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.
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.
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.
-
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.
-
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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RULER: What's the Real Context Size of Your Long-Context Language Models?
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.
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Mamba: Linear-Time Sequence Modeling with Selective State Spaces
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.
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LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding
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).
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Efficiently Modeling Long Sequences with Structured State Spaces
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
Denoising diffusion probabilistic models generate high-quality images by learning to reverse a fixed forward diffusion process, achieving FID 3.17 on CIFAR10.
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Scaling Laws for Neural Language Models
Empirical power-law scaling governs language model loss versus model size, data size, and compute, enabling optimal allocation of training compute.
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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.
-
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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SnapStream: Efficient Long Sequence Decoding on Dataflow Accelerators
SnapStream deploys sparse KV attention in a production inference system on dataflow accelerators, delivering 4x on-chip memory savings for DeepSeek-671B at 128k context with up to 1832 tokens/sec and minimal accuracy loss on LongBench-v2, AIME24, and LiveCodeBench.
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DELTA: Dynamic Layer-Aware Token Attention for Efficient Long-Context Reasoning
DELTA partitions layers into full, delta, and sparse groups to select salient tokens via aggregated attention scores, matching full-attention accuracy on AIME and GPQA while cutting attended tokens up to 4.25x and achieving 1.54x speedup.
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IAFormer: Interaction-Aware Transformer network for collider data analysis
IAFormer uses boost-invariant pairwise quantities and differential attention to create a sparse Transformer that achieves state-of-the-art classification on top-quark and quark-gluon jet datasets while using over an order of magnitude fewer parameters than prior Particle Transformer models.
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Transformer Neural Processes - Kernel Regression
TNP-KR adds a kernel regression transformer block, kernel attention bias, scan attention for translation invariance, and deep kernel attention to achieve lower complexity and state-of-the-art results on meta-regression and related benchmarks.
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FlashAttention-3: Fast and Accurate Attention with Asynchrony and Low-precision
FlashAttention-3 achieves 1.5-2x speedup on H100 GPUs for attention, reaching 740 TFLOPs/s (75% utilization) in FP16 and near 1.2 PFLOPs/s in FP8 while cutting numerical error by 2.6x versus baseline FP8 attention.
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Leave No Context Behind: Efficient Infinite Context Transformers with Infini-attention
Infini-attention combines compressive memory with masked local attention and long-term linear attention inside each Transformer block to support infinite context length with bounded resources.
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Griffin: Mixing Gated Linear Recurrences with Local Attention for Efficient Language Models
Griffin hybrid model matches Llama-2 performance while trained on over 6 times fewer tokens and offers lower inference latency with higher throughput.
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Actions Speak Louder than Words: Trillion-Parameter Sequential Transducers for Generative Recommendations
HSTU-based generative recommenders with 1.5 trillion parameters scale as a power law with compute up to GPT-3 scale, outperform baselines by up to 65.8% NDCG, run 5-15x faster than FlashAttention2 on long sequences, and improve online A/B metrics by 12.4%.
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Vision Mamba: Efficient Visual Representation Learning with Bidirectional State Space Model
Vim is a bidirectional Mamba vision backbone that outperforms DeiT in accuracy on standard tasks while being substantially faster and more memory-efficient for high-resolution images.
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Scalable Diffusion Models with Transformers
DiTs achieve SOTA FID of 2.27 on ImageNet 256x256 by scaling transformer-based latent diffusion models, with performance improving consistently as Gflops increase.
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FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness
FlashAttention reduces GPU high-bandwidth memory accesses in self-attention via tiling, delivering exact attention with lower IO complexity, 2-3x wall-clock speedups on models like GPT-2, and the ability to train on sequences up to 64K long.
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OPT: Open Pre-trained Transformer Language Models
OPT releases open decoder-only transformers up to 175B parameters that match GPT-3 performance at one-seventh the carbon cost, along with code and training logs.
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High-Resolution Image Synthesis with Latent Diffusion Models
Latent diffusion models achieve state-of-the-art inpainting and competitive results on unconditional generation, scene synthesis, and super-resolution by performing the diffusion process in the latent space of pretrained autoencoders with cross-attention conditioning, while cutting computational and
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Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity
Switch Transformers use top-1 expert routing in a Mixture of Experts setup to scale to trillion-parameter language models with constant compute and up to 4x speedup over T5-XXL.
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Scaling Laws for Autoregressive Generative Modeling
Autoregressive transformers follow power-law scaling laws for cross-entropy loss with nearly universal exponents relating optimal model size to compute budget across four domains.
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Rethinking Attention with Performers
Performers approximate full-rank softmax attention in Transformers via FAVOR+ random features for linear complexity, with theoretical guarantees of unbiased estimation and competitive results on pixel, text, and protein tasks.
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DeBERTa: Decoding-enhanced BERT with Disentangled Attention
DeBERTa improves BERT-style models by separating content and relative position in attention and adding absolute positions to the decoder, yielding consistent gains on NLU and NLG tasks and the first single-model superhuman score on SuperGLUE.
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Longformer: The Long-Document Transformer
Longformer uses local windowed attention plus task-specific global attention to achieve linear scaling and state-of-the-art results on long-document language modeling, QA, and summarization after pretraining.
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ALBERT: A Lite BERT for Self-supervised Learning of Language Representations
ALBERT reduces BERT parameters via embedding factorization and layer sharing, adds inter-sentence coherence pretraining, and reaches SOTA on GLUE, RACE, and SQuAD with fewer parameters than BERT-large.
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Augmenting Self-attention with Persistent Memory
Augmenting self-attention with persistent memory vectors allows removal of feed-forward layers from Transformers without degrading performance on character and word level language modeling benchmarks.
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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.