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Deep Learning · Generative Models and Autoencoders

Yu Zhang, Xingzhuo Guo, Haoran Xu, Jialong Wu, Mingsheng Long

Diffusion and flow-based models have enabled significant progress in generation tasks across various modalities and have recently found applications in predictive learning. However, unlike typical generation tasks that encourage sample diversity, predictive learning entails different sources of stochasticity and requires sampling consistency aligned with the ground-truth trajectory, which is a limitation we empirically observe in diffusion models. We argue that a key bottleneck in learning sampling-consistent predictive diffusion models lies in suboptimal predictive ability, which we attribute to the entanglement of condition understanding and target denoising within shared architectures and co-training schemes. To address this, we propose **Foresight Diffusion (ForeDiff)**, a framework for predictive diffusion models that improves sampling consistency by decoupling condition understanding from target denoising. ForeDiff incorporates a separate deterministic predictive stream to process conditioning inputs independently of the denoising stream, and further leverages a pretrained predictor to extract informative representations that guide generation. Extensive experiments on robot video prediction and scientific spatiotemporal forecasting show that ForeDiff improves both predictive accuracy and sampling consistency over strong baselines, offering a promising direction for predictive diffusion models.

Deep Learning · Everything Else

Lukas Rüttgers, Till Aczel, Andreas Plesner, Roger Wattenhofer

Differentiable logic gate networks (DLGNs) exhibit extraordinary efficiency at inference while sustaining competitive accuracy. But vanishing gradients, discretization errors, and high training cost impede scaling these networks. Even with dedicated parameter initialization schemes from subsequent works, increasing depth still harms accuracy. We show that the root cause of these issues lies in the underlying parametrization of logic gate neurons themselves. To overcome this issue, we propose a reparametrization that also shrinks the parameter size logarithmically in the number of inputs per gate. For binary inputs, this already reduces the model size by 4x, speeds up the backward pass by up to 1.86x, and converges in 8.5x fewer training steps. On top of that, we show that the accuracy on CIFAR-100 remains stable and sometimes superior to the original parametrization.

Applications · Time Series

Defu Cao, Wen Ye, Yizhou Zhang, Sam Griesemer, Yan Liu

Time series analysis underpins scientific advances. While specialized models have advanced various time series tasks, scientific domains face unique challenges: limited samples with complex physical dynamics, missing observations, multi-resolution sampling, and requirements for physical consistency. With the increasing demands on generative modeling capabilities, we introduce PINFDiT, a diffusion transformer-based model with physics injection during inference. Our approach combines a transformer backbone for capturing temporal dependencies with a comprehensive masking strategy that addresses imperfect data. The diffusion framework enables high-quality sample generation with inherent generative capability. In addition, our model-free physics-guided correction steers generated samples toward physically consistent solutions using calibrated Langevin dynamics, which balances distribution fidelity and physical law adherence without architectural modifications or retraining. Our evaluation demonstrates PINFDiT's effectiveness across multivariate forecasting with imperfect data, physics knowledge incorporation in data-limited scenarios, zero-shot and fine-tuning performance across diverse domains, establishing it as a proto-foundation model that bridges the gap between general-purpose and domain-specific models.

Deep Learning · Everything Else

Tianshi Zheng, Kiu Wai Tam, Kim Hue Nam Nguyen, Baixuan Xu, Zhaowei Wang, Cheng Jiayang, Hong Ting Tsang, Weiqi Wang, Jiaxin Bai, Tianqing Fang 等

Large language models (LLMs) are emerging as powerful tools for scientific law discovery, a foundational challenge in AI-driven science. However, existing benchmarks for this task suffer from a fundamental methodological trilemma, forcing a trade-off between scientific relevance, scalability, and resistance to memorization. Furthermore, they oversimplify discovery as static function fitting, failing to capture the authentic scientific process of uncovering embedded laws through the interactive exploration of complex model systems. To address these critical gaps, we introduce **NewtonBench**, a benchmark comprising 324 scientific law discovery tasks across 12 physics domains. Our design mitigates the evaluation trilemma by using counterfactual law shifts - systematic alterations of canonical laws - to generate a vast suite of problems that are scalable, scientifically relevant, and memorization-resistant. Moreover, we elevate the evaluation from static function fitting to interactive model discovery, requiring agents to experimentally probe simulated complex systems to uncover hidden principles. Our extensive evaluation of 11 state-of-the-art LLMs reveals a clear but fragile capability for discovery in frontier models: this ability degrades precipitously with increasing system complexity and exhibits extreme sensitivity to observational noise. Notably, we uncover a paradoxical effect of tool assistance: providing a code interpreter can hinder more capable models by inducing a premature shift from exploration to exploitation, causing them to satisfice on suboptimal solutions. These results demonstrate that robust, generalizable discovery in complex, interactive environments remains the core challenge for the future of automated science. By providing a scalable, robust, and scientifically authentic testbed, NewtonBench offers a crucial tool for measuring true progress and guiding the development of next-generation AI agents capable of genuine scientific discovery.

Computer Vision · 3D Rendering & Reconstruction

Jonas Belouadi, Tamy Boubekeur, Adrien Kaiser

Material node graphs are programs that generate the 2D channels of procedural materials, including geometry such as roughness and displacement maps, and reflectance such as albedo and conductivity maps. They are essential in computer graphics for representing the appearance of virtual 3D objects parametrically and at arbitrary resolution. In particular, their directed acyclic graph structure and intermediate states enable a modular, interpretable workflow for interactive appearance modeling. However, creating such graphs remains challenging and typically requires professional training. While recent neural program synthesis approaches attempt to simplify this process, they solely represent graphs as textual programs, failing to capture the inherently visual-spatial nature of node graphs that makes them accessible to humans. To address this gap, we present MultiMat, a multimodal program synthesis framework that leverages large multimodal models to process both visual and textual graph representations for improved generation of procedural material graphs. We train our models on a new dataset of production-quality procedural materials and combine them with a constrained tree search inference algorithm that ensures static correctness while efficiently navigating the program space. Our experimental results show that our multimodal program synthesis method is more efficient in both unconditional and conditional graph synthesis with higher visual quality and fidelity than text-only baselines, establishing new state-of-the-art performance.

Social Aspects · Fairness, Equity, Justice and Safety

Kihyun Kim, Jiawei Zhang, Asuman Ozdaglar, Pablo Parrilo

Conventional preference learning methods often prioritize opinions held more widely when aggregating preferences from multiple evaluators. This may result in policies that are biased in favor of some types of opinions or groups and susceptible to strategic manipulation. To address this issue, we develop a novel preference learning framework capable of aligning aggregate opinions and policies proportionally with the true population distribution of evaluator preferences. Grounded in social choice theory, our approach infers the feasible set of evaluator population distributions directly from pairwise comparison data. Using these estimates, the algorithm constructs a policy that satisfies foundational axioms from social choice theory, namely monotonicity and Pareto efficiency, as well as our newly-introduced axioms of population-proportional alignment and population-bounded manipulability. Moreover, we propose a soft-max relaxation method that smoothly trades off population-proportional alignment with the selection of the Condorcet winner (which beats all other options in pairwise comparisons). Finally, we validate the effectiveness and scalability of our approach through experiments on both tabular recommendation tasks and large language model alignment.

Applications · Chemistry and Drug Discovery

Yang Tan, Wenrui Gou, Bozitao Zhong, Huiqun Yu, liang hong, Bingxin Zhou

Deep learning models have driven significant progress in predicting protein function and interactions at the protein level. While these advancements have been invaluable for many biological applications such as enzyme engineering and function annotation, a more detailed perspective is essential for understanding protein functional mechanisms and evaluating the biological knowledge captured by models. This study introduces VenusX, the first benchmark designed to assess protein representation learning with a focus on fine-grained intra-protein functional understanding. VenusX comprises three major task categories across six types of annotations, including residue-level binary classification, fragment-level multi-class classification, and pairwise functional similarity scoring for identifying critical active sites, binding sites, conserved sites, motifs, domains, and epitopes. The benchmark features over 878,000 samples curated from major open-source databases such as InterPro, BioLiP, and SAbDab. By providing mixed-family and cross-family splits at three sequence identity thresholds, our benchmark enables a comprehensive assessment of model performance on both in-distribution and out-of-distribution scenarios. For baseline evaluation, we assess a diverse set of popular and open-source models, including pre-trained protein language models, sequence-structure hybrids, structure-based methods, and alignment-based techniques. Their performance is reported across all benchmark datasets and evaluation settings using multiple metrics, offering a thorough comparison and a strong foundation for future research. Our code (https://github.com/ai4protein/VenusX), data (https://huggingface.co/collections/AI4Protein/venusx-dataset), and a leaderboard (https://ai4protein.github.io/venusx/) are provided as open-source resources.

Applications · Chemistry and Drug Discovery

Xuan Li, (Andrew) Zhanke Zhou, Zongze Li, Jiangchao Yao, Yu Rong, Lu Zhang, Bo Han

Large language models (LLMs) benefit substantially from supervised fine-tuning (SFT) and reinforcement learning with verifiable rewards (RLVR) in reasoning tasks. However, these recipes perform poorly in instruction-based molecular optimization, where each data point typically provides only a single optimized reference molecule and no step-by-step optimization trajectory. We reveal that answer-only SFT on the reference molecules collapses reasoning, and RLVR provides sparse feedback under similarity constraints due to the model's lack of effective exploration, which slows learning and limits optimization. To encourage the exploration of new molecules while balancing the exploitation of the reference molecules, we introduce **Re**ference-guided **P**olicy **O**ptimization (RePO), an optimization approach that learns from reference molecules without requiring trajectory data. At each update, RePO samples candidate molecules with their intermediate reasoning trajectories from the model and trains the model using verifiable rewards that measure property satisfaction under similarity constraints in an RL manner. Meanwhile, it applies reference guidance by keeping the policy’s intermediate reasoning trajectory as context and training only the answer in a supervised manner. Together, the RL term promotes exploration, while the guidance term mitigates reward sparsity and stabilizes training by grounding outputs to references when many valid molecular edits exist. Across molecular optimization benchmarks, RePO consistently outperforms SFT and RLVR baselines (e.g., GRPO), achieving improvements on the optimization metric (Success Rate $\times$ Similarity), improving balance across competing objectives, and generalizing better to unseen instruction styles. Our code is publicly available at https://github.com/tmlr-group/RePO.

Applications · Chemistry and Drug Discovery

Yiming Yang, Zhiyuan Zhou, Yueming Yin, Hoi-Yeung Li, Adams Kong

Accurate prediction of protein-ligand bioactivity is a cornerstone of modern drug discovery, yet current deep learning methods often struggle with out-of-domain (OOD) generalization. The existing methods rely on access to source data, making them impractical in scenarios where data cannot be accessed due to confidentiality, privacy concerns or intellectual property restrictions. In this paper, we provide the first exploration of a more realistic setting for bioactivity prediction, where models are expected to adapt to out-of-domain distributions without access to source data. Motivated by the critical role of binding-relevant interactions in determining ligand-protein bioactivity, we introduce an uncertainty-weighted consistency strategy, in which original samples with high confidence guide their augmented counterparts by minimizing feature distance. This encourages the model to focus on informative interaction regions while suppressing reliance on spurious or non-causal substructures. To further enhance representation discriminability and prevent feature collapse, we integrate a contrastive optimization objective that pulls together augmented views of the same complex and pushes away views from different complexes. Together, these two components enable the learning of invariant, bioactivity-aware representations, allowing robust adaptation under distribution shifts. Extensive experiments across DTIGN, SIU 0.6, and DrugOOD demonstrate that our framework consistently outperforms state-of-the-art baselines under scaffold, protein, and assay based OOD settings. Especially on the eight subsets of DTIGN, it improves Pearson’s $R$ by 8.2\% and Kendall’s Tau $\tau$ by 5.8\% on average over the best baseline, underscoring its effectiveness as a source data-absent solution for OOD bioactivity prediction.

Applications · Chemistry and Drug Discovery

Ziyang Yu, Wenbing Huang, Yang Liu

Molecular Dynamics (MD) simulations provide a fundamental tool for characterizing molecular behavior at full atomic resolution, but their applicability is severely constrained by the computational cost. To address this, a surge of deep generative models has recently emerged to learn dynamics at coarsened timesteps for efficient trajectory generation, yet they either generalize poorly across systems or, due to limited molecular diversity of trajectory data, fail to fully exploit structural information to improve generative fidelity. Here, we present the Pretrained Variational Bridge (PVB) in an encoder-decoder fashion, which maps the initial structure into a noised latent space and transports it toward stage-specific targets through augmented bridge matching. This unifies training on both single-structure and paired trajectory data, enabling consistent use of cross-domain structural knowledge across training stages. Moreover, for protein-ligand complexes, we further introduce a reinforcement learning-based optimization via adjoint matching that speeds progression toward the holo state, which supports efficient post-optimization of docking poses. Experiments on proteins and protein-ligand complexes demonstrate that PVB faithfully reproduces thermodynamic and kinetic observables from MD while delivering stable and efficient generative dynamics.

Deep Learning · Generative Models and Autoencoders

Robert Gruhlke, Valentin Resseguier, Merveille Talla

We introduce a new class of generative models based on multiplicative score-driven diffusion. In contrast to classical diffusion models that rely on additive Gaussian noise, our construction is driven by skew-symmetric multiplicative noise. It yields conservative forward-backward dynamics inspired by principles of physics. We prove that the forward process converges exponentially fast to a tractable non-Gaussian latent distribution, and we characterize this limit explicitly. A key property of our diffusion is that it preserves the distribution of data norms, resulting in a latent space that is inherently data-aware. Unlike the standard Gaussian prior, this structure better adapts to heavy-tailed and anisotropic data, providing a closer match between latent and observed distributions. On the algorithmic side, we derive the reverse-time stochastic differential equation and associated probability flow, and show that sliced score matching furnishes a consistent estimator for the backward dynamics. This estimation procedure is equivalent to maximizing an evidence lower bound (ELBO), bridging our framework with established variational principles. Empirically, we demonstrate the advantages of our model in challenging settings, including correlated Cauchy distributions and experimental fluid dynamics data (d=1024). Across these tasks, our approach more accurately captures extreme events and tail behavior than classical diffusion models, particularly in the low-data regime. Our results suggest that multiplicative conservative diffusions open a principled alternative to current score-based generative models, with strong potential for domains where rare but critical events dominate.

Applications · Chemistry and Drug Discovery

Jiahui Zhang, Rouyi Wang, Kuangqi Zhou, Tianshu Xiao, Lingyan Zhu, Yaosen Min, Yang Wang

Peptide therapeutics are widely regarded as the “third generation” of drugs, yet progress in peptide Machine Learning (ML) are hindered by the absence of standardized benchmarks. Here we present \textbf{PepBenchmark}, which unifies datasets, preprocessing, and evaluation protocols for peptide drug discovery. PepBenchmark comprises three components: (1) \textbf{PepBenchData}, a well-curated collection comprising 29 canonical-peptide and 6 non-canonical-peptide datasets across 7 groups, systematically covering key aspects of peptide drug development—representing, to the best of our knowledge, the most comprehensive AI-ready dataset resource to date; (2) \textbf{PepBenchPipeline}, a standardized preprocessing pipeline that ensures consistent dataset cleaning, construction, splitting, and feature transformation, mitigating quality issues common in ad hoc pipelines; and (3) \textbf{PepBenchLeaderboard}, a unified evaluation protocol and leaderboard with strong baselines across 4 major methodological families: Fingerprint-based, GNN-based, PLM-based, and SMILES-based models. Together, PepBenchmark provides the first standardized and comparable foundation for peptide drug discovery, facilitating methodological advances and translation into real-world applications. The data and code are publicly available at \href{https://github.com/ZGCI-AI4S-Pep/PepBenchmark/}{\texttt{https://github.com/ZGCI-AI4S-Pep/PepBenchmark/}}.

Shang Zhou, Zihan Zheng, Kaiyuan Liu, Zeyu Shen, Zerui Cheng, Zexing Chen, Hansen He, Jianzhu Yao, Huanzhi Mao, Qiuyang Mang 等

Writing competitive programming problems is exacting. Authors must: set constraints, input distributions, and edge cases that rule out shortcuts; target specific algorithms (e.g., max-flow, dynamic programming, data structures); and calibrate complexity beyond the reach of most competitors. We argue that this makes for an ideal test of general large language model capabilities and study whether they can do this reliably. We introduce AutoCode, which uses multiple rounds of validation to yield competition-grade problem statements and test cases. On held-out problems, AutoCode test suites approach 99% consistency with official judgments, a significant improvement over current state-of-the-art methods like HardTests, which achieve less than 81%. Furthermore, starting with a random seed problem, AutoCode can create novel variants with reference and brute-force solutions. By cross-verifying these generated solutions against test cases, we can further filter out malformed problems. Our system ensures high correctness, as verified by human experts. AutoCode successfully produces novel problems judged by Grandmaster-level (top 0.3%) competitive programmers to be of contest quality.

General Machine Learning · Transfer, Multitask and Meta-learning

Hong Ye Tan, Emma Slade

Dataset distillation aims to find a small synthetic training set, such that training on the synthetic data achieves similar performance to training on a larger training dataset. Early methods solve this by interpreting the distillation problem as a bi-level optimization problem. On the other hand, disentangled methods bypass pixel-space optimization by matching data distributions and using generative techniques, leading to better computational complexity in terms of size of both training and distilled datasets. We demonstrate that by using latent spaces, the empirically successful disentangled methods can be reformulated as an optimal quantization problem, where a finite set of points is found to approximate the underlying probability measure. In particular, we link disentangled dataset distillation methods to the classical problem of optimal quantization, and are the first to demonstrate consistency of distilled datasets for diffusion-based generative priors. We propose Dataset Distillation by Optimal Quantization (DDOQ), based on clustering in the latent space of latent diffusion models. Compared to a similar clustering method D4M, we achieve better performance and inter-model generalization on the ImageNet-1K dataset using the same model and with trivial additional computation, achieving SOTA performance in higher image-per-class settings. Using the distilled noise initializations in a stronger diffusion transformer model, we obtain competitive or SOTA distillation performance on ImageNet-1K and its subsets, outperforming recent diffusion guidance methods.

Deep Learning · Generative Models and Autoencoders

Xuebing Liu, Shanbao Qiao, Roseline Nyange, Dongwook Min, Hyun Kim, Seung-Hoon Na

Large language models (LLMs) can be enhanced with external knowledge through two dominant approaches: (1) **retrieval-augmented generation (RAG)**, which supplements LLMs with in-context retrieved passages, and (2) **parametric knowledge adaptation (PKA)**, which directly updates model parameters with new domain knowledge. Recently, parametric RAG (PRAG) has emerged as a promising framework, extending RAG by translating retrieved passages into parameter updates, thereby mitigating inefficiency and noise sensitivity inherent to RAG. However, existing PRAG methods remain limited to single-pass retrieval, falling short of the **multi-hop RAG** setting that requires iterative retrieval and reasoning. We propose **MergePRAG**(*Orthogonal Merging of Passage-experts for Multi-hop PRAG*), a novel framework that sequentially integrates retrieved passages into LLM parameters through a continual merging mechanism, which is advanced by two key proposals: (1) **orthogonal merging** using the Gram–Schmidt process to minimize conflicts between "passage experts", and (2) **critical-layer parameterization** to efficiently encode in-context passages. Experiments on multi-hop open-domain QA and reasoning-aware knowledge editing show that MergePRAG consistently outperforms both standard and state-of-the-art RAGs as well as existing parametric adaptation methods, achieving superior effectiveness and efficiency. All datasets and code will be released at https://github.com/Liu-Xuebing/MhQA_hypernetwork.

Applications · Everything Else

Yusong Wu, Stephen Brade, Teng Ma, Tia-Jane Fowler, Enning Yang, Berker Banar, Aaron Courville, Natasha Jaques, Anna Huang

Most applications of generative AI involve a sequential interaction in which a person inputs a prompt and waits for a response, and where reaction time and adaptivity are not important factors. In contrast, live jamming is a collaborative interaction that requires real-time coordination and adaptation without access to the other player’s future moves, while preserving diversity to sustain a creative flow. Reinforcement learning post-training enables effective adaptation through on-policy interaction, yet it often reduces output diversity by exploiting coherence-based rewards. This collapse, known as ``reward hacking'', affects many RL post-training pipelines, but is especially harmful in live jamming, where musical creativity relies on dynamic variation and mutual responsiveness. In this paper, we propose a novel adversarial training method on policy-generated trajectories to mitigate reward hacking in RL post-training for melody-to-chord accompaniment. A co-evolving discriminator separates policy trajectories from the data distribution, while the policy maximizes the discriminator output in addition to coherence rewards to prevent collapse to trivial outputs. We evaluate accompaniment quality and output diversity in simulation with both fixed test melodies and learned melody agents, and we conduct a user study with the model deployed in a real-time interactive system with expert musicians. Quantitative evaluation and user feedback demonstrate improved output diversity, harmonic coherence, adaptation speed and user agency. Our results demonstrate a simple yet effective method to mitigate reward hacking in RL post-training of generative sequence models.

Reinforcement Learning · Deep RL

Ezgi Korkmaz

Learning in high-dimensional MDPs with complex state dynamics became possible with the progress achieved in reinforcement learning research. At the same time, deep neural policies have been observed to be highly unstable with respect to the minor variations in their state space, causing volatile and unpredictable behaviour. To alleviate these volatilities, a line of work suggested techniques to cope with this problem via explicitly regularizing the temporal difference loss to ensure local $\epsilon$-invariance in the state space. In this paper, we provide theoretical foundations on the impact of robust, i.e. adversarial, training on reinforcement learning. Our comprehensive theoretical and experimental analysis reveals that standard reinforcement learning inherently learns counterfactual values while recent training techniques that focus on explicitly enforcing $\epsilon$-local invariance cause policies to lose counterfactuality, and further result in learning misaligned and inconsistent values. In connection to this analysis, we further highlight that this line of training methods breaks the core intuition and the true biological inspiration of reinforcement learning, sacrifices essential inherent skills that enable reasoning and generalization, and introduces an intrinsic gap between how natural intelligence understands and interacts with an environment in contrast to AI agents trained via $\epsilon$-local invariance methods. The misalignment, inaccuracy and the loss of counterfactuality revealed in our paper further demonstrate the need to rethink the approach in establishing truly reliable and generalizable reinforcement learning policies.

Deep Learning · Everything Else

Lukas Rauch, René Heinrich, Houtan Ghaffari, Lukas Miklautz, Ilyass Moummad, Bernhard Sick, Christoph Scholz

Although probing frozen models has become a standard evaluation paradigm, self-supervised learning in audio defaults to fine-tuning {when pursuing state-of-the-art on AudioSet}. A key reason is that global pooling creates an information bottleneck causing linear probes to misrepresent the embedding quality: The $\texttt{cls}$-token discards crucial token information about dispersed, localized events in audio. This weakness is rooted in the mismatch between the pretraining objective (globally) and the downstream task (localized). Across a comprehensive benchmark of 13 datasets and 6 spectrogram-based encoders, we investigate the global pooling bottleneck. We introduce binarized prototypical probes: a lightweight and simple pooling method that learns prototypes to perform class-wise information aggregation. Despite its simplicity, our method notably outperforms linear and attentive probing. Our work establishes probing as a competitive and efficient paradigm for evaluating audio SSL models, challenging the reliance on costly fine-tuning.

Deep Learning · Attention Mechanisms

Arthur S. Bianchessi, Yasmin C. Aguirre, Rodrigo C Barros, Lucas S. Kupssinskü

Transformer-based language models rely on positional encoding (PE) to handle token order and support context length extrapolation. However, existing PE methods lack theoretical clarity and rely on limited evaluation metrics to substantiate their extrapolation claims. We propose the Bayesian Attention Mechanism (BAM), a theoretical framework that formulates positional encoding as a prior within a probabilistic model. BAM unifies existing methods (e.g., NoPE and ALiBi) and motivates a new Generalized Gaussian positional prior that substantially improves long-context generalization. Empirically, BAM enables accurate information retrieval at $500\times$ the training context length, outperforming previous state-of-the-art context length generalization by more than $25\times$ in retrieval accuracy while maintaining comparable perplexity and introducing minimal additional parameters.

Theory · Interpretability and Visualization

Jingyi Cui, Qi Zhang, Yifei Wang, Yisen Wang

Sparse autoencoders (SAEs) have recently emerged as a powerful tool for interpreting the features learned by large language models (LLMs). By reconstructing features with sparsely activated networks, SAEs aim to recover complex superposed polysemantic features into interpretable monosemantic ones. Despite their wide applications, it remains unclear under what conditions SAEs can fully recover the ground truth monosemantic features from the superposed polysemantic ones. In this paper, we provide the first theoretical analysis with a closed-form solution for SAEs, revealing that they generally fail to fully recover the ground truth monosemantic features unless the ground truth features are extremely sparse. To improve the feature recovery of SAEs in general cases, we propose a reweighting strategy targeting at enhancing the reconstruction of the ground truth monosemantic features instead of the observed polysemantic ones. We further establish a theoretical weight selection principle for our proposed weighted SAE (WSAE). Experiments across multiple settings validate our theoretical findings and demonstrate that our WSAE significantly improves feature monosemanticity and interpretability.