ICML 2026 Papers

International Conference on Machine Learning

Decision breakdown

6,341papers

Counted from the official paper list; may differ slightly from the number the conference announced.

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Topic: Multimodal LLMs · 1,051 papers · Reset filters

Best of Both Worlds: Multimodal Reasoning and Generation via Unified Discrete Flow Matching

Onkar Kishor Susladkar, Tushar Prakash, Gayatri Deshmukh, Kiet A. Nguyen, Jiaxun Zhang, Adheesh Sunil Juvekar, Tianshu Bao, Lin Chai, Sparsh Mittal, Inderjit S Dhillon, Ismini Lourentzou

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We propose UniDFlow, a unified discrete flow-matching framework for multimodal understanding, generation, and editing. It decouples understanding and generation via task-specific low-rank adapters, avoiding objective interference and representation entanglement, while a novel reference-based multimodal preference alignment optimizes relative outcomes under identical conditioning, improving faithfulness and controllability without large-scale retraining. UniDFlow achieves SOTA performance across eight benchmarks and exhibits strong zero-shot generalization to tasks including inpainting, in-context image generation, reference-based editing, and compositional generation, despite no explicit task-specific training.

Poster
The Hidden Cost of Structured Generation in LLMs: Draft-Conditioned Constrained Decoding

Avinash Reddy, Thayne T. Walker, Jaime S. Ide, Amrit Singh Bedi

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Large language models (LLMs) are increasingly used to generate executable outputs, JSON objects, and API calls, where a single syntax error can make the output unusable. Constrained decoding enforces validity token-by-token via masking and renormalization, but it can distort generation when the model assigns low probability mass to valid continuations, pushing decoding toward locally valid yet semantically incorrect trajectories. We propose \emph{Draft-Conditioned Constrained Decoding (DCCD)}, a simple two-step, training-free inference procedure that decouples semantic planning from structural enforcement: an unconstrained draft is generated first, and constrained decoding is then applied, conditioned on this draft, to guarantee validity. We analyze DCCD through a KL-projection view, showing that draft conditioning increases feasible mass and reduces the cumulative “projection tax” induced by hard constraints, with an optional best-of-$K$ draft selection. Across structured reasoning benchmarks, DCCD improves strict structured accuracy by up to +24 percentage points over standard constrained decoding (e.g., 15.2\% to 39.0\% on GSM8K with a 1B model), and enables smaller model pairs to match or exceed much larger constrained baselines, yielding substantial gains in parameter efficiency.

Poster
Is Code Better Than Language for Algorithmic Reasoning?

Terry Tong, Yu Feng, Surbhi Goel, Dan Roth

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For tool-augmented language models, comparing natural-language reasoning with code-execution pipelines is difficult because the comparison changes both the intermediate representation and the execution mechanism. We separate these factors with an intermediate intervention: the model expresses its reasoning as executable code, and the language model simulates that code in context to produce an answer. On a 40-task verifiable algorithmic benchmark, deterministic code execution outperforms natural-language reasoning by +31.6pp. We observe that the intermediate intervention is not meaningfully different from natural-language reasoning (+0.15pp). These results suggest that, in our evaluated setting, changing the intermediate representation alone does not explain the tool-use advantage, providing evidence for the performance gains requiring reliable external execution. We formalize this intuition with a simple statistical decision-theoretic model that characterizes when execution dominates end-to-end risk in our disentangled trace-generation/execution regime. We validate our theory using a reconstruction intervention that leverages a proxy language model to infer natural-language reasoning traces from code representations, recovering performance comparable to the original natural-language reasoning pipeline. All experiments are at https://github.com/TerryTong-Git/ToolProj.

Poster
Scene Graph Thinking: Reinforcing Structured Visual Reasoning for Multimodal Large Language Models

Zhiwei Yang, Yuanchen Wu, Nan Zhang, Yucong Meng, Ke Yan, Shouhong Ding

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Multimodal Large Language Models (MLLMs) have demonstrated strong perception and reasoning capabilities. However, most existing models focus on isolated objects and neglect structured relationships for efficient target navigation, limiting their performance on visually intensive tasks. To address this challenge, we introduce Scene Graph Thinking (SaGe), a novel paradigm that enables fine-grained and structured visual reasoning through explicit scene-graph representations. Specifically, we first introduce an automated data engine that converts flat image–text corpora into structured scene graphs, where hierarchical entities constitute the nodes and diverse visual relations define the edges. Building upon this, we construct 120K high-quality training data by sampling reasoning traces from scene graphs. Then two-stage graph-aligned post-training paradigms are introduced, where supervised fine-tuning internalizes MLLMs with structured reasoning, and subsequent reinforcement fine-tuning proposes node-as-proxy graph rewards to consolidate efficient graph exploration. With curated data and graph-aligned training, our approach achieves significant improvements across eight multimodal benchmarks, demonstrating strong effectiveness on fine-grained perception and reasoning tasks.

Poster
Open-World LLM Logical Reasoning

Ye Mo, Chuan Zhou, Fengxiang Cheng, Jialin Yu, Liangming Pan, Fenrong Liu, Sheng Zhou, Haoxuan Li, Zhouchen Lin, Philip Torr

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Large Language Models (LLMs) achieve remarkable performance but struggle with complex logical reasoning, particularly in real-world settings. Existing research is largely confined to the closed-world assumption, which posits that all premises required for reasoning are explicitly provided. However, real-world tasks frequently exhibit open-world characteristics, where the provided information is insufficient to infer a conclusion due to missing premises or implicit commonsense knowledge. To address this, we propose OpenIKLR, an Open-world Incomplete-Knowledge-aware Logical Reasoning framework that integrates symbolic logic solvers with LLMs. OpenIKLR first translates natural language into symbolic representations to pinpoint reasoning gaps via a logical solver. It then iteratively generates a minimal set of necessary missing premises using LLMs. To ensure these added premises are both logically sound and factually accurate, we introduce a dual-verification: logic verification via the solver and fact verification via the LLMs. Experiments show that OpenIKLR consistently outperforms existing logical reasoning and RAG baselines across multiple backbones and real-world datasets. The code is available at https://github.com/OpenIKLR/OpenIKLR.

Poster
Steer Where It Matters: Token-Level Visual-Sensitivity Steering for LVLMs Hallucination Mitigation

Ruipeng Zhang, Zhihao Li, C.L.Philip Chen, Tong Zhang

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Large vision language models (LVLMs) have made rapid advancements and are deployed across various applications, yet hallucinations remain a major challenge. Activation steering is appealing due to its minimal training overhead and controllability at inference time. However we found that during autoregressive decoding, visual conditioning affects token prediction sparsely and locally across decoding steps, and many existing methods that average image-versus-no-image differences over the entire sequence dilute these critical signals, yielding low signal-to-noise ratio steering directions. Additionally, many existing methods apply a fixed steering strength, which misallocates the intervention budget, over-perturbs non-critical tokens, and can cause instability. To address these limitations, we propose Token-Level Visual-Sensitivity Steering (TLVS) for hallucination mitigation. Our approach first extract token-level steering vectors and refines them, and then applies fine-grained, visual-sensitivity–adaptive steering only where it matters. This lightweight, plug-and-play mechanism requires only minimal training for calibration and can be applied across diverse vision-language models. It modulates the steering strength at each decoding step, selectively suppressing hallucination-prone spans while preserving evidence-grounded content. We evaluate TLVS on several benchmarks, including POPE, AMBER, CHAIR (COCO), MMHal and HallusionBench, demonstrating consistent improvements over previous steering methods.

Poster
Safe Autoregressive Image Generation with Iterative Self-Improving Codebooks

Yunqi Xue, Zhijiang Li, Philip Torr, Jindong Gu

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Unlike diffusion-based models that operate in continuous latent spaces, autoregressive unified multimodal models produce images by sequentially predicting discretized visual tokens. These tokens are derived from a codebook that maps embeddings to quantized visual patterns. The language-like architecture enables unified multimodal models to effectively capture text conditional information for generation, making them promising for text-to-image tasks. This also raises an interesting question: *how safe are the images generated in such an autoregressive way?* In this work, we propose iterative self-improving codebooks for safe autoregressive generation. We leverage the understanding and judgment capabilities of the unified multimodal model itself to identify unsafe generated images without human annotation. Subsequently, the inherent representations in the codebook are fixed to eliminate harmful mappings. Our method comprises two steps: first, we use the unified model to identify unsafe generations and construct corresponding harmful and safe image-text pairs. These pairs are used to construct the Harmful Space and guide updates to the codebook, thereby eliminating harmful outputs. Second, we perform adaptive fine-tuning on the codebook within the harmless space using safe image-text pairs to ensure the quality of generated images. These two steps are repeated until no further improvement is observed, producing a safety-enhanced model codebook. Without additional external feedback, the safety of models is improved iteratively.

Poster
MoDA: Modulation Adapter for Fine-Grained Visual Understanding in Instructional MLLMs

Wayner Barrios, Andrés Villa, Juan C Leon Alcazar, SouYoung Jin, Bernard Ghanem

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Multimodal Large Language Models (MLLMs) have achieved remarkable success in instruction-following tasks by integrating pretrained visual encoders with large language models (LLMs). However, existing approaches often struggle with fine-grained visual grounding due to semantic entanglement in visual patch representations, where individual patches blend multiple distinct visual elements, making it difficult for models to focus on instruction-relevant details. To address this challenge, we propose MoDA (Modulation Adapter), a lightweight module that enhances visual grounding through instruction-guided channel-wise modulation. Unlike token-level methods such as Q-Former that perform additive feature selection, MoDA operates at the channel level through multiplicative modulation on already-aligned features, enabling fine-grained control over which embedding dimensions are relevant for each instruction. Following the standard LLaVA training protocol, MoDA applies cross-attention between language instructions and pre-aligned visual features, generating dynamic modulation masks without architectural modifications or additional supervision. We evaluate MoDA across 12 benchmarks spanning visual question answering, vision-centric reasoning, and hallucination detection, including recent 2024 benchmarks (MMVP, CV-Bench, MMStar, RealWorldQA), on three distinct MLLM architectures: LLaVA-1.5, LLaVA-MoRE (2025), and Qwen3-VL (2025). MoDA delivers consistent gains across all three families, with +12.0 points on MMVP for the LLaVA-1.5 family and +4.8 points on ScienceQA for the LLaVA-MoRE family, and +4.9 ScienceQA, +4.1 RealWorldQA, and +3.8 GQA on Qwen3-VL, confirming that the gains generalize beyond CLIP-based encoders with minimal overhead (<1% FLOPs). Code is available at https://github.com/waybarrios/MoDA.

Poster
Gram2Token: Enabling Run-time GPU-Native Grammar-Constrained Decoding for LLMs

Hantao Hua, Jiming Su, Hao Tang, Yiping Yao, Feng Zhu

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Grammar-constrained decoding enables large language models (LLMs) to reliably generate structured outputs such as JSON, SQL, and domain-specific programs. Existing systems often enforce constraints by executing byte-level parser logic inside the token-level decoding loop, introducing CPU-side control flow and CPU--GPU synchronization that become bottlenecks under continuous batching. We propose Gram2Token, a GPU-native framework that preprocesses deterministic byte-level grammar execution into token-level transitions before inference. Gram2Token aligns tokenizer byte sequences with grammar transitions through a trie and groups tokens with identical transition outcomes across preprocessed grammar states. These categories yield compact validity masks and transition tables, reducing run-time enforcement to category lookup, masking, and state update rather than parser-style byte traversal. Across four model families under schema-diverse continuous batching, Gram2Token achieves a geometric-mean throughput improvement of 1.38$\times$ over the strongest baseline, with a maximum speedup of 1.85$\times$, at the cost of additional preprocessing and time-to-first-token overhead. Break-even and grammar-complexity analyses show that this overhead is amortized by grammar reuse, longer outputs, and larger batches. These results show that token-level grammar preprocessing is an effective design point for high-throughput structured LLM serving. Code is available at https://github.com/Paradozile/Gram2Token.

Poster
No Data? No Problem: Robust Vision-Tabular Learning with Missing Values

Marta Hasny, Laura Alexandra Daza, Keno Bressem, Maxime Di Folco, Julia Schnabel

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Large-scale medical biobanks provide imaging data complemented by extensive tabular information, such as clinical measurements or demographics. However, this abundance of tabular attributes does not reflect real-world datasets, where only a subset of attributes may be available. This discrepancy calls for methods that remain robust to missing values at inference. To address this challenge, we propose RoVTL (Robust Vision-Tabular Learning), a framework designed to handle any level of tabular data availability, from 0% to 100%. RoVTL comprises two key stages: contrastive pretraining, where we introduce tabular attribute missingness as data augmentation to promote robustness, and downstream task tuning, where tabular missingness is complemented by a novel Tabular More vs. Fewer loss that ranks performance based on the amount of available tabular data. Combined with gated-cross attention fusion module, our tuning approach enables consistent performance across all tabular data completeness scenarios. We evaluate RoVTL on cardiac MRI scans from the UK Biobank, demonstrating superior robustness to missing tabular data compared to prior methods. Furthermore, RoVTL successfully generalizes to an external cardiac MRI dataset for multimodal disease classification, and extends to the natural images domain, achieving robust performance on a car advertisements dataset. The model weights and code are available at https://github.com/marteczkah/RoVTL.

Poster
Weaving Graph over Tokens: Contextualizing Structured Sequences for LLMs

Jiaxuan Chen, Zixing Zhang, Ruijun Mao, Wei Sun, Zhicheng Liang, Yuhang Zhang, Yaxi Liu, Fangxin Wang

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Generative Graph Language Models (GLMs) must reconcile topology with causal language modeling. Linearization obscures multi-hop connectivity, while encoder-based methods bottleneck token-level reasoning during generation. Viewing context modeling as a form of message passing, we introduce **Weaver**, an encoder-free framework that extends the attention mechanism of decoder-only LLMs to enable graph reasoning. Weaver maps graph distances into rotary positional embeddings so that structurally connected nodes become proximate in attention space, propagating information over graph topology as if it were sequential context. To achieve this, we combine: 1) a masking mechanism for causal tokens with graph structures; 2) a unified geometric encoding that couples sequential position and graph distance in joint rotary embeddings (Graph-over-Tokens RoPE); and 3) a design principle to prioritize local information to resolve positional ambiguity under graph symmetries. On zero-shot benchmarks, Weaver achieves state-of-the-art performance among generative GLMs, with gains of up to 30\% over prior generative methods on heterophilic graphs, while matching specialized discriminative models on citation networks---all within a unified decoder-only framework.

Poster
Mantis: Lightweight Foundation Model for Time Series Classification

Vasilii Feofanov, Songkang Wen, Shifeng Xie, Simon Roschmann, Marius Alonso, Hongbo Guo, Romain Ilbert, Malik Tiomoko, Quentin Bouniot, Zeynep Akata, Lujia Pan, Jianfeng Zhang, Ievgen Redko

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While foundation models have revolutionized various domains, their application to time series classification remains rather under-explored, with existing literature predominantly focused on forecasting. To bridge this gap, we introduce \textbf{Mantis}, a transformer-based foundation model pre-trained exclusively on synthetic data via self-supervised contrastive learning. We demonstrate that effective tokenization is critical to unlocking the full potential of transformers, proposing a novel token generator unit. Furthermore, we introduce an enhanced test-time methodology that bridges the performance gap between Mantis and strong specialized approaches by leveraging intermediate-layer representations, self-ensembling, and cross-model embedding fusion. Extensive experiments demonstrate that Mantis establishes a new state-of-the-art, outperforming existing foundation models across four diverse dataset collections covering various application domains.

Poster
SpaCeFormer: Fast Proposal-Free Open-Vocabulary 3D Instance Segmentation

Chris Choy, Junha Lee, Chunghyun Park, Minsu Cho, Jan Kautz

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Open-vocabulary 3D instance segmentation is a core capability for robotics and AR/VR, but prior methods trade one bottleneck for another: multi-stage 2D+3D pipelines aggregate foundation-model outputs at hundreds of seconds per scene, while pseudo-labeled end-to-end approaches rely on fragmented masks and external region proposals. We present SpaCeFormer, a proposal-free space-curve transformer that runs in 0.12–0.30 seconds per scene across standard benchmarks, 2–3 orders of magnitude faster than multi-stage 2D+3D pipelines. We pair it with SpaCeFormer-3M, the largest open-vocabulary 3D instance segmentation dataset (3.0M multi-view-consistent captions over 604K instances from 7.4K scenes) built through multi-view mask clustering and multi-view VLM captioning; it reaches **21× higher mask recall** than prior single-view pipelines (54.3% vs 2.5% at IoU>0.5). SpaCeFormer combines spatial window attention with Morton-curve serialization for spatially coherent features, and uses a RoPE-enhanced decoder to predict instance masks directly from learned queries without external proposals. On ScanNet200 we achieve 11.1 zero-shot mAP, a 2.8× improvement over the prior best proposal-free method; on ScanNet++ and Replica, we reach 22.9 and 24.1 mAP, surpassing all prior methods including those using multi-view 2D inputs.

Poster
Global Geometry Is Not Enough for Vision Representations

Jiwan Chung, Seon Joo Kim

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A common assumption in representation learning is that globally well-distributed embeddings support robust and generalizable representations. This focus has shaped both training objectives and evaluation protocols, implicitly treating global geometry as a proxy for representational competence. While global geometry effectively encodes which elements are present, it is often insensitive to how they are composed. We investigate this limitation by testing the ability of geometric metrics to predict compositional binding across 21 vision encoders. We find that standard geometry-based statistics exhibit near-zero correlation with compositional binding. In contrast, functional sensitivity, as measured by the input-output Jacobian, reliably tracks this capability. We further provide an analytic account showing that this disparity arises from objective design, as existing losses explicitly constrain embedding geometry but leave the local input-output mapping unconstrained. These results suggest that global embedding geometry captures only a partial view of representational competence and establish functional sensitivity as a critical complementary axis for modeling composite structure.

Poster
Beyond Next-Token Alignment: Distilling Multimodal Large Language Models via Token Interactions

Lin Chen, Xiaoke Zhao, Kun Ding, Weiwei Feng, Changtao Miao, Zili Wang, Wenxuan Guo, Ying Wang, Kaiyuan Zheng, Bo Zhang, Zhe Li, Shiming Xiang

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Multimodal Large Language Models (MLLMs) demonstrate impressive cross-modal capabilities, yet their substantial size poses significant deployment challenges. Knowledge distillation (KD) is a promising solution for compressing these models, but existing methods primarily rely on static next-token alignment, neglecting the dynamic token interactions, which embed essential capabilities for multimodal understanding and generation. To this end, we introduce **Align-TI**, a novel KD framework designed from the perspective of **T**oken **I**nteractions. Our approach is motivated by the insight that MLLMs rely on two primary interactions: vision-instruction token interactions to extract relevant visual information, and intra-response token interactions for coherent generation. Accordingly, Align-TI introduces two components: IVA enables the student model to imitate the teacher's instruction-relevant visual information extract capability by aligning on salient visual regions. TPA captures the teacher's dynamic generative logic by aligning the sequential token-to-token transition probabilities. Extensive experiments demonstrate Align-TI's superiority. Notably, our approach achieves 2.6% relative improvement over Vanilla KD, and our distilled Align-TI-2B even outperforms LLaVA-1.5-7B (a much larger MLLM) by 7.0%, establishing a new state-of-the-art distillation framework for training parameter-efficient MLLMs.

Poster
LAST: Bridging Vision-Language and Action Manifolds via Gromov-Wasserstein Alignment

Huaihai Lyu, Chaofan Chen, Yuheng Ji, Xiansheng Chen, Pengwei Wang, Shanghang Zhang, Changsheng Xu

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We formulate the learning of generalist Vision-Language-Action (VLA) models as a Gromov-Wasserstein alignment problem, aiming to map semantically similar VL embeddings to physically similar motion primitives. However, solving this is challenging due to the mathematical heterogeneity between the domains: the semantic space of vision-language is topologically linear and isotropic, while the physical manifold of robotic action is non-Euclidean and anisotropic. As a result, direct regression approaches fail due to the disjoint metric structures of these domains, making standard distance minimization ill-posed. To resolve this incompatibility, we introduce LAST (Lie-algebraic Action Space Tokenizer). LAST reconstructs the action space to establish a more consistent metric alignment between the VL and Action modalities. Specifically, LAST bridges the heterogeneity via two stages: (1) *Global Topological Linearization*, which linearizes the action manifold through Lie-algebraic mapping, converting trajectories into a fixed-length, physically additive representation; and (2) *Local Metric Discretization*, where the representation is discretized hierarchically into schemas and whitened residuals, establishing a mathematical isomorphism with the isotropic Euclidean metric. By addressing the structural mismatch globally and locally, LAST enables VLA models with enhanced convergence and generalizability.

Poster
DeepSight: Long-Horizon World Modeling via Latent States Prediction for End-to-End Autonomous Driving

Lingjun Zhang, Changjie Wu, Linzhe Shi, Jiangyang Li, Jiaxin Liu, Lei Yang, Hang Zhang, Mu Xu, Hong Wang

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End-to-end autonomous driving systems are increasingly integrating Vision-Language Model (VLM) architectures, incorporating text reasoning or visual reasoning to enhance the robustness and accuracy of driving decisions. However, the reasoning mechanisms employed in most methods are direct adaptations from general domains, lacking in-depth exploration tailored to autonomous driving scenarios, particularly within visual reasoning modules. In this paper, we propose a driving world model that performs parallel prediction of latent semantic features for consecutive future frames in the bird’s-eye-view (BEV) space, thereby enabling long-horizon modeling of future world states. We also introduce an efficient and adaptive text reasoning mechanism that utilizes additional social knowledge and reasoning capabilities to further improve driving performance in challenging long-tail scenarios. We present a novel, efficient, and effective approach that achieves state-of-the-art (SOTA) results on the closed-loop Bench2drive benchmark. Codes are available at: https://github.com/hotdogcheesewhite/DeepSight.

Poster
CoGeoAD: Hierarchical Color-Geometric Fusion with Multi-View Attention for Zero-Shot 3D Anomaly Detection

Ke Xu, Xinle Wang, Yanning Hou, Xueliang Ma, Juan Xie, Jianfeng Qiu

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Zero-shot 3D anomaly detection is essential for industrial quality inspection, where labeled anomaly samples are scarce. Meanwhile, existing methods lack an effective mechanism to fuse complementary 2D color images with 3D geometric structures, limiting their ability to detect both surface and structural defects in a unified framework. To address these issues, we propose CoGeoAD, a unified CLIP-based framework that fuses color and geometric features by constructing pixel-aligned paired multi-view images. The framework introduces a Data-Driven Multi-View Attention (MVA) mechanism to adaptively aggregate 3D features and a Multi-Stage Color-Geometric Fusion (MS-CGF) module to hierarchically integrate multi-level features from both modalities. Extensive experiments on the MVTec3D-AD and Eyecandies benchmarks demonstrate that CoGeoAD achieves state-of-the-art performance, effectively capturing both structural and textural anomalies in complex industrial scenarios.

Poster
Seeing to Generalize: How Visual Data Corrects Binding Shortcuts

Nicolás Buzeta, Felipe del Rio, Cristian Hinostroza, Denis Parra, Hans Lobel, Rodrigo Toro Icarte

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Vision Language Models (VLMs) are designed to extend Large Language Models (LLMs) with visual capabilities, yet in this work we observe a surprising phenomenon: VLMs can outperform their underlying LLMs on purely text-only tasks, particularly in long-context information retrieval. To investigate this effect, we build a controlled synthetic retrieval task and find that a transformer trained only on text achieves perfect in-distribution accuracy but fails to generalize out-of-distribution (OOD), while subsequent training on an image-tokenized version of the same task nearly doubles text-only OOD performance. Mechanistic interpretability reveals that visual training changes the model’s internal binding strategy: text-only training encourages positional shortcuts, whereas image-based training disrupts them through spatial translation invariance and other encoder-level inductive biases, forcing the model to adopt a more robust symbolic binding mechanism that persists even after text-only examples are reintroduced. We further characterize how binding strategies vary across training regimes and visual encoders, and show that analogous shifts occur during pre-trained LLM-to-VLM transitions. Our findings suggest that cross‑modal training can enhance reasoning and generalization even for tasks grounded in a single modality.

Poster
Concept Concentration for Faithful Representation Intervention

Hongzheng Yang, Yongqiang Chen, Zeyu Qin, Tongliang Liu, Chaowei Xiao, Kun Zhang, Bo Han

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Representation intervention aims to locate and modify the representations that encode the underlying concepts in Large Language Models (LLMs) to elicit the aligned and expected behaviors. Despite the empirical success, it has never been examined whether one could locate the faithful concepts for intervention. In this work, we explore the question in safety alignment. If the interventions are faithful, the intervened LLMs should erase the harmful concepts and be robust to both in-distribution adversarial prompts and the \textit{out-of-distribution} (OOD) jailbreaks. While it is feasible to erase harmful concepts without degrading the benign utility of LLMs in linear settings, we show that it is \textit{infeasible} in the general non-linear setting. To tackle the issue, we propose \texttt{Concept Concentration} (\texttt{COCA}). \texttt{COCA} refactors the training data with an explicit reasoning process, which first identifies the potential unsafe concepts and then decides the responses. Essentially, \texttt{COCA} simplifies the decision boundary between harmful and benign representations, enabling more effective linear erasure. Extensive experiments with multiple representation intervention methods and model architectures demonstrate that \texttt{COCA} significantly reduces both in-distribution and OOD jailbreak success rates, and meanwhile maintaining strong performance on regular tasks such as math and code generation. Our code is publicly available at: \url{https://github.com/tmlr-group/COCA}.

Poster