Reverse kl divergence. 2020; Bhattacharyya et al.

Reverse kl divergence The other type of explanation you might come across usually relies on information theory to explain the The entry point to learning generative AI fundamentals is through the REVERSE Kullback-Leibler divergence. ruMark Gales: Depa 最近的一个论文 Beyond Reverse KL: Generalizing Direct Preference Optimization with Diverse Divergence Constraints 指出说： 实现与 human 对齐的常见技术是 RLHF，最近的论文提出了 DPO 方法，这种方法是 pler is the reverse KL divergence due to its tractability. For instance, given our distributions \(p\) and \(q\) we define {KL}(q \vert\vert p)\) the backward (or reverse) KL divergence. 16240 Chaoqi Wang, Yibo Jiang, Chenghao Yang, Han Liu, Yuxin Chen forward KL divergence in enhancing model diversity and explores the impact of different divergence constraints. This means that when the target distribution p d(x) contains multiple distant modes, the model p θ(x) trained by reverse KL will underestimate the Gaussian Mixture Reduction Using Reverse Kullback-Leibler Divergence Tohid Ardeshiri, Umut Orguner, Emre Ozkan¨ Abstract—We propose a greedy mixture reduction algorithm which is capable of pruning mixture components as well as merging them based on the Kullback-Leibler divergence (KLD). 이는 기존에 우리가 알던 KL divergence의 형태와 By introducing a compensatory operation using reverse Kullback-Leibler divergence, our method can improve the modeling of the extremely small values in the negative from the teacher and preserve the learning capacity for the positive. infer the value of a random variable given the value of another random variable) as optimization problems (i. [2] See also. We re-formulate KD of LLMs into two stages: first optimizing and objective consisting of implicit reward and reverse KL divergence and then improving the preference probability of teacher outputs over student outputs. optimization problems using reverse Kullback-Leibler (KL) divergence, and derives a new optimization method using forward KL divergence, instead of reverse KL divergence in the optimization problems. where P(X) is the true distribution we want to approximate, Q(X) is the approximate distribution. However, the most significant limitation of reverse KL is the mode collapse phenomenon due to its mode-seeking behavior (Bishop,2006). (2005), re-verse KL is zero forcing because p = 0 forces q=0, and the forward KL tends to model the main mass as requiring q >0 whenever p>0. 変分推論など，Pが真の分布(ex. This can pler is the reverse KL divergence due to its tractability. KL [6] BEYOND REVERSE KL: GENERALIZING DIRECT PREFERENCE OPTIMIZATION WITH DIVERSE DIVERGENCE CONSTRAINTS [7] Rethinking Kullback-Leibler Divergence in Knowledge Distillation for Large Language by maximizing the likelihood – equivalent to minimizing the KL divergence KL[ XkpX]. VB methods allow us to re-write statistical inference problems (i. Figure (1) demonstrates the computational process of the BDD tech-nique. To accelerate generation speed, recent approaches distill a multi-step diffusion model into a single-step student generator via variational score distillation, which matches the distribution of samples generated by the Figure 1. Our main contributions are as follows: • We propose a comprehensive mathematical framework for reverse KL-regularized RLHF with multiple reference models and provide the exact solution for this problem and reverse Kullback-Leibler (KL) divergence as the BC regularizer based on the TD3 algorithm. This is sometimes called the “backward” or “reverse” KL. 1 Supremum of Reverse KL Divergence Between Gaussians The following Theorem 1 gives the supremum of reverse KL divergence when forward KL The KL Divergence could be computed as follows:. 先介绍介绍基础知识，KL散度在 知识蒸馏 KD中有广泛应用，也广为大家所使用。 不过，KL散度并不是对称的，正向KL不 First, we show that the appropriate training criterion for Prior Networks is the reverse KL-divergence between Dirichlet distributions. This addresses issues in the nature of the training data target distributions, enabling prior networks to be successfully trained on classification tasks with arbitrarily many classes, as well as the reverse Kullback-Leibler divergence (RKL) between q and p, i. Why Abstract page for arXiv paper 2309. Reverse KL Let Pand Qbe two distributions with probability density functions pand q, where qis an approximation of p. (), and implement several strategies to optimize the distillation process. (c) We propose to use path gradients and Reverse KL Divergence as Bregman Divergence. 16240: Beyond Reverse KL: Generalizing Direct Preference Optimization with Diverse Divergence Constraints The increasing capabilities of large language models (LLMs) raise opportunities for artificial general intelligence but concurrently amplify safety concerns, such as potential misuse of AI Abstract Kullback-Leiber divergence has been widely used in Knowledge Distillation (KD) to compress Large Language Models (LLMs). However, there are two kinds of KL Divergences: Forward and Reverse. This addresses issues in the nature of the training data target distributions, enabling prior networks to be successfully trained on classification tasks with arbitrarily many classes, as well as 最近的一个论文 Beyond Reverse KL: Generalizing Direct Preference Optimization with Diverse Divergence Constraints 指出说： 实现与 human 对齐的常见技术是 RLHF，最近的论文提出了 DPO 方法，这种方法是 RLHF + Reverse KL 的近似，DPO 的优势是不再需要分两阶段训练 reward 模型进而相比 RLHF The objective is to minimize the reverse KL divergence between the true posterior and the approximate distribution. In particular, we investigate the difference between the forward and reverse KL divergences, with varying degrees of entropy regularization; these are chosen because they KL (p model kp data), which is usually referred to as the reverse KL divergence [20, 11, 13, 28]. . via Reverse KL divergence (RKL) or forward KL divergence (FKL). KL forwardとKL reverseの違い. Forward KL divergence corresponds to $D_{KL}(p|q)$, and reverse corresponds to $D_{KL}(q|p)$. Contrary to prior assertions that reverse Kullback-Leibler (RKL) divergence is mode-seeking and thus preferable over the mean-seeking forward Kullback-Leibler (FKL) divergence, this study empirically and theoretically 文章浏览阅读823次，点赞23次，收藏26次。近来有很多文章尝试做 LLM 的蒸馏，有几篇文章都提到说，使用 Reverse KL 会比 Forward KL 好，并且给出了自己的理由，事实真的如此么？先介绍介绍基础知识，KL 散度在知 This method leverages a reverse KL-divergence-based knowledge distillation approach, ensuring significant forget quality without compromising the model’s overall performance. forward KLKL divergence는 확률 분포 간 거리를 재는 척도로 data distribution p(x)와 model distribution q(x) 간의 거리를 잴 수 있기 때문에 loss function으로 많이 사용한다. We can exchange forward and reverse KL divergence in MPO algorithm. This means that when the target distribution p d(x) contains multiple distant modes, the model p θ(x) trained by reverse KL will underestimate the Phaseless imaging refers to reconstructing an image from its intensity-only measurements, a task complicated by noise and outliers in real-world applications. To address this challenge, we propose RKLD, a novel \textbf{R}everse \textbf{KL}-Divergence-based Knowledge \textbf{D}istillation unlearning algorithm for LLMs targeting the unlearning of personal information. In this paper, we introduce Diffusive KL Divergence (DiKL), a reverse-KL-based divergence that promotes mode-covering behavior, in contrast to the standard reverse KL, which tends to focus on mode-seeking: mode-seeking behavior of reverse KL hinders effective approximation of multi-modal tar-get distributions. We have a few comments and suggestions for the work: The comparison of forward vs reverse KL divergence as the objective criteria resembles the choice of mode vs. In this paper, we develop novel robust phase retrieval algorithms based on the minimization of reverse Kullback-Leibler divergence (RKLD) within the Wirtinger Flow (WF) framework. HTML. We can eliminate such di erence. This addresses issues in the nature of the training data target distributions, enabling prior networks to be successfully trained on classification tasks with arbitrarily many classes, as well as improving out First, we show that the appropriate training criterion for Prior Networks is the \emph{reverse} KL-divergence between Dirichlet distributions. The KL-divergence is an example of a Bregman divergence. When conducting the computation, the KL divergence was separated into two categories, namely forward-KL and reverse-KL, with different components 3 GitHub is where people build software. 2020-08-24. Sampling of a given target density X(x) – sample from the simple distribution Z(z) and minimize a divergence between the distribution generated by the forward-transformation x = FXZ(z) and X(x). In accordance with the following lecture notes, reverse KL can cause q under-estimate the support of p while forward KL can cause the overestimate. reverse KL divergence loss. Using the reverse (exclusive) KL as the variational objective is the common approach, though lately I stumbled upon some interesting works that use the forward (inclusive) KL Gaussian Mixture Reduction Using Reverse Kullback-Leibler Divergence Tohid Ardeshiri, Umut Orguner, Emre Ozkan¨ Abstract—We propose a greedy mixture reduction algorithm which is capable of pruning mixture components as well as merging them based on the Kullback-Leibler divergence (KLD). pler is the reverse KL divergence due to its tractability. To address this, we propose to minimize the reverse KL along diffusion trajectories of both model and target densities. ru RKLD: Reverse KL-Divergence-based Knowledge Distillation for Unlearning Personal Information in Large Language Models. It might happen that the forward KL divergence 1 KL(pjjq) is very small but the reverse KL divergence KL(pjjq) = KL( ) is very large. The typical example for using KL to optimize a distribution To address this, we propose a theoretically grounded approach that replaces forward KL divergence-whose mass-covering behavior risks overfitting to imperfect weak Variational inference: In Bayesian inference, reverse KL is often used to approximate the intractable true posterior distribution with a simpler distribution. Reverse KL divergence's zero-forcing effect prioritizes high-confidence predictions, effectively mitigating the influence of unreliable weak supervision. T, the Kullback-Leibler (KL) divergence [19] is defined as KL(P k Q)= Z X p(x)log p(x) q(x) dx, (1) where p and q are the probability densities of P and Q respectively, and x 2 Rn. Reinforcement learning: In policy optimization, forward KL is used to enforce a trust region, ensuring that the updated policy remains close to the old policy, avoiding large and potentially catastrophic updates. It is also generally difficult to assess the quality of a VI ap-proximation on downstream tasks based on the value of the RKL divergence [Yao et al. However, the most significant limitation of reverse KL is the mode collapse phenomenon due to its mode-seeking behavior (Bishop, 2006). Distributionally Robust Optimization For Language Modeling; Optimizing Language Models for Human Preferences is a Causal Inference Problem; Title: Reverse KL-Divergence Training of Prior Networks: Improved Uncertainty and Adversarial Robustness Author: Andrey Malinin and Mark Gales am969@yandex-team. To address this, we pro-pose to minimize the reverse KL along dif-fusion trajectories of both model and target densities. Fact. 1 Task Definition As mentioned above, different works have different definitions of unlearning. In addition, we provide a statistical analysis of these scenarios. Murphy, "Machine Learning Ying considered three different types of strongly convex functions g i in [28]: Kullback-Leibler divergence, reverse Kullback-Leibler divergence, and Hellinger divergence. In practice, we don't have access to the true distribution, we only have access to NeurIPS 2019: Reverse KL-Divergence Training of Prior Networks: Improved Uncertainty and Adversarial RobustnessCode: PriorNetworksAndrey Malinin: Yandex Research am969@yandex-team. Recently Updated. In particular, we investigate the difference between the forward and reverse KL divergences, with varying degrees of entropy regularization. More than 150 million people use GitHub to discover, fork, and contribute to over 420 million projects. In this blog post, we delve into knowledge distillation techniques for Large Language Models (LLMs), with a particular focus on using Kullback-Leibler (KL) Divergence as the optimization objective. Contrary to prior assertions that reverse Kullback-Leibler (RKL) divergence is mode-seeking and thus preferable over the mean-seeking forward Kullback-Leibler (FKL) divergence, this study empirically and theoretically demonstrates that KL-divergence (KL) is an inappropriate optimization criterion and instead propose to train Prior Networks with the reverse KL-divergence (RKL) between the model and a target Dirichlet distribution. Beyond Reverse KL: Generalizing Direct Preference Optimization with Diverse Divergence Constraints arXiv - CS - Artificial Intelligence Pub Date : 2023-09-28, DOI: arxiv-2309. As stated earlier, KL-divergence is non-symmetric (Shlens, 2014), i. , more diverse state visitation distribution). Contrary to prior assertions that reverse Kullback-Leibler (RKL) divergence is mode-seeking and thus preferable over the mean-seeking forward Kullback-Leibler (FKL) divergence, this study empirically and theoretically demonstrates that I have a question regarding the forward or reverse KL divergence used in variational inference. The function H(p) is non-negative and concave on the space of all reverse Kullback–Leibler divergence KL(q;p) from the normalizing flow model qto the target density pand show a drastic deterioration in approximation quality with growing system size or as a etc. There are two types of KL divergence: forward and reverse. It is, however, necessary to use auxiliary losses, such as cross-entropy, to yield competitive classification performance. These conclusions quantify the approximate symmetry of small KL divergence between Gaussians. KL divergence; I study statistics, machine Hence the need to distinguish the KL-divergence from its dual, the so-called "reverse KL-divergence". Ask Question Asked 1 month ago. (); Agarwal et al. However, by meticulously addressing the Karush–Kuhn–Tucker (KKT) conditions, specif- Robustness to noise and outliers is a desirable trait in phase retrieval algorithms for many applications in imaging and signal processing. For example, it's unclear how RKLD would perform in edge cases where the personal information is deeply intertwined with Divergence f (t) Kullback Leibler (KL) tlog t Reverse KL (RKL) log t Jensen Shannon (JS) (t+1)log(t+1 2)+ tlog t Total variation distance (TVD) 1 2 jt 1j Table 1: Common divergence functions and their corre-sponding choices of f . Forward KL divergence, KL [p k q], encourages the student model to t the entire teacher distribu-tion, including low-probability regions. Kullback-Leiber divergence has been widely used in Knowledge Distillation (KD) to compress Large Language Models (LLMs). TL,DR: We provide a deeper insight into forward KL and reverse KL in the KD for LLM and then propose a novel AKL based on the analysis. 予 如果两者越接近，则KL散度越小，反之则越大。 反向 KL 散度与正向 KL 散度. Both the KL-divergence and the reverse KL-divergence are examples of f-divergences. In Part 1, we introduced the reverse Kullback-Leibler divergence (RKLD) as a loss function for phase retrieval in the presence of noise and outliers. In particular, we investigate the difference between the forward and reverse KL divergences, with varying degrees of entropy regularization; these are chosen because they Training generative models to sample from unnormalized density functions is an important and challenging task in machine learning. Bichen Wang, Yuzhe Zi, Yixin Sun, Yanyan Zhao, Bing Qin. It is a non-symmetric distance function, and each arrangement has its own interesting property, especially when we use it in optimization Definition (Kullback-Leibler divergence) For discrete probability distributions $P$ and $Q$ defined on the same probability space, $\chi$, the Kullback-Leibler divergence from KL Divergence Forward: D KL (p(x)||q(x)) KL Divergence Reverse: D KL (q(x)||p(x)) KL Divergence can be used as a loss function to minimize in deep learning model. More on this choice below. 2 Our Proposed f -DISTILL Framework To this end, we propose a generalized f -DISTILL forward KL and reverse KL in the KD for LLMs and then propose a novel AKL. Contrary to prior assertions that reverse Kullback-Leibler (RKL) divergence is mode-seeking and thus preferable over the mean-seeking forward Kullback-Leibler (FKL) divergence, this study empirically and theoretically demonstrates that Official PyTorch implementation of the paper Training Neural Samplers with Reverse Diffusive KL Divergence. Viewed 7 times 0 $\begingroup$ Throughout I will In other words, the KL divergence from p to q isn’t necessarily the same as from q to p. mean seeking form of the objective in variational inference, respectively (in this case applied with a Dirichlet distribution). KL(P||Q) は「PからQへのdivergence」と読む. KL散度有两种常见的计算方式：正向 KL 散度（Forward KL Divergence）与反向 KL 散度（Reverse KL Divergence）。它们有着不同的优化目标和物理意义。 1. 05 Nov 2019. Knowledge distillation is a powerful tool to reduce model size while maintaining comparable performance, making it especially useful in scenarios with constrained around 1, then the corresponding f-divergence for two distributions pand qis defined as D f(p,q) = E q(x) f p(x) q(x) . I am not clear about the underlying logic. This brings obstacles in the applications This is due to () > whenever () > to make sure KL divergence stays finite. To remember this 이번 포스팅에서는 loss function으로 많이 사용되는 KL divergence 및 cross-entropy에 대해 정리해 보려고 합니다! 1. This addresses issues in the nature of the training data target distributions, enabling prior networks to be successfully trained on classification tasks with arbitrarily many classes, as well as We propose an algorithm to estimate the path-gradient of both the reverse and forward Kullback--Leibler divergence for an arbitrary manifestly invertible normalizing flow. Why it might be preferable to use reverse KL instead of forward KL. 2022). , strong BC regularization on the states with narrow action coverage, and vice versa) but also avoids selecting OOD actions thanks to the Traditional training methods often rely on the reverse Kullback-Leibler (KL) divergence due to its tractability. First, we show that the appropriate training criterion for Prior Networks is the reverse KL-divergence between Dirichlet distributions. Coupled with an RKLD-based spectral initialization technique, we presented three In this work, we investigate approximate greedification when reducing the KL divergence between the parameterized policy and the Boltzmann distribution over action values. A common choice is the reverse KL divergence KL[pXk X]. We then experiment with changing its objective function from forward KL divergence to reverse KL divergence, inspired by Gu et al. The reverse KL without entropy regularization Kullback-Leiber divergence has been widely used in Knowledge Distillation (KD) to compress Large Language Models (LLMs). Forward KL Forward KL(inclusive KL)은 아래와 같이 정의한다. The KL divergence is the most frequent choice in the context of variational inference. 正向 KL 散度定义为： In using the reverse KL divergence above, I've glossed over an important detail: We can't actually compute the second term \(\mathbb{E}_{x \sim q_\theta}[\log p(x)]\) because it requires evaluating the true probability \(p(x)\) of a sample \(x \sim q_\theta\). The algorithm is distinct from the well-known Runnalls In this work, we investigate approximate greedification when reducing the KL divergence between the parameterized policy and the Boltzmann distribution over action values. (We will upload this Technical Note to arXiv shortly; for With this concept, this paper reveals that the optimizations of both value function and policy on the traditional RL are consistent with reverse Kullback–Leibler (KL) divergence optimization (named RKL-RL in this paper). , 2016]. K. The use of reverse KL-divergence is an innovative twist that aligns well with the goal of unlearning sensitive data while retaining useful knowledge. A reverse KL is more appropriate than a forward KL when the policy is misspecified. Essentially, it does not fundamentally enhance the DPO algorithm itself As we can see from KL divergence calculations, q_1 is closer to our Gaussian mixture distribution. PDF. The forward/reverse formulations of KL divergence are distinguished by having mean/mode-seeking behavior. This means that when the target distribution p d(x) contains multiple distant modes, the model p θ(x) trained by reverse KL will underestimate the 渺渺兮予怀，望美人兮天一方. Furthermore, it is also difficult to train Prior Networks using this criterion on complex datasets with many classes. Theoretically, we extend existing bounds and derive tighter lower bounds for both forward and reverse KL divergence, establishing that reverse KL achieves at least comparable guarantees to Kullback-Leibler (KL) divergence; Evidence Lower Bound (ELBO) Rationale. 3 Bringing new insights to existing reinforcement learning algorithm. In sections 3 and 4 of this paper it is shown, both theoretically and empirically on synthetic data, that Reverse Kullback-Leibler Divergence Nazia Afroz Choudhury, Bariscan Yonel, Birsen Yazici Abstract Robustness to noise and outliers is a desirable trait in phase retrieval algo-rithms for many applications in imaging and signal processing. May 30, 2024 Technical Tips . Unfortunately, reverse KL divergence cannot be computed because the expert distribution is unknown. However, the mode-seeking behavior of reverse KL hinders effective approximation of multi-modal target distributions. Traditional training methods often rely on the reverse Kullback-Leibler (KL) divergence due to its tractability. Our experiments on the TOFU unlearning benchmark demonstrate that RKLD outperforms existing methods in both forget quality and model utility, especially with larger First, we show that the appropriate training criterion for Prior Networks is the \emph{reverse} KL-divergence between Dirichlet distributions. 2020; Bhattacharyya et al. Theoretically, we extend existing bounds and derive tighter lower bounds for both forward and reverse KL divergence, establishing that reverse KL achieves at least comparable guarantees to optimization problems using reverse Kullback-Leibler (KL) divergence, and derives a new optimization method using forward KL divergence, instead of reverse KL divergence in the optimization problems. KL divergence는 확률 분포를 대입하는 Different from the reverse KL divergence, we initially find that a naive derivation results in an excessively complex relationship between the reward and optimal policy for other divergences, largely due to the normalizing con-stant. In particular, Equation (1) is known as the forward KL divergence from P to Q, whereas reverse KL divergence refers to KL(Q k P). In this paper, we develop novel robust phase retrieval algorithms based on the minimization DPKD utilizes distribution divergence to represent the preference loss and implicit reward function. This post will try to explain the differences between KL and reverse KL divergences and demonstrate it using a small generative model trained on mixture of KL divergenceについての感覚的なところを備忘用にまとめておく. Firstly, KL divergence is not symmetric. To address this, Abstract. We use a teacher-student distillation setup with the BabyLLaMa model (Timiryasov and Tastet, 2023) as a backbone. (a) Forward and reverse KL divergences being respectively mode covering and mode seeking. In this work, we investigate approximate greedification when reducing the KL divergence between the parameterized policy and the Boltzmann distribution over action values. See (Abdolmaleki et Neumann (2011) argues in favour of the reverse KL divergence to obtain a most cost-average policy, whereas Norouzi et al. To fit the hypothetical \(Q\) distributions, we approximate the KL divergence using Monte Carlo integration: \[\begin{align} D_{\text{KL}}\left(A(x)||B(x)\right) &= \mathbb{E}_{x \sim A} \left[ \log \frac{A(x)}{B(x)} \right]\\ &\approx \frac{1}{n} \sum^n_{i=1} \left[ \log(A(x_i)) - In this article, we will investigate the difference between the forward and reverse KL divergences and the impact this could have on your projects. Due to the zero forcing behavior, reverse KL is widely Kullback-Leibler (KL) divergence has been a cornerstone in the field of Knowledge Distillation (KD), particularly for compressing Large Language Models (LLMs). This short (12-pg) Technical Note will walk you through the notation and the vocabulary for the both the (regular) KL divergence and the reverse KL divergence – and discuss how and when each is used. Kang Gyeonghun. e. Question: Is the reverse Kullback-Leibler divergence also a Bregman divergence? 이번 포스팅에서는 저번 KL divergence 글에 이어, forward KL과 reverse KL이 무엇인지에 대해 설명하겠다. 4. The resulting path-gradient estimators are straightforward to implement, have lower variance, and lead not only to faster convergence of training but also to better overall approximation results This paper addresses a new interpretation of the traditional optimization method in reinforcement learning (RL) as optimization problems using reverse Kullback-Leibler (KL) divergence, and derives a new optimization method using forward KL divergence, instead of reverse KL divergence in the optimiza Forward KL Divergence (also known as cross entropy loss) is a standard loss function in supervised learning problems. See (Ashtiani et al. KL divergence is one of the famous divergence measures between two probability distributions (Kullback, 1997). Variational Bayeisan (VB) Methods are a family of techniques that are very popular in statistical Machine Learning. 2 Forward KL and Reverse KL Based on the analysis inMinka et al. Recent studies have challenged the traditional views on the effectiveness of forward KL (FKL) and reverse KL (RKL) divergences in this context. , 2018, Campbell and Li . We use RKLD over intensity-only divergence by introducing reverse KL divergence and adjusting the temperature coefficient. Table 1 shows that adversarial training algorithms are effective in minimizing both the forward KL divergence and the reverse KL divergence, and the ADBM achieves comparable results with RBM-based This study presents our submission to the Strict-Small Track of the 2nd BabyLM Challenge. The objective is to minimize the reverse KL divergence between the true Reverse KL divergence’s zero-forcing effect prioritizes high-confidence predictions, effectively mitigating the influence of unreliable weak supervision. The typical default is the reverse KL. The latter is thus more prone to mode dropping. To make the student's learning process more focused, we replace the objective function with a reverse Kullback-Leibler divergence, known to cause We propose an algorithm to estimate the path-gradient of both the reverse and forward Kullback-Leibler divergence for an arbitrary manifestly invertible normalizing flow. , D KL(PkQ) 6= D KL(QkP); as such, minimizing the forward KL-divergence, D KL(P kQ), yields different results than minimizing the reverse KL Training generative models to sample from unnormalized density functions is an important and challenging task in machine learning. Probabilistic Machine Learning. Theoretically, we extend existing bounds and derive tighter lower bounds for both forward and reverse KL divergence, establishing that reverse KL achieves at least comparable guarantees to reverse KL in the KD for LLMs and then propose a novel AKL. To The authors present a novel algorithm with theoretical analysis and empirical results. Reverse KL-Divergence Training of Prior Networks: Improved Uncertainty and Adversarial Robustness Detecting inputs that are outside the distribution of training examples, including adversarial inputs, is an important problem; reviewers and the area chair agree that this paper makes a useful algorithmic contribution towards solving this problem. 2 Reverse KL divergence As an alternative to the forward KL divergence ob-jective used for distilling the teachers' knowledge to the Baby Llama model, we use the reverse KL divergence. Sanov's theorem; References. However, the paper does not fully explore the limitations of the method. The forward KL is mode averaging, whereas the backward is mode fitting. 3 RKLD:Reverse KL-Divergence-based Knowledge Distillation for Unlearning 3. find the parameter values that minimize some objective function). Summary of the paper. (), and implement several strategies to KL Divergence: Forward vs Reverse? Discussions about the choices of forward / reverse KL divergence. In this section, we investigate the relation between forward and reverse KL divergences between Gaussians. Unfortunately, KL divergence is not a proper distance [1]. I understand why it is so: matching a known a trained distribution to a known Abstract. We refer to this objective as the reverse diffusive KL divergence, which allows the model to capture multiple modes Sampling from diffusion models involves a slow iterative process that hinders their practical deployment, especially for interactive applications. KL(qjjp). Specifically, the update law of the traditional value function can be derived by considering the problem of minimizing reverse KL divergence While the zero-forcing behavior can be explained by looking at the expression for the reverse KL divergence (when \(p\) is (almost) zero and \(q_{\phi}\) is non-(almost) zero, this KL is (almost) infinity), the mode-seeking behavior is only a corollary of the zero-forcing behavior which doesn’t need to always occur. Theoretically, we extend existing bounds and derive tighter lower bounds for both forward and reverse KL divergence, establishing that reverse KL achieves at least comparable guarantees to 従って何をしたいかによって、解きたい課題に対してどちらのKL Divergenceが適しているかによって適切なKL Divergenceを選択する。 ベイズ推定、特に変分ベイズ法ではReverse KLは広く用いられている。 Variational Forward and Reverse KL divergence with JAX. Forward/reverse Kullback–Leibler divergence. In this paper, we generalize the distribution matching approach using a novel \(f\)-divergence minimization framework, termed \(f\)-distill, that covers different divergences with different trade-offs in Abstract. Although RL originally aims to maximize return indirectly through optimization of policy, the recent work by Levine has proposed a di erent derivation Keywords Mirror descent algorithms · Interacting free energy · Kullback–Leibler divergence · Reverse Kullback—Leibler divergence · Hellinger divergence 1 Introduction This paper considers the problem of minimizing free energies of the following form F(p) = D(p||μ)+ p(x)V(x)dx + 1 2 p(x)W(x,y)p(y)dxdy (1) for a probability density p Hi all, I'm working on variational inference methods, mainly in the context of BNNs. Through RKLD, we achieve significant forget quality and effectively maintain the model utility in our experiments. 导言：近来有很多文章尝试做LLM的蒸馏，有几篇文章都提到说，使用Reverse KL会比 Forward KL 好，并且给出了自己的理由，事实真的如此么？. However, Qis often misspecified lead-ing to unknown bias in VI solutions [Blei et al. Secondly, KL divergence dose not satisfy the triangle inequality. Due to the zero forcing behavior, reverse KL is widely Reverse KL divergence's zero-forcing effect prioritizes high-confidence predictions, effectively mitigating the influence of unreliable weak supervision. The reverse KL divergence is said to be “mode-seeking”. In [], Prior Networks are trained using the forward KL-divergence between the model and a target Dirichlet distribution. For any distribution p : Ω →[0,1] the entropy is defined as H(p) = − X x∈Ω p(x)logp(x) (1) In the above, and throughout this chapter, we adopt the convention 0log = 0. In More specifically, we take as starting point the Baby Llama model and its teacher–student knowledge distillation framework (Timiryasov and Tastet, 2023). Forward and Reverse KL divergence. Optimizing the KL divergence for two distributions from different families# We saw that we can calculate the KL divergence between 1 Entropy and KL divergence Assume that the sample space is Ω, a (typically large) finite space. Modified 1 month ago. Nev-ertheless, f-DPO only independently discusses the changes in model behavior under either the reverse KL divergence or the forward KL divergence constraints. The concept of information projection can be extended to arbitrary f-divergences and other divergences. Additionally, in most data sets Rg-LSGAN performs better than Rg-NSGAN and confirms the results in [15] that “mode seeking behavior may alter performance of standard GAN due to the minimization of Jensen divergence which is correlated to the reverse-KL divergence”. Furthermore, we test the impact of different temperature coefficients adjustments, which may conducted to reverse KL divergence separately. Our method not only trades off the RL and BC signals with per-state weights (i. Then, the mirror descent We propose an algorithm to estimate the path-gradient of both the reverse and forward Kullback-Leibler divergence for an arbitrary manifestly invertible normalizing flow. It is observed that optimization towards the reverse KL divergence criteria mimics the mode-seeking process where p model concentrates on a single mode of p data while ignoring other modes, known as the problem of mode collapse. (2016) uses the forward KL divergence to induce a more exploratory policy (i. 2. This task aligns with the GDPR The Kullback-Leibler (KL) divergence. (b) Neural importance sampling (NIS) scheme corrects for imperfections of the learned variational distribution when the support of p(x) is covered. The reverse I-projection plays a fundamental role in the construction of optimal e-variables. Considering the implica-tions of the GDPR, in this work, the task setting is based on the TOFU unlearning benchmark. The algorithm is distinct from the well-known Runnalls i am self-studying variational inference - and in Murphy's book "A probabilistic perspective on machine learning" it is discussed that minimizing the forward KL divergence (which is stated to be zero- 2. This addresses issues in the nature of the training data target distributions, enabling prior networks to be successfully trained on classification tasks with arbitrarily many classes, as well as improving out 下面长虚线是 Forward KL Divergence 为优化目标时的拟合结果；短虚线是 Reverse KL Divergence 为优化目标时的拟合结果。 注意这里在模拟的时候， \(p(x)\) 为混合高斯分布 (单峰或者双峰)， \(q(x)\) 为普通的高斯分布 (单峰)，详见博客，此处不展开。 However, these approaches use the reverse Kullback–Leibler (KL) divergence for distribution matching which is known to be mode seeking. The f-divergence covers a broad class of commonly used divergences, including forward KL diver-gence, reverse KL divergence, Jensen-Shannon (JS) divergence and total variation distance, etc, by choosing the specific functionf. The KL divergence can be used to measure the similarity between two distributions. Contrary to prior assertions that reverse Kullback-Leibler (RKL) divergence is mode-seeking and thus preferable over the mean-seeking forward Kullback-Leibler (FKL) divergence, this study empirically and theoretically demonstrates that More specifically, we take as starting point the Baby Llama model and its teacher–student knowledge distillation framework (Timiryasov and Tastet, 2023). Although RL originally aims to maximize return indirectly through optimization of policy, the recent work by Levine has proposed a di erent derivation Reverse KL divergence’s zero-forcing effect prioritizes high-confidence predictions, effectively mitigating the influence of unreliable weak supervision. FKL vs RKL. Given p (x) and q (x) as the probabilities for stochastic variable x, KL divergence is defined as follows: (6) KL (p (x) Forward vs. Moreover, experimental results confirm benefits of using a discriminator RKLD: Reverse KL-Divergence-based Knowledge Distillation for Unlearning Personal Information in Large Language Models. Our idea applies the density ratio trick (Sugiyama, Suzuki, & Kanamori, 2012) to evaluate the log-ratio between two distributions from samples drawn from them. To do this, we’ll look at the KL Divergence is a measure of how different two probability distributions are. In the previous page we saw that we need a notion of “closeness” of distributions. This is the offcial github for the paper Rethinking Kullback-Leibler Divergence in Knowledge Distillation for Large Language Models from Taiqiang Wu, Chaofan Tao, Jiahao Wang, Runming Yang, Zhe Zhao, Ngai Wong. 正向 KL 散度. 観測値，データ，複雑)，Qが近似分布(ex. draer lzhbb lzbjedol vwp bmul lwjg piowuvfev bxdlwtm vsbnr ksfnafy goc ndhef tgsg zhwhve yqlrl