This supplementary provides additional experiments as well as details that are required to reproduce our results. These were not included in the main paper due to space limitations. The supplementary is arranged as follows: Section A: Details on Modelling - Section A.1 Details of Theoretical Modelling - Section A.2 Additional Details on CLEAM Algorithm - Section A.3 Details on Fairness Metric - Section A.4 Details of Significance of the Baseline Errors Section B: Deeper Analysis on Error in Fairness Measurement Section C: Validating Statistical Model for Classifier Output - Section C.1 Validation of Sample-Based Estimate vs Model-Based Estimate - Section C.2 Goodness-of-Fit Test: ˆpfrom the Real GANs with Our Theoretical Model Section D: Additional Experimental Results - Section D.1 Experimental Results with Standard Deviation - Section D.2 Experimental Setup for Diversity - Section D.3 Measuring Varying Degrees of Bias (Gender and BlackHair) - Section D.4 Measuring Varying Degrees of ...

S1.1 Step-by-step derivation of min-max optimization in Section 2.2.1 By substituting Eq. 2 into Eq. 1 in the main manuscript, we can obtain the objective function of subscript z (we temporarily drop ifor clarity): J(z) = max Since z might be in high dimensional space, solving such a large system of linear equations under the constraint |z| 1is oftentimes computationally challenging. In order to find a practical solution for z that satisfies the constrained minimization problem in Eq. By setting zl as point of coincidence, we can find a separable majorizer of M(z) by adding the non-negative function (z zl) (βI Gx Gx)(z zl) (S6) 37th Conference on Neural Information Processing Systems (NeurIPS 2023). Note, to unify the format, we use the matrix transpose property in Eq. Then, the next step is to find z RN that minimizes z z 2bz subject to the constraint |z| 1. Let's first consider the simplest case where z is a scalar: argmin If b 1, then the solution is z = b.

The dataset and the baseline code will be made publicly available in a dedicated GitHub repository upon acceptance. License TempEL is distributed under Creative Commons Attribution-ShareAlike 4.0 International license (CCBY-SA 4.0).1 Maintenance The maintenance and extension to further temporal snapshots of TempEL will be carried out by the authors of the paper. Additionally, we will make the code public to create potential new variations and extensions of TempEL using a number of hyperparameters (see Sections A.4 and A.5 for further details). A.2 Datasheet for TempEL In this section we provide a more detailed documentation of the dataset with the intended uses. We base ourselves on the datasheet proposed by [1]. A.2.1 Motivation For what purpose was the dataset created? The TempEL dataset was created to evaluate how the temporal change of anchor mentions and that of target Knowledge Base (KB; i.e., modification or creation of new entities) affects the entity linking (EL) task. This contrasts with the currently existing datasets [9, 7, 8, 6], which are associated with a single version of the target KB such as the Wikipedia 2010 for the widely adopted CoNLL-AIDA[2] dataset. We expect that TempEL will encourage research in devising new models and architectures that are robust to temporal changes both in mentions as well as in the target KBs. Who created the dataset and on behalf of which entity?

A.1 Scenario with only stragglers The hyperparameter settings for Sageflow are shown in Table 1. For the schemes ignore stragglers and wait for stragglers combined with FedAvg, we decayed the learning rate during training. For the FedAsync scheme of [7], we take a polynomial strategy with hyperparameters a= 0.5, α= 0.8, and decayed γ during training. A.2 Scenario with only adversaries Data poisoning and model poisoning attacks: Table 2 describes the hyperparameters for Sageflow with only adversaries, under data poisoning and model poisoning attacks. For RFA of [5], the maximum iteration is set to 10. In this setup, the learning rate is decayed for all three schemes (Sageflow, RFA, FedAvg).

Since the PDE in Eq. 5 in the main manuscript is equivalent to the E-L equation of the quadratic

After 2D ray sampling process depicted in Sec. The total number of parameters of our network is 25M. In Section 3.4 of the main manuscript, we introduce the 3D intersection-aware hand feature This process enables the extraction of global information from the hand joints. Our training process involves the utilization of five distinct types of data samples. In this section, we provide the corresponding table (Tab.

We summarize our methods for computing/estimating the gradient of the log determinant arising inmaximum likelihood training ofrectangular flows. Algorithm 2showstheexactmethod, where jvp(f,z,)denotes computingJ[f](z) usingforward-mode AD,and i Rd isthei-thstandard basis vector, i.e. a one-hot vector with a1 on its i-th coordinate. Note that / θlogdetAθ is computed using backpropagation. Thefor loop is easily parallelized in practice.

We provide additional qualitative comparative results on both ShapeNetandPix3DinFig8,9.

Eqn. 3 represents the solution for a stationary energy with respect to the prospective voltage ŭ Here we consider a generalization of the energy function from the main manuscript that includes arbitrary "connectivity functions" f with parameters θ: E(ŭ Pseudo-code for our vanilla implementation can be found in Algorithm 1. Algorithm 1 Pseudo-code for the multi-layer implementation of Latent Equilibrium (LE) Figure 5: Learning to mimic a teacher microcircuit with LE. For the interneurons, the somatic membrane potentials of the pyramidal neurons in the layer above serve as targets. First, the output rate of the neurons must depend on the prospective voltage: ϕ (u) ϕ (ŭ). Note that this includes also the rates in the calculation of dendritic membrane potentials (Eqns. Learning is split into two stages: first, the learning of the so-called self-predicting state and afterwards the learning of the actual task.