For uniform keys on the d-dimensional sphere, softmax attention becomes selective at inverse temperature scaling β_n* ≍ n^{2/(d-1)}, with explicit limiting laws for attention weights and outputs in each regime.
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Generating Long Sequences with Sparse Transformers
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abstract
Transformers are powerful sequence models, but require time and memory that grows quadratically with the sequence length. In this paper we introduce sparse factorizations of the attention matrix which reduce this to $O(n \sqrt{n})$. We also introduce a) a variation on architecture and initialization to train deeper networks, b) the recomputation of attention matrices to save memory, and c) fast attention kernels for training. We call networks with these changes Sparse Transformers, and show they can model sequences tens of thousands of timesteps long using hundreds of layers. We use the same architecture to model images, audio, and text from raw bytes, setting a new state of the art for density modeling of Enwik8, CIFAR-10, and ImageNet-64. We generate unconditional samples that demonstrate global coherence and great diversity, and show it is possible in principle to use self-attention to model sequences of length one million or more.
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- abstract Transformers are powerful sequence models, but require time and memory that grows quadratically with the sequence length. In this paper we introduce sparse factorizations of the attention matrix which reduce this to $O(n \sqrt{n})$. We also introduce a) a variation on architecture and initialization to train deeper networks, b) the recomputation of attention matrices to save memory, and c) fast attention kernels for training. We call networks with these changes Sparse Transformers, and show they can model sequences tens of thousands of timesteps long using hundreds of layers. We use the same a
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representative citing papers
Attention and LoRA regression losses induce Poincaré inequalities under mild regularization, so SGD-mimicking SDEs converge to minimizers with no assumptions on data or model size.
ArgBench unifies 33 existing datasets into a standardized benchmark for testing LLMs across 46 argumentation tasks and analyzes the impact of prompting techniques and model factors on performance.
Content-based routing succeeds only when models provide bidirectional context and perform pairwise comparisons, with bidirectional Mamba plus rank-1 projection reaching 99.7% precision at linear inference cost.
EQ-VMamba adds rotation-equivariant cross-scan and group Mamba blocks to enforce end-to-end rotation equivariance, yielding better rotation robustness, competitive accuracy, and roughly 50% fewer parameters than non-equivariant baselines across classification, segmentation, and super-resolution.
RULER shows most long-context LMs drop sharply in performance on complex tasks as length and difficulty increase, with only half maintaining results at 32K tokens.
Mamba is a linear-time sequence model using input-dependent selective SSMs that achieves SOTA results across modalities and matches twice-larger Transformers on language modeling with 5x higher inference throughput.
LongBench is the first bilingual multi-task benchmark for long context understanding in LLMs, containing 21 datasets in 6 categories with average lengths of 6711 words (English) and 13386 characters (Chinese).
S4 is an efficient state space sequence model that captures long-range dependencies via structured parameterization of the SSM, achieving state-of-the-art results on the Long Range Arena and other benchmarks while being faster than Transformers for generation.
Denoising diffusion probabilistic models generate high-quality images by learning to reverse a fixed forward diffusion process, achieving FID 3.17 on CIFAR10.
Empirical power-law scaling governs language model loss versus model size, data size, and compute, enabling optimal allocation of training compute.
Meta-Attention introduces per-token Bayesian routing among attention mechanisms via amortised variational inference with a Dirichlet prior, yielding lower projected FLOP cost than prior-free routing on a Tiny LM benchmark.
Derives a blockwise resolvent-style attention operator that exploits structured sparsity for subquadratic O(n^{4/3}d) entity tracking while matching dense accuracy.
SymTrack is the first systematic detection-free framework for scene text tracking that constructs benchmarks from video text spotting datasets and reports up to 11.97% AUC gains over prior trackers.
A transformer with prediction-correction and hierarchical super-token merging unifies simulation of six physical dynamics categories on Lagrangian particles and generalizes to unseen conditions.
QLAM extends state-space models with quantum superposition in the hidden state for linear-time long-sequence modeling and reports consistent gains over RNN and transformer baselines on sequential image tasks.
Dingo-Pop uses a transformer to perform amortized, end-to-end population inference from GW strain data in seconds, bypassing per-event Monte Carlo sampling.
VORT assigns learnable fractional orders to tokens and approximates their power-law retention kernels via sum-of-exponentials for efficient long-range dependency modeling in transformers.
MISA routes to a small subset of indexer heads via block statistics, matching full DSA performance on LongBench with 4-8x fewer heads and 3.82x speedup while recovering over 92% of selected tokens.
SpecEdit accelerates diffusion-based image editing up to 10x by using a low-resolution draft to identify edit-relevant tokens via semantic discrepancies for selective high-resolution denoising.
A cross-attention SAE with sparsemax attention achieves lower reconstruction loss and higher-quality concepts than fixed-sparsity baselines by making activation counts data-dependent.
Contextual entrainment decreases for semantic contexts but increases for non-semantic ones as LLMs scale, following power-law trends with 4x better resistance to misinformation but 2x more copying of arbitrary tokens.
LoSA caches prefix attention for stable tokens in block-wise DLMs and applies sparse attention only to active tokens, preserving near-dense accuracy while achieving 1.54x lower attention density and up to 4.14x speedup.
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citing papers explorer
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Scaling Limits of Long-Context Transformers
For uniform keys on the d-dimensional sphere, softmax attention becomes selective at inverse temperature scaling β_n* ≍ n^{2/(d-1)}, with explicit limiting laws for attention weights and outputs in each regime.
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Convergent Stochastic Training of Attention and Understanding LoRA
Attention and LoRA regression losses induce Poincaré inequalities under mild regularization, so SGD-mimicking SDEs converge to minimizers with no assumptions on data or model size.
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ArgBench: Benchmarking LLMs on Computational Argumentation Tasks
ArgBench unifies 33 existing datasets into a standardized benchmark for testing LLMs across 46 argumentation tasks and analyzes the impact of prompting techniques and model factors on performance.
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When Does Content-Based Routing Work? Representation Requirements for Selective Attention in Hybrid Sequence Models
Content-based routing succeeds only when models provide bidirectional context and perform pairwise comparisons, with bidirectional Mamba plus rank-1 projection reaching 99.7% precision at linear inference cost.
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Rotation Equivariant Mamba for Vision Tasks
EQ-VMamba adds rotation-equivariant cross-scan and group Mamba blocks to enforce end-to-end rotation equivariance, yielding better rotation robustness, competitive accuracy, and roughly 50% fewer parameters than non-equivariant baselines across classification, segmentation, and super-resolution.
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Meta-Attention: Bayesian Per-Token Routing for Efficient Transformer Inference
Meta-Attention introduces per-token Bayesian routing among attention mechanisms via amortised variational inference with a Dirichlet prior, yielding lower projected FLOP cost than prior-free routing on a Tiny LM benchmark.
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Structured-Sparse Attention for Entity Tracking with Subquadratic Sequence Complexity
Derives a blockwise resolvent-style attention operator that exploits structured sparsity for subquadratic O(n^{4/3}d) entity tracking while matching dense accuracy.
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Beyond Detection: A Structure-Aware Framework for Scene Text Tracking
SymTrack is the first systematic detection-free framework for scene text tracking that constructs benchmarks from video text spotting datasets and reports up to 11.97% AUC gains over prior trackers.
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WorldParticle: Unified World Simulation of Lagrangian Particle Dynamics via Transformer
A transformer with prediction-correction and hierarchical super-token merging unifies simulation of six physical dynamics categories on Lagrangian particles and generalizes to unseen conditions.
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QLAM: A Quantum Long-Attention Memory Approach to Long-Sequence Token Modeling
QLAM extends state-space models with quantum superposition in the hidden state for linear-time long-sequence modeling and reports consistent gains over RNN and transformer baselines on sequential image tasks.
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End-to-End Population Inference from Gravitational-Wave Strain using Transformers
Dingo-Pop uses a transformer to perform amortized, end-to-end population inference from GW strain data in seconds, bypassing per-event Monte Carlo sampling.
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VORT: Adaptive Power-Law Memory for NLP Transformers
VORT assigns learnable fractional orders to tokens and approximates their power-law retention kernels via sum-of-exponentials for efficient long-range dependency modeling in transformers.
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MISA: Mixture of Indexer Sparse Attention for Long-Context LLM Inference
MISA routes to a small subset of indexer heads via block statistics, matching full DSA performance on LongBench with 4-8x fewer heads and 3.82x speedup while recovering over 92% of selected tokens.
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SpecEdit: Training-Free Acceleration for Diffusion based Image Editing via Semantic Locking
SpecEdit accelerates diffusion-based image editing up to 10x by using a low-resolution draft to identify edit-relevant tokens via semantic discrepancies for selective high-resolution denoising.
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Improving Sparse Autoencoder with Dynamic Attention
A cross-attention SAE with sparsemax attention achieves lower reconstruction loss and higher-quality concepts than fixed-sparsity baselines by making activation counts data-dependent.
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Better and Worse with Scale: How Contextual Entrainment Diverges with Model Size
Contextual entrainment decreases for semantic contexts but increases for non-semantic ones as LLMs scale, following power-law trends with 4x better resistance to misinformation but 2x more copying of arbitrary tokens.
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LoSA: Locality Aware Sparse Attention for Block-Wise Diffusion Language Models
LoSA caches prefix attention for stable tokens in block-wise DLMs and applies sparse attention only to active tokens, preserving near-dense accuracy while achieving 1.54x lower attention density and up to 4.14x speedup.
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A Hormone-inspired Emotion Layer for Transformer language models (HELT)
HormoneT5 augments T5 with a hormone-inspired block that predicts six continuous emotion values and uses them to modulate responses, reporting over 85% per-hormone accuracy and human preference for emotional quality.
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Free-Range Gaussians: Non-Grid-Aligned Generative 3D Gaussian Reconstruction
Free-Range Gaussians uses flow matching over Gaussian parameters to predict non-grid-aligned 3D Gaussians from multi-view images, enabling synthesis of plausible content in unobserved regions with fewer primitives than grid-aligned methods.
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Cactus: Accelerating Auto-Regressive Decoding with Constrained Acceptance Speculative Sampling
Cactus uses constrained optimization to guarantee bounded divergence from the verifier LLM distribution during speculative sampling, raising acceptance rates without the distortion seen in typical acceptance sampling.
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More than the Sum: Panorama-Language Models for Adverse Omni-Scenes
Panorama-Language Models with a sparse attention module and PanoVQA dataset deliver superior holistic reasoning on 360° adverse omni-scenes compared to stitched pinhole views.
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Scaling Parallel Sequence Models to Foundation-Scale Vision Encoders
C-GSPN scales 2D spatial propagation to foundation vision encoders via a fast CUDA kernel, compressed blocks, and two-stage distillation, matching ViT performance with 15% fewer parameters and 4x block speedup at 2K resolution.
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Approaching I/O-optimality for Approximate Attention
Presents I/O-efficient algorithms for approximate attention with almost-linear cost in n, approaching lower bounds in most parameter regimes.
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Activation-Free Backbones for Image Recognition: Polynomial Alternatives within MetaFormer-Style Vision Models
Polynomial replacements for activations in MLPs, convolutions, and attention within MetaFormer yield PolyNeXt models that match or exceed standard performance on ImageNet, ADE20K, and robustness benchmarks while beating prior polynomial networks.
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PulseCol: Periodically Refreshed Column-Sparse Attention for Accelerating Diffusion Language Models
PulseCol introduces periodically refreshed column-sparse attention to achieve up to 1.95x speedup over FlashAttention in diffusion LLMs with maintained model quality.
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Attention Once Is All You Need: Efficient Streaming Inference with Stateful Transformers
Stateful sessions with incremental KV cache and flash queries allow O(|q|) latency in streaming transformer inference, delivering up to 5.9x speedup over conventional engines while preserving full attention.
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Phasor Memory Networks: Stable Backpropagation Through Time for Scalable Explicit Memory
PMNet uses unitary phasor dynamics and hierarchical anchors to make explicit memory stable for long sequences, matching a 3x larger Mamba model on long-context robustness with a 119M parameter network.
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KV-Fold: One-Step KV-Cache Recurrence for Long-Context Inference
KV-Fold turns frozen transformers into stable long-context models by folding the KV cache across sequence chunks in repeated forward passes.
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Search Your Block Floating Point Scales!
ScaleSearch optimizes block floating point scales via fine-grained search to cut quantization error by 27% for NVFP4, improving PTQ by up to 15 points on MATH500 for Qwen3-8B and attention PPL by 0.77 on Llama 3.1 70B.
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Compute Where it Counts: Self Optimizing Language Models
SOL trains a policy to dynamically control multiple efficiency mechanisms per token via group-relative policy optimization on teacher-forced episodes, yielding better quality at matched average budget than static or random allocation.
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FocuSFT: Bilevel Optimization for Dilution-Aware Long-Context Fine-Tuning
FocuSFT uses an inner optimization loop to adapt fast-weight parameters into a parametric memory that sharpens attention on relevant content, then conditions outer-loop supervised fine-tuning on this representation, yielding gains on long-context benchmarks.
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A Novel Graph-Regulated Disentangling Mamba Model with Sparse Tokens for Enhanced Tree Species Classification from MODIS Time Series
A graph-regulated disentangling Mamba model with sparse tokens achieves 93.94% accuracy classifying tree species from MODIS time series in Alberta and outperforms twelve prior models.
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The Impossibility Triangle of Long-Context Modeling
No model can achieve efficiency, compactness, and recall capacity scaling with sequence length at once, as any two imply a strict bound of O(poly(d)/log V) on recallable facts.
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On the (In-)Security of the Shuffling Defense in the Transformer Secure Inference
An attack aligns differently shuffled intermediate activations from secure Transformer inference queries to recover model weights with low error using roughly one dollar of queries.
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Linear-Time Global Visual Modeling without Explicit Attention
Dynamic parameterization of standard layers can replace explicit attention for linear-time global visual modeling.
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UniBCI: Towards a Unified Pretrained Model for Invasive Brain-Computer Interfaces
UniBCI is a unified pretrained model for invasive neural spike data that uses CST tokenization, IAA attention, and self-supervised masked reconstruction to achieve SOTA downstream performance with better generalization and efficiency.
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Unifying Sparse Attention with Hierarchical Memory for Scalable Long-Context LLM Serving
SPIN co-designs sparse attention with hierarchical memory to achieve 1.66-5.66x higher throughput, 7-9x lower TTFT, and up to 58% lower TPOT than vLLM and original sparse implementations.
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HubRouter: A Pluggable Sub-Quadratic Routing Primitive for Hybrid Sequence Models
HubRouter is a sub-quadratic routing primitive using learned hubs that replaces attention layers in hybrid models while delivering competitive perplexity and large throughput gains.
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An explicit operator explains end-to-end computation in the modern neural networks used for sequence and language modeling
S4D state space models correspond exactly to wave propagation and nonlinear wave interactions in a one-dimensional ring oscillator network, with a closed-form operator describing the complete input-output map.
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DASH-KV: Accelerating Long-Context LLM Inference via Asymmetric KV Cache Hashing
DASH-KV accelerates long-context LLM inference to linear complexity via asymmetric KV cache hashing and mixed-precision retention, matching full attention performance on LongBench.
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AQPIM: Breaking the PIM Capacity Wall for LLMs with In-Memory Activation Quantization
AQPIM performs in-memory product quantization of activations for LLMs on PIM hardware, reducing GPU-CPU communication by 90-98.5% and delivering 3.4x speedup over prior PIM methods.
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Prefill-as-a-Service: KVCache of Next-Generation Models Could Go Cross-Datacenter
PrfaaS enables practical cross-datacenter prefill-decode disaggregation for hybrid-attention models via selective offloading, bandwidth-aware scheduling, and cache-aware placement, yielding 54% higher throughput and 64% lower P90 TTFT than homogeneous baselines in a 1T-parameter case study.
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FreqFormer: Hierarchical Frequency-Domain Attention with Adaptive Spectral Routing for Long-Sequence Video Diffusion Transformers
FreqFormer applies heterogeneous attention (dense global on low frequencies, block-sparse on mid, local on high) plus adaptive spectral routing to reduce attention cost in long-sequence video diffusion transformers.
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In-Place Test-Time Training
In-Place TTT adapts LLM MLP projection matrices at test time with a next-token-aligned objective and chunk-wise updates, enabling better long-context performance as a drop-in enhancement.
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PoM: A Linear-Time Replacement for Attention with the Polynomial Mixer
PoM is a new linear-complexity token mixer using learned polynomials that matches attention performance in transformers while enabling efficient long-sequence processing.
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LSRM: High-Fidelity Object-Centric Reconstruction via Scaled Context Windows
LSRM scales transformer context windows with native sparse attention and geometric routing to deliver high-fidelity feed-forward 3D reconstruction and inverse rendering that approaches dense optimization quality.
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MobileLLM-Flash: Latency-Guided On-Device LLM Design for Industry Scale Deployment
MobileLLM-Flash creates 350M-1.4B parameter LLMs via latency-guided search and attention skipping, delivering up to 1.8x faster prefill and 1.6x faster decode on mobile CPUs with comparable or better quality.
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LPC-SM: Local Predictive Coding and Sparse Memory for Long-Context Language Modeling
LPC-SM is a hybrid architecture separating local attention, persistent memory, predictive correction, and control with ONT for memory writes, showing loss reductions on 158M-parameter models up to 4096-token contexts.
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Voxtral Realtime
Voxtral Realtime is an end-to-end trained streaming ASR model that achieves Whisper-level transcription quality at 480ms delay after scaling pretraining across 13 languages.
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CompilerKV: Risk-Adaptive KV Compression via Offline Experience Compilation
CompilerKV uses offline-compiled retention tables as portable priors to achieve SOTA prefill-only KV compression performance across backbones at low token budgets.