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Deep Learning · Everything Else

Xu Wang, Yan Hu, Wang Benyou, Difan Zou

Sparse Autoencoders (SAEs) are widely used to steer large language models (LLMs), based on the assumption that their interpretable features naturally enable effective model behavior steering. Yet a fundamental question remains: does higher interpretability imply better steering utility? To answer this, we train 90 SAEs across three LLMs (Gemma-2-2B, Qwen-2.5-3B, Gemma-2-9B), spanning five architectures and six sparsity levels. We evaluate interpretability with SAEBench (Karvonen et al., 2025) and steering utility with AxBench (Wu et al., 2025), and analyze rank agreement via Kendall’s rank coefficient $\tau_b$. Our analysis reveals only a relatively weak positive association ($\tau_b \approx 0.298$), indicating that interpretability is an insufficient proxy for steering performance. We conjecture the interpretability–utility gap stems from feature selection: not all SAE features are equally effective for steering. To identify features that truly steer LLM behavior, we propose a novel selection criterion, $\Delta$ Token Confidence, which measures how much amplifying a feature changes the next-token distribution. Our method improves steering performance on three LLMs by **52.52\%** compared to the best prior output score–based criterion (Arad et al., 2025). Strikingly, after selecting features with high $\Delta$ Token Confidence, the correlation between interpretability and utility vanishes ($\tau_b \approx 0$) and can even become negative, further highlighting their divergence for the most effective steering features.

Deep Learning · Generative Models and Autoencoders

Peter Blohm, Vikas Garg

Composing pretrained diffusion models provides a cost-effective mechanism to encode constraints and unlock complex generative capabilities. Prior work relies on crafting compositional operators that seek to extend set-theoretic notions such as union and intersection to diffusion models, e.g., using a product or mixture of the underlying energy functions. We expose the inadequacy and inconsistency of combining these operators in terms of limited mode coverage, biased sampling, instability under negation queries, and failure to satisfy basic compositional laws such as idempotency and distributivity. We introduce a principled calculus grounded in fuzzy logic that resolves these issues. Specifically, we define a general class of conjunction, disjunction, and negation operators that generalize the classical mixtures, illustrating how they circumvent various pathologies and enable precise combinatorial reasoning with score models. Beyond existing methods, the proposed *Dombi* operators yield complex generative outcomes, such as the Exclusive-OR (XOR) of individual scores. We establish rigorous theoretical guarantees on the stability and temperature scaling of Dombi compositions, and derive Feynman-Kac correctors to mitigate the sampling bias in score composition. Empirical results on image generation with stable diffusion and multi-objective molecular generation substantiate the conceptual, theoretical, and methodological benefits. Overall, this work lays the foundation for systematic design, analysis, and deployment of diffusion ensembles. Code is available at [https://github.com/Aalto-QuML/logic-diffusion-composition](https://github.com/Aalto-QuML/logic-diffusion-composition)

Deep Learning · Generative Models and Autoencoders

Hao Huang, Jingtao Ding, Mengqi Liao, Xin Wang, Jinyang Ban, Yuan Yuan, Huaiyu Wan, Yong Li

The widespread adoption of Low-Rank Adaptation (LoRA) for efficient fine-tuning of large language models has created demand for scalable parameter generation methods that can synthesize adaptation weights directly from task descriptions, avoiding costly task-specific training. We present LoRAGen, a structure-aware method for generating LoRA parameters from natural language descriptions. Through empirical analysis of LoRA libraries, we identify two key structural properties of LoRA parameter spaces: non-uniqueness of low-rank decomposition and heterogeneous weight distributions across network modules. These properties necessitate specialized parameter generation methods rather than general weight space learning approaches. LoRAGen employs a latent diffusion model with two innovations: weight-space supervision on full adaptation matrices to handle decomposition non-uniqueness, and a module-aware Mix-of-Experts decoder that adapts to module-specific weight distributions. Experiments show LoRAGen achieves 96.0\% performance relative to task-specific LoRAs on FLAN-T5-large and 72.7\% on Gemma-2-2B-Instruct for in-distribution tasks, while obtaining 40.2\% on zero-shot generation across unseen tasks—surpassing baselines by nearly 5\%. Our work establishes the first structure-aware approach to LoRA generation with insights into adaptation weight space geometry.

General Machine Learning · Causality

Valentyn Melnychuk, Stefan Feuerriegel

Various deep generative models have been proposed to estimate potential outcomes distributions from observational data. However, none of them have the favorable theoretical property of general Neyman-orthogonality and, associated with it, quasi-oracle efficiency and double robustness. In this paper, we introduce a general suite of generative Neyman-orthogonal (doubly-robust) learners that estimate the conditional distributions of potential outcomes. Our proposed generative doubly-robust learners (GDR-learners) are flexible and can be instantiated with many state-of-the-art deep generative models. In particular, we develop GDR-learners based on (a) conditional normalizing flows (which we call GDR-CNFs), (b) conditional generative adversarial networks (GDR-CGANs), (c) conditional variational autoencoders (GDR-CVAEs), and (d) conditional diffusion models (GDR-CDMs). Unlike the existing methods, our GDR-learners possess the properties of quasi-oracle efficiency and rate double robustness, and are thus asymptotically optimal. In a series of (semi-)synthetic experiments, we demonstrate that our GDR-learners are very effective and outperform the existing methods in estimating the conditional distributions of potential outcomes.

Deep Learning · Generative Models and Autoencoders

Sara Kangaslahti, Nihal V. Nayak, Jonathan Geuter, Marco Fumero, Francesco Locatello, David Alvarez-Melis

Large language models (LLMs) are typically deployed under diverse memory and compute constraints. Existing approaches build model families by training each size independently, which is prohibitively expensive and provides only coarse-grained size options. In this work, we identify a novel phenomenon that we call boomerang distillation: starting from a large base model (the teacher), one first distills down to a small student and then progressively reconstructs intermediate-sized models by re-incorporating blocks of teacher layers into the student without any additional training. This process produces zero-shot interpolated models of many intermediate sizes whose performance scales smoothly between the student and teacher, often matching or surpassing pretrained or distilled models of the same size. We further analyze when this type of interpolation succeeds, showing that alignment between teacher and student through pruning and distillation is essential. Boomerang distillation thus provides a simple and efficient way to generate fine-grained model families, dramatically reducing training cost while enabling flexible adaptation across deployment environments. The code and models are available at [https://github.com/dcml-lab/boomerang-distillation](https://github.com/dcml-lab/boomerang-distillation).

Applications · Robotics

Yang Zhang, Chenwei Wang, ouyang lu, Yuan Zhao, Yunfei Ge, Zhenglong Sun, Xiu Li, Chi Zhang, Chenjia Bai, Xuelong Li

Vision-Language-Action (VLA) models pre-trained on large, diverse datasets show remarkable potential for general-purpose robotic manipulation. However, a primary bottleneck remains in adapting these models to downstream tasks, especially when the robot's embodiment or the task itself differs from the pre-training data. This discrepancy leads to a significant mismatch in action distributions, demanding extensive data and compute for effective fine-tuning. To address this challenge, we introduce Align-Then-stEer (ATE), a novel, data-efficient, and plug-and-play adaptation framework. ATE first aligns disparate action spaces by constructing a unified latent space, where a variational autoencoder constrained by reverse KL divergence embeds adaptation actions into modes of the pre-training action latent distribution. Subsequently, it steers the diffusion- or flow-based VLA's generation process during fine-tuning via a guidance mechanism that pushes the model's output distribution towards the target domain. We conduct extensive experiments on cross-embodiment and cross-task manipulation in both simulation and real world. Compared to direct fine-tuning of representative VLAs, our method improves the average multi-task success rate by up to 9.8% in simulation and achieves a striking 32% success rate gain in a real-world cross-embodiment setting. Our work presents a general and lightweight solution that greatly enhances the practicality of deploying VLA models to new robotic platforms and tasks. Our code is released at \url{https://github.com/TeleHuman/Align-Then-Steer}.

Deep Learning · Generative Models and Autoencoders

Yihe Liu, Huibin Wang, Xianming Hu, Pinyi Zhang, Jiahao Xiong, Chenglin Wang, Nuoyi Chen, Hongbo Zhao, Jie Zhang, Kai Zhang

Auto-regressive large language models (LLMs) exhibit a non-trivial capacity to "anticipate'' long-range future tokens despite being trained to predict only one token at a time. Nevertheless, how to systematically profile, enhance and leverage such capacity to practically improve LLM reasoning performance remains unclear. In this paper, we propose **Next Token-Bag Exploitation (Next-ToBE)** to tackle this challenge. Next-ToBE quantifies LLM’s anticipatory capacity by measuring how well tokens in the future window are pre-captured by the model’s current softmax probabilities. This capacity is strongly correlated with LLM generative quality but often suppressed by the rigid one-hot objective in next-token prediction. To address this, we replace the {one-hot target vector} in next-token prediction with a soft target distribution spanning additional future tokens. Specifically, the immediate next token retains the highest importance, while more distant ``look-ahead tokens'' are also included to enrich supervision, with their importance dynamically determined by temporal and semantic relevance patterns to inject forward-looking pressure. Besides, the fitting process emphasizes the model’s intrinsic anticipatory tendency, thus preserving the confidence and fidelity of the pre-trained model to improve training stability. Overall, Next-ToBE not only effectively activates LLM anticipatory capacity through fine-tuning, yielding notable gains in reasoning performance with higher memory and computational efficiency against the MTP baselines, but also shows great potential in pretraining setting by successfully cultivating this capacity from scratch. These highlight its value as an effective strategy to extend the prediction horizon of LLMs, enabling them to see further, and reason better.

Deep Learning · Theory

Shyam Venkatasubramanian, Sean Moushegian, Ahmed Aloui, VAHID TAROKH

Quantifying the limitations of classical neural network architectures is a critically underexplored area of machine learning research. Deriving lower bounds on the optimal performance of these architectures can facilitate improved neural architecture search and overfitting detection. We present an information-theoretic lower bound on the generalization mean squared error of autoencoders with sigmoid activation functions. Through the Estimation Error and Differential Entropy (EEDE) inequality for continuous random vectors, we derive this lower bound, which provides a new perspective on the inherent limitations and capabilities of autoencoders. Our analysis extends to the examination of how this lower bound is influenced by various architectural features and data distribution characteristics. This study enriches our theoretical understanding of autoencoders and has substantial practical implications for their design, optimization, and application in the field of deep learning.

General Machine Learning · Representation Learning

Albert Miao, Chenliang Zhou, Jiawei Zhou, Cengiz Oztireli

Sparse Autoencoders (SAEs) have found human-interpretable features in LLM activations, clarifying how LLMs transform input to output. However, they have rarely been applied outside of text, limiting explorations of feature dynamics. We present the first application of SAEs to the 3D domain, analyzing the features found in 53k 3D objects encoded by a state-of-the-art 3D reconstruction VAE. We observe that the model encodes discrete rather than continuous features, leading to our key finding: the model's feature activations approximate a discrete state space, driven by phase-like transitions. Through this state space framework, we address three otherwise unintuitive behaviors — the preference for positional encoding features, the sigmoidal relationship between feature ablation and reconstruction loss, and the bimodal distribution of phase transition points. This final observation suggests the model redistributes superposition interference to prioritize the high-importance features. Our work not only catalogs and explains unexpected feature dynamics, but also provides a framework to explain the model's learning dynamics. The code is available at https://feature3d.github.io/Dora-SAE/.

Deep Learning · Generative Models and Autoencoders

Jiajia Yu, Junghwan Lee, Yao Xie, Xiuyuan Cheng

Mean-field games (MFGs) study the Nash equilibrium of systems with a continuum of interacting agents, which can be formulated as the fixed-point of optimal control problems. They provide a unified framework for a variety of problems, including both potential and non-potential games, with applications in areas such as generative modeling. Despite their broad applicability, solving high-dimensional MFGs remains a significant challenge due to fundamental computational and analytical obstacles. In this work, we propose a particle-based deep Flow Matching (FM) method to tackle high-dimensional MFG computation. In each iteration of our proximal fixed-point scheme, particles are updated using first-order information, and a flow neural network is trained to match the velocity of the sample trajectories. Theoretically, in the optimal control setting, we prove that our scheme converges to a stationary point sublinearly, and upgrade to linear (exponential) convergence under additional convexity assumptions. Our proof uses FM to induce an Eulerian coordinate (density-based) from a Lagrangian one (particle-based), and this also leads to certain equivalence results between the two formulations for MFGs when the Eulerian solution is sufficiently regular. Our method demonstrates promising experimental performance on MFGs in high dimensions.

Deep Learning · Generative Models and Autoencoders

Yuchen Yang, Wenze Lin, Enhao Huang, Zhixuan Chu, Hongbin zhou, Lan Tao, Yiming Li, Zhan Qin, Kui Ren

Large Language Models (LLMs) have seen remarkable advancements, achieving state-of-the-art results in diverse applications. Fine-tuning, an important step for adapting LLMs to specific downstream tasks, typically involves further training on corresponding datasets. However, a fundamental discrepancy exists between current fine-tuning datasets and the token-level optimization mechanism of LLMs: most datasets are designed at the sentence-level, which introduces token-level noise, causing negative influence to final performance. In this paper, we propose XTF, an explainable token-level noise filtering framework. XTF decomposes the complex and subtle contributions of token-level data to the fine-tuning process into three distinct and explicit attributes (reasoning importance, knowledge novelty, and task relevance), which can be assessed using scoring methods, and then masks the gradients of selected noisy tokens accordingly to optimize the performance of fine-tuned LLMs. We conduct extensive experiments on three representative downstream tasks (math, code and medicine) across 7 mainstream LLMs. The results demonstrate that XTF can significantly improve downstream performance by up to 13.7% compared to regular fine-tuning. Our work highlights the importance of token-level dataset optimization, and demonstrates the potential of strategies based on attribute decomposition for explaining complex training mechanisms.

Deep Learning · Generative Models and Autoencoders

Melika Mobini, Vincent Holst, Floriano Tori, Andres Algaba, Vincent Ginis

Large language models are increasingly used to curate bibliographies, raising the question: are their reference lists distinguishable from human ones? We build paired citation graphs, ground truth and GPT-4o-generated (from parametric knowledge), for 10,000 focal papers ($\approx$ 275k references) from SciSciNet, and added a field-matched random baseline that preserves out-degree and field distributions while breaking latent structure. We compare (i) structure-only node features (degree/closeness/eigenvector centrality, clustering, edge count) with (ii) 3072-D title/abstract embeddings, using an RF on graph-level aggregates and Graph Neural Networks with node features. Structure alone barely separates GPT from ground truth (RF accuracy $\approx$ 0.60) despite cleanly rejecting the random baseline ($\approx$ 0.89--0.92). By contrast, embeddings sharply increase separability: RF on aggregated embeddings reaches $\approx$ 0.83, and GNNs with embedding node features achieve 93\% test accuracy on GPT vs.\ ground truth. We show the robustness of our findings by replicating the pipeline with Claude Sonnet 4.5 and with multiple embedding models (OpenAI and SPECTER), with RF separability for ground truth vs.\ Claude $\approx 0.77$ and clean rejection of the random baseline. Thus, LLM bibliographies, generated purely from parametric knowledge, closely mimic human citation topology, but leave detectable semantic fingerprints; detection and debiasing should target content signals rather than global graph structure.

Deep Learning · Generative Models and Autoencoders

Sijia Liu, Niklas Muennighoff, Kawin Ethayarajh

Online alignment (e.g., GRPO) is generally more performant than offline alignment (e.g., DPO)---but why? Drawing on prospect theory from behavioral economics, we propose a human-centric explanation. We prove that online on-policy sampling better approximates the human-perceived distribution of what the model can produce, and PPO/GRPO-style clipping---originally introduced to just stabilize training---recovers a perceptual bias in how humans perceive probability. In this sense, PPO/GRPO act as perceptual losses already. Our theory further suggests that the online/offline dichotomy is itself incidental to maximizing human utility, since we can achieve the same effect by selectively training on any data in a manner that mimics human perception, rather than restricting ourselves to online on-policy data. Doing so would allow us to post-train more quickly, cheaply, and flexibly without sacrificing performance. To this end, we propose a design pattern that explicitly incorporates perceptual distortions of probability into objectives like DPO/KTO/GRPO, creating $\textit{humanline variants}$ of them. Surprisingly, we find that these humanline variants, even when trained with offline off-policy data, can match the performance of their online counterparts on both verifiable and unverifiable tasks.

Deep Learning · Generative Models and Autoencoders

Yunhong Min, Juil Koo, Seungwoo Yoo, Minhyuk Sung

We introduce BézierFlow, a lightweight training approach for few-step generation with pretrained diffusion and flow models. BézierFlow achieves a 2–3× performance improvement for sampling with $\leq$ 10 NFEs while requiring only 15 minutes of training. Recent lightweight training approaches have shown promise by learning optimal timesteps, but their scope remains restricted to ODE discretizations. To broaden this scope, we propose learning the optimal transformation of the sampling trajectory by parameterizing stochastic interpolant (SI) schedulers. The main challenge lies in designing a parameterization that satisfies critical desiderata, including boundary conditions, differentiability, and monotonicity of the SNR. To effectively meet these requirements, we represent scheduler functions as Bézier functions, where control points naturally enforce these properties. This reduces the problem to learning an ordered set of points in the time range, while the interpretation of the points changes from ODE timesteps to Bézier control points. Across a range of pretrained diffusion and flow models, BézierFlow consistently outperforms prior timestep-learning methods, demonstrating the effectiveness of expanding the search space from discrete timesteps to Bézier-based trajectory transformations.

Deep Learning · Generative Models and Autoencoders

Alexi Gladstone, Ganesh Nanduru, Md Mofijul Islam, Peixuan Han, Hyeonjeong Ha, Aman Chadha, Yilun Du, Heng Ji, Jundong Li, Tariq Iqbal

Inference-time computation, analogous to human System 2 Thinking, has recently become popular for improving model performance. However, most existing approaches suffer from several limitations: they are modality-specific (e.g., working only in text), problem-specific (e.g., verifiable domains like math and coding), or require additional supervision/training on top of unsupervised pretraining (e.g., verifiers or verifiable rewards). In this paper, we ask the question “Is it possible to generalize these System 2 Thinking approaches, and develop models that learn to think solely from unsupervised learning?” We find the answer is yes, by learning to explicitly verify the compatibility between inputs and candidate-predictions, and then re-framing prediction problems as optimization with respect to this verifier. Specifically, we train Energy-Based Transformers (EBTs)---a new class of Energy-Based Models (EBMs)---to assign an energy value to every input and candidate-prediction, enabling predictions through energy minimization until convergence. To support this approach, we introduce several key techniques for stable and parallelizable training, which enable the emergence of strong System 2 Thinking capabilities and scalable EBMs. Across discrete and continuous modalities, we find EBTs outperform the Transformer++ approach, scaling up to 35% faster during pretraining, and improving inference-time performance by up to 29%. EBTs also surpass Diffusion Transformers on image denoising while requiring 99% fewer forward passes. Moreover, System 2 Thinking with EBTs yields larger performance gains on data that is farther out-of-distribution, and EBTs achieve better results than existing models on most downstream tasks despite achieving the same or worse pretraining performance, enabling EBTs to generalize better than existing approaches. Consequently, EBTs are a flexible and exciting new approach for scaling both the learning and thinking capabilities of models.

Theory · Interpretability and Visualization

Chiraag Kaushik, Davis Barch, Andrea Fanelli

The Linear Representation Hypothesis asserts that the embeddings learned by neural networks can be understood as linear combinations of features corresponding to high-level concepts. Based on this ansatz, sparse autoencoders (SAEs) have recently become a popular method for decomposing embeddings into a sparse combination of linear directions, which have been shown empirically to often correspond to human-interpretable semantics. However, recent attempts to apply SAEs to multimodal embedding spaces (such as the popular CLIP embeddings for image/text data) have found that SAEs often learn ``split dictionaries,'' where most of the learned sparse features are essentially unimodal, active only for data of a single modality. In this work, we study how to effectively adapt SAEs for the setting of multimodal embeddings while ensuring multimodal alignment. We first argue that the existence of a split dictionary decomposition on an aligned embedding space implies the existence of a non-split dictionary with improved modality alignment. Then, we propose a new SAE-based approach to multimodal embedding decomposition using cross-modal random masking and group-sparse regularization. We apply our method to popular embeddings for image/text (CLIP) and audio/text (CLAP) data and show that, compared to standard SAEs, our approach learns a more multimodal dictionary while reducing the number of dead neurons and improving feature semanticity. We finally demonstrate how this improvement in alignment of concepts between modalities can enable improvements in the interpretability and control of cross-modal tasks.

Deep Learning · Generative Models and Autoencoders

Zeqi Ye, Qijie Zhu, Molei Tao, Minshuo Chen

Diffusion models have achieved remarkable success across diverse domains, but they remain vulnerable to memorization---reproducing training data rather than generating novel outputs. This not only limits their creative potential but also raises concerns about privacy and safety. While empirical studies have explored mitigation strategies, theoretical understanding of memorization remains limited. We address this gap through developing a dual-separation result via two complementary perspectives: statistical estimation and network approximation. From the estimation side, we show that the ground-truth score function does not minimize the empirical denoising loss, creating a separation that drives memorization. From the approximation side, we prove that implementing the empirical score function requires network size to scale with sample size, spelling a separation compared to the more compact network representation of the ground-truth score function. Guided by these insights, we develop a pruning-based method that reduces memorization while maintaining generation quality in diffusion transformers.

Deep Learning · Generative Models and Autoencoders

Haozheng Luo, Zhuolin Jiang, Md Zahid Hasan, Yan Chen, Soumalya Sarkar

We propose **FROST**, an attention-aware method for efficient reasoning. Unlike traditional approaches, FROST leverages attention weights to prune uncritical reasoning paths, yielding shorter and more reliable reasoning trajectories. Methodologically, we introduce the concept of *reasoning outliers* and design an attention-based mechanism to remove them. Theoretically, FROST preserves and enhances the model’s reasoning capacity while eliminating outliers at the sentence level. Empirically, we validate FROST on four benchmarks using two strong reasoning models (Phi-4-Reasoning and GPT-oss-20B), outperforming state-of-the-art methods such as TALE and ThinkLess. Notably, FROST achieves an average **69.68%** reduction in token usage and a **26.70%** improvement in accuracy over the base model. Furthermore, in evaluations of attention outlier metrics, FROST reduces the maximum infinity norm $\||\mathbf{x}\||_{\infty}$ by **15.97%** and the average kurtosis by **91.09%** compared to the base model.

General Machine Learning · Representation Learning

Yotam Norman, Ron Meir

We propose a novel unsupervised framework for Invariant Risk Minimization (IRM), extending the concept of invariance to settings where labels are unavailable. Traditional IRM methods rely on labeled data to learn representations that are robust to distributional shifts across environments. In contrast, our approach redefines invariance through feature distribution alignment, enabling robust representation learning from unlabeled data. We introduce two methods within this framework: Principal Invariant Component Analysis (PICA), a linear method that extracts invariant directions under Gaussian assumptions, and Variational Invariant Autoencoder (VIAE), a deep generative model that separates environment-invariant and environment-dependent latent factors. Our approach is based on a novel ``unsupervised'' structural causal model and supports environment-conditioned sample-generation and intervention. Empirical evaluations on synthetic dataset, modified versions of MNIST, and CelebA demonstrate the effectiveness of our methods in capturing invariant structure, preserving relevant information, and generalizing across environments without access to labels.

General Machine Learning · Everything Else

Ruixin Guo, Xinyu Li, Hao Zhou, Yang Zhou, Ruoming Jin

Linear autoencoders (LAEs) have gained increasing popularity in recommender systems due to their simplicity and strong empirical performance. Most LAE models, including the Emphasized Denoising Linear Autoencoder (EDLAE) introduced by (Steck, 2020), use quadratic loss during training. However, the original EDLAE only provides closed-form solutions for the hyperparameter choice $b = 0$, which limits its capacity. In this work, we generalize EDLAE objective function into a Decoupled Expected Quadratic Loss (DEQL). We show that DEQL simplifies the process of deriving EDLAE solutions and reveals solutions in a broader hyperparameter range $b > 0$, which were not derived in Steck’s original paper. Additionally, we propose an efficient algorithm based on Miller’s matrix inverse theorem to ensure the computational tractability for the $b > 0$ case. Empirical results on benchmark datasets show that the $b > 0$ solutions provided by DEQL outperform the $b = 0$ EDLAE baseline, demonstrating that DEQL expands the solution space and enables the discovery of models with better testing performance.