ICLR 2026 Papers

International Conference on Learning Representations

Decision breakdown

5,358papers

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

  • Oral
    2244.2%
  • Poster
    5,13495.8%

Browse all papers

Noise-Adaptive Diffusion Sampling for Inverse Problems Without Task-Specific Tuning

Yingzhi Xia, Setthakorn Tanomkiattikun, Liangli Zhen, ZAIWANG GU

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Diffusion models (DMs) have recently shown remarkable performance on inverse problems (IPs). Optimization-based methods can fast solve IPs using DMs as powerful regularizers, but it is susceptible to local minima and noise overfitting. Although DMs can provide strong priors for Bayesian approaches, enforcing measurement consistency during the denoising process leads to manifold infeasibility issues. We propose Noise-space Hamiltonian Monte Carlo (N-HMC), a posterior sampling method that treats reverse diffusion as a deterministic mapping from initial noise to clean images. N-HMC enables comprehensive exploration of the solution space, avoiding local optima. By moving inference entirely into the initial-noise space, N-HMC keeps proposals on the learned data manifold. We provide a comprehensive theoretical analysis of our approach and extend the framework to a noise-adaptive variant (NA-NHMC) that effectively handles IPs with unknown noise type and level. Extensive experiments across four linear and three nonlinear inverse problems demonstrate that NA-NHMC achieves superior reconstruction quality with robust performance across different hyperparameters and initializations, significantly outperforming recent state-of-the-art methods. Code will be made available on GitHub upon publication.

Poster
FREAK: A Fine-grained Hallucination Evaluation Benchmark for Advanced MLLMs

Zhihan Yin, Jianxin Liang, Yueqian Wang, Yifeng Yao, Huishuai Zhang, Dongyan Zhao

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Multimodal Large Language Models (MLLMs) suffer from hallucinations. Existing hallucination evaluation benchmarks are often limited by over-simplified tasks leading to saturated metrics, or insufficient diversity that fails to adequately assess the hallucination extent in state-of-the-art multimodal models. To address this gap, we propose FREAK, a comprehensive multimodal benchmark designed for fine-grained hallucination assessment in MLLMs. Through high-quality photorealistic images featuring fine-grained counter-commonsense edits, FREAK innovatively evaluates hallucination phenomena in detailed visual perception of MLLMs. Extensive experiments on FREAK show severe hallucination issues in SOTA models regarding detailed visual perception. To enable deeper investigation, we curate a controlled subset to indirectly evaluate the model’s ability to perceive target detailed information. Through systematic evaluation of prevailing Chain-of-Thought (CoT) prompting techniques within this task, we reveal critical insights regarding hallucination patterns and model reasoning processes.

Poster
SNAP-UQ: Self-supervised Next-Activation Prediction for Single-Pass Uncertainty in TinyML

Ismail Lamaakal, Chaymae Yahyati, Khalid El Makkaoui, Ibrahim Ouahbi, Yassine Maleh

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Reliable uncertainty estimation is a key missing piece for on-device monitoring in TinyML: microcontrollers must detect failures, distribution shift, or accuracy drops under strict flash/latency budgets, yet common uncertainty approaches (deep ensembles, MC dropout, early exits, temporal buffering) typically require multiple passes, extra branches, or state that is impractical on milliwatt hardware. This paper proposes a novel and practical method, SNAP-UQ, for single-pass, label-free uncertainty estimation based on depth-wise next-activation prediction. SNAP-UQ taps a small set of backbone layers and uses tiny int8 heads to predict the mean and scale of the next activation from a low-rank projection of the previous one; the resulting standardized prediction error forms a depth-wise surprisal signal that is aggregated and mapped through a lightweight monotone calibrator into an actionable uncertainty score. The design introduces no temporal buffers or auxiliary exits and preserves state-free inference, while increasing deployment footprint by only a few tens of kilobytes. Across vision and audio backbones, SNAP-UQ reduces flash and latency relative to early-exit and deep-ensemble baselines (typically $\sim$40--60% smaller and $\sim$25--35% faster), with several competing methods at similar accuracy often exceeding MCU memory limits. On corrupted streams, it improves accuracy-drop event detection by multiple AUPRC points and maintains strong failure detection (AUROC $\approx 0.9$) in a single forward pass. By grounding uncertainty in layer-to-layer dynamics rather than solely in output confidence, SNAP-UQ offers a novel, resource-efficient basis for robust TinyML monitoring. Our code is available at: https://github.com/Ism-ail11/SNAP-UQ

Poster
GuardAlign: Robust Safety Alignment in Multimodal Large Language Models

Xingyu Zhu, Beier Zhu, Junfeng Fang, Shuo Wang, Yin Zhang, Xiang Wang, Xiangnan He

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Multimodal large language models (MLLMs) have achieved remarkable progress in vision–language reasoning tasks, yet ensuring their safety remains a critical challenge. Recent input-side defenses detect unsafe images with CLIP and prepend safety prefixes to prompts, but they still suffer from inaccurate detection in complex scenes and unstable safety signals during decoding. To address these issues, we propose **GuardAlign**, a training-free defense framework that integrates two strategies. First, OT-enhanced safety detection leverages optimal transport to measure distribution distances between image patches and unsafe semantics, enabling accurate identification of malicious regions without additional computational cost. Second, cross-modal attentive calibration strengthens the influence of safety prefixes by adaptively reallocating attention across layers, ensuring that safety signals remain consistently activated throughout generation. Extensive evaluations on six representative MLLMs demonstrate that GuardAlign reduces unsafe response rates by up to 39% on SPA-VL, while preserving utility, achieving an improvement on VQAv2 from 78.51% to 79.21%.

Poster
Neural Hamilton--Jacobi Characteristic Flows for Optimal Transport

Yesom Park, Shu Liu, Mo Zhou, Stanley Osher

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We present a novel framework for solving optimal transport (OT) problems based on the Hamilton--Jacobi (HJ) equation, whose viscosity solution uniquely characterizes the OT map. By leveraging the method of characteristics, we derive closed-form, bidirectional transport maps, thereby eliminating the need for numerical integration. The proposed method adopts a pure minimization framework: a single neural network is trained with a loss function derived from the method of characteristics of the HJ equation. This design guarantees convergence to the optimal map while eliminating adversarial training stages, thereby substantially reducing computational complexity. Furthermore, the framework naturally extends to a wide class of cost functions and supports class-conditional transport. Extensive experiments on diverse datasets demonstrate the accuracy, scalability, and efficiency of the proposed method, establishing it as a principled and versatile tool for OT applications with provable optimality.

Poster
FlexHiNM-GP: Flexible Hierarchical Pruning via Region Allocation and Channel Permutation

YI XIAODIE, Hayun Lee, Dongkun Shin

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N:M sparsity has emerged as a hardware-friendly pruning strategy, notably supported by NVIDIA’s Sparse Tensor Cores. While efficient, its fixed sparsity ratio restricts flexibility, making it difficult to adapt pruning granularity to varying weight importance across layers and architectures. To overcome this limitation, we propose FlexHiNM, a hybrid framework that adaptively partitions each layer into three regions: dense, vector-pruned, and N:M sparse, enabling finer-grained control while preserving hardware compatibility. To better preserve salient weights, we extend this to FlexHiNM-GP, which incorporates Gyro-Permutation, an iterative channel-rearrangement algorithm. Through successive sampling, clustering, and assignment, Gyro-Permutation aligns high-importance weights with structured sparsity patterns and mitigates suboptimal configurations in multi-level pruning. During gradual pruning, FlexHiNM-GP further employs a differentiable masking mechanism based on the Hard Concrete distribution, enabling gradient-based mask learning and preventing over-aggressive early pruning. Experiments on vision and language benchmarks demonstrate that FlexHiNM-GP consistently surpasses strong structured baselines and approaches the performance of unstructured pruning, validating the effectiveness of combining hybrid sparsity with learned masks and permutation strategies.

Poster
A Hierarchical Circuit Symbolic Discovery Framework for Efficient Logic Optimization

Yinqi Bai, Jie Wang, Tong Xialiang, Longdi Pan, Jilai Pan, Mingxuan Yuan, Jianye Hao

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The efficiency of Logic Optimization (LO) has become one of the key bottlenecks in chip design. To prompt efficient LO, many graph-based machine learning (ML) methods, such as graph neural networks (GNNs), have been proposed to predict and prune a large number of ineffective subgraphs of the LO heuristics. However, the high inference cost and limited interpretability of these approaches severely limit their wide application to modern LO tools. To address this challenge, we propose a novel **H**ierarchical C**i**rcuit **S**ymbolic Discovery Framework, namely HIS, to learn a *lightweight* and *interpretable* symbolic function that can *accurately* identify ineffective subgraphs for efficient LO. Specifically, HIS proposes a hierarchical tree structure to represent the circuit symbolic function, where every layer of the symbolic tree performs an efficient and interpretable message passing to capture the structural information of the circuit graph. To learn the hierarchical tree, we propose a circuit symbolic generation framework that leverages reinforcement learning to optimize a structure-aware Transformer model for symbolic token generation. To the best of our knowledge, HIS is *the first* approach to discover an efficient, interpretable, and high-performance symbolic function from the circuit graph for efficient LO. Experiments on two widely used circuit benchmarks show that the learned graph symbolic functions outperform previous state-of-the-art approaches in terms of efficiency and optimization performance. Moreover, we integrate HIS with the Mfs2 heuristic, one of the most time-consuming LO heuristics. Results show that HIS significantly enhances both its efficiency and optimization performance on a CPU-based machine, achieving an average runtime improvement of 27.22% and a 6.95% reduction in circuit size.

Poster
SGD-Based Knowledge Distillation with Bayesian Teachers: Theory and Guidelines

Itai Morad, Nir Shlezinger, Yonina C. Eldar

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Knowledge Distillation (KD) is a central paradigm for transferring knowledge from a large teacher network to a typically smaller student model, often by leveraging soft probabilistic outputs. While KD has shown strong empirical success in numerous applications, its theoretical underpinnings remain only partially understood. In this work, we adopt a Bayesian perspective on KD to rigorously analyze the convergence behavior of students trained with Stochastic Gradient Descent (SGD). We study two regimes: $(i)$ when the teacher provides the exact Bayes Class Probabilities (BCPs); and $(ii)$ supervision with noisy approximations of the BCPs. Our analysis shows that learning from BCPs yields variance reduction and removes neighborhood terms in the convergence bounds compared to one-hot supervision. We further characterize how the level of noise affects generalization and accuracy. Motivated by these insights, we advocate the use of Bayesian deep learning models, which typically provide improved estimates of the BCPs, as teachers in KD. Consistent with our analysis, we experimentally demonstrate that students distilled from Bayesian teachers not only achieve higher accuracies (up to +4.27\%), but also exhibit more stable convergence (up to 30\% less noise), compared to students distilled from deterministic teachers.

Poster
Dynamic Speculative Agent Planning

Yilin Guan, Qingfeng Lan, Fei Sun, Dujian Ding, Devang Acharya, Chi Wang, William Yang Wang, Wenyue Hua

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Despite their remarkable success in complex tasks propelling widespread adoption, large language model based agents still face critical deployment challenges due to prohibitive latency and inference costs. While recent work has explored various methods to accelerate inference, existing approaches suffer from significant limitations: they either fail to preserve performance fidelity, require extensive offline training of router modules, or incur excessive operational costs. Moreover, they provide minimal user control over the tradeoff between acceleration and other performance metrics. To address these gaps, we introduce **Dynamic Speculative Planning** (DSP), an asynchronous online reinforcement learning framework that provides lossless acceleration with substantially reduced costs without requiring additional pre-deployment preparation. DSP explicitly optimizes a joint objective balancing end-to-end latency against dollar cost, allowing practitioners to adjust a single parameter that steers the system toward faster responses, cheaper operation, or any point along this continuum. Experiments on two standard agent benchmarks demonstrate that DSP achieves comparable efficiency to the fastest lossless acceleration method while reducing total cost by 30\% and unnecessary cost up to 60\%. Our code and data are available through \url{https://anonymous.4open.science/r/Dynamic-Speculative-Planning-F574}

Poster
GradShield: Alignment Preserving Finetuning

Zhanhao Hu, Xiao Huang, Patrick Mendoza, Emad A. Alghamdi, Raluca Ada Popa, David Wagner

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Large Language Models (LLMs) pose a significant risk of safety misalignment after finetuning, as models can be compromised by both explicitly and implicitly harmful data. Even some seemingly benign data can inadvertently steer a model towards unsafe behaviors. To address this, we introduce GradShield, a principled filtering method that safeguards LLMs during finetuning by identifying and removing harmful data points before they corrupt the model's alignment. It removes potentially harmful data by computing a Finetuning Implicit Harmfulness Score (FIHS) for each data point and employs an adaptive thresholding algorithm.We apply GradShield to multiple utility fine-tuning tasks combined with different levels of harmful data, and evaluate the safety and utility performance of the resulting LLMs under various metrics. Our results show that GradShield outperforms all baseline methods, as it consistently maintains a low Attack Success Rate (ASR) of under $6\%$, while preserving the utility performance.

Poster
Towards Interpretable Visual Decoding with Attention to Brain Representations

Pinyuan Feng, Hossein Adeli, Wenxuan Guo, Fan L. Cheng, Ethan Hwang, Nikolaus Kriegeskorte

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Recent work has demonstrated that complex visual stimuli can be decoded from human brain activity using deep generative models, helping brain science researchers interpret how the brain represents real-world scenes. However, most current approaches leverage mapping brain signals into intermediate image or text feature spaces before guiding the generative process, masking the effect of contributions from different brain areas on the final reconstruction output. In this work, we propose \textit{NeuroAdapter}, a visual decoding framework that directly conditions a latent diffusion model on brain representations, bypassing the need for intermediate feature spaces. Our method demonstrates competitive visual reconstruction quality on public fMRI datasets compared to prior work, while providing greater transparency into how brain signals shape the generation process. To this end, we contribute an Image–Brain BI-directional interpretability framework (\textit{IBBI}) which investigates cross-attention mechanisms across diffusion denoising steps to reveal how different cortical areas influence the unfolding generative trajectory. Our results highlight the potential of end-to-end brain-to-image decoding and establish a path toward interpreting diffusion models through the lens of visual neuroscience.

Poster
LycheeDecode: Accelerating Long-Context LLM Inference via Hybrid-Head Sparse Decoding

Gang Lin, Dongfang Li, Zhuoen Chen, Yukun Shi, Xuhui Chen, Baotian Hu, Min Zhang

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The proliferation of long-context large language models (LLMs) exposes a key bottleneck: the rapidly expanding key-value cache during decoding, which imposes heavy memory and latency costs. While recent approaches attempt to alleviate this by sharing a single set of crucial tokens across layers, such coarse-grained sharing undermines model performance by neglecting the functional diversity of attention heads. To address this, we propose LycheeDecode, an efficient decoding method centered on a fine-grained hybrid-head attention mechanism that employs a hardware-efficient top-$k$ selection strategy. Specifically, the novel HardKuma-based mechanism partitions attention heads into a small subset of retrieval heads that dynamically identify crucial tokens and a majority of sparse heads that reuse them for efficient computation. Through extensive experiments on leading models like Llama3 and Qwen3 across diverse benchmarks for long-context understanding (e.g., LongBench, RULER) and complex reasoning (e.g., AIME24, OlympiadBench), we demonstrate that LycheeDecode achieves generative quality comparable to, and at times surpassing even the full-attention baseline. Crucially, this is accomplished with up to a 2.7x speedup at a 128K context length. By preserving the functional diversity of attention heads, our fine-grained strategy overcomes the performance bottlenecks of existing methods, providing a powerful and validated pathway to both efficient and high-quality long-context LLM inference. The implementation code, kernels, and models will be publicly available.

Poster
Vivid-VR: Distilling Concepts from Text-to-Video Diffusion Transformer for Photorealistic Video Restoration

Haoran Bai, Xiaoxu Chen, Canqian Yang, Zongyao He, Sibin Deng, Ying Chen

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We present Vivid-VR, a DiT-based generative video restoration method built upon an advanced T2V foundation model, where ControlNet is leveraged to control the generation process, ensuring content consistency. However, conventional fine-tuning of such controllable pipelines frequently suffers from distribution drift due to limitations in imperfect multimodal alignment, resulting in compromised texture realism and temporal coherence. To tackle this challenge, we propose a concept distillation training strategy that utilizes the pretrained T2V model to synthesize training samples with embedded textual concepts, thereby distilling its conceptual understanding to preserve texture and temporal quality. To enhance generation controllability, we redesign the control architecture with two key components: 1) a control feature projector that filters degradation artifacts from input video latents to minimize their propagation through the generation pipeline, and 2) a new ControlNet connector employing a dual-branch design. This connector synergistically combines MLP-based feature mapping with cross-attention mechanism for dynamic control feature retrieval, enabling both content preservation and adaptive control signal modulation. Extensive experiments show that Vivid-VR performs favorably against existing approaches on both synthetic and real-world benchmarks, as well as AIGC videos, achieving impressive texture realism, visual vividness, and temporal consistency.

Poster
Task-Related Token Compression in Multimodal Large Language Models from an Explainability Perspective

Lei Lei, Jie Gu, Xiaokang Ma, Chu Tang, Jingmin Chen, Tong Xu

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Existing Multimodal Large Language Models (MLLMs) process a large number of visual tokens, leading to significant computational costs and inefficiency. Instruction-related visual token compression demonstrates strong task relevance, which aligns well with MLLMs’ ultimate goal of instruction following. Previous works generally assume that visual tokens achieve better vision–language alignment in the shallow layers of LLMs, which have led to task-related token compression being primarily applied in intermediate LLM layers. In contrast, our study reveals that with proper selection, task-related token compression is feasible at the input stage of LLM with negligible performance loss. This new paradigm significantly reduces task-irrelevant visual tokens and its model-agnostic design enables application without modifying the LLM architecture. Specifically, we suggest that explainability methods for transformer-based architechtures can evaluate the global importance of each visual token with respect to the given instruction, which can effectively guide the task-related token compression for MLLMs. Furthermore, we propose to learn a mapping from the attention map of the first LLM layer to the explanation results, thereby avoiding the need for a full inference pass. Interestingly, this mapping can be learned using a simple and lightweight convolutional network, whose training is efficient and independent of MLLMs. Extensive experiments on 13 image and video benchmarks across three leading MLLMs (Qwen2-VL, LLaVA-OneVision, and VILA1.5) demonstrate the remarkable effectiveness and strong generalization of our approach. Additionally, our new compression paradigm achieves faster inference with reductions in both prefilling time and KV-cache memory.

Poster
Efficient Differentiable Contact Model with Long-range Influence

Xiaohan Ye, Kui Wu, Taku Komura, zherong pan

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With the maturation of differentiable physics, its role in various downstream applications—such as model-predictive control, robotic design optimization, and neural PDE solvers—has become increasingly important. However, the derivative information provided by differentiable simulators can exhibit abrupt changes or vanish altogether, impeding the convergence of gradient-based optimizers. In this work, we demonstrate that such erratic gradient behavior is closely tied to the design of contact models. We further introduce a set of properties that a contact model must satisfy to ensure well-behaved gradient information. Lastly, we present a practical contact model for differentiable rigid-body simulators that satisfies all of these properties while maintaining computational efficiency. Our experiments show that, even from simple initializations, our contact model can discover complex, contact-rich control signals, enabling the successful execution of a range of downstream locomotion and manipulation tasks.

Poster
Confident Block Diagonal Structure-Aware Invariable Graph Completion for Incomplete Multi-view Clustering

Shuping Zhao, Yulong Chen, Jie Wen, Lunke Fei, Jinrong Cui, Tingting Chai

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Multi-view clustering (MVC) adopts complementary information from multiple views to reveal the underlying structure of the data. However, the conventional MVC-based methods remain a crucial challenge on the incomplete multi-view clustering (IMVC) tasks, when some views of the multi-view data are missing. Particularly, current IMVC methods suffer from two main limitations: 1) they focused on recovering the missing data, yet often overlooked the potential inaccuracies in imputed values caused by the absence of true label information; 2) the recovered features were learned from the complete data, neglecting the distributional discrepancy between the complete and incomplete instances. In order to tackle these issues, in this paper, a confident block diagonal structure-aware invariable graph completion-based incomplete multi-view clustering method (CBDS_IMVC) is proposed. Specifically, we first design a confident-aware missing-view inferring strategy, where the confident block diagonal structures (CBDS) are learned to guarantee that recovered instances of all views have the same strict invariable local structure with the constraint of CBDS. Subsequently, we proposed an invariable graph completion strategy to learn the intrinsic structure across all views. Each parts are jointly trained, complementing and promoting each other to achieve the optimum together. Compared to other state-of-the-art methods, the proposed CBDS_IMVC demonstrates superior performance across multiple benchmark datasets.

Poster
QuoKA: Query-Oriented KV Selection for Efficient LLM Prefill

Dalton Jones, Junyoung Park, Matthew J Morse, Mingu Lee, Matthew Harper Langston, Christopher Lott

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We present QuoKA: Query-oriented KV selection for efficient attention, a training-free and hardware agnostic sparse attention algorithm for accelerating transformer inference under chunked prefill. While many queries focus on a smaller group of keys in the attention operator, we observe that queries with low cosine similarity with respect to the mean query interact more strongly with more keys and have the greatest contribution to final attention logits. By prioritizing these low cosine similarity queries, the behavior of full attention during the prefill stage can be closely approximated. QuoKA leverages this observation, accelerating attention by (1) first retaining a small set of representative queries and (2) then subselecting the keys most aligned with those queries. Through experiments on Needle-In-A-Haystack, LongBench, RULER, and Math500, we show that, while realizing a 3× reduction in time-to-first-token, 5× speedup in attention on Nvidia GPUs and up to nearly a 7× speedup on Intel Xeon CPUs, QuoKA achieves near-baseline accuracy, utilizing 88% fewer key-value pairs per attention evaluation.

Poster
Fewer Weights, More Problems: A Practical Attack on LLM Pruning

Kazuki Egashira, Robin Staab, Thibaud Gloaguen, Mark Vero, Martin Vechev

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Model pruning, i.e., removing a subset of model weights, has become a prominent approach to reducing the memory footprint of large language models (LLMs) during inference. Notably, popular inference engines, such as vLLM, enable users to conveniently prune downloaded models before they are deployed. While the utility and efficiency of pruning methods have improved significantly, the security implications of pruning remain underexplored. In this work, for the first time, we show that modern LLM pruning methods can be maliciously exploited. In particular, an adversary can construct a model that appears benign yet, once pruned, exhibits malicious behaviors. Our method is based on the idea that the adversary can compute a proxy metric that estimates how likely each parameter is to be pruned. With this information, the adversary can first inject a malicious behavior into those parameters that are unlikely to be pruned. Then, they can repair the model by using parameters that are \textit{likely} to be pruned, effectively canceling out the injected behavior in the unpruned model. We demonstrate the severity of our attack through extensive evaluation on five models; after any of the pruning in vLLM are applied (Magnitude, Wanda, and SparseGPT), it consistently exhibits strong malicious behaviors in a diverse set of attack scenarios (success rates of up to 95.7% for jailbreak, 98.7% for benign instruction refusal, and 99.5% for targeted content injection). Our results reveal a critical deployment-time security gap and underscore the urgent need for stronger security awareness in model compression.

Poster
Foundation Visual Encoders Are Secretly Few-Shot Anomaly Detectors

Guangyao Zhai, Yue Zhou, Xinyan Deng, Lars Heckler-Kram, Nassir Navab, Benjamin Busam

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Few-shot anomaly detection streamlines and simplifies industrial safety inspection. However, limited samples make accurate differentiation between normal and abnormal features challenging, and even more so under category-agnostic conditions. Large-scale pre-training of foundation visual encoders has advanced many fields, as the enormous quantity of data helps to learn the general distribution of normal images. We observe that the anomaly amount in an image directly correlates with the difference in the learnt embeddings and utilize this to design a few-shot anomaly detector termed FoundAD. This is done by learning a nonlinear projection operator onto the natural image manifold. The simple operator acts as an effective tool for anomaly detection to characterize and identify out-of-distribution regions in an image. Extensive experiments show that our approach supports multi-class detection and achieves competitive performance compared to other approaches, while surpassing them in model size and inference efficiency. Backed up by evaluations with multiple foundation encoders, including fresh DINOv3, we believe this idea broadens the perspective on foundation features and advances the field of few-shot anomaly detection. Our code will be made public.

Poster
Directed Semi-Simplicial Learning with Applications to Brain Activity Decoding

Manuel Lecha, Andrea Cavallo, Francesca Dominici, Ran Levi, Alessio Del Bue, Elvin Isufi, Pietro Morerio, Claudio Battiloro

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Graph Neural Networks (GNNs) excel at learning from pairwise interactions but often overlook multi-way and hierarchical relationships. Topological Deep Learning (TDL) addresses this limitation by leveraging combinatorial topological spaces, such as simplicial or cell complexes. However, existing TDL models are restricted to undirected settings and fail to capture the higher-order directed patterns prevalent in many complex systems, e.g., brain networks, where such interactions are both abundant and functionally significant. To fill this gap, we introduce Semi-Simplicial Neural Networks (SSNs), a principled class of TDL models that operate on semi-simplicial sets---combinatorial structures that encode directed higher-order motifs and their directional relationships. To enhance scalability, we propose Routing-SSNs, which dynamically select the most informative relations in a learnable manner. We theoretically characterize SSNs by proving they are strictly more expressive than standard graph and TDL models, and they are able to recover several topological descriptors. Building on previous evidence that such descriptors are critical for characterizing brain activity, we then introduce a new principled framework for brain dynamics representation learning centered on SSNs. Empirically, we test SSNs on 4 distinct tasks across 13 datasets, spanning from brain dynamics to node classification, showing competitive performance. Notably, SSNs consistently achieve state-of-the-art performance on brain dynamics classification tasks, outperforming the second-best model by up to 27\%, and message passing GNNs by up to 50\% in accuracy. Our results highlight the potential of topological models for learning from structured brain data, establishing a unique real-world case study for TDL. Code and data are uploaded as supplementary material.

Poster