context stringlengths 250 4.36k | A stringlengths 250 4.85k | B stringlengths 250 4.12k | C stringlengths 250 3.69k | D stringlengths 250 8.2k | label stringclasses 4
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\prime\prime}(x)+\frac{(\Delta x)^{3}}{3!}f^{\prime\prime\prime}(x)\approx 0.italic_f ( italic_x + roman_Δ italic_x ) ≈ italic_f ( italic_x ) + roman_Δ italic_x italic_f start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT ( italic_x ) + divide start_ARG ( roman_Δ italic_x ) start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT end_ARG s... | \frac{f^{\prime\prime}(x)}{f^{\prime}(x)}\right)roman_Δ italic_x = - divide start_ARG italic_f ( italic_x ) end_ARG start_ARG italic_f start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT ( italic_x ) end_ARG / ( 1 - divide start_ARG italic_f ( italic_x ) end_ARG start_ARG 2 italic_f start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT ... | ^{2}}{6}\frac{f^{\prime\prime\prime}(x)}{f^{\prime}(x)}\approx 0,1 + divide start_ARG roman_Δ italic_x end_ARG start_ARG 2 end_ARG divide start_ARG italic_f start_POSTSUPERSCRIPT ′ ′ end_POSTSUPERSCRIPT ( italic_x ) end_ARG start_ARG italic_f start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT ( italic_x ) end_ARG + divide sta... | \prime\prime}(x)+\frac{(\Delta x)^{3}}{3!}f^{\prime\prime\prime}(x)\approx 0.italic_f ( italic_x + roman_Δ italic_x ) ≈ italic_f ( italic_x ) + roman_Δ italic_x italic_f start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT ( italic_x ) + divide start_ARG ( roman_Δ italic_x ) start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT end_ARG s... | {\prime}(x)}\left(h_{0}(x)\frac{f(x)}{f^{\prime}(x)}+h_{1}(x)\right)\right].roman_Δ italic_x = - divide start_ARG italic_f ( italic_x ) end_ARG start_ARG italic_f start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT ( italic_x ) end_ARG / [ 1 + divide start_ARG 1 end_ARG start_ARG 2 italic_h start_POSTSUBSCRIPT 2 end_POSTSUBSCR... | B |
0&I_{d-4}\end{array}\right)\text{for $d$ even or }x=I_{d}\text{ for $d$ odd}.italic_x = ( start_ARRAY start_ROW start_CELL italic_x start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT end_CELL start_CELL 0 end_CELL end_ROW start_ROW start_CELL 0 end_CELL start_CELL italic_I start_POSTSUBSCRIPT italic_d - 4 end_POSTSUBSCRIPT end_CE... | 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... | Note that a small variation of these standard generators for SL(d,q)SL𝑑𝑞\textnormal{SL}(d,q)SL ( italic_d , italic_q ) are used in Magma [14] as well
as in algorithms to verify presentations of classical groups, see [12], where only the generator v𝑣vitalic_v is slightly different in the two scenarios when d𝑑ditali... | The lower-unitriangular matrices u1subscript𝑢1u_{1}italic_u start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT and u2subscript𝑢2u_{2}italic_u start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT are returned as words in the Leedham-Green–O’Brien standard generators [11] for SL(d,q)SL𝑑𝑞\textnormal{SL}(d,q)SL ( italic_d , italic_q ) define... | Finally, we construct a second MSLP, described in Section 3.5, that writes a diagonal matrix h∈SL(d,q)ℎSL𝑑𝑞h\in\textnormal{SL}(d,q)italic_h ∈ SL ( italic_d , italic_q ) as a word in the standard generators of SL(d,q)SL𝑑𝑞\textnormal{SL}(d,q)SL ( italic_d , italic_q ) (when evaluated with these generators as input)... | B |
To show the existence and uniqueness of solutions for (21), we proceed by parts. The existence of solution for the first equation follows from Lemma LABEL:l:lrmsystem. Solving the second equation is equivalent to (22), and such system is well-posed due to the coercivity of (⋅,T⋅)∂𝒯H(\cdot,T\cdot)_{{\partial\mathcal{T}... |
The key to approximate (25) is the exponential decay of Pw𝑃𝑤Pwitalic_P italic_w, as long as w∈H1(𝒯H)𝑤superscript𝐻1subscript𝒯𝐻w\in{H^{1}({\mathcal{T}_{H}})}italic_w ∈ italic_H start_POSTSUPERSCRIPT 1 end_POSTSUPERSCRIPT ( caligraphic_T start_POSTSUBSCRIPT italic_H end_POSTSUBSCRIPT ) has local support. That al... |
It is essential for the performing method that the static condensation is done efficiently. The solutions of (22) decay exponentially fast if w𝑤witalic_w has local support, so instead of solving the problems in the whole domain it would be reasonable to solve it locally using patches of elements. We note that the ide... |
Above, and in what follows, c𝑐citalic_c denotes an arbitrary constant that does not depend on H𝐻Hitalic_H, ℋℋ{\mathscr{H}}script_H, hℎhitalic_h, 𝒜𝒜\mathcal{A}caligraphic_A, depending only on the shape regularity of the elements of 𝒯Hsubscript𝒯𝐻{\mathcal{T}_{H}}caligraphic_T start_POSTSUBSCRIPT italic_H end_POST... | Except for (ii), all steps above above can be performed efficiently as the matrices involved are sparse and either local or independent of hℎhitalic_h. Solving (25) on the other hand involves computing the hℎhitalic_h-dependent, global operator P𝑃Pitalic_P, leading to a dense matrix in (25). From now on, we concentrat... | D |
We remark that the previously best known algorithms for finding the minimum area / perimeter all-flush triangle
take nearly linear time [6, 1, 2, 3, 23], that is, O(nlogn)𝑂𝑛𝑛O(n\log n)italic_O ( italic_n roman_log italic_n ) or O(nlog2n)𝑂𝑛superscript2𝑛O(n\log^{2}n)italic_O ( italic_n roman_log start_POSTSUP... | in the Rotate-and-Kill process,
and we are at the beginning of another iteration (b′,c′)superscript𝑏′superscript𝑐′(b^{\prime},c^{\prime})( italic_b start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT , italic_c start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT ) satisfying (2). | Then, during the Rotate-and-Kill process, the pair (eb,ec)subscript𝑒𝑏subscript𝑒𝑐(e_{b},e_{c})( italic_e start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT , italic_e start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT ) will meet all pairs that are not DEAD, which implies that the algorithm finds the minimum perimeter (all-... | Using a Rotate-and-Kill process (which is shown in Algorithm 5),
we find out all the edge pairs and vertex pairs in 𝖴r,s,tsubscript𝖴𝑟𝑠𝑡\mathsf{U}_{r,s,t}sansserif_U start_POSTSUBSCRIPT italic_r , italic_s , italic_t end_POSTSUBSCRIPT that are not G-dead. | The inclusion / circumscribing problems usually admit the property that the set of locally optimal solutions are pairwise interleaving [6]. Once this property is admitted and k=3𝑘3k=3italic_k = 3, we show that
an iteration process (also referred to as Rotate-and-Kill) can be applied for searching all the locally optim... | D |
For analyzing the employed features, we rank them by importances using RF (see 3). The best feature is related to sentiment polarity scores. There is a big difference between the sentiment associated to rumors and the sentiment associated to real events in relevant tweets. In specific, the average polarity score of new... | at an early stage. Our fully automatic, cascading rumor detection method follows
the idea on focusing on early rumor signals on text contents; which is the most reliable source before the rumors widely spread. Specifically, we learn a more complex representation of single tweets using Convolutional Neural Networks, tha... |
It has to be noted here that even though we obtain reasonable results on the classification task in general, the prediction performance varies considerably along the time dimension. This is understandable, since tweets become more distinguishable, only when the user gains more knowledge about the event. | CrowdWisdom: Similar to [18], the core idea is to leverage the public’s common sense for rumor detection: If there are more people denying or doubting the truth of an event, this event is more likely to be a rumor. For this purpose, [18] use an extensive list of bipolar sentiments with a set of combinational rules. In... |
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 |
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 ... | We should not rely on plateauing of the training loss or on the loss (logistic or exp or cross-entropy) evaluated on a validation data, as measures to decide when to stop. Instead, we should look at the 00–1111 error on the validation dataset. We might improve the validation and test errors even when when the decrease ... | Let ℓℓ\ellroman_ℓ be the logistic loss, and 𝒱𝒱\mathcal{V}caligraphic_V be an independent validation set, for which ∃𝐱∈𝒱𝐱𝒱\exists\mathbf{x}\in\mathcal{V}∃ bold_x ∈ caligraphic_V such that 𝐱⊤𝐰^<0superscript𝐱top^𝐰0\mathbf{x}^{\top}\hat{\mathbf{w}}<0bold_x start_POSTSUPERSCRIPT ⊤ end_POSTSUPERSCRIPT over^ start_... | The follow-up paper (Gunasekar et al., 2018) studied this same problem with exponential loss instead of squared loss. Under additional assumptions on the asymptotic convergence of update directions and gradient directions, they were able to relate the direction of gradient descent iterates on the factorized parameteriz... | decreasing loss, as well as for multi-class classification with cross-entropy loss. Notably, even though the logistic loss and the exp-loss behave very different on non-separable problems, they exhibit the same behaviour for separable problems. This implies that the non-tail
part does not affect the bias. The bias is a... | A |
For analysing the employed features, we rank them by importances using RF (see 4). The best feature is related to sentiment polarity scores. There is a big bias between the sentiment associated to rumors and the sentiment associated to real events in relevant tweets. In specific, the average polarity score of news even... | We use the same dataset described in Section 4.1. In total –after cutting off 180 events for pre-training single tweet model – our dataset contains 360 events and 180 of them are labeled as rumors. As a rumor is often of a long circurlating story (friggeri2014rumor, ), this results in a rather long time span. In this w... | To construct the training dataset, we collected rumor stories from the rumor tracking websites snopes.com and urbanlegends.about.com. In more detail, we crawled 4300 stories from these websites. From the
story descriptions we manually constructed queries to retrieve the relevant tweets for the 270 rumors with highest i... |
Training data for single tweet classification. An event might include sub-events for which relevant tweets are rumorous. To deal with this complexity, we train our single-tweet learning model only with manually selected breaking and subless events from the above dataset. In the end, we used 90 rumors and 90 news assoc... | The time period of a rumor event is sometimes fuzzy and hard to define. One reason is a rumor may have been triggered for a long time and kept existing, but it did not attract public attention. However it can be triggered by other events after a uncertain time and suddenly spreads as a bursty event. E.g., a rumor999htt... | A |
\mathcal{C}_{k})\mathsf{f^{*}}_{m}(\bar{a})italic_s italic_c italic_o italic_r italic_e ( over¯ start_ARG italic_a end_ARG ) = ∑ start_POSTSUBSCRIPT italic_m ∈ italic_M end_POSTSUBSCRIPT italic_P ( caligraphic_C start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT | italic_e , italic_t ) italic_P ( caligraphic_T start_POSTSU... | to add additional features from ℳ1superscriptℳ1\mathcal{M}^{1}caligraphic_M start_POSTSUPERSCRIPT 1 end_POSTSUPERSCRIPT. The feature vector
of ℳLR2superscriptsubscriptℳ𝐿𝑅2\mathcal{M}_{LR}^{2}caligraphic_M start_POSTSUBSCRIPT italic_L italic_R end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT consists of ... | RQ3. We demonstrate the results of single models and our ensemble model in Table 4. As also witnessed in RQ2, SVMall𝑆𝑉subscript𝑀𝑎𝑙𝑙SVM_{all}italic_S italic_V italic_M start_POSTSUBSCRIPT italic_a italic_l italic_l end_POSTSUBSCRIPT, will all features, gives a rather stable performance for both NDCG and Recall... |
We propose two sets of features, namely, (1) salience features (taking into account the general importance of candidate aspects) that mainly mined from Wikipedia and (2) short-term interest features (capturing a trend or timely change) that mined from the query logs. In addition, we also leverage click-flow relatednes... | 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... | C |
RL [Sutton and Barto, 1998] has been successfully applied to a variety of domains,
from Monte Carlo tree search [Bai et al., 2013] and hyperparameter tuning for complex optimization in science, engineering and machine learning problems [Kandasamy et al., 2018; Urteaga et al., 2023], | SMC weights are updated based on the likelihood of the observed rewards:
wt,a(m)∝pa(yt|xt,θt,a(m))proportional-tosuperscriptsubscript𝑤𝑡𝑎𝑚subscript𝑝𝑎conditionalsubscript𝑦𝑡subscript𝑥𝑡superscriptsubscript𝜃𝑡𝑎𝑚w_{t,a}^{(m)}\propto p_{a}(y_{t}|x_{t},\theta_{t,a}^{(m)})italic_w start_POSTSUBSCRIPT italic_t , it... | we propagate forward the sequential random measure pM(θt,a|ℋ1:t)subscript𝑝𝑀conditionalsubscript𝜃𝑡𝑎subscriptℋ:1𝑡p_{M}(\theta_{t,a}|\mathcal{H}_{1:t})italic_p start_POSTSUBSCRIPT italic_M end_POSTSUBSCRIPT ( italic_θ start_POSTSUBSCRIPT italic_t , italic_a end_POSTSUBSCRIPT | caligraphic_H start_POSTSUBSCRIPT 1 : ... | the fundamental operation in the proposed SMC-based MAB Algorithm 1
is to sequentially update the random measure pM(θt,a|ℋ1:t)subscript𝑝𝑀conditionalsubscript𝜃𝑡𝑎subscriptℋ:1𝑡p_{M}(\theta_{t,a}|\mathcal{H}_{1:t})italic_p start_POSTSUBSCRIPT italic_M end_POSTSUBSCRIPT ( italic_θ start_POSTSUBSCRIPT italic_t , itali... | The techniques used in these success stories are grounded on statistical advances on sequential decision processes and multi-armed bandits.
The MAB crystallizes the fundamental trade-off between exploration and exploitation in sequential decision making. | D |
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. | 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. | 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. | 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. | 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... | A |
The images presented during the acquisition of saliency maps in all aforementioned datasets are largely based on natural scenes. Stimuli of CAT2000 additionally fall into predefined categories such as Action, Fractal, Object, or Social. Together with the corresponding fixation patterns, they constituted the input and ... | To assess the predictive performance for eye tracking measurements, the MIT saliency benchmark Bylinskii et al. (2015) is commonly used to compare model results on two test datasets with respect to prior work. Final scores can then be submitted on a public leaderboard to allow fair model ranking on eight evaluation met... | We normalized the model output such that all values are non-negative with unit sum. The estimation of saliency maps can hence be regarded as a probability distribution prediction task as formulated by Jetley et al. (2016). To determine the difference between an estimated and a target distribution, the Kullback-Leibler ... | Various measures are used in the literature and by benchmarks to evaluate the performance of fixation models. In practice, results are typically reported for all of them to include different notions about saliency and allow a fair comparison of model predictions Kümmerer et al. (2018); Riche et al. (2013). A set of nin... | 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... | C |
In this work, we have answered several open questions about the string parameter of the locality number. Our main tool was to relate the locality number to the graph parameters cutwidth and pathwidth via suitable reductions. As an additional result, our reductions also pointed out an interesting relationship between th... | The main results are presented in Sections 4, 5 and 6. First, in Section 4, we present the reductions from Loc to Cutwidth and vice versa, and we discuss the consequences of these reductions. Then, in Section 5, we show how Loc can be reduced to Pathwidth, which yields an approximation algorithm for computing the local... |
In this section, we introduce polynomial-time reductions from the problem of computing the locality number of a word to the problem of computing the cutwidth of a graph, and vice versa. This establishes a close relationship between these two problems (and their corresponding parameters), which lets us derive several u... | Many existing algorithms constructing path decompositions are of theoretical interest only, and this disadvantage carries over to the possible algorithms computing the locality number or cutwidth (see Section 6) based on them. However, the reduction of 5.7 is also applicable in a purely practical scenario, since any ki... |
While our focus is on theoretical results in form of lower and upper complexity bounds, we stress here that the reductions may also be of practical interest, since they allow to transform any practical pathwidth or cutwidth algorithm into a practical algorithm for computing the locality number (or to transform a pract... | D |
Every ROI was identified using a combination of three CNNs, each analyzing one orthogonal image plane.
While a single CNN predicted the presence of a specific ROI in the given plane, the combination of their results provided a 3D bounding box around it. | Using a set of handcrafted image features together with features derived from a pretrained VGGnet with five layers, they build a classification scheme to map a given CT slice to the relevant level.
Each feature group was used to train a separate SVM classifier and predicted labels are then combined in a linear model, a... | Patients were assigned to one of five standard cardiovascular risk categories based on the Agatston score.
Authors from the same group created a method[232] for the detection of calcifications in low-dose chest CT using a CNN for anatomical location and another CNN for calcification detection. | In their article Moradi et al.[204] address the problem of detection of vertical position for a given cardiac CT slice.
They divide the body area depicted in chest CT into nine semantic categories each representing an area most relevant to the study of a disease. | In their article Hong et al.[201] trained a DBN using image patches for the detection, segmentation and severity classification of Abdominal Aortic Aneurysm region in CT images.
Liu et al.[202] used an FCN with twelve layers for left atrium segmentation in 3D CT volumes and then refined the segmentation results of the ... | C |
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... |
In this paper our focus was to demonstrate the capability and generality of SimPLe only across a suite of Atari games, however, we believe similar methods can be applied to other environments and tasks which is one of our main directions for future work. As a long-term challenge, we believe that model-based reinforcem... | Human players can learn to play Atari games in minutes (Tsividis et al., 2017). However, some of the best model-free reinforcement learning algorithms require tens or hundreds of millions of time steps – the equivalent of several weeks of training in real time. How is it that humans can learn these games so much faster... | Our predictive model has stochastic latent variables so it can be applied in highly stochastic environments. Studying such environments is an exciting direction for future work, as is the study of other ways in which the predictive neural network model could be used. Our approach uses the model as a learned simulator a... | Oh et al. (2015) and Chiappa et al. (2017) show that learning predictive models of Atari 2600 environments is possible using appropriately chosen deep learning architectures. Impressively, in some cases the predictions maintain low L2subscript𝐿2L_{2}italic_L start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT error over timespans... | A |
A high level overview of these combined methods is shown in Fig. 1.
Although we choose the EEG epileptic seizure recognition dataset from University of California, Irvine (UCI) [13] for EEG classification, the implications of this study could be generalized in any kind of signal classification problem. | For the CNN modules with one and two layers, xisubscript𝑥𝑖x_{i}italic_x start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT is converted to an image using learnable parameters instead of some static procedure.
The one layer module consists of one 1D convolutional layer (kernel sizes of 3333 with 8888 channels). | The two layer module consists of two 1D convolutional layers (kernel sizes of 3333 with 8888 and 16161616 channels) with the first layer followed by a ReLU activation function and a 1D max pooling operation (kernel size of 2222).
The feature maps of the last convolutional layer for both modules are then concatenated al... | Here we also refer to CNN as a neural network consisting of alternating convolutional layers each one followed by a Rectified Linear Unit (ReLU) and a max pooling layer and a fully connected layer at the end while the term ‘layer’ denotes the number of convolutional layers.
| Architectures of all bdsubscript𝑏𝑑b_{d}italic_b start_POSTSUBSCRIPT italic_d end_POSTSUBSCRIPT remained the same, except for the number of the output nodes of the last linear layer which was set to five to correspond to the number of classes of D𝐷Ditalic_D.
An example of the respective outputs of some of the m𝑚mita... | C |
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 10: The Cricket robot tackles a step of height h using rolling locomotion mode, negating the need for a transition to the walking mode. The total energy consumed throughout the entire step negotiation process in rolling locomotion stayed below the preset threshold value. This threshold value was established bas... | Figure 11: The Cricket robot tackles a step of height 2h, beginning in rolling locomotion mode and transitioning to walking locomotion mode using the rear body climbing gait. The red line in the plot shows that the robot tackled the step in rolling locomotion mode until the online accumulated energy consumption of the ... |
The whole-body climbing gait involves utilizing the entire body movement of the robot, swaying forwards and backwards to enlarge the stability margins before initiating gradual leg movement to overcome a step. This technique optimizes stability during the climbing process. To complement this, the rear-body climbing ga... | 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... | C |
Furthermore, we show an interesting difference between the standard advice model and the model we introduce: in the former, an advice bit can be at least as powerful as a random bit, since an advice bit can effectively simulate any efficient choice of a random bit. In contrast, we show that in our model, there are situ... |
In this work we focus on the online computation with advice. Our motivation stems from observing that, unlike the real world, the advice under the known models is often closer to “fiat” than “recommendation”. Our objective is to propose a model which allows the possibility of incorrect advice, with the objective of ob... | We begin in Section 2 with a simple, yet illustrative online problem as a case study, namely the ski rental problem.
Here, we give a Pareto-optimal algorithm with only one bit of advice. We also show that this algorithm is Pareto-optimal even in the space of all (deterministic) algorithms with advice of any size. |
All the above results pertain to deterministic online algorithms. In Section 6, we study the power of randomization in online computation with untrusted advice. First, we show that the randomized algorithm of Purohit et al. [29] for the ski rental problem Pareto-dominates any deterministic algorithm, even when the lat... | While our work addresses issues similar to [24] and [29], in that trusted advice is related to consistency whereas untrusted advice is related to robustness, it differs in two significant aspects: First, our ideal objective is to identify an optimal
family of algorithms, and we show that in some cases (ski rental, onli... | D |
It is true that more elaborated methods that simultaneously learn the classification model and the policy to stop reading could have been used, such as in [Dulac-Arnold et al., 2011, Yu et al., 2017].
However, for the moment it is clear that this very simple approach is effective enough to outperform the remainder meth... | This discriminating power of words can also be appreciated from a more qualitative point of view in the word-clouds of the top-100 selected words by global value shown in Figure 5.
From this figure it is possible to observe that the most frequent terms, i.e. the biggest ones on (b), were also selected by IG𝐼𝐺IGitali... | global value (green) in relation to the local value (orange) for the “depressed” category. The abscissa represents individual words arranged in order of frequency.
Note that the zone in which stop words are located (close to 0 in the abscissa) the local value is very high (since they are highly frequent words) but the ... | It is also worth mentioning that this is a vital and very relevant aspect: if we value these specific words, as is usual, only by their local probability 242424Which is the case, for instance, with Multinomial Naive Bayes. (or frequency), as shown in (b), they will always have almost “no value” since, naturally, their ... | In order to get a better understanding of the rationale behind the good behavior of our framework, it is important to go into more details on the mechanisms used to weight words.
In Figure 4 we can empirically corroborate that the global value correctly captures the significance and discriminating power of words since,... | D |
DEF-A achieves its best performance when λ=0.3𝜆0.3\lambda=0.3italic_λ = 0.3. In comparison, GMC+ outperforms DEF-A across different λ𝜆\lambdaitalic_λ values and shows a preference for a larger λ𝜆\lambdaitalic_λ (e.g., 0.5).
In the following experiments, we set λ𝜆\lambdaitalic_λ as 0.3 for DEF-A and 0.5 for GMC+. λ=... | 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... |
In this paper, we propose a novel method, called global momentum compression (GMC), for sparse communication in distributed learning. To the best of our knowledge, this is the first work that introduces global momentum for sparse communication in DMSGD. Furthermore, to enhance the convergence performance when using mo... | 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... | Figure 2(b), 2(c) and 2(d) show the distances to the global optimal point when using different s𝑠sitalic_s for the case when d=20𝑑20d=20italic_d = 20. We can find that, compared with the local momentum methods, the global momentum method GMC converges faster and more stably.
| B |
For the purposes of this paper we use a variation of the database444https://archive.ics.uci.edu/ml/datasets/Epileptic+Seizure+Recognition in which the EEG signals are split into segments with 178178178178 samples each, resulting in a balanced dataset that consists of 11500115001150011500 EEG signals in total.
| We then split the 11500115001150011500 signals into 76%percent7676\%76 %, 12%percent1212\%12 % and 12%percent1212\%12 % (8740,1380,13808740138013808740,1380,13808740 , 1380 , 1380 signals) as training, validation and test data respectively and normalize in the range [0,1]01[0,1][ 0 , 1 ] using the global max and min.
F... | We use one signal from each of 15 signal datasets from Physionet listed in the first column of Table I.
Each signal consists of 12000120001200012000 samples which in turn is split in 12121212 signals of 1000100010001000 samples each, to create the training (6666 signals), validation (2222 signals) and test datasets (44... | During supervised learning the weights of the kernels are frozen and a one layer fully connected network (FNN) is stacked on top of the reconstruction output of the SANs.
The FNN is trained for an additional 5555 epochs with the same batch size and model selection procedure as with SANs and categorical cross-entropy as... | The first two fully connected layers are followed by a ReLU while the last one produces the predictions.
The CNN is trained for an additional 5555 epochs with the same batch size and model selection procedure as with SANs and categorical cross-entropy as the loss function. | A |
Figure 15: τ𝜏\tauitalic_τ and m𝑚mitalic_m’s impact on the probability of altering strategies ω=(e1τ)m𝜔superscriptsuperscript𝑒1𝜏𝑚\omega=(e^{\frac{1}{\tau}})^{m}italic_ω = ( italic_e start_POSTSUPERSCRIPT divide start_ARG 1 end_ARG start_ARG italic_τ end_ARG end_POSTSUPERSCRIPT ) start_POSTSUPERSCRIPT italic_m end... | In the large-scale UAV ad-hoc networks, the number of UAVs is another feature that should be investigated. Since the demanding channel’s capacity should not be more than the channel’s size we provide, we limit the number of UAVs in the tolerance range which satisfies that each UAV’s channel selection is contented. In t... | Since the UAV ad-hoc network game is a special type of potential game, we can apply the properties of the potential game in the later analysis. Some algorithms that have been applied in the potential game can also be employed in the UAV ad-hoc network game. In the next section, we investigate the existing algorithm wit... |
Fig. 12 shows how the number of UAVs affect the computation complexity of SPBLLA. Since the total number of UAVs is diverse, the goal functions are different. The goal functions’ value in the optimum states increase with the growth in UAVs’ number. Since goal functions are the summation function of utility functions, ... |
1: Initialization: Selecting an arbitrary power and altitude profile s∈S𝑠𝑆s\in Sitalic_s ∈ italic_S and arbitrary channels for each UAV, the number of UAVs in a channel must be less than Cmaxsubscript𝐶𝑚𝑎𝑥C_{max}italic_C start_POSTSUBSCRIPT italic_m italic_a italic_x end_POSTSUBSCRIPT. | A |
\mathbf{v}}+\frac{\dot{p}}{\gamma-1}+\frac{1}{\mu_{0}r^{2}}\left(\nabla\psi%
\cdot\left(\nabla\dot{\psi}\right)+f\dot{f}\right)divide start_ARG italic_m start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT over˙ start_ARG italic_n end_ARG bold_v start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT end_ARG start_ARG 2 end_ARG + italic... | \frac{\gamma p}{\gamma-1}\mathbf{v}+\frac{(\mathbf{v}\cdot\nabla\psi)}{\mu_{0}%
r^{2}}\nabla\psi- ∇ ⋅ ( divide start_ARG italic_m start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT italic_n bold_v start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT end_ARG start_ARG 2 end_ARG bold_v + divide start_ARG italic_γ italic_p end_ARG sta... | \mathbf{v}}+\frac{\dot{p}}{\gamma-1}+\frac{1}{\mu_{0}r^{2}}\left(\nabla\psi%
\cdot\left(\nabla\dot{\psi}\right)+f\dot{f}\right)divide start_ARG italic_m start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT over˙ start_ARG italic_n end_ARG bold_v start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT end_ARG start_ARG 2 end_ARG + italic... | 𝐯˙=−𝐯⋅∇𝐯+1ρ(−∇p−∇⋅𝝅¯+𝐉×𝐁)˙𝐯⋅𝐯∇𝐯1𝜌∇𝑝⋅∇¯𝝅𝐉𝐁\dot{\mathbf{v}}=-\mathbf{v}\cdot\nabla\mathbf{v}+\frac{1}{\rho}\left(-\nabla p%
-\nabla\cdot\underline{\boldsymbol{\pi}}+\mathbf{J\times}\mathbf{B}\right)over˙ start_ARG bold_v end_ARG = - bold_v ⋅ ∇ bold_v + divide start_ARG 1 end_ARG start_ARG italic_ρ end_ARG ... | −[mi𝐯22∇⋅(n𝐯)+ρ𝐯⋅∇𝐯22]delimited-[]⋅subscript𝑚𝑖superscript𝐯22∇𝑛𝐯⋅𝜌𝐯∇superscript𝐯22\displaystyle-\left[\frac{m_{i}\mathbf{v}^{2}}{2}\nabla\cdot(n\mathbf{v})+\rho%
\mathbf{v}\cdot\nabla\frac{\mathbf{v}^{2}}{2}\right]- [ divide start_ARG italic_m start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT bold_v start_P... | D |
When using the framework, one can further require reflexivity on the comparability functions, i.e. f(xA,xA)=1A𝑓subscript𝑥𝐴subscript𝑥𝐴subscript1𝐴f(x_{A},x_{A})=1_{A}italic_f ( italic_x start_POSTSUBSCRIPT italic_A end_POSTSUBSCRIPT , italic_x start_POSTSUBSCRIPT italic_A end_POSTSUBSCRIPT ) = 1 start_POSTSUBSCRIP... | Indeed, in practice the meaning of the null value in the data should be explained by domain experts, along with recommendations on how to deal with it.
Moreover, since the null value indicates a missing value, relaxing reflexivity of comparability functions on null allows to consider absent values as possibly | When using the framework, one can further require reflexivity on the comparability functions, i.e. f(xA,xA)=1A𝑓subscript𝑥𝐴subscript𝑥𝐴subscript1𝐴f(x_{A},x_{A})=1_{A}italic_f ( italic_x start_POSTSUBSCRIPT italic_A end_POSTSUBSCRIPT , italic_x start_POSTSUBSCRIPT italic_A end_POSTSUBSCRIPT ) = 1 start_POSTSUBSCRIP... | fA(u,v)=fB(u,v)={1if u=v≠nullaif u≠null,v≠null and u≠vbif u=v=null0otherwise.subscript𝑓𝐴𝑢𝑣subscript𝑓𝐵𝑢𝑣cases1if 𝑢𝑣null𝑎formulae-sequenceif 𝑢null𝑣null and 𝑢𝑣𝑏if 𝑢𝑣null0otherwise.f_{A}(u,v)=f_{B}(u,v)=\begin{cases}1&\text{if }u=v\neq\texttt{null}\\
a&\text{if }u\neq\texttt{null},v\neq\texttt{null}... | Intuitively, if an abstract value xAsubscript𝑥𝐴x_{A}italic_x start_POSTSUBSCRIPT italic_A end_POSTSUBSCRIPT of ℒAsubscriptℒ𝐴\mathcal{L}_{A}caligraphic_L start_POSTSUBSCRIPT italic_A end_POSTSUBSCRIPT is interpreted as 1111 (i.e., equality)
by hAsubscriptℎ𝐴h_{A}italic_h start_POSTSUBSCRIPT italic_A end_POSTSUBSCRIPT... | A |
In this paper, we introduce and conduct an empirical analysis of an alternative approach to mitigate variance and overestimation phenomena using Dropout techniques. Our main contribution is an extension to the DQN algorithm that incorporates Dropout methods to stabilize training and enhance performance. The effectivene... |
Deep neural networks are the state of the art learning models used in artificial intelligence. The large number of parameters in neural networks make them very good at modelling and approximating any arbitrary function. However the larger number of parameters also make them particularly prone to over-fitting, requirin... |
It’s the original Dropout method. It was introduced in 2012. Standard Dropout provides a simple technique for avoiding over-fitting in fully connected neural networks[12]. During each training phase, each neuron is excluded from the network with a probability p. Once trained, in the testing phase the full network is u... |
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... |
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... | A |
Figure 14 contains a simple overlap scenario, with the ground truth and the predicted binary masks with a spatial resolution 5×5555\times 55 × 5. Let black pixels denote the object to be segmented. The confusion matrix for this can be constructed as shown in Table 1. Using the expressions above, we can calculate the me... | Next, we briefly discuss the most popular and widely used datasets for the semantic segmentation of natural images. These datasets cover various categories of scenes, such as indoor and outdoor environments, common objects, urban street view as well as generic scenes. For a comprehensive review of the natural image dat... | Guo et al. (2018) provided a review of deep learning based semantic segmentation of images, and divided the literature into three categories: region-based, fully convolutional network (FCN)-based, and weakly supervised segmentation methods. Hu et al. (2018b) summarized the most commonly used RGB-D datasets for semantic... |
Creating large 2D and 3D publicly available medical benchmark datasets for semantic image segmentation such as the Medical Segmentation Decathlon (Simpson et al., 2019). Medical imaging datasets are typically much smaller in size than natural image datasets (Jin et al., 2020), and the curation of larger public dataset... |
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. | A |
The best case is the bipartite graph, where the MAXCUT is known and it cuts all the graph edges.
The partition 𝐳𝐳{\mathbf{z}}bold_z found by our spectral algorithm on bipartite graphs is optimal, i.e., γ(𝐳)=MAXCUT/|ℰ|=1𝛾𝐳MAXCUTℰ1\gamma({\mathbf{z}})=\texttt{\small{MAXCUT}}{}/|\mathcal{E}|=1italic_γ ( bold_z ) = M... | We recall that in those cases the MAXCUT is unknown and the gaps between the lower bound (0.5) and the upper bound (λmaxs/2subscriptsuperscript𝜆𝑠max2\lambda^{s}_{\text{max}}/2italic_λ start_POSTSUPERSCRIPT italic_s end_POSTSUPERSCRIPT start_POSTSUBSCRIPT max end_POSTSUBSCRIPT / 2) can be arbitrarily large.
| From Fig. 9(b) we notice that the graphs 𝐀(1)superscript𝐀1{\mathbf{A}}^{(1)}bold_A start_POSTSUPERSCRIPT ( 1 ) end_POSTSUPERSCRIPT and 𝐀(2)superscript𝐀2{\mathbf{A}}^{(2)}bold_A start_POSTSUPERSCRIPT ( 2 ) end_POSTSUPERSCRIPT in GRACLUS have additional nodes that are disconnected.
As discussed in Sect. V, these are ... | We recall that in those cases the MAXCUT is unknown and the gaps between the lower bound (0.5) and the upper bound (λmaxs/2subscriptsuperscript𝜆𝑠max2\lambda^{s}_{\text{max}}/2italic_λ start_POSTSUPERSCRIPT italic_s end_POSTSUPERSCRIPT start_POSTSUBSCRIPT max end_POSTSUBSCRIPT / 2) can be arbitrarily large.
| In graphs that are close to be bipartite or, in general, that have a very sparse and regular connectivity, a large percentage of edges can be cut if the nodes are partitioned correctly.
Indeed, for these graphs the MAXCUT is usually large and is closer to the upper-bound in (11). | D |
Additionally, the experiment shows that the training is very robust to overfitting even when the number of parameters in the network increases.
When combining the generated data and original data, the accuracy on Car and Covertype improves with an increasing number of training examples. | We analyze the performance by training random forests for each dataset and evaluating neural random forest imitation with different network architectures.
A variety of network architectures with different depths, widths, and additional layers such as Dropout have been studied. In this work, we focus on two-hidden-layer... | NRFI with and without the original data is shown for different network architectures. The smallest architecture has 2222 neurons in both hidden layers and the largest 128128128128. For NRFI (gen-ori), we can see that a network with 16161616 neurons in both hidden layers (NN-16-16) is already sufficient to learn the dec... | Overall, the experiment shows that the accuracy increases with an increasing number of neurons in both layers and NRFI is robust to different network architectures.
NRFI is capable of generating a large variety of unique examples from random forests which have been initially trained on a limited amount of data. | Additionally, the experiment shows that the training is very robust to overfitting even when the number of parameters in the network increases.
When combining the generated data and original data, the accuracy on Car and Covertype improves with an increasing number of training examples. | C |
Coupled with powerful function approximators such as neural networks, policy optimization plays a key role in the tremendous empirical successes of deep reinforcement learning (Silver et al., 2016, 2017; Duan et al., 2016; OpenAI, 2019; Wang et al., 2018). In sharp contrast, the theoretical understandings of policy opt... | 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... | for any function f:𝒮→ℝ:𝑓→𝒮ℝf:{\mathcal{S}}\rightarrow\mathbb{R}italic_f : caligraphic_S → blackboard_R. By allowing the reward function to be adversarially chosen in each episode, our setting generalizes the stationary setting commonly adopted by the existing work on value-based reinforcement learning (Jaksch et al.... |
Broadly speaking, our work is related to a vast body of work on value-based reinforcement learning in tabular (Jaksch et al., 2010; Osband et al., 2014; Osband and Van Roy, 2016; Azar et al., 2017; Dann et al., 2017; Strehl et al., 2006; Jin et al., 2018) and linear settings (Yang and Wang, 2019b, a; Jin et al., 2019;... |
A line of recent work (Fazel et al., 2018; Yang et al., 2019a; Abbasi-Yadkori et al., 2019a, b; Bhandari and Russo, 2019; Liu et al., 2019; Agarwal et al., 2019; Wang et al., 2019) answers the computational question affirmatively by proving that a wide variety of policy optimization algorithms, such as policy gradient... | D |
Targeting the same problem, Lin et al. (2023) introduced activation-aware weight quantization, which exploits the fact that the weights of large language models are not equally important.
They propose to guide the selection of important weights by activation magnitudes (rather than weight magnitudes) and protecting sal... | Liu et al. (2019b) have replicated several experiments of pruning approaches (see Section 3.2) and they observed that the typical workflow of training, pruning, and fine-tuning is often not necessary and only the discovered sparsity structure is important.
In particular, they show for several pruning approaches that ra... | By injecting additive noise to the deterministic weights before rounding, one can compute probabilities of the weights being rounded to specific values in a predefined discrete set.
Subsequently, these probabilities are used to differentiably round the weights using the Gumbel-softmax approximation (Jang et al., 2017). | They introduce a mixture of log-uniform priors whose mixtures are centered at predefined quantization values.
Consequently, the approximate posterior also concentrates at these values such that weights can be safely quantized without requiring a fine-tuning procedure. | At forward propagation, the weights are stochastically quantized to either binary weights w∈{−1,1}𝑤11w\in\{-1,1\}italic_w ∈ { - 1 , 1 } or ternary weights w∈{−1,0,1}𝑤101w\in\{-1,0,1\}italic_w ∈ { - 1 , 0 , 1 } to remove the need for multiplications at all.
During backpropagation, inputs and hidden neurons are quantiz... | C |
In Section 8, we reprove Rips and Gromov’s result about the contractibility of the Vietoris-Rips complex of hyperbolic geodesic metric spaces, by using our method consisting of isometric embeddings into injective metric spaces. As a result, we will be able to bound the length of intervals in Vietoris-Rips persistence b... | In [64], Liu studies the mapping properties of the filling radius. His results can be interpreted as providing certain guarantees for how the filling radius changes under multiplicative distortion of metrics. Here we study the effect of additive distortion.
| Of central interest in topological data analysis has been the question of providing a complete characterization of the Vietoris-Rips persistence barcodes of spheres of different dimensions. Despite the existence of a complete answer to the question for the case of 𝕊1superscript𝕊1\mathbb{S}^{1}blackboard_S start_POSTS... |
In Section 9, we give some applications of our ideas to the filling radius of Riemannian manifolds and also study consequences related to the characterization of spheres by their persistence barcodes and some generalizations and novel stability properties of the filling radius. |
In this section, we recall the notions of spread and filling radius, as well as their relationship. In particular, we prove a number of statements about the filling radius of a closed connected manifold. Moreover, we consider a generalization of the filling radius and also define a strong notion of filling radius whic... | C |
Anna uses the Dimension Correlation in order to determine the role of the data set’s dimensions in the outcome of the projection. She interactively draws a polyline with her mouse following the pattern from the benign cases to the malignant ones, as shown in Figure 6(c). By looking at the Dimension Correlation view (se... | Anna uses the Dimension Correlation in order to determine the role of the data set’s dimensions in the outcome of the projection. She interactively draws a polyline with her mouse following the pattern from the benign cases to the malignant ones, as shown in Figure 6(c). By looking at the Dimension Correlation view (se... |
When she looks at the main view again, one thing catches her eye: there is quite a difference in density between the two large clusters of points (as shown by the points’ colors in Figure 6(c)). The cluster to the left (mostly malignant cases) has low density in general, as opposed to the cluster to the right (mostly ... | Anna loads the data into t-viSNE and starts the hyper-parameter exploration with a grid search. After the execution, she sees several projections that accurately separate the two classes. As she does not have any special preference, she selects the top-left projection, because the projections are sorted from best to wo... | In the second case (2) (not included due to space constraints), she spotted that there is a pattern of a rapid increase in the “clump thickness” (more than 80% correlation) when going from the middle-left side to the bottom side of the cluster with the benign classified points.
“This is new,” she thinks. These connecti... | D |
The crucial decision in differential vector movement is how the differential vector (namely, the intensity and direction of the movement) is calculated. This differential vector could be calculated so as to move the reference solution to another solution (usually a better one), or as a lineal combination of other diff... |
Algorithms within this category do not resort to representative solutions of the entire population (such as the current best), but they only consider solutions of a subset or group of the solutions in the population. When the differential movement considers both a group and a representative of all the population, the ... | This category is further divided into subcategories as a function of the above decision, i.e. which solutions are considered to create the movement vector. It should be noted that some algorithms can be classified into more than one subcategory. For instance, a particle’s update in the PSO solver is affected by the glo... |
In this group (the most populated in this second taxonomy), the different movement of each solution is only influenced by a small group of representative solutions. It is often the case that these representative solutions are selected to be the best solutions found by the algorithm (as per the objective of the problem... | Tables 18, 19, 20, 21, 22, 23 and 24 show the different algorithms in this subcategory. An exemplary algorithm of this category that has been a major meta-heuristic solver in the history of the field is PSO [80]. In this solver, each solution or particle is guided by the global current best solution and the best soluti... | 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. | (1) Via extending the generative graph models into general type data, GAE is naturally employed as the basic representation learning model and weighted graphs can be further applied to GAE as well. The connectivity distributions given by the generative perspective also inspires us to devise a novel architecture for dec... | To apply graph convolution on unsupervised learning, GAE is proposed [20].
GAE firstly transforms each node into latent representation (i.e., embedding) via GCN, and then aims to reconstruct some part of the input. GAEs proposed in [20, 29, 22] intend to reconstruct the adjacency via decoder while GAEs developed in [21... | D |
The measurement methodology underlying SMap uses active probes, some sent from spoofed as well as from real source IP addresses to popular services on the tested networks. The spoofed source IP addresses belong to the tested networks (similarly to the Spoofer Project (Beverly and Bauer, 2005)). The idea behind our met... |
SMap consists of the orchestrator which coordinates and synchronises the prober hosts. The prober hosts receive the dataset of networks to be scanned for spoofability from the orchestrator. The probers then run IPID, PMTUD and DNS lookup tests against the services on the dataset list. SMap applies one test at a time f... |
We define the result of SMap evaluation successful (i.e., true positive) if at least one of the three tests outputs that the tested network does not filter spoofed packets: either the IPID value on the server in the tested network was incremented as expected (IPID test) or we receive a query at our domain (DNS test) o... | Methodology. The core idea of the Path MTU Discovery (PMTUD) based tool is to send the ICMP Packet too Big (PTB) message from a spoofed source IP address, belonging to the tested network, and in the 8 bytes payload of the ICMP to insert the real IP address belonging to the prober. If the network does not enforce ingres... |
Methodology. We use services that assign globally incremental IPID values. The idea is that globally incremental IPID [RFC6864] (Touch, 2013) values leak traffic volume arriving at the service and can be measured by any Internet host. Given a server with a globally incremental IPID on the tested network, we sample the... | A |
Machine learning applications frequently deal with data-generating processes that change over time. Applications in such nonstationary environments include power use forecasting, recommendation systems, and environmental sensors [9]. Semisupervised learning, which has received a lot of attention in the sensor communit... | While natural systems cope with changing environments and embodiments well, they form a serious challenge for artificial systems. For instance, to stay reliable over time, gas sensing systems must be continuously recalibrated to stay accurate in a changing physical environment. Drawing motivation from nature, this pape... | Biology frequently deals with drift [16]. For instance olfactory systems are constantly adapting, predominantly through feedback mechanisms. This section details some such models from computer science and neuroscience [17]. One example is the KIII model, a dynamic network resembling the olfactory bulb and feedforward a... |
One prominent feature of the mammalian olfactory system is feedback connections to the olfactory bulb from higher-level processing regions. Activity in the olfactory bulb is heavily influenced by behavioral and value-based information [19], and in fact, the bulb receives more neural projections from higher-level regio... |
The purpose of this study was to demonstrate that explicit representation of context can allow a classification system to adapt to sensor drift. Several gas classifier models were placed in a setting with progressive sensor drift and were evaluated on samples from future contexts. This task reflects the practical goal... | B |
Our algorithm is a dynamic program, where we define a subproblem for each separator
index i𝑖iitalic_i, and each set of endpoints B∈ℬi𝐵subscriptℬ𝑖B\in\mathcal{B}_{i}italic_B ∈ caligraphic_B start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT. The value of A[i,B]𝐴𝑖𝐵A[i,B]italic_A [ italic_i , italic_B ] is defined as f... | A(1)[i,B]:={A representative set containing pairs (M,x), where M is a perfect matching on B∈ℬi(1) and x is a real number equal to the minimum total length of a path cover of P0∪⋯∪Pi−1∪B realizing the matching Massignsuperscript𝐴1𝑖𝐵casesA representative set containing pairs (M,x), where M is a perfect matching on B∈... | A(2)[i,B]:={A representative set containing pairs (M,x), where M is a perfect matching on B∈ℬi(2) and x is a real number equal to the minimum total length of a path cover of P0∪⋯∪Pi−1∪B realizing the matching M.assignsuperscript𝐴2𝑖𝐵casesA representative set containing pairs (M,x), where M is a perfect matching on B... |
A[i,B]:={A representative set containing pairs (M,x), where M is a perfect matching on B∈ℬi and x is a real number equal to the minimum total length of a path cover of P0∪⋯∪Pi−1∪B realizing the matching M.assign𝐴𝑖𝐵casesA representative set containing pairs (M,x), where M is a perfect matching on B∈ℬi and x is a re... |
A[i,B]:={A representative set containing pairs (M,x), where M is a perfect matching on B and x is a real number equal to the minimum total length of a path cover of P0∪⋯∪Pi−1∪B realizing the matching M.assign𝐴𝑖𝐵casesA representative set containing pairs (M,x), where M is a perfect matching on B and x is a real num... | D |
The first author was supported by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through an FCT post-doctoral fellowship (SFRH/BPD/121469/2016) and the projects UID/MAT/00297/2013 (Centro de Matemática e Aplicações) and PTDC/MAT-PUR/31174/2017.
| The first author was supported by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through an FCT post-doctoral fellowship (SFRH/BPD/121469/2016) and the projects UID/MAT/00297/2013 (Centro de Matemática e Aplicações) and PTDC/MAT-PUR/31174/2017.
| idempotent or both homogeneous (with respect to the presentation given by the generating automaton), then S⋆T⋆𝑆𝑇S\star Titalic_S ⋆ italic_T is an automaton semigroup.
For her Bachelor thesis [19], the third author modified the construction in [3, Theorem 4] to considerably relax the hypothesis on the base semigroups: | 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... |
During the research and writing for this paper, the second author was previously affiliated with FMI, Centro de Matemática da Universidade do Porto (CMUP), which is financed by national funds through FCT – Fundação para a Ciência e Tecnologia, I.P., under the project with reference UIDB/00144/2020, and the Dipartiment... | D |
This work was supported in part by AFOSR grant [FA9550-18-1-0121], NSF award #1909696, and a gift from Adobe Research. We thank NVIDIA for the GPU donation. The views and conclusions contained herein are those of the authors and should not be interpreted as representing the official policies or endorsements of any spon... | Our regularization method, which is a binary cross entropy loss between the model predictions and a zero vector, does not use additional cues or sensitivities and yet achieves near state-of-the-art performance on VQA-CPv2. We set the learning rate to: 2×10−6r2superscript106𝑟\frac{2\times 10^{-6}}{r}divide start_ARG 2 ... | We compare the baseline UpDn model with HINT and SCR-variants trained on VQAv2 or VQA-CPv2 to study the causes behind the improvements. We report mean accuracies across 5555 runs, where a pre-trained UpDn model is fine-tuned on subsets with human attention maps and textual explanations for HINT and SCR respectively. Fu... |
We compare four different variants of HINT and SCR to study the causes behind the improvements including the models that are fine-tuned on: 1) relevant regions (state-of-the-art methods) 2) irrelevant regions 3) fixed random regions and 4) variable random regions. For all variants, we fine-tune a pre-trained UpDn, whi... | Following Selvaraju et al. (2019), we train HINT on the subset with human-based attention maps Das et al. (2017), which are available for 9% of the VQA-CPv2 train and test sets. The same subset is used for VQAv2 too. The learning rate is set to 2×10−52superscript1052\times 10^{-5}2 × 10 start_POSTSUPERSCRIPT - 5 end_PO... | C |
We use the byte pair encoding tokenization technique utilized in RoBERTa and retain its cased vocabulary. We did not create a new vocabulary since the two vocabularies are not significantly different and any out-of-vocabulary words can be represented and tuned for the privacy domain using the byte pair encoding vocabu... |
Prior collections of privacy policy corpora have led to progress in privacy research. Wilson et al. (2016) released the OPP-115 Corpus, a dataset of 115 privacy policies with manual annotations of 23k fine-grained data practices, and they created a baseline for classifying privacy policy text into one of ten categorie... |
For the data practice classification task, we leveraged the OPP-115 Corpus introduced by Wilson et al. (2016). The OPP-115 Corpus contains manual annotations of 23K fine-grained data practices on 115 privacy policies annotated by legal experts. To the best of our knowledge, this is the most detailed and widely used da... | For each topic, we identified a corresponding entry from the OPP-115 annotation scheme (Wilson et al., 2016), which was created by legal experts to label the contents of privacy policies. While Wilson et al. (2016) followed a bottom-up approach and identified different categories from analysis of data practices in priv... |
It is likely that the divergence between OPP-115 categories and LDA topics comes from a difference in approaches: the OPP-115 categories represent themes that privacy experts expected to find in privacy policies, which diverge from the actual distribution of themes in this text genre. Figure 2 shows the percentage of ... | B |
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 ... | Figure 6: The process of exploration of distinct algorithms in hypotheticality stance analysis. (a) presents the selection of appropriate validation metrics for the specification of the data set. (b) aggregates the information after the exploration of different models and shows the active ones which will be used for th... | E2 added that, after some initial training period (because the system could be a bit overwhelming in the beginning), the power of visualization in StackGenVis for supporting the analytical process is impressive.
E3 raised the question: “why not select the best, or a set of the best models of an algorithm, according to ... | 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 ... |
In this paper, we introduced an interactive VA system, called StackGenVis, for the alignment of data, algorithms, and models in stacking ensemble learning. The adaptation of an already-existing knowledge generation model leads us to stable design goals and analytical tasks that were realized by StackGenVis. With the c... | B |
We thus have 3333 cases, depending on the value of the tuple
(p(v,[010]),p(v,[323]),p(v,[313]),p(v,[003]))𝑝𝑣delimited-[]010𝑝𝑣delimited-[]323𝑝𝑣delimited-[]313𝑝𝑣delimited-[]003(p(v,[010]),p(v,[323]),p(v,[313]),p(v,[003]))( italic_p ( italic_v , [ 010 ] ) , italic_p ( italic_v , [ 323 ] ) , italic_p ( italic_v... | Then, by using the adjacency of (v,[013])𝑣delimited-[]013(v,[013])( italic_v , [ 013 ] ) with each of
(v,[010])𝑣delimited-[]010(v,[010])( italic_v , [ 010 ] ), (v,[323])𝑣delimited-[]323(v,[323])( italic_v , [ 323 ] ), and (v,[112])𝑣delimited-[]112(v,[112])( italic_v , [ 112 ] ), we can confirm that | p(v,[013])=p(v,[313])=p(v,[113])=1𝑝𝑣delimited-[]013𝑝𝑣delimited-[]313𝑝𝑣delimited-[]1131p(v,[013])=p(v,[313])=p(v,[113])=1italic_p ( italic_v , [ 013 ] ) = italic_p ( italic_v , [ 313 ] ) = italic_p ( italic_v , [ 113 ] ) = 1.
Similarly, when f=[112]𝑓delimited-[]112f=[112]italic_f = [ 112 ], | 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 | {0¯,1¯,2¯,3¯,[013],[010],[323],[313],[112],[003],[113]}.¯0¯1¯2¯3delimited-[]013delimited-[]010delimited-[]323delimited-[]313delimited-[]112delimited-[]003delimited-[]113\{\overline{0},\overline{1},\overline{2},\overline{3},[013],[010],[323],[313],%
[112],[003],[113]\}.{ over¯ start_ARG 0 end_ARG , over¯ start_ARG 1 end... | C |
For both BLEU and C Score, Jac Score is around 1 in each cluster, which means the persona descriptions are not similar. The dialogue quantity also seems similar among different clusters. So we can conclude that data quantity and task profile does not have a major impact on the fine-tuning process.
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To answer RQ1, we compare the changing trend of the general language model and the task-specific adaptation ability during the training of MAML to find whether there is a trade-off problem. (Figure 1) We select the trained parameter initialization at different MAML training epochs and evaluate them directly on the met... | 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... | 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... | 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... | 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_... | 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... | 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... | 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... |
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. | D |
There are other logics, incomparable
in expressiveness with 𝖥𝖮Pres2subscriptsuperscript𝖥𝖮2Pres\mathsf{FO}^{2}_{\textup{Pres}}sansserif_FO start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT Pres end_POSTSUBSCRIPT, where periodicity of the spectrum has been proven [17]. The | There are other logics, incomparable
in expressiveness with 𝖥𝖮Pres2subscriptsuperscript𝖥𝖮2Pres\mathsf{FO}^{2}_{\textup{Pres}}sansserif_FO start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT Pres end_POSTSUBSCRIPT, where periodicity of the spectrum has been proven [17]. The | The paper [4] shows decidability for a logic with incomparable expressiveness: the quantification allows a more powerful
quantitative comparison, but must be guarded – restricting the counts only of sets of elements that are adjacent to a given element. | Related one-variable fragments in which we have only a
unary relational vocabulary and the main quantification is ∃Sxϕ(x)superscript𝑆𝑥italic-ϕ𝑥\exists^{S}x~{}\phi(x)∃ start_POSTSUPERSCRIPT italic_S end_POSTSUPERSCRIPT italic_x italic_ϕ ( italic_x ) are known to be decidable (see, e.g. [2]), and their decidability ... | In addition, to make the main line of argument clearer, we consider only the finite graph case in the body of the paper,
which already implies decidability of the finite satisfiability of 𝖥𝖮Pres2subscriptsuperscript𝖥𝖮2Pres\mathsf{FO}^{2}_{\textup{Pres}}sansserif_FO start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT start_... | B |
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... |
at the mean-field limit with ϵ→0+→italic-ϵsuperscript0\epsilon\rightarrow 0^{+}italic_ϵ → 0 start_POSTSUPERSCRIPT + end_POSTSUPERSCRIPT and m→∞→𝑚m\rightarrow\inftyitalic_m → ∞. Such a correspondence allows us to use the PDE solution ρtsubscript𝜌𝑡\rho_{t}italic_ρ start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT in (3.... | The key to our analysis is a mean-field perspective, which allows us to associate the evolution of a finite-dimensional parameter with its limiting counterpart over an infinite-dimensional Wasserstein space (Villani, 2003, 2008; Ambrosio et al., 2008; Ambrosio and Gigli, 2013). Specifically, by exploiting the permutati... | 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... | The proof of Proposition 3.1 is based on the propagation of chaos (Sznitman, 1991; Mei et al., 2018, 2019).
In contrast to Mei et al. (2018, 2019), the PDE in (3.4) can not be cast as a gradient flow, since there does not exist a corresponding energy functional. Thus, their analysis is not directly applicable to our se... | B |
We explore the use of LSTMs to connect layers in stacked deep architectures for Transformers: we show how residual connections can be replaced by LSTMs connecting self-, cross- and masked self-attention layers. In contrast to standard LSTMs that process token sequences, we refer to the use of LSTMs in connecting stacke... | We suggest that selectively aggregating different layer representations of the Transformer may improve the performance, and propose to use depth-wise LSTMs to connect stacked (sub-) layers of Transformers. We show how Transformer layer normalization and feed-forward sub-layers can be absorbed by depth-wise LSTMs, while... | We explore the use of LSTMs to connect layers in stacked deep architectures for Transformers: we show how residual connections can be replaced by LSTMs connecting self-, cross- and masked self-attention layers. In contrast to standard LSTMs that process token sequences, we refer to the use of LSTMs in connecting stacke... |
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-... | The computation of depth-wise LSTM is the same as the conventional LSTM except that depth-wise LSTM connects stacked Transformer layers instead of tokens in a token sequence as in conventional LSTMs. The gate mechanisms in the original LSTM are to enhance its ability in capturing long-distance relations and to address ... | A |
so that, for all i,j,k∈I𝑖𝑗𝑘𝐼i,j,k\in Iitalic_i , italic_j , italic_k ∈ italic_I with k≤j≤i𝑘𝑗𝑖k\leq j\leq iitalic_k ≤ italic_j ≤ italic_i, we have
fi,i=idXisubscript𝑓𝑖𝑖subscriptidsubscript𝑋𝑖f_{i,i}=\mathrm{id}_{X_{i}}italic_f start_POSTSUBSCRIPT italic_i , italic_i end_POSTSUBSCRIPT = roman_id start_POSTSUBS... | uniqueness in 𝐓𝐨𝐩𝐓𝐨𝐩\mathbf{Top}bold_Top. This shows that {fi:X→Xi}i∈Isubscriptconditional-setsubscript𝑓𝑖→𝑋subscript𝑋𝑖𝑖𝐼\{f_{i}\colon X\to X_{i}\}_{i\in I}{ italic_f start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT : italic_X → italic_X start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT } start_POSTSUBSCRIPT ita... | Assume that {fi:X→(𝒞,τi)}i∈Isubscriptconditional-setsubscript𝑓𝑖→𝑋𝒞subscriptτ𝑖𝑖𝐼\{f_{i}:X\to(\mathcal{C},\uptau_{i})\}_{i\in I}{ italic_f start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT : italic_X → ( caligraphic_C , roman_τ start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ) } start_POSTSUBSCRIPT italic_i ∈ italic_... | If {fi:X→Xi}i∈Isubscriptconditional-setsubscript𝑓𝑖→𝑋subscript𝑋𝑖𝑖𝐼\{f_{i}\colon X\to X_{i}\}_{i\in I}{ italic_f start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT : italic_X → italic_X start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT } start_POSTSUBSCRIPT italic_i ∈ italic_I end_POSTSUBSCRIPT
is the limit of ℱℱ\mathcal... | The projective limit of a projective system ℱℱ\mathcal{F}caligraphic_F
is an object X𝑋Xitalic_X with maps fi:X→Xi:subscript𝑓𝑖→𝑋subscript𝑋𝑖f_{i}\colon X\to X_{i}italic_f start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT : italic_X → italic_X start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT | D |
(1) Overall, the ordinal distortion estimation significantly outperforms the distortion parameter estimation in both convergence and accuracy, even if the amount of training data is 20% of that used to train the learning model. Note that we only use 1/4 distorted image to predict the ordinal distortion. As we pointed o... |
Global Perception Module: For the global perception module, its architecture can be divided into two sub-networks, a backbone network, and a header network. Specifically, the general representation of the global distortion context is extracted using the backbone network composed of convolutional layers. This represent... | (1) Overall, the ordinal distortion estimation significantly outperforms the distortion parameter estimation in both convergence and accuracy, even if the amount of training data is 20% of that used to train the learning model. Note that we only use 1/4 distorted image to predict the ordinal distortion. As we pointed o... |
(2) For each backbone network, the layer depths of VGG16, InceptionV3, and ResNet50 are 23, 159, and 168, respectively. These architectures represent the different extraction abilities of image features. As illustrated in Fig. 6, the distortion parameter estimation achieves the lowest error (0.15) using InceptionV3 as... |
To exhibit the performance fairly, we employ three common network architectures VGG16, ResNet50, and InceptionV3 as the backbone networks of the learning model. The proposed MDLD metric is used to express the distortion estimation error due to its unique and fair measurement for distortion distribution. To be specific... | C |
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 3 shows the validation perplexity of the three methods with a small batch size of 20 and a large batch size of 2000. In small-batch training, SNGM and LARS achieve validation perplexity comparable to that of MSGD. Meanwhile, in large-batch training, SNGM achieves better performance than MSGD and LARS. | Table 6 shows the test perplexity of the three methods with different batch sizes. We can observe that for small batch size, SNGM achieves test perplexity comparable to that of MSGD, and for large batch size, SNGM is better than MSGD. Similar to the results of image classification, SNGM outperforms LARS for different b... | showed that existing SGD methods with a large batch size will lead to a drop in the generalization accuracy of deep learning models. Figure 1
shows a comparison of training loss and test accuracy between MSGD with a small batch size and MSGD with a large batch size. We can find that large-batch training indeed | 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... | A |
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 |
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... |
III. The co-existence of random graphs, subgradient measurement noises, additive and multiplicative communication noises are considered. Compared with the case with only a single random factor, the coupling terms of different random factors inevitably affect the mean square difference between optimizers’ states and an... | (Lemma 3.1).
To this end, we estimate the upper bound of the mean square increasing rate of the local optimizers’ states at first (Lemma 3.2). Then we substitute this upper bound into the Lyapunov function difference inequality of the consensus error, and obtain the estimated convergence rate of mean square consensus (... | As a result, the existing methods are no longer applicable. In fact, the inner product of the subgradients and the error between local optimizers’ states and the global optimal solution inevitably exists in the recursive inequality of the conditional mean square error, which leads the nonegative supermartingale converg... | I. The local cost functions in this paper are not required to be differentiable and the subgradients only satisfy the linear growth condition.
The inner product of the subgradients and the error between local optimizers’ states and the global optimal solution inevitably exists in the recursive inequality of the conditi... | B |
Given a microdata table T𝑇Titalic_T, the mutual cover strategy partitions T𝑇Titalic_T into groups, calculates a random output table on each QI attribute for the records in every group, and generates random values according to probabilities in the random output tables.
| Specifically, there are three main steps in the proposed approach. First, MuCo partitions the tuples into groups and assigns similar records into the same group as far as possible. Second, the random output tables, which control the distribution of random output values within each group, are calculated to make similar ... | Given a microdata table T𝑇Titalic_T, the mutual cover strategy partitions T𝑇Titalic_T into groups, calculates a random output table on each QI attribute for the records in every group, and generates random values according to probabilities in the random output tables.
| 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... |
For instance, suppose that we add another QI attribute of gender as shown in Figure 4, the mutual cover strategy first divides the records into groups in which the records in the same group cover for each other by perturbing their QI values. Then, the mutual cover strategy calculates a random output table on each QI a... | D |
Due to limited mask representation of HTC, we move on to SOLOv2, which utilizes much larger mask to segment objects. It builds an efficient yet simple instance segmentation framework, outperforming other segmentation methods like TensorMask Chen et al. (2019c), CondInst Tian et al. (2020) and BlendMask Chen et al. (20... | 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. “... | As shown in Table 3, all PointRend models achieve promising performance. Even without ensemble, our PointRend baseline, which yields 77.38 mAP, has already achieved 1st place on the test leaderboard. Note that several attempts, like BFP Pang et al. (2019) and EnrichFeat, give no improvements against PointRend baseline,... | 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... | 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.... | C |
(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... |
where for A⊆[n]𝐴delimited-[]𝑛A\subseteq[n]italic_A ⊆ [ italic_n ], |A|𝐴|A|| italic_A | denotes the cardinality of A𝐴Aitalic_A. This object, especially for boolean functions, is a deeply studied one and quite influential (but this is not the reason for the name…) in several directions. We refer to [O] for some info... |
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... |
In version 1 of this note, which can still be found on the ArXiv, we showed that the analogous version of the conjecture for complex functions on {−1,1}nsuperscript11𝑛\{-1,1\}^{n}{ - 1 , 1 } start_POSTSUPERSCRIPT italic_n end_POSTSUPERSCRIPT which have modulus 1111 fails. This solves a question raised by Gady Kozma s... | For the significance of this conjecture we refer to the original paper [FK], and to Kalai’s blog [K] (embedded in Tao’s blog) which reports on all significant results concerning the conjecture. [KKLMS] establishes a weaker version of the conjecture. Its introduction is also a good source of information on the problem.
| D |
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... |
In practice, the transition function ℙℙ\mathbb{P}blackboard_P is unknown, and the state space might be so large that it is impossible for the learner to fully explore all states. If we parametrize the action-value function in a linear form as ⟨ϕ(⋅,⋅),𝒘⟩bold-italic-ϕ⋅⋅𝒘\langle\bm{\phi}(\cdot,\cdot),\bm{w}\rangle⟨ bo... |
After showing the action-value function estimate is the optimistic upper bound of the optimal action-value function, we can derive the dynamic regret bound within one epoch via recursive regret decomposition. The dynamic regret within one epoch for Algorithm 1 with the knowledge of B𝜽,ℰsubscript𝐵𝜽ℰB_{\bm{\theta},\m... |
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... |
Our proposed algorithm LSVI-UCB-Restart has two key ingredients: least-squares value iteration with upper confidence bound to properly handle the exploration-exploitation trade-off (Jin et al., 2020), and restart strategy to adapt to the unknown nonstationarity. Our algorithm is summarized in Algorithm 1. From a high-... | D |
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... | Singapore is a city-state with an open economy and diverse population that shapes it to be an attractive and vulnerable target for fake news campaigns (Lim, 2019). As a measure against fake news, the Protection from Online Falsehoods and Manipulation Act (POFMA) was passed on May 8, 2019, to empower the Singapore Gover... | Many studies worldwide have observed the proliferation of fake news on social media and instant messaging apps, with social media being the more commonly studied medium. In Singapore, however, mitigation efforts on fake news in instant messaging apps may be more important. Most respondents encountered fake news on inst... | Fake news is news articles that are “either wholly false or containing deliberately misleading elements incorporated within its content or context” (Bakir and McStay, 2018). The presence of fake news has become more prolific on the Internet due to the ease of production and dissemination of information online (Shu et a... | 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 |
Our method represents a standard KG embedding approach capable of generating embeddings for various tasks. This distinguishes it from most inductive methods that either cannot produce entity embeddings [22, 23, 25], or have entity embeddings conditioned on specific relations/entities [20, 21]. While some methods attem... |
Unlike many inductive methods that are solely evaluated on datasets with unseen entities, our method aims to produce high-quality embeddings for both seen and unseen entities across various downstream tasks. To our knowledge, decentRL is the first method capable of generating high-quality embeddings for different down... |
We conduct experiments to explore the impact of the numbers of unseen entities on the performance in open-world entity alignment. We present the results on the ZH-EN datasets in Figure 6. Clearly, the performance gain achieved by leveraging our method significantly increases when there are more unseen entities. For ex... | 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... |
Our method represents a standard KG embedding approach capable of generating embeddings for various tasks. This distinguishes it from most inductive methods that either cannot produce entity embeddings [22, 23, 25], or have entity embeddings conditioned on specific relations/entities [20, 21]. While some methods attem... | A |
To validate the effectiveness of our method, we compare the proposed method with the following self-supervised exploration baselines. Specifically, we conduct experiments to compare the following methods: (i) VDM. The proposed self-supervised exploration method. (ii) ICM [10]. ICM first builds an inverse dynamics mode... | We compare the model complexity of all the methods in Table I. VDM, RFM, and Disagreement use a fixed CNN for feature extraction. Thus, the trainable parameters of feature extractor are 0. ICM estimates the inverse dynamics for feature extraction with 2.21M parameters. ICM and RFM use the same architecture for dynamics... |
To validate the effectiveness of our method, we compare the proposed method with the following self-supervised exploration baselines. Specifically, we conduct experiments to compare the following methods: (i) VDM. The proposed self-supervised exploration method. (ii) ICM [10]. ICM first builds an inverse dynamics mode... |
(i) For the network architecture, the important hyper-parameters include the dimensions of latent space Z𝑍Zitalic_Z, the dimensions of state features d𝑑ditalic_d, and the use of skip-connection between the prior and generative networks. We add an ablation study in Tab. IV to perform a grid search. The result shows t... |
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... | A |
However, even if P𝑃Pitalic_P is unisolvent, as is well known and shown in our previous work [51], the inversion of the matrix V𝑉Vitalic_V becomes numerically ill-conditioned
when represented in the canonical basis qα(x)=xαsubscript𝑞𝛼𝑥superscript𝑥𝛼q_{\alpha}(x)=x^{\alpha}italic_q start_POSTSUBSCRIPT italic_α end... | Therefore, alternative interpolation schemes with better numerical condition and lower computational complexity are desirable.
While previous approaches to addressing this problem relied on tensorial interpolation schemes [33, 48, 59, 75], we here propose a different approach. | Though, approximations of lower accuracy might be reached faster then by polynomial interpolation, this makes these approaches incapable for answering Question 1 when higher-precision
approximations are required. The multivariate polynomial interpolation method presented here reaches this goal. | This allowed us to extend the classic 1D Newton and Lagrange interpolation methods to multivariate
schemes in a numerically stable and efficient way, resulting in a practically implemented algorithm with 𝒪(|A|2)𝒪superscript𝐴2\mathcal{O}(|A|^{2})caligraphic_O ( | italic_A | start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIP... | where the Chebyshev extremes Chebn0superscriptsubscriptCheb𝑛0\mathrm{Cheb}_{n}^{0}roman_Cheb start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT defined in Eq. (7.1) are Leja ordered [61].
Since these PAsubscript𝑃𝐴P_{A}italic_P start_POSTSUBSCRIPT italic_A end_POSTSUBSCRIPT for... | A |
As a result, the sample complexity for estimating the Wasserstein distance W(μ,ν)𝑊𝜇𝜈W(\mu,\nu)italic_W ( italic_μ , italic_ν ) up to ϵitalic-ϵ\epsilonitalic_ϵ sub-optimality gap is of order 𝒪~(ϵd∨2)~𝒪superscriptitalic-ϵ𝑑2\tilde{\mathcal{O}}(\epsilon^{d\lor 2})over~ start_ARG caligraphic_O end_ARG ( italic_ϵ st... | The orthogonal constraint on the projection mapping A𝐴Aitalic_A is for normalization, such that any two different projection mappings have distinct projection directions.
The projected Wasserstein distance can also be viewed as a special case of integral probability metric with the function space | The max-sliced Wasserstein distance is proposed to address this issue by finding the worst-case one-dimensional projection mapping such that the Wasserstein distance between projected distributions is maximized.
The projected Wasserstein distance proposed in our paper generalizes the max-sliced Wasserstein distance by ... | The 1111-Wasserstein distance can be viewed as a special IPM with ℱ=Lip1ℱsubscriptLip1\mathcal{F}=\text{Lip}_{1}caligraphic_F = Lip start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT, where the Rademacher complexity of ℱℱ\mathcal{F}caligraphic_F is given by [42, Example 4]:
| Motivated by Example 1, we propose the projected Wasserstein distance in Definition 2 to improve the sample complexity.
This distance can be viewed as a special IPM with the function space defined in (1), a collection of 1111-Lipschitz functions in composition with an orthogonal k𝑘kitalic_k-dimensional linear mapping. | D |
VAE-type DGMs use amortized variational inference to learn an approximate posterior qϕ(H|x)subscript𝑞italic-ϕconditional𝐻𝑥q_{\phi}(H|x)italic_q start_POSTSUBSCRIPT italic_ϕ end_POSTSUBSCRIPT ( italic_H | italic_x ) by maximizing an evidence lowerbound (ELBO) to the log-marginal likelihood of the data under the mod... | 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... | Deep generative models (DGMs) such as variational autoencoders (VAEs) [dayan1995helmholtz, vae, rezende2014stochastic] and generative adversarial networks (GANs) [gan] have enjoyed great success at modeling high dimensional data such as natural images. As the name suggests, DGMs leverage deep learning to model a data g... |
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... | Amortization of the inference is achieved by parameterising the variational posterior with another deep neural network (called the encoder or the inference network) that outputs the variational posterior parameters as a function of X𝑋Xitalic_X. Thus, after jointly training the encoder and decoder, a VAE model can perf... | D |
If a pair of lines of the same color is connected, 1, if broken, the sequence pair of states of the red line (α𝛼\alphaitalic_α) and blue line (β𝛽\betaitalic_β) determines the transmitted digital signal. Thus, signal cables require one transistor for switching action at the end. When introducing the concept of an inve... | 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... | If a pair of lines of the same color is connected, 1, if broken, the sequence pair of states of the red line (α𝛼\alphaitalic_α) and blue line (β𝛽\betaitalic_β) determines the transmitted digital signal. Thus, signal cables require one transistor for switching action at the end. When introducing the concept of an inve... |
The NOT gate can be operated in a logic-negative operation through one ‘twisting’ as in a 4-pin. To be exact, the position of the middle ground pin is fixed and is a structural transformation that changes the position of the remaining two true and false pins. |
The structural computer used an inverted signal pair to implement the reversal of a signal (NOT operation) as a structural transformation, i.e. a twist, and four pins were used for AND and OR operations as a series and parallel connection were required. However, one can think about whether the four pin designs are the... | D |
Hence any function xnsuperscript𝑥𝑛x^{n}italic_x start_POSTSUPERSCRIPT italic_n end_POSTSUPERSCRIPT with gcd(n,q−1)≠1𝑔𝑐𝑑𝑛𝑞11gcd(n,q-1)\neq 1italic_g italic_c italic_d ( italic_n , italic_q - 1 ) ≠ 1, under the action of 𝐊𝐊\mathbf{K}bold_K settles down to the function xq−1superscript𝑥𝑞1x^{q-1}italic_x start... |
In this section, we aim to compute the possible cycle lengths of the PP through the linear representation defined in (10). As discussed in Section 1.3, given a polynomial f(x)𝑓𝑥f(x)italic_f ( italic_x ), we associate a dynamical system through a difference equation of the form |
In this section, we provide examples of estimating the possible orbit lengths of permutation polynomials in the form of Dickson polynomials Dn(x,α)subscript𝐷𝑛𝑥𝛼D_{n}(x,\alpha)italic_D start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT ( italic_x , italic_α ) [10] of degree n𝑛nitalic_n through the linear representati... | The work [19] also provides a computational framework to compute the cycle structure of the permutation polynomial f𝑓fitalic_f by constructing a matrix A(f)𝐴𝑓A(f)italic_A ( italic_f ), of dimension q×q𝑞𝑞q\times qitalic_q × italic_q through the coefficients of the (algebraic) powers of fksuperscript𝑓𝑘f^{k}italic... | The paper is organized as follows. Section 2 focuses on linear representation for maps over finite fields 𝔽𝔽\mathbb{F}blackboard_F, develops conditions for invertibility, computes the compositional inverse of such maps and estimates the cycle structure of permutation polynomials. In Section 3, this linear representat... | A |
Since feature selection often comes at a cost in terms of stability (Xu \BOthers., \APACyear2012), it is to be expected that view selection stability (Φ^^Φ\hat{\Phi}over^ start_ARG roman_Φ end_ARG) is higher for meta-learners that select more views. The results of two meta-learners do not align with this pattern, name... | The results of applying MVS with the seven different meta-learners to the colitis data can be observed in Table 2. In terms of raw test accuracy the nonnegative lasso is the best performing meta-learner, followed by the nonnegative elastic net and the nonnegative adaptive lasso. In terms of AUC and H, the best performi... |
Since feature selection often comes at a cost in terms of stability (Xu \BOthers., \APACyear2012), it is to be expected that view selection stability (Φ^^Φ\hat{\Phi}over^ start_ARG roman_Φ end_ARG) is higher for meta-learners that select more views. The results of two meta-learners do not align with this pattern, name... |
The true positive rate in view selection for each of the meta-learners can be observed in Figure 2. Ignoring the interpolating predictor for now, nonnegative ridge regression has the highest TPR, which is unsurprising seeing as it performs feature selection only through its nonnegativity constraints. Nonnegative ridge... | The results for the breast cancer data can be observed in Table 3. The interpolating predictor and the lasso are the best performing meta-learners in terms of all three classification measures, with the interpolating predictor having higher test accuracy and H, and the lasso having higher AUC. However, the interpolatin... | D |
This example highlights the fundamental difference between proximity-based and dependency-based methods. Dependency-based methods focus on identifying anomalies based on underlying relationships between variables, whereas proximity-based methods rely on object similarity in terms of proximity. In cases like this, where... | To address these gaps, this paper introduces a Dependency-based Anomaly Detection framework (DepAD) to provide a general approach to dependency-based anomaly detection. For each phase of the DepAD framework, this paper analyzes what and how to utilize the off-the-shelf techniques in the context of anomaly detection. We... |
Despite that research [7, 4] has shown the promise of dependency-based anomaly detection, there are still certain research gaps in this area that need attention. Firstly, existing dependency-based methods represent only a fraction of a much larger potential combinations of supervised methods and scoring functions for ... | A common way of examining dependency deviations in the dependency-based approach is to check the difference between the observed value and the expected value of an object, where the expected value is estimated based on the underlying dependency between variables [7, 4, 5]. Thus, dependency-based approach naturally lead... | We propose a dependency-based anomaly detection framework, DepAD, to provide a general approach to dependency-based anomaly detection. DepAD offers a holistic approach to guide the development of dependency-based anomaly detection methods. DepAD is effective and adaptable, utilizing off-the-shelf techniques for diverse... | C |
For an intuitive understanding of the choice model, consider an example of an online furniture retailer that offers N𝑁Nitalic_N distinct products where the ithsuperscript𝑖𝑡ℎi^{th}italic_i start_POSTSUPERSCRIPT italic_t italic_h end_POSTSUPERSCRIPT product has an attribute vector xisubscript𝑥𝑖x_{i}italic_x start_P... |
Motivated by these issues, we consider the dynamic assortment optimization problem. In every round, the retailer offers a subset (assortment) of products to a consumer and observes the consumer response. Consumers purchase (at most one product from each assortment) products that maximize their utility, and the retaile... | 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... |
The rest of this section is organized as follows: We first describe the related literature and qualitative significance of the parameter κ𝜅\kappaitalic_κ. Then, we highlight our contributions and end the section by contrasting them with recent notable research works. |
In this section we compare the empirical performance of our proposed algorithm CB-MNL with the previous state of the art in the MNL contextual bandit literature: UCB-MNL[Oh & Iyengar, 2021] and TS-MNL[Oh & Iyengar, 2019] on artificial data. We focus on performance comparison for varying values of parameter κ𝜅\kappait... | C |
Inspired by FPN [22], which computes multi-scale features with different levels, we propose a cross-scale graph pyramid network (xGPN). It progressively aggregates features from cross scales as well as from the same scale at multiple network levels via a hybrid module of a temporal branch and a graph branch. As shown ... |
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... | We provide ablation study for the key components VSS and xGPN in VSGN to verify their effectiveness on the two datasets in Table 3 and 4, respectively. The baselines are implemented by replacing each xGN module in xGPN with a layer of Conv1d(3,2)Conv1d32\textrm{Conv1d}(3,2)Conv1d ( 3 , 2 ) and ReLU, and not using cutt... | Cross-scale graph network. The xGN module contains a temporal branch to aggregate features in a temporal neighborhood, and a graph branch to aggregate features from intra-scale and cross-scale locations. Then it pools the aggregated features into a smaller temporal scale. Its architecture is illustrated in Fig. 4. The ... | To further improve the boundaries generated from Mlocsubscript𝑀𝑙𝑜𝑐M_{loc}italic_M start_POSTSUBSCRIPT italic_l italic_o italic_c end_POSTSUBSCRIPT, we design Madjsubscript𝑀𝑎𝑑𝑗M_{adj}italic_M start_POSTSUBSCRIPT italic_a italic_d italic_j end_POSTSUBSCRIPT inspired by FGD in [24]. For each updated anchor seg... | C |
Another open issue is the avoidance of hyperparameter tuning per se, as noted by E3. The goal of the tool is not to explore or bring insights about the individual sets of hyperparameters of the models or algorithms, but instead we focus on the search for new powerful models and implicitly store their hyperparameters.
T... | Evolutionary optimization and majority-voting ensembles inspired us to focus on the three aforementioned questions that constitute open research challenges. In this paper, we present a visual analytics (VA) tool, called VisEvol (see VisEvol: Visual Analytics to Support Hyperparameter Search through Evolutionary Optimiz... | Another open issue is the avoidance of hyperparameter tuning per se, as noted by E3. The goal of the tool is not to explore or bring insights about the individual sets of hyperparameters of the models or algorithms, but instead we focus on the search for new powerful models and implicitly store their hyperparameters.
T... |
In this paper, we presented VisEvol, a VA tool with the aim to support hyperparameter search through evolutionary optimization. With the utilization of multiple coordinated views, we allow users to generate new hyperparameter sets and store the already robust hyperparameters in a majority-voting ensemble. Exploring th... | (iv) control the evolutionary process by setting the number of models that will be used for crossover and mutation in each algorithm (VisEvol: Visual Analytics to Support Hyperparameter Search through Evolutionary Optimization(b)); and
(v) compare the performances of the best so far identified ensemble against the acti... | C |
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... | Consensus protocols form an important field of research that has a strong connection with Markov chains [18].
Consensus protocols are a set of rules used in distributed systems to achieve agreement among a group of agents on the value of a variable [19, 20, 21, 22]. | Consensus protocols, in contrast to Markov chains, operate without the limitations of non-negative nodes and edges or the requirement for the sum of nodes to equal one [18]. This broader scope enables consensus protocols to address a significantly wider range of problem spaces.
Therefore, there is a significant interes... |
Markov chains and consensus protocols share a close relationship. The rich theory of Markov chains has proven to be valuable in analyzing specific consensus protocols. Notable works such as [23, 24, 25, 26] have leveraged Markov chain theory to provide insights and analysis for consensus protocols. | There are comprehensive survey papers that review the research on consensus protocols [19, 20, 21, 22]. In many scenarios, the network topology of the consensus protocol is a switching topology due to failures, formation reconfiguration, or state-dependence. There is a large number of papers that propose consensus prot... | A |
Other learning methods rely on a given template for each class [25] or local neighbourhood encoding to learn a compact representation [39].
The recently conducted SHREC correspondence contest on isometric and non-isometric 3D shapes [20] revealed that there is still room for improvement in both fields. | Although multi-matchings obtained by synchronisation procedures are cycle-consistent, the matchings are often spatially non-smooth and noisy, as we illustrate in Sec. 5.
From a theoretical point of view, the most appropriate approach for addressing multi-shape matching is based on a unified formulation, where cycle con... | 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... | There are various works that particularly target the matching of multiple shapes. In [30, 32], semidefinite programming relaxations are proposed for the multi-shape matching problem. However, due to the employed lifting strategy, which drastically increases the number of variables, these methods are not scalable to lar... |
The multi-matching problem is relatively well-studied for generic settings, e.g. for matching multiple graphs [79, 78, 65, 6, 69, 77], or matching keypoints in image collections [76, 72, 42]. A desirable property of multi-matchings is cycle consistency (which we will formally define in Sec. 3.1). | D |
Directed path graphs are characterized by Gavril [9], in the same article he also gives the first recognition algorithms that has O(n4)𝑂superscript𝑛4O(n^{4})italic_O ( italic_n start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT ) time complexity. In the above cited article, Monma and Wei [18] give the second characterizati... | A graph is an interval graph if it is the intersection graph of a family of intervals on the real line; or, equivalently, the intersection graph of a family of subpaths of a path. Interval graphs are characterized by Lekkerkerker and Boland [15] as chordal graphs with no asteroidal triples, where an asteroidal triple i... | 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... |
Path graphs and directed path graphs are classes of graphs between interval graphs and chordal graphs. A graph is a chordal graph if it does not contain a hole as an induced subgraph, where a hole is a chordless cycle of length at least four. Gavril [8] proves that a graph is chordal if and only if it is the intersect... |
A clique is a clique separator if its removal disconnects the graph in at least two connected components. A graph with no clique separator is called atom. For example, every cycle has no clique separator, and the butterfly/hourglass graph has two cliques and it is an atom. In [18] it is proved that an atom is a path g... | C |
Our idea proposed in this paper can be extended in many directions. Building the theoretical framework for Mixed-SLIMapprosubscriptSLIM𝑎𝑝𝑝𝑟𝑜\mathrm{SLIM}_{appro}roman_SLIM start_POSTSUBSCRIPT italic_a italic_p italic_p italic_r italic_o end_POSTSUBSCRIPT and Mixed-SLIMτapprosubscriptSLIM𝜏𝑎𝑝𝑝𝑟𝑜\mathr... |
The ego-networks dataset contains more than 1000 ego-networks from Facebook, Twitter, and GooglePlus. In an ego-network, all the nodes are friends of one central user and the friendship groups or circles (depending on the platform) set by this user can be used as ground truth communities. The SNAP ego-networks are ope... | In this section, four real-world network datasets with known label information are analyzed to test the performances of our Mixed-SLIM methods for community detection. The four datasets can be downloaded from
http://www-personal.umich.edu/~mejn/netdata/. For the four datasets, the true labels are suggested by the origi... | Funding. Qing’s work was supported by High level personal project of Jiangsu Province (JSSCBS20211218). Wang’s work was supported by the Fundamental Research Funds for the Central Universities, Nankai University, 63221044 and the National Natural Science Foundation of China (Grant 12001295).
| In this section, we first introduce the main algorithm mixed-SLIM which can be taken as a natural extension of the SLIM (SLIM, ) to the mixed membership community detection problem. Then we discuss the choice of some tuning parameters in the proposed algorithm.
| C |
In contrast, the feasible set of distributional optimization is the Wasserstein space on a subset 𝒳𝒳\mathcal{X}caligraphic_X of ℝdsuperscriptℝ𝑑\mathbb{R}^{d}blackboard_R start_POSTSUPERSCRIPT italic_d end_POSTSUPERSCRIPT, which is an infinite-dimensional manifold.
As a result, unlike | variational inference (Gershman and Blei, 2012; Kingma and Welling, 2019), policy optimization (Sutton et al., 2000; Schulman et al., 2015; Haarnoja et al., 2018), and GAN (Goodfellow et al., 2014; Arjovsky et al., 2017), and has achieved tremendous empirical successes.
However, | See, e.g., Welling and Teh (2011); Chen et al. (2014); Ma et al. (2015); Chen et al. (2015); Dubey et al. (2016); Vollmer et al. (2016); Chen et al. (2016); Dalalyan (2017); Chen et al. (2017); Raginsky et al. (2017); Brosse et al. (2018); Xu et al. (2018); Cheng and Bartlett (2018); Chatterji et al. (2018); Wibisono (... | See, e.g., Cheng et al. (2017); Cheng and Bartlett (2018); Xu et al. (2018); Durmus et al. (2019) and the references therein for the analysis of the Langevin MCMC algorithm.
Besides, it is shown that (discrete-time) Langevin MCMC can be viewed as (a discretization of) the Wasserstein gradient flow of KL[p(z),p(z|x))... | See, e.g., Udriste (1994); Ferreira and Oliveira (2002); Absil et al. (2009); Ring and Wirth (2012); Bonnabel (2013); Zhang and Sra (2016); Zhang et al. (2016); Liu et al. (2017); Agarwal et al. (2018); Zhang et al. (2018); Tripuraneni et al. (2018); Boumal et al. (2018); Bécigneul and Ganea (2018); Zhang and Sra (2018... | B |
(2) Modelling Latent Coordination with Neighbors: In our method, the neighbor information is available only in training, and the decoders are abandoned in execution. Only using individual observation as the input of policy may ignore the latent neighbors information. As shown in Eq. 1, the observation transition is cau... |
In this section, we propose Meta Variationally Intrinsic Motivated (MetaVIM) method to achieve Eq. 1 and Eq. 2, as illustrated in Fig. 3. MetaVIM employs latent variable to represent each task to make the reward, observation transition and policy functions shareable. At the same time, MetaVIM makes the approximations ... | 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... | may cause learning non-stationary because the agent may receive different rewards and observation transitions for the same action at the same observation. In this case, the received rewards and observation transitions of the current agent could not be well predicted only conditioned on its own observations and performe... | As stated in Eq. 2, the non-stationary learning often causes the observation transition and received rewards unpredictable only conditioned on individual observation and action. Conversely, we hope the learned policy makes them be predicted stably.
To achieve this goal, we design a novel intrinsic reward based on VAE, ... | D |
\mathbf{x}_{j})^{\dagger}italic_J start_POSTSUBSCRIPT rank- italic_r end_POSTSUBSCRIPT ( bold_x start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT ) start_POSTSUPERSCRIPT † end_POSTSUPERSCRIPT italic_J start_POSTSUBSCRIPT rank- italic_r end_POSTSUBSCRIPT ( bold_x start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT ) italic_J st... | J(𝐱j−1)Jrank-r(𝐱j−1)†𝐽subscript𝐱𝑗1subscript𝐽rank-rsuperscriptsubscript𝐱𝑗1†\displaystyle J(\mathbf{x}_{j-1})\,J_{\mbox{\scriptsize rank-$r$}}(\mathbf{x}_%
{j-1})^{\dagger}italic_J ( bold_x start_POSTSUBSCRIPT italic_j - 1 end_POSTSUBSCRIPT ) italic_J start_POSTSUBSCRIPT rank- italic_r end_POSTSUBSCRIPT ( bold... | })\,J_{\mbox{\scriptsize rank-$r$}}(\mathbf{x})^{\dagger}\big{\|}_{2}\,\|J(%
\mathbf{x})-J(\mathbf{y})\|_{2}≤ ∥ italic_J start_POSTSUBSCRIPT rank- italic_r end_POSTSUBSCRIPT ( bold_x ) italic_J start_POSTSUBSCRIPT rank- italic_r end_POSTSUBSCRIPT ( bold_x ) start_POSTSUPERSCRIPT † end_POSTSUPERSCRIPT ∥ start_POSTSUBSCR... | \mathbf{x}_{j})^{\dagger}italic_J start_POSTSUBSCRIPT rank- italic_r end_POSTSUBSCRIPT ( bold_x start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT ) start_POSTSUPERSCRIPT † end_POSTSUPERSCRIPT italic_J start_POSTSUBSCRIPT rank- italic_r end_POSTSUBSCRIPT ( bold_x start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT ) italic_J st... | =Jrank-r(𝐱j−1)Jrank-r(𝐱j−1)†absentsubscript𝐽rank-rsubscript𝐱𝑗1subscript𝐽rank-rsuperscriptsubscript𝐱𝑗1†\displaystyle~{}~{}=~{}~{}J_{\mbox{\scriptsize rank-$r$}}(\mathbf{x}_{j-1})\,J%
_{\mbox{\scriptsize rank-$r$}}(\mathbf{x}_{j-1})^{\dagger}= italic_J start_POSTSUBSCRIPT rank- italic_r end_POSTSUBSCRIPT ( bol... | A |
Adaptive(w𝑤witalic_w) improves upon FirstFit and BestFit when w𝑤witalic_w takes values in the shorter range [2000,4000].
For “Schwerin”, Adaptive(w𝑤witalic_w) always performs better, which can be explained by the discussion in Section 6.3. For “Wäscher”, Adaptive(w𝑤witalic_w) does not offer any advantage over |
As explained earlier, FirstFit and BestFit perform very well in practice, and we use them as benchmarks for comparing our algorithms. As often in offline bin packing, we also report the L2 lower bound (?, ?) as a lower-bound estimation of the optimal offline bin packing solution. That is, no algorithm, online or offli... | sh=3𝑠ℎ3sh=3italic_s italic_h = 3, or a file from the GI Benchmark), we generate 20 random sequences of length 106superscript10610^{6}10 start_POSTSUPERSCRIPT 6 end_POSTSUPERSCRIPT.
For each sequence, we compute FirstFit, BestFit, and the L2𝐿2L2italic_L 2 lower bound. The average costs of these algorithms, over the ... | FirstFit and BestFit. However, these two baseline algorithms are remarkably close to the L2𝐿2L2italic_L 2 lower bound, which means that they output essentially optimal packings for this benchmark, and which in turn leaves very little room for any potential improvement.
| These algorithms are variants of the classic Harmonic algorithm (?), which places items of approximately equal sizes, according to a harmonic sequence, in the same bin.
The currently best algorithm is the Advanced Harmonic (AH) algorithm, which has a competitive ratio of 1.57829 (?), whereas the best-known lower bound ... | C |
Practically speaking, our approach transforms the embedding of point cloud obtained from the base model to parametrize the bijective function represented by the MLP network. This function aims to find a mapping between a canonical 2D patch to the 3D patch on the surface of the target mesh. We condition the positioning ... |
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... |
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... |
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... | 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... | D |
For non-strongly convex-concave case, distributed SPP with local and global variables were studied in [41], where the authors proposed a subgradient-based algorithm for non-smooth problems with O(1/N)𝑂1𝑁O(1/\sqrt{N})italic_O ( 1 / square-root start_ARG italic_N end_ARG ) convergence guarantee (N𝑁Nitalic_N is the n... |
For non-strongly convex-concave case, distributed SPP with local and global variables were studied in [41], where the authors proposed a subgradient-based algorithm for non-smooth problems with O(1/N)𝑂1𝑁O(1/\sqrt{N})italic_O ( 1 / square-root start_ARG italic_N end_ARG ) convergence guarantee (N𝑁Nitalic_N is the n... | Now we show the benefits of representing some convex problems as convex-concave problems on the example of the Wasserstein barycenter (WB) problem and solve it by the DMP algorithm. Similarly to Section (3), we consider a SPP in proximal setup and introduce Lagrangian multipliers for the common variables. However, in t... | Paper [61] introduced an Extra-gradient algorithm for distributed multi-block SPP with affine constraints. Their method covers the Euclidean case and the algorithm has O(1/N)𝑂1𝑁O(1/N)italic_O ( 1 / italic_N ) convergence rate.
Our paper proposes an algorithm based on adding Lagrangian multipliers to consensus constr... |
We proposed a decentralized method for saddle point problems based on non-Euclidean Mirror-Prox algorithm. Our reformulation is built upon moving the consensus constraints into the problem by adding Lagrangian multipliers. As a result, we get a common saddle point problem that includes both primal and dual variables. ... | C |
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. |
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... | where L^=D^tD^^𝐿superscript^𝐷𝑡^𝐷\hat{L}=\hat{D}^{t}\hat{D}over^ start_ARG italic_L end_ARG = over^ start_ARG italic_D end_ARG start_POSTSUPERSCRIPT italic_t end_POSTSUPERSCRIPT over^ start_ARG italic_D end_ARG is the lower right |V|−1×|V|−1𝑉1𝑉1|V|-1\times|V|-1| italic_V | - 1 × | italic_V | - 1 submatrix of the ... |
The remainder of this section is dedicated to express the problem in the context of the theory of cycle bases, where it has a natural formulation, and to describe an application. Section 2 sets some notation and convenient definitions. In Section 3 the complete graph case is analyzed. Section 4 presents a variety of i... |
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]. | A |
Fix a simplicial complex K𝐾Kitalic_K, a value δ∈(0,1]𝛿01\delta\in(0,1]italic_δ ∈ ( 0 , 1 ], and integers b≥1𝑏1b\geq 1italic_b ≥ 1 and m>μ(K)𝑚𝜇𝐾m>\mu(K)italic_m > italic_μ ( italic_K ). If ℱℱ\mathcal{F}caligraphic_F is a sufficiently large (K,b)𝐾𝑏(K,b)( italic_K , italic_b )-free cover such that πm(ℱ)≥δ(|ℱ|m)... |
It is known that the Helly number of a (K,b)𝐾𝑏(K,b)( italic_K , italic_b )-free cover is bounded from above in terms of K𝐾Kitalic_K and b𝑏bitalic_b [18] 222The bound on Helly number of (K,b)-free cover directly follows from a combination of Proposition 30 and Lemma 26 in [18]., as is the Radon number [35, Proposit... |
Through a series of papers [18, 35, 22], the Helly numbers, Radon numbers, and fractional Helly numbers for (⌈d/2⌉,b)𝑑2𝑏(\lceil d/2\rceil,b)( ⌈ italic_d / 2 ⌉ , italic_b )-covers in ℝdsuperscriptℝ𝑑\mathbb{R}^{d}blackboard_R start_POSTSUPERSCRIPT italic_d end_POSTSUPERSCRIPT were bounded in terms of d𝑑ditalic_d and... | One immediate application of Theorem 1.2 is the reduction of fractional Helly numbers. For instance, it easily improves a theorem444[35, Theorem 2.3] was not phrased in terms of (K,b)𝐾𝑏(K,b)( italic_K , italic_b )-free covers but readily generalizes to that setting, see Section 1.4.1. of Patáková [35, Theorem 2.3] in... |
Note that the constant number of points given by the (p,q)𝑝𝑞(p,q)( italic_p , italic_q )-theorem in this case depends not only on p𝑝pitalic_p, q𝑞qitalic_q, and d𝑑ditalic_d, but also on b𝑏bitalic_b. For the setting of (1,b)1𝑏(1,b)( 1 , italic_b )-covers in surfaces555By a surface we mean a compact 2-dimensional ... | C |
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) ... | Visual support for the task of feature subset selection requires displaying information on different levels of granularity; highly detailed views are not optimal because they do not scale well with many features. For instance, the tool by Hohman et al. [63] facilitates the visual comparison of feature distributions for... | A use case present in a visual diagnosis tool revealed that feature generation involving the combination of two features is capable of a slight increase in performance [30]. The authors tested the same mathematical operations as in our system (i.e., addition, subtraction, multiplication, and division), but the generati... | Figure 7: Engineering features for improved predictive performance. From the pre-training phase, we detect that most of the instances belong to the Best slice (a.4), then the Worst slice (a.1), followed by the remaining slices (a.3 and a.2). In view (b), we validate every feature by working in synergy with the table he... |
Figure 1: Selecting important features, transforming them, and generating new features with FeatureEnVi: (a) the horizontal beeswarm plot for manually slicing the data space (which is sorted by predicted probabilities) and continuously checking the migration of data instances throughout the process; (b) the table heat... | A |
In machining, positioning systems need to be fast and precise to guarantee high productivity and quality. Such performance can be achieved by model predictive control (MPC) approach tailored for tracking a 2D contour [1, 2], however requiring precise tuning and good computational abilities of the associated hardware. ... | 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... | This paper demonstrated a hierarchical contour control implementation for the increase of productivity in positioning systems. We use a contouring predictive control approach to optimize the input to a low level controller. This control framework requires tuning of multiple parameters associated with an extensive numbe... |
In machining, positioning systems need to be fast and precise to guarantee high productivity and quality. Such performance can be achieved by model predictive control (MPC) approach tailored for tracking a 2D contour [1, 2], however requiring precise tuning and good computational abilities of the associated hardware. ... | 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... | A |
Existing datasets for assessing bias mitigation methods do not enable analysis of multiple bias sources, e.g., Colored MNIST only tests for color versus class bias. To address this, we created the Biased MNIST dataset, which requires recognizing digits while remaining robust to multiple sources of biases i.e., other fa... | Results on a simpler setting. We further study bias exploitation on CelebA. For this, we plot improvement over the standard model (IOSM𝐼𝑂𝑆𝑀IOSMitalic_I italic_O italic_S italic_M) in Fig. 5, which is the accuracy gain over the standard model on each dataset group. The improvements in blond (minority group) incur... |
For example, in systems trained to infer hair color on the CelebA dataset [43], the majority group of non-blond males occurs 50505050 times more than the minority group of blond males, resulting in systems incorrectly predicting non-blond as hair color for the minority group. | CelebA. We show accuracy for each group of CelebA in Table. A3. SD and GDRO obtain the highest accuracies. As discussed previously, we observe trade-offs between blond and non-blond classes with the improvements in the rare blond class incurring degradations in the non-blond class.
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The CelebA dataset [43] of celebrity faces is widely used to assess bias mitigation techniques [55, 56, 46, 50]. Following earlier work, it is used for binary hair color classification (blond or non-blond), which is correlated with gender. There are two major bias sources: a) class imbalance, with non-blond occurring ... | D |
2) A robust regression function to learn the mappings from appearance feature to human gaze. It is non-trivial to map the high-dimensional eye appearance to the low-dimensional gaze. Many regression functions have been used to regress gaze from appearance, e.g., local linear interpolation [21] and adaptive linear regre... | Figure 1: Deep learning-based gaze estimation relies on simple devices but complex algorithms to estimate human gaze. It usually uses off-the-shelf cameras to capture facial appearance, and employs deep learning algorithms to regress gaze from the appearance. According to this pipeline, we survey current deep learning-... | In this paper, we provide a systematic review of appearance-based gaze estimation methods using deep learning algorithms.
As shown in Fig. 1, we discuss these methods from four perspectives: 1) deep feature extraction, 2) deep neural network architecture design, 3) personal calibration, and 4) device and platform. | Recently, deep learning-based methods have gained popularity as they offer several advantages over conventional appearance-based methods. These methods use convolution layers or transformers [22] to automatically extract high-level gaze features from images. Deep learning models are also highly non-linear and can fit t... | In this survey, we present a comprehensive overview of deep learning-based gaze estimation methods. Unlike the conventional gaze estimation methods that requires dedicated devices, the deep learning-based approaches regress the gaze from the eye appearance captured by web cameras. This makes it easy to implement the al... | C |
The rest of this paper is organized as follows: Section 2 presents the related works. In Section 3 we present the motivation and contribution of the paper. The proposed method is detailed in Section 4. Experimental results are presented in Section 5. Conclusion ends the paper. |
Occlusion is a key limitation of real-world 2D face recognition methods. Generally, it comes out from wearing hats, eyeglasses, masks as well as any other objects that can occlude a part of the face while leaving others unaffected. Thus, wearing a mask is considered the most difficult facial occlusion challenge since ... | 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... | The COVID-19 can be spread through contact and contaminated surfaces, therefore, the classical biometric systems based on passwords or fingerprints are not anymore safe. Face recognition is safer without any need to touch any device. Recent studies on coronavirus have proven that wearing a face mask by a healthy and in... |
Occlusion removal approach: In order to avoid a bad reconstruction process, these approaches aim to detect regions found to be occluded in the face image and discard them completely from the feature extraction and classification process. Segmentation based approach is one of the best methods that detect firstly the oc... | A |
Our process typing judgment is itself mixed inductive-coinductive [DA09]—we introduce the auxiliary judgment 𝒱;𝒞;Γ⊢∞e¯P::(y:A)\mathcal{V};\mathcal{C};\Gamma\vdash_{\infty}^{\overline{e}}P::(y:A)caligraphic_V ; caligraphic_C ; roman_Γ ⊢ start_POSTSUBSCRIPT ∞ end_POSTSUBSCRIPT start_POSTSUPERSCRIPT over¯ start_ARG ital... |
We conjecture that finite-time typechecking only requires restricting our type system (including equality of equirecursive types [DP20a]) to circular derivations, which can be represented as finite trees with loops, provided decidable arithmetic (e.g., Presburger). Such a restricted system may be put in correspondence... | Sized types are compositional: since termination checking is reduced to an instance of typechecking, we avoid the brittleness of syntactic termination checking. However, we find that ad hoc features for implementing size arithmetic in the prior work can be subsumed by more general arithmetic refinements [DP20b, XP99], ... |
Our system is closely related to the sequential functional language of Lepigre and Raffalli [LR19], which utilizes circular typing derivations for a sized type system with mixed inductive-coinductive types, also avoiding continuity checking. In particular, their well-foundedness criterion on circular proofs seems to c... | Implementation: we are interested in developing a convenient surface language (perhaps a functional one [PP20]) for SAX and implementing our type system, following Rast [DP20a], an implementation of resource-aware session types that includes arithmetic refinements. Perhaps various validity conditions of infinite proofs... | A |
There are two extra challenges that need to be addressed. For one thing, considering that the original purpose of cloud’s involvement is to help resource-constrained owners efficiently share their media contents, the owner-side overhead needs to be carefully controlled to ensure that owners can obtain sig-nificant reso... |
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... | Thirdly, there are also studies that deal with both privacy-protected access control and traitor tracing. Xia et al. [26] introduced the watermarking technique to privacy-protected content-based ciphertext image retrieval in the cloud, which can prevent the user from illegally distributing the retrieved images. However... |
As discussed above, AFP seems to solve Problems 2 and 3 perfectly. However, this is no longer the case when media contents are remotely hosted by the cloud since existing AFP schemes were designed without taking the cloud’s involvement into consideration. Thus it remains to be further explored how to develop a novel A... |
In this paper, facing these problems and challenges, we set out to solve them. First, to achieve data protection and access control, we adopt the lifted-ElGamal based PRE scheme, as discussed in [16, 17, 18, 19, 20], whose most prominent characteristic is that it satisfies the property of additive homomorphism. Then t... | D |
The selected feature interactions of order-3 and order-4 are mostly not overlapped in the correctly predicted instance (a). In instance (a), our model selects relevant feature fields (Gender, Age, ReleaseTime, WatchTime) for Genre in order-3, while selects the other two feature fields (Occupation, Gender) in order-4.
H... | We find that in the first layer, which models the second order feature interactions, these feature fields are hard to distinguish when selecting the beneficial interactions. This suggests that almost all the second-order feature interactions are useful, which also why we sample all of them in the first layer, i.e., m1=... | The selected feature interactions of order-3 and order-4 are mostly not overlapped in the correctly predicted instance (a). In instance (a), our model selects relevant feature fields (Gender, Age, ReleaseTime, WatchTime) for Genre in order-3, while selects the other two feature fields (Occupation, Gender) in order-4.
H... | Since the features along with selected beneficial feature interactions are treated as a graph, it can provide human readable interpretations on the prediction. Here we visualize heat maps of estimated edge weights of two cherry-pick instances on MovieLens-1M dataset in Fig. 4. We show the measured edge weights of each ... | This proves that our model can indeed select meaningful feature combination and model feature interactions of increasing orders with multiple layers in most cases, rather than select the redundant feature combinations of same feature fields.
We can also find some meaningful feature combinations in common cases. For exa... | D |
Linear Minimization Oracle (LMO): Given 𝐝∈ℝn𝐝superscriptℝ𝑛\mathbf{d}\in\mathbb{R}^{n}bold_d ∈ blackboard_R start_POSTSUPERSCRIPT italic_n end_POSTSUPERSCRIPT, return argmin𝐱∈𝒳⟨𝐱,𝐝⟩subscriptargmin𝐱𝒳𝐱𝐝\operatorname*{argmin}\limits_{\mathbf{x}\in\mathcal{X}}\left\langle\mathbf{x}%
,\mathbf{d}\right\rangleroman_... | Table 1:
Number of iterations needed to achieve an ε𝜀\varepsilonitalic_ε-optimal solution for Problem 1.1. We denote line search by LS, zeroth-order oracle by ZOO, second-order oracle by SOO, domain oracle by DO, local linear optimization oracle by LLOO, and the assumption that 𝒳𝒳\mathcal{X}caligraphic_X is polyhed... |
The FOO and LMO oracles are standard in the FW literature. The ZOO oracle is often implicitly assumed to be included with the FOO oracle; we make this explicit here for clarity. Finally, the DO oracle is motivated by the properties of generalized self-concordant functions. It is reasonable to assume the availability o... | This means that Theorems 2.4 and 2.6 effectively bound the number of ZOO, FOO, DO, and LMO oracle calls needed to achieve a target primal gap or Frank-Wolfe gap accuracy ε𝜀\varepsilonitalic_ε as a function of Tνsubscript𝑇𝜈T_{\nu}italic_T start_POSTSUBSCRIPT italic_ν end_POSTSUBSCRIPT and ε𝜀\varepsilonitalic_ε; note... | If either of these two checks fails, we simply do not move: the algorithm sets 𝐱t+1=𝐱tsubscript𝐱𝑡1subscript𝐱𝑡\mathbf{x}_{t+1}=\mathbf{x}_{t}bold_x start_POSTSUBSCRIPT italic_t + 1 end_POSTSUBSCRIPT = bold_x start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT in Line 6 of Algorithm 1.
As customary, we assume short-circ... | B |
Furthermore, we make some important observations about invariants that are preserved by operations of our algorithm which we will use later.
In Section 4, we prove the correctness of our algorithm. The approximation analysis as well as the proof of the pass complexity can be found in Section 5. In Section 6 we provide ... | Furthermore, we make some important observations about invariants that are preserved by operations of our algorithm which we will use later.
In Section 4, we prove the correctness of our algorithm. The approximation analysis as well as the proof of the pass complexity can be found in Section 5. In Section 6 we provide ... | In this section, we give a brief outline of our approach and discuss the challenges we overcome.
As the basic building block, we follow the classic approach by Hopcroft and Karp [HK73] of iteratively finding short augmenting paths to improve a 2222-approximate matching that can easily be found by a greedy algorithm. | The basic building block in the search for augmenting paths is to find semi-matchings between the vertices and their matched neighbors such that each vertex has a small amount of neighbors in the semi-matching.
In the case of bipartite graphs, they show that their method of searching for augmenting paths in a graph def... |
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... | B |
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... | 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... | Recently, several compression methods have been proposed for distributed and federated learning, including [28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40].
Recent works have tried to combine the communication compression methods with decentralized optimization. |
In decentralized optimization, efficient communication is critical for enhancing algorithm performance and system scalability. One major approach to reduce communication costs is considering communication compression, which is essential especially under limited communication bandwidth. | B |
where x1,…,xMsubscript𝑥1…subscript𝑥𝑀x_{1},\ldots,x_{M}italic_x start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT , … , italic_x start_POSTSUBSCRIPT italic_M end_POSTSUBSCRIPT and y1,…,yMsubscript𝑦1…subscript𝑦𝑀y_{1},\ldots,y_{M}italic_y start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT , … , italic_y start_POSTSUBSCRIPT italic_M end... | 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... | Unlike (2), the formulation (1) penalizes not the difference with the global average, but the sameness with other connected local nodes. Thereby the decentralized case can be artificially created in centralized architecture, e.g., if we want to create the network and W𝑊Witalic_W matrix to connect only some clients bas... |
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... | Note that in the proposed formulation (1) we consider both the centralized and decentralized cases. In the decentralized setting, all nodes are connected within a network, and each node can communicate/exchange information only with their neighbors in the network. While the centralized architecture consists of master-s... | D |
Correlation is achieved via a trusted external entity (correlation device) which samples a joint action from a public CE joint distribution. Each player is given their action in secret. The properties of the CE means that no individual player is motivated to deviate from the suggested action. If there are deviation ac... | 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 ... | Figure 1: The solution landscape for the traffic lights game. The solid polytope shows the space of CE joint strategies, and the dotted surface shows factorizable joint strategies. NEs are where the surface and polytope intersect. There are three unsatisfying NEs: mixed spends most of its time waiting and does not avoi... | The set of (C)CEs forms a convex polytope, and therefore any strictly convex function could uniquely select amongst this set. The literature only provides one such example: MECE (Ortiz et al., 2007) which has a number of appealing properties, but was found to be slow to solve large games. There is a gap in the literatu... |
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... | A |
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 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 ... | 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 ... | 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... | C |
For each u∈χ−1(𝖢˙)𝑢superscript𝜒1˙𝖢u\in\chi^{-1}(\mathsf{\dot{C}})italic_u ∈ italic_χ start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT ( over˙ start_ARG sansserif_C end_ARG ) we perform a number of 𝒪(n+m)𝒪𝑛𝑚\mathcal{O}(n+m)caligraphic_O ( italic_n + italic_m )-time operations and run the dynamic programming algo... | Similar to the algorithm from Lemma 5.8, we can use two (n+m,𝒪(k5z2))𝑛𝑚𝒪superscript𝑘5superscript𝑧2(n+m,\mathcal{O}(k^{5}z^{2}))( italic_n + italic_m , caligraphic_O ( italic_k start_POSTSUPERSCRIPT 5 end_POSTSUPERSCRIPT italic_z start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ) )-universal sets to create a set of c... |
Using the previous lemmas the problem of finding a reducible single-tree FVC reduces to finding a coloring that properly colors a simple reducible FVC. We generate a set of colorings that is guaranteed to contain at least one such coloring. To generate this set we use the concept of a universal set. | Note that the condition |NG(F)|≤|C|+1subscript𝑁𝐺𝐹𝐶1|N_{G}(F)|\leq|C|+1| italic_N start_POSTSUBSCRIPT italic_G end_POSTSUBSCRIPT ( italic_F ) | ≤ | italic_C | + 1 trivially holds for any single-tree FVC. We will show that, given a reducible FVC (C,F)𝐶𝐹(C,F)( italic_C , italic_F ), we can efficiently reduce to a s... |
Given a multigraph G𝐺Gitalic_G and coloring χ𝜒\chiitalic_χ of G𝐺Gitalic_G that properly colors some simple reducible FVC (C,F)𝐶𝐹(C,F)( italic_C , italic_F ), a reducible FVC (C′,F′)superscript𝐶normal-′superscript𝐹normal-′(C^{\prime},F^{\prime})( italic_C start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT , italic_F st... | B |
The existing generative image composition methods can be divided into two groups: token-to-object methods and object-to-object methods.
The first group of methods [79, 100] learn token-to-object mapping conditioned on the background information. Inspired by [129], they adapt a pretrained diffusion model to a subject by... |
Training diffusion model requires massive training triplets of foregrounds, backgrounds, and ground-truth real images. Previous works [183, 141] proposed to crop the foregrounds from real images and perturb the foregrounds (e.g., color transfer, geometric transformation), so that we can have perturbed foreground, mask... | In some previous works [154, 29], object placement is used as data augmentation strategy to facilitate the downstream tasks (e.g., object detection, instance segmentation). Therefore, they make use of existing object detection and instance segmentation datasets [89, 28, 21, 38]. In particular, the foregrounds are cropp... |
The second group of methods [183, 141, 205, 16, 191, 187] learn object-to-object mapping conditioned on the background information. They train a diffusion model on abundant pairs of foregrounds and backgrounds, so that it can be directly applied to a new pair of foreground and background at test time. In [183, 141], t... | object placement to find suitable scale and location for the foreground, and use image blending to refine the boundary between foreground and background. Then, we use image harmonization to adjust the foreground illumination and shadow generation to generate plausible shadow for the foreground.
Recently, as the diffusi... | C |
Table II presents the statistics of the processed sub-datasets. It is worth noting that the cities in CityNet exhibit diverse properties. For instance, Beijing, Shanghai, Shenzhen, and Chongqing have large maps with more than 1000 regions (|ℛc|>1000subscriptℛ𝑐1000|\mathcal{R}_{c}|>1000| caligraphic_R start_POSTSUBSCRI... | In addition to the collection and processing of data, it is essential to identify and quantify the correlations between sub-datasets in CityNet to gain insights into the effective utilization of the multi-modal data. In this section, we leverage data mining tools to explore and visualize the relationships between servi... | Our analyses and experiments on CityNet have yielded valuable insights for researchers. Our studies have confirmed the correlations among sub-datasets and have demonstrated that urban modeling and analyses can be enhanced by appropriately utilizing the mutual knowledge among correlated sub-datasets. To this end, we hav... | In the present study, we have introduced CityNet, a multi-modal dataset specifically designed for urban computing in smart cities, which incorporates spatio-temporally aligned urban data from multiple cities and diverse tasks. To the best of our knowledge, CityNet is the first dataset of its kind, which provides a comp... | The paper is structured as follows. Section II outlines the pre-processing procedure of all sub-datasets in CityNet, along with their basic statistics. In Section III, we employ data mining tools to reveal and elucidate the correlations between contexts and service data. In Section IV, we conduct machine learning exper... | A |
Figure 3: R2superscript𝑅2R^{2}italic_R start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT-coefficients for a selection of data sets. For every model 2 variants are shown (except for NN and RF): trained on the full data set and on half of the data set (as for the conformalized models). The fully trained models are indicated ... | For each of the selected models, Fig. 4 shows the best five models in terms of average width, excluding those that do not (approximately) satisfy the coverage constraint (2). This figure shows that there is quite some variation in the models. There is not a clear best choice. Because on most data sets the models produc... | In Fig. 1, both the coverage degree, average width and R2superscript𝑅2R^{2}italic_R start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT-coefficient are shown. For each model, the data sets are sorted according to increasing R2superscript𝑅2R^{2}italic_R start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT-coefficient (averaged over th... |
Figure 3: R2superscript𝑅2R^{2}italic_R start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT-coefficients for a selection of data sets. For every model 2 variants are shown (except for NN and RF): trained on the full data set and on half of the data set (as for the conformalized models). The fully trained models are indicated ... | The results for the conformalized models are the same as for the those trained on half of the data set, since conformal prediction is a post-hoc method. Therefore, only the fully-trained and conformalized models are shown. Here again it is clear that the uncalibrated models do not approximately saturate the validity co... | D |
These constitute the main ideas of the CP representation \parencitehsiao21aaai,
which has at least the following two advantages over its REMI counterpart: 1) the number of time steps needed to represent a MIDI piece is much reduced, since the tokens are merged into a “super token” (a.k.a. a “compound word” \parencitehs... | For fine-tuning, we create training, validation and test splits for each of the three datasets of the downstream tasks with the 8:1:1 ratio at the piece level (i.e., all the 512-token sequences from the same piece are in the same split).
With the same batch size of 12, we fine-tune the pre-trained our model for each ta... | 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... |
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. | In addition to REMI, we experiment with the “token grouping” idea of the compound word (CP) representation \parencitehsiao21aaai, to reduce the length of the token sequences.
We depict the two adopted token representations in Fig. 1 and provide some details below. | C |
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... |
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... |
Therefore, the only possible backward carry from the block of type A to the block of type B has to be in the form (0,0,1)001(0,0,1)( 0 , 0 , 1 ). However, this will be combined with a block (0,1,0)010(0,1,0)( 0 , 1 , 0 ) from Z(S)𝑍𝑆Z(S)italic_Z ( italic_S ) – thus, the sum of the blocks from Z(S)𝑍𝑆Z(S)italic_Z (... | In any way, the forward carry to the (i+1)𝑖1(i+1)( italic_i + 1 )-th block cannot exceed (1,1,0)110(1,1,0)( 1 , 1 , 0 ). However, since the (i+1)𝑖1(i+1)( italic_i + 1 )-th blocks of Z(S)𝑍𝑆Z(S)italic_Z ( italic_S ) and Z(S2)𝑍subscript𝑆2Z(S_{2})italic_Z ( italic_S start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT ) are (0,... | Finally, note that the aforementioned forward carry resulting from backward carry appears in the block which has to be equal to (0,0,1)001(0,0,1)( 0 , 0 , 1 ) (as it has to be the second case above), so it turns it into (1,0,1)101(1,0,1)( 1 , 0 , 1 ) and it does not generate any future carries.
| D |
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