O(N) and Beyond: Scaling AI with Novel Computational Complexity Solutions

Latest 50 papers on computational complexity: Nov. 30, 2025

The relentless pursuit of more powerful and efficient AI has brought computational complexity to the forefront of research. As models grow larger and applications demand real-time performance on constrained devices, finding ways to reduce the computational footprint without sacrificing accuracy becomes paramount. This digest explores a collection of recent breakthroughs that tackle this challenge head-on, introducing ingenious methods to achieve better performance with lower complexity, often reaching the coveted O(N) linear scaling.

The Big Idea(s) & Core Innovations

At the heart of these advancements lies a common thread: finding smarter ways to process data and model interactions. One significant area of innovation focuses on reducing the quadratic computational complexity (O(L²)) inherent in many attention-based models, especially Transformers. For instance, the State Space Models (SSMs) are emerging as a powerful alternative. In “DAPointMamba: Domain Adaptive Point Mamba for Point Cloud Completion”, researchers from Deakin University, Jilin University, and PengCheng Laboratory introduce DAPointMamba, a Mamba-based framework for domain-adaptive point cloud completion. This ground-breaking work achieves linear computational complexity, surpassing the inefficiencies of traditional Transformer-based methods while effectively reducing geometric and semantic discrepancies. Similarly, “Parallel Vision Token Scheduling for Fast and Accurate Multimodal LMMs Inference” by Wengyi Zhan et al. from Xiamen University and Rakuten Asia introduces ParVTS, a training-free scheduling framework that prunes up to 88.9% of non-essential visual tokens in multimodal LLMs, reducing FLOPs by 70% and achieving up to 1.77x speedup without O(L²) complexity.

Another critical innovation is in efficient data representation and processing. In “Frequency-Aware Token Reduction for Efficient Vision Transformer”, Dong-Jae Lee et al. from KAIST and NAVER AI Lab propose a frequency-aware token reduction strategy for Vision Transformers (ViTs). By selectively retaining high-frequency tokens and aggregating low-frequency ones, they significantly reduce computational cost while mitigating issues like rank collapsing and over-smoothing. This highlights the importance of preserving crucial signal components in a computationally efficient manner. Parallel to this, “F-INR: Functional Tensor Decomposition for Implicit Neural Representations” from Friedrich Schiller University Jena introduces functional tensor decomposition as a new paradigm for INRs. This framework, developed by Sai Karthikeya Vemuri et al., accelerates training by up to 20x and improves fidelity by breaking down large networks into smaller, axis-specific sub-networks.

Beyond neural network architectures, the quest for efficiency extends to optimization and data analysis. Alessandro Agnetis et al., from Università di Siena and KU Leuven, tackle the “The Unreliable Job Selection and Sequencing Problem”, proving its NP-hardness but also deriving polynomial solutions for special cases and proposing exact algorithms that handle up to 10,000 jobs in minutes. This demonstrates how even in complex stochastic scheduling, intelligent problem decomposition can lead to remarkable efficiency gains. In a similar vein, Kazuki Nakajima et al. from Tokyo Metropolitan University, The University of Osaka, and National Institute of Informatics demonstrate the prevalence of “Learning Multi-Order Block Structure in Higher-Order Networks”, showing that accounting for order-dependent structural details improves predictive performance and interpretability, moving beyond single-order models.

Under the Hood: Models, Datasets, & Benchmarks

These papers showcase a range of specialized models, novel datasets, and optimized benchmarks:

• DAPointMamba: A Mamba-based UDA framework for domain-adaptive point cloud completion, achieving linear computational complexity. It utilizes Cross-Domain Patch-Level Scanning and Spatial/Channel SSM Alignment. No public code repository was explicitly mentioned, but the paper ID suggests it may be available.
• MobileI2V: A lightweight diffusion model from Huazhong University of Science and Technology for fast, high-resolution image-to-video generation on mobile devices. It features a hybrid linear-softmax attention architecture and composite timestep distillation. Code available at https://github.com/hustvl/MobileI2V.
• Ent-Prog: An efficient training framework from Stanford University et al. for diffusion models in human video generation. It uses Conditional Entropy Inflation (CEI) and an adaptive progressive schedule. Code: https://github.com/changlin31/Ent-Prog.
• Low-Rank GEMM: A system from Metere Consulting, LLC that uses low-rank matrix approximations and FP8 precision for efficient matrix multiplication, reducing complexity from O(n³) to O(n²r). Code: https://github.com/metereconsulting/gemm_lora_fp8.
• RASTP: Representation-Aware Semantic Token Pruning by Tianyu Zhan et al. from Zhejiang University for generative recommendation systems, leveraging semantic saliency and attention centrality to prune less informative tokens. Code: https://github.com/Yuzt-zju/RASTP.
• OptimizedDP: A software toolbox from Simon Fraser University for optimal control and dynamic programming, designed for efficient high-dimensional computations using level-set methods and value iteration. Code: https://github.com/SFU-MARS/optimized_dp.
• HSTAN (Hierarchical Spatio-Temporal Attention Network) and DRTA (Dynamic Risk Threshold Adjustment): A framework by Haoran Hu et al. from Chongqing University of Posts and Telecommunications for forward collision warning, achieving high accuracy with low computational complexity (12.3ms inference time) on the NGSIM dataset. Code: https://github.com/huhaoran/HSTAN.
• LAE (Lightweight Autoencoder): A model from Memorial University and Benha University by Ahmad A. Aziz El-Banna and Octavia A. Dobre for position-assisted beam prediction in mmWave ISAC systems, reducing operations by 83% while maintaining accuracy. This leverages real-world data from the DeepSense6G project.
• LCB-CV-UNet: An advanced deep learning architecture by NGC13009 for High Dynamic Range (HDR) radar signal processing, focusing on weak target detection and noise suppression. Code available at https://github.com/NGC13009/ComPlex.
• SAOT (Spectral Transformer): A hybrid spectral Transformer framework from **Hong Kong Baptist University and A*STAR by Chenhong Zhou et al.** that combines Wavelet and Fourier attention mechanisms for solving PDEs, demonstrating state-of-the-art results on six operator learning benchmarks. Code: https://github.com/chenhong-zhou/SAOT.
• HyperMOSBM: A multi-order hypergraph stochastic block model for higher-order networks from Tokyo Metropolitan University et al. that accounts for order-dependent structural details. Code: https://doi.org/10.5281/zenodo.17713331.
• δ-core subsampling: A novel subsampling method by Gabriel Minian et al. from University of California, Berkeley, ETH Zurich, and Google Research for Topological Data Analysis (TDA) based on strong collapse, producing more accurate subsamples with lower computational costs. Code: https://github.com/stolzbernadette/Outlier-robust-subsampling-techniques-for-persistent-homology.
• RISC-V Based TinyML Accelerator: A specialized hardware accelerator by Author A and Author B from University of Example and Institute of Advanced Computing for depthwise separable convolutions in edge AI, focusing on memory access patterns and control flow for low-power computing. Code: https://github.com/SpinalHDL/VexRiscv.

Impact & The Road Ahead

The implications of these advancements are profound. From enabling real-time, high-resolution video generation on mobile phones with MobileI2V: Fast and High-Resolution Image-to-Video on Mobile Devices to improving safety in autonomous vehicles with the efficient collision warning system in “Hierarchical Spatio-Temporal Attention Network with Adaptive Risk-Aware Decision for Forward Collision Warning in Complex Scenarios”, the push for computational efficiency is directly translating into practical, impactful AI applications. The ability to prune tokens, optimize memory, or decompose complex problems into linear-time sub-problems means that powerful AI models can be deployed in resource-constrained environments, widening their accessibility and utility.

Looking ahead, the focus on O(N) complexity and beyond suggests a future where AI systems are not just intelligent but also inherently sustainable and scalable. Papers like “Energy Scaling Laws for Diffusion Models: Quantifying Compute and Carbon Emissions in Image Generation” highlight the critical need to quantify and reduce the environmental impact of AI, providing frameworks for more sustainable development. The exploration of theoretical limits, as seen in “Information Physics of Intelligence: Unifying Logical Depth and Entropy under Thermodynamic Constraints”, also promises to redefine our understanding of intelligence itself, paving the way for fundamentally more efficient architectures. As these innovations mature, we can expect a new generation of AI that is not only smarter but also leaner, faster, and more accessible than ever before.