black line: the threshold from [28] indicating the value of λmaxs/2subscriptsuperscript𝜆𝑠max2\lambda^{s}_{\text{max}}/2italic_λ start_POSTSUPERSCRIPT italic_s end_POSTSUPERSCRIPT start_POSTSUBSCRIPT max end_POSTSUBSCRIPT / 2 below which one should switch to the random cut to obtain a solution ≥0.53absent0.53\geq 0.53... | We replicate for each graph type the experiment in Sect. IV-B, which illustrates how the size of the cut obtained with the proposed algorithm changes as we randomly add edges.
Fig. 11 reports in blue the size of the cut associated with the partition yielded by the spectral algorithm; in orange the size of the cut yield... | B |
In contrast to neural networks, random forests are very robust to overfitting due to their ensemble of multiple decision trees. Each decision tree is trained on randomly selected features and samples.
Random forests have demonstrated remarkable performance in many domains (Fernández-Delgado et al., 2014). | Decision trees learn rules by splitting the data. The rules are easy to interpret and additionally provide an importance score of the features.
Random forests (Breiman, 2001) are an ensemble method consisting of multiple decision trees, with each decision tree being trained using a random subset of samples and features... | While the generated decision rules are simple and interpretable, the orthogonal separation of the feature space can also be disadvantageous on other datasets, especially with correlated features (Menze et al., 2011).
Additionally, random forests are not differentiable and cannot be fine-tuned with gradient-based optimi... | The number of parameters of the networks becomes enormous as the number of nodes grows exponentially with the increasing depth of the decision trees.
Additionally, many weights are set to zero so that an inefficient representation is created. Due to both reasons, the mappings do not scale and are only applicable to sim... | (1) We enable the generation of neural networks with very few training examples.
(2) The resulting network can be used as a warm start, is fully differentiable, and allows further end-to-end fine-tuning. (3) The generated network can be easily integrated into any trainable pipeline (e.g., jointly with feature extractio... | B |
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... |
Our work is closely related to another line of work (Even-Dar et al., 2009; Yu et al., 2009; Neu et al., 2010a, b; Zimin and Neu, 2013; Neu et al., 2012; Rosenberg and Mansour, 2019a, b) on online MDPs with adversarially chosen reward functions, which mostly focuses on the tabular setting. | Assuming the transition dynamics are known but only the bandit feedback of the received rewards is available, the work of Neu et al. (2010a, b); Zimin and Neu (2013) establishes an H2|𝒜|T/βsuperscript𝐻2𝒜𝑇𝛽H^{2}\sqrt{|\mathcal{A}|T}/\betaitalic_H start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT square-root start_ARG |... |
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;... | B |
On the contrary, GPUs feature large register files and aim to hide memory latency by leveraging parallel slackness.
Another critical aspect of loop-back architectures is low compute utilization, which can potentially occur if certain layer or operation types do not fit the static compute array (i.e., if operation size ... | The results reveal that quantization does not provide throughput improvements on this processor.
This is mainly due to the efficient floating-point units within the CPU in combination with fast on-chip memory and the high overhead resulting from performing low-bit-width computations. | The advantage of their approach is that weight assignments need not be stored explicitly since they are given implicitly by the hashing function.
The authors show a memory footprint reduction by a factor of 10 while keeping the prediction quality essentially unaffected. | The advantage of such a generic compute architecture is that they allow arbitrary operations in combination with productive code generation since the hardware does not need to be optimized for a certain task.
Continuous improvements in semi-conductor and processor technology are the main improvement factor of such infe... | While domain-specific accelerators, such as Google’s TPU, excel in their specific performance, they are usually limited to a set of specific operations and are neither flexible in terms of data types nor sparse calculations. Furthermore, in particular for the TPU, experimentation is often hindered due to limitations in... | C |
{v0,v27}+{v27,v28}+{v28,v14}+{v14v29}+{v29,v23}+{v23,v30}+{v30,v31}+{v31,v0},subscript𝑣0subscript𝑣27subscript𝑣27subscript𝑣28subscript𝑣28subscript𝑣14subscript𝑣14subscript𝑣29subscript𝑣29subscript𝑣23subscript𝑣23subscript𝑣30subscript𝑣30subscript𝑣31subscript𝑣31subscript𝑣0\displaystyle\quad\{v_{0},v_{27}\}+\... | 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
|
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 | 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... |
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 | A |
A DR method is an algorithm that projects a high-dimensional data set to a low-dimensional representation, preserving the structure of the original data as much as possible.
Most of these algorithms have some (or many) hyper-parameters that may considerably affect their results, but setting them correctly is not a triv... | 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... | Fujiwara et al. [44] proposed the contrasting clusters in PCA (ccPCA) method to find which dimensions contributed more to the formation of a selected cluster and why it differs from the rest of the dataset, based on information on separation and internal vs. external variability. We have similar goals, but approach the... | A DR method is an algorithm that projects a high-dimensional data set to a low-dimensional representation, preserving the structure of the original data as much as possible.
Most of these algorithms have some (or many) hyper-parameters that may considerably affect their results, but setting them correctly is not a triv... | A few other tools have been proposed throughout the years that incorporate these techniques to deal with the problem of supporting the exploration of multidimensional data with DR. In Subsection 2.4, we discuss their goals and trade-offs, and compare them with t-viSNE.
| D |
Topologies: A promising research direction is to jointly consider topologies and ensemble strategies to leverage the superior explorative/exploitative powers of ensembles and also topologies for population-based metaheuristics to achieve better solutions than other solvers. | We should pause and reflect on which research directions should be pursued in the future in regard to bio-inspired optimization and related areas, as there are other remarkable fields to be noted as direct applications for bio-inspired optimization. In [3], the authors show a full discussion of the status of the field ... |
Surrogate model-assisted optimization: This area has promising research lines of investigation with highly dimensional search spaces and DL models, where there is a need to alleviate high computational efforts, with evaluation times that range from hours to days per experiment. |
From a design perspective, nature- and bio-inspired optimization algorithms are usually conceived after observing a natural process or the behavioral patterns of biological organisms, which are then converted into a computational optimization algorithm. New discoveries in Nature and the undoubted increase of worldwide... |
Going deeper into the creation of Machine Learning (ML) and Deep Learning (DL) models: Although most algorithms have been developed in recent years, the impact of EAs, a classical family of algorithms, has risen in the last few years. Their use in ML has been widely studied both for the design of models [615] and also... | B |
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 ... | 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... | (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... | C |
∙∙\bullet∙ Traffic load. Network scans, such as (Lyon, 2009; Durumeric et al., 2013; Kührer et al., 2014), require exchanging packets with a large number of Internet networks as well as IP addresses inside the networks. To avoid scanning the Internet we periodically download a dataset of a full scan of the Internet don... | Limitations of filtering studies. The measurement community provided indispensable studies for assessing “spoofability” in the Internet, and has had success in detecting the ability to spoof in some individual networks using active measurements, e.g., via agents installed on those networks (Mauch, 2013; Lone et al., 20... |
∙∙\bullet∙ Consent of the scanned. It is often impossible to request permission from owners of all the tested networks in advance, this challenge similarly applies to other Internet-wide studies (Lyon, 2009; Durumeric et al., 2013, 2014; Kührer et al., 2014). Like the other studies, (Durumeric et al., 2013, 2014), we ... | 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... | ∙∙\bullet∙ Traffic load. Network scans, such as (Lyon, 2009; Durumeric et al., 2013; Kührer et al., 2014), require exchanging packets with a large number of Internet networks as well as IP addresses inside the networks. To avoid scanning the Internet we periodically download a dataset of a full scan of the Internet don... | B |
Experiments in this paper used the gas sensor drift array dataset [7]. The data consists of 10 sequential collection periods, called batches. Every batch contains between 161161161161 to 3,60036003{,}6003 , 600 samples, and each sample is represented by a 128-dimensional feature vector; 8 features each from 16 metal ox... | Experiments in this paper used the gas sensor drift array dataset [7]. The data consists of 10 sequential collection periods, called batches. Every batch contains between 161161161161 to 3,60036003{,}6003 , 600 samples, and each sample is represented by a 128-dimensional feature vector; 8 features each from 16 metal ox... |
The current design of the context-based network relies on labeled data because the odor samples for a given class are presented as ordered input to the context layer. However, the model can be modified to be trained on unlabeled data, simply by allowing arbitrary data samples as input to the context layer. This design... | 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... |
Two processing steps were applied to the data used by all models included in this paper. The first preprocessing step was to remove all samples taken for gas 6, toluene, because there were no toluene samples in batches 3, 4, and 5. Data was too incomplete for drawing meaningful conclusions. Also, with such data missin... | D |
The goal would be to obtain an algorithm with running time 2O(f(δ)n)superscript2𝑂𝑓𝛿𝑛2^{O(f(\delta)\sqrt{n})}2 start_POSTSUPERSCRIPT italic_O ( italic_f ( italic_δ ) square-root start_ARG italic_n end_ARG ) end_POSTSUPERSCRIPT, where f(n)=O(n1/6)𝑓𝑛𝑂superscript𝑛16f(n)=O(n^{1/6})italic_f ( italic_n ) = italic... | First of all, the ΔisubscriptΔ𝑖\Delta_{i}roman_Δ start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT are now independent.
Second, as we will prove next, the expected running time of an algorithm on a uniformly distributed point set can be bounded by the expected running time of that algorithm on a point set generated this ... | In the second step, we therefore describe a method to generate the random point set in a different way, and we show how to relate the expected running times in these two settings.
In the third step, we will explain which changes are made to the algorithm. | 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... | We believe that our algorithm can serve as the basis of an algorithm solving such a problem, under the assumption that the point sets are dense enough to ensure that the solution will generally follow these curves / segments. Making this precise, and investigating how the running time depends on the number of line segm... | D |
The problem of presenting (finitely generated) free groups and semigroups in a self-similar way has a long history [15]. A self-similar presentation in this context is typically a faithful action on an infinite regular tree (with finite degree) such that, for any element and any node in the tree, the action of the elem... |
There is a quite interesting evolution of constructions to present free groups in a self-similar way or even as automaton groups (see [15] for an overview). This culminated in constructions to present free groups of arbitrary rank as automaton groups where the number of states coincides with the rank [18, 17]. While t... |
There are quite a few results on free (and related) products of self-similar or automaton groups (again see [15] for an overview) but many of them present the product as a subgroup of an automaton/self-similar group and, thus, loose the self-similarity property. An exception here is a line of research based on the Bel... | 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... | The construction used to prove Theorem 6 can also be used to obtain results which are not immediate corollaries of the theorem (or its corollary for automaton semigroups in 8). As an example, we prove in the following theorem that it is possible to adjoin a free generator to every self-similar semigroup without losing ... | A |
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... |
The usage of visual cues and sensitivities in existing methods is superfluous because the results indicate that performance improves through degradation of training accuracy. We hypothesize that simple regularization that does not rely on cues or sensitivities can also achieve large performance gains for VQA-CP. To te... |
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... | 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... | 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 ... | B |
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... |
For the question answering task, we leveraged the PrivacyQA corpus (Ravichander et al., 2019). PrivacyQA consists of 1,750 questions about the contents of privacy policies from 35 privacy documents. While crowdworkers were asked to come up with privacy related questions based on public information about an application... |
The 1,600 labelled documents were randomly divided into 960 documents for training, 240 documents for validation and 400 documents for testing. Using 5-fold cross-validation, we tuned the hyperparameters for the models separately with the validation set and then used the held-out test set to report the test results. D... | Document Classification. Some of the web pages in the English language candidate document set may not have been privacy policies and instead simply satisfied our URL selection criteria. To separate privacy policies from other web documents we used a supervised machine learning approach. Two researchers in the team labe... | The complete set of documents was divided into 97 languages and an unknown language category. We found that the vast majority of documents were in English. We set aside candidate documents that were not identified as English by Langid and were left with 2.1 million candidates.
| B |
The second expert (E2) is a senior researcher in software engineering and applied ML working in a government research institute and as an adjunct professor. He has worked with ML for the past 7 years, and 2 years with stacking ensemble learning. The third expert (E3) is the head of applied ML in a large multinational c... | Workflow. E1, E2, and E3 agreed that the workflow of StackGenVis made sense.
They all suggested that data wrangling could happen before the algorithms’ exploration, but also that it is usual to first train a few algorithms and then, based on their predictions, wrangle the data. | Another positive opinion from E3 was that, with a few adaptations to the performance metrics, StackGenVis could work with regression or even ranking problems.
E3 also mentioned that supporting feature generation in the feature selection phase might be helpful. Finally, E1 suggested that the circular barcharts could onl... | (ii) in the next algorithm exploration phase, we compare and choose specific ML algorithms for the ensemble and then proceed with their particular instantiations, i.e., the models;
(iii) during the data wrangling phase, we manipulate the instances and features with two different views for each of them; (iv) model explo... | Thus, it is considered an iterative process: the expert might start with the algorithms’ exploration and move to the data wrangling, or vice versa. “The former approach is even more suitable for your VA system, because you use the accuracy of the base ML models as feedback/guidance to the expert in order to understand ... | A |
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 | 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 | (E𝐂,(2¯,(u2,[013])))superscript𝐸𝐂¯2subscript𝑢2delimited-[]013(E^{\mathbf{C}},(\overline{2},(u_{2},[013])))( italic_E start_POSTSUPERSCRIPT bold_C end_POSTSUPERSCRIPT , ( over¯ start_ARG 2 end_ARG , ( italic_u start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT , [ 013 ] ) ) ),
(E𝐂,((u1,[112]),(u2,[010])))superscript𝐸𝐂subscr... | cannot be adjacent to 2¯¯2\overline{2}over¯ start_ARG 2 end_ARG nor 3¯¯3\overline{3}over¯ start_ARG 3 end_ARG,
and so f′superscript𝑓′f^{\prime}italic_f start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT is [013]delimited-[]013[013][ 013 ] or [010]delimited-[]010[010][ 010 ]. | 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 | D |
To answer RQ3, we conduct experiments on different data quantity and task similarity settings. We compare two baselines with MAML :
Transformer/CNN, which pre-trains the base model (Transformer/CNN) on the meta-training set and evaluates directly on the meta-testing set, and Transformer/CNN-F, which fine-tunes Transfor... | Model-Agnostic Meta-Learning (MAML) [Finn et al., 2017] is one of the most popular meta-learning methods. It is trained on plenty of tasks (i.e. small data sets) to get a parameter initialization which is easy to adapt to target tasks with a few samples. As a model-agnostic framework, MAML is successfully employed in d... | To answer RQ3, we conduct experiments on different data quantity and task similarity settings. We compare two baselines with MAML :
Transformer/CNN, which pre-trains the base model (Transformer/CNN) on the meta-training set and evaluates directly on the meta-testing set, and Transformer/CNN-F, which fine-tunes Transfor... | Task similarity. In Persona and Weibo, each task is a set of dialogues for one user, so tasks are different from each other. We shuffle the samples and randomly divide tasks to construct the setting that tasks are similar to each other. For a fair comparison, each task on this setting also has 120 and 1200 utterances o... | Data Quantity. In Persona, we evaluate Transformer/CNN, Transformer/CNN-F and MAML on 3 data quantity settings: 50/100/120-shot (each task has 50, 100, 120 utterances on average). In Weibo, FewRel and Amazon, the settings are 500/1000/1500-shot, 3/4/5-shot and 3/4/5-shot respectively (Table 2).
When the data quantity i... | D |
As αisubscript𝛼𝑖\alpha_{i}italic_α start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT and βjsubscript𝛽𝑗\beta_{j}italic_β start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT is the quantization of azimuth angle and elevation angle, respectively, the indexes of the optimal codewords ik*superscriptsubscript𝑖𝑘i_{k}^{*}italic_... | Multiuser-resultant Receiver Subarray Partition: As shown in Fig. 3, the r-UAV needs to activate multiple subarrays to serve multiple t-UAVs at the same time. Assuming that an element can not be contained in different subarrays, then the problem of activated CCA subarray partition rises at the r-UAV side for the fast m... |
Figure 6: The subarray patterns on the cylinder and the corresponding expanded cylinder. (a) The t-UAV subarray partition pattern. (b) The r-UAV subarray partition pattern with conflict. (c) The r-UAV subarray partition pattern without conflict. (d) The t-UAV subarray partition pattern with beamwidth selection. | The t-UAV needs to select an appropriate codeword 𝒗(i,j,𝒮)𝒗𝑖𝑗𝒮\boldsymbol{v}(i,j,\mathcal{S})bold_italic_v ( italic_i , italic_j , caligraphic_S ) from our proposed codebook 𝒱ksubscript𝒱𝑘\mathcal{V}_{k}caligraphic_V start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT to solve the subarray partition and AWV selecti... | According to (20), the codeword 𝒗(i,j,𝒮)𝒗𝑖𝑗𝒮\boldsymbol{v}(i,j,\mathcal{S})bold_italic_v ( italic_i , italic_j , caligraphic_S ) includes both the beam pattern information and the subarray pattern information. The beam pattern information mainly includes the beam angle (αi,βj)subscript𝛼𝑖subscript𝛽𝑗(\alpha_{i... | B |
We start in this section by giving proofs only for the 1111-color case, without the completeness requirement. While this case does not directly correspond to any formula used in the proof of Theorem 3.7 (since matrices (4) have 2 rows even when there are no binary predicates), this case gives the flavor of the argument... | We start in this section by giving proofs only for the 1111-color case, without the completeness requirement. While this case does not directly correspond to any formula used in the proof of Theorem 3.7 (since matrices (4) have 2 rows even when there are no binary predicates), this case gives the flavor of the argument... | The requirement that M¯|N¯conditional¯𝑀¯𝑁\bar{M}|\bar{N}over¯ start_ARG italic_M end_ARG | over¯ start_ARG italic_N end_ARG is extra big enough ensures that we have enough edges to perform the edge swapping.
This completes the proof for case 2 when the assumptions (a1) and (a2) hold. | This will be bootstrapped to the multi-color case in later sections. Note that the 1111-color case with the completeness requirement is not very interesting, and also not useful for the general case: completeness states that every node on
the left must be connected, via the unique edge relation, to every node on the ri... | 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 | C |
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... |
Contribution. Going beyond the NTK regime, we prove that, when the value function approximator is an overparameterized two-layer neural network, TD and Q-learning globally minimize the mean-squared projected Bellman error (MSPBE) at a sublinear rate. Moreover, in contrast to the NTK regime, the induced feature represe... | 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... | 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... | In this section, we extend our analysis of TD to Q-learning and policy gradient. In §6.1, we introduce Q-learning and its mean-field limit. In §6.2, we establish the global optimality and convergence of Q-learning. In §6.3, we further extend our analysis to soft Q-learning, which is equivalent to policy gradient.
| A |
In this paper, we replace residual connections of the Transformer with depth-wise LSTMs, to selectively manage the representation aggregation of layers benefiting performance while ensuring convergence of the Transformer. Specifically, we show how to integrate the computation of multi-head attention networks and feed-... | We show that the 6-layer Transformer using depth-wise LSTM can bring significant improvements in both WMT tasks and the challenging OPUS-100 multilingual NMT task. We show that depth-wise LSTM also has the ability to support deep Transformers with up to 24242424 layers, and that the 12-layer Transformer using depth-wis... |
Notably, on the En-De task, the 12-layer Transformer with depth-wise LSTM already outperforms the 24-layer vanilla Transformer, suggesting efficient use of layer parameters. On the Cs-En task, the 12-layer model with depth-wise LSTM performs on a par with the 24-layer baseline. Unlike in the En-De task, increasing dep... |
When using the depth-wise RNN, the architecture is quite similar to the standard Transformer layer without residual connections but using the concatenation of the input to the encoder/decoder layer with the output(s) of attention layer(s) as the input to the last FFN sub-layer. Table 2 shows that the 6-layer Transform... | Our experiments with the 6-layer Transformer show that our approach using depth-wise LSTM can achieve significant BLEU improvements in both WMT news translation tasks and the very challenging OPUS-100 many-to-many multilingual translation task over baselines. Our deep Transformer experiments demonstrate that: 1) the de... | D |
^{\circ}\!\left(X\right)\right\}caligraphic_K start_POSTSUPERSCRIPT ∘ end_POSTSUPERSCRIPT ( italic_Y ) ⊇ { italic_U ∩ italic_Y ∣ italic_U ∈ caligraphic_K start_POSTSUPERSCRIPT ∘ end_POSTSUPERSCRIPT ( italic_X ) }.
Note that this stronger property is preserved | on ⟨⟦𝖥𝖮[σ]⟧𝒟≤2∩τ⊆i⟩\langle\llbracket\mathsf{FO}[\upsigma]\rrbracket_{\mathcal{D}_{\leq 2}}\cap%
\uptau_{\subseteq_{i}}\rangle⟨ ⟦ sansserif_FO [ roman_σ ] ⟧ start_POSTSUBSCRIPT caligraphic_D start_POSTSUBSCRIPT ≤ 2 end_POSTSUBSCRIPT end_POSTSUBSCRIPT ∩ roman_τ start_POSTSUBSCRIPT ⊆ start_POSTSUBSCRIPT italic_i end_PO... | ⟨Fin(σ),τ≤,𝖥𝖮[σ]⟩Finσsubscriptτ𝖥𝖮delimited-[]σ\left\langle\operatorname{Fin}(\upsigma),\uptau_{\leq},\mathsf{FO}[\upsigma]\right\rangle⟨ roman_Fin ( roman_σ ) , roman_τ start_POSTSUBSCRIPT ≤ end_POSTSUBSCRIPT , sansserif_FO [ roman_σ ] ⟩ is a lpps.
| ⟨𝒟≤2,τ⊆i,𝖥𝖮[σ]⟩subscript𝒟absent2subscriptτsubscript𝑖𝖥𝖮delimited-[]σ\left\langle\mathcal{D}_{\leq 2},\uptau_{\subseteq_{i}},\mathsf{FO}[\upsigma]\right\rangle⟨ caligraphic_D start_POSTSUBSCRIPT ≤ 2 end_POSTSUBSCRIPT , roman_τ start_POSTSUBSCRIPT ⊆ start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT end_POSTSUBSCRIPT ... | ⟨Struct(σ),τ⊆i,𝖥𝖮[σ]⟩Structσsubscriptτsubscript𝑖𝖥𝖮delimited-[]σ\left\langle\operatorname{Struct}(\upsigma),\uptau_{\subseteq_{i}},\mathsf{FO}%
[\upsigma]\right\rangle⟨ roman_Struct ( roman_σ ) , roman_τ start_POSTSUBSCRIPT ⊆ start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT end_POSTSUBSCRIPT , sansserif_FO [ roman_... | C |
In the training stage, we crop each distorted image into four distortion elements and learn the parameters of the neural network using all data. Note that this training process is data-independent, where each part of the entire image is fed into the network one by one without the data correlation. In the test stage, w... | 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... | Evaluation Metrics: Crucially, evaluating the performance of different methods with reasonable metrics benefits experimental comparisons. In the distortion rectification problem, the corrected image can be evaluated with the peak signal-to-noise ratio (PSNR) and the structural similarity index (SSIM). For the evaluatio... | In contrast to RMSE, MDLD is more suitable for parameter evaluation due to the uniqueness of the distortion distribution. Moreover, RMSE fails to evaluate the different numbers and attributes of estimated parameters for different camera models. Thanks to the objective description of the distortion, MDLD is capable of e... |
As listed in Table II, our approach significantly outperforms the compared approaches in all metrics, including the highest metrics on PSNR and SSIM, as well as the lowest metric on MDLD. Specifically, compared with the traditional methods [23, 24] based on the hand-crafted features, our approach overcomes the scene l... | B |
We use a pre-trained ViT 555https://huggingface.co/google/vit-base-patch16-224-in21k [4] model and fine-tune it on the CIFAR-10/CIFAR-100 datasets.
The experiments are implemented based on the Transformers 666https://github.com/huggingface/transformers framework. We fine-tune the model with 20 epochs. | Many methods have been proposed for improving the performance of SGD with large batch sizes. The works in [7, 33]
proposed several tricks, such as warm-up and learning rate scaling schemes, to bridge the generalization gap under large-batch training settings. Researchers in [11] | We don’t use training tricks such as warm-up [7]. We adopt the linear learning rate decay strategy as default in the Transformers framework.
Table 5 shows the test accuracy results of the methods with different batch sizes. SNGM achieves the best performance for almost all batch size settings. | 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... | B |
When the algorithm terminates with Cs=∅subscript𝐶𝑠C_{s}=\emptysetitalic_C start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT = ∅, Lemma 5.2 ensure the solution zfinalsuperscript𝑧finalz^{\text{final}}italic_z start_POSTSUPERSCRIPT final end_POSTSUPERSCRIPT is integral. By Lemma 5.5, any client j𝑗jitalic_j with d(j,S)>... | Brian Brubach was supported in part by NSF awards CCF-1422569 and CCF-1749864, and by research awards from Adobe. Nathaniel Grammel and Leonidas Tsepenekas were supported in part by NSF awards CCF-1749864 and CCF-1918749, and by research awards from Amazon and Google. Aravind Srinivasan was supported in part by NSF awa... |
do FA←{ijA|j∈HA and FI∩GπIj=∅}←subscript𝐹𝐴conditional-setsubscriptsuperscript𝑖𝐴𝑗𝑗subscript𝐻𝐴 and subscript𝐹𝐼subscript𝐺superscript𝜋𝐼𝑗F_{A}\leftarrow\{i^{A}_{j}~{}|~{}j\in H_{A}\text{ and }F_{I}\cap G_{\pi^{I}j}=\emptyset\}italic_F start_POSTSUBSCRIPT italic_A end_POSTSUBSCRIPT ← { italic_i star... | For instance, during the COVID-19 pandemic, testing and vaccination centers were deployed at different kinds of locations, and access was an important consideration [18, 20]; access can be quantified in terms of different objectives including distance, as in our work. Here,
ℱℱ\mathcal{F}caligraphic_F and 𝒞𝒞\mathcal{C... | FAs¯←{ijA|j∈HA and FI∩GπIj=∅}←subscriptsuperscript𝐹¯𝑠𝐴conditional-setsubscriptsuperscript𝑖𝐴𝑗𝑗subscript𝐻𝐴 and subscript𝐹𝐼subscript𝐺superscript𝜋𝐼𝑗F^{\bar{s}}_{A}\leftarrow\{i^{A}_{j}~{}|~{}j\in H_{A}\text{ and }F_{I}\cap G_{%
\pi^{I}j}=\emptyset\}italic_F start_POSTSUPERSCRIPT over¯ start_ARG italic_s... | A |
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... |
II. The structure of the networks among optimizers is modeled by a more general sequence of random digraphs. The sequence of random digraphs is conditionally balanced, and the weighted adjacency matrices are not required to have special statistical properties such as independency with identical distribution, Markovian... | We have studied the distributed stochastic subgradient algorithm for the stochastic optimization by networked nodes to cooperatively minimize a sum of convex cost functions.
We have proved that if the local subgradient functions grow linearly and the sequence of digraphs is conditionally balanced and uniformly conditio... |
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... | 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... | C |
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 ... | 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... |
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... | 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 ... | B |
3D-FUTURE dataset is a recently public large-scale indoor dataset with 34 categories. Following the official splits, we adopt 12,144 images for training, 2,024 for validation and 6,072 for testing. From the size distribution of bounding boxes in 3D-FUTURE and COCO shown in Figure 1, the medium object size of 3D-FUTURE ... | Table 2: PointRend’s step-by-step performance on our own validation set (splitted from the original training set). “MP Train” means more points training and “MP Test” means more points testing. “P6 Feature” indicates adding P6 to default P2-P5 levels of FPN for both coarse prediction head and fine-grained point head. “... | 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.... | 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... | PointRend performs point-based segmentation at adaptively selected locations and generates high-quality instance mask. It produces smooth object boundaries with much finer details than previously two-stage detectors like MaskRCNN, which naturally benefits large object instances and complex scenes. Furthermore, compared... | A |
I(f)<1,andH(|f^|2)>nn+1logn.formulae-sequence𝐼𝑓1and𝐻superscript^𝑓2𝑛𝑛1𝑛I(f)<1,\ \ {\mbox{and}}\ \ H(|\hat{f}|^{2})>\frac{n}{n+1}\log n.italic_I ( italic_f ) < 1 , and italic_H ( | over^ start_ARG italic_f end_ARG | start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ) > divide start_ARG italic_n end_ARG start_ARG ita... | 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... | (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... | C |
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 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... |
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... | B |
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... |
In general, respondents possess a competent level of digital literacy skills with a majority exercising good news sharing practices. They actively verify news before sharing by checking with multiple sources found through the search engine and with authoritative information found in government communication platforms,... | 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... |
There is a very strong, negative correlation between the media sources of fake news and the level of trust in them (ref. Figures 1 and 2) which is statistically significant (r(9)=−0.81𝑟90.81r(9)=-0.81italic_r ( 9 ) = - 0.81, p<.005𝑝.005p<.005italic_p < .005). Trust is built on transparency and truthfulness, and t... | 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... | C |
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