WriteSAE introduces sparse autoencoders with rank-1 matrix atoms for recurrent state updates, allowing replacement tests that outperform deletion on 92.4% of positions and a formula predicting logit changes with R²=0.98.
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Retentive Network: A Successor to Transformer for Large Language Models
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abstract
In this work, we propose Retentive Network (RetNet) as a foundation architecture for large language models, simultaneously achieving training parallelism, low-cost inference, and good performance. We theoretically derive the connection between recurrence and attention. Then we propose the retention mechanism for sequence modeling, which supports three computation paradigms, i.e., parallel, recurrent, and chunkwise recurrent. Specifically, the parallel representation allows for training parallelism. The recurrent representation enables low-cost $O(1)$ inference, which improves decoding throughput, latency, and GPU memory without sacrificing performance. The chunkwise recurrent representation facilitates efficient long-sequence modeling with linear complexity, where each chunk is encoded parallelly while recurrently summarizing the chunks. Experimental results on language modeling show that RetNet achieves favorable scaling results, parallel training, low-cost deployment, and efficient inference. The intriguing properties make RetNet a strong successor to Transformer for large language models. Code will be available at https://aka.ms/retnet.
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- abstract In this work, we propose Retentive Network (RetNet) as a foundation architecture for large language models, simultaneously achieving training parallelism, low-cost inference, and good performance. We theoretically derive the connection between recurrence and attention. Then we propose the retention mechanism for sequence modeling, which supports three computation paradigms, i.e., parallel, recurrent, and chunkwise recurrent. Specifically, the parallel representation allows for training parallelism. The recurrent representation enables low-cost $O(1)$ inference, which improves decoding throughp
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representative citing papers
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.
Test-time training with KV binding reduces to learned linear attention.
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.
VMamba introduces a state-space vision backbone using 2D selective scanning across four routes to achieve linear complexity and strong performance on image tasks.
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.
Hypic enables position-independent KV/state reuse on hybrid-attention LLMs via cached segment transitions, seam-window repair, and inter-instance segment parallelism, cutting TTFT 3.25x over prefix caching.
Tapered Language Models monotonically decrease MLP width across depth with a cosine schedule, yielding better perplexity and downstream performance than uniform-width baselines across multiple architectures and scales at no extra cost.
LongSpike integrates fractional-order state-space modeling into spiking neural networks, enabling better long-sequence performance than prior SNNs on LRA, WikiText-103, and Speech Commands benchmarks while retaining sparse computation.
Derives μP-style scaling rules for Gated Delta Networks and validates stable learning-rate transfer in language model pre-training experiments.
AURA-Mem uses an action-gated recurrent memory trained on closed-loop action error to deliver constant 4,224-byte state and 5-9x fewer writes than baselines while matching base policy success on LIBERO-Long.
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.
QGS introduces query-item pair encoding and query-conditioned prediction with a linear HSTU encoder and HFG-Attention to reduce noise from query switches in generative search ranking, reporting online gains in a commercial system.
Tensor Cache augments sliding-window attention with an eviction-fed outer-product associative memory and a training correction to improve long-context performance under bounded memory.
KVBuffer reduces linear attention decoding latency by up to 45% and increases speculative decoding throughput 5x by buffering keys/values for flexible chunked and parallel computation.
Chem-GMNet uses sphere-native embeddings, DualSKA attention, and SH-FFN layers to match or beat ChemBERTa-2 on MoleculeNet tasks with fewer parameters and sometimes no pretraining.
TIDES reconciles selective SSM expressivity with continuous-time physical discretization by moving input dependence onto the state matrix, enabling native irregular time series handling and achieving SOTA on UEA and Physiome-ODE benchmarks.
Lighthouse Attention enables faster long-context pre-training via gradient-free symmetrical hierarchical compression of QKV while preserving causality, followed by a short full-attention recovery that yields lower loss than standard full-attention training.
Adding temporal memory via LIF, precision-weighted gating, and anticipatory prediction to MoE routers recovers effective expert selection at distribution transitions, with ablation confirming a super-additive beta-ant interaction.
A neural covariance estimator enables fully blind, direction-preserving MIMO speech enhancement that improves over mask-based baselines and approaches oracle performance with fewer parameters.
Multiscreen replaces softmax attention with screening to provide absolute query-key relevance, resulting in models with 30% fewer parameters that maintain stable performance at long contexts.
Exact Flow Linear Attention derives a closed-form exact update for delta-rule linear attention from continuous-time dynamics, removing Euler discretization error while preserving linear complexity and structure.
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.
citing papers explorer
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WriteSAE: Sparse Autoencoders for Recurrent State
WriteSAE introduces sparse autoencoders with rank-1 matrix atoms for recurrent state updates, allowing replacement tests that outperform deletion on 92.4% of positions and a formula predicting logit changes with R²=0.98.
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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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Test-Time Training with KV Binding Is Secretly Linear Attention
Test-time training with KV binding reduces to learned linear attention.
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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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VMamba: Visual State Space Model
VMamba introduces a state-space vision backbone using 2D selective scanning across four routes to achieve linear complexity and strong performance on image tasks.
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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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HYPIC: Accelerating Hybrid-Attention LLM Serving with Position-Independent Caching
Hypic enables position-independent KV/state reuse on hybrid-attention LLMs via cached segment transitions, seam-window repair, and inter-instance segment parallelism, cutting TTFT 3.25x over prefix caching.
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Tapered Language Models
Tapered Language Models monotonically decrease MLP width across depth with a cosine schedule, yielding better perplexity and downstream performance than uniform-width baselines across multiple architectures and scales at no extra cost.
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LongSpike: Fractional Order Spiking State Space Models for Efficient Long Sequence Learning
LongSpike integrates fractional-order state-space modeling into spiking neural networks, enabling better long-sequence performance than prior SNNs on LRA, WikiText-103, and Speech Commands benchmarks while retaining sparse computation.
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Unlocking Feature Learning in Gated Delta Networks at Scale
Derives μP-style scaling rules for Gated Delta Networks and validates stable learning-rate transfer in language model pre-training experiments.
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AURA: Action-Gated Memory for Robot Policies at Constant VRAM
AURA-Mem uses an action-gated recurrent memory trained on closed-loop action error to deliver constant 4,224-byte state and 5-9x fewer writes than baselines while matching base policy success on LIBERO-Long.
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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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From Item-Only to Query-Item: Query-Conditioned Generative Search with QGS in Quark
QGS introduces query-item pair encoding and query-conditioned prediction with a linear HSTU encoder and HFG-Attention to reduce noise from query switches in generative search ranking, reporting online gains in a commercial system.
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Tensor Cache: Eviction-conditioned Associative Memory for Transformers
Tensor Cache augments sliding-window attention with an eviction-fed outer-product associative memory and a training correction to improve long-context performance under bounded memory.
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KVBuffer: IO-aware Serving for Linear Attention
KVBuffer reduces linear attention decoding latency by up to 45% and increases speculative decoding throughput 5x by buffering keys/values for flexible chunked and parallel computation.
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Chem-GMNet: A Sphere-Native Geometric Transformer for Molecular Property Prediction
Chem-GMNet uses sphere-native embeddings, DualSKA attention, and SH-FFN layers to match or beat ChemBERTa-2 on MoleculeNet tasks with fewer parameters and sometimes no pretraining.
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TIDES: Implicit Time-Awareness in Selective State Space Models
TIDES reconciles selective SSM expressivity with continuous-time physical discretization by moving input dependence onto the state matrix, enabling native irregular time series handling and achieving SOTA on UEA and Physiome-ODE benchmarks.
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Long Context Pre-Training with Lighthouse Attention
Lighthouse Attention enables faster long-context pre-training via gradient-free symmetrical hierarchical compression of QKV while preserving causality, followed by a short full-attention recovery that yields lower loss than standard full-attention training.
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Affinity Is Not Enough: Recovering the Free Energy Principle in Mixture-of-Experts
Adding temporal memory via LIF, precision-weighted gating, and anticipatory prediction to MoE routers recovers effective expert selection at distribution transitions, with ablation confirming a super-additive beta-ant interaction.
-
Direction-Preserving MIMO Speech Enhancement Using a Neural Covariance Estimator
A neural covariance estimator enables fully blind, direction-preserving MIMO speech enhancement that improves over mask-based baselines and approaches oracle performance with fewer parameters.
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Screening Is Enough
Multiscreen replaces softmax attention with screening to provide absolute query-key relevance, resulting in models with 30% fewer parameters that maintain stable performance at long contexts.
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Exact Flow Linear Attention: Exact Solution from Continuous-Time Dynamics
Exact Flow Linear Attention derives a closed-form exact update for delta-rule linear attention from continuous-time dynamics, removing Euler discretization error while preserving linear complexity and structure.
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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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Graph Retention Networks for Dynamic Graphs
Graph Retention Networks extend retention to dynamic graphs to enable parallelizable training, O(1) inference, and chunkwise long-term training while delivering competitive performance with major efficiency gains.
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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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Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality
Transformers and SSMs are unified through structured state space duality, producing a 2-8X faster Mamba-2 model that remains competitive with Transformers.
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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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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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The Key to Going Linear: Analysis-Driven Transformer Linearization
Delta-rule linear attention faithfully approximates softmax attention through key-dependent rank-1 projections, enabling efficient post-hoc linearization of LLMs up to 32B parameters.
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CARVE: Content-Aware Recurrent with Value Efficiency for Chunk-Parallel Linear Attention
Key-axis-only content-aware erase plus a scalar write gate restores WY-form chunk training for delta-rule models and improves 1.3B language-model quality over GDN-2.
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Test-Time Training with Next-Token Prediction
TTT-NTP adapts pretrained LLMs at test time by training fast weights to match next-position hidden states from the forward pass, yielding consistent gains on long-context benchmarks across Llama, Mistral, and Qwen models.
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Architecture-Aware Reinforcement Learning Makes Sliding-Window Attention Competitive in Math Reasoning
Reinforcement learning after SFT conversion narrows the performance gap between sliding-window attention and full self-attention on math reasoning benchmarks while preserving linear complexity.
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You Only Index Once: Cross-Layer Sparse Attention with Shared Routing
CLSA shares both KV cache and routing indices across decoder layers to amortize top-k selection, delivering up to 7.6x decoding speedup and 17.1x throughput at 128K context while preserving accuracy.
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Dynamic Short Convolutions Improve Transformers
Dynamic short convolutions applied to key/query/value projections and linear layers in Transformers yield consistent performance gains and 1.33-1.60x compute advantages over standard models on language modeling from 150M to 2B parameters.
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Don't Read Everything: A Curvature-Conditioned Query for Linear Attention
CCQ adds a curvature-based query contraction to linear attention backbones, improving perplexity, retrieval, and long-context performance on GLA and Gated DeltaNet at low extra cost.
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FlowNar: Scalable Streaming Narration for Long-Form Videos
FlowNar achieves bounded memory and 3x higher throughput for streaming narration on Ego4D, EgoExo4D, and EpicKitchens100 by combining dynamic historical context removal with a Cross Linear Attentive Memory module.
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SANA-Streaming: Real-time Streaming Video Editing with Hybrid Diffusion Transformer
SANA-Streaming delivers 1280x704 streaming video editing at 24 FPS end-to-end on an RTX 5090 using hybrid DiT blocks, cycle-reverse training, and mixed-precision quantization.
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Forget Less, Generalize More: Unifying Temporal and Structural Adaptation for Dynamic Graphs
DSRD unifies temporal and structural adaptation for dynamic graphs via a single recurrent retentive state with learnable time-sensitivity parameters in the decay kernels.
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Discontinuous Galerkin Neural Operator for Pathology Defocus Deblurring
DGNO parameterizes integral kernels with discontinuous Galerkin elements for heterogeneous defocus deblurring in pathology images and reports superior performance over prior methods.
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Gated DeltaNet-2: Decoupling Erase and Write in Linear Attention
Gated DeltaNet-2 decouples channel-wise erase and write gates in linear attention, generalizing prior DeltaNet and KDA models while showing stronger results on language modeling and long-context retrieval at 1.3B scale.
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Towards Understanding Self-Pretraining for Sequence Classification
Self-pretraining improves Transformer sequence classification by enabling learning of proximity-biased attention from positional encodings that label supervision alone cannot easily acquire from random starts.
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LT2: Linear-Time Looped Transformers
LT2 introduces looped transformers with linear-time attention (linear, sparse, and hybrid variants) that match or exceed standard looped transformer quality at linear complexity, including a converted 1.4B model competitive with larger industry models.
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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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OSDN: Improving Delta Rule with Provable Online Preconditioning in Linear Attention
OSDN adds online diagonal preconditioning to the Delta Rule, preserving chunkwise parallelism while proving super-geometric convergence and delivering 32-39% recall gains at 340M-1.3B scales.
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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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The Routing and Filtering Structure of Attention
Attention decomposes into low-rank routing and symmetric filtering; disentangled S-D attention reveals a spectral cascade allowing early-layer linearization at under 5% perplexity cost.
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Elastic Attention Cores for Scalable Vision Transformers
VECA learns effective visual representations using core-periphery attention where patches interact exclusively via a resolution-invariant set of learned core embeddings, achieving linear O(N) complexity while maintaining competitive performance.
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The Transformer as a Polar State Estimator
The paper casts the standard Transformer block with RoPE as a first-order approximation of a radial–tangential state estimator and introduces a Polar Transformer variant that retains the discarded geometric corrections.
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Priming: Hybrid State Space Models From Pre-trained Transformers
Priming transfers knowledge from pre-trained Transformers to hybrid SSM-attention models, recovering performance with minimal additional tokens and showing Gated KalmaNet outperforming Mamba-2 on long-context reasoning at 32B scale.