ICML 2026 论文列表

International Conference on Machine Learning

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6,341篇论文

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RTInfer: Real-Time Inference of Multiple DNNs on Edge GPUs

Renjie Li, Tong Sun, Yi Gao, Wei Dong

展开摘要

While edge GPUs are increasingly used for latency-critical DNN tasks, limited resources often fail to meet strict real-time (RT) requirements under concurrent workloads. Existing preemption and early-exit mechanisms often underutilize GPU resources through single-task queuing and sacrifice excessive accuracy during task bursts. To address this, we propose RTInfer, a novel system that enables concurrent RT task execution while balancing throughput and accuracy. RTInfer integrates an accuracy-calibrated lightweight variant co-optimization to generate efficient models, a memory-layout-aware scheduler to mitigate fragmentation during preemption, and an on-demand loading strategy to minimize host-to-GPU latency. Extensive evaluations demonstrate that RTInfer outperforms state-of-the-art methods by reducing average deadline miss rate (DMR) from 32.8\% to 0\% and improving accuracy by up to 56.5\%.

Poster
Rethinking Depth Pruning for Vision Transformers: A Heterogeneity-Aware Perspective

Zhenfeng Su, Kang Zhao, Han Bao, Tao Yuan, Zhongzhe Hu, Xianzhi Yu, Wenxuan Wang

展开摘要

While prior studies have successfully compressed vision Transformers (ViTs) through various pruning techniques, most have concentrated on width pruning to achieve significant reductions in model size. Depth pruning, which removes entire layers from a ViT, is notoriously difficult for accuracy recovery despite its potential to deliver higher speedups, limiting the acceleration achieved by existing joint width-and-depth pruning methods. In this work, we reveal that the failure of existing depth pruning methods lies in their neglect of heterogeneity between different layers, and we introduce HetDPT, a heterogeneity-aware depth pruning method that avoids dimension mismatch. Comprehensive experiments on ImageNet-1K, CIFAR-100, COCO, and ADE20K validate our method: HetDPT achieves a 1.58$\times$ speedup for DeiT-B while maintaining accuracy and a 1.39$\times$ speedup for DeiT-S with nearly no accuracy degradation. Furthermore, when combined with width pruning, HetDPT+ sets a new state-of-the-art record in extreme ViT pruning, enhancing the acceleration ratio from 4.24$\times$ to 5.19$\times$ for the Isomorphic-Pruning-2.6G configuration while maintaining near-lossless accuracy; our code is available at \url{https://github.com/Efficient-AI-for-All/HetDPT}.

Poster
Stem: Rethinking Causal Information Flow in Sparse Attention

Lin Niu, Xin Luo, Linchuan Xie, Yifu Sun, Guanghua Yu, Jianchen Zhu, S. Kevin Zhou

展开摘要

The quadratic computational complexity of self-attention remains a fundamental bottleneck for scaling Large Language Models (LLMs) to long contexts, particularly during the pre-filling phase. In this paper, we rethink the causal attention mechanism from the perspective of information flow. Due to causal constraints, tokens at initial positions participate in the aggregation of every subsequent token. However, existing sparse methods typically apply a uniform top-$k$ selection across all token positions within a layer, ignoring the cumulative dependency of token information inherent in causal architectures. To address this, we propose Stem, a novel, plug-and-play sparsity module aligned with information flow. First, Stem employs the Token Position-Decay strategy, applying position-dependent top-$k$ within each layer to retain initial tokens for recursive dependencies. Second, to preserve information-rich tokens, Stem utilizes the Output-Aware Metric. It prioritizes high-impact tokens based on approximate output magnitude. Extensive evaluations demonstrate that Stem achieves superior accuracy with reduced computation and pre-filling latency. Code is available at https://anonymous.4open.science/r/stem-254ENLXL.

Poster
CVSearch: Empowering Multimodal LLMs with Cognitive Visual Search for High-Resolution Image Perception

Liupeng Li, Haoqian Kang, Zhenyu Lu, Jinpeng Wang, Bin CHEN, Ke Chen, Yaowei Wang

展开摘要

High-resolution (HR) image perception presents a key bottleneck for multimodal large language models (MLLMs). While visual search offers a promising solution, existing methods struggle with the trade-off between coverage and efficiency. Visual expert-assisted search is efficient but prone to blind spots when proposals fail, whereas scan-based search guarantees coverage at the cost of computational redundancy and semantic fragmentation. To address this dilemma, we introduce CVSearch, a training-free adaptive framework that dynamically schedules search strategies via an Assess-then-Search workflow. Specifically, CVSearch first invokes expert-assisted search when global information is insufficient, and only triggers a novel semantic-aware scanning mechanism upon failure. Distinct from rigid grid partitioning, this efficient scanning paradigm incorporates Semantic Guided Adaptive Patching to decompose images into semantically consistent regions, effectively mitigating object fragmentation. Furthermore, we devise a Dynamic Bottom-Up Search strategy driven by a Visual Complexity prior to enable efficient and precise iterative exploration of local details. Extensive experiments on HR benchmarks demonstrate that CVSearch achieves state-of-the-art accuracy while substantially improving search efficiency. Code is released at https://github.com/liliupeng28/ICML26-CVSearch.

Poster
UniPercept: Towards Unified Perceptual-Level Image Understanding across Aesthetics, Quality, Structure, and Texture

Shuo Cao, Jiayang Li, Xiaohui Li, Yuandong Pu, Kaiwen Zhu, Yuanting Gao, Siqi Luo, Yi Xin, Qi Qin, Yu Zhou, Xiangyu Chen, Wenlong Zhang, Bin Fu, Yu Qiao, Yihao Liu

展开摘要

Multimodal large language models (MLLMs) have achieved remarkable progress in visual understanding tasks such as visual grounding, segmentation, and captioning. However, their ability to perceive perceptual-level image features remains limited. In this work, we present UniPercept-Bench, a unified framework for perceptual-level image understanding across three key domains: Aesthetics, Quality, Structure and Texture. We establish a hierarchical definition system and construct large-scale datasets to evaluate perceptual-level image understanding. Based on this foundation, we develop a strong baseline UniPercept trained via Domain-Adaptive Pre-Training and Task-Aligned RL, enabling robust generalization across both Visual Rating (VR) and Visual Question Answering (VQA) tasks. UniPercept outperforms existing MLLMs on perceptual-level image understanding and can serve as a plug-and-play reward model for text-to-image generation. This work defines perceptual-level image understanding in the era of MLLMs and, through the introduction of a comprehensive benchmark together with a strong baseline, provides a solid foundation for advancing perceptual-level multimodal image understanding.

Spotlight
T2AV-Compass: Towards Unified Evaluation for Text-to-Audio-Video Generation

Zhe Cao, Tao Wang, Jiaming Wang, Yanghai Wang, Yuanxing Zhang, Jiahao Wang, Jialu Chen, Miao Deng, Chenxi Liao, Yize Zhang, Yubin Guo, Zhaoxiang Zhang, Jiaheng Liu

展开摘要

Text-to-Audio-Video (T2AV) generation aims to synthesize temporally coherent video and semantically synchronized audio from natural language, yet its evaluation remains fragmented, often relying on unimodal metrics or narrowly scoped benchmarks that fail to capture cross-modal alignment, instruction following, and perceptual realism under complex prompts. To address this limitation, we present T2AV-Compass, a unified benchmark for comprehensive evaluation of T2AV systems, consisting of 500 diverse and complex prompts constructed via a taxonomy-driven pipeline to ensure semantic richness and physical plausibility. Besides, T2AV-Compass introduces a dual-level evaluation framework that integrates objective signal-level metrics for video quality, audio quality, and cross-modal alignment with a subjective MLLM-as-a-Judge protocol for instruction following and realism assessment. Extensive evaluation of 15 representative T2AV systems reveals that even the strongest models fall substantially short of human-level realism and cross-modal consistency, with persistent failures in audio realism, fine-grained synchronization, instruction following, etc. These results indicate significant improvement room for future models and highlight the value of T2AV-Compass as a challenging and diagnostic testbed for advancing text-to-audio-video generation.

Poster
Asymptotically Fast Clebsch-Gordan Tensor Products with Vector Spherical Harmonics

YuQing Xie, Ameya Daigavane, Mit Kotak, Tess Smidt

展开摘要

$E(3)$-equivariant neural networks have proven to be extremely effective in a wide range of 3D modeling tasks. A fundamental operation of such networks is the tensor product, which allows interaction between different feature types. Because this operation scales poorly, there has been considerable work towards accelerating this interaction. However, recently [Xie et al. 2025](https://openreview.net/forum?id=EvIwwGYTLc) have pointed out that most speedups come from a reduction in expressivity rather than true algorithmic improvements on computing Clebsch-Gordan tensor products. A modification of Gaunt tensor product ([Luo et al.](https://openreview.net/forum?id=mhyQXJ6JsK)) can give a true asymptotic speedup but is incomplete and misses many interactions. In this work, we provide the first complete algorithm which truly provides asymptotic benefits Clebsch-Gordan tensor products. For full CGTP, our algorithm brings runtime complexity from the naive $O(L^6)$ to $O(L^4\log^2 L)$, close to the lower bound of $O(L^4)$. We first show how generalizing fast Fourier based convolution naturally leads to the previously proposed Gaunt tensor product ([Luo et al.](https://openreview.net/forum?id=mhyQXJ6JsK)). To remedy antisymmetry issues, we generalize from scalar signals to irrep valued signals, giving us tensor spherical harmonics. We prove a generalized Gaunt formula for the tensor harmonics. Finally, we show that we only need up to vector valued signals to recover the missing interactions of Gaunt tensor product.

Poster
OmniFit: Bridging Modalities via Layer-Adaptive Token Compression for Omnimodal Large Language Models

Zining Wang, Zhihang Yuan, Yingjie Zhai, Wenshuo Li, Han Shu, Ruihao Gong, Jinyang Guo, Xianglong Liu

展开摘要

Emerging Omni-modal Large Language Models (OmniLLMs) enable real-time interaction across video, audio, and text but suffer from prohibitive computational costs due to the quadratic complexity of processing continuous streaming inputs. Existing token compression strategies remain suboptimal as they typically rely on biased modality-centric priors or enforce uniform retention policies, neglecting the heterogeneity across layers and the critical role of cross-modality alignment. To address these challenges, we propose OmniFit, a training-free framework that decouples interaction profiling from inference execution. OmniFit incorporates Layer-Adaptive Heterogeneity Profiling (LAHP) to dynamically allocate computational budgets based on layer-wise redundancy and modality preferences, preserving tokens according to the characteristics of each layer. Furthermore, we introduce Alignment-Rectified Token Selection (ARTS), a lightweight mechanism that efficiently identifies tokens semantically aligned with cross-modal cues. Extensive experiments on 3 model series across 10 benchmarks demonstrate that OmniFit establishes a new Pareto frontier, retaining 98\% of model performance with only 20\% token usage and achieves up to 2.31$\times$ end-to-end inference speedup and 2.5$\times$ VRAM saving, significantly outperforming state-of-the-art methods.

Spotlight
PAMD: Structured Adaptive Distances for Bisimulation Representations in Visual Reinforcement Learning

Daegyeong Roh, Juho Bae, Han-Lim Choi

展开摘要

Many visual reinforcement learning (RL) algorithms learn representations by matching latent distances to a behavioral distance induced by reward and transition similarity. In practice, the choice of the latent distance can strongly affect performance: using a fixed, pre-specified global norms (e.g., $\ell_p$ norms or other hand-designed metrics) may be overly restrictive to capture the behavioral distance. In contrast, unconstrained pairwise distances may admit degenerate solutions that drive the metric loss down without improving the representation. To address this gap, we introduce **PAMD: Pairwise Adaptive Mahalanobis Distance**, which parameterizes a positive-definite, pair-conditioned metric for measuring latent state similarity. PAMD is a simple plug-in for existing bisimulation-based methods, offering a more expressive yet structured alternative to fixed, pre-specified latent distances. We empirically validate our method on visual MuJoCo continuous-control tasks, where final performance of several recent bisimulation-based RL algorithms is substantially improved when equipped with the distance we propose.

Poster
Modeling Temporal scRNA-seq Data with Latent Gaussian Process and Optimal Transport

Mehmet Yigit Balik, Harri Lähdesmäki

展开摘要

Single-cell RNA sequencing provides insights into gene expression at single-cell resolution, yet inferring temporal processes from these static snapshot measurements remains a fundamental challenge. Current approaches utilizing neural differential equations and flows are sensitive to overfitting and lack careful considerations of biological variability. In this work, we propose a generative framework that models population trends using a latent heteroscedastic Gaussian process (GP) approximated by Hilbert space methods. To address the absence of genuine cell trajectories, we leverage an optimal transport (OT) objective that aligns generated and observed population distributions. Our method explicitly captures biological heterogeneity by incorporating cell-specific latent time and cell type conditioning to disentangle temporal asynchrony and trajectories to different cell types. We demonstrate state-of-the-art performance on complex interpolation and extrapolation benchmarks and introduce a novel gradient-based strategy for inferring perturbation trajectories.

Poster
BLOCK-EM: Preventing Emergent Misalignment via Latent Blocking

Muhammed Ustaomeroglu, Guannan Qu

展开摘要

Emergent misalignment can arise when a language model is fine-tuned on a narrowly scoped supervised objective: the model learns the target behavior, yet also develops undesirable out-of-domain behaviors. We investigate a mechanistic approach to preventing emergent misalignment by identifying a small set of internal features that reliably control the misaligned behavior and then discouraging the model from strengthening these features during fine-tuning. Across six fine-tuning domains, blocking (i.e., constraining) a fixed set of features achieves up to 95\% relative reduction in emergent misalignment with no degradation in model quality or target-task performance. We strengthen validity with disjoint selection/evaluation splits, multiple independent judges, multiple random seeds for key settings, quality metrics, and extensive ablations demonstrating that the reduction in misalignment is specific to the identified mechanism. We also characterize a limiting regime in which misalignment re-emerges under prolonged fine-tuning, present evidence consistent with rerouting through alternative features or layers, and evaluate modifications that partially restore the misalignment-blocking effect. Overall, our results show that targeted training-time constraints on internal mechanisms can mitigate emergent misalignment without degrading target-task performance.

Poster
SOTAlign: Semi-Supervised Alignment of Unimodal Vision and Language Models via Optimal Transport

Simon Roschmann, Paul KRZAKALA, Sonia Mazelet, Quentin Bouniot, Zeynep Akata

展开摘要

The Platonic Representation Hypothesis posits that neural networks trained on different modalities converge toward a shared statistical model of the world. Recent work exploits this convergence by aligning frozen pretrained vision and language models with lightweight alignment layers, but typically relies on contrastive losses and millions of paired samples. In this work, we ask whether meaningful alignment can be achieved with substantially less supervision. We introduce a semi-supervised setting in which pretrained unimodal encoders are aligned using a small number of image-text pairs together with large amounts of unpaired data. To address this challenge, we propose SOTAlign, a two-stage framework that first recovers a coarse shared geometry from limited paired data using a linear teacher, and then refines the alignment on unpaired samples via an optimal-transport-based divergence that transfers relational structure without overconstraining the target space. Unlike existing semi-supervised methods, SOTAlign effectively leverages unpaired images and text, learning robust joint embeddings across datasets and encoder pairs, and significantly outperforming supervised and semi-supervised baselines.

Poster
Demystifying Action Space Design for Robotic Manipulation Policies

Yuchun Feng, Jinliang Zheng, Zhihao Wang, Dongxiu Liu, Jianxiong Li, Jiangmiao Pang, Tai Wang, Xianyuan Zhan

展开摘要

The specification of the action space plays a pivotal role in imitation-based robotic manipulation policy learning, fundamentally shaping the optimization landscape of policy learning. While recent advances have focused heavily on scaling training data and model capacity, the choice of action space remains guided by ad-hoc heuristics or legacy designs, leading to an ambiguous understanding of robotic policy design philosophies. To address this ambiguity, we conducted a large-scale and systematic empirical study, confirming that the action space does have significant and complex impacts on robotic policy learning. We dissect the action design space along temporal and spatial axes, facilitating a structured analysis of how these choices govern both policy learnability and control stability. Based on 13,000+ real-world rollouts on a bimanual robot and evaluation on 500+ trained models over four scenarios, we examine the trade-offs between absolute vs. delta representations, and joint-space vs. task-space parameterizations. Our large-scale results suggest that properly designing the policy to predict delta actions consistently improves performance, while joint-space and task-space representations offer complementary strengths, favoring control stability and generalization, respectively.

Poster
Batched Contextual Reinforcement

Bangji Yang, Hongbo Ma, Jiajun Fan, Ge Liu

展开摘要

Large Language Models (LLMs) employing Chain-of-Thought reasoning achieve strong performance but suffer from excessive token consumption that inflates inference costs. Existing efficiency methods—such as explicit length penalties, difficulty estimators, or multi-stage curricula—either degrade reasoning quality or require complex training pipelines. We introduce **Batched Contextual Reinforcement (BCR)**, a minimalist, single-stage training paradigm that unlocks efficient reasoning through a simple structural modification: training the model to solve N problems simultaneously within a shared context window, rewarded purely by per-instance accuracy. This formulation creates an implicit token budget that yields several key findings: (1) We identify a novel _task-scaling law_: as the number of concurrent problems N increases at inference time, per-problem token usage decreases monotonically---a phenomenon that arises purely at inference, holds for models both before and after training, and is unrelated to accuracy or the training procedure. BCR makes this regime practical by degrading accuracy far more gracefully than baselines as N grows, establishing N as a controllable throughput dimension. (2) BCR challenges the traditional accuracy-efficiency trade-off by demonstrating a "free lunch" phenomenon at standard single-problem (N=1) inference. Across both 1.5B and 4B model families, BCR reduces token usage by 15.8\% to 62.6\% while consistently maintaining or improving accuracy across five major mathematical benchmarks (e.g., +13.3\% on AIME25 for the 4B model). (3) Qualitative analyses reveal emergent self-regulated efficiency, where models autonomously eliminate redundant metacognitive loops without explicit length supervision. (4) Crucially, we empirically demonstrate that implicit budget constraints successfully circumvent the adversarial gradients and catastrophic optimization collapse inherent to explicit length penalties, offering a highly stable, constraint-based alternative for length control. These results establish BCR as a highly practical framework, demonstrating how simple structural training incentives can unlock latent high-density reasoning modes in LLMs.

Poster
Re-FORC: Adaptive Reward Prediction for Efficient Chain-of-Thought Reasoning

Renos Zabounidis, Aditya Golatkar, Michael Kleinman, Alessandro Achille, Wei Xia, Stefano Soatto

展开摘要

We propose Re-FORC, an adaptive reward prediction method that, given a query, enables prediction of the expected future rewards as a function of the number of future thinking tokens. Re-FORC trains a lightweight adapter on reasoning models, demonstrating improved prediction with longer reasoning and larger models. Re-FORC enables: 1) early stopping of unpromising reasoning chains, reducing compute by up to 24\% compared to fixed-budget cutoffs, while maintaining accuracy, 2) optimized model and thinking length selection that outperforms the largest model alone---reaching 1.7 percentage points higher peak accuracy while needing up to 12\% less compute to match the largest model's accuracy, 3) adaptive test-time scaling, which increases accuracy by 8.8 percentage points (on average at maximum compute) over confidence-based baselines. Re-FORC allows dynamic reasoning with length control via cost-per-token thresholds while estimating computation time upfront.

Poster
Training-Free Coverless Multi-Image Steganography with Access Control

Minyeol Bae, Si-Hyeon Lee

展开摘要

Coverless Image Steganography (CIS) hides information without explicitly modifying a cover image, providing strong imperceptibility and inherent robustness to steganalysis. However, existing CIS methods largely lack robust access control, making it difficult to selectively reveal different hidden contents to different authorized users. Such access control is critical for scalable and privacy-sensitive information hiding in multi-user settings. We propose MIDAS (Multi-Image Diffusion-based Access-controlled Steganography), a training-free diffusion-based CIS framework that enables multi-image hiding with user-specific access control via latent-level fusion. MIDAS introduces a Random Basis mechanism to suppress residual structural information, together with a theoretical analysis of information leakage, and a Latent Vector Fusion module that reshapes aggregated latents to better align with the diffusion process. Experimental results demonstrate that MIDAS consistently outperforms existing training-free CIS baselines in access control functionality, stego image quality and diversity, robustness to noise, and resistance to steganalysis, establishing a practical and scalable approach to access-controlled coverless steganography.

Poster
Mitigating Label Shift in Tabular In-Context Learning via Test-Time Posterior Adjustment

Seunghan Lee

展开摘要

TabPFN has recently gained attention as a foundation model for tabular datasets, achieving strong performance by leveraging in-context learning on synthetic data. However, we find that TabPFN is vulnerable to label shift, often overfitting to the majority class in the training dataset. To address this limitation, we propose DistPFN, the first test-time posterior adjustment method designed for tabular foundation models. DistPFN rescales predicted class probabilities by downweighting the influence of the training prior (i.e., the class distribution of the context) and emphasizing the contribution of the model’s predicted posterior, without architectural modification or additional training. We further introduce DistPFN-T, which incorporates temperature scaling to adaptively control the adjustment strength based on the discrepancy between prior and posterior. We evaluate our methods on over 250 OpenML datasets, demonstrating substantial improvements for various TabPFN-based models in classification tasks under label shift, while maintaining strong performance in standard settings without label shift. Code is available at this repository: https://github.com/seunghan96/DistPFN.

Poster
Required Spine Optional Limbs: Heterogeneous Federated Learning via Backbone-sharing and Activation-guided Selection

Mingsheng Cao, Hongliang Chen, Ming Hu, Fei Gao, Qiaolong Ding, Wenke Huang, Xiaofei Xie, Junlong Zhou

展开摘要

Although Federated Learning (FL) offers advantages in privacy-preserving for cross-device collaborative learning, its practical deployment remains severely constrained by heterogeneous hardware resources and non-IID (non-independent and identically distributed) data across devices. Sub-model extraction has emerged as a widely adopted strategy for enabling collaborative training among devices with heterogeneous models. However, existing sub-model extraction methods in FL typically rely on coarse-grained stochastic selection or rigid rule-based neuron selection, which severely limits training performance. Specifically, stochastic strategies lead to severe parameter conflicts under non-IID data distributions, while rule-based approaches lack diversity in neuron selection per device, preventing comprehensive parameter optimization. To address this problem, this paper presents a novel sub-model extraction-based FL framework, named SpineFL, which adopts a backbone-sharing mechanism and an activation-guided pruning strategy for sub-model extraction. Specifically, SpineFL decomposes each global model layer into two portions: i) a mandatory backbone shared by all the sub-models to maintain model generalization, and ii) a dynamic portion for sub-model extraction. SpineFL adopts the activation-guided selection strategy to probabilistically select neurons according to their activation frequency from the dynamic portion to generate sub-model, where neurons exhibiting higher historical activation are more likely to be included, thereby simultaneously addressing parameter conflicts while preserving selection diversity. Experimental results demonstrate that compared with state-of-the-art heterogeneous FL methods, SpineFL can achieve up to 3.28% accuracy improvement.

Spotlight
Reward Redistribution for CVaR MDPs using a Bellman Operator on L-infinity

Aneri Muni, Vincent Taboga, Esther Derman, Pierre-Luc Bacon, Erick Delage

展开摘要

Tail-end risk measures such as static conditional value-at-risk (CVaR) are used in safety-critical applications to prevent rare, yet catastrophic events. Unlike risk-neutral objectives, the static CVaR of the return depends on entire trajectories without admitting a recursive Bellman decomposition in the underlying Markov decision process. A classical resolution relies on state augmentation with a continuous variable. However, unless restricted to a specialized class of admissible value functions, this formulation induces sparse rewards and degenerate fixed points. In this work, we propose a novel formulation of the static CVaR objective based on augmentation. Our alternative approach leads to a Bellman operator with: (1) dense per-step rewards; (2) contracting properties on the full space of bounded value functions. Building on this theoretical foundation, we develop risk-averse value iteration and model-free Q-learning algorithms that rely on discretized augmented states. We further provide convergence guarantees and approximation error bounds due to discretization. Empirical results demonstrate that our algorithms successfully learn CVaR-sensitive policies and achieve effective performance-safety trade-offs.

Spotlight
On Minimum Depth and Width of Floating-Point Neural Networks for Representing Floating-Point Functions

Sejun Park, Yeachan Park, Geonho Hwang

展开摘要

Research on the expressive power of neural networks has identified the minimum depth and width of neural networks that enable universal approximation and memorization. However, existing results are derived under exact arithmetic and cannot be directly applied to real implementations on computers, which can only use a finite set of numbers and inexact machine operations with round-off errors. In this work, we study floating-point ReLU networks that have floating-point parameters and use floating-point operations. Specifically, we investigate their minimum depth and width to represent all functions from the set of floating-point vectors $\mathbb F^d$ to the set of floating-point numbers $\mathbb F$. We first show that the minimum depth for representing all functions from $\mathbb F^d$ to $\mathbb F$ is exactly three, where two layers can be sufficient if we consider a smaller domain and/or codomain. We further show that the minimum width for representing all functions from $\mathbb F^d$ to $\mathbb F$ lies between $2d$ and $2d+4$. In addition, if we restrict the domain to non-negative floats, it lies between $d$ and $d+4$, where it can be smaller for a smaller domain, even beyond $d$. Our results show that the existing results analyzed under exact arithmetic do not extend to the floating-point setup.

Spotlight