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 |
Table 4 presents the results of conventional entity alignment. decentRL achieves state-of-the-art performance, surpassing all others in Hits@1 and MRR. AliNet [39], a hybrid method combining GCN and GAT, performs better than the methods solely based on GAT or GCN on many metrics. Nonetheless, across most metrics and da... | GNN-based methods [13, 37, 38, 39, 40, 41, 42] introduce relation-specific composition operations to combine neighbors and their corresponding relations before performing neighborhood aggregation. They usually leverage existing GNN models, such as GCN and GAT [43, 44], to aggregate an entity’s neighbors. It is worth no... | In this work, we propose Decentralized Attention Network for knowledge graph embedding and introduce self-distillation to enhance its ability to generate desired embeddings for both known and unknown entities. We provide theoretical justification for the effectiveness of our proposed learning paradigm and conduct compr... |
Although GCN and GAT are generally regarded as inductive models for graph representation learning, our analysis in previous sections suggests their limited applicability on relational KG embedding. In further validation of this, we compare the performance of decentRL with AliNet and GAT on datasets containing new enti... | Figure 4 shows the experimental results. decentRL outperforms both GAT and AliNet across all metrics. While its performance slightly decreases compared to conventional datasets, the other methods experience even greater performance drops in this context. AliNet also outperforms GAT, as it combines GCN and GAT to aggreg... | C |
In this work, we consider self-supervised exploration without extrinsic reward. In such a case, the above trade-off narrows down to a pure exploration problem, aiming at efficiently accumulating information from the environment. Previous self-supervised exploration typically utilizes ‘curiosity’ based on prediction-err... |
The related exploration methods aim to remove the stochasticity of the dynamics rather than modeling it. For example, Inverse Dynamics [10], Random Features [11], and EMI [30] learn a feature space to remove the task-irrelevant information in feature space such as white-noise. Curiosity-Bottleneck [31] and Dynamic Bot... |
An ordinary encoder-decoder based dynamics model that makes deterministic predictions often fails to capture the multimodality and stochasticity in dynamics and outputs an averaged prediction. An intuitive example is given in Fig. 1, there are two roads (one from the left, and the other from the right) to reach the go... |
In this paper, we propose the Variational Dynamic Model (VDM), which models the multimodality and stochasticity of the dynamics explicitly based on conditional variational inference. VDM considers the environmental state-action transition as a conditional generative process by generating the next-state prediction unde... | We observe that our method performs the best in most of the games, in both the sample efficiency and the performance of the best policy. The reason our method outperforms other baselines is the multimodality in dynamics that the Atari games usually have. Such multimodality is typically caused by other objects that are ... | A |
+1)}\|_{C^{0}(\Omega)}}{2^{n}(n+1)!}\,,\,\,\,P_{A}=\mathrm{Cheb}_{n}^{1\mathrm%
{st}}\,.| italic_f ( italic_x ) - italic_Q start_POSTSUBSCRIPT italic_f , italic_A end_POSTSUBSCRIPT ( italic_x ) | ≤ divide start_ARG | italic_f start_POSTSUPERSCRIPT ( italic_n + 1 ) end_POSTSUPERSCRIPT ( italic_ξ start_POSTSUBSCRIPT ital... | Our result in Eq. (7.8) provides a similar bound on the approximation error in m𝑚mitalic_mD whenever the k𝑘kitalic_k-th derivatives of f𝑓fitalic_f are known or bounded.
However, usually these bounds are unknown. By validating the proposed Trefethen approximation rates in the next section, we even though provide a po... | Recently, Lloyd N. Trefethen [83] proposed a way of delivering a potential solution to the problem: For continuous functions f:Ω⟶ℝ:𝑓⟶Ωℝf:\Omega\longrightarrow\mathbb{R}italic_f : roman_Ω ⟶ blackboard_R
that are analytic in the unbounded Trefethen domain (a genralization of a Bernstein ellipse) Nm,ρ⊊Ω=[−1,1]msubscript�... | This result states that any sufficiently smooth function f𝑓fitalic_f can be approximated by piecewise polynomial functions, which allows to approximate f𝑓fitalic_f by Hermite or spline interpolation.
Generalizations of this result rely on this fact and are formulated in a similar manner [23, 24, 26]. | Furthermore, so far none of these approaches is known to reach the optimal Trefethen approximation rates when requiring the number of nodes of the underlying tensorial grids to
scale sub-exponential with space dimension. As the numerical experiments in Section 8 suggest, we believe that only non-tensorial grids are abl... | A |
In the second case, the distributions μ𝜇\muitalic_μ and ν𝜈\nuitalic_ν are both d𝑑ditalic_d-dimensional Gaussian distributions with the same mean vector but different covariance metrics, where d∈{30,60}𝑑3060d\in\{30,60\}italic_d ∈ { 30 , 60 }.
More specifically, μ=𝒩(0,Id)𝜇𝒩0subscript𝐼𝑑\mu=\mathcal{N}(0,I_{d})i... | In other words, we only scale the first two diagonal entries in the covariance matrix of ν𝜈\nuitalic_ν to make the hypothesis testing problem difficult to perform.
We compare the performance of the PW test with the MMD test discussed in [20], where the kernel function is chosen to be the standard Gaussian kernel with ... | Several data-efficient two-sample tests [20, 21, 22] are constructed based on Maximum Mean Discrepancy (MMD), which quantifies the distance between two distributions by introducing test functions in a Reproducing Kernel Hilbert Space (RKHS).
However, it is pointed out in [23] that when the bandwidth is chosen based on ... | However, the two-sample tests based on concentration inequalities in Section III give conservative results in practice. We examine the two-sample tests using the projected Wasserstein distance via the permutation approach.
Specifically, we permute the collected data points for Np=100subscript𝑁𝑝100N_{p}=100italic_N st... | The last two plots correspond to covariance-shifted Gaussian distributions, where Fig. 1c) examines the power for different n𝑛nitalic_n with fixed d=60𝑑60d=60italic_d = 60, and Fig. 1d) examines the power for different d𝑑ditalic_d with fixed n=75𝑛75n=75italic_n = 75.
We can see that the power of all methods increas... | A |
Prior work in unsupervised DR learning suggests the objective of learning statistically independent factors of the latent space as means to obtain DR. The underlying assumption is that the latent variables H𝐻Hitalic_H can be partitioned into independent components C𝐶Citalic_C (i.e. the disentangled factors) and corre... | While the aforementioned models made significant progress on the problem, they suffer from an inherent trade-off between learning DR and reconstruction quality. If the latent space is heavily regularized, not allowing enough capacity for the nuisance variables, reconstruction quality is diminished. On the other hand, i... | Specifically, we apply a DGM to learn the nuisance variables Z𝑍Zitalic_Z, conditioned on the output image of the first part, and use Z𝑍Zitalic_Z in the normalization layers of the decoder network to shift and scale the features extracted from the input image. This process adds the details information captured in Z𝑍Z... | Prior work in unsupervised DR learning suggests the objective of learning statistically independent factors of the latent space as means to obtain DR. The underlying assumption is that the latent variables H𝐻Hitalic_H can be partitioned into independent components C𝐶Citalic_C (i.e. the disentangled factors) and corre... |
The model has two parts. First, we apply a DGM to learn only the disentangled part, C𝐶Citalic_C, of the latent space. We do that by applying any of the above mentioned VAEs111In this exposition we use unspervised trained VAEs as our base models but the framework also works with GAN-based or FLOW-based DGMs, supervise... | A |
Furthermore, we propose Simulation Metric (DFS) based on deep-first search (DFS) that enables easy implementation and testing of complex structural computer Circuits. This confirmed the feasibility of this study in an experiment based on an XOR gate produced by combining NAND, AND and OR gates.
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And it is expected that this research can be applied to the development of artificial intelligence technologies such as deep learning in the future. In other words, it is expected that the idea of structural computers will be applied to semiconductors that generate a lot of heat, such as Computer Vision task[8][9][10]... | We will look at the inputs through 18 test cases to see if the circuit is acceptable. Next, it verifies with DFS that the output is possible for the actual pin connection state. As mentioned above, the search is carried out and the results are expressed by the unique number of each vertex. The result is as shown in Tab... | Optical logic aggregates can be designed in the same way as in Implementation of Structural Computer Using Mirrors and Translucent Mirrors, and for the convenience of expression and the exploration of mathematical properties (especially their association with matrices), the number shown in Fig. 5 can be applied to the ... | The structure-based computer mentioned in this paper are based on Boolean Algebra, a system commonly applied to digital computers. Boolean algebra is a concept created by George Boole (1815-1854) of the United Kingdom that expresses the True and False of logic 1 and 0, and mathematically describes digital electrical si... | A |
Given a polynomial function f(x)𝑓𝑥f(x)italic_f ( italic_x ) over a finite field 𝔽𝔽\mathbb{F}blackboard_F (or 𝔽nsuperscript𝔽𝑛\mathbb{F}^{n}blackboard_F start_POSTSUPERSCRIPT italic_n end_POSTSUPERSCRIPT), determine if it is a permutation over 𝔽𝔽\mathbb{F}blackboard_F (𝔽nsuperscript𝔽𝑛\mathbb{F}^{n}blackboard... | The paper primarily addresses the problem of linear representation, invertibility, and construction of the compositional inverse for non-linear maps over finite fields. Though there is vast literature available for invertibility of polynomials and construction of inverses of permutation polynomials over 𝔽𝔽\mathbb{F}b... | Given a polynomial function f(x)𝑓𝑥f(x)italic_f ( italic_x ) over a finite field 𝔽𝔽\mathbb{F}blackboard_F (or 𝔽nsuperscript𝔽𝑛\mathbb{F}^{n}blackboard_F start_POSTSUPERSCRIPT italic_n end_POSTSUPERSCRIPT), determine if it is a permutation over 𝔽𝔽\mathbb{F}blackboard_F (𝔽nsuperscript𝔽𝑛\mathbb{F}^{n}blackboard... | Given an 1111-parameter family of maps over 𝔽𝔽\mathbb{F}blackboard_F, determine if it is parametrically invertible over 𝔽𝔽\mathbb{F}blackboard_F. It is also shown in this paper that the compositional inverse of a 1111-parameter family of permutation polynomials is also a 1111-parameter family of permutation polynom... | We developed a linear representation theory for functions over 𝔽𝔽\mathbb{F}blackboard_F in the previous section. This section extends the idea to a family of functions over 𝔽𝔽\mathbb{F}blackboard_F defined through a 𝔽𝔽\mathbb{F}blackboard_F-valued parameter. The well-known Dickson polynomial is one such motivatin... | C |
Stacked penalized logistic regression (StaPLR) (Van Loon \BOthers., \APACyear2020) is a method specifically developed to tackle the joint classification and view selection problem. Compared with a variant of the lasso for selecting groups of features (the so-called group lasso (M. Yuan \BBA Lin, \APACyear2007)), StaPLR... | For this purpose, one would ideally like to use an algorithm that provides sparsity, but also algorithmic stability in the sense that given two very similar data sets, the set of selected views should vary little. However, sparse algorithms are generally not stable, and vice versa (Xu \BOthers., \APACyear2012).
An exam... | In this article we investigated how different view-selecting meta-learners affect the performance of multi-view stacking. In our simulations, the interpolating predictor often performed worse than the other meta-learners on at least one outcome measure. For example, when the sample size was larger than the number of vi... | In high-dimensional biomedical studies, a common goal is to create an accurate classification model using only a subset of the features (Y. Li \BOthers., \APACyear2018). A popular approach to this type of joint classification and feature selection problem is to apply penalized methods such as the lasso (Tibshirani, \AP... | A particular challenge of the aforementioned joint classification and view selection problem is its inherent trade-off between accuracy and sparsity. For example, the most accurate model may not perform the best in terms of view selection. In fact, the prediction-optimal amount of regularization causes the lasso to sel... | D |
Compared to other methods, IEPC exhibits a notably lower reduction rate, which, we believe, contributes to its unstable performance. The experimental results in Figure 3 indicate that when considering only linear prediction models, IEPC performs better with regularization techniques such as LASSO and Ridge, as opposed ... |
It is worth noting that the key difference between the two DepAD methods (FBED-CART-PS and FBED-CAR-Sum) and ALSO lies in their relevant variable selection phase. The two DepAD methods learn and use the MB of a variable as its relevant variables, while ALSO, for each variable, uses all other variables as the variable’... | In conclusion, the relevant variable selection phase of the DepAD framework is crucial for identifying optimal predictors for the target variable in anomaly detection. Striking a balance between selecting too many or too few variables is essential for maintaining prediction accuracy. When the ground-truth relevant vari... |
Table 6 presents the reduction rates achieved by each of the five techniques. The reduction rate is computed as 1 minus the ratio of the number of relevant variables selected to the total number of variables in a dataset. The results reveal substantial variations in reduction rates among the different techniques for t... |
Among the filter feature selection methods, causal feature selection methods [31, 29, 32] are recommended choices as they identify the causal factors of a target variable, offering better interpretability. These methods select the parents and children (PC) or Markov blanket (MB) of a target variable in a Bayesian netw... | B |
At the start of the interaction, when no contexts have been observed, θ^tsubscript^𝜃𝑡\hat{\theta}_{t}over^ start_ARG italic_θ end_ARG start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT is well-defined by Eq (5) when λt>0subscript𝜆𝑡0\lambda_{t}>0italic_λ start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT > 0. Therefore, th... | where pessimism is the additive inverse of the optimism (difference between the payoffs under true parameters and those estimated by CB-MNL). Due to optimistic decision-making and the fact that θ∗∈Ct(δ)subscript𝜃subscript𝐶𝑡𝛿\theta_{*}\in C_{t}(\delta)italic_θ start_POSTSUBSCRIPT ∗ end_POSTSUBSCRIPT ∈ italic_C star... |
Comparison with Oh & Iyengar [2019] The Thompson Sampling based approach is inherently different from our Optimism in the face of uncertainty (OFU) style Algorithm CB-MNL. However, the main result in Oh & Iyengar [2019] also relies on a confidence set based analysis along the lines of Filippi et al. [2010] but has a m... | In this paper, we build on recent developments for generalized linear bandits (Faury et al. [2020]) to propose a new optimistic algorithm, CB-MNL for the problem of contextual multinomial logit bandits. CB-MNL follows the standard template of optimistic parameter search strategies (also known as optimism in the face of... | Algorithm 1 follows the template of in the face of uncertainty (OFU) strategies [Auer et al., 2002, Filippi et al., 2010, Faury et al., 2020]. Technical analysis of OFU algorithms relies on two key factors: the design of the confidence set and the ease of choosing an action using the confidence set.
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Up-scaling a video could transform a short action into a long one, but may lose important information for localization. Thus both the original scale and the enlarged scale have their limitations and advantages. The original video scale contains the original intact information, while the enlarged one is easier for the ... | Specifically, we propose a Video self-Stitching Graph Network (VSGN) for improving performance of short actions in the TAL problem. Our VSGN is a multi-level cross-scale framework that contains two major components: video self-stitching (VSS); cross-scale graph pyramid network (xGPN). In VSS, we focus on a short period... |
Multi-scale input. The magnification process may inevitably impair the information in the clip, thus the original video clip, which contains the original intact information, is also necessary. To take advantage of the complementary properties of both scales, we design a video stitching technique to piece them together... |
2) We propose a novel temporal action localization framework VSGN, which features two key components: video self-stitching (VSS); cross-scale graph pyramid network (xGPN). For effective feature aggregation, we design a cross-scale graph network for each level in xGPN with a hybrid module of a temporal branch and a gra... |
In this paper, to tackle the challenging problem of large action scale variation in the temporal action localization (TAL) problem, we target short actions and propose a multi-level cross-scale solution called video self-stitching graph network (VSGN). It contains a video self-stitching (VSS) component that generates ... | A |
Hyperparameter optimization (also called hyperparameter tuning) is the process of selecting appropriate values of hyperparameters for machine learning (ML) models, often independently for each data set, to achieve their best possible results.
Although time consuming, this process is required for the vast majority of ML... | Important contributions of this research include the formalization of primary concepts [CDM15], the identification of methods for assessing hyperparameter importance [JWXY16, PBB19, vRH17, HHLB13, HHLB14, vRH18], and resulting libraries and frameworks for specific hyperparameter optimization methods [KGG∗18, THHLB13]. ... | Visualization tools have been implemented for sequential-based, bandit-based, and population-based approaches [PNKC21], and for more straightforward techniques such as grid and random search [LCW∗18]. Evolutionary optimization, however, has not experienced similar consideration by the InfoVis and VA communities, with t... | One common focus of related work is the hyperparameter search for deep learning models. HyperTuner [LCW∗18] is an interactive VA system that enables hyperparameter search by using a multi-class confusion matrix for summarizing the predictions and setting user-defined ranges for multiple validation metrics to filter out... | Numerous techniques exist that try to solve this challenge, such as the well-known grid search, random search [BB12], and Bayesian optimization that belong to the generic type of sequential-based methods [BBBK11, SSW∗16]. Other proposed methods include bandit-based approaches [FKH18, LJD∗17], population-based methods [... | D |
The fundamental idea underlying MCMC algorithms is to synthesize a Markov chain that converges to a specified steady-state distribution.
Random sampling of a large state space while adhering to a predefined probability distribution is the predominant use of MCMC algorithms. | The current literature covers a broad spectrum of methodologies for Markov chain synthesis, incorporating both heuristic approaches and optimization-based techniques [4, 5, 6]. Each method provides specialized algorithms tailored to the synthesis of Markov chains in alignment with specific objectives or constraints.
Ma... | This algorithm treats the spatial distribution of swarm agents, called the density distribution, as a probability distribution and employs the Metropolis-Hastings (M-H) algorithm to synthesize a Markov chain that guides the density distribution toward a desired state.
The probabilistic guidance algorithm led to the dev... | Unlike the homogeneous Markov chain synthesis algorithms in [4, 7, 5, 6, 8, 9], the Markov matrix, synthesized by our algorithm, approaches the identity matrix as the probability distribution converges to the desired steady-state distribution. Hence the proposed algorithm attempts to minimize the number of state transi... | In this section, we apply the DSMC algorithm to the probabilistic swarm guidance problem and provide numerical simulations that show the convergence rate of the DSMC algorithm is considerably faster as compared to the previous Markov chain synthesis algorithms in [7] and [14].
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We have proven that the IsoMuSh algorithm is convergent in the objective f(⋅,⋅)𝑓⋅⋅f(\cdot,\cdot)italic_f ( ⋅ , ⋅ ). However, we did not establish convergence of the variables U𝑈Uitalic_U and Q𝑄Qitalic_Q. In this context, we note that there are equivalence classes of U𝑈Uitalic_U and Q𝑄Qitalic_Q that lead to the sa... |
We presented a novel formulation for the isometric multi-shape matching problem. Our main idea is to simultaneously solve for shape-to-universe matchings and shape-to-universe functional maps. By doing so, we generalise the popular functional map framework to multi-matching, while guaranteeing cycle consistency, both ... | In contrast, HiPPI and our method require shape-to-universe representations. To obtain these, we use synchronisation to extract the shape-to-universe representation from the pairwise transformations. By doing so, we obtain the initial U𝑈Uitalic_U and Q𝑄Qitalic_Q. We refer to this method of synchronising the ZoomOut r... | Similar to the previous section, we want to impose cycle consistency on the pairwise functional maps 𝒞ijsubscript𝒞𝑖𝑗\mathcal{C}_{ij}caligraphic_C start_POSTSUBSCRIPT italic_i italic_j end_POSTSUBSCRIPT.
We do so by defining a shape-to-universe functional map 𝒞isubscript𝒞𝑖\mathcal{C}_{i}caligraphic_C start_POSTS... | A shortcoming when applying the mentioned multi-shape matching approaches to isometric settings is that they do not exploit structural properties of isometric shapes. Hence, they lead to suboptimal multi-matchings, which we experimentally confirm in Sec. 5. One exception is the recent work on spectral map synchronisati... | A |
If there exists a polynomial algorithm that tests if a graph G𝐺Gitalic_G is a path graph and returns a clique path tree of G𝐺Gitalic_G when the answer is “yes”, then there exists an algorithm with the same complexity to test if a graph is a directed
path graph. |
In this section we introduce some results and notations in [1], that give a new characterization of path graphs resumed in Theorem 6. Indirectly, some of these results allow us to efficiently recognize directed path graphs too (see Section 5 and Theorem 9). | On the side of directed path graphs, at the state of art, our algorithm is the only one that does not use the results in [4], in which it is given a linear time algorithm able to establish whether a path graph is a directed path graph too (see Theorem 5 for further details). Thus, prior to this paper, it was necessary ... | The paper is organized as follows. In Section 2 we present the characterization of path graphs and directed path graphs given by Monma and Wei [18], while in Section 3 we explain the characterization of path graphs by Apollonio and Balzotti [1]. In Section 4 we present our recognition algorithm for path graphs, we prov... | interval graphs ⊂ rooted path graphs ⊂ directed path graphs ⊂ path graphs ⊂ chordal graphs.interval graphs ⊂ rooted path graphs ⊂ directed path graphs ⊂ path graphs ⊂ chordal graphs\text{interval graphs $\subset$ rooted path graphs $\subset$ directed path %
graphs $\subset$ path graphs $\subset$ chordal graphs}.interva... | A |
In experiments 1(a) and 1(b), we study how the fraction of pure nodes affects the behaviors of these mixed membership community detection methods under MMSB and DCMM, respectively. We fix (x,ρ)=(0.4,0.1)𝑥𝜌0.40.1(x,\rho)=(0.4,0.1)( italic_x , italic_ρ ) = ( 0.4 , 0.1 ) and let n0subscript𝑛0n_{0}italic_n start_POSTSUB... |
Panels (e) and (f) of Figure 1 report the numerical results of these two sub-experiments. They suggest that estimating the memberships becomes harder as the purity of mixed nodes decreases. Mixed-SLIM and Mixed-SCORE perform similarly and both two approaches perform better than OCCAM and GeoNMF under the MMSB setting.... |
Numerical results of these two sub-experiments are shown in panels (c) and (d) of Figure 1. From subfigure (c), under the MMSB model, we can find that Mixed-SLIM, Mixed-SCORE, OCCAM, and GeoNMF have similar performances, and as ρ𝜌\rhoitalic_ρ increases they all perform poorer. Under the DCMM model, the mixed Humming ... |
Numerical results of these two sub-experiments are shown in panels (a) and (b) of Figure 1, respectively. From the results in subfigure 1(a), it can be found that Mixed-SLIM performs similarly to Mixed-SCORE while both two methods perform better than OCCAM and GeoNMF under the MMSB setting. Subfigure 1(b) suggests tha... |
The numerical results are given by the last two panels of Figure 1. Subfigure 1(k) suggests that Mixed-SLIM, Mixed-SCORE, and GeoNMF share similar performances and they perform better than OCCAM under the MMSB setting. the proposed Mixed-SLIM significantly outperforms the other three methods under the DCMM setting. | C |
For any functional F:ℳ→ℝ:𝐹→ℳℝF\colon\mathcal{M}\rightarrow\mathbb{R}italic_F : caligraphic_M → blackboard_R, we let gradFgrad𝐹\operatorname{{\mathrm{grad}}}Froman_grad italic_F denote the functional gradient of F𝐹Fitalic_F with respect to the Riemannian metric g𝑔gitalic_g.
| To study optimization problems on the space of probability measures, we first introduce the background knowledge of the Riemannian manifold and the Wasserstein space. In addition, to analyze the statistical estimation problem that arises in estimating the Wasserstein gradient, we introduce the reproducing kernel Hilber... | Here the statistical error is incurred in estimating the Wasserstein gradient by solving the dual maximization problem using functions in a reproducing kernel Hilbert space (RKHS) with finite data, which converges sublinearly to zero as the number of particles goes to infinity.
Therefore, in this scenario, variational ... | Second, when the Wasserstein gradient is approximated using RKHS functions and the objective functional satisfies the PL condition, we prove that the sequence of probability distributions constructed by variational transport converges linearly to the global minimum of the objective functional, up to certain statistical... | we prove that variational transport constructs a sequence of probability distributions that converges linearly to the global minimizer of the objective functional up to a statistical error due to estimating the Wasserstein gradient with finite particles. Moreover, such a statistical error converges to zero as the numbe... | A |
To make the policy transferable, traffic signal control is also modeled as a meta-learning problem in [14, 49, 36]. Specifically, the method in [14] performs meta-learning on multiple independent MDPs and ignores the influences of neighbor agents. A data augmentation method is proposed in [49] to generates diverse traf... | Secondly, even for a specific task, the received rewards and observations are uncertain to the agent, as illustrated in Fig. 1, which make the policy learning unstable and non-convergent. Even if the agent performs the same action on the same observation at different timesteps, the agent may receive different rewards a... | Intrinsic motivation methods have been widely studied in the literature, such as handling the difficult-to-learn dilemma in sparse reward environments [51] or trading off the exploration and exploitation in non-sparse reward scenarios [50]. Most of the intrinsic reward approaches can be classified into two classes. The... |
Besides the above two classes, other intrinsic reward methods are mainly task-oriented and for a specific purpose. For example, the method in [19] uses the discrepancy between the marginal policy and the conditional policy as the intrinsic reward for encouraging agents to have a greater social impact on others. The er... | Before formulating the problem, we firstly design the learning paradigm by analyzing the characteristics of the traffic signal control (TSC). Due to the coordination among different signals, the most direct paradigm may be centralized learning. However, the global state information in TSC is not only highly redundant a... | B |
Then, for every 𝐱0∈Sτ(𝐱∗)subscript𝐱0subscript𝑆𝜏subscript𝐱\mathbf{x}_{0}\,\in\,S_{\tau}(\mathbf{x}_{*})bold_x start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ∈ italic_S start_POSTSUBSCRIPT italic_τ end_POSTSUBSCRIPT ( bold_x start_POSTSUBSCRIPT ∗ end_POSTSUBSCRIPT ), we have
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‖𝐱k+1−𝐱0‖2subscriptnormsubscript𝐱𝑘1subscript𝐱02\displaystyle\|\mathbf{x}_{k+1}-\mathbf{x}_{0}\|_{2}∥ bold_x start_POSTSUBSCRIPT italic_k + 1 end_POSTSUBSCRIPT - bold_x start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ∥ start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT | ≤‖𝐱k+1−𝐱k‖2+⋯+‖𝐱1−𝐱0‖2absentsubscriptnormsubscript𝐱𝑘1subscript𝐱𝑘2⋯subscriptnormsubscript𝐱1subscript𝐱02\displaystyle~{}~{}\leq~{}~{}\|\mathbf{x}_{k+1}-\mathbf{x}_{k}\|_{2}+\cdots+\|%
\mathbf{x}_{1}-\mathbf{x}_{0}\|_{2}≤ ∥ bold_x start_POSTSUBSCRIPT italic_k + 1 end_POSTSUBSCRIPT - bold_x start_POSTSUBSCRIPT it... | 𝐱1=𝐱0−A†(A𝐱0−𝐛)=A†𝐛+(I−A†A)𝐱0subscript𝐱1subscript𝐱0superscript𝐴†𝐴subscript𝐱0𝐛superscript𝐴†𝐛𝐼superscript𝐴†𝐴subscript𝐱0\mathbf{x}_{1}~{}~{}=~{}~{}\mathbf{x}_{0}-A^{\dagger}\,(A\,\mathbf{x}_{0}-%
\mathbf{b})~{}~{}=~{}~{}A^{\dagger}\,\mathbf{b}+(I-A^{\dagger}\,A)\,\mathbf{x}% | ‖𝐱1−𝐱∗‖normsubscript𝐱1subscript𝐱\displaystyle\|\mathbf{x}_{1}-\mathbf{x}_{*}\|∥ bold_x start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - bold_x start_POSTSUBSCRIPT ∗ end_POSTSUBSCRIPT ∥
≤‖𝐱1−𝐱0‖2+‖𝐱0−𝐱∗‖2absentsubscriptnormsubscript𝐱1subscript𝐱02subscriptnormsubscript𝐱0subscript𝐱2\displaystyle~{}~{}\leq~{}~{}\|\mat... | D |
The second type of benchmarks is generated from the BPPLIB library (?), a collection of bin packing benchmarks used in various works on (offline) algorithms for bin packing. In particular, we report results on the benchmarks “GI” (?), “Schwerin” (?), “Randomly_Generated” (?), “Schoenfield_Hard28” (?) and “Wäscher” (?).... | As illustrated in Figure 3(c), the smaller the parameter λ𝜆\lambdaitalic_λ, the better the performance of Hybrid(λ𝜆\lambdaitalic_λ); in particular, ProfilePacking performs the best, which suggests that for inputs from a small set of item sizes, it is beneficial to choose a small value of λ𝜆\lambdaitalic_λ. This can ... |
In this work, we focus on the online variant of bin packing, in which the set of items is not known in advance but is rather revealed in the form of a sequence. Upon the arrival of a new item, the online algorithm must either place it into one of the currently open bins, as long as this action does not violate the bin... |
In this section, we present an experimental evaluation of the performance of our algorithms111The code on which the experiments are based is available at https://github.com/shahink84/BinPackingPredictions.. Specifically, in Section 6.1 we describe the benchmarks and the input generation model; in Section 6.2, we expan... | We set the bin capacity to k=100𝑘100k=100italic_k = 100, and we also scale down each item to the closest integer in [1,k]1𝑘[1,k][ 1 , italic_k ].
This choice is relevant for applications such as Virtual Machine placement (Section 5.1), as explained in Section 5.1. We generate two classes of input sequences. | D |
Efficient 3D object representations are fundamental building blocks of many computer vision and machine learning applications, ranging from robotic manipulation (Kehoe et al., 2015) to autonomous driving (Yang et al., 2018a). Contemporary 3D registration devices, such as LIDARs and depth cameras, generate these represe... |
We compare the results with the existing solutions that aim at point cloud generation: latent-GAN (Achlioptas et al., 2017), PC-GAN (Li et al., 2018), PointFlow (Yang et al., 2019), HyperCloud(P) (Spurek et al., 2020a) and HyperFlow(P) (Spurek et al., 2020b). We also consider in the experiment two baselines, HyperClou... |
Patch-based approaches (Yang et al., 2018b; Groueix et al., 2018; Bednarik et al., 2020; Deng et al., 2020b) are much more flexible and enable modeling virtually any surfaces, including those with a non-disk topology. It is achieved using parametric mappings to transform 2D patches into a set of 3D shapes. The first d... | In literature, there exist a huge variety of 3D shape reconstruction models. The most popular ones are dense, pixel-wise depth maps, or normal maps (Eigen et al., 2014; Bansal et al., 2016; Bednarik et al., 2018; Tsoli et al., 2019; Zeng et al., 2019), point clouds (Fan et al., 2017; Qi et al., 2017b; Yang et al., 2018... |
Recently proposed object representations address this pitfall of point clouds by modeling object surfaces with polygonal meshes (Wang et al., 2018; Groueix et al., 2018; Yang et al., 2018b; Spurek et al., 2020a, b). They define a mesh as a set of vertices that are joined with edges in triangles. These triangles create... | D |
O(n2εnlnnmaxi,jCij2χ).𝑂superscript𝑛2𝜀𝑛𝑛subscript𝑖𝑗superscriptsubscript𝐶𝑖𝑗2𝜒O\left(\frac{n^{2}}{\varepsilon}\sqrt{n\ln n}\max_{i,j}C_{ij}^{2}\chi\right).italic_O ( divide start_ARG italic_n start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT end_ARG start_ARG italic_ε end_ARG square-root start_ARG italic_n ro... | parameter γ𝛾\gammaitalic_γ to solve the WB problem.
We ran the IBP and the ADCWB algorithms with different values of the regularization parameter γ𝛾\gammaitalic_γ starting from γ=0.1𝛾0.1\gamma=0.1italic_γ = 0.1 and gradually decreasing its value to γ=10−4𝛾superscript104\gamma=10^{-4}italic_γ = 10 start_POSTSUPERSCR... |
We demonstrate the performance of the DMP algorithm on different network architectures with different conditional number χ𝜒\chiitalic_χ: complete graph, star graph, cycle graph and the Erdős-Rényi random graphs with the probability of edge creation p=0.5𝑝0.5p=0.5italic_p = 0.5 and p=0.4𝑝0.4p=0.4italic_p = 0.4 under... | We comment on the complexity of the DMP algorithm compared to the existing state-of-the-art methods: the iterative Bregman projections (IBP) algorithm, its accelerated versions and primal dual algorithm (ADCWB), see Table 1. All of these methods use entropic regularization of Wasserstein metric with parameter γ𝛾\gamma... | Finally, we show how the proposed method can be applied to prominent problem of computing Wasserstein barycenters to tackle the problem of instability of regularization-based approaches under a small value of regularizing parameter. The idea is based on the saddle point reformulation of the Wasserstein barycenter probl... | C |
The set of cycles of a graph has a vector space structure over ℤ2subscriptℤ2\mathbb{Z}_{2}blackboard_Z start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT, in the case of undirected graphs, and over ℚℚ\mathbb{Q}blackboard_Q, in the case of directed graphs [5]. A basis of such a vector space is denoted cycle basis and its dimensio... | In the case that we can find some non-star spanning tree T𝑇Titalic_T of
G𝐺Gitalic_G such that ∩(T)<∩(Ts)𝑇subscript𝑇𝑠\cap(T)<\cap(T_{s})∩ ( italic_T ) < ∩ ( italic_T start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT ) then, we can “simplify” the instance by removing the interbranch cycle-edges with respect to T𝑇Tital... |
In the introduction of this article we mentioned that the MSTCI problem is a particular case of finding a cycle basis with sparsest cycle intersection matrix. Another possible analysis would be to consider this in the context of the cycle basis classes described in [6]. |
The length of a cycle is its number of edges. The minimum cycle basis (MCB) problem is the problem of finding a cycle basis such that the sum of the lengths (or edge weights) of its cycles is minimum. This problem was formulated by Stepanec [7] and Zykov [8] for general graphs and by Hubicka and Syslo [9] in the stric... |
Different classes of cycle bases can be considered. In [6] the authors characterize them in terms of their corresponding cycle matrices and present a Venn diagram that shows their inclusion relations. Among these classes we can find the strictly fundamental class. | D |
In this respect, the case of convex lattice sets, that is, sets of the form C∩ℤd𝐶superscriptℤ𝑑C\cap\mathbb{Z}^{d}italic_C ∩ blackboard_Z start_POSTSUPERSCRIPT italic_d end_POSTSUPERSCRIPT where C𝐶Citalic_C is a convex set in ℝdsuperscriptℝ𝑑\mathbb{R}^{d}blackboard_R start_POSTSUPERSCRIPT italic_d end_POSTSUPERSCRIP... | We first prove, in Section 3, that complexes with a forbidden simplicial homological minor also have a forbidden grid-like homological minor.
The proof uses the stair convexity of Bukh et al. [8] to build, in a systematic way, chain maps from simplicial complexes to cubical complexes. We then adapt, in Section 4, the m... | The support of a chain σ𝜎\sigmaitalic_σ, denoted supp(σ)supp𝜎\operatorname{supp}(\sigma)roman_supp ( italic_σ ), in a simplicial complex is the set of simplices with nonzero coefficients in σ𝜎\sigmaitalic_σ. We say that two chains σ𝜎\sigmaitalic_σ and τ𝜏\tauitalic_τ have overlapping supports if there exists a sim... | In this paper, we show that the gap observed for convex lattice sets occurs in the broad topological setting of triangulable spaces with a forbidden homological minor, a notion introduced by Wagner [37] as a higher-dimensional analogue of the familiar notion of graph minors [34].
| Theorem 1.1
depends on p𝑝pitalic_p, q𝑞qitalic_q, K𝐾Kitalic_K and b𝑏bitalic_b (but, as usual, is independent of the size of the cover). Moreover, while the Helly number of a (K,b)𝐾𝑏(K,b)( italic_K , italic_b )-free cover can grow with b𝑏bitalic_b (it is at least (b−1)(μ(K)+2)𝑏1𝜇𝐾2(b-1)(\mu(K)+2)( italic_b - ... | C |
Feature transformation usually denotes less sophisticated modifications over the features [14]. Some of the standard transformations also supported by our approach are: (1) rounding, (2) binning, (3) scaling, (4) logarithmic transformations, (5) exponential transformations, and (6) power functions. In this scenario, ML... | There is a rather large body of existing work on automatic feature selection techniques [16, 19, 17]. However, one limitation is that features can be redundant if there is a strong correlation among them, and the correlation coefficient is unable to characterize nonlinear relationships. Thus, this is a problem where th... | Next, as XGBoost [29] is a nonlinear ML algorithm, we also train a linear classifier (a logistic regression [83] model with the default Scikit-learn’s hyperparameters [84]) to compute the coefficients matrix and then use Recursive Feature Elimination (RFE) [40] to rank the features from the best to the worst in terms o... |
Various visualization techniques have been proposed for the task of feature selection, including correlation matrices [42, 43], radial visualizations [44, 45, 46], scatterplots [47], scatterplot matrices [48], feature ranking [49, 50, 51, 52, 53, 54, 55, 56], feature clustering [57], and dimensionality reduction (DR) ... |
Feature selection is about choosing a subset of features from the pool of features available by that time. Feature selection methods can be generally divided into four high-level categories: (1) filter methods, (2) wrapper methods, (3) embedded methods, and (4) hybrid methods [16, 17, 18]. Our feature selection strate... | D |
The goal is to tune the parameters of the MPC-based planning unit without introducing any modification in the structure of the underlying control system.
We leverage the repeatability of the system, which is higher than the integrated encoder error of 3μm3𝜇𝑚3\mu m3 italic_μ italic_m, | which is an MPC-based contouring approach to generate optimized tracking references. We account for model mismatch by automated tuning of both the MPC-related parameters and the low level cascade controller gains, to achieve precise contour tracking with micrometer tracking accuracy. The MPC-planner is based on a combi... | MPC accounts for the real behavior of the machine and the axis drive dynamics can be excited to compensate for the contour error to a big extent, even without including friction effects in the model [4, 5]. High-precision trajectories or set points can be generated prior to the actual machining process following variou... | To bring the model close to the real system, we unify the terms required for the contour control formulation with the velocity and acceleration for each axis from the identified, discretized state-space model from (4).
Also, we include the path progress sksubscript𝑠𝑘s_{k}italic_s start_POSTSUBSCRIPT italic_k end_POST... | The physical system is a 2-axis gantry stage for (x,y)𝑥𝑦(x,y)( italic_x , italic_y ) positioning with industrial grade actuators and sensors [14].
The plant can be modeled as a mass-spring-damper system with two masses linked with a damper and a spring for capturing imperfection and friction in the transmitting movem... | D |
An interesting observation was that a weaker architecture, CNNs, were able to ignore position bias, whereas a more powerful architecture, CoordConv, resorted to exploiting this bias resulting in worse performance. While the community has largely focused on training procedures for bias mitigation, an exciting avenue fo... | We have pointed to issues with the existing bias mitigation approaches, which alter the loss or use resampling. An orthogonal avenue for attacking bias mitigation is to use alternative architectures. Neuro-symbolic and graph-based systems could be created that focus on learning and grounding predictions on structured c... | Deep learning systems are trained to minimize their loss on a training dataset. However, datasets often contain spurious correlations and hidden biases which result in systems that have low loss on the training data distribution, but then fail to work appropriately on minority groups because they exploit and even ampli... | Without bias mitigation mechanisms, standard models (StdM) often use spurious bias variables for inference, rather than developing invariance to them, which often results in their inability to perform well on minority patterns [27, 11, 3, 61]. To address this, several bias mitigation mechanisms have been proposed, and ... |
An interesting observation was that a weaker architecture, CNNs, were able to ignore position bias, whereas a more powerful architecture, CoordConv, resorted to exploiting this bias resulting in worse performance. While the community has largely focused on training procedures for bias mitigation, an exciting avenue fo... | A |
The first two types of methods estimate gaze based on geometric features such as contours, reflection and eye corners. The geometric features can be accurately extracted with the assistance of dedicated devices, e.g., infrared cameras.
More concretely, the 2D eye feature regression method learns a mapping function from... | The 3D eye model recovery-based methods usually require personal calibration to recover person-specific parameters such as iris radius and kappa angle.
While these methods often achieve high accuracy, they require dedicated devices such as infrared cameras. |
It is non-trivial to learn an accurate and universal gaze estimation model. Conventional 3D eye model recovery methods usually build a unified gaze model including subject-specific parameters such as eyeball radius [28]. They perform a personal calibration to estimate these subject-specific parameters. In the field of... | The eye model is fitted with geometric features, such as the infrared corneal reflections [28, 29], pupil center [30] and iris contours [31]. However, they usually require a personal calibration process for each subject, since the eye model contains subject-specific parameters such as cornea radius, kappa angles.
| The first two types of methods estimate gaze based on geometric features such as contours, reflection and eye corners. The geometric features can be accurately extracted with the assistance of dedicated devices, e.g., infrared cameras.
More concretely, the 2D eye feature regression method learns a mapping function from... | C |
Inspired by the high performance of CNN based methods that have strong robustness to illumination, facial expression, and facial occlusion changes, we propose in this paper an occlusion removal approach and deep CNN based model to address the problem of masked face recognition during the COVID-19 pandemic. Motivations... | Experimental results are carried out on Real-world Masked Face Recognition Dataset (RMFRD) and Simulated Masked Face Recognition Dataset (SMFRD) presented in wang2020masked . We start by localizing the mask region. To do so, we apply a cropping filter in order to obtain only the informative regions of the masked face (... |
Real-World-Masked-Face-Dataset wang2020masked is a masked face dataset devoted mainly to improve the recognition performance of the existing face recognition technology on the masked faces during the COVID-19 pandemic. It contains three types of images namely, Masked Face Detection Dataset (MFDD), Real-world Masked F... | The obtained high accuracy compared to other face recognizers is achieved due to the best features extracted from the last convolutional layers of the pre-trained models, and the high efficiency of the proposed BoF paradigm that gives a lightweight and more discriminative power comparing to classical CNN with softmax f... | To tackle these problems, we distinguish two different tasks namely: face mask recognition and masked face recognition. The first one checks whether the person is wearing a mask or no. This can be applied in public places where the mask is compulsory. Masked face recognition, on the other hand, aims to recognize a face... | A |
recursive definitions of the form y←fi¯x¯=Pf(i¯,x¯,y)←𝑦𝑓¯𝑖¯𝑥subscript𝑃𝑓¯𝑖¯𝑥𝑦y\leftarrow f~{}\overline{i}~{}\overline{x}=P_{f}(\overline{i},\overline{x},y)italic_y ← italic_f over¯ start_ARG italic_i end_ARG over¯ start_ARG italic_x end_ARG = italic_P start_POSTSUBSCRIPT italic_f end_POSTSUBSCRIPT ( over¯ s... | There are eight kinds of processes: two for the structural rules (identity and cut), one for each combination of type polarity (positive or negative) and rule type (left or right), one for definition calls, and one for unreachable code.
{defi}[Process] |
The first two kinds of processes correspond to the identity and cut rules. Values V𝑉Vitalic_V and continuations K𝐾Kitalic_K are specified on a per-type-and-rule basis in the following two tables. Note the address variable x𝑥xitalic_x distinguished by each rule. |
where the arithmetic variables in 𝒱𝒱\mathcal{V}caligraphic_V are free in the constraints (arithmetic formulas) in 𝒞𝒞\mathcal{C}caligraphic_C, the types in ΓΓ\Gammaroman_Γ, the process P𝑃Pitalic_P, and type C𝐶Citalic_C; moreover, the address variables in ΓΓ\Gammaroman_Γ, which are free in P𝑃Pitalic_P, stand for ... |
The first rule for →→\to→ corresponds to the identity rule and copies the contents of one cell into another. The second rule, which is for cut, models computing with futures [Hal85]: it allocates a new cell to be populated by the newly spawned P𝑃Pitalic_P. Concurrently, Q𝑄Qitalic_Q may read from said new cell, which... | B |
Figure 13: The comparison of cloud-side computational efficiency between FairCMS-I and FairCMS-II. The bars and polyline correspond to the left and right Y-axes, respectively. The time consumed by FairCMS-II is 100 times the reading on the Y-axis. (a) Efficiency comparison under different number of users. (b) Efficien... | The owner-side efficiency and scalability performance of FairCMS-II are directly inherited from FairCMS-I, and the achievement of the three security goals of FairCMS-II is also shown in Section VI. Comparing to FairCMS-I, it is easy to see that in FairCMS-II the cloud’s overhead is increased considerably due to the ado... | Finally, the comparison between the two proposed schemes and the existing relevant schemes is summarized in Table I. As can be seen therein, the two proposed schemes FairCMS-I and FairCMS-II have advantages over the existing works. In addition, the two proposed schemes offer owners the flexibility to choose. If the sec... |
This paper solves the three problems faced by cloud media sharing and proposes two schemes FairCMS-I and FairCMS-II. FairCMS-I gives a method to transfer the management of LUTs to the cloud, enabling the calculation of each user’s D-LUT in the ciphertext domain and its subsequent distribution. However, utilizing the s... | Second, we compare the cloud-side efficiency of FairCMS-I and FairCMS-II, and the results are presented in Fig. 13. As shown therein, the cloud-side efficiency of FairCMS-I is significantly higher than that of FairCMS-II, thus validating our analysis in Section VII. The main reason for the cloud-side efficiency gain of... | D |
It should be noted that fssubscript𝑓𝑠f_{s}italic_f start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT is invariant to the order of its input, i.e., fs(𝐞i,𝐞j)=fs(𝐞j,𝐞i)subscript𝑓𝑠subscript𝐞𝑖subscript𝐞𝑗subscript𝑓𝑠subscript𝐞𝑗subscript𝐞𝑖f_{s}(\mathbf{e}_{i},\mathbf{e}_{j})=f_{s}(\mathbf{e}_{j},\mathbf{e}_{i... | To overcome this limitation, we replace the edge set E𝐸Eitalic_E with weighted adjacency 𝐏𝐏\mathbf{P}bold_P, where pijsubscript𝑝𝑖𝑗p_{ij}italic_p start_POSTSUBSCRIPT italic_i italic_j end_POSTSUBSCRIPT is interpreted as the probability of (vi,vj)∈Esubscript𝑣𝑖subscript𝑣𝑗𝐸(v_{i},v_{j})\in E( italic_v start_POS... |
From the estimated edge weighted matrix 𝐏(k)superscript𝐏𝑘\mathbf{P}^{(k)}bold_P start_POSTSUPERSCRIPT ( italic_k ) end_POSTSUPERSCRIPT at each layer, we then sample the beneficial feature interactions, which is also to sample the neighborhood for each feature field. | where 𝐏(k)[i,:]superscript𝐏𝑘𝑖:\mathbf{P}^{(k)}[i,:]bold_P start_POSTSUPERSCRIPT ( italic_k ) end_POSTSUPERSCRIPT [ italic_i , : ] denotes the i𝑖iitalic_i-th column of matrix 𝐏(k)superscript𝐏𝑘\mathbf{P}^{(k)}bold_P start_POSTSUPERSCRIPT ( italic_k ) end_POSTSUPERSCRIPT at k𝑘kitalic_k-th layer, 𝐏(k)[i,−idxi]s... | At each layer of GraphFM, we select the beneficial feature interactions and treat them as edges in a graph. Then we utilize a neighborhood/interaction aggregation operation to encode the interactions into feature representations.
By design, the highest order of feature interaction increases at each layer and is determi... | B |
which is reminiscient of the 𝒪(Lf𝒳D2/t)𝒪superscriptsubscript𝐿𝑓𝒳superscript𝐷2𝑡\mathcal{O}(L_{f}^{\mathcal{X}}D^{2}/t)caligraphic_O ( italic_L start_POSTSUBSCRIPT italic_f end_POSTSUBSCRIPT start_POSTSUPERSCRIPT caligraphic_X end_POSTSUPERSCRIPT italic_D start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT / italic_t )... |
Furthermore, with this simple step size we can also prove a convergence rate for the Frank-Wolfe gap, as shown in Theorem 2.6. More specifically, the minimum of the Frank-Wolfe gap over the run of the algorithm converges at a rate of 𝒪(1/t)𝒪1𝑡\mathcal{O}(1/t)caligraphic_O ( 1 / italic_t ). The idea of the proof is... | For AFW, we can see that the algorithm either chooses to perform what is known as a Frank-Wolfe step in Line 7 of Algorithm 5
if the Frank-Wolfe gap g(𝐱)𝑔𝐱g(\mathbf{x})italic_g ( bold_x ) is greater than the away gap ⟨∇f(𝐱t),𝐚t−𝐱t⟩∇𝑓subscript𝐱𝑡subscript𝐚𝑡subscript𝐱𝑡\left\langle\nabla f(\mathbf{x}_{t}),\m... | We can make use of the proof of convergence in primal gap to prove linear convergence in Frank-Wolfe gap. In order to do so, we recall a quantity formally defined in Kerdreux et al. [2019] but already implicitly used earlier in Lacoste-Julien & Jaggi [2015] as:
| Moreover, as the upper bound on the Bregman divergence holds for ν=2𝜈2\nu=2italic_ν = 2 regardless of the value of d2(𝐱,𝐲)subscript𝑑2𝐱𝐲d_{2}(\mathbf{x},\mathbf{y})italic_d start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT ( bold_x , bold_y ), we can modify the proof of Theorem 2.4 to obtain a convergence rate of the form:... | A |
In the semi-streaming model, which is the most commonly established variant of the graph stream model, the algorithm is given O~(n)~𝑂𝑛\widetilde{O}(n)over~ start_ARG italic_O end_ARG ( italic_n )222The O~~𝑂\widetilde{O}over~ start_ARG italic_O end_ARG hides poly-logarithmic terms, thus O~(n)=n⋅poly(logn)~𝑂𝑛⋅𝑛... |
In the first pass, we apply a simple greedy algorithm to find a maximal matching, hence a 2222-approximation. This 2222-approximate maximum matching is our starting matching. The rest of our algorithm is divided into multiples phases. In each phase, we iteratively improve the approximation ratio of our current matchin... |
It is known that finding an exact matching requires linear space in the size of the graph and hence it is not possible to find an exact maximum matching in the semi-streaming model [FKM+04], at least for sufficiently dense graphs. Nevertheless, this result does not apply to computing a good approximation to the maximu... |
Given a graph on n𝑛nitalic_n vertices, there is a deterministic (1+ε)1𝜀(1+\varepsilon)( 1 + italic_ε )-approximation algorithm for maximum matching that runs in poly(1/ε)poly1𝜀\operatorname{poly}(1/\varepsilon)roman_poly ( 1 / italic_ε ) passes in the semi-streaming model. |
Let ΔΔ\Deltaroman_Δ be an upper bound on the structure size and h(ε)|M|ℎ𝜀𝑀h(\varepsilon)|M|italic_h ( italic_ε ) | italic_M | be the maximum number of active nodes at the end of a phase. Fix a phase. Let k≥3𝑘3k\geq 3italic_k ≥ 3 be an integer parameter. Let M𝑀Mitalic_M be the matching at the beginning of that ph... | B |
}^{n}f_{i}(\bm{\mathit{x}}),roman_min start_POSTSUBSCRIPT bold_italic_x ∈ blackboard_R start_POSTSUPERSCRIPT italic_p end_POSTSUPERSCRIPT end_POSTSUBSCRIPT italic_f ( bold_italic_x ) = divide start_ARG 1 end_ARG start_ARG italic_n end_ARG ∑ start_POSTSUBSCRIPT italic_i = 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic... |
The communication between all the agents is modeled by directed graphs. Given a strongly connected graph 𝒢=(𝒩,ℰ)𝒢𝒩ℰ\mathcal{G}=\left(\mathcal{N},\mathcal{E}\right)caligraphic_G = ( caligraphic_N , caligraphic_E ) with ℰ⊂𝒩×𝒩ℰ𝒩𝒩\mathcal{E}\subset\mathcal{N}\times\mathcal{N}caligraphic_E ⊂ caligraphic_N × caligra... | Many methods have been proposed to solve the problem (1) under various settings on the optimization objectives, network topologies, and communication protocols.
The paper [10] developed a decentralized subgradient descent method (DGD) with diminishing stepsizes to reach the optimum for convex objective functions over a... | The n𝑛nitalic_n agents are connected through a general directed network and only communicate directly with their immediate neighbors.
The problem (1) has received much attention in recent years due to its wide applications in distributed machine learning [1, 2, 3], multi-agent target seeking [4, 5], and wireless netwo... | For example, the rapid development of distributed machine learning involves data whose size is getting increasingly large, and they are usually stored across multiple computing agents that are spatially distributed. Centering large amounts of data is often undesirable due to limited communication resources and/or priva... | C |
\tfrac{\lambda}{2}\|\sqrt{W}Y\|^{2}\right\}{ ∑ start_POSTSUBSCRIPT italic_m = 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_M end_POSTSUPERSCRIPT italic_f start_POSTSUBSCRIPT italic_m end_POSTSUBSCRIPT ( italic_x start_POSTSUBSCRIPT italic_m end_POSTSUBSCRIPT , italic_y start_POSTSUBSCRIPT italic_m end_POSTSUBSCRIPT... | Certainly, we want to reduce the number of communications (or calls the regularizer gradient) as much as possible.
This is especially important when the problem (1) is a fairly personalized (λ≪Lmuch-less-than𝜆𝐿\lambda\ll Litalic_λ ≪ italic_L) and information from other nodes is not significant. To solve this problem ... | To the best of our knowledge, this paper is the first to consider decentralized personalized federated saddle point problems, propose optimal algorithms and derives the computational and communication lower bounds for this setting. In the literature, there are works on general (non-personalized) SPPs. We make a detaile... |
In this paper, we present a novel formulation for the Personalized Federated Learning Saddle Point Problem (1). This formulation incorporates a penalty term that accounts for the specific structure of the network and is applicable to both centralized and decentralized network settings. Additionally, we provide the low... | or open-source codes). This definition comes from the standard results, that for smooth functions the stepsize ∼1Lsimilar-toabsent1𝐿\sim\frac{1}{L}∼ divide start_ARG 1 end_ARG start_ARG italic_L end_ARG. We do not say that this is a good definition of L𝐿Litalic_L, but we only need it for the intuition. We also mentio... | A |
This highlights the main drawback of MW(C)CE which does not select for unique solutions (for example, in constant-sum games all solutions have maximum welfare). One selection criterion for NEs is maximum entropy Nash equilibrium (MENE) (Balduzzi et al., 2018), however outside of the two-player constant-sum setting, th... |
The new solution concept MG(C)CE is rooted in the powerful principles of entropy and margin maximisation. Therefore it is a simple solution that makes limited assumptions, and is robust to many possible counter strategies (Jaynes, 1957). The MG(C)CE defines a family of unique solutions parameterized by ϵitalic-ϵ\epsil... | There are two important solution concepts in the space of CEs. The first is Maximum Welfare Correlated Equilibrium (MWCE) which is defined as the CE that maximises the sum of all player’s payoffs. An MWCE can be obtained by solving a linear program, however the MWCE may not be unique and therefore does not fully solve ... | MG(C)CE, however, is the solution to a quadratic program, and therefore can be solved in polynomial time. Furthermore, if the assumption is made that the solution is full-support, the algorithm’s variables scale better than the number of σ𝜎\sigmaitalic_σ parameters.
| MG(C)CE can provide solutions in general-support and, similar to MECE, MG(C)CE permits a scalable representation when the solution is full-support. Under this scenario, the distribution inequality constraint variables, β𝛽\betaitalic_β, are inactive, are equal to zero, can be dropped, and the α𝛼\alphaitalic_α variable... | D |
Given η>0𝜂0\eta>0italic_η > 0 and a query q𝑞qitalic_q, the Gaussian mechanism with noise parameter η𝜂\etaitalic_η returns its empirical mean q(s)𝑞𝑠{q}\left(s\right)italic_q ( italic_s ) after adding a random value, sampled from an unbiased Gaussian distribution with variance η2superscript𝜂2\eta^{2}italic_η start... | Since achieving posterior accuracy is relatively straightforward, guaranteeing Bayes stability is the main challenge in leveraging this theorem to achieve distribution accuracy with respect to adaptively chosen queries. The following lemma gives a useful and intuitive characterization of the quantity that the Bayes sta... | In this section, we give a clean, new characterization of the harms of adaptivity. Our goal is to bound the distribution error of a mechanism that responds to queries generated by an adaptive analyst.
This bound will be achieved via a triangle inequality, by bounding both the posterior accuracy and the Bayes stability ... |
In order to leverage Lemma 3.5, we need a stability notion that implies Bayes stability of query responses in a manner that depends on the actual datasets and the actual queries (not just the worst case). In this section we propose such a notion and prove several key properties of it. Missing proofs from this section ... | Using the first part of the lemma, we guarantee Bayes stability by bounding the correlation between specific q𝑞qitalic_q and K(⋅,v)𝐾⋅𝑣{K}\left(\cdot,v\right)italic_K ( ⋅ , italic_v ) as discussed in Section 6. The second part of this Lemma implies that bounding the appropriate divergence is necessary and sufficient... | B |
However, we argue that these results on kernelization do not explain the often exponential speed-ups (e.g. [3], [5, Table 6]) caused by applying effective preprocessing steps to non-trivial algorithms. Why not? A kernelization algorithm guarantees that the input size is reduced to a function of the parameter k𝑘kitali... |
However, we argue that these results on kernelization do not explain the often exponential speed-ups (e.g. [3], [5, Table 6]) caused by applying effective preprocessing steps to non-trivial algorithms. Why not? A kernelization algorithm guarantees that the input size is reduced to a function of the parameter k𝑘kitali... |
We start by motivating the need for a new direction in the theoretical analysis of preprocessing. The use of preprocessing, often via the repeated application of reduction rules, has long been known [3, 4, 44] to speed up the solution of algorithmic tasks in practice. The introduction of the framework of parameterized... | We therefore propose the following novel research direction: to investigate how preprocessing algorithms can decrease the parameter value (and hence search space) of FPT algorithms, in a theoretically sound way. It is nontrivial to phrase meaningful formal questions in this direction. To illustrate this difficulty, not... | We have taken the first steps into a new direction for preprocessing which aims to investigate how and when a preprocessing phase can guarantee to identify parts of an optimal solution to an 𝖭𝖯𝖭𝖯\mathsf{NP}sansserif_NP-hard problem, thereby reducing the running time of the follow-up algorithm. Aside from the techni... | C |
Object placement [2, 24, 65, 154, 197] tends to seek for reasonable location, size, and shape by predicting the foreground transformation to avoid the abovementioned inconsistencies. Previous object placement methods [197, 154] mainly predict simple form of spatial transformation, that is, shifting and scaling the fore... | After compositing a new image with foreground and background, there exist many issues that could make the composite image unrealistic and thus significantly degrade its quality. These issues can be summarized as the inconsistency between foreground and background, which can be divided into appearance inconsistency, geo... | Figure 2: The quality of composite image is degraded by the appearance inconsistency, geometric inconsistency, and semantic inconsistency. Each type of inconsistency involves a number of issues. Each sub-task targets at addressing one or more issues.
| The semantic inconsistency is including but not limited to: 1) the foreground appears at a semantically unreasonable place (e.g., a zebra is placed in the living room); 2) the foreground has unreasonable interactions with other objects or people (e.g., a person is riding a motorbike, but the person and the motorbike ar... | Object placement aims to paste the foreground on the background with suitable location, size, and shape. As shown in Fig. 4, the cases of unreasonable object placement are including but not limited to: a) the foreground object has inappropriate size (e.g., the dog is too large); b) the foreground object has unreasonabl... | C |
Table VII presents the results of our inter-city transfer learning experiments. Specifically, we report the results obtained by training our models using both full and 3-day target data, which correspond to the lower and upper bounds of errors, respectively. Furthermore, we also include the results of fine-tuning and R... |
Degradation under data scarcity. Our findings reveal that when only 3-day training data are available, non-deep learning models such as LR achieve similar performances as compared to using full data, whereas LSTM models suffer from an increased error rate of 50%, as observed in the case of Chengdu. This suggests that ... |
As depicted in Table V, deep learning models can generate highly accurate predictions when provided with ample data. However, the level of digitization varies significantly among cities, and it is likely that many cities may not be able to construct accurate deep learning prediction models due to a lack of data. One e... |
Deep Learning or Not: When provided with ample data (e.g., 10 days, 1-2 months), deep learning models such as CNN, LSTM, GCN, and GAT exhibit superior performance compared to traditional time-series forecasting methods such as HA and LR. This highlights the potency of deep learning in spatio-temporal predictions and t... | Among the methods studied, HA and LR are traditional time series forecasting models, while CNN and LSTM are deep learning models designed for Euclidean structures (such as grid networks). By contrast, GCN and GAT are graph deep learning models that leverage additional region-wise connections, such as POI and road conne... | A |
Most of the data sets were obtained from the UCI repository Dua2019 . Specific references are given in Table 2. This table also shows the number of data points and (used) features and the skewness and (Pearson) kurtosis of the response variable. All data sets were standardized (both features and target variables) befor... | Neural network: A standard neural network point predictor was chosen as a baseline model. Early stopping as for the ensemble methods was used as a regularization method. Furthermore, dropout with p=0.1𝑝0.1p=0.1italic_p = 0.1 and L2superscript𝐿2L^{2}italic_L start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT-regularization w... | Deep ensembles: The ensemble consisted of 5 estimators and the adversarial step size equalled 0.01 times the range of the corresponding dimension (cf. lakshminarayanan2017simple ). At training time L2superscript𝐿2L^{2}italic_L start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT-regularization with λ=10−6𝜆superscript106\lambd... | Neural network quantile regression: The same softening factor w=2𝑤2w=2italic_w = 2 as in romano2019conformalized ; sesia2020comparison was used. The early stopping criterion for neural networks was also modified to work with the average length and coverage degree of the prediction intervals instead of the loss functi... |
All neural networks were constructed using the default implementations fromPyTorch pytorch . The general architecture for all neural-network-based models was fixed. The Adam optimizer was used for weight optimization with a fixed learning rate of 5×10−45superscript1045\times 10^{-4}5 × 10 start_POSTSUPERSCRIPT - 4 end... | D |
The results show that MusicBERT achieves a testing accuracy of 37.25% for style classification and 77.78% for emotion classification. Specifically, in the style classification task, MusicBERT exhibits clear signs of overfitting and falls short in performance when compared to our model (81.75%). This outcome can be attr... |
To train Transformers, it is required that all input sequences have the same length. For both REMI and CP, we divide the token sequence for each entire piece into a number of shorter sequences with equal sequence length 512, zero-padding those at the end of a piece to 512 with an appropriate number of Pad tokens. |
Tab. 2 also shows that “our model (performance)+++CP” outperforms “our model (score)+++CP” greatly for the two sequence-level tasks, style classification and emotion classification. This matches our intuition as the two tasks are highly related to performance styles and expressions of the piano pieces. | To study whether the accuracy gain comes simply from a longer musical context enjoyed by CP, we also train “our model (performance)+++CP” with a sequence of length 128, obtaining 95.43, 80.32 and 64.04 accuracies for three-class melody classification, style classification and emotion classification, respectively.
We no... | In particular, the combination of our model (score) and CP, referred to as “our model (score)+CP” hereafter, exhibits the highest accuracy in the two note-level tasks. Additionally, the combination of our model (performance) and CP, denoted as “our model (performance)+CP”, achieves the best result in the style classifi... | C |
Otherwise, F𝐹Fitalic_F has a leaf v∈A𝑣𝐴v\in Aitalic_v ∈ italic_A with a neighbor u∈B𝑢𝐵u\in Bitalic_u ∈ italic_B. We can assign c(v)=a2𝑐𝑣subscript𝑎2c(v)=a_{2}italic_c ( italic_v ) = italic_a start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT, c(u)=b2𝑐𝑢subscript𝑏2c(u)=b_{2}italic_c ( italic_u ) = italic_b start_POSTSU... | The linear running time follows directly from the fact that we compute c𝑐citalic_c only once and we can pass additionally through recursion the lists of leaves and isolated vertices in an uncolored induced subtree. The total number of updates of these lists is proportional to the total number of edges in the tree, hen... | Next, let us count the total number of jumps necessary for finding central vertices over all loops in Algorithm 1. As it was stated in the proof of Lemma 2.2, while searching for a central vertex we always jump from a vertex to its neighbor in a way that decreases the largest remaining component by one. Thus, if in the... |
Now, observe that if the block to the left is also of type A, then a respective block from Z(S)𝑍𝑆Z(S)italic_Z ( italic_S ) is (0,1,0)010(0,1,0)( 0 , 1 , 0 ) – and when we add the backward carry (0,0,1)001(0,0,1)( 0 , 0 , 1 ) to it, we obtain the forward carry to the rightmost block. And regardless of the value of t... | To obtain the total running time we first note that each of the initial steps – obtaining (R,B,Y)𝑅𝐵𝑌(R,B,Y)( italic_R , italic_B , italic_Y ) from Corollary 2.11 (e.g. using Algorithm 1), contraction of F𝐹Fitalic_F into F′superscript𝐹normal-′F^{\prime}italic_F start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT, and findi... | A |
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