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+# Denoising Diffusion Variational Inference: Diffusion Models as Expressive Variational Posteriors
+
+Wasu Top Piriyakulkij*1, Yingheng Wang*1, Volodymyr Kuleshov1,2
+
+1Department of Computer Science, Cornell University
+
+2The Jacobs Technion-Cornell Institute, Cornell Tech
+
+{wp237, yw2349, kuleshov}@cornell.edu
+
+# Abstract
+
+We propose denoising diffusion variational inference (DDVI), a black-box variational inference algorithm for latent variable models which relies on diffusion models as flexible approximate posteriors. Specifically, our method introduces an expressive class of diffusion-based variational posteriors that perform iterative refinement in latent space; we train these posteriors with a novel regularized evidence lower bound (ELBO) on the marginal likelihood inspired by the wake-sleep algorithm. Our method is easy to implement (it fits a regularized extension of the ELBO), is compatible with black-box variational inference, and outperforms alternative classes of approximate posteriors based on normalizing flows or adversarial networks. We find that DDVI improves inference and learning in deep latent variable models across common benchmarks as well as on a motivating task in biology— inferring latent ancestry from human genomes—where it outperforms strong baselines on 1000 Genomes dataset.
+
+# 1 Introduction
+
+We are interested in amortized black-box variational inference problems of the form
+
+$$
+\begin{array}{l} \log p _ {\boldsymbol {\theta}} (\mathbf {x}) \geq \max  _ {\boldsymbol {\phi}} \mathbb {E} _ {q _ {\boldsymbol {\phi}} (\mathbf {z} | \mathbf {x})} \left[ \log p _ {\boldsymbol {\theta}} (\mathbf {x}, \mathbf {z}) - \log q _ {\boldsymbol {\phi}} (\mathbf {z} | \mathbf {x}) \right] \\ := \max  _ {\phi} \operatorname {E L B O} (\mathbf {x}, \boldsymbol {\theta}, \phi), \tag {1} \\ \end{array}
+$$
+
+in which we approximate the marginal likelihood log $p _ { \pmb { \theta } } ( \mathbf { x } )$ of a latent variable model $p _ { \pmb { \theta } } ( \mathbf { x } , \mathbf { z } )$ with an evidence lower bound $\mathrm { E L B O } ( \mathbf { x } , \theta , \phi )$ that is a function of an approximate variational posterior $q _ { \phi } ( \mathbf { z } | \mathbf { x } )$ . We assume that $p _ { \theta }$ factorizes as $p _ { \pmb { \theta } } ( \mathbf { x } | \mathbf { z } ) \bar { p } _ { \pmb { \theta } } ( \mathbf { z } )$ and admits efficient sampling: examples of such $p _ { \pmb { \theta } }$ include Bayesian networks, topic models (Blei, $\mathrm { N g }$ , and Jordan 2003), variational autoencoders (VAEs), and broad classes of $p _ { \theta }$ defined via modern probabilistic programming frameworks (Gordon et al. 2014).
+
+Maximizing $\mathrm { E L B O } ( \mathbf { x } , \pmb { \theta } , \phi )$ over $\phi$ yields a variational posterior $q _ { \phi } ( \mathbf { z } | \mathbf { x } )$ that approximates $p _ { \pmb { \theta } } ( \mathbf { z } | \mathbf { x } )$ as well as a tight bound on log $p _ { \pmb { \theta } } ( \mathbf { x } )$ that serves as a learning objective for $p _ { \pmb { \theta } }$ . The approximation gap log $\begin{array} { r } { p _ { \theta } ( \mathbf { x } ) ~ - ~ \mathrm { m a x } _ { \phi } \mathrm { E L B O } ( \mathbf { x } , \theta , \phi ) } \end{array}$ equals precisely
+
+*Equal contribution. Author order is randomly assigned and reshuffled across revisions to indicate equal contribution. Copyright $^ ©$ 2025, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.
+
+$\begin{array} { r } { \operatorname* { m i n } _ { \phi } \mathrm { K L } \big ( q _ { \phi } ( \mathbf { z } | \mathbf { x } ) | | p _ { \theta } ( \mathbf { z } | \mathbf { x } ) \big ) } \end{array}$ , which motivates the design of expressive classes of posteriors $q _ { \phi } ( \mathbf { z } | \mathbf { x } )$ that reduce this gap. Recent efforts leverage modern generative models— including normalizing flows (Rezende and Mohamed 2015; Kingma et al. 2016) and generative adversarial networks (Goodfellow et al. 2014; Makhzani et al. 2015)—as expressive model families for $q _ { \phi }$ that tighten the ELBO.
+
+This work seeks to further improve variational inference via expressive posteriors based on diffusion models (Ho, Jain, and Abbeel 2020; Song et al. 2020). Diffusion methods have become the de-facto standard for high-quality image synthesis (Rombach et al. 2022; Gokaslan et al. 2024). Here, we use diffusion in latent space to parameterize $q _ { \phi } ( \mathbf { z } | \mathbf { x } )$ . We train this distribution with a denoising diffusion-like objective that does not involve adversarial training (Makhzani et al. 2015) or constrained invertible normalizing flow architectures (Kingma et al. 2016). Samples from $q _ { \phi } ( \mathbf { z } | \mathbf { x } )$ are obtained via iterative refinement of $\mathbf { z }$ , starting from a Gaussian distribution, and gradually forming one that is multi-modal and complex.
+
+Our work expands upon existing diffusion-based approximate inference methods (Berner, Richter, and Ullrich 2022; Zhang and Chen 2021; Vargas, Grathwohl, and Doucet 2023; Zhang et al. 2023; Richter, Berner, and Liu 2023; Sendera et al. 2024; Akhound-Sadegh et al. 2024) that focus on the task of drawing samples from unnormalized distributions $\tilde { p } ( { \mathbf z } )$ and estimating the partition function $\begin{array} { r } { Z = \int _ { \mathbf { z } } \tilde { p } ( \mathbf { z } ) d \mathbf { z } } \end{array}$ . While these methods are applicable in our setting—we set the unnormalized $\tilde { p } ( { \mathbf z } )$ to $p _ { \pmb { \theta } } ( \mathbf { x } , \mathbf { z } )$ such that $Z = p _ { \pmb { \theta } } ( \mathbf { x } )$ —they do not make use of characteristics of $p _ { \pmb { \theta } }$ that are common in many types of models (VAEs, Bayes networks, etc.), namely the factorization $p _ { \pmb { \theta } } ( \mathbf { x } | \mathbf { z } ) p _ { \pmb { \theta } } ( \mathbf { z } )$ and efficient sampling. We find that leveraging these properties yields simpler algorithms that avoid backpropagating through a sampling process, and that are fast enough to perform learning in addition to inference.
+
+Specifically, we propose denoising diffusion variational inference (DDVI), an approximate inference algorithm defined by a class of approximate posterior distribution based on diffusion and a learning objective inspired by the wakesleep algorithm (Hinton et al. 1995) that implements regularized variational inference. We also derive extensions of our method to semi-supervised learning and clustering.
+
+Our method is easy to implement (it fits a regularized ex-
+
+tension of the ELBO), is compatible with black-box variational inference, and outperforms alternative classes of approximate posteriors based on normalizing flows or adversarial networks.
+
+We evaluate DDVI on synthetic benchmarks and on a real problem in biological data analysis—inferring human ancestry from genetic data. Our method outperforms strong baselines on 1000 Genomes dataset (Siva 2008) and learns a lowdimensional latent space that preserves biologically meaningful structure (Haghverdi, Buettner, and Theis 2015).
+
+Contributions. In summary, this work introduces denoising diffusion variational inference, an approximate inference algorithm defined by two components: a class of approximate posteriors $q ( \mathbf { z } | \mathbf { x } )$ parameterized by diffusion, and a lower bound on the marginal likelihood inspired by wake-sleep. We complement DDVI with extensions to semisupervised learning and clustering. Our method is especially suited for probabilistic programming, representation learning, and dimensionality reduction, where it outperforms alternative methods based on normalizing flows and adversarial training.
+
+# 2 Background
+
+Deep Latent Variable Models Latent variable models (LVMs) $p _ { \pmb { \theta } } ( \mathbf { x } , \mathbf { z } )$ are usually fit by optimizing the evidence lower bound (ELBO)
+
+$$
+\log p _ {\boldsymbol {\theta}} (\mathbf {x}) \geq \mathbb {E} _ {q _ {\boldsymbol {\phi}} (\mathbf {z} | \mathbf {x})} [ \log p _ {\boldsymbol {\theta}} (\mathbf {x} | \mathbf {z}) ] - \mathrm {K L} (q _ {\boldsymbol {\phi}} (\mathbf {z} | \mathbf {x}) | | p _ {\boldsymbol {\theta}} (\mathbf {z})),
+$$
+
+which serves as a tractable surrogate for the marginal loglikelihood (MLL). The gap between the MLL and the ELBO equals precisely $\operatorname { K L } ( q _ { \phi } ( \mathbf { z } | \mathbf { x } ) | | p _ { \pmb { \theta } } ( \mathbf { z } | \mathbf { x } ) )$ —thus, a more expressive $q _ { \phi } ( \mathbf { z } | \mathbf { x } )$ may better fit the true posterior and induce a tighter ELBO (Kingma and Welling 2013).
+
+Expressive variational posteriors can be formed by choosing more expressive model families—including auxiliary variable methods (Maaløe et al. 2016), MCMC-based methods (Salimans, Kingma, and Welling 2015), normalizing flows (Rezende and Mohamed 2015)—or improved learning objectives—e.g., adversarial or sample-based losses (Makhzani et al. 2015; Zhao, Song, and Ermon 2017; Si, Bishop, and Kuleshov 2022; Si et al. 2023).
+
+The wake-sleep algorithm (Hinton et al. 1995) optimizes an alternative objective
+
+$$
+\mathbb {E} _ {q _ {\phi} (\mathbf {z} | \mathbf {x})} \left[ \log p _ {\boldsymbol {\theta}} (\mathbf {x} | \mathbf {z}) \right] - \operatorname {K L} \left(p _ {\boldsymbol {\theta}} (\mathbf {z} | \mathbf {x}) \mid \mid q _ {\phi} (\mathbf {z} | \mathbf {x})\right),
+$$
+
+in which the KL divergence term is reversed. The learning procedure for wake-sleep involves alternating between ”wake” phases where the recognition model is updated and ”sleep” phases where the generative model is refined.
+
+Denoising Diffusion Models A diffusion model is defined via a user-specified noising process $q$ that maps data $\mathbf { x } _ { \mathrm { 0 } }$ into a sequence of $T$ variables ${ \bf y } _ { 1 : T } = { \bf y } _ { 1 } , . . . , { \bf y } _ { T }$ that represent increasing levels of corruption to $\mathbf { x } _ { \mathrm { 0 } }$ . We obtain $\mathbf { y } _ { 1 : T }$ by applying a Markov chain $\begin{array} { r } { \dot { q } ( \mathbf { y } _ { 1 : T } | \mathbf { x } _ { 0 } ) = \prod _ { t = 1 } ^ { T } q ( \mathbf { y } _ { t } | \mathbf { y } _ { t - 1 } ) } \end{array}$ , where we define $\mathbf { y } _ { 0 } ~ = ~ \mathbf { x } _ { 0 }$ for convenience. When $\mathbf { x } _ { \mathrm { 0 } }$ is a continuous vector, a standard choice of transition kernel is $q ( \mathbf { x } _ { t } \ \mid \ \mathbf { x } _ { t - 1 } ) \ = \ { \mathcal { N } } ( \mathbf { y } _ { t } ; { \sqrt { \alpha _ { t } } } \mathbf { y } _ { t - 1 } , { \sqrt { 1 - \alpha _ { t } } } \mathbf { I } )$ , which is a
+
+Gaussian centered around a copy of $\mathbf { y } _ { t - 1 }$ to which we added noise following a schedule $0 < \pmb { \alpha } _ { 1 } < \pmb { \alpha } _ { 2 } < . . . < \pmb { \alpha } _ { T } = 1$ .
+
+A diffusion model can then be represented as a latent variable distribution $p ( \mathbf { x } _ { 0 } , \mathbf { y } _ { 1 : T } )$ that factorizes as $\begin{array} { r } { p ( \mathbf { x } _ { 0 } , \mathbf { y } _ { 1 : T } ) = p ( \mathbf { y } _ { T } ) \prod _ { t = 0 } ^ { T - 1 } p _ { \pmb { \theta } } ( \mathbf { y } _ { t } \mid \mathbf { y } _ { t + 1 } ) } \end{array}$ (again using $\mathbf { y } _ { 0 }$ as shorthand for $\mathbf { x } _ { \mathrm { 0 } }$ ). This model seeks to approximate the reverse of the forward diffusion $q$ and map noise $\mathbf { y } _ { T }$ into data $\mathbf { x } _ { \mathrm { 0 } }$ .
+
+The true reverse of the process $q$ cannot be expressed in closed form; as such, we parameterize $p _ { \theta }$ with $\pmb { \theta }$ trained by maximizing the ELBO:
+
+$$
+\begin{array}{l} \log p _ {\boldsymbol {\theta}} \left(\mathbf {x} _ {0}\right) \geq \mathbb {E} _ {q} \left[ \log p _ {\boldsymbol {\theta}} \left(\mathbf {x} _ {0} \mid \mathbf {x} _ {1}\right) - \sum_ {t = 2} ^ {T} \mathrm {K L} \left(q _ {t} \mid \mid p _ {t}\right) \right] \tag {2} \\ - \operatorname {K L} \left(q \left(\mathbf {x} _ {T} \mid \mathbf {x} _ {0}\right) \mid \mid p \left(\mathbf {x} _ {T}\right)\right) \\ \end{array}
+$$
+
+where $q _ { t } , p _ { t }$ denote the distributions $q ( \mathbf { x } _ { t - 1 } | \mathbf { x } _ { t } , \mathbf { x } _ { 0 } )$ and $p _ { \pmb { \theta } } ( \mathbf { x } _ { t - 1 } | \mathbf { x } _ { t } )$ , respectively.
+
+# 3 Variational Inference With Denoising Diffusion Models
+
+We introduce denoising diffusion variational inference (DDVI), which improves variational inference with diffusion-based techniques.
+
+The goal of DDVI is to fit a latent variable model $p _ { \pmb { \theta } } ( \mathbf { x } , \mathbf { z } )$ . We assume that $p _ { \theta }$ factorizes as $p _ { \pmb { \theta } } ( \mathbf { x } | \mathbf { z } ) p _ { \pmb { \theta } } ( \mathbf { z } )$ and admits efficient sampling: examples of such $p _ { \theta }$ include Bayesian networks and variational autoencoders (VAEs) (Kingma and Welling 2013).
+
+Our approach is comprised of three components:
+
+1. A modeling family of approximate posteriors $q _ { \phi } ( \mathbf { z } | \mathbf { x } )$ based on diffusion;   
+2. A learning objective formed by a regularized ELBO;   
+3. An optimization algorithm inspired by wake-sleep.
+
+The $q _ { \phi } ( \mathbf { z } | \mathbf { x } )$ iteratively refines latents $\mathbf { z }$ , starting from a Gaussian distribution. The learning objective trains $q _ { \phi } ( \mathbf { z } | \mathbf { x } )$ to reverse a used-specified forward diffusion process.
+
+# 3.1 Modeling Family: Diffusion-Based Posteriors
+
+DDVI performs variational inference using a family of approximate posteriors $\begin{array} { r } { q _ { \phi } ( \mathbf { z } | \mathbf { x } ) = \int _ { \mathbf { y } } q _ { \phi } ( \mathbf { z } | \mathbf { \bar { y } } , \mathbf { x } ) q _ { \phi } ( \mathbf { \bar { y } } | \mathbf { x } ) d \mathbf { \bar { y } } } \end{array}$ , which themselves contain latent variables $\mathbf { y } \in \mathcal { V }$ . The models $q _ { \phi } ( \mathbf { z } | \mathbf { y } , \mathbf { x } ) , q _ { \phi } ( \mathbf { y } | \mathbf { x } )$ must have tractable densities and support gradient-based optimization over $\phi$ .
+
+We choose the latent $\begin{array} { r l r } { { \bf y } } & { { } = } & { \left( { \bf y } _ { 1 } , { \bf y } _ { 2 } , . . . , { \bf y } _ { T } \right) } \end{array}$ to be a vector of $T$ variables that represent progressively simplified versions of $\mathbf { z }$ , with $\mathbf { y } _ { T }$ corresponding to a simple distribution (e.g., a Gaussian). The model $\begin{array} { r l r } { q _ { \phi } ( \mathbf { y } , \mathbf { \bar { z } } | \mathbf { x } ) } & { { } = } & { q _ { \phi } ( \mathbf { z } | \mathbf { y } _ { 1 } , \mathbf { \bar { x } } ) \prod _ { t = 1 } ^ { T - 1 } q _ { \phi } ( \mathbf { y } _ { t } | \mathbf { y } _ { t + 1 } , \mathbf { x } ) } \end{array}$ transforms $\mathbf { y } _ { T }$ into $\mathbf { z }$ via iterative refinement. To sample from $q _ { \phi }$ , we first sample $\mathbf { y } _ { T }$ —this is an easier task since we can define $\mathbf { y } _ { T }$ to have a simple (e.g., Gaussian) distribution—and then by sampling from the denoising model $\begin{array} { r } { q _ { \phi } ( \mathbf { z } | \mathbf { y } _ { 1 } , \mathbf { x } ) \prod _ { t = 1 } ^ { T - 1 } q _ { \phi } ( \mathbf { y } _ { t } | \mathbf { \bar { y } } _ { t + 1 } , \mathbf { x } ) } \end{array}$ - .
+
+We define the relationship between y and $\mathbf { z }$ via a forward diffusion process $r ( { \bf \hat { y } } | { \bf z } , { \bf x } ) = { \hat { r } } ( { \bf y } _ { 1 : T } | { \bf z } , { \bf x } ) = $
+
+![](images/89bc4e11d0890276231236c68fc50b136b9530041131a0047a4887455f421887.jpg)  
+Figure 1: Denoising diffusion variational inference in a VAE. Between the encoder and decoder, we have a diffusion model to map a simple distribution into a complex distribution over latents.
+
+$\begin{array} { r } { r ( { \bf y } _ { 1 } | { \bf z } , { \bf x } ) \prod _ { t = 1 } ^ { T - 1 } r ( { \bf y } _ { t + 1 } | { \bf y } _ { t } , { \bf x } ) } \end{array}$ , which transforms z—the latent whose intractable posterior we seek to approximate— into $\mathbf { y } _ { T }$ , whose posterior is easier to model (possibly conditioned on x). Examples of $r$ include Gaussian forward diffusion processes and discrete noising processes (Austin et al. 2021). The model $q _ { \phi }$ is trained to approximately reverse this forward diffusion process.
+
+# 3.2 Learning Objective: A Markovian ELBO
+
+The standard approach to fit auxiliary-variable generative models (Maaløe et al. 2016) is to apply the ELBO twice:
+
+$$
+\begin{array}{l} \log p _ {\boldsymbol {\theta}} (\mathbf {x}) \geq \log p _ {\boldsymbol {\theta}} (\mathbf {x}) - \mathrm {K L} \left(q _ {\phi} (\mathbf {z} | \mathbf {x}) \left\| p _ {\boldsymbol {\theta}} (\mathbf {z} | \mathbf {x})\right) \right. (3) \\ \geq \log p _ {\boldsymbol {\theta}} (\mathbf {x}) - \operatorname {K L} \left(q _ {\phi} (\mathbf {z} | \mathbf {x}) | | p _ {\boldsymbol {\theta}} (\mathbf {z} | \mathbf {x})\right) (4) \\ - \mathbb {E} _ {q _ {\phi} (\mathbf {z} | \mathbf {x})} \left[ \mathrm {K L} \left(q _ {\phi} (\mathbf {y} | \mathbf {x}, \mathbf {z}) \mid \mid r (\mathbf {y} | \mathbf {x}, \mathbf {z})\right) \right] \\ = \mathbb {E} _ {q _ {\phi} (\mathbf {y}, \mathbf {z} | \mathbf {x})} [ \log p _ {\theta} (\mathbf {x} | \mathbf {z}) ] (5) \\ - \operatorname {K L} \left(q _ {\phi} (\mathbf {y}, \mathbf {z} | \mathbf {x}) \mid \mid r (\mathbf {y} | \mathbf {x}, \mathbf {z}) p (\mathbf {z})\right) \\ \end{array}
+$$
+
+In Equation (3), we applied the ELBO over z, and in Equation (4) we applied the ELBO over the latent y of $q$ (see Appendix J for the derivation). Notice that the gap between the ELBO and $\log p _ { \pmb { \theta } } ( \mathbf { x } )$ is $\begin{array} { r } { \mathrm { K L } ( q _ { \phi } ( \mathbf { z } | \mathbf { x } ) | | p _ { \theta } ( \mathbf { z } | \mathbf { x } ) ) + } \end{array}$ $\mathbb { E } _ { q _ { \phi } ( \mathbf { z } | \mathbf { x } ) } [ \mathrm { K L } ( q _ { \phi } ( \mathbf { y } | \mathbf { x } , \mathbf { z } ) | | r ( \mathbf { y } | \mathbf { x } , \mathbf { z } ) ) ]$ . Thus, if we correctly match $q$ and $r$ , we will achieve a tight bound.
+
+Analyzing the ELBO Optimizing Equation (5) requires tractably dealing with the prior regularization term $\bar { \mathcal { L } } _ { \mathrm { r e g } } ( \mathbf { x } , \pmb \theta , \phi ) : = - \mathbf { K } \bar { \mathbf { L } } \big ( q _ { \phi } ( \mathbf { y } , \mathbf { z } | \mathbf { x } ) | | r ( \mathbf { y } | \bar { \mathbf { x } } , \mathbf { z } ) p ( \mathbf { z } ) \big )$ , which we equivalently rewrite as:
+
+$$
+\mathcal {L} _ {\text {r e g}} = \mathbb {E} _ {q _ {\phi} (\mathbf {y}, \mathbf {z} | \mathbf {x})} \left[ \log \left(r (\mathbf {y} | \mathbf {x}, \mathbf {z}) p (\mathbf {z})\right) \right] + H (q). \tag {6}
+$$
+
+We can expand the first term by leveraging the Markov structure of $r , q$ to rewrite $\mathcal { L } _ { \mathrm { r e g } }$ as the likelihood of samples from the reverse diffusion process $q$ under the forward process $r$ .
+
+$$
+\mathcal {L} _ {\mathrm {r e g}} = \sum_ {t = 1} ^ {T} \mathbb {E} _ {q} \left[ \log \left(r \left(\mathbf {y} _ {t} \mid \mathbf {y} _ {t - 1}, \mathbf {x}\right) \right] + \mathbb {E} _ {q} \left[ \log p (\mathbf {z}) \right] + H (q), \right.
+$$
+
+where $\mathbf { y } _ { 0 } : = \mathbf { z } $ . We refer to optimizing the Markovian ELBO as unregularized DDVI, the first instance of our method.
+
+The noise process $r$ defines prior regularization terms for each $\mathbf { y } _ { t }$ . This provides extra supervision for learning $q$ in the form of trajectories from latents $\mathbf { y } _ { T }$ to $\mathbf { y } _ { 1 }$ ; this extra supervision helps $q$ fit complex non-Gaussian posteriors.
+
+The term H(q) = − $\begin{array} { r l r } { \bar { H ( q ) } } & { { } = } & { - \sum _ { t = 1 } ^ { T + 1 } \mathbb { E } _ { q } [ \log \bar { q } _ { \phi } ( \mathbf { y } _ { t - 1 } | \mathbf { y } _ { t } , \mathbf { x } ) ] } \end{array}$ PT +1t=1 Eq[log qϕ(yt−1|yt, x)] denotes the entropy. For example, when each term $q _ { \phi } ( \mathbf { y } _ { t - 1 } | \mathbf { y } _ { t } , \mathbf { x } )$ is Gaussian, it is computed as
+
+$$
+H (q) = \sum_ {t = 1} ^ {T + 1} \mathbb {E} _ {q} \left[ \frac {d}{2} \left(1 + \log (2 \pi)\right) + \frac {1}{2} \log | \Sigma_ {\phi} (\mathbf {y} _ {t}, \mathbf {x}) | \right]
+$$
+
+where $d$ is the dimension of $\mathbf { y }$ and we use the notation ${ \bf y } _ { T + 1 } = { \bf x }$ . It is also common to leave the variance $\Sigma _ { \phi }$ fixed, in which case $H ( q )$ is a constant.
+
+# 3.3 Refining the Objective: A Regularized ELBO
+
+Notice that optimizing $\mathcal { L } _ { \mathrm { r e g } }$ involves sampling from the approximate reverse process $\mathbf { \bar { \rho } } _ { q \phi } ( \mathbf { y } , \mathbf { z } | \mathbf { x } )$ to match the true reverse process $r ( \mathbf { y } | \mathbf { z } , \mathbf { x } )$ : this is the opposite of diffusion training, where we would sample from $r$ to fit $q$ . This type of on-policy learning of $q$ has been studied in the context of approximate inference (Zhang and Chen 2021); however, it requires backpropagating through $T$ samples, which may hamper training, and it optimizes a mode-covering divergence that may struggle to fit complex $p ( \mathbf { z } )$ .
+
+Adding Wake-Sleep Regularization to the ELBO We propose to further improve the ELBO via off-policy diffusion-like training. Our new objective is the ELBO in Equation (5) augmented with a regularizer ${ \mathcal { L } } _ { \mathrm { s l e e p } } ( \phi )$ .
+
+$$
+\begin{array}{l} \log p _ {\boldsymbol {\theta}} (\mathbf {x}) \geq \underbrace {\mathbb {E} _ {q _ {\phi} (\mathbf {y} , \mathbf {z} \mid \mathbf {x})} \left[ \log p _ {\boldsymbol {\theta}} (\mathbf {x} \mid \mathbf {z}) \right]} _ {\text {w a k e / r e c o n s . t e r m} \mathcal {L} _ {\text {r e c}} (\mathbf {x}, \boldsymbol {\theta}, \phi)} \tag {7} \\ \underbrace {- \operatorname {K L} \left(q _ {\phi} (\mathbf {y} , \mathbf {z} | \mathbf {x}) | | r (\mathbf {y} | \mathbf {x} , \mathbf {z}) p (\mathbf {z})\right)} _ {\text {p r i o r r e g u l a r i z a t i o n t e r m} \mathcal {L} _ {\text {r e g}} (\mathbf {x} , \boldsymbol {\theta} , \phi)} \\ \underbrace {- \mathbb {E} _ {p _ {\boldsymbol {\theta}} (\mathbf {x})} [ \mathrm {K L} (p _ {\boldsymbol {\theta}} (\mathbf {z} | \mathbf {x}) | | q _ {\boldsymbol {\phi}} (\mathbf {z} | \mathbf {x})) ]} _ {\text {s l e e p t e r m} \mathcal {L} _ {\text {s l e e p}} (\boldsymbol {\phi})} \\ \end{array}
+$$
+
+The optimization of the regularizer ${ \mathcal { L } } _ { \mathrm { s l e e p } } ( \phi )$ is similar to the sleep phase of wake-sleep, and closely resembles diffusion model training (see below). As in wake-sleep, ${ \mathcal { L } } _ { \mathrm { s l e e p } } ( \phi )$ is optimized over $\phi$ only, the $\mathbf { x }$ are sampled from $p$ .
+
+From Wake-Sleep to Diffusion Regularization Computing $\mathcal { L } _ { \mathrm { s l e e p } } ( \phi )$ still involves intractable distributions $p _ { \pmb { \theta } } ( \mathbf { z } | \mathbf { x } )$ , $q _ { \phi } ( \mathbf { \dot { z } } | \mathbf { x } )$ . To optimize ${ \mathcal { L } } _ { \mathrm { s l e e p } } ( \phi )$ , we introduce another lower bound ${ \mathcal { L } } _ { \mathrm { d i f f } } ( \phi )$ , which we call the denoising diffusion loss (for reasons that will become apparent shortly):
+
+$$
+\begin{array}{l} \mathcal {L} _ {\text {s l e e p}} (\phi) = - \mathbb {E} _ {p _ {\theta} (\mathbf {x})} \left[ \mathrm {K L} \left(p _ {\theta} (\mathbf {z} \mid \mathbf {x}) \mid \mid q _ {\phi} (\mathbf {z} \mid \mathbf {x})\right) \right] \tag {8} \\ = \mathbb {E} _ {p _ {\boldsymbol {\theta}} (\mathbf {x}, \mathbf {z})} \left[ \log q _ {\boldsymbol {\phi}} (\mathbf {z} | \mathbf {x}) \right] + \bar {H} (p _ {\boldsymbol {\theta}}) \\ \geq \mathbb {E} _ {p _ {\boldsymbol {\theta}} (\mathbf {x}, \mathbf {z})} \left[ \mathbb {E} _ {r} [ \log \frac {q _ {\boldsymbol {\phi}} (\mathbf {y} , \mathbf {z} | \mathbf {x})}{r (\mathbf {y} | \mathbf {z} , \mathbf {x})} ] \right] + \bar {H} (p _ {\boldsymbol {\theta}}) \\ = \mathcal {L} _ {\text {d i f f}} (\phi) \\ \end{array}
+$$
+
+In Equation (8), we applied the ELBO with $r ( \mathbf { y } | \mathbf { z } , \mathbf { x } )$ playing the role of the variational posterior over the latent $\mathbf { y }$ in $q _ { \phi } \mathrm { ; } \bar { H } ( p _ { \theta } )$ is the expected conditional entropy of $p _ { \pmb { \theta } } ( \mathbf { z } | \mathbf { x } )$ , a constant that does not depend on $\phi$ .
+
+We can further simplify ${ \mathcal { L } } _ { \mathrm { d i f f } } ( \phi )$ by leveraging the Markov structure of the forward and reverse processes $r , q$ . Recall that each $\mathbf { y } = ( \mathbf { y } _ { 1 } , \mathbf { y } _ { 2 } , . . . , \mathbf { y } _ { T } )$ can be a vector of $T$ latents, which we also denote as $\mathbf { y } _ { 1 : T }$ , and that $r ( { \bf y } _ { 1 : T } | { \bf z } , { \bf x } ) =$ $\begin{array} { r } { \prod _ { t = 1 } ^ { T } r ( \mathbf { y } _ { t } | \mathbf { y } _ { t - 1 } , \mathbf { x } ) } \end{array}$ , where $\mathbf { y } _ { 0 } = \mathbf { z }$ and also $q _ { \phi } ( \mathbf { y } , \mathbf { z } | \mathbf { x } ) =$ ${ \begin{array} { r } { q _ { \phi } ( \mathbf { y } _ { 0 : T } | \mathbf { x } ) = q _ { \phi } ( \mathbf { y } _ { T } | \mathbf { x } ) \prod _ { t = 1 } ^ { T } q _ { \phi } ( \mathbf { y } _ { t - 1 } | \mathbf { y } _ { t } , \mathbf { x } ) } \end{array} }$ .
+
+We may use the Markov structure in $q , r$ to rewrite ${ \mathcal { L } } _ { \mathrm { d i f f } } ( \phi )$ as a sum of $T$ terms, one per Markov step. The derivation is identical to that used to obtain the ELBO of a diffusion model (Sohl-Dickstein et al. 2015), and yields an expression of the same form:
+
+$$
+\begin{array}{l} \mathcal {L} _ {\text {d i f f}} (\phi) = \mathbb {E} _ {r} \left[ \log q _ {\phi} (\mathbf {z} | \mathbf {y} _ {1}, \mathbf {x}) - \sum_ {t = 2} ^ {T} \mathrm {K L} \left(r _ {t} \mid \mid q _ {t}\right) \right] \tag {9} \\ - \operatorname {K L} \left(r \left(\mathbf {y} _ {T} \mid \mathbf {z}, \mathbf {x}\right) \mid \mid q _ {\phi} \left(\mathbf {y} _ {T} \mid \mathbf {x}\right)\right) + \bar {H} \left(p _ {\theta}\right). \\ \end{array}
+$$
+
+where $r _ { t } , q _ { t }$ denote the distributions $r \left( \mathbf { y } _ { t - 1 } | \mathbf { y } _ { t } , \mathbf { y } _ { 0 } , \mathbf { x } \right)$ and $q _ { \phi } ( \mathbf { y } _ { t - 1 } | \mathbf { y } _ { t } , \mathbf { x } )$ (see Appendix K for the derivation).
+
+Regularized DDVI Objective We define the full DDVI objective ${ \mathcal { L } } _ { \mathrm { d d v i } }$ to be the sum of the aforementioned terms:
+
+$$
+\mathcal {L} _ {\mathrm {d d v i}} (\mathbf {x}, \boldsymbol {\theta}, \phi) = \mathcal {L} _ {\mathrm {r e c}} (\mathbf {x}, \boldsymbol {\theta}, \phi) + \mathcal {L} _ {\mathrm {r e g}} (\mathbf {x}, \boldsymbol {\theta}, \phi) + \mathcal {L} _ {\mathrm {d i f f}} (\phi)
+$$
+
+Terms $\mathcal { L } _ { \mathrm { r e g } }$ and ${ \mathcal { L } } _ { \mathrm { d i f f } }$ may be weighted by hyper-parameters βr $_ \mathrm { g } , \beta _ { \mathrm { d i f f } } \ \mathrm { ~ > ~ 0 ~ }$ , as in the $\beta$ -VAE framework. In our experiments, $\beta _ { \mathrm { r e g } } = \beta _ { \mathrm { d i f f } } = 1$ unless otherwise specified. Note that since $\mathcal { L } _ { \mathrm { d i f f } } \leq \mathcal { L } _ { \mathrm { s l e e p } } \leq 0$ , $\mathcal { L } ( \mathbf { x } , \pmb { \theta } , \phi )$ is a valid lower bound on $\log p _ { \pmb { \theta } } ( \mathbf { x } )$ that is tight when $q _ { \phi } ( \mathbf { z } | \mathbf { x } ) = p _ { \pmb { \theta } } ( \mathbf { z } | \mathbf { x } )$ .
+
+# 3.4 Optimization: Extending Wake-Sleep
+
+We may optimize $\mathcal { L } _ { \mathrm { d d v i } } ( \mathbf { x } , \theta , \phi )$ using gradient descent by alternating between ELBO optimization and taking sleep steps (see Appendix A for full details):
+
+1. Sample x from data, take gradient step on $\theta , \phi$ optimizing $\mathcal { L } _ { \mathrm { r e c } } ( \mathbf { x } , \pmb { \theta } , \phi ) + \mathcal { L } _ { \mathrm { r e g } } ( \mathbf { x } , \pmb { \theta } , \phi )$ (the “wake” step);   
+2. Sample $\mathbf { z } , \mathbf { x }$ from $p _ { \theta }$ and take a gradient step on $\phi$ optimizing ${ \mathcal { L } } _ { \mathrm { d i f f } } ( \phi )$ (the “sleep” step).
+
+Again, terms may be weighted by $\beta _ { \mathrm { r e g } } , \beta _ { \mathrm { d i f f } } > 0$ . Note that by maximizing ${ \mathcal { L } } _ { \mathrm { d i f f } } ( \phi )$ , we fit $q _ { \phi } ( \mathbf { z } | \mathbf { \bar { x } } )$ to $p _ { \pmb { \theta } } ( \mathbf { z } | \mathbf { x } )$ via the forward KL divergence; similarly, by optimizing $\mathcal { L } _ { \mathrm { r e c } } + \mathcal { L } _ { \mathrm { r e g } }$ (the ELBO), we fit $q _ { \phi } ( \mathbf { z } | \mathbf { x } )$ to $p _ { \pmb { \theta } } ( \mathbf { z } | \mathbf { x } )$ via the reverse KL divergence. Thus, optimizing $\mathcal { L } ( \mathbf { x } , \pmb { \theta } , \phi )$ encourages $q _ { \phi } ( \mathbf { z } | \mathbf { x } )$ to approximate $p _ { \pmb { \theta } } ( \mathbf { z } | \mathbf { x } )$ , and when the two are equal, the bound ${ \mathcal { L } } _ { \mathrm { d d v i } }$ on $\log p _ { \theta } ( \mathbf { x } )$ is tight.
+
+Simplified Wake-Sleep We also consider a light-weight algorithm, in which $r ( \mathbf { y } | \mathbf { z } )$ and $q _ { \phi } ( \mathbf { y } , \mathbf { z } )$ do not depend on x. This scenario admits the following optimization procedure:
+
+1. Sample x from data and compute gradient on $\theta , \phi$ optimizing $\mathcal { L } _ { \mathrm { r e c } } ( \mathbf { x } , \pmb { \theta } , \phi ) + \mathcal { L } _ { \mathrm { r e g } } ( \bar { \mathbf { x } } , \pmb { \theta } , \bar { \phi } )$ .   
+2. Sample z from $p ( \mathbf { z } )$ and compute gradient on $\phi$ optimizing ${ \mathcal { L } } _ { \mathrm { d i f f } } ( \phi )$ ; take step on weighted sum of both gradients.
+
+In this case, ${ \mathcal { L } } _ { \mathrm { d i f f } }$ requires only sampling from $p ( \mathbf { z } )$ , and the entire loss ${ \mathcal { L } } _ { \mathrm { d d v i } }$ can be optimized end-to-end using gradient descent. This algorithm is simpler (there is no separate sleep phase); however, $q _ { \phi } ( \mathbf { z } | \mathbf { x } )$ may not perfectly approximate $p _ { \pmb { \theta } } ( \mathbf { z } | \mathbf { x } )$ when $r ( \mathbf { y } \vert \mathbf { z } )$ and $q _ { \phi } ( \mathbf { z } | \mathbf { y } )$ do not depend on x, hence $\mathcal { L }$ may no longer be a tight bound.
+
+Practical Considerations A common type of noising process compatible with this bound when $\mathbf { z }$ is continuous is Gaussian diffusion, where we define √ $\mathcal { N } ( \mathbf { y } _ { t } ; \sqrt { 1 - \alpha _ { t } } \mathbf { y } _ { t - 1 } , \alpha _ { t } \mathbf { I } )$ t for a suitable schedule $r ( \mathbf { y } _ { t } | \mathbf { y } _ { t - 1 } ) =$ $( \alpha _ { t } ) _ { t = 1 } ^ { T }$ . We then adopt the parameterization $q _ { \phi } ( \mathbf { y } _ { t - 1 } | \mathbf { y } _ { t } , \mathbf { x } ) =$ $\mathcal { N } ( \mathbf { y } _ { t - 1 } ; \mu _ { \phi } ( \mathbf { y } _ { t } , \mathbf { x } , t ) , \Sigma _ { \phi } ( \mathbf { y } _ { t } , \mathbf { x } , t ) )$ . It is then common to parameterize $q _ { \phi }$ with a noise prediction network $\epsilon _ { \phi }$ (Ho, Jain, and Abbeel 2020); the sum of KL divergences√ can be approximated by $\mathbb { E } _ { t , \epsilon _ { t } \sim r ( \mathbf { y } _ { 0 } , t ) } | | \epsilon _ { t } - \epsilon _ { \phi } ( \sqrt { \bar { \alpha _ { t } } } \mathbf { y } _ { 0 } \ +$ $\sqrt { 1 - \bar { \alpha _ { t } } } \epsilon _ { t } , \mathbf { x } , t ) | | ^ { 2 }$ . Other extensions include discrete denoising processes (Austin et al. 2021; Sahoo et al. 2024; Schiff et al. 2024). In the wake-sleep setting, we know both endpoints $\mathbf { y } _ { T } \sim \mathbf { \boldsymbol { q } } ( \cdot | \mathbf { x } )$ and $\mathbf { y } _ { 0 } ~ = ~ \mathbf { z }$ of the diffusion process, opening the possibility for applying optimal transport techniques (Cuturi 2013; De Bortoli et al. 2021).
+
+# 4 Extensions
+
+# 4.1 Semi-Supervised Learning
+
+Following Makhzani et al. (2015), we extend our algorithm to the semi-supervised learning setting where some data points have labels denoted by $l$ . We assume the user provides a model of the form $p _ { \pmb { \theta } } ( \mathbf { x } , \mathbf { y } , \mathbf { z } , l ) \ =$ $\begin{array} { r } { p _ { \pmb { \theta } } ( \mathbf { x } | \mathbf { z } , l ) \bar { r } ( \mathbf { y } | \mathbf { z } , l ) p _ { \pmb { \theta } } ( \mathbf { z } | l ) p ( l ) } \end{array}$ ; we set the variational distributions to $q _ { \phi } ( \mathbf { z } | \mathbf { x } , \mathbf { y } , l ) , q _ { \phi } ( \mathbf { y } | \mathbf { x } ) , q _ { \phi } ( l | \mathbf { x } )$ $q _ { \phi } ( \mathbf { z } | \mathbf { x } , \mathbf { y } , l )$ . In this setting, we consider two cases, depending on whether the label is observed (Kingma et al. 2014). We extend Equation (7) to incorporate the label $l$ corresponding to a data point as follows:
+
+$$
+\begin{array}{l} \mathcal {L} _ {\text {s e m i}} = \mathbb {E} _ {q _ {\phi} (\mathbf {y}, \mathbf {z} | \mathbf {x}, l)} \left[ \log p _ {\boldsymbol {\theta}} (\mathbf {x} | \mathbf {z}, l) \right] \tag {10} \\ - \operatorname {K L} \left(q _ {\phi} (\mathbf {y}, \mathbf {z} | \mathbf {x}, l) | | p _ {\theta} (\mathbf {y}, \mathbf {z} | l)\right) \\ - \mathbb {E} _ {p _ {\theta} (\mathbf {x})} \left[ \mathrm {K L} \left(p _ {\theta} (\mathbf {z} | \mathbf {x}, l) \mid \mid q _ {\phi} (\mathbf {z} | \mathbf {x}, l)\right) \right] \\ \end{array}
+$$
+
+When the label $c$ cannot be observed, we treat it as a latent variable and modify the learning objective $\chi _ { \mathrm { s e m i } } =$ $\begin{array} { r } { \sum _ { c } q _ { \phi } ( l | \mathbf { x } ) \mathcal { L } _ { \mathrm { s e m i } } ( \mathbf { x } , l , \pmb { \theta } , \phi ) \ + \ \mathrm { K L } ( q _ { \phi } ( l | \mathbf { x } ) | | p ( l ) ) } \end{array}$ . Therefore, we can conclude a marginal likelihood on our
+
+dataset as follows: $\begin{array} { r } { \tilde { \mathcal { L } } _ { \mathrm { s e m i } } ~ = ~ \sum _ { ( \mathbf { x } , l ) \in L } \mathcal { L } _ { \mathrm { s e m i } } ( \mathbf { x } , l , \pmb \theta , \phi ) \ + } \end{array}$ $\begin{array} { r } { \sum _ { \mathbf { x } \in U } \mathcal { U } _ { \mathrm { s e m i } } ( \mathbf { x } , \pmb { \theta } , \phi ) } \end{array}$ . where $L$ and $U$ are the sets of data with and without labels, respectively.
+
+We also want to guarantee that all model parameters can be learned in all cases, including $q _ { \phi } ( l | \mathbf { x } )$ , such that this posterior can be applied as a classifier during inference. Thus, we combine the marginal likelihood with a classification loss to form an extended learning objective: $\tilde { \mathcal { L } } _ { \mathrm { s e m i } _ { \alpha } } =$ $\tilde { \mathcal { L } } _ { \mathrm { s e m i } } + \boldsymbol { \alpha } \cdot \mathbb { E } _ { \tilde { p } ( \mathbf { x } , l ) } \left[ - \log q _ { \phi } ( l | \mathbf { x } ) \right]$
+
+# 4.2 Clustering
+
+We have further extended our algorithm to encompass the clustering paradigm. We propose two distinct strategies. In the first approach, we simply formulate a model in which $p _ { \pmb { \theta } } ( \mathbf { z } )$ is a mixture of desired priors. The means of these priors are characterized by $\pmb \theta$ . From these means, cluster membership, denoted as c can be deduced. This approach requires no alteration to the existing learning objective.
+
+Alternatively, the second method retains the original prior, but introduces an additional latent cluster variable c where $\textstyle \sum _ { i } c _ { i } \ = \ 1$ . Thus, the model can be specified as $p _ { \theta } ( \mathbf { x } , \mathbf { y } , \mathbf { \overline { { z } } } , \mathbf { c } ) \ = \ p _ { \theta } ( \mathbf { x } | \mathbf { z } , \mathbf { c } ) r ( \mathbf { y } | \mathbf { z } ) p _ { \theta } ( \mathbf { z } ) p ( \mathbf { c } )$ with $p ( \mathbf { c } ) ~ =$ $D i r ( \epsilon )$ . Consequently, the variational distributions become $q _ { \phi } ( { \bf z } | { \bf y } , { \bf c } , { \bf x } ) , q _ { \phi } ( { \bf y } , { \bf c } | { \bf x } )$ . This yields the objective:
+
+$$
+\begin{array}{l} \mathcal {L} _ {\mathrm {c l u s}} (\mathbf {x}) = \mathbb {E} _ {q \phi (\mathbf {y}, \mathbf {z}, \mathbf {c} \mid \mathbf {x})} \left[ \log p _ {\theta} (\mathbf {x} \mid \mathbf {z}, \mathbf {c}) \right] \tag {11} \\ - \operatorname {K L} \left(q _ {\phi} (\mathbf {y}, \mathbf {z}, \mathbf {c} | \mathbf {x}) | | p _ {\theta} (\mathbf {y}, \mathbf {z}, \mathbf {c})\right) \\ - \mathbb {E} _ {p _ {\theta} (\mathbf {x})} \left[ \mathrm {K L} \left(p _ {\theta} (\mathbf {z} | \mathbf {x}) \mid \mid q _ {\phi} (\mathbf {z} | \mathbf {x})\right) \right] \\ \end{array}
+$$
+
+Expectations over small numbers of classes c are done analytically; larger c require backpropagating through discrete sampling (Jang, Gu, and Poole 2016; Sahoo et al. 2023).
+
+# 5 Experiments
+
+We compare DDVI with Auto-Encoding Variational Bayes (AEVB) (Kingma and Welling 2013), AEVB with inverse autoregressive flow posteriors (AEVB-IAF) (Kingma et al. 2016), Adversarial Auto-Encoding Bayes (AAEB) (Makhzani et al. 2015), and Path Integral Sampler (PIS) (Zhang and Chen 2021) on MNIST (Lecun et al. 1998) and CIFAR-10 (Krizhevsky and Hinton 2009) in unsupervised and semi-supervised learning settings, and also on the Thousand Genomes dataset (Siva 2008). We also compare with Hierachical Auto-Encoding Variational Bayes (H-AEVB) (Ranganath, Tran, and Blei 2016; Vahdat and Kautz 2020) in unsupervised setting. We discuss the computational costs of all methods in Appendix D. The priors, model architecture, and training details can also be founded in Appendix H. All results below are reported with $9 5 \%$ confidence interval using 3 different seeds.
+
+# 5.1 Unsupervised learning
+
+We start with synthetic experiments that are aimed at benchmarking the expressivity of diffusion-based posteriors and their ability to improve fitting $p$ , a distribution with a complex structured prior, like one might find in probabilistic programming, scientific analysis, or other applications. We fit a
+
+model $p _ { \pmb { \theta } } ( \mathbf { x } , \mathbf { z } )$ on the MNIST and CIFAR-10 datasets with three priors $p ( \mathbf { z } )$ : pinwheel, swiss roll, and square and report our results in Table 1 and 7. The model distribution $p _ { \theta }$ is instantiated by a deep Gaussian latent variable model (DGLVM) with multi-layer perceptrons (MLPs) on MNIST and convolutional neural networks (CNNs) on CIFAR-10 (see the details of model architecture in Appendix G).
+
+Our first set of metrics (ELBO and MMD) seeks to evaluate the learned generative model $p _ { \theta }$ is good. In the ELBO calculation, we average the reconstruction loss across image pixels. We use MMD to measure sample quality: we generate images with the trained model and calculate MMD between the generated images and test images using a mixture of Gaussian kernel with sigma equal to [2, 5, 10, 20, 40, 80]. We only report MMD for MNIST, since CIFAR-10 generated samples are very low-quality for all methods because the latent dimension is 2.
+
+Our last metric seeks to directly evaluate the expressivity of the posterior. We measure latent negative log-likelihood (Latent NLL) by fitting a kernel density estimator (KDE) on the latents produced by the model with test data as input and compute the log-likelihood of the latents sampled from the prior under the fitted KDE.
+
+From Table 1 and Table 7 in Appendix, we see our method DDVI achieve best ELBO in all but one scenario, in which it still performs competitively. We also see strong results in Latent NLL and k-nearest neighbors classification accuracy of the latents (Acc). in many scenarios, except for swiss roll where AAEB does well. We present visualizations on MNIST using the baselines and our method in Figure 2.
+
+# 5.2 Semi-supervised Learning
+
+We also evaluate the performance of our method and the baselines under semi-supervised learning setting where some labels are observed (1,000 for MNIST and 10,000 for CIFAR-10) and the partitions of the priors are known.
+
+For this setting, we evaluate ELBO, Latent NLL, and Acc. We choose classification accuracy since classification is a common downstream task for semi-supervised learning. We use the same set of priors and baselines. Details on how we partition each prior into $p _ { \pmb { \theta } } ( \mathbf { z } | \mathbf { x } , l )$ can be founded in Appendix F. The partitions defined for our priors are local parts of the priors. We note that unlike unsupervised learning, we use the simplified sleep term in our objective for this setting (see Appendix B for details), since $q _ { \phi }$ already gets extra information from l here.
+
+The results are shown in Table 2 and Table 8 in Appendix. DDVI mostly outperforms the baselines across different priors and metrics, especially on CIFAR-10 where DDVI is best across the board. For MNIST, DDVI always achieves the best ELBO, and it also performs competitively with other baselines in classification accuracy. We also show the visualizations of the latents in Figure 3 where DDVI matches the prior almost perfectly.
+
+# 5.3 Clustering and Visualization for Genotype Analysis
+
+In this section, we report results on an real-world task in genome analysis. Visualizing genotype data reveals patterns
+
+![](images/787a79ade10ce638b9bc2d0c9da756af227b744fd49732da0a467651cafead46.jpg)  
+Figure 2: Unsupervised visualization on MNIST using three priors (pinwheel, swiss roll, and square). Each color indicates a class.
+
+Table 1: Unsupervised learning on MNIST. We report ELBO, MMD between generated images and test images, and latent negative log-likelihood (Latent NLL) with pinwheel, swiss roll, and square priors.   
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">Pinwheel</td><td colspan="3">Swiss Roll</td><td colspan="3">Square</td></tr><tr><td>ELBO</td><td>MMD</td><td>Latent NLL</td><td>ELBO</td><td>MMD</td><td>Latent NLL</td><td>ELBO</td><td>MMD</td><td>Latent NLL</td></tr><tr><td>AEVB</td><td>-12.13 ± 0.41</td><td>0.77 ± 0.04</td><td>1.68 ± 0.31</td><td>-14.80 ± 0.23</td><td>0.78 ± 0.17</td><td>5.65 ± 1.58</td><td>-7.85 ± 0.29</td><td>1.10 ± 0.66</td><td>2.78 ± 0.61</td></tr><tr><td>AEVB-IAF</td><td>-4.19 ± 0.05</td><td>0.77 ± 0.00</td><td>1.64 ± 0.73</td><td>-5.10 ± 0.30</td><td>0.61 ± 0.15</td><td>4.43 ± 1.09</td><td>-3.97 ± 0.22</td><td>0.75 ± 0.12</td><td>1.68 ± 0.27</td></tr><tr><td>AAEB</td><td>N/A</td><td>0.68 ± 0.02</td><td>1.54 ± 0.19</td><td>N/A</td><td>0.52 ± 0.03</td><td>3.34 ± 0.16</td><td>N/A</td><td>0.80 ± 0.02</td><td>2.46 ± 0.46</td></tr><tr><td>H-AEVB</td><td>-7.03 ± 3.13</td><td>0.74 ± 0.02</td><td>2.25 ± 3.02</td><td>-7.21 ± 4.62</td><td>0.70 ± 0.22</td><td>4.04 ± 4.62</td><td>-5.71 ± 3.05</td><td>0.76 ± 0.21</td><td>2.22 ± 2.03</td></tr><tr><td>PIS</td><td>-7.83 ± 0.64</td><td>0.75 ± 0.14</td><td>6.50 ± 1.11</td><td>-9.83 ± 0.61</td><td>0.61 ± 0.03</td><td>2.40 ± 1.01</td><td>-7.06 ± 0.06</td><td>0.77 ± 0.04</td><td>3.67 ± 0.08</td></tr><tr><td>DDVI</td><td>-3.88 ± 0.96</td><td>0.67 ± 0.04</td><td>1.27 ± 0.21</td><td>-5.03 ± 0.58</td><td>0.62 ± 0.33</td><td>3.86 ± 0.17</td><td>-3.79 ± 0.14</td><td>0.66 ± 0.07</td><td>1.56 ± 0.09</td></tr></table>
+
+in the latent ancestry of individuals. We instantiate DDVI with a deep Gaussian latent variable model (DGLVM) and compare it against with the three strong clustering baselines using the 1000 Genomes dataset. We also report visualizations from three dimensionality reduction algorithms: PCA, TSNE, and UMAP. For each clustering algorithm, we seek to discover up to 20 clusters. We report quantitative results in terms of cluster purity, cluster completeness, and normalized mutual information (NMI). There is an inherent tradeoff between cluster purity completeness. The overall clustering performance can be captured with NMI.
+
+In Table 3, we see that DDVI attains the best performance on cluster purity and NMI. For cluster completeness, VAE and AAE have better means but much larger confidence interval. Furthermore, we visualize our genotype clustering results in latent space, shown in Figure 4, and also report results from classical dimensionality reduction and visualization methods that do not perform clustering (PCA (Wold, Esbensen, and Geladi 1987), t-SNE (Van der Maaten and Hinton 2008), and UMAP (McInnes, Healy, and Melville 2018)). The legend of Figure 4 can be founded at Figure 5 in Appendix.
+
+# 6 Discussion
+
+Diffusion vs. Normalizing Flows Our approach is most similar to flow-based approximators (Rezende and Mohamed 2015; Kingma et al. 2016); in fact when $T \to \infty$ , our diffusion-based posterior effectively becomes a continuoustime normalizing flow (Song, Meng, and Ermon 2020). However, classical flow-based methods require invertible architectures for each flow layer: this constrains their expressivity and requires backpropagating through potentially a very deep network. Our approach, on the other hand, trains a model (a continuous-time flow when $T \to \infty$ ) via a denoising objective (similar to score matching) that does not require invertible architectures and effectively admits an infinite number of layers (with weight sharing). This model is trained not by backpropagating through the ELBO, but rather via an auxiliary diffusion loss term (effectively, a score matching objective).
+
+Despite training with a modified loss, we observe in Section 5 that a diffusion model with an expressive denoising architecture yields an improved ELBO relative to regular flows. Also, our modified loss based on the forward KL divergence reduces posterior collapse (i.e., all modes of the prior are covered well), and thus produces better samples.
+
+![](images/9ff4eda1985a1233ec206fb2b0905c45e6104d74dc27d366de74b8b6d437501e.jpg)  
+Figure 3: Semi-supervised visualization on MNIST with 1,000 labels using three different priors (pinwheel, swiss roll, and square). Each a indicates one class.
+
+Table 2: Semi-supervised learning on MNIST (1,000 labels). We report ELBO, accuracy using KNN $\mathrm { K } { = } 2 0$ ) classifier (Acc), and latent negative log-likelihood (Latent NLL) with pinwheel, swiss roll, and square priors.   
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">Pinwheel</td><td colspan="3">Swiss Roll</td><td colspan="3">Square</td></tr><tr><td>ELBO</td><td>Acc</td><td>Latent NLL</td><td>ELBO</td><td>Acc</td><td>Latent NLL</td><td>ELBO</td><td>Acc</td><td>Latent NLL</td></tr><tr><td>AEVB</td><td>-11.15 ± 0.53</td><td>0.93 ± 0.01</td><td>1.36 ± 0.03</td><td>-15.29 ± 1.33</td><td>0.68 ± 0.01</td><td>4.60 ± 0.23</td><td>-10.26 ± 0.25</td><td>0.86 ± 0.01</td><td>1.68 ± 0.02</td></tr><tr><td>AEVB-IAF</td><td>-2.10 ± 0.26</td><td>0.95 ± 0.00</td><td>1.06 ± 0.03</td><td>-5.38 ± 1.78</td><td>0.90 ± 0.02</td><td>2.75 ± 0.14</td><td>-2.67 ± 0.83</td><td>0.91 ± 0.01</td><td>0.90 ± 0.02</td></tr><tr><td>AAEB</td><td>N/A</td><td>0.89 ± 0.01</td><td>1.55 ± 0.01</td><td>N/A</td><td>0.88 ± 0.01</td><td>3.07 ± 0.05</td><td>N/A</td><td>1.94 ± 0.38</td><td>0.76 ± 0.13</td></tr><tr><td>DDVI</td><td>-0.24 ± 0.13</td><td>0.95 ± 0.00</td><td>1.06 ± 0.01</td><td>-2.89 ± 0.33</td><td>0.92 ± 0.01</td><td>2.09 ± 0.00</td><td>0.02 ± 0.09</td><td>0.90 ± 0.01</td><td>1.49 ± 0.03</td></tr></table>
+
+Table 3: Quantitative genotype clustering results.   
+
+<table><tr><td>Method</td><td>Cluster Purity</td><td>Cluster Completeness</td><td>NMI</td></tr><tr><td>AEVB</td><td>0.28 ± 0.02</td><td>0.78 ± 0.16</td><td>0.59 ± 0.08</td></tr><tr><td>AEVB-IAF</td><td>0.29 ± 0.04</td><td>0.73 ± 0.06</td><td>0.55 ± 0.06</td></tr><tr><td>AAEB</td><td>0.37 ± 0.06</td><td>0.76 ± 0.11</td><td>0.63 ± 0.02</td></tr><tr><td>DDVI</td><td>0.45 ± 0.03</td><td>0.75 ± 0.05</td><td>0.66 ± 0.04</td></tr></table>
+
+Diffusion vs. Other Generative Models Variational posteriors based on GANs (Makhzani et al. 2015) also admit expressive architectures and require only sample-based access to the prior $p ( \mathbf { z } )$ . Our diffusion-based approach admits a more stable loss, and is potentially more expressive, as it effectively supports an infnite number of layers (with shared parameters when $T \to \infty$ ). Unlike GANs, our models also admit explicit likelihoods and allow us to compute the ELBO for model evaluation. Our approach is similar to variational MCMC (Salimans, Kingma, and Welling 2015); however, we train with a better objective augmented with a diffusion loss, and we adopt improved architectures with shared weights across layers.
+
+Diffusion for Approximate Inference Existing diffusionbased approximate inference methods (Berner, Richter, and Ullrich 2022; Zhang and Chen 2021; Vargas, Grathwohl,
+
+and Doucet 2023; Zhang et al. 2023; Richter, Berner, and Liu 2023; Sendera et al. 2024; Akhound-Sadegh et al. 2024) focus on the task of drawing samples from unnormalized distributions $\tilde { p } ( { \mathbf z } )$ and estimating the partition function $\begin{array} { r } { Z = \int _ { \mathbf { z } } \tilde { p } ( \mathbf { z } ) d \mathbf { z } } \end{array}$ . While these methods are applicable in our setting—we set the unnormalized $\tilde { p } ( { \mathbf z } )$ to $p _ { \pmb { \theta } } ( \mathbf { x } , \mathbf { z } )$ such that $Z = p _ { \pmb { \theta } } ( \mathbf { x } )$ —they also tackle a more challenging problem (drawing samples from energy-based models) in more general classes of models (arbitrary unnormalized distributions). In contrast, we focus on restricted but still important classes of models (VAEs, Bayes networks, etc.), and we solve more challenging sets of tasks (e.g., maximumlikelihood learning) by using properties of $p _ { \pmb { \theta } }$ (the factorization $p _ { \pmb { \theta } } ( \mathbf { x } | \mathbf { z } ) p _ { \pmb { \theta } } ( \mathbf { z } )$ and efficient sampling from $p _ { \theta }$ ).
+
+Our algorithms are also simpler. For example, diffusion sampling methods require backpropagating through a sampling process to minimize the reverse $\mathrm { K L } ( q _ { \phi } | | p _ { \theta } )$ , which poses challenges with optimization and credit assignment. Some methods based on Schrodinger bridges require an iterative optimization process generalizing the sinkhorn algorithm or computationally expensive on-policy or off-policy (Malkin et al. 2022) trajectory-based optimization. In contrast, DDVI optimizes the forward ${ \mathrm { K L } } ( { \bar { p } } _ { \theta } | | q _ { \phi } )$ using simple gradient-based optimization that directly emulates diffusionbased training.
+
+![](images/a23a59ce2b9999b6abebaa98b7fa829298deb6d669ea02bdf134913e4f9df19a.jpg)  
+Figure 4: Visualization of genotype clusters. A color represents one ethnicity.
+
+# 7 Related Work
+
+Latent Diffusion Vahdat, Kreis, and Kautz (2021); Wehenkel and Louppe (2021); Rombach et al. (2022) perform diffusion in the latent space of a VAE. Their goal is high sample quality, and they introduce into $p$ hierarchical latents with simple Gaussian priors.
+
+Our goal is different: we seek to fit a $p$ with structured latents (e.g., in probabilistic programming or in science applications, users introduce prior knowledge via handcrafted $p _ { \ell }$ ), and we improve variational inference in this structured model by introducing auxiliary latents into $q$ . Recent work (Preechakul et al. 2022; Zhang, Zhao, and Lin 2022; Wang et al. 2023) has also melded auto-encoders with diffusion models, focusing on semantically meaningful lowdimensional latents in a diffuser $p$ . Cohen et al. (2022) crafts a diffusion bridge linking a continuously coded vector to a non-informative prior distribution.
+
+Diffusion for Approximate Inference Diffusion sampling (Berner, Richter, and Ullrich 2022; Zhang and Chen 2021; Vargas, Grathwohl, and Doucet 2023; Zhang et al. 2023; Richter, Berner, and Liu 2023; Sendera et al. 2024; Akhound-Sadegh et al. 2024) mainly focuses on the task of drawing samples from unnormalized distributions and estimating the partition function. These works draw connections between diffusion (learning the denoising process) and stochastic control (learning the Follmer drift). Some other ¨ works (Zhang et al. 2023; Akhound-Sadegh et al. 2024; Sendera et al. 2024) use continuous generative flow networks (GFlowNets) – deep reinforcement learning algorithms adapted to variational inference that offers stable offpolicy training and thus flexible exploration. While this work is applicable to our setting, it does not rely on the structure
+
+of $p ( \mathbf { x } , \mathbf { z } )$ available to us, namely tractable sampling in $p$
+
+Dimensionality Reduction Latent variable models in general are an attractive alternative to visualization methods like PCA, Sparse PCA, NMF, UMAP, and t-SNE (Wold, Esbensen, and Geladi 1987; Kuleshov 2013; Lee and Seung 2000; McInnes, Healy, and Melville 2018; Van der Maaten and Hinton 2008). Domain-specific knowledge can be injected through the prior, and deep neural networks can be utilized to achieve a more expressive mapping from the data space to the latent space. Nevertheless, downsides of LVMs are that they are more computationally expensive and require careful hyperparameter tuning.
+
+# 8 Conclusion
+
+While this paper focuses on applications of DDVI to dimensionality reduction and visualization, there exist other tasks for the algorithm, e.g., density estimation or sample quality. Accurate variational inference has the potential to improve downstream applications of generative modeling, e.g., decision making (Nguyen and Grover 2022; Deshpande and Kuleshov 2023), meta-learning (Rastogi et al. 2023), or causal effect estimation (Deshpande et al. 2022).
+
+Since our learning objective differs from the ELBO (it adds a regularizer), we anticipate gains on models whose training benefits from regularization, but perhaps not on all models. Also, attaining competitive likelihood estimation requires architecture improvements that are orthogonal to this paper. However, our ability to generate diverse samples and achieve class separation in latent space hints at the method’s potential on these tasks.
+
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+
+# A Pseudocode
+
+Here we provide a pseudocode to illustrate the training process of DDVI.
+
+Algorithm 1: DDVI Pseudocode   
+1: (Optional) Pre-train $p_{\theta}(\mathbf{x}|\mathbf{z})$ and $q_{\phi}(\mathbf{y}|\mathbf{x})$ with DDVI but with unconditional diffusion model $q_{\phi}(\mathbf{z}|\mathbf{y})$ 2: for epoch $= 1,\ldots ,n$ do  
+3: for $\mathbf{x}_1,\ldots ,\mathbf{x}_k\sim p_{\mathcal{D}}(\mathbf{x})$ do  
+4: $\mathbf{y}_i\sim q_{\phi}(\mathbf{y}|\mathbf{x}_i)$ and $\mathbf{z}_i\sim q(\mathbf{z}|\mathbf{y}_i,\mathbf{x}_i)$ for $i = 1,\ldots ,k$ 5: Optimize $\theta ,\phi$ with respect to a Monte Carlo estimate of $\mathbb{E}_{q_{\phi}(\mathbf{y},\mathbf{z}|\mathbf{x})}[\log p_{\theta}(\mathbf{x}|\mathbf{z})] - \mathrm{KL}(q_{\phi}(\mathbf{y},\mathbf{z}|\mathbf{x})||p_{\theta}(\mathbf{y},\mathbf{z}))$ for each $\mathbf{x}_i$ 6: for iteration $= 1,\ldots ,m$ do  
+7: $\mathbf{z}_1,\ldots ,\mathbf{z}_k\sim p(\mathbf{z})$ 8: $\hat{\mathbf{x}}_i\sim p(\mathbf{x}|\mathbf{z}_i)$ for $i = 1,\ldots ,k$ 9: $\mathbf{y}_i\sim r(\mathbf{y}|\mathbf{z}_i)$ for $i = 1,\ldots ,k$ 10: Optimize $\phi$ using the standard diffusion noise prediction loss on $q_{\phi}(\mathbf{z}|\mathbf{y}_i,\hat{\mathbf{x}}_i)$ 11: end for  
+12: end for  
+13: end for
+
+# B Simplifying Wake-Sleep
+
+In wake-sleep, sampling x from $p _ { \pmb { \theta } }$ to obtain gradients for the sleep term introduces computational overhead. To address this issue, we propose wake-sleep in latent space, an algorithm that optimizes an approximation $\hat { \mathcal { L } } ( \mathbf { x } , \pmb \theta , \phi )$ of $\mathcal { L }$ :
+
+$$
+\hat {\mathcal {L}} (\mathbf {x}, \boldsymbol {\theta}, \phi) = \underbrace {\mathbb {E} _ {q _ {\phi} (\mathbf {y} , \mathbf {z} \mid \mathbf {x})} \left[ \log p _ {\boldsymbol {\theta}} (\mathbf {x} \mid \mathbf {z}) \right]} _ {\text {w a k e / r e c o n s t r . t e r m} \mathcal {L} _ {\text {r e c}} (\mathbf {x}, \boldsymbol {\theta}, \phi)} \underbrace {- \mathrm {K L} \left(q _ {\phi} (\mathbf {y} , \mathbf {z} \mid \mathbf {x}) \left\| p _ {\boldsymbol {\theta}} (\mathbf {y} , \mathbf {z}) \right.\right)} _ {\text {p r i o r r e g u l a r i z a t i o n t e r m} \mathcal {L} _ {\text {r e g}} (\mathbf {x}, \boldsymbol {\theta}, \phi)} \underbrace {- \mathrm {K L} \left(p _ {\boldsymbol {\theta}} (\mathbf {z}) \left\| q _ {\boldsymbol {\phi}} (\mathbf {z} \mid \mathbf {x}) \right.\right)} _ {\text {l a t e n t s l e e p t e r m} \mathcal {L} _ {\text {s l e e p}} (\mathbf {x}, \boldsymbol {\phi})}. \tag {12}
+$$
+
+We have replaced ${ \mathcal { L } } _ { \mathrm { s l e e p } } ( \phi )$ with a latent sleep term $\mathcal { L } _ { \mathrm { s l e e p } } ( \mathbf { x } , \phi )$ , in which $\mathbf { x }$ is given, and we only seek to fit the true reverse noising process $r ( \mathbf { z } | \mathbf { y } )$ independently of $\mathbf { x }$ . We can similarly show that
+
+$$
+\begin{array}{l} \mathcal {L} _ {\text {s l e e p}} (\mathbf {x}, \phi) = \mathbb {E} _ {p _ {\theta} (\mathbf {z})} \left[ \log q _ {\phi} (\mathbf {z} | \mathbf {x}) \right] + \bar {H} \left(p _ {\theta}\right) \geq \mathbb {E} _ {p _ {\theta} (\mathbf {z}) r (\mathbf {y} | \mathbf {z})} \left[ \log \left(q _ {\phi} (\mathbf {y}, \mathbf {z} | \mathbf {x}) / r (\mathbf {y} | \mathbf {z})\right) \right] + \bar {H} \left(p _ {\theta}\right) (13) \\ = - \mathbb {E} _ {p _ {\theta} (\mathbf {z})} \left[ \mathrm {K L} \left(r (\mathbf {y} \mid \mathbf {z}) \left\| q _ {\phi} (\mathbf {y} \mid \mathbf {z}, \mathbf {x}) \right\}\right) - \mathrm {K L} \left(p _ {\theta} (\mathbf {z}) \left\| q (\mathbf {z} \mid \mathbf {x})\right)\right), \right. (14) \\ \end{array}
+$$
+
+where $\bar { H } ( p _ { \theta } )$ is an entropy term constant in $\phi$ . Thus, we minimize the forward KL divergence by sampling $\mathbf { z }$ , and applying the noising process to get y; the $q _ { \phi }$ is fit to denoise $\mathbf { z }$ from y as in Equation 8.
+
+We optimize our bound on $\hat { \mathcal { L } } ( x , \theta , \phi )$ end-to-end using minibatch gradient descent over θ, ϕ. While the wake term is a reconstruction loss as in wake-sleep, the sleep term generates latent samples $\mathbf { z } , \mathbf { y }$ from $r ( \mathbf { y } | \mathbf { z } ) p _ { \pmb { \theta } } ( \mathbf { z } )$ (by analogy with $p _ { \pmb { \theta } } ( \mathbf { x } | \mathbf { z } ) p _ { \pmb { \theta } } ( \mathbf { z } )$ in normal wake-sleep); the denoiser $q _ { \phi }$ is trained to recover z from y. Thus, we perform wake-sleep in latent space, which obviates the need for alternating wake and sleep phases, and allows efficient end-to-end training. A limitation of this approximation is that the sleep term does not fit $q _ { \phi }$ to the true $p _ { \pmb { \theta } } ( \mathbf { z } | \mathbf { x } , \mathbf { y } )$ , and as a consequence $\hat { L }$ is not a tight lower bound on $\log p _ { \pmb { \theta } } ( \mathbf { x } )$ . We may think of $\bar { \mathcal { L } } _ { \mathrm { s l e e p } } ( \mathbf { x } , \phi )$ as a regularizer to the ELBO.
+
+# C Comparision of Methods
+
+We provide a comprehensive comparison of different methods in Table 4. Vahdat, Kreis, and Kautz (2021); Wehenkel and Louppe (2021); Rombach et al. (2022) perform diffusion in the latent space of a VAE to improve the efficiency of image generation. Their goal is high sample quality, and they introduce into $p$ hierarchical latents with simple Gaussian priors. Our goal is different: we seek a method to fit a $p$ with structured latents (e.g., in probabilistic programming or in science applications, users introduce prior knowledge via hand-crafted $p$ ), and we improve variational inference in this structured model by introducing auxiliary latents into $q$ .
+
+Recent work (Preechakul et al. 2022; Zhang, Zhao, and Lin 2022; Wang et al. 2023) has also melded auto-encoders with diffusion models, focusing on semantically meaningful low-dimensional latents in a diffuser $p$ . Cohen et al. (2022) crafts a diffusion bridge linking a continuous coded vector to a non-informative prior distribution.
+
+# D Computational Cost Analysis
+
+We conduct a computational cost analysis between the baselines and DDVI with various timesteps on the genotype clustering/visualization experiments. Table 5 shows that DDVI outperforms baselines at all timestamps and continues to improve after the baselines have plateaued.
+
+<table><tr><td>Model</td><td>Training Objective</td><td>Approximating Family</td><td>Sample-based Prior</td><td>Auxiliary Variable</td><td>Tasks</td><td>Simplified Graphical Illustration</td></tr><tr><td>AEVB</td><td>ELBO</td><td>Diagonal Gaussian</td><td>X</td><td>X</td><td>Density estimation</td><td>x→z→x</td></tr><tr><td>AEVB-IAF</td><td>ELBO</td><td>Normalizing flow</td><td>X</td><td>✓</td><td>Density estimation / Visualization</td><td>x→z0→zT→x</td></tr><tr><td>AAEB</td><td>Adversarial training</td><td>Adversarial generator</td><td>✓</td><td>X</td><td>Visualization</td><td>x→z→x</td></tr><tr><td>H-AEVB-(IAF)</td><td>ELBO</td><td>Factorial Normal / Normalizing flow</td><td>X</td><td>✓</td><td>Density estimation / High-quality sample generation</td><td>x→z0→zT→z0→x</td></tr><tr><td>ADGM</td><td>ELBO</td><td>Non-Gaussian</td><td>X</td><td>✓</td><td>Density estimation</td><td>x→a→z→x</td></tr><tr><td>LDM</td><td>ELBO</td><td>Diagonal Gaussian</td><td>X</td><td>✓</td><td>High-quality sample generation</td><td>x→z0→zT→z0→x</td></tr><tr><td>LSGM</td><td>ELBO &amp; score matching</td><td>Diagonal Gaussian</td><td>X</td><td>✓</td><td>High-quality sample generation</td><td>x→z0→zT→z0→x</td></tr><tr><td>DDVI</td><td>ELBO &amp; sleep term</td><td>Denoising diffusion</td><td>✓</td><td>✓</td><td>Density estimation / Visualization</td><td>x→zT(y)→z0(z)→x</td></tr></table>
+
+Table 4: Comparison of DDVI to other relevant methods. x represents the original data input to the model. z denotes the latent (hidden) representation of the input data. a represents an auxiliary variable introduced in some models (like ADGM) to capture additional aspects of the data distribution or to assist in the model’s learning process.   
+Table 5: Computational cost trade-off on 1kgenome: NMI vs wall-clock training time   
+
+<table><tr><td rowspan="2">Method</td><td colspan="6">NMI values at different wall-clock training times</td></tr><tr><td>NMI @ 10 min</td><td>NMI @ 20 min</td><td>NMI @ 30 min</td><td>NMI @ 40 min</td><td>NMI @ 50 min</td><td>NMI @ 60 min</td></tr><tr><td>AEVB</td><td>0.52</td><td>0.52</td><td>0.52</td><td>0.52</td><td>0.52</td><td>0.52</td></tr><tr><td>AEVB-IAF</td><td>0.54</td><td>0.52</td><td>0.52</td><td>0.52</td><td>0.52</td><td>0.52</td></tr><tr><td>AAEB</td><td>0.61</td><td>0.57</td><td>0.57</td><td>0.57</td><td>0.57</td><td>0.57</td></tr><tr><td>DDVI (T=5)</td><td>warm up</td><td>0.63</td><td>0.63</td><td>0.66</td><td>0.66</td><td>0.66</td></tr><tr><td>DDVI (T=10)</td><td>warm up</td><td>0.64</td><td>0.68</td><td>0.70</td><td>0.70</td><td>0.70</td></tr><tr><td>DDVI (T=20)</td><td>warm up</td><td>0.50</td><td>0.51</td><td>0.56</td><td>0.64</td><td>0.68</td></tr><tr><td>DDVI (T=50)</td><td>warm up</td><td>0.52</td><td>0.54</td><td>0.51</td><td>0.59</td><td>0.59</td></tr></table>
+
+# E Connections to Diffusion Samplers
+
+Diffusion sampling (Berner, Richter, and Ullrich 2022; Zhang and Chen 2021; Vargas, Grathwohl, and Doucet 2023; Zhang et al. 2023; Richter, Berner, and Liu 2023; Sendera et al. 2024; Akhound-Sadegh et al. 2024) mainly focuses on the task of drawing samples from unnormalized distributions and estimating the partition function. These works draw connections between diffusion (learning the denoising process) and stochastic control (learning the Follmer drift), leading to several approaches, e.g., ¨ path integral sampler (PIS) (Zhang and Chen 2021), denoising diffusion sampler (DDS) (Vargas, Grathwohl, and Doucet 2023), and time-reversed diffusion sampler (DIS) (Berner, Richter, and Ullrich 2022), which have been unified by Richter, Berner, and Liu (2023). Some other works (Zhang et al. 2023; Akhound-Sadegh et al. 2024) use continuous generative flow networks (GFlowNets) – deep reinforcement learning algorithms adapted to variational inference that offers stable off-policy training and thus flexible exploration. Sendera et al. (2024) benchmarked these previous diffusion-structured amortized inference methods and studied how to improve credit assignment in diffusion samplers, which refers to the propagation of learning signals from the target density to the parameters of earlier sampling steps. Overall, there are indeed some strong connections between these works and ours:
+
+• They also focus on variational methods that directly fit a parametric family of tractable distributions (given by controlled SDEs) to the target density.   
+• They cast the density estimation/sampling problem into an optimization problem over a control objective, which learns control drifts (and diffusion) parameterized by neural networks.
+
+But we would like to clarify that there are also some clear differences between them:
+
+• The diffusion-structured samplers only focus on density estimation/sampling but ignore the problem of learning a generative model, which is one of the main focuses of our work. We aim to perform more accurate variational inference using an auxiliary variable model augmented by diffusion models to improve generative modeling. In our setting, $p _ { \theta } ( z | x )$ is a moving target density, as we jointly learn $\pmb \theta$ with $\phi$ , as opposed to a static target density that diffusion-structured samplers are designed to solve.   
+• To tackle the challenge of credit assignment – propagating weak learning signals through the sampling trajectory, the techniques proposed in diffusion-structured samplers are mostly based on partial trajectory information, which has higher training costs over on-policy (Zhang and Chen 2021) or off-policy (Malkin et al. 2022) trajectory-based optimization. Instead, we introduce a wake-sleep optimization algorithm and its simplified version to alleviate the weak learning signal issue and optimize the evidence lower bound in a better way.   
+• In Equation 8, we are minimizing the forward KL divergence $\mathrm { K L } ( p _ { \theta } | | q _ { \phi } )$ , where diffusion samplers are minimizing the reverse $\mathrm { K L } ( q _ { \phi } | | p _ { \theta } )$ .
+
+We also summarize the connections and differences in the table below.
+
+Table 6: Comparison of Diffusion-structured Samplers, GFlowNet-based Approaches, and DDVI   
+
+<table><tr><td></td><td>Diffusion Samplers (Berner, Richter, and Ullrich 2022; Zhang and Chen 2021; Vargas, Grathwohl, and Doucet 2023; Akhound-Sadegh et al. 2024)</td><td>GFlowNet-based (Zhang et al. 2023; Richter, Berner, and Liu 2023; Sendera et al. 2024; Malkin et al. 2022)</td><td>DDVI (ours)</td></tr><tr><td>Tasks</td><td>Sampling, density estimation</td><td>Sampling, density estimation</td><td>Learning, Sampling, Dimensionality reduction</td></tr><tr><td>Model Family for p</td><td>Any energy-based</td><td>Any energy-based</td><td>Latent with tractable p(x|z), p(z)</td></tr><tr><td>Model Family for q</td><td>Markov chain</td><td>Markov chain</td><td>Markov chain</td></tr><tr><td>Objective Algorithm</td><td>KL(q||p) with regularizer Gradient descent (with reference process), importance sampling</td><td>Trajectory balance objective RL-motivated off-policy optimization (replay buffers, Thompson sampling, etc.)</td><td>KL(p||q) with ELBO Gradient descent with wake-sleep</td></tr><tr><td>Compatible Models</td><td>Anything energy-based</td><td>Anything energy-based</td><td>LDA, deep latent-variable models</td></tr><tr><td>Applications</td><td>Sampling from physics-based models, model selection based on NLL</td><td>Sampling from physics-based models, model selection based on NLL</td><td>Probabilistic programming, visualization</td></tr></table>
+
+# F Priors
+
+Below we describe the sampling process for each prior.
+
+Pinwheel. This distribution was used in (Johnson et al. 2016). We define the number of clusters to be 10. For semi-supervised learning experiments, this prior is partitioned into 10 partitions, each partition being a cluster.
+
+Swiss Roll. This distribution was used in (Marsland 2014). For semi-supervised learning experiments, this prior is partitioned into 10 partitions. The samples from the prior can actually be characterized by a single scalar representing how far you are long the swiss roll from the center. The paritioning is done by creating 10 equal-length intervals in this 1D space.
+
+Square. This distribution has the shaped of a square going from -1 to 1 in both axes. Each position on the square can be characterized by a single scalar representing how far you are from the top left corner. Sampling is done by sampling the position uniformly and turn the 1D position to 2D latent. We add noise $\sigma = 0 . 0 6$ to the prior. For semi-supervised learning experiments, this prior is partitioned into 10 partitions. The partitioning is done by creating 10 equal-length intervals in the 1D position space.
+
+AEVB and AEVB-IAF requires that we can evaluate the prior density. To do this, for all priors, we evaluate the density by fitting a kernel density estimator with mixture of gaussian kernel with bandwidth equal to 0.005, 0.008, 0.01, 0.03, and 0.05.
+
+# G Model Architecture
+
+All methods use the same architecture for encoder $q _ { \phi } ( \mathbf { z } | \mathbf { x } )$ and decoder $p _ { \pmb { \theta } } ( \mathbf { x } | \mathbf { z } )$ , excluding the extra parts specific to each method which we describe below, for the same dataset. For MNIST, the encoder and decoder are multi-layer perceptron with
+
+Chinese Dai in Xishuangbanna, China   
+Han Chinese in Bejing,China   
+Japanese in Tokyo, Japan   
+Kinh in Ho Chi Minh City, Vietnam   
+Southern Han Chinese, China   
+Bengali in Bangladesh   
+Gujarati Indian in Houston,TX   
+Indian Telugu in the UK   
+Punjabi in Lahore,Pakistan
+
+Sri Lankan Tamil in the UK   
+African Ancestry in Southwest US   
+African Caribbean in Barbados   
+Esan in Nigeria   
+Gambian in Western Division, The Gambia   
+Luhya in Webuye, Kenya   
+Mende in Sierra Leone   
+Yoruba in Ibadan, Nigeria   
+British in England and Scotland
+
+Finnish in Finland   
+Iberian populations in Spain   
+Toscani in taly   
+Utahresidents with Norther and Westem European ancestry   
+Colombian in Medellin, Colombia   
+Mexican Ancestry in Los Angeles, California   
+Peruvian in Lima, Peru   
+Puerto Rican in Puerto Rico
+
+Figure 5: Legend showing what ethnicity each color corresponds to in the 1000 Genomes dataset
+
+two hidden layers, each with 1000 hidden units. For CIFAR-10, the encoder is a 4-layer convolutional neural network with (16, 32, 64, 128) channels with a linear layer on top, and the decoder is a 4-layer tranposed convolutional neural network with (64, 32, 16, 3) channels where a linear layer is used to first turn the feature dimension from 2 to 64.
+
+AEVB-IAF employs 4 IAF transformations on top of the encoder, each is implemented with a 4-layer MADE. The number of hidden units in MADE is 128. The ordering is reversed between every other IAF transformation.
+
+AAEB has a discriminator, used in adversarial training, which is a multi-layer perceptron with two hidden layers, each with 1000 hidden units.
+
+DDVI has a diffusion model on top of the encoder. The time-conditioned reverse diffusion distribution is implemented with a 5-layer time-conditioned multi-layer perceptron, each with 128 hidden units. A time-conditioned linear layer learns an additional embedding for each timestep and adds it to the output of the linear layer.
+
+# H Training Details
+
+For training, we update the parameters for each batch of inputs by alternating between the ELBO phase (optimizing $\pmb { \theta }$ and $\phi$ with respect to the ELBO, i.e., the reconstruction term and the prior matching term) and the sleep phase (optimizing $\phi$ with respect to the sleep term). We use Adam optimizer and latent size of 2 for all of our experiments. Each algorithm takes roughly 2 hours on a single Nvidia GeForce RTX 3090 to complete one run of experiment. The training details of each algorithm are detailed below:
+
+AEVB. The batch size is set to 128. The number of epochs is 200 for unsupervised and clustering experiments and 50 for semi-supervised experiments. The learning rate is 0.0001. The loss is BCE for MNIST and CIFAR-10 experiments and MSE for genotype analysis experiments. For semi-supervised MNIST experiments, the kl divergence weight is set to be 0.01, while for semi-supervised CIFAR-10 experiments, the kl divergence weight is set to be 0.01. For other experiments, the KL divergence weight is set with a schedule linear on number of epochs going from 0 to 0.01. We also have a weight of 5 multiplied to the prior density.
+
+AEVB-IAF. The batch size, number of epochs, learning rate, loss, KL divergence weight, and prior density weight are the same as VAE. The context size, i.e., the size of features used to initialize the flow layers for different datat point, is 10.
+
+AAEB. The batch size is set to 128. The number of epochs is 200 for all experiments. The learning rate is 0.0002. The loss is MSE for all experiments. To stabilize the training, we add noise to the input to the discriminator with sigma 0.3 at the start and lower it by 0.1 for every 50 epochs. The noise equals to 0 at epoch 150.
+
+DDVI. The batch size is set to 128 for most experiments, except for semi-supervied experiments where the batch size is 1024. The number of epochs is 200 for unsupervised and clustering experiments and 30 for semi-supervised experiments. The learning rate is 0.0001. The loss is BCE for MNIST and CIFAR-10 experiments and MSE for genotype analysis experiments. For unsupervised MNIST and CIFAR-10 experiments, the KL divergence weight is set to 0.003. For semi-supervised MNIST experiment, we use KL divergence weight of 0.1. For semi-supervised CIFAR-10 experiment, we use KL divergence weight of 0.5. For clustering experiment, we use KL divergence weight of 0.005. The number of timesteps is 20 for unsupervised and clustering experiments and 100 for semi-supervised experiments.
+
+# I Genotype Analysis Experiments Details
+
+Before inputting the data points into any of the visualization methods, we first pre-process it by running a PCA and keep only the first 1000 principal components of the data points. We further divide the features by 30 for all latent variables model methods.
+
+The legend of the 1000 Genomes Visualization plot can be found at Figure 5.
+
+# J ELBO for Auxiliary-Variable Generative Models
+
+We aim to derive the lower bound for the log-likelihood $\log p _ { \pmb { \theta } } ( \mathbf { x } )$ by introducing auxiliary variables and applying the Evidence Lower Bound (ELBO) twice.
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">Pinwheel</td><td colspan="2">Swiss Roll</td><td colspan="2">Square</td></tr><tr><td>ELBO</td><td>Latent NLL</td><td>ELBO</td><td>Latent NLL</td><td>ELBO</td><td>Latent NLL</td></tr><tr><td>AEVB</td><td>-12.96 ± 1.81</td><td>3.26 ± 0.60</td><td>-12.87 ± 4.55</td><td>6.25 ± 1.58</td><td>-7.91 ± 0.11</td><td>2.91 ± 0.17</td></tr><tr><td>AEVB-IAF</td><td>-3.24 ± 0.16</td><td>1.71 ± 0.84</td><td>-4.03 ± 0.73</td><td>5.51 ± 0.51</td><td>-2.10 ± 0.31</td><td>1.71 ± 0.77</td></tr><tr><td>AAEB</td><td>N/A</td><td>1.70 ± 0.41</td><td>N/A</td><td>3.18 ± 0.22</td><td>N/A</td><td>1.67 ± 0.17</td></tr><tr><td>H-AEVB</td><td>-4.42 ± 0.46</td><td>1.69 ± 0.17</td><td>-5.36 ± 0.77</td><td>5.74 ± 0.55</td><td>-2.86 ± 0.11</td><td>1.64 ± 0.09</td></tr><tr><td>PIS</td><td>-2.92 ± 1.23</td><td>3.61 ± 0.62</td><td>-4.14 ± 0.49</td><td>7.14 ± 0.14</td><td>-4.85 ± 0.06</td><td>3.91 ± 0.06</td></tr><tr><td>DDVI</td><td>-1.38 ± 0.44</td><td>1.75 ± 0.53</td><td>-3.05 ± 0.65</td><td>5.66 ± 2.63</td><td>-2.47 ± 0.30</td><td>1.58 ± 0.09</td></tr></table>
+
+Table 7: Unsupervised learning on CIFAR-10. We report ELBO and latent negative log-likelihood (Latent NLL) with pinwheel, swiss roll, and square priors.   
+Table 8: Semi-supervised learning on CIFAR-10 (10,000 labels). We report ELBO, accuracy using KNN $\mathrm { K } { = } 2 0$ ) classifier (Acc), and latent negative log-likelihood (Latent NLL) with pinwheel, swiss roll, and square priors.   
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">Pinwheel</td><td colspan="3">Swiss Roll</td><td colspan="3">Square</td></tr><tr><td>ELBO</td><td>Acc</td><td>Latent NLL</td><td>ELBO</td><td>Acc</td><td>Latent NLL</td><td>ELBO</td><td>Acc</td><td>Latent NLL</td></tr><tr><td>AEVB</td><td>-17.14 ± 1.46</td><td>0.30 ± 0.05</td><td>2.32 ± 0.27</td><td>-17.89 ± 5.21</td><td>0.20 ± 0.07</td><td>6.56 ± 2.25</td><td>-13.30 ± 1.50</td><td>0.30 ± 0.05</td><td>1.95 ± 0.28</td></tr><tr><td>AEVB-IAF</td><td>-5.70 ± 0.07</td><td>0.47 ± 0.01</td><td>1.62 ± 0.05</td><td>-5.53 ± 2.82</td><td>0.28 ± 0.08</td><td>6.82 ± 1.90</td><td>-4.41 ± 0.53</td><td>0.36 ± 0.01</td><td>1.58 ± 0.15</td></tr><tr><td>AAEB</td><td>N/A</td><td>0.25 ± 0.01</td><td>1.77 ± 0.14</td><td>N/A</td><td>0.23 ± 0.01</td><td>3.38 ± 0.30</td><td>N/A</td><td>0.23 ± 0.04</td><td>1.74 ± 0.15</td></tr><tr><td>DDVI</td><td>-1.60 ± 0.29</td><td>0.49 ± 0.01</td><td>1.09 ± 0.05</td><td>-4.13 ± 1.51</td><td>0.47 ± 0.09</td><td>2.29 ± 0.08</td><td>-1.73 ± 0.64</td><td>0.49 ± 0.01</td><td>1.48 ± 0.02</td></tr></table>
+
+Introduce the latent variable z and apply the ELBO:
+
+$$
+\begin{array}{l} \log p _ {\boldsymbol {\theta}} (\mathbf {x}) = \log \int p _ {\boldsymbol {\theta}} (\mathbf {x}, \mathbf {z}) d \mathbf {z} (15) \\ \geq \mathbb {E} _ {q _ {\phi} (\mathbf {z} | \mathbf {x})} \left[ \log \frac {p _ {\theta} (\mathbf {x} , \mathbf {z})}{q _ {\phi} (\mathbf {z} | \mathbf {x})} \right] \quad \text {(b y J e s s e n s i n e q u a l i t y)} (16) \\ = \mathbb {E} _ {q _ {\phi} (\mathbf {z} | \mathbf {x})} \left[ \log p _ {\theta} (\mathbf {x} | \mathbf {z}) \right] - \operatorname {K L} \left(q _ {\phi} (\mathbf {z} | \mathbf {x}) \| p (\mathbf {z})\right) (18) \\ \end{array}
+$$
+
+Then, introduce an auxiliary variable y and apply the ELBO again:
+
+$$
+\begin{array}{l} \log p _ {\boldsymbol {\theta}} (\mathbf {x}) \geq \mathbb {E} _ {q _ {\boldsymbol {\phi}} (\mathbf {z} | \mathbf {x})} \left[ \log p _ {\boldsymbol {\theta}} (\mathbf {x} | \mathbf {z}) \right] - \operatorname {K L} \left(q _ {\boldsymbol {\phi}} (\mathbf {z} | \mathbf {x}) \| p (\mathbf {z})\right) (19) \\ = \mathbb {E} _ {q _ {\phi} (\mathbf {z} | \mathbf {x})} \left[ \log p _ {\boldsymbol {\theta}} (\mathbf {x} | \mathbf {z}) \right] - \mathbb {E} _ {q _ {\phi} (\mathbf {z} | \mathbf {x})} \log q _ {\phi} (\mathbf {z} | \mathbf {x}) + \mathbb {E} _ {q _ {\phi} (\mathbf {z} | \mathbf {x})} \log p (\mathbf {z}) (20) \\ \geq \mathbb {E} _ {q _ {\phi} (\mathbf {z} | \mathbf {x})} \left[ \mathbb {E} _ {q _ {\phi} (\mathbf {y} | \mathbf {x}, \mathbf {z})} \left[ \log p _ {\theta} (\mathbf {x} | \mathbf {z}) \right] \right] - \mathbb {E} _ {q _ {\phi} (\mathbf {z} | \mathbf {x})} \left[ \mathbb {E} _ {q _ {\phi} (\mathbf {y} | \mathbf {x}, \mathbf {z})} \left[ \log \frac {q _ {\phi} (\mathbf {y} , \mathbf {z} | \mathbf {x})}{r (\mathbf {y} | \mathbf {x} , \mathbf {z})} \right] \right] + \mathbb {E} _ {q _ {\phi} (\mathbf {z} | \mathbf {x})} \left[ \mathbb {E} _ {q _ {\phi} (\mathbf {y} | \mathbf {x}, \mathbf {z})} \left[ \log p (\mathbf {z}) \right] \right] (21) \\ = \mathbb {E} _ {q _ {\phi} (\mathbf {y}, \mathbf {z} | \mathbf {x})} \left[ \log p _ {\theta} (\mathbf {x} | \mathbf {z}) \right] - \operatorname {K L} \left(q _ {\phi} (\mathbf {y}, \mathbf {z} | \mathbf {x}) \parallel r (\mathbf {y} | \mathbf {x}, \mathbf {z}) p (\mathbf {z})\right) (22) \\ \end{array}
+$$
+
+# K Diffusion Regularization
+
+We begin with the definition of ${ \mathcal { L } } _ { \mathrm { d i f f } } ( \phi )$ , derived as a lower bound on $\mathcal { L } _ { \mathrm { s l e e p } } ( \phi )$
+
+$$
+\mathcal {L} _ {\text {d i f f}} (\phi) = \mathbb {E} _ {p _ {\boldsymbol {\theta}} (\mathbf {x}, \mathbf {z})} \left[ \mathbb {E} _ {r} \left[ \log \frac {q _ {\boldsymbol {\phi}} (\mathbf {y} , \mathbf {z} \mid \mathbf {x})}{r (\mathbf {y} \mid \mathbf {z} , \mathbf {x})} \right] \right] + \bar {H} (p _ {\boldsymbol {\theta}}).
+$$
+
+To simplify ${ \mathcal { L } } _ { \mathrm { d i f f } }$ , we leverage the Markov structure of the forward process $r ( \mathbf { y } | \mathbf { z } , \mathbf { x } )$ and the reverse process $q _ { \phi } ( \mathbf { y } , \mathbf { z } | \mathbf { x } )$
+
+The forward process $r ( \mathbf { y } | \mathbf { z } , \mathbf { x } )$ is decomposed as:
+
+$$
+r \left(\mathbf {y} _ {1: T} \mid \mathbf {z}, \mathbf {x}\right) = \prod_ {t = 1} ^ {T} r \left(\mathbf {y} _ {t} \mid \mathbf {y} _ {t - 1}, \mathbf {x}\right),
+$$
+
+where $\mathbf { y } _ { 0 } = \mathbf { z }$
+
+The reverse process $q _ { \phi } ( \mathbf { y } , \mathbf { z } | \mathbf { x } )$ is decomposed as:
+
+$$
+q _ {\phi} (\mathbf {y}, \mathbf {z} | \mathbf {x}) = q _ {\phi} (\mathbf {y} _ {0: T} | \mathbf {x}) = q _ {\phi} (\mathbf {y} _ {T} | \mathbf {x}) \prod_ {t = 1} ^ {T} q _ {\phi} (\mathbf {y} _ {t - 1} | \mathbf {y} _ {t}, \mathbf {x}),
+$$
+
+Table 9: Unsupervised learning on MNIST, including the results of DDVI without the sleep term.   
+
+<table><tr><td>Method</td><td>Latent NLL - Pinwheel</td><td>Latent NLL - Swiss Roll</td><td>Latent NLL - Square</td></tr><tr><td>AEVB</td><td>1.68 ± 0.31</td><td>5.65 ± 1.58</td><td>2.78 ± 0.61</td></tr><tr><td>AEVB-IAF</td><td>1.64 ± 0.73</td><td>4.43 ± 1.09</td><td>1.68 ± 0.27</td></tr><tr><td>AAEB</td><td>-</td><td>-</td><td>-</td></tr><tr><td>H-AEVB</td><td>2.25 ± 3.02</td><td>4.04 ± 4.62</td><td>2.22 ± 2.03</td></tr><tr><td>DDVI</td><td>1.27 ± 0.21</td><td>3.86 ± 1.17</td><td>1.56 ± 0.09</td></tr><tr><td>DDVI (w/o sleep term)</td><td>2.12</td><td>5.25</td><td>2.97</td></tr></table>
+
+where $\mathbf { y } _ { 0 } = \mathbf { z }$ and $\mathbf { y } _ { 1 : T }$ are increasingly noisy versions of $\mathbf { z }$ .
+
+Substituting the factorizations of $r$ and $q _ { \phi }$ into the definition of ${ \mathcal { L } } _ { \mathrm { d i f f } } ( \phi )$ , and rewriting the logarithm and rearranging terms, we have:
+
+$$
+\begin{array}{l} \mathcal {L} _ {\mathrm {d i f f}} (\phi) = \mathbb {E} _ {p _ {\boldsymbol {\theta}} (\mathbf {x}, \mathbf {z})} \left[ \mathbb {E} _ {r (\mathbf {y} _ {1: T} | \mathbf {z}, \mathbf {x})} \left[ \log \frac {q _ {\phi} (\mathbf {y} _ {T} | \mathbf {x}) \prod_ {t = 1} ^ {T} q _ {\phi} (\mathbf {y} _ {t - 1} | \mathbf {y} _ {t} , \mathbf {x})}{\prod_ {t = 1} ^ {T} r (\mathbf {y} _ {t} | \mathbf {y} _ {t - 1} , \mathbf {x})} \right] \right] + \bar {H} (p _ {\boldsymbol {\theta}}) \\ = \mathbb {E} _ {r (\mathbf {y} _ {1: T}, \mathbf {z}, \mathbf {x})} \left[ \log q _ {\phi} (\mathbf {z} | \mathbf {y} _ {1}, \mathbf {x}) - \sum_ {t = 2} ^ {T} \mathrm {K L} (r _ {t} | | q _ {t}) \right] - \mathrm {K L} (r (\mathbf {y} _ {T} | \mathbf {z}, \mathbf {x}) | | q _ {\phi} (\mathbf {y} _ {T} | \mathbf {x})) + \bar {H} (p _ {\pmb {\theta}}) \\ \end{array}
+$$
+
+Here, $\log q _ { \phi } ( { \bf z } | { \bf y } _ { 1 } , { \bf x } )$ corresponds to the reconstruction term for the initial latent state $\mathbf { z }$ , while the summation represents the KL divergence between the forward and reverse processes at each intermediate step. $r _ { t } = r ( \mathbf { y } _ { t - 1 } | \mathbf { y } _ { t } , \mathbf { z } , \mathbf { x } )$ is the conditional forward distribution at step $t$ , $q _ { t } = q _ { \phi } ( \mathbf { y } _ { t - 1 } | \mathbf { y } _ { t } , \mathbf { x } )$ is the reverse process distribution at step t. $H ( p _ { \theta } )$ is the expected conditional entropy of $p _ { \pmb { \theta } } ( \mathbf { z } | \mathbf { x } )$ , a constant that does not depend on $\phi$ .
+
+This form mirrors the ELBO derivation for diffusion models (Sohl-Dickstein et al. 2015), where each step in the Markov chain contributes a KL divergence term, and the reconstruction term arises from the connection between the noisy latent variables and the original data.

paper_markdowns/bamboo-00153.md

@@ -0,0 +1,523 @@
+# LiON: Learning Point-wise Abstaining Penalty for LiDAR Outlier DetectioN Using Diverse Synthetic Data
+
+Shaocong $\mathbf { X } \mathbf { u } ^ { 1 , 2 * }$ , Pengfei $\mathbf { L i } ^ { 1 \ast }$ , Qianpu Sun1, Xinyu Liu1, Yang Li1, Shihui $\mathbf { G u o } ^ { 2 \dagger }$ , Zhen Wang3, Bo Jiang3, Rui Wang3, Kehua Sheng3, Bo Zhang3, Li Jiang4, Hao Zhao1†, Yilun Chen1
+
+1Tsinghua University, 2Xiamen University, 3Didi Chuxing, 4Chinese University of Hong Kong, ShenZhen
+
+# Abstract
+
+LiDAR-based semantic scene understanding is an important module in the modern autonomous driving perception stack. However, identifying outlier points in a LiDAR point cloud is challenging as LiDAR point clouds lack semantically-rich information. While former SOTA methods adopt heuristic architectures, we revisit this problem from the perspective of Selective Classification, which introduces a selective function into the standard closed-set classification setup. Our solution is built upon the basic idea of abstaining from choosing any inlier categories but learns a point-wise abstaining penalty with a margin-based loss. Apart from learning paradigms, synthesizing outliers to approximate unlimited real outliers is also critical, so we propose a strong synthesis pipeline that generates outliers originated from various factors: object categories, sampling patterns and sizes. We demonstrate that learning different abstaining penalties, apart from pointwise penalty, for different types of (synthesized) outliers can further improve the performance. We benchmark our method on SemanticKITTI and nuScenes and achieve SOTA results. Codes are available at https://github.com/Daniellli/LiON/.
+
+# Introduction
+
+LiDAR outlier detection (Li and Dong 2023) complements LiDAR semantic segmentation (Wang et al. 2024), aiming to enhance the model’s ability to recognize outliers without compromising its inlier segmentation performance.
+
+This task is important and practical. Traditional segmentation methods (Wang et al. 2024, Li, Shum, and Breckon 2024) assume that the samples in the training and test sets belong to the same set of categories. Thus, these models are trained on inlier categories and tend to classify all inputs into one of the inlier categories. However, this assumption fails in real-world scenarios where outliers are present. For example, as shown in Fig. 1-(a), the model may randomly classify furniture that has not been seen in training, leading to disastrous consequences in the downstream planning stage.
+
+While 2D outlier detection has made significant strides, including optimizing inlier prediction (Tian et al. 2022, Liu
+
+![](images/1ef9969ad90602ca337c50de1eaaf7587ca9d9bddd1f50d8ac445596509162bf.jpg)
+
+![](images/269ff9cee90a4c3153e6e4506e2718b5a5083e73e736cb454e956b92a4dc9cd7.jpg)  
+(a) Segmentation model's random classification of furniture in the road
+
+![](images/7516b666e93e0a4bb2504dd23d6bbded41f0ae8db3d07841b0a2151737f0e4e2.jpg)
+
+![](images/d085ff228f7d6373db662722ca24aa8a4c54764e3342a1fce11789f6541c699d.jpg)  
+(b) Synthesis Method Comparison   
+Figure 1: (a). The semantic segmentation model fails to identify furniture because the training set does not include such objects; (b). Comparison of our ShapeNet outlier synthesis method and the former resize outlier synthesis method.
+
+et al. 2023, Miao et al. 2024), addressing outlier class imbalance (Choi, Jeong, and Choi 2023), evolving from pixelwise to mask-based outlier detection methods (Zhang et al. 2024, Rai et al. 2023, Nayal et al. 2023, Zhang et al. 2024), developing promptable outlier detectors (Zhao et al. 2024, Li et al. 2024, Zhou et al. 2022), and utilizing model ensembling (Liu et al. 2024), the field of LiDAR outlier detection is still in its early stages (Li and Dong 2023). Seminal work REAL (Cen et al. 2022) proposes randomly choosing and resizing objects existing in the scene to synthesize outliers to approximate unlimited real outliers. For example, as shown in the left panel of Fig. 1-(b), the car is chosen and shrunk. This is viable but fail to represent the long-tail distribution of real outliers, in two regards. Firstly, objects from existing road scene understanding datasets are limited in category. Secondly, naive resizing violates the sampling pattern of real LiDAR sensors: points on enlarged objects get sparser while those on shrunk objects get denser. This leads to a shortcut problem: the model may find a trivial solution to distinguish outliers from inliers solely using point sparsity.
+
+Besides, REAL empirically finds 2D outlier detection methods (Hendrycks and Gimpel 2018, Hendrycks et al. 2019, Gal and Ghahramani 2016) perform poorly in the 3D domain, as a large number of outliers are predicted as inliers with high confidence scores . To alleviate this phenomenon, in addition to the Cross Entropy (CE) loss, REAL designs a
+
+Calibration Cross Entropy(CCE) loss to calibrate the outlier probabilities in inlier prediction. However, we empirically find that CCE alleviates this at the cost of accuracy in predicting inliers. As shown in the right panel of Fig. 4, with CCE, the outlier probabilities of inlier points, which account for the vast majority of the total points, become very high (higher than 0.1), which is undesirable.
+
+To address these issues, in this work, we propose a novel method LiON, aiming to mitigate the lack of semanticallyrich information in LiDAR point clouds for outlier detection. We contribute from two perspectives: learning and data.
+
+Learning. We reformulate the LiDAR outlier detection problem by applying Selective Classification (SC) principles (Feng et al. 2023, Chow 1970) and introduce a point-wise abstaining penalty learning paradigm to address the problem of unclear distinction in point clouds. While inspired by SC, our method differs significantly from SC in our point-wise design. Specifically, a diverse calibration factor is learned in a point-wise manner to more effectively capture subtle differences within a point cloud and calibrate the relationship between inlier and outlier classifiers. As a result, we mitigate the unclear distinction in point clouds caused by their lack of semantically-rich information by learning a diverse factor in a point-wise manner.
+
+Data. Inspired by outlier exposure (Hendrycks, Mazeika, and Dietterich 2019), we propose introducing objects from an external dataset, ShapeNet (Chang et al. 2015), into existing scenes to synthesize outliers. ShapeNet, with its wide spectrum of categories and diverse geometries, can compensate for the long-tail distribution of real outliers. To ensure the realism of synthesized outliers, we take the LiDAR sampling pattern into consideration when merging randomly selected ShapeNet objects into road scenes. As illustrated in the right of Fig. 1-(b), our synthesized outliers are precisely aligned with objects in the scene with respect to point sparsity and occlusion. In this way, we mitigate the lack of semantically-rich information in LiDAR point clouds by utilizing realistic, ShapeNet outliers with diverse geometries.
+
+Finally, the risk-coverage evaluation metrics associated with SC are also adapted for this task to serve as supplementary metrics of the holistic metrics AUPR/AUROC/mIoUold , allowing us to gain a deeper understanding of the performance gains. These metrics are also a key to narrow the gap between academic and industrial communities. This is because these metrics allow us to identify the rejection threshold that incurs the least cost but yields the highest gain (coverage), which is very important for industrial applications.
+
+Our contributions can be summarized as follows:
+
+• We propose a point-wise abstaining penalty learning paradigm using the principle of SC to calibrate the relationship between inlier and outlier classifiers in a pointwise manner. Additionally, the risk-coverage evaluation metrics associated with SC are adapted for this problem, serving as supplementary metrics to the holistic metrics AUPR/AUROC/mIoUold.   
+• We utilize ShapeNet objects to synthesize realistic and diverse outliers to approximate unlimited real outliers.   
+• Our method has achieved new SOTA performance for Li-
+
+DAR outlier detection not only in previously established outlier detection metrics, but also in the risk-coverage curve metric, on SemanticKITTI and NuScenes.
+
+# Related Works
+
+Outlier Detection in Autonomous Driving. Outlier detection is vital for ensuring the safety of ego-cars in openworld environments by identifying outlier objects. Extensive research has been conducted in 2D perception, specifically with semantic segmentation models. Unsupervised methods (Jung et al. 2021, Bevandic et al. 2021) involve ´ post-processing predicted logits from frozen segmentation models to detect outliers. Supervised methods (Tian et al. 2022, Grcic, Bevandi ´ c, and ´ Segvi ˇ c 2022, Chan, Rottmann, ´ and Gottschalk 2021) utilize auxiliary datasets like COCO (Lin et al. 2014) to synthesize outlier objects in training images (e.g., Cityscapes (Cordts et al. 2016)) and retrain the segmentation model using outlier exposure (Hendrycks, Mazeika, and Dietterich 2019, Zhou et al. 2024).
+
+While significant advancements have been made in 2D outlier detection, the exploration in the context of LiDAR point clouds remains limited. Cen et al. (2022) use resize synthesis pipeline and calibration loss to achieve the discrimination of outlier points. However, their focus primarily revolves around the open-world segmentation setting without extensively analyzing calibration effectiveness. Li and Dong (2023) propose an adversarial prototype framework that improves performance but involves complex network design and computationally expensive training. Considering these limitations, we present our method and substantiate its effectiveness through extensive experiments.
+
+Selective Classification. SC can be broadly classified into two groups: 1) the first group focuses on addressing SC through the use of additional heads/logits (Geifman and El-Yaniv 2017, 2019, Liu et al. 2019, Feng et al. 2023, Gal and Ghahramani 2016, Chow 1970); 2) the second group tackles SC through cost-sensitive classification techniques (Charoenphakdee et al. 2021, Mozannar and Sontag 2020). Motivated by the extra head/logits design, resembling outlier detection, we design a new outlier detector from the perspective of SC and utilize SC’s evaluation metrics as alternative performance measures for our outlier detector.
+
+Synthetic Data. Due to the limited availability and high cost associated with acquiring high-quality real-world datasets, synthetic data has been extensively employed in the field of scene understanding (Su et al. 2015, Movshovitz-Attias, Kanade, and Sheikh 2016, Zhang et al. 2017b, Handa et al. 2016, McCormac et al. 2017, Zhang et al. 2017a, Song et al. 2017, Gao et al. 2021, 2024a,b, 2023, Xu et al. 2024, Ding et al. 2024). In this work, we introduce ShapeNet objects into the existing scene to effectively compensate for the lack of semantically-rich information in point clouds.
+
+# Preliminaries: Selective Classification
+
+We first formalize the definition of SC and put different methods under a unified lens. Experimentally, the riskcoverage trade-off analysis that comes along with this
+
+![](images/62f8aa1595ab9cd59d7bdd07b54e2839ef96c211422c62d4d734811a7a183136.jpg)  
+Figure 2: Method pipeline: a point cloud containing outliers synthesized by ShapeNet is processed by a feature extractor to obtain features. These features are then used by inlier and outlier classifiers to predict class logits.
+
+framework, allows us to reveal in-depth differences between methods.
+
+Definition. In SC, our goal is to learn predictive models that know what they do not know or when they should abstain1 from making decisions. Here we consider a generic SC definition, which is agnostic of network and application. A supervised classification task is formulated as follows. Let $\mathcal { X }$ be any feature space and $\mathcal { V }$ a label space. In LiDAR outlier detection, $\mathcal { X }$ could be point clouds, and $\mathcal { V }$ could be class labels2 of each point cloud. Let $P ( \mathcal X , \mathcal y )$ be a distribution over $\mathcal { X } \times \mathcal { V }$ . A model $f : \mathcal { X }  \mathcal { Y }$ is called a prediction function and its true risk used to evaluate the performance of $f$ w.r.t. $P$ is ${ \cal R } ( f ) : = { \cal E } _ { P ( \mathcal { X } , \mathcal { Y } ) } [ \ell ( f ( { \bf x } ) , { \bf y } ) ]$ , where $\ell :$ $\mathcal { V } \times \mathcal { V }  \mathbb { R } ^ { + }$ is a given loss function, for example, the Cross Entropy (CE) loss. Given a labeled set ${ \cal S } _ { m } = \{ ( { \bf x _ { i } } , { \bf y _ { i } } ) \} _ { i = 1 } ^ { m }$ sampled i.i.d. from $P ( \mathcal X , \mathcal y )$ , the empirical risk of the classifier $f$ is $\begin{array} { r } { \hat { r } ( f | S _ { m } ) : = \frac { 1 } { m } \sum _ { i = 1 } ^ { m } \ell ( f ( \bar { \mathbf { x _ { i } } } ) , \mathbf { y _ { i } } ) } \end{array}$ .
+
+Apart from risk, another important concept in the SC formulation is coverage. A selective model (El-Yaniv et al. 2010) is a pair $( f , g )$ , where $f$ is a prediction function, and $g : \mathcal { X }  \{ 0 , 1 \}$ is a selective function, which serves as a binary qualifier for $f$ as follows:
+
+$$
+(f, g) (\mathbf {x}) := \left\{ \begin{array}{l l} f (\mathbf {x}), & \text {i f} g (\mathbf {x}) = 1 \\ \text {A B S T A I N}, & \text {i f} g (\mathbf {x}) = 0 \end{array} \right. \tag {1}
+$$
+
+Thus, the selective model abstains from prediction at $\mathbf { x }$ iff $g ( \mathbf { x } ) = 0$ . A soft selection function can also be considered, where $g : \mathcal { X }  [ 0 , 1 ]$ , and decisions can be taken probabilistically or deterministically (e.g., using a threshold). The introduction of a selective function $g$ allows us to define coverage. Specifically, coverage is defined to be the ratio of the non-abstained subset within set $P$ to the entirety of $P$ , which can be formulated as:
+
+$$
+\phi (g) := E _ {P} [ g (\mathbf {x}) ] \tag {2}
+$$
+
+Accordingly, the standard risk for a classifier $f$ can be augmented into the selective risk of $( f , g )$ as
+
+$$
+R (f, g) := \frac {E _ {P} [ \ell (f (\mathbf {x}) , \mathbf {y}) g (\mathbf {x}) ]}{\phi (g)} \tag {3}
+$$
+
+Clearly, the risk of a selective model can be traded-off for coverage. The performance profile of such a model can be
+
+specified by its risk–coverage curve, defined to be the risk as a function of coverage.
+
+Finally, we clarify that the continuous risk and coverage defined above are calculated using a fixed set in practice. For any given labeled set $S _ { m }$ , the empirical selective risk is
+
+$$
+\hat {r} (f, g \mid S _ {m}) := \frac {\frac {1}{m} \sum_ {i = 1} ^ {m} \ell \left(f \left(\mathbf {x} _ {\mathbf {i}}\right) , \mathbf {y} _ {\mathbf {i}}\right) g \left(\mathbf {x} _ {\mathbf {i}}\right)}{\phi (g \mid S _ {m})} \tag {4}
+$$
+
+and the empirical coverage is
+
+$$
+\hat {\phi} (g | S _ {m}) := \frac {1}{m} \sum_ {i} ^ {m} g \left(\mathbf {x} _ {\mathbf {i}}\right) \tag {5}
+$$
+
+Remark. Later we will put methods under the unified lens of SC and use the risk-coverage curve to analyze them.
+
+# Method
+
+LiDAR semantic segmentation is the task of assigning a class label from a predefined class label set to each point in a given point cloud. LiDAR outlier detection, on the other hand, is an extension to semantic segmentation, which aims to identify points that do not belong to the predefined inlier label set. While the seminal work proposes a viable solution REAL, we revisit this issue through the unified lens of SC and propose a solution that effectively mitigates the problem of unclear distinctions in point clouds. Apart from the learning paradigm, we design a novel outlier synthesis pipeline that leverages the richness of the ShapeNet and adheres to the realistic LiDAR distribution to compensate for the lack of semantically-rich information in point clouds.
+
+# Network Architecture Overview
+
+As shown in Fig. 2, the input point cloud $\mathbf { x } \in \mathbb { R } ^ { n \times 3 }$ , sampled from $S _ { m }$ , is denoted on the left with ShapeNet objects integrated into it. Then, $\mathbf { x }$ is fed into the feature extractor $\psi$ followed by an inlier classifier $f$ to predict the inlier logit $\hat { \mathbf { y } } \in \mathbb { R } ^ { n \times c }$ , where $c$ is the number of inlier classes. An outlier classifier $g$ is used to predict the outlier logit $\hat { \mathbf { o } } \in \mathbb { R } ^ { n \times 1 }$ . As such, $( f , g )$ instantiates a selective model mentioned above. These operations can be expressed as follows:
+
+$$
+\hat {\mathbf {y}} := f (\psi (\mathbf {x})) \quad \hat {\mathbf {o}} := g (\psi (\mathbf {x}))
+$$
+
+$$
+\tilde {\mathbf {y}} := [ \hat {\mathbf {y}}, \hat {\mathbf {o}} ] := \left\{\tilde {\mathbf {y}} _ {\mathbf {i}} := [ \hat {y} _ {i}, \hat {o} _ {i} ] \Big | i = 1, \dots , n \right\}
+$$
+
+$$
+\begin{array}{l} \mathbf {p} := \left\{p _ {i, j} = \frac {e ^ {\tilde {y} _ {i , j}}}{\sum_ {k = 1} ^ {c + 1} e ^ {\tilde {y} _ {i , k}}} \left| i = 1, \dots , n; j = 1, \dots , c + 1 \right. \right\} \\ \mathbf {p} ^ {\mathbf {y}}, \mathbf {p} ^ {\mathbf {o}} := \mathbf {p} \tag {6} \\ \end{array}
+$$
+
+Here, the operation $[ \cdot ]$ denotes concatenation. Prediction probability $\mathbf { p } \in [ 0 , 1 ] ^ { n \times ( c + 1 ) }$ consists of inlier probability $\mathbf { p } ^ { \mathbf { y } } \in [ 0 , 1 ] ^ { n \times c }$ and outlier probability $\mathbf { p ^ { o } } \in [ 0 , 1 ] ^ { \overline { { n } } \times 1 }$ .
+
+# Revisiting the REAL Formulation
+
+Cen et al. (2022) introduces the first LiDAR outlier detector, REAL. Their added dummy classifiers can also be thought of as $g$ , under the SC framework, but there is a key difference. They observe that numerous real outliers are wrongly classified as inlier classes with high probabilities. To address
+
+Table 1: Removing CCE in REAL can actually improve the outlier detection metrics on SemanticKITTI.   
+
+<table><tr><td>CE</td><td>CCE</td><td>AUPR</td><td>AUROC</td><td>mIoUold</td></tr><tr><td>✓</td><td>✓</td><td>20.00</td><td>84.90</td><td>57.80</td></tr><tr><td>✓</td><td></td><td>26.68</td><td>87.60</td><td>58.28</td></tr></table>
+
+this issue, they propose a Calibration Cross Entropy (CCE) loss function to drive the outlier logit of the inlier sample to the second largest. We formalize3 this loss as follows:
+
+$$
+\begin{array}{l} \ell := \frac {1}{m} \sum_ {S _ {m}} \frac {1}{n} \sum_ {i = 1} ^ {n} \left\{\underbrace {- \log p _ {i , y _ {i}}} _ {\mathrm {C E}} \right. \\ \left. \underbrace {- \lambda \mathbb {I} \left(y _ {i} \neq c + 1\right) \log \frac {e ^ {\tilde {y} _ {i , c + 1}}}{\sum_ {k = 1 \& k \neq y _ {i}} ^ {c + 1} e ^ {\tilde {y} _ {i , k}}}} _ {\text {C C E}} \right\} \tag {7} \\ \end{array}
+$$
+
+Here, $y _ { i } \in \{ 1 , \ldots , c , c + 1 \}$ signifies the ground truth corresponding to $x _ { i } \in { \bf x }$ , where $\{ 1 , \ldots , c \}$ represents inlier class labels while $\{ c + 1 \}$ indicates the outlier class label. y and x are sampled i.i.d. from $S _ { m }$ . I(·) is the indicator function. $\lambda$ is a hyperparameter. A notable fact is that REAL does not provide an ablation study for this CCE loss and as shown in Tab. 1, removing this CCE loss can indeed improve standard outlier detection metrics. But why this happens cannot be understood through metrics like AUPR or AUROC, highlighting the need to revisit REAL under the lens of SC.
+
+We use Fig. 4 as an intuitive case to analyze the negative impact of the CCE loss. It illustrates sample numbers within different $\mathbf { p ^ { o } }$ intervals for both inliers and outliers. By removing the CCE loss, sample number in the extremely low interval [0, 0.1] grows significantly for both inliers and outliers. This is desirable for inliers but not for outliers. As shown by the red increase number, 9.8 million samples change to a desirable state while 1.7 million samples change to a undesirable state, and this large difference explains why the collective metrics in Tab. 1 become better.
+
+The reason why this in-depth statistics (Fig. 4) can reveal the negative impact of CCE is that different $\mathbf { p ^ { o } }$ values are investigated separately. And, the SC framework provides the principled tool risk-coverage curve to conduct this kind of analysis, because different coverage is achieved through selecting different thresholds on $\mathbf { p ^ { o } }$ . More principled analyses that reveal reasons behind phenomena like Tab. 1 can be found in the experiments section.
+
+# Point-wise Abstaining Penalty Learning
+
+Point-wise upgrade. The reason why the disadvantages of CCE exceed its benefits is its sub-optimal calibration for the inlier probabilities $\mathbf { p } ^ { \mathbf { y } }$ and the outlier probabilities $\mathbf { p ^ { o } }$ . Inspired by ‘learning to abstain’ (Liu et al. 2019), where the calibration between the reject and non-reject options is adeptly handled, we propose our new learning paradigm. Specifically, Liu et al. (2019) employs a fixed calibrating
+
+factor to achieve this. While this may suffice for imagelevel SC, it is inadequate for point-wise outlier detection. This is because, in LiDAR outlier detection, we need a different calibrating factor for each point to capture the subtle differences between them, such as between remote (sparse) and near (dense) points, as well as between inlier and outlier points. Therefore, we upgrade this fixed calibrating factor to a point-wise one, defined as abstaining penalty $\alpha$ , and introduce a point-wise penalty loss to supervise the network to learn the subtle differences between various points, which can be expressed as follows:
+
+$$
+\begin{array}{l} \alpha := \left\{\alpha_ {i} = - \log \left(\sum_ {j = 1} ^ {c} e ^ {\hat {y} _ {i, j}}\right) | i = 1, \dots , n \right\} \\ \ell^ {\text {p e n a l t y}} := \frac {1}{m} \sum_ {S _ {m}} \frac {1}{n} \sum_ {i = 1} ^ {n} \left\{\mathbb {I} \left(y _ {i} \neq c + 1\right) \max  \left(\alpha_ {i} - m _ {\text {i n}}, 0\right) \right. \\ \left. + \mathbb {I} \left(y _ {i} = c + 1\right) \max  \left(m _ {\text {o u t}} - \alpha_ {i}, 0\right) \right\} \tag {8} \\ \end{array}
+$$
+
+As shown in Fig. 5-(c), the hyperparameters $m _ { \mathrm { i n } }$ and $m _ { \mathrm { o u t } }$ ensure that the inliers are associated with penalties lower than $m _ { \mathrm { i n } }$ , while the outliers exhibit penalties higher than $m _ { \mathrm { o u t } }$ . Note that in our experiments, the penalties are negative and we set the value of $m _ { \mathrm { i n } }$ to -12, and $m _ { \mathrm { o u t } }$ to -6.
+
+Moreover, our new ‘learning to abstain’ formulation for this task with this point-wise penalty is defined as follows:
+
+$$
+\ell^ {\text {a b s t a i n}} :=
+$$
+
+$$
+\frac {1}{m} \sum_ {S _ {m}} \frac {1}{n} \sum_ {i = 1} ^ {n} \left\{- \mathbb {I} \left(y _ {i} \neq c + 1\right) \log \left\{p _ {i, y _ {i}} ^ {y} + \underbrace {p _ {i} ^ {o}} _ {\text {a b s t a i n i n g t e r m}} \right\} \right. \text {f o r i n l i e r s a m p l e s}
+$$
+
+$$
+\underbrace {- \mathbb {I} \left(y _ {i} = c + 1\right) \sum_ {j = 1} ^ {c} \log \left\{p _ {i , j} ^ {y} + \underbrace {\frac {p _ {i} ^ {o}}{(- \alpha_ {i}) ^ {2}}} _ {\text {a b s t a i n i n g t e r m}} \right\}} \}
+$$
+
+{zfor outlier samples
+
+(9)
+
+Intuition. Minimizing the point-wise penalty loss Eq. (8) results in assigning lower $\alpha _ { i }$ to inliers, thereby leading to higher valutribution of $( - \bar { \alpha } _ { i } ) ^ { 2 }$ effectively suppresses the con-to play a dominant role in the $p _ { i } ^ { o }$ $p _ { i , y _ { i } } ^ { y }$ point-wise abstain loss Eq. (9). Likewise, higher $\alpha _ { i }$ are allocated to outliers, resulting in lower values of $( - \alpha _ { i } ) ^ { 2 }$ . This allows $p _ { i } ^ { o }$ to play a dominant role and, consequently, suppresses the contribution of $\{ p _ { i , j } ^ { y } | j = 1 , \ldots , c \}$ in the pointwise abstain loss Eq. (9). Since this learning paradigm is defined in a point-wise manner, it has the potential to capture the subtle difference between inliers and outliers despite LiDAR point clouds lack semantically-rich information.
+
+The total loss can be expressed as follows:
+
+$$
+\ell^ {\text {t o t a l}} := \lambda^ {\text {a b s t a i n}} \ell^ {\text {a b s t a i n}} + \lambda^ {\text {p e n a l t y}} \ell^ {\text {p e n a l t y}} \tag {10}
+$$
+
+![](images/972e944d61787fa41689774a5f45f9f8e3a1cb3f76df3c6670b29b7d439c616f.jpg)
+
+![](images/f8ee46ed93ea6e14db6bb37bd3f626178314d4f17153f2ffa6e15bf19a212376.jpg)
+
+![](images/c394deef05de2e8fa59c92a6d3d1912c90827346bd440f43f151fff16d1828cf.jpg)
+
+![](images/a666a8b818a0d96703d567cd660b2d8380af56f056e218b4433634226bd92f90.jpg)
+
+![](images/8fec6714b146a33a42d55118fa45728c9dd40111b223a8e05d5d515b3cec7153.jpg)
+
+![](images/a3efa39dc7e89123c79cef32e782b75da069e3055abc9eda3c4429d52ed9d9f1.jpg)
+
+![](images/cd0b1c6ad8d552b692bf614e6e07837d19af75d56ef35241b0ab31e5aca329be.jpg)  
+(c) rotating   
+  
+(e) putting on ground   
+(f) resampling   
+Figure 3: Our outlier synthesis pipeline: (a) loading a ShapeNet object; (b) randomly moving it away from the scene center; (c) randomly rotating it around the gravity direction; (d) randomly resizing it; (e) putting it on ground; (f) resampling points on the object to blend into the scene. We repeat this pipeline on the fly $G$ times for inserting $G$ objects.
+
+![](images/12bc8a78abe7074680171008109d01c4d369529098479fe5266feabe1dc13c36.jpg)  
+2D scene   
+(a) loading   
+(b) moving
+
+![](images/3eeef3fd1db07b5966e78306d0198e867b0a8440f003fa4074a4c9f220dbab54.jpg)  
+Figure 4: Statistics of outlier probability $\mathbf { p ^ { o } }$ for inlier and outlier samples under different settings of REAL on SemanticKITTI. For inliers, we would like to observe more samples with $\mathbf { p ^ { o } } \in [ 0 , 0 . 1 ]$ , while for outliers, less samples with $\mathbf { p ^ { o } } \in [ 0 , 0 . 1 ]$ is desirable.
+
+# Outlier Synthesis Pipeline
+
+REAL synthesizes outliers by resizing the objects presenting in existing scene, as depicted in the left panel of Fig. 1- (b). However, we observe that this synthesis pipeline fails to represent the real outlier in two aspects: 1) the limited variety of objects in the existing scene makes it challenging to compensate for the lack of semantically-rich information through resizing; 2) learning from these synthesized outliers may lead to a model that classifies real outliers solely based on point sparsity. As such, we resort to an additional dataset, ShapeNet, which consists of 220,000 models classified into 3,135 categories. As shown in Fig. 3, we repeat the synthesis pipeline for $G$ times to insert $G$ outlier objects. For each object, there are six steps as follows:
+
+(a) To synthesize diverse outliers, we first randomly decide the number of outlier objects $G$ according to a Binomial distribution4. The specific distribution used is Binomial(20, 0.3). We then load $G$ objects from ShapeNet into the given scene x, where the probability of not adding any object into $\mathbf { x }$ is also considered.   
+(b) Then, for each object $\mathbf { s } \in \mathbb { R } ^ { l \times 3 }$ , we move s $\in \mathbb { R } ^ { l \times 3 }$ away from scene center $x ^ { c }$ , alone the $\mathbf { X }$ -axis by $d ^ { x } \sim$ Uniform $( r ^ { \operatorname* { m i n } } , 0 . 8 * r ^ { \operatorname* { m a x } } ) ^ { 5 }$ that $r ^ { \mathrm { m i n } }$ is the distance of the closest point from $x ^ { c }$ and $r ^ { \mathrm { m a x } }$ is the furthest point from $x ^ { c }$ .   
+(c) Next, we rotate s around $x ^ { c }$ on the xy-plane (around the gravity direction) for $d ^ { \mathrm { l o n } } \sim \mathrm { U n i f o r m } ( 0 , 3 6 0 )$ $( 0 , 3 6 0 )$ degrees and denote the resulting object as $\mathbf { s } = ( \mathbf { u } , \mathbf { v } , \mathbf { w } )$ . There is a probability that s does not overlap with $\mathbf { x }$ , after moving and rotating. Therefore, if s is positioned outside of $\mathbf { x }$ , the subsequent steps are not carried out and we move on the next
+
+object. Specifically, we stop synthesis process if:
+
+$$
+\min  \left\{\left| \bar {u} - i \right| + \left| \bar {v} - j \right| \right\} > \Delta , (i, j, k) \in \mathbf {x} \tag {11}
+$$
+
+Here, $\bar { u }$ and $\bar { v }$ represent the mean u and mean v of $s$ , respectively. We set $\Delta$ to 1 in our experiments.
+
+(d) Then, since the objects from ShapeNet tend to be smaller in size compared to those in the existing scene, we proceed to resize s by a factor of $k \sim \mathrm { U n i f o r m } ( 1 , 7 )$ .   
+(e) Following this, we put s on ground by setting its last axis to $\tilde { \mathbf { w } } = \mathbf { w } - \Delta _ { w }$ , where $\Delta _ { w }$ represents the distance between the bottom of s and the point on x that are the closest to s along the gravity direction and falls into the x-y plane projection of $s$ . The resulting object is $\mathbf { s } = ( \mathbf { u } , \mathbf { v } , \tilde { \mathbf { w } } )$ .   
+(f) Finally, to consider the realistic LiDAR’s sampling pattern, we merge s into $\mathbf { x }$ by adjusting the radii of x. Specifically, we represent s and $\mathbf { x }$ using spherical coordinates:
+
+$$
+\begin{array}{l} \mathbf {s} \overline {{\mathbf {s}}} = \left\{s _ {j} = \left(\operatorname {l o n} _ {j}, \operatorname {l a t} _ {j}, \mathrm {r} _ {j}\right) \mid j = 1, \dots , l \right\} \\ \mathbf {x} := \left\{x _ {k} = \left(\operatorname {l o n} _ {k}, \operatorname {l a t} _ {k}, \mathrm {r} _ {k}\right) \mid k = 1, \dots , n \right\} \tag {12} \\ \end{array}
+$$
+
+Here, the lon represents longitude, lat represents latitude, and r represents radius. For each $x _ { k }$ , we replace $\mathbf { r } _ { k }$ with $\boldsymbol { \mathrm { r } } _ { j }$ if $s _ { j }$ satisfy $| \mathrm { l o n } _ { k } - \mathrm { l o n } _ { j } | < \Delta _ { \mathrm { l o n } }$ and $\vert \mathrm { l a t } _ { k } - \mathrm { l a t } _ { j } \vert < \Delta _ { \mathrm { l a t } }$ . During our experiment, we set $\Delta _ { \mathrm { l o n } }$ to 0.02 and $\bar { \Delta } _ { \mathrm { l a t } }$ to 0.2. When multiple $s _ { j }$ satisfy the above criterion, we use their smallest r to replace $\mathbf { r } _ { k }$ .
+
+# Dynamic Penalty
+
+As shown in Fig. 1-(b), the outliers synthesized through resizing are further from the inlier data distribution in terms of point sparsity compared to those synthesized by our pipeline. Hence, to maximize the benefits of the point-wise learning paradigm, we introduce a dynamic penalty loss that handles points in a customized manner:
+
+$$
+\ell^ {\text {d y n a m i c p e n a l t y}} :=
+$$
+
+$$
+\begin{array}{l} \frac {1}{m} \sum_ {S _ {m}} \frac {1}{n} \sum_ {i = 1} ^ {n} \left\{\mathbb {I} \left(y _ {i} \neq c + 1 \& y _ {i} \neq c + 2\right)\right) \max  \left(\alpha_ {i} - \beta_ {\mathrm {i n}} m _ {\mathrm {i n}}, 0\right) \\ + \mathbb {I} \left(y _ {i} = c + 1\right) \max  \left(\beta_ {\text {r o u t}} m _ {\text {r o u t}} - \alpha_ {i}, 0\right) \\ \left. \left. + \mathbb {I} \left(y _ {i} = c + 2\right) \max  \left(\beta_ {\text {s o u t}} m _ {\text {s o u t}} - \alpha_ {i}, 0\right) \right\} \right. \tag {13} \\ \end{array}
+$$
+
+The $\{ c + 2 \}$ denotes the outlier class label generated by ShapeNet. The weight parameter $\beta$ associated with the threshold $m$ is initialized as 1 and is learnable. In our experimental setting, we set the value of $m _ { \mathrm { s o u t } }$ to $^ { - 7 }$ , and $m _ { \mathrm { r o u t } }$ to -6. Consequently, the total loss becomes:
+
+$$
+\ell^ {\text {t o t a l}} := \lambda^ {\text {a b s t a i n}} \ell^ {\text {a b s t a i n}} + \lambda^ {\text {d y n a m i c p e n a l t y}} \ell^ {\text {d y n a m i c p e n a l t y}} \tag {14}
+$$
+
+Table 2: Comparisons with previous methods. C3D refers to the base segmentation model, Cylinder3D (Zhu et al. 2021). Comparisons with APF on NuScenes are not conducted, as the results are unavailable and its code is not publicly released.   
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">SemanticKITTI (Behley et al. 2019)</td><td colspan="3">NuScenes (Caesar et al. 2020)</td></tr><tr><td>AUPR</td><td>AUROC</td><td>mIoUold</td><td>AUPR</td><td>AUROC</td><td>mIoUold</td></tr><tr><td>Closed-set C3D</td><td>-</td><td>-</td><td>58.00</td><td>-</td><td>-</td><td>58.70</td></tr><tr><td>C3D + MSP (Hendrycks and Gimpel 2018)</td><td>6.70</td><td>74.00</td><td>58.00</td><td>4.30</td><td>76.70</td><td>58.70</td></tr><tr><td>C3D + MaxLogit (Hendrycks et al. 2019)</td><td>7.60</td><td>70.50</td><td>58.00</td><td>8.30</td><td>79.40</td><td>58.70</td></tr><tr><td>C3D + MC-Dropout (Gal and Ghahramani 2016)</td><td>7.40</td><td>74.70</td><td>58.00</td><td>14.90</td><td>82.60</td><td>58.70</td></tr><tr><td>C3D + REAL (Cen et al. 2022)</td><td>20.08</td><td>84.90</td><td>57.80 (0.20 ↓)</td><td>21.20</td><td>84.50</td><td>56.80</td></tr><tr><td>C3D + APF (Li and Dong 2023)</td><td>36.10</td><td>85.60</td><td>57.30 (0.70 ↓)</td><td>-</td><td>-</td><td>-</td></tr><tr><td>C3D + LiON (ours)</td><td>44.68 (8.58 ↑)</td><td>92.69 (7.09 ↑)</td><td>57.56 (0.44 ↓)</td><td>31.58 (10.38 ↑)</td><td>95.24 (10.74 ↑)</td><td>59.11 (0.41 ↑)</td></tr></table>
+
+![](images/a0ce28b64f95ea20e61a8a6728faeb64ac1f2875d7d593077048a3a0d721b5fd.jpg)  
+Figure 5: (a). Comparison with the SOTA using the Risk-Coverage curves; (b). Comparison with different outlier synthesis pipeline using the risk-coverage curve; (c). Relationship between point-wise penalty loss and penalty $\alpha$ .
+
+# Experiments
+
+# Dataset
+
+SemanticKITTI (Behley et al. 2019) is a driving-scene dataset designed for point cloud segmentation. The point clouds are collected using the Velodyne-HDLE64 LiDAR in Germany. The dataset consists of 22 sequences, with sequences 00 to 10 utilized as the training set, sequence 08 serves as the validation set, and sequences 11 to 21 used as the test set. After merging classes with different moving statuses and ignoring classes with a small number of points, 19 classes remain for training and evaluation. Consistent with prior work, we designate {other-vehicle} as outlier class.
+
+NuScenes (Caesar et al. 2020) consists of 1000 scenes, each lasting 20 seconds, captured using a 32-beam LiDAR sensor, which leads to its challenging nature (a sparser Li-DAR point cloud makes the classification task more difficult). It contains 40,000 frames sampled at $2 0 \mathrm { H z }$ and has official training and validation splits. After merging similar classes and removing rare/useless classes including ‘ego-car’, there are 16 remaining classes for training and evaluation. The classes designated as outliers include {barrier, constructive-vehicle, traffic-cone, trailer}.
+
+# Evaluation Metric
+
+Traditional evaluation metrics: Consistent with previous work (Cen et al. 2022), we employ inlier mean intersection over union $\mathrm { ( m I o U _ { o l d } ) }$ metric to evaluate the performance of inlier classification, while the AUPR and AUROC are utilized to assess the performance of outlier classification.
+
+New evaluation metrics: The loss-based selective risk (Eq. (4)) is sub-optimal for serving as an evaluation metric for point-wise classification task because it is not sensitive to the class imbalance which is crucial in this task. Thus, we upgrade it into mIoU-based selective risk, as shown below:
+
+$$
+\hat {r} (f, g \mid S _ {m}) := \frac {1 0 0 - \mathrm {m I o U} _ {\text {o l d}} ^ {S _ {m} \mid g}}{\phi (g \mid S _ {m})} \tag {15}
+$$
+
+Here, $\mathrm { m I o U } _ { \mathrm { o l d } } ^ { S _ { m } | g }$ represents the $\mathrm { m I o U _ { o l d } }$ calculated for the sub-dataset $\hat { S } _ { m }$ under the selective model condition $g$ . Through this upgradation, the selective risk becomes more comparable, as $\hat { r } ~ \in ~ [ 0 , 1 0 0 ]$ , and the mIoU inherently accounts for sensitivity to class imbalance. Furthermore, the definitions of selective AUPR and AUROC can be found in the appendix. With these new evaluation metrics, we can draw risk/AUPR/AUROC-coverage curves to obtain deeper understanding of model performance.
+
+# Comparisons with State-of-the-art Methods
+
+We use Cylinder3D (Zhu et al. 2021) as the baseline segmentation model to ensure a fair comparison. The computational cost remains low with the addition of an outlier detection head, achieving 7 fps on a single NVIDIA 3090 GPU.
+
+Quantitative comparison: As illustrated in Tab. 2, our method achieves a new SOTA in outlier class segmentation for SemanticKITTI and NuScenes, surpassing the previous SOTA by a significant margin. Specifically, our method achieves an AUPR of 44.68 and an AUROC of 92.69, which exceeds the previous SOTA scores by 8.58 and 7.09 in SemanticKITTI. Moreover, our method achieves an AUPR of 31.58 and an AUROC of 95.24 in NuScenes, which exceeds the previous SOTA scores by 10.38 and 10.74, respectively.
+
+Qualitative comparison: Qualitative results, as illustrated in Fig. 6, demonstrate that our method not only locates the outliers more accurately but also does so with greater confidence compared to REAL. Furthermore, in NuScenes (Fig. 6-right ), our method accurately identifies the ‘ego-car’ as outliers, although this category is not incorporated into the training and evaluation phases. These findings provide further evidence of the superiority of our method.
+
+Comparison between LiON and the previous SOTA (APF) from another perspective: In addition to better quantitative results, LiON is easier to implement and requires less computational cost compared to APF. LiON can be implemented by simply adding an extra classifier to an arbitrary LiDAR-based segmentation network and training the
+
+![](images/7d3d05cd597c23d00686351cee6bc8695b8cf4563db05b71f3663dd4351370c1.jpg)
+
+![](images/2d86681769b89247f6af90015f81415c19573b834190cfdc2bf682d77b494d23.jpg)
+
+![](images/698a2b5d6fbde73cacffd4933f73c3ce9a1eceac1dfab0a2997af50a70e24e99.jpg)
+
+![](images/5f65e234552b7a0b84fa43c354e05e798a44abab5f97e13c7736464a9550f635.jpg)  
+  
+■ unlabeled and others ignored ■bicyclt
+
+![](images/81ca7ce4beed0a317dc7424e459e18c753eb32bb08447beac0f8f1317e7b3199.jpg)
+
+![](images/5a42e42c2c3fc2bb7155f95e7609a1811734ec7ee625168f94a54f171b721180.jpg)
+
+![](images/bdab7dd609a0d7cc15e158ba9b220143e9e644984a69016575cf2f0b87919364.jpg)  
+  
+Groun   
+d truth   
+Inlier predi   
+ding vege   
+ction (ours) n (ours)   
+etatio
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+?? (REAL)
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+truc
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+■ bicy
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+rclist
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+■road
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+![](images/4cc202fbacb657d6b5593359ca824dd26df8990333a6cbb057856072dac569e0.jpg)  
+Final predi   
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+ction (ou   
+traffic-sign
+
+![](images/a4f0840cbd43de326a0085d3bcc6364e0b8f76624c6cf2ffb8e8b7f6d5bd57ee.jpg)
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+![](images/8f11a2a5974fcff4bc36b2d42b883a3319fa16b390c7b72493d33091de3d2dc4.jpg)
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+![](images/0351ded27a5c3dfb755a653ce847d6b091e0ef8b00d2c4870bfea89417c2122e.jpg)  
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+Figure 6: Qualitative comparison results for SemanticKITTI (left) and NuScenes (right); Inlier prediciton indicates semantic segmentation; The final prediction is obtained by integrating the inlier prediction with $\mathbf { p ^ { o } }$ using a threshold of 0.5.
+
+Table 3: Ablations for dynamic penalty setting in SemanticKITTI.   
+
+<table><tr><td>Penalty</td><td>Dynamic Penalty</td><td>AUPR ↑</td><td>AUROC ↑</td><td>mIoUold ↑</td></tr><tr><td>✓</td><td></td><td>43.69</td><td>92.51</td><td>57.47</td></tr><tr><td></td><td>✓</td><td>44.68</td><td>92.69</td><td>57.56</td></tr></table>
+
+network in a single stage using our novel learning paradigm and two different outlier synthesis pipelines. In contrast, APF requires not only an arbitrary segmentation network but also several learnable prototypes, a prototypical constraint module, a generator, a discriminator, and an adversarial mapper, which significantly increase computational costs. Further, APF relies on a two-stage training process, complicating the reproducibility of its results.
+
+Risk-Coverage curve comparison: As shown in Fig. 5- (a), the problem of the CE&CCE, analyzed above, is reflected as a high risk at high coverages, while the CE exhibits an unstable trend when coverage decreases. In contrast, our method achieves a highly competitive risk compared to them at high coverages. With decreasing coverage, our method shows a consistent decline to a plateau in risk.
+
+Why our method achieve a higher risk compared to REAL when coverage is below $9 0 \% 2$ (purple dotted line) This is because our method rejects most real outlier samples/points when coverage exceeds $90 \%$ . This is proved by that the threshold set to achieve $90 \%$ coverage is 0.0051, indicating that all samples with a predicted outlier probability higher than 0.0051 are rejected. This means that when coverage is around $90 \%$ , the outlier probabilities of the remaining samples are relatively small, and there are few real outliers left. Therefore, to further decrease the coverage, our method tends to reject more true inliers than true outliers.
+
+However, we believe that robust performance in high coverage is more critical than in low coverage due to the fact that the outlier objects are rare in the real world.
+
+# Ablation Study
+
+Effectiveness of dynamic abstaining penalty. As demonstrated in Tab. 3, the penalty setting is denoted by Eq. (10), while the dynamic penalty setting is represented by Eq. (14). The dynamic penalty setting achieves the best performance.
+
+Table 4: Ablation study on outlier synthesis pipeline in SemanticKITTI.   
+
+<table><tr><td>ShapeNet</td><td>Resize</td><td>AUPR</td><td>AUROC</td><td>mIoUold</td></tr><tr><td>✓</td><td></td><td>29.14 (14.55 ↓)</td><td>89.56 (2.95 ↓)</td><td>57.31 (0.16 ↓)</td></tr><tr><td></td><td>✓</td><td>41.82 (1.87 ↓)</td><td>93.04 (0.53 ↑)</td><td>57.30 (0.17 ↓)</td></tr><tr><td>✓</td><td>✓</td><td>43.69</td><td>92.51</td><td>57.47</td></tr></table>
+
+These results provide evidence for the effectiveness of our dynamic penalty design.
+
+Effectiveness of outlier synthesis pipeline. As shown in Tab. 4, excluding the ShapeNet synthesis pipeline results in a decrease in AUPR by 1.87 and an increase in AUROC by 0.53. Moreover, the AUPR and AUROC drop significantly by 14.55 and 2.95, respectively, without the resize synthesis pipeline. This raises the question of whether ShapeNet synthesis pipeline is trivial.
+
+There are two types of real outliers: those that are distant from the inlier distribution (referred to as far real outliers) and those that lie closer to the inlier distribution (referred to as near real outliers). As shown in Fig. 5-(b), the resize synthesis pipeline shows an initial decrease in risk followed by an increase. This occurs because this pipeline can approximate the far real outlier distribution but struggles with approximating the near real outlier distribution.
+
+On the other hand, our ShapeNet synthesis pipeline exhibits a consistent reduction in risk as the coverage decreases, as it can synthesize outliers that approximate both near and far real outlier distributions. The former result from considering the LiDAR sampling pattern, while the latter stem from considering the diversity of real outliers.
+
+# Conclusion
+
+In this work, we first revisit previous methods using the unified lens of selective classification and propose a new formulation which effectively captures the subtle differences between inliers and outliers. Then, we design a novel outlier synthesis pipeline to synthesize diverse and realistic outliers, compensating for the lack of semantically-rich information in point clouds. Experimental results demonstrate the superiority of our method across both traditional outlier detection metrics and newly introduced metrics. Our method has achieved SOTA performance on public benchmark datasets.
+
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paper_markdowns/bamboo-00248.md

@@ -0,0 +1,410 @@
+# Task-level Distributionally Robust Optimization for Large Language Model-based Dense Retrieval
+
+Guangyuan $\mathbf { M } \mathbf { a } ^ { 1 , 2 * }$ , Yongliang Ma3, Xing Wu1,2, Zhenpeng $\mathbf { S u } ^ { 1 , 2 }$ , Ming Zhou3, Songlin Hu1,2†
+
+1Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China
+
+2School of Cyber Security, University of Chinese Academy of Sciences, Beijing, China
+
+3Langboat Technology, Beijing, China
+
+{maguangyuan,wuxing,suzhenpeng,husonglin}@iie.ac.cn, {mayongliang,zhouming}@langboat.com
+
+# Abstract
+
+Large Language Model-based Dense Retrieval (LLM-DR) optimizes over numerous heterogeneous fine-tuning collections from different domains. However, the discussion about its training data distribution is still minimal. Previous studies rely on empirically assigned dataset choices or sampling ratios, which inevitably lead to sub-optimal retrieval performances. In this paper, we propose a new task-level Distributionally Robust Optimization (tDRO) algorithm for LLM-DR fine-tuning, targeted at improving the universal domain generalization ability by end-to-end reweighting the data distribution of each task. The tDRO parameterizes the domain weights and updates them with scaled domain gradients. The optimized weights are then transferred to the LLM-DR finetuning to train more robust retrievers. Experiments show optimal improvements in large-scale retrieval benchmarks and reduce up to $30 \%$ dataset usage after applying our optimization algorithm with a series of different-sized LLM-DR models.
+
+Code — https://github.com/ma787639046/tdro
+
+Datasets — https://huggingface.co/tdro-llm
+
+# Introduction
+
+Dense retrieval (Karpukhin et al. 2020) recalls relevant documents from large-sized candidate pools with the similarity search (Mussmann and Ermon 2016) of query-passage embeddings. The recent bloom of Large Language Modelbased Dense Retrieval (LLM-DR) (Wang et al. 2024a; Meng et al. 2024; Muennighoff et al. 2024) promotes remarkable retrieval abilities with better foundation models (Touvron et al. 2023; Bai et al. 2023; Jiang et al. 2023) and large-scale training collections (Wang et al. 2024a; Xiao et al. 2023).
+
+LLM-DR fine-tuning learns LLM-based retrieval models with heterogeneous training collections (Reimers 2019) from multiple domains with different learning difficulties. The data distribution of training collections, i.e. a mixture of data with chosen datasets or sampling ratio on each dataset, significantly influences the general retrieval performances of dense retrievers (Oren et al. 2019; Meng et al. 2024). However, the choice or sampling ratio of the training sets still
+
+![](images/4188454e48a6b5eb0d32667c9349dd2ce6b605434a47c7517a321d776b56f2d9.jpg)  
+Figure 1: Task-level Distributionally Robust Optimization for Large Language Model-based Dense Retrieval.
+
+relies heavily on intuitional assessments. It’s hard to decide whether an empirical assigned data sampling ratio is optimal for the models to perform well, i.e. robust to all tasks. Nowadays, the robustness of data distributional optimization for LLM-DR is still very limited.
+
+Distributionally Robust Optimization (DRO) (Oren et al. 2019; Sagawa et al. 2019; Piratla, Netrapalli, and Sarawagi 2022) receives extensive discussions for battling unbalanced data composition. GroupDRO (Sagawa et al. 2019), the most popular algorithm for DRO, optimizes on the worst-case loss of the corresponding domain, which picks a domain with the highest loss at each training step and up-weights the loss of this domain. Although there was an attempt (Yu et al. 2022) to utilize vanilla GroupDRO or variants of DRO algorithm (Piratla, Netrapalli, and Sarawagi 2022) for dense retrieval fine-tuning, the optimization is limited to a small BERTbased model over clustered groups of one single dataset, i.e. MS-MARCO (Nguyen et al. 2016), which fails to generalize to LLM-DR fine-tuning with multiple heterogeneous training collections. It’s profitable to solve the data distribution issue of LLM-DR in an end-to-end manner like DRO, but such a study is still left for further exploration.
+
+The existing DRO algorithms (Oren et al. 2019; Sagawa et al. 2019; Piratla, Netrapalli, and Sarawagi 2022), such as GroupDRO, are theoretically incompatible with LLM-DR fine-tuning due to different batch sampling strategies and incommensurable loss scales. Firstly, DRO requires all
+
+Table 1: Comparison of loss scales for Yahoo answers (Title-Answer) (Zhang, Zhao, and LeCun 2015), MS-MARCO (Nguyen et al. 2016), and DuReader (Qiu et al. 2022) datasets. The model used here is Qwen1.5-0.5B trained with uniform data sampling ratios for 1k steps.   
+
+<table><tr><td>Dataset</td><td>Loss</td></tr><tr><td>Yahoo answers (Title-Answer)</td><td>3.9257</td></tr><tr><td>MS-MARCO</td><td>1.3312</td></tr><tr><td>DuReader</td><td>0.6925</td></tr></table>
+
+domain data mandatory in one batch for end-to-end comparisons. It dynamically reweights the training losses based on the worst-case group and derives the robust-optimized proxy model as the final model directly. However, the LLM-DR fine-tuning collects the heterogeneous sets in a homogeneous batching method (Meng et al. 2024) during its finetuning, which means only one domain can be collected to the whole batch to ensure that in-batch negatives are sampled from the same task. What’s worse, the heterogeneous collections used by LLM-DRs have significantly different loss scales. If directly applying the DRO algorithms (Sagawa et al. 2019; Yu et al. 2022; Piratla, Netrapalli, and Sarawagi 2022) to LLM-DRs, the models will always bias towards the domain with the highest training loss, i.e. worst case loss, which will hurt the fine-tuning process. As is shown in Table 1, the loss of Yahoo answers with a Qwen1.5-0.5B retriever is three times over MS-MARCO and five times over DuReader. Directly using worst-case loss will make the model always biased towards Yahoo, rather than MS-MARCO or DuReader.
+
+To tackle the above optimization problems for LLM-DR, we develop a new task-level Distributionally Robust Optimization (tDRO) algorithm that aims at improving the general domain adaption ability across multiple tasks1. Firstly, to coordinate with different batch sampling strategies, our algorithm separates the DRO optimization and LLM-DR fine-tuning as is presented in Figure 1. Instead of directly learning a robust model (Oren et al. 2019; Sagawa et al. 2019), such separation first learns domain weights with a proxy model via the DRO algorithm and then transfers learned domain weights to LLM-DR fine-tuning. The proxy model is initialized from a small-sized LM, e.g. Qwen1.5- 0.5B (Bai et al. 2023). It receives uniformly sampled training collections within an input batch, computes contrastive losses of each domain, and uses them as the gradients of domain weights. Then it transfers the learned weight or merely chooses the top-weighted datasets all LLM-DR model finetunings with different sizes. This separation shares several benefits: We can sample all domains within a batch in the tDRO stage and use task-homogeneous batching in the finetuning stage, which makes DRO work well while not hurting the final retrieval performances of LLM-DRs. Also, a smallsized LM can be used in tDRO optimizations to reduce com-
+
+putational overheads.
+
+Secondly, as discussed above, the heterogeneous domains have different loss scales. To make a comparable measurement of domain running losses, we use a trained LLM-DR model, e.g. Qwen1.5-0.5B with uniform data sampling ratios, as the reference model and forward it with the same inputs. We compute the relative loss measurement by dividing the proxy loss with reference loss. Intuitively, the relative loss measurement represents the improving headroom for the corresponding domains. Higher gradients will up-weight more corresponding domain weights.
+
+To verify the effectiveness of the tDRO algorithm, we conduct data distribution optimization on open-sourced sentence transformers training data (Reimers 2019). We test on three large-scale retrieval benchmarks to fully assess the universal retrieval abilities across different languages and domains, including multilingual MIRACL (Zhang et al. 2023), cross-lingual MKQA (Longpre, Lu, and Daiber 2021), and monolingual BeIR (Thakur et al. 2021). Experiments shows steady improvements with less dataset usage after applying tDRO optimization.
+
+# Algorithm
+
+# Problem Statement
+
+Assume the training collections $D ^ { t r a i n }$ of LLM-DR finetuning are composed of $k$ individual datasets, each of them is assigned with a domain weight $\alpha$ , representing a choice of probability distribution $P _ { \alpha }$ over joint training collections:
+
+$$
+P _ {\alpha} = \sum_ {g = 1} ^ {k} \alpha_ {g} \mathrm {U} \left(D _ {g} ^ {t r a i n}\right), s. t. \sum_ {g = 1} ^ {k} \alpha_ {g} = 1. \tag {1}
+$$
+
+U is a uniform distributional sampling function. And $\alpha _ { g } \mathrm { U } ( D _ { g } ^ { t r a i n } )$ means sampling from such distribution with weight $\alpha _ { g }$ for group $g$ , which is also called $\alpha$ -covered probability distribution (Oren et al. 2019). The goal of LLM-DR data distributional optimization is to find an optimal distribution $P _ { \alpha }$ , or a choice of weights $\alpha$ specifically, enabling the model to perform well on all downstream tasks $D ^ { t e s t }$ . Note that downstream tasks $D ^ { t e s t }$ are not necessarily identical to the fine-tuning sets $D ^ { t r a i n }$ .
+
+# Task-level Distributionally Robust Optimization
+
+The task-level Distributionally Robust Optimization (tDRO) algorithm parameterizes domain weights $\alpha$ and tries to learn the best choice of $\alpha$ for all tasks in an end-to-end manner. The tDRO holds a basic assumption for solving the data distributional optimization of LLM-DR: In a scenario with multiple independent and identically distributed (iid) task collections, if a model is robust to the training phase, then it will be robust to most of the test sets. Thus like most DRO algorithms (Oren et al. 2019; Sagawa et al. 2019; Piratla, Netrapalli, and Sarawagi 2022), tDRO operates on the robustness of training collections for universal adaption abilities. The whole optimization pipeline includes a separate tDRO stage and LLM-DR fine-tuning stage.
+
+![](images/f258216033c5b23f10b63f135ce68d0f7216a940d4457991e5857c9b99861536.jpg)  
+A) Fitting single domain data in one batch.
+
+![](images/eb84456af8ffce4ddf91e18e085d6dafb20758c237c7fd37a00c80230c2afe69.jpg)  
+B) Fitting multiple domain data in one batch.   
+Figure 2: Different batch sampling strategies and negative types for A) LLM-DR Fine-tuning and B) Distributionally Robust Optimization.
+
+InfoNCE Loss tDRO treats each dataset as a task (or domain) at minimal granularity and trains a proxy model with parameters $\theta _ { p r o x y }$ to adaptively compare and update the domain weights at the task level. At each training step $t$ , a batch of training data with domain sampling probabilities $1 / k$ is forwarded through the proxy model. By extracting hidden states from the last token position, each batch item comprises a query representation $q$ , a positive document representation $d ^ { + }$ , and several hard negative $( H N )$ document representations $d _ { H N } ^ { - }$ . InfoNCE loss (van den Oord, Li, and Vinyals 2018), i.e. contrastive loss, is used to calculate losses of the proxy model for each group:
+
+$$
+\mathcal {L} ^ {p r o x y} = - \log \frac {e ^ {q \cdot d ^ {+} / \tau}}{e ^ {q \cdot d ^ {+} / \tau} + \sum e ^ {q \cdot d _ {H N} ^ {-} / \tau}}, \tag {2}
+$$
+
+where $\tau$ is a contrastive temperature. In-batch negative sampling is not an option for tDRO because different tasks could induce false negatives and reduce negative qualities.
+
+Optimization Objective tDRO learns domain weights $\alpha$ with a dual-optimization objective, which minimizes the supremum of the $\alpha$ -weighted sum of group loss measurements. Such an objective ensures universal robustness by lowering the upper bound of the worst groups:
+
+$$
+\min  _ {\theta} \sup  _ {\alpha} \sum_ {g = 1} ^ {k} \alpha_ {g} \mathcal {M} _ {g} \left(\theta_ {p r o x y}; q, d ^ {+}, d ^ {-}\right), \tag {3}
+$$
+
+where group loss measurement $\mathcal { M } _ { g }$ is a scalar corresponding to averaged losses, representing the improving headrooms for each group. Following the previous DRO framework (Sagawa et al. 2019), the above object is optimized by interleaving the updates of weights $\alpha$ and proxy model parameters $\theta$ .
+
+Weights Update For weights update, tDRO optimizes the above object by up-weighting the corresponding domain weights with exponential gradient ascent:
+
+$$
+\alpha_ {g} ^ {t} = \alpha_ {g} ^ {t - 1} e ^ {\eta_ {\alpha} \mathcal {M} _ {g}}, \tag {4}
+$$
+
+where $\eta _ { \alpha }$ is the learning rate for domain weights. As a common optimation practice, gradient normalization is used on the above gradients to ensure stable weight updates. Intuitively, a higher loss measurement induces more upweighting of the corresponding group. After the update of $\alpha$ , a re-normalization is performed to ensure $\textstyle \sum _ { g = 1 } ^ { k } \alpha _ { g } = 1$ .
+
+Relative Loss Measurement The key component of tDRO is how to derive a balanced and comparable loss measurement $\mathcal { M } _ { g }$ . GroupDRO directly uses the average group loss $\mathbb { E } ( \mathcal { L } _ { g } ^ { p r o x y } )$ as the loss measurement, where $\mathbb { E }$ is the arithmetic mean function. However, as presented in Table 1, the averaged contrastive losses of each group are not comparable. Directly using the average group loss will always make the proxy model biased toward one group with the highest loss. To solve the above issue, we introduce a trained reference model $_ { r e f }$ , forward it with the same inputs, compute reference loss as Formula (2), and divide the proxy loss with reference loss to dynamically scale the average group loss. This design is called relative loss measurement.
+
+$$
+\mathcal {M} _ {g} = \mathbb {E} \left(\mathcal {L} _ {g} ^ {p r o x y}\right) / \mathbb {E} \left(\mathcal {L} _ {g} ^ {r e f}\right). \tag {5}
+$$
+
+The reference model is frozen and will not be updated during the tDRO stage. In our implementation, we initialize the reference model with Qwen1.5-0.5B (Bai et al. 2023) and train with uniform sampling weights on all training sets. The training setting of the reference model follows the LLM-DR fine-tuning recipe, which will be described later.
+
+Proxy Model Update After updating domain weights, the proxy model is updated with $\alpha$ -weighted contrastive loss.
+
+$$
+\theta^ {t} = \theta^ {t - 1} - \alpha_ {g} \eta_ {\theta} \nabla_ {\theta}, \tag {6}
+$$
+
+where $\eta _ { \theta }$ is the learning rate of the proxy model, and $\nabla _ { \theta }$ is the gradient of proxy model obtained by backpropagation. The AdamW optimizer can be used for fast convergence.
+
+# LLM-DR Fine-tuning
+
+LLM-DR fine-tuning also uses contrastive loss to pull positive representations together and push negative representa-
+
+Table 2: Training datasets information. Note that strict deduplication is performed on all training sets with Simhash (Manku, Jain, and Sarma 2007) to ensure no overlap between training and testing sets.   
+
+<table><tr><td>Dataset</td><td>Language</td><td>Category</td><td>Deduped Size</td></tr><tr><td>agnews (Corso, Gulli, and Romani 2005)</td><td>English</td><td>News</td><td>1,157,745</td></tr><tr><td>AllNLI (Bowman et al. 2015; Williams, Nangia, and Bowman 2018)</td><td>English</td><td>NLI</td><td>277,230</td></tr><tr><td>altlex (Hidey and McKeown 2016)</td><td>English</td><td>Wikipedia Pair</td><td>112,696</td></tr><tr><td>amazon_review_2018 (Ni, Li, and McAuley 2019)</td><td>English</td><td>Amazon</td><td>999,999</td></tr><tr><td>cnn_dailymail (See, Liu, and Manning 2017)</td><td>English</td><td>News</td><td>311,971</td></tr><tr><td>codesearchnet (Husain et al. 2019)</td><td>English</td><td>Github</td><td>1,375,067</td></tr><tr><td>dureader (Liu et al. 2021)</td><td>Chinese</td><td>Web Collections</td><td>86,395</td></tr><tr><td>eli5_question_answer (Fan et al. 2019)</td><td>English</td><td>Reddit</td><td>325,390</td></tr><tr><td>gooaq_pairs (Khashabi et al. 2021)</td><td>English</td><td>Web Collections</td><td>3,012,347</td></tr><tr><td>hotpotqa (Yang et al. 2018)</td><td>English</td><td>Wikipedia QA</td><td>85,000</td></tr><tr><td>medmcqa (Pal, Umapathi, and Sankarasubbu 2022)</td><td>English</td><td>Medical</td><td>160,865</td></tr><tr><td>miracl (Zhang et al. 2023)</td><td>16 languages</td><td>Multilingual Wikipedia</td><td>32,405</td></tr><tr><td>mr_tydi(combined (Zhang et al. 2021)</td><td>11 languages</td><td>Multilingual Wikipedia</td><td>48,475</td></tr><tr><td>msmarco (Nguyen et al. 2016)</td><td>English</td><td>Web Collections</td><td>502,854</td></tr><tr><td>nq (Kwiatkowski et al. 2019)</td><td>English</td><td>Wikipedia QA</td><td>58,800</td></tr><tr><td>quora Duplicate triples (Iyer, Dandekar, and Csernai 2012)</td><td>English</td><td>Forum Duplicates</td><td>97,011</td></tr><tr><td>searchQA_top5_snippets (Dunn et al. 2017)</td><td>English</td><td>Web Collections</td><td>117,219</td></tr><tr><td>sentence-compression (Filippova and Altun 2013)</td><td>English</td><td>News</td><td>180,000</td></tr><tr><td>SimpleWiki (Coster and Kauchak 2011)</td><td>English</td><td>Wikipedia Pair</td><td>102,225</td></tr><tr><td>squad_pairs (Rajpurkar et al. 2016)</td><td>English</td><td>Wikipedia QA</td><td>87,595</td></tr><tr><td>stackexchange Duplicate_title-body (da Silva, Paixão, and de Almeida Maia 2018)</td><td>English</td><td>Forum Duplicates</td><td>250,516</td></tr><tr><td>t2ranking (Xie et al. 2023b)</td><td>Chinese</td><td>Web Collections</td><td>200,376</td></tr><tr><td>trivia (Joshi et al. 2017)</td><td>English</td><td>Wikipedia QA</td><td>60,370</td></tr><tr><td>xsum (Narayan, Cohen, and Lapata 2018)</td><td>English</td><td>News</td><td>226,711</td></tr><tr><td>yahoo_answers_title_answer (Zhang, Zhao, and LeCun 2015)</td><td>English</td><td>Yahoo</td><td>1,198,018</td></tr></table>
+
+tions away. But it uses completely different batch sampling strategies and negative types from tDRO, which is one of the reasons that previous DRO algorithms like GroupDRO are theoretically incompatible with LLM-DR fine-tuning.
+
+LLM-DR Batching Strategy As is shown in Figure 2A, LLM-DR fine-tuning fits the data from one single domain in each batch to ensure the quality of in-batch negatives. This batching strategy is also called task-homogeneous batching (Meng et al. 2024). As is a common practice, LLM-DR trains with large batch sizes, e.g. 2048 in our implementation, and three types of negatives, including hard negatives $( H N )$ , in-batch negatives $( I B N )$ , and cross-batch negatives $( C B N )$ . Large batch size enables contrastive learning of LLM-DR using more negatives, especially in-batch and cross-batch negatives. Hard negatives are provided by individual datasets, which are mined from existing retrieval systems like BM25 (Robertson et al. 1994) or dense retrievers (Karpukhin et al. 2020). In-batch negatives are samples from other data items within a batch. Cross-batch negatives are samples gathered from other GPU batches. Overall, the contrastive loss $( \mathcal { L } ^ { C L } )$ for LLM-DR is formulated as follows.
+
+$$
+\mathcal {L} ^ {C L} = - \log \frac {e ^ {q \cdot d ^ {+} / \tau}}{e ^ {q \cdot d ^ {+} / \tau} + \sum e ^ {q \cdot \{d _ {H N} ^ {-} ; d _ {I B N} ^ {-} ; d _ {C B N} ^ {-} \} / \tau}}. \tag {7}
+$$
+
+However, tDRO compares and updates domain weights in an end-to-end manner, thus it requires fitting all domain data in one batch. As displayed in Figure 2B, The training batch
+
+is composed of all domains, while the in-batch/cross-batch negatives are not used in tDRO.
+
+# Experiments
+
+# Experiment Settings
+
+Datasets A total of 25 individual datasets are used in our experiments, covering categories of Wikipedia, web collection, news, GitHub, yahoo, etc. Most of them are directly taken from sentence transformers training data (Reimers 2019). BGE-large-en-1.5 (Xiao et al. 2023) is used to mine negatives if the original datasets (several English datasets) have no negatives provided. Several popular multilingual datasets are also included in the training sets, including MIRACL (Zhang et al. 2023) and Mr.Tydi (Zhang et al. 2021). All information about datasets is listed in Table 2.
+
+Settings For the tDRO algorithm, both the proxy and reference models are initialized from Qwen1.5-0.5B (Bai et al. 2023) for computational efficiency. tDRO is performed with a total batch size of 2048, query & document maximum sequence lengths of 128 & 512, a proxy model learning rate ηθ of 1e-4, contrastive temperature $\tau$ of 0.002, weights learning rate $\eta _ { \alpha }$ of 2e-2, and seed of 42. The weights from the tDRO stage are directly transferred to LLM-DR fine-tuning. Two weight transfer strategies are utilized:
+
+1. Top-rated dataset selection: Use the Top-rated datasets and discard the datasets with lower weights. This helps reduce dataset usage.
+
+Table 3: Retrieval performances and corresponding gains of tDRO algorithm on MIRACL dev, MKQA test, and BeIR test benchmarks. The highest retrieval scores and average performance gains are marked as bold. *Significant improvements $( \mathsf { p } \leq$ 0.01) over the corresponding baseline. MS-MARCO in BeIR uses the dev split because there is no public test label.   
+
+<table><tr><td>Benchmark (# Dataset)</td><td colspan="2">MIRACL (18)</td><td colspan="2">MKQA (25)</td><td>BeIR (15)</td></tr><tr><td>Metric</td><td>nDCG@10</td><td>Recall@100</td><td>Accuracy@10</td><td>Accuracy@100</td><td>nDCG@10</td></tr><tr><td colspan="6">Uniform Sampling Baselines</td></tr><tr><td>Qwen-0.5B</td><td>45.8</td><td>80.5</td><td>43.1</td><td>61.3</td><td>47.5</td></tr><tr><td>Qwen-1.8B</td><td>50.9</td><td>84.7</td><td>45.0</td><td>64.0</td><td>48.8</td></tr><tr><td>Qwen-4B</td><td>55.9</td><td>88.7</td><td>53.7</td><td>70.2</td><td>51.8</td></tr><tr><td>Qwen-7B</td><td>59.6</td><td>90.6</td><td>58.7</td><td>73.6</td><td>52.3</td></tr><tr><td>Mistral-7B</td><td>61.3</td><td>91.6</td><td>59.8</td><td>72.8</td><td>55.2</td></tr><tr><td>Llama3-8B</td><td>64.1</td><td>92.8</td><td>64.0</td><td>75.8</td><td>55.0</td></tr><tr><td colspan="6">tDRO - Dataset Selection Top-70%</td></tr><tr><td>Qwen-0.5B</td><td>48.7* (+2.9)</td><td>82.1* (+1.6)</td><td>45.4* (+2.3)</td><td>62.3* (+1.0)</td><td>48.9* (+1.4)</td></tr><tr><td>Qwen-1.8B</td><td>54.1* (+3.2)</td><td>86.6* (+1.9)</td><td>48.6* (+3.6)</td><td>65.6* (+1.6)</td><td>50.2* (+1.4)</td></tr><tr><td>Qwen-4B</td><td>58.6* (+2.7)</td><td>90.0* (+1.3)</td><td>57.0* (+3.3)</td><td>71.4* (+1.2)</td><td>52.6* (+0.8)</td></tr><tr><td>Qwen-7B</td><td>61.6* (+2.0)</td><td>91.4* (+0.8)</td><td>59.9* (+1.2)</td><td>73.8 (+0.2)</td><td>53.3* (+1.0)</td></tr><tr><td>Mistral-7B</td><td>63.8* (+2.5)</td><td>92.4* (+0.8)</td><td>62.5* (+2.7)</td><td>73.8* (+1.0)</td><td>55.2 (+0.0)</td></tr><tr><td>Llama3-8B</td><td>66.4* (+2.3)</td><td>93.5* (+0.7)</td><td>66.0* (+2.0)</td><td>76.4* (+0.6)</td><td>55.1 (+0.1)</td></tr><tr><td>Avg Gains</td><td>+2.6</td><td>+1.2</td><td>+2.5</td><td>+0.9</td><td>+0.8</td></tr><tr><td colspan="6">tDRO - Sample Ratio Reweighting</td></tr><tr><td>Qwen-0.5B</td><td>49.1* (+3.3)</td><td>82.7* (+2.2)</td><td>45.5* (+2.4)</td><td>62.2* (+0.9)</td><td>48.3* (+0.8)</td></tr><tr><td>Qwen-1.8B</td><td>53.6* (+2.7)</td><td>86.5* (+1.8)</td><td>50.5* (+5.5)</td><td>66.8* (+2.8)</td><td>49.7* (+0.9)</td></tr><tr><td>Qwen-4B</td><td>58.4* (+2.5)</td><td>90.0* (+1.3)</td><td>57.8* (+4.1)</td><td>72.0* (+1.8)</td><td>51.9 (+0.1)</td></tr><tr><td>Qwen-7B</td><td>61.0* (+1.4)</td><td>91.1 (+0.5)</td><td>59.8* (+1.1)</td><td>73.6 (+0.0)</td><td>52.4 (+0.1)</td></tr><tr><td>Mistral-7B</td><td>63.4* (+2.1)</td><td>92.4* (+0.8)</td><td>62.8* (+3.0)</td><td>74.0* (+1.2)</td><td>55.4 (+0.2)</td></tr><tr><td>Llama3-8B</td><td>66.3* (+2.2)</td><td>93.4* (+0.6)</td><td>67.0* (+3.0)</td><td>76.8* (+1.0)</td><td>55.0 (+0.0)</td></tr><tr><td>Avg Gains</td><td>+2.4</td><td>+1.2</td><td>+3.2</td><td>+1.3</td><td>+0.4</td></tr></table>
+
+![](images/9ae19cd854fad85e60520b1fe0a262b48c9d1ce4d311713cf83ffae47e958a6e.jpg)  
+Figure 3: Weights comparison among baseline, tDRO, and other loss measurement designs.
+
+# 2. Sample Ratio Reweighting: Directly use the weights to reweight the sample ratios of datasets.
+
+We conduct weights transfer on Qwen-1.5 0.5B, 1.8B, 4B, 7B (Bai et al. 2023), Mistral-0.1-7B (Jiang et al. 2023) and Llama3-8B (Touvron et al. 2023) for LLM-DR fine-tuning. Contrastive learning is performed with the same batch size, sequence lengths, model learning rate (1e-4), and contrastive temperature as stated before. Gradient cache (Gao et al. 2021), flash attention 2 (Dao 2023), full-shard data paral-
+
+lel (FSDP), activation checkpointing and low-rank adapter (LoRA) (Hu et al. 2022) with $r = 8 , \alpha = 3 2$ and dropout ratio of 0.1 are used to reduce GPU memory usage. Following the previous work (Wang et al. 2024a; Su et al. 2023), prompt instructions are added on the query side for multitasks during training and evaluation. All trainings are performed on 8 NVIDIA H800 GPUs with 4.5 hours for tDRO and less than 10 hours for all LLM-DR fine-tunings.
+
+Table 4: Retrieval scores among state-of-the-art retrievers. *We take the released BeIR scores without GPT data for fair comparisons.   
+
+<table><tr><td>Benchmark</td><td>Enhance</td><td>MIRACL</td><td>MKQA</td><td>BeIR</td></tr><tr><td>Metric → 
+Models ↓</td><td>Special 
+Pre-train</td><td>nDCG@10</td><td>Acc@100</td><td>nDCG@10</td></tr><tr><td>BM25</td><td></td><td>31.9</td><td>39.9</td><td>41.7</td></tr><tr><td>mContiever</td><td>✓</td><td>43.1</td><td>67.9</td><td>46.0</td></tr><tr><td>mE5-large-inst</td><td>✓</td><td>64.6</td><td>70.2</td><td>52.3</td></tr><tr><td>E5-Mistral*</td><td></td><td>62.2</td><td>68.6</td><td>52.7</td></tr><tr><td colspan="5">tDRO + LLM-DR Llama3-8B</td></tr><tr><td>Top-70%</td><td></td><td>66.4</td><td>76.4</td><td>55.1</td></tr><tr><td>Reweighting</td><td></td><td>66.3</td><td>76.8</td><td>55.0</td></tr></table>
+
+Baselines and Benchmarks To compare the performance changes after tDRO optimization, we choose LLM-DR with uniform sampling weights2 as baselines. All other settings are kept the same. Note that results from some recent state-of-the-art retrievers, including BM25 (Robertson et al. 1994), mContriever/Contriever (Izacard et al. 2021), E5- Mistral-7b (Wang et al. 2024a), and Multilingual-e5-largeinstruct (Wang et al. 2024b) are also added to our results. But we DO NOT seek to compare with them. Some of them utilize multiple training enhancements, such as data synthesis with ChatGPT and special pre-trainings (Wang et al. 2023; Wu et al. 2023; Ma et al. 2024a) for retrieval, which is an unfair comparison to our experiments and out of the research scope for our paper.
+
+MIRACL (Zhang et al. 2023), MKQA (Longpre, Lu, and Daiber 2021), and BeIR (Thakur et al. 2021) are used as main retrieval benchmarks. MIRACL is a huge multilingual retrieval benchmark across 18 languages with 13K queries and 90M passages. Cross-lingual benchmark MKQA holds 25 different languages of parallel Wikipedia queries. Following (Chen et al. 2024), the cross-lingual retrieval is performed by using queries (6.6k for each) of different languages to recall relevant English Wikipedia with 2.7M passages3. BeIR is a heterogeneous English retrieval benchmark with 15 public datasets and 34M documents, covering a wide range of retrieval domains and text symmetries. MIR-ACL is reported with nDCG $@ 1 0$ and Recall $@ 1 0 0$ . MKQA is reported with Accuacy $@ \{ 1 0 , 1 0 0 \}$ (Acc). Examing performances at threshold 10 assess the top-ranking ability and threshold 100 for recalling capacity at a larger window. BeIR is reported with nDCG $@ 1 0$ by following the original paper (Thakur et al. 2021). The whole evaluation takes around 30 hours with 8 NVIDIA H800 GPUs for the largest LLM-DR retriever, Llama3-8B.
+
+# Results
+
+Retrieval benchmarks on multilingual, cross-lingual, and monolingual English retrieval are conducted and listed in
+
+Table 5: Ablation studies on sampling strategy choices and group loss designs.   
+
+<table><tr><td></td><td>BEIR</td><td>MIRACL</td><td>MKQA</td></tr><tr><td>Metric</td><td>nDCG@10</td><td>nDCG@10</td><td>Acc@100</td></tr><tr><td>Qwen-0.5B-Baseline</td><td>47.5</td><td>45.8</td><td>61.3</td></tr><tr><td colspan="4">Sampling Strategy Choices for tDRO</td></tr><tr><td colspan="4">Dataset Selection</td></tr><tr><td>w/ Bottom-50%</td><td>45.2-2.3</td><td>44.6-1.2</td><td>60.7-0.6</td></tr><tr><td>w/ Top-60%</td><td>48.4+0.9</td><td>48.2+2.4</td><td>62.0+0.7</td></tr><tr><td>w/ Top-70%</td><td>48.9+1.4</td><td>48.7+2.9</td><td>62.3+1.0</td></tr><tr><td>w/ Top-80%</td><td>48.9+1.4</td><td>47.8+2.0</td><td>62.1+0.8</td></tr><tr><td>Samping Ratio Reweighting</td><td>48.3+0.8</td><td>49.1+3.3</td><td>62.2+0.9</td></tr><tr><td>Loss Reweighting</td><td>48.2+0.7</td><td>46.3+0.5</td><td>61.2-0.1</td></tr><tr><td colspan="4">Loss Measurements (w/ Sampling Ratio Reweighting)</td></tr><tr><td>Lproxy/ Lref</td><td>48.3+0.8</td><td>49.1+3.3</td><td>62.2+0.9</td></tr><tr><td>Lproxy - Lref</td><td>47.5-0.0</td><td>45.3-0.5</td><td>60.1+1.2</td></tr><tr><td>Lproxy</td><td>47.2-0.3</td><td>47.0+1.2</td><td>61.5+0.2</td></tr></table>
+
+Table 3. tDRO optimized domain weights are listed in Figure 3. Top- $70 \%$ is the optimal line for the top-rated dataset selection strategy. Ablation on the percentages of dataset selection will be presented later.
+
+tDRO Boosts Retrieval Performances. tDRO boosts the universal retrieval performances of LLM-DR on a series of different-sized base LLM, including Qwen-1.5 (0.5B, 1.8B, 4B, 7B), Mistral-0.1 7B, and Llama3 8B. Both the top-rated dataset selection and the sample ratio reweighting strategies work well on most retrieval benchmarks with significant performance gains. The improvements in multilingual MIRACL and cross-lingual MKQA retrieval are attributed to the up-weighting of multilingual datasets, e.g. MIRACL.
+
+tDRO Balances Data Usages As is shown in Figure 3, although multilingual training sets are less than monolingual sets, tDRO balances the lingual distribution differences by top-rating the multilingual MIRACL and T2-Ranking. In contrast, tDRO down-weights 9 monolingual English datasets (Nearly $30 \%$ amounts) to less than 0.01. If we remove less-weighted datasets and keep only the Top- $70 \%$ sets, the results on multilingual, cross-lingual, and monolingual retrieval benchmarks even get significantly better, although less data is involved in LLM-DR fine-tuning. This is attributed to the end-to-end task-level data distribution optimization by tDRO, which balances the data distribution and helps LLM-DR training to focus on more useful and challenging data. Notably, as shown in Table 4, tDRO-optimized LLM-DR gets leading performances without using further enhancements, such as GPT4 data synthesis and special pretraining.
+
+# Analysis
+
+# Weight Transfering Strategies
+
+According to Table 5, top-rated dataset selection reaches peak performances with Top- $70 \%$ datasets. On the contrary, using Bottom- $50 \%$ significantly hurts the performances. This strategy is stable on nearly all benchmarks. However, as is shown in Table 3, some monolingual results seem to reach peak levels without further gains, such as Mistral-7B and Llama3-8B for BeIR. This phenomenon only occurs in LLMs with larger parameters $\mathrm { ( > 7 B ) }$ on BeIR. A potential explanation could be that larger LLMs have stronger capacities to tolerate the data weight changes when plenty of monolingual data is provided. Under this circumstance, large LLMs can perform evenly well.
+
+Sample ratio reweighting has more performance gains on MKQA than the selection strategy because it incurs more sampling probabilities on multilingual datasets, e.g. MIR-ACL and T2-Ranking, as displayed in Figure 3. However, such over-weighting on multilingual datasets is also the reason for no significant gains on monolingual BeIR of large LLMs, e.g. Qwen-4B, 7B, Mistral-7B, and Llama3-8B.
+
+Additionally, we also test re-scaling contrastive losses of LLM-DR with transferred weights. However, such loss reweighting improves BeIR but has no gains on MIRACL and MKQA. A potential reason could be that loss reweighting only changes the loss scale, but does not import more multilingual data because the data sampling ratios are unchanged.
+
+# Loss Measurement Designs
+
+Loss measurement is the key design to get proper domain loss scales. tDRO utilizes relative loss measurement by dividing the proxy loss with the reference loss. We also tested two additional choices:
+
+1. Minus the proxy loss with reference loss. This design is also called group excess loss in DRO (Oren et al. 2019). But obviously, the minus operation could not scale the big loss differences of heterogeneous collections for LLM-DR fine-tuning.   
+2. Directly using proxy loss.
+
+As is shown in Table 5, these two loss measurements hurt the performances. This is attributed to the incomparable loss scales of different datasets. According to Figure 3, both measurements over-prefer Yahoo significantly, because of the biggest loss scale of Yahoo as shown in Table 1.
+
+# Related Works
+
+# Large Language Model-based Dense Retrieval (LLM-DR)
+
+Dense retrieval (DR) has gained significant improvements in recent years because of the rapid developments of large language models (LLM) (Ouyang et al. 2022; Touvron et al. 2023; Bai et al. 2023; Jiang et al. 2023) and growing collections of heterogeneous training data (Reimers 2019). In short, the model parameter is growing, and the datasets are increasing. Sentence-T5 (Ni et al. 2022) first scales the
+
+foundation models to billon parameter T5 and gains good abilities of sentence embeddings. RepLLaMA and RankLLaMA (Ma et al. 2024b) first finetune retrievers and re-rankers on Llama2 with a single MS-MARCO dataset and get remarkable improvements over a series of smallsized baseline retrievers. E5-Mistral (Wang et al. 2024a) utilizes 500k GPT3.5/4 synthesized training data and 15 wellcollected datasets to fine-tune the retriever, further pushing the boundary of retrieval abilities. It also transfers these data to specially pre-trained small-sized model mE5 (Wang et al. 2024b) for state-of-the-art (SOTA) multilingual performances. However, the utilization of training collection for LLM-DR still relies on intuitional assessments. As discussed in this paper, empirical assigned data choices or sampling ratios, e.g. uniform sampling, incur sub-optimal performances.
+
+# Distributionally Robust Optimization (DRO)
+
+Distributionally Robust Optimization (DRO) is an effective way to battle unbalanced data distributions. Topic CVaR (Oren et al. 2019), first proposes to minimize the worst-case loss of each topic. (Sagawa et al. 2019) proposes a gradientbased GroupDRO algorithm and successfully improves the worse-group accuracies. DoReMi (Xie et al. 2023a) utilizes GroupDRO in LLM pre-training with minimax optimization for improving perplexities and downstream accuracies. CGD algorithm (Piratla, Netrapalli, and Sarawagi 2022) introduces the inter-group interactions into GroupDRO by substituting the worst-case loss with the inner product score of group gradients.
+
+Research on DRO for dense retrieval is still minimal. COCO-DR (Yu et al. 2022) combines pre-training method coCondenser (Gao and Callan 2022) and CGD algorithm to battle the distribution shifts on both the document and query side. However, its scope is limited to small-sized BERT models over clustered groups of one single MS-MARCO (Nguyen et al. 2016) dataset. Our study aims to solve the optimization problem of data distribution in LLM-DR finetuning, which end-to-end reweights each dataset for optimal performance.
+
+# Conclusion
+
+Large language model-based dense retrieval (LLM-DR) utilizes multiple heterogeneous training datasets in fine-tuning. Previous studies rely on empirical assessments to decide the sampling ratios of each dataset, which incurs unbalanced training data distribution and leads to sub-optimal performances. In our study, we propose a new task-level Distributionally Robust Optimization (tDRO) algorithm to improve the domain generalization ability by end-to-end reweighting the data distribution of each dataset. Experiments on largescale retrieval benchmarks show steady improvements with less dataset usage.
+
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+
+# Appendix
+
+# Training Hyper-parameters
+
+To facilitate the reproducibility of our work, we arrange all hyper-parameters or experiment settings here for tDRO optimization and LLM-DR fine-tuning.
+
+Table 6: Training hyper-parameters for tDRO optimization and LLM-DR fine-tuning.   
+
+<table><tr><td></td><td>tDRO</td><td>LLM-DR</td></tr><tr><td>Base model</td><td>Qwen1.50.5B</td><td>Any LLMs</td></tr><tr><td>Representation Pooling</td><td>Last token</td><td>Last token</td></tr><tr><td>Batch size</td><td>2048</td><td>2048</td></tr><tr><td>Maxlen (query)</td><td>128</td><td>128</td></tr><tr><td>Maxlen (document)</td><td>512</td><td>512</td></tr><tr><td>Training steps</td><td>1k</td><td>1k</td></tr><tr><td>Warmup steps</td><td>100</td><td>100</td></tr><tr><td>Model LR ηθ</td><td>1e-4</td><td>1e-4</td></tr><tr><td>Model LR Scheduler</td><td>Cosine</td><td>Cosine</td></tr><tr><td>Model min LR ratio</td><td>0.1</td><td>0.1</td></tr><tr><td>Model Optimizer</td><td>AdamW</td><td>AdamW</td></tr><tr><td>Weights LR ηα</td><td>2e-2</td><td>-</td></tr><tr><td>Weights LR Scheduler</td><td>Constant</td><td>-</td></tr><tr><td>Half precision</td><td>BF16</td><td>BF16</td></tr><tr><td>Negative types</td><td>Hard</td><td>Hard+in/cross-batch</td></tr><tr><td>Contrastive temperature τ</td><td>0.002</td><td>0.002</td></tr><tr><td>LoRA r</td><td>8</td><td>8</td></tr><tr><td>LoRA α</td><td>32</td><td>32</td></tr><tr><td>LoRA dropout</td><td>0.1</td><td>0.1</td></tr></table>
+
+# Full Baseline Losses
+
+The losses of the Qwen1.5-0.5B LLM-DR baseline model are presented below, which is the full version of Table 1. This model is trained with the uniform data sampling ratio for 1k steps with hyper-parameters in Table 6. As discussed in the Introduction Section, severe differences in loss scales exist in LLM-DR fine-tuning among different tasks. Thus tDRO proposes to use relative loss measurement for rescaling the running loss scales and derive the proper improving headroom for data distributional optimization.
+
+Table 7: Full loss scales of the Qwen1.5-0.5B LLM-DR baseline model.   
+
+<table><tr><td>Task</td><td>Loss</td><td>Task</td><td>Loss</td></tr><tr><td>yahoo_answers</td><td>3.9257</td><td>hotpotqa</td><td>1.1098</td></tr><tr><td>amazon_review_2018</td><td>2.9479</td><td>codesearchnet</td><td>0.8673</td></tr><tr><td>miracl</td><td>2.2658</td><td>dureader</td><td>0.6925</td></tr><tr><td>nq</td><td>2.1364</td><td>searchQA_top5_snippets</td><td>0.6387</td></tr><tr><td>eli5_question_answer</td><td>2.1336</td><td>xsum</td><td>0.4839</td></tr><tr><td>medmcqa</td><td>2.1148</td><td>squad_pairs</td><td>0.2786</td></tr><tr><td>Trivia</td><td>1.8961</td><td>AllNLI</td><td>0.2707</td></tr><tr><td>agnews</td><td>1.5894</td><td>quora Duplicate SNMP triplets</td><td>0.1549</td></tr><tr><td>t2ranking</td><td>1.5815</td><td>sentence-compression</td><td>0.0496</td></tr><tr><td>stackexchange_duplicates</td><td>1.3679</td><td>cnn_dailymail</td><td>0.0465</td></tr><tr><td>msmarco</td><td>1.3312</td><td>SimpleWiki</td><td>0.0248</td></tr><tr><td>mr_tydi(combined</td><td>1.3301</td><td>altlex</td><td>0.0163</td></tr><tr><td>gooaq_pairs</td><td>1.2492</td><td></td><td></td></tr></table>
+
+# Prompted Embeddings
+
+Instead of directly encoding the embeddings from textual inputs, our work adds a prompt description before query input to suit different tasks for LLM-DR retrieval. Following (Wang et al. 2024a), we did NOT add prompts on the document side to allow us to reuse the pre-built document index across different task scenarios. Such prompted embedding strategy is a common practice for LLM-DR fine-tuning (Wang et al. 2024a; Su et al. 2023), which is useful for multitasking. The basic format of the prompted query is:
+
+# Instruct: {prompt}\nQuery: {query text}
+
+Different prompts for each task are listed as follows. Note that one dataset or task may have multiple prompts for diversity consideration.
+
+# Prompts for Training Sets
+
+1. agnews: Given a news title, retrieve the news descriptions that match the title   
+2. AllNLI(1): Given a premise, retrieve a hypothesis that is entailed by the premise   
+3. AllNLI(2): Retrieve semantically similar text.   
+4. altlex(1): Given a sentence, retrieve a paraphrase Wikipedia sentence   
+5. altlex(2): Given a passage, retrieve a Wikipedia passage that forms paraphrase pairs   
+6. amazon review 2018(1): Given a title, retrieve the corresponding reviews from Amazon   
+7. amazon review 2018(2): Given a title, retrieve a Amazon review   
+8. cnn dailymail: Given highlight sentences, retrieve an relevant article that match the sentences   
+9. codesearchnet: Given a comment of the function code, retrieve the corresponding code blocks   
+10. dureader: Given a Chinese search query, retrieve web passages that answer the question   
+11. eli5 question answer: Provided a user question, retrieve the highest voted answers on Reddit ELI5 forum   
+12. gooaq pairs: Given a web search query, retrieve the corresponding answers from Google   
+13. hotpotqa: Given a multi-hop question, retrieve documents that can help answer the question   
+14. medmcqa(1): Given a medical query, retrieve relevant passages that answer the query   
+15. medmcqa(2): Given a medical question, retrieve passages that answer the question   
+16. miracl(1): Given a question, retrieve Wikipedia passages that answer the question   
+17. miracl(2): Retrieve Wikipedia passages that answer the question   
+18. mr tydi combined(1): Given a question, retrieve Wikipedia passages that answer the question   
+19. mr tydi combined(2): Retrieve Wikipedia passages that answer the question   
+20. msmarco: Given a web search query, retrieve relevant passages that answer the query
+
+21. nq(1): Given a question, retrieve Wikipedia passages that answer the question   
+22. nq(2): Retrieve Wikipedia passages that answer the question   
+23. quora duplicates triplets(1): Given a question, retrieve questions that are semantically equivalent to the given question   
+24. quora duplicates triplets(2): Find questions that have the same meaning as the input question   
+25. searchQA top5 snippets(1): Given a question, retrieve text snippets that answer the question   
+26. searchQA top5 snippets(2): Retrieve text snippets that answer the question   
+27. sentence-compression: Given a sentence, retrieve a short sentence that is semantically equivalent to the given sentence   
+28. SimpleWiki(1): Given a Wikipedia sentence, retrieve sentences that are semantically equivalent to the given sentence   
+29. SimpleWiki(2): Retrieve semantically similar text.   
+30. squad pairs(1): Given a question, retrieve Wikipedia passages that answer the question   
+31. squad pairs(2): Retrieve Wikipedia passages that answer the question   
+32. stackexchange duplicates title-body: Retrieve duplicate questions and passages from StackOverflow forum   
+33. t2ranking: Given a Chinese search query, retrieve web passages that answer the question   
+34. trivia(1): Given a question, retrieve Wikipedia passages that answer the question   
+35. trivia(2): Retrieve Wikipedia passages that answer the question   
+36. xsum: Given a news summary, retrieve articles that match the summary   
+37. yahoo answers title answer: Given a title, retrieve Yahoo answers that match the title
+
+# Prompts for Multilingual / Cross-lingual Benchmarks
+
+1. MIRACL (18 languages): Given a question, retrieve Wikipedia passages that answer the question   
+2. MKQA (25 languages): Given a question, retrieve Wikipedia passages that answer the question
+
+# Prompts for English BeIR Benchmarks
+
+Most of the prompts for BeIR are taken from Mistral-E5 (Wang et al. 2024a) for reproducibility.
+
+1. ArguAna: Given a claim, find documents that refute the claim   
+2. ClimateFEVER: Given a claim about climate change, retrieve documents that support or refute the claim   
+3. CQADupStack: Given a question, retrieve detailed question descriptions from Stackexchange that are duplicates to the given question   
+4. DBPedia: Given a query, retrieve relevant entity descriptions from DBPedia
+
+5. FEVER: Given a claim, retrieve documents that support or refute the claim   
+6. FiQA2018: Given a financial question, retrieve user replies that best answer the question   
+7. HotpotQA: Given a multi-hop question, retrieve documents that can help answer the question   
+8. MSMARCO: Given a web search query, retrieve relevant passages that answer the query   
+9. NFCorpus: Given a question, retrieve relevant documents that best answer the question   
+10. NQ: Given a question, retrieve Wikipedia passages that answer the question   
+11. Quora: Given a question, retrieve questions that are semantically equivalent to the given question   
+12. SCIDOCS: Given a scientific paper title, retrieve paper abstracts that are cited by the given paper   
+13. SciFact: Given a scientific claim, retrieve documents that support or refute the claim   
+14. Touche2020: Given a question, retrieve detailed and persuasive arguments that answer the question   
+15. TRECCOVID: Given a query on COVID-19, retrieve documents that answer the query
+
+# Domain Weights of Different Designs
+
+Here we list the domain weights of tDRO and other loss measurement designs in Table 8, which is a detailed version of Figure 3.
+
+Table 8: Detailed domain weights among baseline, tDRO, and other loss measurement designs.   
+
+<table><tr><td rowspan="2">Experiments → 
+Dataset (25 in total) ↓</td><td rowspan="2">Baseline</td><td rowspan="2">tDRO 
+Lproxy/ Lref</td><td colspan="2">Other Designs</td></tr><tr><td>Lproxy - Lref</td><td>Lproxy</td></tr><tr><td>miracl</td><td>0.0400</td><td>0.1314</td><td>0.1376</td><td>0.1193</td></tr><tr><td>medmcqa</td><td>0.0400</td><td>0.0940</td><td>0.0886</td><td>0.0807</td></tr><tr><td>t2ranking</td><td>0.0400</td><td>0.0885</td><td>0.0629</td><td>0.0651</td></tr><tr><td>nq</td><td>0.0400</td><td>0.0875</td><td>0.0618</td><td>0.0615</td></tr><tr><td>eli5</td><td>0.0400</td><td>0.0847</td><td>0.0767</td><td>0.0807</td></tr><tr><td>yahoo_answers</td><td>0.0400</td><td>0.0838</td><td>0.1537</td><td>0.1935</td></tr><tr><td>msmarco</td><td>0.0400</td><td>0.0713</td><td>0.0546</td><td>0.0411</td></tr><tr><td>trivia</td><td>0.0400</td><td>0.0623</td><td>0.0561</td><td>0.0532</td></tr><tr><td>gooaq_pairs</td><td>0.0400</td><td>0.0600</td><td>0.0509</td><td>0.0344</td></tr><tr><td>agnews</td><td>0.0400</td><td>0.0563</td><td>0.0541</td><td>0.0430</td></tr><tr><td>stackexchange_dups</td><td>0.0400</td><td>0.0472</td><td>0.0285</td><td>0.0242</td></tr><tr><td>amazon_review_2018</td><td>0.0400</td><td>0.0425</td><td>0.0750</td><td>0.1056</td></tr><tr><td>mr_tydi(combined</td><td>0.0400</td><td>0.0252</td><td>0.0202</td><td>0.0181</td></tr><tr><td>codesearchnet</td><td>0.0400</td><td>0.0154</td><td>0.0129</td><td>0.0156</td></tr><tr><td>hotpotqa</td><td>0.0400</td><td>0.0131</td><td>0.0174</td><td>0.0186</td></tr><tr><td>dreader</td><td>0.0400</td><td>0.0110</td><td>0.0152</td><td>0.0112</td></tr><tr><td>squad_pairs</td><td>0.0400</td><td>0.0072</td><td>0.0104</td><td>0.0060</td></tr><tr><td>searchQA_top5_snippets</td><td>0.0400</td><td>0.0066</td><td>0.0082</td><td>0.0080</td></tr><tr><td>xsum</td><td>0.0400</td><td>0.0063</td><td>0.0063</td><td>0.0062</td></tr><tr><td>quora Duplicate</td><td>0.0400</td><td>0.0019</td><td>0.0023</td><td>0.0028</td></tr><tr><td>sentence-compression</td><td>0.0400</td><td>0.0011</td><td>0.0022</td><td>0.0027</td></tr><tr><td>cnn_dailymail</td><td>0.0400</td><td>0.0009</td><td>0.0014</td><td>0.0025</td></tr><tr><td>SimpleWiki</td><td>0.0400</td><td>0.0007</td><td>0.0011</td><td>0.0023</td></tr><tr><td>altlex</td><td>0.0400</td><td>0.0006</td><td>0.0009</td><td>0.0019</td></tr><tr><td>AllNLI</td><td>0.0400</td><td>0.0005</td><td>0.0006</td><td>0.0016</td></tr></table>
+
+# Full Retrieval Performances
+
+Here we list the full retrieval scores for MIRACL, MKQA, and BeIR in Table 9, Table 10, and Table 11, which is a detailed version of Table 3.
+
+Table 9: Multilingual retrieval performance on MIRACL dev sets with 18 languages (measured by nDCG@10). *Significant improvements $( \mathtt { p } \le 0 . 0 1 )$ over the corresponding baseline.   
+
+<table><tr><td>Model</td><td>ar</td><td>bn</td><td>de</td><td>en</td><td>es</td><td>fa</td><td>fi</td><td>fr</td><td>hi</td><td>id</td><td>ja</td><td>ko</td><td>ru</td><td>sw</td><td>te</td><td>th</td><td>yo</td><td>zh</td><td>Avg</td><td>Gain</td></tr><tr><td>BM25</td><td>39.5</td><td>48.2</td><td>12.0</td><td>26.7</td><td>7.7</td><td>28.7</td><td>45.8</td><td>11.5</td><td>35.0</td><td>29.7</td><td>31.2</td><td>37.1</td><td>25.6</td><td>35.1</td><td>38.3</td><td>49.1</td><td>56.1</td><td>17.5</td><td>31.9</td><td></td></tr><tr><td>mContrever</td><td>52.5</td><td>50.1</td><td>40.8</td><td>36.4</td><td>41.8</td><td>21.5</td><td>60.2</td><td>31.4</td><td>28.6</td><td>39.2</td><td>42.4</td><td>48.3</td><td>39.1</td><td>56.0</td><td>52.8</td><td>51.7</td><td>41.5</td><td>41.0</td><td>43.1</td><td></td></tr><tr><td>mE5-large-inst</td><td>76.8</td><td>73.8</td><td>55.7</td><td>51.5</td><td>53.2</td><td>56.4</td><td>77.4</td><td>53.0</td><td>60.2</td><td>52.0</td><td>69.1</td><td>65.4</td><td>67.9</td><td>72.4</td><td>83.5</td><td>78.6</td><td>60.4</td><td>55.2</td><td>64.6</td><td></td></tr><tr><td>E5-Mistral</td><td>73.3</td><td>70.3</td><td>54.0</td><td>57.3</td><td>52.2</td><td>52.1</td><td>74.7</td><td>55.2</td><td>52.1</td><td>52.7</td><td>66.8</td><td>61.8</td><td>67.7</td><td>68.4</td><td>73.9</td><td>74.0</td><td>58.8</td><td>54.0</td><td>62.2</td><td></td></tr><tr><td colspan="21">Uniform Sampling Baselines</td></tr><tr><td>Qwen-0.5B</td><td>57.8</td><td>45.0</td><td>41.1</td><td>41.1</td><td>43.6</td><td>32.1</td><td>56.2</td><td>38.6</td><td>29.4</td><td>41.4</td><td>47.1</td><td>51.9</td><td>44.4</td><td>42.9</td><td>60.0</td><td>57.3</td><td>47.7</td><td>46.7</td><td>45.8</td><td></td></tr><tr><td>Qwen-1.8B</td><td>62.0</td><td>51.9</td><td>47.2</td><td>43.2</td><td>45.9</td><td>39.9</td><td>62.4</td><td>43.4</td><td>40.9</td><td>45.0</td><td>51.1</td><td>53.6</td><td>51.3</td><td>51.5</td><td>61.9</td><td>62.6</td><td>50.9</td><td>51.4</td><td>50.9</td><td></td></tr><tr><td>Qwen-4B</td><td>67.7</td><td>59.8</td><td>52.1</td><td>47.5</td><td>49.5</td><td>44.8</td><td>69.3</td><td>45.1</td><td>46.3</td><td>49.0</td><td>56.3</td><td>58.7</td><td>58.5</td><td>57.7</td><td>66.7</td><td>68.0</td><td>56.2</td><td>53.5</td><td>55.9</td><td></td></tr><tr><td>Qwen-7B</td><td>72.2</td><td>68.6</td><td>53.6</td><td>50.5</td><td>49.6</td><td>48.8</td><td>71.8</td><td>47.3</td><td>51.7</td><td>49.7</td><td>63.0</td><td>64.4</td><td>63.0</td><td>61.9</td><td>71.9</td><td>72.1</td><td>56.6</td><td>55.8</td><td>59.6</td><td></td></tr><tr><td>Mistral-7B</td><td>73.5</td><td>70.5</td><td>55.6</td><td>54.0</td><td>51.2</td><td>48.2</td><td>74.6</td><td>51.7</td><td>53.5</td><td>51.6</td><td>65.0</td><td>62.6</td><td>67.5</td><td>68.8</td><td>72.8</td><td>71.8</td><td>57.5</td><td>53.6</td><td>61.3</td><td></td></tr><tr><td>Llama3-8B</td><td>76.6</td><td>74.1</td><td>56.3</td><td>54.1</td><td>52.0</td><td>52.6</td><td>76.7</td><td>50.2</td><td>62.7</td><td>51.9</td><td>66.8</td><td>64.4</td><td>67.4</td><td>74.7</td><td>77.9</td><td>78.0</td><td>62.4</td><td>54.6</td><td>64.1</td><td></td></tr><tr><td colspan="21">tDRO - Dataset Selection Top-70%</td></tr><tr><td>Qwen-0.5B</td><td>60.9</td><td>47.4</td><td>43.9</td><td>46.8</td><td>45.7</td><td>33.0</td><td>59.4</td><td>42.6</td><td>29.6</td><td>43.4</td><td>51.8</td><td>54.0</td><td>48.1</td><td>46.4</td><td>64.1</td><td>60.4</td><td>48.5</td><td>50.7</td><td>48.7*</td><td>+2.9</td></tr><tr><td>Qwen-1.8B</td><td>66.1</td><td>57.8</td><td>48.6</td><td>47.9</td><td>46.9</td><td>42.7</td><td>65.4</td><td>45.2</td><td>43.1</td><td>47.1</td><td>56.2</td><td>55.3</td><td>54.6</td><td>56.6</td><td>68.2</td><td>66.7</td><td>52.0</td><td>53.9</td><td>54.1*</td><td>+3.2</td></tr><tr><td>Qwen-4B</td><td>69.8</td><td>64.3</td><td>53.9</td><td>51.4</td><td>51.3</td><td>45.8</td><td>71.4</td><td>48.5</td><td>49.3</td><td>49.9</td><td>60.9</td><td>61.0</td><td>60.7</td><td>61.7</td><td>69.3</td><td>70.6</td><td>58.8</td><td>56.7</td><td>58.6*</td><td>+2.7</td></tr><tr><td>Qwen-7B</td><td>74.2</td><td>70.1</td><td>53.9</td><td>54.6</td><td>51.4</td><td>49.9</td><td>73.2</td><td>49.6</td><td>53.3</td><td>51.1</td><td>66.9</td><td>65.4</td><td>64.8</td><td>66.8</td><td>73.5</td><td>74.1</td><td>57.4</td><td>58.5</td><td>61.6*</td><td>+2.0</td></tr><tr><td>Mistral-7B</td><td>74.9</td><td>74.9</td><td>55.3</td><td>58.8</td><td>52.7</td><td>50.7</td><td>75.6</td><td>54.2</td><td>56.8</td><td>52.6</td><td>68.7</td><td>62.8</td><td>69.1</td><td>71.3</td><td>75.6</td><td>75.4</td><td>60.9</td><td>57.3</td><td>63.8*</td><td>+2.5</td></tr><tr><td>Llama3-8B</td><td>77.9</td><td>75.8</td><td>56.7</td><td>58.0</td><td>55.5</td><td>55.2</td><td>78.1</td><td>54.5</td><td>64.6</td><td>53.5</td><td>71.0</td><td>66.5</td><td>70.4</td><td>75.1</td><td>79.8</td><td>80.7</td><td>63.5</td><td>57.6</td><td>66.4*</td><td>+2.3</td></tr><tr><td colspan="21">tDRO - Sample Ratio Reweighting</td></tr><tr><td>Qwen-0.5B</td><td>60.8</td><td>49.9</td><td>44.5</td><td>47.6</td><td>46.8</td><td>33.9</td><td>58.2</td><td>43.9</td><td>29.2</td><td>43.4</td><td>52.4</td><td>54.3</td><td>48.3</td><td>45.6</td><td>62.0</td><td>60.0</td><td>49.5</td><td>53.1</td><td>49.1*</td><td>+3.3</td></tr><tr><td>Qwen-1.8B</td><td>64.9</td><td>58.0</td><td>49.7</td><td>47.3</td><td>47.7</td><td>41.8</td><td>64.0</td><td>47.1</td><td>40.2</td><td>46.1</td><td>56.4</td><td>55.1</td><td>53.9</td><td>54.4</td><td>65.7</td><td>65.4</td><td>51.7</td><td>56.0</td><td>53.6*</td><td>+2.7</td></tr><tr><td>Qwen-4B</td><td>69.7</td><td>63.8</td><td>53.8</td><td>52.1</td><td>51.5</td><td>45.1</td><td>70.0</td><td>50.4</td><td>48.2</td><td>50.1</td><td>61.1</td><td>59.9</td><td>61.2</td><td>60.0</td><td>68.5</td><td>70.9</td><td>57.0</td><td>58.3</td><td>58.4*</td><td>+2.5</td></tr><tr><td>Qwen-7B</td><td>73.7</td><td>69.9</td><td>53.6</td><td>53.7</td><td>51.4</td><td>49.3</td><td>71.4</td><td>50.4</td><td>51.1</td><td>50.2</td><td>65.4</td><td>64.7</td><td>64.5</td><td>64.0</td><td>73.3</td><td>74.0</td><td>58.2</td><td>58.6</td><td>61.0*</td><td>+1.4</td></tr><tr><td>Mistral-7B</td><td>75.4</td><td>72.5</td><td>55.0</td><td>57.7</td><td>53.4</td><td>51.1</td><td>74.4</td><td>53.3</td><td>56.5</td><td>52.7</td><td>67.1</td><td>63.8</td><td>68.9</td><td>71.4</td><td>74.2</td><td>74.3</td><td>61.0</td><td>58.7</td><td>63.4*</td><td>+2.1</td></tr><tr><td>Llama3-8B</td><td>78.2</td><td>75.9</td><td>56.0</td><td>58.3</td><td>54.5</td><td>55.1</td><td>77.2</td><td>54.6</td><td>62.7</td><td>54.1</td><td>72.0</td><td>67.8</td><td>68.6</td><td>75.7</td><td>78.5</td><td>80.5</td><td>64.3</td><td>59.0</td><td>66.3*</td><td>+2.2</td></tr></table>
+
+Table 10: Cross-lingual retrieval performance on MKQA test sets with 25 languages (measured by Accuacy $@ 1 0 0 )$ ).   
+
+<table><tr><td>Model</td><td>ar</td><td>da</td><td>de</td><td>es</td><td>fi</td><td>fr</td><td>he</td><td>hu</td><td>it</td><td>ja</td><td>km</td><td>ko</td><td>ms</td><td>nl</td><td>no</td><td>pl</td><td>pt</td><td>ru</td><td>sv</td><td>th</td><td>tr</td><td>vi</td><td>zh_cn</td><td>zh_hk</td><td>zh_tw</td><td>Avg</td><td>Gain</td></tr><tr><td>BM25</td><td>18.9</td><td>49.3</td><td>35.4</td><td>43.4</td><td>46.3</td><td>45.3</td><td>26.9</td><td>38.2</td><td>45.2</td><td>24.5</td><td>27.8</td><td>27.9</td><td>55.9</td><td>56.2</td><td>52.1</td><td>40.8</td><td>44.9</td><td>33.2</td><td>54.6</td><td>37.8</td><td>45.8</td><td>46.6</td><td>31.0</td><td>35.0</td><td>33.5</td><td>39.9</td><td></td></tr><tr><td>mContriever</td><td>58.2</td><td>73.9</td><td>71.7</td><td>72.6</td><td>70.2</td><td>72.8</td><td>63.8</td><td>69.7</td><td>72.3</td><td>64.8</td><td>26.8</td><td>59.7</td><td>74.1</td><td>73.7</td><td>73.5</td><td>71.6</td><td>72.0</td><td>69.8</td><td>73.2</td><td>66.9</td><td>71.1</td><td>70.9</td><td>68.1</td><td>68.0</td><td>67.9</td><td>67.9</td><td></td></tr><tr><td>mE5-large-inst</td><td>66.2</td><td>76.5</td><td>76.0</td><td>75.6</td><td>72.3</td><td>76.7</td><td>61.3</td><td>73.8</td><td>76.5</td><td>61.9</td><td>44.9</td><td>46.9</td><td>76.1</td><td>77.8</td><td>76.3</td><td>76.4</td><td>76.5</td><td>75.9</td><td>77.0</td><td>70.8</td><td>74.1</td><td>75.6</td><td>64.6</td><td>62.8</td><td>61.9</td><td>70.2</td><td></td></tr><tr><td>E5-Mistral-7b</td><td>56.4</td><td>76.9</td><td>76.0</td><td>76.9</td><td>70.0</td><td>77.3</td><td>44.1</td><td>74.0</td><td>76.5</td><td>63.9</td><td>31.2</td><td>57.3</td><td>75.9</td><td>78.3</td><td>75.9</td><td>75.8</td><td>76.7</td><td>73.7</td><td>77.4</td><td>63.8</td><td>71.4</td><td>70.0</td><td>67.4</td><td>62.9</td><td>64.3</td><td>68.6</td><td></td></tr><tr><td colspan="28">Uniform Sampling Baselines</td></tr><tr><td>Qwen-0.5B</td><td>47.4</td><td>66.2</td><td>66.7</td><td>67.8</td><td>54.7</td><td>70.1</td><td>46.8</td><td>54.0</td><td>65.4</td><td>58.1</td><td>38.3</td><td>47.8</td><td>66.2</td><td>69.8</td><td>64.1</td><td>61.8</td><td>66.3</td><td>61.8</td><td>67.2</td><td>58.8</td><td>57.8</td><td>65.2</td><td>71.0</td><td>70.0</td><td>69.6</td><td>61.3</td><td></td></tr><tr><td>Qwen-1.8B</td><td>52.4</td><td>69.1</td><td>69.1</td><td>70.3</td><td>59.5</td><td>71.0</td><td>48.8</td><td>58.7</td><td>67.4</td><td>59.5</td><td>39.8</td><td>53.9</td><td>69.3</td><td>72.8</td><td>66.7</td><td>65.6</td><td>68.4</td><td>65.6</td><td>69.7</td><td>60.7</td><td>61.6</td><td>65.0</td><td>72.7</td><td>71.1</td><td>71.8</td><td>64.0</td><td></td></tr><tr><td>Qwen-4B</td><td>60.0</td><td>75.0</td><td>73.3</td><td>74.9</td><td>68.6</td><td>75.6</td><td>58.0</td><td>68.9</td><td>74.5</td><td>70.7</td><td>48.1</td><td>54.7</td><td>73.7</td><td>76.4</td><td>73.6</td><td>72.7</td><td>74.3</td><td>73.0</td><td>74.8</td><td>67.4</td><td>69.1</td><td>72.4</td><td>75.5</td><td>74.3</td><td>75.4</td><td>70.2</td><td></td></tr><tr><td>Qwen-7B</td><td>66.7</td><td>76.8</td><td>76.1</td><td>76.7</td><td>71.4</td><td>77.6</td><td>64.3</td><td>72.4</td><td>75.6</td><td>74.3</td><td>52.4</td><td>67.0</td><td>75.8</td><td>78.4</td><td>75.3</td><td>75.1</td><td>76.8</td><td>76.6</td><td>76.8</td><td>73.5</td><td>72.2</td><td>75.8</td><td>77.5</td><td>76.3</td><td>77.6</td><td>73.6</td><td></td></tr><tr><td>Mistral-7B</td><td>63.6</td><td>78.1</td><td>77.1</td><td>78.0</td><td>71.8</td><td>78.3</td><td>57.5</td><td>75.8</td><td>76.9</td><td>73.6</td><td>39.5</td><td>68.7</td><td>77.4</td><td>78.9</td><td>76.5</td><td>77.2</td><td>77.4</td><td>77.3</td><td>78.1</td><td>70.7</td><td>73.7</td><td>72.8</td><td>74.8</td><td>72.8</td><td>73.1</td><td>72.8</td><td></td></tr><tr><td>Llama3-8B</td><td>72.1</td><td>78.1</td><td>77.8</td><td>78.1</td><td>76.3</td><td>78.4</td><td>73.5</td><td>76.0</td><td>77.3</td><td>77.1</td><td>50.8</td><td>72.1</td><td>78.6</td><td>79.2</td><td>77.3</td><td>77.8</td><td>78.1</td><td>78.0</td><td>78.3</td><td>77.6</td><td>76.7</td><td>77.3</td><td>76.7</td><td>75.5</td><td>76.5</td><td>75.8</td><td></td></tr><tr><td colspan="28">tDRO - Dataset Selection Top-70%</td></tr><tr><td>Qwen-0.5B</td><td>48.3</td><td>67.4</td><td>68.0</td><td>69.1</td><td>55.4</td><td>70.7</td><td>48.2</td><td>54.3</td><td>66.9</td><td>59.3</td><td>38.9</td><td>49.1</td><td>67.1</td><td>71.2</td><td>65.5</td><td>63.1</td><td>67.3</td><td>63.2</td><td>68.6</td><td>59.4</td><td>58.7</td><td>65.9</td><td>71.9</td><td>70.8</td><td>70.3</td><td>62.3*</td><td>+1.0</td></tr><tr><td>Qwen-1.8B</td><td>54.4</td><td>70.1</td><td>70.3</td><td>71.5</td><td>61.6</td><td>72.3</td><td>50.6</td><td>60.8</td><td>69.6</td><td>62.5</td><td>43.0</td><td>54.7</td><td>69.8</td><td>72.9</td><td>68.2</td><td>67.2</td><td>70.2</td><td>66.8</td><td>71.6</td><td>62.8</td><td>62.9</td><td>66.7</td><td>73.8</td><td>72.7</td><td>72.9</td><td>65.6*</td><td>+1.6</td></tr><tr><td>Qwen-4B</td><td>63.3</td><td>75.5</td><td>74.2</td><td>75.9</td><td>69.3</td><td>76.1</td><td>62.0</td><td>70.2</td><td>75.5</td><td>70.8</td><td>47.6</td><td>61.6</td><td>74.4</td><td>76.8</td><td>74.4</td><td>73.6</td><td>75.1</td><td>74.5</td><td>75.7</td><td>69.2</td><td>70.0</td><td>73.7</td><td>76.0</td><td>74.8</td><td>75.3</td><td>71.4*</td><td>+1.2</td></tr><tr><td>Qwen-7B</td><td>67.7</td><td>77.2</td><td>76.4</td><td>76.8</td><td>71.5</td><td>77.6</td><td>63.4</td><td>73.2</td><td>76.2</td><td>74.7</td><td>52.8</td><td>65.3</td><td>75.8</td><td>78.5</td><td>75.7</td><td>75.4</td><td>77.1</td><td>76.7</td><td>77.3</td><td>74.3</td><td>72.6</td><td>76.4</td><td>77.7</td><td>76.7</td><td>77.8</td><td>73.8</td><td>+0.2</td></tr><tr><td>Mistral-7B</td><td>65.6</td><td>78.3</td><td>77.8</td><td>78.3</td><td>72.9</td><td>78.4</td><td>61.4</td><td>76.2</td><td>77.6</td><td>75.5</td><td>42.9</td><td>71.7</td><td>77.5</td><td>78.8</td><td>77.0</td><td>77.5</td><td>77.6</td><td>77.9</td><td>78.3</td><td>72.2</td><td>74.2</td><td>74.0</td><td>75.8</td><td>73.8</td><td>74.1</td><td>73.8*</td><td>+1.0</td></tr><tr><td>Llama3-8B</td><td>73.0</td><td>78.3</td><td>78.3</td><td>78.4</td><td>76.1</td><td>78.7</td><td>74.1</td><td>76.5</td><td>77.9</td><td>77.4</td><td>57.8</td><td>73.5</td><td>78.3</td><td>79.3</td><td>77.6</td><td>77.9</td><td>78.1</td><td>78.0</td><td>78.4</td><td>78.6</td><td>77.0</td><td>77.7</td><td>77.4</td><td>76.1</td><td>76.8</td><td>76.4*</td><td>+0.6</td></tr><tr><td colspan="28">tDRO - Sample Ratio Reweighting</td></tr><tr><td>Qwen-0.5B</td><td>48.6</td><td>67.4</td><td>67.3</td><td>68.9</td><td>55.0</td><td>70.6</td><td>47.9</td><td>53.3</td><td>66.4</td><td>59.9</td><td>39.1</td><td>48.8</td><td>67.3</td><td>70.9</td><td>65.1</td><td>63.1</td><td>67.8</td><td>63.1</td><td>68.2</td><td>59.9</td><td>58.4</td><td>65.4</td><td>71.8</td><td>71.0</td><td>70.5</td><td>62.2*</td><td>+0.9</td></tr><tr><td>Qwen-1.8B</td><td>55.3</td><td>71.8</td><td>71.7</td><td>70.8</td><td>62.0</td><td>72.6</td><td>52.8</td><td>61.5</td><td>71.7</td><td>66.1</td><td>43.8</td><td>56.7</td><td>70.3</td><td>74.4</td><td>69.6</td><td>67.7</td><td>71.0</td><td>68.0</td><td>72.6</td><td>64.2</td><td>63.8</td><td>69.2</td><td>75.0</td><td>73.8</td><td>74.3</td><td>66.8*</td><td>+2.8</td></tr><tr><td>Qwen-4B</td><td>63.5</td><td>76.2</td><td>75.4</td><td>76.5</td><td>70.4</td><td>76.6</td><td>62.1</td><td>70.5</td><td>75.9</td><td>73.1</td><td>48.2</td><td>60.8</td><td>74.1</td><td>77.5</td><td>74.7</td><td>73.9</td><td>76.1</td><td>75.0</td><td>76.4</td><td>69.9</td><td>70.5</td><td>73.5</td><td>77.1</td><td>75.9</td><td>76.9</td><td>72.0*</td><td>+1.8</td></tr><tr><td>Qwen-7B</td><td>66.9</td><td>77.1</td><td>76.8</td><td>76.5</td><td>71.3</td><td>77.5</td><td>61.8</td><td>72.3</td><td>76.1</td><td>75.3</td><td>53.7</td><td>64.9</td><td>75.3</td><td>78.5</td><td>75.7</td><td>75.4</td><td>76.7</td><td>76.9</td><td>77.0</td><td>73.9</td><td>72.3</td><td>75.8</td><td>77.9</td><td>77.0</td><td>78.1</td><td>73.6</td><td>+0.0</td></tr><tr><td>Mistral-7B</td><td>65.3</td><td>78.3</td><td>77.8</td><td>78.6</td><td>72.8</td><td>78.7</td><td>61.3</td><td>76.5</td><td>77.9</td><td>75.6</td><td>43.6</td><td>71.4</td><td>77.5</td><td>79.1</td><td>77.2</td><td>78.1</td><td>78.8</td><td>78.1</td><td>78.6</td><td>72.3</td><td>74.4</td><td>74.0</td><td>75.7</td><td>73.7</td><td>74.6</td><td>74.0*</td><td>+1.2</td></tr><tr><td>Llama3-8B</td><td>74.2</td><td>78.5</td><td>78.4</td><td>78.4</td><td>76.6</td><td>78.9</td><td>74.5</td><td>76.8</td><td>78.5</td><td>78.0</td><td>59.2</td><td>74.4</td><td>78.5</td><td>79.5</td><td>77.7</td><td>77.9</td><td>78.4</td><td>78.6</td><td>78.8</td><td>78.8</td><td>77.1</td><td>77.8</td><td>77.7</td><td>76.6</td><td>77.2</td><td>76.8*</td><td>+1.0</td></tr></table>
+
+Table 11: English retrieval performance on BeIR test sets (except MS-MARCO, which uses dev set.) with 15 datasets (measured by nDCG@10). †E5-Mistral-7b scores without using GPT synthesis data are listed here for fairness consideration.   
+
+<table><tr><td>Model</td><td>ArguAna</td><td>CQADup</td><td>C-FEVER</td><td>DBPedia</td><td>FEVER</td><td>FiQA</td><td>HotpotQA</td><td>MSMARCO</td><td>NFCorpus</td><td>NQ</td><td>Quora</td><td>SCIDOCS</td><td>SciFact</td><td>T-COVID</td><td>Touche</td><td>Avg</td><td>Gain</td></tr><tr><td>BM25</td><td>31.5</td><td>29.9</td><td>21.3</td><td>31.3</td><td>75.3</td><td>23.6</td><td>60.3</td><td>22.8</td><td>32.5</td><td>32.9</td><td>78.9</td><td>15.8</td><td>66.5</td><td>65.6</td><td>36.7</td><td>41.7</td><td></td></tr><tr><td>Contriever</td><td>44.6</td><td>34.5</td><td>23.7</td><td>41.3</td><td>75.8</td><td>32.9</td><td>63.8</td><td>36.8</td><td>32.8</td><td>49.8</td><td>86.5</td><td>16.5</td><td>67.7</td><td>59.6</td><td>23.0</td><td>46.0</td><td></td></tr><tr><td>mE5-large-inst</td><td>55.5</td><td>42.7</td><td>29.8</td><td>38.4</td><td>78.0</td><td>47.7</td><td>69.3</td><td>40.4</td><td>35.6</td><td>57.7</td><td>89.1</td><td>18.7</td><td>71.9</td><td>82.0</td><td>27.3</td><td>52.3</td><td></td></tr><tr><td>E5-Mistral-7b†</td><td>62.5</td><td>42.9</td><td>25.2</td><td>47.7</td><td>73.1</td><td>54.5</td><td>75.6</td><td>42.9</td><td>35.3</td><td>57.3</td><td>89.5</td><td>19.0</td><td>74.7</td><td>70.8</td><td>19.1</td><td>52.7</td><td></td></tr><tr><td colspan="18">Uniform Sampling Baselines</td></tr><tr><td>Qwen-0.5B</td><td>55.4</td><td>41.5</td><td>24.4</td><td>34.8</td><td>64.3</td><td>39.3</td><td>62.2</td><td>32.5</td><td>34.4</td><td>47.5</td><td>87.7</td><td>18.5</td><td>68.9</td><td>73.9</td><td>26.6</td><td>47.5</td><td></td></tr><tr><td>Qwen-1.8B</td><td>54.6</td><td>44.1</td><td>25.6</td><td>36.6</td><td>69.3</td><td>44.3</td><td>65.0</td><td>32.9</td><td>36.9</td><td>47.8</td><td>87.6</td><td>19.8</td><td>70.5</td><td>75.2</td><td>22.4</td><td>48.8</td><td></td></tr><tr><td>Qwen-4B</td><td>57.9</td><td>47.7</td><td>26.1</td><td>41.3</td><td>75.3</td><td>49.6</td><td>70.6</td><td>35.9</td><td>38.2</td><td>53.3</td><td>87.9</td><td>22.0</td><td>74.3</td><td>77.2</td><td>19.7</td><td>51.8</td><td></td></tr><tr><td>Qwen-7B</td><td>58.4</td><td>49.8</td><td>25.7</td><td>41.3</td><td>75.0</td><td>51.5</td><td>72.7</td><td>36.1</td><td>39.1</td><td>55.0</td><td>88.5</td><td>22.3</td><td>76.0</td><td>73.5</td><td>19.7</td><td>52.3</td><td></td></tr><tr><td>Mistral-7B</td><td>59.6</td><td>50.6</td><td>26.6</td><td>45.2</td><td>78.5</td><td>58.6</td><td>78.8</td><td>39.0</td><td>42.0</td><td>60.6</td><td>88.7</td><td>22.3</td><td>79.2</td><td>77.9</td><td>20.4</td><td>55.2</td><td></td></tr><tr><td>Llama3-8B</td><td>58.2</td><td>51.3</td><td>27.0</td><td>44.2</td><td>79.0</td><td>57.7</td><td>78.9</td><td>38.5</td><td>41.3</td><td>60.6</td><td>89.0</td><td>22.9</td><td>78.6</td><td>75.8</td><td>21.3</td><td>55.0</td><td></td></tr><tr><td colspan="18">tDRO - Dataset Selection Top-70%</td></tr><tr><td>Qwen-0.5B</td><td>55.2</td><td>41.8</td><td>25.2</td><td>37.8</td><td>72.2</td><td>41.7</td><td>63.9</td><td>33.4</td><td>35.6</td><td>49.4</td><td>84.8</td><td>18.7</td><td>69.4</td><td>76.9</td><td>27.3</td><td>48.9*</td><td>+1.4</td></tr><tr><td>Qwen-1.8B</td><td>56.8</td><td>44.8</td><td>26.4</td><td>37.4</td><td>76.8</td><td>46.0</td><td>67.0</td><td>33.0</td><td>37.1</td><td>51.9</td><td>86.8</td><td>19.9</td><td>72.5</td><td>73.9</td><td>22.8</td><td>50.2*</td><td>+1.4</td></tr><tr><td>Qwen-4B</td><td>59.0</td><td>46.9</td><td>26.7</td><td>41.4</td><td>80.1</td><td>51.1</td><td>72.2</td><td>36.3</td><td>38.6</td><td>56.3</td><td>87.7</td><td>21.6</td><td>75.2</td><td>75.8</td><td>19.6</td><td>52.6*</td><td>+0.8</td></tr><tr><td>Qwen-7B</td><td>59.2</td><td>49.6</td><td>25.5</td><td>40.9</td><td>77.8</td><td>53.6</td><td>73.9</td><td>36.0</td><td>40.0</td><td>57.8</td><td>87.2</td><td>22.3</td><td>77.2</td><td>75.6</td><td>22.2</td><td>53.3*</td><td>+1.0</td></tr><tr><td>Mistral-7B</td><td>53.3</td><td>50.3</td><td>25.5</td><td>44.4</td><td>81.9</td><td>59.7</td><td>79.1</td><td>39.7</td><td>41.9</td><td>63.4</td><td>87.0</td><td>21.4</td><td>77.1</td><td>79.4</td><td>23.9</td><td>55.2</td><td>+0.0</td></tr><tr><td>Llama3-8B</td><td>56.9</td><td>51.5</td><td>28.1</td><td>45.0</td><td>81.1</td><td>57.8</td><td>80.0</td><td>38.9</td><td>41.6</td><td>61.9</td><td>87.8</td><td>22.1</td><td>78.2</td><td>75.7</td><td>19.7</td><td>55.1</td><td>+0.1</td></tr><tr><td colspan="18">tDRO - Sample Ratio Reweighting</td></tr><tr><td>Qwen-0.5B</td><td>55.6</td><td>40.5</td><td>22.0</td><td>37.0</td><td>70.5</td><td>42.2</td><td>60.9</td><td>34.2</td><td>34.9</td><td>51.1</td><td>84.5</td><td>18.0</td><td>69.7</td><td>78.0</td><td>25.2</td><td>48.3*</td><td>+0.8</td></tr><tr><td>Qwen-1.8B</td><td>57.2</td><td>44.1</td><td>23.6</td><td>37.3</td><td>73.0</td><td>47.0</td><td>62.3</td><td>34.1</td><td>37.5</td><td>53.1</td><td>86.3</td><td>19.5</td><td>72.9</td><td>74.0</td><td>23.0</td><td>49.7*</td><td>+0.9</td></tr><tr><td>Qwen-4B</td><td>59.9</td><td>46.3</td><td>24.4</td><td>41.5</td><td>76.1</td><td>51.4</td><td>67.5</td><td>36.8</td><td>38.8</td><td>57.5</td><td>87.4</td><td>21.7</td><td>76.4</td><td>73.7</td><td>19.1</td><td>51.9</td><td>+0.1</td></tr><tr><td>Qwen-7B</td><td>57.4</td><td>48.6</td><td>24.7</td><td>40.8</td><td>76.4</td><td>51.6</td><td>69.3</td><td>37.3</td><td>39.9</td><td>59.4</td><td>87.2</td><td>21.7</td><td>77.4</td><td>75.9</td><td>18.5</td><td>52.4</td><td>+0.1</td></tr><tr><td>Mistral-7B</td><td>55.6</td><td>49.1</td><td>25.7</td><td>44.1</td><td>80.1</td><td>60.6</td><td>75.6</td><td>41.1</td><td>41.5</td><td>63.2</td><td>86.0</td><td>21.9</td><td>78.6</td><td>81.6</td><td>25.9</td><td>55.4</td><td>+0.2</td></tr><tr><td>Llama3-8B</td><td>51.9</td><td>50.6</td><td>28.9</td><td>42.9</td><td>81.7</td><td>56.9</td><td>75.8</td><td>39.9</td><td>41.2</td><td>63.1</td><td>87.9</td><td>22.2</td><td>78.7</td><td>80.5</td><td>22.5</td><td>55.0</td><td>+0.0</td></tr></table>

paper_markdowns/bamboo-00323.md

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+# Beyond True or False: Retrieval-Augmented Hierarchical Analysis of Nuanced Claims
+
+Priyanka Kargupta*, Runchu Tian*, Jiawei Han
+
+Department of Computer Science, University of Illinois at Urbana-Champaign
+
+{pk36, runchut2, hanj}@illinois.edu
+
+# Abstract
+
+Claims made by individuals or entities are oftentimes nuanced and cannot be clearly labeled as entirely "true" or false—as is frequently the case with scientific and political claims. However, a claim (e.g., "vaccine A is better than vaccine B") can be dissected into its integral aspects and sub-aspects (e.g., efficacy, safety, distribution), which are individually easier to validate. This enables a more comprehensive, structured response that provides a well-rounded perspective on a given problem while also allowing the reader to prioritize specific angles of interest within the claim (e.g., safety towards children). Thus, we propose CLAIMSPECT, a retrieval-augmented generation-based framework for automatically constructing a hierarchy of aspects typically considered when addressing a claim and enriching them with corpus-specific perspectives. This structure hierarchically partitions an input corpus to retrieve relevant segments, which assist in discovering new sub-aspects. Moreover, these segments enable the discovery of varying perspectives towards an aspect of the claim (e.g., support, neutral, or oppose) and their respective prevalence (e.g., "how many biomedical papers believe vaccine A is more transportable than B?"). We apply CLAIMSPECT to a wide variety of real-world scientific and political claims featured in our constructed dataset, showcasing its robustness and accuracy in deconstructing a nuanced claim and representing perspectives within a corpus. Through real-world case studies and human evaluation, we validate its effectiveness over multiple baselines.
+
+# 1 Introduction
+
+Scientific and political topics increasingly being consumed in the form of concise, attention-grabbing claims which lack the nuance needed to represent complex realities (Vosoughi et al., 2018; Allcott and Gentzkow, 2017; Lazer et al., 2018). Such claims are frequently oversimplified or confidently stated, despite being valid only under specific conditions or when evaluated from
+
+![](images/0eb63612010847f938ef4401664011cb92338447aa1efd64ed2bd06051254781.jpg)  
+Claim: "Vaccine A is better than Vaccine B"   
+Figure 1: An example hierarchy of a nuanced claim being deconstructed into aspects. Each node is enriched with relevant excerpts, the affirmative/neutral/opposing perspectives, and their respective evidence.
+
+certain perspectives. For instance, a claim like "vaccine A is better than vaccine B" may appear straightforward but becomes inherently nuanced when specific aspects, such as efficacy, safety, and distribution logistics, are considered. Moreover, the ambiguous and fragmented nature of information shared on such platforms often allows such claims to be twisted or reframed as "true" or "false" to support conflicting narratives, complicating the task of verifying their validity (Sharma et al., 2019; Pennycook and Rand, 2021).
+
+Stance detection categorizes textual opinions as supportive, neutral, or opposing relative to a target (Mohammad et al., 2016). However, documents—especially those in a scientific domain—often present a range of stances across various aspects of a claim. For instance, as illustrated in Figure 1, a study might find Vaccine A safer for adults than Vaccine B while highlighting its significantly greater logistical challenges for widespread distribution. In this case, the paper supports the claim regarding “safety for adults” (note: not “safety” in its entirety) but opposes it concerning distribution. This complexity renders stance detection at the document level ineffective for nuanced, multifaceted claims.
+
+Fact-checking models often validate claims by retrieval
+
+ing evidence from large corpora or using web-integrated language models (Thorne et al., 2018; Popat et al., 2018; Zhang and Gao, 2023). While some methods now offer varied factuality judgements like "mostly true" or "half-true" (Zhang and Gao, 2023), these are less effective in scientific contexts. Especially in evolving areas, fine-grained scientific claims may be unsubstantiated due to a lack of research or scientific consensus, rather than being outright false. This distinction is vital, as it highlights areas needing further exploration. For example, in Figure 1, relevant paper excerpts mapped to the "Safety for Adults" node show that an 80:20 ratio of affirmative to opposing stances towards the sub-aspect claim suggests consensus, whereas a 60:40 ratio or sparse data signals limited research or disagreement. Such insights, crucial for understanding gaps in knowledge, are often overlooked by existing fact-checking frameworks.
+
+We address these challenges using CLAIMSPECT, a framework which systematically deconstructs and analyzes claims by leveraging large language models (LLMs). ClaimSpect hierarchically partitions a claim into a tree of aspects and sub-aspects, enabling structured validation and the discovery of perspectives. This is accomplished by adopting the following principles:
+
+Principle #1: Claim trees capture the multidimensionality inherent in nuanced topics. As opposed to considering a single target claim and the full document, we must first determine the relevant aspects discussed within the corpus itself in order to discover more targeted subclaims. However, it is essential to retain the hierarchical nature of such aspects. This is demonstrated in Figure 1, where certain aspects that are difficult to validate (e.g., "safety") can typically be partitioned until they reach "atomic" sub-aspects that are more commonly considered (e.g., "safety for children", "safety for adults", and "safety for elderly"). Furthermore, these hierarchical relationships are often also reflected in how we naturally navigate formulating our own perspective towards a given topic (either individually or collectively): parse through the existing knowledge on a topic, consider different sub-angles of the problem based on this knowledge, retrieve more sub-angle specific knowledge, develop our opinions accordingly, and aggregate them to a high-level opinion (Perony et al., 2013; Chen et al., 2022). Thus, this brings us to our next principle.
+
+Principle #2: Iterative, discriminative retrieval enhances LLM-based tree construction. LLMs have recently shown promise in automatic taxonomy enrichment and expansion, organizing data into hierarchies of categories and subcategories similar to our target aspect hierarchy (Shen et al., 2024b; Zeng et al., 2024b). However, these approaches often rely on general knowledge existing within the LLM's pre-training dataset, overlooking corpus-specific insights crucial for (1) uncovering fine-grained sub-aspects prevalent in domain-specific data, and (2) ensuring alignment with the task of determining corpus-wide consensus. To address this, we leverage retrieval-augmented generation (RAG), which
+
+has recently made advances in knowledge-intensive tasks by integrating external corpora or databases into the generation process (Lewis et al., 2020; Gao et al., 2023). We introduce an iterative RAG approach, which dynamically constructs the aspect hierarchy by retrieving relevant segments for an aspect node, using them to discover new sub-aspects. This ensures the taxonomy aligns closely with corpus-specific discussions of claims, aspects, and perspectives.
+
+We note that noisy retrieval often hinders reasoning performance (Shen et al., 2024a). In our setting, this may occur when certain retrieved excerpts overlap multiple semantically similar aspect nodes (e.g., "safety for children" vs. "safety for adults"), introducing noise when determining sub-aspects for only one aspect. To mitigate this, we introduce a discriminative ranking mechanism that prioritizes segments discussing a single aspect in-depth, enhancing sub-aspect discovery and the final aspect hierarchy.
+
+Principle #3: Perspectives enrich understanding beyond stance and consensus. For each aspect node in the hierarchy, we identify and cluster papers based on their stance (affirmative, neutral, opposing) using hierarchical text classification and stance detection. These clusters reveal not only the presence or absence of consensus but also the key perspectives within each stance. For example, as shown in Figure 1, the affirmative perspective might highlight Vaccine A's lower rate of severe allergic reactions in adults, while the opposition focuses on its higher incidence of blood clotting. These perspectives offer transparency, uncover potential research gaps (e.g., if $80\%$ of the affirmative papers do not address these blood clotting incidents), and provide critical context for framing nuanced claims.
+
+Overall, CLAIMSPECT utilizes a structured approach to deconstruct a nuanced claim into a hierarchy of aspects, targeting a holistic approach considering all aspects which could be used to validate the root claim. The framework comprises the following steps: (1) aspect-discriminative retrieval, (2) iterative sub-aspect discovery, and (3) classification-based perspective discovery. Our contributions can be summarized as:
+
+- From the best of our knowledge, CLAIMSPECT is the first work to formally deconstruct claims into a hierarchical structure of aspects to determine consensus.   
+- We construct two novel datasets of real-world, scientific and political nuanced claims and corresponding corpora.   
+- Through experiments and case studies on real-world domains, we demonstrate that ClaimSpect performs hierarchical consensus analysis significantly more effectively than the baselines.
+
+Reproducibility: We provide our dataset and source code<sup>1</sup> to facilitate further studies.
+
+# 2 Related Works
+
+Fact Checking. Fact-checking models (Thorne et al., 2018; Popat et al., 2018; Atanasova et al., 2019; Karadzhov et al., 2017) have leveraged external evidence to validate claims, but often treat claims as monolithic statements. Web-integrated methods (Zhang and Gao, 2023; Karadzhov et al., 2017) attempt to enrich fact-checking with additional context, but still fail to account for nuanced claims that cannot be clearly validated without considering a diverse range of claim sub-aspects and their varying levels of evidence. In contrast, CLAIMSPECT acknowledges the nuance behind certain claims, utilizing a corpus to help identify the various aspects that would be considered when validating a claim—enabling a more multi-faceted and interpretable analysis. We note that CLAIMSPECT does not aim to validate a given claim—it simply aims to deconstruct the claim into a hierarchy of aspects which could be used to validate it, posing potential perspectives towards the aspect of the claim, grounded in the corpus. We also note the adjacent task of evidence retrieval, where existing work explores organizing evidence according to a fixed and flat (non-hierarchical) set of aspects: populations, interventions, and outcomes (Wadhwa et al., 2023).
+
+LLM-Based Taxonomy Generation. Recent advances in taxonomy generation (Shen et al., 2024b; Zeng et al., 2024b; Chen et al., 2023; Zeng et al., 2024a; Sun et al., 2024) have demonstrated the potential of large language models for structuring information hierarchically. However, these methods typically rely on static, domain-agnostic knowledge, limiting their adaptability to construct rich, fine-grained taxonomies (Sun et al., 2024). CLAIMSPECT addresses these limitations through corpus-aware, aspect-discriminative retrieval and iterative sub-aspect discovery, constructing a rich taxonomy of aspects that is aligned with a corpus. This allows us to identify the relevant segments to both a given aspect but also a perspective towards that aspect.
+
+Stance Detection Traditional stance detection (Mohammad et al., 2016) classifies opinions as supportive, neutral, or opposing towards a target (e.g., claim). However, these approaches typically assign a single stance to an entire document, overlooking the nuanced, aspect-specific stances present within many claims, especially in scientific and political contexts. Recent works (Zhang and Gao, 2023) have introduced more fine-grained judgments (e.g., "mostly true"), but similar to fact-checking methods, they often fail to capture the multi-faceted nature and rationale behind certain stances. By exploiting its constructed aspect hierarchy, CLAIMSPECT is able to infer viable supportive, neutral, and opposing perspectives towards an aspect and its associated papers.
+
+# 3 Methodology
+
+Illustrated in Figure 2, CLAIMSPECT consists of the following steps: (1) aspect-discriminative retrieval, (2) iterative sub-aspect discovery, and (3) classification-based perspective discovery.
+
+# 3.1 Preliminaries
+
+# 3.1.1 Task Definition
+
+We assume that as input, the user provides a claim $t_0$ (e.g., "Vaccine A is better than Vaccine B") and a corpus $D$ . In order to better reflect real-world settings, we do not assume that each document $d \in D$ is relevant to $t_0$ .
+
+Definition 1 (CLAIM) A statement or assertion that expresses a position, which may require validation or scrutiny. It often encapsulates multiple dimensions that contribute to its overall truthfulness or validity.
+
+Definition 2 (ASPECT) A specific component or dimension of a claim that can be independently analyzed or evaluated.
+
+ClaimSpect aims to output a hierarchy of aspects $T$ , where each aspect node (e.g., "safety") within the hierarchy can be considered as a descendant subclaim $t_i$ of the root user-specified claim, $t_0$ (e.g., "A is a safer vaccine than B"). In other words, each aspect node $t_i$ should reflect a relevant aspect that is important to consider when evaluating the root claim $t_0$ .
+
+# 3.1.2 Document Preprocessing
+
+For each $d \in D$ , we assume we have its full textual content (e.g., a full scientific paper). In order to have smaller, context-preserving units of text for our framework to retrieve, we segment each $d$ into chunks using the widely-recognized text segmentation method, C99 (Choi, 2000). This method labels sentences with matching tags if they pertain to the same topical group, which assists with retaining consecutive discussion of an aspect to a single segment.
+
+# 3.1.3 Initial Coarse-Grained Aspect Discovery
+
+Given our weak supervision setting, where only the root claim $t_0$ is provided, we first generate reliable, coarse-grained aspects to guide the retrieval-augmented hierarchy construction. These aspects are typically commonsense and do not require domain expertise to identify. Preliminary experiments confirm that LLMs can reliably identify them based on their expansive background knowledge alone. Thus, we prompt an LLM to generate coarse-grained aspects $t_i^0 \in T^0$ (e.g., efficacy, safety, and distribution in Figure 1) that will serve as the children of $t_0 \in T$ . For each aspect $t_i^0$ , the model outputs its label, significance to $t_0$ , and a list of $n = 10$ relevant keywords. This initial subtree forms the foundation of our framework. The full prompt is in Appendix B.1.
+
+# 3.2 Aspect-Discriminative Retrieval
+
+In order to construct a rich, coarse-to-fine aspect hierarchy that is aligned with the corpus, we must identify similarly rich reference material from our corpus. In general, noisy retrieval often hinders reasoning performance (Shen et al., 2024a), which may negatively impact discovering subaspects of a given node. Thus, in order to discover each subaspect $t_j^i$ of an aspect node $t_i$ , we must determine which segments $S_i$ from our corpus
+
+![](images/f5bab797fce3fbe54cb4f5ed2c63770ea14aa0076d0c5e5541d2427506695c31.jpg)  
+Figure 2: CLAIMSPECT deconstructs a nuanced claim into a hierarchy of aspects typically considered for validating the claim. We automatically discover the set of perspectives towards each aspect from the corpus.
+
+$D$ discuss $t_i$ . However, not all segments are equally informative for discovering subaspects.
+
+Specifically, a high-quality, discriminative segment $s_i$ for node $t_i$ contains the following features: (1) $s_i$ discusses $t_i$ in depth and (2) $s_i$ does not discuss $t_i$ 's siblings in breadth or depth. For instance, in Figure 1, a segment regarding the side effects observed within a clinical trial of Vaccine A and B on both children and adults discusses "safety" in more depth than if it only mentioned children. Furthermore, for discovering subaspects of "safety for children", a segment which independently discusses the safety for both children and adults would introduce additional noise into the subaspect generation process. Overall, it is important to rank these segments such that we select a set which minimizes the noise we introduce into the retrieval-augmented discovery of subaspects, while maximizing the number of subaspects which we can discover. We formalize our discriminative ranking mechanism in the sections below:
+
+# 3.2.1 Retrieval-Augmented Keyword Enrichment
+
+In order to determine whether a segment discusses an aspect $t_i$ in depth, we must first further enrich our understanding of $t_i$ . We propose performing a retrieval-augmented keyword-based enrichment of $t_i$ , where each keyword is likely to occur within segments relevant to $t_i$ and, thus, reflects either explicitly or implicitly the sub-aspects of $t_i$ . For example, for the "efficacy" aspect, the corresponding keywords are: neutralization, immune stimulation, post-dose antibody response, and waning immunity. First, we use a retrieval embedding model to select the top- $n$ segments (based on cosine-similarity) from the entire corpus that are relevant to a $t_i$ -specific query (its root, name, description, and keywords from Section 3.1.3):
+
+Claim: $[t_0]$ ; Aspect: $[t_i]$ ; [generated description of $t_i$ ]; $\text{Aspect Keywords: [generated keywords of } t_i$ ].
+
+We provide these initial top $n$ segments in addition to the root claim $t_0$ , the aspect label $t_i$ , and its description to the LLM in-context to identify $2k$ keywords. Given the same information and these keywords, we then
+
+merge similar or duplicate terms, while filtering irrelevant terms—explicitly prompting the model to provide solely $k$ keywords. This set of terms $w \in W_i$ ; $|W_i| = k$ , grounds our discriminative segment ranking for node $t_i$ . We provide these two prompts in Appendix B.2.
+
+# 3.2.2 Discriminative Segment Ranking
+
+In order to determine the most discriminative segments $S_{i}$ for aspect node $t_{i}$ , we first collect an initial large pool of segments using the same retrieval embedding-based method as Section 3.2.1. Our subsequent goal is to rank a segment $s \in S_{i}$ based on its discriminativeness:
+
+- Target Score: Reward $s$ based on its likelihood to contain all relevant subaspects $t_j^i$ of $t_i$ .   
+- Distractor Score: Penalize $s$ based on the degree and depth of other sibling aspects that it discusses.
+
+We assume that $t_i$ 's' keywords $W_i$ implicitly and/or explicitly reflect many of its subaspects. Thus, we use them to approximate the depth of an aspect-specific discussion. We convert each keyword $w_i$ into a descriptive query: "[ $w_i$ ] with respect to [all ancestor nodes of $w_i$ ]". By integrating the ancestors into the query, we influence the retention of $t_i$ 's hierarchical context; for example, we specifically reward a segment if it discusses "the safety of Vaccine A and B", as opposed to merely "safety". We embed each keyword query $\text{emb}(w \in W_i)$ using the retrieval embedding model, in addition to embedding each segment $\text{emb}(s) \in S_i$ .
+
+More formally, we are given an aspect node $t_i^h$ , which is a child of parent node $t_h$ and sibling node of $t_j \in T_{\neq i}^h$ . We are also provided with a segment embedding $\text{emb}(s) \in S_i$ , all keyword query embeddings of $t_i^h$ , $\text{emb}(w) \in W_i$ , and all sibling keyword query embeddings, $\text{emb}(w) \in W_{\neq i}^h$ . We compute the discriminative rank based on the following:
+
+Definition 3 (TARGET SCORE) A segment $s_i$ is rewarded based on a weighted average $(H)$ of its degree of similarity to all keywords $w \in W_i$ , implying a deeper discussion of node $t_i$ and its subaspects.
+
+$$
+\begin{array}{l} \mathbf {p} \left(s _ {i}, W _ {i}\right) = H \left(\left[ \operatorname {s i m} \left(e m b \left(s _ {i}\right), e m b (w)\right) \mid w \in W _ {i} \right]\right), \\ \text {w h e r e} H (X) = \frac {\sum_ {r = 1} ^ {| X |} \frac {1}{r} x _ {r}}{\sum_ {r = 1} ^ {| X |} \frac {1}{r}} \tag {1} \\ \end{array}
+$$
+
+We compute a weighted average based on Zipf's Law (Powers, 1998), where a word indexed at the $r$ -th position will have a weight of $1 / r$ . This weighted average of the segment-keyword similarities is based on the assumption that the model will implicitly generate the keywords from most to least significant-- in other words, we weight the first term $w_{1} \in W_{i}$ the highest, while weighing $w_{|X|}$ the lowest. For example, if $s_{i}$ had similarities of $[0.9, 0, 0]$ to $W_{i} = \{w_{1}, w_{2}, w_{3}\}$ , then $\mathbf{p}(s_{i}, W_{i}) = 0.5363$ . On the other hand, if the similarities were $[0.7, 0.8, 0.7]$ , $\mathbf{p}(s_{i}, W_{i}) = 0.7272$ . Overall, the target score will indicate a segment's discussion depth of aspect node $t_{i}$ -- how many keywords it aligns with and to what degree.
+
+Definition 4 (DISTRACTOR SCORE) A segment $s_i$ is penalized based on the breadth and depth of siblings discussed. The breadth is indicated by the mean target scoring between $s_i$ and each $W_j$ of $t_j \in T_{\neq i}^h$ . The depth is indicated by the max target scoring between $s_i$ and each $W_j$ of $t_j \in T_{\neq i}^h$ .
+
+$$
+\begin{array}{l} \mathbf {n} \left(s _ {i}, T _ {\neq i} ^ {h}\right) = 0. 5 \times \left(\frac {1}{\left| T _ {\neq i} ^ {h} \right|} \sum_ {j = 1} ^ {\left| T _ {\neq i} ^ {h} \right|} p \left(s _ {i}, W _ {j}\right)\right) \tag {2} \\ + 0. 5 \times \left(\max  _ {j = \left[ 1, \left| T _ {\neq i} ^ {h} \right| \right]} \left(p \left(s _ {i}, W _ {j}\right)\right)\right) \\ \end{array}
+$$
+
+We utilize the target and distractor scores to compute our overall discriminativeness score, which weighs the proximity between a segment and its target aspect, relative to its overall and individual proximity to its distractor, sibling aspects.
+
+Definition 5 (DISCRIMINATIVENESS SCORE) A segment $s_i$ is rewarded based on a weighted average $(H)$ of its degree of similarity to all keywords $w \in W_i$ , while being penalized based on the breadth and depth of siblings discussed.
+
+$$
+\mathbf {d} \left(s _ {i}, W ^ {h}\right) = \frac {\beta \times p \left(s _ {i} , W _ {i} ^ {h}\right)}{\gamma \times n \left(s _ {i} , T _ {\neq i} ^ {h}\right)} \tag {3}
+$$
+
+In Equation 3, $\mathbf{d}(s_i, W^h)$ grows proportional to the target score, while falling proportional to the distractor score. We include the $\beta$ and $\gamma$ scaling factors for each in case users would like to customize their degree of reward or penalty. Ultimately, we rank each segment $s \in S_i$ based on its discriminativeness score, taking the top- $k$ segments which feature the richest discussion of target aspect $t_i$ in order to discover its subaspects.
+
+# 3.3 Iterative Subaspect Discovery
+
+In order to expand our aspect hierarchy, we iteratively exploit our aspect-discriminative retrieval as knowledge which grounds the LLM's subaspect discovery. Given the aspect node $t_i$ , its description, its corresponding
+
+discriminative segments $S_{i}$ , and the root claim $t_0$ , we prompt the model to determine a set of at minimum two and at maximum $k$ subaspects for aspect $t_0$ . We provide this prompt in Appendix B.3.
+
+Definition 6 (SUBASPECT) A more granular component of a parent aspect $t_i$ that further refines $t_i$ 's evaluation and would be considered when specifically addressing the root claim $t_0$ .
+
+Each subaspect is represented in the same manner specified in Section 3.1.3: its label, description, and keywords. We continue constructing our aspect hierarchy in a top-down fashion, as detailed in Algorithm 1.
+
+# Algorithm 1 Iterative Subaspect Discovery
+
+Require: Root Claim $t_0$ , Corpus $D$ , max_depth $= l$
+
+1: $T =$ initialize_tree $\left( {t}_{0}\right) \left\{  {\bar{T}.\text{depth} = 0}\right\}$   
+2: $t_i^0 \in T^0 \gets \text{coarse\_grained\_aspects}(t_0)$ {Section 3.1.3}   
+3: $q = \text{queue}(T^0)$   
+4: while $len(q) > 0$ and $T.\mathrm{depth}\leq l$ do   
+5: $t_i \gets pop(q)$   
+6: enrich_node $(t_0,t_i,D)$ {Section 3.2.1}   
+7: $S_{i} \gets \mathrm{rank\_segments}(t_{0}, t_{i}, D)$ {Section 3.2.2}   
+8: $t_j^i \in T^i \gets \text{subaspect\_discovery}(t_0, t_i, S_i)$   
+9: $q.\mathrm{append}(T^i)$   
+10: end while   
+11: return $T$
+
+Ultimately, the output of Algorithm 1 is our final aspect hierarchy, serving as the basis for our consensus determination and perspective discovery process.
+
+# 3.4 Classification-Based Perspective Discovery
+
+With the aspect hierarchy constructed, we must identify the complete set of corpus segments that (1) pertain to the root claim $t_0$ and (2) align with an aspect node in hierarchy $T$ . Pinpointing papers discussing aspect node $t_i$ allows us to infer their perspective on $t_i$ and assess the presence and extent of consensus. However, as noted in Section 3.1.1, we cannot assume all corpus segments are relevant to the root claim—an assumption made in LLM-based taxonomy-guided hierarchical classification works (Zhang et al., 2024a). Thus, we must first filter out claim-irrelevant segments.
+
+Filtering. A naive approach determines segment relevance per node via in-context prompting, but this scales poorly. Instead, we frame relevance filtering as a binary search problem, identifying the relevance-irrelevance boundary. Specifically, we embed the claim label $t_0$ ( $\text{emb}(t_0)$ ) and each child aspect $t_i^0 \in T^0$ ( $\text{emb}([aspect\_label]$ with respect to $[t_0])$ ), computing the claim representation as:
+
+$$
+\mathbf {c} _ {0} = \frac {1}{2} \left(e m b \left(t _ {0}\right) + \frac {\sum_ {i = 1} ^ {| T ^ {0} |} e m b \left(t _ {i} ^ {0}\right)}{| T ^ {0} |}\right) \tag {4}
+$$
+
+We rank the encoded segments by cosine-similarity to $\mathbf{c}_0$ and use binary search to find the index $r$ where fewer than $\delta \%$ of segments in a $\pm n$ window are relevant. This rank $r$ serves as our threshold, filtering out lower-ranked segments and retaining only those relevant to $t_0(S_0^{\prime})$ .
+
+This optimization significantly reduces the quantity of relevance judgments necessary; the relevancy prompt is in Appendix B.4.
+
+Hierarchical Text Classification. With $S_0'$ and $T$ , we apply taxonomy-guided hierarchical classification to determine $S_i'$ for each aspect node $t_i \in T$ . Since our focus is retrieval-guided aspect hierarchy construction rather than classification, we adopt a recent LLM-based hierarchical classification model (Zhang et al., 2024a), which enriches taxonomy nodes (e.g., adding keywords) to support its top-down classification of $S_i'$ to $t_i$ .
+
+Perspective & Consensus Discovery. The final step of our pipeline is to determine the primary perspectives $P_{i} = \{a_{i},o_{i}\}$ towards each aspect node $t_i$ where $a_{i}$ is the overarching supportive perspective and $o_{i}$ is the opposing perspective. We also seek to identify the papers which hold each of these perspectives $(D_{i} = D_{i}^{\mathrm{supp}}\cup D_{i}^{\mathrm{opp}}\cup D_{i}^{\mathrm{neutral}})$ , accounting for papers which do not hold any clear perspective towards $t_i$ .
+
+Definition 7 (PERSPECTIVE) A descriptive viewpoint expressed toward a specific aspect $t_i$ of claim $t_0$ in the form of an implicit or explicit stance towards $t_i$ (e.g., support, neutral, or oppose) and optionally, a rationale.
+
+We do not assume that $D_{i}^{\mathrm{supp}}, D_{i}^{\mathrm{opp}}$ , and $D_{i}^{\mathrm{neutral}}$ are non-overlapping, as they may have multiple segments indicating different perspectives. For example, a segment $s_{i}^{\prime} \in S_{i}^{\prime}$ mapped to "Safety for Elders" may discuss a clinical trial showing increased anaphylactic shock in older patients when taking Vaccine A. However, another segment from the same paper may also note severe hives from Vaccine B. Thus, we allow for such flexibility.
+
+Recent studies have shown LLMs demonstrate powerful abilities in stance detection (Zhang et al., 2024b; Lan et al., 2024). Consequently, in order to discover these perspectives, we prompt the model to first determine the stance of each segment $s_i' \in S_i'$ :
+
+- Supports Claim: $s_i'$ either implicitly or explicitly indicates that the claim is true with respect to $t_i$ .   
+- Neutral to Claim: $s_i'$ is relevant to the claim and aspect, but does not indicate whether the claim is true with respect to $t_i$ .   
+- Opposes Claim: $s_i'$ either implicitly or explicitly indicates that the claim is false with respect to $t_i$ .
+
+This forms the segment sets: $S_{i}^{\mathrm{supp}}$ , $S_{i}^{\mathrm{neutral}}$ , and $S_{i}^{\mathrm{opp}}$ . We ask the model to summarize the perspective (stance and rationale) of each segment set: $P_{i}$ . Both prompts are provided in Appendix B.5. Since we retain the original paper source of each segment, we are able to construct $D_{i}$ for each node $t_{i}$ . This indicates consensus; for instance, how many papers in $D$ held perspective $p_{i}^{\mathrm{supp}}$ towards aspect $t_{i}$ . As our final output, we have the aspect hierarchy $T$ , the set of perspectives $P_{i}$ , and their corresponding papers $D_{i}$ .
+
+# 4 Experimental Design
+
+We explore CLAIMSPECT's performance on an open-source model, Llama-3.1-8B-Instruct (∞).
+
+We sample from the top $1\%$ of the tokens and set the temperature based on the nature of the given task (same setting across all samples); we include these settings in Appendix C. We set the maximum depth of the aspect hierarchy to $l = 3$ .
+
+# 4.1 Dataset
+
+In order to evaluate CLAIMSPECT's abilities to deconstruct nuanced claims into a hierarchy of aspects and identify their corresponding perspectives, we construct two novel, large-scale datasets specific to our task, applied to both political (World Relations) and scientific (Biomedical) domains. To construct this dataset, we first manually collect $\sim 50$ reference materials discussing (1) security-related international conflicts, and (2) biomedical safety-related studies. Then, we used GPT-4 (OpenAI et al., 2024) to generate nuanced claims based on these materials. Subsequently, we used the Semantic Scholar API (Allen Institute for AI, 2025) to collect meta information relevant literature based on these claims. Then, based on this meta information, we filtered the collected literature and retrieved the full texts. This way, for each claim, we obtained a corresponding literature repository. We show the statistics of each of these datasets in Table 1. More details about the dataset construction can be found in Appendix D, including a human study for validating the quality of the generated claims and their associated papers in Appendix D.5.
+
+Table 1: # of claims, papers, and segments per dataset.   
+
+<table><tr><td>Dataset</td><td>Claims</td><td>Papers</td><td>Segments</td></tr><tr><td>World Relations</td><td>140</td><td>9,525</td><td>1,081,241</td></tr><tr><td>Biomedical</td><td>50</td><td>3,719</td><td>428,833</td></tr><tr><td>Total</td><td>190</td><td>13,244</td><td>1,510,074</td></tr></table>
+
+# 4.2Baselines
+
+Our primary motivation for CLAIMSPECT is to demonstrate its capabilities of deconstructing a nuanced claim into an aspect hierarchy and identifying corresponding perspectives. However, no existing methods tackle this novel task. Consequently, we choose to implement and compare our method with both RAG-driven and LLM-only approaches, detailed below. We run each baseline using both Llama $(\infty)$ and GPT-4o-mini ( $\mathbb{O}$ ):
+
+1. RAG-Based: Given a claim and definition of an aspect hierarchy, we use the claim as a query to retrieve relevant documents. We then provide the documents in-context when prompt the LLM to generate the aspect hierarchy.   
+2. Iterative RAG-Based: Given the claim, the definition of an aspect hierarchy, and the name/description of the current node $t_i$ , we construct a detailed query to retrieve node-specific
+
+Table 2: Comparison between ClaimSpect and all baselines. Sibling granularity (Sib) is normalized; all others are scaled by 100. Since Iterative Zero-Shot is not grounded with a corpus, there are no associated segments to each node. Thus, we omit its segment relevance scores (Seg). We bold the top score and underline the second-highest.   
+
+<table><tr><td rowspan="2">Method</td><td colspan="5">World Relations</td><td colspan="5">Biomedical</td></tr><tr><td>Rel</td><td>Path</td><td>Sib</td><td>Unique</td><td>Seg</td><td>Rel</td><td>Path</td><td>Sib</td><td>Unique</td><td>Seg</td></tr><tr><td>Iterative Zero-Shot</td><td>97.85</td><td>41.94</td><td>58.01</td><td>72.96</td><td>—</td><td>98.33</td><td>44.44</td><td>57.04</td><td>77.17</td><td>—</td></tr><tr><td>Iterative RAG</td><td>97.18</td><td>45.34</td><td>59.01</td><td>74.25</td><td>42.79</td><td>97.14</td><td>45.93</td><td>59.08</td><td>76.17</td><td>27.11</td></tr><tr><td>Iterative Zero-Shot</td><td>98.60</td><td>42.88</td><td>64.04</td><td>76.01</td><td>—</td><td>97.89</td><td>41.56</td><td>62.09</td><td>77.55</td><td>—</td></tr><tr><td>Iterative RAG</td><td>97.40</td><td>52.30</td><td>66.45</td><td>76.59</td><td>46.93</td><td>94.37</td><td>50.07</td><td>64.21</td><td>77.05</td><td>31.82</td></tr><tr><td>CLAIMSPECT</td><td>95.30</td><td>78.24</td><td>85.26</td><td>87.62</td><td>43.23</td><td>97.95</td><td>75.10</td><td>74.80</td><td>86.26</td><td>27.39</td></tr><tr><td>CLAIMSPECT - No Disc</td><td>99.00</td><td>79.75</td><td>82.64</td><td>85.43</td><td>49.47</td><td>96.07</td><td>76.26</td><td>74.39</td><td>87.69</td><td>39.03</td></tr></table>
+
+relevant documents. We then provide these documents in-context to prompt the LLM for generating the children subaspects $t_j^i$ of aspect $t_i$ .
+
+We also conduct an ablation study, No Discriminative (No Disc), where we remove discriminative ranking and instead replace it with a semantic similarity-based ranking. For this, we compute the semantic similarity between each segment and our $t_i$ -specific query from Section 3.2.1.
+
+# 4.3 Evaluation Metrics
+
+We design a thorough automatic evaluation suite using GPT-4o-mini to determine the quality of our generated taxonomies, using both node-level and taxonomy-level metrics. For each judgment, we ask the LLM to provide additional rationalization:
+
+- (Node-Wise) Node Relevance: For each aspect node $t_i$ and its respective path within the hierarchy, what is its relevance to the claim $t_0$ ? Scored 0/1.   
+- (Node-Wise) Path Granularity: Does the path to node $t_i$ preserve the hierarchical relationships between its entities (is each child $t_j^i$ more specific than the parent $t_i$ )? Scored 0/1.   
+- (Level-Wise) Sibling Granularity: For each set of siblings $T^i$ within the hierarchy, does the overall set reflect the same level of specificity relative to their parent aspect $t_i$ ? Scored from 1 to 4 (all different $\rightarrow$ some $\rightarrow$ most $\rightarrow$ all same).   
+- (Node-Wise) Uniqueness: Does the aspect node $t_i$ have other overlapping nodes within the hierarchy $T$ ? Scored 0/1.   
+- (Node-Wise) Segment Quality: How many segments $s \in S_i'$ are relevant to the claim $t_0$ and aspect $t_i$ ? We compute the average proportion of relevant segments per node.
+
+In addition to automatically evaluating our aspect hierarchy, we also conduct a supplementary human evaluation on 50 perspectives and their sampled segments, which CLAIMSPECT identifies from the corpus (Section 5.2).
+
+# 5 Experimental Results
+
+# 5.1 Overall Performance & Analysis
+
+Tables 2-3 demonstrate several key advantages of CLAIMSPECT over the baselines across various node and level-wise metrics for both the World Relations and Biomedical datasets. CLAIMSPECT is able to strongly enforce the hierarchical structure of the generated aspect hierarchy while preserving relevance to the corpus. Below, we present our core findings and insights. We also provide a breakdown of ClaimSpect's computational efficiency in Appendix E. Finally, we additionally conducted a human-automatic evaluation agreement study in Appendix A.
+
+CLAIMSPECT excels in granular aspect discovery. As shown in Table 2, CLAIMSPECT significantly outperforms the baselines in metrics associated with node-level structure, particularly outperforming Iterative RAG by $72.6\%$ and $63.51\%$ in preserving hierarchical relationships (path granularity) and by $44.48\%$ and $26.61\%$ in maintaining uniform sibling-level specificity (sibling granularity) for both datasets respectively. This demonstrates the method's ability to retrieve and organize aspects at targeted levels of granularity. These gains are similarly observed with the GPT-based baselines, despite relying on a closed-source model. We attribute this gain to ClaimSpect's iterative subaspect discovery (Section 3.3) being integrated with its aspect-discriminative retrieval mechanism (Section 3.2), where the pool of segments grounding the subaspect discovery is iteratively updated based on the given aspect node. We can see that the No Disc ablation does experience some loss in granularity quality. It is important to note that No Disc does experience competitive and, at times, better performance; this is likely due to it considering more segments, which may or may not discuss multiple aspects. In contrast, the baseline methods retrieve broader, less focused segments, reducing their ability to discover fine-grained sub-aspects. Overall, this demonstrates that ClaimSpect is able to deconstruct a claim into a well-structured hierarchy of aspects.
+
+Table 3: Pairwise comparisons between all methods for each dataset. Each value is the percentage of samples within each dataset where the method is considered better. $E$ -Tie denotes Explicit Tie; $I$ -Tie denotes Implicit Tie.   
+
+<table><tr><td rowspan="2">Method Pair (A vs. B)</td><td colspan="4">World Relations</td><td colspan="4">Biomedical</td></tr><tr><td>A Wins</td><td>B Wins</td><td>E-Tie</td><td>I-Tie</td><td>A Wins</td><td>B Wins</td><td>E-Tie</td><td>I-Tie</td></tr><tr><td>Zero-Shot ∩ vs RAG ∩</td><td>0.00</td><td>33.06</td><td>0.00</td><td>66.94</td><td>2.22</td><td>22.22</td><td>0.00</td><td>75.55</td></tr><tr><td>Zero-Shot ∩ vs CLAIMSPECT ∩</td><td>0.00</td><td>97.58</td><td>0.00</td><td>2.42</td><td>0.00</td><td>95.55</td><td>2.22</td><td>2.22</td></tr><tr><td>RAG ∩ vs CLAIMSPECT ∩</td><td>0.81</td><td>90.32</td><td>0.00</td><td>8.87</td><td>0.00</td><td>95.55</td><td>0.00</td><td>4.44</td></tr><tr><td>No Disc ∩ vs CLAIMSPECT ∩</td><td>21.43</td><td>30.00</td><td>0.00</td><td>48.57</td><td>24.00</td><td>28.00</td><td>0.00</td><td>48.00</td></tr><tr><td>Zero-Shot ∩ vs RAG ∩</td><td>0.00</td><td>36.00</td><td>0.00</td><td>64.00</td><td>0.71</td><td>47.14</td><td>0.00</td><td>52.14</td></tr><tr><td>Zero-Shot ∩ vs CLAIMSPECT ∩</td><td>0.00</td><td>98.00</td><td>0.00</td><td>2.00</td><td>0.00</td><td>96.43</td><td>0.00</td><td>3.57</td></tr><tr><td>RAG ∩ vs CLAIMSPECT ∩</td><td>0.00</td><td>90.00</td><td>0.00</td><td>10.00</td><td>7.14</td><td>72.14</td><td>0.71</td><td>20.00</td></tr></table>
+
+![](images/ba326f5a4c88389329cdacda1361124a1774ab03e8dc07107c22d06bad0524da.jpg)  
+Figure 3: A constructed Biomedical aspect hierarchy. All nodes and their # of segments from levels 1-2 are included; a subset of the third level is highlighted. The # of papers mapped to each perspective is provided in parentheses.
+
+CLAIMSPECT constructs a rich aspect hierarchy while preserving relevance. In Table 2, we observe that ClaimSpect's constructed hierarchy features nodes that are $14.40\%$ and $11.23\%$ more unique than the top baseline on each dataset, respectively. This indicates that ClaimSpect's hierarchies are richer in aspect quality, experiencing less overlap between aspects across the tree and supported by an increase in segment quality. Despite this significant boost in uniqueness, ClaimSpect only experiences a $3.35\%$ and $0.386\%$ drop from the top baseline in aspect node relevance for the World Relations and Biomedical datasets, respectively. This highlights the strength of ClaimSpect's retrieval-augmented keyword enrichment and aspect-discriminative retrieval (Sections 3.2.1 and 3.2), which prioritize segments that thoroughly discuss a single aspect rather than shallow descriptions of multiple aspects. This allows us to discover a richer set of unique and relevant subaspects at each level, throughout the hierarchy.
+
+CLAIMSPECT is overwhelmingly preferred over baselines. Table 3 presents pairwise comparisons between CLAIMSPECT and the baseline methods. These
+
+comparisons are judged by an LLM that is shown the aspect hierarchy outputs of methods $A$ and $B$ in both possible orders: $A$ vs. $B$ and $B$ vs. $A$ . The LLM may (1) prefer either method $A$ or $B$ , (2) declare an explicit tie $(E-Tie)$ , or (3) indicate an implicit tie $(I-Tie)$ , which occurs when the preferred method changes depending on the order of presentation (e.g., $A$ wins in $A$ vs. $B$ , but $B$ wins in $B$ vs. $A$ ) (Shi et al., 2024).
+
+Across both datasets, CLAIMSPECT exhibits a clear advantage, being preferred $92.95\%$ of the time, with a $6.69\%$ average inconsistency rate across all settings and datasets. Specifically, when compared with Zero-Shot $\infty$ , CLAIMSPECT is judged superior in $97.58\%$ and $95.55\%$ of cases for World Relations and Biomedical datasets, respectively. Even against RAG $\text{圆}$ , CLAIMSPECT outperforms in $90.00\%$ and $72.14\%$ of samples. This is a stark contrast from the lack of strong preference between the baselines themselves, indicated by the $64.66\%$ average implicit tie rate—implying that there is no obvious qualitative preference between the two. Finally, we show that ClaimSpect and No Disc are similarly preferred, with ClaimSpect preferred slightly more
+
+often. Overall, these results validate that CLAIMSPECT constructs significantly more meaningful aspect hierarchies relevant to the claim.
+
+# 5.2 Perspective Discovery Analysis
+
+CLAIMSPECT identifies nuanced, corpus-specific perspectives. We showcase a qualitative analysis of a nuanced claim's aspect hierarchy, highlighting certain subtrees and the root node's extracted perspectives, in Fig. 3. We observe each coarse-grained aspect (yellow nodes) well represents the various angles of the root claim that would be considered in validating it: what long-term vaccine studies currently exist, what is the current mRNA technology, and how is genetic impact currently assessed? We see that the path-specific dependencies are reflected within the descriptions of each aspect (e.g., "mRNA Interaction with Host Genome" involves both mRNA technology and potential genetic impact risks). Furthermore, these hierarchical relationships and claim relevance are preserved even in the final layer of the hierarchy (e.g., "mRNA Interaction with Host Genome" $\rightarrow$ "mRNA degradation patterns"). Finally, we see that the perspectives mapped to the root node are informative, providing justification behind each stance. Note that ClaimSpect maps segments to each perspective, allowing us to identify the original paper sources and ultimately provide a corpus-specific estimate of the consensus. Overall, this deconstructed view of the claim provides a means to identify which and to what degree certain aspects have been explored (e.g., mRNA Technology has been more explored within the corpus compared to Genetic Impact Assessment).
+
+Table 4: Human validation on the percentage of perspectives discovered by CLAIMSPECT which are grounded in at least one of $k$ associated segments. $k = \#$ of segments considered. We provide the number of samples for each setting in parenthesis.   
+
+<table><tr><td>k</td><td>World Relations</td><td>Biomedical</td></tr><tr><td>5</td><td>72% (50)</td><td>72% (50)</td></tr><tr><td>10</td><td>80% (20)</td><td>82% (20)</td></tr><tr><td>15</td><td>85% (19)</td><td>89% (9)</td></tr></table>
+
+Human annotators validate the grounding of discovered perspectives. To assess the validity of the perspectives discovered by CLAIMSPECT, we apply human evaluation to evaluate whether these perspectives are effectively grounded in the corpus. We randomly sampled perspectives along with their associated $k$ segments (each aspect node has three ass from the generated results across two datasets. The evaluation metric used was whether at least one segment in $k$ could provide grounding background knowledge for the corresponding perspective. As shown in Table 4, we found that the vast majority of cases (85% and 89% for each dataset respectively) are supported by specific literature segments. Furthermore, we can see that the support rate
+
+steadily increases as we retrieve more segments that are mapped to the perspective. This shows the perspectives identified by CLAIMSPECT are largely supported by the corpus.
+
+# 6 Conclusion
+
+Our work introduces CLAIMSPECT, a novel framework for deconstructing nuanced claims into a hierarchy of corpus-specific aspects and perspectives. By integrating iterative, aspect-discriminative retrieval with hierarchical sub-aspect discovery and perspective clustering, CLAIMSPECT provides a structured, comprehensive view of complex claims. Our experiments on two novel, large-scale datasets demonstrate that CLAIMSPECT constructs rich, corpus-aligned aspect hierarchies that are enriched with diverse and informative perspectives. This highlights its effectiveness as a scalable and adaptable method for nuanced claim analysis across domains.
+
+# 7 Limitations & Future Work
+
+The primary contribution of CLAIMSPECT is our retrieval-augmented framework for constructing an aspect hierarchy relevant for validating a nuanced claim. In order to demonstrate the hierarchy's potential, we apply it to the task of perspective discovery, involving (1) identifying which segments from the corpus are relevant to a given aspect node, (2) determining the stance (or lack thereof) of the segment towards the claim and aspect, and (3) discovering the potential perspective of each of the stance-based segment clusters. Consequently, this step relies heavily upon an existing hierarchical classification model (Zhang et al., 2024a), as we do not claim novelty with respect to classification. Similarly, our classification-based perspective discovery (Section 3.4) is reliant on the LLM's fine-grained stance detection abilities—although prior work (Zhang et al., 2024b; Lan et al., 2024) has shown precedence for its capabilities. Thus, the performance of the hierarchical classification and stance detection serves as a bottleneck to our method's performance. For example, if the LLM-based stance detection has a high recall but low precision for detecting segments which support the aspect of claim, then the method may overestimate the consensus behind a certain perspective within the corpus. Likewise, if the detection has a high precision but lower recall, it may underestimate the consensus. Nonetheless, our work aims to, overall, motivate the need to structure the aspects of certain nuanced claims before diving straight into their validation.
+
+Hierarchically analyzing nuanced claims opens up doors to many new avenues of research. First, CLAIMSPECT can be integrated with more systematic and/or tool-integrated fact validation systems, in an effort to build a more robust fact-checking system. Furthermore, CLAIMSPECT can be applied to more targeted retrieval or question answering tasks where a question, similar to a nuanced claim, cannot easily be answered and may
+
+benefit from a more structured output (similar to an aspect hierarchy).
+
+# 8 Acknowledgements
+
+This work was supported by the National Science Foundation Graduate Research Fellowship. The work was also supported in part by the BRIES Program No. HR0011-24-3-0325. This research used the DeltaAI advanced computing and data resource, which is supported by the National Science Foundation (award OAC 2320345) and the State of Illinois. DeltaAI is a joint effort of the University of Illinois at Urbana-Champaign and its National Center for Supercomputing Applications. We thank Peter Bautista, Spencer Lynch, and Svitlana Volkova from Aptima, Inc. for their discussions on our work. We also thank Mihir Kavishwar for early ideation discussions.
+
+# References
+
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+Google Scholar. 2025. Google Scholar. https:// scholar.google.com. Accessed: 2025-02-15.
+
+Georgi Karadzhov, Preslav Nakov, Lluis Marquez, Alberto Barron-Cedeno, and Ivan Koychev. 2017. Fully automated fact checking using external sources. In Proceedings of the International Conference Recent Advances in Natural Language Processing, RANLP 2017, pages 344-353, Varna, Bulgaria. INCOMA Ltd.   
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+Patrick Lewis, Ethan Perez, Aleksandra Piktus, Fabio Petroni, Vladimir Karpukhin, Naman Goyal, Heinrich Kuttler, Mike Lewis, Wen-tau Yih, Tim Rocktäschel, et al. 2020. Retrieval-augmented generation for knowledge-intensive nlp tasks. Advances in Neural Information Processing Systems, 33:9459-9474.   
+Saif M Mohammad, Svetlana Kiritchenko, Parinaz Sobhani, Xiaodan Zhu, and Colin Cherry. 2016. Semeval-2016 task 6: Detecting stance in tweets. In Proceedings of the 10th International Workshop on Semantic Evaluation (SemEval-2016), pages 31-41.   
+OpenAI, :, Aaron Hurst, Adam Lerer, Adam P. Goucher, Adam Perelman, Aditya Ramesh, Aidan Clark, AJ Ostrow, Akila Welihinda, et al. 2024. Gpt-4o system card. Preprint, arXiv:2410.21276.   
+Jason Alan Palmer. 2024. pdftotext.   
+Gordon Pennycook and David G Rand. 2021. The psychology of fake news. *Trends in Cognitive Sciences*, 25(5):388-402.   
+Nicolas Perony, René Pfitzner, Ingo Scholtes, Claudio J Tessone, and Frank Schweitzer. 2013. Enhancing consensus under opinion bias by means of hierarchical decision making. Advances in Complex Systems, 16(06):1350020.   
+Kashyap Popat, Subhabrata Mukherjee, Jannik Strötgen, and Gerhard Weikum. 2018. Declare: Debunking fake news and false claims using evidence-aware deep learning. In Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing, pages 22-32.   
+David M. W. Powers. 1998. Applications and explanations of Zipf's law. In New Methods in Language Processing and Computational Natural Language Learning.   
+PubMed. 2025. PubMed. https://pubmed.ncbi.nlm.nih.gov. Accessed: 2025-02-15.   
+Karishma Sharma, Feng Qian, He Jiang, Natali Ruchansky, Minghui Zhang, and Yan Liu. 2019. Combating
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+fake news: A survey on identification and mitigation techniques. ACM Transactions on Intelligent Systems and Technology (TIST), 10(3):1-42.   
+Xiaoyu Shen, Rexhina Blloshmi, Dawei Zhu, Jiahuan Pei, and Wei Zhang. 2024a. Assessing "implicit" retrieval robustness of large language models. In Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing, pages 8988-9003, Miami, Florida, USA. Association for Computational Linguistics.   
+Yanzhen Shen, Yu Zhang, Yunyi Zhang, and Jiawei Han. 2024b. A unified taxonomy-guided instruction tuning framework for entity set expansion and taxonomy expansion. arXiv preprint arXiv:2402.13405.   
+Lin Shi, Chiyu Ma, Wenhua Liang, Weicheng Ma, and Soroush Vosoughi. 2024. Judging the judges: A systematic investigation of position bias in pairwise comparative assessments by llms. arXiv preprint arXiv:2406.07791.   
+Yushi Sun, Hao Xin, Kai Sun, Yifan Ethan Xu, Xiao Yang, Xin Luna Dong, Nan Tang, and Lei Chen. 2024. Are large language models a good replacement of taxonomies? arXiv preprint arXiv:2406.11131.   
+James Thorne, Andreas Vlachos, Christos Christodoulopoulos, and Arpit Mittal. 2018. FEVER: a large-scale dataset for fact extraction and VERIFICATION. In Proceedings of the 2018 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long Papers), pages 809-819, New Orleans, Louisiana. Association for Computational Linguistics.   
+Soroush Vosoughi, Deb Roy, and Sinan Aral. 2018. The spread of true and false news online. Science, 359(6380):1146-1151.   
+Somin Wadhwa, Vivek Khetan, Silvio Amir, and Byron Wallace. 2023. RedHot: A corpus of annotated medical questions, experiences, and claims on social media. In Findings of the Association for Computational Linguistics: EACL 2023, pages 809-827, Dubrovnik, Croatia. Association for Computational Linguistics.   
+Qingkai Zeng, Yuyang Bai, Zhaoxuan Tan, Shangbin Feng, Zhenwen Liang, Zhihan Zhang, and Meng Jiang. 2024a. Chain-of-layer: Iteratively prompting large language models for taxonomy induction from limited examples. In Proceedings of the 33rd ACM International Conference on Information and Knowledge Management, pages 3093-3102.   
+Qingkai Zeng, Yuyang Bai, Zhaoxuan Tan, Zhenyu Wu, Shangbin Feng, and Meng Jiang. 2024b. Codetaxo: Enhancing taxonomy expansion with limited examples via code language prompts. arXiv preprint arXiv:2408.09070.   
+Xuan Zhang and Wei Gao. 2023. Towards LLM-based fact verification on news claims with a hierarchical step-by-step prompting method. In Proceedings of
+
+the 13th International Joint Conference on Natural Language Processing and the 3rd Conference of the Asia-Pacific Chapter of the Association for Computational Linguistics (Volume 1: Long Papers), pages 996-1011, Nusa Dua, Bali. Association for Computational Linguistics.   
+Yunyi Zhang, Ruozhen Yang, Xueqiang Xu, Rui Li, Jinfeng Xiao, Jiaming Shen, and Jiawei Han. 2024a. Teleclass: Taxonomy enrichment and llm-enhanced hierarchical text classification with minimal supervision. arXiv preprint arXiv:2403.00165.   
+Zhao Zhang, Yiming Li, Jin Zhang, and Hui Xu. 2024b. Llm-driven knowledge injection advances zero-shot and cross-target stance detection. In Proceedings of the 2024 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume 2: Short Papers), pages 371-378.
+
+# A Human Annotator Background and Human-Automatic Alignment for Evaluation
+
+We perform a human evaluation study to show the alignment between humans and GPT-4o-mini for evaluation. We use two human evaluators to evaluate randomly sampled cases for each of our proposed metrics: node relevance, path granularity, sibling granularity, uniqueness and segment quality. Our human evaluators are two volunteer graduate researchers (one PhD student and Masters student), with one having a background in Biology + NLP (critical for our biomedical task evaluation). We used the following instructions to help guide them in the evaluation task, with an initial "training" period where the evaluators could familiarize themselves with the task (e.g., aspect taxonomies and their expected hierarchical relationships) and discuss examples with one another, but the full evaluation period was conducted independently:
+
+1. General Instruction: Claims made by individuals or entities are often nuanced and cannot always be strictly categorized as entirely 'true' or 'false', particularly in scientific and political contexts. Instead, a claim can be broken down into its core aspects and sub-aspects, which are easier to evaluate individually.   
+2. Node Relevance: Given the claim: [claim], decide whether this path from the aspect tree is relevant to the analysis of the claim: [path] $\rightarrow$ relevant or irrelevant?   
+3. Path Granularity: Given the claim: [claim], decide whether this path from the aspect tree has good granularity: [path]. Check whether the child node is a more specific subaspect of the parent node. $\rightarrow$ granular or non-granular?   
+4. Sibling Granularity: Given the claim: [claim'], decide whether these siblings from parent node [parent] have good granularity. $\rightarrow$ <proportion of granular siblings>   
+5. Uniqueness: Normally, we want the aspects and sub-aspects to be unique in the taxonomy. Given the claim: [claim], count how many nodes in this taxonomy are largely overlapping or almost equivalent. $\rightarrow$ <total count of overlapping nodes>   
+6. Segment Quality: Given the claim: [claim], evaluate the quality of these segments for aspect [aspect node label]. [list of mapped segments] $\rightarrow$ <total count of relevant segments to aspect node>
+
+Since ClaimSpect has consistently high scores on "Node Relevance" and "Uniqueness" (not very many nodes are irrelevant or overlapping across the entire taxonomy), the scores from both the LLM and evaluators have very low variance. This greatly limits both Cohen's
+
+and Intraclass Correlation Coefficient (high instability). Nonetheless, the evaluators have a $100\%$ and $96.97\%$ agreement rate respectively. We choose Cohen's $\kappa$ or ICC based on the ordinal/continuous versus categorical nature of the metric.
+
+1. The weighted $\kappa$ for Path Granularity is $0.62 \rightarrow$ substantial agreement   
+2. The $ICC1k$ for Sibling Granularity is $0.7806 \rightarrow$ good reliability   
+3. The $ICC2k$ for Segment Quality is $0.7578 \rightarrow$ good reliability
+
+We also show the agreement rate below on 100 different samples across all metrics in Table 5.
+
+Table 5: Human-Automatic Agreement rates across different metrics.   
+
+<table><tr><td></td><td>Rel</td><td>Path</td><td>Sib</td><td>Unique</td><td>Seg</td></tr><tr><td>Agreement Rate</td><td>100%</td><td>85%</td><td>87.5%</td><td>96.97%</td><td>82%</td></tr></table>
+
+We can see that the LLM evaluation and human evaluators have a high degree of alignment. We note that segment quality features the lowest alignment (albeit still a relatively high rate), likely due to the more fine-grained text understanding abilities required for verifying segment alignment to the parent node (where oftentimes, segments can be quite semantically dissimilar or only discuss a "sub-aspect" of the node). Nonetheless, through these results, we can see that **our autoevaluation is reliable**.
+
+# B Prompt Template
+
+In this section, we present the prompts used in different modules of CLAIMSPECT.
+
+# B.1 Coarse-Grained Aspect Discovery
+
+This is the prompt used to generate coarse-grained aspects for the root claim, including their labels, description, and relevant keywords to structure the initial retrieval-augmented hierarchy.
+
+# Prompt
+
+For the topic, {topic}, output the list of up to $\{\mathbf{k}\}$ aspects in JSON format.
+
+# B.2 Retrieval-Augmented Keyword Enrichment
+
+Following are the prompts used for retrieval-augmented keyword enrichment, instructing the LLM to refine and filter aspect-specific keywords for improved segment ranking.
+
+# Prompt (Extraction)
+
+The claim is: {claim}. You are analyzing it with a focus on the aspect {aspect_name}. The aspect, {aspect_name}, can be described as the following: {aspect_description}
+
+Please extract at most $\{2^{*}\mathrm{max\_}$ keyword_num} keywords related to the aspect {aspect_name} from the following documents: {contents} Ensure that the extracted keywords are diverse, specific, and highly relevant to the given aspect. Only output the keywords and seperate them with comma. Your output should be in JSON format.
+
+# Prompt (Filtering)
+
+Our claim is '\{claim\}'. With respective to the target aspect '\{aspect_name\}' identify $\{\mathrm{min\_keyword\_num}\}$ to $\{\mathrm{max\_keyword\_num}\}$ relevant keywords from the provided list: $\{\mathrm{key}$ wordCandidates}.
+
+{aspect_name} : {aspect_description}
+
+Merge terms with similar meanings, exclude relatively irrelevant ones, and output only the final keywords separated by commas.
+
+Your output should be in JSON format.
+
+# B.3 Iterative Subaspect Discovery
+
+Following is the prompt used to iteratively guide the LLM in discovering and expanding subaspects for each aspect node based on discriminative retrieval and root claim context.
+
+# Prompt
+
+Output the list of up to $\{\mathbf{k}\}$ subaspects of parent aspect $\{$ aspect $\}$ that would be considered when evaluating the claim, $\{$ topic $\}$ . claim: $\{$ topic $\}$ parent\_aspect: $\{$ aspect $\}$ ; $\{$ aspect\_description $\}$ path_to_parent\_aspect: $\{$ aspect_path $\}$ Provide your output in the following JSON format.
+
+# B.4 Relevance Filtering
+
+Following is the prompt used for relevance filtering, leveraging binary search on cosine-similarity rankings to efficiently identify and retain only the most relevant segments for each aspect.
+
+# Prompt
+
+I am currently analyzing a claim based on a segment from the literature from several different aspects. The segment is: {segment} The claim is: {claim} The aspects are: {aspects} Please help me determine whether this segment is related to the claim so that I can analyze this claim based on it from at least one of these aspects. Your output should be 'Yes' or 'No' in JSON format.
+
+# B.5 Perspective Discovery
+
+Following are prompts used to for determining segment stances (support, neutral, or oppose) and summarizing perspectives, including rationales, for each aspect.
+
+# Prompt
+
+You are a stance detector, which determines the stance that a segment from a scientific paper has towards an aspect of a specific claim. Oftentimes, scientific papers do not provide explicit, outright stances, so your job is to figure out what stance the data or statement that they are presenting implies. Segment: {segment(content}
+
+What is the segment's stance specifically with respect to {aspect_name} for if {claim}? {aspect_name} can be described as {aspect_description}. Claim: {claim} Aspect to consider: {aspect_name}: {aspect_description} Path to aspect: {aspect_path}
+
+Your stance options are the following: - supports_claim: The segment either implicitly or explicitly indicates that claim is true specific to the given aspect. - neutral_to_claim: The segment is relevant to the claim and aspect, but does not indicate whether the claim is true specific to the given aspect. - opposes_claim: The segment either implicitly or explicitly indicates that the claim is false specific to the given aspect. - irrelevant_to_claim: The segment does not contain relevant information on the claim and the aspect.
+
+# C Generation Settings
+
+This section details the temperature values used in various stages of our process and their respective roles.
+
+# C.1 Overview of Temperature Settings
+
+- Coarse-Grained Aspect Discovery (0.3): Used to generate high-level aspects related to the claim. A lower temperature ensures structured and deterministic output.   
+- Subaspect Discovery (0.7): Used for identifying subaspects from ranked segments. A higher temperature allows for more diversity while maintaining coherence.
+
+- OpenAI Chat Models (GPT-4o (OpenAI et al., 2024), GPT-4o-mini (OpenAI et al., 2024)) (0.3): Applied in various stages where GPT-4o models are used (e.g., aspect generation, classification), ensuring consistent responses.   
+- Subaspect Discovery (Aspect Ranking and Retrieval) (0.7): Used when extracting subaspects from ranked segments to balance creativity with relevance.
+
+# C.2 General Trends
+
+- Lower temperature (0.3) is used for structured and deterministic tasks such as aspect generation and classification.   
+- Higher temperature (0.7) is applied to subaspect discovery, where diversity and exploration are beneficial.
+
+# D Dataset Construction
+
+To evaluate the effectiveness of CLAIMSPECT, our nuanced claims analysis, we constructed two datasets covering two key domains: political (World Relations) and scientific (Biomedical). The dataset construction process consists of the following steps:
+
+# D.1 Manual Seed Collection
+
+We begin by manually collecting a set of seed claims from reliable sources such as Google Scholar (Google Scholar, 2025) and PubMed (PubMed, 2025). Specifically, we collect material from 7 papers in the World Relations domain and 50 papers in the Biomedical domain. These initial materials serve as a context or specific topics for generating nuanced claims.
+
+# D.2 Nuanced Claims Generation
+
+Using the literature collected in the previous step and definition of nuanced claims as context, we prompt GPT-4 (OpenAI et al., 2024) to generate nuanced claims related to the topics within these papers. To ensure diversity in claim perspectives, we employ two sets of prompts: one for generating claims that align with the perspectives in the literature and another for generating claims that diverge from them. The specific prompts used are detailed below.
+
+# Positive Claim Generation Prompt
+
+Scientific or political claims are often nuanced and multifaceted, rarely lending themselves to simple "yes" or "no" answers. To answer such questions effectively, claims must be broken into specific aspects for in-depth analysis, with evidence drawn from relevant scientific literature. We are currently studying such claims using this corpus: {context}
+
+Task: Generate 10 nuanced and diverse claims based on this corpus. The claims should adhere to the following criteria:
+
+1. Diversity: The claims should be sufficiently varied: they should involve diverse sub-topics in the context   
+2. Complexity: The claims should be complex and controversial (and not necessity true), requiring multi-aspect analysis rather than simplistic treatment. Avoid overly straightforward or simplistic claims.   
+3. Research Feasibility: The claims should not be too specific and should pertain to topics with a likely body of existing literature to support evidence-based exploration.   
+4. Concision: The claims should be concise and focused in one short sentence.   
+5. Completeness: The claims should be complete and not require additional context to understand. Output: Provide the claims as a list.
+
+# Negative Claim Generation Prompt
+
+Scientific or political claims are often nuanced and multifaceted, rarely lending themselves to simple "yes" or "no" answers. To answer such questions effectively, claims must be broken into specific aspects for in-depth analysis, with evidence drawn from relevant scientific literature. We are currently studying such claims using this corpus:
+
+{context}
+
+Task: Generate 10 nuanced and diverse claims based on this corpus. The claims should adhere to the following criteria:
+
+1. Diversity: The claims should be sufficiently varied: they should involve diverse sub-topics in the context   
+2. Complexity: The claims should be complex and controversial (and not necessity true), requiring multi-aspect analysis rather than simplistic treatment. Avoid overly straightforward or simplistic claims.   
+3. Research Feasibility: The claims should not be too specific and should pertain to topics with a likely body of existing literature to support evidence-based exploration.   
+4. Concision: The claims should be concise and focused in one short sentence.   
+5. Completeness: The claims should be complete and not require additional context to understand.   
+6. The claims should be against the point of view in the context.
+
+Output: Provide the claims as a list.
+
+We find that the generated nuanced claims are of high quality. They are content-rich, specific, and difficult to classify as simply true or false, aligning well with our task requirements. Below are some example claims from our datasets.
+
+# Claims for World Relations
+
+1. International collaborations under the Global Nuclear Security Program prioritize geopolitical alliances over immediate nuclear threat reduction.   
+2. Counteracting WMDs through international partnerships creates dependency and may hinder national self-sufficiency in threat reduction capabilities.   
+3. The effectiveness of the biological threat reduction component is questionable given the rise and global spread of emerging biological threats.
+
+# Claims for Biomedical Domain
+
+1. COVID-19 vaccine safety evaluations are compromised by inconsistent application of evidence standards across different data sources like RCTs and VAERS.   
+2. The rigid adherence to optimized distribution plans might inhibit the flexibility needed to respond to unforeseen disruptions in the vaccine supply chain.   
+3. Keeping manufacturing costs secret is essential for protecting proprietary processes and innovations in the pharmaceutical industry.
+
+# D.3 Meta Information Collection
+
+To support the corpus-based analysis of each claim, we retrieve relevant literature using the Semantic Scholar API (Allen Institute for AI, 2025).
+
+Since our claims are highly nuanced and involve multiple concepts, directly searching for claims themselves does not yield useful matches based on literature titles and abstracts. To address this, we first perform keyword extraction for each claim. We then use the extracted keywords to query the Semantic Scholar API and retrieve up to 1000 related literature entries for each claim.
+
+# D.4 Filtering and Full-Text Collection
+
+After obtaining the literature metadata, we first filter out entries with missing fields and retain the top 100 most relevant papers based on relevance. We then utilize the provided PDF URLs to download the full-text of the selected literature and convert them into plain text with pdftotext (Palmer, 2024). As a result, we obtain a comprehensive textual literature repository for each claim, ensuring a rich contextual foundation for further analysis.
+
+This structured approach ensures a robust dataset suitable for nuanced claims analysis across the domains.
+
+# D.5 Human Validation of Generated Claims and Assigned Papers
+
+We conducted a human evaluation study for validating 40 total claims—20 on each dataset. We define the following binary criteria for claim validation:
+
+1. Nuanced: Is the claim obviously true or false?   
+2. Relevant: Is the claim relevant to the topic (biomedical/world relations)?   
+3. Corpus-Aligned@k: At least $k$ papers are relevant to the claim within the corpus (this is computed on $k = 5$ and $k = 10$ )
+
+We show the validation results in Table 6, which demonstrates the nuanced nature of the generated claims, their relevancy, and the presence of $k$ papers aligned to each claim.
+
+Table 6: Human validation of claim quality across datasets.   
+
+<table><tr><td>Metric</td><td>World Relations</td><td>Biomedical</td></tr><tr><td>Nuanced</td><td>0.9</td><td>1.0</td></tr><tr><td>Relevant</td><td>1.0</td><td>1.0</td></tr><tr><td>Corpus-Aligned@5</td><td>0.95</td><td>0.8</td></tr><tr><td>Corpus-Aligned@10</td><td>0.65</td><td>0.65</td></tr></table>
+
+# E Computational Efficiency
+
+We specify the components of CLAIMSPECT's framework and their corresponding computational efficiency across the entire pipeline below. We consider the number of nodes within a full aspect hierarchy as $n$ and the total number of segments within the corpus as $S$ . We additionally provide rough time estimates based on an average sample.
+
+- Coarse-Grained Aspect Discovery (Section 3.1.3)
+
+-A single LLM call: $O(1)$
+
+- Aspect-Discriminative Retrieval (Section 3.2)
+
+- Retrieval-Augmented Keyword Enrichment (Section 3.2.1)
+
+* Embedding the segments using the retrieval model takes the most amount of time $(O(S))$ , but this can be computed offline given a knowledge base. Retrieval itself is quite efficient since it is embedding-based, and we use cosine-similarity to determine relevance (an efficient computation, especially in high-dimensional scenarios).
+
+* Enrich each node: $O(N) \to 10$ seconds per node
+
+-Discriminative Segment Ranking (Section 3.2.2)
+
+* We only compute the ranking on the top-100 segments, so this operation's efficiency is constant: $O(1)$
+
+* The target score and distractor score computation scales according to the number of aspects throughout the tree (since their # of associated keywords is constant): $O(N) \rightarrow 6$ seconds for each node
+
+- Iterative Subaspect Discovery (Section 3.3)
+
+- A single prompt per aspect node in hierarchy: $O(N)$
+
+- Classification-Based Perspective Discovery (Section 3.4)
+
+- As mentioned in lines 442-446, "we reframe relevance filtering as a binary search problem" intentionally to optimize the efficiency of this
+
+module. Thus, instead of sequentially determining claim relevancy for each segment, we sort the segments (which have more than 500 characters) and use binary search $(O(\log S))$ to find the boundary of relevance-irrelevance. This leads to $O(S\log S)$ efficiency due to the sorting function $\rightarrow 5$ seconds during runtime, due to Python optimizations.
+
+* Perspective Discovery involves prompting the LLM for each filtered segment's stance: $O(S) \rightarrow 3$ minutes
+
+We specifically use vLLM to optimize our LLM batched generation. To construct a claim with 39 nodes and a max depth of 3, it takes approximately 20 minutes to run on two NVIDIA RTX A6000s. We can see that in total, the core framework operations take 13 minutes and 42 seconds, with the remaining time dedicated to embedding computations (which can be done offline).

paper_markdowns/bamboo-00423.md

@@ -0,0 +1,518 @@
+# Graph of Records: Boosting Retrieval Augmented Generation for Long-context Summarization with Graphs
+
+Haozhen Zhang $^{1*}$ and Tao Feng and Jiaxuan You
+
+University of Illinois at Urbana-Champaign
+
+{haozhenz,taofeng2,jiaxuan}@illinois.edu, $^1$ wazh24@gmail.com
+
+# Abstract
+
+Retrieval-augmented generation (RAG) has revitalized Large Language Models (LLMs) by injecting non-parametric factual knowledge. Compared with long-context LLMs, RAG is considered an effective summarization tool in a more concise and lightweight manner, which can interact with LLMs multiple times using diverse queries to get comprehensive responses. However, the LLM-generated historical responses, which contain potentially insightful information, are largely neglected and discarded by existing approaches, leading to suboptimal results. In this paper, we propose graph of records (GoR), which leverages historical responses generated by LLMs to enhance RAG for long-context global summarization. Inspired by the retrieve-then-generate paradigm of RAG, we construct a graph by establishing an edge between the retrieved text chunks and the corresponding LLM-generated response. To further uncover the intricate correlations between them, GoR features a graph neural network and an elaborately designed BERTScore-based objective for self-supervised model training, enabling seamless supervision signal backpropagation between reference summaries and node embeddings. We comprehensively compare GoR with 12 baselines across four long-context summarization datasets, and the results indicate that our proposed method reaches the best performance (e.g., $15\%$ , $8\%$ , and $19\%$ improvement over retrievers w.r.t. Rouge-L, Rouge-1, and Rouge-2 on the WCEP dataset). Extensive experiments further demonstrate the effectiveness of GoR. Code is available at https://github.com/ulab-uiuc/GoR
+
+# 1 Introduction
+
+Large Language Models (LLMs) have recently achieved remarkable performance across sorts of language modeling tasks (Achiam et al., 2023;
+
+AI@Meta, 2024). Among them, the long-context global summarization task is of great importance, which requires ultra-long context understanding capabilities of LLMs (Li et al., 2024a; Liu et al., 2024b). Current attempts to accomplish this task mainly include long-context LLMs (Touvron et al., 2023; GLM et al., 2024; Li* et al., 2023; Tworkowski et al., 2023) and retrieval-augmented generation (RAG) (Ram et al., 2023; Yu et al., 2023; Trivedi et al., 2022; Jiang et al., 2023b; Asai et al., 2023). In comparison with long-context LLMs that expand their context window to accommodate long-context inputs, RAG performs a cost-effective retrieve-then-generate paradigm and provides a few retrieved short text chunks from a long document to LLMs. In a running RAG system, there are usually a large number of historical user queries and LLM-generated responses for a long document. Nevertheless, these historical responses, which contain informative task-related content, are mostly neglected without sufficient utilization by current RAG approaches.
+
+Unfortunately, utilizing LLM historical responses for long-context global summarization presents two major challenges. (1) Sophisticated yet implicit correlations between historical responses and text. Given a long document, there will inevitably be complicated correlations among plentiful user queries (e.g., logical correlations), which are further inherited by LLM-generated responses and the retrieved text chunks. However, uncovering these correlations is non-trivial since most text embeddings from language models (e.g., SBERT (Reimers and Gurevych, 2019)) or retrievers (Karpukhin et al., 2020) concentrate on semantic similarity, which faces degrading performance in this case. (2) Lack of supervision signal. In contrast with local (e.g., query-based) summarization (Zhong et al., 2021; Wang et al., 2022a) that includes golden reference text as labels, global summarization needs to be considered from the perspec
+
+tive of the long document as a whole and only has global reference summaries, which complicates the direct backpropagation of effective, accurate, and deterministic supervision signals to optimize the model towards a few relevant text chunks.
+
+Based on the above observations, we propose graph of records (GoR), which utilizes and organizes LLM historical responses as a graph of records for enhancing long-context global summarization in RAG. In detail, we first leverage LLMs to simulate some user queries conditioned on arbitrary text chunks in a long document to obtain historical responses under the paradigm of RAG, and an edge is then created between the retrieved text chunks and the LLM-generated response to construct a graph of records. To learn fine-grained correlations among nodes, we employ a graph neural network and reuse the simulated user queries with the corresponding source text chunk as self-supervised training data. Intuitively, we hope the node embeddings can be adaptively learned to reflect the semantic and logical correlations with a given query. Inspired by the wellreceived BERTScore (Zhang et al., 2019) that quantifies the semantic similarity between two paragraphs of text, we rely on it to rank the nodes according to their similarity with the self-supervised label of a given simulated query. In this way, node embeddings can benefit the indirect supervision signal from the self-supervised labels and be flexibly optimized using a contrastive loss and a pair-wise ranking loss based on the node rankings. In the experiments, we adopt four long-context summarization datasets, and the results demonstrate the superiority and effectiveness of our proposed method. For example, we show that GoR outperforms retrievers by $15\%$ , $8\%$ , and $19\%$ w.r.t. Rouge-L, Rouge-1, and Rouge-2, respectively, on the WCEP dataset. We also provide detailed comparisons and insightful analyses through extensive experiments, further showcasing the effectiveness of our approach. Our contributions are summarized as follows:
+
+- We propose graph of records (GoR), which utilizes and organizes LLM-generated historical responses as a graph of records to strengthen RAG for long-context global summarization. We reveal that the fine-grained correlations between LLM historical responses and text chunks from long documents can be uncovered and utilized effectively to improve RAG performance.
+
+- We leverage a graph neural network and design a BERTScore-based objective to optimize node embeddings, which can be adaptively learned in a self-supervised manner to reflect the semantic and complex correlations with input queries. Furthermore, the indirect supervision signal from self-supervised labels is crucial and conducive to the effective optimization of node embeddings.
+
+- We evaluate our proposed method on four long-context summarization datasets, and the results show that GoR outperforms several competitive baselines by a significant margin. Extensive experiments and detailed analysis verify the superiority of GoR.
+
+# 2 Graph of Records
+
+In this section, we first present some necessary backgrounds in Section 2.1. Then, we describe our proposed method sequentially through three sections, i.e., Graph Construction (Section 2.2), BERTScore-based Objective for Self-supervised Training (Section 2.3), and Retrieval from the Graph for Summarization (Section 2.4).
+
+# 2.1 Preliminaries
+
+Retrieval-augmented Generation (RAG) (Ram et al., 2023) can typically be summarized into the following two processes. (1) Retrieval. Give a long document which consists of several split text chunks $\mathbf{C} = \{\mathbf{c_i}\}_{i = 1}^{|C|}$ as retrieval corpus, RAG first employs a retriever (e.g., Contriever (Izacard et al., 2021)) to retrieve $\mathbf{K}$ text chunks that are most relevant to a given query $\mathbf{q}$ based on semantic similarity. The retriever typically embeds the query $\mathbf{q}$ and a text chunk $\mathbf{c}$ from $\mathbf{C}$ using a query encoder $\mathbf{E_q}(\cdot)$ and a context encoder $\mathbf{E_c}(\cdot)$ , respectively, and quantify their semantic similarity by the dot product operation described as $\mathrm{Sim}(\mathbf{q},\mathbf{c}) = \mathbf{E_q}(\mathbf{q})^T\cdot \mathbf{E_c}(\mathbf{c})$ . (2) Generation. The retrieved text chunks are fed into LLMs with the query $\mathbf{q}$ to obtain the final response $\mathbf{r}$ . The whole process can be described as:
+
+$$
+\mathbf {r} = \mathrm {G e n e r a t i o n} (\mathbf {q}, \{\mathbf {c _ {1}}, \dots , \mathbf {c _ {K}} \}),
+$$
+
+$$
+\left\{\mathbf {c} _ {\mathbf {1}}, \dots , \mathbf {c} _ {\mathbf {K}} \right\} = \operatorname {R e t r i e v a l} (\mathbf {q} | \mathbf {C}). \tag {1}
+$$
+
+Graph Neural Networks. Graph Neural Networks (GNNs) (Kipf and Welling, 2016) stand out for their excellent representation learning ability
+
+on graph data. GNNs update node embeddings iteratively by aggregating messages from their neighboring nodes. Generally, the $l$ -th layer of GNNs can be formalized as:
+
+$$
+\begin{array}{l} \mathbf {h} _ {v} ^ {(l)} = \operatorname {A G G} ^ {(l)} \left(\mathbf {h} _ {v} ^ {(l - 1)}, \operatorname {M S G} ^ {(l)} \left(\left\{\mathbf {h} _ {u} ^ {(l - 1)}, \right. \right. \right. \tag {2} \\ u \in N (v) \}; \theta_ {m} ^ {l}); \theta_ {a} ^ {l}) \cdot \\ \end{array}
+$$
+
+where $\mathbf{h}_u^{(l)}\in \mathbb{R}^{d_l}$ is the embedding vector of nodes $u$ in layer $l$ and the dimension is $d_{l}$ $\mathrm{MSG}^{(l)}(\cdot)$ is a message computation function parameterized by $\theta_{m}^{l}$ and $\mathrm{AGG}^{(l)}(\cdot)$ is a message aggregation function parameterized by $\theta_{a}^{l}$ in layer $l$
+
+# 2.2 Graph Construction
+
+In this section, we describe how to organize LLM historical responses into a graph of records by simulating user queries.
+
+Query Simulation. User queries play a very critical role in the design of GoR since LLM historical responses generated by lots of repetitive, nonsense, or meaningless questions are inherently not beneficial for summarization. One solution is to use doc2query (Nogueira et al., 2019) to simulate queries for a long document, but the generated results inevitably suffer from simplicity and rigidity due to the limited text generation capabilities of T5 (Raffel et al., 2020). To this end, we directly turn to LLMs for query simulation with temperature sampling instead of greedy decoding for generating meaningful, insightful, and diverse questions. Specifically, we split a long document into several text chunks C following the standard procedure of RAG and prompt LLMs to generate a query $\mathbf{q}^{\mathrm{s}}$ based on a randomly selected text chunk $\mathbf{c}^{\mathrm{s}}$ . We repeat the above process until a certain number of non-duplicate queries are generated, which are gathered in pairs with the corresponding text chunks to form a corpus $\mathbf{T} = \{(\mathbf{q}_i^{\mathrm{s}},\mathbf{c}_i^{\mathrm{s}})\}_{i = 1}^{|T|}$ for further model training (Section 2.3).
+
+Organize LLM Historical Responses into A Graph. After obtaining simulated queries, we utilize them to perform RAG on the long document. LLM-generated responses during this process include informative and valuable understanding, summarizing, and answering of retrieved text chunks in the long document. Moreover, since there may exist sophisticated correlations among simulated queries, the text chunks and responses can inherit these features and potentially assist in answering a more comprehensive query, especially global sum
+
+marization that needs to be understood from a holistic perspective. Nevertheless, it is a significant challenge to find correlations among complex and massive text at the linguistic level and the embeddings from language models (e.g., SBERT (Reimers and Gurevych, 2019)) or retrievers (Karpukhin et al., 2020) focus on semantic similarity, which also suffers from poor performance in this case. To this end, we propose to break out of this dilemma by organizing these historical responses into a graph.
+
+Inspired by the retrieve-then-generate process of RAG, we can connect the retrieved chunks to the corresponding response generated by LLMs since they are naturally relevant in content. Sequentially, during the i-th round RAG, given the simulated query $\mathbf{q_i^s}$ , we expand the retrieval corpus $\mathbf{C}$ with previously generated responses $\{\mathbf{r}_1,\dots ,\mathbf{r}_{i - 1}\}$ and then build an edge between each retrieved chunk $\mathbf{c_j}\in \{\mathbf{c}_1,\dots ,\mathbf{c_K}\}$ and the newly generated LLM response $\mathbf{r_i}$ , resulting in $\mathbf{K}$ edges constructed in each round. Note that we append the responses generated by each round of RAG to the retrieval corpus because they contain more refined knowledge compared with the text chunks from $\mathbf{C}$ and can help LLMs generate comprehensive responses in a self-evolving manner. Formally, the i-th round RAG on simulated queries $\{\mathbf{q}_i^{\mathbf{s}}\}_{i = 1}^{\left|\mathbf{T}\right|}$ can be described as:
+
+$$
+\mathbf {r} _ {\mathbf {i}} = \operatorname {G e n e r a t i o n} \left(\mathbf {q} _ {\mathbf {i}} ^ {\mathbf {s}}, \left\{\mathbf {c} _ {\mathbf {1}}, \dots , \mathbf {c} _ {\mathbf {K}} \right\}\right),
+$$
+
+$$
+\left\{\mathbf {c} _ {1}, \dots , \mathbf {c} _ {K} \right\} = \operatorname {R e t r i e v a l} \left(\mathbf {q} _ {\mathbf {i}} ^ {\mathbf {s}} \mid \mathbf {C}, \left\{\mathbf {r} _ {1}, \dots , \mathbf {r} _ {\mathbf {i} - 1} \right\}\right). \tag {3}
+$$
+
+In this way, the LLM-generated responses serve as bridges to connect the originally scattered text chunks $\mathbf{C}$ so that the fine-grained and sophisticated correlations among them can be better modeled and explored. Furthermore, we can potentially leverage historical responses generated by LLMs and enhance the quality of future LLM responses.
+
+# 2.3 BERTScore-based Objective for Self-supervised Training
+
+So far, we have constructed a graph using LLM-generated historical responses during RAG given the simulated queries. The key in this section lies in designing a reasonable and effective objective function for model optimization. Considering that some random walk (Grover and Leskovec, 2016) or propagation-based (Zhu and Ghahramani, 2002) algorithms are not differentiable, we turn to graph neural networks (GNNs) for learning node embed
+
+![](images/5c35d82a0ad85ac9cc9f7be99a3781d6f4f848fc5bb2dff459db20700adcc1e1.jpg)  
+Figure 1: GoR model architecture. GoR randomly selects text chunks $\mathbf{c}_i$ from long documents to feed into LLMs for query simulation, which are saved as a self-supervised training corpus $\mathbf{T}$ and further used for graph construction inspired by the retrieve-then-generate paradigm in RAG. For model training, GoR leverages GNNs to obtain node embeddings and calculate their similarities to the query embedding. Finally, GoR features contrastive learning and pair-wise ranking objectives based on the node ranking list $\mathbf{M}_i$ derived from BERTScore calculation.
+
+dings, which are backpropagation-friendly. Intuitively, given a global summarization query $\mathbf{q}$ , our ultimate optimization goal is to make the learned node embeddings adaptively reflect the similarity with the query embedding $\mathbf{E}_{\mathbf{q}}(\mathbf{q})$ by taking the complicated correlations among nodes into account. However, in global summarization tasks, there are essentially no text chunk indices as labels to indicate which nodes are most relevant for a query since it needs to consider the long document as a whole. Another naive solution is to use global reference summaries as labels, but there is a gap in supervision signal backpropagation between them and node embeddings because we still need to find out which nodes are most relevant to them.
+
+Therefore, inspired by BERTScore (Zhang et al., 2019), which measures the semantic similarity between the reference and the generated text, we propose to use it to rank all nodes based on the similarity with reference summaries. By this means, BERTScore fills the gap in the backpropagation so that node embeddings can benefit the indirect supervision signal from the reference summaries. Nevertheless, global reference summaries contain broad information about long documents, making them highly semantically relevant to many nodes, which will confuse the model optimization direction and degrade the performance (we will discuss it in Section 3.5).
+
+Contrastive Loss Driven by BERTScore.
+
+Based on the above observations, we directly reuse the simulated queries $\mathbf{T} = \{(\mathbf{q}_i^{\mathbf{s}},\mathbf{c}_i^{\mathbf{s}})\}_{i = 1}^{|\mathbf{T}|}$ to serve as self-supervised training data, in which the text chunk $\mathbf{c}_i^{\mathbf{s}}$ is highly relevant to the query $\mathbf{q}_i^{\mathbf{s}}$ and has more focused content. Given node embeddings output by the last $L$ -th layer of GNNs, for the $i$ -th query $\mathbf{q}_i^{\mathbf{s}}$ , we rank them according to the similarity with the $i$ -th text chunk $\mathbf{c}_i^{\mathbf{s}}$ and obtain a node embedding ranking list $\mathbf{M}_i$ :
+
+$$
+\mathbf {M} _ {i} = \left[ \mathbf {h} _ {+} ^ {(L)}, \mathbf {h} _ {1} ^ {(L)}, \dots , \mathbf {h} _ {| \mathbf {C} | + | \mathbf {T} |} ^ {(L)} \right], \tag {4}
+$$
+
+where $\mathbf{h}_{+}^{(L)}$ stands for the node embedding with highest similarity. Note that we utilize the context encoder $\mathbf{E}_{\mathbf{c}}(\cdot)$ from the retriever to initialize node embeddings for simplicity. Then, we regard $\mathbf{h}_{+}^{(L)}$ as the positive while the rest in $\mathbf{M}_i$ as negative samples to conduct contrastive learning using InfoNCE (van den Oord et al., 2018), which brings the query $\mathbf{q}_i^{\mathrm{s}}$ and the positive sample $\mathbf{h}_{+}^{(L)}$ closer in the semantic embedding space. We formulate the contrastive training objective as follows:
+
+$$
+s (\mathbf {q}, \mathbf {h}) = \exp \left(\mathbf {E} _ {\mathbf {q}} (\mathbf {q}) ^ {\top} \mathbf {h} / \tau\right), \tag {5}
+$$
+
+$$
+\mathcal {L} _ {\mathrm {C L}} = - \frac {1}{| \mathbf {T} |} \sum_ {j = 1} ^ {| \mathbf {T} |} \log \frac {s \left(\mathbf {q} _ {j} ^ {\mathbf {s}} , \mathbf {h} _ {+} ^ {(L)}\right)}{s \left(\mathbf {q} _ {j} ^ {\mathbf {s}} , \mathbf {h} _ {+} ^ {(L)}\right) + \sum_ {i = 1} ^ {| \mathbf {M} _ {j} - 1 |} s \left(\mathbf {q} _ {j} ^ {\mathbf {s}} , \mathbf {h} _ {i} ^ {(L)}\right)} \tag {6}
+$$
+
+where $\tau$ is the temperature coefficient. Note that in the optimization pipeline of GoR, we conduct minibatch training on the graph level, and each graph is associated with an independent self-supervised training dataset $\mathbf{T}$ . We also leverage in-batch negatives from other graphs since the nodes in them are completely irrelevant content from other long documents (it is not shown in Formula 6 for brevity).
+
+Auxiliary Pair-wise Ranking Loss. In the above-described contrastive loss $\mathcal{L}_{\mathrm{CL}}$ , although we impose constraints on positive and negative samples, the ranking of negative samples themselves is not well utilized. Inspired by LambdaRank (Burges, 2010), we further introduce an auxiliary pair-wise ranking loss on the ranking list $\mathbf{M}_i$ , which can be formulated as:
+
+$$
+\begin{array}{l} \mathcal {L} _ {\mathrm {R A N K}} = \frac {1}{| \mathbf {T} |} \sum_ {k = 1} ^ {| \mathbf {T} |} \sum_ {\mathbf {h} _ {i} ^ {(L)}, \mathbf {h} _ {j} ^ {(L)} \in \mathbf {M} _ {k}} \\ \mathbb {I} _ {\mathrm {r} \left(\mathbf {h} _ {j} ^ {(L)}\right) > \mathrm {r} \left(\mathbf {h} _ {i} ^ {(L)}\right)} \log \left(1 + \frac {s \left(\mathbf {q} _ {k} ^ {\mathbf {s}} , \mathbf {h} _ {j} ^ {(L)}\right)}{s \left(\mathbf {q} _ {k} ^ {\mathbf {s}} , \mathbf {h} _ {i} ^ {(L)}\right)}\right), \tag {7} \\ \end{array}
+$$
+
+where $\mathrm{r}(\cdot)$ denotes the ranking index (e.g., $\mathrm{r}(\mathbf{h}_{+}^{(L)}) < \mathrm{r}(\mathbf{h}_{1}^{(L)})$ ). Given $\mathbf{h}_{i}^{(L)}, \mathbf{h}_{j}^{(L)} \in \mathbf{M}_{k}$ that satisfies $\mathrm{r}(\mathbf{h}_{j}^{(L)}) > \mathrm{r}(\mathbf{h}_{i}^{(L)})$ , the pair-wise ranking loss will explicitly optimize in the direction of $\mathbf{E}_{\mathbf{q}}(\mathbf{q}_{k}^{\mathbf{s}})^{\top} \mathbf{h}_{j}^{(L)} < \mathbf{E}_{\mathbf{q}}(\mathbf{q}_{k}^{\mathbf{s}})^{\top} \mathbf{h}_{i}^{(L)}$ , thus imposing stricter constraints to the pair-wise ranking.
+
+Overall Training Objective. To sum up, the overall training objective can be formulated as:
+
+$$
+\mathcal {L} = \mathcal {L} _ {\mathrm {C L}} + \alpha \cdot \mathcal {L} _ {\mathrm {R A N K}}. \tag {8}
+$$
+
+where $\alpha \in [0,1]$ is a hyper-parameter. It is worth noting that GoR's training costs are lightweight since the only trainable module is GNNs, and no human-crafted labels are needed.
+
+# 2.4 Retrieval from the Graph for Summarization
+
+During the graph construction phase, we have already obtained a graph consisting of nodes that represent both the text chunks $\mathbf{c}$ from the long document and the responses $\mathbf{r}$ generated by LLMs during the RAG process. These nodes collectively form the retrieval corpus used by GoR during inference. After GNN training, each node is associated with a learned embedding vector that captures not only its semantic content but also its contextual
+
+and structural relationships with other nodes in the graph. These learned embeddings replace the original text embeddings produced by conventional retrievers (e.g., Contriever (Izacard et al., 2021)), enabling the model to incorporate richer relational information among document chunks, which is especially beneficial for the summarization task. During inference for global summarization, the process begins with encoding the query into an embedding using the same retriever. We then compute the similarity (via inner product) between the query embedding and all node embeddings in the graph. The top-K most relevant nodes, comprising both document chunks and LLM-generated responses, are retrieved based on this similarity score. These selected nodes, along with the query, are then fed into the LLM to generate the final summary.
+
+Overall, the retrieval process in GoR mirrors that of standard dense retrievers, with the key distinction being the use of graph-enhanced node embeddings and the inclusion of generated responses in the retrieval corpus. This approach allows GoR to better exploit both content and structural cues for improved summarization performance.
+
+# 3 Experiments
+
+# 3.1 Experimental Setup
+
+Datasets. We evaluate our proposed method on four long-context summarization datasets, i.e., AcademicEval (Feng et al., 2024), QMSum (Zhong et al., 2021), WCEP (Gholipour Ghalandari et al., 2020), and BookSum (Krysciński et al., 2021). Among them, AcademicEval collects scientific papers from arXiv for abstract writing, given the long inputs of its main body. QMSum is a query-based summarization dataset, and we only use "general queries" for evaluating global summarization. WCEP is a multi-document summarization dataset about news events, while BookSum features long-form narrative summarization. For metrics, we adopt Rouge-1 (R-1), Rouge-2 (R-2), and Rouge-L (R-L) (Lin, 2004) to assess the text alignment between the reference summaries and the predicted content generated by GoR.
+
+Implementation Details. Following the standard procedure of RAG, we adopt TokenTextSplitter from LangChain to split each long document into text chunks. Each chunk has a size of 256, and the chunk overlapping is 32. We generate 30 queries for each long document using Mixtral-8x7B-Instruct-v0.1 (Jiang et al., 2024), and the
+
+Table 1: Experimental results on QMSum, AcademicEval, WCEP, and BookSum datasets over long-context global summarization tasks w.r.t. Rouge-L (R-L), Rouge-1 (R-1), and Rouge-2 (R-2). Note that the average LLM input token length of GoR and retriever-based baselines is $6 \times 256$ ( $\approx 1.5\mathrm{K}$ ). (BOLD indicates the best score)   
+
+<table><tr><td rowspan="2">Model</td><td colspan="3">QMSum</td><td colspan="3">AcademicEval</td><td colspan="3">WCEP</td><td colspan="3">BookSum</td></tr><tr><td>R-L</td><td>R-1</td><td>R-2</td><td>R-L</td><td>R-1</td><td>R-2</td><td>R-L</td><td>R-1</td><td>R-2</td><td>R-L</td><td>R-1</td><td>R-2</td></tr><tr><td>Node2Vec</td><td>18.5</td><td>31.8</td><td>6.3</td><td>19.3</td><td>38.3</td><td>10.6</td><td>13.9</td><td>20.1</td><td>6.3</td><td>13.6</td><td>27.4</td><td>4.6</td></tr><tr><td>BM25</td><td>18.4</td><td>32.1</td><td>6.1</td><td>20.4</td><td>39.6</td><td>11.3</td><td>15.5</td><td>22.6</td><td>7.3</td><td>13.7</td><td>26.7</td><td>4.9</td></tr><tr><td>TF-IDF</td><td>18.3</td><td>31.2</td><td>6.3</td><td>19.5</td><td>38.0</td><td>10.6</td><td>15.3</td><td>22.3</td><td>7.3</td><td>13.6</td><td>26.6</td><td>4.9</td></tr><tr><td>Contriever</td><td>19.1</td><td>32.7</td><td>7.7</td><td>23.6</td><td>44.8</td><td>16.0</td><td>15.7</td><td>23.5</td><td>7.7</td><td>14.4</td><td>29.8</td><td>5.5</td></tr><tr><td>DPR</td><td>18.6</td><td>32.1</td><td>6.7</td><td>20.9</td><td>41.4</td><td>13.2</td><td>15.6</td><td>22.5</td><td>7.5</td><td>13.8</td><td>27.1</td><td>4.8</td></tr><tr><td>Dragon</td><td>19.2</td><td>33.5</td><td>7.7</td><td>23.5</td><td>43.8</td><td>15.1</td><td>14.6</td><td>21.8</td><td>6.8</td><td>13.7</td><td>27.2</td><td>4.8</td></tr><tr><td>SBERT</td><td>19.0</td><td>33.0</td><td>7.4</td><td>23.4</td><td>45.2</td><td>15.8</td><td>13.7</td><td>20.5</td><td>5.5</td><td>14.4</td><td>29.5</td><td>5.4</td></tr><tr><td>BM25+DPR</td><td>18.3</td><td>31.8</td><td>6.6</td><td>19.9</td><td>39.0</td><td>10.8</td><td>15.7</td><td>22.1</td><td>7.6</td><td>14.1</td><td>28.9</td><td>5.4</td></tr><tr><td>Gemma-8K</td><td>19.8</td><td>33.5</td><td>7.3</td><td>21.9</td><td>42.0</td><td>12.9</td><td>15.6</td><td>21.9</td><td>7.7</td><td>12.8</td><td>23.4</td><td>4.2</td></tr><tr><td>Mistral-8K</td><td>19.6</td><td>31.2</td><td>7.2</td><td>21.6</td><td>41.6</td><td>13.1</td><td>16.7</td><td>24.2</td><td>8.8</td><td>13.5</td><td>26.2</td><td>5.3</td></tr><tr><td>Full Context</td><td>19.4</td><td>33.1</td><td>6.8</td><td>21.5</td><td>41.1</td><td>12.5</td><td>14.4</td><td>21.0</td><td>7.1</td><td>14.4</td><td>28.9</td><td>5.9</td></tr><tr><td>Thought-R</td><td>19.0</td><td>33.9</td><td>7.6</td><td>22.0</td><td>42.6</td><td>13.2</td><td>15.2</td><td>22.4</td><td>7.4</td><td>14.2</td><td>29.5</td><td>5.7</td></tr><tr><td>GoR (Ours)</td><td>19.8</td><td>34.5</td><td>7.8</td><td>24.7</td><td>46.5</td><td>17.3</td><td>18.1</td><td>25.4</td><td>9.2</td><td>14.9</td><td>31.5</td><td>6.6</td></tr></table>
+
+temperature coefficient is set to 0.5 by default in the query simulation stage. For RAG, we use Contriever (Izacard et al., 2021) for query and document embedding and retrieve 6 text chunks by default, which are fed into LLaMA-2-7b-chat (Touvron et al., 2023) with greedy decoding to generate predicted summaries. In the training stage, we initialize the graph neural network as a two-layer graph attention network (GAT) (Veličković et al., 2017), with a 768-dim hidden dimension following the default setting of most retrievers.
+
+Baselines. To have a comprehensive evaluation, we compare our proposed GoR with dozens of baselines, including (1) Random Walk based Node Embedding (i.e., Node2Vec (Grover and Leskovec, 2016)), (2) Sparse Retriever (i.e., BM25 (Robertson et al., 2009) and TF-IDF (Ramos et al., 2003)), (3) Dense Retriever (i.e., Contriever (Izacard et al., 2021), DPR (Karpukhin et al., 2020), Dragon (Lin et al., 2023), and Sentence-BERT (SBERT) (Reimers and Gurevych, 2019), (4) Hybrid Retriever (i.e., BM25+DPR with Reciprocal Rerank Fusion), (5) Long-context LLMs (i.e., Gemma-8K (Team et al., 2024) and Mistral8K (Jiang et al., 2023a)), (6) Full Context (i.e., feeds all inputs to LLMs for summary generation), and (7) Thought Retriever (Thought-R) (Feng
+
+et al., 2024). Appendix A elucidates more details.
+
+# 3.2 Main Results
+
+We conduct comprehensive experiments on QMSum, AcademicEval, WCEP, and BookSum datasets compared with dozens of baselines to evaluate the long-context global summarization capabilities of our proposed method. The results are shown in Table 1.
+
+GoR consistently outperforms retriever-based methods. From Table 1, our proposed GoR beats sparse retrievers, dense retrievers, and hybrid retrievers in every aspect. Thanks to the constructed graph, which integrates text chunks from long documents and LLM historical responses into a whole, node embeddings can better reflect the complicated correlations with given queries, thus significantly improving the retrieval performance of GoR. Moreover, the informative content of historical responses may also enhance the summarization task.
+
+GoR shows superiority over long-context LLMs. We compare Gemma-8K and Mistral-8K with a longer context window to accommodate long-context inputs. However, longer inputs may contain minor information, and long-context LLMs struggle with this situation. In contrast, GoR can effectively differentiate key and topic-related content in long texts using learned node embeddings and achieve better results with shorter input lengths.
+
+Additional Findings. (1) Node2Vec produces unsatisfactory results, and the node embeddings
+
+Table 2: LLM Evaluation w.r.t. overall win rates on the QMSum, AcademicEval, WCEP, and BookSum datasets. Note that there are very few test samples that contain some security-sensitive information that causes DeepSeek-R1 to be unable to return valid evaluation information. We directly skip these samples.   
+
+<table><tr><td colspan="2">QMSum</td><td colspan="2">AcademicEval</td><td colspan="2">WCEP</td><td colspan="2">BookSum</td></tr><tr><td>BM25</td><td>GoR</td><td>BM25</td><td>GoR</td><td>BM25</td><td>GoR</td><td>BM25</td><td>GoR</td></tr><tr><td>38.7%</td><td>61.3%</td><td>30.0%</td><td>70.0%</td><td>70.4%</td><td>29.6%</td><td>35.5%</td><td>64.5%</td></tr><tr><td>TF-IDF</td><td>GoR</td><td>TF-IDF</td><td>GoR</td><td>TF-IDF</td><td>GoR</td><td>TF-IDF</td><td>GoR</td></tr><tr><td>40.6%</td><td>59.4%</td><td>33.3%</td><td>66.7%</td><td>66.7%</td><td>33.3%</td><td>41.9%</td><td>58.1%</td></tr><tr><td>Contriever</td><td>GoR</td><td>Contriever</td><td>GoR</td><td>Contriever</td><td>GoR</td><td>Contriever</td><td>GoR</td></tr><tr><td>51.6%</td><td>48.4%</td><td>53.3%</td><td>46.7%</td><td>48.1%</td><td>51.9%</td><td>54.8%</td><td>45.2%</td></tr><tr><td>Gemma-8K</td><td>GoR</td><td>Gemma-8K</td><td>GoR</td><td>Gemma-8K</td><td>GoR</td><td>Gemma-8K</td><td>GoR</td></tr><tr><td>6.5%</td><td>93.5%</td><td>16.7%</td><td>83.3%</td><td>37.0%</td><td>63.0%</td><td>12.9%</td><td>87.1%</td></tr><tr><td>Mistral-8K</td><td>GoR</td><td>Mistral-8K</td><td>GoR</td><td>Mistral-8K</td><td>GoR</td><td>Mistral-8K</td><td>GoR</td></tr><tr><td>12.9%</td><td>87.1%</td><td>40.0%</td><td>60.0%</td><td>37.0%</td><td>63.0%</td><td>22.6%</td><td>77.4%</td></tr></table>
+
+cannot be optimized effectively since it is based on a non-differentiable algorithm. (2) Although Thought Retriever demonstrates competitive results, it is still inferior to GoR due to the lack of exploration of the correlations between retrieved text chunks and LLM-generated responses. (3) Since the context window length limit of LLMs is exceeded, "Full Context" truncates the long-context input, thus losing some information that may be important for global summarization, resulting in suboptimal results.
+
+Overall, GoR achieves the best results compared with various baselines, demonstrating the effectiveness of our proposed method.
+
+# 3.3 LLM Evaluation
+
+To enable a more comprehensive automatic evaluation of GoR, inspired by LLM-as-a-Judge (Gu et al., 2024), we adopt DeepSeek-R1 (Guo et al., 2025) to assess the summaries generated by GoR and competitive baselines. Following (Edge et al., 2024) and (Guo et al., 2024), we evaluate from three perspectives: comprehensiveness, diversity, and empowerment. The LLM is instructed to provide an overall judgment based on these criteria to determine the better summary.
+
+To reduce evaluation costs, we select representative and strong baselines for LLM evaluation on the QMSum, AcademicEval, WCEP, and BookSum datasets. Table 2 reports the overall win rates, i.e., the proportion of summaries judged better under pairwise comparison. Evaluation prompts are provided in Appendix D.
+
+From Table 2, we observe the following. (1) GoR consistently outperforms other methods across all datasets, demonstrating stronger com
+
+prehensiveness, diversity, and informativeness. (2) Contriever performs comparably, with results close to GoR. (3) Long-context LLMs like Gemma-8K and Mistral-8K fall significantly behind, suggesting that GoR's graph-based retrieval yields more relevant and refined content, especially when input length is limited.
+
+In summary, GoR delivers superior performance in LLM evaluation compared to other baselines.
+
+# 3.4 Ablation Study
+
+To investigate how each component of GoR contributes to its performance, we conduct an ablation experiment, and the results are shown in Table 3.
+
+From Table 3, we can draw several conclusions. (1) Directly using the text embeddings from the retriever without training leads to degraded performance (i.e., w/o train), highlighting the effectiveness of the learned node embeddings. (2) Both the contrastive loss $\mathcal{L}_{\mathrm{CL}}$ and pair-wise ranking loss $\mathcal{L}_{\mathrm{RANK}}$ significantly improve performance. The pair-wise ranking loss imposes stricter ranking constraints on node embeddings, making effective use of the indirect supervision signal from the self-supervised reference summaries. (3) In-batch negatives are crucial to the performance of contrastive learning. Removing in-batch negatives (i.e., w/o in-b neg) leads to a significant drop in results. (4) Compared with self-supervised training, we utilize global reference summaries as labels to conduct supervised training (i.e., w/ sup), and the results are significantly worse than the self-supervised setting. We will further discuss it in Section 3.5.
+
+In general, GoR's reasonable module design enables it to achieve superior performance.
+
+Table 3: Ablation study on the WCEP and BookSum datasets w.r.t. R-L, R-1, and R-2.   
+
+<table><tr><td rowspan="2">Variant</td><td colspan="3">WCEP</td><td colspan="3">BookSum</td></tr><tr><td>R-L</td><td>R-1</td><td>R-2</td><td>R-L</td><td>R-1</td><td>R-2</td></tr><tr><td>w/o train</td><td>15.3</td><td>22.4</td><td>7.4</td><td>13.7</td><td>27.7</td><td>4.7</td></tr><tr><td>w/o \(\mathcal{L}_{\text{CL}}\)</td><td>14.7</td><td>21.9</td><td>7.2</td><td>14.1</td><td>28.8</td><td>5.1</td></tr><tr><td>w/o \(\mathcal{L}_{\text{RANK}}\)</td><td>16.6</td><td>24.2</td><td>8.2</td><td>14.0</td><td>28.0</td><td>4.9</td></tr><tr><td>w/o in-b neg</td><td>17.2</td><td>24.9</td><td>8.8</td><td>13.3</td><td>26.3</td><td>5.2</td></tr><tr><td>w/ sup</td><td>15.5</td><td>22.8</td><td>7.3</td><td>13.8</td><td>29.0</td><td>5.2</td></tr><tr><td>GoR</td><td>18.1</td><td>25.4</td><td>9.2</td><td>14.9</td><td>31.5</td><td>6.6</td></tr></table>
+
+# 3.5 Discussions
+
+Impact of the Number of Simulated Queries During Training. Query Simulation is a crucial stage in our method design, and we will examine how the number of simulated queries used during training affects learning performance. In particular, we explore this effect by gradually increasing the number of simulated queries used in training. We present the results in Figure 2. Overall, R-L shows an upward trend as the number of simulated queries increases. Nevertheless, since fewer queries cover less relevant content from long documents, the curves of each dataset have some fluctuations, indicating the occurrence of underfitting.
+
+In general, 30 simulated queries can optimize the model well across these four datasets, which indicates that our proposed GoR is cost-effective. Nevertheless, increasing the number of simulated queries may still potentially further improve the performance of the model. Due to budget constraints, we will leave this for future work.
+
+![](images/5b595c56774080b686eb6c015154805d0a413943ce14b3c4a9315fbb329a9049.jpg)  
+Figure 2: Impact of the number of simulated queries during training w.r.t. R-L. We show the results on the QMSum and WCEP datasets.
+
+Supervised Training on Global Summarization Queries. To dive deeper into the differences between self-supervised and supervised training, we carry out additional experiments using global reference summaries. Specifically, we utilize global summarization queries and reference summaries to serve as a training corpus under the
+
+supervised setting. As there is only one global summarization query for each long document, we replicate it multiple times to match the quantity of self-supervised training data, thus eliminating the impact of the quantity difference. We present the results on the BookSum dataset in Figure 3, and the Entropy denotes the entropy of the similarity distribution between queries and node embeddings.
+
+From Figure 3, it is evident that in the self-supervised setting, the loss is consistently lower than in the supervised setting. This suggests that the global reference summaries are highly correlated with many nodes, causing most nodes to exhibit a high semantic similarity with the global query. As a result, this confuses the model's optimization direction. Additionally, the entropy curve shows that the entropy in the supervised setting is consistently higher than in the self-supervised setting, indicating that the model struggles to select the most similar node. In contrast, the self-supervised label, derived from a specific part of a long document, contains more focused content, effectively guiding the model's optimization.
+
+![](images/9eddabbcc393c135ae7480e89a3e62e3bf5358e32714d40c3b26c3fd1758a139.jpg)
+
+![](images/fbf222247dbc1f63d6fea21521a52c7e90fafec4b4eddb3ef8245a8c2f50b1e0.jpg)  
+Figure 3: Differences between self-supervised and supervised training w.r.t. loss and entropy on the BookSum dataset.
+
+Inference Efficiency Analysis. To investigate the inference efficiency of GoR, we conduct extensive experiments on the WCEP dataset and present the results w.r.t. the inference time per query in Table 4. Note that since the LLM used in our experiment is consistent, we ignore the inference time brought by the LLM itself.
+
+From Table 4, we can draw the following conclusion. (1) Since GoR's only trainable module is GNN, GoR's inference efficiency is very high, and almost no additional noticeable latency is introduced. (2) Although GoR's inference time is longer than some baselines, it only increases by a few hundred milliseconds. Considering the significant performance improvement brought by GoR in Table 1, this tiny time overhead is almost negligible in practical applications.
+
+Table 4: Inference efficiency analysis w.r.t. inference time per query on the WCEP dataset.   
+
+<table><tr><td>Baselines</td><td>Node2Vec</td><td>BM25</td><td>Contriever</td><td>SBERT</td><td>BM25+DPR</td><td>Thought-R</td><td>GoR (ours)</td></tr><tr><td>Inference Time (s)</td><td>9.4</td><td>0.02</td><td>0.20</td><td>0.01</td><td>0.04</td><td>0.3</td><td>0.58</td></tr></table>
+
+# 4 Related Work
+
+Long-context Summarization using LLMs. In recent years, LLMs have shown impressive capabilities in long-context modeling (Achiam et al., 2023; AI@Meta, 2024; Team et al., 2024; Jiang et al., 2024). Summarizing lengthy documents with LLMs primarily involves two approaches: retrieval-augmented generation (RAG) (Ram et al., 2023; Yu et al., 2023) and long-context LLMs (GLM et al., 2024; Li* et al., 2023; Tworkowski et al., 2023). Long-context LLMs feature a large context window length to accommodate long-context inputs. However, they may suffer from severe performance degradation when accessing some local key details in the middle of long contexts (Liu et al., 2024b). Conversely, RAG emerges as a promising approach for cost-effective long-context summarization. By equipping with a retriever (Karpukhin et al., 2020; Robertson et al., 2009), RAG can first perform a relevance search based on user queries and then feed the retrieved text into LLMs for summary. For a recent example, GraphRAG (Edge et al., 2024) conducts query-focused summarization by setting up a graph index and detecting graph communities for summary generation.
+
+Nevertheless, most current RAG approaches still focus on enhancing LLMs' reasoning and question-answering capabilities, which only require retrieving locally relevant information (Trivedi et al., 2022; Jiang et al., 2023b; Asai et al., 2023; Li et al., 2023; Zheng et al., 2023). In comparison, our proposed method stands out from these methods by focusing on LLMs' global summarization capability of long-context inputs.
+
+Graph-assisted Retrieval-augmented Language Models. As one of the effective structures for modeling data relations, graphs have recently been used to enhance the performance of retrieval-augmented language models on various QA tasks. EtD (Liu et al., 2024a) features a graph neural network (GNN) to traverse a knowledge graph hop by hop to discover more relevant knowledge, thus enhancing LLM generation quality. GNN-RAG (Mavromatis and Karypis, 2024) learns to rea
+
+son over graphs using GNNs, and retrieves answer candidates for a given question. PG-RAG (Liang et al., 2024) constructs pseudo-graphs with a retrieval indexer by prompting LLMs to organize document knowledge in a self-learning manner. G-RAG (Dong et al., 2024) proposes to rerank documents by learning graph representation on abstract meaning representation graphs, while GNN-Ret (Li et al., 2024b) refines semantic distances between documents and queries by modeling relationships among related passages. ToG (Sun et al., 2023) and KGP (Wang et al., 2024) treat LLMs as agents to traverse and reason over knowledge graphs in an iterative way, while RoG (Luo et al., 2023) first generates plans for retrieval and then conducts reasoning. G-Retriever (He et al., 2024) transforms retrieved knowledge subgraphs into graph embeddings by training a graph encoder and textualizes subgraphs to serve as inputs of LLMs.
+
+Different from the above, GraphRAG (Edge et al., 2024) sets up a graph index for query-focused summarization, which aligns more closely with our approach. Compared with GraphRAG, which is time-consuming and suffers from huge computational costs, GoR is lightweight and only draws on a few LLM historical responses with efficient training to achieve competitive performance.
+
+# 5 Conclusion
+
+In this work, we introduce a method named graph of records (GoR) to improve long-context global summarization in retrieval-augmented generation by utilizing LLM-generated historical responses. Intuitively, we establish connections between text chunks retrieved from long documents and LLM-generated historical responses to create a graph of records. To uncover complex correlations between these connections, we use a graph neural network and develop a BERTScore-based objective for self-supervised training, enabling seamless supervision signal backpropagation between self-supervised reference summaries and node embeddings. Our experiments on four long-context summarization datasets show that GoR significantly outperforms various baselines, demonstrating its effectiveness.
+
+# 6 Limitations
+
+Despite the superiority of our proposed method, GoR has some limitations. (1) Due to a limited budget, we only simulate and generate a small number of user queries, which may cause a bottleneck in further model optimization. (2) The simulated queries may not accurately reflect the real-world distribution, as they do not account for the possibility of users asking many meaningless questions. Therefore, a filtering process may be necessary, which we leave for future work.
+
+To promote sharing and communication in the academic community, we also share some insights about simulated queries here. Given the powerful evaluation capabilities of LLMs, many works utilize LLM-as-a-Judge and treat LLMs as evaluators. Intuitively, in practical applications, we can first use some simple rule-based filtering strategies to preliminarily screen the meaningless questions raised by users, and then use LLM-as-a-Judge to evaluate the remaining questions and judge their quality from multiple dimensions (such as diversity, complexity, inspiration, etc.), which not only takes into account performance but also ensures a certain efficiency in real multi-user scenarios.
+
+# Acknowledgments
+
+We sincerely appreciate the support from Amazon grant funding project #120359, "GRAG: Enhance RAG Applications with Graph-structured Knowledge", and Meta gift funding project "PERM: Toward Parameter Efficient Foundation Models for Recommenders"
+
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+Yu Wang, Nedim Lipka, Ryan A Rossi, Alexa Siu, Ruiyi Zhang, and Tyler Derr. 2024. Knowledge graph prompting for multi-document question answering. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pages 19206-19214.   
+Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, Fei Xia, Ed Chi, Quoc V Le, Denny Zhou, et al. 2022. Chain-of-thought prompting elicits reasoning in large language models. Advances in neural information processing systems, 35:24824-24837.   
+Felix Wu, Amauri Souza, Tianyi Zhang, Christopher Fifty, Tao Yu, and Kilian Weinberger. 2019. Simplifying graph convolutional networks. In International Conference on Machine Learning, pages 6861-6871.   
+Keyulu Xu, Weihua Hu, Jure Leskovec, and Stefanie Jegelka. 2019. How powerful are graph neural networks? In International Conference on Learning Representations.   
+Ling Yang, Zhaochen Yu, Tianjun Zhang, Shiyi Cao, Minkai Xu, Wentao Zhang, Joseph E Gonzalez, and Bin Cui. 2024. Buffer of thoughts: Thought-augmented reasoning with large language models. arXiv preprint arXiv:2406.04271.   
+Shunyu Yao, Dian Yu, Jeffrey Zhao, Izhak Shafran, Tom Griffiths, Yuan Cao, and Karthik Narasimhan. 2024. Tree of thoughts: Deliberate problem solving with large language models. Advances in Neural Information Processing Systems, 36.   
+Zichun Yu, Chenyan Xiong, Shi Yu, and Zhiyuan Liu. 2023. Augmentation-adapted retriever improves generalization of language models as generic plug-in. arXiv preprint arXiv:2305.17331.   
+Tianyi Zhang, Varsha Kishore, Felix Wu, Kilian Q Weinberger, and Yoav Artzi. 2019. Bertscore: Evaluating text generation with bert. arXiv preprint arXiv:1904.09675.   
+Huaixiu Steven Zheng, Swaroop Mishra, Xinyun Chen, Heng-Tze Cheng, Ed H Chi, Quoc V Le, and Denny Zhou. 2023. Take a step back: Evoking reasoning via abstraction in large language models. arXiv preprint arXiv:2310.06117.
+
+Ming Zhong, Da Yin, Tao Yu, Ahmad Zaidi, Mutethia Mutuma, Rahul Jha, Ahmed Hassan Awadallah, Asli Celikyilmaz, Yang Liu, Xipeng Qiu, et al. 2021. Qsum: A new benchmark for query-based multi-domain meeting summarization. arXiv preprint arXiv:2104.05938.   
+Xiaojin Zhu and Zoubin Ghahramani. 2002. Learning from labeled and unlabeled data with label propagation. ProQuest number: information to all users.
+
+# A Experimental Details
+
+# A.1 Dataset
+
+We present dataset statistics in Table 5. Due to the limited budget, we randomly select training and test samples for the training and test set and calculate the average input and output token lengths using the LLaMA-2 tokenizer (Touvron et al., 2023) (samples with short input lengths are filtered out).
+
+We evaluate our proposed method on four longcontext summarization datasets, i.e., AcademicEval (Feng et al., 2024), QMSum (Zhong et al., 2021), WCEP (Gholipour Ghalandari et al., 2020), and BookSum (Krysciński et al., 2021).
+
+- QMSum (Zhong et al., 2021). QMSum is a query-based summarization dataset that features lengthy meeting transcripts, specific queries, and general queries. Specific queries focus on query-based summarization, and general queries are questions that summarize the entire meeting transcript, such as "Summarize the whole meeting." We only use "general queries" for evaluating global summarization.   
+- AcademicEval (Feng et al., 2024). AcademicEval collects scientific papers from arXiv for abstract and related work writing. We use the abstract writing subset, which provides the main body of a paper as input and generates the predicted abstract.   
+- WCEP (Gholipour Ghalandari et al., 2020). WCEP is a multi-document summarization dataset about news events, which requires comprehensive consideration of the contents of multiple documents.   
+- BookSum (Krysciński et al., 2021). BookSum features long-form narrative summarization, which covers source documents from the literature domain and includes highly abstractive human-written summaries.
+
+# A.2 Baselines
+
+We present detailed descriptions of adopted baselines.
+
+- Node2Vec (Grover and Leskovec, 2016). Node2Vec generates node embeddings for graphs by simulating biased random walks to capture both local and global structural properties of nodes.
+
+- BM25 (Robertson et al., 2009), TF-IDF (Ramos et al., 2003). BM25 ranks documents based on term frequency, inverse document frequency, and document length normalization, while TF-IDF evaluates the importance of a term in a document relative to a corpus by combining term frequency and inverse document frequency.   
+- Contriever (Izacard et al., 2021), DPR (Karpukhin et al., 2020), Dragon (Lin et al., 2023), SBERT (Reimers and Gurevych, 2019). Contriever is a self-supervised dense retriever that learns unsupervised document embeddings for information retrieval, DPR (Dense Passage Retriever) is a bi-encoder model that retrieves relevant passages by training on question-passage pairs, Dragon is a dense retrieval model optimized through diverse augmentation for generalizable dense retrieval, and SBERT (Sentence-BERT) is a modification of BERT that generates semantically meaningful sentence embeddings for tasks like similarity and clustering using a siamese network structure.   
+- BM25+DPR. BM25+DPR with Reciprocal Rerank Fusion is a hybrid retrieval method that combines the strengths of BM25's lexical matching and DPR's dense embeddings by reranking results from both models using a reciprocal rank fusion strategy to improve retrieval accuracy.   
+- Gemma-8K (Team et al., 2024), Mistral-8K (Jiang et al., 2023a). Gemma-8K and Mistral-8K are LLMs with relatively long context window lengths.   
+- Full Context. We feed all inputs to LLMs for summary generation. If the input length exceeds the context window limit, we randomly sample continuous text spans of maximum length multiple times to feed into LLMs and calculate the average result.   
+- Thought-R (Feng et al., 2024). Thought Retriever (Thought-R) generates thoughts for a series of simulated queries and appends them to the retrieval corpus as high-level knowledge.
+
+Table 5: Dataset statistics   
+
+<table><tr><td>Dataset</td><td>#Train</td><td>#Test</td><td>Average Input Token Length</td><td>Average Output Token Length</td></tr><tr><td>QMSum (Zhong et al., 2021)</td><td>162</td><td>30</td><td>17K</td><td>0.1K</td></tr><tr><td>AcademicEval (Feng et al., 2024)</td><td>400</td><td>30</td><td>13K</td><td>0.3K</td></tr><tr><td>WCEP (Gholipour Ghalandari et al., 2020)</td><td>400</td><td>30</td><td>11K</td><td>0.05K</td></tr><tr><td>BookSum (KrySciński et al., 2021)</td><td>400</td><td>30</td><td>16K</td><td>1K</td></tr></table>
+
+# A.3 Additional Explanation on Training Objective
+
+Given a graph that consists of document chunks and response nodes, we expect that the learned node embeddings $\mathbf{h}_v^{(L)}$ can adaptively reflect the semantic similarity to a given query $\mathbf{q}$ . In other words, we expect that we can select the node $\mathbf{v}$ with the largest semantic similarity to $\mathbf{q}$ according to the formula $\mathrm{Sim}(\mathbf{q},\mathbf{v}) = \mathbf{E}_{\mathbf{q}}(\mathbf{q})^T\cdot \mathbf{h}_v^{(L)}$ . To this end, we need to find out which node has the highest semantic similarity with $\mathbf{q}$ and use this as a supervision signal for model optimization. Therefore, we utilize BERTScore (Zhang et al., 2019) to obtain a node ranking list $\mathbf{M}_i$ , which exactly serves as supervision signals.
+
+$$
+\mathbf {M} _ {i} = \left[ \mathbf {h} _ {+} ^ {(L)}, \mathbf {h} _ {1} ^ {(L)}, \dots , \mathbf {h} _ {| \mathbf {C} | + | \mathbf {T} |} ^ {(L)} \right] \tag {9}
+$$
+
+For contrastive loss in Equation 6, we regard $\mathbf{h}_{+}^{(L)}$ as the positive and $[\mathbf{h}_1^{(L)},\dots ,\mathbf{h}_{|\mathbf{C}| + |\mathbf{T}|}^{(L)}]$ as the negatives to conduct contrastive learning (van den Oord et al., 2018). For a given query $\mathbf{q}$ , the contrastive learning objective will bring $\mathbf{E}_{\mathbf{q}}(\mathbf{q})$ and $\mathbf{h}_{+}^{(L)}$ closer in the semantic embedding space while increasing the distance between $\mathbf{E}_{\mathbf{q}}(\mathbf{q})$ and $[\mathbf{h}_1^{(L)},\dots ,\mathbf{h}_{|\mathbf{C}| + |\mathbf{T}|}^{(L)}]$ (the symbols are simplified here for convenience of description).
+
+Similarly, in Equation 7, we expect to impose a stricter constraint on the learned node embedding based on the node ranking list $\mathbf{M}_i$ . Although Equation 6 shortens the semantic distance between $\mathbf{E}_{\mathbf{q}}(\mathbf{q})$ and $\mathbf{h}_+^{(L)}$ , it does not take into account the relative ranking between negative samples. For example, the semantic similarity between $\mathbf{E}_{\mathbf{q}}(\mathbf{q})$ and $\mathbf{h}_1^{(L)}$ is higher than that between $\mathbf{h}_2^{(L)}$ . Formally, given $\mathbf{h}_i^{(L)}$ , $\mathbf{h}_j^{(L)} \in \mathbf{M}_i$ that satisfies $\mathrm{rank}(\mathbf{h}_j^{(L)}) > \mathrm{rank}(\mathbf{h}_i^{(L)})$ , Equation 7 will explicitly optimize in the direction of $\mathbf{E}_{\mathbf{q}}(\mathbf{q})^\top \mathbf{h}_j^{(L)} < \mathbf{E}_{\mathbf{q}}(\mathbf{q})^\top \mathbf{h}_i^{(L)}$ , thus imposing stricter constraints to the pair-wise ranking.
+
+# A.4 Additional Implementation Details
+
+In the stage of graph construction, due to the number and randomness of the simulated queries, there may be some isolated nodes, and we just keep them in the graph with self-loop edges. During model optimization, BERTScore is pre-computed for efficient training.
+
+In the training stage, we use the Adam optimizer for model training and gradually decay the learning rate from 1e-3 to 0 with the LambdaLR scheduler. We present detailed hyper-parameters on QMSum, AcademicEval, WCEP, and BookSum datasets in Table 6. We implement our proposed method using PyTorch and Deep Graph Library (DGL), and all the experiments are conducted on a single RTX 3080 GPU. As for LLMs, we rely on API calling from Together AI<sup>3</sup> to obtain responses.
+
+For metrics, we adopt Rouge-1 (R-1), Rouge-2 (R-2), and Rouge-L (R-L) (Lin, 2004) to assess the text alignment between the reference summaries and the predicted content generated by our proposed method. If a global summarization query has multiple reference summaries, we calculate the Rouge-L/1/2 of the predicted summary and all references, respectively, and take the maximum value as the final evaluation result. We follow this setting in all experiments, including the baseline evaluation.
+
+# A.5 More Comparison Experiments
+
+We conduct extensive experiments on GovReport (Huang et al., 2021) and SQuALITY (Wang et al., 2022a) datasets, and the results are shown in Table 7, which demonstrate our proposed GoR is still competitive among baselines on these two datasets.
+
+# A.6 More Ablation Experiments
+
+We conduct extensive ablation experiments on QMSum (Zhong et al., 2021) and AcademicEval (Feng
+
+<table><tr><td>Datasets</td><td>QMSum</td><td>AcademicEval</td><td>WCEP</td><td>BookSum</td></tr><tr><td>#GAT Layers</td><td>2</td><td>2</td><td>2</td><td>2</td></tr><tr><td>#GAT Heads</td><td>4</td><td>4</td><td>4</td><td>4</td></tr><tr><td>Batch Size</td><td>32</td><td>32</td><td>32</td><td>32</td></tr><tr><td>Epoch</td><td>150</td><td>150</td><td>150</td><td>150</td></tr><tr><td>Learning Rate</td><td>1e-3</td><td>1e-3</td><td>1e-3</td><td>1e-3</td></tr><tr><td>Hidden Dimension</td><td>768</td><td>768</td><td>768</td><td>768</td></tr><tr><td>Dropout Rate</td><td>0.2</td><td>0.0</td><td>0.1</td><td>0.2</td></tr><tr><td>Loss Coefficient α</td><td>0.9</td><td>0.6</td><td>0.7</td><td>0.2</td></tr></table>
+
+Table 6: Hyper-parameters   
+Table 7: Experimental results on GovReport and SQuALITY datasets over long-context global summarization tasks w.r.t. Rouge-L (R-L), Rouge-1 (R-1), and Rouge-2 (R-2). Note that the average LLM input token length of GoR and retriever-based baselines is $6 \times 256$ , which is about $1.5\mathrm{K}$ . (BOLD indicates the best score)   
+
+<table><tr><td rowspan="2">Model</td><td colspan="3">GovReport</td><td colspan="3">SQuALITY</td></tr><tr><td>R-L</td><td>R-1</td><td>R-2</td><td>R-L</td><td>R-1</td><td>R-2</td></tr><tr><td>Node2Vec</td><td>18.1</td><td>36.7</td><td>12.4</td><td>17.0</td><td>32.9</td><td>7.7</td></tr><tr><td>BM25</td><td>18.2</td><td>39.2</td><td>13.0</td><td>17.0</td><td>31.4</td><td>8.1</td></tr><tr><td>TF-IDF</td><td>18.1</td><td>39.2</td><td>12.8</td><td>17.0</td><td>31.4</td><td>8.1</td></tr><tr><td>Contriever</td><td>20.2</td><td>39.8</td><td>17.6</td><td>16.8</td><td>32.6</td><td>8.3</td></tr><tr><td>DPR</td><td>19.1</td><td>39.4</td><td>15.5</td><td>17.4</td><td>33.1</td><td>8.4</td></tr><tr><td>Dragon</td><td>19.6</td><td>38.2</td><td>16.0</td><td>16.2</td><td>29.6</td><td>7.5</td></tr><tr><td>SBERT</td><td>20.0</td><td>39.8</td><td>15.8</td><td>17.1</td><td>32.1</td><td>7.8</td></tr><tr><td>BM25+DPR</td><td>19.4</td><td>37.4</td><td>15.0</td><td>16.6</td><td>31.5</td><td>7.4</td></tr><tr><td>Gemma-8K</td><td>17.4</td><td>33.8</td><td>11.4</td><td>12.9</td><td>19.7</td><td>5.8</td></tr><tr><td>Mistral-8K</td><td>16.0</td><td>28.9</td><td>9.4</td><td>16.9</td><td>32.2</td><td>8.1</td></tr><tr><td>Full Context</td><td>18.4</td><td>39.1</td><td>13.8</td><td>17.8</td><td>34.0</td><td>8.8</td></tr><tr><td>Thought-R</td><td>20.4</td><td>40.3</td><td>17.0</td><td>17.3</td><td>32.0</td><td>8.0</td></tr><tr><td>GoR (Ours)</td><td>20.9</td><td>41.4</td><td>16.8</td><td>17.8</td><td>34.0</td><td>8.5</td></tr></table>
+
+et al., 2024) datasets, and the results are shown in Table 8.
+
+Table 8: Ablation study on QMSum and AcademicEval datasets w.r.t. R-L, R-1, and R-2.   
+
+<table><tr><td rowspan="2">Variant</td><td colspan="3">QMSum</td><td colspan="3">AcademicEval</td></tr><tr><td>R-L</td><td>R-1</td><td>R-2</td><td>R-L</td><td>R-1</td><td>R-2</td></tr><tr><td>w/o train</td><td>18.2</td><td>33.0</td><td>7.6</td><td>23.3</td><td>45.0</td><td>15.5</td></tr><tr><td>w/o \(\mathcal{L}_{\text{CL}}\)</td><td>18.4</td><td>33.3</td><td>6.9</td><td>23.5</td><td>44.9</td><td>15.5</td></tr><tr><td>w/o \(\mathcal{L}_{\text{RANK}}\)</td><td>19.6</td><td>33.1</td><td>7.8</td><td>23.1</td><td>44.4</td><td>15.1</td></tr><tr><td>w/o in-b neg</td><td>19.8</td><td>34.7</td><td>7.8</td><td>24.5</td><td>46.4</td><td>16.5</td></tr><tr><td>w/ sup</td><td>18.1</td><td>32.3</td><td>6.9</td><td>21.4</td><td>43.3</td><td>13.9</td></tr><tr><td>GoR</td><td>19.8</td><td>34.5</td><td>7.8</td><td>24.7</td><td>46.5</td><td>17.3</td></tr></table>
+
+study their impact on learning node embeddings, including GCN (Kipf and Welling, 2016), SGC (Wu et al., 2019), GIN (Xu et al., 2019), and GraphSAGE (Hamilton et al., 2017). Our findings, illustrated in Figure 4, show that GAT outperforms the other architectures. This is because GAT considers the significance of neighboring nodes when updating node embeddings, allowing the model to effectively capture essential information from the nodes. Among the other architectures, GraphSAGE performs poorly due to its unstable neighbor sampling mechanism.
+
+# A.7 Impact of GNN Architectures
+
+GNNs play a vital role in learning node embeddings. we explore various GNN architectures to
+
+Overall, GAT reaches the best results, which shows that considering the importance of neighboring nodes is effective in mining complicated correlations and is critical to improving performance.
+
+![](images/fe017e65355e50068e540c21e0acb4bd9d3392de36cd96a27abf3ed78d6eda5e.jpg)
+
+![](images/3990ead253c9484377566813e360cbd6ca4fef57b6bd3d13825b815f7be212cb.jpg)  
+Figure 4: Impact of GNN architectures w.r.t. R-L, R-1, and R-2. The left figure shows results on the WCEP dataset, while the right one shows results with the BookSum dataset.
+
+# A.8 Impact of the Number of Simulated Queries During Training
+
+We show additional results on the AcademicEval and BookSum datasets in Figure 5.
+
+![](images/5085fc4a7e1504e0603f5055f7b0bd54e5b274ef95592e38638c7403477fc3a8.jpg)
+
+![](images/91c96a1b0a670a9ee8614688d36465bd454dd33a2ede50fdcfeffb3ae13c5f0c.jpg)  
+Figure 5: Impact of the number of simulated queries during training w.r.t. R-L. We show the additional results on the AcademicEval and BookSum datasets.
+
+# A.9 Supervised Training on Global Summarization Queries
+
+We show additional results on the WCEP dataset in Figure 6.
+
+![](images/15c0337a5a0ab52f21ed43e4605cc0dcaea0a581661bcbb22ce5c19ca1df035b.jpg)
+
+![](images/e68b1578249f1e440433c97eae37c1d090492e127d59c3fc2465d0abacd16709.jpg)  
+Figure 6: Differences between self-supervised and supervised training w.r.t. loss and entropy. We show the loss and entropy curve during training on the WCEP dataset.
+
+# B Additional Related Work
+
+Historical Response Utilization of LLMs. Little work has been done on this under-explored topic.
+
+Thought-retriever (Feng et al., 2024) saves the historical responses of each user-LLM interaction as high-level and informative thoughts to expand the retrieval corpus for future user queries. However, the intricate correlations among thoughts are neglected, leaving room for further improvement.
+
+Another line of work is the Chain-of-Thought (CoT), which is similar to our approach in terms of utilizing LLM historical responses and has been regarded as an effective means to enhance the reasoning ability of LLM during inference time in recent years. Few-shot CoT (Wei et al., 2022) and zero-shot CoT (Kojima et al., 2022) elicit intermediate reasoning paths by prompting LLMs with several demonstrations or just appending "Let's think step by step." Self-consistency (Wang et al., 2022b) samples diverse reasoning paths and conducts a majority vote to obtain the final answer. ToT (Yao et al., 2024) and GoT (Besta et al., 2024) take a further step by integrating a tree or graph structure to manage its historical reasoning paths, enabling more flexible reasoning and reflection of LLMs. By memorizing the solution paradigms of various queries into different templates, BoT (Yang et al., 2024) pushes LLM's reasoning ability to a new level. Although the above-mentioned CoT-series approaches improve the reasoning capabilities of LLMs by utilizing chains of intermediate reasoning responses, they usually concentrate on one specific QA-type query and cannot generalize to and benefit other queries. Moreover, only a small number of historical reasoning responses are retained for the final generation, while most of the rest are just discarded.
+
+# C Case Study
+
+In this section, we provide a case study of GoR and other baseline methods' summarization.
+
+# The Summary Generated by GoR
+
+An asteroid called 1999 KW4 will make a close approach to Earth this weekend, with its own small moon in tow. The asteroid is estimated to be around $1.5\mathrm{km}$ wide and will be roughly 3.2 million miles from Earth at its closest point. NASA astronomers are interested in studying the asteroid due to its close proximity and the fact that it is a binary system, meaning it has its own moon. The last time the asteroid will make a close approach to Earth will be in 2036. Additionally, a recent study using data from NASA's Kepler Space Telescope suggests that comets may have delivered water to Earth, as the ratio of two types of water molecules on comets matches that in Earth's oceans. The new algorithm used in the study is more sensitive to small planets the size of Earth and could help in the search for Earth-like planets.
+
+# The Summary Generated by Contriever
+
+Asteroid 2019 JH7 recently flew past Earth, and NASA observed that the asteroid's trajectory falls under the "Earth Close Approach" category. The observations made by NASA's Jet Propulsion Laboratory (JPL) in Pasadena, California, suggest that comets could have delivered water to Earth. The study found that the ratio of two types of water molecules on the comet matches that in the Earth's oceans, which could imply that comets delivered a large fraction of water to the outer reaches of the solar system. The observations made using data from the SOFIA telescope suggest that all comets could have a heavy-to-regular water ratio similar to Earth's oceans, which could imply that comets delivered some water to Earth. Previously, measuring this ratio was difficult, and ground and space telescopes could only study this level of detail in comets when they pass near Earth.
+
+# Reference Summary
+
+Binary Aten asteroid (66391) 1999 KW4 and its minor-planet moon make their closest-ever recorded flyby of Earth at 3.2 million miles away. The asteroid will approach even closer at 0.0155 AU (2,320,000 km) from Earth in 2036, and is the largest asteroid to approach Earth until (4953) 1990 MU in June 2027.
+
+From the above example, we can draw conclusions. (1) GoR summarizes several keywords that appear in the reference summary, such as "1999 KW4" and "3.2 million miles", etc., but Contriever fails to extract this crucial information. (2) From a global perspective, the summary generated by GoR is more relevant and consistent with the reference summary. However, the summary generated by Contriever focuses too much on local details and ignores the main idea of the original article.
+
+# D LLM Prompts
+
+In this section, we present LLM prompts used in GoR, including user query simulation, RAG, and LLM-as-a-Judge prompts.
+
+# D.1 LLM Prompts for User Query Simulation
+
+# Prompt for User Query Simulation
+
+You are a great questioner of any text, and are adept at asking valuable and insightful questions. Your goal is to generate 1 summary question for the text provided below. The generated summary question should try to simulate the tone of human questions as much as possible, and make sure that the generated question must be interrogative sentences and a summary question. Important! Please make sure this text must be a complete and non-redundant answer to the generated summary question. Please directly output the generated summary question, do not output irrelevant text.
+
+DOCUMENT:
+
+{document}
+
+# LLM-as-a-Judge Prompt - Instruction
+
+# Role
+
+You are an expert tasked with evaluating two answers to the same question based on four criteria: Comprehensiveness, Diversity, and Empowerment.
+
+# Goal
+
+You will evaluate two answers to the same question based on four criteria: Comprehensiveness, Diversity, and Empowerment.
+
+Comprehensiveness: How much detail does the answer provide to cover all aspects and details of the question?
+
+Diversity: How varied and rich is the answer in providing different perspectives and insights on the question?
+
+Empowerment: How well does the answer help the reader understand and make informed judgments about the topic?
+
+For each criterion, choose the better answer (either Answer 1 or Answer 2) and explain why. Then, select an overall winner based on these three categories.
+
+# D.2 LLM Prompts for RAG
+
+# RAG Prompt
+
+Refer to the following supporting materials and answer the question with brief but complete explanations.
+
+SUPPORTING MATERIALS:  
+{materials}
+
+QUESTION: {question}
+
+# D.3 LLM Prompts for LLM-as-a-Judge
+
+We construct LLM-as-a-Judge prompts following (Edge et al., 2024) and (Guo et al., 2024) with some minor changes.
+
+# LLM-as-a-Judge Prompt - Input
+
+Here is the question: {query}
+
+Here are the two answers: Answer 1: {answer1}; Answer 2: {answer2}
+
+Evaluate both answers using the three criteria listed above and provide detailed explanations for each criterion.
+
+Avoiding any potential bias and ensuring that the order in which the answers were presented does not affect your judgment.
+
+Output your evaluation in the following JSON format:
+
+{{"Comprehensiveness": {{"Winner": "[Answer 1 or Answer 2]", "Explanation": ["Provide explanation here"]}}},
+
+"Diversity": {{ "Winner": "[Answer 1 or Answer 2]", "Explanation": ["Provide explanation here"]}},
+
+"Empowerment": {{ "Winner": "[Answer 1 or Answer 2]", "Explanation": ["Provide explanation here"]}},
+
+"Overall Winner": {{"Winner": ["Answer 1 or Answer 2"], "Explanation": ["Summarize why this answer is the overall winner based on the three criteria"]}}}}
+
+# E Broader Impacts
+
+In the era of LLMs, countless interactions take place between users and these models on a daily basis, resulting in the generation of a vast amount of historical responses. Our proposed method demonstrates that these historical responses hold significant potential and can be effectively leveraged to further improve the quality of future responses generated by LLMs. By analyzing and reusing these past outputs, we can not only refine and enhance the overall performance of the models but also reduce computational overhead. This approach highlights the untapped value of historical data in optimizing response generation while making the process more efficient and resource-friendly.

paper_markdowns/bamboo-00448.md

@@ -0,0 +1,509 @@
+# Interactive Evolution: A Neural-Symbolic Self-Training Framework For Large Language Models
+
+Fangzhi Xu $^{1,2,5*}$ Qiushi Sun $^{3}$ Kanzhi Cheng $^{4}$ Jun Liu $^{1,5,6\dagger}$ Yu Qiao $^{2}$ Zhiyong Wu $^{2\dagger}$
+
+$^{1}$ School of Computer Science and Technology, Xi'an Jiaotong University $^{2}$ Shanghai AI Lab $^{3}$ The University of Hong Kong $^{4}$ Nanjing University $^{5}$ Ministry of Education Key Laboratory of Intelligent Networks and Network Security $^{6}$ Shaanxi Province Key Laboratory of Big Data Knowledge Engineering {fangzhixu98, whucs2013wzy}@gmail.com liukeen@xjtu.edu.cn
+
+# Abstract
+
+One of the primary driving forces contributing to the superior performance of Large Language Models (LLMs) is the extensive availability of human-annotated natural language data, which is used for alignment fine-tuning. This inspired researchers to investigate self-training methods to mitigate the extensive reliance on human annotations. However, the current success of self-training has been primarily observed in natural language scenarios, rather than in the increasingly important neural-symbolic scenarios. To this end, we propose an environment-guided neural-symbolic self-training framework named ENVISIONS. It aims to overcome two main challenges: (1) the scarcity of symbolic data, and (2) the limited proficiency of LLMs in processing symbolic language. Extensive evaluations conducted on three distinct domains demonstrate the effectiveness of our approach. Additionally, we have conducted a comprehensive analysis to uncover the factors contributing to ENVISIONS's success, thereby offering valuable insights for future research in this area.
+
+# 1 Introduction
+
+Large Language Models (LLMs) (Achiam et al., 2023; Team et al., 2023) have undergone extensive training using massive data, enabling them to possess remarkable capabilities across diverse domains. One of the main recipes of LLMs' success is the post-pretraining effort to achieve alignment with downstream tasks (Taori et al., 2023; Yin et al., 2023). The effective alignment primarily relies on the accessibility of a substantial volume of expensive human-annotated data, employing techniques such as Supervised Fine-Tuning
+
+(SFT) (Ivison et al., 2023) or Reinforcement Learning from Human Feedback (RLHF) (Ouyang et al., 2022). Recently, there has been a growing interest in developing self-training methods that enable fine-tuning of LLMs without human annotations, thereby reducing cost and streamlining the training process (Yuan et al., 2024).
+
+Notable progress has been made in self-training techniques for natural language (NL) scenarios (Chen et al., 2024; Rosset et al., 2024), where researchers focus on improving LLMs by synthesizing their own natural language input-output pairs. However, in recent years, there has been a growing emphasis on delegating tasks to external tools/environments to expand the capability boundaries of LLMs. The shift in focus necessitates the generation of a symbolic intermediate representation $a$ that can be executed in the environment to faithfully produce the desired output $y$ . This neural-symbolic framework (Xu et al., 2024) has achieved significant success in complex planning (Liu et al., 2023a), mathematical reasoning (Gou et al., 2023), robotic planning (Hu et al., 2023), and agentic tasks (Zheng et al., 2023; Wu et al., 2024). In contrast to the abundance of NL annotation data $(x - y)$ , curating symbolic annotation $(x - a - y)$ is significantly more challenging and costly due to the scarcity and inherent complexity of symbolic language (SL). In this paper, we delve into the exploration of effective self-training methods for LLMs within complex neural-symbolic scenarios, all without human-annotated symbolic data.
+
+Current self-training approaches in empowering LLMs in SL-centric scenarios fall into two categories, each with its own drawbacks. Distill-then-Finetune (Ivison et al., 2023; Xu et al., 2023a), shown in Fig. 1(a), entails fine-tuning a less powerful LLM using distilled data obtained from a teacher LLM, such as GPT-4 (Achiam et al., 2023).
+
+![](images/d1e97fb4ac547ab80c5bdc1e332b0a5e362be43bcfe319523b9f6a9c40ecfc00.jpg)
+
+![](images/7781899a45525e61e95c54d515ad4cd58f0a4e7f7ce078f2b07192b851ee5a80.jpg)
+
+![](images/8bf17d5888b5ee40f32c766dc788f6384828ce7e80931759d643ca540cec9dc8.jpg)  
+Figure 1: Weak-to-strong paradigms. (a) Distill-then-Finetune paradigm. (b) Reinforced Self-Training methods. (c) Environment-guided Self-Training paradigm.
+
+Although this method is simple yet effective, its application is constrained by the requirement of an already existing stronger LLM and the associated high costs. Furthermore, the performance of the student LLM is upper-bounded by the capabilities of the teacher LLM. Reinforced Self-Training (Gulcehre et al., 2023; Singh et al., 2023), as shown in Fig. 1 (b), iteratively improves a weak LLM by leveraging reinforcement learning algorithms (Rafailov et al., 2024), guided by customized reward models. Nevertheless, reinforced methods are constrained by their inefficiency in training and/or reliance on human annotations for reward model training.
+
+To address the limitations of previous approaches, this work focuses on two key challenges: enhancing the proficiency of LLMs in processing SL and eliminating the requirement for human-annotated data. Illustrated in Figure 1 (c), the proposed approach, called Environment-guided (Env-guided) self-training, involves iterative training of LLMs through interactions with an embodied environment. Built upon the approach, we propose an ENV-guIded Self-traIning framework fOr Neural Symbolic scenarios, named ENVISIONS. As an example, consider the training of LLMs for web browsing, i.e., training a web agent. Given a web manipulation task $x$ , the agent generates multiple candidate actions $a \in \mathcal{A}$ and executes these actions within the web browser, resulting in both correct and incorrect outcomes. A self-rewarding algorithm is designed to post-process the agent's trajectories and create contrastive training pairs. These correct-incorrect trajectory pairs, along with a self-refining loss, are utilized to empower the LLMs to self-improve.
+
+Through the Env-guided self-training approach, the LLMs leverage the interactive nature of the embodied environment to generate trajectories and learn symbolic language processing abilities, mitigating the need for human annotations. Through ex
+
+tensive evaluation, we found that ENVISIONS can consistently convert an existing LLM to a stronger one without reliance on existing stronger models or reward models. It's also worth noting that ENVISIONS and previous methods are not mutually exclusive, but we leave it as a future work to explore their synergy.
+
+We highlight our contributions as follows:
+
+(1) A neural-symbolic self-training framework: We propose a novel framework ENVISIONS for neural-symbolic self-training. The proposed framework can eliminate the need for human annotation or a stronger teacher model during self-training.   
+(2) Comprehensive evaluations and analysis: We extensively evaluate ENVISIONS across three domains to showcase its superiority over existing self-training methods. Our thorough analysis uncovers the reasons behind ENVISIONS's exceptional performance, highlighting its potential as a new paradigm for neural-symbolic self-training.   
+(3) Insights on Env-guided neural-symbolic self-training: Our research provides valuable insights, supported by evidence, into the training process of Env-guided neural-symbolic self-training. These findings pave the way for future researches.
+
+# 2 Related Work
+
+Self-Training Methods. Self-training (Tao et al., 2024; Cao et al., 2024), offers a promising avenue for models to learn from their own outputs, reducing reliance on extensive human annotations. Recent advances (Gulcehre et al., 2023) leverage well-trained reward models to filter better training samples, and optimize the policy via reinforced self-training (Singh et al., 2023; Liu et al., 2023b). However, these approaches heavily rely on a strong reward model, which limits its applicability and training efficiency. Following the success of DPO (Rafailov et al., 2024), self-play frameworks have emerged as a new path that implicitly models the preferences among unlabeled rationales in iterative DPO styles (Chen et al., 2024; Rosset et al., 2024; Yuan et al., 2024). Nevertheless, these RL methods still face efficiency issues (Wang et al., 2023a). Beyond RL, previous works (Zelikman et al., 2022; Ni et al., 2022) optimize policy models within iterative SFT frameworks, yet neglecting the value of negative samples. Notably, previous efforts merely focus on the NL scenarios, but fail to apply in neural-symbolic settings.
+
+Data Synthesis with LLMs. Obtaining high-quality reasoning traces to optimize LLMs has been a long-standing challenge (Mukherjee et al., 2023). Beyond well-established approaches utilizing data augmentation strategies to obtain diversified training data (Deng et al., 2023; Lee et al., 2024; Huang et al., 2025a). Recent efforts (Yue et al., 2023; Zeng et al., 2023; Cheng et al., 2024) primarily distill strong LLMs (Achiam et al., 2023; Anil et al., 2023) to generate novel samples in the given format. They either generate more diverse samples from seed data through self-instruct (Wang et al., 2023b) or enhance diversity through sample rewriting (Wei et al., 2023; Xu et al., 2025). However, current works mainly employ proprietary LLMs for data synthesis, which is a cost.
+
+Neural-Symbolic Integration for LLMs. Neural-symbolic methods synergize the powerful generation capacity of LLMs with the reliability and interpretability of symbolic systems. Typically, PAL/PoT (Gao et al., 2023; Chen et al., 2023) synthesize executable programs as intermediate reasoning steps to solve numerical problems. This strategy of delegating problems to external solvers (e.g., Python interpreter), has gained significant traction (Xu et al., 2024; Sun et al., 2024; Huang et al., 2025b). For instance, (Gou et al., 2023) and (Pan et al., 2023) apply neural code generation and symbolic execution on math and logical reasoning respectively. Beyond reasoning, recent endeavors have extended the application into agent scenarios (Xu et al., 2023b; Qin et al., 2023) and leverage external feedback from the environment (Zheng et al., 2023; Yang et al., 2024) for refinement. However, these approaches mainly optimize LLM usage rather than providing autonomous self-improvement.
+
+# 3 Methodology
+
+# 3.1 Preliminaries
+
+In neural-symbolic scenarios, based on the NL input $x$ , LLMs are required to produce symbolic solution $a$ to obtain the desired output $y$ through the execution in the environment ENV. To adapt the weak LLMs to such complex settings and curate extensive $(x, a, y)$ pairs, we propose to iteratively interact with ENV for self-improving LLMs. For each iteration $i$ , the LLM $\pi_{\theta_i}$ will be provided with the task data set $\{(x^{(i)}, y^{(i)})\}$ , with $J$ input-output pairs. Without loss of generality, we assume the samples keep static between iterations.
+
+Our framework ENVISIONS, presented in Fig. 2, is specifically designed to address two key challenges: (1) the scarcity of SL data and (2) the limited proficiency of LLMs in SL. Data scarcity limitation is addressed by the online exploration stage (Step 1-7). To convert LLMs from weak to strong in addressing SL, we employ LLM training using a carefully designed loss function and filtered data (Step 8-10). To simplify the expression, we omit the indicator of iteration $i$ in the symbols. The overall procedure of ENVISIONS is also concluded in the pseudocode of Appendix D.
+
+# 3.2 Online Exploration for SL Scarcity
+
+Given the limited annotated SL data, ENVISIONS enables the policy LLM to autonomously generate symbolic solutions by interacting with the environment ENV. This process is named Online Exploration, which includes three main aspects 1) self-exploration (Step ①-③); 2) self-refinement (Step ④-⑥); and 3) self-rewarding (Step ⑦).
+
+Self-exploration. Given the NL input $x$ , the policy model $\pi_{\theta}$ first generates $K$ diverse symbolic outputs (Step ①), formulated as $\{a_{k}\}_{k=1}^{K} \sim \pi_{\theta}(\cdot|x)$ . These intermediate outputs will be executed in ENV (Step ②) to obtain the binary feedback $\{b_{k}\}_{k=1}^{K}$ based on $y$ (Step ③). This procedure allows $\pi_{\theta}$ to explore the environment autonomously and search for diverse symbolic solutions.
+
+Self-refinement. Considering the complexity of SL, solutions generated by the LLM may contain mistakes in symbolic format, which significantly impair the efficiency of exploration. To address this, we utilize the above self-explored solutions $\{a_k\}_{k=1}^K$ as references to regenerate new refined symbolic solutions (Step ④), formulated as $\{\widetilde{a}_k\}_{k=1}^K \sim \pi_\theta(\cdot|x; a_k)$ . Similarly, these outputs will be executed in ENV (Step ⑤) and receive the corresponding binary reward $\{\widetilde{b}_k\}_{k=1}^K$ (Step ⑥).
+
+Self-rewarding. Feedback from ENV merely gives the binary rewards. However, it remains challenging to discern preferences among various positive solutions or obtain valuable feedback from negative solutions. Motivated by it, we propose a soft reward score through sequence output probabilities with the following calculation:
+
+$$
+r = \bar {p} _ {\theta} (a | x) = \frac {1}{\left\| a \right\|} \sum_ {t} \log p _ {\theta} \left(a _ {t} \mid x; a _ {<   t}\right), \tag {1}
+$$
+
+where $||a||$ is the length of the symbolic solution $a$ . Based on this definition, the soft self-rewards
+
+![](images/4964e9f9a64e662597b4e9e32bdc0027cdcca9664d254794455d7f7bb2b58763.jpg)  
+Figure 2: The neural-symbolic self-training framework ENVISIONS. $\rightarrow$ denotes self-exploration process (Step ①-③), $\rightarrow$ indicates self-refinement (Step ④-⑥), and $\rightarrow$ is self-rewarding (Step ⑦). $a$ is the solution, and $b$ is the binary feedback from the environment based on the execution of $a$ .
+
+of $a_{k}$ and $\widetilde{a}_k$ are derived respectively as $r_k$ and $\widetilde{r}_k$ Considering that no extra reward model is involved, we name it self-rewarding1 (Step ⑦).
+
+# 3.3 Data Selection and Training Strategies
+
+After the online exploration stage, the candidate trajectories are constructed as $T_{k} = (x,y,a_{k},b_{k},r_{k})$ and $\widetilde{T}_k = (x,y,\widetilde{a}_k,\widetilde{b}_k,\widetilde{r}_k)$ , which are sourced from self-exploration and self-refinement respectively. Next, we select premium trajectories for training the LLM $\pi_{\theta_i}$ .
+
+Trajectory filtering and candidate pool updating. To control the candidate number and maintain high-quality trajectories, we select the superior one from $T_{k}$ and $\widetilde{T}_k$ to update the candidate pool (Step ⑧). To facilitate automatic selection, we incorporate binary rewards and self-rewards for assessment. Following the principle of prioritizing execution correctness, we derive the filtered trajectory $T_{k}^{*}$ :
+
+$$
+\begin{array}{l} T _ {k} ^ {*} = (x, y, a _ {k} ^ {*}, b _ {k} ^ {*}, r _ {k} ^ {*}) \\ = \left\{ \begin{array}{l l} \left(x, y, a _ {k}, b _ {k}, r _ {k}\right), & \text {i f} b _ {k} = 1 \text {a n d} \widetilde {b} _ {k} = 0, \\ \left(x, y, a _ {k}, b _ {k}, r _ {k}\right), & \text {i f} b _ {k} = \widetilde {b} _ {k} \text {a n d} r _ {k} > \widetilde {r} _ {k}, \\ \left(x, y, \widetilde {a} _ {k}, \widetilde {b} _ {k}, \widetilde {r} _ {k}\right), & \text {o t h e r w i s e .} \end{array} \right. \tag {2} \\ \end{array}
+$$
+
+Notably, our filter strategy still maintains some trajectories with incorrect solutions but relatively higher rewards. These trajectories will serve as hard negative samples for the subsequent steps.
+
+Supervised fine-tuning on positive solutions. As we have explored diverse trajectories in ENV, an intuitive way to bootstrap the performance of LLMs is fine-tuning with the positive solutions. Therefore, for each input $x$ , we can retrieve the
+
+positive trajectories (i.e., $b = 1$ ) from the candidate pool. Giving priority to more valuable solutions, we rank the trajectories in descending order based on self-rewards, resulting in the positive set $S^{+}$ . To mitigate overfitting, we enforce a maximum of $N_{1}$ positive-only solutions sampled for each input $x$ :
+
+$$
+\begin{array}{l} U _ {1} = \{(x, a _ {m} ^ {+}) \mid m \leq \min  \left(N _ {1}, \left| S ^ {+} \right|\right) \tag {3} \\ \left. \left. \text {a n d} T _ {m} ^ {+} \in S ^ {+} \right\} \right. \\ \end{array}
+$$
+
+where $m \in \mathbb{Z}^+$ means the index in the ranked set and $|\cdot|$ returns the number of trajectories in the given set. $T_m^+ = (x, y, a_m^+, b_m^+ r_m^+)$ denotes the trajectories in $S^+$ . Following the principle of MLE, the optimized loss function can be written as:
+
+$$
+\mathcal {L} _ {1} = - \sum_ {(x, a ^ {+}) \sim U _ {1}} \log p _ {\theta} \left(a ^ {+} \mid x\right) \tag {4}
+$$
+
+RL-free loss to learn from mistakes. Under the neural-symbolic setting, negative solutions may comprise a substantial portion of exploration trajectories, while also offering valuable insights for model enhancement. ENVISIONS explores motivating the policy LLM to learn from mistakes during the weak-to-strong process. We can obtain the ranked negative set $S^{-}$ from the candidate pool. For each input $x$ , at most $N_{2}$ positive-negative pairs will be constructed from $S^{+}$ and $S^{-}$ :
+
+$$
+\begin{array}{l} U _ {2} = \left\{\left(x, a _ {m} ^ {+}, a _ {m} ^ {-}\right) \mid T _ {m + \left| U _ {1} \right|} ^ {+} \in S ^ {+} \text {a n d} T _ {m} ^ {-} \in S ^ {-} \right. \\ \text {a n d} m \leq \min  \left(N _ {2}, \left| S ^ {+} \right| - N _ {1}, \left| S ^ {-} \right|\right) \}, \tag {5} \\ \end{array}
+$$
+
+where $T_{m}^{-} = (x,y,a_{m}^{-},b_{m}^{-}r_{m}^{-})$ denotes the trajectories in $S^{-}$ . Limited by the difficulty and complexity of optimizing models in an RL manner (e.g., DPO (Rafailov et al., 2024)), it is challenging for reinforced-based methods (Chen et al., 2024; Rosset et al., 2024) to quickly adapt to the SL scenarios.
+
+Therefore, we design the following contrastive RL-free loss function:
+
+$$
+\mathcal {L} _ {2} = - \sum_ {(x, a ^ {+}, a ^ {-}) \sim U _ {2}} \log p _ {\theta} \left(a ^ {+} \mid x; a ^ {-}\right) \tag {6}
+$$
+
+It brings two main advantages: (1) the ability of self-refinement is acquired, which benefits the scalability to complex cases; (2) compared to reinforced losses, superior training efficiency is achieved. Finally, the overall loss function of each iteration is simply designed as $\mathcal{L} = \mathcal{L}_1 + \mathcal{L}_2$ .
+
+# 4 Experiments
+
+# 4.1 Datasets
+
+We evaluate the proposed framework on three distinct domains, each with its own environment: web agents (Chrome browser), math reasoning (Python compiler), and logical reasoning (Pyke engine). For agentic tasks, we select the widely-used web navigation benchmark MiniWob++ (Liu et al., 2018). For the math reasoning domain, we include: GSM8K (Cobbe et al., 2021), MATH (Hendrycks et al., 2021), GSM-Hard (Gao et al., 2023), SVAMP (Patel et al., 2021), and AsDiv (Miao et al., 2020). For logical reasoning tasks, we include ProofWriter (Tajord et al., 2021) and RuleTaker (Clark et al., 2021). To evaluate the generalization capability of our method, we reserve some datasets for out-of-distribution evaluation as shown in Table 1. Refer to Appendix A.2 for details.
+
+# 4.2 Baselines and Training Details
+
+Following the categorization of Figure 1, we consider the respective three lines of baselines. All baselines are reproduced under the same codebase for a fair comparison.
+
+Distill-then-Finetune. GPT-4 and Claude-2 are selected as strong teacher LLMs in this approach. By prompting teacher LLMs, we obtain the symbolic trajectories with correct answers to fine-tune LLMs. Due to the high time and financial cost of calling API, each input will be prompted only once.
+
+Reinforced Self-Training. We implement two RL-based self-training baselines: Self-Rewarding (Yuan et al., 2024) and iterative SFT+DPO. For the former, we follow the official implementation to first warm up the weak LLM using human annotation from OpenAssistant (Kopf et al., 2024). The latter is a variation of ENVISIONS that mainly separates the training into
+
+two stages, with positive solutions for SFT and positive-negative pairs for DPO.
+
+Env-guided Self-Training. Since there is no existing baseline for this approach, we consider extending the NL-centric self-training method STaR (Zelikman et al., 2022) to support neural-symbolic scenarios. It is worth noting that STaR only uses positive samples for behavior cloning. For the methods under this paradigm (including ENVISIONS) we optimize LLM from scratch in each iteration with the updated training samples.
+
+Except for Distill-then-Finetune baselines, all other methods utilize few-shot prompting to acquire training samples as a cold start. The few-shot numbers for the web agent, math, and logic domains are set to 1, 3, and 1 respectively. We also include few-shot results on weak LLM for comparison. For a fair evaluation, all baselines are optimized to generate symbolic outputs (e.g., Python code) rather than natural language outputs, following PoT style (Chen et al., 2023). Please refer to Appendix A for other details.
+
+We use LLaMA2-Chat 7B/13B models for the evaluation. At each generation step (i.e., Step ①, ④), the candidate size $K$ is set to 5. The total iteration number for web agent, math, and logic tasks is set to 5, 10, and 8 respectively, unless otherwise stated. For each input, $N_{1}$ and $N_{2}$ are fixed to 10 and 2 respectively. All the self-training experiments are implemented on 8*A100 of 80GB VRAM. Please refer to Appendix A.1 for other details.
+
+# 4.3 Main Results
+
+Table 2 presents the evaluation results. For supplementary experiments on other backbone LLMs, please refer to Section 4.5 and Appendix C.3.
+
+ENVISIONS presents consistent superiority over strong baselines. Evolving from LLaMA2-Chat, ENVISIONS notably boosts average performance by $30.00\%$ and $24.95\%$ for the 7B and 13B variants, respectively. Compared with Distill-then-Finetune methods, $5.66\% - 7.13\%$ gains are obtained. Apart from its superior performance, ENVISIONS presents scalability without the associated costs of using strong LLMs. It exhibits clear advantages over Reinforced Self-Training and other Env-guided Self-Training methods, delivering average gains of $2.78\% - 14.47\%$ . The competitive performances, with the training efficiency, makes ENVISIONS stand out among these strong baselines.
+
+Table 1: Details and statistics of evaluated domains. #Samples denotes the number of input samples per iteration. Static? indicates whether the input data remains the same across all iterations.   
+
+<table><tr><td>Domains</td><td>Held-in Tasks</td><td>Held-out Tasks</td><td>#Samples</td><td>Static ?</td><td>Env.</td></tr><tr><td>Web Agent</td><td>MiniWob++</td><td>-</td><td>2,200</td><td>No</td><td>Chrome browser</td></tr><tr><td>Math Reasoning</td><td>GSM8K, MATH</td><td>GSM-H, SVAMP, AsDiv</td><td>13,492</td><td>Yes</td><td>Python compiler</td></tr><tr><td>Logic Reasoning</td><td>ProofWriter</td><td>RuleTaker</td><td>3,600</td><td>Yes</td><td>Pyke engine</td></tr></table>
+
+Table 2: Main Results on Agent, Math Reasoning and Logical Reasoning domain. Notably, we report the average performance across extensive tasks in MiniWob++ benchmark (refer to Appendix C.8 for details). Is Held-out? row distinguishes the held-in and held-out tasks. Avg. column reports the averaged performances on all tasks.   
+
+<table><tr><td rowspan="2">Models</td><td rowspan="2">Agent MiniWob++</td><td colspan="5">Math Reasoning</td><td rowspan="2" colspan="2">Logical Reasoning ProofWriter RuleTaker</td><td rowspan="2">Avg.</td></tr><tr><td>GSM8K</td><td>MATH</td><td>GSM-H</td><td>SVAMP</td><td>ASDiv</td></tr><tr><td>Is Held-out?</td><td>X</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td></td></tr><tr><td colspan="10">LLaMA2-Chat (7B)</td></tr><tr><td>LLaMA2-Chat (few-shot)</td><td>51.14</td><td>12.21</td><td>1.32</td><td>10.69</td><td>22.00</td><td>25.86</td><td>34.83</td><td>47.44</td><td>25.69</td></tr><tr><td>Distill-then-Finetune</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>GPT-4 + LLaMA2-Chat</td><td>81.14</td><td>53.07</td><td>18.84</td><td>47.84</td><td>66.80</td><td>68.75</td><td>34.33</td><td>48.88</td><td>52.46</td></tr><tr><td>Claude-2 + LLaMA2-Chat</td><td>82.80</td><td>52.69</td><td>18.17</td><td>44.88</td><td>70.50</td><td>69.85</td><td>36.17</td><td>49.17</td><td>53.03</td></tr><tr><td>Reinforced Self-Training</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Self-Rewarding</td><td>69.39</td><td>40.03</td><td>10.70</td><td>31.69</td><td>58.20</td><td>61.55</td><td>32.17</td><td>50.04</td><td>44.22</td></tr><tr><td>Iterative SFT+DPO</td><td>77.05</td><td>54.81</td><td>14.75</td><td>47.08</td><td>70.10</td><td>66.22</td><td>49.00</td><td>58.82</td><td>54.73</td></tr><tr><td>Env-guided Self-Training</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>STaR + Env.</td><td>83.71</td><td>58.23</td><td>15.97</td><td>46.63</td><td>67.50</td><td>68.46</td><td>50.17</td><td>58.60</td><td>55.91</td></tr><tr><td>ENVISIONS</td><td>85.38</td><td>58.98</td><td>19.00</td><td>48.52</td><td>72.40</td><td>69.80</td><td>52.83</td><td>62.63</td><td>58.69</td></tr><tr><td colspan="10">LLaMA2-Chat (13B)</td></tr><tr><td>LLaMA2-Chat (few-shot)</td><td>60.00</td><td>34.87</td><td>6.07</td><td>28.96</td><td>45.00</td><td>46.61</td><td>35.83</td><td>51.50</td><td>38.61</td></tr><tr><td>Distill-then-Finetune</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>GPT-4 + LLaMA2-Chat</td><td>80.15</td><td>62.85</td><td>23.64</td><td>53.98</td><td>73.00</td><td>73.52</td><td>34.17</td><td>50.61</td><td>56.49</td></tr><tr><td>Claude-2 + LLaMA2-Chat</td><td>84.77</td><td>62.24</td><td>23.47</td><td>52.08</td><td>76.30</td><td>74.05</td><td>36.00</td><td>48.45</td><td>57.17</td></tr><tr><td>Reinforced Self-Training</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Self-Rewarding</td><td>74.55</td><td>50.80</td><td>13.97</td><td>41.24</td><td>74.10</td><td>71.37</td><td>37.33</td><td>56.66</td><td>52.50</td></tr><tr><td>Iterative SFT+DPO</td><td>82.73</td><td>63.84</td><td>22.32</td><td>50.57</td><td>77.30</td><td>70.94</td><td>51.00</td><td>59.47</td><td>59.77</td></tr><tr><td>Env-guided Self-Training</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>STaR + Env.</td><td>85.15</td><td>63.61</td><td>20.57</td><td>53.37</td><td>74.70</td><td>74.76</td><td>52.33</td><td>60.33</td><td>60.60</td></tr><tr><td>ENVISIONS</td><td>87.12</td><td>68.31</td><td>26.04</td><td>57.54</td><td>78.30</td><td>75.52</td><td>54.83</td><td>60.84</td><td>63.56</td></tr></table>
+
+Env-guided Self-Training exhibits strong scalability to neural-symbolic scenarios. Compared to the other two approaches, Env-guided Self-Training is more applicable to complex neural-symbolic scenarios, especially in agentic tasks where NL-centric methods inherently exhibit limitations. Besides the great performances of ENViRONS, previous methods STaR can also benefit from the supervision signals acquired in ENV, which helps the evolution progress.
+
+# 4.4 Evolution Progress
+
+In Figure 3, we present the iterative evolution curves of the self-training frameworks with LLaMA2-Chat (13B) as the LLM, which clearly shows the procedure of weak-to-strong transformation. We leave the discussion on the evolution of both performance and explored sample numbers with the 7B version in Appendix C.1.
+
+ENVIATIONS combines high evolutionary efficiency and sustainability. In the initial iterations, ENVISIONS demonstrates swift adaptability to different scenarios. This indicates that exceptional performance can be achieved with minimal time for data collection in ENVISIONS. Additionally, ENVISIONS stands out as a more sustainable option when compared to other baselines. For instance, in math reasoning tasks of Fig. 3(b), all baseline methods achieve saturated performance levels by $6^{th}$ iteration. However, our framework continues to exhibit evolutionary progress.
+
+Reinforced baselines are largely flawed during iterations. The incorporation of reinforced loss (e.g., DPO) brings difficulty in optimization and greatly restricts the evolutionary scales of the LLM to adapt to the neural-symbolic scenarios. Self-Rewarding exhibits largely reduced benefits during iterations, in contrast to its impressive performance in NL-centric tasks. For Iterative SFT+DPO, the
+
+![](images/fd0aa654b0923ea1cc5d3fe346623624853106d2eb6b17df4a7cf8fb5a07ac5a.jpg)
+
+![](images/a0422c688b568013ed74b5e8578554eeb1a5437faca1edc8188fade9b2e40d0d.jpg)  
+Figure 3: Performance evolution of self-training methods on LLaMA2-Chat 13B model. Reinforced Self-Training approaches are represented by dashed lines, while Env-guided ones are in solid lines.   
+Figure 4: Generalization to different LLMs. The performances on math reasoning tasks are reported.
+
+SFT stage boosts the ability in effective exploration. However, the subsequent DPO stage imposes a slight improvement while significantly reduce the training efficiency.
+
+# 4.5 Generalization to Various Backbones
+
+To demonstrate the generalizability, we apply ENViRONS to enhance two additional base LLMs on mathematical reasoning tasks: (1) DeepSeekChat (DeepSeek-AI, 2024) model of 7B size, which is a foundational LLM and (2) Llemma (Azerbayev et al., 2023), a competent domain-specific LLM optimized for math reasoning. Figure 4 shows the comparisons with Few-shot Prompting and Distill GPT4-then-Finetune. It is observed that our framework still works for strong foundation LLMs, with $9.20\%$ and $14.78\%$ performance boosts for DeepSeek-Chat and Llemma respectively. This demonstrates that our framework can not only convert LLMs from weak to strong, but also elevate LLMs from strong to stronger.
+
+# 5 Analysis
+
+This section will make an in-depth analysis of the underlying reason behind ENVISIONS's success.
+
+# 5.1 What is the Impact of Key Components?
+
+Some key components are ablated independently to verify their effectiveness in Table 3. w/o self-refine ablates both the self-refinement process (i.e., Step 4-6) and $\mathcal{L}_2$ . w/o self-rewards replaces the trajectory ranking on the self-rewarding strategy with random sampling. w/o long-term memory only utilizes the generated trajectories from the current iteration for training. w/o $\mathcal{L}_2$ loss ablates the optimization with positive-negative pairs.
+
+Of these components, self-refine-oriented optimizations (i.e., self-refinement and $\mathcal{L}_2$ loss) play key roles in boosting the performances. As one of the key contributions, the design of $\mathcal{L}_2$ loss leads to $3.10\% - 4.57\%$ improvements in ENVISIONS. It makes full use of negative trajectories while maintaining training efficiency in an RL-free style. Especially in agent tasks, ENVISIONS benefits a lot from $\mathcal{L}_2$ loss, with $3.49\% - 5.53\%$ gains.
+
+# 5.2 What is Behind the Superiority?
+
+We provide in-depth evidence and analysis on the superiority of ENVISIONS from three distinctive views: (1) exploratory ability and stability; (2) log probability margin between positive and negative solutions; and (3) diversity of synthetic samples. The analysis is on LLaMA2-Chat 7B and we leave the discussion of 13B in Appendix C.6.
+
+Balanced exploratory ability and stability are key to success in weak-to-strong. To effectively navigate the environment and acquire new skills autonomously, two factors are crucial: 1) promptly resolving extensive samples to collect correct trajectories, and 2) minimizing the potential loss of knowledge from previously solved samples. We employ two metrics exploratory ability and stability to evaluate the LLM (both of them are the higher, the better). Refer to Appendix B for definition de
+
+Table 3: Ablation studies on key components.   
+
+<table><tr><td rowspan="2">Models</td><td rowspan="2">Agent MiniWob++</td><td colspan="5">Math Reasoning</td><td colspan="2">Logical Reasoning</td><td rowspan="2">Avg.</td></tr><tr><td>GSM8K</td><td>MATH</td><td>GSM-H</td><td>SVAMP</td><td>ASDiv</td><td>ProofWriter</td><td>RuleTaker</td></tr><tr><td colspan="10">LLaMA-2-Chat (7B)</td></tr><tr><td>ENVISIONS</td><td>85.38</td><td>58.98</td><td>19.00</td><td>48.52</td><td>72.40</td><td>69.80</td><td>52.83</td><td>62.63</td><td>58.69</td></tr><tr><td>w/o self-refine</td><td>84.92</td><td>56.86</td><td>18.20</td><td>48.14</td><td>68.70</td><td>67.89</td><td>42.00</td><td>58.60</td><td>55.66</td></tr><tr><td>w/o self-reward</td><td>84.47</td><td>58.61</td><td>18.75</td><td>47.92</td><td>71.10</td><td>68.46</td><td>47.33</td><td>59.61</td><td>57.03</td></tr><tr><td>w/o candidate pool</td><td>83.86</td><td>57.77</td><td>17.55</td><td>47.16</td><td>70.90</td><td>68.03</td><td>49.17</td><td>59.18</td><td>56.70</td></tr><tr><td>w/o L2loss</td><td>81.89</td><td>55.88</td><td>18.90</td><td>47.16</td><td>67.60</td><td>67.75</td><td>47.67</td><td>57.88</td><td>55.59</td></tr><tr><td colspan="10">LLaMA-2-Chat (13B)</td></tr><tr><td>ENVISIONS</td><td>87.12</td><td>68.31</td><td>26.04</td><td>57.54</td><td>78.30</td><td>75.52</td><td>54.83</td><td>60.84</td><td>63.56</td></tr><tr><td>w/o self-refine</td><td>84.24</td><td>65.96</td><td>24.95</td><td>55.34</td><td>77.70</td><td>73.90</td><td>51.00</td><td>57.59</td><td>61.34</td></tr><tr><td>w/o self-reward</td><td>85.45</td><td>67.02</td><td>25.59</td><td>55.57</td><td>77.80</td><td>74.05</td><td>51.50</td><td>60.69</td><td>62.21</td></tr><tr><td>w/o candidate pool</td><td>85.61</td><td>66.89</td><td>24.19</td><td>53.07</td><td>77.20</td><td>72.90</td><td>51.33</td><td>58.96</td><td>61.27</td></tr><tr><td>w/o L2loss</td><td>81.59</td><td>63.08</td><td>20.00</td><td>51.18</td><td>74.30</td><td>71.23</td><td>50.33</td><td>60.19</td><td>58.99</td></tr></table>
+
+![](images/cfcd7d02808fc44bf19893f8a9a254d6fe7e1692054cca0c50c29855a0c6a2d0.jpg)  
+(a)
+
+![](images/1f5239a298e6db889f73cef8845dba54870a009ce917050de5b946c0923e0399.jpg)  
+(b)
+
+![](images/5aa62da7bd4b78fc480dea5778006507e222db5131fac6af761321273ee815fb.jpg)  
+(c)   
+Figure 5: In-depth analysis from three perspectives. Plots in fig.(b) correspond to the methods represented by the same colors in fig.(a).
+
+tails. In Figure 5(a), ENVISIONS demonstrates remarkable performance in achieving a balance between exploratory ability and stability. By leveraging the candidate pool and self-rewards, ENVISIONS effectively retains high-quality positive solutions during training, significantly mitigating the issue of forgetting previous trajectories. Additionally, the RL-free loss $\mathcal{L}_2$ enables flexible updates of the LLM, enhancing its exploration capabilities.
+
+Clearly distinguishing positive and negative solutions can help the LLM optimization. During the optimization process, it is inevitable for the log probability of both positive and negative trajectories to increase simultaneously (Hong et al., 2024). However, clearly keeping the probability margins $(\Delta \log p)$ between positive-negative pairs is crucial to facilitate the optimization. Fig. 5(b) shows the analysis of $\Delta \log p$ during iterations. It is observed ENVISIONS keeps the margin within a reasonable range, while reinforced methods exhibit a rapid decrease in $\Delta \log p$ . It indicates the unsuitability of DPO to the exploration setting and the importance of feedback from ENV. Notably, $S_{\text{TA}} + \text{Env}$
+
+fails to keep the stable margins in the math domain, since it merely utilizes positive data for training, which fails to distinguish negative ones and leads to overfitting on the limited number of solutions. Such finding corresponds to the lack of exploratory ability in Fig. 5(a).
+
+Diverse trajectories are what you need for selftraining. In Fig. 5(c), we compare the number of correct and unique trajectories by the last iteration. It demonstrates the huge strengths of ENVISIONS in synthesizing diverse trajectories. It largely surpasses Reinforced Self-Training approaches, which is one of the underlying reasons for our superiority. In fact, the LLM updates in RL methods are restricted by KL constraints, which ultimately impact the diversity of the generated trajectories. Moreover, Distill GPT-4 and Distill Claude2 lead to 10,831 and 8,561 diverse trajectories with one iteration. Since repeatedly calling strong LLMs involves extremely high cost and cumbersome prompt optimizations, they are far from sustainable compared with ENVISIONS.
+
+# 6 Conclusion
+
+This paper focuses on converting LLMs from weak to strong in increasingly promising neural-symbolic scenarios, without human-annotated symbolic training data. In view of two key challenges, i.e., 1) the scarcity of symbolic training data, and 2) the inherent weakness of LLMs in addressing SL, we conclude the env-guided self-training approach. Built on it, we propose a novel neural-symbolic self-training framework ENVISIONS. Extensive experiments across three domains verify the remarkable performances. In-depth analysis on the superiority of ENVISIONS from three distinctive views provide novel insights for future researches.
+
+# Acknowledgement
+
+This work was supported by National Key Research and Development Program of China (2022YFC3303600), National Natural Science Foundation of China (No. 62137002, 62293550, 62293553, 62293554, 62437002, 62477036, 62176209, 62176207), "LENOVO-XJTU" Intelligent Industry Joint Laboratory Project, Shaanxi Undergraduate and Higher Education Teaching Reform Research Program (No. 23BY195), and Xi'an Jiaotong University City College Research Project (No. 2024Y01), Project of China Knowledge Centre for Engineering Science and Technology, the Youth AI Talents Fund of China Association of Automation (Grant No.HBRC-JKYZD-2024-311).
+
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+Jianing Wang, Qiushi Sun, Nuo Chen, Chengyu Wang, Jun Huang, Ming Gao, and Xiang Li. 2023a. Uncertainty-aware parameter-efficient self-training for semi-supervised language understanding. In *Findings of the Association for Computational Linguistics: EMNLP* 2023, pages 7873-7884, Singapore. Association for Computational Linguistics.   
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+Jerry Wei, Le Hou, Andrew Lampinen, Xiangning Chen, Da Huang, Yi Tay, Xinyun Chen, Yifeng Lu, Denny Zhou, Tengyu Ma, and Quoc Le. 2023. Symbol tuning improves in-context learning in language models.
+
+In Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing, pages 968-979, Singapore. Association for Computational Linguistics.   
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+Can Xu, Qingfeng Sun, Kai Zheng, Xiubo Geng, Pu Zhao, Jiazhan Feng, Chongyang Tao, and Daxin Jiang. 2023a. Wizardlm: Empowering large language models to follow complex instructions. arXiv preprint arXiv:2304.12244.   
+Fangzhi Xu, Qika Lin, Jiawei Han, Tianzhe Zhao, Jun Liu, and Erik Cambria. 2025. Are large language models really good logical reasoners? a comprehensive evaluation and beyond. IEEE Transactions on Knowledge and Data Engineering.   
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+
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+
+# A Implementation Details
+
+In this section, we provide some details of the implementation.
+
+# A.1 Training Details
+
+The SFT training in both our framework and baselines is conducted on 8*A100 with a maximum length of 2,048. They are optimized and accelerated with Deepspeed Zero3 and FlashAttention2. The AdamW optimizer (Loshchilov and Hutter, 2017) is leveraged with a Linear learning rate of 2e-5. The SFT training epoch number of each iteration is set to 2, 1, 2 for agent, math reasoning, and logic reasoning tasks respectively.
+
+For the DPO training stage in baseline methods, it is also conducted on 8*A100 with a maximum length of 2,048. The Linear learning rate is 5e-7 with a warm-up ratio of 0.1. The epoch number for each domain is the same as the SFT stage.
+
+# A.2 Test Tasks and Benchmark
+
+The experiments in the main paper primarily cover three domains: web agent, math reasoning, and logic reasoning. We have concluded some key details in Table 1. In Table 4, we attach extra information on the test tasks and benchmark.
+
+Unless otherwise stated, all these test tasks are evaluated under the zero-shot setting. For MiniWob++ benchmark, we select 44 tasks for the test (Cheng et al., 2024), each with 30 randomly generated samples. All the above settings are consistent among all baseline methods.
+
+# B Definition of Exploratory Ability and Stability
+
+(1) Whether the policy LLM can rapidly explore large amounts of correct samples, and (2) whether it can mitigate the issue of forgetting previously-solved samples are two key factors to evaluate LLMs in interacting with the environment. We define Exploratory Ability (EA) and Stability (STB) respectively as the metrics. The calculation of the metrics is defined as follows:
+
+Suppose that we have the input set $M$ . In the $i^{th}$ iteration, the solved sample (with correct trajectories) constitute of set $M_{i}$ . $\bigcup_{j = 1}^{i - 1}M_{j}$ contains all the previously-solved samples from the iteration 1 to $i - 1$ . And $M_{i}\cup \bigcup_{j = 1}^{i - 1}M_{j}$ comprises the overlapped successful samples between the current iteration and preceding iterations. $M_{i}\setminus \bigcup_{j = 1}^{i - 1}M_{j}$ denotes the sample set that are newly solved in the
+
+current iteration $i$ . Based on the definition, we accumulate to obtain the overall EA and STB of the entire process:
+
+$$
+\mathrm {E A} = \sum_ {i = 2} ^ {T} \frac {\left| M _ {i} \backslash \bigcup_ {j = 1} ^ {i - 1} M _ {j} \right|}{\left| \bigcup_ {j = 1} ^ {i - 1} M _ {j} \right|}, \tag {7}
+$$
+
+$$
+\mathrm {S T B} = \sum_ {i = 2} ^ {T} \frac {\left| M _ {i} \cap \bigcup_ {j = 1} ^ {i - 1} M _ {j} \right|}{\left| \bigcup_ {j = 1} ^ {i - 1} M _ {j} \right|}
+$$
+
+where $|\cdot|$ is the number of samples in the given set. $T$ is the total number of iterations.
+
+Take the process of 2 iterations as an example, suppose the iteration 1 explores 1,000 correct samples. Iteration 2 obtains 1200 correct samples, including 800 previously-solved samples and 400 newly-solved samples. Then, $\mathrm{EA} = 400 / 1000$ and $\mathrm{STB} = 800 / 1000$ .
+
+# C Supplementary Results
+
+# C.1 Evolution Progress
+
+Apart from the performance evolution curves with the LLaMA2-Chat 13B model presented in Figure 3, we expand the discussion on the 7B version. In Figure 6, we visualize the evolution progress of self-training methods on both the model performance and the number of explored samples. The explored sample denotes that one input $x$ is solved by at least one generated symbolic solution $a_{k}$ (i.e., $b_{k} = 1$ ). We count the number of explored samples at each iteration to make the figure.
+
+From the results, the performances of the frameworks are positively correlated with the ability to continuously explore correct trajectories. ENVISIONS presents great superiority, especially in the logic reasoning tasks. Compared with our proposed Env-guided Self-Training approach, Reinforced Self-Training approach appears to be weaker at exploring new samples. This finding is consistent with Figure 5 in the main paper.
+
+# C.2 Scaling of $K$
+
+The hyper-parameter $K$ controls the number of generated candidate symbolic solutions at each generation step. In the main results, we only implement $K = 5$ for illustration.
+
+In Table 5, we present performances under various choices of $K$ , including 2, 5, 10, and 15. Considering the training cost, we only include LLaMA2-Chat (7B) as the base LLM. From the results, we conclude the following takeaways:
+
+<table><tr><td>Domains</td><td>Task name</td><td>Is Held-out?</td><td>#Test Samples</td><td>Beam Size</td><td>Max. Length</td><td>Sources</td></tr><tr><td>Web Agent</td><td>MiniWob++</td><td></td><td>30 (×44 tasks)</td><td>1</td><td>2,048</td><td>Liu et al. (2018)</td></tr><tr><td rowspan="5">Math Reasoning</td><td>GSM8K</td><td></td><td>1,319</td><td>2</td><td>2,048</td><td>Cobbe et al. (2021)</td></tr><tr><td>MATH</td><td></td><td>4,001</td><td>2</td><td>2,048</td><td>Hendrycks et al. (2021)</td></tr><tr><td>GSM-Hard</td><td>✓</td><td>1,319</td><td>2</td><td>2,048</td><td>Gao et al. (2023)</td></tr><tr><td>SVAMP</td><td>✓</td><td>1,000</td><td>2</td><td>2,048</td><td>Patel et al. (2021)</td></tr><tr><td>AsDiv</td><td>✓</td><td>2,096</td><td>2</td><td>2,048</td><td>Miao et al. (2020)</td></tr><tr><td rowspan="2">Logic Reasoning</td><td>ProofWriter</td><td></td><td>600</td><td>1</td><td>4,096</td><td>Tajord et al. (2021)</td></tr><tr><td>RuleTaker</td><td>✓</td><td>1,389</td><td>1</td><td>4,096</td><td>Clark et al. (2021)</td></tr></table>
+
+Table 4: Details of test tasks and benchmarks.   
+Table 5: Scaling of $K$ with LLaMA2-Chat (7B) as the base LLM. In the main results, we implement $K = 5$ for illustration.   
+
+<table><tr><td rowspan="2">Models</td><td rowspan="2">Agent MiniWob++</td><td colspan="5">Math Reasoning</td><td colspan="2">Logical Reasoning</td><td rowspan="2">Avg.</td></tr><tr><td>GSM8K</td><td>MATH</td><td>GSM-H</td><td>SVAMP</td><td>ASDiv</td><td>ProofWriter</td><td>RuleTaker</td></tr><tr><td>K=2</td><td>78.56</td><td>53.60</td><td>17.37</td><td>44.96</td><td>67.20</td><td>66.84</td><td>35.17</td><td>49.82</td><td>51.69</td></tr><tr><td>K=5</td><td>85.38</td><td>58.98</td><td>19.00</td><td>48.52</td><td>72.40</td><td>69.80</td><td>52.83</td><td>62.63</td><td>58.69</td></tr><tr><td>K=10</td><td>79.24</td><td>58.30</td><td>21.89</td><td>48.29</td><td>67.90</td><td>69.75</td><td>53.50</td><td>61.99</td><td>57.61</td></tr><tr><td>K=15</td><td>79.55</td><td>57.47</td><td>23.72</td><td>46.63</td><td>69.80</td><td>70.28</td><td>54.83</td><td>59.54</td><td>57.73</td></tr></table>
+
+Moderate value of $K$ leads to the optimal performances. When $K = 5$ , ENVISIONS demonstrates superior performances, especially on agentic tasks (i.e., MiniWob++ benchmark). However, when reducing the value of $K$ (i.e., $K = 2$ ), the overall performances of ENVISIONS drop a lot. It indicates that keeping a moderate number of candidate solutions in each generation step benefits the self-training process.
+
+Scaling of $K$ does not bring significant improvements. Scaling $K$ from 5 to 10 and 15 does bring improvements on some challenging tasks (e.g., MATH). However, this observation is not consistent across various tasks. Generally, the average performances remain stable with $K$ increasing.
+
+# C.3 Generalization to Other Backbones
+
+In Section 4.5 of the main paper, we have presented the generalization of ENVISIONS to various backbones. The promising results in mathematical domains demonstrate that ENVISIONS is compatible with a wide range of LLMs (from weak LLMs to stronger ones).
+
+To further support our claims, we supplement the experiments on another popular LLM backbone Mistral-Instruct-v0.2 (7B). Limited by selftraining time cost, we only implement it in the agentic domain. We include the strong baselines of $STaR + Env$ , and iterative $SFT + DPO$ for comparisons. Table 6 presents the experimental results.
+
+It is observed that the superiority of ENVISIONS
+
+Table 6: Averaged performances on MiniWob++ benchmark. All these methods are based on Mistral-Instructv0.2 (7B) model.   
+
+<table><tr><td>Methods</td><td>MiniWob++</td><td>Δ</td></tr><tr><td>Few-shot Prompting</td><td>51.44</td><td>+26.51</td></tr><tr><td>iterative SFT+DPO</td><td>73.18</td><td>+4.77</td></tr><tr><td>STaR+Env.</td><td>65.00</td><td>+12.95</td></tr><tr><td>ENVISSIONS</td><td>77.95</td><td>-</td></tr></table>
+
+with the Mistral backbone is also obvious. The generalization capability is further verified. Compared with the previous SOTA method $\text{STaR+Env.}$ , ENVISIONS achieves $12.95\%$ superiority over it. And it also outperforms reinforced self-training baseline iterative $\text{SFT+DPO}$ baseline by $4.77\%$ .
+
+# C.4 Results on latest powerful LLM
+
+To verify the effectiveness and generalization capability of ENVISIONS, we supplement the implementation of ENVISIONS on the latest opensource LLM - LLaMA3.1 in Table 7.
+
+From the results, ENVISIONS still works for the powerful LLaMA3.1-8B model in the mathematical reasoning tasks. It improves performances by large margins and presents superiority over strong baselines.
+
+It is observed that some previous SOTA methods fail to generalize well to LLaMA3.1. It is worth noting that current trending LLMs (e.g., LLaMA3.1) may be widely contaminated by the
+
+![](images/6d78b060cc712e620cd3e3d9dff45338c08bada220225a1b7e59a507210860ea.jpg)
+
+![](images/640f994c5fce42bdf2e24d33e73c25e891fefacf1e346b591fb8220e338095ca.jpg)  
+(a) Evolution of performance.   
+(b) Evolution of explored sample numbers.   
+Figure 6: Evolution curves on LLaMA2-Chat 7B version across agent, math, and logic reasoning domains. (a) is the performance evolution progress. (b) denotes the evolution of explored sample numbers.
+
+Table 7: Performances on LLaMA3.1.   
+
+<table><tr><td></td><td>GSM8K</td><td>MATH</td><td>GSM-H</td><td>Avg.</td></tr><tr><td>Is Held-out ?</td><td>X</td><td>X</td><td>√</td><td>-</td></tr><tr><td colspan="5">LLaMA3.1-Chat (8B)</td></tr><tr><td>Few-shot</td><td>60.27</td><td>39.57</td><td>50.95</td><td>50.26</td></tr><tr><td>Distill GPT-4</td><td>63.08</td><td>38.47</td><td>53.07</td><td>51.54</td></tr><tr><td>ETO</td><td>66.64</td><td>39.29</td><td>59.06</td><td>55.00</td></tr><tr><td>STaR + Env.</td><td>69.60</td><td>36.69</td><td>66.11</td><td>57.47</td></tr><tr><td>ENVISSIONS</td><td>83.32</td><td>42.13</td><td>69.14</td><td>64.86</td></tr></table>
+
+training corpus (e.g., GSM8K) or have been exposed to similar training corpus. That is why we chose to experiment on the Llemma or Mistral base model to evaluate its generalization capability in the original manuscript.
+
+# C.5 Inference-Time Optimization
+
+One of the unique advantages of RL-free loss is the inference-time self-refinement, which can be obtained with traditional contrastive learning works. Table 8 presents the results.
+
+The experimental results show that ENVISIONS can benefit a lot from the optimization of self-refinement (RL-free loss), while other baselines
+
+Table 8: Inference-time optimization. We apply self-refinement strategy to the self-training methods and report the performances on five mathematical datasets.   
+
+<table><tr><td></td><td>GSM8K</td><td>MATH</td><td>GSM-H</td><td>SVAMP</td><td>AsDiv</td></tr><tr><td>iterative SFT+DPO</td><td>54.81</td><td>14.75</td><td>47.08</td><td>70.10</td><td>66.22</td></tr><tr><td>+Self-refine</td><td>55.11</td><td>14.82</td><td>47.38</td><td>71.10</td><td>66.36</td></tr><tr><td>STaR+Env.</td><td>58.23</td><td>18.82</td><td>48.45</td><td>67.50</td><td>68.46</td></tr><tr><td>+Self-refine</td><td>58.30</td><td>18.87</td><td>48.52</td><td>67.60</td><td>68.51</td></tr><tr><td>ENVISSIONS</td><td>58.98</td><td>19.00</td><td>48.52</td><td>72.40</td><td>69.80</td></tr><tr><td>+Self-refine</td><td>60.65</td><td>19.70</td><td>49.81</td><td>73.60</td><td>70.61</td></tr></table>
+
+can hardly conduct effective self-refinement.
+
+# C.6 Detailed Analysis From Three Views
+
+In the section 5.2 of the main paper, we make a analysis on What is behind the superiority of ENVISIONS. We present the analysis with LLaMA2-Chat (7B) model as backbone from three distinctive views: (1) exploratory ability and stability; (2) log probability margin between positive and negative solutions; and (3) diversity of synthetic samples. Here, we supplement the results on the LLaMA2-Chat (13B) model. The main findings are consistent with the 7B model:
+
+Balanced exploratory ability and stability are key to success in weak-to-strong. We employ
+
+![](images/3893025676bd9f6a7d93a550d8613bb51bd2acf39ec28587475972fe90f143c2.jpg)  
+(a)
+
+![](images/6ec5c16652a5a5f21fcca0fe8e313af0a5bfba4c9b7cfa0fe79fcef1a31d2834.jpg)  
+(b)
+
+![](images/1e7610f415cb9ec80a5d977db99eb56811720fe7b75133d492b9e52b2d94c2ed.jpg)  
+(c)
+
+![](images/a17ab367cbafc254e997673a101d1867a8939c4c167fbb13a9457ab82f92c32f.jpg)  
+(d)
+
+![](images/f346fae3a1258ef21e30e72ce0a07f956d23fdaa01bcb3c0ac57f9ae334e7c22.jpg)  
+(e)
+
+![](images/e63a7fbff219402a1944d647a76365e8849173c808434f7ef941637aa0473902.jpg)  
+(f)   
+Figure 7: In-depth analysis from three perspectives. The first row (i.e., (a),(b),(c)) and the second row (i.e., (d),(e),(f)) represent the results on LLaMA2-Chat (7B) and LLaMA2-Chat (13B) respectively. Plots in fig.(b),(e) correspond to the methods represented by the same colors in fig.(a),(d).
+
+two metrics exploratory ability and stability to evaluate the LLM (both of them are the higher, the better). Appendix B gives definition details. In both Fig. 7(a) and (d), ENVISIONS demonstrates remarkable performance in achieving a balance between exploratory ability and stability. By leveraging the candidate pool and self-rewards, ENVISIONS effectively retains high-quality positive solutions during training, significantly mitigating the issue of forgetting previous trajectories. Notably, reinforced self-training methods consistently exhibit unstable performance.
+
+Clearly distinguishing positive and negative solutions can help the LLM optimization. Clearly keeping the probability margins $(\Delta \log p)$ between positive-negative pairs is crucial to facilitate the optimization. Fig. 7 (b) and (e) shows the analysis of $\Delta \log p$ during iterations. It is observed ENVISIONS keeps the margin within a reasonable range, while reinforced methods exhibit a rapid decrease in $\Delta \log p$ . It indicates the unsuitability of DPO to the exploration setting and the importance of feedback from ENV. Such finding corresponds to the
+
+lack of exploratory ability in Fig. 7(a) and (d).
+
+Diverse trajectories are what you need for self-training. In Fig. 7 (c) and (f), we compare the number of correct and unique trajectories by the last iteration. It demonstrates the huge strengths of ENVISIONS in synthesizing diverse trajectories. It largely surpasses Reinforced Self-Training approaches. Notably, LLM updates in RL methods are restricted by KL constraints, which ultimately impact the diversity of the generated trajectories. Moreover, Distill GPT-4 and Distill Claude2 lead to 10,831 and 8,561 diverse trajectories. Since repeatedly calling strong LLMs involves extremely high costs, they are far from sustainable compared with ENVISIONS.
+
+# C.7 How does the Training Recipe Matter in Iterative Self-Exploration?
+
+In each iteration of ENVISIONS, we optimize the policy LLM from scratch (e.g., LLaMA2-Chat) with the updated training trajectories. Such a training recipe is expected to bring stability to the training process, compared with the strategy of contin
+
+Table 9: Comparisons between training strategies. Cont. column denotes the performances of ENVISIONS under the continual training setting.   
+
+<table><tr><td>Tasks</td><td>Cont.</td><td>ENVISIONS</td><td>Δ</td></tr><tr><td colspan="4">LLaMA-2-Chat (7B)</td></tr><tr><td>Agent</td><td>78.18</td><td>85.38</td><td>+7.20</td></tr><tr><td>Math Reasoning</td><td>51.20</td><td>53.74</td><td>+2.54</td></tr><tr><td>Logic Reasoning</td><td>46.20</td><td>57.73</td><td>+11.53</td></tr><tr><td>Average</td><td>53.32</td><td>58.69</td><td>+5.37</td></tr></table>
+
+uous training based on previous checkpoints. Table. 9 presents the performance comparisons. Obvious superiority of ENVISIONS is observed across these three domains, with an average improvement of $5.37\%$ . Training from previous checkpoints does affect the exploration. For the RL-based self-training method, the training of the policy LLM is constrained within the range of the reference model by the KL term. In order to enable continuous evolution, the policy LLM is required to be updated from the checkpoint of the previous iteration. It is also one of the main causes of their sub-optimal performances.
+
+# C.8 MiniWob++ Results Per Tasks
+
+Table 11 shows the performance of ENVISIONS on each of the 44 MiniWob++ tasks.
+
+# C.9 Comparison with more SOTA baselines
+
+To better verify the effectiveness of ENVIRONs, we supplement one more SOTA baseline ETO (Song et al., 2024) for comparison. The results show consistent superiority in math reasoning tasks.
+
+Table 10: Comparisons with another SOTA baseline ETO on math reasoning tasks.   
+
+<table><tr><td>Tasks</td><td>GSM8K</td><td>GSM-H</td><td>MATH</td><td>SVAMP</td><td>AsDiv</td><td>Avg.</td></tr><tr><td colspan="7">LLaMA-2-Chat (7B)</td></tr><tr><td>ETO</td><td>50.04</td><td>15.75</td><td>45.49</td><td>68.10</td><td>65.36</td><td>48.95</td></tr><tr><td>ENVISSIONS</td><td>58.98</td><td>19.00</td><td>48.52</td><td>72.40</td><td>69.80</td><td>53.74</td></tr></table>
+
+# D Pseudocode of ENVISIONS
+
+The self-training framework ENVISIONS can be expressed in Algorithm 1.
+
+# E Prompt of Self-Refinement
+
+We provide the prompt for the self-refinement. Below is an example of the math reasoning task.
+
+# [INPUT]
+
+You are provided with a Python code to solve the given problem. You can either repair and refine it, or simply return the original solution.
+
+The question is:
+
+<question>
+
+The current Python code is:
+
+<negative solution>
+
+The solution code is:
+
+[OUTPUT]
+
+<positive solution>
+
+Table 11: Detailed performances on 44 MiniWob++ tasks.   
+
+<table><tr><td></td><td>1-shot</td><td>Distill GPT4</td><td>Distill Claude2</td><td>STAR+Env.</td><td>Self-Rewarding</td><td>iter. SFT+DPO</td><td>Ours</td></tr><tr><td colspan="8">LLaMA-2-Chat (7B)</td></tr><tr><td>choose-date</td><td>0.00</td><td>0.00</td><td>0.00</td><td>0.00</td><td>0.00</td><td>0.00</td><td>0.00</td></tr><tr><td>choose-list</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td></tr><tr><td>click-button</td><td>0.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>96.67</td><td>100.00</td></tr><tr><td>click-button-sequence</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>96.67</td></tr><tr><td>click-checkboxes</td><td>20.00</td><td>100.00</td><td>96.67</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td></tr><tr><td>click-checkboxes-large</td><td>20.00</td><td>86.67</td><td>96.67</td><td>86.67</td><td>66.67</td><td>100.00</td><td>100.00</td></tr><tr><td>click-checkboxes-soft</td><td>0.00</td><td>6.67</td><td>30.00</td><td>50.00</td><td>0.00</td><td>63.33</td><td>76.67</td></tr><tr><td>click-checkboxes-transfer</td><td>56.67</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td></tr><tr><td>click-collapsible</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td></tr><tr><td>click-color</td><td>53.33</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td></tr><tr><td>click-dialog</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>0.00</td><td>100.00</td><td>100.00</td></tr><tr><td>click-dialog-2</td><td>0.00</td><td>26.67</td><td>73.33</td><td>100.00</td><td>73.33</td><td>100.00</td><td>100.00</td></tr><tr><td>click-link</td><td>73.33</td><td>93.33</td><td>93.33</td><td>93.33</td><td>93.33</td><td>93.33</td><td>93.33</td></tr><tr><td>click-option</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td></tr><tr><td>click-scroll-list</td><td>56.67</td><td>100.00</td><td>100.00</td><td>100.00</td><td>96.67</td><td>100.00</td><td>100.00</td></tr><tr><td>click-shades</td><td>93.33</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td></tr><tr><td>click-shape</td><td>0.00</td><td>70.00</td><td>53.33</td><td>63.33</td><td>16.67</td><td>50.00</td><td>70.00</td></tr><tr><td>click-tab</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>96.67</td><td>56.67</td><td>100.00</td></tr><tr><td>click-test</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td></tr><tr><td>click-test-2</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td></tr><tr><td>click-widget</td><td>96.67</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td></tr><tr><td>copy-paste</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td></tr><tr><td>copy-paste-2</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td></tr><tr><td>enter-date</td><td>3.33</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td></tr><tr><td>enter-password</td><td>96.67</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td></tr><tr><td>enter-text</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td></tr><tr><td>enter-text-dynamic</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td></tr><tr><td>enter-time</td><td>0.00</td><td>30.00</td><td>0.00</td><td>0.00</td><td>0.00</td><td>0.00</td><td>43.33</td></tr><tr><td>focus-text</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td></tr><tr><td>focus-text-2</td><td>33.33</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td></tr><tr><td>guess-number</td><td>6.67</td><td>0.00</td><td>6.67</td><td>10.00</td><td>6.67</td><td>10.00</td><td>10.00</td></tr><tr><td>identify-shape</td><td>0.00</td><td>56.67</td><td>80.00</td><td>100.00</td><td>56.67</td><td>50.00</td><td>100.00</td></tr><tr><td>multi-Layouts</td><td>3.33</td><td>96.67</td><td>86.67</td><td>100.00</td><td>76.67</td><td>96.67</td><td>100.00</td></tr><tr><td>multi-orderings</td><td>0.00</td><td>93.33</td><td>100.00</td><td>100.00</td><td>80.00</td><td>100.00</td><td>100.00</td></tr><tr><td>navigate-tree</td><td>60.00</td><td>60.00</td><td>60.00</td><td>60.00</td><td>60.00</td><td>60.00</td><td>60.00</td></tr><tr><td>read-table</td><td>70.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td></tr><tr><td>search-engine</td><td>3.33</td><td>100.00</td><td>100.00</td><td>100.00</td><td>43.33</td><td>0.00</td><td>100.00</td></tr><tr><td>simple-algebra</td><td>6.67</td><td>50.00</td><td>63.33</td><td>80.00</td><td>6.67</td><td>3.33</td><td>73.33</td></tr><tr><td>simple-arithmetic</td><td>0.00</td><td>86.67</td><td>90.00</td><td>100.00</td><td>40.00</td><td>73.33</td><td>96.67</td></tr><tr><td>social-media-all</td><td>30.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td></tr><tr><td>simple-checkboxes</td><td>26.67</td><td>86.67</td><td>96.67</td><td>90.00</td><td>43.33</td><td>90.00</td><td>93.33</td></tr><tr><td>simple-checkboxes-soft</td><td>0.00</td><td>3.33</td><td>46.67</td><td>90.00</td><td>20.00</td><td>60.00</td><td>90.00</td></tr><tr><td>click-checkboxes-transfer</td><td>10.00</td><td>100.00</td><td>96.67</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td></tr><tr><td>click-checkboxes-large</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td></tr><tr><td>click-color</td><td>56.67</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td></tr><tr><td>click-dialog</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td></tr><tr><td>click-signature</td><td>0.00</td><td>6.67</td><td>6.67</td><td>6.67</td><td>6.67</td><td>6.67</td><td>6.67</td></tr><tr><td>use-spinner</td><td>0.00</td><td>6.67</td><td>6.67</td><td>6.67</td><td>6.67</td><td>0.00</td><td>0.00</td></tr><tr><td>Average</td><td>51.14</td><td>81.14</td><td>82.80</td><td>83.71</td><td>69.47</td><td>77.05</td><td>85.38</td></tr><tr><td colspan="8">LLaMA-2-Chat (13B)</td></tr><tr><td>choose-date</td><td>0.00</td><td>0.00</td><td>0.00</td><td>0.00</td><td>0.00</td><td>0.00</td><td>0.00</td></tr><tr><td>choose-list</td><td>96.67</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td></tr><tr><td>click-button</td><td>96.67</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>96.67</td><td>100.00</td></tr><tr><td>click-button-sequence</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td></tr><tr><td>click-checkboxes</td><td>30.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td></tr><tr><td>click-checkboxes-large</td><td>26.67</td><td>86.67</td><td>96.67</td><td>90.00</td><td>43.33</td><td>90.00</td><td>93.33</td></tr><tr><td>click-checkboxes-soft</td><td>0.00</td><td>3.33</td><td>46.67</td><td>90.00</td><td>20.00</td><td>60.00</td><td>90.00</td></tr><tr><td>click-checkboxes-transfer</td><td>10.00</td><td>100.00</td><td>96.67</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td></tr></table>
+
+Algorithm 1: A Neural-Symbolic Self-Training Framework ENVISIONS   
+Input: Data pair $\{(x,y)\}$ , environment ENV, candidate trajectory pool POOL, weak LLM $\pi_{\theta_0}$ , number of generated samples $K$ , number of iteration $T$ .  
+Output: Strong LLM $\pi_{\theta}^{*}$ .  
+// Initialize $\pi_{\theta} \gets \pi_{\theta_0}$ // Start the Loop  
+for $i = 1$ to $T$ do  
+for each $x$ in the input do  
+// 1-Online Exploration  
+Generate $K$ symbolic solutions with self-rewards: $\{a_k\}_{k=1}^K$ , $\{r_k\}_{k=1}^K \sim \pi_{\theta}(\cdot|x)$ .  
+Get binary rewards by executing in ENV: $\{b_k\}_{k=1}^K \gets \mathbb{I}[\mathbf{ENV}(a_k) == y]$ .  
+Generate self-refined solutions with self-rewards: $\{\widetilde{a}_k\}_{k=1}^K$ , $\{\widetilde{r}_k\}_{k=1}^K \sim \pi_{\theta}(\cdot|x;a_k)$ .  
+Get binary rewards by executing in ENV: $\{\widetilde{b}_k\}_{k=1}^K \gets \mathbb{I}[\mathbf{ENV}(\widetilde{a}_k) == y]$ .  
+Let $T_k = (x,y,a_k,b_k,r_k)$ , $\widetilde{T}_k = (x,y,\widetilde{a}_k,\widetilde{b}_k,\widetilde{r}_k)$ denote the collected trajectories.  
+// 2-Traj. Filtering and Candidate Pool Updating  
+Filter the superior trajectory $T_k^*$ from $T_k$ and $\widetilde{T}_k$ with binary rewards and self-rewards.  
+Update the candidate pool with $T_k^*$ .  
+end  
+// 3-Training  
+Rank and retrieve positive-only training set $U_1$ and positive-negative pairs $U_2$ from POOL.  
+Optimize $\pi_{\theta_0}$ to $\pi_{\theta}^*$ with $\mathcal{L} = -\sum_{(x,a^+) \sim U_1} \log p_{\theta_0}(a^{|x}) - \sum_{(x,a^+,a^-) \sim U_2} \log p_{\theta_0}(a^{|x};a^-)$ .  
+Update the policy LLM for the next iteration: $\pi_{\theta} \gets \pi_{\theta}^*$ end  
+// Output the enhanced LLM  
+Return $\pi_{\theta}^*$ ;

paper_markdowns/bamboo-00492.md

@@ -0,0 +1,370 @@
+# LongRecipe: Recipe for Efficient Long Context Generalization in Large Language Models
+
+Zhiyuan Hu $^{1*}$ , Yuliang liu $^{2,3*}$ , Jinman Zhao $^{4}$ , Suyuchen Wang $^{5}$ , Yan Wang $^{7}$ , Wei Shen $^{3}$ , Qing Gu $^{3}$ , Anh Tuan Luu $^{6}$ , See-Kiong Ng $^{1}$ , Zhiwei Jiang $^{3}$ , Bryan Hooi $^{1\dagger}$
+
+$^{1}$ National University of Singapore, $^{2}$ Shanghai Innovation Institute $^{3}$ Nanjing University,
+
+<sup>4</sup>University of Toronto, <sup>5</sup>Mila, Québec AI Institute / Université de Montréal,
+
+$^{6}$ Nanyang Technological University, $^{7}$ The University of Hong Kong
+
+zhiyuan_hu@u.nus.edu, bhooi@comp.nus.edu.sg
+
+# Abstract
+
+Large language models (LLMs) face significant challenges in handling long-context tasks because of their limited effective context window size during pretraining, which restricts their ability to generalize over extended sequences. Meanwhile, extending the context window in LLMs through post-pretraining is highly resource-intensive. To address this, we introduce LongRecipe, an efficient training strategy for extending the context window of LLMs, including impactful token analysis, position index transformation, and training optimization strategies. It simulates long-sequence inputs while maintaining training efficiency and significantly improves the model's understanding of long-range dependencies. Experiments on three types of LLMs show that LongRecipe can utilize long sequences while requiring only $30\%$ of the target context window size, and reduces computational training resource over $85\%$ compared to full sequence training. Furthermore, LongRecipe also preserves the original LLM's capabilities in general tasks. Ultimately, we can extend effective context window of open-source LLMs from $8k$ to $128k$ , achieving performance close to GPT-4 with just one day of dedicated training using a single GPU with $80G$ memory. Our code is released at https://github.com/zhiyuanhubj/LongRecipe.
+
+# 1 Introduction
+
+LLMs are crucial for NLP tasks. However, they face challenges in applications involving long context, such as in-context learning (Brown et al., 2020), long document summarization (Koh et al., 2022), long-form QA (Krishna et al., 2021), document-level retrieval (Callan, 1994) and and multi-modal QA (Yang et al., 2025a,b). These challenges stem from their limited effective context
+
+window size during the pretraining process, making long-context generalization difficult.
+
+A straightforward approach is to continually pretrain or fine-tune these models on long context input (Fu et al., 2024). However, expanding the context window usually results in a quadratic increase in computational and memory costs. According to the training setup in (Fu et al., 2024), extending the Llama-2 7B model's context window from 4k to 80k using 8 A100 GPUs (80G each) takes five days. The costs of resources and time increase significantly for larger models and more extended training periods. In addition to the methods mentioned, there are techniques aimed at extending the length of the context window more efficiently during fine-tuning, including PI (Chen et al., 2023), Yarn (Peng et al., 2024), and LongLoRA (Chen et al., 2024b). However, these techniques still require full-length fine-tuning, meaning they must fine-tune with the context of the target length, which is both memory- and time-intensive. Meanwhile, Randomized Positional Encoding Scheme (Ruoss et al., 2023) and PoSE (Zhu et al., 2023) simulate longer inputs within a fixed window by adjusting position indices, allowing LLMs that are trained on shorter contexts to be extended to longer context windows. However, randomized position embeddings in (Ruoss et al., 2023) disrupt local sentence structures by exaggerating the dependency lengths between neighboring tokens. PoSE, on the other hand, only considers two chunks to mimic the position index, consistently omitting longer dependencies in the sequence. This distortion creates a significant generalization gap in understanding token relationships across the sequence when extending LLMs to a long context window.
+
+To address the aforementioned issues and further uncover the potential of efficient training for long-context generalization in LLMs, we present LongRecipe, an efficient framework designed to enhance long-context capabilities in models. Long
+
+Rotary Position Embeddings have been shown to effectively encode positional information ....... (Long Sequence of Input)
+
+![](images/2ed181048e42e8b64af432d5c541f73a156b0e055afcd19392aceab853b699cf.jpg)  
+Figure 1: Method Overview
+
+context generalization depends on token distances set by position indexes, which are then combined with token representations. LongRecipe is primarily focused on optimizing the learning process by efficiently handling both position indexes and token representations. Our framework introduces Impactful Token Analysis to identify tokens that significantly influence long-text training. By focusing on these tokens, we extract shorter segments from long-text corpora, reducing text length while preserving key information. We then apply Position Index Transformation to simulate long-sequence positional indices using these shortened texts, extending the model's ability to handle long sequences without needing actual long texts. Additionally, we implement training optimizations — pretraining data replay and model merging — to enhance the model's long-text processing capabilities. As illustrated in Figure 1, LongRecipe compares the logits of output tokens from an untuned LLM with those from a tuned LLM within a longer context. This reveals significant token logit changes from long context generalization training. Sentences or paragraphs with these tokens are selected, upsampled, and segmented with continuous positional indices, then used to train the LLM, effectively extending its context window. This method efficiently captures key changes in long-context training while improving training efficiency by streamlining samples. The position index transformation also sharpens the
+
+model's understanding of long-range dependencies and sequences in extended texts.
+
+To validate the effectiveness of LongRecipe, we conduct the empirical evaluation with Llama3-8B, Mistral-7B, Qwen2-7B on Multi-Needle In A Haystack (gkamradt, 2023), RULER (Hsieh et al., 2024) and LongBench (Bai et al., 2023). Applied with LongRecipe, we can extend the effective context window of an open-source LLM from 8k or 32k to 80k or 128k. The experimental results demonstrate that LongRecipe achieves an average improvement of approximately $5.5\%$ across four metrics in three types of models, with context windows 80k and 128k. Additionally, using as little as $30\%$ of the tokens with around 1/8 of the GPU computational resources can achieve nearly the same performance as full context window training. Currently, we can extend an open-source LLM's context window from 8k to 128k, matching GPT-4-Turbo's performance with just one day of training on a single H100 GPU. Furthermore, we test the performance of our method in general tasks, including MMLU (Hendrycks et al., 2021), GSM8K (Cobbe et al., 2021), and HumanEval (Chen et al., 2021) to assess if our method impacts LLMs' general abilities, showing it largely preserves their original performance. To summarize, our contributions are as follows:
+
+- We introduce LongRecipe, leveraging impactful token analysis and position index transfor
+
+mation to fully uncover the potential of efficient training for long context generalization.
+
+- LongRecipe uses training strategies of the pretraining data replay and model merging to enable LLMs to preserve the original foundational abilities and enhance long context generalization ability stably.   
+- Experiments on context lengths from 8k-128k across three types of LLMs validate LongRecipe's effectiveness.
+
+# 2 Preliminary
+
+The approach that is widely used in previous pretrained language models such as BERT (Devlin et al., 2018) is to add position embedding vectors to word embedding vectors directly. For a sequence of tokens represented as $w_{1}, w_{2}, \dots, w_{L}$ , with their corresponding embeddings $\mathbf{x}_1, \mathbf{x}_2, \dots, \mathbf{x}_L$ , let $\mathbf{p}_1, \mathbf{p}_2, \dots, \mathbf{p}_L$ be absolute position embedding, the position encoding of query $(\mathbf{q})$ and $\text{key}(\mathbf{k})$ are $\mathbf{q}_m = W_q(\mathbf{x}_m + \mathbf{p}_m)$ and $\mathbf{k}_n = W_k(\mathbf{x}_n + \mathbf{p}_n)$ . Then the unnormalized attention scores are calculated by dot-producting two vectors: $score(\mathbf{q}_m, \mathbf{k}_n) = \mathbf{q}_m^T \cdot \mathbf{k}_n$ .
+
+Rotary Position Embedding (RoPE) (Su et al., 2024) is proposed to integrate relative positional information by modulating the query and key vectors in the attention mechanism. Let $D$ denote the dimension of hidden layers, the transformations applied are as follows:
+
+$$
+\mathbf {q} _ {m} = W _ {q} \mathbf {x} _ {m} \cdot e ^ {i m \theta} \tag {1}
+$$
+
+$$
+\mathbf {k} _ {n} = W _ {k} \mathbf {x} _ {n} \cdot e ^ {i n \theta} \tag {2}
+$$
+
+where $W_{q}$ and $W_{k}$ are $|D| \times |D|$ projection matrices, $m$ and $n$ are the positions of the tokens, and $\theta$ is a constant that adjusts the rotation based on token positions.
+
+$$
+\theta_ {i} = 1 0 0 0 0 ^ {\frac {- 2 i}{D}}
+$$
+
+RoPE operation on $\vec{q} = W_{q}\mathbf{x}_{m}$ results $\mathbf{q}_m =$
+
+$$
+\left[ \begin{array}{c} q _ {0} \\ q _ {1} \\ \vdots \\ q _ {D - 2} \\ q _ {D - 1} \end{array} \right] \otimes \left[ \begin{array}{c} \cos m \theta_ {0} \\ \cos m \theta_ {0} \\ \vdots \\ \cos m \theta_ {\frac {D}{2} - 1} \\ \cos m \theta_ {\frac {D}{2} - 1} \end{array} \right] + \left[ \begin{array}{c} q _ {1} \\ q _ {0} \\ \vdots \\ q _ {D - 1} \\ q _ {D - 2} \end{array} \right] \otimes \left[ \begin{array}{c} - \sin m \theta_ {0} \\ \sin m \theta_ {0} \\ \vdots \\ - \sin m \theta_ {\frac {D}{2} - 1} \\ \sin m \theta_ {\frac {D}{2} - 1} \end{array} \right]
+$$
+
+The real part of the inner product between $\mathbf{q}_m$ and $\mathbf{k}_n$ captures the relative positional information, facilitating the model's understanding of token distances.
+
+# 3 Related Works
+
+Position Encoding Various position encoding methods have been proposed to support extrapolation beyond the pretraining window, such as AL-iBi (Press et al., 2022), xPos (Sun et al., 2023), and KERPLE (Chi et al., 2022) introduce bias terms, scaling, or kernel-based functions to improve length generalization.
+
+RoPE (Su et al., 2024) and CoPE (Golovneva et al., 2024), two widely used mechanisms, introduce more structured encoding strategies. RoPE applies fixed-frequency complex rotations to query and key vectors, encoding absolute positions in a way that allows relative position differences to emerge naturally through phase shifts. Unlike methods that explicitly model relative positions or learn position embeddings, RoPE is nonparametric, architecture-free, and enables smooth extrapolation by design.
+
+Efficient Pretraining or Fine-tuning Methods Position Interpolation (PI)(Chen et al., 2023) downsizes position indices of long text to the original window size. NTK Interpolation(Peng and Quesnelle, 2023) adjusts rotation speed for small positions and linear interpolation for large ones. YaRN (Peng et al., 2024) improves NTK Interpolation with NTK-by-parts scaling to accommodate different RoPE features. Resonance RoPE (Wang et al., 2024a) refines RoPE features with integer wavelengths, improving upon YaRN for better out-of-distribution position recognition. LMInfinite (Han et al., 2024) encodes absolute positions for starter tokens and masks middle tokens, retaining relative positions for rare tokens. Randomized Positional Embedding (Ruoss et al., 2023) simulates long text input with shorter texts by randomly selecting position indices. PoSE (Zhu et al., 2023) uses a fixed context window, dividing it into chunks with skipping bias terms, enabling adaptation to all positions within the target length. CREAM (Wu et al., 2024) builds upon PoSE and proposes a truncated Gaussian sampling strategy to address the "Lost-in-the-Middle" issue, enabling the model to better capture middle-position information during fine-tuning without exceeding the original context window. LongLoRA (Chen et al., 2024b) replaces ordinary attention with shift short attention. Temp Lora (Wang et al., 2024b) integrates context details into a temporary Lora module, incrementally trained with previously generated text. SelfExtend (Jin et al., 2024) and DCA
+
+(An et al., 2024) convert the attention computation for long sequences into chunk-based modules to achieve the training-free extension.
+
+# 4 Methodology
+
+# 4.1 Impactful Token Analysis
+
+Consider a base large language model $H$ with a context window size $L$ . This model is further trained to extend its context window to $L'$ , resulting in a new model denoted as $H'$ . Using the LongRecipe methodology, we can calculate the logit offset for each token by comparing the differences between the logits produced by $H$ and $H'$ . We then identify the token types with the most significant changes in logits to serve as anchors for selecting sentences containing these token types, which are then used for upsampling.
+
+Formally, for each token $t$ , we condition both the base model $H$ and the extended model $H'$ on the preceding prompt $x < t$ to obtain the logit probability scores $S_{H}(t \mid x < t)$ and $S_{H'}(t \mid x < t)$ , respectively. These scores represent the final unnormalized logits from the language modeling head over the vocabulary. The distribution of logit probability changes is then given by:
+
+$$
+\begin{array}{l} p \left(X _ {t} \mid x <   t\right) = \operatorname {s o f t m a x} \left[ S _ {H ^ {\prime}} \left(X _ {t} \mid x <   t\right) \right. \\ \left. - S _ {H} \left(X _ {t} \mid x <   t\right) \right] \tag {3} \\ \end{array}
+$$
+
+To formally describe the process of selecting token types with the most significant logit changes, we define a significance score $\Delta (t)$ for each token type $t$ as:
+
+$$
+\begin{array}{l} \Delta (t) = \sum_ {i = 1} ^ {N} \left| S _ {H ^ {\prime}} \left(X _ {t} ^ {(i)} \mid x <   t ^ {(i)}\right) \right. \\ - S _ {H} \left(X _ {t} ^ {(i)} \mid x <   t ^ {(i)}\right) | \tag {4} \\ \end{array}
+$$
+
+where $N$ represents the total number of samples. We then rank all token types by their significance score $\Delta (t)$ , and select the token types with the highest scores as anchors. The selected tokens are used to identify and upsample sentences that contain these tokens.
+
+Intuitively, we aggregate the distributions across all samples to derive the statistics of token types whose logit probability changes are most significant. We select the top $20\%$ of tokens based on their significance scores $\Delta(t)$ at each position (e.g., the $i$ -th token in the sample). We then calculate the frequency of each token type (part-of-speech).
+
+Subsequently, for a given sample, we first remove sentences that do not contain these token types, which generally constitute a significant portion of the total sentences. Then, from the remaining sentences, we select a fixed number of tokens to use for further training.
+
+# 4.2 Position Index Transformation
+
+We aim to utilize the current data with context window $L$ to enable the model with larger input context length $\hat{L}$ by further continual pretraining in the data with synthesized position indices. Let $S$ be the original sequence. We define a function $\mathbf{seg}: S \to \{s_1, s_2, \ldots, s_N\}$ that partitions $S$ into $N$ segments, where each segment $s_i$ can be either a sentence or a paragraph, for $1 \leq i \leq N$ . The function $\mathbf{seg}$ satisfies the following conditions:
+
+$$
+S = s _ {1} \cup s _ {2} \cup \dots \cup s _ {N} \tag {5}
+$$
+
+The union of all segments reconstructs the original sequence and segments are disjoint:
+
+$$
+s _ {i} \cap s _ {j} = \emptyset \quad \text {f o r a l l} \quad i \neq j \tag {6}
+$$
+
+To vary the spacing between each segment, we will randomly skip some position indices from 0 to $M$ , where $M$ is a parameter of our method. When $M = 0$ , the position indices of the two segments will be continuous.
+
+We start by defining $\mathbf{pos}(s_i)$ as the position index of the first token of segment $s_i$ . For each segment, the position indices are sequentially increased by 1 for each token within that segment. The position index of the first token in the first segment is set to 0, i.e., $\mathbf{pos}(s_1) = 0$ .
+
+For subsequent segments, we introduce a random skip represented by a function $g(s_{i})$ which takes values from $0, 1, \ldots, M$ . This function represents the gap before the start of segment $s_{i}$ and is determined randomly for each segment. Thus, the position index of the first token of segment $s_{i}$ , for $i \geq 2$ , can be defined recursively as follows:
+
+$$
+\operatorname {p o s} \left(s _ {i}\right) = \operatorname {p o s} \left(s _ {i - 1}\right) + \left| s _ {i - 1} \right| + g \left(s _ {i}\right) + 1 \tag {7}
+$$
+
+Where $|s_{i-1}|$ represents the number of tokens in segment $s_{i-1}$ . We repeat this process until the position index of the last token of the last segment $s_N$ does not exceed $\hat{L}$ .
+
+To achieve comprehensive coverage of the target context window, we re-sample both the length and skipping term of every chunk for each training example.
+
+# 4.3 Training Optimization Strategies
+
+When we extend the effective context window of LLMs, we also want to enable the LLMs with strong general abilities within their original context window. Therefore, we explore the below two training optimization strategies to achieve that.
+
+Pretraining Data Replaying In this module, we address the issue of maintaining a model's general capabilities during post-training by employing a Pretraining Data Replay strategy. Specifically, we define two datasets: $\mathcal{D}_1$ , which represents the original pretraining data, and $\mathcal{D}_2$ , which is a replay dataset derived from $\mathcal{D}_1$ . Both $\mathcal{D}_1$ and $\mathcal{D}_2$ share the same distribution.
+
+The replay dataset $\mathcal{D}_2$ is used for further training after the model undergoes long-sequence extension training. This process is intended to help the model recover and reinforce its general capabilities that may have been affected during the length extension training. Formally, during the replay phase, the model is trained on $\mathcal{D}_2$ to restore and enhance its generalization abilities: $\Theta_{\mathrm{replay}} = \mathrm{Train}(\Theta_{\mathrm{extended}},\mathcal{D}_2)$ . Here, $\Theta_{\mathrm{extended}}$ represents the model after it has undergone long-sequence extension training, and $\Theta_{\mathrm{replay}}$ is the model after the replay phase using $\mathcal{D}_2$ .
+
+Model Merging To maintain the general abilities of original LLMs trained in short context window, we utilize a model merging technique to integrate the capabilities of two distinct models: one that is the original model without context window extension $(\Theta^{(o)})$ and another that is trained with longer context and pretraining data replaying $(\Theta^{(replay)})$ . We use two hyperparameters $\lambda_{1}$ and $\lambda_{2}$ to retains the general abilities of original models and the long context generalization of tuned model. The merged model can be represented by the following equation:
+
+$$
+\Theta_ {\text {m e r g e}} = \lambda_ {1} \Theta^ {(o)} + \lambda_ {2} \Theta^ {(\text {r e p l a y})} \tag {8}
+$$
+
+# 5 Experimental Setup
+
+# 5.1 Baselines
+
+We use the following long context training method as our baseline:
+
+1. Full-length Text Training (FLT). We train the LLMs using a corpus that contains the full target context length. This approach serves as a baseline for comparing the performance and observing any potential loss when applying our method.
+
+2. Randomized Positional Encoding Scheme (RPES) (Ruoss et al., 2023) simulates the positions of longer sequences and randomly selects an ordered subset to match the longer length.   
+3. Positional Skip-wisE (PoSE) (Zhu et al., 2023) simulates long inputs using a fixed context window. It divides the original context window into two chunks and applies distinct skipping bias terms to manipulate the position indices of each chunk. These bias terms and the lengths of the chunks are changed for each training example, enabling the model to adapt to positions within the target length.
+
+# 5.2 Dataset and Evaluation
+
+Dataset for Training We use the dataset in the work (Fu et al., 2024) as training set. The dataset derived from SlimPajama (Cerebras, 2023), incorporates domain balancing and length upsampling. This dataset includes 80k samples and 128k tokens for each, we use 10k samples in the experiments for all baselines.
+
+Benchmarks of Long Context Generalization We use the following benchmarks to evaluate our method:
+
+1. The Needle In A Haystack (NIAH) framework (gkamradt, 2023) tests LLMs' ability to retrieve hidden information by embedding a "needle" (fact) within a "haystack" (long document). As the current LLMs can almost perform perfectly in a single-needle retrieval task, we use a more challenging multi-needle retrieval task to evaluate LLMs' ability, namely NIAH(M).   
+2. RULER (Hsieh et al., 2024) offers flexible sequence lengths and task complexities with 13 sub-task categories, including retrieval and question answering.
+
+We supplement more details about these benchmark in Appendix E.
+
+Datasets for Assessment of Fundamental Abilities of LLMs We use three benchmarks to test if the continual pretraining process affects LLMs' fundamental abilities within their original context length:
+
+1. MMLU covers 57 subjects across STEM, the humanities, the social sciences, philosophy,
+
+law, medicine and more (Hendrycks et al., 2021). It serves as a comprehensive benchmark for evaluating a model's general language understanding and broad factual knowledge.
+
+2. GSM8K (Cobbe et al., 2021) is a benchmark of grade school-level math word problems that test a model's ability to perform multi-step arithmetic reasoning. The dataset contains 7,473 training problems and 1,319 test problems, each requiring multiple computation steps to arrive at the correct answer.
+
+3. HumanEval (Chen et al., 2021) is a code generation benchmark consisting of 164 handwritten programming problems. It evaluates a model's ability to generate correct and semantically accurate Python code.
+
+# 5.3 Setup
+
+Long Context Training We train the LLMs using samples with $30\%$ of the extended context window length and optimize efficiency with FlashAttention 2 (Dao et al., 2022) and DeepSpeed Zero 3 (Aminabadi et al., 2022). To further train the LLMs with longer context window, we utilize Accelerator of Huggingface (Face) and Sequence Parallel technique (e.g. DeepSpeed-Ulysses (Jacobs et al., 2023) and Ring Attention (Liu et al., 2023; Zhu)) to optimize the GPU memory demands. More details including RoPE scaling, Batch Size, Hours to Train and others are in Appendix B.
+
+Pretraining Data Replay We use WizardLM-evol-instruct-70k (Luo et al., 2023) and Magicoder-OSS-Instruct-75K(Wei et al., 2024), totally with 68M tokens. Based on the findings in (Yang et al., 2024b), replaying $5\%$ to $10\%$ of the post-training dataset is considered the optimal configuration. For our setup, we use a batch size of 96, a learning rate of 5e-6, and a decay rate of 0.1. Model Merging We set $\lambda_{1}$ and $\lambda_{2}$ as 0.5, hence it would be the average weight for model merging.
+
+LLMs We test various LLMs to evaluate our approach, including Llama3 (Meta.AI, 2024), Mistral (Mistral.AI, 2024), Qwen2 (Yang et al., 2024a), GPT-4 (OpenAI: Josh Achiam et al., 2023), Gemini-1.5-Pro (Reid et al., 2024) and others. Information about all models is in Appendix C.
+
+# 6 Experimental Performance
+
+# 6.1 Long Context Generalization
+
+The LongRecipe method shows an average improvement of $6.6\%$ over RPES and $7.8\%$ over PoSE in the NIAH(M) task. In the RULER evaluation, LongRecipe outperforms RPES by $2.9\%$ and PoSE by $4.7\%$ . Especially, in the NIAH task, Llama3-8B-I (80k) shows a $10.1\%$ improvement with LongRecipe over PoSE. In the RULER task, Mistral7B (128k) improves by $11.9\%$ . In addition, our method remains competitive on Llama3-8B and Qwen2 while outperforming others on Mistral on LongBench (Bai et al., 2023), which is the first bilingual benchmark for long context understanding. We report the results of the experiments and provide further discussion in Appendix A.
+
+Compared to the performance of current closed-source and open-source LLMs with a 128k context window, LongRecipe not only surpasses base models like Yi-9B, Llama3.1-8B, and the instruction model Qwen2-7B-Instruct but also achieves performance comparable to Gradient-Llama3-8B, which uses four times the tokens and full-length training. Additionally, LongRecipe approaches the performance levels of GPT-4.
+
+# 6.2 Maintaining General Abilities
+
+Table 1 shows that LLMs can nearly maintain their general abilities with short inputs, as seen by the minor performance drop in MMLU. Despite some remaining gaps in mathematical (GSM8K) and programming (HumanEval) abilities, the model merging and pretraining data replay strategy successfully restored approximately $75\%$ and $65\%$ of the original capabilities.
+
+# 6.3 Ablation Study
+
+Benefits of Impactful Token Analysis and Position Index Transformation As shown in Table 3, the performance will drop significantly in NIAH(M) and RULER metrics when we randomly select sentence from long sequence (LongRecipe (Random T)) rather than using analyzed token pattern. Additionally, the application of Position Index Transformation can bring average $3.3\%$ improvement from PoSE to LongRecipe (w/o T).
+
+Effect of Pre-training Data Replay and Model Merging for Maintaining General Abilities In Table 2, comparing the models before and after replaying shows noticeable improvement, partic
+
+Table 1: Performance of different methods in long context generalization tasks and general abilities benchmarks. FLT* in Qwen2-7B denotes the Qwen2-7B base model combined with YARN and DCA methods for targeting the context window, as detailed in their technical report. In 'Other LLMs' part, the models above dashed line are the base model and blow are instruction tuned models. All the experiment results of FLT, RPES and PoSE are implemented by us.   
+
+<table><tr><td rowspan="2">Model</td><td rowspan="2">Length</td><td rowspan="2">Method</td><td colspan="2">Long Context Generalization</td><td colspan="3">General Abilities</td></tr><tr><td>NIAH(M)</td><td>RULER</td><td>MMLU</td><td>GSM8K</td><td>HumanEval</td></tr><tr><td rowspan="9">Llama3-8B-I</td><td>8k</td><td>Base Model</td><td>-</td><td>-</td><td>65.7</td><td>71.4</td><td>37.5</td></tr><tr><td rowspan="4">80k</td><td>FLT</td><td>82.3</td><td>75.7</td><td>62.2</td><td>54.5</td><td>32.7</td></tr><tr><td>RPES</td><td>71.8</td><td>71.4</td><td>61.4</td><td>53.1</td><td>15.4</td></tr><tr><td>PoSE</td><td>68.8</td><td>69.9</td><td>62.6</td><td>58.2</td><td>25.6</td></tr><tr><td>LongRecipe</td><td>78.9</td><td>74.5</td><td>63.0</td><td>57.9</td><td>29.3</td></tr><tr><td rowspan="4">128k</td><td>FLT</td><td>73.2</td><td>75.8</td><td>58.3</td><td>50.9</td><td>16.5</td></tr><tr><td>RPES</td><td>72.7</td><td>71.5</td><td>59.2</td><td>46.0</td><td>16.8</td></tr><tr><td>PoSE</td><td>80.1</td><td>75.3</td><td>61.9</td><td>51.1</td><td>21.1</td></tr><tr><td>LongRecipe</td><td>82.6</td><td>76.0</td><td>62.1</td><td>54.9</td><td>24.2</td></tr><tr><td rowspan="8">Mistral-7B</td><td>32k</td><td>Base Model</td><td>-</td><td>-</td><td>55.7</td><td>28.4</td><td>31.1</td></tr><tr><td rowspan="4">80k</td><td>FLT</td><td>43.0</td><td>57.4</td><td>52.6</td><td>25.2</td><td>25.6</td></tr><tr><td>RPES</td><td>60.4</td><td>65.1</td><td>51.8</td><td>27.4</td><td>24.7</td></tr><tr><td>PoSE</td><td>64.7</td><td>65.0</td><td>54.9</td><td>29.4</td><td>27.6</td></tr><tr><td>LongRecipe</td><td>64.7</td><td>67.2</td><td>53.7</td><td>28.0</td><td>27.6</td></tr><tr><td rowspan="3">128k</td><td>RPES</td><td>41.9</td><td>52.5</td><td>52.8</td><td>26.5</td><td>24.8</td></tr><tr><td>PoSE</td><td>35.9</td><td>46.3</td><td>53.4</td><td>25.9</td><td>22.6</td></tr><tr><td>LongRecipe</td><td>53.4</td><td>58.2</td><td>53.1</td><td>26.0</td><td>24.2</td></tr><tr><td rowspan="9">Qwen2-7B</td><td>32k</td><td>Base Model</td><td>-</td><td>-</td><td>66.1</td><td>58.3</td><td>20.3</td></tr><tr><td rowspan="4">80k</td><td>FLT*</td><td>64.7</td><td>69.5</td><td>68.4</td><td>63.1</td><td>27.4</td></tr><tr><td>RPES</td><td>73.7</td><td>68.9</td><td>65.7</td><td>55.1</td><td>16.0</td></tr><tr><td>PoSE</td><td>70.0</td><td>66.7</td><td>66.6</td><td>58.9</td><td>17.7</td></tr><tr><td>LongRecipe</td><td>79.5</td><td>70.8</td><td>65.7</td><td>57.2</td><td>19.1</td></tr><tr><td rowspan="4">128k</td><td>FLT*</td><td>52.7</td><td>51.3</td><td>68.4</td><td>63.1</td><td>27.4</td></tr><tr><td>RPES</td><td>64.6</td><td>64.6</td><td>65.5</td><td>56.1</td><td>14.8</td></tr><tr><td>PoSE</td><td>58.5</td><td>60.1</td><td>67.1</td><td>58.2</td><td>20.9</td></tr><tr><td>LongRecipe</td><td>65.8</td><td>64.8</td><td>65.9</td><td>58.7</td><td>17.3</td></tr><tr><td rowspan="12">Other LLMs</td><td rowspan="12">128k</td><td>Llama3.1-8B</td><td>72.0</td><td>69.8</td><td>62.0</td><td>41.8</td><td>38.4</td></tr><tr><td>Yi-9B-200k</td><td>65.7</td><td>62.3</td><td>42.5</td><td>51.3</td><td>21.3</td></tr><tr><td>Yi-34B-200k</td><td>84.9</td><td>77.3</td><td>76.3</td><td>67.2</td><td>23.2</td></tr><tr><td>Qwen2-7B-Instruct</td><td>38.8</td><td>52.5</td><td>69.5</td><td>55.6</td><td>43.3</td></tr><tr><td>Gradient-Llama3-8B</td><td>89.6</td><td>78.4</td><td>59.4</td><td>49.9</td><td>13.4</td></tr><tr><td>Llama3.1-8B-Instruct</td><td>89.0</td><td>77.7</td><td>73.0</td><td>84.5</td><td>72.6</td></tr><tr><td>GLM4-9B-Chat-1M</td><td>90.2</td><td>79.9</td><td>74.7</td><td>84.0</td><td>70.1</td></tr><tr><td>Llama3.1-70B-Instruct</td><td>68.3</td><td>66.6</td><td>86.0</td><td>95.1</td><td>80.5</td></tr><tr><td>Qwen2-72B-Instruct</td><td>83.4</td><td>53.7</td><td>84.2</td><td>89.5</td><td>64.6</td></tr><tr><td>Gradient-Llama3-70B</td><td>79.2</td><td>72.1</td><td>72.5</td><td>73.4</td><td>33.5</td></tr><tr><td>GPT-4</td><td>76.2</td><td>81.2</td><td>80.5</td><td>93.0</td><td>73.2</td></tr><tr><td>Gemini-1.5-Pro</td><td>82.0</td><td>94.4</td><td>81.9</td><td>91.7</td><td>71.9</td></tr></table>
+
+cularly on the GSM8K dataset. By further merging with the original model, we can enhance the model's general capabilities, as seen in the MMLU performance (63% vs. 65.7%). Although there are still some gaps in mathematical (GSM8K) and coding (HumanEval) capabilities, the model merging and pretraining data replaying successfully recovers approximately 75% and 65% of the original abilities.
+
+Performance Comparison Based on Various Number of Tokens As the number of tokens per sample increases, the performance of each sample improves consistently. However, the benefit gained from increasing the number of tokens (i.e., extend
+
+ing the context length) diminishes. Even when we increase the token ratio from $30\%$ to $100\%$ , only around $1\%$ improvement can be obtained. This is particularly evident in the results of Llama3-8B for a 128-token context window, as shown in Table 1, where we achieve even better performance than FLT with $100\%$ of the tokens.
+
+# 6.4 Analysis
+
+Distance Among Tokens and Continual Length of Segments We suppose the effectiveness of position index transformation stems from improving distances among token while maintaining local information via continual segment. Therefore, we
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">Before Replaying</td><td colspan="3">After Replaying</td><td colspan="3">After Model Merging</td></tr><tr><td>MMLU</td><td>GSM8K</td><td>HE</td><td>MMLU</td><td>GSM8K</td><td>HE</td><td>MMLU</td><td>GSM8K</td><td>HE</td></tr><tr><td>FLT</td><td>58.1</td><td>39.7</td><td>20.9</td><td>58.2</td><td>47.2</td><td>17.5</td><td>62.2</td><td>54.5</td><td>32.3</td></tr><tr><td>RPES</td><td>54.0</td><td>33.6</td><td>15.2</td><td>59.7</td><td>46.7</td><td>3.3</td><td>61.8</td><td>53.9</td><td>12.6</td></tr><tr><td>PoSE</td><td>58.1</td><td>39.1</td><td>17.0</td><td>60.7</td><td>49.5</td><td>5.7</td><td>62.6</td><td>58.2</td><td>25.6</td></tr><tr><td>LongRecipe</td><td>58.6</td><td>42.7</td><td>20.1</td><td>62.1</td><td>50.9</td><td>6.7</td><td>63.0</td><td>57.9</td><td>29.3</td></tr></table>
+
+Table 2: Performance of different stages in long context generalization training, pretraining data replaying and model merging. HE represents HumanEval. All experiments are conducted using the Llama3-8B-instruct model, with $30\%$ of tokens utilized within an 80k token target context window.   
+
+<table><tr><td>Method</td><td>NIAH(M)</td><td>RULER</td></tr><tr><td>PoSE</td><td>68.8</td><td>69.9</td></tr><tr><td>LongRecipe (w/o T)</td><td>71.9</td><td>71.7</td></tr><tr><td>LongRecipe (Random T)</td><td>70.1</td><td>69.8</td></tr><tr><td>LongRecipe</td><td>78.9</td><td>74.5</td></tr></table>
+
+Table 3: Performance of different ablation settings, LongRecipe (w/o T) uses the short exiting samples as PoSE and apply position index transformation on it. LongRecipe (Random T) select the sentence randomly from long sequence of sample and construct a new short samples. All experiments are based on Llama3-8B-instruct and we use $30\%$ tokens of 80k target context window.   
+Table 4: We conduct context window extension experiments using Llama3-8B-I with an 80k token length. Starting from $10\%$ , which represents 8k tokens per sample, $20\%$ corresponds to 16k tokens, $30\%$ to 24k tokens, and $40\%$ to 32k tokens. The $100\%$ configuration utilizes the entire long sample.   
+
+<table><tr><td>Ratio</td><td>NIAH(M)</td><td>RULER</td></tr><tr><td>10%</td><td>65.3</td><td>67.4</td></tr><tr><td>20%</td><td>70.9</td><td>70.7</td></tr><tr><td>30%</td><td>78.9</td><td>74.5</td></tr><tr><td>40%</td><td>72.0</td><td>71.0</td></tr><tr><td>100%</td><td>82.3</td><td>75.7</td></tr></table>
+
+calculated average distance among tokens and average continuous segment length for each methods.
+
+As shown in Figure 2, the LongRecipe approach achieves approximately twice the token distance compared to PoSE in the 128k setting. Additionally, LongRecipe maintains an average continuous segment length of 88, which helps the LLM recognize local dependency structures. In contrast, the average continuous segment length with RPES is nearly 0, disrupting local sentence structures.
+
+This chart displays the frequency distribution and relative relationships of parts of speech for tokens with significant logits changes across different positions in the text. NUM (numerals) has the high-
+
+![](images/7603bf3d8304926cd83d09b14a600a8b2123a2bc07d5cd6da3605c66ccfc8b1a.jpg)  
+Figure 2: Comparison of average distance among tokens for different methods and context window.
+
+est frequency, stabilizing around 0.4 throughout the text. In contrast, other parts of speech have significantly lower frequencies. For example, PRON (pronouns) and AUX (auxiliary verbs) have frequencies around 0.15, while CCONJ (conjunctions) and ADP (adpositions) have frequencies around 0.1. The frequency of NUM is approximately 2.67 times that of PRON and AUX and about 4 times that of CCONJ and ADP. These findings suggest that long-context tuning has varying effects on different token types, which further reinforces the motivation behind our method.
+
+Analysis of Token Type In the LongRecipe approach, we first compare the change in token logits before and after tuning the long context window. We then select the top $20\%$ of tokens that exhibit the most significant change at each index. These selected tokens are further analyzed for their part of speech distribution patterns. The results of this analysis are presented in Figure 3.
+
+Do Coherence and Cohesion Matter in Long Context Generalization? In this work, we select sentences from long samples based on analyzed token patterns, which may impact semantic coherence and cohesion. However, our current results
+
+![](images/dd2f89c078306545976d6a441fa3ea0915a1d0c2e1af526aa009859931801735.jpg)  
+Figure 3: Frequency Distribution of Parts of Speech for Tokens with Significant Logits Changes Across Text Positions. INTJ (Interjection), SYM (Symbol), ADP (Adposition), AUX (Auxiliary), PRON (Pronoun), CCONJ (Conjunction), NUM (Numeral)
+
+based on LongRecipe can match or even surpass those from some full-length samples, suggesting that coherence and cohesion may not be as critical for long-context training. To further investigate this, we utilize the Long Dependency Score (Chen et al., 2024a) to assess the long dependencies in different datasets, which may be more crucial for long context training. After calculation, PoSE and RPES, which use the same existing short samples, achieved a score of 12.07, while the data constructed by LongRecipe and that concatenated from several short documents in FLT scored 17.88. Since the data used in FLT is concatenated rather than naturally occurring long context, the semantic quality is not satisfactory. LongRecipe does not significantly harm the long dependencies required for long-context training, even though it may influence coherence and cohesion to some extent.
+
+Furthermore, during the pretraining process, the model primarily focuses on learning grammar and semantics. However, in the post-training phase on long texts, the model has already acquired grammar and semantic knowledge, so the focus may shift to capturing long dependencies among tokens. At this stage, it is possible to ignore certain tokens that are less important. These sentence might significantly influence overal semantic but contribute little to the learning of more complex attention patterns across longer sequences. Although this approach may slightly affect the model's general capabilities, the impact is minimal, and the model can quickly recover. More importantly, we can leverage LongRecipe method to achieve the efficient training for long context training.
+
+# 7 Conclusion
+
+In this work, we presented LongRecipe, a novel and efficient framework for extending the context window of LLMs to enhance their performance on long-context tasks. By integrating impactful token analysis, position index transformation, and training strategies, LongRecipe effectively simulates long-sequence inputs while maintaining training efficiency. Our extensive experiments on various LLMs, with extended context windows in 80k to 128k, demonstrated that LongRecipe could achieve substantial improvements in long-context generalization with significantly reduced computational resources. Notably, the method requires only $30\%$ of the target context window size and cuts down training costs over $85\%$ compared to full-length post-training. Moreover, LongRecipe preserves the original capabilities of the LLMs in general tasks, ensuring a balanced enhancement of both long-range dependency understanding and foundational model performance. These results highlight LongRecipe as a general and scalable solution for efficient long-context adaptation in LLMs.
+
+# 8 Limitation and Ongoing Work
+
+Supervised Fine-Tuning (SFT) While our current post-training approach, based on instruction or base models, yields satisfactory performance in NIAH and RULER, the absence of SFT still creates a gap between our method and the state-of-the-art (SOTA) LLMs. Recently, the release of LongWriter (Zhipu, 2024) for long-context SFT presents a promising option for further enhancing our finetuning process. Integrating such long-context SFT techniques into our pipeline is a promising direction for bridging the remaining performance gap.
+
+Longer Context Generalization The latest LLMs have pushed the boundaries of long-context capabilities to handle up to 1 million tokens, enabling users to input vast amounts of data. We plan to train and release models with 512k and 1M token capacities using the effective training strategies outlined in LongRecipe. This approach will further enhance the generalization of our method. Such scaling not only benchmarks the robustness of our method but also brings it closer to real-world long-document applications.
+
+# References
+
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+
+Yushi Bai, Yuxiao Dong, Zehan Qi, Zhaoyu Wang, Zhen Yang, Zhengxiao Du, Zhenyu Hou, and Zihan Wang. 2024. Chatglm: A family of large language models from glm-130b to glm-4 all tools. Preprint, arXiv:2406.12793.   
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+
+Tong Wu, Yanpeng Zhao, and Zilong Zheng. 2024. An efficient recipe for long context extension via middle-focused positional encoding. In *The Thirty-eighth Annual Conference on Neural Information Processing Systems*.   
+An Yang, Baosong Yang, Binyuan Hui, Bo Zheng, Bowen Yu, Chang Zhou, Chengpeng Li, Chengyuan Li, Dayiheng Liu, Fei Huang, et al. 2024a. Qwen2 technical report. arXiv preprint arXiv:2407.10671.   
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+Zhipu. 2024. Longwriter.   
+Dawei Zhu, Nan Yang, Liang Wang, Yifan Song, Wenhao Wu, Furu Wei, and Sujian Li. 2023. Pose: Efficient context window extension of llms via positional skip-wise training. arXiv preprint arXiv:2309.10400.   
+Zilin Zhu. Zigzag-ring-attention. https://github.com/zhuzilin/ring-flash-attention.
+
+# A LongBench Experiment Results
+
+Shown by Table 5, our method remains competitive on Llama3-8B and Qwen2 while outperforming others on Mistral. Additionally, as mentioned in the section Limitation and Ongoing Work, our current experiments involve post-continual pretraining but have not yet included supervised fine-tuning (SFT). In future work, we will conduct SFT experiments and include the results in the next version to further validate the effectiveness of LongRecipe in the whole process of post-training.
+
+For LongBench, we report the average score across all 21 subsets for the models.
+
+Table 5: LongBench scores for different models and methods on 80k length experiments.   
+
+<table><tr><td>Model</td><td>Method</td><td>LongBench</td></tr><tr><td rowspan="4">Llama3-8B-I</td><td>FLT</td><td>28.1</td></tr><tr><td>RPES</td><td>27.3</td></tr><tr><td>PoSE</td><td>26.7</td></tr><tr><td>LongRecipe</td><td>25.5</td></tr><tr><td rowspan="4">Mistral-7B</td><td>FLT</td><td>17.7</td></tr><tr><td>RPES</td><td>21.8</td></tr><tr><td>PoSE</td><td>22.3</td></tr><tr><td>LongRecipe</td><td>23.7</td></tr><tr><td rowspan="4">Qwen2-7B</td><td>FLT</td><td>17.7</td></tr><tr><td>RPES</td><td>26.8</td></tr><tr><td>PoSE</td><td>27.7</td></tr><tr><td>LongRecipe</td><td>26.2</td></tr></table>
+
+# B Training Setup
+
+We elaborate the setup of our training method in Table 6.
+
+# C Models
+
+We select in total 15 models for evaluation and analysis. We assess two commercial close-source GPT-4 and Gemini-1.5, and 13 open-source models. The details are demonstrated in Table 7.
+
+# D Pseudo Code for Position Index Transformation
+
+# Algorithm 1 Position Index Transformation
+
+1: Initialize:   
+2: Initialize source length $L_{s}$ and target length $L_{t}$   
+3: Load dataset $\mathcal{D}$ with each sample having length $L_{s}$   
+4: Position Index Transformation:   
+5: for each sample $S$ in $\mathcal{D}$ do   
+6: Split $S$ into $N$ sentences based on delimiters. '..? \n'   
+7: Initialize a list $\mathcal{L}$ of length $L_{t}$ , filled with zeros   
+8: Randomly select $N - 1$ distinct positions in $\mathcal{L}$   
+9: Insert the first sentence at position 0 and each of the remaining sentences at the selected $N - 1$ positions in $\mathcal{L}$   
+10: Flatten $\mathcal{L}$ by removing zeros, and the indices of the non-zero elements represent the new position indexes   
+11: end for   
+12: Save New Position Indexes
+
+# E Details about Long Context Benchmarks
+
+NIAH (M) and RULER: For NIAH (M), we report the average score across three tasks in RULER: niah-multikey, niahMULTIvalue, and niahMULTIquery. For RULER, we present the average score for all 13 subsets with Llama3-8B-Instruct and Mistral-7B-v0.3, and the average score for 12 subsets (excluding Variable Tracking) with Qwen2-7B.
+
+Table 6: Training Configuration Details   
+
+<table><tr><td>Model</td><td colspan="2">Llama3-8B</td><td colspan="2">Qwen2-7B</td></tr><tr><td>Extended Context Length</td><td>80k</td><td>128k</td><td>80k</td><td>128k</td></tr><tr><td>Training Sample Length</td><td>24k</td><td>38.4k</td><td>24k</td><td>38.4k</td></tr><tr><td>RoPE scaling (Dynamic NTK)</td><td>48.9M</td><td>131.5M</td><td>13.5M</td><td>13.5M</td></tr><tr><td>RoPE factor (Dynamic NTK)</td><td>10</td><td>16</td><td>4</td><td>4</td></tr><tr><td>Batch Size</td><td>96</td><td>96</td><td>96</td><td>96</td></tr><tr><td>Steps</td><td>104</td><td>104</td><td>104</td><td>104</td></tr><tr><td>Total Tokens</td><td>240M</td><td>384M</td><td>240M</td><td>384M</td></tr><tr><td>Learning Rate</td><td>5e-5</td><td>5e-5</td><td>5e-5</td><td>5e-5</td></tr><tr><td># GPUs and Type</td><td>1×A800/H100</td><td>2×A800/H100</td><td>1×A800/H100</td><td>1×A800/H100</td></tr><tr><td>Total GPU Memory</td><td>56G</td><td>104G</td><td>64G</td><td>72G</td></tr><tr><td>Total CPU Memory</td><td>148G</td><td>172G</td><td>168G</td><td>208G</td></tr><tr><td>Hours to Train</td><td>26/16</td><td>30/20</td><td>23/15</td><td>44/28</td></tr></table>
+
+Table 7: Information of evaluated and analyzed models.   
+
+<table><tr><td>Model</td><td>Size</td><td>Context Length</td><td>Huggingface (Wolf et al., 2019) / API</td></tr><tr><td>GPT-4 (OpenAI: Josh Achiam et al., 2023)</td><td>-</td><td>128K</td><td>gpt-4-1106-preview</td></tr><tr><td>Gemini-1.5-Pro (Reid et al., 2024)</td><td>-</td><td>1M</td><td>gemini-1.5-pro</td></tr><tr><td>Llama3-8B-I (Meta.AI, 2024)</td><td>8B</td><td>8K</td><td>meta-llama/Meta-Llama-3-8B-Instruct</td></tr><tr><td>Llama3.1-8B (Meta.AI, 2024)</td><td>8B</td><td>128K</td><td>meta-llama/Meta-Llama-3.1-8B</td></tr><tr><td>Llama3.1-8B-Instruct (Meta.AI, 2024)</td><td>8B</td><td>128K</td><td>meta-llama/Meta-Llama-3.1-8B-Instruct</td></tr><tr><td>Llama3.1-70B-Instruct (Meta.AI, 2024)</td><td>70B</td><td>128K</td><td>meta-llama/Meta-Llama-3.1-70B-Instruct</td></tr><tr><td>Qwen2-7B (Yang et al., 2024a)</td><td>7B</td><td>128K</td><td>Qwen/Qwen2-72B-Instruct</td></tr><tr><td>Qwen2-7B-Instruct (Yang et al., 2024a)</td><td>7B</td><td>128K</td><td>Qwen/Qwen2-7B-Instruct</td></tr><tr><td>Qwen2-7B-Instruct (Yang et al., 2024a)</td><td>72B</td><td>128K</td><td>Qwen/Qwen2-72B-Instruct</td></tr><tr><td>Yi-9B-200k (Young et al., 2024)</td><td>9B</td><td>200K</td><td>01-ai/Yi-34B-200K</td></tr><tr><td>Yi-34B-200k (Young et al., 2024)</td><td>34B</td><td>200K</td><td>01-ai/Yi-34B-200K</td></tr><tr><td>Mistral-7B (Mistral.AI, 2024)</td><td>7B</td><td>32K</td><td>mistralai/Mistral-7B-Instruct-v0.3</td></tr><tr><td>GLM4-9B-Chat-1M (GLM et al., 2024)</td><td>9B</td><td>1M</td><td>THUDM/glm-4-9b-chat-1m</td></tr><tr><td>Gradient-Llama3-8B (AI, 2024)</td><td>8B</td><td>1M</td><td>gradientai/Llama-3-8B-InstructGradient-1048k</td></tr><tr><td>Gradient-Llama3-70B (AI, 2024)</td><td>70B</td><td>1M</td><td>gradientai/Llama-3-70B-InstructGradient-1048k</td></tr></table>

paper_markdowns/bamboo-00497.md

@@ -0,0 +1,410 @@
+# MA-COIR: Leveraging Semantic Search Index and Generative Models for Ontology-Driven Biomedical Concept Recognition
+
+Shanshan Liu $^{1,2}$ , Noriki Nishida $^{1}$ , Rumana Ferdous Munne $^{1}$ , Narumi Tokunaga $^{1}$ , Yuki Yamagata $^{3,4}$ , Kouji Kozaki $^{5}$ , Yuji Matsumoto $^{1}$ ,
+
+$^{1}$ RIKEN AIP $^{2}$ University of Tsukuba $^{3}$ RIKEN R-IH $^{4}$ RIKEN BRC
+
+$^{5}$ Osaka Electro-Communication University
+
+{shanshan.liu, noriki.nishida, rumanaferdous.munne, narumi.tokunaga,
+
+yuki.yamagata, yuji.matsumoto} @riken.jp
+
+kozaki@osakac.ac.jp
+
+# Abstract
+
+Recognizing biomedical concepts in the text is vital for ontology refinement, knowledge graph construction, and concept relationship discovery. However, traditional concept recognition methods, relying on explicit mention identification, often fail to capture complex concepts not explicitly stated in the text. To overcome this limitation, we introduce MA-COIR, a framework that reformulates concept recognition as an indexing-recognition task. By assigning semantic search indexes (ssIDs) to concepts, MA-COIR resolves ambiguities in ontology entries and enhances recognition efficiency. Using a pretrained BART-based model fine-tuned on small datasets, our approach reduces computational requirements to facilitate adoption by domain experts. Furthermore, we incorporate large language models (LLMs)-generated queries and synthetic data to improve recognition in low-resource settings. Experimental results on three scenarios (CDR, HPO, and HOIP) highlight the effectiveness of MA-COIR in recognizing both explicit and implicit concepts without the need for mention-level annotations during inference, advancing ontology-driven concept recognition in biomedical domain applications. Our code and constructed data are available at https://github.com/s1-633/macoir-master.
+
+# 1 Introduction
+
+Automatic recognition of biological concepts in the text aids experts in refining ontologies and consolidating domain knowledge. As structured knowledge evolves to include increasingly complex concepts (Gargano, 2023; Yamagata et al., 2024), identifying concepts often requires significant expert analysis. Traditional Concept Recognition (CR) methods are inadequate for supporting tasks such as ontology-driven knowledge graph construction, efficient literature retrieval for specific concepts,
+
+![](images/5cd1018f522b58221b73dc5e63cb275da3067ff56083b66d55de43d388a8a301.jpg)  
+Figure 1: Concept recognition by MA-COIR follows the default workflow indicated by purple arrows. When an LLM generates simplified queries from a given passage, additional processes, denoted by blue arrows, are incorporated. When "6-2-8-0-5" is generated, "HOIP_0004832: TNF signalling" is predicted as a concept within the query.
+
+and the discovery of novel relationships between concepts.
+
+Typically, recognizing ontology concepts in passages or sentences relies on identifying mentions - text spans where concepts appear. When mentions are provided, Entity Disambiguation (ED) can be applied to match each mention to a single entity or none at all (Wu et al., 2020; Jiang et al., 2024; Wang et al., 2023; OAKlib, 2023). When mentions are unknown, recognition may be achieved through a pipeline beginning with Named Entity Recognition (NER) to identify mentions, followed by ED to resolve these predictions (Shlyk et al., 2024; Caufield et al., 2024). Alternatively, end-to-end Entity Linking (EL) approaches can yield a series of (mention, entity) pairs (Kolitsas et al., 2018; Cao et al., 2020; Luo et al., 2021).
+
+With advancements in Large Language Models (LLMs), several LLM-based pipeline methods for NER and ED have been introduced (Shlyk et al., 2024; Caufield et al., 2024). In-context learning (ICL) techniques reduce annotation requirements; however, a substantial performance gap remains between ICL and fully supervised methods (Shlyk
+
+et al., 2024). While mention-based queries are typically generated to retrieve concepts, the limitation of this approach becomes evident when complex concepts do not appear explicitly as "mentions" within the text, rendering aforementioned mention-based recognition methods ineffective in real-world applications.
+
+We propose MA-COIR (Mention-Agnostic Concept Recognition through an IndexingRecognition Framework), a framework for recogni-nizing biomedical concepts explicitly or implicitly mentioned in the text. Inspired by prior works (Tay et al., 2022; Jiang et al., 2024), we reformulate the concept recognition (CR) task into an indexingrecognition paradigm. This approach assigns each concept a semantic search index (ssID) and trains a neural model to predict ssIDs corresponding to concepts described in the input text (see Fig. 1).
+
+By generating ssIDs instead of literal concept names, the framework resolves ambiguities caused by identical concept names within ontologies (e.g., concepts sharing preferred names but differing definitions). Additionally, the semantic alignment between concepts and their assigned indexes enhances model learning, enabling more powerful recognition.
+
+Our method leverages a pretrained BART-based language model fine-tuned on a small dataset, thereby reducing computational demands and improving accessibility for domain experts. Furthermore, we explore LLM-generated queries and synthetic data, demonstrating the framework's utility in low-resource settings for real-world concept extraction tasks. Results across datasets (CDR, HPO, and HOIP) demonstrate the effectiveness of our framework.
+
+Our contributions are:
+
+- We propose MA-COIR, a novel framework for recognizing both explicit and implicit biomedical concepts without the need for prior identification of specific mentions, thereby reducing reliance on labor-intensive annotations needed for entity recognizer training.   
+- To the best of our knowledge, we are the first to integrate a semantic search index into biomedical concept recognition, improving generative model learning and enabling more efficient recognition.   
+- We demonstrate the utility of query and training data generated by an LLM in concept
+
+recognition tasks, providing a reference framework for efficient recognition in low-resource settings.
+
+# 2 Related work
+
+Biomedical Concept Recognition. In recent years, biomedical CR methods have largely followed two main approaches. The first approach involves fully-, weakly-, or self-supervised learning methods based on pretrained language models, such as domain-specific BERT or BART models (Liu et al., 2021; Lee et al., 2019; Yuan et al., 2022; Zhang et al., 2022), and fine-tuned these models on small annotated datasets (Luo et al., 2021). The second approach leverages the strong generalization capabilities of LLMs to perform NER and ED tasks in zero- or few-shot settings (Wang et al., 2023). Existing biomedical CR methods that operate without mention annotations are LLM-based. For instance, (Caufield et al., 2024) explored a schema guiding LLMs to perform NER with specified constraints, using (OAKlib, 2023) for subsequent ED tasks. (Shlyk et al., 2024) proposed the REAL framework, which combines LLM-based zero-shot NER with an ED method using retrieval-augmented generation (RAG). (El Khettari et al., 2024) developed an ICL demonstration selection strategy to generate concept names closely aligned with ontology terms, subsequently linking them based on the similarity between generated names and ontology terms.
+
+Hierarchical Indexing. Hierarchical indexing has proven effective in handling large output spaces, as seen in applications like extreme multi-label classification (Zhang et al., 2021; Kharbanda et al., 2022) and document retrieval (Tay et al., 2022). By organizing labels or documents into tree-structured hierarchies based on semantic relationships, these methods improve computational efficiency and prediction performance. Notably, in the context of biomedical CR, well-defined concept taxonomies already exist through ontologies, offering a natural foundation for hierarchical organization. However, the application of hierarchical indexing in this field remains relatively unexplored despite its potential benefits.
+
+# 3 Methodology
+
+# 3.1 Task formulation
+
+Let $O$ represent a set of concepts $\{C_1, \dots, C_n\}$ defined within a domain ontology. Given a query text
+
+![](images/226039e4c967e8b151c740ae6ad0f6fb96d766d07d4c1624d31f7590167c2051.jpg)  
+Figure 2: Indexing Phase in MA-COIR: A semantic search index (ssID) is assigned based on a label tree derived from the domain ontology. Through hierarchical clustering, the ssID for the concept "HOIP_0004832: TNF signaling" is "6-2-8-0-5".
+
+$Q$ , the CR task aims to identify a subset of concepts $\{C_1', \dots, C_p'\}$ from the ontology that are referenced in the text.
+
+We approach the CR task as an end-to-end generative process. First, we assign each concept $C$ a unique semantic search index (ssID). Then, our model generates one or more ssIDs for the input text $Q$ , thereby retrieving the concepts are presented in the text.
+
+# 3.2 Concept Indexing
+
+As illustrated in Fig. 2, each concept $C$ is represented as a vector $E_{C}$ , obtained by encoding its canonical name $Name_{C}$ using a text encoder. Given our focus on the biomedical domain, we select SapBERT (Liu et al., 2021) as the text encoder. The representation $E_{C}$ is derived by averaging the last hidden states for the tokens in $Name_{C}$ .
+
+$$
+X _ {C} = \operatorname {T e x t E n c o d e r} \left(\operatorname {N a m e} _ {C}\right) \in \mathbb {R} ^ {l \times H} \quad (1)
+$$
+
+$$
+E _ {C} = \operatorname {a v g} \left(X _ {C}\right) \in \mathbb {R} ^ {H} \tag {2}
+$$
+
+where $l$ is the token length, and $H$ is the dimension of each token's embedding.
+
+Starting with the ROOT node that encompasses all concepts in the target ontology, we construct a label tree using a top-down hierarchical clustering process. Specifically, if a node contains
+
+more than $g$ elements, we divide it into $\leq m$ categories until each leaf node corresponds to a single concept (with $g = 10, m = 10$ in this study)<sup>2</sup> by K-means algorithm implemented with Scikit-learn (Pedregosa et al., 2011). Each node is assigned an index based on its category, forming a sequence of "semantic search indexes" (ssIDs) that encode semantic information from each concept's representation.
+
+# 3.3 Concept Recognition
+
+During recognition phase following the indexing process, the input may consist of a passage (e.g., a paragraph of one PubMed article), a sentence, or a span (mention or concept name), while the output is a text sequence listing ssIDs (e.g., "6-2-8-0-5; 9-6-6-9-5;"). Each ssID is separated by a semicolon (";"), as illustrated in Fig. 1.
+
+To effectively map natural language text to a formatted sequence, we selected a BART-based pretrained language model (facebook/bart-large) (Lewis et al., 2019). This model, with its encoder-decoder architecture and cross-attention mechanism, is well-suited for our tasks.
+
+To ensure the BART-based model generates valid ssID sequences, we apply a constrained decoder that filters the output to retain only valid ssIDs. The decoder's vocabulary $T$ is restricted to ssID tokens. The token embedding $e_t$ for each token $t \subset T$ is obtained from the embedding layer LmEmbedding of the language model $LM$ :
+
+$$
+e _ {t} = L m E m b e d d i n g (t) \in \mathbb {R} ^ {H} \tag {3}
+$$
+
+where $H$ is the dimension of a token's embedding.
+
+At the $i$ -th time step, the decoder selects the token with the highest score based on the token embedding $e_t$ and the last hidden state $h_i$ . One feature $h_{i,t}$ is computed using a one-layer linear classifier:
+
+$$
+h _ {i} = L M \left(\hat {y} _ {i - 1}\right) \in \mathbb {R} ^ {H} \tag {4}
+$$
+
+$$
+h _ {i, t} = W _ {t} ^ {o} h _ {i} + b ^ {o} \tag {5}
+$$
+
+where $W^{o}$ is the weight and $b^{o}$ is the bias of the classifier.
+
+Another feature $e_{i,t}$ is the dot product of $e_t$ and $h_i$ , representing the relevance between the token $t$ and $h_i$ :
+
+$$
+e _ {i, t} = e _ {t} h _ {i} \tag {6}
+$$
+
+![](images/9e2dc824f034790bbdc709ee62f721fff848db8f4b19216d98453c7270577486.jpg)  
+Figure 3: An example of constructing a claim-concept instance is as follows: Given a passage, we prompt the LLM to breakdown the passage into several claims. For one claim, we then perform excerpt mining. Next, we match these mined excerpts to the passage's annotated concepts by assessing semantic similarity. If an excerpt closely aligns with an annotated concept, we pair the concept with the claim. In this example, seven concepts are paired with a single claim, forming a claim-concept instance.
+
+The final score of the token $t$ is the average of two features:
+
+$$
+z _ {i, t} = \operatorname {a v g} \left(e _ {i, t}, h _ {i, t}\right) \tag {7}
+$$
+
+$$
+\hat {y} _ {i} = \arg \max  _ {t} \left(\sigma \left(z _ {i, t}\right)\right) \tag {8}
+$$
+
+where $h_{i,t},e_{i,t},z_{i,t}\in \mathbb{R}^{1},\sigma$ is the Softmax function. The model parameters are optimized by minimizing the CrossEntropyLoss $(y,\hat{y})$
+
+Our preliminary experiments revealed that using only one canonical name-ssID pair to introduce a concept into the model did not provide strong performance. It is crucial to incorporate synonym-, mention-, and passage-ssID pairs for model improvement if they are available. Therefore, our model is trained on various input-output pairs. When the input is a span and the output is the ssID of a single concept, the model learns "indexing". When the input is a longer text and the output includes multiple ssIDs for the concepts are presented in the input, the model is trained for "recognition".
+
+# 3.4 Multi-level queries generated by LLMs
+
+Biomedical concepts are more challenging to recognize when the query is a passage compared to a sentence or span. By extracting shorter segments (e.g., sentences, phrases) from a passage, the model
+
+can better identify concepts that are difficult to capture when the query is a passage. Our framework, MA-COIR, is trained to process multiple levels of queries, enabling the integration of results from various query types derived from a passage into the final predictions.
+
+In this study, we employ an open-source LLM - llama-3-8b (AI@Meta, 2024), to generate simplified queries from passages. For the CDR and HPO datasets, where concepts are associated with specific "mentions", the model generates concept names to serve as queries. Given that HOIP concepts are not consistently expressed as phrases, we use the model to transform passages into sentence-level claims and span-level concept names.
+
+Claims are prioritized over segmented sentences because they encapsulate the passage's meaning in a coherent and self-contained manner, facilitating comprehension and recognition. In contrast, segmented sentences often lack sufficient context, leading to ambiguity. Claims provide the necessary abstraction and semantic synthesis, aligning more effectively with downstream tasks that rely on conceptual understanding.
+
+The concept name generation is performed under a 10-shot ICL setting. For a given passage in the test set, we randomly select 10 passage-concept
+
+Table 1: Statistics of instances.   
+
+<table><tr><td>Split</td><td>Data</td><td>Passage</td><td>Claim</td><td>Concept</td><td>Mention</td></tr><tr><td rowspan="3">Train</td><td>CDR</td><td>500</td><td>-</td><td>1,328</td><td>2,672</td></tr><tr><td>HPO</td><td>182</td><td>-</td><td>416</td><td>926</td></tr><tr><td>HOIP</td><td>225</td><td>682</td><td>337</td><td>-</td></tr><tr><td rowspan="3">Test</td><td>CDR</td><td>500</td><td>-</td><td>2,778</td><td>4,600</td></tr><tr><td>HPO</td><td>23</td><td>-</td><td>159</td><td>237</td></tr><tr><td>HOIP</td><td>37</td><td>165</td><td>265</td><td>-</td></tr></table>
+
+pairs from the training set as demonstrations of the prompt. $^{3}$ Claim generation is done in a zero-shot setting due to the lack of annotated passage-claim pairs. Prompts we used are provided in Appendix Fig. 5.
+
+# 3.5 Data augmentation
+
+After breaking down the passage into claims using an LLM on the HOIP dataset, we generate claimssID pairs from the training set for semi-supervised learning. This data construction follows a common weakly supervised NER approach, consisting of two steps:
+
+- Excerpt mining: Identify noun phrases and excerpts consisting of “a noun phrase and a verb linked to that noun phrase” using the dependency tree of a generated claim. We use spaCy (Honnibal and Montani, 2017) as the dependency parser.   
+- Labeling function: Represent each excerpt similarly to how a concept or query is represented, then compute the cosine similarity between the excerpt and annotated concepts from the passage. If any excerpt in the claim has a cosine similarity $\geq 0.5$ to a gold concept, that concept is assigned to the claim.
+
+Many matched excerpts only capture part of the meaning of the corresponding concept. Pairing the entire claim (which the excerpt appears) with the concept reduces noise compared to pairing the excerpt alone with the concept. An example of constructing a claim-concept instance is shown in Fig. 3.
+
+# 4 Experiments
+
+# 4.1 Datasets
+
+Target concepts in an ontology are expressed frequently either as mentions or not. The motivation
+
+for proposing MA-COIR is to apply a pragmatic approach for the latter. To evaluate the framework's effectiveness in both cases, we conduct experiments on the three datasets.
+
+CDR The pair of the MeSH $^{4}$ and BC5CDR dataset (Li et al., 2016). The 2015 version of the MeSH vocabulary includes 258K terms and BC5CDR comprises 1,500 passages annotated with MeSH terms based on entity mentions. MeSH is not a formally defined ontology, evaluating performance on this scenario establishes a reference for the lower bound of ontological content.
+
+HPO The pair of Human Phenotype Ontology (HPO) (Gargano, 2023) $^5$ and HPO GSC+ dataset published by Lobo et al. (2017). The latest version of the HPO ontology includes over 19,000 concepts. The HPO GSC+ dataset comprises 228 PubMed abstracts and 1,933 mention annotations, each mention linked to a concept.
+
+HOIP The pair of Homeostasis Imbalance Process (HOIP) ontology (Yamagata et al., 2024) and HOIP dataset (El Khettari et al., 2024). The ontology includes over 60,000 concepts related to homeostasis imbalance processes, of which 44,439 biological process concepts are target concepts.
+
+The dataset consists of 362 passages extracted from PubMed papers. Each passage is annotated with biological process concepts from the HOIP ontology. Mention annotations of concepts are not provided. Notably, a concept may be annotated based on its relevance to a process mentioned in the passage, even if the concept is not stated in the passage (this relevance may depend on the annotator's background knowledge).
+
+We conduct training with the original train/dev set, and evaluation with a refined test set containing only explicitly mentioned concepts.
+
+# 4.2 Comparison system
+
+XR-Transformer. Prior to MA-COIR, no supervised biomedical CR model directly generated a list of ontology concepts from free text. By treating concepts as labels, CR task can be naturally framed as an instance of extreme multi-label text classification (XMC), where a passage is assigned multiple relevant ontology terms. We adopt XR-Transformer (Zhang et al., 2021), a state-of-the-art
+
+XMC model with top-tier performance across multiple public benchmarks, as a strong baseline.
+
+kNN-searcher. Given the lack of existing approaches that do not use mentions for CR, we selected a straightforward baseline method: the top-k Nearest Neighbor (kNN) search, which can retrieve candidate concepts based on a given query. As the way we represent a concept $E_{C}$ that described in Section 3.2, we get the representation of the query $E_{Q}$ by the TextEncoder:
+
+$$
+X _ {Q} = \operatorname {T e x t E n c o d e r} (Q) \in \mathbb {R} ^ {l \times H} \tag {9}
+$$
+
+$$
+E _ {Q} = \operatorname {a v g} \left(X _ {Q}\right) \in \mathbb {R} ^ {H} \tag {10}
+$$
+
+where $l$ is the token length of the query, and $H$ is the dimension of a token's embedding.
+
+With $E_{Q}$ and representations of all concepts $\{E_{C_1},\dots,E_{C_n}\}$ as input vectors, we implemented Faiss (Douze et al., 2024) for a fast vector search of $E_{Q}$ among large-scale concept spaces, by calculated similarity based on Euclidean distance. The kNN-searcher may return a candidate even if its distance from the query is large, when no other concepts closer to the query exceed the distance of the candidate. To mitigate false positives, we classify retrieved concepts with a similarity score $< 0.6$ as non-predictions.
+
+Additionally, we conduct a comparative analysis of our approach against (Shlyk et al., 2024) and (El Khettari et al., 2024) under a controlled setup. Details are described in Section 6.4.
+
+# 4.3 Setups
+
+We trained MA-COIR and XR-Transformer using passage-, name-, and synonym-ssID pairs for all three datasets. When annotated mentions or generated claims were available, the model was trained with mention- and claim-ssID pairs. The models trained with synthetic claim-ssID pairs is referred to as MA-COIR-a and XR-Transformer-a. For checkpoint selection, we used only passage-ssID pairs from the development set. Evaluation involved testing the model with various types of queries, including passages, gold mentions (for CDR and HPO), generated claims (only for HOIP), and generated concept names. The statistics for the instances are provided in Table 1. Hyperparameters are listed in Appendix A.1.
+
+# 4.4 Evaluation metrics
+
+We evaluate all models using precision (Pre), recall (Rec), and micro F1-score (F1), measured across
+
+different query levels. For MA-COIR, we use beam search to generate top- $k$ concept sequences per query. Each sequence is segmented into ssID-like spans using semicolons as delimiters. Spans not matching any defined ssID are discarded. All valid spans across $k$ sequences are then merged and deduplicated to form the final prediction set. When multiple queries are derived from a single passage, their predictions are aggregated and compared against the gold annotations for that passage.
+
+To ensure a fair comparison, passage-level input for the kNN-searcher is the same full-text passage used by MA-COIR, rather than shorter fragments obtained via "excerpt mining" we described in Section 3.5.
+
+# 5 Results
+
+Tables 2 and 3 summarize model performance across three biomedical concepts. On both CDR and HPO, MA-COIR consistently achieves the best F1 scores with passage-level inputs (47.6 and 60.0, respectively), while kNN-searcher and XR-Transformer perform best with span-level inputs. In the more challenging HoIP setting, MA-COIR-a and XR-Transformer-a outperform kNN-searcher, with XR-Transformer-a achieving the highest F1 for passage- and claim-level inputs ((19.8 and 23.4), and MA-COIR leading in the span-level setting (26.8). We analyze results from three complementary perspectives: concept type, input granularity, and real-world applicability.
+
+Concept Type. The three datasets involve concept spaces of increasing complexity—from chemical and drug names (CDR), to phenotype abnormalities (HPO), and finally to abstract homeostasis imbalance processes (HoIP).
+
+In CDR, most gold concepts are explicitly mentioned in text or have close surface-level synonyms, making the kNN-searcher highly effective. However, HPO concepts such as "Abnormality of body height" or "Abnormal platelet morphology" are semantically richer and less likely to appear verbatim. Here, supervised models like MA-COIR and XR-Transformer gain a clear edge by leveraging learned task-specific information.
+
+HoIP presents the greatest challenge: many target concepts are abstract, fine-grained, and rarely expressed via identifiable mentions, challenging to recognize even for experts (e.g., "dysregulation of matrix metalloproteinase secretion"). In addition, HoIP lacks mention-ssID training pairs, limiting
+
+<table><tr><td rowspan="2">Dataset</td><td rowspan="2">k</td><td rowspan="2">Query</td><td colspan="3">MA-COIR</td><td colspan="3">XR-Transformer</td><td colspan="3">kNN-searcher</td></tr><tr><td>Pre</td><td>Rec</td><td>F1</td><td>Pre</td><td>Rec</td><td>F1</td><td>Pre</td><td>Rec</td><td>F1</td></tr><tr><td rowspan="9">CDR</td><td rowspan="3">1</td><td>Passage</td><td>51.0</td><td>44.6</td><td>47.6</td><td>79.6</td><td>11.6</td><td>20.3</td><td>13.3</td><td>0.1</td><td>0.1</td></tr><tr><td>Mention</td><td>67.2</td><td>72.0</td><td>69.5</td><td>67.1</td><td>71.4</td><td>69.1</td><td>75.5</td><td>82.5</td><td>78.9</td></tr><tr><td>Concept</td><td>57.2</td><td>41.2</td><td>47.9</td><td>57.2</td><td>41.5</td><td>48.1</td><td>63.5</td><td>48.2</td><td>54.8</td></tr><tr><td rowspan="3">5</td><td>Passage</td><td>36.5</td><td>49.6</td><td>42.0</td><td>45.3</td><td>33.1</td><td>38.3</td><td>12.5</td><td>0.1</td><td>0.2</td></tr><tr><td>Mention</td><td>17.1</td><td>74.8</td><td>27.9</td><td>13.8</td><td>73.6</td><td>23.3</td><td>18.9</td><td>92.0</td><td>31.3</td></tr><tr><td>Concept</td><td>15.2</td><td>44.2</td><td>22.6</td><td>12.4</td><td>44.4</td><td>19.4</td><td>16.5</td><td>56.1</td><td>25.5</td></tr><tr><td rowspan="3">10</td><td>Passage</td><td>29.9</td><td>52.0</td><td>37.9</td><td>26.7</td><td>39.0</td><td>31.7</td><td>10.5</td><td>0.1</td><td>0.2</td></tr><tr><td>Mention</td><td>9.2</td><td>75.5</td><td>16.4</td><td>7.1</td><td>74.1</td><td>13.0</td><td>11.4</td><td>93.1</td><td>20.3</td></tr><tr><td>Concept</td><td>8.3</td><td>45.4</td><td>14.0</td><td>6.4</td><td>44.8</td><td>11.2</td><td>9.9</td><td>57.3</td><td>16.9</td></tr><tr><td rowspan="9">HPO</td><td rowspan="3">1</td><td>Passage</td><td>67.7</td><td>53.8</td><td>60.0</td><td>91.3</td><td>13.5</td><td>23.5</td><td>33.3</td><td>0.6</td><td>1.3</td></tr><tr><td>Mention</td><td>85.6</td><td>80.1</td><td>82.8</td><td>88.1</td><td>85.3</td><td>86.6</td><td>70.7</td><td>71.2</td><td>70.9</td></tr><tr><td>Concept</td><td>65.9</td><td>57.1</td><td>61.2</td><td>65.2</td><td>57.7</td><td>61.2</td><td>58.5</td><td>50.6</td><td>54.3</td></tr><tr><td rowspan="3">5</td><td>Passage</td><td>60.8</td><td>57.7</td><td>59.2</td><td>61.7</td><td>45.5</td><td>52.4</td><td>11.1</td><td>0.6</td><td>1.2</td></tr><tr><td>Mention</td><td>21.2</td><td>84.0</td><td>33.8</td><td>19.2</td><td>87.8</td><td>31.5</td><td>21.3</td><td>87.8</td><td>34.3</td></tr><tr><td>Concept</td><td>18.5</td><td>66.7</td><td>29.0</td><td>15.4</td><td>66.0</td><td>25.0</td><td>18.1</td><td>66.7</td><td>28.4</td></tr><tr><td rowspan="3">10</td><td>Passage</td><td>54.1</td><td>59.6</td><td>56.7</td><td>43.9</td><td>64.7</td><td>52.3</td><td>7.7</td><td>0.6</td><td>1.2</td></tr><tr><td>Mention</td><td>12.4</td><td>87.2</td><td>21.7</td><td>9.9</td><td>87.8</td><td>17.7</td><td>13.9</td><td>89.1</td><td>24.0</td></tr><tr><td>Concept</td><td>11.0</td><td>73.7</td><td>19.2</td><td>8.2</td><td>67.9</td><td>14.6</td><td>11.0</td><td>67.9</td><td>18.9</td></tr></table>
+
+Table 2: Results of the top- $k$ generated sequences by MA-COIR and the top- $k$ retrieved concepts by the XR-transformer and kNN-searcher on the CDR and the HPO. "mention" are gold annotated mentions of a passage. "concept" are generated concepts by the LLM given a passage. Red values indicate the highest F1 score achieved for each query type on a given dataset.   
+Table 3: Results of the top- $k$ generated sequences by MA-COIR and the top- $k$ retrieved concepts by the XR-Transformer and kNN-searcher on the HOIP dataset. "claim" and "concept" refer to generated claims and concepts, produced by the LLM given a passage. Red values indicate the highest F1 score achieved for each query type.   
+
+<table><tr><td rowspan="2">k</td><td rowspan="2">Query</td><td colspan="3">MA-COIR</td><td colspan="3">MA-COIR-a</td><td colspan="3">XR-Transformer-a</td><td colspan="3">kNN-searcher</td></tr><tr><td>Pre</td><td>Rec</td><td>F1</td><td>Pre</td><td>Rec</td><td>F1</td><td>Pre</td><td>Rec</td><td>F1</td><td>Pre</td><td>Rec</td><td>F1</td></tr><tr><td rowspan="3">1</td><td>Passage</td><td>11.1</td><td>25.0</td><td>15.4</td><td>13.0</td><td>27.3</td><td>17.6</td><td>32.4</td><td>13.6</td><td>19.2</td><td>6.7</td><td>2.3</td><td>3.4</td></tr><tr><td>Claim</td><td>8.2</td><td>21.6</td><td>11.9</td><td>14.1</td><td>30.7</td><td>19.3</td><td>19.8</td><td>28.4</td><td>23.4</td><td>6.7</td><td>8.0</td><td>7.3</td></tr><tr><td>Concept</td><td>18.2</td><td>46.6</td><td>26.2</td><td>18.5</td><td>48.9</td><td>26.8</td><td>17.8</td><td>45.5</td><td>25.6</td><td>13.0</td><td>35.2</td><td>19.0</td></tr><tr><td rowspan="3">5</td><td>Passage</td><td>8.6</td><td>34.1</td><td>13.8</td><td>11.0</td><td>39.8</td><td>17.2</td><td>14.6</td><td>30.7</td><td>19.8</td><td>2.1</td><td>3.4</td><td>2.6</td></tr><tr><td>Claim</td><td>6.0</td><td>45.5</td><td>10.7</td><td>7.4</td><td>47.7</td><td>12.8</td><td>6.5</td><td>45.5</td><td>11.4</td><td>3.8</td><td>17.0</td><td>6.3</td></tr><tr><td>Concept</td><td>6.4</td><td>64.8</td><td>11.6</td><td>6.7</td><td>68.2</td><td>12.1</td><td>5.5</td><td>64.8</td><td>10.1</td><td>5.0</td><td>56.8</td><td>9.1</td></tr><tr><td rowspan="3">10</td><td>Passage</td><td>7.2</td><td>36.4</td><td>12.0</td><td>9.8</td><td>45.5</td><td>16.2</td><td>10.0</td><td>42.0</td><td>16.2</td><td>2.4</td><td>6.8</td><td>3.6</td></tr><tr><td>Claim</td><td>4.7</td><td>54.5</td><td>8.7</td><td>5.9</td><td>59.1</td><td>10.7</td><td>4.2</td><td>55.7</td><td>7.8</td><td>2.6</td><td>17.0</td><td>4.4</td></tr><tr><td>Concept</td><td>3.9</td><td>69.3</td><td>7.4</td><td>4.4</td><td>78.4</td><td>8.4</td><td>3.0</td><td>69.3</td><td>5.7</td><td>3.3</td><td>62.5</td><td>6.2</td></tr></table>
+
+supervised grounding. $^{7}$ As a result, all models struggle, but the gap between supervised and unsupervised methods widens. This underscores a key insight: concept complexity and the mentioned way are critical determinants of method suitability.
+
+Input Granularity. MA-COIR excels with passage-level inputs, outperforming XR-Transformer by large margins on CDR (47.6 vs. 38.3) and HPO (60.0 vs. 52.4), and achieving stronger recall on HoIP. The kNN-searcher, by contrast, underperforms in this setting due to poor alignment between full passages and span-based embeddings.
+
+At the span-level, performance varies: MA-
+
+COIR outperforms XR-Transformer when given gold mentions on CDR, but lags slightly on HPO. When using concept names generated by LLMs, MA-COIR matches or exceeds XR-Transformer. This reflects the robustness of MA-COIR to input variation and highlights a key practical strength: in real applications, gold mentions are unavailable, and LLM-generated spans often differ in granularity from ontology entries, making retrieval harder. MA-COIR's adaptability makes it better suited for such realistic, mention-free scenarios.
+
+Practical Considerations. On CDR and HPO, MA-COIR demonstrates strong and consistent performance, proving its effectiveness for real-world biomedical CR. On HoIP, XR-Transformer-a achieves slightly higher F1 than MA-COIR-a (19.8 vs. 17.6). This is largely due to the dataset's statistics: each passage contains, on average, 7.2 gold
+
+concepts. XR-Transformer-a's fixed- $k$ retrieval (with $k = 5$ ) benefits from limiting false positives, whereas MA-COIR-a uses beam search to generate unbounded concept sequences, trading off precision for recall. In practice, however, concept density varies across documents, and setting an optimal $k$ is non-trivial, limiting the robustness of fixed- $k$ methods like XR-Transformer.
+
+On span-level CDR tasks, MA-COIR and XR-Transformer perform comparably, but both fall short of kNN-searcher when provided with gold mentions. On HPO, kNN-searcher is only competitive when given gold mentions and big $k$ values (e.g., $k = 5$ or 10). Further analysis (Appendix A.3) reveals that MA-COIR struggles to recognize unseen concepts lacking training exposure—an issue shared with XR-Transformer. In contrast, kNN-searcher remains unaffected. Nonetheless, we believe this limitation can be mitigated via data synthesis strategies: our preliminary experiments confirm the feasibility of using synthetic samples to improve MA-COIR's generalization.
+
+Summary. MA-COIR delivers strong performance across diverse concept types and input settings. While training data coverage remains a limitation, this can be addressed with scalable augmentation techniques. Given its flexibility, robustness to input variation, and effectiveness even without gold mentions, MA-COIR offers a practical and reliable solution for biomedical CR.
+
+# 6 Analysis
+
+# 6.1 Effectiveness of ssID
+
+To verify the effectiveness of ssID, we compared it with other types of indexes can be used for the recognition on the HOIP.
+
+- Random ID: Randomly assign a number to each concept as an index. The index ranges from 0 to the number of all ontology concepts.   
+- Ontology ID: The unique ID of each concept in the ontology is used as the index. Like "HOIP_0004832" is the ontology ID of "TNF signaling", and the index for generation.   
+- ssID (name): As described in Section 3.2.   
+- ssID (+hypernyms): The indexes are based on constructing a label tree using the concatenation of the representation of a name of each
+
+Table 4: Results of the top-1 generated sequence using various index types with the passage queries on the HOIP dataset by MA-COIR.   
+
+<table><tr><td>Index type</td><td>Pre</td><td>Rec</td><td>F1</td></tr><tr><td>Random ID</td><td>7.8</td><td>31.8</td><td>12.5</td></tr><tr><td>Ontology ID</td><td>6.7</td><td>47.7</td><td>11.8</td></tr><tr><td>ssID (name)</td><td>11.1</td><td>25.0</td><td>15.4</td></tr><tr><td>ssID (+hybernyms)</td><td>9.7</td><td>20.5</td><td>13.1</td></tr></table>
+
+![](images/f020469c73ff4e68b5153061df97a15b9ce0e0074dbab7f26a4a13fb4662b7aa.jpg)  
+Figure 4: F1 scores by MA-COIR between complex query (passage) and the average of the simpler set of queries (claim/concept) from top-1 generated sequence using different indexes on the HOIP.
+
+concept, and the average of the representations of its hypernyms. The hypernymy and hyponymy relations is known from the ontology. Let $U_{C}$ denote a set of concepts that are hypernyms of concept $C$ defined in the ontology. The representation of the concept $C$ used for label tree construction changed from eq. 2 to eq. 4.
+
+$$
+E _ {U _ {C i}} = \operatorname {a v g} \left(X _ {U _ {C i}}\right) \in \mathbb {R} ^ {H} \tag {11}
+$$
+
+$$
+E _ {C} = \left[ \operatorname {a v g} \left(X _ {C}\right): \operatorname {a v g} \left(E _ {U _ {C}}\right) \right] \tag {12}
+$$
+
+where “:” is the concatenation operation, $H$ is the dimension of a token's embedding, $E_{C} \in \mathbb{R}^{2 \times H}$ .
+
+The experimental results are summarized in Table 4. Both Random ID and Ontology ID performed well on span-level queries, providing higher recall compared to ssIDs. On the other hand, using ssID (name) achieved the highest precision and F1 scores for passage-level queries. As shown in Fig. 4, ssID-based indexing demonstrates robustness across both complex and simple queries, whereas Random ID and Ontology ID perform optimally only on shorter queries. In the absence of tools to retrieve non-passage level information, ssID is clearly the superior choice.
+
+# 6.2 Effectiveness of data augmentation
+
+The results for the MA-COIR-a are presented in Table 3. Incorporating claim-ssID pairs, as described
+
+Table 5: Results of the top-1 generated sequence by MA-COIR-a on HOIP.   
+
+<table><tr><td>Query</td><td>Pre</td><td>Rec</td><td>F1</td></tr><tr><td>passage</td><td>13.0</td><td>27.3</td><td>17.6</td></tr><tr><td>+ claim</td><td>12.5</td><td>45.5</td><td>19.7</td></tr><tr><td>+ concept</td><td>12.3</td><td>64.8</td><td>20.7</td></tr><tr><td>+ concept</td><td>14.7</td><td>61.4</td><td>23.7</td></tr></table>
+
+Table 6: Comparison between our methods and previous works. "HOIP-o" refers to the original test set.   
+
+<table><tr><td>Dataset</td><td>Method</td><td>Pre</td><td>Rec</td><td>F1</td></tr><tr><td rowspan="4">HPO</td><td>REAL-1st hit</td><td>40.0</td><td>49.0</td><td>44.0</td></tr><tr><td>REAL-GPT3.5</td><td>68.0</td><td>48.0</td><td>56.0</td></tr><tr><td>kNN-searcher</td><td>58.5</td><td>50.6</td><td>54.3</td></tr><tr><td>MA-COIR</td><td>63.4</td><td>54.5</td><td>58.6</td></tr><tr><td rowspan="3">HOIP-o</td><td>ICL-Llama</td><td>43.1</td><td>11.8</td><td>18.6</td></tr><tr><td>kNN-searcher</td><td>42.0</td><td>13.9</td><td>20.9</td></tr><tr><td>MA-COIR</td><td>23.7</td><td>19.6</td><td>21.5</td></tr></table>
+
+in Section 3.5, leads to improvements across all metrics for all query types. F1 scores for claim-queries increase by 4.6 points compared to MA-COIR. Across all query types, the improvement in recall exceeds that in precision, indicating that the added data is both accurate (with minimal noise, which helps maintain precision) and diverse, benefiting all query types.
+
+# 6.3 Combination of different-level queries
+
+The results of combining predictions of various types of queries are presented in Table 5. While the accuracy of decomposing full passages into shorter units is low, MA-COIR captures additional concepts that are difficult to detect from full-length inputs alone. The predictions from different query levels exhibit partial but non-trivial overlap, revealing their complementary strengths.
+
+Each query type offers distinct advantages. Aggregating predictions across all levels yields substantial gains. Recall improves significantly from $(27.3 \to 45.5 \to 64.8)$ when integrating all three, underscoring the value of multi-level querying.
+
+# 6.4 More comparisons
+
+Our framework operates under different setups compared to previous studies that were validated on the same dataset. We provide results using a more comparable setting to ensure fair evaluation (see Table 6).
+
+For HPO dataset, REAL (Shlyk et al., 2024)
+
+reports results for two approaches: for an LLM generated mention, selecting the top-1 candidate from three candidates provided to GPT-3.5 (REAL-GPT3.5) or taking the top-1 concept retrieved by kNN searching (REAL-1st hit). For comparison, we report the results by MA-COIR trained without mention-ssID pairs and the kNN-searcher we implemented using concept queries with $k = 1$ .
+
+For HOIP dataset, El Khettari et al. (2024) report the results of a similarity-based kNN search for concepts generated by llama-3-8b in its few-shot setting (ICL-Llama). After retrieval, they filtered out out-of-dataset predictions. We replicated their approach by using their generated concepts as queries and applying the same filter with kNN-searcher and setting $k = 1$ .
+
+From the results of REAL-1st hit and kNN-searcher on HPO (F1: 44.0/54.3), as well as kNN-searcher on concepts from ICL-Llama and our generated concepts (F1: 18.6/20.9) on HOIP-o, we can infer that the quality of our generated concepts and the representation of concepts/query is consistent with previous methods.
+
+The removal of out-of-dataset concepts significantly reduced false positives in similarity-based methods, improving precision to over 40.0 on the HOIP-o. In contrast, MA-COIR does not predict concepts never appeared in the training phase, such post-processing does not provide benefits.
+
+Overall, our supervised recognizer, MA-COIR, outperforms unsupervised LLM-based solutions like REAL-GPT3.5 and ICL-Llama.
+
+# 7 Conclusion
+
+We present the MA-COIR framework, a flexible and implementable solution for recognizing both simple and complex biomedical concepts explicitly or implicitly appeared in scientific texts, without requiring specific mention information. The framework meets the needs of domain experts, as demonstrated by experiments on three vocabulary/ontology-dataset pairs. We introduce efficient methods for obtaining queries at various levels and data augmentation using an LLM and proving their efficacy in low-resource scenarios. MA-COIR's adaptability to multi-level queries enhances its practical utility. We further provide an in-depth analysis of biomedical concept recognition and potential directions for future improvement.
+
+# Limitations
+
+Although we would like MA-COIR to generate ssIDs for unseen concepts based on semantic similarities with seen concepts, results indicate that it lacks this capability. This restricts the model's applicability to the available dataset. Given that the annotated dataset contains significantly fewer concepts than the full ontology, further framework refinement is needed to allow comprehensive processing across different input levels and consistent mapping of all ontology concepts and their indexes.
+
+It is essential to develop validation datasets that align with the needs of domain experts. In the HPO and HOIP test sets, the low proportion of unseen concepts limits the evaluation of the model's generalization to out-of-dataset concepts. Without observing MA-COIR's performance decline on the CDR dataset, this limitation might have gone unrecognized.
+
+Last but not least, the performance of MA-COIR also depends on query quality. There is a substantial gap between results for concept names generated by an LLM and those derived from gold annotated mentions. Although we have not fully explored LLM-based query generation, it is unrealistic to expect consistent query quality across specialized biomedical domains. Thus, it is critical to both improve the model's robustness to lower-quality queries and identify ways to generate high-quality queries.
+
+# References
+
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+Nicola De Cao, Gautier Izacard, Sebastian Riedel, and Fabio Petroni. 2020. Autoregressive entity retrieval. CoRR, abs/2010.00904.   
+J Harry Caufield, Harshad Hegde, Vincent Emonet, Nomi L Harris, Marcin P Joachimiak, Nicolas Ma-tentzogl, HyeongSik Kim, Sierra Moxon, Justin T Reese, Melissa A Haendel, Peter N Robinson, and Christopher J Mungall. 2024. Structured Prompt Interrogation and Recursive Extraction of Semantics (SPIRES): a method for populating knowledge bases using zero-shot learning. Bioinformatics, 40(3):btae104.   
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+Oumaima El Khettari, Noriki Nishida, Shanshan Liu, Rumana Ferdous Munne, Yuki Yamagata, Solen
+
+Quiniou, Samuel Chaffron, and Yuji Matsumoto. 2024. Mention-agnostic information extraction for ontological annotation of biomedical articles. In Proceedings of the 23rd Workshop on Biomedical Natural Language Processing, pages 457-473, Bangkok, Thailand. Association for Computational Linguistics.   
+Michael A et al. Gargano. 2023. The human phenotype ontology in 2024: phenotypes around the world. *Nucleic Acids Research*, 52(D1):D1333–D1346.   
+Matthew Honnibal and Ines Montani. 2017. spaCy 2: Natural language understanding with Bloom embeddings, convolutional neural networks and incremental parsing. To appear.   
+Jyun-Yu Jiang, Wei-Cheng Chang, Jiong Zhang, Chojui Hsieh, and Hsiang-Fu Yu. 2024. Entity disambiguation with extreme multi-label ranking. In Proceedings of the ACM on Web Conference 2024, pages 4172-4180.   
+Siddhant Kharbanda, Atmadeep Banerjee, Erik Schultheis, and Rohit Babbar. 2022. Cascadexml: Rethinking transformers for end-to-end multi-resolution training in extreme multi-label classification. Advances in neural information processing systems, 35:2074-2087.   
+Nikolaos Kolitsas, Octavian-Eugen Ganea, and Thomas Hofmann. 2018. End-to-end neural entity linking. In Proceedings of the 22nd Conference on Computational Natural Language Learning, pages 519-529, Brussels, Belgium. Association for Computational Linguistics.   
+Jinhyuk Lee, Wonjin Yoon, Sungdong Kim, Donghyeon Kim, Sunkyu Kim, Chan Ho So, and Jaewoo Kang. 2019. BioBERT: a pre-trained biomedical language representation model for biomedical text mining. Bioinformatics, 36(4):1234-1240.   
+Mike Lewis, Yinhan Liu, Naman Goyal, Marjan Ghazvininejad, Abdelrahman Mohamed, Omer Levy, Veselin Stoyanov, and Luke Zettlemoyer. 2019. BART: denoising sequence-to-sequence pre-training for natural language generation, translation, and comprehension. CoRR, abs/1910.13461.   
+Jiao Li, Yueping Sun, Robin J. Johnson, Daniela Sciaky, Chih-Hsuan Wei, Robert Leaman, Allan Peter Davis, Carolyn J. Mattingly, Thomas C. Wiegers, and Zhiyong Lu. 2016. Biocreative V CDR task corpus: a resource for chemical disease relation extraction. Database J. Biol. Databases Curation, 2016.   
+Fangyu Liu, Ehsan Shareghi, Zaiqiao Meng, Marco Basaldella, and Nigel Collier. 2021. Self-alignment pretraining for biomedical entity representations. In Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, pages 4228-4238, Online. Association for Computational Linguistics.
+
+Manuel Lobo, Andre Lamurias, and Francisco M. Couto. 2017. Identifying human phenotype terms by combining machine learning and validation rules. BioMed Research International, 2017(1):8565739.
+
+Ling Luo, Shankai Yan, Po-Ting Lai, Daniel Veltri, Andrew Oler, Sandhya Xirasagar, Rajarshi Ghosh, Morgan Similuk, Peter N Robinson, and Zhiyong Lu. 2021. Phenotagger: a hybrid method for phenotype concept recognition using human phenotype ontology. Bioinformatics, 37(13):1884-1890.
+
+OAKlib. 2023. Ontology access kit (oak).
+
+F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay. 2011. Scikit-learn: Machine learning in Python. Journal of Machine Learning Research, 12:2825-2830.
+
+Darya Shlyk, Tudor Groza, Marco Mesiti, Stefano Montanelli, and Emanuele Cavalleri. 2024. REAL: A retrieval-augmented entity linking approach for biomedical concept recognition. In Proceedings of the 23rd Workshop on Biomedical Natural Language Processing, pages 380-389, Bangkok, Thailand. Association for Computational Linguistics.
+
+Yi Tay, Vinh Q. Tran, Mostafa Dehghani, Jianmo Ni, Dara Bahri, Harsh Mehta, Zhen Qin, Kai Hui, Zhe Zhao, Jai Gupta, Tal Schuster, William W. Cohen, and Donald Metzler. 2022. Transformer memory as a differentiable search index. Preprint, arXiv:2202.06991.
+
+Qinyong Wang, Zhenxiang Gao, and Rong Xu. 2023. Exploring the in-context learning ability of large language model for biomedical concept linking. Preprint, arXiv:2307.01137.
+
+Ledell Wu, Fabio Petroni, Martin Josifoski, Sebastian Riedel, and Luke Zettlemoyer. 2020. Zero-shot entity linking with dense entity retrieval. In EMNLP.
+
+Yuki Yamagata, Tatsuya Kushida, Shuichi Onami, and Hiroshi Masuya. 2024. Homeostasis imbalance process ontology: a study on COVID-19 infectious processes.
+
+Hongyi Yuan, Zheng Yuan, Ruyi Gan, Jiaxing Zhang, Yutao Xie, and Sheng Yu. 2022. BioBART: Pretraining and evaluation of a biomedical generative language model. In Proceedings of the 21st Workshop on Biomedical Language Processing, pages 97-109, Dublin, Ireland. Association for Computational Linguistics.
+
+Jiong Zhang, Wei-Cheng Chang, Hsiang-Fu Yu, and Inderjit Dhillon. 2021. Fast multi-resolution transformer fine-tuning for extreme multi-label text classification. Advances in Neural Information Processing Systems, 34:7267-7280.
+
+Table 7: Hyperparameters of the recognizer.   
+
+<table><tr><td>Item</td><td>Value</td></tr><tr><td>model_card</td><td>facebook/bart-large</td></tr><tr><td>learning_rate</td><td>1e-5</td></tr><tr><td>num_epoch</td><td>50</td></tr><tr><td>batch_size</td><td>4</td></tr><tr><td>max_length_of_tokens</td><td>1024</td></tr></table>
+
+Sheng Zhang, Hao Cheng, Shikhar Vashishth, Cliff Wong, Jinfeng Xiao, Xiaodong Liu, Tristan Naumann, Jianfeng Gao, and Hoifung Poon. 2022. Knowledge-rich self-supervision for biomedical entity linking. In Findings of the Association for Computational Linguistics: EMNLP 2022, pages 868-880, Abu Dhabi, United Arab Emirates. Association for Computational Linguistics.
+
+# A Appendix
+
+# A.1 Hyperparameters
+
+The BART-based language model (facebook/bart-large) used in MA-COIR for recognition is trained with hyperparameters listed in the Table 7.
+
+The hyperparameters of the K-Means clustering algorithm used for hierarchical clustering process, are $g$ and $m$ , while $g$ is the maximum number of the elements covered by a node when we can stop further dividing the node into smaller clusters. $m$ is the number of clusters when we divide the elements in a node. For example, when $g = 10$ , $m = 10$ , if there are 9 elements in the current node, we do not divide the elements in this node by clustering; if there are 18 elements in the current node, we will do a clustering for these elements, so that these elements will be categorized into $m = 10$ clusters.
+
+In this work, we set $g = 10$ , $m = 10$ . Our choice is based on two main considerations: (1) Empirical evidence: Preliminary experiments using the DSI-inspired configuration ( $g = 10$ , $m = 100$ ) resulted in lower F1 scores on the HOIP validation set, compared to the current setting. (2) Structural consistency: Using decimal numbering (0-9) aligns naturally with our hierarchical "ssID" design, which organizes concepts into 10 branches per level, facilitating both interpretability and implementation.
+
+For the training of XR-Transformer, we implement the model with the library pecos $^8$ , setting the hyperparameters provided by the authors, as those have already been tuned. The architecture of the Transformers model we used in the experiments is BERT.
+
+![](images/c3602d64ad9530b192365c37efa85b1c6028bc6f00f8e4680302e424bfcafd1a.jpg)  
+Figure 5: Prompt template for generating concept names / claims for passage. A prompt consists of task instruction, output format instruction, several demonstrations and the query.
+
+Table 8: Recalls on the seen and unseen concepts of the top- $k$ generated sequences by MA-COIR.   
+
+<table><tr><td rowspan="2">k</td><td rowspan="2">Query</td><td colspan="2">CDR</td><td colspan="2">HPO</td></tr><tr><td>Seen</td><td>Unseen</td><td>Seen</td><td>Unseen</td></tr><tr><td rowspan="3">1</td><td>passage</td><td>57.2</td><td>0.3</td><td>60.0</td><td>0.0</td></tr><tr><td>mention</td><td>92.4</td><td>0.0</td><td>89.3</td><td>0.0</td></tr><tr><td>concept</td><td>52.9</td><td>0.0</td><td>63.6</td><td>0.0</td></tr><tr><td rowspan="3">5</td><td>passage</td><td>63.6</td><td>0.3</td><td>64.3</td><td>0.0</td></tr><tr><td>mention</td><td>95.2</td><td>2.9</td><td>92.1</td><td>12.5</td></tr><tr><td>concept</td><td>56.3</td><td>1.5</td><td>74.3</td><td>0.0</td></tr><tr><td rowspan="3">10</td><td>passage</td><td>66.6</td><td>0.4</td><td>66.4</td><td>0.0</td></tr><tr><td>mention</td><td>95.8</td><td>4.0</td><td>95.0</td><td>18.8</td></tr><tr><td>concept</td><td>57.7</td><td>2.2</td><td>80.7</td><td>12.5</td></tr></table>
+
+# A.2 LLM Application
+
+We applied a large language model llama-3-8b for query generation. For all concept generation tasks, the prompt consists of "instruction", "n demonstrations" under the n-shot setting, and the passage. The prompts we used for concept name generation on CDR, HPO and HOIP are shown in Fig. 5. For claim generation, the prompt template we used for a passage on HOIP is shown in Fig. 5. The generation is conducted in a zero-shot scenario cause there is no annotated data for passage-claim pairs.
+
+# A.3 Performance on seen and unseen concepts
+
+Upon examining MA-COIR's performance on both seen (concepts appeared in the training set) and unseen concepts (concepts only appeared in the test set), we found that the performance gap between it and the kNN-searcher is primarily due to its inability to recognize unseen concepts. As presented in the Table 8, when we evaluated the model on unseen concepts, MA-COIR achieved a recall of nearly 0.0 on both the CDR and the HPO.
+
+# A.4 Training data for "Indexing" capability of the recognizer
+
+The indexing capability of the model refers to the model's ability to generate the correct ssID for the query when it is a span. On datasets labelled with
+
+Table 9: Results on CDR with different training data. "All" contains passage-ssIDs pairs, name-ssID pairs, synonym-ssID pairs and mention-ssID pairs constructed from the original training set.   
+
+<table><tr><td>Data</td><td>Query</td><td>Pre</td><td>Rec</td><td>F1</td></tr><tr><td rowspan="3">All</td><td>passage</td><td>51.0</td><td>44.6</td><td>47.6</td></tr><tr><td>mention</td><td>67.2</td><td>72.0</td><td>69.5</td></tr><tr><td>concept</td><td>57.2</td><td>41.2</td><td>47.9</td></tr><tr><td rowspan="3">- mention</td><td>passage</td><td>36.1</td><td>30.5</td><td>33.1</td></tr><tr><td>mention</td><td>39.5</td><td>42.8</td><td>41.1</td></tr><tr><td>concept</td><td>32.4</td><td>22.3</td><td>26.4</td></tr><tr><td rowspan="3">- synonym</td><td>passage</td><td>48.2</td><td>42.3</td><td>45.0</td></tr><tr><td>mention</td><td>67.4</td><td>72.0</td><td>69.6</td></tr><tr><td>concept</td><td>58.2</td><td>41.4</td><td>48.3</td></tr><tr><td>- mention</td><td>passage</td><td>36.0</td><td>30.5</td><td>33.0</td></tr><tr><td>- synonym</td><td>mention</td><td>41.9</td><td>44.8</td><td>43.3</td></tr><tr><td></td><td>concept</td><td>37.6</td><td>24.8</td><td>29.9</td></tr></table>
+
+mentions, in addition to the canonical names and synonyms of a concept in the ontology that can be used to train model indexing capabilities, mentions are also very effective data. We conducted an ablation study on the CDR dataset to confirm the impact of synonym- and mention-ssID information on the model's ability to recognize concepts. The results can be seen in Table 9.
+
+After removing the mention-ssID data, the model's performance dropped significantly; removing the synonym-ssID data, the performance on the passage-level query dropped less and even improved on the span-level query. This illustrates that the way a concept is expressed within a particular application (passage) is important for capturing the relationship between the concept and the ssID. Not only the indexing capability are influenced by removing mention data, but also the recognition on the passage query (↓ 14.5 F1 score). The slight improvement after removing synonym-ssID pairs indicates how different the common expressions written in scientific papers and the technical terms of a concept are. Using synonyms to enrich concept information makes the query and a concept further apart in representation.

paper_markdowns/bamboo-00498.md

@@ -0,0 +1,606 @@
+# MAM: Modular Multi-Agent Framework for Multi-Modal Medical Diagnosis via Role-Specialized Collaboration
+
+Yucheng Zhou, Lingran Song, Jianbing Shen*
+
+SKL-IOTSC, CIS, University of Macau
+
+yucheng.zhou@connect.um.edu.mo, jianbingshen@um.edu.mo
+
+# Abstract
+
+Recent advancements in medical Large Language Models (LLMs) have showcased their powerful reasoning and diagnostic capabilities. Despite their success, current unified multimodal medical LLMs face limitations in knowledge update costs, comprehensiveness, and flexibility. To address these challenges, we introduce the Modular Multi-Agent Framework for Multi-Modal Medical Diagnosis (MAM). Inspired by our empirical findings highlighting the benefits of role assignment and diagnostic discernment in LLMs, MAM decomposes the medical diagnostic process into specialized roles: a General Practitioner, Specialist Team, Radiologist, Medical Assistant, and Director, each embodied by an LLM-based agent. This modular and collaborative framework enables efficient knowledge updates and leverages existing medical LLMs and knowledge bases. Extensive experimental evaluations conducted on a wide range of publicly accessible multimodal medical datasets, incorporating text, image, audio, and video modalities, demonstrate that MAM consistently surpasses the performance of modality-specific LLMs. Notably, MAM achieves significant performance improvements ranging from $18\%$ to $365\%$ compared to baseline models. Our code is released at https://github.com/yczhou001/MAM.
+
+# 1 Introduction
+
+Large Language Models (LLMs) have recently demonstrated remarkable reasoning capabilities (Radford, 2018; OpenAI, 2023; Touvron et al., 2023a; Yang et al., 2024; Zhang et al., 2023b; Shao et al., 2024; Zhang et al., 2023a). Beyond demonstrating impressive language reasoning and generation capabilities, LLMs are expanded to process diverse modalities, e.g., images, audio, and
+
+video (Liu et al., 2023a; Chu et al., 2023; Zhang et al., 2023a). This formidable reasoning capacity holds significant promise for addressing problems in medical diagnostics.
+
+For medical practice, physicians are confronted with a deluge of heterogeneous medical data, encompassing textual reports, medical images, cardiac sounds, and even surgical video recordings. Accurately extracting critical information from this complex data to arrive at precise diagnoses places a significant cognitive burden and challenge on clinicians. Furthermore, the growth in the volume of medical diagnostic data provides a substantial foundation for the training of LLMs. Consequently, the development of LLMs to enhance medical diagnostic workflows is crucial.
+
+However, many efforts are directed towards constructing unified multimodal medical large models (Li et al., 2023; Thawakar et al., 2024; Deng et al., 2024). While these models have shown some progress in integrating multimodal information, they suffer from two limitations. Firstly, for unified models, each knowledge update is cost, often requiring substantial computational resources to retrain the entire model. Secondly, unified models lack modularity and flexibility, necessitating a single model to exhibit sufficient performance across various medical diagnostic tasks to satisfy demands. To explore the capabilities of existing domain-specific LLMs, we conducted an empirical study. Our findings indicate that role assignment significantly enhances the diagnostic abilities of LLMs, and LLMs possess the potential to discern the correct diagnosis from multiple ones.
+
+To overcome the aforementioned limitations of unified multimodal medical LLMs and to better emulate the collaborative approach of human medical teams, we propose the Multi-Agent Framework for Multi-Modal Medical Diagnosis (MAM). Instead of pursuing an "omnipotent" unified model, MAM framework decomposes the medical diag
+
+nostic process into several specialized roles and designs LLM-based agents for each role. These agents include: a General Practitioner agent responsible for initial triage, a Specialist Team agent providing domain-expert opinions, a Radiologist agent specializing in medical image analysis, a Medical Assistant agent aiding information retrieval and knowledge management, and a Director agent responsible for coordinating and synthesizing diagnostic opinions. The core advantages of the MAM framework lie in its modular design and collaborative workflow. The modular agent design enables more granular and efficient knowledge updates and model maintenance, without requiring global retraining. The framework also allows MAM to easily integrate and leverage various existing medical models and specialized knowledge bases.
+
+In the experiments, we evaluate our MAM framework in multimodal medical diagnosis tasks through comprehensive experiments on several publicly available multimodal medical datasets. Experimental results demonstrate that the MAM framework consistently outperforms specific-modal LLMs across various medical datasets and data modalities. In addition, we conduct ablation studies, consistency analysis, and sensitivity analyses regarding the number of discussion rounds and roles to gain deeper insights into the roles of individual components and the operational mechanisms of the framework.
+
+# 2 Related Work
+
+# 2.1 LLM-based Multi-Agent
+
+With the rapid advancement of LLMs, their application across various tasks has become increasingly widespread (Radford, 2018; OpenAI, 2023; Touvron et al., 2023a; Yang et al., 2024; Zhang et al., 2023b; Shao et al., 2024; Zhang et al., 2023a; Zhou et al., 2025, 2024a). These LLMs, outstanding in natural language processing, have been widely adapted to different tasks (Wang et al., 2024a; Yue et al., 2024; Yang et al., 2024; Zhou et al., 2024b; Hu et al., 2025). However, for relatively complex tasks, the capabilities of a single LLM may not achieve the desired effect. In order to solve complex tasks beyond the function of a single LLM, LLM-based multi-agent systems are developed (Liu et al., 2023c; Zhao et al., 2024; Talebirad and Nadiri, 2023). In (Wu et al., 2024), the author investigates the effectiveness of using LLM-based Multi-Agent to solve mathematical problems
+
+through dialogue, and MathChat is proposed as a conversational problem-solving solution designed for mathematical problems. In software engineering, the MAGIS (Tao et al., 2024) framework enables the collaboration of various agents in the planning and coding process to solve GITHUB problems. In the field of finance, inspired by the organizational structure of effective investment firms in the real world, FinCon (Yu et al., 2024) is developed to accomplish a variety of financial tasks.
+
+The emergence of these LLM-based Multi-Agent systems points to a common conclusion that LLM-based Multi-Agents are well adapted for reasoning (Zhao et al., 2024; Talebirad and Nadiri, 2023; Wu et al., 2024; Tao et al., 2024), decision making (Liu et al., 2023c; Yu et al., 2024), etc. This adaptability makes them essential in the medical domain where interdisciplinary knowledge and multi-step problem solving are required.
+
+# 2.2 Medical LLM
+
+Due to the remarkable performance of LLMs in different tasks (Zhang et al., 2023b; Shao et al., 2024; Zhang et al., 2023a), various medical LLMs have been developed to solve a wide range of medical problems (Bao et al., 2023; Zhao et al., 2024; Ye et al., 2023; Fleming et al., 2024). As a comprehensive solution, DISC-MedLLM (Bao et al., 2023) utilizes LLM to deliver accurate and realistic medical responses in end-to-end conversational healthcare services. As the first LLaMA based Chinese medical LLM, Zhongjing (Zhao et al., 2024) has implemented the training pipeline from continuous pre-training, SFT, to Reinforcement Learning from Human Feedback (RLHF), where pre-training enhances medical knowledge and RLHF further improves instruction compliance and safety. Through a multi-stage training approach that combines domain-specific continuous pre-training (DCPT), SFT, and Direct Preference Optimization (DPO), Qilin-Med (Ye et al., 2023) shows substantial performance gains as a medical LLM.
+
+Moreover, medical field is characterized by the presence of multimodal information, including diverse data types such as text, images, audios, etc. To make full use of these diverse data types, multimodal medical large models have been created (Li et al., 2023; Thawakar et al., 2024; Deng et al., 2024; Liu et al., 2023b; Chen et al., 2024). In LLaVA-Med (Li et al., 2023), the authors propose a cost-effective way to train a visual language con
+
+<table><tr><td>Dataset</td><td>Direct</td><td>Assigned Roles</td></tr><tr><td>MedQA (Jin et al., 2020)</td><td>30.8</td><td>50.6 (+19.8)</td></tr><tr><td>PubMedQA (Jin et al., 2019)</td><td>48.5</td><td>87.0 (+38.5)</td></tr><tr><td>PathVQA (He et al., 2020)</td><td>40.1</td><td>46.6 (+6.5)</td></tr><tr><td>PMC-VQA (Zhang et al., 2023c)</td><td>24.0</td><td>29.0 (+5.0)</td></tr><tr><td>DeepLesion (Yan et al., 2017)</td><td>11.1</td><td>40.0 (+28.9)</td></tr><tr><td>NIH (Wang et al., 2017)</td><td>12.6</td><td>50.7 (+38.1)</td></tr><tr><td>Brain Tumor (Bhuvaji et al., 2020)</td><td>80.2</td><td>98.2 (+18.0)</td></tr><tr><td>Heartbeat (Bentley et al., 2011)</td><td>43.9</td><td>62.5 (+18.6)</td></tr><tr><td>SoundDr (Hoang et al., 2023)</td><td>25.0</td><td>45.4 (+20.4)</td></tr><tr><td>MedVidQA (Gupta et al., 2022)</td><td>55.3</td><td>69.7 (+14.4)</td></tr></table>
+
+Table 1: Performance comparison of "Direct" and "Assigned Roles" prompting methods across multi-modal medical tasks. The blue numbers indicate the performance improvement.
+
+versational assistant that can answer open-ended research questions on biomedical images. In the task area of radiology, XrayGPT (Thawakar et al., 2024) was developed, which is a new conversational medical visual language model that can analyze and answer open-ended questions about chest radiographs. In the field of ophthalmology, OphGLM (Deng et al., 2024) has built a large multimodal model of ophthalmology, contributing to the clinical application of ophthalmology.
+
+# 3 Empirical Study
+
+# 3.1 The Significance of Assigned Roles in Medical Diagnosis with LLMs
+
+Experimental Setting. We investigate the impact of assigned roles on the performance of Large Language Models (LLMs) in multimodal medical diagnosis. Our experiments leverage a diverse collection of publicly available medical datasets, encompassing text, image, audio, and video modalities. Specifically, we utilize the following datasets: Brain Tumor (Bhuvaji et al., 2020) (394 cases), DeepLesion (Yan et al., 2017) (225 cases), Heartbeat (Bentley et al., 2011) (461 cases), MedQA (Jin et al., 2020) (200 cases), MedVidQA (Gupta et al., 2022) (284 cases), NIH Chest X-rays (Wang et al., 2017) (215 cases), PathVQA (He et al., 2020) (200 cases), PMC-VQA (Zhang et al., 2023c) (200 cases), PubMedQA (Jin et al., 2019) (200 cases), and SoundDr (Hoang et al., 2023) (240 cases). We use these datasets to evaluate the capabilities of LLMs in handling multimodal medical diagnostic tasks. We employ Qwen-Audio-Chat (Chu et al., 2023) for audio tasks, Medichat-Llama3-8B (sethuiyer, 2024) for text tasks, HuatuoGPT-Vision-7B (Chen et al., 2024) for image tasks, and VideoLLaMA2-7B (Cheng et al., 2024b) for video tasks. LLMs can assign roles in input prompts.
+
+<table><tr><td>Dataset</td><td>Expectation</td><td>Reasoning</td></tr><tr><td>MedQA (Jin et al., 2020)</td><td>46.9</td><td>49.3 (+2.4)</td></tr><tr><td>PubMedQA (Jin et al., 2019)</td><td>54.0</td><td>72.6 (+18.6)</td></tr><tr><td>PathVQA (He et al., 2020)</td><td>50.0</td><td>91.7 (+41.7)</td></tr><tr><td>PMC-VQA (Zhang et al., 2023c)</td><td>41.7</td><td>62.5 (+20.8)</td></tr><tr><td>DeepLesion (Yan et al., 2017)</td><td>52.5</td><td>57.5 (+5.0)</td></tr><tr><td>NIH (Wang et al., 2017)</td><td>44.0</td><td>46.0 (+2.0)</td></tr><tr><td>Brain Tumor (Bhuvaji et al., 2020)</td><td>55.1</td><td>73.9 (+18.8)</td></tr><tr><td>Heartbeat (Bentley et al., 2011)</td><td>50.2</td><td>54.0 (+3.8)</td></tr><tr><td>SoundDr (Hoang et al., 2023)</td><td>48.1</td><td>55.7 (+7.6)</td></tr><tr><td>MedVidQA (Gupta et al., 2022)</td><td>46.0</td><td>50.0 (+4.0)</td></tr></table>
+
+Table 2: LLM Diagnostic Discernment: Comparing Expected vs. Reasoning Accuracy. This table shows the performance of LLMs in selecting the correct diagnosis from a set of plausible alternatives. "Expectation" represents random selection accuracy, while "Reasoning" reflects the LLM's accuracy in identifying the correct diagnosis.
+
+Table 1 compares two prompting strategies: "Direct" and "Assigned Roles". The "Direct" is without role assignment, while the "Assigned Roles" approach creates a physician role using a specific prompt (see Appendix B). The results indicate a consistent and significant performance improvement across all datasets using the "Assigned Roles" prompting strategy, with gains ranging from $5.0\%$ (PMC-VQA) to $38.5\%$ (PubMedQA). This suggests that role context enhances LLMs' ability to interpret and reason about medical data, improving diagnostic accuracy. Even in datasets with high baseline performance (e.g., Brain Tumor), role assignment provides a noticeable benefit. Furthermore, role assignment is particularly effective for tasks requiring deeper medical context and domain-specific knowledge.
+
+# 3.2 LLMs' Capability to Discern Correct Reasoning Outcomes
+
+To evaluate the reasoning capabilities of LLMs, we designed an experiment to assess their ability to identify the correct diagnosis from a set of plausible alternatives. Using the "Assigned Roles" prompting strategy, we generated three diagnostic outputs for each instance in the datasets. The datasets were pre-filtered to include only instances where at least one of the three diagnoses was correct, establishing a baseline "Expectation" representing random selection accuracy. The "Reasoning" column in Table 2 reflects the LLMs' accuracy in explicitly selecting the correct diagnosis from three generated options. Results show that the "Reasoning" accuracy consistently exceeds the "Expectation" across all datasets, with improvements ranging from $2.0\%$ (NIH) to $41.7\%$ (PathVQA). This demonstrates
+
+![](images/74c0364c100d0278b4a877db3f8c21354d6ba5ba796151cbcffad8472fb3484e.jpg)  
+Figure 1: Overview of our MAM Framework for multi-modal medical diagnosis.
+
+that LLMs possess reasoning capabilities beyond random selection, particularly in complex visual question answering tasks like PathVQA and PMCVQA. The consistent positive delta across datasets indicates LLMs' potential to evaluate and refine their outputs to identify accurate conclusions.
+
+# 4 Method
+
+Based on our preliminary empirical studies, we observed that augmenting Large Language Models (LLMs) with specific medical roles significantly enhances their diagnostic performance. Furthermore, LLMs demonstrate a notable capacity to reason and synthesize correct diagnoses from diverse diagnostic opinions. Inspired by these findings, we propose the Multi-Agent Medical (MAM) framework, shown in Figure 1. This framework aims to transform multi-modal medical diagnosis into a collaborative endeavor, thereby amplifying the diagnostic capabilities of existing models. It comprises five key roles, each embodied by an LLM-based agent, working synergistically within a defined workflow: ① General Practitioner: Responsible for initial Disease Type Classification and Referral to Specialist. ② Specialist Team: Charged with providing Diagnostic Opinions on specific medical conditions and actively participating in discussions. ③ Radiologist: Tasked with analyzing medical images and contributing to diagnostic discussions. ④ Medical Assistant: Responsible for retrieving and summarizing relevant medical information from databases. ⑤ Director: Synthesizes discussion reports and reviews the quality of medical diagnoses.
+
+In our framework, multi-modal medical inputs are initially directed to the General Practitioner, who performs disease classification and subsequently refers the case to the relevant Specialist Team. The Specialist Teams will decompose and anonymize the medical problem. The Medical Assistant then retrieves and summarizes pertinent information from medical databases based on the decomposed problem. Subsequently, the Director orchestrates discussions among the Specialist Team, where each specialist presents their diagnostic opinion. The Director then synthesizes these opinions and the database summaries into a comprehensive report. The Specialist Team reviews this report and votes on whether to endorse it. In cases of disagreement, the process iteratively re-enters the Specialist Team discussion phase. Otherwise, upon reaching a consensus, the Director derives the final diagnosis based on the synthesized report.
+
+# 4.1 Doctor Agent Role Design
+
+General Practitioner The General Practitioner agent is designed to mimic the role of a primary care physician in a clinical setting. Upon receiving multi-modal medical inputs, this agent is responsible for the initial triage, performing Disease Type Classification to categorize the medical case. Crucially, it then determines the appropriate Referral to Specialist, directing cases to the relevant Specialist Team based on the initial classification.
+
+Specialist Team The Specialist Team is composed of multiple agents, each representing a specialist in a specific medical domain. These agents
+
+are tasked with providing Diagnostic Opinions relevant to their expertise. They engage in discussions, sharing their perspectives and interpretations of the medical case. Furthermore, Specialist Team members participate in a voting process to reach a consensus on the synthesized diagnostic report.
+
+Radiologist The Radiologist agent specializes in the interpretation of medical images, such as X-rays and CT scans. Its primary responsibility is to analyze these images and provide imaging-based insights to the other agents. The Radiologist communicates with the Specialist Team and the Director, offering expertise in image analysis to aid in diagnosis and treatment planning.
+
+Medical Assistant The Medical Assistant agent plays a crucial role in information management. Its responsibilities include processing medical data to facilitate retrieval of relevant information from medical databases. Furthermore, the Medical Assistant summarizes the retrieved information, providing concise summaries.
+
+Director The Director agent serves as the orchestrator and synthesizer within the MAM framework. This agent is responsible for reviewing the diagnostic opinions provided by the Specialist Team and the Radiologist. It synthesizes the discussion outcomes from the Specialist Team into a comprehensive report. Crucially, the Director derives the final diagnosis based on the synthesized report, specifically when a consensus is reached among the Specialist Team through voting.
+
+# 4.2 Collaborative Diagnosis Process
+
+The MAM framework orchestrates a collaborative diagnostic process initiated upon receiving multimodal medical inputs. Let $M = \{m_{1},m_{2},\dots,m_{k}\}$ represent the multi-modal medical input, where $m_{i}$ denotes the $i$ -th modality.
+
+Initial Triage and Referral: The General Practitioner agent $(G)$ receives the multi-modal input $M$ . $G$ performs Disease Type Classification to categorize the medical case into a disease type $d$ . This can be represented as:
+
+$$
+d = C ^ {G} (M) \tag {1}
+$$
+
+where $C^G$ denotes the disease type classification function performed by agent $G$ .
+
+Based on the classified disease type $d$ , $G$ determines the appropriate Specialist Team $S =$
+
+$\{s_1,s_2,\ldots ,s_n\}$ for referral. This referral process can be represented by:
+
+$$
+S = R ^ {G} (d) \tag {2}
+$$
+
+where $R^G$ is the referral function by agent $G$ , and $S$ is the set of specialist agents $s_i$ .
+
+Problem Decomposition and Anonymization: The Specialist Team $S$ receives the medical case and decomposes the problem into a set of subproblems $P = \{p_1, p_2, \dots, p_m\}$ . Anonymization is performed concurrently. This decomposition is represented by:
+
+$$
+P = D ^ {S} (M) \tag {3}
+$$
+
+where $D^S$ is the problem decomposition function by Specialist Team $S$ .
+
+Information Retrieval: The Medical Assistant agent $(A)$ utilizes the decomposed problem $P$ to retrieve relevant medical information. Let $I_r$ represent the retrieved information, obtained through:
+
+$$
+I _ {r} = \operatorname {R e t r i e v e} ^ {A} (P) \tag {4}
+$$
+
+where $\mathrm{Retrieve}^A$ is the information retrieval function by agent $A$ . Since we do not have access to a real hospital database, the retrieval process is conducted using the Google API. The query used for retrieval is based on the decomposed and anonymized problem $P$ , ensuring no privacy leakage. $A$ then summarizes the retrieved information into a concise summary $I_s$ :
+
+$$
+I _ {s} = \operatorname {S u m m a r i z e} ^ {A} \left(I _ {r}\right) \tag {5}
+$$
+
+where $\mathrm{Summarize}^A$ is the summarization function by agent $A$ .
+
+Diagnostic Opinion Generation and Discussion: Each specialist $s_i \in S$ and the Radiologist agent (Rad) independently generate their diagnostic opinions based on the multi-modal input $M$ , and the information summary $I_s$ . Let $O_{s_i}$ be the diagnostic opinion of specialist $s_i$ and $O_{Rad}$ be the opinion of the Radiologist. Opinions are generated through:
+
+$$
+O _ {s _ {i}} = \operatorname {D i a g} ^ {s _ {i}} \left(M, I _ {s}\right) \quad \forall s _ {i} \in S \tag {6}
+$$
+
+$$
+O _ {R a d} = \operatorname {D i a g} ^ {R a d} (M) \tag {7}
+$$
+
+where $\mathrm{Diag}^{s_i}$ and $\mathrm{Diag}^{Rad}$ are the diagnostic opinion generation functions for specialist $s_i$ and Radiologist Rad, respectively. The Director agent (Dir) orchestrates a discussion.
+
+Algorithm 1 Consensus and Iteration Process  
+1: while No Consensus do  
+2: Specialist Team $S$ and Radiologist $Rad$ present and discuss diagnostic opinions $\{O_{si}\}_{si \in S}$ and $O_{Rad}$ .  
+3: Director $Dir$ synthesizes a report $R_p = \text{SynthDir}(\{O_{si}\}_{si \in S}, O_{Rad}, I_s)$ .  
+4: Specialist Team $S$ reviews report $R_p$ .  
+5: for each specialist $s_i \in S$ do  
+6: Specialist $s_i$ votes $v_i \in \{0,1\}$ on endorsing $R_p$ .  
+7: end for  
+8: Calculate total endorsement votes $V = \sum_{i=1}^{n} v_i$ .  
+9: if $V == n$ then  
+10: Consensus Reached $\leftarrow$ True.  
+11: else  
+12: Consensus Reached $\leftarrow$ False.  
+13: end if  
+14: end while  
+15: return Consensus Reached
+
+Report Synthesis and Review: The Director agent (Dir) synthesizes the diagnostic opinions $\{O_{s_1},O_{s_2},\dots,O_{s_n},O_{Rad}\}$ and the information summary $I_{s}$ into a comprehensive diagnostic report $R_{p}$ . This synthesis is performed by:
+
+$$
+R _ {p} = \operatorname {S y n t h} ^ {D i r} \left(\left\{O _ {s _ {i}} \right\} _ {s _ {i} \in S}, O _ {R a d}, I _ {s}\right) \tag {8}
+$$
+
+where $\mathrm{Synth}^{Dir}$ is the synthesis function by agent $Dir$ . The Specialist Team $S$ reviews $R_{p}$ and votes on endorsement. Let $v_{i} \in \{0,1\}$ be the vote of specialist $s_{i}$ .
+
+Consensus and Iteration: The Director agent checks for consensus. Let $V = \sum_{i=1}^{n} v_{i}$ be the total endorsement votes. If $V = n$ (assuming $n = 3$ in your algorithm), the description seems to be a typo, it should be consensus of all specialists which is $V = n$ , consensus is reached.
+
+Final Diagnosis Derivation: Upon reaching consensus, the Director agent derives the final diagnosis $D_{final}$ based on $R_{p}$ . This is performed by:
+
+$$
+D _ {f i n a l} = \operatorname {D i a g n o s i s} ^ {D i r} \left(R _ {p}\right) \tag {9}
+$$
+
+where $\text{Diagnosis}^{Dir}$ is the diagnosis derivation function by agent $Dir$ . $D_{final}$ is the output of the MAM framework.
+
+Table 3: Performance comparison of different LLMs on text-based medical datasets.   
+
+<table><tr><td>Method</td><td>MedQA</td><td>PubMedQA</td></tr><tr><td>LLaMA-7B (Touvron et al., 2023b)</td><td>18.6</td><td>37.2</td></tr><tr><td>DAPT-7B (Gururangan et al., 2020)</td><td>25.7</td><td>44.1</td></tr><tr><td>MedAlpaca-7B (Han et al., 2023)</td><td>29.3</td><td>51.2</td></tr><tr><td>AdaptLLM-7B (Cheng et al., 2024a)</td><td>30.5</td><td>56.8</td></tr><tr><td>LLaMA-3-8B (AI@Meta, 2024)</td><td>29.6</td><td>43.6</td></tr><tr><td>Medichat-Llama3-8B (sethuiyer, 2024)</td><td>30.8</td><td>48.5</td></tr><tr><td>MAM</td><td>40.0</td><td>84.0</td></tr></table>
+
+# 5 Experiments
+
+# 5.1 Setup
+
+Text-based Evaluation. For text-based evaluation, we used MedQA (Jin et al., 2020) and PubMedQA (Jin et al., 2019). We selected 200 English four-option multiple-choice questions from MedQA (Jin et al., 2020) and 200 question-answer pairs from PubMedQA (Jin et al., 2019). We compared MAM against LLMs: LLaMA-7B (Touvron et al., 2023b), DAPT-7B (Gururangan et al., 2020), MedAlpaca-7B (Han et al., 2023), AdaptLLM-7B (Cheng et al., 2024a), LLaMA-3-8B (AI@Meta, 2024), and Medichat-Llama3-8B (sethuiyer, 2024).
+
+Image-based Evaluation. For image evaluation, we used Brain Tumor (Bhuvaji et al., 2020) (test set, 394 cases), DeepLesion (Yan et al., 2017) (225 cases from 9 categories), NIH Chest X-rays (Wang et al., 2017) (215 cases), PathVQA (He et al., 2020) (200 cases), and PMC-VQA (Zhang et al., 2023c) (200 pairs). Compared LVLMs include LLaVA-7B (Liu et al., 2023a), Qwen2-VL-7B (Wang et al., 2024b), LLaVA-Med-7B (Li et al., 2023), QilinMed-VL-13B (Liu et al., 2023b), and HuatuoGPTVision-7B (Chen et al., 2024).
+
+Audio-based Evaluation. For audio evaluation, we used Heartbeat (Bentley et al., 2011) (clinical trial data, 461 instances) and SoundDr (Hoang et al., 2023) (240 instances). MAM is compared with Qwen-Audio-Chat (Chu et al., 2023).
+
+Video-based Evaluation. For video evaluation, we used MedVidQA (Temporal Segment Prediction test set, 284 data points (Gupta et al., 2022)). We preprocessed it into yes/no questions using original and alternative video segments. MAM is compared with video-LLMs: LLaVA-Next-Video-7B (Zhang et al., 2024), Qwen2-VL-7B (Wang et al., 2024b), and VideoLLaMA2-7B (Cheng et al., 2024b).
+
+<table><tr><td>Method</td><td>Pa</td><td>PMC</td><td>DL</td><td>NIH</td><td>BT</td></tr><tr><td>LLaVA-7B (Liu et al., 2023a)</td><td>7.3</td><td>6.2</td><td>2.6</td><td>4.2</td><td>34.6</td></tr><tr><td>Qwen2-VL-7B (Wang et al., 2024b)</td><td>29.5</td><td>10.6</td><td>3.6</td><td>6.3</td><td>52.6</td></tr><tr><td>LLaVA-Med-7B (Li et al., 2023)</td><td>36.3</td><td>19.8</td><td>8.5</td><td>9.2</td><td>73.7</td></tr><tr><td>Qilin-Med-VL-13B (Liu et al., 2023b)</td><td>39.2</td><td>22.5</td><td>11.3</td><td>11.4</td><td>80.6</td></tr><tr><td>HuatuoGPT-Vision-7B (Chen et al., 2024)</td><td>40.1</td><td>24.0</td><td>11.1</td><td>12.6</td><td>80.2</td></tr><tr><td>MAM</td><td>47.6</td><td>32.5</td><td>35.1</td><td>58.6</td><td>97.9</td></tr></table>
+
+Table 4: Performance comparison of different LVLMs on various image-based medical datasets. "Pa", "PMC", "BT" and "DL" denote "PathVQA", "PMC-VQA", "Brain Tumor" and "DeepLesion".   
+Table 5: Performance comparison of audio-LLMs on audiobased medical datasets.   
+
+<table><tr><td>Method</td><td>Heartbeat</td><td>SoundDr</td></tr><tr><td>Qwen-Audio-Chat (Chu et al., 2023)</td><td>34.9</td><td>25.0</td></tr><tr><td>MAM</td><td>64.0</td><td>47.9</td></tr></table>
+
+# 5.2 Main Results
+
+Our comprehensive experiments across text, image, audio, and video medical data demonstrate the superior performance of the MAM framework. As shown in Table 3-6, MAM consistently outperforms strong competitors across all modalities and achieves significant performance improvements ranging from $18\%$ to $365\%$ compared to baseline models. For text-based medical question answering (Table 3), MAM significantly surpasses baseline LLMs on MedQA and PubMedQA datasets, demonstrating enhanced medical text understanding. In image-based diagnosis (Table 4), MAM achieves top accuracy across PathVQA, PMCVQA, DeepLesion, NIH Chest X-rays, and Brain Tumor datasets, with particularly substantial gains on DeepLesion and NIH Chest X-rays. Audiobased results on Heartbeat and SoundDr datasets (Table 5) show MAM's clear advantage over audiOLLM baselines in medical audio interpretation. For video-based medical question answering on MedVidQA (Table 6), MAM achieves leading accuracy, outperforming all video-LLM competitors. These results collectively demonstrate MAM's efficacy in multi-modal medical diagnosis, highlighting the benefits of its collaborative multi-agent approach.
+
+# 5.3 Ablation Study
+
+To evaluate the contribution of each component in the MAM framework, we conducted an ablation study, with results shown in Table 7. The study systematically assesses the impact of incrementally adding key functionalities, starting from a baseline "Direct" approach (using the baseline LLM directly for diagnosis) and progressively in
+
+Table 6: Performance comparison of different video-LLMs on the Video-based medical dataset.   
+
+<table><tr><td>Method</td><td>MedVidQA</td></tr><tr><td>LLaVA-Next-Video-7B (Zhang et al., 2024)</td><td>51.5</td></tr><tr><td>Qwen2-VL-7B (Wang et al., 2024b)</td><td>54.8</td></tr><tr><td>VideoLLaMA2-7B (Cheng et al., 2024b)</td><td>55.3</td></tr><tr><td>MAM</td><td>74.3</td></tr></table>
+
+Table 7: Ablation study of our MAM framework. The "Direct" represents the baseline. From left to right, we incrementally add functions. "+Retrieval" is our full MAM framework.   
+
+<table><tr><td>Dataset</td><td>Direct</td><td>+Roles</td><td>+Discussion</td><td>+Retrival</td></tr><tr><td colspan="5">Incrementally Added Function →</td></tr><tr><td>MedQA</td><td>30.8</td><td>31.0</td><td>32.5</td><td>40.0</td></tr><tr><td>PubMedQA</td><td>48.5</td><td>69.5</td><td>77.0</td><td>84.0</td></tr><tr><td>PathVQA</td><td>40.1</td><td>46.0</td><td>47.0</td><td>47.6</td></tr><tr><td>PMC-VQA</td><td>24.0</td><td>26.0</td><td>32.0</td><td>32.5</td></tr><tr><td>DeepLesion</td><td>11.1</td><td>33.8</td><td>34.7</td><td>35.1</td></tr><tr><td>NIH</td><td>12.6</td><td>36.0</td><td>38.6</td><td>58.6</td></tr><tr><td>Brain Tumor</td><td>80.2</td><td>92.4</td><td>97.0</td><td>97.9</td></tr><tr><td>Heartbeat</td><td>34.9</td><td>35.1</td><td>49.5</td><td>64.0</td></tr><tr><td>SoundDr</td><td>25.0</td><td>32.9</td><td>43.3</td><td>47.9</td></tr><tr><td>MedVidQA</td><td>55.3</td><td>58.0</td><td>60.6</td><td>74.3</td></tr></table>
+
+tegrating agent roles (+Roles), inter-agent discussion (+Discussion), and information retrieval (+Retrieval), representing the complete MAM framework. The results reveal consistent performance improvements across all datasets as each component is added. The introduction of agent roles (+Roles) shows significant gains over the baseline, emphasizing the value of role specialization. Enabling discussion (+Discussion) further enhances performance, demonstrating the benefits of collaborative reasoning. Most notably, the full MAM framework (+Retrieval) achieves the highest performance, highlighting the synergistic effects of role specialization, collaborative discussion, and information retrieval. The substantial improvement from “+Discussion” to “+Retrieval” underscores the critical role of the Medical Assistant in enhancing diagnostic accuracy through relevant medical knowledge. These findings confirm the efficacy of each MAM component and their combined impact on multi-modal medical diagnosis.
+
+# 5.4 Consistency
+
+To evaluate the MAM framework's behavior, we analyzed its prediction consistency compared to the "Direct" approach. Consistency is defined as the percentage of instances where MAM's final prediction aligns with a correct prediction from the "Direct" method. This metric assesses MAM's
+
+Table 8: Consistency of prediction results from baseline (Direct) and MAM. Rows with lighter cyan color indicate datasets where MAM has relatively lower performance.   
+
+<table><tr><td>Dataset</td><td>Consistency</td><td>MAM</td></tr><tr><td>MedQA (Jin et al., 2020)</td><td>34.4</td><td>40.0</td></tr><tr><td>PubMedQA (Jin et al., 2019)</td><td>74.2</td><td>84.0</td></tr><tr><td>PathVQA (He et al., 2020)</td><td>50.0</td><td>47.6</td></tr><tr><td>PMC-VQA (Zhang et al., 2023c)</td><td>14.6</td><td>32.5</td></tr><tr><td>DeepLesion (Yan et al., 2017)</td><td>12.0</td><td>35.1</td></tr><tr><td>NIH (Wang et al., 2017)</td><td>59.3</td><td>58.6</td></tr><tr><td>Brain Tumor (Bhuvaji et al., 2020)</td><td>97.5</td><td>97.9</td></tr><tr><td>Heartbeat (Bentley et al., 2011)</td><td>70.2</td><td>64.0</td></tr><tr><td>SoundDr (Hoang et al., 2023)</td><td>60.0</td><td>47.9</td></tr><tr><td>MedVidQA (Gupta et al., 2022)</td><td>67.5</td><td>74.3</td></tr></table>
+
+ability to retain and reinforce correct baseline predictions while correcting errors. Table 8 compares the consistency scores with MAM's overall performance across datasets. Results indicate a positive correlation between MAM's performance and consistency. For instance, datasets, where MAM performs well, show high consistency, suggesting MAM effectively builds on the "Direct" method's correct predictions. In contrast, datasets with lower performance, such as PMC-VQA and DeepLesion lower consistency. This implies that when the "Direct" achieves lower accuracy, MAM may introduce changes that slightly reduce consistency with the original correct predictions. Nevertheless, MAM generally outperforms the "Direct" method overall, as shown in Table 7 and Table 8, indicating that its refinements enhance diagnostic accuracy despite occasional deviations from the baseline's correct predictions. This demonstrates that MAM actively improves predictions through its collaborative, knowledge-augmented framework rather than merely replicating the "Direct" approach.
+
+# 5.5 Discussion Time and Performance
+
+We investigated the impact of iterative discussions on diagnostic accuracy by evaluating performance across different discussion rounds, as illustrated in Figure 2. For Brain Tumor, performance improved in early rounds, indicating that iterative discussions enhance accuracy for complex cases. However, extending discussions beyond a few rounds did not consistently yield further gains. For MedQA and PathVQA, performance fluctuated, with peak accuracy often achieved within the first two or three rounds. PMC-VQA experienced a performance decline in the final round, suggesting potential overfitting or dataset-specific issues. Results imply that while initial discussions can refine diagnoses, ex
+
+![](images/a4e0ed0121839df07a3fdf7e812c9c65eddf67f0f80f897ed025517e18028ee0.jpg)
+
+![](images/05d18c21d2a3e2364d10907b8778add63f3976a1d89ecef9ba726c5e956bf16e.jpg)
+
+![](images/3c49c1d7aee36711f811120bbfcc0707ac85f5fc4b048c2aff388513730e61fc.jpg)
+
+![](images/881111470074011242707f4d2211712e6e0521cfa521cfd9396b9aa1307b10ae.jpg)
+
+![](images/96f826a8938ea613f230b928054329d87b36127e8e7064e6c7ac7a1981e35b10.jpg)  
+Figure 2: Performance with different times of discussion $(\leq 3)$ in our MAM pipeline across various datasets.
+
+![](images/817d2b87603007634b5e727f3afe5938a237798c87ad26c7f8102f6b3815efc6.jpg)
+
+![](images/aa9a7dee9b980778a13e002c7fa07ba51f8dff7ba954bca6ca79c9698e506fa4.jpg)
+
+![](images/ebc84c293dd80c2ddbf852ff266019ac4590132374f9d35f0a2d499094a6beac.jpg)  
+Figure 3: Performance with different number of roles in our MAM pipeline across various datasets.
+
+cessive rounds introduce noise or dilute accurate initial opinions. Limiting discussions can balance collaborative benefits and avoid over-discussion.
+
+# 5.6 Impact of Role Number
+
+We investigate the effect of role granularity by varying the number of agents in MAM (Figure 3). Performance generally followed an inverted U-shape: increasing roles from 1 ("Direct") to 3 significantly improved results, highlighting the benefit of role specialization. However, further increasing to 5 roles led to a performance decrease across datasets. This suggests an optimal level of role granularity exists. While role specialization is beneficial, excessive roles may introduce redundancy or overhead, hindering diagnosis. A moderately specialized framework with 3 roles appears to strike a better balance than either a single-agent approach or an overly complex multi-agent system, indicating that streamlined role specialization is crucial for effective collaborative medical diagnosis.
+
+# 5.7 Recall of Retrieval
+
+To evaluate the Medical Assistant's information retrieval module, we first measured recall, defined as
+
+Table 9: "Recall" indicates the proportion of instances where the retrieved content includes the correct answer. "Answer Correct" represents the accuracy of the final answer under the retrieved content that encompasses the correct answer.   
+
+<table><tr><td>Dataset</td><td>Recall</td><td>Answer Correct</td></tr><tr><td>DeepLesion (Yan et al., 2017)</td><td>31.7</td><td>53.4</td></tr><tr><td>Heartbeat (Bentley et al., 2011)</td><td>34.0</td><td>58.8</td></tr><tr><td>NIH (Wang et al., 2017)</td><td>12.1</td><td>46.2</td></tr></table>
+
+the proportion of retrieved medical documents containing information necessary to correctly answer diagnostic questions. As shown in Table 9, recall varies across datasets, ranging from $12.1\%$ for NIH to $34.0\%$ for Heartbeat. These results indicate that while the module retrieves relevant information in some cases, significant improvement is needed. Imperfect recall may stem from limitations in retrieval algorithms, incomplete medical databases, or challenges in formulating effective search queries for diverse medical questions. Enhancing recall is critical for ensuring the availability of necessary information for downstream diagnostic tasks.
+
+# 5.8 Impact from Retrieval Content
+
+Complementary to evaluating retrieval recall, we examined the impact of retrieved content on diagnostic accuracy by calculating the conditional probability of obtaining a correct answer when the retrieved documents contained the necessary information. This metric, labeled "Answer Correct" in Table 9, assesses the MAM framework's ability to leverage retrieved information effectively. As shown in Table 9, the "Answer Correct" is consistently higher than the corresponding accuracy of the "+"Discussion" (without retrieval) in Table 7. For instance, in the NIH dataset, the "Answer Correct" $(46.2\%)$ significantly surpasses the "Discussion" $(38.6\%)$ . It demonstrates that when relevant information is retrieved, the MAM framework is more likely to arrive at a correct diagnosis. However, the "Answer Correct" is not perfect, demonstrating the importance of improving retrieval and LLM's reasoning capabilities.
+
+# 5.9 Case Study
+
+Figure 4 shows a case of multimodal input from DeepLesion, comparing the outputs from the baseline and our framework. The baseline model produced incorrect results, whereas our framework delivered correct predictions. Our framework begins by identifying the input modality and determining the data type. Based on this information,
+
+it generates three expert roles to engage in up to three rounds of dialogue to discuss potential solutions. Concurrently, the Medical Assistant formulates queries for web retrieval. After processing the retrieved data, the Director reviews the discussion and retrieval records, synthesizes the insights into a summary, and presents it to the expert team for voting. The Director then uses the voting results and summary to make the final diagnosis. As shown in the process discussed in Figure 4, it is evident that although not all expert roles prioritized the correct answer initially, the structured approach of discussions and voting leads to an accurate resolution, which demonstrates effectiveness of our framework, demonstrating its ability of decision-making in complex medical scenarios.
+
+# 6 Conclusion
+
+This study introduces the Multi-Agent Framework for Multi-Modal Medical Diagnosis (MAM), addressing the limitations of unified multimodal medical LLMs. MAM employs a modular, collaborative approach, assigning specialized roles, i.e., General Practitioner, Specialist Team, Radiologist, Medical Assistant, and Director, to distinct LLM-based agents. This structure enhances knowledge updates, leverages specialized expertise, and adapts to diverse medical tasks and modalities. Extensive evaluations on multimodal medical datasets demonstrate MAM's superiority, outperforming modality-specific LLMs by $18\%$ to $365\%$ . Future work will integrate advanced knowledge retrieval and evaluate MAM in real-world clinical settings.
+
+# Limitations
+
+The performance of MAM is fundamentally constrained by the capabilities of the underlying LLMs utilized for each agent role. Inherent limitations such as model biases, knowledge gaps, or reasoning inaccuracies within these LLMs may propagate through the framework, potentially compromising diagnostic outcomes. MAM's architecture allows for flexible switching of base models, which could mitigate some limitations in future applications. The other limitation of the current study is the absence of real-world clinical validation, which presents substantial challenges in terms of resource allocation and human expertise required for comprehensive evaluation. We acknowledge this limitation and propose to address it through clinical validation studies in our future work.
+
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+Yangyang Yu, Zhiyuan Yao, Haohang Li, Zhiyang Deng, Yuechen Jiang, Yupeng Cao, Zhi Chen, Jordan W. Suchow, Zhenyu Cui, Rong Liu, Zhaozhuo Xu, Denghui Zhang, Koduvayur Subbalakshmi, Guojun Xiong, Yueru He, Jimin Huang, Dong Li, and Qianqian Xie. 2024. Fincon: A synthesized LLM multi-agent system with conceptual verbal reinforcement for enhanced financial decision making. In Advances in Neural Information Processing Systems 38: Annual Conference on Neural Information Processing Systems 2024, NeurIPS 2024, Vancouver, BC, Canada, December 10 - 15, 2024.   
+Shengbin Yue, Shujun Liu, Yuxuan Zhou, Chenchen Shen, Siyuan Wang, Yao Xiao, Bingxuan Li, Yun Song, Xiaoyu Shen, Wei Chen, Xuanjing Huang, and Zhongyu Wei. 2024. Lawllm: Intelligent legal system with legal reasoning and verifiable retrieval. In Database Systems for Advanced Applications - 29th International Conference, DASFAA 2024, Gifu, Japan, July 2-5, 2024, Proceedings, Part V, volume 14854 of Lecture Notes in Computer Science, pages 304-321. Springer.   
+Hang Zhang, Xin Li, and Lidong Bing. 2023a. Video-llama: An instruction-tuned audio-visual language model for video understanding. In Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing, EMNLP 2023 - System Demonstrations, Singapore, December 6-10, 2023, pages 543-553. Association for Computational Linguistics.   
+Hongbo Zhang, Junying Chen, Feng Jiang, Fei Yu, Zhihong Chen, Guiming Chen, Jianquan Li, Xiangbo Wu, Zhiyi Zhang, Qingying Xiao, Xiang Wan, Benyou Wang, and Haizhou Li. 2023b. Huatuogpt, towards taming language model to be a doctor. In Findings of the Association for Computational Linguistics: EMNLP 2023, Singapore, December 6-10, 2023, pages 10859-10885. Association for Computational Linguistics.   
+Xiaoman Zhang, Chaoyi Wu, Ziheng Zhao, Weixiong Lin, Ya Zhang, Yanfeng Wang, and Weidi Xie. 2023c. PMC-VQA: visual instruction tuning for medical visual question answering. CoRR, abs/2305.10415.
+
+Yuanhan Zhang, Bo Li, haotian Liu, Yong jae Lee, Liangke Gui, Di Fu, Jiashi Feng, Ziwei Liu, and Chunyuan Li. 2024. Llava-last: A strong zero-shot video understanding model.   
+Andrew Zhao, Daniel Huang, Quentin Xu, Matthieu Lin, Yong-Jin Liu, and Gao Huang. 2024. Expel: LLM agents are experiential learners. In Thirty-Eighth AAAI Conference on Artificial Intelligence, AAAI 2024, Thirty-Sixth Conference on Innovative Applications of Artificial Intelligence, IAAI 2024, Fourteenth Symposium on Educational Advances in Artificial Intelligence, EAAI 2014, February 20-27, 2024, Vancouver, Canada, pages 19632-19642. AAAI Press.   
+Yucheng Zhou, Xiang Li, Qianning Wang, and Jianbing Shen. 2024a. Visual in-context learning for large vision-language models. In *Findings of the Association for Computational Linguistics*, ACL 2024, Bangkok, Thailand and virtual meeting, August 11-16, 2024, pages 15890-15902. Association for Computational Linguistics.   
+Yucheng Zhou, Jianbing Shen, and Yu Cheng. 2025. Weak to strong generalization for large language models with multi-capabilities. In The Thirteenth International Conference on Learning Representations, ICLR 2025, Singapore, April 24-28, 2025. OpenReview.net.   
+Yucheng Zhou, Jihai Zhang, Guanjie Chen, Jianbing Shen, and Yu Cheng. 2024b. Less is more: Vision representation compression for efficient video generation with large language models.
+
+# A Case Study
+
+Figure 4 shows the comparison results between the baseline model and our framework under the same sample input from DeepLesion (Yan et al., 2017) dataset.
+
+# B Prompt
+
+# Image Type Classification Prompt
+
+1. Please answer with a single word: What kind of medical image is this? X-Ray, CT, MRI, Pathology, Biomedical.   
+2. Please answer with a single word: What part of the human body does this image show? Brain, bone, abdomen, mediastinum, liver, lung, kidney, soft tissue, pelvis.
+
+# Audio Type Classification Prompt
+
+Please answer with a single word: What kind of audio is this? Cardiovascular, Respiratory.
+
+# Video Type Classification Prompt
+
+Please answer with a single word: What kind of video is this? Sports, Rehabilitation, Emergency.
+
+# Text Type Classification Prompt
+
+System prompt: You are given a question, please select a question type according to the given question. Input: The question is {question_text}. Which kind of question is this? Anaesthesia, Anatomy, Biochemistry, Dental, ENT, FM, O&G, Medicine, Microbiology, Ophthalmology, Orthopaedics, Pathology, Pediatrics, Pharmacology, Physiology, Psychiatry, Radiology, Skin, PSM, Surgery, Unknown. Output example:
+
+The question type is \*\*Anaesthesia\*\*.
+
+# Role Generation Prompt
+
+Given a disease type, generate a system prompt that assigns tasks to relevant medical roles, including **Specialist Doctor**, **Radiologic Technologist**, etc, from the perspective of a General Practitioner.
+
+Input: The modality type is {modality_type}, the disease type is {disease_type}, and the patient question is {question}.
+
+Output:
+
+A system prompt that:
+
+Identifies the relevant Specialist Doctor(s), Radiologic Technologist(s), and other Specialist(s) for the given disease type.
+
+Assigns tasks to each identified role, specifying the necessary actions, tests, or examinations required for diagnosis and treatment.
+
+Output example:
+
+**Specialist Doctor** (Pulmonologist):
+
+- Assess Patient's Health: Evaluate patient's function and overall health.   
+- Use {modality_type} Studies: Utilize expertise in the {disease_type} domains to diagnose diseases.   
+- Analyze Patient History and Symptoms: Determine the cause and severity of diseases by analyzing patient's medical history and symptoms.
+
+# Get Discuss Prompt
+
+You are a $\{\text{role\_name}\}$ , responsible for the following tasks: $\{\text{role\_responsibilities}\}$ . Please thoughtfully express your views for the following question. Input:   
+**Question type**: {disease_type}.   
+**Question**: {question}.   
+Example output:   
+**Assessment Steps**:   
+- Initial Assessment: [Provide a detailed overview of the initial assessment process]   
+- Diagnostic Studies (e.g., imaging, lab tests): [Include relevant details about any studies conducted]   
+- Additional Considerations: [Mention any other pertinent factors or evaluations]   
+**Possible Answers**:   
+- Answer 1: [Briefly explain answer 1]   
+Reasoning: [Briefly describe the corresponding reason for answer 1]   
+- Answer 2: [Briefly explain answer 2]   
+Reasoning: [Briefly describe the corresponding reason for answer 2]   
+- Answer 3: [Briefly explain answer 3]   
+Reasoning: [Briefly describe the corresponding reason for answer 3]   
+**Conclusion**: [Summarize the findings and provide a final recommendation or insight]
+
+# Get Summarize Prompt
+
+You are a specialized doctor serving as the moderator of this meeting. Please provide a detailed summary of the discussions that have taken place.
+
+Example output:   
+**Possible Answers**:   
+- Answer 1: [Briefly explain answer 1]   
+- Answer 2: [Briefly explain answer 2]   
+- Answer 3: [Briefly explain answer 3]   
+**Agreements**:   
+- [Description of any agreements reached]   
+**Disagreements**:   
+- [Description of any disagreements that were noted]   
+**Conclusions**:   
+- [Final thoughts or conclusions drawn from the discussion]   
+Input: The question is {question}. The previous discussion of the meeting includes: {discussion}.
+
+# Get Vote Prompt
+
+You are a $\{\text{role\_name}\}$ , responsible for the following tasks: $\{\text{role\_responsibilities}\}$ .
+
+Please answer just using "yes" or "no" according to the following questions and the corresponding summary and the contents of the given file(if any).
+
+Input: The question is {question}, and the summary of the discussion is: {summary} Do you agree with the summary above? Please answer just using "yes" or "no".
+
+# Get Review Prompt
+
+Question: Is there any medical reasoning errors, redundant statements, or invalid outputs in the following paragraph? Please answer just using "yes" or "no". Please read the rollowing paragraph: {dis}
+
+# Get Multimodal Description Prompt
+
+Please describe this {modality_type} briefly in 100 words:
+
+# Get Search Summarize Prompt
+
+Please summarize the following search results briefly in 200 words: {search_result}
+
+# Get Diagnosis Prompt
+
+Input: Based on the provided image/video.audio (if applicable) and the meeting record, please provide answer to the following question.  
+Question: {ques}.  
+Meeting record: {record}.
+
+# Get Overall Review Prompt
+
+Input: You're a medical assistant. Please check whether the answer to this question is reasonable, if it is, please answer "yes", if not, please answer "no".  
+Question: {ques}.  
+Answer: {record}.
+
+![](images/48d6f65eefd055f15d867ab3105a23d437ac3208714fcc6bc00abad2a07c623b.jpg)  
+Example output of baseline model:   
+Multimodal Input
+
+Question: Please select one of the following labels that best describes the lesion: bone, abdomen, mediastinum, liver, lung, kidney, soft tissue, pelvis
+
+![](images/7e8fc5af99e115a6cad0139c6c32e016e82ea8afd9b8235a3177239158802a6f.jpg)  
+Diagnosis
+
+Answer: soft tissue
+
+![](images/e8e4e607839bdf4cc16db3d3384db2aecb4f3083347d762049e61670b8b1a8c3.jpg)  
+Example output of our framework:   
+Multimodal Medical Input
+
+![](images/961d26ae70d1a0babe2f5821520125e7b9fd75997098b7e5a4000dce957c0de4.jpg)
+
+Question: Please select one of the following labels that best describes the lesion: bone, abdomen, mediastinum, liver, lung, kidney, soft tissue, pelvis
+
+Modality: Image
+
+![](images/bd13f0a1f27e3e590ba4c3f79129c2cef14abe27e3f845cc0a632b981f87792c.jpg)
+
+![](images/9db197f07d3520e86e54fd9bd4c2fdc03b5fe38a338a0044dc672f4c295629f8.jpg)
+
+Referral to Specialist
+
+Type: CT
+
+![](images/9f5f54dd611e984107e5cf6ea7175c9d8b2f2ab5d10424ab4b57394edbdfeae3.jpg)
+
+Medical Assistant
+
+# Meeting/Debate
+
+![](images/80766377206a79aa6a378344a2091b2c7b0d580a5a984047592abf1005bf7581.jpg)  
+Diagnostic Opinion
+
+**Assessment Steps:**
+
+- Initial Assessment: The image provided is a cross-sectional view of the thoracic region, showing structures such as lungs and mediastinum.
+
+- Diagnostic Studies (e.g., imaging): This appears to be an axial CT scan slice through the chest at the level of the heart and great vessels.
+
+**Possible Answers:**
+
+# 1. Mediastinum:
+
+- Reasoning: The lesion in question seems located centrally within the thorax between the two lung fields, which corresponds with the anatomical location of the mediastinum on this type of imaging study.
+
+2. Lung:
+
+- Reasoning: ...
+
+![](images/55b9f655b56170948060cfec34495a70fbfc02d79d0da62597924b9676e399c2.jpg)  
+Diagnostic Opinion
+
+**Assessment Steps**:   
+- Initial Assessment: The image provided is a cross-sectional CT scan of the thorax, focusing on the lungs.   
+- Diagnostic Studies (e.g., imaging): This appears to be an axial slice from a chest computed tomography (CT) scan with contrast enhancement.   
+- Additional Considerations: No other specific information or clinical context has been given.   
+Director of Review   
+#
+
+**Possible Answers**:
+
+1. Lung   
+Reasoning: The lesion in question is located within one of the lung fields as seen in this transverse section of the thoracic cavity.   
+2. Mediastinum   
+Reasoning: ...
+
+![](images/7c42bf63c4f93e9ff33a3c67f785f95aa004809ab0ae92bf3d26eecb926870c8.jpg)
+
+![](images/ab267c4418cd8e1ef29e3c054a97234a0fac8eeb6feb5418d6ece1040dc45cc1.jpg)  
+Specialist Team
+
+![](images/c057095ef1a4f46820d4086ed22e38be28ff0d704d9417b9916eb92b18b24353.jpg)
+
+![](images/4e96ddae138e2810a52c65fccf56286c029f60d374bac0cd08c48c47aaed6785.jpg)
+
+![](images/b15d1f9cdffa0a875bdfdde02d40fcd3c6cbae1e9da9fc3f1f40b996f6a5c14d.jpg)  
+Summary of Search Results
+
+1. Pulmonary Embolism (PE): This article discusses PE, a condition where a blood clot (thrombus) blocks blood flow in the lung arteries. It highlights the complications arising from ...   
+2.Major Aortopulmonary Collateral Arteries (MAPCAs): This article focuses on MAPCAs, which are congenital blood vessels connecting the aorta to the pulmonary vascular system...   
+3.Lung Metastases Imaging: This overview highlights the frequency of pulmonary metastasis, which occurs in $20 - 54\%$ of extrathoracic malignancies...
+
+![](images/51d6ca788e9d72eda44960fdcfd024dc4e561b6c767a1f3915b6cbdca810eae6.jpg)  
+Summary Report
+
+**Possible Answers**:
+
+- Answer 1: The image provided is a cross-sectional CT scan of the chest, showing both lungs and part of the mediastinum. The...   
+- Answer 2: ...   
+- Answer 3: ...   
+- Answer 4: ...   
+**Agreements**:
+
+- The majority of the participants agreed that the lesion in question is located within the
+
+# mediastinum
+
+**Disagreements**:   
+- Some participants suggested that the lesion could be located within the lung tissue itself, while others thought it might be a soft tissue lesion.   
+**Conclusions**:
+
+- Based on the analysis, the most appropriate label describing the lesion present in the sample falls under 'mediastinum'. It suggests potential involvement of lymphatic or other mediastinal structures, warranting further investigation through clinical correlation and potentially additional imaging studies.
+
+![](images/de167178bb29171c8c06410671ad43bb228ef205f5003c3361a5ce0667524f7b.jpg)  
+Diagnostic Opinion
+
+**Assessment Steps**:   
+- Initial Assessment: The image provided is a cross-sectional CT scan of the chest, showing both lungs and part of the mediastinum.   
+- Diagnostic Studies (e.g., imaging): This appears to be an axial slice from a computed tomography (CT) scan focusing on the thoracic region.   
+Based on this analysis:   
+**Possible Answers**:   
+1. **Mediastinum**:   
+- Reasoning: The lesion in question seems located centrally within the chest cavity between the two lung fields, which corresponds with the anatomical location of the mediastinum where structures such as lymph nodes are commonly found.   
+2. **Lung**:   
+- Reasoning: ...
+
+![](images/c5152f1d72e239cfa8ee658bbb8ae0ec6fd2105966f4f98ce214ac36b3afbb25.jpg)  
+Diagnosis
+
+Final Answer:
+
+mediastinum
+
+![](images/659324c4f6989822c4d96556928a493227831183d442aae57c4061fae330c2c9.jpg)  
+Summary Report
+
+![](images/e07def203d0a571eb07e8b6f256d360fab424b19614b7affb54a24ca14582308.jpg)
+
+Summary Report
+
+![](images/ce41736d47d17a290a0810bbe36cdc24349298cc0e947f7223960e6d7c25d310.jpg)
+
+![](images/c11706b4bdc17fee79a465ae75f9eeb9a9313b44c1c87085ee94e4289d781f39.jpg)
+
+![](images/4c2dc5a9fbbb46284a0cbbd35bab9d7446d99f5da8da7d270c790b6eeb430211.jpg)
+
+![](images/f06f52ad5741e73579cb420486f932ae2b862f23c9b053693c2c6609ff2f798e.jpg)  
+Figure 4: Case Study.

paper_markdowns/bamboo-00566.md

@@ -0,0 +1,587 @@
+# Ranked Voting based Self-Consistency of Large Language Models
+
+Weiqin Wang, Yile Wang*, Hui Huang
+
+College of Computer Science and Software Engineering, Shenzhen University here1swqw@gmail.com, wangyile@szu.edu.cn, hhzhiyan@gmail.com
+
+# Abstract
+
+Majority voting is considered an effective method to enhance chain-of-thought reasoning, as it selects the answer with the highest "self-consistency" among different reasoning paths (Wang et al., 2023). However, previous chain-of-thought reasoning methods typically generate only a single answer in each trial, thereby ignoring the possibility of other potential answers. As a result, these alternative answers are often overlooked in subsequent voting processes. In this work, we propose to generate ranked answers in each reasoning process and conduct ranked voting among multiple ranked answers from different responses, thereby making the overall self-consistency more reliable. Specifically, we use three ranked voting methods: Instant-runoff voting, Borda count voting, and mean reciprocal rank voting. We validate our methods on six datasets, including three multiple-choice and three open-ended question-answering tasks, using both advanced open-source and closed-source large language models. Extensive experimental results indicate that our proposed method outperforms the baselines, showcasing the potential of leveraging the information of ranked answers and using ranked voting to improve reasoning performance. The code is available at https://github.com/szu-tera/RankedVotingSC.
+
+# 1 Introduction
+
+Large language models (LLMs) have shown strong performance in recent years (Ouyang et al., 2022; OpenAI, 2023; Dubey et al., 2024; Yang et al., 2024; DeepSeek-AI, 2024). Chain-of-thought prompting (Wei et al., 2022) further improves the performance of LLMs in commonsense (Talmor et al., 2019) and mathematical (Cobbe et al., 2021) reasoning tasks. Building on these advancements, Wang et al. (2023) propose a majority voting based
+
+Question: Which material is most suitable for making high-voltage power cables? (A) Iron; (B) Copper; (C) Rubber; (D) Glass.
+
+(a) Single Answers and Majority Voting
+
+![](images/96049a0aa13d08f6cdf786877d59303c190fc813fbb0f874d310b45d9cb438e7.jpg)
+
+(b) Ranked Answers by Likelihood
+
+![](images/d5752be712ef559a1822ca1dca1978acaa9108559c2e4da354578d4f508d7924.jpg)  
+Figure 1: Example of (a) majority voting based self-consistency among single answers (Wang et al., 2023) and (b) ranked answers in four responses by models.
+
+self-consistency approach, which leverages multiple reasoning paths through sampling to identify the most self-consistent answer, thereby improving the reasoning performance of LLMs.
+
+An example of majority voting based self-consistency is shown in Figure 1(a). In four responses by the model, option (A) was answered twice, (B) and (C) were each answered once, therefore (A) is considered the answer with the highest "self-consistency". In each response, the model replies with only one option, thereby omitting the possibility and priority of other options, which may introduce biases in the following majority voting process. In this work, we consider obtaining ranked answers instead of only a single answer in each response and employ ranked voting based self-consistency from multiple ranked answers, which we hope can lead to more reliable self-consistency and better reasoning performance.
+
+![](images/bb8e541c81d8b00741d3d5f212b0f5272a71c3e75852c3925fa5cf0d56105c1e.jpg)
+
+![](images/9ea457a923230a8388aece4a3b16a28d99d65784bc6bd18f15619e33581071c4.jpg)
+
+![](images/c776762866253df7a4d52495e0d64ed46ed8ff3c0aa1d8d3141c84650469782e.jpg)
+
+![](images/2e174179ec7948df48ce1597cc799cc6e4b802a7f834e52aac5b9bc13b6db626.jpg)  
+Figure 2: Examples of the procedures for three ranked voting methods. (a) The obtained ranked answers $(k = 8)$ . (b) Instant-runoff voting. (c) Borda count voting. (d) Mean reciprocal rank voting.
+
+We show the example of ranked answers in Figure 1(b). The model generates the possibility ranking of all options each time. In this case, we find that option (B) ranks in the top two positions in all four responses, while option (A) ranks last in two responses. Considering the overall results, option (A) may not be the best suitable final answer.
+
+To further decide the best answer according to the ranking information, we attempt to use ranked voting to determine the most appropriate answer based on the obtained ranked answers in responses. Ranked voting has been widely used in election systems. Specifically, we use three ranking voting methods to facilitate the final answer, including instant-runoff voting (Cary, 2011), Borda count voting (Emerson, 2013), and mean reciprocal rank voting. The first two methods are widely used in elections, while the latter one is related with the ranking-based MRR metric. We consider these ranked voting based approaches, compared with majority voting on single answers, can provide more reliable final answer by leveraging the ranking information of ordered answers.
+
+We validate our ranked voting based self-consistency by using advanced LLMs, including four open-source models LLaMa-3 (Dubey et al., 2024), Qwen-2.5 (Yang et al., 2024), Gemma2 (Team Gemma et al., 2024), Phi-3 (Abdin et al., 2024), and two closed-source models GPT
+
+3.5 (OpenAI, 2022) and GPT-4 (OpenAI, 2023). Empirical results show that our method consistently outperforms baselines on three multiple-choice and three open-ended question-answering datasets.
+
+# 2 Method
+
+We first introduce the majority voting based self-consistency baseline (§2.1) and propose obtaining the ranked answers in each LLMs' response (§2.2). Then we provide detailed descriptions to three ranked voting methods as shown in Figure 2, including instant-runoff voting (§2.3), Borda count voting (§2.4), and mean reciprocal rank voting (§2.5). In the final we briefly present overall comparison and how to handle tie votes (§2.7).
+
+# 2.1 Majority Voting based Self-Consistency
+
+Given a model $\mathcal{M}$ and question $\mathcal{Q}$ , following chain-of-thought reasoning (Wei et al., 2022), we have
+
+$$
+\mathcal {R}, \mathcal {A} = \mathcal {M} \left(\mathcal {Q} _ {1}, r _ {1}, a _ {1} \dots , \mathcal {Q} _ {n}, r _ {n}, a _ {n}, \mathcal {Q}\right), \tag {1}
+$$
+
+where $\{\mathcal{Q}_j, r_j, a_j\}_{j=1}^n$ are questions, reasoning paths, and answers in few-shot examples, respectively. $\mathcal{R}$ and $\mathcal{A}$ are generated reasoning path and answer of the question $\mathcal{Q}$ .
+
+Wang et al. (2023) further propose finding the most "consistent" answer among multiple responses. In particular, by setting a high decoding temperature (e.g., $\tau = 0.7$ ), the final answer is the
+
+# Multiple-Choice Question-Answering
+
+/* Few-Shot Examples */
+
+Question: [...] $(\mathcal{Q}_j)$
+
+Answer: [...] $(a_{j}^{r_{1}}\succ a_{j}^{r_{2}}\succ a_{j}^{r_{3}}\succ a_{j}^{r_{4}})$
+
+/* Test Question */
+
+Question: George wants to warm his hands quickly by rubbing them. Which skin surface will produce the most heat? (A) dry palms. (B) wet palms. (C) palms covered with oil. (D) palms covered with lotion. (Q)
+
+Answer: Heat is generated by friction when two surfaces rub together. The amount of friction depends on the dryness and texture of the surfaces. Dry palms have [...] . Wet palms reduce [...] . Palms covered with oil lower [...] , and palms covered with lotion reduce [...] . The ranking of options by likelihood is: $\mathrm{A} > \mathrm{B}$ $> \mathrm{D} > \mathrm{C}$ $\left( {\mathcal{A}}^{r1} \succ  {\mathcal{A}}^{r2} \succ  {\mathcal{A}}^{r3} \succ  {\mathcal{A}}^{r4}\right)$
+
+# Open-Ended Question-Answering
+
+/* Few-Shot Examples */
+
+Question: [...] $(\mathcal{Q}_j)$
+
+Answer: [...] $(a_j^{r_1} \succ a_j^{r_2} \succ a_j^{r_3} \succ a_j^{r_4} \succ a_j^{r_5})$
+
+/* Test Question */
+
+Question: The language used in Cameroon is $(\mathcal{Q})$
+
+Answer: Cameroon is a multilingual country located in Central Africa. However, the official languages of the country are French and English. While many indigenous languages are also spoken, they do not have the same status as the official languages. The ranking of answers by likelihood is: French
+
+> English > Pidgin English > Fulfulde > Hausa.
+
+$(\mathcal{A}^{r_1}\succ \mathcal{A}^{r_2}\succ \mathcal{A}^{r_3}\succ \mathcal{A}^{r_4}\succ \mathcal{A}^{r_5})$
+
+Table 1: The examples to obtain ranked answers $\mathcal{A}^r$ (colored in blue) on multiple-choice and open-ended question-answering tasks in few-shot settings.
+
+majority voting results across $k$ possible solutions $\{\mathcal{R}_i,\mathcal{A}_i\}_{i = 1}^k$ in totally $k$ responses:
+
+$$
+\mathcal {A} _ {\text {f i n a l}} ^ {\text {m a j o r i t y}} = \operatorname {a r g m a x} _ {\mathcal {A}} \sum_ {i = 1} ^ {k} \mathbb {1} \left(\mathcal {A} _ {i} = \mathcal {A}\right). \tag {2}
+$$
+
+# 2.2 From Single Answer to Ranked Answers
+
+In Eq. 1, $\mathcal{A}$ usually indicates a single answer such as a specific option in multiple-choice question-answering. However, it is difficult to reflect the possibility of other options from the single answer $\mathcal{A}$ . Thus, we consider obtaining the ranked answers $\mathcal{A}^r$ , which contains multiple ranked candidates according to the preference of LLMs:
+
+$$
+\mathcal {R}, \mathcal {A} ^ {r} = \mathcal {M} \left(\mathcal {Q} _ {1}, r _ {1}, a _ {1} ^ {r} \dots , \mathcal {Q} _ {n}, r _ {n}, a _ {n} ^ {r}, \mathcal {Q}\right), \tag {3}
+$$
+
+# Algorithm 1 Instant-Runoff Voting
+
+Input: Ranked answers $\mathrm{ANS} = \{\mathcal{A}_1^r,\dots,\mathcal{A}_k^r\}$
+
+Output: Final answer WINNER
+
+while True do
+
+CURRWINNER = MostFirstChoice(ANS)
+
+if Count(CURRWINNER) > k/2 then
+
+return CURRWINNER
+
+end if
+
+for $j$ in $1,\ldots ,k$ do
+
+$\mathcal{A}_j^r = \text{EliminateTheLastOne}(\mathcal{A}_j^r)$
+
+end for
+
+$\mathsf{ANS} = \{\mathcal{A}_1^r,\dots,\mathcal{A}_k^r\}$
+
+end while
+
+where $\{\mathcal{Q}_j, r_j, a_j^r\}_{j=1}^n$ are questions, reasoning paths, and ranked answers in few-shot examples, respectively. $\mathcal{R}$ and $\mathcal{A}^r$ are generated reasoning path and ranked answers of the question $\mathcal{Q}$ . The ranked answers $\{a_j^r\}_{j=1}^n$ and $\mathcal{A}^r$ includes $m$ ranked candidate answers:
+
+$$
+\begin{array}{l} a _ {j} ^ {r} = a _ {j} ^ {r _ {1}}, a _ {j} ^ {r _ {2}}, \dots , a _ {j} ^ {r _ {m}}, \\ \mathcal {A} ^ {r} = \mathcal {A} ^ {r _ {1}}, \mathcal {A} ^ {r _ {2}}, \dots , \mathcal {A} ^ {r _ {m}}, \\ \end{array}
+$$
+
+where $a_{j}^{r_{1}}\succ a_{j}^{r_{2}}\succ \dots \succ a_{j}^{r_{m}}$ and $\mathcal{A}^{r_1}\succ \mathcal{A}^{r_2}\succ \dots \succ \mathcal{A}^{r_m}$ indicate that $a_{j}^{r_{1}}$ or $\mathcal{A}^{r_1}$ is the most possible answer, $a_{j}^{r_{m}}$ or $\mathcal{A}^{r_m}$ is the least possible answer in corresponding responses, respectively.
+
+Examples of Ranked Answers. For obtaining the ranked answers $\mathcal{A}^r$ , we design the demonstrations in few-shot settings and show two examples in Table 1 on both multiple-choice and open-ended question-answering scenarios.
+
+Ranked Voting. Instead of majority voting, we leverage the information of ranked answers and get the final answer according to $k$ possible ranked solutions $\{\mathcal{A}_i^r\}_{i=1}^k = \{\mathcal{A}_i^{r_1}, \mathcal{A}_i^{r_2}, \dots, \mathcal{A}_i^{r_m}\}_{i=1}^k$ :
+
+$$
+\mathcal {A} _ {\text {f i n a l}} ^ {\text {r a n k e d}} = \text {R A N K V O T E} \left(\mathcal {A} _ {1} ^ {r}, \mathcal {A} _ {2} ^ {r}, \dots , \mathcal {A} _ {k} ^ {r}\right), \tag {5}
+$$
+
+where RANKVOTE indicates three ranked voting methods we used, as shown in Figure 2. We describe them in detail in the following subsections.
+
+# 2.3 Instant-Runoff Voting
+
+Instant-runoff voting (IRV) is a voting system that allows voters to rank candidates in order of preference (Cary, 2011). The main idea of IRV is to eliminate the candidate with the fewest votes in each round until a candidate receives a majority (more than $50\%$ ) of the votes. In a situation where the number of votes is relatively balanced, this voting
+
+method can determine the most suitable candidate through multiple rounds of selection. We provide the IRV procedure in Algorithm 1 and a specific example below.
+
+For example, consider the following ranked answers: “ $a > b > c$ ” appearing on 3 responses, “ $b > c > a$ ” appearing on 2 responses, and “ $c > a > b$ ” appearing on 3 responses, respectively. In the initial round, candidate “ $a$ ” and “ $c$ ” each secure 3 first-choice votes (37.5%), while “ $b$ ” garners only 2 first-choice votes (25%). Since no candidate achieves a majority of votes, the candidate “ $b$ ” is eliminated due to the fewest first-choice votes. The second-choice votes from the responses that originally ranked “ $b$ ” first are redistributed to “ $c$ ”, resulting in “ $c$ ” accumulating a total of 5 first-choice votes (62.5%). Meanwhile, “ $a$ ” retains its 3 first-choice votes (37.5%). Consequently, “ $c$ ” emerges as the winner with a clear majority.
+
+# 2.4 Borda Count Voting
+
+Borda count voting (BCV) is a positional voting rule that gives each candidate a number of points (i.e., Borda count) based on their ranking (Emerson, 2013). Suppose we have $m$ ranked answers $\mathcal{A}^{r_1}, \mathcal{A}^{r_2}, \dots, \mathcal{A}^{r_m}$ , the Borda count for candidate $\mathcal{A}$ is calculated as follows:
+
+$$
+\operatorname {B o r d a C o u n t} (\mathcal {A}) = \sum_ {i = 1} ^ {k} \left(m - \operatorname {r a n k} _ {\mathcal {A}} \left(\mathcal {A} _ {i} ^ {r}\right) + 1\right), \tag {6}
+$$
+
+where $\mathrm{rank}_{\mathcal{A}}(\mathcal{A}_i^r)$ is the rank of candidate $\mathcal{A}$ in the ranked answers $\mathcal{A}_i^r = \mathcal{A}_i^{r_1},\mathcal{A}_i^{r_2},\dots,\mathcal{A}_i^{r_m}$ from the $i$ -th response. For example, for ranked answers " $a\succ b\succ c$ " and " $b\succ c\succ a$ ", the Borda count for candidates " $a$ ", " $b$ ", and " $c$ " are $3 + 1 = 4$ , $2 + 3 = 5$ , and $1 + 2 = 3$ , respectively. The final answer $\mathcal{A}_{\mathrm{final}}^{\mathrm{BCV}}$ is the select candidate with the largest Borda count:
+
+$$
+\mathcal {A} _ {\text {f i n a l}} ^ {\mathrm {B C V}} = \operatorname {a r g m a x} _ {\mathcal {A}} \operatorname {B o r d a C o u n t} (\mathcal {A}). \tag {7}
+$$
+
+# 2.5 Mean Reciprocal Rank Voting
+
+The mean reciprocal rank (MRR) is a metric used in information retrieval to evaluate the effectiveness of search algorithms. For a sample of queries, it is calculated as the average of the multiplicative inverse of the rank of the first correct candidate: 1 for the first place, $1/2$ for the second place, etc. Inspired by such rank-aware metrics, we consider evaluating the answer according to its place in multiple ranked answers, and obtain the final answer according to the MRR scores in $k$ responses, which
+
+we called mean reciprocal rank voting (MRRV). In particular, for a candidate answer $a$ , we calculate the corresponding MRR score as follows:
+
+$$
+\operatorname {M R R} (\mathcal {A}) = \frac {1}{k} \sum_ {i = 1} ^ {k} \frac {1}{\operatorname {r a n k} _ {\mathcal {A}} \left(\mathcal {A} _ {i} ^ {r}\right)}, \tag {8}
+$$
+
+where $\mathrm{rank}_{\mathcal{A}}(\mathcal{A}_i^r)$ is the rank of candidate $\mathcal{A}$ in the ranked answers $\mathcal{A}_i^r = \mathcal{A}_i^{r_1},\mathcal{A}_i^{r_2},\dots,\mathcal{A}_i^{r_m}$ from the $i$ -th response. For example, for ranked answers " $a\succ c\succ b$ " and " $b\succ a\succ c$ " in two responses, the MRR scores for candidates " $a$ ", " $b$ ", and " $c$ " are $\frac{1}{2}(\frac{1}{1}+\frac{1}{2})=0.75$ , $\frac{1}{2}(\frac{1}{3}+\frac{1}{1})=0.66$ , $\frac{1}{2}(\frac{1}{2}+\frac{1}{3})=0.42$ , respectively. MRR score of 1.00 indicates that the corresponding candidate is always ranked first. The final answer $\mathcal{A}_{\mathrm{final}}^{\mathrm{MRRV}}$ is the selected candidate with the highest MRR score:
+
+$$
+\mathcal {A} _ {\text {f i n a l}} ^ {\text {M R R V}} = \operatorname {a r g m a x} _ {\mathcal {A}} \text {M R R} (\mathcal {A}). \tag {9}
+$$
+
+# 2.6 Construction of Few-Shot Examples
+
+Constructing few-shot examples for our method is straightforward. The primary criterion we follow is to ensure strong semantic relevance between the question and its relevant candidates. To demonstrate how to construction an examples, we show one example in Table 2. A high-quality example should not only justify the correct answer, but also assess the plausibility of the other candidates in addressing the question, as well as their semantic relevance to it. We refer to such an example as a template. Once created, the template can be reused to construct additional examples for other questions. To scale up the few-shot example set, we begin by using existing examples as few-shot, and
+
+# An Example Prompt for Constructing Few-Shot
+
+Question: What home entertainment equipment requires cable? (A) radio shack (B) substation (C) television (D) cabinet
+
+Answer: The most likely answer is a television, as it commonly requires cable for broadcasting or streaming services. A substation and radio shack are unrelated to home entertainment equipment, and a cabinet is purely for storage, not requiring a cable for its function. The most likely answer is (C). The ranking of options by likelihood is: $\mathrm{C} > \mathrm{B} > \mathrm{A} > \mathrm{D}$ .
+
+Table 2: A few-shot example for question answering, showing the rationale and a candidate ranking based on semantic relevance (explanation highlighted in blue).
+
+then leverage large language models to automatically generate additional demonstrations, requiring only minimal human verification.
+
+# 2.7 Overall Comparison and Tiebreaker Rule
+
+Comparison of Methods. The ranked voting methods IRV, BCV, and MRRV are different from each other. Specifically, IRV can be regarded as an elimination-based ranked voting, while BCV and MRRV can be seen as ranked voting with different weighting schemes. In Figure 2, all three methods arrive at the same final answer (C). However, in practice, their results may vary due to the specific outcomes of ranked answers.
+
+Tiebreaker Rules. Although ties are rare in voting outcomes, they may occur particularly for complex questions. Compared with self-consistency baseline, our ranking-based approach mitigates this issue by incorporating preference ranking information (see details in §4). To ensure rigor, we handle tie scenarios through confidence scoring for all methods, including the baseline: when multiple candidates receive equal votes, we compute each answer's confidence score $S_{i} = \sum_{t=1}^{n} \log(p(\mathcal{C}_{i,t}))$ , where $\mathcal{C}_{i,t}$ denotes the $t$ -th token's predicted probability in the $i$ -th candidate. The final selection chooses the candidate with the highest sum of logarithmic probabilities. For closed-source models, we defer to the model itself to select the best answer from the candidates.
+
+# 3 Experiments
+
+# 3.1 Settings
+
+Datasets. We validate our method on six tasks across different domains. The three multiple-choice QA tasks include: CommonsenseQA (Talmor et al., 2019) is a multiple-choice question answering dataset that requires different types of commonsense knowledge. ARC-Challenge (Clark et al., 2018) includes genuine grade-school level, multiple-choice science questions. AQUARAT (Ling et al., 2017) is a multiple-choice QA dataset which involves five-options algebraic word problems with rationales. We also evaluate on three open-ended QA tasks form Big-bench (Srivastava et al., 2023): WikiData involves performing open-domain cloze-style question answering. Date Understanding aims to measure models' ability to understand date-related information. Word Unscrambling asks models to unscramble the given letters to form an English word. We list examples
+
+of each dataset in Appendix A.
+
+Models. We compare with widely-used LLMs, including open-source models LLaMA-3 (Dubey et al., 2024), Qwen-2.5 (Yang et al., 2024), Gemma2 (Team Gemma et al., 2024), and Phi-3 (Abdin et al., 2024), as well as closed-source GPT3.5-turbo (OpenAI, 2022) and GPT-4-turbo (OpenAI, 2023) models. For open-source models, we use both lightweight $(2\mathrm{B}\sim 4\mathrm{B})$ and medium-sized $(7\mathrm{B}\sim 9\mathrm{B})$ models for comprehensive evaluations, and the checkpoints are listed in Appendix B.
+
+Baseline Methods. We compare with the following baselines: Few-Shot-CoT (Wei et al., 2022) with chain-of-thought reasoning. Best-of-N (Stiennon et al., 2020) involves sampling multiple solutions and selecting the best one based on the scores of a fine-tuned Qwen2.5-7B (Yang et al., 2024) reward model. Few-Shot-CoT-SC (Wang et al., 2023) uses majority voting for aggregating multiple answers. Adaptive-SC (Aggarwal et al., 2023) uses dynamic number of responses instead of fixed ones.
+
+Implementation Details. For all tasks, we use LM-evaluation-harness (Gao et al., 2024) for fair comparison. Following Wei et al. (2022), we set the number of few-shot examples $n = 8$ and decoding temperature $\tau = 0.7$ for baselines and our methods. Considering the budget constraints, we set the number of responses $k = 8$ in main experiments.
+
+# 3.2 Main Results
+
+2B~4B Open-Source LLMs. The results are shown in Table 3. Overall, our method demonstrates improved average performance across various datasets and models, surpassing all baseline methods. Compared to the Few-Shot-CoT-SC, our three ranked voting methods achieve an average improvement of $3.32\%$ with LLaMA-3.2-3B and $4.95\%$ with Qwen-2.5-3B. Our method also outperforms Best-of-N, which relies on a reward model to enhance generation quality and incurs additional computational overhead.
+
+Across different tasks, we achieve the largest improvement when performing data understanding tasks using Qwen-2.5-3B. Compared to Few-Shot-CoT-SC, the improvement can reach $10.84\%$ to $12.46\%$ . This suggests that, in contrast to providing a single answer for majority voting, offering multiple candidate answers along with their ranking and conducting ranked voting can offer more useful context.
+
+We also find that the majority voting based self
+
+Table 3: Comparison between baselines and our method (in gray) across open-source LLMs with 2B~4B parameters. In each column, the best results are in bold, and the second-best results are underlined. The subscript values represent the differences from Few-Shot-CoT-SC baseline.   
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">Multiple-Choice QA (Accuracy)</td><td colspan="3">Open-Ended QA (Exact Match)</td><td rowspan="2">Average</td></tr><tr><td>CommonsenseQA</td><td>ARC-Challenge</td><td>AQUA-RAT</td><td>WikiData</td><td>Date Understanding</td><td>Word Unscrambling</td></tr><tr><td colspan="8">(LLAMA-3.2-3B)</td></tr><tr><td>Few-Shot-CoT</td><td>71.99</td><td>78.67</td><td>58.27</td><td>66.67</td><td>57.72</td><td>25.33</td><td>59.78</td></tr><tr><td>Best-of- N</td><td>74.61</td><td>80.63</td><td>67.72</td><td>70.83</td><td>63.69</td><td>26.50</td><td>64.00</td></tr><tr><td>Few-Shot-CoT-SC</td><td>73.46</td><td>80.54</td><td>61.81</td><td>73.67</td><td>60.98</td><td>24.33</td><td>62.47</td></tr><tr><td>Adaptive-SC</td><td>74.20</td><td>80.89</td><td>64.17</td><td>73.33</td><td>61.25</td><td>26.33</td><td>63.36</td></tr><tr><td>Instant-Runoff Voting</td><td>74.86+1.40</td><td>81.31+0.77</td><td>69.29+7.48</td><td>74.00+0.33</td><td>64.23+3.25</td><td>27.67+3.34</td><td>65.23+2.76</td></tr><tr><td>Borda Count Voting</td><td>74.69+1.23</td><td>80.55+0.01</td><td>67.32+5.51</td><td>77.00+3.33</td><td>60.16-0.82</td><td>28.33+4.00</td><td>64.67+2.20</td></tr><tr><td>Mean Reciprocal Rank Voting</td><td>74.45+0.99</td><td>81.40+0.86</td><td>71.26+9.45</td><td>76.00+2.32</td><td>62.60+1.62</td><td>29.00+4.67</td><td>65.79+3.32</td></tr><tr><td colspan="8">(QWEN-2.5-3B)</td></tr><tr><td>Few-Shot-CoT</td><td>77.15</td><td>71.42</td><td>70.87</td><td>69.00</td><td>42.55</td><td>6.67</td><td>56.28</td></tr><tr><td>Best-of-N</td><td>77.97</td><td>75.90</td><td>75.39</td><td>70.67</td><td>50.14</td><td>8.00</td><td>59.68</td></tr><tr><td>Few-Shot-CoT-SC</td><td>77.89</td><td>76.96</td><td>77.95</td><td>72.67</td><td>47.97</td><td>7.33</td><td>60.13</td></tr><tr><td>Adaptive-SC</td><td>77.48</td><td>78.07</td><td>77.17</td><td>72.67</td><td>48.78</td><td>7.67</td><td>60.31</td></tr><tr><td>Instant-Runoff Voting</td><td>78.95+1.06</td><td>83.45+6.49</td><td>79.13+1.18</td><td>74.67+2.00</td><td>60.70+12.73</td><td>11.67+4.34</td><td>64.76+4.63</td></tr><tr><td>Borda Count Voting</td><td>78.38+0.49</td><td>83.19+6.23</td><td>80.31+2.36</td><td>76.33+3.66</td><td>58.81+10.84</td><td>11.33+4.00</td><td>64.72+4.59</td></tr><tr><td>Mean Reciprocal Rank Voting</td><td>78.79+0.90</td><td>83.70+6.74</td><td>79.92+1.97</td><td>75.33+2.66</td><td>60.43+12.46</td><td>12.33+5.00</td><td>65.08+4.95</td></tr><tr><td colspan="8">(GEMMA-2-2B)</td></tr><tr><td>Few-Shot-CoT</td><td>69.53</td><td>71.33</td><td>36.61</td><td>72.67</td><td>36.04</td><td>24.33</td><td>51.75</td></tr><tr><td>Best-of-N</td><td>70.76</td><td>73.59</td><td>42.32</td><td>72.17</td><td>37.40</td><td>20.83</td><td>52.84</td></tr><tr><td>Few-Shot-CoT-SC</td><td>69.29</td><td>71.42</td><td>36.22</td><td>73.67</td><td>37.67</td><td>21.67</td><td>51.66</td></tr><tr><td>Adaptive-SC</td><td>70.76</td><td>73.46</td><td>33.46</td><td>74.33</td><td>37.13</td><td>23.00</td><td>52.02</td></tr><tr><td>Instant-Runoff Voting</td><td>71.50+2.21</td><td>74.74+3.32</td><td>44.49+8.27</td><td>75.67+2.00</td><td>37.94+0.27</td><td>23.00+1.33</td><td>54.56+2.90</td></tr><tr><td>Borda Count Voting</td><td>70.93+1.67</td><td>73.12+1.70</td><td>42.52+6.30</td><td>77.67+4.00</td><td>37.40-0.27</td><td>22.00+0.33</td><td>53.94+2.28</td></tr><tr><td>Mean Reciprocal Rank Voting</td><td>71.42+2.13</td><td>72.18+0.76</td><td>42.91+6.69</td><td>77.33+3.66</td><td>39.02+1.35</td><td>22.67+1.00</td><td>54.26+2.60</td></tr><tr><td colspan="8">(PHI-3-4B)</td></tr><tr><td>Few-Shot-CoT</td><td>74.53</td><td>86.86</td><td>66.54</td><td>76.00</td><td>62.87</td><td>24.67</td><td>65.25</td></tr><tr><td>Best-of-N</td><td>76.29</td><td>86.35</td><td>74.41</td><td>71.50</td><td>60.70</td><td>22.33</td><td>65.26</td></tr><tr><td>Few-Shot-CoT-SC</td><td>75.84</td><td>90.13</td><td>73.62</td><td>77.33</td><td>66.12</td><td>23.33</td><td>67.73</td></tr><tr><td>Adaptive-SC</td><td>75.76</td><td>88.57</td><td>71.26</td><td>77.67</td><td>65.31</td><td>24.00</td><td>67.09</td></tr><tr><td>Instant-Runoff Voting</td><td>78.54+2.70</td><td>90.70+0.57</td><td>74.41+0.79</td><td>79.00+2.34</td><td>66.40+0.28</td><td>27.00+3.67</td><td>69.34+1.61</td></tr><tr><td>Borda Count Voting</td><td>78.71+2.87</td><td>88.23-1.90</td><td>75.20+1.58</td><td>78.67+1.34</td><td>63.96-2.16</td><td>27.00+3.67</td><td>68.63+0.90</td></tr><tr><td>Mean Reciprocal Rank Voting</td><td>78.95+3.11</td><td>90.44+0.31</td><td>75.20+1.58</td><td>80.00+2.67</td><td>65.58-0.54</td><td>27.00+3.67</td><td>69.53+1.80</td></tr></table>
+
+consistency does not always help. For example, the performance drops (25.33→24.33, 24.33→21.67, and 24.67→23.33) on word unscrambling task. This indicates that for some tasks, due to the difficulty of problems and the inherent limitations of LLMs, majority voting based self-consistency does not always lead to improvements. Overall, our ranked voting based self-consistency generally outperforms majority voting based methods such as Few-Shot-CoT-SC and Adaptive-SC.
+
+7B~9B Open-Source LLMs. The results are shown in Table 4. Similarly, our methods achieved the best and second-best results, indicating that they are still effective on the medium-size LLMs of ranked voting. Across different scenarios, compared to Few-Shot-CoT-SC, LLaMa-3-8B achieves an average performance improvement of $2.68\%$ to $3.51\%$ . Compared to the 2B~4B lightweight LLMs, the overall improvement has slightly decreased, possibly due to the increase in the LLMs' inherent capacity.
+
+Closed-Source LLMs. The results are shown in Table 5. Our method achieves an average accuracy of $76.69\%$ and $87.41\%$ on gpt-3.5-turbo-0125 and
+
+gpt-4-turbo-2024-04-09, respectively, outperforming the best baseline methods by $3.4\%$ and $0.48\%$ . These two results reflect the differences in GPT-3.5 and GPT-4. Similar to the open-source models, we see large improvements on GPT-3.5, while on the state-of-the-art GPT-4 model, the gains from voting across multiple responses decrease. Nevertheless, our ranking voting method still performs slightly better than the baselines.
+
+# 4 Analyses
+
+We further analyze our proposed method from different perspectives. Unless otherwise specified, we conduct experiments on CommonsenseQA and WikiData using LLaMa-3-8B.
+
+The Impact of $k$ . Figure 3 shows the performance of different number of samples $k$ . For CommonsenseQA, under different settings of $k$ , ranked voting methods consistently outperform majority voting based self-consistency. Moreover, compared with baseline with $k = 12$ or more, our method achieves better results when $k = 8$ , and its performance improves as $k$ increases. In contrast, the baseline shows limited improvement as $k$ increases.
+
+Table 4: Comparison between baselines and our method (in gray) across open-source LLMs with 7B~9B parameters.   
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">Multiple-Choice QA (Accuracy)</td><td colspan="3">Open-Ended QA (Exact Match)</td><td rowspan="2">Average</td></tr><tr><td>CommonsenseQA</td><td>ARC-Challenge</td><td>AQUA-RAT</td><td>WikiData</td><td>Date Understanding</td><td>Word Unscrambling</td></tr><tr><td colspan="8">(LLAMA-3-8B)</td></tr><tr><td>Few-Shot-CoT</td><td>78.13</td><td>84.13</td><td>62.99</td><td>78.33</td><td>70.19</td><td>25.67</td><td>66.67</td></tr><tr><td>Best-of-N</td><td>79.03</td><td>85.15</td><td>72.44</td><td>77.83</td><td>69.92</td><td>26.83</td><td>68.53</td></tr><tr><td>Few-Shot-CoT-SC</td><td>78.71</td><td>86.77</td><td>66.93</td><td>80.00</td><td>71.82</td><td>24.00</td><td>68.04</td></tr><tr><td>Adaptive-SC</td><td>78.95</td><td>86.95</td><td>68.50</td><td>79.67</td><td>71.00</td><td>25.33</td><td>68.40</td></tr><tr><td>Instant-Runoff Voting</td><td>79.12+0.41</td><td>87.29+0.52</td><td>74.02+7.09</td><td>80.00+0.00</td><td>72.09+0.27</td><td>35.00+11.00</td><td>71.25+3.21</td></tr><tr><td>Borda Count Voting</td><td>79.69+0.98</td><td>87.12+0.35</td><td>70.87+3.94</td><td>80.33+0.33</td><td>71.00-0.82</td><td>35.33+11.33</td><td>70.72+2.68</td></tr><tr><td>Mean Reciprocal Rank Voting</td><td>79.36+0.65</td><td>87.46+0.69</td><td>75.20+8.27</td><td>80.67+0.67</td><td>71.27-0.45</td><td>35.33+11.33</td><td>71.55+3.51</td></tr><tr><td colspan="8">(QWEN-2.5-7B)</td></tr><tr><td>Few-Shot-CoT</td><td>83.29</td><td>87.80</td><td>80.31</td><td>68.00</td><td>68.29</td><td>17.00</td><td>67.45</td></tr><tr><td>Best-of-N</td><td>84.32</td><td>89.04</td><td>82.87</td><td>69.00</td><td>70.05</td><td>23.17</td><td>69.74</td></tr><tr><td>Few-Shot-CoT-SC</td><td>84.28</td><td>89.16</td><td>84.65</td><td>70.33</td><td>70.73</td><td>21.00</td><td>70.03</td></tr><tr><td>Adaptive-SC</td><td>84.68</td><td>89.25</td><td>83.46</td><td>71.33</td><td>70.46</td><td>22.33</td><td>70.25</td></tr><tr><td>Instant-Runoff Voting</td><td>84.77+0.49</td><td>89.16+0.00</td><td>85.04+0.39</td><td>77.67+7.34</td><td>71.27+0.54</td><td>24.00+3.00</td><td>71.98+1.95</td></tr><tr><td>Borda Count Voting</td><td>84.52+0.24</td><td>89.25+0.09</td><td>84.25-0.40</td><td>79.33+9.00</td><td>70.73+0.00</td><td>23.33+2.33</td><td>71.90+1.87</td></tr><tr><td>Mean Reciprocal Rank Voting</td><td>84.93+0.65</td><td>87.80-1.36</td><td>85.83+1.18</td><td>78.67+8.34</td><td>71.27+0.54</td><td>24.00+3.00</td><td>72.08+2.05</td></tr><tr><td colspan="8">(GEMMA-2-9B)</td></tr><tr><td>Few-Shot-CoT</td><td>80.75</td><td>88.05</td><td>63.39</td><td>78.00</td><td>77.24</td><td>45.67</td><td>72.18</td></tr><tr><td>Best-of-N</td><td>80.22</td><td>88.52</td><td>71.46</td><td>77.50</td><td>76.29</td><td>43.17</td><td>72.86</td></tr><tr><td>Few-Shot-CoT-SC</td><td>80.10</td><td>89.59</td><td>67.32</td><td>81.33</td><td>78.05</td><td>44.33</td><td>73.45</td></tr><tr><td>Adaptive-SC</td><td>81.41</td><td>86.77</td><td>66.93</td><td>80.67</td><td>77.78</td><td>45.67</td><td>73.20</td></tr><tr><td>Instant-Runoff Voting</td><td>83.21+3.11</td><td>89.68+0.09</td><td>72.83+5.51</td><td>82.67+1.34</td><td>78.59+0.54</td><td>46.33+2.00</td><td>75.55+2.10</td></tr><tr><td>Borda Count Voting</td><td>82.96+1.86</td><td>89.33-0.26</td><td>70.87+3.55</td><td>83.33+2.00</td><td>79.40+1.35</td><td>46.00+1.67</td><td>75.31+1.86</td></tr><tr><td>Mean Reciprocal Rank Voting</td><td>83.05+2.95</td><td>89.25-0.34</td><td>72.44+5.12</td><td>83.00+1.67</td><td>78.32+0.27</td><td>46.33+2.00</td><td>75.40+1.95</td></tr><tr><td colspan="8">(PHI-3-7B)</td></tr><tr><td>Few-Shot-CoT</td><td>80.43</td><td>91.47</td><td>65.75</td><td>79.33</td><td>68.56</td><td>27.67</td><td>68.87</td></tr><tr><td>Best-of-N</td><td>80.79</td><td>91.30</td><td>77.17</td><td>77.17</td><td>73.04</td><td>29.67</td><td>71.52</td></tr><tr><td>Few-Shot-CoT-SC</td><td>81.24</td><td>91.89</td><td>73.62</td><td>79.33</td><td>73.71</td><td>28.33</td><td>71.35</td></tr><tr><td>Adaptive-SC</td><td>81.16</td><td>91.98</td><td>74.02</td><td>79.00</td><td>73.17</td><td>29.67</td><td>71.50</td></tr><tr><td>Instant-Runoff Voting</td><td>81.98+0.74</td><td>92.24+0.35</td><td>77.17+3.55</td><td>80.00+0.67</td><td>75.34+1.63</td><td>30.33+2.00</td><td>72.84+1.49</td></tr><tr><td>Borda Count Voting</td><td>82.31+1.07</td><td>91.81-0.08</td><td>75.20+1.58</td><td>80.00+0.67</td><td>75.61+1.90</td><td>28.33+0.00</td><td>72.21+0.86</td></tr><tr><td>Mean Reciprocal Rank Voting</td><td>82.15+0.91</td><td>91.98+0.09</td><td>77.17+3.55</td><td>81.00+1.67</td><td>75.34+1.63</td><td>28.67+0.34</td><td>72.72+1.37</td></tr></table>
+
+Table 5: Comparison between baselines and our method (in gray) across closed-source GPT-3.5 and GPT-4 models.   
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">Multiple-Choice QA (Accuracy)</td><td colspan="3">Open-Ended QA (Exact Match)</td><td rowspan="2">Average</td></tr><tr><td>CommonsenseQA</td><td>ARC-Challenge</td><td>AQUA-RAT</td><td>WikiData</td><td>Date Understanding</td><td>Word Unscrambling</td></tr><tr><td colspan="8">(GPT-3.5-TURBO-0125)</td></tr><tr><td>Few-Shot-CoT</td><td>79.85</td><td>86.65</td><td>58.27</td><td>78.00</td><td>58.27</td><td>49.50</td><td>68.42</td></tr><tr><td>Best-of-N</td><td>80.34</td><td>87.86</td><td>72.44</td><td>79.83</td><td>61.11</td><td>58.17</td><td>73.29</td></tr><tr><td>Few-Shot-CoT-SC</td><td>79.61</td><td>87.54</td><td>69.49</td><td>79.00</td><td>57.99</td><td>54.50</td><td>71.36</td></tr><tr><td>Adaptive-SC</td><td>79.77</td><td>88.25</td><td>70.67</td><td>79.33</td><td>58.40</td><td>54.50</td><td>71.82</td></tr><tr><td>Instant-Runoff Voting</td><td>80.84+1.23</td><td>89.33+1.79</td><td>70.67+1.18</td><td>82.00+3.00</td><td>68.97+10.98</td><td>66.50+12.00</td><td>76.30+4.94</td></tr><tr><td>Borda Count Voting</td><td>80.92+1.31</td><td>89.59+2.05</td><td>68.90-0.59</td><td>81.50+2.50</td><td>68.70+10.71</td><td>67.67+13.17</td><td>76.21+4.85</td></tr><tr><td>Mean Reciprocal Rank Voting</td><td>81.00+1.39</td><td>89.25+1.71</td><td>71.06+1.57</td><td>82.33+3.33</td><td>68.83+10.84</td><td>67.67+13.17</td><td>76.69+5.33</td></tr><tr><td colspan="8">(GPT-4-TURBO-2024-04-09)</td></tr><tr><td>Few-Shot-CoT</td><td>86.32</td><td>93.69</td><td>80.31</td><td>82.00</td><td>88.08</td><td>78.67</td><td>84.84</td></tr><tr><td>Best-of-N</td><td>87.39</td><td>94.70</td><td>85.43</td><td>82.33</td><td>86.99</td><td>81.67</td><td>86.42</td></tr><tr><td>Few-Shot-CoT-SC</td><td>87.39</td><td>95.30</td><td>86.22</td><td>83.00</td><td>88.35</td><td>81.33</td><td>86.93</td></tr><tr><td>Adaptive-SC</td><td>87.22</td><td>95.21</td><td>86.22</td><td>82.67</td><td>88.62</td><td>81.00</td><td>86.82</td></tr><tr><td>Instant-Runoff Voting</td><td>87.47+0.08</td><td>97.01+1.71</td><td>86.61+0.39</td><td>83.00+0.00</td><td>88.35+0.00</td><td>82.00+0.67</td><td>87.41+0.48</td></tr><tr><td>Borda Count Voting</td><td>87.31-0.08</td><td>96.84+1.54</td><td>85.04-1.18</td><td>83.33+0.33</td><td>88.35+0.00</td><td>81.67+0.34</td><td>87.09+0.16</td></tr><tr><td>Mean Reciprocal Rank Voting</td><td>87.31-0.08</td><td>97.01+1.71</td><td>86.22+0.00</td><td>83.00+0.00</td><td>88.62+0.27</td><td>81.67+0.34</td><td>87.30+0.37</td></tr></table>
+
+For WikiData, the results of instant-runoff voting and baseline are similar, while the other two methods consistently achieve an accuracy improvement of $0.5 \sim 1.0$ with different settings of $k$ .
+
+Robustness Analysis. The performance of LLMs is relatively sensitive to the order of examples in few-shot setting, such as exhibiting some recency bias (Zhao et al., 2021). We randomly shuffled the order of few-shot $(n = 8)$ examples and conducted four experiments, and the results are shown in Figure 4. For both CommonsenseQA and WikiData,
+
+the performance of our method surpasses that of the baseline consistently, and it exhibits relatively smaller variance, indicating that our approach leverages additional ranking information to yield more robust results.
+
+Compare the Impact of Ranked Answers and the Impact of Ranked Voting. To investigate whether the improvement stems from the ranking of answers or the ranked voting, we conducted experiments with the settings where only a single response with ranked answers is provided, taking
+
+![](images/9b7cb405737d2afb2d6f69784353eaf085958225636adca53c99a57b6abe3b9b.jpg)  
+Figure 3: Comparison of methods with different number of responses $k$ .
+
+![](images/085114fdc53ca63d9fd8812be83a15ad9b4df9eceb7366bd2cd876325dcd2bdc.jpg)  
+Figure 4: Comparison of methods with different shuffled examples for few-shot learning.
+
+![](images/f66ac416bfce9974458106f85798b851156d121f2dcadbcaa65765702f38b3b8.jpg)  
+Figure 5: The impact of ranked answers (in blue dashed box) and ranked voting (in red dashed box). Ranked voting is more effective and capable of delivering substantial and reliable improvements.
+
+the top-ranked answer as the final result. In this setting, the voting mechanisms are not employed. The results are shown in Figure 5. We find that the ranked answers along do not lead to consistent improvement, even making the results worse on WikiData. The gap between ranked voting and majority voting is much larger than that between Few-Shot-CoT (w/ ranked answers) and Few-Shot-CoT (w/ single answer), indicating that ranked voting can indeed enhance the model's performance.
+
+The Impact of the Number of Candidates. We observed that the number of candidates can significantly affect the performance of ranked voting methods. To systematically examine this effect, we select a set of values $\mathcal{C} = 1,2,3,4,5$ and conduct experiments using our approach under each candidate setting.
+
+As shown in Figure 6, we find that the performance of our methods is positively correlated with
+
+![](images/581251a47fb8c5635a3390fdefba763cfec6ab191be25d4481eaac66b0715c8d.jpg)  
+Figure 6: Performance comparison of SC and ranked voting methods (IRV, BCV, MRRV) under different candidate numbers $c$ (Since SC does not incorporate the concept of ranking candidates, its performance remains constant and thus appears as a flat line).
+
+Table 6: The tie rates for different voting methods.   
+
+<table><tr><td rowspan="2">Datasets</td><td rowspan="2">Majority Voting</td><td colspan="3">Ranked Voting</td></tr><tr><td>IRV</td><td>BCV</td><td>MRRV</td></tr><tr><td>CommonsenseQA</td><td>5.08%</td><td>3.77%</td><td>4.42%</td><td>2.29%</td></tr><tr><td>WikiData</td><td>4.33%</td><td>4.33%</td><td>4.00%</td><td>3.67%</td></tr></table>
+
+the number of candidates $c$ : as $c$ increases, the performance also improves. On CommonsenseQA, our methods surpass the baseline with only $c = 2$ candidates, and by $c = 4$ , all ranked voting strategies consistently outperform SC. On WikiData, even with $c = 1$ , ranked methods already achieve better performance than SC, and their accuracy continues to rise as more candidates are considered. These results demonstrate that incorporating a richer set of candidate responses allows our ranked approaches to extract stronger reasoning signals, leading to improved robustness and generalization across tasks. Moreover, increasing the number of candidates effectively encourages the model to explore a broader solution space, promoting deeper reasoning and more diverse perspectives during the generation process.
+
+The Impact of Ranking Information on Tie Situations. Both majority voting and ranked voting may result in ties among multiple candidates, which can lead to confusing and incorrect answers. The ranked voting methods leverage ranking information, which effectively reduces the occurrence of ties, as confirmed by our experiments.
+
+The results are shown in Table 6, we find that there are $4.33\% \sim 5.08\%$ ties in majority voting based self-consistency, while our methods reduce this to $2.29\% \sim 4.33\%$ . Among the three ranked voting methods, the weighting-based methods (BCV and MRRV) are less likely to result in ties compared to the elimination-based method (IRV). The difference arises from the vote aggregation mechanisms. Weighting-based methods assign varying
+
+confidence scores to candidate answers, reducing the likelihood of ties. In contrast, IRV iteratively eliminates lower-ranked options, which can lead to ties when multiple answers have similar rankings.
+
+# 5 Related Work
+
+Chain-of-Thought Reasoning. Chain-of-thought (CoT) have shown effectiveness for eliciting the reasoning ability of LLMs through generating rationales in contexts (Wei et al., 2022; Kojima et al., 2022; Chen et al., 2023; Zhang et al., 2023). Although the generated rationales improve the performance, previous studies focus on designing prompts for certain tasks. For example, Yao et al. (2023) and Besta et al. (2024) further propose tree-of-thought (ToT) and graph-of-thought (GoT) for solving search-style or elaborate problems, respectively. These works usually generate a single final answer in each trial and there is a lack of study on prompting the model to generate multiple possible answers and corresponding priority relationships.
+
+Self-Consistency of LLMs. Wang et al. (2023) propose self-consistency to improve chain-of-thought reasoning, a decoding method that improves the accuracy of LLMs by taking the majority vote among multiple answers generated through diverse reasoning paths. Aggarwal et al. (2023) further propose adaptive self-consistency to reduce the computational cost for obtain diverse reasoning paths, which dynamically adjusts the number of responses based on the model's confidence using a stopping criteria. Xiong et al. (2023) introduce inter-consistency among LLMs for multi agents collaboration. Wang et al. (2024) introduce soft self-consistency in long-duration interactive tasks for language model agents. Huang et al. (2024) enhance the coding ability of LLMs through multiple-perspective self-consistency. As a comparison, these methods rely on majority voting for specific tasks and ignore the possibility of multiple potential answers, which could offer useful information for obtaining the final correct answer in general reasoning and question-answering tasks.
+
+Ranked Voting. Ranked voting expresses the preferences of voters by ranking multiple candidates, organizing selections on an ordinal scale, which has been widely applied in elections, competitions, and recommendation systems (Myatt, 2007; Colomer, 2013). Similar ideas have also been applied to enhance the performance of neural models. Schwartz (2021) propose using an ensemble method to aggre
+
+gate predictions from multiple MRR and NDCG based models. Liu et al. (2024) proposes pairwise-preference search to address bias in text evaluation by constructing a global ranking. Zhao et al. (2024) introduces general electoral decision-making interface to enhance collaboration among multiple LLM agents through ordinal preferential voting. In recent years, ranking systems have also been valued and proposed to be introduced into more NLP benchmarks (Colombo et al., 2022; Rofin et al., 2023) and Chatbot arenas (Min et al., 2025). Tang et al. (2024) similarly leverage multiple generations via permutation self-consistency to enhance ranking robustness, though their focus is on mitigating positional bias rather than vote-based aggregation.
+
+# 6 Conclusion
+
+We introduce ranked voting based self-consistency to enhance the reasoning performance of large language models. Our method outperforms traditional majority voting techniques by generating and incorporating ranking information among multiple candidate answers during the reasoning process. The proposed method improves the reliability of self-consistency and boosts the performance. Extensive experiments demonstrate the effectiveness of our method, as it consistently outperforms baselines across a variety of multiple-choice and open-ended question-answering datasets, using both open-source and closed-source LLMs.
+
+# Limitations
+
+First, ranked voting has a rich history and comes in many forms. In our main experiments, we demonstrate three effective ranked voting strategies for large language models, however, there are some other ranked voting methods show limited improvement in datasets we used. For example, in the Appendix C, we introduce approval voting and find that this method performs similarly to majority voting when applied to ranked answers from models. Second, as shown in Figure 6, the number of candidates in the ranked answers may have an impact on the performance. Increasing the number of candidates allows a broader range of potential options to be considered, which could improve the accuracy of the final decision. In this work, we enable the model to autonomously rank a small set of options or open-ended generated candidates (usually $4\sim 5$ ), without imposing additional constraints by designing prompts to expand the candidate pool.
+
+# Acknowledgments
+
+This work was supported in parts by NSFC (62306161, U21B2023), Guangdong Basic and Applied Basic Research Foundation (2023B1515120026), DEGP Innovation Team (2022KCXTD025), and Scientific Development Funds from Shenzhen University.
+
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+Aarohi Srivastava, Abhinav Rastogi, Abhishek Rao, Abu Awal Md Shoeb, Abubakar Abid, Adam Fisch, Adam R Brown, Adam Santoro, Aditya Gupta, Adrià Garriga-Alonso, et al. 2023. Beyond the imitation game: Quantifying and extrapolating the capabilities of language models. Transactions on Machine Learning Research. Featured Certification.   
+Nisan Stiennon, Long Ouyang, Jeffrey Wu, Daniel Ziegler, Ryan Lowe, Chelsea Voss, Alec Radford, Dario Amodei, and Paul F Christiano. 2020. Learning to summarize with human feedback. In Advances in Neural Information Processing Systems, volume 33, pages 3008-3021. Curran Associates, Inc.   
+Alon Talmor, Jonathan Herzig, Nicholas Lourie, and Jonathan Berant. 2019. CommonsenseQA: A question answering challenge targeting commonsense knowledge. In Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers), pages 4149-4158, Minneapolis, Minnesota. Association for Computational Linguistics.   
+Raphael Tang, Crystina Zhang, Xueguang Ma, Jimmy Lin, and Ferhan Ture. 2024. Found in the middle: Permutation self-consistency improves listwise ranking in large language models. In Proceedings of the 2024 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume 1: Long
+
+Papers), pages 2327-2340, Mexico City, Mexico. Association for Computational Linguistics.   
+Team Gemma, Morgane Riviere, Shreya Pathak, Pier Giuseppe Sessa, Cassidy Hardin, Surya Bhupatiraju, Léonard Hussenot, Thomas Mesnard, Bobak Shahriari, Alexandre Ramé, et al. 2024. Gemma 2: Improving open language models at a practical size. arXiv preprint arXiv:2408.00118.   
+Han Wang, Archiki Prasad, Elias Stengel-Eskin, and Mohit Bansal. 2024. Soft self-consistency improves language models agents. In Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers), pages 287-301, Bangkok, Thailand. Association for Computational Linguistics.   
+Xuezhi Wang, Jason Wei, Dale Schuurmans, Quoc V Le, Ed H. Chi, Sharan Narang, Aakanksha Chowdhery, and Denny Zhou. 2023. Self-consistency improves chain of thought reasoning in language models. In The Eleventh International Conference on Learning Representations.   
+Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, brian richter, Fei Xia, Ed Chi, Quoc V Le, and Denny Zhou. 2022. Chain-of-thought prompting elicits reasoning in large language models. In Advances in Neural Information Processing Systems, volume 35, pages 24824-24837. Curran Associates, Inc.   
+Kai Xiong, Xiao Ding, Yixin Cao, Ting Liu, and Bing Qin. 2023. Examining inter-consistency of large language models collaboration: An in-depth analysis via debate. In Findings of the Association for Computational Linguistics: EMNLP 2023, pages 7572-7590, Singapore. Association for Computational Linguistics.   
+An Yang, Baosong Yang, Beichen Zhang, Binyuan Hui, Bo Zheng, Bowen Yu, Chengyuan Li, Dayiheng Liu, Fei Huang, Haoran Wei, et al. 2024. Qwen2.5 technical report. arXiv preprint arXiv:2412.15115.   
+Shunyu Yao, Dian Yu, Jeffrey Zhao, Izhak Shafran, Thomas L. Griffiths, Yuan Cao, and Karthik R Narasimhan. 2023. Tree of thoughts: Deliberate problem solving with large language models. In Thirty-seventh Conference on Neural Information Processing Systems.   
+Yifan Zhang, Jingqin Yang, Yang Yuan, and Andrew Chi-Chih Yao. 2023. Cumulative reasoning with large language models. arXiv preprint arXiv:2308.04371.   
+Xiutian Zhao, Ke Wang, and Wei Peng. 2024. An electoral approach to diversify LLM-based multiagent collective decision-making. In Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing, pages 2712-2727, Miami, Florida, USA. Association for Computational Linguistics.
+
+# CommonsenseQA (1221)
+
+Question: What must someone do before they shop?
+
+Options: (A) get money (B) have money (C) bring cash
+
+(D) go to market (E) bring cash
+
+Answer: (A).
+
+# ARC-Challenge (1172)
+
+Question: There is a very slight change in gravity at the top of a mountain. Which property would most likely be less at the top of a mountain?
+
+Options: (A) mass (B) weight (C) body density (D) body temperature
+
+Answer: (B).
+
+# AQUA-RAT (254)
+
+Question: I have a money pouch containing Rs. 700.
+
+There are equal number of 25 paise coins, 50 paise coins and one rupee coins. How many of each are there?
+
+Options: (A) 453 (B) 651 (C) 400 (D) 487 (E) 286
+
+Answer: (C).
+
+# WikiData (300)
+
+Question: The language of The Rise and Fall of Ziggy.  
+Stardust and the Spiders from Mars is
+
+Answer: English.
+
+# Date Understanding (369)
+
+Question: Jane got her job in 2016. Today is her 3-year work anniversary. She still remember that on Dec 2, her second day at work, she spilled coffee on her laptop. What is the date today in MM/DD/YYYY?
+
+Answer: 12/01/2019.
+
+# Word Unscrambling (300)
+
+Question: The word eptnerrreenu is a scrambled version of the English word
+
+Answer: entrepreneur.
+
+Table 7: Examples of each dataset, the numbers in brackets denote the number of evaluation questions.   
+
+<table><tr><td>Zihao Zhao, Eric Wallace, Shi Feng, Dan Klein, and Sameer Singh. 2021. Calibrate before use: Improving few-shot performance of language models. In Proceedings of the 38th International Conference on Machine Learning, volume 139 of Proceedings of Machine Learning Research, pages 12697–12706. PMLR.</td></tr></table>
+
+# A Examples of Datasets
+
+We list examples of different datasets in Table 7. For CommonsenseQA, we evaluated all instances from the validation set since the test set does not provide answers. For ARC-Challenge, AQUARAT, and Date Understanding, we tested on all instances from the test set. For WikiData and Word Unscrambling, we randomly sampled 300 instances from the test set for evaluation.
+
+# B Checkpoints of Models
+
+The checkpoints of open-source models in our experiments are shown in Table 8.
+
+# C More Results of Other Ranked Voting based Methods
+
+Approval Voting. In addition to the three voting methods discussed in the main pages, we introduce an additional approach called approval voting (Laslier and Vander Straeten, 2003). This voting system enables participants to express their stance on an issue—whether to approve or disapprove. To streamline this process, approval voting assumes that higher-ranked answers are more likely to be accepted as correct. Therefore, we establish a threshold $t$ : answers ranked before this threshold are considered approved, while those ranked after are deemed disapproved:
+
+$$
+\begin{array}{l} \begin{array}{c} \mathcal {A} _ {1: t} ^ {r} = \mathcal {A} ^ {r _ {1}}, \mathcal {A} ^ {r _ {2}}, \dots , \mathcal {A} ^ {r _ {t}}, \\ 4 x \end{array} \tag {10} \\ \mathcal {A} _ {\mathrm {a p p r o v e d}} ^ {r} = \mathcal {A} _ {1: t} ^ {r}. \\ \end{array}
+$$
+
+Next, we conduct majority voting to select the answer with the most supporters, where each approval vote carries equal weight in the majority voting process. In the experiments, we set the threshold $t = 2$ .
+
+Results. Table 9 shows the performance of approval voting. It is evident that in certain cases, approval voting outperforms self-consistency and can even achieve the best performance. For example, in the WikiData task, LLaMA-3-8B attains the highest performance using approval voting. However, this method has its limitations as well, since it is not particularly stable. Although it performs well in some situations, it may sometimes underperform compared to Few-Shot-CoT.
+
+# D Results of Multiple Experimental Runs
+
+The standard deviation results for multiple experimental runs are shown in Table 10. The comparable and relatively small standard deviations between baseline and ours indicate the stability of the implementation and our ranked voting methods.
+
+# E Case Study
+
+We show cases of the ranked voting on Common-senseQA in Table 11, Table 12, and Table 13.
+
+Table 8: Checkpoints of open-source models in our experiments. Note that LLaMA-3 series only include 8B and 70B models, while LLaMA-3.2 series include 1B, 3B, 11B, and 90B models. Therefore, in our experiments, we use LLaMA-3-8B and LLaMA-3.2-3B for validating on the LLaMA models.   
+
+<table><tr><td>Model</td><td>Checkpoints</td></tr><tr><td>LLaMA-3.2-3B</td><td>https://huggingface.co/meta-llama/Llama-3.2-3B-Instruct</td></tr><tr><td>LLaMA-3-8B</td><td>https://huggingface.co/meta-llama/Meta-Llama-3-8B-Instruct</td></tr><tr><td>Qwen-2.5-3B</td><td>https://huggingface.co/Qwen/Qwen2.5-3B-Instruct</td></tr><tr><td>Qwen-2.5-7B</td><td>https://huggingface.co/Qwen/Qwen2.5-7B-Instruct</td></tr><tr><td>Gemma-2-2B</td><td>https://huggingface.co/google/gemma-2-2b-it</td></tr><tr><td>Gemma-2-9B</td><td>https://huggingface.co/google/gemma-2-9b-it</td></tr><tr><td>Phi-3-4B</td><td>https://huggingface.co.microsoft/Phi-3-mini-4k-instruct</td></tr><tr><td>Phi-3-7B</td><td>https://huggingface.co.microsoft/Phi-3-small-8k-instruct</td></tr></table>
+
+Table 9: Results for approval voting using open-source LLMs, where the overall improvement is limited.   
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">Multiple-Choice QA (Accuracy)</td><td colspan="3">Open-Ended QA (Exact Match)</td><td rowspan="2">Average</td></tr><tr><td>CommonsenseQA</td><td>ARC-Challenge</td><td>AQUA-RAT</td><td>WikiData</td><td>Date Understanding</td><td>Word Unscrambling</td></tr><tr><td colspan="8">(LLAMA-3-8B)</td></tr><tr><td>Few-Shot-CoT</td><td>78.13</td><td>84.13</td><td>62.99</td><td>78.33</td><td>70.19</td><td>25.67</td><td>66.67</td></tr><tr><td>Few-Shot-CoT-SC</td><td>78.71</td><td>86.77</td><td>66.93</td><td>80.00</td><td>71.82</td><td>24.00</td><td>68.04</td></tr><tr><td>Approval Voting</td><td>77.48-1.23</td><td>83.96-2.81</td><td>65.35-1.58</td><td>80.67+0.67</td><td>69.38-2.44</td><td>34.67+10.67</td><td>68.58+0.54</td></tr><tr><td colspan="8">(QWEN-2.5-7B)</td></tr><tr><td>Few-Shot-CoT</td><td>83.29</td><td>87.80</td><td>80.31</td><td>68.00</td><td>68.29</td><td>17.00</td><td>67.45</td></tr><tr><td>Few-Shot-CoT-SC</td><td>84.28</td><td>89.16</td><td>84.65</td><td>70.33</td><td>70.73</td><td>21.00</td><td>70.03</td></tr><tr><td>Approval Voting</td><td>83.46-0.82</td><td>87.20-1.96</td><td>76.77-7.88</td><td>78.33+8.00</td><td>69.65-1.08</td><td>22.33+1.33</td><td>69.62-0.41</td></tr><tr><td colspan="8">(GEMMA-2-9B)</td></tr><tr><td>Few-Shot-CoT</td><td>80.75</td><td>88.05</td><td>63.39</td><td>78.00</td><td>77.24</td><td>45.67</td><td>72.18</td></tr><tr><td>Few-Shot-CoT-SC</td><td>80.10</td><td>89.59</td><td>67.32</td><td>81.33</td><td>78.05</td><td>44.33</td><td>73.45</td></tr><tr><td>Approval Voting</td><td>82.64+2.54</td><td>88.99-0.60</td><td>67.32+0.00</td><td>82.00+0.67</td><td>76.15-1.90</td><td>46.33+2.00</td><td>73.91+0.46</td></tr><tr><td colspan="8">(PHI-3-7B)</td></tr><tr><td>Few-Shot-CoT</td><td>80.43</td><td>91.47</td><td>65.75</td><td>79.33</td><td>68.56</td><td>27.67</td><td>68.87</td></tr><tr><td>Few-Shot-CoT-SC</td><td>81.24</td><td>91.89</td><td>73.62</td><td>79.33</td><td>73.71</td><td>28.33</td><td>71.35</td></tr><tr><td>Approval Voting</td><td>80.92-0.32</td><td>90.36-1.53</td><td>67.72-5.90</td><td>80.67+1.34</td><td>70.73-2.98</td><td>27.67-0.66</td><td>69.68-1.67</td></tr></table>
+
+Table 10: The standard deviation results in subscripts of multiple experimental runs.   
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">Multiple-Choice QA</td><td colspan="3">Open-Ended QA</td></tr><tr><td>CommonsenseQA</td><td>ARC-Challenge</td><td>AQUA-RAT</td><td>WikiData</td><td>Date Understanding</td><td>Word Unscrambling</td></tr><tr><td colspan="7">(LLAMA-3.2-3B)</td></tr><tr><td>Few-Shot-CoT-SC</td><td>73.46±0.3</td><td>80.54±0.4</td><td>61.81±0.3</td><td>73.67±0.2</td><td>60.98±0.5</td><td>24.33±0.6</td></tr><tr><td>Instant-Runoff Voting</td><td>74.86±0.2</td><td>81.31±0.2</td><td>69.29±0.3</td><td>74.00±0.4</td><td>64.23±0.4</td><td>27.67±0.7</td></tr><tr><td>Borda Count Voting</td><td>74.69±0.2</td><td>80.55±0.2</td><td>67.32±0.2</td><td>77.00±0.4</td><td>60.16±0.8</td><td>28.33±0.7</td></tr><tr><td>Mean Reciprocal Rank Voting</td><td>74.45±0.1</td><td>81.40±0.3</td><td>71.26±0.3</td><td>76.00±0.4</td><td>62.60±0.9</td><td>29.00±0.6</td></tr><tr><td colspan="7">(QWEN-2.5-3B)</td></tr><tr><td>Few-Shot-CoT-SC</td><td>77.89±0.2</td><td>76.96±0.18</td><td>77.95±0.2</td><td>72.67±0.2</td><td>47.97±0.4</td><td>7.33±0.02</td></tr><tr><td>Instant-Runoff Voting</td><td>78.95±0.2</td><td>83.45±0.3</td><td>79.13±0.1</td><td>74.67±0.1</td><td>60.70±0.5</td><td>11.67±0.5</td></tr><tr><td>Borda Count Voting</td><td>78.38±0.2</td><td>83.19±0.5</td><td>80.31±0.4</td><td>76.33±0.1</td><td>58.81±0.5</td><td>11.33±0.6</td></tr><tr><td>Mean Reciprocal Rank Voting</td><td>78.79±0.3</td><td>83.70±0.4</td><td>79.92±0.1</td><td>75.33±0.1</td><td>60.43±0.4</td><td>12.33±0.6</td></tr><tr><td colspan="7">(GEMMA-2-2B)</td></tr><tr><td>Few-Shot-CoT-SC</td><td>69.29±0.2</td><td>71.42±0.2</td><td>36.22±0.2</td><td>73.67±0.2</td><td>37.67±0.9</td><td>21.67±0.5</td></tr><tr><td>Instant-Runoff Voting</td><td>71.50±0.2</td><td>74.74±0.4</td><td>44.49±0.1</td><td>75.67±0.4</td><td>37.94±0.2</td><td>23.00±0.3</td></tr><tr><td>Borda Count Voting</td><td>70.93±0.2</td><td>73.12±0.3</td><td>42.52±0.2</td><td>77.67±0.5</td><td>37.40±0.4</td><td>22.00±0.5</td></tr><tr><td>Mean Reciprocal Rank Voting</td><td>71.42±0.2</td><td>72.18±0.3</td><td>42.91±0.1</td><td>77.33±0.5</td><td>39.02±0.4</td><td>22.67±0.4</td></tr><tr><td colspan="7">(PHY-3-4B)</td></tr><tr><td>Few-Shot-CoT-SC</td><td>75.84±0.3</td><td>90.13±0.2</td><td>73.62±0.5</td><td>77.33±0.2</td><td>66.12±0.5</td><td>23.33±0.5</td></tr><tr><td>Instant-Runoff Voting</td><td>78.54±0.3</td><td>90.70±0.3</td><td>74.41±0.1</td><td>79.00±0.4</td><td>66.40±0.4</td><td>27.00±1.1</td></tr><tr><td>Borda Count Voting</td><td>78.71±0.3</td><td>88.23±0.2</td><td>75.20±0.3</td><td>78.67±0.3</td><td>63.96±0.9</td><td>27.00±1.3</td></tr><tr><td>Mean Reciprocal Rank Voting</td><td>78.95±0.3</td><td>90.44±0.2</td><td>75.20±0.3</td><td>80.00±0.3</td><td>65.58±0.4</td><td>27.00±1.2</td></tr><tr><td colspan="7">(LLAMA-3-8B)</td></tr><tr><td>Few-Shot-CoT-SC</td><td>78.71±0.2</td><td>86.77±0.2</td><td>66.93±0.3</td><td>80.00±0.3</td><td>71.82±0.8</td><td>24.00±0.6</td></tr><tr><td>Instant-Runoff Voting</td><td>79.12±0.2</td><td>87.29±0.2</td><td>74.02±0.3</td><td>80.00±0.2</td><td>72.09±0.3</td><td>35.00±0.6</td></tr><tr><td>Borda Count Voting</td><td>79.69±0.2</td><td>87.12±0.2</td><td>70.87±0.3</td><td>80.33±0.4</td><td>71.00±0.4</td><td>35.33±1.0</td></tr><tr><td>Mean Reciprocal Rank Voting</td><td>79.36±0.2</td><td>87.46±0.2</td><td>75.20±0.3</td><td>80.67±0.4</td><td>71.27±0.6</td><td>35.33±1.1</td></tr><tr><td colspan="7">(QWEN-2.5-7B)</td></tr><tr><td>Few-Shot-CoT-SC</td><td>84.28±0.1</td><td>89.16±0.2</td><td>84.65±0.1</td><td>70.33±0.5</td><td>70.73±0.7</td><td>21.00±0.3</td></tr><tr><td>Instant-Runoff Voting</td><td>84.77±0.2</td><td>89.16±0.2</td><td>85.04±0.1</td><td>77.67±0.3</td><td>71.27±0.3</td><td>24.00±0.4</td></tr><tr><td>Borda Count Voting</td><td>84.52±0.3</td><td>89.25±0.2</td><td>84.25±0.3</td><td>79.33±0.3</td><td>70.73±0.4</td><td>23.33±0.3</td></tr><tr><td>Mean Reciprocal Rank Voting</td><td>84.93±0.2</td><td>87.80±0.2</td><td>85.83±0.2</td><td>78.67±0.3</td><td>71.27±0.4</td><td>24.00±0.3</td></tr><tr><td colspan="7">(GEMMA-2-9B)</td></tr><tr><td>Few-Shot-CoT-SC</td><td>80.10±0.1</td><td>89.59±0.2</td><td>67.32±0.2</td><td>81.33±0.3</td><td>78.05±0.2</td><td>44.33±0.4</td></tr><tr><td>Instant-Runoff Voting</td><td>83.21±0.1</td><td>89.68±0.2</td><td>72.83±0.2</td><td>82.67±0.4</td><td>78.59±0.2</td><td>46.33±0.4</td></tr><tr><td>Borda Count Voting</td><td>82.96±0.1</td><td>89.33±0.1</td><td>70.87±0.2</td><td>83.33±0.1</td><td>79.40±0.1</td><td>46.00±0.4</td></tr><tr><td>Mean Reciprocal Rank Voting</td><td>83.05±0.2</td><td>89.25±0.1</td><td>72.44±0.2</td><td>83.00±0.2</td><td>78.32±0.1</td><td>46.33±0.4</td></tr><tr><td colspan="7">(PHI-3-7B)</td></tr><tr><td>Few-Shot-CoT-SC</td><td>81.24±0.4</td><td>91.89±0.1</td><td>73.62±0.3</td><td>79.33±0.2</td><td>73.71±0.5</td><td>28.33±0.8</td></tr><tr><td>Instant-Runoff Voting</td><td>81.98±0.2</td><td>92.24±0.1</td><td>77.17±0.2</td><td>80.00±0.4</td><td>75.34±0.4</td><td>30.33±0.8</td></tr><tr><td>Borda Count Voting</td><td>82.31±0.2</td><td>91.81±0.2</td><td>75.20±0.3</td><td>80.00±0.5</td><td>75.61±0.5</td><td>28.33±0.7</td></tr><tr><td>Mean Reciprocal Rank Voting</td><td>82.15±0.2</td><td>91.98±0.1</td><td>77.17±0.2</td><td>81.00±0.4</td><td>75.34±0.3</td><td>28.67±0.7</td></tr><tr><td colspan="7">(GPT-3.5-TURBO-0125)</td></tr><tr><td>Few-Shot-CoT-SC</td><td>79.61±0.2</td><td>87.54±0.1</td><td>69.49±0.3</td><td>79.00±0.1</td><td>57.99±0.4</td><td>54.50±0.2</td></tr><tr><td>Instant-Runoff Voting</td><td>80.84±0.1</td><td>89.33±0.1</td><td>70.67±0.2</td><td>82.00±0.3</td><td>68.97±0.5</td><td>66.50±0.3</td></tr><tr><td>Borda Count Voting</td><td>80.92±0.1</td><td>89.59±0.1</td><td>68.90±0.2</td><td>81.50±0.2</td><td>68.70±0.5</td><td>67.67±0.4</td></tr><tr><td>Mean Reciprocal Rank Voting</td><td>81.00±0.1</td><td>89.25±0.1</td><td>71.06±0.2</td><td>82.33±0.3</td><td>68.83±0.5</td><td>67.67±0.3</td></tr><tr><td colspan="7">(GPT-4-TURBO-2024-04-09)</td></tr><tr><td>Few-Shot-CoT-SC</td><td>87.39±0.1</td><td>95.30±0.1</td><td>86.22±0.2</td><td>83.00±0.1</td><td>88.35±0.3</td><td>81.33±0.0</td></tr><tr><td>Instant-Runoff Voting</td><td>87.47±0.1</td><td>97.01±0.1</td><td>86.61±0.1</td><td>83.00±0.2</td><td>88.35±0.2</td><td>82.00±0.0</td></tr><tr><td>Borda Count Voting</td><td>87.31±0.1</td><td>96.84±0.1</td><td>85.04±0.2</td><td>83.33±0.2</td><td>88.35±0.2</td><td>81.67±0.1</td></tr><tr><td>Mean Reciprocal Rank Voting</td><td>87.31±0.1</td><td>97.01±0.1</td><td>86.22±0.1</td><td>83.00±0.2</td><td>88.62±0.2</td><td>81.67±0.1</td></tr></table>
+
+# CommonsenseQA
+
+Question: Dance can be elegant and specific, or you can just have fun and what?
+
+Options: (A) falling down (B) trip (C) fall down (D) move around (E) celebrate.
+
+Ground-Truth Label: D
+
+# Self-Consistency Answer through Majority Voting: A. X
+
+# Our Ranked Answers:
+
+Response 1: The answer should focus on an action that represents a casual, carefree approach, contrasting with the elegance and precision of dance. "Trip" fits well because it conveys a playful or carefree moment that can happen when you're not focusing on being precise. This aligns with the idea of just having fun. The ranking of options by likelihood is: $\mathrm{B} > \mathrm{D} > \mathrm{E} > \mathrm{C} > \mathrm{A}$ .
+
+Response 2: The answer should be the action that is the opposite of being elegant and specific, which implies a more casual or carefree approach. Of the above choices, the closest match is "just have fun and fall down", which implies a more playful and carefree attitude. The ranking of options by likelihood is: $\mathrm{A} > \mathrm{D} > \mathrm{E} > \mathrm{C} > \mathrm{B}$ .
+
+Response 3: The answer should be the phrase that describes the opposite of elegance, which is a more casual and carefree way of dancing. Of the above choices, "falling down" implies a loss of control and a more playful approach to dancing. The ranking of options by likelihood is: $\mathrm{A} > \mathrm{E} > \mathrm{D} > \mathrm{C} > \mathrm{B}$ .
+
+Response 4: The answer should be a phrase that describes an action that is carefree and fun, which is a common aspect of dancing. The ranking of options by likelihood is: $\mathrm{E} > \mathrm{D} > \mathrm{A} > \mathrm{C} > \mathrm{B}$ .
+
+Response 5: The answer should be the action that is often associated with having fun while dancing. Of the above choices, "move around" is a general action that is often done while having fun and dancing, without any specific technique or elegance. The ranking of options by likelihood is: $\mathrm{D} > \mathrm{E} > \mathrm{A} > \mathrm{C} > \mathrm{B}$ .
+
+Response 6: The answer should be the opposite of "elegant and specific", which implies a more carefree and casual attitude towards dancing. Of the above choices, "just have fun" is closely related to "move around" in a playful way. The ranking of options by likelihood is: $\mathrm{D} > \mathrm{E} > \mathrm{A} > \mathrm{C} > \mathrm{B}$ .
+
+Response 7: The answer should be the action that is often associated with having fun while dancing. Of the above choices, "have fun" is often associated with "celebrate". The ranking of options by likelihood is: $\mathrm{E} > \mathrm{D} > \mathrm{A} > \mathrm{C} > \mathrm{B}$ .
+
+Response 8: The answer should be the opposite of "elegant" and "specific", which implies a more casual or playful approach to dance. The ranking of options by likelihood is: $\mathrm{A} > \mathrm{E} > \mathrm{D} > \mathrm{C} > \mathrm{B}$ .
+
+# Instant-Runoff Voting: D.
+
+# Instant-Runoff Voting Procedure:
+
+Round 1:
+
+$\mathrm{B} > \mathrm{D} > \mathrm{E} > \mathrm{C} > \mathrm{A} \times 1$
+
+$\mathrm{A} > \mathrm{D} > \mathrm{E} > \mathrm{C} > \mathrm{B} \times 1$
+
+$\mathrm{A} > \mathrm{E} > \mathrm{D} > \mathrm{C} > \mathrm{B} \times 2$
+
+$\mathrm{E} > \mathrm{D} > \mathrm{A} > \mathrm{C} > \mathrm{B} \times 2$
+
+$\mathrm{D} > \mathrm{E} > \mathrm{A} > \mathrm{C} > \mathrm{B} \times 2$
+
+Count: A (3 times), B (1 times), C (0 times), D (2 times), E (2 times). No option gets more than half the votes, and C has the fewest, so C is eliminated.
+
+Round 2:
+
+$\mathrm{B} > \mathrm{D} > \mathrm{E} > \mathrm{A} \times 1$
+
+$\mathrm{A} > \mathrm{D} > \mathrm{E} > \mathrm{B} \times 1$
+
+$\mathrm{A} > \mathrm{E} > \mathrm{D} > \mathrm{B} \times 2$
+
+$\mathrm{E} > \mathrm{D} > \mathrm{A} > \mathrm{B} \times 2$
+
+$\mathrm{D} > \mathrm{E} > \mathrm{A} > \mathrm{B} \times 2$
+
+Count: A (3 times), B (1 times), D (2 times), E (2 times). No option gets more than half the votes, and B has the fewest, so B is eliminated.
+
+Round 3:
+
+$\mathrm{D} > \mathrm{E} > \mathrm{A} \times 1 \xrightarrow{\text{merge}} \mathrm{D} > \mathrm{E} > \mathrm{A} \times 3$
+
+$\mathrm{A} > \mathrm{D} > \mathrm{E} \times 1$ $\mathrm{A} > \mathrm{D} > \mathrm{E} \times 1$
+
+$\mathrm{A} > \mathrm{E} > \mathrm{D} \times 2 \quad \mathrm{A} > \mathrm{E} > \mathrm{D} \times 2$
+
+$\mathrm{E} > \mathrm{D} > \mathrm{A} \times 2$ $\mathrm{E} > \mathrm{D} > \mathrm{A} \times 2$
+
+$\mathrm{D} > \mathrm{E} > \mathrm{A} \times 2$
+
+Count: A (3 times), D (3 times), E (2 times). No option gets more than half the votes, and E has the fewest, so E is eliminated.
+
+Round 4:
+
+$\mathrm{D} > \mathrm{A} \times 1 \xrightarrow{\text{merge}} \mathrm{D} > \mathrm{A} \times 5$
+
+$\mathrm{A} > \mathrm{D} \times 3$
+
+A>D×2
+
+$\mathrm{D} > \mathrm{A}\times 2$
+
+$\mathrm{D} > \mathrm{A}\times 2$
+
+Count: A (3 times), D (5 times). D gets more than half the votes, so D is the winner.
+
+Table 11: Example of instant-runoff voting on CommonsenseQA.
+
+Table 12: Example of Borda count voting voting on CommonsenseQA.   
+
+<table><tr><td>CommonsenseQA</td></tr><tr><td>Question: Danny found an old film in a sealed what?</td></tr><tr><td>Options: (A) clingfilm (B) disneyland (C) cave (D) cabinet (E) movie.</td></tr><tr><td>Ground-Truth Label: D</td></tr><tr><td>Self-Consistency Answer through Majority Voting: A. X</td></tr><tr><td>Our Ranked Answers:</td></tr><tr><td>Response 1: The answer should be the container where the film was found. Of the above choices, clingfilm and cabinet are both plausible containers, but sealed clingfilm is more likely to preserve an old film. The ranking of options by likelihood is: A &gt; D &gt; C &gt; E &gt; B.</td></tr><tr><td>Response 2: The answer should be the place where an old film would likely be stored. Of the above choices, a sealed cabinet makes the most sense for storing old films. The ranking of options by likelihood is: D &gt; C &gt; A &gt; E &gt; B.</td></tr><tr><td>Response 3: The answer should be a place where an old film could be found, likely in a sealed container. Of the above choices, a cabinet is a common place to store things, and it could be sealed. The ranking of options by likelihood is: D &gt; C &gt; A &gt; E &gt; B.</td></tr><tr><td>Response 4: The answer should be the item that is used to seal something. Of the above choices, clingfilm is used to seal things. The ranking of options by likelihood is: A &gt; D &gt; C &gt; E &gt; B.</td></tr><tr><td>Response 5: The answer should be a container or packaging that can be sealed. Of the above choices, clingfilm is a type of plastic wrap that can be sealed. The ranking of options by likelihood is: A &gt; D &gt; C &gt; E &gt; B.</td></tr><tr><td>Response 6: The answer should be the container that is typically sealed to keep things inside. Of the above choices, clingfilm is a type of plastic wrap used to seal things. The ranking of options by likelihood is: A &gt; D &gt; C &gt; E &gt; B.</td></tr><tr><td>Response 7: The answer should be a container or object that can be sealed. Of the above choices, clingfilm (also known as plastic wrap) is commonly used to seal items. The ranking of options by likelihood is: A &gt; D &gt; C &gt; E &gt; B.</td></tr><tr><td>Response 8: The answer should be the container where an old film could be stored and sealed. Of the above choices, the most likely container is a cabinet. The ranking of options by likelihood is: D &gt; C &gt; A &gt; E &gt; B.</td></tr><tr><td>Borda Count Voting: D. ✓</td></tr><tr><td>Borda Count Voting Calculation:</td></tr><tr><td>A: 5 + 3 + 3 + 5 + 5 + 5 + 5 + 3 = 34</td></tr><tr><td>B: 1 + 1 + 1 + 1 + 1 + 1 + 1 = 8</td></tr><tr><td>C: 3 + 4 + 4 + 3 + 3 + 3 + 3 + 4 = 27</td></tr><tr><td>D: 4 + 5 + 5 + 4 + 4 + 4 + 4 + 5 = 35 ✓</td></tr><tr><td>E: 2 + 2 + 2 + 2 + 2 + 2 + 2 = 16</td></tr></table>
+
+# CommonsenseQA
+
+Question: The man acted ridiculous at the funeral, what attitude should he have taken?
+
+Options: (A) straightforward (B) serious (C) solemn (D) somber (E) funny.
+
+Ground-Truth Label: C
+
+# Self-Consistency Answer through Majority Voting: B. X
+
+# Our Ranked Answers:
+
+Response 1: The most likely attitude to take at a funeral is solemn. This word implies a sense of respect and seriousness that is appropriate for such a setting. The other options, such as straightforward, serious, and somber, are all related to seriousness and respect, but "funny" would be inappropriate and insensitive. The ranking of options by likelihood is: $\mathrm{C} > \mathrm{D} > \mathrm{A} > \mathrm{E} > \mathrm{B}$ .
+
+Response 2: The most appropriate attitude for the man to take at a funeral would be "serious" or "somber". Funeral are solemn occasions requiring a display of respect for the deceased and the grieving process. Funny or straight-forward would be inappropriate. The ranking of options by likelihood is: $\mathrm{B} > \mathrm{C} > \mathrm{D} > \mathrm{E} > \mathrm{A}$ .
+
+Response 3: The most appropriate demeanor at a funeral is one of solemnity, as it is a moment for grieving and honoring the departed. Words like straightforward, serious, and somber all reflect an attitude of respect and mourning, while funny would be seen as unsuitable and disrespectful. The ranking of options by likelihood is: $\mathrm{C} > \mathrm{D} > \mathrm{E} > \mathrm{A} > \mathrm{B}$ .
+
+Response 4: The most likely answer is (B) serious, as a funeral is a somber occasion and a serious attitude is appropriate and respectful. The other options, like straightforward, solemn, and somber, are less likely to be the correct response to a funeral. The ranking of options by likelihood is: $\mathrm{B} > \mathrm{C} > \mathrm{A} > \mathrm{D} > \mathrm{E}$ .
+
+Response 5: The most likely attitude to take at a funeral is (B) serious, as this is a time of mourning and respect, and a funeral is a solemn occasion. The other options, such as straightforward, somber, and funny, are less appropriate for such an event. The ranking of options by likelihood is: $\mathrm{B} > \mathrm{E} > \mathrm{A} > \mathrm{C} > \mathrm{D}$ .
+
+Response 6: The most appropriate attitude for the man to have taken at a funeral would be "somber", as it reflects a sense of respect and sadness appropriate for such a solemn occasion. The other options, while potentially applicable in other contexts, are not the best match for a funeral, which is generally a time for mourning and reflection. The ranking of options by likelihood is: $\mathrm{D} > \mathrm{C} > \mathrm{E} > \mathrm{A} > \mathrm{B}$ .
+
+Response 7: The most likely attitude to take at a funeral is solemn, as it is a time for mourning and respect for the deceased. Straightforward, serious, and somber are all synonyms for showing respect and mourning, while funny would be inappropriate and disrespectful. The ranking of options by likelihood is: $\mathrm{C} > \mathrm{B} > \mathrm{D} > \mathrm{A} > \mathrm{E}$ .
+
+Response 8: The most likely attitude the man should have taken is (B) serious, as funerals are somber occasions requiring respect and solemnity. The other options, such as straightforward, solemn, and somber, are less appropriate for such an event. The ranking of options by likelihood is: $\mathrm{B} > \mathrm{C} > \mathrm{D} > \mathrm{E} > \mathrm{A}$ .
+
+# Mean Reciprocal Rank Voting: C.
+
+Mean Reciprocal Rank Voting Calculation:
+
+$$
+\begin{array}{l} A: \frac {1}{8} \left(\frac {1}{3} + \frac {1}{5} + \frac {1}{4} + \frac {1}{3} + \frac {1}{3} + \frac {1}{4} + \frac {1}{4} + \frac {1}{5}\right) = 0. 2 6 8 7 5 \\ \mathrm {B}: \frac {1}{8} \left(\frac {1}{5} + 1 + \frac {1}{5} + 1 + 1 + \frac {1}{5} + \frac {1}{2} + 1\right) = 0. 6 3 7 5 \\ \mathrm {C}: \frac {1}{8} \left(1 + \frac {1}{2} + 1 + \frac {1}{2} + \frac {1}{4} + \frac {1}{2} + 1 + \frac {1}{2}\right) = 0. 6 5 6 2 5 \checkmark \\ \mathrm {D}: \frac {1}{8} \left(\frac {1}{2} + \frac {1}{3} + \frac {1}{2} + \frac {1}{4} + \frac {1}{5} + 1 + \frac {1}{3} + \frac {1}{3}\right) = 0. 4 3 1 2 5 \\ \mathrm {E}: \frac {1}{8} \left(\frac {1}{4} + \frac {1}{4} + \frac {1}{3} + \frac {1}{5} + \frac {1}{2} + \frac {1}{3} + \frac {1}{5} + \frac {1}{4}\right) \approx 0. 2 8 9 5 8 \\ \end{array}
+$$
+
+Table 13: Example of mean reciprocal rank voting on CommonsenseQA.

paper_markdowns/bamboo-01210.md

@@ -0,0 +1,477 @@
+# Detecting Knowledge Boundary of Vision Large Language Models by Sampling-Based Inference
+
+Zhuo Chen $^{1}$ , Xinyu Wang $^{2*}$ , Yong Jiang $^{2*}$ , Zhen Zhang $^{2}$ , Xinyu Geng $^{2}$ , Pengjun Xie $^{2}$ , Fei Huang $^{2}$ , Kewei Tu $^{1*}$
+
+$^{1}$ School of Information Science and Technology, ShanghaiTech University $^{1}$ Shanghai Engineering Research Center of Intelligent Vision and Imaging $^{2}$ Institute for Intelligent Computing, Alibaba Group chenzhuo@shanghaiitech.edu.cn
+
+# Abstract
+
+Despite the advancements made in Vision Large Language Models (VLLMs), like text Large Language Models (LLMs), they have limitations in addressing questions that require real-time information or are knowledge-intensive. Indiscriminately adopting Retrieval Augmented Generation (RAG) techniques is an effective yet expensive way to enable models to answer queries beyond their knowledge scopes. To mitigate the dependence on retrieval and simultaneously maintain, or even improve, the performance benefits provided by retrieval, we propose a method to detect the knowledge boundary of VLLMs, allowing for more efficient use of techniques like RAG. Specifically, we propose a method with two variants that fine-tune a VLLM on an automatically constructed dataset for boundary identification. Experimental results on various types of Visual Question Answering datasets show that our method successfully depicts a VLLM's knowledge boundary, based on which we are able to reduce indiscriminate retrieval while maintaining or improving the performance. In addition, we show that the knowledge boundary identified by our method for one VLLM can be used as a surrogate boundary for other VLLMs. Code will be released at https://github.com/Chord-Chen-30/VLLM-KnowledgeBoundary
+
+# 1 Introduction
+
+The great advancements in language models have led to the integration of image encoding and understanding capabilities (Achiam et al., 2023; Lu et al., 2024; Wang et al., 2024), significantly enhancing the performance of a series of pre-trained Vision Large Language Models (VLLMs) in tasks involving Visual Question Answering (VQA). Despite these advancements, akin to Large Language Models (LLMs) (Touvron et al., 2023; Workshop et al., 2022; Brown et al., 2020; Zhang et al., 2024b),
+
+![](images/6560a0587ffc2654a952df3aac822de31401be0396b02899ade5f1fdd54f03cc.jpg)  
+Figure 1: VLLMs Knowledge Boundary concept. The black part represents all the knowledge humans have explored, and the orange and green parts represent knowledge possessed by VLLMs and knowledge that can be retrieved from external sources respectively. They overlap in some areas and the boundary between them remains unclear. The overall knowledge boundary of VLLMs can be differentiated into two parts that overlap with knowledge between RAG and world knowledge. Our method aims to identify both, and we conduct experiments to validate the potential VQA performance improvements using RAG.
+
+VLLMs remain constrained by the boundaries of their knowledge (Lin and Byrne, 2022). As a result, their ability to accurately respond to content outside the model's knowledge scope, such as knowledge-intensive questions, real-time news, and queries with dynamic answers, is considerably limited.
+
+Some works study the knowledge boundary of text LLMs (Li et al., 2025; Cheng et al., 2024; Zhang et al., 2024b; Ren et al., 2023) via prompt-based or SFT-based methods. As of yet, there has been little research on the methodology for determining the knowledge boundaries of VLLMs. In practical applications, to answer VQA queries outside its knowledge scope, indiscriminately employing Retrieval Augmented Generation (RAG) techniques is often a viable solution. Although this approach has been proven to enhance the (V)LLMs' performance (Wang et al., 2021; Lewis et al., 2020; Chen et al., 2017), the comprehensive reliance on
+
+retrieval methods incurs significant latency due to the retrieval steps and the introduction of excessively long inputs (Chevalier et al., 2023; Zhang et al., 2024a; Chen et al., 2024).
+
+To mitigate the dependence on retrieval for answering questions and simultaneously maintain, or improve, the performance benefits provided by retrieval, we aim to develop a method that can depict the knowledge boundary of a VLLM. In this paper, we employ a method with two variants to delineate the knowledge boundaries of a VLLM by fine-tuning a VLLM on data constructed based on sampling the responses of the VLLM.
+
+With the ability to depict the knowledge boundary of a VLLM, we then adopt RAG techniques to validate the accuracy of the identified boundary in various held-out datasets. We conduct experiments using a variety of VQA datasets, including three knowledge-intensive datasets, two non-knowledge-intensive datasets, and one mixed dataset. After determining whether a query falls within the knowledge boundary, we use RAG to assess the potential improvements the retrieved information provides to the queries falling out of the knowledge boundary. Our experimental results reveal that on a mixed dataset, which contains both non-knowledge-intensive and knowledge-intensive queries simulating real situations, our method outperforms the indiscriminative use of RAG (denoted "All RAG") and prompt-based baseline with $50.67\%$ retrieval reduction. The fine-tuned knowledge boundary model lowers the retrieving ratio on less knowledge-intensive data and obtains close or even better performance compared to the "All RAG" setting. Besides, we show that the fine-tuned VLLM for boundary identification for one VLLM can be used as a surrogate boundary identifier for other VLLMs.
+
+To sum up, our contributions are as follows:
+
+1. We propose a method with two variants that detects the knowledge boundary of a VLLM.   
+2. Experimental results show that we maintain, or even improve, the performance of the VLLM on various types of data while lowering the ratio of using RAG, and our method outperforms the "All RAG" setting and other baselines on a dataset simulating real situations.   
+3. We show that the knowledge boundary for one VLLM can be used as a surrogate boundary for other VLLMs, to reduce retrieval while maintaining or improving the performance.
+
+# 2 Method
+
+We propose a method with two variants that fine-tunes a VLLM, which can depict the hard or soft knowledge boundary of VLLMs. The proposed method relies only on (V)LLMs and does not require manual annotation. In the following sections, we first introduce the background and necessary notations. Then we give details on constructing two types of datasets for fine-tuning a VLLM for knowledge boundary approximation.
+
+# 2.1 Background
+
+Consider a Visual Question Answering query $\mathbf{q}$ with gold text answer $\mathbf{a}$ , where $\mathbf{q}$ contains image(s) $\mathbf{q}_i$ and a text query $\mathbf{q}_t$ . Also, contexts $\mathbf{k}$ related to $\mathbf{q}$ can be retrieved from a given corpus, where $\mathbf{k}$ can refer to the collection of both texts and images. Given a VL model, parameterized by $\theta$ , we can answer the query with or without RAG by running decoding (Dec) on the model:
+
+$$
+\begin{array}{l} \boldsymbol {y} _ {\boldsymbol {n}} = \operatorname {D e c} _ {\theta} (\boldsymbol {y} | \boldsymbol {q}) \tag {1} \\ \boldsymbol {y} _ {r} = \operatorname {D e c} _ {\theta} (\boldsymbol {y} | \boldsymbol {q}, \boldsymbol {k}) \\ \end{array}
+$$
+
+where $\pmb{k}$ might also contain prompts connecting related content and it is omitted here for simplicity.
+
+It is acknowledged that VLLMs have a limited knowledge scope (Lin and Byrne, 2022; Wu et al., 2022), denoted as $S$ , and the boundary is a rather vague concept and is hard to depict accurately.
+
+# 2.2 Sampling
+
+To approximate whether a query $q$ should lie in VLLMs' knowledge scope $S$ , we run repeated sampling of a VLLM and collect its outputs. The sampling methods include but are not limited to, top-p sampling and top-k sampling. These sampling-based methods are widely adopted to study the model's knowledge boundary problems (Li et al., 2025; Zhang et al., 2024b; Cheng et al., 2024). By running $R$ times sampling, we obtain $R$ outputs given query $q$ :
+
+$$
+\boldsymbol {y} ^ {(i)} = D e c _ {\theta} (\boldsymbol {y} | \boldsymbol {q}), i \in \{1, 2, \dots , R \} \tag {2}
+$$
+
+After obtaining the $R$ predictions, a text LLM is prompted<sup>1</sup> to evaluate each prediction $y^{(i)}$ where the gold answer is also given. Subsequently a score $s_i \in [s_w, s_c]$ is provided by this text LLM. We define the score range within $s_w$ and $s_c$ , where
+
+![](images/4187963f5e9e793fa998f18a40416d2219856662c8a46b42cf6f9fd976f8c7a9.jpg)  
+Figure 2: Method illustration of training a Knowledge Boundary model.
+
+$s_c$ indicates a perfectly correct answer and $s_w$ indicates a wrong answer. Then an average score is calculated over $R$ scores, indicating the overall performance of this query:
+
+$$
+s = \operatorname {m e a n} \left(s _ {i}\right), i \in \{1, 2, \dots , R \} \tag {3}
+$$
+
+and we note that $s$ is also $\in [s_w, s_c]$ .
+
+# 2.3 Training
+
+The score $s$ is used to construct the knowledge boundary training data. We differentiate our method into two variants. A VLLM is adopted to train on the knowledge boundary training data. We denote the parameters by $\phi$ .
+
+Hard Knowledge Boundary By setting a threshold $\epsilon$ , we deem the queries with score $s \geq \epsilon$ inside the knowledge boundary $S$ and the rest outside $S$ . The query $\mathbf{q}$ , together with proper prompts $P_h$ , will be constructed into a training sample $\mathbf{x}(\mathbf{q}, P_h)$ as shown in Sec. A.1. For any $\mathbf{x}(\mathbf{q}, P_h)$ in the training dataset, we define the training objective $J_h$ w.r.t. $\phi$ as follows:
+
+$$
+\begin{array}{l} J _ {h} (\phi) = - \sum_ {\boldsymbol {x} (\boldsymbol {q}, P _ {h}): \boldsymbol {q} \notin S} \log P _ {\phi} \left(\text {" T r u e "} \mid \boldsymbol {x} (\boldsymbol {q}, P _ {h})\right) \\ - \sum_ {\boldsymbol {x} \left(\boldsymbol {q}, P _ {h}\right): \boldsymbol {q} \in S} \log P _ {\phi} \left(\text {" F a l s e "} \mid \boldsymbol {x} \left(\boldsymbol {q}, P _ {h}\right)\right) \tag {4} \\ \end{array}
+$$
+
+where $P_{\phi}(a|b)$ stands for the probability model $\phi$ predicts on $a$ given input $b$ . $\phi$ is optimized by minimizing $J_{h}(\phi)$ .
+
+Soft Knowledge Boundary Setting a threshold to binarily classify the queries might be an overly rigid method and there is no room for adjustment when the knowledge boundary model performs poorly in possibly unseen scenarios unless we adjust $\epsilon$ and retrain the model. Thus, we also propose
+
+a method that can depict a softer boundary. Recall that for query $\mathbf{q}$ , the average score $s$ over $R$ model predictions ranges in $[s_w, s_c]$ , where $s_w$ indicates a wrong answer and $s_c$ indicates a correct one. We linearly flip the score, for example, the new score $s' = s_w$ represents a strong tendency for external knowledge while $s' = s_c$ represents a refusal to external knowledge.
+
+The query $\mathbf{q}$ , together with prompts $P_{s}$ , will be constructed into a training sample $\mathbf{x}(\mathbf{q}, P_{s})$ as shown in Sec. A.1. For any $\mathbf{x}(\mathbf{q}, P_{s})$ in the training dataset, we define the training objective as follows:
+
+$$
+J _ {s} (\phi) = - \sum_ {\boldsymbol {x} (\boldsymbol {q}, P _ {s})} \log P _ {\phi} \left(s ^ {\prime} \mid \boldsymbol {x} (\boldsymbol {q}, P _ {s})\right) \tag {5}
+$$
+
+where $\phi$ is optimized by minimizing $J_{s}(\phi)$
+
+By optimizing objective 4, we get a Hard Knowledge Boundary model $HKB_{\phi}$ that can take a VQA sample and predict a binary output "True" or "False" indicating whether the RAG technique can help solve this query. Similarly, a Soft Knowledge Boundary model $SKB_{\phi}$ that can predict a soft score, ranging from $s_w$ to $s_c$ , is trained by optimizing objective 5:
+
+$$
+H K B _ {\phi} (\boldsymbol {x} (\boldsymbol {q}, P _ {h})) = \text {T r u e} / \text {F a l s e} \tag {6}
+$$
+
+$$
+S K B _ {\phi} (\boldsymbol {x} (\boldsymbol {q}, P _ {s})) \in [ s _ {w}, s _ {c} ]
+$$
+
+# 2.4 Application of RAG in Our Method
+
+An indicator function is defined to map the prediction of a Hard/Soft Knowledge Boundary model to a real search decision:
+
+$$
+\mathbb {I} (\boldsymbol {q}, \boldsymbol {k}) = \left\{ \begin{array}{l} \boldsymbol {k}, \text {i f} H K B _ {\phi} (\boldsymbol {x} (\boldsymbol {q}, P _ {h})) = = \text {t r u e} \\ \text {o r} S K B _ {\phi} (\boldsymbol {x} (\boldsymbol {q}, P _ {s})) \geq \epsilon \\ \text {N o n e , e l s e} \end{array} \right. \tag {7}
+$$
+
+Then we can combine the decoding with or without RAG stated in equation 1 into:
+
+$$
+\boldsymbol {y} _ {\boldsymbol {k} \boldsymbol {b}} = \operatorname {D e c} _ {\theta , \phi} (\boldsymbol {y} | \boldsymbol {q}, \mathbb {I} (\boldsymbol {q}, \boldsymbol {k})) \tag {8}
+$$
+
+<table><tr><td>Source</td><td># Samples</td><td>Model</td><td>Avg. Score ± std.</td></tr><tr><td rowspan="2">InfoSeek</td><td rowspan="2">216000</td><td>QW</td><td>1.82± 1.17</td></tr><tr><td>DS</td><td>1.86± 1.28</td></tr><tr><td rowspan="2">OK-VQA</td><td rowspan="2">9009</td><td>QW</td><td>3.70± 1.48</td></tr><tr><td>DS</td><td>4.92± 0.47</td></tr><tr><td rowspan="2">VQAv2.0</td><td rowspan="2">108000</td><td>QW</td><td>4.27± 1.36</td></tr><tr><td>DS</td><td>4.50± 1.22</td></tr><tr><td rowspan="2">MMBench (en)</td><td rowspan="2">4329</td><td>QW</td><td>3.92± 1.72</td></tr><tr><td>DS</td><td>4.08± 1.65</td></tr><tr><td rowspan="2">MME</td><td rowspan="2">2374</td><td>QW</td><td>4.15± 1.63</td></tr><tr><td>DS</td><td>4.15± 1.64</td></tr></table>
+
+Table 1: Training set sources and statistics. Answers are sampled from Qwen-VL-7B-Chat (QW) (Bai et al., 2023) DeepSeek-VL-7B-Chat (DS) (Lu et al., 2024) respectively. Scores are evaluated by Qwen-Max (Team, 2024)
+
+# 3 Experiment
+
+# 3.1 Setup
+
+# 3.1.1 Training Data
+
+With method stated in Sec. 2.2 and 2.3, we adopt InfoSeek (Chen et al., 2023), OK-VQA (Marino et al., 2019), VQAv2.0 (Goyal et al., 2017), MMBench (Liu et al., 2025), and MME (Fu et al., 2023) to construct the training set where we randomly sample two subsets from InfoSeek and VQAv2.0 respectively due to their large sizes. Table 1 presents the detailed sizes for each dataset we use along with the average scores $s$ . In our experiments $s_w = 1$ and $s_c = 5$ . We adopt all these datasets to increase the diversity of queries as much as possible. A detailed description of each dataset is stated in Sec. A.2.
+
+# 3.1.2 Test Data
+
+As we aim to construct a model that can take various input queries and make good judgments about the knowledge boundary, we adopt held-out data to evaluate the final VQA performance. We summarize the overall RAG Effect on each data in Table 2 and a brief introduction as follows.
+
+Life VQA We collect a set of VQA data from people's daily lives and extract the ones current VLLMs do not perform well, which is used to verify whether our model decides to resort to RAG for help. We will release this data along with the code and name it Life VQA.
+
+Private VQA is an internal dataset spanning broad categories, including animals, plants, architecture, geographic locations, etc. Due to the complexity of the backgrounds and the presence of
+
+<table><tr><td>Test Data</td><td>RAG Effect</td></tr><tr><td>Life VQA</td><td>High</td></tr><tr><td>Private VQA</td><td>Medium</td></tr><tr><td>Dyn-VQA</td><td>High</td></tr><tr><td>NoCaps</td><td>Low</td></tr><tr><td>Visual7W</td><td>Low</td></tr><tr><td>Mix</td><td>?</td></tr></table>
+
+Table 2: Test data property illustration of whether RAG is helpful in answering the queries.
+
+multiple objects, this collection poses a notable challenge for advanced visual reasoning and understanding. This dataset will not be released for now.
+
+Dyn-VQA is released by Li et al. (2024) and contains three types of questions: questions with rapidly changing answers, questions requiring multi-modal knowledge and multi-hop questions. This dataset is a challenging one in our evaluation. Gold query is annotated by Li et al. (2024) that combines the text query and image to be used to retrieve useful information.
+
+NoCaps (Agrawal et al., 2019) is an open-domain image captioning dataset derived from Open Images (Krasin et al., 2017), focusing on generating captions for a diverse array of objects and scenes. We sample a subset of size 500.
+
+Visual7W (Zhu et al., 2016) is a VQA dataset containing images from COCO (Lin et al., 2014), paired with seven types of questions (who, what, when, where, how, why and which). It aims to evaluate models' abilities in object recognition and deeper reasoning within visual contexts.
+
+Mix is a composite dataset consisting of 100 samples from each of the aforementioned datasets. It is designed to integrate the characteristics of each dataset and simulate real-world scenarios. Thus the effect of RAG on this dataset is mixed and hard to predict intuitively.
+
+# 3.1.3 Use of RAG
+
+We aim not only to locate the queries that need RAG to answer better but also to adopt retrieval techniques to verify the final VQA performance with the search decision $HKB_{\phi}$ and $SKB_{\phi}$ defined in equations 6. We note that although there are various options for retrieval, such as text search
+
+Table 3: Main results of Qwen-VL-Chat. Scores are shown in columns except for the % ones. Metrics are evaluated by Qwen-Max (LLM) and Token Accuracy (Acc.). Underlines mark the results that outperform three baseline “No RAG”, “All RAG” and “Prompt-based” settings. Boldface marks the best results.   
+
+<table><tr><td>Dataset</td><td>Metric</td><td>No RAG</td><td>All RAG</td><td>Prompt-based</td><td>%</td><td>HKB</td><td>%</td><td>SKB</td><td>%</td><td>Human</td><td>%</td></tr><tr><td rowspan="2">Life VQA</td><td>LLM</td><td>30.00</td><td>40.70</td><td>33.89</td><td>12.75%</td><td>40.64</td><td>96.64%</td><td>36.78</td><td>61.74%</td><td>39.33</td><td>71.14%</td></tr><tr><td>Acc.</td><td>17.80</td><td>36.11</td><td>21.38</td><td>12.75%</td><td>36.11</td><td>96.64%</td><td>29.44</td><td>61.74%</td><td>33.36</td><td>71.14%</td></tr><tr><td rowspan="2">Private VQA</td><td>LLM</td><td>22.90</td><td>24.35</td><td>24.95</td><td>14.80%</td><td>24.50</td><td>99.20%</td><td>22.89</td><td>67.80%</td><td>24.20</td><td>72.00%</td></tr><tr><td>Acc.</td><td>16.26</td><td>18.40</td><td>17.26</td><td>14.80%</td><td>18.40</td><td>99.20%</td><td>17.35</td><td>67.80%</td><td>18.55</td><td>72.00%</td></tr><tr><td rowspan="2">Dyn-VQA ch</td><td>LLM</td><td>19.16</td><td>38.95</td><td>19.70</td><td>6.38%</td><td>37.94</td><td>95.66%</td><td>36.53</td><td>84.26%</td><td>28.89</td><td>46.95%</td></tr><tr><td>Acc.</td><td>23.41</td><td>43.06</td><td>24.37</td><td>6.38%</td><td>42.71</td><td>95.66%</td><td>40.97</td><td>84.26%</td><td>33.13</td><td>46.95%</td></tr><tr><td rowspan="2">Dyn-VQA en</td><td>LLM</td><td>21.60</td><td>34.93</td><td>23.51</td><td>14.13%</td><td>33.30</td><td>89.79%</td><td>32.06</td><td>76.08%</td><td>25.73</td><td>29.51%</td></tr><tr><td>Acc.</td><td>25.64</td><td>41.87</td><td>27.58</td><td>14.13%</td><td>40.66</td><td>89.79%</td><td>38.51</td><td>76.08%</td><td>30.83</td><td>29.51%</td></tr><tr><td rowspan="2">NoCaps</td><td>LLM</td><td>50.13</td><td>30.37</td><td>50.13</td><td>0.00%</td><td>42.50</td><td>38.40%</td><td>50.13</td><td>0.00%</td><td>50.13</td><td>0.00%</td></tr><tr><td>Acc.</td><td>40.50</td><td>30.72</td><td>40.50</td><td>0.00%</td><td>36.95</td><td>38.40%</td><td>40.50</td><td>0.00%</td><td>40.50</td><td>0.00%</td></tr><tr><td rowspan="2">Visual7W</td><td>LLM</td><td>54.48</td><td>52.04</td><td>55.32</td><td>31.36%</td><td>52.95</td><td>35.37%</td><td>54.27</td><td>2.96%</td><td>54.53</td><td>0.52%</td></tr><tr><td>Acc.</td><td>44.34</td><td>44.94</td><td>44.18</td><td>31.36%</td><td>44.32</td><td>35.37%</td><td>44.68</td><td>2.96%</td><td>44.34</td><td>0.52%</td></tr><tr><td rowspan="2">Mix</td><td>LLM</td><td>34.44</td><td>38.60</td><td>34.98</td><td>12.67%</td><td>39.59</td><td>76.83%</td><td>39.93</td><td>49.33%</td><td>38.29</td><td>38.33%</td></tr><tr><td>Acc.</td><td>26.13</td><td>32.39</td><td>27.23</td><td>12.67%</td><td>32.73</td><td>76.83%</td><td>30.98</td><td>49.33%</td><td>31.02</td><td>38.33%</td></tr></table>
+
+and image search, we do not design detailed methods to determine the best option in this paper. Instead, we directly use text search (Google) for DynVQA and image search (Bing) for the rest for better retrieval information quality towards answering the question. We note that Dyn-VQA is a challenging dataset that exhibits multi-hop property, therefore we use the golden query Li et al. (2024) have summarized for retrieving useful information.
+
+In the following sections, the "No RAG" setting refers to the performance of only VLLMs and no retrieval information is given, and "All RAG" refers to always incorporating RAG. "Prompt-based" refers to prompting the model that is sampled to adopt RAG or not.
+
+# 3.1.4 Base Models
+
+When constructing the training set according to the method stated in Sec. 2.2, we experiment with Qwen-VL-7B-Chat and DeepSeek-VL-7B-Chat that are used to be sampled $R = 30$ times and finetuned according to Sec. 2.3 respectively. Refer to Sec. A.3 for detailed training settings. Qwen-Max is prompted to score the $R$ predictions to get scores $s_i$ where we adopt $s_w = 1$ and $s_c = 5$ referenced from Liu (2022).
+
+For Visual Question Answering, we first evaluate the performance of the original models to be sampled. In addition, we seek to validate whether the identified knowledge boundary can function as a surrogate boundary for other VLLMs since
+
+constructing training datasets through sampling (Sec. 2.3) on (larger) models can be prohibitively expensive. We further validate the surrogate knowledge boundary on the following VLLMs, Qwen-VL-Max (Bai et al., 2023), Qwen-VL-2 (Wang et al., 2024) and GPT-4o (Hurst et al., 2024), to evaluate its potential for generalizing across different VLLMs.
+
+# 3.2 Main Results
+
+We present our main results of Qwen-VL-7B-Chat in Table 3 and results of DeepSeek-VL-7B-Chat in Appendix A.6. In this section, we focus on the results of Qwen.
+
+Metrics LLM represents that the score is evaluated by a text LLM, Qwen-Max, given the model prediction and gold answer. Metrics Acc. refers to token accuracy which involves determining the proportion of tokens in the model's predictions that match the tokens in the gold answer. Both Scores range from 0 to 100 and a higher score indicates a higher performance. The $\%$ columns refer to the ratio of data that our knowledge boundary model predicts to lie beyond the VLLM's knowledge boundaries. The "Human" column represents the corresponding statistics where the Knowledge Boundary model is trained on the human-labeled data mentioned in Sec. 3.1.1, and we deem it a reference result.
+
+First, the results in the Mix row, which considers all kinds of VQA queries in our setting and simu
+
+Table 4: Knowledge Boundary model (Qwen-VL-7B-Chat) as a surrogate boundary identifier for other VLLMs.   
+
+<table><tr><td></td><td>Metric: LLM</td><td>No RAG</td><td>All RAG</td><td>Prompt-based</td><td>%</td><td>HKB</td><td>%</td><td>SKB</td><td>%</td><td>Human</td><td>%</td></tr><tr><td rowspan="4">Life VQA</td><td>Ds.-VL-Chat</td><td>25.54</td><td>47.38</td><td>27.68</td><td>12.75%</td><td>46.91</td><td>96.64%</td><td>41.21</td><td>61.74%</td><td>41.61</td><td>71.14%</td></tr><tr><td>Qwen-VL-Max</td><td>43.26</td><td>56.38</td><td>45.97</td><td>12.75%</td><td>56.85</td><td>96.64%</td><td>53.86</td><td>61.74%</td><td>55.23</td><td>71.14%</td></tr><tr><td>Qwen-VL-2</td><td>42.55</td><td>54.43</td><td>46.28</td><td>12.75%</td><td>54.03</td><td>96.64%</td><td>52.28</td><td>61.74%</td><td>53.96</td><td>71.14%</td></tr><tr><td>GPT-4o</td><td>47.52</td><td>55.47</td><td>48.26</td><td>12.75%</td><td>56.14</td><td>96.64%</td><td>54.83</td><td>61.74%</td><td>54.90</td><td>71.14%</td></tr><tr><td rowspan="4">Private VQA</td><td>Ds.-VL-Chat</td><td>23.01</td><td>27.06</td><td>23.89</td><td>14.80%</td><td>26.94</td><td>99.20%</td><td>26.19</td><td>67.80%</td><td>25.83</td><td>72.00%</td></tr><tr><td>Qwen-VL-Max</td><td>35.20</td><td>41.90</td><td>38.30</td><td>14.80%</td><td>41.68</td><td>99.20%</td><td>40.45</td><td>67.80%</td><td>43.18</td><td>72.00%</td></tr><tr><td>Qwen-VL-2</td><td>35.16</td><td>38.02</td><td>36.57</td><td>14.80%</td><td>37.84</td><td>99.20%</td><td>35.85</td><td>67.80%</td><td>38.25</td><td>72.00%</td></tr><tr><td>GPT-4o</td><td>39.70</td><td>38.21</td><td>40.06</td><td>14.80%</td><td>37.85</td><td>99.20%</td><td>38.83</td><td>67.80%</td><td>40.21</td><td>72.00%</td></tr><tr><td rowspan="4">Dyn-VQA ch</td><td>Ds.-VL-Chat</td><td>21.62</td><td>44.10</td><td>22.98</td><td>6.38%</td><td>42.92</td><td>95.66%</td><td>40.99</td><td>84.26%</td><td>34.24</td><td>46.95%</td></tr><tr><td>Qwen-VL-Max</td><td>32.97</td><td>51.24</td><td>34.23</td><td>6.38%</td><td>50.86</td><td>95.66%</td><td>48.24</td><td>84.26%</td><td>43.33</td><td>46.95%</td></tr><tr><td>Qwen-VL-2</td><td>32.78</td><td>50.74</td><td>34.02</td><td>6.38%</td><td>50.48</td><td>95.66%</td><td>48.19</td><td>84.26%</td><td>43.05</td><td>46.95%</td></tr><tr><td>GPT-4o</td><td>41.91</td><td>56.31</td><td>42.53</td><td>6.38%</td><td>56.31</td><td>95.66%</td><td>54.49</td><td>84.26%</td><td>48.95</td><td>46.95%</td></tr><tr><td rowspan="4">Dyn-VQA en</td><td>Ds.-VL-Chat</td><td>25.58</td><td>38.10</td><td>27.19</td><td>14.13%</td><td>36.86</td><td>89.79%</td><td>36.32</td><td>76.08%</td><td>29.44</td><td>29.51%</td></tr><tr><td>Qwen-VL-Max</td><td>37.19</td><td>43.98</td><td>38.32</td><td>14.13%</td><td>43.09</td><td>89.79%</td><td>42.78</td><td>76.08%</td><td>39.48</td><td>29.51%</td></tr><tr><td>Qwen-VL-2</td><td>37.12</td><td>44.20</td><td>37.17</td><td>14.13%</td><td>42.47</td><td>89.79%</td><td>42.32</td><td>76.08%</td><td>40.07</td><td>29.51%</td></tr><tr><td>GPT-4o</td><td>45.41</td><td>50.93</td><td>45.24</td><td>14.13%</td><td>49.88</td><td>89.79%</td><td>48.75</td><td>76.08%</td><td>47.14</td><td>29.51%</td></tr><tr><td rowspan="4">NoCaps</td><td>Ds.-VL-Chat</td><td>63.67</td><td>59.81</td><td>63.67</td><td>0.00%</td><td>61.23</td><td>38.40%</td><td>63.67</td><td>0.00%</td><td>63.67</td><td>0.00%</td></tr><tr><td>Qwen-VL-Max</td><td>62.10</td><td>49.66</td><td>62.10</td><td>0.00%</td><td>57.09</td><td>38.40%</td><td>62.10</td><td>0.00%</td><td>62.10</td><td>0.00%</td></tr><tr><td>Qwen-VL-2</td><td>62.10</td><td>49.93</td><td>62.10</td><td>0.00%</td><td>56.93</td><td>38.40%</td><td>62.10</td><td>0.00%</td><td>62.10</td><td>0.00%</td></tr><tr><td>GPT-4o</td><td>61.43</td><td>63.98</td><td>61.43</td><td>0.00%</td><td>62.12</td><td>38.40%</td><td>61.43</td><td>0.00%</td><td>61.43</td><td>0.00%</td></tr><tr><td rowspan="4">Visual7W</td><td>Ds.-VL-Chat</td><td>58.34</td><td>57.29</td><td>57.26</td><td>31.36%</td><td>57.85</td><td>35.37%</td><td>58.13</td><td>2.96%</td><td>58.28</td><td>0.52%</td></tr><tr><td>Qwen-VL-Max</td><td>58.37</td><td>55.51</td><td>62.11</td><td>31.36%</td><td>57.10</td><td>35.37%</td><td>58.25</td><td>2.96%</td><td>58.30</td><td>0.52%</td></tr><tr><td>Qwen-VL-2</td><td>58.16</td><td>54.41</td><td>62.19</td><td>31.36%</td><td>56.66</td><td>35.37%</td><td>57.85</td><td>2.96%</td><td>58.02</td><td>0.52%</td></tr><tr><td>GPT-4o</td><td>52.96</td><td>47.06</td><td>51.82</td><td>31.36%</td><td>50.87</td><td>35.37%</td><td>52.89</td><td>2.96%</td><td>52.87</td><td>0.52%</td></tr><tr><td rowspan="4">Mix</td><td>Ds.-VL-Chat</td><td>34.96</td><td>45.18</td><td>35.71</td><td>12.67%</td><td>45.08</td><td>76.83%</td><td>43.35</td><td>49.33%</td><td>42.20</td><td>38.33%</td></tr><tr><td>Qwen-VL-Max</td><td>46.54</td><td>49.26</td><td>47.30</td><td>12.67%</td><td>50.64</td><td>76.83%</td><td>51.06</td><td>49.33%</td><td>52.05</td><td>38.33%</td></tr><tr><td>Qwen-VL-2</td><td>46.36</td><td>47.89</td><td>47.46</td><td>12.67%</td><td>49.31</td><td>76.83%</td><td>49.29</td><td>49.33%</td><td>51.41</td><td>38.33%</td></tr><tr><td>GPT-4o</td><td>51.44</td><td>52.90</td><td>50.57</td><td>12.67%</td><td>54.10</td><td>76.83%</td><td>52.97</td><td>49.33%</td><td>55.27</td><td>38.33%</td></tr></table>
+
+lates a real situation, show that our methods outperform all other baseline and reference settings. Our $HKB$ method lowers the retrieval demand by $23.17\%$ , and the $SKB$ method lowers it by $50.67\%$ .
+
+Second, as shown by the $\%$ columns and the RAG Effect we summarized in Table 2, our Knowledge Boundary models succeed in predicting a high ratio on test data when RAG can effectively aid in answering the query, and it lowers the ratio for data where the queries tend to fall within the knowledge scope of a VLLM.
+
+Third, on the first four datasets where RAG can (greatly) enhance the VQA performance, we show that with our $HKB$ and $SKB$ , the performance is close to that achieved with the "All RAG" setting. For example, with the $SKB$ model, Qwen-VL-Chat archives a 32.06 LLM score on the Dyn-VQA (en) dataset with $76.08\%$ RAG ratio, whereas the "All RAG" setting achieves 34.93. With the $HKB$ model, Qwen-VL-Chat exceeds the "All RAG" setting on Private VQA, even though we note that "All RAG" is a strong setting on this data.
+
+At last, on the NoCaps and Visual7W datasets where VLLMs can perform well without RAG and RAG tends to supply noise, our method can identify a much lower search ratio. Specifically, the search ratio from $SKB$ is close to or equal to zero.
+
+# 4 Analysis
+
+In this section, we present five analytical experiments. The first shows the performance of other VLLMs if we employ the identified knowledge boundary as a surrogate. The second shows how the RAG ratio and VQA performance are affected by the threshold defined in the $SKB$ variant. The third presents the efficiency of our method. The fourth is a case study showing cases with different Knowledge Boundary model predictions (inside or outside the knowledge boundary). The last shows the accuracy of VLLM boundary identification on held-in data at training time.
+
+# 4.1 Surrogate Boundary for Other VLLMs
+
+We assemble around 340 thousand VQA samples from various domains discussed in Sec. 3.1.1. Sam
+
+![](images/e1086cb7accf8bfae191ba3deba56c94497d63d5f1cf1c4d05b487ac35fc1252.jpg)
+
+![](images/f531448c8cb2dc9247525e428b03c3602ce85bb5caacd59ba73ea63fe03bcb7e.jpg)
+
+![](images/7cc1d3a231df9903691669fc5d841d26896fca80e76ae0760b099b0e5c14ea7a.jpg)
+
+![](images/84648a019535feab17058f5c21ceccf2f05e55dc509da0d14e9c7d7d0ab15cb8.jpg)
+
+![](images/2ed83ee1246d25bb5b4cc96339acc965e21e1c0887f675c56b0490b514c417f1.jpg)
+
+![](images/032c78987efeaa630796a2230ff4ba96fe5051924c399d56ead8bb00b04a6feb.jpg)  
+Figure 3: Effect of $\epsilon$ . The lighter dashed lines accordingly indicate the performance under each base model's "No RAG" setting. Knowledge Boundary model is Qwen-VL-7B-Chat.
+
+pling each data thirty times is prohibitively expensive for closed-source VLLMs. While VLLMs (e.g., Qwen-VL, DeepSeek-VL) may intuitively exhibit different knowledge scopes, this overlap is expected given their shared pretraining corpora (e.g., LAION (Schuhmann et al., 2022), COCO (Lin et al., 2014)), similar visual encoder architectures (e.g., CLIP variants), and common textual knowledge from large-scale web data. Besides, queries regarding recently occurring news events typically fall outside the knowledge boundaries of any model. Thus, we conduct an experiment that validates whether the identified knowledge boundary can function as a surrogate boundary for other VLLMs.
+
+The experimental results with Qwen as a boundary model are presented in Table 4 and Table 11. The results with DeepSeek as a boundary model are presented in Appendix A.7.
+
+From Table 4 Mix row, Qwen-VL-Max, Qwen-VL-2 and GPT-4o achieve better performance than all three baseline settings. Deepseek-VL-7B-Chat remains competitive to the "All RAG" setting with LLM metric and outperforms all other settings in Table 11 Mix row. For other datasets, we show that the previously identified knowledge boundary can help maintain the performance with a reduced RAG ratio. For example, GPT-4o achieves 54.83 with only $61.74\%$ RAG ratio while the "All RAG" setting achieves 55.47 on the Life VQA dataset.
+
+Deepseek-VL-7B-Chat maintains its performance on the Dyn-VQA (en) dataset compared to the "All RAG" setting and keeps a clear margin compared to the "No RAG" setting with a $23.92\%$ retrieving deduction.
+
+# 4.2 Effect of $\epsilon$ for $SKB$
+
+In Sec 3.2, we show the result of the $SKB$ method with the least RAG ratio, i.e., $\epsilon$ is set to maintain a low tendency to resort to RAG. Here we show how the overall VQA performance is affected by $\epsilon$ . The results of three datasets are illustrated in Fig. 3. The leftmost point of the horizontal axis corresponds to the "All RAG" setting (with $\epsilon = s_w$ ), while the rightmost point represents the minimal search ratio. Light-coloured dashed lines depict the "No RAG" setting. For the left two data in Fig 3, where RAG can greatly affect the performance, our methods can maintain a clear margin between the "No RAG" setting and obtain a relatively stable performance with a decreased search ratio. For the Mix data where all types of data are fused, our methods can still lower the search ratio while maintaining, or improving, the performance.
+
+# 4.3 Efficiency
+
+Our method incorporates an additional forward pass for each VQA example for knowledge boundary identification. We report the overall efficiency in Table 6 on the Mix dataset, where the All RAG
+
+Cases where the model predicts to be out of the knowledge boundary
+
+Question: How many World Series titles has the team won?
+
+![](images/d71baf6a331e2e5f1a183f96d19cb585b2f0df907f6e21cd93df7952332324df.jpg)
+
+Prediction w/o retrieval: The Houston Astros have won one World Series title, in 2017. $\rightarrow$ (incorrect)
+
+Prediction w/ retrieval: The Houston Astros have won two World Series titles. $\rightarrow$ (correct) (Source: Dyn-VQA (en))
+
+Question: Who is the current Prime Minister of this country?
+
+![](images/719fe03dd48f7ce3a39491fece6b48278e19282f2a456c0a284677a7d5fe287c.jpg)
+
+Prediction w/o retrieval: The current Prime Minister of the United Kingdom is Rishi Sunak. $\rightarrow$ (incorrect)
+
+Prediction w/ retrieval: The current Prime Minister of the United Kingdom is Keir Starmer. $\rightarrow$ (correct) (Source: Dyn-VQA (en))
+
+Cases where the model predicts to be in the knowledge boundary
+
+Question: Can you add a caption to the image using a phrase? For example: A little girl in a white jacket and sandals.
+
+![](images/94e2d82f04c510af45b9dce67f985faadda2d7e10f8c01ea20af88d39d3502d3.jpg)
+
+Prediction w/o retrieval: A blue jay perched on a tree branch. $\rightarrow$ (correct)
+
+Prediction w/ retrieval: A blue and white bird perched on a tree branch. $\rightarrow$ (correct) (Source: NoCaps)
+
+Question: How is the boat staying ashore?
+
+![](images/8ae4737d345447b6356d4c3b006fdaf38695d566100150b5f851e5371ee6a8c6.jpg)
+
+Prediction w/o retrieval: The boat is staying ashore by being tied to a wooden post with a yellow rope. The rope is wrapped around the post and secured, preventing the boat from drifting back into the water. $\rightarrow$ (correct)
+
+Prediction w/ retrieval: It is tied to a tree with rope. $\rightarrow$ (correct) (Source: Visual7W)
+
+Table 5: Cases when the model predicts whether the VQA queries are in VLLMs' knowledge boundary. Base model is Qwen-VL-Max.   
+
+<table><tr><td></td><td>Model</td><td>All RAG</td><td>HKB (Mix)</td><td>SKB (Mix)</td></tr><tr><td rowspan="2">Time (s)</td><td>QW</td><td rowspan="2">619.20</td><td>598.13</td><td>427.85</td></tr><tr><td>DS</td><td>386.61</td><td>326.74</td></tr><tr><td rowspan="2">Improvement (%)</td><td>QW</td><td rowspan="2">-</td><td>3.40%</td><td>30.90%</td></tr><tr><td>DS</td><td>37.56%</td><td>47.23%</td></tr></table>
+
+Table 6: Efficiency illustration of Knowledge Boundary model Qwen-VL-7B-Chat (QW) and DeepSeek-VL-7B-Chat (DS). Time row shows the time spent before generating the answer in the VQA task.
+
+<table><tr><td>Model</td><td>Fold</td><td>Human-labeled</td><td>Hard</td><td>Soft</td></tr><tr><td rowspan="2">QW</td><td>Train</td><td>96.25</td><td>90.50</td><td>88.41</td></tr><tr><td>Val.</td><td>-</td><td>91.16</td><td>88.96</td></tr><tr><td rowspan="2">DS</td><td>Train</td><td>96.25</td><td>93.91</td><td>92.10</td></tr><tr><td>Val</td><td>-</td><td>93.76</td><td>92.11</td></tr></table>
+
+Table 7: Training and validation results on the held-in dataset. Metrics are shown in the accuracy defined in ms-swift package. We have a limited number of human-labeled samples thus we do not set a validation set for "Human-labeled" setting.
+
+setting always uses RAG (calls to the search engines included) and does not perform the forward pass, and $HKB / SKB$ refers to partially performing RAG according to our model's predictions with forward-pass time included.
+
+# 4.4 Case Study
+
+This section shows four cases with different Knowledge Boundary model predictions (inside or outside the knowledge boundary). In the left column of Table 5, the Knowledge Boundary model predicts that they are outside the knowledge boundary, and the retrieval indeed helps the model correct its response. In the right column, we show two examples cases that our Knowledge Boundary model predicts to be in the knowledge boundary and thus do not need retrieval.
+
+# 4.5 Performance of Knowledge Boundary Identification on Held-In Data
+
+The training results of the Knowledge Boundary model are shown in Table 7. We show that by training Qwen-VL-7B-Chat (QW) and DeepSeek-VL-7B-Chat (DS), they succeed in modeling the knowledge boundary on held-in data we constructed according to Sec. 2.3.
+
+# 5 Related Work
+
+# 5.1 Knowledge Boundary Study of Text LLM
+
+As the LLMs are applied to a wider range of fields, users expect them to perform well on any query. However, inevitably, the knowledge embedded within LLMs does not automatically update over time, resulting in certain queries consistently falling outside the model's knowledge boundaries.
+
+Some works study the Knowledge Boundaries of text LLMs. A commonly used approach prompts LLMs to output content like "I don't know" (Li et al., 2025; Cheng et al., 2024; Ren et al., 2023). Alternatively, another approach is to construct a dataset and perform Supervised Fine-Tuning (SFT) (Zhang et al., 2024b; Cheng et al., 2024; Li et al., 2025). Both aforementioned types of approaches focus on making the models express "I know" or "I don't know". Most aforementioned works find that prompt-based methods are poorly performed.
+
+We contend that this task is actually challenging for two primary reasons. First, regarding whether a model can itself articulate its own knowledge boundaries, considerable debate persists in current research. For example, Ren et al. (2023) states that LLMs struggle to perceive their factual knowledge boundary, and tend to be overconfident, however, Cheng et al. (2024) conclude that the AI assistant can, to a significant extent, identify what it does not know. Second, it is difficult to verify the accuracy of the predicted boundaries.
+
+# 5.2 Retrieval-Augmented Generation
+
+The RAG technique is widely adopted to help models answer certain queries needing external information in both texts (Jeong et al., 2024; Chen et al., 2024; Lewis et al., 2020) and image-text scenarios (Lin and Byrne, 2022; Wu et al., 2022). However, current RAG techniques are far from being perfect for enhancing (V)LLMs in all settings. For example, Zhang et al. (2024b) finds that for math reasoning and code questions, RAG usually brings noise rather than useful information, and thus RAG may even yield adverse effects. Therefore, more effective utilization of RAG can not only result in savings of time and computational resources but also enhance performance in certain scenarios.
+
+# 6 Conclusion
+
+In this paper, we introduce a method with two variants that fine-tunes VLLMs on automatically constructed datasets for boundary identification. This method mitigates the reliance on RAG techniques, which introduce significant latency and long input sequences. Our experiments across diverse held-out VQA datasets, including knowledge-intensive, non-knowledge-intensive, and mixed datasets, demonstrate that our method not only maintains or enhances VLLM performance but also lowers the RAG ratio. Additionally, the fine-tuned
+
+knowledge boundary exhibits versatility by functioning as a surrogate for other VLLM series, facilitating retrieval reduction without compromising performance. These findings underscore the efficacy of our method in optimizing the balance between retrieval dependence and model performance, paving the way for more efficient and effective deployment of VLLMs in practical applications.
+
+# 7 Limitations
+
+In this paper, we do not design detailed methods to distinguish the search type, such as text search and image search, towards answering a VQA sample. Experiments utilizing training data sampled from larger VLLMs are currently lacking. Both limitations will be addressed in our future work. Moreover, our current method is not yet able to reliably distinguish errors stemming from visual misrecognition (e.g., incorrect object identification or multi-view ambiguity) from knowledge gaps.
+
+# Acknowledgment
+
+This work was supported by Alibaba Group through Alibaba Innovative Research Program and the Core Facility Platform of Computer Science and Communication, SIST, ShanghaiTech University.
+
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+
+# A Appendix
+
+# A.1 Training Examples
+
+Hard Knowledge Boundary Query $\mathbf{q}$ , together with prompts $P_{h}$ (in blue), will be constructed into a training sample $\mathbf{x}(\mathbf{q}, P_{h})$ as follows:
+
+You are an assistant capable of deciding whether a search is needed in a multimodal question-answering scenario. Below, I will provide you with a multimodal question that includes a text question and an image link. Please respond with "true" or "false," indicating whether a search is necessary (true) or not (false) to answer this multimodal question.  
+<ST_1>  
+Text question: $q_t$ <Image>: $q_i$ <ST_2>
+
+Soft Knowledge Boundary Query $\mathbf{q}$ , together with prompts $P_{s}$ (in blue), will be constructed into a training sample $\mathbf{x}(\mathbf{q}, P_{s})$ as follows:
+
+```txt
+You are an assistant capable of deciding whether a search is needed in a multimodal question-answering scenario. Below, I will provide you with a multimodal question that includes a text question and an image link. Please respond with a score ranging from 1.0 to 5.0 indicating whether a search is necessary or not to answer this multimodal question. 
+```
+
+Follow these guidelines for scoring:
+
+- Your score has to be between 1.0 and 5.0, where 1.0 stands for an unnecessary search and 5.0 stands for a necessary search.   
+- The score does not have to be integer.
+
+Example Response: 4.0
+
+<ST_1>
+
+Text question: $\mathbf{q}_t$
+
+<Image>: $\pmb{q}_i$
+
+<ST_2>
+
+Your score:
+
+Table 8: Detailed hyperparameters. Grad. Accum. stands for gradient accumulation steps.   
+
+<table><tr><td>Base Model</td><td>Qwen- &amp; DeepSeek-VL-7B-Chat</td></tr><tr><td>LoRA</td><td>Q, K, V</td></tr><tr><td>LoRA Rank</td><td>8</td></tr><tr><td>LoRA Alpha</td><td>32</td></tr><tr><td>Learning Rate</td><td>1e-4</td></tr><tr><td>Optimizer</td><td>AdamW</td></tr><tr><td>LR Scheduler</td><td>Linear</td></tr><tr><td>Precision</td><td>bf16</td></tr><tr><td>Batch Size</td><td>1</td></tr><tr><td>Grad. Accum.</td><td>16</td></tr><tr><td>GPU</td><td>NVIDIA A100-SXM4-80GB</td></tr></table>
+
+# A.2 Training Dataset Description
+
+Below is a brief description of each dataset (for training).
+
+InfoSeek is designed to assess the capability of models to seek and incorporate external information for question answering. It features a variety of queries that necessitate fact retrieval and reasoning that go beyond the provided context.
+
+OK-VQA is a dataset where images are paired with open-ended questions that require answers stemming from general knowledge that extends beyond the image alone.
+
+VQAv2.0 is a comprehensive VQA dataset that requires interpretation or understanding of the visual content. It features a diverse and balanced range of answers.
+
+MMBench is a benchmarking suite for evaluating multi-modal understanding, ensuring that multimodal machine learning systems can effectively process and synthesize data from different sources.
+
+MME is focused on tasks related to multi-modal entity recognition and extraction. The dataset contains annotations of text and images with multimodal entities that need to be identified or linked.
+
+Human-Labeled A group of annotators is asked to annotate whether RAG can help solve a VQA sample. We construct this data to form a reference setting.
+
+# A.3 Training Details and Hyperparameters
+
+Recall that our methods need to train a VLLM, parameterized by $\phi$ , as a Knowledge Boundary
+
+Table 9: LLM evaluation consistency between QwenMax and GPT-4o on Mix dataset. Scores range from 0 to 100.   
+
+<table><tr><td>Scoring LLM Setting</td><td colspan="2">Qwen-Max GPT-4o No RAG</td><td colspan="2">Qwen-Max GPT-4o All RAG</td></tr><tr><td>Ds.-VL-Chat</td><td>34.96</td><td>32.88</td><td>45.18</td><td>45.70</td></tr><tr><td>Qwen-VL-Chat</td><td>34.44</td><td>32.62</td><td>38.60</td><td>38.34</td></tr><tr><td>Qwen-VL-Max</td><td>46.54</td><td>45.88</td><td>49.26</td><td>48.45</td></tr><tr><td>GPT-4o</td><td>51.44</td><td>51.72</td><td>52.90</td><td>50.58</td></tr></table>
+
+model discussed in Sec. 2.3. In experiments, we adopt LoRA (Hu et al., 2021) to optimize $\phi$ and the related hyperparameters are shown in Table 8. We note that our method does not rely heavily on tuning hyperparameters. We just choose intuitive values and it works fairly well.
+
+# A.4 Training and Evaluation Cost
+
+Based on our training settings, the training time for both Qwen-VL-Chat-7B and DeepSeek-VL-Chat-7B takes around 10 hours on 1 A100. Besides, the API call costs are as follows:
+
+1. Training data construction: 339,712 calls to Qwen-Max (for scoring).   
+2. Retrieve information from the web: $\sim 3000$ calls to Bing/Google (for test set evaluation).   
+3. Test set inference: $\sim 3,000$ calls to GPT-4o and $\sim 3,000$ calls to Qwen-VL-Max   
+4. Test set LLM (Qwen-Max) evaluation: $\sim 6,000$ calls (No RAG & All RAG settings)
+
+# A.5 LLM Evaluation Consistency
+
+We report the LLM evaluation consistency on the Mix dataset with No RAG and All RAG settings in Table 9. We note that the scores of all other settings can be derived from these two settings with the "Use RAG or not" decisions. It can be observed that, under these settings, the maximum difference in the average scores between GPT-4o and Qwen-Max is within 3.
+
+# A.6 Main Results on DeepSeek
+
+We present our main results of DeepSeek-VL-7B-Chat in Table 10. For both the $HKB$ and $SKB$ methods, DeepSeek performs more confidently than Qwen, and it tends to predict a lower ratio of resorting to RAG. On the Mix dataset, DeepSeek also well maintains the performance with the $SKB$ method compared to the All RAG setting and outperforms the Prompt-based method. In addition, compared to Qwen, DeepSeek better utilizes
+
+human-labeled data to depict the knowledge boundary and obtains the best result among all settings.
+
+# A.7 Supplementary Results of "Surrogate Boundary" Experiments
+
+We provide the supplementary experimental results for Sec 4.1 where the token accuracy metrics are shown in Table 11. It can be concluded that similar conclusions can be drawn as in Sec 4.1. The experiment where DeepSeek-VL-7B-Chat is trained for surrogate boundary prediction is shown in Table 12 and 13.
+
+# A.8 Supplementary Results on MMMU Dataset
+
+In this section, we show the experimental results of our methods on a challenging dataset, $\mathsf{MMMU}^3$ (Yue et al., 2024) in Table 14. MMMU is a dataset containing VQA samples demanding college-level subject knowledge and deliberate reasoning, and it is hard to verify the knowledge boundary that our methods depict by simply adopting RAG.
+
+The results in Table 14 show that the Knowledge Boundary model trained by human-labeled data helps achieve the best performance. It verifies that the aforementioned Human-labeled training data is effective. In addition, we show that our methods also exhibit substantial potential within this setting, in which both the $HKB$ and $SKB$ models predict a high search ratio over MMMU. We contend that the suboptimal performance of this dataset arises because it lies beyond the knowledge boundaries, which are challenging to validate using RAG, as delineated by the white dashed lines in Fig. 1. We present the performance of each of the 30 subjects in the MMMU validation set in Fig 4. The first row shows the LLM evaluation results, and the second shows the token accuracy metric. We can see that in most subjects "Human" setting succeeds in obtaining a higher performance than both "All RAG" and "No RAG" settings.
+
+Table 10: Main results of DeepSeek-VL-7B-Chat.   
+
+<table><tr><td>Dataset</td><td>Metric</td><td>No RAG</td><td>All RAG</td><td>Prompt-based</td><td>%</td><td>HKB</td><td>%</td><td>SKB</td><td>%</td><td>Human</td><td>%</td></tr><tr><td rowspan="2">Life VQA</td><td>LLM</td><td>25.81</td><td>47.35</td><td>33.36</td><td>30.20%</td><td>35.81</td><td>46.31%</td><td>42.18</td><td>73.83%</td><td>47.21</td><td>96.64%</td></tr><tr><td>Acc.</td><td>10.82</td><td>36.79</td><td>20.84</td><td>30.20%</td><td>24.81</td><td>46.31%</td><td>31.93</td><td>73.83%</td><td>36.79</td><td>96.64%</td></tr><tr><td rowspan="2">Private VQA</td><td>LLM</td><td>22.80</td><td>27.28</td><td>23.93</td><td>21.20%</td><td>25.45</td><td>27.60%</td><td>26.03</td><td>56.40%</td><td>27.08</td><td>88.20%</td></tr><tr><td>Acc.</td><td>15.51</td><td>19.75</td><td>16.38</td><td>21.20%</td><td>17.70</td><td>27.60%</td><td>17.75</td><td>56.40%</td><td>19.57</td><td>88.20%</td></tr><tr><td rowspan="2">Dyn-VQA ch</td><td>LLM</td><td>21.32</td><td>44.20</td><td>25.63</td><td>12.48%</td><td>28.29</td><td>27.00%</td><td>37.81</td><td>79.10%</td><td>43.54</td><td>97.42%</td></tr><tr><td>Acc.</td><td>20.74</td><td>46.91</td><td>24.15</td><td>12.48%</td><td>28.07</td><td>27.00%</td><td>41.18</td><td>79.10%</td><td>46.23</td><td>97.42%</td></tr><tr><td rowspan="2">Dyn-VQA en</td><td>LLM</td><td>24.90</td><td>38.36</td><td>25.63</td><td>12.73%</td><td>29.41</td><td>33.57%</td><td>32.31</td><td>60.56%</td><td>37.77</td><td>96.78%</td></tr><tr><td>Acc.</td><td>24.37</td><td>43.28</td><td>26.51</td><td>12.73%</td><td>30.22</td><td>33.57%</td><td>35.49</td><td>60.56%</td><td>43.01</td><td>96.78%</td></tr><tr><td rowspan="2">NoCaps</td><td>LLM</td><td>63.10</td><td>59.39</td><td>62.95</td><td>2.00%</td><td>63.12</td><td>0.20%</td><td>61.40</td><td>32.40%</td><td>62.50</td><td>6.20%</td></tr><tr><td>Acc.</td><td>43.89</td><td>40.45</td><td>43.62</td><td>2.00%</td><td>43.88</td><td>0.20%</td><td>42.50</td><td>32.40%</td><td>43.48</td><td>6.20%</td></tr><tr><td rowspan="2">Visual7W</td><td>LLM</td><td>58.54</td><td>57.68</td><td>58.17</td><td>2.44%</td><td>58.24</td><td>7.67%</td><td>58.16</td><td>10.98%</td><td>56.98</td><td>54.70%</td></tr><tr><td>Acc.</td><td>46.55</td><td>46.62</td><td>46.40</td><td>2.44%</td><td>46.27</td><td>7.67%</td><td>46.55</td><td>10.98%</td><td>46.18</td><td>54.70%</td></tr><tr><td rowspan="2">Mix</td><td>LLM</td><td>35.07</td><td>45.37</td><td>37.17</td><td>13.50%</td><td>39.38</td><td>25.00%</td><td>42.46</td><td>54.83%</td><td>45.63</td><td>74.50%</td></tr><tr><td>Acc.</td><td>25.81</td><td>35.23</td><td>28.11</td><td>13.50%</td><td>29.08</td><td>25.00%</td><td>33.23</td><td>54.83%</td><td>35.83</td><td>74.50%</td></tr></table>
+
+Table 11: Knowledge Boundary model (Qwen-VL-7B-Chat) as a surrogate boundary identifier for other VLLMs. Results evaluated by token accuracy.   
+
+<table><tr><td></td><td>Metric: Acc.</td><td>No RAG</td><td>All RAG</td><td>Prompt-based</td><td>%</td><td>HKB</td><td>%</td><td>SKB</td><td>%</td><td>Human</td><td>%</td></tr><tr><td rowspan="4">Life VQA</td><td>Ds.-VL-Chat</td><td>10.82</td><td>36.79</td><td>14.12</td><td>12.75%</td><td>36.12</td><td>96.64%</td><td>30.97</td><td>61.74%</td><td>30.50</td><td>71.14%</td></tr><tr><td>Qwen-VL-Max</td><td>24.21</td><td>42.30</td><td>27.66</td><td>12.75%</td><td>41.96</td><td>96.64%</td><td>38.37</td><td>61.74%</td><td>38.20</td><td>71.14%</td></tr><tr><td>Qwen-VL-2</td><td>23.06</td><td>41.05</td><td>27.64</td><td>12.75%</td><td>40.71</td><td>96.64%</td><td>37.27</td><td>61.74%</td><td>37.05</td><td>71.14%</td></tr><tr><td>GPT-4o</td><td>31.72</td><td>40.85</td><td>32.81</td><td>12.75%</td><td>40.85</td><td>96.64%</td><td>38.47</td><td>61.74%</td><td>41.88</td><td>71.14%</td></tr><tr><td rowspan="4">Private VQA</td><td>Ds.-VL-Chat</td><td>15.51</td><td>19.75</td><td>16.65</td><td>14.80%</td><td>19.75</td><td>99.20%</td><td>18.20</td><td>67.80%</td><td>18.51</td><td>72.00%</td></tr><tr><td>Qwen-VL-Max</td><td>27.93</td><td>28.14</td><td>28.08</td><td>14.80%</td><td>28.29</td><td>99.20%</td><td>27.68</td><td>67.80%</td><td>28.96</td><td>72.00%</td></tr><tr><td>Qwen-VL-2</td><td>27.69</td><td>30.72</td><td>27.75</td><td>14.80%</td><td>30.87</td><td>99.20%</td><td>28.96</td><td>67.80%</td><td>31.13</td><td>72.00%</td></tr><tr><td>GPT-4o</td><td>31.12</td><td>27.02</td><td>30.88</td><td>14.80%</td><td>26.87</td><td>99.20%</td><td>27.72</td><td>67.80%</td><td>29.10</td><td>72.00%</td></tr><tr><td rowspan="4">Dyn-VQA ch</td><td>Ds.-VL-Chat</td><td>20.74</td><td>46.91</td><td>22.37</td><td>6.38%</td><td>46.05</td><td>95.66%</td><td>44.13</td><td>84.26%</td><td>33.60</td><td>46.95%</td></tr><tr><td>Qwen-VL-Max</td><td>31.53</td><td>46.73</td><td>33.53</td><td>6.38%</td><td>46.38</td><td>95.66%</td><td>44.82</td><td>84.26%</td><td>39.79</td><td>46.95%</td></tr><tr><td>Qwen-VL-2</td><td>31.52</td><td>46.70</td><td>33.52</td><td>6.38%</td><td>46.28</td><td>95.66%</td><td>44.69</td><td>84.26%</td><td>39.85</td><td>46.95%</td></tr><tr><td>GPT-4o</td><td>36.46</td><td>51.27</td><td>37.32</td><td>6.38%</td><td>50.85</td><td>95.66%</td><td>49.4</td><td>84.26%</td><td>42.45</td><td>46.95%</td></tr><tr><td rowspan="4">Dyn-VQA en</td><td>Ds.-VL-Chat</td><td>24.37</td><td>43.28</td><td>26.80</td><td>14.13%</td><td>42.08</td><td>89.79%</td><td>40.61</td><td>76.08%</td><td>31.67</td><td>29.51%</td></tr><tr><td>Qwen-VL-Max</td><td>37.54</td><td>45.27</td><td>38.03</td><td>14.13%</td><td>44.30</td><td>89.79%</td><td>43.55</td><td>76.08%</td><td>39.40</td><td>29.51%</td></tr><tr><td>Qwen-VL-2</td><td>37.37</td><td>45.16</td><td>37.25</td><td>14.13%</td><td>43.84</td><td>89.79%</td><td>43.48</td><td>76.08%</td><td>40.66</td><td>29.51%</td></tr><tr><td>GPT-4o</td><td>43.33</td><td>49.71</td><td>42.40</td><td>14.13%</td><td>48.48</td><td>89.79%</td><td>47.66</td><td>76.08%</td><td>45.07</td><td>29.51%</td></tr><tr><td rowspan="4">NoCaps</td><td>Ds.-VL-Chat</td><td>43.89</td><td>40.45</td><td>43.89</td><td>0.00%</td><td>42.76</td><td>38.40%</td><td>43.89</td><td>0.00%</td><td>43.89</td><td>0.00%</td></tr><tr><td>Qwen-VL-Max</td><td>37.47</td><td>34.55</td><td>37.47</td><td>0.00%</td><td>36.75</td><td>38.40%</td><td>37.47</td><td>0.00%</td><td>37.47</td><td>0.00%</td></tr><tr><td>Qwen-VL-2</td><td>37.26</td><td>34.61</td><td>37.26</td><td>0.00%</td><td>36.35</td><td>38.40%</td><td>37.26</td><td>0.00%</td><td>37.26</td><td>0.00%</td></tr><tr><td>GPT-4o</td><td>32.12</td><td>36.25</td><td>32.12</td><td>0.00%</td><td>33.22</td><td>38.40%</td><td>32.12</td><td>0.00%</td><td>32.12</td><td>0.00%</td></tr><tr><td rowspan="4">Visual7W</td><td>Ds.-VL-Chat</td><td>46.55</td><td>46.62</td><td>46.29</td><td>31.36%</td><td>46.03</td><td>35.37%</td><td>46.58</td><td>2.96%</td><td>46.55</td><td>0.52%</td></tr><tr><td>Qwen-VL-Max</td><td>46.07</td><td>44.44</td><td>48.63</td><td>31.36%</td><td>45.16</td><td>35.37%</td><td>46.13</td><td>2.96%</td><td>46.07</td><td>0.52%</td></tr><tr><td>Qwen-VL-2</td><td>45.94</td><td>43.86</td><td>48.47</td><td>31.36%</td><td>45.06</td><td>35.37%</td><td>45.99</td><td>2.96%</td><td>45.94</td><td>0.52%</td></tr><tr><td>GPT-4o</td><td>41.59</td><td>37.16</td><td>40.09</td><td>31.36%</td><td>39.41</td><td>35.37%</td><td>41.80</td><td>2.96%</td><td>41.48</td><td>0.52%</td></tr><tr><td rowspan="4">Mix</td><td>Ds.-VL-Chat</td><td>25.81</td><td>35.23</td><td>26.55</td><td>12.67%</td><td>35.38</td><td>76.83%</td><td>33.06</td><td>49.33%</td><td>32.73</td><td>38.33%</td></tr><tr><td>Qwen-VL-Max</td><td>32.35</td><td>34.78</td><td>33.00</td><td>12.67%</td><td>35.48</td><td>76.83%</td><td>34.84</td><td>49.33%</td><td>35.51</td><td>38.33%</td></tr><tr><td>Qwen-VL-2</td><td>32.59</td><td>35.56</td><td>33.27</td><td>12.67%</td><td>36.29</td><td>76.83%</td><td>35.62</td><td>49.33%</td><td>36.33</td><td>38.33%</td></tr><tr><td>GPT-4o</td><td>34.52</td><td>35.96</td><td>33.99</td><td>12.67%</td><td>35.90</td><td>76.83%</td><td>35.86</td><td>49.33%</td><td>36.49</td><td>38.33%</td></tr></table>
+
+Table 12: Knowledge Boundary model (DeepSeek-VL-7B-Chat) as a surrogate boundary identifier for other VLLMs. Results evaluated by LLM.   
+
+<table><tr><td></td><td>Metric: LLM</td><td>No RAG</td><td>All RAG</td><td>Prompt-based</td><td>%</td><td>HKB</td><td>%</td><td>SKB</td><td>%</td><td>Human</td><td>%</td></tr><tr><td rowspan="4">Life VQA</td><td>Qwen-VL-Chat</td><td>31.14</td><td>42.85</td><td>33.62</td><td>30.20%</td><td>37.08</td><td>46.31%</td><td>41.78</td><td>73.83%</td><td>43.05</td><td>96.64%</td></tr><tr><td>Qwen-VL-Max</td><td>44.09</td><td>56.64</td><td>46.51</td><td>30.20%</td><td>48.59</td><td>46.31%</td><td>54.16</td><td>73.83%</td><td>56.51</td><td>96.64%</td></tr><tr><td>Qwen-VL-2</td><td>42.95</td><td>54.23</td><td>45.00</td><td>30.20%</td><td>48.66</td><td>46.31%</td><td>53.36</td><td>73.83%</td><td>54.23</td><td>96.64%</td></tr><tr><td>GPT-4o</td><td>47.45</td><td>56.38</td><td>53.15</td><td>30.20%</td><td>54.16</td><td>46.31%</td><td>55.37</td><td>73.83%</td><td>56.11</td><td>96.64%</td></tr><tr><td rowspan="4">Private VQA</td><td>Qwen-VL-Chat</td><td>24.45</td><td>26.16</td><td>25.21</td><td>21.20%</td><td>25.35</td><td>27.60%</td><td>26.08</td><td>56.40%</td><td>26.01</td><td>88.20%</td></tr><tr><td>Qwen-VL-Max</td><td>36.84</td><td>42.97</td><td>36.45</td><td>21.20%</td><td>39.16</td><td>27.60%</td><td>42.26</td><td>56.40%</td><td>43.73</td><td>88.20%</td></tr><tr><td>Qwen-VL-2</td><td>36.76</td><td>38.20</td><td>36.65</td><td>21.20%</td><td>38.52</td><td>27.60%</td><td>39.37</td><td>56.40%</td><td>39.03</td><td>88.20%</td></tr><tr><td>GPT-4o</td><td>40.13</td><td>38.72</td><td>39.15</td><td>21.20%</td><td>40.59</td><td>27.60%</td><td>40.76</td><td>56.40%</td><td>39.56</td><td>88.20%</td></tr><tr><td rowspan="4">Dyn-VQA ch</td><td>Qwen-VL-Chat</td><td>37.73</td><td>44.68</td><td>38.44</td><td>12.48%</td><td>40.31</td><td>27.00%</td><td>39.63</td><td>79.10%</td><td>43.85</td><td>97.42%</td></tr><tr><td>Qwen-VL-Max</td><td>32.67</td><td>50.85</td><td>35.11</td><td>12.48%</td><td>37.20</td><td>27.00%</td><td>46.62</td><td>79.10%</td><td>50.32</td><td>97.42%</td></tr><tr><td>Qwen-VL-2</td><td>45.95</td><td>50.91</td><td>46.33</td><td>12.48%</td><td>48.03</td><td>27.00%</td><td>46.42</td><td>79.10%</td><td>50.13</td><td>97.42%</td></tr><tr><td>GPT-4o</td><td>42.10</td><td>56.51</td><td>44.55</td><td>12.48%</td><td>44.80</td><td>27.00%</td><td>51.99</td><td>79.10%</td><td>56.23</td><td>97.42%</td></tr><tr><td rowspan="4">Dyn-VQA en</td><td>Qwen-VL-Chat</td><td>22.07</td><td>35.23</td><td>23.58</td><td>12.73%</td><td>26.91</td><td>33.57%</td><td>30.06</td><td>60.56%</td><td>34.27</td><td>96.78%</td></tr><tr><td>Qwen-VL-Max</td><td>19.41</td><td>39.90</td><td>22.86</td><td>12.73%</td><td>24.71</td><td>33.57%</td><td>36.01</td><td>60.56%</td><td>39.44</td><td>96.78%</td></tr><tr><td>Qwen-VL-2</td><td>37.90</td><td>44.29</td><td>38.58</td><td>12.73%</td><td>40.45</td><td>33.57%</td><td>40.11</td><td>60.56%</td><td>43.58</td><td>96.78%</td></tr><tr><td>GPT-4o</td><td>32.73</td><td>51.17</td><td>35.25</td><td>12.73%</td><td>37.36</td><td>33.57%</td><td>47.15</td><td>60.56%</td><td>50.65</td><td>96.78%</td></tr><tr><td rowspan="4">NoCaps</td><td>Qwen-VL-Chat</td><td>50.46</td><td>30.41</td><td>50.00</td><td>2.00%</td><td>50.48</td><td>0.20%</td><td>44.43</td><td>32.40%</td><td>49.48</td><td>6.20%</td></tr><tr><td>Qwen-VL-Max</td><td>62.04</td><td>49.63</td><td>61.82</td><td>2.00%</td><td>61.92</td><td>0.20%</td><td>57.63</td><td>32.40%</td><td>61.16</td><td>6.20%</td></tr><tr><td>Qwen-VL-2</td><td>61.88</td><td>49.84</td><td>61.66</td><td>2.00%</td><td>61.78</td><td>0.20%</td><td>57.44</td><td>32.40%</td><td>60.92</td><td>6.20%</td></tr><tr><td>GPT-4o</td><td>61.58</td><td>64.51</td><td>61.68</td><td>2.00%</td><td>61.56</td><td>0.20%</td><td>62.00</td><td>32.40%</td><td>61.68</td><td>6.20%</td></tr><tr><td rowspan="4">Visual7W</td><td>Qwen-VL-Chat</td><td>55.53</td><td>54.52</td><td>55.45</td><td>2.44%</td><td>55.76</td><td>7.67%</td><td>55.31</td><td>10.98%</td><td>55.01</td><td>54.70%</td></tr><tr><td>Qwen-VL-Max</td><td>61.72</td><td>58.16</td><td>61.59</td><td>2.44%</td><td>61.27</td><td>7.67%</td><td>61.08</td><td>10.98%</td><td>59.04</td><td>54.70%</td></tr><tr><td>Qwen-VL-2</td><td>61.81</td><td>58.07</td><td>61.58</td><td>2.44%</td><td>61.25</td><td>7.67%</td><td>61.23</td><td>10.98%</td><td>58.78</td><td>54.70%</td></tr><tr><td>GPT-4o</td><td>53.34</td><td>47.44</td><td>53.30</td><td>2.44%</td><td>52.71</td><td>7.67%</td><td>52.70</td><td>10.98%</td><td>49.97</td><td>54.70%</td></tr><tr><td rowspan="4">Mix</td><td>Qwen-VL-Chat</td><td>34.58</td><td>39.03</td><td>35.54</td><td>13.50%</td><td>37.12</td><td>25.00%</td><td>39.76</td><td>54.83%</td><td>42.61</td><td>74.50%</td></tr><tr><td>Qwen-VL-Max</td><td>46.13</td><td>49.02</td><td>46.47</td><td>13.50%</td><td>47.43</td><td>25.00%</td><td>48.98</td><td>54.83%</td><td>51.39</td><td>74.50%</td></tr><tr><td>Qwen-VL-2</td><td>46.26</td><td>47.84</td><td>46.64</td><td>13.50%</td><td>48.17</td><td>25.00%</td><td>48.55</td><td>54.83%</td><td>50.13</td><td>74.50%</td></tr><tr><td>GPT-4o</td><td>51.21</td><td>52.70</td><td>51.81</td><td>13.50%</td><td>52.28</td><td>25.00%</td><td>52.04</td><td>54.83%</td><td>53.42</td><td>74.50%</td></tr></table>
+
+![](images/3e1dfc95fe9c6b9a8f028102f7416e37aa93e4063b8d6469ff08955e100525a8.jpg)
+
+![](images/15e27279c04b6b2b36b947d34b1228bc5aa2d94847a61cb10a844828311af6a3.jpg)
+
+![](images/3dbcbc1c236044c2a4823c10ff300f1c9b4c4f8a8f9a30e034ac4d2a36983272.jpg)
+
+![](images/b0f949c01647cdf7f3ad7da68a95c06a19f3a1c90a5842e185982ebd1e0ebfed.jpg)  
+Figure 4: Qwen-VL-Max and Qwen-VL-2 performance on the MMMU validation set with the Knowledge Boundary model trained on Human-labeled data.
+
+Table 13: Knowledge Boundary model (DeepSeek-VL-7B-Chat) as a surrogate boundary identifier for other VLLMs. Results were evaluated by token accuracy.   
+
+<table><tr><td></td><td>Metric: Acc.</td><td>No RAG</td><td>All RAG</td><td>Prompt-based</td><td>%</td><td>HKB</td><td>%</td><td>SKB</td><td>%</td><td>Human</td><td>%</td></tr><tr><td rowspan="4">Life VQA</td><td>Qwen-VL-Chat</td><td>17.80</td><td>36.11</td><td>23.68</td><td>30.20%</td><td>28.05</td><td>46.31%</td><td>34.43</td><td>73.83%</td><td>36.78</td><td>96.64%</td></tr><tr><td>Qwen-VL-Max</td><td>25.42</td><td>42.30</td><td>30.09</td><td>30.20%</td><td>32.83</td><td>46.31%</td><td>38.38</td><td>73.83%</td><td>42.07</td><td>96.64%</td></tr><tr><td>Qwen-VL-2</td><td>25.29</td><td>41.05</td><td>29.77</td><td>30.20%</td><td>33.75</td><td>46.31%</td><td>38.48</td><td>73.83%</td><td>40.83</td><td>96.64%</td></tr><tr><td>GPT-4o</td><td>31.72</td><td>40.85</td><td>36.49</td><td>30.20%</td><td>38.53</td><td>46.31%</td><td>40.01</td><td>73.83%</td><td>42.19</td><td>96.64%</td></tr><tr><td rowspan="4">Private VQA</td><td>Qwen-VL-Chat</td><td>16.26</td><td>18.40</td><td>17.28</td><td>21.20%</td><td>18.11</td><td>27.60%</td><td>18.34</td><td>56.40%</td><td>18.90</td><td>88.20%</td></tr><tr><td>Qwen-VL-Max</td><td>27.12</td><td>28.14</td><td>26.77</td><td>21.20%</td><td>27.94</td><td>27.60%</td><td>28.18</td><td>56.40%</td><td>28.31</td><td>88.20%</td></tr><tr><td>Qwen-VL-2</td><td>27.04</td><td>30.72</td><td>27.89</td><td>21.20%</td><td>28.78</td><td>27.60%</td><td>29.94</td><td>56.40%</td><td>30.95</td><td>88.20%</td></tr><tr><td>GPT-4o</td><td>31.12</td><td>27.02</td><td>29.74</td><td>21.20%</td><td>30.78</td><td>27.60%</td><td>29.73</td><td>56.40%</td><td>28.24</td><td>88.20%</td></tr><tr><td rowspan="4">Dyn-VQA ch</td><td>Qwen-VL-Chat</td><td>37.37</td><td>45.16</td><td>38.25</td><td>12.48%</td><td>39.83</td><td>27.00%</td><td>39.37</td><td>79.10%</td><td>44.84</td><td>97.42%</td></tr><tr><td>Qwen-VL-Max</td><td>31.66</td><td>46.70</td><td>34.29</td><td>12.48%</td><td>35.11</td><td>27.00%</td><td>42.80</td><td>79.10%</td><td>46.35</td><td>97.42%</td></tr><tr><td>Qwen-VL-2</td><td>43.33</td><td>49.71</td><td>43.68</td><td>12.48%</td><td>45.47</td><td>27.00%</td><td>45.17</td><td>79.10%</td><td>49.28</td><td>97.42%</td></tr><tr><td>GPT-4o</td><td>36.46</td><td>51.27</td><td>38.75</td><td>12.48%</td><td>39.78</td><td>27.00%</td><td>46.96</td><td>79.10%</td><td>51.13</td><td>97.42%</td></tr><tr><td rowspan="4">Dyn-VQA en</td><td>Qwen-VL-Chat</td><td>25.64</td><td>41.87</td><td>27.33</td><td>12.73%</td><td>31.66</td><td>33.57%</td><td>35.00</td><td>60.56%</td><td>41.63</td><td>96.78%</td></tr><tr><td>Qwen-VL-Max</td><td>23.41</td><td>43.06</td><td>26.81</td><td>12.73%</td><td>29.04</td><td>33.57%</td><td>39.36</td><td>60.56%</td><td>42.57</td><td>96.78%</td></tr><tr><td>Qwen-VL-2</td><td>37.54</td><td>45.27</td><td>37.52</td><td>12.73%</td><td>40.05</td><td>33.57%</td><td>40.50</td><td>60.56%</td><td>44.95</td><td>96.78%</td></tr><tr><td>GPT-4o</td><td>31.66</td><td>46.73</td><td>34.25</td><td>12.73%</td><td>34.93</td><td>33.57%</td><td>42.96</td><td>60.56%</td><td>46.39</td><td>96.78%</td></tr><tr><td rowspan="4">NoCaps</td><td>Qwen-VL-Chat</td><td>40.50</td><td>30.72</td><td>40.39</td><td>2.00%</td><td>40.49</td><td>0.20%</td><td>37.88</td><td>32.40%</td><td>39.92</td><td>6.20%</td></tr><tr><td>Qwen-VL-Max</td><td>37.47</td><td>34.55</td><td>37.44</td><td>2.00%</td><td>37.42</td><td>0.20%</td><td>36.47</td><td>32.40%</td><td>37.22</td><td>6.20%</td></tr><tr><td>Qwen-VL-2</td><td>37.26</td><td>34.61</td><td>37.30</td><td>2.00%</td><td>37.21</td><td>0.20%</td><td>36.21</td><td>32.40%</td><td>37.04</td><td>6.20%</td></tr><tr><td>GPT-4o</td><td>32.12</td><td>36.25</td><td>32.23</td><td>2.00%</td><td>32.12</td><td>0.20%</td><td>32.96</td><td>32.40%</td><td>32.35</td><td>6.20%</td></tr><tr><td rowspan="4">Visual7W</td><td>Qwen-VL-Chat</td><td>44.34</td><td>44.94</td><td>44.26</td><td>2.44%</td><td>44.64</td><td>7.67%</td><td>44.86</td><td>10.98%</td><td>45.11</td><td>54.70%</td></tr><tr><td>Qwen-VL-Max</td><td>49.41</td><td>45.13</td><td>49.39</td><td>2.44%</td><td>49.28</td><td>7.67%</td><td>48.13</td><td>10.98%</td><td>46.04</td><td>54.70%</td></tr><tr><td>Qwen-VL-2</td><td>49.71</td><td>44.19</td><td>49.48</td><td>2.44%</td><td>49.58</td><td>7.67%</td><td>48.43</td><td>10.98%</td><td>45.51</td><td>54.70%</td></tr><tr><td>GPT-4o</td><td>41.59</td><td>37.16</td><td>41.76</td><td>2.44%</td><td>40.96</td><td>7.67%</td><td>40.91</td><td>10.98%</td><td>39.10</td><td>54.70%</td></tr><tr><td rowspan="4">Mix</td><td>Qwen-VL-Chat</td><td>26.13</td><td>32.39</td><td>28.00</td><td>13.50%</td><td>29.55</td><td>25.00%</td><td>32.46</td><td>54.83%</td><td>34.06</td><td>74.50%</td></tr><tr><td>Qwen-VL-Max</td><td>32.35</td><td>34.78</td><td>32.91</td><td>13.50%</td><td>33.17</td><td>25.00%</td><td>35.12</td><td>54.83%</td><td>35.96</td><td>74.50%</td></tr><tr><td>Qwen-VL-2</td><td>32.45</td><td>35.56</td><td>33.51</td><td>13.50%</td><td>33.86</td><td>25.00%</td><td>35.88</td><td>54.83%</td><td>36.63</td><td>74.50%</td></tr><tr><td>GPT-4o</td><td>34.52</td><td>35.96</td><td>35.17</td><td>13.50%</td><td>35.77</td><td>25.00%</td><td>35.86</td><td>54.83%</td><td>36.24</td><td>74.50%</td></tr></table>
+
+Table 14: Results evaluated by LLM on MMMU validation set.   
+
+<table><tr><td></td><td></td><td>No RAG</td><td>All RAG</td><td>Human</td><td>%</td><td>HKB</td><td>%</td><td>SKB</td><td>%</td></tr><tr><td rowspan="4">MMMU</td><td>Qwen-VL-Chat</td><td>20.12</td><td>20.28</td><td>21.24</td><td>6.88%</td><td>20.35</td><td>97.08%</td><td>20.18</td><td>61.26%</td></tr><tr><td>Qwen-VL-Max</td><td>51.33</td><td>41.37</td><td>52.67</td><td>6.88%</td><td>41.46</td><td>97.08%</td><td>44.40</td><td>61.26%</td></tr><tr><td>Qwen-VL-2</td><td>51.45</td><td>42.39</td><td>51.93</td><td>6.88%</td><td>42.54</td><td>97.08%</td><td>45.61</td><td>61.26%</td></tr><tr><td>GPT-4o</td><td>56.60</td><td>56.64</td><td>57.36</td><td>6.88%</td><td>56.92</td><td>97.08%</td><td>56.91</td><td>61.26%</td></tr></table>

paper_markdowns/bamboo-01266.md

@@ -0,0 +1,320 @@
+# IG-Pruning: Input-Guided Block Pruning for Large Language Models
+
+Kangyu Qiao $^{1,3}$ , Shaolei Zhang $^{1,3}$ , Yang Feng $^{1,2,3\dagger}$
+
+<sup>1</sup>Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences (ICT/CAS)
+
+$^{2}$ Key Laboratory of AI Safety, Chinese Academy of Sciences   
+<sup>3</sup> University of Chinese Academy of Sciences, Beijing, China
+
+{qiaokangyu24s, zhangshaolei20z, fengyang}@ict.ac.cn
+
+# Abstract
+
+With the growing computational demands of large language models (LLMs), efficient inference has become increasingly critical for practical deployment. Depth pruning has emerged as a promising approach for reducing the computational costs of large language models by removing transformer layers. However, existing methods typically rely on fixed block masks, which can lead to suboptimal performance across different tasks and inputs. In this paper, we propose IG-Pruning, a novel input-aware block-wise pruning method that dynamically selects layer masks at inference time. Our approach consists of two stages: (1) Discovering diverse mask candidates through semantic clustering and $L_{0}$ optimization, and (2) Implementing efficient dynamic pruning without the need for extensive training. Experimental results demonstrate that our method consistently outperforms state-of-the-art static depth pruning methods, making it particularly suitable for resource-constrained deployment scenarios.
+
+# 1 Introduction
+
+Large Language Models (LLMs) (Brown et al., 2020; AI@Meta, 2024; QwenTeam, 2025; Zhang et al., 2024b, 2023a) have demonstrated remarkable capabilities across a wide range of natural language processing tasks. However, their immense model size and computational demands present significant deployment challenges (Wang et al., 2024; Zhou et al., 2024), particularly in resource-constrained environments and for latency-sensitive real-time inference scenarios. To address this, pruning techniques have become a crucial area of research (Ma et al., 2023; Sun et al., 2023; Frantar and Alistarh, 2023; Ashkboos et al., 2024; Fang et al., 2024; Ling et al., 2024; Zhang et al., 2023b; Gu et al., 2021), being highly favored due to their potential for reducing parameters for efficient inference.
+
+![](images/ed4d74df512e83e90e4512a85c211d1cfaf65144a39ba2bad12c817e7054771a.jpg)  
+Figure 1: Different Mask structure can lead to similar perplexity scores but exhibit significant performance variations across different downstream tasks.
+
+As large LLMs continue to scale in size, researchers have identified significant redundancy within their layer structures. Studies from Liu et al. (2023); Men et al. (2024); Gromov et al. (2024) reveal that word embeddings in adjacent layers often change slightly due to residual connection, suggesting that selective layer removal may have minimal impact on performance. These findings have motivated increasing research interest in discovering effective depth pruning strategies for LLMs, which aim to reduce the number of transformer layers or blocks in the model architecture while maintaining performance. In recent years, depth pruning methods (Song et al., 2024; Sieberling et al., 2024; Kim et al., 2024; Ling et al., 2024) have emerged as a promising approach for reducing LLM computational costs. Compared with fine-grained structured pruning methods (which remove the neurons or channels), depth pruning has demonstrated superior computational efficiency advantages in practical deployments (Kim et al., 2024).
+
+However, a critical limitation of existing depth
+
+pruning methods is their reliance on a fixed layer pruning mask determined offline based on global layer importance metrics at a given sparsity level. This static approach is problematic because different fixed pruning masks, even at the same sparsity level, can exhibit significant performance variations across different downstream tasks. For instance, we observe that perplexity (PPL) is commonly used as a saliency metric for layer pruning (Sieberling et al., 2024; Kim et al., 2024), but as illustrated in Figure 1, different mask structures can achieve similar perplexity scores while exhibiting substantially different performance across various downstream tasks. To overcome these limitations and enable adaptive computation pathways, researchers have explored various dynamic routing approaches (Elhoushi et al., 2024; Fan et al., 2024; Del Corro et al.; Schuster et al., 2022; Raposo et al., 2024; Tan et al., 2024; Wu et al., 2024). However, most existing methods perform dynamic routing at the token level, which introduces significant drawbacks: they lack comprehensive understanding of sentence-level semantics, potentially leading to globally inconsistent routing decisions. Furthermore, these approaches typically incur substantial computational overhead from frequent token-level routing calls and require extensive training of additional router networks alongside the original model parameters, making them computationally expensive and time-consuming to implement.
+
+To address the challenges identified in existing works, we propose IG-Pruning, a novel blockwise pruning method that dynamically selects layer masks based on input characteristics at inference time. Our approach consists of two stages: (1) a semantic clustering-based mask discovery stage that identifies diverse, high-quality mask candidates while capturing global information through rapidly converging trainable masks, and (2) a lightweight inference-time routing mechanism that requires no additional training of the base model parameters, enabling efficient dynamic adaptation to varying inputs.
+
+Extensive evaluations demonstrate that our approach consistently outperforms state-of-the-art static pruning methods across different sparsity levels and model architectures on various zero-shot tasks. For Llama-3-8B at $25\%$ sparsity, IG-Pruning preserves $87.18\%$ of dense model performance, surpassing the best baseline by 10.86 percentage points. Similarly, for Qwen-3-8B, IG-Pruning maintains $96.01\%$ of dense model perfor
+
+mance at $13.9\%$ sparsity, compared to $90.37\%$ for the best baseline.
+
+Our method trains only mask parameters while keeping model weights frozen, enabling rapid adaptation with minimal computational overhead. During inference stage, it incurs negligible routing overhead by efficiently skipping unimportant layers; and these advancements provide a viable path toward deploying powerful LLMs in environments with limited computational resources.
+
+# 2 Related Work
+
+Most static depth pruning approaches focus on calculating saliency scores for each transformer block, and removing layers according to these scores. Commonly used saliency metrics include cosine similarity (Song et al., 2024; Men et al., 2024), magnitude, second-order derivatives (Kim et al., 2024), and perplexity (Sieberling et al., 2024). These works calculate layer importance as if they are independent of others, which ignores the coupling connections between layers. As discovered in Fan et al. (2024), contiguous middle layers often exhibit similar saliency scores, which inspired Chen et al. (2024) to use small FFN or transformer blocks to replace contiguous layers. EvoPress (Sieberling et al., 2024) found that lower per-layer error does not necessarily lead to better performance, and proposed an evolutionary search algorithm to generate offspring from parent masks, then select better candidates with lower perplexity or KL divergence. Rather than directly removing layers, LaCO (Yang et al., 2024) collapses consecutive redundant model layers via layer averaging. MKA (Liu et al., 2024a) transforms layer activations into low-dimensional manifolds using diffusion kernel algorithms and evaluates saliency using the NPIB metric.
+
+Beyond one-shot pruning approaches, dynamically skipping unimportant layers during inference has also emerged as a promising research direction. Early approaches include early skipping (Del Corro et al.; Zhu et al., 2024), early exit (Elhoushi et al., 2024), and periodic skipping (Liu et al., 2024b). However, these methods typically require routers for each layer and demand elaborate training of original weights to recover performance. Dynamic skipping has also been adopted in long-context and multimodal models. Adaskip (He et al., 2024) focused on adaptive layer skipping for long-context models, accelerating both prefetching and decoding phases. RoE (Wu et al., 2024) employs token-wise
+
+![](images/2f0479a4efb6dd76c6ff05862a9992e5b378dda65bdf9e8334927a25f4099187.jpg)  
+Figure 2: Overview of our method. The approach consists of two stages: (1) Preparing mask candidates through input clustering and soft mask training; (2) Dynamic pruning that selects the appropriate mask for each input at inference time. This enables efficient computation by selectively skipping layers based on input characteristics while maintaining model performance.
+
+routing for multimodal LLMs and trains low-rank adapters to replace the skipped layers.
+
+# 3 Method
+
+As illustrated in Figure 2, our framework consists of two main stages: (1) Mask candidate discovery and (2) Dynamic routing. In the first stage, we cluster the semantic space of inputs and train clusterspecific masks using hard concrete distributions, resulting in diverse yet high-quality mask candidates that each specialize in handling different input patterns. During the second stage, at inference time, we employ a lightweight routing mechanism that maps each input to its most semantically similar cluster and applies the corresponding pre-trained mask, enabling efficient dynamic adaptation without requiring additional training of router networks or base model parameters.
+
+# 3.1 Stage 1: Discovering Mask Candidates
+
+In the first stage, we aim to discover a set of effective mask candidates for dynamic routing. Unlike existing routing methods that typically employ per-layer router networks to make skip decisions, we propose a global routing strategy that dynamically
+
+selects routing paths from a carefully curated candidate mask set.
+
+We design our mask candidate discovery process to satisfy two key requirements: Quality: Masks must maintain strong general language generation capabilities. Diversity: The candidate set must provide sufficient variety to handle different input patterns effectively.
+
+To meet these requirements, we leverage hard concrete distribution to model transformer block masks to capture global routing information, and apply $L_{0}$ optimization with cluster-specific calibration data, generating masks that cover diverse computational needs.
+
+Input Clustering. First, an encoder is used to encode each sentence $x_{i}$ in the calibration dataset into a fixed-dimensional embedding vector $e_{i}$ :
+
+$$
+e _ {i} = \operatorname {E n c o d e r} \left(x _ {i}\right) \tag {1}
+$$
+
+where $x_{i}$ represents the $i$ -th input, and $e_{i} \in \mathbb{R}^{d}$ , with $d$ being the dimension of the embedding vector. Next, the K-means algorithm is applied to cluster all embedding vectors $e_{1}, e_{2}, \ldots, e_{M}$ where $M$ is the size of the calibration set. The K-means algorithm aims to find $N$ clusters $S =$
+
+$\{S_1,S_2,\ldots ,S_N\}$ that minimize the within-cluster sum of squares:
+
+$$
+\arg \min  _ {S} \sum_ {k = 1} ^ {N} \sum_ {e _ {i} \in S _ {k}} \left\| e _ {i} - \mu_ {k} \right\| ^ {2} \tag {2}
+$$
+
+where $\mu_{k}$ is the centroid of cluster $S_{k}$ . This results in $N$ cluster centers, each representing a class of semantically similar input sentences.
+
+Mask Training. Hard concrete distribution (Louizos et al., 2018; Xia et al., 2022, 2024) has been widely adopted in structured pruning. Following prior work, we incorporate hard concrete distribution to model transformer block masks, and use $L_{0}$ optimization to generate layer masks, enabling joint learning of all layer masks while incorporating global information.
+
+For each cluster $S_{k}$ , we train a dedicated layer mask $z^{(k)} \in \mathbb{R}^{B}$ using hard concrete distribution and Lagrangian sparsity, where $B$ is the total number of blocks in the model (for block-wise pruning, $B = 2L$ where $L$ is the number of transformer layers, representing both attention and FFN blocks separately). Specifically, the masks $z^{(k)}$ are modeled as follows:
+
+First, for each block $i$ in the model, sample $u_{i}^{(k)}$ from a uniform distribution:
+
+$$
+u _ {i} ^ {(k)} \sim \operatorname {U n i f o r m} (0, 1), \quad i \in \{1, 2, \dots , B \} \tag {3}
+$$
+
+Then, compute the soft mask value $s_i^{(k)}$ for each block using the sigmoid function:
+
+$$
+s _ {i} ^ {(k)} = \sigma \left(\frac {1}{\beta} \log \frac {u _ {i} ^ {(k)}}{1 - u _ {i} ^ {(k)}} + \log \alpha_ {i} ^ {(k)}\right) \tag {4}
+$$
+
+Stretch the soft mask values to a specific interval $[l,r]$ :
+
+$$
+\tilde {s} _ {i} ^ {(k)} = s _ {i} ^ {(k)} \times (r - l) + l \tag {5}
+$$
+
+Finally, obtain the hardened mask $z_{i}^{(k)}$ for each block by clipping:
+
+$$
+z _ {i} ^ {(k)} = \min  (1, \max  (0, \tilde {s} _ {i} ^ {(k)})) \tag {6}
+$$
+
+The complete mask vector for cluster $k$ is then $z^{(k)} = [z_1^{(k)}, z_2^{(k)}, \ldots, z_B^{(k)}]$ , where each element corresponds to a specific transformer block in the model. During training, these mask values are soft (continuous values between 0 and 1), functioning as scaling parameters. During inference, they are binarized to either 0 (block skipped) or 1 (block executed).
+
+Here, $\sigma$ denotes the sigmoid function. The temperature $\beta$ is fixed hyperparameter, and $l < 0, r > 0$ are two constants that stretch the sigmoid function output. $\alpha_{i}^{(k)}$ are the main learnable parameters for i-th block mask value in cluster $k$ .
+
+We enforce a target sparsity via a Lagrangian term. Let $s_{\mathrm{target}}$ be the target sparsity and $t^{(k)}$ be the current sparsity of mask $z^{(k)}$ (computed as the proportion of zeroes in the mask), the Lagrangian penalty term $L_{s}^{(k)}$ is:
+
+$$
+L _ {s} ^ {(k)} = \lambda_ {1} ^ {(k)} \left(t ^ {(k)} - s _ {\text {t a r g e t}}\right) + \lambda_ {2} ^ {(k)} \left(t ^ {(k)} - s _ {\text {t a r g e t}}\right) ^ {2} \tag {7}
+$$
+
+For the $k$ -th cluster, the optimization objective for its mask parameters $\log \alpha^{(k)}$ is to minimize:
+
+$$
+L _ {\text {t o t a l}} ^ {(k)} = \sum_ {x _ {j} \in S _ {k}} L _ {\mathrm {L M}} \left(x _ {j}; W \odot z ^ {(k)}\right) + L _ {s} ^ {(k)} \tag {8}
+$$
+
+where $L_{\mathrm{LM}}$ is the language modeling loss and $W$ represents the model weights.
+
+Routing Decision. To implement dynamic routing decisions, we maintain an embedding pool for each semantic cluster to represent the cluster's features. These embeddings $c_{k}$ are initialized using the cluster centers $\mu_{k}$ . During inference, for each input sequence, we first extract its embedding representation $e_{x}$ through the encoder, then calculate the Euclidean distance between this embedding and each cluster embedding $c_{k}$ . Based on the calculated distances, we select the most similar cluster as the best match for that input:
+
+$$
+k ^ {*} = \arg \min  _ {k} \left\| e _ {x} - c _ {k} \right\| _ {2} ^ {2}, k \in \{1, 2, \dots , N \} \tag {9}
+$$
+
+After determining the best matching cluster, we directly adopt the trained mask corresponding to that cluster as the final execution mask for input $x$ :
+
+$$
+M ^ {x} = z ^ {(k ^ {*})} \tag {10}
+$$
+
+where $z^{(k^*)}$ is the binary mask vector associated with cluster $k^*$ , containing all block-level mask values.
+
+Dynamic Routing for FFN and Attention Blocks. Our dynamic routing approach employs different strategies for Feed-Forward layers and Attention layers. During training, the layer mask values are soft, functioning as scaling parameters that directly multiply with the outputs of FFN and Attention components. This enables gradient-based
+
+optimization through backpropagation. During inference, we use hard binary masks containing only 0 and 1, where FFN layers are completely skipped when the corresponding mask value is 0. For Attention layers, the approach is more nuanced due to the necessity of maintaining key-value caches for autoregressive generation. When an Attention layer is marked for skipping, we still compute the key and value projections to maintain the KV cache, but we bypass the computationally expensive scaled dot-product operation between queries and keys. Specifically, for a transformer layer $i$ with mask value $M_{i}^{x} = 0$ , the FFN computation $\mathrm{FFN}(x_{i})$ is entirely skipped, while for Attention, we compute $K = W_{K}x_{i}$ and $V = W_{V}x_{i}$ for the cache but skip $\mathrm{Attention}(Q,K,V) = \mathrm{softmax}(QK^T / \sqrt{d})V$ . This selective computation strategy preserves the model's autoregressive capabilities while reducing computational overhead.
+
+# 4 Experiment
+
+# 4.1 Experimental Setup
+
+Datasets and Evaluation Metrics. Following prior work, we use lm-evaluation-harness (Gao et al., 2023) to evaluate our method on six widely-used zero-shot tasks: OpenBookQA (Mihaylov et al., 2018), which tests elementary-level science reasoning requiring the combination of facts with commonsense knowledge; Winogrande (Sakaguchi et al., 2021), a large-scale adversarial dataset for testing pronoun disambiguation through commonsense reasoning; HellaSwag (Zellers et al., 2019), which challenges models to select plausible scenario completions through commonsense inference; PIQA (Bisk et al., 2020), focused on physical commonsense knowledge; and the ARC dataset (Clark et al., 2018), divided into ARC-Easy and ARC-Challenge subsets for testing scientific reasoning at different difficulty levels. Llama-3-8B (AI@Meta, 2024) and Qwen-3-8B (QwenTeam, 2025) are used as our base models, and we use all-MiniLM-L6-v2 from sentence transformer (Reimers and Gurevych, 2019) as sentence encoder. For calibration data for clustering and layer mask training, we use fineweb-edu (Lozhkov et al., 2024), which contains high quality synthetic data used for LLM pretraining.
+
+Baselines and Setups. To evaluate our dynamic block pruning approach against static methods, we select three representative block pruning techniques for comparison:
+
+- SLEB (Song et al., 2024): A method that iteratively eliminates redundant transformer blocks based on cosine similarity between adjacent layers.
+
+- ShortenedLlama (Kim et al., 2024): An approach that uses magnitude, second-order derivatives, or perplexity to measure block-level importance. After identifying unimportant blocks, this method removes them in a single pass.
+
+- EvoPress (Sieberling et al., 2024): A technique leveraging evolutionary algorithms to search for optimal pruning masks with improved perplexity or KL divergence. Starting with a random initial configuration, in each generation it mutates the compression levels of selected layers and retains the best candidates according to a fitness function. This approach yields better results but incurs higher computational costs.
+
+For all baseline methods, we perform one-shot pruning that identifies and eliminates redundant transformer blocks without retraining, and we use wikitext2 (Merit et al., 2016) as calibration set for baselines.
+
+# 4.2 Main Results
+
+IG-Pruning consistently outperforms all baseline methods across all evaluated sparsity configurations for both Llama-3-8B and Qwen-3-8B models. In this paper, the sparsity level is defined as the ratio of the number of skipped blocks to the total number of blocks in the model. For Llama-3-8B at $12.5\%$ sparsity, IG-Pruning maintains $98.29\%$ of the dense model performance, surpassing the best baseline (EvoPress) by 6.36 percentage points. This advantage becomes even more significant at $25\%$ sparsity, where IG-Pruning achieves $87.18\%$ of dense performance compared to the best baseline at $76.32\%$ representing a 10.86 percentage point improvement. Similarly, for Qwen-3-8B, IG-Pruning preserves $96.01\%$ of dense model performance at $13.9\%$ sparsity, compared to $90.37\%$ for the best baseline. These consistent improvements across different model architectures demonstrate the inherent advantage of our dynamic routing strategy over static pruning methods.
+
+Table 1: Zero-shot evaluation results on Llama-3-8B and Qwen-3-8B across multiple sparsity levels.   
+
+<table><tr><td>Model</td><td>Sparsity</td><td>Method</td><td>OBQA</td><td>WG</td><td>HS</td><td>PIQA</td><td>ARC-E</td><td>ARC-C</td><td>Average</td><td>Percentage</td></tr><tr><td rowspan="13">Llama-3-8B</td><td>0%</td><td>Dense</td><td>44.6</td><td>73.24</td><td>79.16</td><td>80.79</td><td>77.82</td><td>53.24</td><td>68.14</td><td>100%</td></tr><tr><td rowspan="4">12.5%</td><td>SLEB</td><td>38.6</td><td>69.45</td><td>70.71</td><td>77.63</td><td>70.28</td><td>43.00</td><td>61.61</td><td>90.42%</td></tr><tr><td>ShortenedLlama</td><td>39.2</td><td>61.56</td><td>66.84</td><td>76.33</td><td>67.63</td><td>38.57</td><td>58.36</td><td>85.64%</td></tr><tr><td>EvoPress</td><td>41.2</td><td>70.17</td><td>72.03</td><td>77.75</td><td>71.00</td><td>43.69</td><td>62.64</td><td>91.93%</td></tr><tr><td>IG-Pruning</td><td>43.6</td><td>72.93</td><td>77.26</td><td>79.38</td><td>77.06</td><td>51.62</td><td>66.98</td><td>98.29%</td></tr><tr><td rowspan="4">25%</td><td>SLEB</td><td>33.8</td><td>53.90</td><td>57.96</td><td>72.25</td><td>57.32</td><td>31.56</td><td>51.13</td><td>75.04%</td></tr><tr><td>EvoPress</td><td>32.8</td><td>57.93</td><td>58.16</td><td>71.06</td><td>58.38</td><td>33.70</td><td>52.01</td><td>76.32%</td></tr><tr><td>ShortenedLlama</td><td>33.6</td><td>53.91</td><td>57.98</td><td>72.31</td><td>57.15</td><td>31.74</td><td>51.12</td><td>75.01%</td></tr><tr><td>IG-Pruning</td><td>40.0</td><td>68.98</td><td>67.53</td><td>76.12</td><td>63.43</td><td>40.36</td><td>59.40</td><td>87.18%</td></tr><tr><td rowspan="4">37.5%</td><td>SLEB</td><td>28.4</td><td>52.24</td><td>46.46</td><td>65.77</td><td>46.96</td><td>28.41</td><td>44.71</td><td>65.61%</td></tr><tr><td>EvoPress</td><td>28.2</td><td>51.22</td><td>45.58</td><td>65.18</td><td>48.15</td><td>28.50</td><td>44.47</td><td>65.26%</td></tr><tr><td>ShortenedLlama</td><td>28.6</td><td>52.41</td><td>45.90</td><td>64.69</td><td>42.68</td><td>27.47</td><td>43.63</td><td>64.02%</td></tr><tr><td>IG-Pruning</td><td>31.8</td><td>58.01</td><td>49.63</td><td>65.94</td><td>48.44</td><td>30.38</td><td>47.37</td><td>69.51%</td></tr><tr><td rowspan="13">Qwen-3-8B</td><td>0%</td><td>Dense</td><td>41.8</td><td>67.96</td><td>74.93</td><td>77.48</td><td>80.77</td><td>56.40</td><td>66.56</td><td>100%</td></tr><tr><td rowspan="4">13.9%</td><td>SLEB</td><td>37.4</td><td>60.85</td><td>62.45</td><td>77.52</td><td>74.45</td><td>47.09</td><td>59.96</td><td>90.09%</td></tr><tr><td>ShortenedLlama</td><td>37.0</td><td>59.27</td><td>61.82</td><td>75.14</td><td>71.00</td><td>45.14</td><td>58.23</td><td>87.49%</td></tr><tr><td>EvoPress</td><td>39.0</td><td>61.96</td><td>67.76</td><td>75.57</td><td>70.33</td><td>46.25</td><td>60.15</td><td>90.37%</td></tr><tr><td>IG-Pruning</td><td>39.8</td><td>65.82</td><td>69.44</td><td>77.09</td><td>77.35</td><td>53.92</td><td>63.90</td><td>96.01%</td></tr><tr><td rowspan="4">25%</td><td>SLEB</td><td>36.6</td><td>56.35</td><td>53.95</td><td>72.47</td><td>65.36</td><td>37.20</td><td>53.66</td><td>80.62%</td></tr><tr><td>EvoPress</td><td>37.0</td><td>58.08</td><td>57.18</td><td>71.43</td><td>62.28</td><td>38.65</td><td>54.10</td><td>81.29%</td></tr><tr><td>ShortenedLlama</td><td>35.6</td><td>53.99</td><td>52.20</td><td>70.84</td><td>64.69</td><td>36.43</td><td>52.29</td><td>78.56%</td></tr><tr><td>IG-Pruning</td><td>35.6</td><td>60.46</td><td>61.65</td><td>73.39</td><td>68.94</td><td>44.80</td><td>57.47</td><td>86.35%</td></tr><tr><td rowspan="4">36.1%</td><td>SLEB</td><td>29.6</td><td>52.40</td><td>44.02</td><td>65.77</td><td>51.68</td><td>31.39</td><td>45.81</td><td>68.82%</td></tr><tr><td>EvoPress</td><td>31.6</td><td>52.17</td><td>45.29</td><td>62.95</td><td>51.09</td><td>29.18</td><td>45.38</td><td>68.18%</td></tr><tr><td>ShortenedLlama</td><td>28.2</td><td>50.91</td><td>37.08</td><td>61.75</td><td>46.13</td><td>25.43</td><td>41.58</td><td>62.48%</td></tr><tr><td>IG-Pruning</td><td>32.6</td><td>53.43</td><td>49.17</td><td>65.83</td><td>54.21</td><td>32.17</td><td>47.90</td><td>71.96%</td></tr></table>
+
+# 4.3 Analysis
+
+Mask Training Efficiency. In Stage 1 of our approach, model parameters remain frozen while only layer mask parameters undergo optimization. We set a higher learning rate for $L_{0}$ module, enabling rapid mask convergence without extensive training periods. For our experiments, we sample 1,000 examples from each cluster for training, utilizing 4 NVIDIA H800 GPUs. Hyperparameters can be found in Appendix 5. For configurations with sparsity levels below $25\%$ across 16 clusters, all masks can be trained in approximately 15 minutes. Higher sparsity $(37\%)$ requires around one hour of training time for mask convergence. Our method requires training, but it only trains the block mask parameters, while the parameters in the original models are frozen. Therefore, it doesn't require excessive memory, which has been tested successfully on a single RTX 3090 for 8B model.
+
+Block-level vs. Layer-level Pruning. To investigate the impact of pruning granularity on model performance, we conducted comprehensive experiments comparing block-level and layer-level prun
+
+![](images/aceaa68141f1de074c17e2e2a5ec0d37a65350bbd167bd98fe9d365791bd90df.jpg)  
+Figure 3: Results on average zero-shot task performance of Llama-3-8B, with block and layer pruning.
+
+ing across different sparsity configurations. As shown in Figure 3, block-level pruning consistently outperforms layer-level pruning across all tasks, with performance advantages that vary based on sparsity levels. The gap between these approaches is most significant at sparsity levels around $20\%$ , where block pruning demonstrates substantially better performance. This suggests that independently pruning Attention and FFN components provides the model with greater flexibility to maintain critical capabilities while reducing computational costs.
+
+![](images/07b20a5b1147ef718c21e4a6c4c4b2e3b51888ee9f1d6376b0b8e5501cfd9d76.jpg)
+
+![](images/c57cdcbfc138115bdb9f717523da94a61fd7361be9510555bf913f181a5c47da.jpg)
+
+![](images/144caeb2a1f697a053d45e31d866a1f74d8a8bb7e6a5a535ae4f9e0650d2a313.jpg)
+
+![](images/8ec5e366e01d2e26fa126498dc18a1f8e868792cf8d7e86c0fce90a58b928241.jpg)  
+Figure 4: Block mask visualization of Llama-3-8B(left) and Qwen-3-8B(right) with 16 clusters and $25\%$ sparsity. Upper part is FFN Block and the lower part is Attention Block. The color indicates the mask value, with 1 being blue and 0 being yellow.
+
+Interestingly, the performance differential diminishes as sparsity decreases. At sparsity levels higher than $40\%$ , the differences become minimal, and in specific tasks such as Winogrande, layer-level pruning occasionally outperforms block-level pruning. To better understand the results, we analyze the layer masks. Visualization in Figure 4 reveals that Llama attention blocks are more likely to be pruned compared to FFN blocks, especially in middle layers, aligning with previous observations about layer representation similarity in Men et al. (2024). This phenomenon also exists in the Qwen-3 model, but shows a more balanced distribution between attention and FFN blocks. Additionally, attention masks are more separate for Qwen, with no long ranges of consecutive blocks being masked. We analyzed the mask distribution at various sparsity levels and found this phenomenon was commonly observed. This suggests that, in higher sparsity settings, retaining the FFN blocks is more beneficial for model performance, as they are more likely to contain important information. For higher sparsity levels, more FFN blocks are pruned, leading to similar performance between block-level and layer-level pruning.
+
+Computational Efficiency Analysis. To quantify efficiency improvements, we measured FLOPs (floating point operations) for Llama-3-8B with different sparsity settings, as shown in Table 2. Our analysis reveals that block-wise pruning provides significant computational savings while maintaining model performance. At $25\%$ sparsity, our ap
+
+proach reduces the computational cost to $89.8\%$ of the dense model, representing a reasonable tradeoff between efficiency and effectiveness. As sparsity increases to $37.5\%$ , computational requirements drop to $75.8\%$ of the original model.
+
+Table 2: Computational efficiency at different sparsity for block-wise pruning. The FLOPs values represent the computational cost, while the percentage shows the proportion relative to the dense model.   
+
+<table><tr><td>Sparsity</td><td>FLOPs</td><td>Per%</td><td>Sparsity</td><td>FLOPs</td><td>Per%</td></tr><tr><td>0%</td><td>32.94T</td><td>100.0%</td><td>21.88%</td><td>31.01T</td><td>94.1%</td></tr><tr><td>3.12%</td><td>32.66T</td><td>99.1%</td><td>25.00%</td><td>29.57T</td><td>89.8%</td></tr><tr><td>6.25%</td><td>32.39T</td><td>98.3%</td><td>28.12%</td><td>28.71T</td><td>87.2%</td></tr><tr><td>9.38%</td><td>32.11T</td><td>97.5%</td><td>31.25%</td><td>27.27T</td><td>82.8%</td></tr><tr><td>12.50%</td><td>31.84T</td><td>96.7%</td><td>34.38%</td><td>26.41T</td><td>80.2%</td></tr><tr><td>15.62%</td><td>31.56T</td><td>95.8%</td><td>37.50%</td><td>24.97T</td><td>75.8%</td></tr><tr><td>18.75%</td><td>31.29T</td><td>95.0%</td><td>40.62%</td><td>24.69T</td><td>74.9%</td></tr></table>
+
+# 4.3.1 Analyze clustering effectiveness
+
+Number of Clusters. To investigate how the number of clusters affects model performance, we conducted experiments with varying cluster counts $(N = 4, 8, 16)$ at different sparsity levels, as shown in Figure 5. The results demonstrate a clear trend: as the number of clusters increases, overall performance improves consistently across all pruning configurations. At lower sparsity, models with 16 clusters achieve an average performance of $66.98\%$ compared to $61.05\%$ with 8 clusters and $63.82\%$ with 4 clusters. This advantage becomes even more pronounced at higher sparsity levels. With sparsity of $37.5\%$ , the 16-cluster configuration outperforms the 4-cluster variant by 10.64 percentage
+
+![](images/3f96b7dc9f77faf21cffb5e9c77b0a0c3078a25656fc56f384e90bf56d3ac533.jpg)  
+Figure 5: Impact of cluster number on performance across evaluation tasks. Results on average zero-shot task performance on Llama-3-8B, with cluster $N = 4, 8,$ and 16.
+
+points. This pattern confirms that a higher number of clusters enables more specialized mask combinations tailored to different input types. With more clusters, the model can develop a more diverse set of computational paths, each optimized for specific semantic patterns in the input data. The performance improvements with increased cluster count provide strong evidence supporting our hypothesis that dynamic routing significantly benefits model effectiveness by enabling adaptive computation. Rather than forcing all inputs through a single pruned structure, our approach leverages the complementary strengths of mask combinations, explained why our dynamic pruning strategy consistently outperforms static pruning methods.
+
+Calibration Data Quality. The quality of calibration data proves critical for effective mask training, as demonstrated in our ablation studies (Table 3). We found that using high-quality, diverse pretraining data from fineweb-edu (Lozhkov et al., 2024) yields the best results, achieving an average score of 59.40. In contrast, using wikitext2, the calibration dataset for baseline models, leads to a significant performance degradation, with the average score dropping to 55.85. Also, instruction dataset in Gou et al. (2023), achieved a competitive score of 58.20 but was still lower than fineweb-edu. Our experiments demonstrate that clustering semantically-rich texts creates more meaningfully differentiated clusters, enabling the discovery of truly specialized computational paths. This finding highlights the importance of data diversity and representational richness in training effective dynamic routing mechanisms.
+
+To verify that the observed performance enhancement is attributable to our proposed method
+
+Table 3: Ablation results on Llama-3-8B with $25\%$ sparsity across different datasets. Comparing with fineweb-edu, instruction set show minor difference, while wikitext cause average score degradation.   
+
+<table><tr><td>Dataset</td><td>OBQA</td><td>WG</td><td>HS</td><td>PIQA</td><td>ARC-E</td><td>ARC-C</td><td>Average</td></tr><tr><td>Instruction</td><td>36.4</td><td>68.27</td><td>68.14</td><td>73.06</td><td>63.38</td><td>39.93</td><td>58.20</td></tr><tr><td>Wikitext2</td><td>39.0</td><td>63.06</td><td>64.12</td><td>73.07</td><td>60.19</td><td>35.67</td><td>55.85</td></tr><tr><td>Fineweb-edu</td><td>40.0</td><td>68.98</td><td>67.53</td><td>76.12</td><td>63.43</td><td>40.36</td><td>59.40</td></tr></table>
+
+Table 4: Comparison with baseline models on different datasets. Our method outperforms the baseline (SLEB) regardless of the dataset used.   
+
+<table><tr><td>Method</td><td>Dataset</td><td>OBQA</td><td>WG</td><td>HS</td><td>PIQA</td><td>ARC-E</td><td>ARC-C</td><td>Average</td></tr><tr><td>SLEB</td><td>Wikitext2</td><td>33.8</td><td>53.95</td><td>57.96</td><td>72.25</td><td>57.32</td><td>31.56</td><td>51.13</td></tr><tr><td>SLEB</td><td>Fineweb-edu</td><td>33.0</td><td>52.56</td><td>57.19</td><td>72.79</td><td>56.60</td><td>32.84</td><td>50.83</td></tr><tr><td>IG-Pruning</td><td>Wikitext2</td><td>39.0</td><td>63.06</td><td>64.12</td><td>73.07</td><td>60.19</td><td>35.67</td><td>55.85</td></tr><tr><td>IG-Pruning</td><td>Fineweb-edu</td><td>40.0</td><td>68.98</td><td>67.53</td><td>76.12</td><td>63.43</td><td>40.36</td><td>59.40</td></tr></table>
+
+rather than the calibration data, we benchmarked the SLEB baseline on both the wikitext2 and fineweb-edu datasets. As detailed in Table 4, the baseline's performance did not improve when using fineweb-edu. Crucially, our method continues to outperform the baseline even when using wikitext2. This evidence indicates that the performance gains originate from our method's dynamic architecture and its ability to leverage high-quality data, rather than from an unfair data advantage.
+
+# 5 Conclusion
+
+We introduced IG-Pruning, a novel approach for efficient LLM inference through input-adaptive dynamic block pruning. Our method addresses critical limitations of static pruning, and demonstrates that IG-Pruning consistently outperforms state-of-the-art static pruning methods across various configurations and model architectures. Our approach offers four key advantages: (1) improved accuracy through input-adaptive computation that tailors pruning decisions to specific input characteristics, (2) efficient training that keeps model weights frozen while only optimizing lightweight mask parameters, (3) minimal inference overhead via a simple yet effective semantic-based routing mechanism, and (4) flexible block-level pruning granularity that allows independent treatment of attention and FFN components. The success of IG-Pruning highlights the importance of input-adaptive computation in efficient LLM deployment and represents a promising direction for developing high-performing LLMs for resource-constrained environments.
+
+# Limitations
+
+The performance heavily depends on clustering quality, potentially diminishing if semantic clusters aren't effectively differentiated. Moreover, the result is sensitive to calibration data quality, as instruction datasets led to performance degradation compared to diverse pretraining data. Also, our evaluation focused primarily on specific zero-shot tasks, leaving generalization to other task types or domain-specific applications less thoroughly validated. Additionally, the method introduces sensitivity to multiple hyperparameters, including $L_{0}$ regularization, lagrangian parameters, and cluster numbers. Finally, our work does not investigate the impact of block pruning on model factuality. Removing computational blocks risks eliminating components that are critical for factual recall, which may increase the model's propensity for hallucination. A promising direction for future work would be to combine our dynamic pruning strategy with hallucination mitigation techniques. For instance, integrating methods like TruthX (Zhang et al., 2024a), which enhances truthfulness by editing internal model representations, or Truth-Aware Context Selection (Yu et al., 2024), which filters untruthful information from the input context. Such an approach could lead to models that are not only efficient but also more robust and factually reliable.
+
+# Acknowledgements
+
+We thank all the anonymous reviewers for their insightful and valuable comments on this paper. This work was supported by the grant from the National Natural Science Foundation of China (No. 62376260).
+
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+
+# A Hyperparameter
+
+The hyperparameters we use in our experiments are listed in Table 5.
+
+Table 5: Hyperparameters used in our experiments.   
+
+<table><tr><td>Hyperparameter</td><td>Value</td></tr><tr><td>Batch Size</td><td>32</td></tr><tr><td>L0 Module Learning Rate</td><td>0.1</td></tr><tr><td>Lagrangian Learning Rate</td><td>0.1</td></tr><tr><td>ε</td><td>1e-6</td></tr><tr><td>1/β</td><td>2/3</td></tr><tr><td>l</td><td>-0.1</td></tr><tr><td>r</td><td>1.1</td></tr><tr><td>Number of Clusters</td><td>16, 8, 4</td></tr><tr><td>Calibration Data Size for each cluster</td><td>1000</td></tr><tr><td>Clustering Stage Sequence Length</td><td>4096</td></tr><tr><td>Mask Training Sequence Length</td><td>512</td></tr></table>
+
+# B More results on various models
+
+To further validate the generalizability and robustness of our approach, we conducted additional experiments on a wider range of models, including Llama-3.2-3B (Table 6), Llama-3.2-1B (Table 7), and Qwen-3-4B (Table 8). Across all tested models and architectures, the input-adaptive nature of IG-Pruning allows it to retain significantly more of the original model's performance compared to baselines, especially at moderate sparsity levels. As sparsity becomes extremely high, the performance of both methods naturally converges. These comprehensive results validate that our dynamic approach is a consistently superior and more robust solution for model pruning.
+
+Table 6: Results on Llama-3.2-3B.   
+
+<table><tr><td>Model</td><td>Sparsity</td><td>Method</td><td>OpenBookQA</td><td>Winogrande</td><td>Hellaswag</td><td>PIQA</td><td>ARC-E</td><td>ARC-C</td><td>Average</td><td>Percentage(%)</td></tr><tr><td rowspan="7">Llama-3.2-3B</td><td>0% (0/28)</td><td>Dense</td><td>43.20</td><td>69.38</td><td>73.73</td><td>77.27</td><td>71.84</td><td>45.99</td><td>63.55</td><td>100%</td></tr><tr><td rowspan="2">14% (4/28)</td><td>SLEB</td><td>35.80</td><td>58.45</td><td>58.20</td><td>73.12</td><td>57.02</td><td>33.70</td><td>52.71</td><td>82.94%</td></tr><tr><td>IG-Pruning</td><td>41.40</td><td>66.45</td><td>68.20</td><td>75.95</td><td>68.13</td><td>43.34</td><td>60.58</td><td>95.32%</td></tr><tr><td rowspan="2">25% (7/28)</td><td>SLEB</td><td>25.00</td><td>53.82</td><td>46.67</td><td>68.28</td><td>50.96</td><td>29.01</td><td>46.79</td><td>73.63%</td></tr><tr><td>IG-Pruning</td><td>36.40</td><td>57.76</td><td>60.14</td><td>71.87</td><td>54.88</td><td>33.19</td><td>52.36</td><td>82.40%</td></tr><tr><td rowspan="2">39% (11/28)</td><td>SLEB</td><td>26.80</td><td>51.06</td><td>37.26</td><td>61.58</td><td>40.02</td><td>24.65</td><td>40.23</td><td>63.30%</td></tr><tr><td>IG-Pruning</td><td>28.00</td><td>49.83</td><td>38.52</td><td>61.53</td><td>38.17</td><td>24.40</td><td>40.07</td><td>63.05%</td></tr></table>
+
+Table 7: Results on Llama-3.2-1B.   
+
+<table><tr><td>Model</td><td>Sparsity</td><td>Method</td><td>OpenBookQA</td><td>Winogrande</td><td>Hellaswag</td><td>PIQA</td><td>ARC-E</td><td>ARC-C</td><td>Average</td><td>Percentage(%)</td></tr><tr><td rowspan="7">Llama-3.2-1B</td><td>0% (0/16)</td><td>Dense</td><td>37.40</td><td>60.36</td><td>63.64</td><td>74.43</td><td>60.27</td><td>36.26</td><td>55.38</td><td>100%</td></tr><tr><td rowspan="2">12.5% (2/16)</td><td>SLEB</td><td>30.60</td><td>55.16</td><td>48.74</td><td>68.55</td><td>48.48</td><td>28.41</td><td>46.66</td><td>84.24%</td></tr><tr><td>IG-Pruning</td><td>35.00</td><td>60.45</td><td>59.65</td><td>72.79</td><td>57.32</td><td>33.87</td><td>53.18</td><td>96.02%</td></tr><tr><td rowspan="2">25% (4/16)</td><td>SLEB</td><td>27.80</td><td>51.63</td><td>37.50</td><td>63.11</td><td>40.19</td><td>23.72</td><td>40.65</td><td>73.40%</td></tr><tr><td>IG-Pruning</td><td>27.00</td><td>54.78</td><td>40.30</td><td>62.08</td><td>40.24</td><td>27.22</td><td>41.94</td><td>75.72%</td></tr><tr><td rowspan="2">37.5% (6/16)</td><td>SLEB</td><td>27.00</td><td>49.88</td><td>29.90</td><td>56.03</td><td>30.93</td><td>22.01</td><td>35.96</td><td>64.93%</td></tr><tr><td>IG-Pruning</td><td>24.40</td><td>50.98</td><td>30.90</td><td>56.31</td><td>30.72</td><td>25.08</td><td>36.40</td><td>65.72%</td></tr></table>
+
+Table 8: Results on Qwen-3-4B.   
+
+<table><tr><td>Model</td><td>Sparsity</td><td>Method</td><td>OpenBookQA</td><td>Winogrande</td><td>Hellaswag</td><td>PIQA</td><td>ARC-E</td><td>ARC-C</td><td>Average</td><td>Percentage(%)</td></tr><tr><td rowspan="7">Qwen-3-4B</td><td>0% (0/36)</td><td>Dense</td><td>40.40</td><td>65.82</td><td>68.42</td><td>75.13</td><td>53.75</td><td>53.75</td><td>59.55</td><td>100%</td></tr><tr><td rowspan="2">14% (5/36)</td><td>SLEB</td><td>35.40</td><td>56.19</td><td>57.36</td><td>72.85</td><td>65.78</td><td>39.84</td><td>54.57</td><td>91.64%</td></tr><tr><td>IG-Pruning</td><td>37.60</td><td>62.58</td><td>59.76</td><td>73.55</td><td>68.35</td><td>44.62</td><td>57.74</td><td>96.97%</td></tr><tr><td rowspan="2">25% (9/36)</td><td>SLEB</td><td>32.20</td><td>53.03</td><td>46.94</td><td>67.46</td><td>58.37</td><td>31.22</td><td>48.20</td><td>80.95%</td></tr><tr><td>IG-Pruning</td><td>35.80</td><td>56.43</td><td>53.78</td><td>69.85</td><td>60.01</td><td>39.07</td><td>52.49</td><td>88.15%</td></tr><tr><td rowspan="2">36% (13/36)</td><td>SLEB</td><td>29.80</td><td>53.43</td><td>39.54</td><td>62.67</td><td>47.01</td><td>26.79</td><td>43.21</td><td>72.56%</td></tr><tr><td>IG-Pruning</td><td>30.60</td><td>54.69</td><td>42.74</td><td>63.65</td><td>47.26</td><td>28.66</td><td>44.60</td><td>74.90%</td></tr></table>