context stringlengths 250 4.14k | A stringlengths 250 3.94k | B stringlengths 250 5.14k | C stringlengths 250 4.12k | D stringlengths 250 4.03k | label stringclasses 4
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τ(G)=1|V|∏i=2|V|λi=12|E|∏i=1|V|di∏i=2|V|λ̄i⋅\displaystyle\tau(G)=\frac{1}{|V|}\prod\limits_{i=2}^{|V|}\lambda_{i}=\frac{1}%
{2|E|}\prod\limits_{i=1}^{|V|}d_{i}\prod\limits_{i=2}^{|V|}\lambdabar_{i}\cdotitalic_τ ( italic_G ) = divide start_ARG 1 end_ARG start_ARG | italic_V | end_ARG ∏ start_POSTSUBSCRIPT italic_i = 2 ... | As both of the structural descriptors have important applications in graph theory, networking systems, molecular chemistry, and other related fields, researchers have taken a strong interest in the Kirchhoff indices and degree-Kirchhoff indices of graphs in recent years. Finding the explicit formulae for the Kirchhoff ... | We obtain the formulae for the total count of spanning trees of Pnsubscript𝑃𝑛P_{n}italic_P start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT and Pn′subscriptsuperscript𝑃′𝑛P^{\prime}_{n}italic_P start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT using the Theorem 4 as follows.
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The formulae of the degree-Kirchhoff index of linear hexagonal chains [9], hexagonal Möbius chains [16], linear crossed hexagonal chains [18], linear polyomino chains [8], cylinder phenylene chains [17], random polygonal chains [13], generalized phenylenes [25], cylinder, and Möbius octagonal chain [15], linear pentag... | Being motivated by the success of the Wiener index, nearly after four decades, in 1993,19931993,1993 , Klein and Randić put forward a novel structure-descriptor topological index, known as the Kirchhoff index [11]. The Kirchhoff index of a graph G𝐺Gitalic_G is calculated using the formula Kf(G)=12∑i=1|V|∑j=1|V|rijK... | A |
As in the case of Theorem 2, tksuperscript𝑡𝑘t^{k}italic_t start_POSTSUPERSCRIPT italic_k end_POSTSUPERSCRIPT protects against all actions with lower cost and t1superscript𝑡1t^{1}italic_t start_POSTSUPERSCRIPT 1 end_POSTSUPERSCRIPT protects against all actions with higher cost.
| Section 3.1 confirmed that it can be advantageous for the principal to offer ambiguous contracts.
To quantify the extent of the potential gains, we introduce the notion of the ambiguity gap, defined as the worst-case ratio between the principal’s utility with and without ambiguity. |
Section 4 uses the concept of an ambiguity gap—the largest possible ratio of the principal’s payoff under an optimal ambiguous contract to that of an optimal classic contract—to quantify how much the principal gains by exploiting ambiguity. In general, this ratio can be arbitrarily large. When all rewards are positive... |
We first describe the classic setting, in which a contract, denoted by ⟨t,i⟩𝑡𝑖\langle t,i\rangle⟨ italic_t , italic_i ⟩, is a payment function t𝑡titalic_t and a recommended action i∈[n]𝑖delimited-[]𝑛i\in[n]italic_i ∈ [ italic_n ]. The interpretation is that the principal posts a contract, the agent observes the c... |
Section 6 shows that the advantages of ambiguity disappear if the agent can mix over actions. The ability to mix provides the agent with more alternative actions, tightening the incentive constraints enough to dissipate any advantage the principal gains from ambiguous contracts. As explained by Raiffa, (1961) in his a... | A |
The desired bound then follows from Lemma 2.7. We note that this application of Lemma 2.7 does require the starting distribution of 𝑺𝑺\bm{S}bold_italic_S to be product, but we can apply it even if the intermediate distributions of 𝑺𝑺\bm{S}bold_italic_S conditioned on some of the responses is non-product. This is b... | In Section 5, we generalize these ideas to other choices of m𝑚mitalic_m. Feldman and Steinke also show how to bound the mutual information using ALOOKL stability, corresponding to Theorem 7 in the case of m=1𝑚1m=1italic_m = 1 [FS18]. Our techniques are similar to theirs, appropriately generalized for m>1𝑚1m>1italic_... | The starting point of our analysis is a new notion of algorithmic stability. We require the algorithm’s output to be stable even if a large portion of the dataset is removed. This definition generalizes [FS18]’s notion of “Average leave-one-out KL stability,” which is equivalent to the below with m=1𝑚1m=1italic_m = 1.... |
This definition generalizes ALOOKL (Definition 2.1) stability, which corresponds to ALMOKL stability with m=1𝑚1m=1italic_m = 1. At first glance, this more general definition seems harder to satisfy because ℳ′superscriptℳ′\mathcal{M}^{\prime}caligraphic_M start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT must predict the be... | In this subsection, we prove Lemma 5.3. This proof uses many of the ideas from Feldman and Steinke’s proof of a similar result in the special case where m=1𝑚1m=1italic_m = 1 [FS18]. Just like them, we use the following fact that states the “center” of a collection of probability, as measured by minimizing the average ... | A |
Let t≥1𝑡1t\geq 1italic_t ≥ 1. Two graphs G𝐺Gitalic_G and H𝐻Hitalic_H are homomorphism indistinguishable over ℒt+superscriptsubscriptℒ𝑡\mathcal{L}_{t}^{+}caligraphic_L start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT start_POSTSUPERSCRIPT + end_POSTSUPERSCRIPT if and only if they are t𝑡titalic_t-equivalent. |
Let t≥1𝑡1t\geq 1italic_t ≥ 1. The classes ℒtsubscriptℒ𝑡\mathcal{L}_{t}caligraphic_L start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT and ℒt+superscriptsubscriptℒ𝑡\mathcal{L}_{t}^{+}caligraphic_L start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT start_POSTSUPERSCRIPT + end_POSTSUPERSCRIPT are inner-product compatible. | In this work, the authors introduced tools for constructing systems of equations characterising homomorphism indistinguishably over classes of labelled graphs.
A requirement of these tools is that the graph class in question is inner-product compatible [grohe_homomorphism_2022, Definition 24]. | Despite this, our approach is different from [grohe_homomorphism_2022, rattan_weisfeiler_2023] in the sense that here the graph classes ℒtsubscriptℒ𝑡\mathcal{L}_{t}caligraphic_L start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT and ℒt+superscriptsubscriptℒ𝑡\mathcal{L}_{t}^{+}caligraphic_L start_POSTSUBSCRIPT italic_t en... | the feasibility of various systems of equations associated to graphs like the Sherali–Adams relaxation of ISO(G,H)ISO𝐺𝐻\operatorname{ISO}(G,H)roman_ISO ( italic_G , italic_H ) was characterised in terms of homomorphism indistinguishability over certain graph classes.
We continue this line of research by characterisi... | B |
The lab is equipped with an OptiTrack motion capture system, which functions in the outside-in [39] tracking principle. 6 motion cameras are mounted around the experiment zone to take 2D aligned pictures of passive markers on objects, according to the position of retroreflective markers on 2D frames to calculate the r... |
Figure 3: Design of the experiment: 1) OptiTrack Cameras, 2) Spot Trajectory. The Spot will always move from B to A if not still. Without gaze, in forward conditions, the Spot is facing A point; in sideways conditions, the Spot is vertical to line AB, facing the participant side, and in backward conditions, the Spot i... |
Our robot in this experiment is the Spot from Boston Dynamics. It comes with built-in autonomous walking, inspecting, and avoidance functions. Compared to the general model, this one is mounted with a robotic arm on its back, which gives it the appearance of a dog with the gripper as its head (see in Figure 1). There ... | Sideway orientation is the most special condition in all three moving cases because it gives participants the sense of moving in a vertical direction instead of the original path.
The head of the Spot points vertically toward the participant’s trajectory so that the Spot will move orthogonally to its orientation. Peopl... | The participant should start from position C and move towards the Table in position D to deliver the yellow cup, during which a non-contact interaction between the participant and the Spot was recorded by the motion capture cameras. In the non-stationary conditions, the Spot robot started moving from B to A the moment ... | B |
This section presents a simulation study of human inverse kinematics (IK) using the methods described above. To generate a trajectory, it is essential to ensure that both the starting and final points are within the workspace of the lower limb, as illustrated in Figure 4. According to [24], the average walking speed f... | Cyclic Coordinate Descent (CCD) is an iterative algorithm used to solve inverse kinematics problems. Yotchon et al. [13] proposed a hybrid approach combining the CCD method with a differential evolution algorithm, a metaheuristic optimization technique, to tackle inverse kinematics challenges. This combined method reli... |
The results of the inverse kinematics simulation for the lower limbs using the Cyclic Coordinate Descent (CCD) method are shown in Figure 5. To determine the position error illustrated in Figure 6, we used these results along with the forward kinematics described in Equation (5) to generate the end effector trajectory... |
This subsection explores the use of neural networks to find inverse kinematics (IK) solutions for the human leg. Shah et al. [22] applied deep artificial neural networks to solve the IK problem for a 5-axis serial link robotic manipulator. They achieved an accuracy where the deviation between the end effector and the ... |
Regarding the Levenberg-Marquardt Damped Least Squares (LMDLS) technique, the simulation results are shown in Figures 9 and 10. This method incurs a high computational cost, primarily due to the complexity of the human leg’s structure. Figure 11 displays the angular joint values obtained using the optimization algorit... | B |
A property of digraphs is a set of finite digraphs closed under isomorphism. A digraph G𝐺Gitalic_G is ε𝜀\varepsilonitalic_ε-far from having a property ΦΦ\Phiroman_Φ if any digraph G′superscript𝐺′G^{\prime}italic_G start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT on the vertex set V(G)𝑉𝐺V(G)italic_V ( italic_G ) that d... |
Unfortunately, the dependence on ε𝜀\varepsilonitalic_ε can be quite bad already in the case of undirected graphs: the known upper bounds in the Alon-Shapira theorem are wowzer functions due to the iterated involvement of Szemerédi’s regularity lemma. Following Alon and Fox [7], we call a property easily testable if f... | The goal of this paper is to study testability of finite posets as special digraphs. By a poset, we mean a set equipped with a partial order ≺precedes\prec≺ that is anti-reflexive and transitive. Alon, Ben-Eliezer and Fischer [1] proved that hereditary (closed under induced subgraphs) classes of ordered graphs are stro... | Alon and Shapira [4] proved that every monotone property of undirected graphs (that is, closed under the removal of edges and vertices) is strongly testable, see Lovász and Szegedy for an analytic approach [22], while Rödl and Schacht generalized this to hypergraphs [23], see also Austin and Tao [8]. Similar results ha... | The relationship between local and global properties of structures is a central theme in combinatorics and computer science. Since the work of Rubinstein and Sudan [25], testing properties by sampling a small number of elements is an emerging research area.
A classical result of this kind is the triangle removal lemma ... | C |
In the initial step, the system applies named-entity recognition on textual input data.
Probabilistic models and microtask crowdsourcing are combined to accomplish entity linking with a quality outperforming models without a human-in-the-loop paradigm [304]. | A type ranking step is performed to achieve fine-grained type associations of entities by leveraging the textual surrounding of entities as well as the current KG type hierarchy [305].
Relation Extraction utilizes distant supervision and an aggregated piecewise convolution network which is trained on existing relations... | The first relies on the fact that entities close in the embedding probably share the same type.
Relying on relationship information the second mechanism learns entity type embeddings by replacing the subject and object entity in a triple for their corresponding type. | The processing of semi-structured and unstructured data introduces the need for knowledge extraction methods to determine structured entities and their relations as well as their transformation into the KG graph data model. Data integration and canonicalization involve methods to determine corresponding or matching ent... | For incremental ER the task is to match sets of new entities from one or several sources with the current version of the KG which is typically very large and contains entities of different types. It is thus beneficial to know the type of new entities from previous steps in the KG construction pipeline so that only KG e... | A |
D˙T=ϵd˙2t+ϵd2t˙subscript˙𝐷𝑇italic-ϵ˙𝑑2𝑡italic-ϵ𝑑2˙𝑡\dot{D}_{T}=\epsilon\frac{\dot{d}}{2}t+\epsilon\frac{d}{2}\dot{t}over˙ start_ARG italic_D end_ARG start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT = italic_ϵ divide start_ARG over˙ start_ARG italic_d end_ARG end_ARG start_ARG 2 end_ARG italic_t + italic_ϵ divi... | Furthermore, the dual quaternion method helps to avoid the gimbal lock phenomenon. Gimbal lock is a loss of one degree of freedom (1-DOF) in 3D space that occurs when using Euler angles [4]. For example, suppose a rigid body rotates in 3D space in the order Z, Y, and X, and the angle of rotation about the Y-axis is 90... |
This section focuses on the dynamic description of the lower limb shown in Figure 2 using the Dual Quaternion-based recursive Newton-Euler method. This method involves calculating the velocities and accelerations of the center of mass of each link, known as twists, based on the positions, velocities, and accelerations... |
In this section, the Forward Kinematics (FK) of the lower limbs, depicted in Figure 1, using dual quaternions is established. FK involves computing the positions and orientations of the end-effector in task space from the axes and angles of the joint rotations. The lower limb is decomposed into four segments: the pelv... | In this paper, the dual quaternion-based theory is applied to the kinematics and dynamics study of the 7-DOF human lower limbs in 3D space. Subsequently, the artificial neural networks method is used to solve the inverse kinematics problem. The efficiency of the artificial neural networks method is verified using the j... | C |
Nevertheless, when the objective function is non-convex, a stationary point may be a saddle point or even a local maximum, which might not be desirable. Another common issue is that first-order methods typically have a slow convergence rate, especially when the problem is ill-conditioned. Therefore, they may not be sui... | We consider the variance-reduced cubic Newton method from (Zhou et al., 2019) (referred to as “full VR”), its lazy version where we do not update the snapshot Hessian (“Lazy VR”), the stochastic Cubic Newton method (“SCN”),
the Cubic Newton algorithm (“CN”), Gradient Descent with line search (“GD") and Stochastic Gradi... | We consider again a diagonal neural network and estimate the time costs needed for computing its gradient, Hessian, decomposing the Hessian, and solving the cubic subproblem. Figure 6 shows that the average cost of computing the Hessian is significantly higher than the cost of computing one gradient, and the quotient g... |
To address these challenges, we can take into account second-order information (the Hessian matrix) and apply Newton’s method (see, e.g., (Nesterov, 2018)). Among the many versions of this algorithm, the Cubic Newton method (Nesterov & Polyak, 2006) is one of the most theoretically established. With the Cubic Newton m... | Figure 2: Cubic Newton method with and without using the helper function hℎhitalic_h. For m=1𝑚1m=1italic_m = 1, this is simply the classic Cubic Newton method. To give an intuitive meaning to the plot, 1m1𝑚\frac{1}{m}divide start_ARG 1 end_ARG start_ARG italic_m end_ARG is the percentage of labeled data used during t... | C |
We consider two mobile network operators X and Y who provide service to K𝐾Kitalic_K and Q𝑄Qitalic_Q UEs, respectively. The UEs are arbitrarily distributed over a single cell covering the same geographical area, and operators X and Y use non-overlapping frequency bands. | The base stations (BSs) of operators X and Y (referred to as BS-X and BS-Y, respectively) and the UEs are equipped with a single antenna, and all the channels in the systems undergo frequency-flat fading.111Extension to general cases with multiple antennas and frequency selective channels does not change the main messa... | Now, due to the independence of the channels of the users served by operators X and Y, the phase configuration used by operator X to serve its own users appears as a random phase configuration of the IRS for any UE served by operator Y. In the sequel, we quantify the impact of the IRS on the throughput achieved by the ... | In this paper, we analyzed the effect of deploying an IRS on the performance of an OOB operator that has no control over the IRS. We showed that while the IRS optimally serves the in-band UEs, it simultaneously, and at no additional cost, enhances the quality of the channels of the OOB UEs. This enhancement in the OOB ... | As mentioned earlier, in this work, we consider a scenario where operator X deploys and controls an IRS in order to enhance the throughput of the users being served by it, and are interested in the effect of the IRS on an operator Y that is providing services in a different frequency band. Thus, in order to serve the k... | A |
Besides, Fig. 1(right) and Fig. 2(right) also show histograms of effects I(S|𝒙)𝐼conditional𝑆𝒙I(S|\boldsymbol{x})italic_I ( italic_S | bold_italic_x ) over different samples5, where S𝑆Sitalic_S was extracted as a salient concept.
We found that the same interaction concept usually made similar effects on different ... | Figure 1: Visualization of interaction concepts S𝑆Sitalic_S extracted by PointNet on different samples in the ShapeNet dataset.
The histograms show the distribution of interaction effects I(S|𝒙)𝐼conditional𝑆𝒙I(S|\boldsymbol{x})italic_I ( italic_S | bold_italic_x ) over samples in the “motorbike” category, where S... | Some concepts frequently appear in different samples and make salient effects, while other concepts only appear in very few concepts.
Therefore, we use the frequency of the concept α(S)𝛼𝑆\alpha(S)italic_α ( italic_S ) as a weight to compute the average discrimination power of all concepts, which is given as β¯≜∑S[α... |
Figure 5: The average discrimination power of concepts in different frequency intervals, i.e. α∈(0.0,0.2],(0.2,0.4],…,(0.8,1.0]𝛼0.00.20.20.4…0.81.0\alpha\in(0.0,0.2],(0.2,0.4],...,(0.8,1.0]italic_α ∈ ( 0.0 , 0.2 ] , ( 0.2 , 0.4 ] , … , ( 0.8 , 1.0 ]. | Fig. 5 shows the average discrimination power of concepts in different frequency intervals.
We found that the average discrimination power β¯¯𝛽\bar{\beta}over¯ start_ARG italic_β end_ARG of concepts was usually higher than 0.80.80.80.8, which verified the discrimination power of extracted concepts. | C |
Interactive concepts vs. cognitive concepts and other interaction metrics. Although the Harsanyi interactive concept seems partially aligned with humans’ cognition to some extent (Cheng et al. 2021b), we do not think such interactive concepts exactly fit humans’ cognition. More crucially, the mathematical generalizati... | Complexity (order) of interactive concepts.
The complexity of the interactive concept S𝑆Sitalic_S is defined as the number of input variables contained in the concept, which is also termed as the order of the concept, i.e., order(S)=|S|order𝑆𝑆\textit{order}(S)=|S|order ( italic_S ) = | italic_S |. | Therefore, a high-order interactive concept contains a large number of input variables, and represents a complex concept.
In this way, we use the high inconsistency to noises of high-order concepts to explain the high over-fitting risk of high-order concepts. | In general, a DNN’s representation complexity is different from the cognitive complexity. For example, let us consider a small ball concept consisting of a few pixels (low-order concept) and a large ball concept consisting of massive pixels (high-order concept) in images. These two balls have similar cognitive difficul... |
Although there is a common intuition that more complex representations usually lead to over-fitting, this study uses an analytic inconsistency of concepts to explain the connection between the complexity of interactive concepts and their generalization power. The complexity of an interactive concept S𝑆Sitalic_S is de... | C |
We conducted experiments with MNIST, the most commonly used datasets in the field of image classification. We used MNIST datasets in torchvision and used 2 layered Networks which is optimized using SGD on a batch size of 64 with a learning rate of 0.001 and a momentum of 0.5 with random seed of 10. We confirmed that ou... | We conducted experiments with MNIST, the most commonly used datasets in the field of image classification. We used MNIST datasets in torchvision and used 2 layered Networks which is optimized using SGD on a batch size of 64 with a learning rate of 0.001 and a momentum of 0.5 with random seed of 10. We confirmed that ou... | ReLU (Rectified Linear Units) is mainly used in the fields of vision classification. In classification, ordinarilly more layers is better in deep learning. On datasets such as MNIST, even simple CNNs with three layers can achieve high classification performance. However, for more challenging datasets such as CIFAR10, s... |
The robust property of MoLU is to approach rapidly to the value of minimum of a loss function without losing stability. This is a truly useful characteristic when training long time-series data by using NeuralODEs(Neural Ordinary Differential Equations). To prove the performance of MoLU, we conducted experiment on Neu... |
We conducted experiment on CIFAR10 which is more challenging model than MNIST in classification fields. ResNet18 which is optimized using SGD on a batch size of 32 with a learning rate of 0.001, momentum of 0.9 is used for the experiment with random seed of 10. Our activation function converges rapidly with respect to... | D |
In a nutshell, this technique amounts to traverse in a depth-first search manner an implicit solution tree where nodes are solutions, and where edges are defined by some parent-child relation between solutions.
During the traversal, children are obtained by merging trees having adjacent roots along the limit cycle. | A notable feature of this algorithm is that it can moreover be adapted in order to produce the successor (or predecessor) of any given solution in O(n2)𝑂superscript𝑛2O(n^{2})italic_O ( italic_n start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ) time as well, and only needs linear space.
This procedure is then used as a s... | Thus, in general, reverse search only needs memory space that is linear in the height of the solution tree times the space needed to generate children.
As of the delay, it only depends on the time needed to compute the parent and the delay needed to generate children when using folklore tricks such as the alternating o... | We can now exploit the algorithms of Theorem 3.1, and more specifically our ability to generate the successor of a given component, as a subroutine for the efficient generation of arbitrary (non necessarily connected) functional digraphs. In order to avoid generating multiple isomorphic digraphs, we first define an app... | There is a O(n2)𝑂superscript𝑛2O(n^{2})italic_O ( italic_n start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT )-delay and linear space algorithm generating all connected n𝑛nitalic_n-vertex functional digraphs.
Moreover, given any such functional digraph, we can generate its successor (resp., predecessor) in the enumeration... | A |
Then, to apply the approximation theory result (20), we recall that, by the hypotheses of this lemma, and (18), T†∈Hηk+1(Ω;Ω)superscript𝑇†superscriptsubscript𝐻𝜂𝑘1ΩΩT^{\dagger}\in H_{\eta}^{k+1}(\Omega;\Omega)italic_T start_POSTSUPERSCRIPT † end_POSTSUPERSCRIPT ∈ italic_H start_POSTSUBSCRIPT italic_η end_POSTSUBSCR... |
In this section we numerically validate the approximation results obtained in Section 4 for various realizations of the abstract algorithm of Section 2. Sections 5.1–5.2 investigate the algorithm that minimizes the Wasserstein distance, while Section 5.3 investigates the Kullback-Leibler divergence between pullback me... |
To derive analogous error bounds to those for pushforward measures in Section 4, we first present an abstract result to bound the KL divergence between a target measure and an approximate pullback measure. An application of this theorem to derive convergence results for an increasing class of monotone and triangular m... | the applied analysis of the backward transport for triangular maps on unbounded domains by minimizing the KL
divergence. Our analysis for triangular maps relies on a specialized stability result, Theorem 8.3, which is analogous to the general Theorem 2.1 for the backward transport problem. However, due to the triangula... | and C>0𝐶0C>0italic_C > 0 is a constant independent of 𝒯^^𝒯\widehat{\mathcal{T}}over^ start_ARG caligraphic_T end_ARG. We note that T†superscript𝑇†T^{\dagger}italic_T start_POSTSUPERSCRIPT † end_POSTSUPERSCRIPT can be taken to be any transport map that satisfies the exact pushforward relation T♯†η=νsubscriptsupersc... | B |
Table 2 shows that our uni-modal non-ensemble learning MMA-MRNNet (that exploits only the visual information and does not employ any ensemble learning) outperforms all other methods by large margins (although some methods are multimodal ones or even ensembles). Let us also note that all baseline and state-of-the-art me... |
The performance of the proposed MMA method was evaluated against several state-of-the-art approaches across multiple datasets (Aff-Wild2, AffectNet and EmotioNet), as detailed in Table 5. The MMA component consistently outperformed by large margins all methods on all tasks (7 basic expression recognition, AU detection... | The Multiple Models of Affect (MMA) extractor component processes an input video X by extracting affective representations from each frame using three distinct models of affect. Specifically, the MMA is a Multi-Task Learning (MTL) CNN model that concurrently performs: (i) continuous affect estimation in terms of valenc... | Initially, we used only single-task affective representations (extracted from MMA) as input to the RNN. We then tested combinations of two tasks (e.g., VA & AUs), and finally, we utilized the affective representations from all three tasks concurrently. The results are summarized in Table 3, where we present only the be... | MMA-MRNNet comprises two primary components: the Multiple Models of Affect (MMA) extractor and the Masked RNN and Routing Network (MRNN). The MMA component is a Multi-Task Learning (MTL) CNN that extracts affective representations from each frame by concurrently estimating valence-arousal (VA), recognizing the 7 basic ... | C |
A conformity function is a mapping ρ:ℝd×𝒴×Ω→ℝ:𝜌→superscriptℝ𝑑𝒴Ωℝ\rho:\mathbb{R}^{d}\times\mathscr{Y}\times\Omega\to\mathbb{R}italic_ρ : blackboard_R start_POSTSUPERSCRIPT italic_d end_POSTSUPERSCRIPT × script_Y × roman_Ω → blackboard_R such that ρ(x,y)=ρ(x,y,⋅)𝜌𝑥𝑦𝜌𝑥𝑦bold-⋅\rho(x,y)=\rho(x,y,\,\boldsymbol{\... | Under the data exchangeability assumption, the sequence of conformity scores {Si}i≥1subscriptsubscript𝑆𝑖𝑖1\{S_{i}\}_{i\geq 1}{ italic_S start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT } start_POSTSUBSCRIPT italic_i ≥ 1 end_POSTSUBSCRIPT is exchangeable.
| In general, the coverage indicators Zisubscript𝑍𝑖Z_{i}italic_Z start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT are dependent random variables, since for all future observables the corresponding conformal prediction sets in Definition 3 are defined in terms of the same calibration sample conformity score S(⌈(1−α)(n+1)... |
Conformity functions are agnostic to the choice of the specific models or algorithms used to construct μ^^𝜇\hat{\mu}over^ start_ARG italic_μ end_ARG, ξ^psubscript^𝜉𝑝\hat{\xi}_{p}over^ start_ARG italic_ξ end_ARG start_POSTSUBSCRIPT italic_p end_POSTSUBSCRIPT, and π^^𝜋\hat{\pi}over^ start_ARG italic_π end_ARG in Exa... |
Note that the regularity of a specific conformity function ρ𝜌\rhoitalic_ρ is contextual, being inherently dependent on the distribution of the underlying data sequence. Technically, we can always avoid ties among the sequence of conformity scores almost surely by introducing a properly constructed ancillary tie-break... | D |
}}.over~ start_ARG bold_f end_ARG start_POSTSUBSCRIPT italic_i italic_j end_POSTSUBSCRIPT = typewriter_MLP ( bold_f start_POSTSUBSCRIPT italic_i italic_j end_POSTSUBSCRIPT ) ∈ blackboard_R start_POSTSUPERSCRIPT italic_D start_POSTSUBSCRIPT roman_e end_POSTSUBSCRIPT end_POSTSUPERSCRIPT , over~ start_ARG bold_r end_ARG s... |
As shown in Fig. 2 (b), previous works aggregate local features directly [30, 16, 9, 10, 12] or only consider positional relations [11] as the correlation between neighboring pairs. These methods may be biased because the semantic relation is also critical in assessing the importance of each neighbor. |
Variant A is a baseline strategy directly using max pooling to aggregate single-scale features in the neighborhood space. Based on this, variant B aggregates neighbor information separately at multiple scales and then sums them together to obtain multi-scale features. It achieves slight improvements on both tasks, dem... | Compared to point-based counterparts, our model outperforms state-of-the-art methods and gains a notable improvement (1.9%percent\%% increase) than the second place on the challenging N-Caltech101 dataset, demonstrating the effectiveness of EVSTr. As shown in Fig. 5, we further provide the visualization of feature repr... |
Recent graph-based approaches [16, 9, 10] construct point-wise graphs on downsampled event streams and exploit graph neural networks (GNNs) to extract event features. Considering that the point-wise relationship of events is susceptible to noise signal [31], voxel-wise GNNs [11, 12] first convert an event stream into ... | A |
In addition, a new uncertainty computation strategy was evaluated, showing that it can be used for on-the-fly quality measurements. The reconstructions were furthermore validated with more than 400 grasps, demonstrating the usability of shape completion in a core robotic task.
| In Fig. 6, the results for the precision of the reconstruction are shown. The single-object experiments are shown in black. We can see that the trends of both JS and CD are the same as for the simulation, even though we can notice noise in some touches. In yellow, the results for multi-object experiments are shown. Aga... | After collision, new visual information is saved, segmented and added to the point cloud for the touched object, together with the haptic information (box (7), lines 17-21). To make sure that we segment the correct object, the RGB-D information is cropped with the bounding box found for the given object in the last ite... |
We will first describe the module for the shape creation itself. In [1] the IGR network was used as a standalone library. To perform more efficiently and to be able to handle more objects at once, we modified it to be more compatible with the whole ecosystem (under Robot Operating System (ROS)). The module contains t... | The results in the real setup are negatively affected by the noise induced by the contact events—the collision is detected with a certain delay, the object moves, and the new pose is not re-estimated perfectly. This could be mitigated in two ways. First, the most effective will be faster contact detection. In the curre... | D |
Clones are sets of finitary operations that include all projections and are closed under composition (see [14, 25, 26]). They play a significant role in universal algebra, as the set of all term operations of an algebra always constitutes a clone, and, in fact, every clone is of this form.
Therefore, comparing clones o... | For countable structures classified as ω𝜔\omegaitalic_ω-categorical, the polymorphism clone carries a substantial amount of information. In [6] primitive positive bi-interpretability of two ω𝜔\omegaitalic_ω-categorical structures A𝐴Aitalic_A and B𝐵Bitalic_B is linked to the isomorphism of their polymorphism clones ... | In addition to their significance in universal algebra, clones also play an important role in the study of first-order structures. The polymorphism clone of a first-order structure, containing all finitary operations that preserve the structure, holds valuable information and serves as a powerful analytical tool.
Clone... | Clones are sets of finitary operations that include all projections and are closed under composition (see [14, 25, 26]). They play a significant role in universal algebra, as the set of all term operations of an algebra always constitutes a clone, and, in fact, every clone is of this form.
Therefore, comparing clones o... | In this framework the nullary operators 𝖾isubscript𝖾𝑖\mathsf{e}_{i}sansserif_e start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT are the projections, and the q𝑞qitalic_q’s operators are the compositions of ω𝜔\omegaitalic_ω-operations. The universe of a FCA (resp. ℵ0subscriptℵ0\aleph_{0}roman_ℵ start_POSTSUBSCRIPT 0 e... | B |
This motivates the following iterative algorithm for finding a pairwise disjoint collection of s𝑠sitalic_s-t𝑡titalic_t mincuts: (1) Find the leftmost s𝑠sitalic_s-t𝑡titalic_t mincut X𝑋Xitalic_X in Hs,tsubscript𝐻𝑠𝑡H_{s,t}italic_H start_POSTSUBSCRIPT italic_s , italic_t end_POSTSUBSCRIPT, (2) identify the set Einv... | In the cut-finding step (Lines 10-14), the algorithm then finds the leftmost minimum s𝑠sitalic_s-t𝑡titalic_t cut amongst valid path edges. Notice that, for each s𝑠sitalic_s-t𝑡titalic_t path in 𝒫s,tsubscript𝒫𝑠𝑡\mathcal{P}_{s,t}caligraphic_P start_POSTSUBSCRIPT italic_s , italic_t end_POSTSUBSCRIPT, removing its ... | In other words, as the algorithm makes progress, no minimum s𝑠sitalic_s-t𝑡titalic_t cut—that is disjoint from the ones found so far by the algorithm—has edges to the left of the minimum s𝑠sitalic_s-t𝑡titalic_t cut found by the algorithm at the present iteration. Next, we show that this implies the maximality of the... |
The algorithm works by traversing the graph from left to right in iterations while marking the vertices it visits. Initially, all vertices are unmarked, except for s𝑠sitalic_s. Each iteration consists of two parts: a marking step, and a cut-finding step. In the marking step (Lines 3-9), the algorithm identifies curre... |
Let C^^𝐶\hat{C}over^ start_ARG italic_C end_ARG denote the solution returned by the algorithm. First, we show that C^^𝐶\hat{C}over^ start_ARG italic_C end_ARG contains only disjoint cuts. This follows from the fact that a cut can only be found amongst valid edges at any given iteration, and once an edge has been inc... | C |
We also show how to lower bound information between probabilities over general spaces with information between probabilities over finite sequences using uniformly enumerable disjoint open sets. We provide an means to upper bound the probabilities between general spaces using computable non-probabilistic measure covers... | We extend conservation to Borel measures over T0subscript𝑇0T_{0}italic_T start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT, second countable topologies. We restrict our attention to such topologies which can be represented by a tuple (X,ℬ,ν)𝑋ℬ𝜈(X,\mathcal{B},\nu)( italic_X , caligraphic_B , italic_ν ) where X𝑋Xitalic_X is a ... | We prove conservation of probabilities over successively general spaces. This includeds finite sequences, infinite sequences, and T0subscript𝑇0T_{0}italic_T start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT, second countable topologies. Conservation of probabilities over the case of finite and infinite sequences follow directly... | The average information between probability measures is small, less than the complexity of the averaging. This is true in the discrete and continuous case. For the discrete case, an enumerable sequence of uniformly computable probability measures over a general space is a sequence of measures {μi}subscript𝜇𝑖\{\mu_{i}... | The advantage to the topological approach used in this paper is that a very general topology can be used. The only assumption needed is that the topology needs to have the T0subscript𝑇0T_{0}italic_T start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT property and a computable countable basis. Typical requirements in computability... | D |
Different normalization techniques, including activation normalization, weight normalization, and gradient normalization, are employed to enhance the training performance of DNNs.
To normalize activations, the most common technique is Batch Normalization (BN) [4]. BN has been proposed to solve the problem caused by the... | Based on the Mixture Normalization (MN) hypothesis proposed by [6] (ref. to Figure 1), our Context Normalization (CN) approach operates under a similar assumption that data can be effectively represented by a mixture of multiple components, as opposed to batch normalization (BN) [4]). In the Context Normalization (CN)... | If the samples within the mini-batch are from the same distribution, the transformation in Equation (1) generates a zero mean and unit variance distribution. This zero-mean and unit-variance constraint allows stabilizing the distribution of the activations and thus benefits training.
This mini-batch-wise approach makes... | Mixture Normalization
In the context of deep neural networks (DNNs), the distribution of activations is almost certain to have multiple modes of variation due to the non-linearities. The batch normalization (BN) [4] hypothesis that a Gaussian distribution can model the generative process of mini-batch samples is less v... | BN and its few extensions can be studied from the viewpoint of Fisher kernels that arise from generative probability models. Kalayeh and al. [6] show that assuming samples within a mini-batch are from the same probability density function, then BN is identical to the Fisher vector of a Gaussian distribution. More speci... | D |
This paper considers the importance of disentangling foreground and background features in OOD detection and proposes to leverage background features to enhance the OOD detection methods that are based on foreground features. To this end, we introduce a novel generic framework, called DFB, that can Disentangle the Fore... | Temperature T𝑇Titalic_T in Synthesizing Foreground and Background OOD Scores. One key challenge in plugging existing foreground OOD scores into DFB in Eq. (7) is the diverse range of different foreground OOD scores yielded by the existing methods. Fig. 6 the variants of DFB of using different temperature T𝑇Titalic_T ... | The Reasons behind the Effectiveness of DFB. We aim to understand the effectiveness of DFB from two perspectives, including the foreground and background OOD scoring, and the latent features learned in DFB, with the results on the Textures dataset reported in Figs. 4 and 5 respectively. We can see in Fig. 4 that the ba... | As depicted in Fig. 1, the proposed DFB effectively disentangles foreground and background features. In the ID data CIFAR10, DFB can more accurately locate the ID objects than the vanilla classifier. In the OOD data CIFAR100, which contains significant foreground objects, DFB successfully disentangle between the foregr... | on OOD benchmarks such as Places356 and Textures where significant background differences are presented compared to the in-distribution background. This demonstrates that DFB can effectively learn the in-distribution background features that can be used to detect OOD samples from the background aspect. Nevertheless, BG... | C |
In this paper, we present a framework for post-processing images which have undergone low-light image enhancement. The enhancement of low-light images often reveals a variety of degradations which are hidden in the dark, and thus a need for post-processing is introduced. Furthermore, each low-light enhancement techniqu... |
LPDM proposed in this study also models the conditional distribution between low-light and normally-exposed images; however, we use the diffusion paradigm to achieve this. Furthermore, we repurpose the function of a DM to be used as a noise detector. Therefore, LPDM provides a subtractable estimation of the noise in a... | As seen in Eq. 5, DMs are trained to make predictions for ϵbold-italic-ϵ\bm{\epsilon}bold_italic_ϵ. We examine the value of predicting ϵbold-italic-ϵ\bm{\epsilon}bold_italic_ϵ by changing the model to predict 𝒙0subscript𝒙0\bm{x}_{0}bold_italic_x start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT directly, and we name this model... |
This study was supported by the National Research Foundation (NRF), South Africa, Thuthuka Grant Number 13819413. The authors acknowledge the Centre for High Performance Computing (CHPC), South Africa, for providing computational resources to this research project. | Section V-A describes the datasets used in this study; Section V-B defines the configuration of LPDM and the training parameters used for all experiments; Section V-C provides detail on the LLIE models selected for comparison with LPDM; in order to achieve a fair comparison, we compare our approach to alternative denoi... | C |
Our results have far-reaching implications. When it comes to government practices of digital services, the concept of "online only" has already been challenged by scholars relying on the fact that people of certain characteristics, particularly age, are less likely to be able to get online, and therefore there must be ... | In the game sessions, players are given two Wikipedia pages as the source and the target in each game. To reduce the disparities in prior knowledge among the participants, the source and target pages are chosen to be similarly distanced (2 or 3 steps away on the Wikipedia network) pages about renowned individuals from ... | Encoding the participants’ answers to the questions in the survey (see encoding details in the Supplementary Material), we end up with 18 control variables characterizing the participants by the six groups of questions specified above, 5 control variables indicating the game, game type (Speed-race or Least-clicks), rou... |
Our study exhibits several limitations. Firstly, to enhance the robustness of our results, we should consider integrating additional variables that measure participants’ engagement, working memory, anxiety levels, and objective spatial abilities, which could potentially impact navigation performance. Secondly, it’s im... | In addition, our observations indicate that individual characteristics, including sex, ethnicity, native language, political stance, and reported spatial navigation skills, significantly influence navigation performance in one type of game (with time or distance constraints) but not the other. To fully understand these... | C |
The resulting tracks still have information at generator-level.
The promotion to high-level quantities, namely the application of the resolution effects due to, for example, multiple scattering phenomena, is carried out by GAN systems trained with binary cross-entropy as loss function and equipped with skip connections... | GlobalPID classifiers, obtained in real data by combining RICH and MUON responses with information from the calorimeter system and features of the reconstructed tracks, are parameterized using similar GAN-based architectures that take as input what produced by the RICH-GAN and MUON-GAN models.
Lastly, the efficiency of... | Combining stacks of GBDT and GAN models, Lamarr provides the high-level response of the LHCb tracking and PID systems.
To validate the ultra-fast simulation approach the chosen machine-learning-based models are trained on detailed simulated samples and the output of Lamarr is compared to the reference distributions as ... | The high-level response of the RICH and MUON systems are reproduced using the particles kinematic information provided by the Lamarr tracking modules and a description of the detector occupancy, for example based on the total number of tracks traversing the detector.
The loss function adopted to train the PID-GAN model... |
As mentioned in the previous Section, the validation of the ultra-fast philosophy of Lamarr is based on the comparison between the distributions obtained from models trained on detailed simulation and the ones resulting from standard simulation strategies. | C |
To evaluate our proposed framework, we conducted benchmark tests. Due to the lack of established evaluation strategies for this novel pretraining paradigm, we designed a series of evaluation experiments, including internal tasks (e.g., contact map prediction and distribution alignment quality assessment) to demonstrate... |
We propose leveraging pretrained protein language model to train protein structure models using cross-modal contrastive learning . Our approach demonstrates superior performances in various evaluation tasks. However, challenges remain, including the scope of language model transfer, data efficiency, generalization, co... | By rethinking the protein representations, we observe that the success of sequence-based models is due to large-scale data and the guidance provided by self-supervised signals. Considering there is a natural pairing relationship between structure and sequence, establishing this relationship can help guide structural le... | ∙∙\bullet∙ We propose an cross-modal protein representation framework, establishing a novel deep alignment relationship between sequences and structures. For the first time, we pretrain protein structural models under the guidance of rich prior language knowledge from pretrained protein sequence models.
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Inspired by advances in cross-modal pretraining (e.g., CLIP [22], Context-to-Vector [30]), we introduce a novel cross-modal contrastive protein learning (CCPL). This method calculates contrastive loss between two independently pretrained encoders, maximizing the similarity between paired protein structures and sequenc... | C |
Figure 1: In (a), conventional KGE models that use high-dimensional entity representations equal to enlarging the width of the embedding layer. But we tend to achieve parameter efficiency by increasing the depth of the embedding network, i.e., a narrower embedding layer (low-dimensional entity representations) plus th... | To accurately preserve the complex structural information of knowledge graphs, conventional KGE methods (e.g., TransE [4]) seek to increase the embedding dimension for better expressiveness and adopt high-dimensional entity/relation representations. However, since the scale of model parameters grows linearly with the r... |
Some methods attempt to improve parameter efficiency by reducing the embedding dimension, and the key problem is how to maintain model expressiveness. Meanwhile, since entities normally are much more than relations in many knowledge graphs, they mostly reduce the dimension of entity representations. One type of method... | The accuracy of link prediction of the proposed LifeNet-based methods and compared conventional methods are shown in Table II. We observe that TransE, TransH, DistMult, and ComplEx all obtain higher link prediction accuracy with 512 embedding dimensions than with 16 embedding dimensions, due to the increased expressive... | As the results show, the LiftNet-based methods save 68.4%percent68.468.4\%68.4 % to 96.9%percent96.996.9\%96.9 % model parameters or the original models. Since the parameter size of LiftNet is negligible (324 parameters), the level of parameter efficiency is mainly affected by the ratio of entities to relations in the ... | A |
This paper focused on multipartite entanglement distribution for a quantum network connected through links that exhibit a trade-off between entanglement generation rate and fidelity. This is the case with hash-based quantum purification protocols [11] and with photonic models [12]. Two entanglement distribution models ... |
This work was supported in part by the European Union’s Horizon 2020 Research and Innovation Program through the Project Quantum Internet Alliance (QIA) under Grant 820445, and in part by FCT - Fundação para a Ciência e Tecnologia, I.P. by project references QuNetMed 2022.05558.PTDC, with DOI identifier https://doi.or... |
The quantum Internet has the potential to allow capabilities and services that would be impossible in classical networks. To name a few, it opens doors to theoretically fully secure communications, enhanced sensing, and distributed quantum computation [1]. A quantum Internet aims to create entanglement between remote ... | Figure 5: Multipartite routing runtime analysis. Simulation of three-partite entanglement distribution for photonic quantum networks in an Erdős-Rényi network (ER) and a random geometric graph (RGG) topology, an average degree ⟨k⟩=10delimited-⟨⟩𝑘10\langle k\rangle=10⟨ italic_k ⟩ = 10 for the single, (a-b), and flow, (... |
Figure 4: Bipartite routing runtime analysis. Simulation of bipartite entanglement distribution for photonic quantum networks with an Erdős-Rényi network (ER) and a random geometric graph (RGG) topology, an average degree ⟨k⟩=6delimited-⟨⟩𝑘6\langle k\rangle=6⟨ italic_k ⟩ = 6 and 10101010 (blue lines), for the single,... | A |
Fig. 7 illustrates the BLER performance of polar codes and PAC codes constructed by different methods with N=256𝑁256N=256italic_N = 256, K=128𝐾128K=128italic_K = 128 and L=16𝐿16L=16italic_L = 16, where polar+ and PAC+ are the construction methods in [27] for polar codes and PAC codes, respectively. | The simulation results show that the proposed MWD sequence is suitable for constructing polar codes for short code length and has about 0.80.80.80.8dB performance gain for code length 256256256256 and list size 16161616 at code rate 0.50.50.50.5 and BLER 10−3superscript10310^{-3}10 start_POSTSUPERSCRIPT - 3 end_POSTSUP... | Then, in Lemma 5, we prove the polar codes obeying the PO with the MWD sequence have the optimum performance evaluated by the MWUB in the high SNR region.
In Lemma 6, we prove the MWD sequence is nested, which means that the MWD sequence can be used similarly to the polar sequence in 5G [4]. | The CRC-polar codes constructed by MWD sequence shows 0.170.170.170.17dB and 0.140.140.140.14dB performance gains with L=32𝐿32L=32italic_L = 32 and L=128𝐿128L=128italic_L = 128 at BLER 10−5superscript10510^{-5}10 start_POSTSUPERSCRIPT - 5 end_POSTSUPERSCRIPT compared with the polar sequence, respectively.
The perform... | In Fig. 7, we observe that both the polar code and the PAC code constructed by the MWD sequence have the optimum performance among the MWD sequence, the polar sequence and the method in [27].
Specifically, the PAC code constructed by MWD sequence has about 0.140.140.140.14dB performance gain at BLER 10−3superscript1031... | D |
That is, the value of the game with signals cannot be larger than that of the classic search game without signals.
Since the value of this classic search game on a tree is equal to its total length μ𝜇\muitalic_μ (Gal, 1979), this must be an upper bound for the value of the search game with signals on a tree. | The rooted tree of Figure 1 has two branch nodes, A𝐴Aitalic_A and O𝑂Oitalic_O.
The recursion works backwards from penultimate nodes to the root, so we start with the subtree at A𝐴Aitalic_A: the arcs AL1𝐴subscript𝐿1AL_{1}italic_A italic_L start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT and AL2𝐴subscript𝐿2AL_{2}italic_A... | We observe that as p𝑝pitalic_p goes to 1111 and q𝑞qitalic_q to 00, the distribution of λ¯¯𝜆\bar{\lambda}over¯ start_ARG italic_λ end_ARG becomes concentrated on the leaf node at greatest distance from O𝑂Oitalic_O, and D𝐷Ditalic_D converges to that distance. As p𝑝pitalic_p goes to 1/2121/21 / 2, the distribution o... |
We define the mean depth D𝐷Ditalic_D of a rooted tree, with respect to a given probability measure λ𝜆\lambdaitalic_λ on its leaf nodes, as the mean distance from the root to the set ℒℒ\mathcal{L}caligraphic_L of leaf nodes, weighted with respect to λ𝜆\lambdaitalic_λ. More precisely, we define |
where the penultimate equality follows from the fact that λ¯¯𝜆\bar{\lambda}over¯ start_ARG italic_λ end_ARG is a probability distribution on ℒℒ\mathcal{L}caligraphic_L and the final equality follows from the fact that the leaf nodes of Q𝑄Qitalic_Q and Q′superscript𝑄′Q^{\prime}italic_Q start_POSTSUPERSCRIPT ′ end_PO... | C |
Images need to be not only anatomically correct but diagnostically correct as well.
Training a model like Stable Diffusion for medical imaging requires a large, varied, and ideally public dataset of images with captions, similar to those used for training on natural images [Schuhmann et al. (2022)]. | Several other works studied text-to-image latent diffusion models for medical imaging Chambon et al. (2022a); Akrout et al. (2023).
Closest to our work is Chambon et al. (2022b), where the authors explore various methods to adapt a pre-trained Stable Diffusion model to chest X-ray generation. | However, practical challenges, such as ethical and legal impediments to sharing medical data, particularly for unstructured radiology reports, complicate this endeavor [Scheibner et al. (2021), Bovenberg et al. (2020)].
For one of the few public datasets of this caliber that exists, MIMIC-CXR, Chambon et al. have demon... | Pre-trained models are often trained on 2D RGB datasets, but many medical imaging modalities are 3D.
Recently, studies such as Khader et al. (2023) and Pinaya et al. (2022) have trained diffusion models from scratch on 3D data or even on 4D data Kim and Ye (2022), and Han et al. (2023) use diffusion models conditioned ... | Images need to be not only anatomically correct but diagnostically correct as well.
Training a model like Stable Diffusion for medical imaging requires a large, varied, and ideally public dataset of images with captions, similar to those used for training on natural images [Schuhmann et al. (2022)]. | B |
Composition Correctness Evaluation. In this task, we assess the consistency of the generated 3D assets across two views, focusing on both semantic consistency and multi-view consistency. We collected four groups of samples, each comprising 3D assets generated by Latent-NeRF, SJC, and our method, using the same text pro... |
In our study, we employ the CLIP score as the primary evaluation metric to assess the congruence between the generated 3D assets and the associated text prompts. This score, commonly used in text-to-image generation research as noted in studies [38, 65, 55], is derived from the cosine similarity between the embeddings... | Composition Correctness Evaluation. In this task, we assess the consistency of the generated 3D assets across two views, focusing on both semantic consistency and multi-view consistency. We collected four groups of samples, each comprising 3D assets generated by Latent-NeRF, SJC, and our method, using the same text pro... | Object Identification. For this task, we selected four samples of 3D assets generated using our method, comprising a total of seven objects. Participants were then asked to identify the objects depicted in these assets. To evaluate the multi-object generation and combination capabilities of our approach, we calculated ... | Generative Quality Evaluation. We provided four groups of generated 3D assets (refer to the supplementary material) to each participant. For each group, the 3D assets were created using Latent-NeRF, SJC, and our method, all based on the same text prompt. Participants were then asked to assess the quality of these gener... | D |
In the following overview, we mainly focus on general-purpose generators. However, the literature has also proposed more specialized solutions to fill specific needs in the community. For example, Beer et al., (2019) present a data generator for subspace clustering, Gan and Tao, (2015) evaluates density-based clusteri... | The generators OCLUS (Steinley and Henson, (2005)) and GenRandomClust (Qiu and Joe, (2006)) focus on providing more sophisticated overlap control compared to previous generators. GenRandomClust extends the generator of Milligan and Cooper, (1985) by managing overlaps between clusters with different ellipsoidal shapes a... |
MDCGen (Iglesias et al., (2019) is a feature-rich generator that supports many desiderata in cluster analysis, such as overlap control, different probability distributions, subspace clusters, and the ability to add noise points. In particular, it is nice to be able to place noise points away from the clusters, which i... | Milligan and Cooper, (1985) implements a generator for generating several clusters in up to 8 dimensions. The method enforces an upper bound on cluster overlap by limiting overlap in the first dimension, but does not otherwise provide control over high-level geometric structure.
| Like other existing generators, OCLUS does not aspire to helping the user establish the overall geometric characteristics of synthetic data sets. To generate a data set, the user must provide a covariance matrix for each cluster, the desired overlaps between all pairs of clusters, and a design matrix specifying which c... | C |
Although DEGREE is effective with the oracle information, it struggles to filter out the ‘invalid’ events in the oracle-free setting, resulting in an almost zero (2.18%) trigger classification F1. This indicates that the information leaked in the template significantly contributes to the performance of DEGREE.
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We conduct experiments on two variants of the ACE05 benchmark under the oracle-free setting to evaluate our COFFEE. The results demonstrate that the template-based baselines heavily rely on the additional oracle information, whereas our COFFEE exhibits superior empirical performance over these baselines in the absence... | In this work, we study a more realistic setting of the event extraction task, namely the oracle-free event extraction, where no additional information beyond the context is required for event inference. To address this task, we propose a generation-based event extraction framework called COFFEE. Our COFFEE introduces a... | In this study, we propose a novel Contrastive Oracle-Free Framework for Event Extraction (COFFEE), which addresses the event extraction task without using any oracle information. Our COFFEE consists of two parts, a generator that performs the extraction of events and a selector that aims to refine the generated results... | Our proposed COFFEE outperforms the classification-based approach OneIE and the generation-based approaches Text2Event, BARTGen, and DEGREE in both the presence and absence of oracle information across all four metrics. This demonstrates that our COFFEE can effectively leverage the input context to extract event frames... | D |
where ϕ:[0,κ2]→ℝ+:italic-ϕ→0superscript𝜅2superscriptℝ\phi:\left[0,\kappa^{2}\right]\rightarrow\mathbb{R}^{+}italic_ϕ : [ 0 , italic_κ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ] → blackboard_R start_POSTSUPERSCRIPT + end_POSTSUPERSCRIPT is a non-decreasing index function such that ϕ(0)=0italic-ϕ00\phi(0)=0italic_ϕ... |
This is a standard assumption to control the noise such that the tail probability decays fast (Lin and Cevher, 2020a; Fischer and Steinwart, 2020). It is satisfied for, for instance, the Gaussian noise with bounded variance or sub-Gaussian noise. Some literature (e.g., Steinwart et al. 2009; Pillaud-Vivien et al. 2018... | Since the convergence rates and the minimax optimality of spectral algorithms in the well specified case are clear, a large amount of literature studied the misspecified spectral algorithms. Among these work, Steinwart et al. (2009); Dicker et al. (2017); Pillaud-Vivien et al. (2018); Fischer and Steinwart (2020); Celi... | In addition, we also notice a line of work which studies the learning curves of kernel ridge regression (Spigler et al., 2020; Bordelon et al., 2020; Cui et al., 2021) and crossovers between different noise magnitudes. At present, their results all rely on a Gaussian design assumption (or some variation), which is a ve... |
General spectral algorithms in the setting of kernel methods were first proposed and studied by Rosasco et al. (2005); Caponnetto (2006); Bauer et al. (2007); Gerfo et al. (2008). A large class of regularization methods are introduced collectively as spectral algorithms and are characterized through the corresponding ... | C |
From the results presented in Table 1, it is clear that our proposed method is capable of comparable empirical performance to many of the existing methods for simplifying point clouds. The GP-based approach outperforms the AIVS baseline across all experiments and metrics, and outperforms the PC-Simp baseline on all but... | In order to evaluate the performance of our method in comparison to other simplification techniques, we firstly use each simplified point cloud obtained from three object level point clouds to form simplified meshes, using screened Poisson surface reconstruction [17]. We can then compute the reconstruction errors betwe... |
Table 1: Empirical results and total runtimes (time taken by surface variation computation and simplification) for all tested simplification methods and point clouds. We report the maximum and mean Hausdorff distances between the original meshes, and the meshes reconstructed from the simplified point clouds. Also repo... |
Furthermore, we validate our technique’s feature-sensitive approach on real-world scanning datasets captured using different acquisition devices. Firstly, we use a desk scene point cloud from the NYU Depth V2 dataset, derived from RGBD data acquired using RGB and Depth cameras from Microsoft Kinect. This cloud and the... |
Table 1: Empirical results for all tested simplification methods for the remaining point clouds. We report the maximum and mean Hausdorff distances between the original meshes, and the meshes reconstructed from the simplified point clouds. Also reported is the average surface variation over each simplified point cloud... | B |
Training on full resolution (FullRes):
We implemented a distributed version of the proposed architecture that splits the task to two GPUs if necessary. This allows for training directly on full resolution (2563superscript2563256^{3}256 start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT) data, given that the expensive speciali... | 2563superscript2563256^{3}256 start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT images, we distribute the model over 2 GPUs. The methods HalfRes and PatchDDM were trained on one GPU only.
The optimizer we used was AdamW [Loshchilov and Hutter(2017)] with the default parameters. | For three spatial dimensions (i.e. 3D) this means that reducing the
input size from 2563superscript2563256^{3}256 start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT to 1283superscript1283128^{3}128 start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT results in a reduction | of 1×1×1\textmm3111\text𝑚superscript𝑚31\times 1\times 1\text{mm}^{3}1 × 1 × 1 italic_m italic_m start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT, resulting in a total scan size of 240×240×155240240155240\times 240\times 155240 × 240 × 155, which we padded to a size of 256×256×256256256256256\times 256\times 256256 × 25... | Training on full resolution (FullRes):
We implemented a distributed version of the proposed architecture that splits the task to two GPUs if necessary. This allows for training directly on full resolution (2563superscript2563256^{3}256 start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT) data, given that the expensive speciali... | B |
Adaptive learning rate design for fast model convergence: To the best of our knowledge, this paper is the first to investigate the closed-form design of an adaptive learning rate for each client at each local epoch by introducing an aggregated gradient term into the SGD-based local updating rules. Furthermore, to mitig... | From the objective function Ui(T)subscript𝑈𝑖𝑇U_{i}(T)italic_U start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ( italic_T ) in Eqs. (9)-(10), we observe that the learning rate ηi,ltsuperscriptsubscript𝜂𝑖𝑙𝑡\eta_{i,l}^{t}italic_η start_POSTSUBSCRIPT italic_i , italic_l end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic... | Decentralized adaptive learning rate design via mean-field terms: To address the challenge of inter-client information exchange during local training epochs, we introduce two mean-field estimators to approximate the average local parameters and gradients of all clients over time, based on which, a decentralized adaptiv... |
(Mean-Field Terms) To figure out the optimal decentralized learning rate for each client, we introduce two mean-field terms to respectively estimate the average local gradients and parameters of all clients at the l𝑙litalic_l-th local epoch of global iteration t𝑡titalic_t, where t∈{0,1,…,T}𝑡01…𝑇t\in\{0,1,\ldots,T\... |
In this section, we first derive the optimal decentralized adaptive learning rate ηi,ltsuperscriptsubscript𝜂𝑖𝑙𝑡\eta_{i,l}^{t}italic_η start_POSTSUBSCRIPT italic_i , italic_l end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_t end_POSTSUPERSCRIPT in closed-form for each client by introducing mean-field terms ϕ𝟏,𝒍𝒕s... | B |
LLaMA-Adapter can be generalized to image-conditioned generation as a multi-modal LLM, achieving competitive results on various visual question answering benchmarks.
On traditional vision and language tasks, our zero-initialized attention also attains favorable fine-tuning performance, which indicates strong generaliza... | The gating mechanism is initialized by zeros, and controls the feature interaction between prompt and word tokens, within the process of attention calculation.
Such a strategy can first preserve the original knowledge in LLaMA, and progressively inject the new instructional signals during training. |
Zero-shot Multi-modal Evaluation. To verify the out-of-domain generation ability of our approach, we conduct a two-stage multi-modal training, and then evaluate three benchmarks (MME (Fu et al., 2023), MMBench (Liu et al., 2023c), LVLM-eHub (Xu et al., 2023)) in a zero-shot manner. For the first stage, we utilize the ... |
To this end, we adopt a learnable gating factor, denoted as glsubscript𝑔𝑙g_{l}italic_g start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT, to adaptively control the importance of SlKsuperscriptsubscript𝑆𝑙𝐾S_{l}^{K}italic_S start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_K end_POSTSUPERSCRI... |
This work is partially supported by the National Key R&D Program of China (NO.2022ZD0161100), the National Natural Science Foundation of China (No.62206272), the Centre for Perceptual and Interactive Intelligence (CPII) Ltd under the Innovation and Technology Commission (ITC)’s InnoHK, and General Research Fund of Hon... | D |
VQA results on two open-ended datasets are shown in Table 2.
To enable S-ViLM to deal with the VQA task, we add a fusion head adapted from BUTD (Anderson et al., 2018) by integrating video and text features with simple linear layers. Then a classifier is inserted after the fusion module to perform question answering as... | Compared with previous methods which leverage particular architectures for VQA or include a complicated fusion encoder, S-ViLM is the most efficient and flexible for various vision-language tasks.
S-ViLM achieves better performance than competing methods with the accuracy of 43.5% (+1.4%) and 46.4% (+0.5%) on MSRVTT-QA... | Pre-training datasets. To analyze of effects of pre-training datasets, we report the model performances on selected downstream tasks in Table 5.
In particular, the same model pre-trained on VideoCC achieves the best performance in zero-shot retrieval on MSR-VTT, compared with HowTo100M and WebVid-2M. | S-ViLM also achieves performance gain when the model is fine-tuned on the target MSR-VTT dataset, which further validates advantages of the pre-trained model.
Note that S-ViLM performs favorably against existing methods despite the much smaller size of the pre-training data used in S-ViLM than those in baselines, such ... | In particular, when pre-trained on the same VideoCC dataset, S-ViLM leads to better performance than MCQ. The significant improvement over MCQ shows that our techniques do help to learn better features for downstream tasks.
It is also worth noting that pre-training on VideoCC and ActivityNet performs consistently bette... | A |
Results with multilingual BERT representations in Table 2 show our method’s effectiveness. (Trends with XLM-R are consistent; Appendix A.1.2). Under random sampling evaluation (left block), ContraSim shows superior results over other similarity measures, despite being evaluated on language pairs it hasn’t seen at train... |
We use two multilingual models: multilingual BERT (Devlin et al., 2019)444https://huggingface.co/bert-base-multilingual-cased and XLM-R (Conneau et al., 2020a). We use the XNLI dataset (Conneau et al., 2018), which has natural language inference examples, parallel in multiple languages. Each example in our dataset is ... | We experimentally evaluate ContraSim on standard benchmark for similarity measures – the layer prediction benchmark Kornblith et al. (2019), and two new benchmarks we introduce in this paper: the multilingual benchmark and the image–caption benchmark. In experiments with both language and vision models and multiple dat... | We trained a different encoder for each model, as opposed to the single encoder we trained in all other experiments. This enables ContraSim to be used with representations with different dimensions. Results are summarized in Table 3. We report results with FAISS sampling. Across all pairs, ContraSim achieves superior r... | To further analyze this, we compare the original multilingual representations from the last layer with their projections by ContraSim’s trained encoder.
Figure 4 shows UMAP (McInnes et al., 2018) projections for 10 English sentences and 10 Arabic sentences, before and after ContraSim encoding. The ContraSim encoder was... | D |
In this paper, we focus on calibration methods that both recover rotation and remove distortion from a single image, as specified in Table 1. A pioneering learning-based method was proposed by López-Antequera et al. [36] to address rotation and distortion based on Brown’s quartic polynomial models [6]. Wakai and Yamas... | Synthetic images.
Figure 16 shows the additional qualitative results obtained on synthetic images. Similarly to Figure 6 (main paper), our results are the most similar to the ground-truth images. By contrast, the quality of the recovered images that contain a few arcs was notably degraded when the geometry-based method... | Geometry-based calibration methods can estimate the camera rotation and distortion from a distorted image [3, 35, 44, 65]. However, it is difficult for geometry-based methods to calibrate cameras from images that contain few artificial objects because these methods need to detect many arcs to estimate the VPs. Therefor... | For a Manhattan world, Wildenauer et al. [65] proposed a pioneering geometry-based calibration method from a single image using a constraint based on parallel scene lines. This method addressed distortion using a one-parameter division model [16]. A geometry-based calibration method has been proposed to improve calibra... |
In this paper, we focus on calibration methods that both recover rotation and remove distortion from a single image, as specified in Table 1. A pioneering learning-based method was proposed by López-Antequera et al. [36] to address rotation and distortion based on Brown’s quartic polynomial models [6]. Wakai and Yamas... | C |
η¯1,…,η¯ν−1subscript¯𝜂1…subscript¯𝜂𝜈1\mkern 1.5mu\overline{\mkern-1.5mu\eta\mkern 1.5mu}\mkern 1.5mu_{1},\ldots,%
\mkern 1.5mu\overline{\mkern-1.5mu\eta\mkern 1.5mu}\mkern 1.5mu_{\nu-1}over¯ start_ARG italic_η end_ARG start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT , … , over¯ start_ARG italic_η end_ARG start_POSTSUBSCRIPT ... | We have provided necessary and sufficient conditions for the synchronization of identical linear SISO systems, with a guaranteed convergence rate,
both in the continuous-time and in the discrete-time case. Our conditions do not require any assumption on the graph, whose topology is just assumed to be time-invariant. Mo... |
Our conditions do not require any assumptions on the graph connectivity properties. Still, if we require the synchronization set to be a non-trivial solution, we can consider connected graphs without loss of generality; in fact, for a disconnected graph, synchronization can be achieved (without information exchange) o... |
Given an assigned convergence rate α⋆≥0superscript𝛼⋆0{\alpha^{\star}}\geq 0italic_α start_POSTSUPERSCRIPT ⋆ end_POSTSUPERSCRIPT ≥ 0 of the solutions towards the attractor 𝒜𝒜\mathcal{A}caligraphic_A, we state a list of necessary and sufficient conditions for (continuous- or discrete-time) α⋆superscript𝛼⋆{\alpha^{\s... | identical LTI systems of arbitrary order, connected through an arbitrary graph topology.
Here, we provide this result by introducing a list of necessary and sufficient conditions for uniform global exponential synchronization with guaranteed convergence rate both in the continuous-time and in the discrete-time case. | A |
Finding 9. We find support for HRQ4𝑅subscript𝑄4{}_{{RQ}_{4}}start_FLOATSUBSCRIPT italic_R italic_Q start_POSTSUBSCRIPT 4 end_POSTSUBSCRIPT end_FLOATSUBSCRIPT. Though incorrect conversions are not directly attributable to the use of unusual operators, they may be attributable to operator sequences.
| We omitted measurements of model size, adversarial robustness, and prediction accuracy, to focus instead on measuring the common failure modes (crashing and behavioral differences) identified in our failure analysis.
Our analysis reveals that converters can successfully convert many real model but synthetic models are ... | This indicates the failing models will often contain common operator patterns, suggesting families of sequences that cause errors.
Finally, our comparison of test suite and mismatching models (\Circled3\Circled3\Circled{3}3 in Table 12) shows that the failing models share few sequences with the models used in converte... | Behavioural Differences: We observed a large fraction of behavioural differences (incorrect output) with synthetic models. Compared to real models, which had 20 instances, synthetic models had 320 instances where the inference results exceeded the threshold. The majority of these instances were observed in the tf2onnx ... | Macro analysis: Real and Synthetic models are converted and then differences are measured. For synthetic models, we used tf2onnx or torch.onnx directly.
For real models we used HuggingFace’s converter, which does preprocessing and then calls those converters. | D |
Input-Output Adaptation: Based on the motion reference received (e.g. position, velocity, angle, etc.) in a specific reference frame, the module transforms this input into the desired coordinated frame of the loaded plugin. Similarly, some reference changes can be needed before sending the actuator commands to the aer... | To facilitate the implementation of different aerial platforms, Aerostack2 incorporates an AerialPlatform abstract class responsible for managing the capabilities associated with the direct integration of various aerial platforms into the framework. This abstraction facilitates the integration of new platforms into the... |
In this approach, each component is managed by a function manager, which is responsible for loading the plugins with each specific algorithm and managing how they interact with the rest of the framework. The plugin selector can also provide meta-control features, such as plugin replacement, whereas the input and outpu... |
TF tree generation: The module is in charge of generating the transformation trees [17] that will be used for the rest of the framework, allowing the system to represent information in different coordinate frames. This module is also in charge of managing the origin of the coordinated system in a multi-robot system. | Table IV shows the components used in both simulation and real experiments. For this mission, since we will use HITL simulation, all the modules remained the same in both experiments. In this case, the Web GUI is the component in charge of generating and uploading the mission that each drone is going to perform. We use... | C |
In general, computer scientists have always been fascinated by the possibility of building machines able to express themselves through writing, e.g., by composing poems and short stories, creating paintings, and so on. In particular, the rise of automatic text generation was contextual to the birth of personal computer... | LLMs can involve re-training through plug-and-play attribute classifiers (Dathathri et al., 2020); re-training to produce paragraphs coherent with a given outline (Rashkin et al., 2020); fine-tuning with specific corpora for writing specific text (Sawicki et al., 2022, Wertz and Kuhn, 2022); or fine-tuning to maximize ... | In particular, deep language models, i.e., probabilistic models of in-context token occurrences trained on a corpus of text with deep learning, easily allow the sampling of new text, facilitating and automating natural language generation. For instance, recurrent neural networks with long-short term memory (LSTM) (Hoch... | In order to be able to be part of the never-ending creative cycle mentioned above, LLMs should constantly adapt. Continual learning (Kirkpatrick et al., 2017, Shin et al., 2017) for LLMs (Sun et al., 2020, Wu et al., 2022) represents a promising direction, yet unexplored for creative applications.
| These models tend to scale poorly to long sequences, and they are often unable to capture the entire context. For this reason, current state-of-the-art language models make use of attention (Bahdanau et al., 2015) and transformers (Vaswani et al., 2017). In recent years, several models based on these mechanisms have be... | B |
(a) Existing SFUDA object detection works utilize feature alignment or sample generation to help with the pseudo labeling. These approaches mainly focus on exploiting the source model. (b) Our proposed SUP-ICI utilizes instance-level contrastive learning (CL) to make use of the foreground-background semantic informatio... |
Deep learning has achieved remarkable success in various object detection tasks. In the medical field, deep networks are able to reach clinical expert-level performance, e.g. pulmonary nodule detection [1, 2], etc. Nonetheless, these networks are usually domain-specific. In other words, they work well when the trainin... | However, medical data often involve private information, which makes them not shareable. Consequently, traditional UDA methods, which often rely on access to labeled source data, are not directly applicable in this context.
Thus in this paper, we aim at the more realistic but challenging source-free unsupervised domain... | Source-free unsupervised domain adaptation (SFUDA) denotes the setting of adapting to the target domain given only a well-trained source model and unlabeled target data. One stream of the SFUDA methods is implicitly aligning the feature distribution of the source and target domain using the generative adversarial netwo... | Unsupervised domain adaptation (UDA) is a practical setting where the labeled source data are provided for adapting to the unlabeled target data. Most existing methods adopt feature alignment for UDA object detection. In [3], the authors build image-level and instance-level domain classifiers to implement feature align... | B |
Once a feasible solution of 𝜽𝜽\bm{\theta}bold_italic_θ is obtained, the values for 𝐩Rsuperscript𝐩𝑅\mathbf{p}^{R}bold_p start_POSTSUPERSCRIPT italic_R end_POSTSUPERSCRIPT and the output of ϕRsuperscriptitalic-ϕ𝑅\phi^{R}italic_ϕ start_POSTSUPERSCRIPT italic_R end_POSTSUPERSCRIPT, i.e., the objective value of the de... | Lastly, we discuss the differentiability properties of the function in (12) since training the network architecture in Fig. 1 requires a backward pass that can calculate the gradients in (13). This is a nuanced point since both (12) and the layers used in neural networks are not everywhere differentiable.
Here, we show... | Theorem 4.3 shows that the gauge map is differentiable with respect to the output of the neural layers, and hence enables the computation of backpropagation gradients in (13) and the training of the architecture in Fig. 1.
In the next section, we validate the effectiveness of the proposed learning architecture on a mod... |
Figure 2: In the RLD problem, non-negative orthant constraints can be enforced using ReLU activation in the last neural layer. For the reserve scheduling problem, the Tanh activation is used at the last neural layer and then the hypercubic output is passed through the transformation layers in | In this paper, we overcome the challenge in policy design and solve two-stage DCOPF problems by presenting a neural network (NN)-based architecture that is computationally efficient and also guarantees the feasibility of learned solutions. In particular, our architecture involves two neural networks, one each for the f... | A |
The basis for our approach is to note that, intuitively, a suitable prior should reflect a belief that the higher the semantic similarity between pairs of inputs, the more likely these inputs are to have the same label. Therefore, rather than inspecting the prior predictive at single points in input space, we examine ... | In practice, we can utilise ideas from contrastive learning to learn models with prior predictive distributions that reflect the semantics of different input pairs.
The high-level idea is thus to use prior knowledge in the form of data augmentations, for which we believe that the semantic content of the data should be ... | Note that this is of course only a reasonable assumption in cases where we believe to have sufficiently good knowledge of semantic similarity in our data domain. That is, we need to have a set of data augmentations for the contrastive tasks, for which we can be reasonably certain that the true labels in our downstream ... | Another related line of work is concerned with learning invariances from data in Bayesian models using the marginal likelihood (van der Wilk et al., 2018; Immer et al., 2022). This case is essentially the opposite of our setting, as there, the labels are known but the augmentations are learned, while in our case, the a... | In Fig. 4, we see that the methods that leverage unlabelled data perform the best. In particular, the self-supervised BNN with BALD acquisition achieves the highest accuracy across most numbers of labels, and substantially outperforms the deep ensemble. This confirms the benefit of incorporating unlabelled data in acti... | B |
I(ri):=F(ri)−F(ri−1).assign𝐼subscript𝑟𝑖𝐹subscript𝑟𝑖𝐹subscript𝑟𝑖1{I}(r_{i}):={F}(r_{i})-{F}(r_{i-1}).italic_I ( italic_r start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ) := italic_F ( italic_r start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ) - italic_F ( italic_r start_POSTSUBSCRIPT italic_i - 1 end_POSTSUB... | Under H0subscript𝐻0H_{0}italic_H start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT, the local ecdf’s are equal in distribution and 𝒮¯Tsubscript¯𝒮𝑇\bar{\mathscr{S}}_{T}over¯ start_ARG script_S end_ARG start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT approximates the common cdf 𝒮𝒮\mathscr{S}script_S. Under HAsubscript𝐻𝐴H_{A}... | The finite sample performance and the presence of outliers is particularly relevant in our context since genomic data applications are typically in the regime of T<100𝑇100T<100italic_T < 100 and n<10K𝑛10𝐾n<10Kitalic_n < 10 italic_K.
In Section 4.2.1, we elaborate on this and introduce a data-adaptive function that ... | which characterizes the measure ν~tsubscript~𝜈𝑡\tilde{\nu}_{t}over~ start_ARG italic_ν end_ARG start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT up to isometry by subsection 3.2. In order to test the hypothesis that the marginal distribution is constant over time against the alternative of the distribution being time-de... | However, the cdf is time-dependent under the alternative and an aggregrate F𝐹Fitalic_F at most reflects the average distribution pattern.
To construct the weight function, we need an empirical version of the most suitable choice for F𝐹Fitalic_F in our case. For this, we use the time-averaged empirical cdf | D |
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