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Knowledge distillation (KD) is an effective model compression method that can transfer the internal capabilities of large language models (LLMs) to smaller ones. However, the multi-modal probability distribution predicted by teacher LLMs causes difficulties for student models to learn. In this paper, we first demonstrate the importance of multi-modal distribution alignment with experiments and then highlight the inefficiency of existing KD approaches in learning multi-modal distributions. To address this problem, we propose Ranking Loss based Knowledge Distillation (RLKD), which encourages the consistency of the ranking of peak predictions between the teacher and student models. By incorporating word-level ranking loss, we ensure excellent compatibility with existing distillation objectives while fully leveraging the fine-grained information between different categories in peaks of two predicted distribution. Experimental results demonstrate that our method enables the student model to better learn the multi-modal distributions of the teacher model, leading to a significant performance improvement in various downstream tasks.

Several recent works have focused on carrying out non-asymptotic convergence analyses for AC algorithms. Recently, a two-timescale critic-actor algorithm has been presented for the discounted cost setting in the look-up table case where the timescales of the actor and the critic are reversed and only asymptotic convergence shown. In our work, we present the first two-timescale critic-actor algorithm with function approximation in the long-run average reward setting and present the first finite-time non-asymptotic as well as asymptotic convergence analysis for such a scheme. We obtain optimal learning rates and prove that our algorithm achieves a sample complexity of {$\mathcal{\tilde{O}}(\epsilon^{-(2+\delta)})$ with $\delta >0$ arbitrarily close to zero,} for the mean squared error of the critic to be upper bounded by $\epsilon$ which is better than the one obtained for two-timescale AC in a similar setting. A notable feature of our analysis is that we present the asymptotic convergence analysis of our scheme in addition to the finite-time bounds that we obtain and show the almost sure asymptotic convergence of the (slower) critic recursion to the attractor of an associated differential inclusion with actor parameters corresponding to local maxima of a perturbed average reward objective. We also show the results of numerical experiments on three benchmark settings and observe that our critic-actor algorithm performs the best amongst all algorithms.

Use real word data to evaluate the performance of the electrocardiographic markers of GEH as features in a machine learning model with Standard ECG features and Risk Factors in Predicting Outcome of patients in a population referred to a tertiary cardiology hospital. Patients forwarded to specific evaluation in a cardiology specialized hospital performed an ECG and a risk factor anamnesis. A series of follow up attendances occurred in periods of 6 months, 12 months and 15 months to check for cardiovascular related events (mortality or new nonfatal cardiovascular events (Stroke, MI, PCI, CS), as identified during 1-year phone follow-ups. The first attendance ECG was measured by a specialist and processed in order to obtain the global electric heterogeneity (GEH) using the Kors Matriz. The ECG measurements, GEH parameters and risk factors were combined for training multiple instances of XGBoost decision trees models. Each instance were optmized for the AUCPR and the instance with higher AUC is chosen as representative to the model. The importance of each parameter for the winner tree model was compared to better understand the improvement from using GEH parameters. The GEH parameters turned out to have statistical significance for this population specially the QRST angle and the SVG. The combined model with the tree parameters class had the best performance. The findings suggest that using VCG features can facilitate more accurate identification of patients who require tertiary care, thereby optimizing resource allocation and improving patient outcomes. Moreover, the decision tree model's transparency and ability to pinpoint critical features make it a valuable tool for clinical decision-making and align well with existing clinical practices.

Population protocols are a model of distributed computation in which an arbitrary number of indistinguishable finite-state agents interact in pairs to decide some property of their initial configuration. We investigate the behaviour of population protocols under adversarial faults that cause agents to silently crash and no longer interact with other agents. As a starting point, we consider the property ``the number of agents exceeds a given threshold $t$'', represented by the predicate $x \geq t$, and show that the standard protocol for $x \geq t$ is very fragile: one single crash in a computation with $x:=2t-1$ agents can already cause the protocol to answer incorrectly that $x \geq t$ does not hold. However, a slightly less known protocol is robust: for any number $t' \geq t$ of agents, at least $t' - t+1$ crashes must occur for the protocol to answer that the property does not hold. We formally define robustness for arbitrary population protocols, and investigate the question whether every predicate computable by population protocols has a robust protocol. Angluin et al. proved in 2007 that population protocols decide exactly the Presburger predicates, which can be represented as Boolean combinations of threshold predicates of the form $\sum_{i=1}^n a_i \cdot x_i \geq t$ for $a_1,...,a_n, t \in \mathbb{Z}$ and modulo prdicates of the form $\sum_{i=1}^n a_i \cdot x_i \bmod m \geq t $ for $a_1, \ldots, a_n, m, t \in \mathbb{N}$. We design robust protocols for all threshold and modulo predicates. We also show that, unfortunately, the techniques in the literature that construct a protocol for a Boolean combination of predicates given protocols for the conjuncts do not preserve robustness. So the question remains open.

We study the problem of drawing samples from a logconcave distribution truncated on a polytope, motivated by computational challenges in Bayesian statistical models with indicator variables, such as probit regression. Building on interior point methods and the Dikin walk for sampling from uniform distributions, we analyze the mixing time of regularized Dikin walks. Our contributions are threefold. First, for a logconcave and log-smooth distribution with condition number $\kappa$, truncated on a polytope in $\mathbb{R}^n$ defined with $m$ linear constraints, we prove that the soft-threshold Dikin walk mixes in $\widetilde{O}((m+\kappa)n)$ iterations from a warm initialization. It improves upon prior work which required the polytope to be bounded and involved a bound dependent on the radius of the bounded region. Moreover, we introduce the regularized Dikin walk using Lewis weights for approximating the John ellipsoid. We show that it mixes in $\widetilde{O}((n^{2.5}+\kappa n)$. Second, we extend the mixing time guarantees mentioned above to weakly log-concave distributions truncated on polytopes, provided that they have a finite covariance matrix. Third, going beyond worst-case mixing time analysis, we demonstrate that soft-threshold Dikin walk can mix significantly faster when only a limited number of constraints intersect the high-probability mass of the distribution, improving the $\widetilde{O}((m+\kappa)n)$ upper bound to $\widetilde{O}(m + \kappa n)$. Additionally, per-iteration complexity of regularized Dikin walk and ways to generate a warm initialization are discussed to facilitate practical implementation.

The partitioned approach for the numerical integration of power system differential algebraic equations faces inherent numerical stability challenges due to delays between the computation of state and algebraic variables. Such delays can compromise solution accuracy and computational efficiency, particularly in large-scale system simulations. We present an $O(h^2)$-accurate prediction scheme for algebraic variables based on forward and backward difference formulas, applied before the correction step of numerical integration. The scheme improves the numerical stability of the partitioned approach while maintaining computational efficiency. Through numerical simulations on a lightly damped single machine infinite bus system and a large-scale 140-bus network, we demonstrate that the proposed method, when combined with variable time-stepping, significantly enhances the numerical stability, solution accuracy, and computational performance of the simulation. Results show reduced step rejections, fewer nonlinear solver iterations, and improved accuracy compared to conventional approaches, making the method particularly valuable for large-scale power system dynamic simulations.

The B-spline copula function is defined by a linear combination of elements of the normalized B-spline basis. We develop a modified EM algorithm, to maximize the penalized pseudo-likelihood function, wherein we use the smoothly clipped absolute deviation (SCAD) penalty function for the penalization term. We conduct simulation studies to demonstrate the stability of the proposed numerical procedure, show that penalization yields estimates with smaller mean-square errors when the true parameter matrix is sparse, and provide methods for determining tuning parameters and for model selection. We analyze as an example a data set consisting of birth and death rates from 237 countries, available at the website, ''Our World in Data,'' and we estimate the marginal density and distribution functions of those rates together with all parameters of our B-spline copula model.

The use of neural networks for solving differential equations is practically difficult due to the exponentially increasing runtime of autodifferentiation when computing high-order derivatives. We propose $n$-TangentProp, the natural extension of the TangentProp formalism \cite{simard1991tangent} to arbitrarily many derivatives. $n$-TangentProp computes the exact derivative $d^n/dx^n f(x)$ in quasilinear, instead of exponential time, for a densely connected, feed-forward neural network $f$ with a smooth, parameter-free activation function. We validate our algorithm empirically across a range of depths, widths, and number of derivatives. We demonstrate that our method is particularly beneficial in the context of physics-informed neural networks where \ntp allows for significantly faster training times than previous methods and has favorable scaling with respect to both model size and loss-function complexity as measured by the number of required derivatives. The code for this paper can be found at //github.com/kyrochi/n\_tangentprop.

In the burgeoning field of medical imaging, precise computation of 3D volume holds a significant importance for subsequent qualitative analysis of 3D reconstructed objects. Combining multivariate calculus, marching cube algorithm, and binary indexed tree data structure, we developed an algorithm for efficient computation of intrinsic volume of any volumetric data recovered from computed tomography (CT) or magnetic resonance (MR). We proposed the 30 configurations of volume values based on the polygonal mesh generation method. Our algorithm processes the data in scan-line order simultaneously with reconstruction algorithm to create a Fenwick tree, ensuring query time much faster and assisting users' edition of slicing or transforming model. We tested the algorithm's accuracy on simple 3D objects (e.g., sphere, cylinder) to complicated structures (e.g., lungs, cardiac chambers). The result deviated within $\pm 0.004 \text{cm}^3$ and there is still room for further improvement.

The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.