Daily Papers

Speculative decoding accelerates autoregressive generation by drafting multiple tokens per step, yet feature-based drafters rely on target hidden features whose contextual emphasis may not align with the needs of subsequent draft positions. Hybrid linear attention (HLA) models maintain compact recurrent states that accumulate historical associations, offering an efficient source of complementary context for speculative drafting. We introduce ReaDy, the first speculative decoding method, to the best of our knowledge, to leverage HLA recurrent states for position-specific context retrieval during drafting. ReaDy equips each draft position with a learned query to retrieve supplementary context directly from the target's committed recurrent states. A lightweight state reader integrates this context into draft representations through residual updates, while low-rank state reads and fused operators keep additional computation and I/O overhead low. Building on DSpark's parallel backbone and sequential prediction head, ReaDy employs a lightweight two-stage adaptation strategy, with reader capacity, state sources, and residual placement examined through ablation studies. Across seven benchmarks spanning mathematics, code generation, and dialogue, ReaDy achieves an average 3.16times decoding speedup over autoregressive decoding with Qwen3.8-27B on a single NVIDIA B200 GPU. It outperforms DSpark on every benchmark, improving throughput by 7.97% and acceptance length by 8.50% on average. Our code is available at https://github.com/StartLuxLabs/ReaDy.

Recurrent neural networks (RNNs) compress the historical context into a memory state of fixed size, thus allowing for constant-time inference. The memory state size is a crucial factor in their performance, as exemplified by the strong performance and resurgence of linear attention, which extends the vector-valued hidden states of ordinary RNNs to matrix-valued hidden states. Crucially, linear attention does so in a parameter-efficient way, in particular by using an outer product of the key and value vectors to write to the matrix-valued hidden state. We generalize this construction and propose triadic linear attention, which writes the triadic outer product of a key, a second key, and a value, into a third-order (i.e., 3D) tensor state, and reads from it by contracting both key axes with two queries. An E-dimensional second key thus yields an E-fold increase in state size while adding only two projections. Triadic linear attention is compatible with data-dependent forgetting, the delta rule, and chunkwise-parallel training. Applied to Gated DeltaNet and scalar-gated linear attention, triadic linear attention substantially improves long-context language modeling and recall, outperforming alternatives that enlarge the state.

Modern language models are built primarily from Transformers, recurrent models, and their hybrid architectures. Transformers rely on token-level attention memories, while recurrent models such as state space models (SSMs) and linear attention maintain compact recurrent states. These architectures are typically instantiated separately or interleaved at the layer level, leaving open whether a shared memory representation can support both recurrent compression and attention-style retrieval. We study this question through the state space duality (SSD) view of Mamba-2, where the SSM state can be interpreted as a compressed associative key--value (KV) cache. We observe that Mamba-2 decodes token-conditioned values from this state but does not decode token-conditioned keys. Based on this observation, we propose DART (Decoded Attention over Recurrent sTates), which retains the chunk state contributions produced by the Mamba-2 chunked scan as chunk state memories, decodes token-conditioned keys and values from these memories, and performs state-memory attention (SMA) over the resulting KV pairs. The retrieved output is then combined with the native Mamba-2 output through a gated residual connection. DART supports practical training by reusing the Mamba-2 chunked scan and implementing SMA as a FlashAttention-style computation. Our analysis and experiments show that DART substantially reduces the length-dependent inference cache compared with a matched attention baseline (e.g., 75% savings when the chunk size is S=256 and the state size is N=128). Compared with Mamba-2, DART substantially improves associative recall and retrieval while preserving general language-modeling quality.

Linear attention and state-space models provide linear-time sequence modeling, but their recurrent memory remains a second-order tensor (a matrix), limiting the order of interactions that can be represented in the state. We introduce the RunningTensor, which generalizes this memory to an order-o tensor, updated by a rank-1 outer product and read by contracting against o-1 vector queries. Order 2 recovers linear attention; we study order 3 as a proof of concept, retaining both recurrent and parallel forms while remaining linear in sequence length T and improving working memory capacity from O(W^2) to O(W^o). On synthetic multi-query associative recall, RunningTensor outperforms linear-attention and SSM baselines. After pretraining, it also improves performance on language-understanding and non-synthetic retrieval tasks, suggesting that higher-order recurrent state can provide useful additional memory capacity beyond matrix-valued state.

Linear attention replaces growing KV caches with fixed-size recurrent states, yet these persistent states can become a substantial memory bottleneck under concurrent serving. Directly quantizing recurrent states to low precision often leads to severe accuracy degradation, as quantization errors propagate through successive state updates. We discover that the impact of these errors depends on two complementary dimensions: temporally, errors in long-lived memory can persist across many decoding steps; spatially, errors in different key rows affect model outputs differently, while state magnitudes vary substantially along both rows and columns. Motivated by these observations, we propose STEPQuant, a spatial-temporal post-training quantization framework for Delta-rule recurrent states. STEPQuant allocates precision according to error magnitude and memory lifetime, and jointly fits key-row and value-column scales based on state distributions and key-row impact on output error. Experiments on Qwen3.8-27B and Kimi-Linear-48B-A3B-Instruct across both long- and short-generation benchmarks show that STEPQuant closely matches FP32-state accuracy under a nominal 6-bit budget and outperforms uniform INT8 in its 4-bit configuration. Integrated into SGLang with optimized GPU kernels, 6-bit STEPQuant achieves over 5x recurrent-state compression and reduces total serving memory by up to 68.7%. Our code is available at https://github.com/Dreamer-Toby/STEPQuant.

Softmax attention stores key and value vectors for every preceding token, causing inference memory to grow with sequence length. Recent language models incorporating Gated DeltaNet (GDN) or Kimi Delta Attention (KDA) reduce this cost by replacing the KV cache in most layers with fixed-size recurrent states. However, these recurrent states are commonly stored in FP32 and consume substantial GPU memory; their updates are memory-bandwidth bound and contribute significantly to decoding latency. To our knowledge, we are the first to study post-training quantization of recurrent states in GDN and KDA based language models. We find that uniform quantization provides a poor accuracy--storage trade-off: INT8 and FP8 already degrade accuracy on complex reasoning tasks, while INT4 and NVFP4 reduce it to near zero. We further find that most quantization-error energy is concentrated in a small subset of channels and that the relative decay strength of state channels remains stable across prompts and tasks. Motivated by these findings, DAMP uses both quantization-error energy and decay-based persistence to identify high-risk channels during offline calibration. It stores these channels at higher precision and the remainder in INT8. We evaluate DAMP on Qwen3.6-35B and Kimi-Linear-48B across six benchmarks covering mathematical reasoning, general reasoning, and code generation. At 9.9 bits per state value, DAMP maintains average accuracy close to the FP32 baseline. DAMP reduces recurrent-state storage by 69.1%, accelerates the recurrent-state update kernel by up to 2.01x, and lowers full-model TPOT by up to 10.9%.

Looped language models reuse physical Transformer blocks across logical depth, but established architectures entangle recurrence placement, input injection, and recurrent state organization. We isolate these axes in models trained from scratch at matched parameter scale, logical depth, and token budgets, and then test whether the resulting design principles transfer to resident- and active-parameter-matched Mixture-of-Experts (MoE) models. The prelude-recurrent block-coda sandwich architecture consistently improves performance on context extraction and reasoning-intensive tasks. Input injection primarily enhances knowledge retrieval and context utilization, whereas random initialization and separate H/L recurrent states provide mixed or negative returns. Taken together, these results favor the Huginn-style design: at the 730M-parameter and 336B-token scale, the complete Huginn architecture outperforms Ouro across all ten benchmarks. The advantages of Huginn over Ouro transfer to MoE models. At the 8BA0.8B (32BA3B when unrolled) scale trained on 500B tokens, Huginn outperforms Ouro on nearly all benchmarks spanning knowledge, reasoning, and coding, while also exhibiting more balanced expert routing. Under matched training and inference FLOPs, the Huginn-style model uses 75% fewer resident parameters than a 112-layer feedforward MoE baseline. Despite its smaller physical parameters, it outperforms the feedforward baseline on DROP and GSM8K, matches it on MATH500, and remains competitive on the other benchmarks.

Looped Transformers achieve parameter efficiency by repeatedly executing a shared block across recurrent loops. Each loop yields an intermediate representation decodable for the same next token, yet standard decoding discards earlier states. Because earlier loops embody less computation, recurrence inherently supplies aligned weak-and-strong prediction pairs without auxiliary models or external training. We introduce LoopCD, a training-free contrastive decoding framework that guides token selection by contrasting the final prediction with an earlier recurrent pass, operating either in logit space with one extra output pass (LoopCD-Logits) or in hidden-state space with zero output overhead (LoopCD-Hidden). Across four looped Transformer families, LoopCD delivers substantial, consistent gains at full recurrent depth: LoopCD-Logits raises Ouro-2.6B-Thinking's AIME 2024 pass@1 from 61.88% to 73.33%, while LoopCD-Hidden lifts Huginn's HumanEval pass@1 from 22.56% to 31.71%. Crucially, these performance gains enable halving the number of recurrent loops while still matching or exceeding full-depth unguided baselines, reducing forward FLOPs by 22.5% to 48.2%. By transforming intermediate recurrent states into effective guidance signals, LoopCD achieves superior decoding quality while substantially reducing inference compute.

Every recurrence of a looped language model adds cost in training, decoding, prefill, and reinforcement learning (RL). The closer recurrent states get to fixed points, the less the path to them matters. This enables truncated backpropagation in training; terminal key-value (KV) sharing for decoding with almost no loss in accuracy; a distilled student that prefills up to 1.79x faster; and RL updates that compute gradients from saved rollout states, 2x faster than backpropagating through the replayed trajectory. We therefore improve the two components of training that shape these fixed points: the depth prior and input injection. Fixed-depth training breaks KV sharing, and Huginn's broad depth prior supports sharing but dilutes supervision at the target depth more than sharing requires; we learn the prior from prediction feedback, with an entropy term that keeps it broad. Existing injection schemes let the state's component along the input amplify or cancel the injection; we remove this component with orthogonal injection. From 100M to 1.6B parameters, the learned prior and orthogonal injection lower perplexity at every scale relative to Huginn's prior and existing injection schemes, respectively. At 1.6B, the learned prior with a 3x smaller KV cache matches the downstream average of fixed-depth training with the full cache.

State-space models (SSMs) offer efficient sequence modeling but lag behind Transformers on benchmarks that require in-context retrieval. Prior work links this gap to a small set of attention heads, termed Gather-and-Aggregate (G&A), which SSMs struggle to reproduce. We propose *retrieval-aware distillation*, which converts a pretrained Transformer into a hybrid student by preserving only these retrieval-critical heads and distilling the rest into recurrent heads. We identify the essential heads via ablation on a synthetic retrieval task, producing a hybrid with sparse, non-uniform attention placement. We show that preserving **just 2% of attention heads recovers over 95% of teacher performance on retrieval-heavy tasks** (10 heads in a 1B model), requiring far fewer heads than hybrids that retain at least 25%. We further find that large recurrent states often compensate for missing retrieval: once retrieval is handled by these heads, the SSM backbone can be simplified with limited loss, even with an 8times reduction in state dimension. By reducing both the attention cache and the SSM state, the resulting hybrid is 5--6times more memory-efficient than comparable hybrids, closing the Transformer--SSM gap at a fraction of the memory cost.

Looped Transformers achieve strong performance with compact parameter sizes by repeatedly applying a shared stack of Transformer blocks across recurrent depths. However, they incur higher decoding latency than standard Transformer models of comparable parameter size because shared weights are accessed at every recurrent depth. To improve decoding efficiency, self-speculative decoding is particularly well suited to Looped Transformers, as their intermediate recurrent states can directly provide draft predictions without an auxiliary draft model. We therefore propose LoopSpec, a training-free self-speculative decoding framework tailored for Looped Transformers. LoopSpec extracts draft tokens from early recurrent states and operates in a pipelined manner, overlapping draft generation of future tokens with target verification of the current token. To improve draft accuracy without excessive compute overhead, we introduce a selective second proposal from deeper recurrent depth while ensuring lossless decoding under both greedy and sampling regimes. Furthermore, we derive the optimal proposal depths in closed form and show the prediction matches measurement. Across reasoning and coding benchmarks, LoopSpec achieves up to 6.83times inference speedup across diverse Looped Transformers.

In retrieval-augmented generation and agentic LLM serving, prompts are assembled from independent segments into long contexts, making the prefill stage dominate per-request cost. Two directions have emerged to reduce this cost: position-independent caching (PIC) admits KV reuse for non-contiguous segments shared across requests, while hybrid-attention models cut computation by replacing most full-attention layers with linear attention. However, they cannot coexist: applying existing PIC methods to hybrid-attention models breaks down because per-token KV-cache reuse primitives do not transfer to the per-request recurrent state. We present Hypic, the first system to accelerate hybrid-attention LLM serving with position-independent caching. For linear-attention layers, we identify the segment-cumulative transition operator as the missing algebraic primitive and cache it alongside each segment's zero-start end-state, enabling near-exact and constant-time composition of independently cached segments. For the remaining full-attention layers, existing PIC methods also fail because linear layers do not expose the per-token hidden states needed for selective recomputation. We show that the largest deviations concentrate at segment beginnings and construct a small seam window that propagates hidden states through the hybrid-attention stack to repair cross-segment attention. Finally, Hypic introduces segment parallelism, which exploits PIC's segment-level self-containment to parallelize cache-miss prefill across instances, turning long cold requests into an accelerable workload. Evaluated across four hybrid-attention models and five workloads, Hypic reduces time-to-first-token by 3.25times on average and improves QPS by 1.66times over Prefix Cache, while preserving task quality with a 1.71-point gap from Full Recompute.

JEV models make multimodal decisions by directly scoring candidates. Although the common context is encoded once, candidate evaluation can still repeat matching token histories, duplicate inference states, and execute the full backbone. In this paper, we study these sources of redundancy and present FastJEV for compact candidate evaluation. We jointly organize history reuse and state storage, since sharing computation requires preserving states for later branches. We first introduce shared context anchoring to reuse recurrent initial states and omit unused final recurrent caches. We extend this reuse through candidate prefix sharing, retaining the intermediate states needed by subsequent branches. To further reduce the depth of these paths, we apply decision guided pruning based on relative score changes measured on a small unlabeled set. Our method retains full context encoding and all candidates without additional training. We evaluate FastJEV across three OmniJev model sizes on five public benchmarks and reconstructed LIBERO-10 offline questions. At the selected pruning budgets, the complete method reduces candidate depth by 43.75% to 45.83%, while retaining 93.66% to 97.52% of the original task scores on average across the six evaluation sets. Through controlled experiments, we show how candidate overlap and branching structure affect the execution cost of history reuse. In our implementation, candidate prefix sharing can reduce repeated computation while increasing latency. These findings motivate designing sharing granularity and execution schedules together for efficient JEV inference.

Test-Time Training (TTT) models context dependencies by adapting part of the model's weights (referred to as fast weights) during inference. This fast weight, akin to recurrent states in RNNs, stores temporary memories of past tokens in the current sequence. Existing TTT methods struggled to show effectiveness in handling long-context data, due to their inefficiency on modern GPUs. The TTT layers in many of these approaches operate with extremely low FLOPs utilization (often <5%) because they deliberately apply small online minibatch sizes (e.g., updating fast weights every 16 or 64 tokens). Moreover, a small minibatch implies fine-grained block-wise causal dependencies in the data, unsuitable for data beyond 1D ordered sequences, like sets or N-dimensional grids such as images or videos. In contrast, we pursue the opposite direction by using an extremely large chunk update, ranging from 2K to 1M tokens across tasks of varying modalities, which we refer to as Large Chunk Test-Time Training (LaCT). It improves hardware utilization by orders of magnitude, and more importantly, facilitates scaling of nonlinear state size (up to 40% of model parameters), hence substantially improving state capacity, all without requiring cumbersome and error-prone kernel implementations. It also allows easy integration of sophisticated optimizers, e.g. Muon for online updates. We validate our approach across diverse modalities and tasks, including novel view synthesis with image set, language models, and auto-regressive video diffusion. Our approach can scale up to 14B-parameter AR video diffusion model on sequences up to 56K tokens. In our longest sequence experiment, we perform novel view synthesis with 1 million context length. We hope this work will inspire and accelerate new research in the field of long-context modeling and test-time training. Website: https://tianyuanzhang.com/projects/ttt-done-right

Linear attention enables efficient long-context autoregressive decoding by compressing history into recurrent states, but this compression can make selective access to sparse and distant information difficult. Existing chunk-based extensions increase memory capacity, yet learned chunk-mixing coefficients may remain fixed with respect to input content and therefore cannot adapt historical access to each query. We introduce Hybrid Linear Attention (HLA), a query-dependent chunk-level attention mechanism for Gated DeltaNet (GDN). HLA represents each completed chunk as an exact affine state transition and computes content-dependent routing gates from compact, self-attentively pooled representatives. Each gate interpolates the corresponding historical transition with the identity map, controlling both the chunk's additive memory and its transformation of earlier states. Effective-support regularization further encourages concentrated routing for sparse inference. We evaluate HLA under both pretrained adaptation and from-scratch training. Across Qwen3.5 models from 0.8B to 9B, HLA consistently improves over native GDN and fixed chunk mixing, with gains of up to 5.57 percentage points on LongBench-V2 and 3.97 points on RULER. In a controlled from-scratch 1.3B setting trained for 100B tokens with a 4K context, HLA also improves RULER performance from 4K to 32K, with gains increasing from 0.83 points at 4K to 4.22 points at 32K. These results demonstrate that query-dependent composition of recurrent memory improves long-context modeling and remains effective beyond the training context while using compact per-chunk affine summaries. Project page: https://caesarhhh.github.io/hla/

Recurrent neural networks typically compress information into a single vector-valued recurrent state, forcing short-term computation and long-term retention to share the same representation. Past extensions alleviate this bottleneck by increasing the memory capacity or separating timescales, but lack the combination of rapid neuron-level processing and longer-term retention found in biology. To that end, we introduce the Continuous Memory Machine (CMM), a recurrent architecture with matrix-valued short- and long-term memory states serving distinct functional roles. Building on the Continuous Thought Machine (CTM), the CMM's short-term memory tracks recent neural activity, with uniquely parameterized neuron-level models learning to use these activity patterns for computation. A persistent long-term memory stores information for later use, with a Transformer jointly updating both memory stores, providing an expressive bidirectional read--write mechanism such that each store can reorganize its own contents and both read from and write to the other. Across algorithmic, in-context learning, and recurrent reasoning tasks, the CMM outperforms a broad suite of baselines, exhibiting stronger generalization than prior memory-augmented networks while preserving the CTM's interpretable attention patterns. Code is available at https://github.com/SakanaAI/continuous-memory-machines.

In this paper, we argue that looped Transformers need their own residual connections to prevent performance degradation as the number of iterations grows. We observe that increasing loop iterations can reduce reasoning accuracy: noisy state updates overwrite correct intermediate deductions and even undo completed solutions. This leaves subsequent iterations to recover lost information from an already degraded representation: once an error arises in an earlier loop, often as a result of long-range propagation through the recurrence, later loops find it difficult to correct. In this paper, we introduce InfiLoop, a loop-native residual connection that learns which past computations to retain and how much to accept from each new update. InfiLoop combines content-based weighting with learned temporal decay to maintain a running summary of recurrent states. An exact streaming recurrence keeps its persistent aggregation memory constant as the loop count grows. The resulting adaptive update suppresses unreliable proposals and preserves useful intermediate states. Across extensive reasoning tasks, a 7M-parameter InfiLoop model outperforms existing recursive architectures, reaching 97.9% exact accuracy on Sudoku-Extreme, and 13.6% pass@2 on ARC-AGI-2. Notably, on Sudoku-Extreme, InfiLoop continues to improve with test-time looping beyond 20,000 effective steps, showing that added depth translates directly into stronger reasoning. Our code is available at https://github.com/pixeli99/InfiLoop.

Vision-and-language navigation (VLN) enables the agent to navigate to a remote location following the natural language instruction in 3D environments. To represent the previously visited environment, most approaches for VLN implement memory using recurrent states, topological maps, or top-down semantic maps. In contrast to these approaches, we build the top-down egocentric and dynamically growing Grid Memory Map (i.e., GridMM) to structure the visited environment. From a global perspective, historical observations are projected into a unified grid map in a top-down view, which can better represent the spatial relations of the environment. From a local perspective, we further propose an instruction relevance aggregation method to capture fine-grained visual clues in each grid region. Extensive experiments are conducted on both the REVERIE, R2R, SOON datasets in the discrete environments, and the R2R-CE dataset in the continuous environments, showing the superiority of our proposed method.

While Transformer-based models have demonstrated remarkable language modeling performance, their high complexities result in high costs when processing long contexts. In contrast, recurrent neural networks (RNNs) such as linear attention and state space models have gained popularity due to their constant per-token complexities. However, these recurrent models struggle with tasks that require accurate recall of contextual information from long contexts, because all contextual information is compressed into a constant-size recurrent state. Previous works have shown that recall ability is positively correlated with the recurrent state size, yet directly training RNNs with larger recurrent states results in high training costs. In this paper, we introduce StateX, a training pipeline for efficiently expanding the states of pre-trained RNNs through post-training. For two popular classes of RNNs, linear attention and state space models, we design post-training architectural modifications to scale up the state size with no or negligible increase in model parameters. Experiments on models up to 1.3B parameters demonstrate that StateX efficiently enhances the recall and in-context learning ability of RNNs without incurring high post-training costs or compromising other capabilities.

Streaming 3D reconstruction from extremely long videos requires estimating camera motion and scene geometry online under bounded memory and computation. Early streaming models achieve causal, bounded-cost inference using finite context buffers or compact recurrent states, yet their estimates often deteriorate as sequences grow. Recent methods improve long-horizon stability by coupling short-range context with persistent or multi-level long-range memory. We pursue a different route: we keep the learned temporal state strictly local and formulate predictions whose targets remain independent of sequence length. We present ABot-Recon, a simple streaming model that caches KV features from only the preceding 11 frames. It predicts a point map in the current camera coordinate system together with an adjacent-frame relative pose. These predictions remain equivariant under changes of reference frame, and global poses and geometry are recovered through sequential composition. To reduce accumulated drift, a lightweight temporal refiner improves relative rotations using recent visual and motion context, while a composition-aware pose loss supervises multi-step pose composition. Extensive evaluations on challenging long-sequence benchmarks demonstrate the superior long-horizon performance of our local-context approach. On Oxford Spires, ABot-Recon achieves an ATE of 4.35 m and an RPE-R of 0.12^circ, reducing both errors by approximately 40\% relative to the best prior results.

Long-horizon manipulation is partially observable: the information needed to choose the next action may appear only in observations from minutes earlier. Existing memory mechanisms: retrieval banks, learned compressors, recurrent states must decide what to keep from the past before knowing what a future decision will require. This was motivated by the assumption that minute-scale history is too large to process directly, which modern VLM backbones no longer make true. In this work, we introduce SimpleMemVLA, a VLA without a dedicated memory module. It keeps the sampled history intact and passes it to the backbone in the timestamped video format the backbone was pretrained to process; the hidden states of a generated sub-task then form the only channel from history to a standard flow-matching action head. Since consecutive decisions share most of their history, prefilling the shared prefix during action execution keeps latency close to a single-frame VLA. SimpleMemVLA sets a new state of the art on four memory benchmarks without cost on general-purpose control. Holding the backbone and training setup fixed, it outperforms retrieval, compression and recurrent-state mechanisms by a wide margin, and causal interventions confirm that the policy genuinely reads its history. Code available at https://github.com/wadeKeith/SimpleMemVLA

Linear RNNs offer linear-time sequence processing and constant-memory decoding, but their fixed-size recurrent states must accommodate all past key--value associations. Existing forgetting mechanisms and Delta Rule updates reduce interference by selectively clearing or correcting the state, yet earlier associations can still become difficult to retrieve. We introduce CyFA (Cyclic Flow Attention), a Linear RNN with relative-time-partitioned memory. At each step, a learned clock controls the cyclic transport applied jointly to the key and value states before the current key--value pair enters the age-zero slot, thereby organizing stored associations across relative-time slots. We further derive an exact change to absolute-clock coordinates that expresses CyFA as two scalar-decay linear attention recurrences and enables efficient chunk-wise training. Across 400M--1.4B pretraining experiments with matched recurrent-state sizes, CyFA improves recall-intensive performance while maintaining competitive language modeling and high computational efficiency. At 400M, CyFA outperforms KDA on FDA (42.60 vs. 26.07) while requiring only 46.7% and 48.3% of KDA's forward and backward core-operator execution times, respectively. Our code is publicly available at https://github.com/Chyxx/CyclicFlowAttention{this https URL}.

Autoregressive (AR) large language models (LLMs) have achieved broad practical success, but sequential decoding remains a key bottleneck for low-latency deployment. Recent efficient-inference work has progressed along two axes: reducing the cost of each model invocation through efficient architectures, and reducing serial decoding steps through parallel generation. Hybrid attention backbones address the former, while diffusion language models (dLLMs) pursue the latter via iterative parallel denoising. Combining these advantages remains challenging: AR-to-dLLM conversion often fails to preserve seed-checkpoint capability, and hybrid-attention recurrent states and masking constraints make diffusion training and serving nontrivial. We present FLARE, a systematic conversion framework for hybrid-attention LLMs. Our analysis identifies transfer data quality as the primary determinant of capability preservation, outweighing loss formulation and attention-mask design. The resulting framework combines a token-equal AR-and-diffusion objective, hardware-aware kernels, and unified inference, enabling one checkpoint to support both AR-style verified decoding and diffusion-style parallel denoising. Starting from strong AR checkpoints with limited post-training data, FLARE is competitive with leading open-source dLLMs across model scales and delivers consistent throughput gains over open-source dLLM baselines in single-GPU concurrent serving. Our results further suggest that practical dLLMs are limited not only by decoding algorithms, but also by transfer data quality and the training inefficiency of current block-diffusion objectives, motivating joint design of data, objectives, architectures, and inference systems.

Long-horizon video world models require persistent memory to preserve scene consistency over extended rollouts. Softmax attention retains the full generation history through a growing KV cache, whereas recurrent linear attention compresses history into fixed-size states with substantially lower memory cost. However, we identify severe long-range forgetting in Gated DeltaNet (GDN), where information from distant but relevant scenes is progressively attenuated by subsequent state updates. To address this limitation, we propose HLA-WM, a training-free hybrid linear-attention framework that combines coarse-grained geometry-guided retrieval with fine-grained recurrent linear-state computation. HLA-WM exploits the affine structure of GDN to cache compact chunk-wise transition summaries, retrieve scene-relevant historical chunks using camera geometry, and recompose them into query-specific recurrent states. On the 60-second SANA-WM-Bench, HLA-WM improves all six aggregate revisit-consistency and camera-control metrics of the base autoregressive generator without additional training, including a 0.74 dB PSNR gain and a 28.5% reduction in rotation error. The improvements persist after downstream refinement and generalize to MBench-A, where HLA-WM consistently improves all three revisit-consistency metrics across all four subsets and all evaluated inference modes over 547 samples. At a 60-second context, HLA-WM reduces historical-state memory by 12times relative to full KV caching while incurring at most a 1.6% reduction in inference throughput. These results demonstrate that selectively addressable recurrent memory can improve long-range scene recall while preserving the efficiency advantages of GDN. Project page: https://caesarhhh.github.io/hla-wm/

Can one language model hand its live memory to another without the receiver rereading the context? We demonstrate useful persistent hybrid-state transfer across one architecture-matched Qwen3.5 4B-to-9B sibling pair. To our knowledge, this is the first demonstrated cross-model handoff of persistent recurrent inference state between differently sized hybrid language models without target prefix replay. Translated attention KV alone leaves a large gap; adding the Gated DeltaNet (GDN) persistent-state package lowers teacher-forced negative log-likelihood (NLL), the average next-token log-loss, by 0.747 nats/token (95% paired document bootstrap CI [0.6921, 0.8047]), improving all 64 PG19 documents. Direct recurrent and convolution reuse outperforms the tested learned GDN maps, consistent with partial functional compatibility of persistent-state coordinates. A fresh component factorial selects translated KV with direct recurrent and convolution state. An additional 434,176-parameter correction improves that base on 64 fresh web documents: continuation loss is 0.076 nats/token above native 9B (excess NLL), Jensen-Shannon (JS) divergence is 0.022, and native context recovery (NCR) is 0.918. Corrected 9B significantly beats continued 4B inference while processing zero historical prefix tokens. Evidence covers one direction, one geometry-matched Base-model pair, and 4K teacher-forced continuation; the near-native gate failed, the 16K branch was not run, and free-generation equivalence and a general state interface remain unproven.

Efficiently modeling sequences with infinite context length has been a long-standing problem. Past works suffer from either the quadratic computation complexity or the limited extrapolation ability on length generalization. In this work, we present Samba, a simple hybrid architecture that layer-wise combines Mamba, a selective State Space Model (SSM), with Sliding Window Attention (SWA). Samba selectively compresses a given sequence into recurrent hidden states while still maintaining the ability to precisely recall memories with the attention mechanism. We scale Samba up to 3.8B parameters with 3.2T training tokens and show that Samba substantially outperforms the state-of-the-art models based on pure attention or SSMs on a wide range of benchmarks. When trained on 4K length sequences, Samba can be efficiently extrapolated to 256K context length with perfect memory recall and show improved token predictions up to 1M context length. As a linear-time sequence model, Samba enjoys a 3.73x higher throughput compared to Transformers with grouped-query attention when processing user prompts of 128K length, and 3.64x speedup when generating 64K tokens with unlimited streaming. A sample implementation of Samba is publicly available in https://github.com/microsoft/Samba.

Mobile displays refresh at 90-120 Hz, yet most video is encoded at 24-30 frames per second; real-time frame-rate doubling requires each synthesized frame within 33.3 ms on mobile neural processing units. We show that mainstream flow-based video frame interpolation faces three structural deployment barriers on mobile accelerators: spatial sampling operators exceed the frame budget or lack hardware support, iterative flow refinement collapses under 8-bit post-training quantization, and memory-bound operators dominate the inference graph. ANVIL addresses these barriers by reusing motion vectors already computed by the H.264 decoder to prealign input frames, removing learned optical flow, spatial sampling, and iterative accumulation from the accelerator graph. The remaining residual is refined by a convolution-dominated network whose inference graph is composed almost entirely of compute-bound operators. On a Snapdragon 8 Gen 3 device, ANVIL achieves 12.8 ms 1080p network inference in 8-bit integer precision; an open-source Android player sustains 28.4 ms median end-to-end latency per interpolated frame pair over 54,623 consecutively logged samples during 30-minute continuous playback. Per-operator causal analysis identifies quantized accumulation on recurrent flow states as a key mechanism behind integer quantization failure in iterative methods. The current design targets H.264 playback scenarios with decoder-exposed motion vectors.

Fast Weight Programmers (FWPs) encode temporal dependencies through dynamically updated parameters rather than recurrent hidden states. Quantum FWPs (QFWPs) extend this idea with variational quantum circuits (VQCs), but existing implementations rely on multi-qubit architectures that are difficult to scale on noisy intermediate-scale quantum (NISQ) devices and expensive to simulate classically. We propose gated QKAN-FWP, a fast-weight framework that integrates FWP with Quantum-inspired Kolmogorov-Arnold Network (QKAN) using single-qubit data re-uploading circuits as learnable nonlinear activation, known as DatA Re-Uploading ActivatioN (DARUAN). We further introduce a scalar-gated fast-weight update rule that stabilizes parameter evolution, supported by a theoretical analysis of its adaptive memory kernel, geometric boundedness, and parallelizable gradient paths. We evaluate the framework across time-series benchmarks, MiniGrid reinforcement learning, and highlight real-world solar cycle forecasting as our main practical result. In the long-horizon setting with 528-month input window and 132-month forecast horizon, our 12.5k-parameter model achieves lower scaled Mean Square Error (MSE), peak amplitude error, and peak timing error than a suite of classical recurrent baselines with up to 13x more parameters, including Long Short-Term Memory (LSTM) networks (25.9k-89.1k parameters), WaveNet-LSTM (167k), Vanilla recurrent neural network (11.5k), and a Modified Echo State Network (132k). To validate NISQ compatibility, we further deploy the trained fast programmer on IonQ and IBM Quantum processors, recovering forecasting accuracy within 0.1% relative MSE of the noiseless simulator at 1024 shots. These results position gated QKAN-FWP as a scalable, parameter-efficient, and NISQ-compatible approach to quantum-inspired sequence modeling.

Latent chain-of-thought compresses reasoning by replacing visible reasoning traces with continuous hidden-state recurrence, but existing formulations are difficult to optimize with standard on-policy reinforcement learning (RL) and hard to interpret causally. Our key insight is that a single pair of explicit boundary tokens can address both issues at once: discrete entry and exit anchors make the latent block compatible with standard on-policy RL, and the same anchors offer a natural foothold for mechanistic analysis. Motivated by this, we propose SWITCH, a switchable latent reasoning framework. The model emits <swi> to enter latent mode and </swi> to exit. Because the boundaries are ordinary discrete tokens, the GRPO policy ratio is well-defined at every decision point. The same anchors also expose the latent steps to direct probing and causal intervention. We train the model with a visible-to-latent curriculum and a Switch-GRPO objective that propagates gradients through recurrent latent computation. SWITCH consistently outperforms prior hidden-state-recurrence latent reasoning approaches at similar scale. Mechanistic analysis through the boundary tokens further reveals three findings: (i) <swi> is a sharply localised, learned switching policy rather than a stylistic artefact; (ii) the latent step it opens performs problem-specific, causally important computation rather than acting as an inert placeholder; and (iii) that computation is concentrated at a single hidden-state transition on entry. Together, these results show that hidden-state-recurrence latent reasoning is both RL-trainable and open to direct mechanistic analysis, including of how on-policy RL itself improves the model from the inside.

Dynamic graph neural networks (DGNNs) that operate on snapshot sequences typically fall into one of two categories. Temporal-first approaches build per-node temporal embeddings and only afterwards perform spatial aggregation, whereas Spatial-first approaches invert this order, feeding the output of a graph convolution into a downstream temporal module. In either case, the rigid sequencing forces the second stage to consume an already-compressed summary produced by the first, ruling out joint reasoning over topology and evolution; concretely, the message-passing operator never gets to weight a neighbor's contribution by that neighbor's past trajectory. This paper introduces SiST-GNN (Simultaneous Spatial-Temporal GNN), which fuses the two signals inside a single message-passing operation rather than chaining them. Concretely, at each snapshot we maintain a recurrent hidden state per node that summarises its history, pair it with the node's current feature vector, and treat the pair as two nodes joined by a cross-time edge; running a standard graph convolution on this temporally augmented graph yields the updated representation. Our empirical study spans nine public baselines and fourteen model-dataset combinations, covering both fixed-split and live-update evaluation regimes. Across every public benchmark, SiST-GNN sets a new state of the art in link prediction task over the strongest prior method by 109--277% in the fixed-split setting and by 68--194% in the live-update setting. We additionally construct three dynamic node-classification tasks by discretising the underlying continuous-time event streams; here SiST-GNN beats the leading discrete-time (DTDG) baseline by 7--22% and matches continuous-time (CTDG) methods that consume the raw events directly.

Complex structured reasoning tasks often require additional computation, yet current language models obtain it mainly by increasing parameter scale or by serializing intermediate steps as chain-of-thought (CoT) tokens. The former raises training and deployment costs, while the latter ties reasoning computation to autoregressive output length. We introduce Penelope, an efficient latent-reasoning framework for pretrained decoder-only Transformers that localizes recurrent computation to a selected decoder interval. The lower decoder prefix is evaluated once to construct a problem-conditioned boundary memory, which is then iteratively refined through time-modulated GRU dynamics and recurrent readout states before answer generation. A progressive CoT-to-latent curriculum transfers visible reasoning into this internal recurrent path, allowing additional computation to be allocated in latent space without repeatedly executing the complete decoder or generating a long intermediate trace. Experiments on open-source structured-reasoning benchmarks show that, at validation-selected latent budgets, Penelope attains competitive accuracy relative to established latent-reasoning models while reducing measured inference latency. These results show that latent refinement can be localized to a narrow decoder interval, reducing repeated full-decoder execution without generating a long visible reasoning trace and providing a practical accuracy-efficiency tradeoff for decoder-only Transformer models.

Modern Recurrent Neural Networks (RNNs), such as RWKV, are distinguished by their powerful short-range modeling capabilities and efficient fixed-size states, which constitute a core advantage over standard Transformers. However, there is a significant lack of research into their internal state as an editable knowledge representation. To fill this gap, we first explore the representational properties of the RWKV state by proposing the DREAMSTATE framework. This framework utilizes a conditional Diffusion Transformer (DiT) to directly model the probability manifold of the state, enabling its generation and editing. The structural nature of this representation is validated through t-SNE visualizations and controlled generation experiments. After successfully uncovering and modeling the state's representational potential, we further propose a novel hybrid architecture that combines the local advantages of RNNs with global context adaptability. This architecture features a parallel DiT that processes a variable-length global context to dynamically generate and adjust the core recurrent module's WKV parameters, transforming the fixed recurrence mechanism into a context-aware dynamic function. Experiments demonstrate that this hybrid model can be trained stably via a multi-objective loss, validating its design feasibility. Our work not only opens a new research direction for RNN state representation but also provides a concrete architectural reference for future model design. The code is publicly available at: https://huggingface.co/2dgx41s/DreamState.

Effectively modeling long spatiotemporal sequences is challenging due to the need to model complex spatial correlations and long-range temporal dependencies simultaneously. ConvLSTMs attempt to address this by updating tensor-valued states with recurrent neural networks, but their sequential computation makes them slow to train. In contrast, Transformers can process an entire spatiotemporal sequence, compressed into tokens, in parallel. However, the cost of attention scales quadratically in length, limiting their scalability to longer sequences. Here, we address the challenges of prior methods and introduce convolutional state space models (ConvSSM) that combine the tensor modeling ideas of ConvLSTM with the long sequence modeling approaches of state space methods such as S4 and S5. First, we demonstrate how parallel scans can be applied to convolutional recurrences to achieve subquadratic parallelization and fast autoregressive generation. We then establish an equivalence between the dynamics of ConvSSMs and SSMs, which motivates parameterization and initialization strategies for modeling long-range dependencies. The result is ConvS5, an efficient ConvSSM variant for long-range spatiotemporal modeling. ConvS5 significantly outperforms Transformers and ConvLSTM on a long horizon Moving-MNIST experiment while training 3X faster than ConvLSTM and generating samples 400X faster than Transformers. In addition, ConvS5 matches or exceeds the performance of state-of-the-art methods on challenging DMLab, Minecraft and Habitat prediction benchmarks and enables new directions for modeling long spatiotemporal sequences.

The dominant speech separation models are based on complex recurrent or convolution neural network that model speech sequences indirectly conditioning on context, such as passing information through many intermediate states in recurrent neural network, leading to suboptimal separation performance. In this paper, we propose a dual-path transformer network (DPTNet) for end-to-end speech separation, which introduces direct context-awareness in the modeling for speech sequences. By introduces a improved transformer, elements in speech sequences can interact directly, which enables DPTNet can model for the speech sequences with direct context-awareness. The improved transformer in our approach learns the order information of the speech sequences without positional encodings by incorporating a recurrent neural network into the original transformer. In addition, the structure of dual paths makes our model efficient for extremely long speech sequence modeling. Extensive experiments on benchmark datasets show that our approach outperforms the current state-of-the-arts (20.6 dB SDR on the public WSj0-2mix data corpus).

Constructing states from sequences of observations is an important component of reinforcement learning agents. One solution for state construction is to use recurrent neural networks. Back-propagation through time (BPTT), and real-time recurrent learning (RTRL) are two popular gradient-based methods for recurrent learning. BPTT requires complete trajectories of observations before it can compute the gradients and is unsuitable for online updates. RTRL can do online updates but scales poorly to large networks. In this paper, we propose two constraints that make RTRL scalable. We show that by either decomposing the network into independent modules or learning the network in stages, we can make RTRL scale linearly with the number of parameters. Unlike prior scalable gradient estimation algorithms, such as UORO and Truncated-BPTT, our algorithms do not add noise or bias to the gradient estimate. Instead, they trade off the functional capacity of the network for computationally efficient learning. We demonstrate the effectiveness of our approach over Truncated-BPTT on a prediction benchmark inspired by animal learning and by doing policy evaluation of pre-trained policies for Atari 2600 games.

The Linear Representation Hypothesis (LRH) states that neural networks learn to encode concepts as directions in activation space, and a strong version of the LRH states that models learn only such encodings. In this paper, we present a counterexample to this strong LRH: when trained to repeat an input token sequence, gated recurrent neural networks (RNNs) learn to represent the token at each position with a particular order of magnitude, rather than a direction. These representations have layered features that are impossible to locate in distinct linear subspaces. To show this, we train interventions to predict and manipulate tokens by learning the scaling factor corresponding to each sequence position. These interventions indicate that the smallest RNNs find only this magnitude-based solution, while larger RNNs have linear representations. These findings strongly indicate that interpretability research should not be confined by the LRH.

Recently, recurrent models such as state space models and linear attention have become popular due to their linear complexity in the sequence length. Thanks to their recurrent nature, in principle they can process arbitrarily long sequences, but their performance sometimes drops considerably beyond their training context lengths-i.e. they fail to length generalize. In this work, we provide comprehensive empirical and theoretical analysis to support the unexplored states hypothesis, which posits that models fail to length generalize when during training they are only exposed to a limited subset of the distribution of all attainable states (i.e. states that would be attained if the recurrence was applied to long sequences). Furthermore, we investigate simple training interventions that aim to increase the coverage of the states that the model is trained on, e.g. by initializing the state with Gaussian noise or with the final state of a different input sequence. With only 500 post-training steps (sim 0.1% of the pre-training budget), these interventions enable length generalization for sequences that are orders of magnitude longer than the training context (e.g. 2klongrightarrow 128k) and show improved performance in long context tasks, thus presenting a simple and efficient way to enable robust length generalization in general recurrent models.

Language model agents increasingly operate over long interaction streams, requiring online adaptation to distribution shifts through continual learning. However, existing agent harnesses typically either evolve their states only through forward information flow or rely on additional replay or validation data for harness optimization. To address this, we propose ReHarness, a recurrent harness framework for agentic continual learning that complements forward read and write with backward revision under a strictly online streaming protocol. We ask what information could have been captured differently in the harness state to better inform the current instance in the stream. Specifically, after each instance, we leverage the resulting trajectory as feedback to revise the reflections retrieved for that instance, thereby propagating feedback backward through the textual harness state. Across three continual learning benchmarks and three language model backbones, ReHarness consistently outperforms strong raw-context baselines, memory- and reflection-based methods, and prompt optimization approaches. Further analysis shows that ReHarness produces source-grounded and meaningful revisions, corrects overgeneralized or outdated experience under distribution shifts, and improves both stability and plasticity during continual learning.

Existing dialog system models require extensive human annotations and are difficult to generalize to different tasks. The recent success of large pre-trained language models such as BERT and GPT-2 (Devlin et al., 2019; Radford et al., 2019) have suggested the effectiveness of incorporating language priors in down-stream NLP tasks. However, how much pre-trained language models can help dialog response generation is still under exploration. In this paper, we propose a simple, general, and effective framework: Alternating Roles Dialog Model (ARDM). ARDM models each speaker separately and takes advantage of the large pre-trained language model. It requires no supervision from human annotations such as belief states or dialog acts to achieve effective conversations. ARDM outperforms or is on par with state-of-the-art methods on two popular task-oriented dialog datasets: CamRest676 and MultiWOZ. Moreover, we can generalize ARDM to more challenging, non-collaborative tasks such as persuasion. In persuasion tasks, ARDM is capable of generating human-like responses to persuade people to donate to a charity.

Objective: Patient notes in electronic health records (EHRs) may contain critical information for medical investigations. However, the vast majority of medical investigators can only access de-identified notes, in order to protect the confidentiality of patients. In the United States, the Health Insurance Portability and Accountability Act (HIPAA) defines 18 types of protected health information (PHI) that needs to be removed to de-identify patient notes. Manual de-identification is impractical given the size of EHR databases, the limited number of researchers with access to the non-de-identified notes, and the frequent mistakes of human annotators. A reliable automated de-identification system would consequently be of high value. Materials and Methods: We introduce the first de-identification system based on artificial neural networks (ANNs), which requires no handcrafted features or rules, unlike existing systems. We compare the performance of the system with state-of-the-art systems on two datasets: the i2b2 2014 de-identification challenge dataset, which is the largest publicly available de-identification dataset, and the MIMIC de-identification dataset, which we assembled and is twice as large as the i2b2 2014 dataset. Results: Our ANN model outperforms the state-of-the-art systems. It yields an F1-score of 97.85 on the i2b2 2014 dataset, with a recall 97.38 and a precision of 97.32, and an F1-score of 99.23 on the MIMIC de-identification dataset, with a recall 99.25 and a precision of 99.06. Conclusion: Our findings support the use of ANNs for de-identification of patient notes, as they show better performance than previously published systems while requiring no feature engineering.

Transformers are highly parallel but are limited to computations in the TC^0 complexity class, excluding tasks such as entity tracking and code execution that provably require greater expressive power. Motivated by this limitation, we revisit non-linear Recurrent Neural Networks (RNNs) for language modeling and introduce Matrix-to-Matrix RNN (M^2RNN): an architecture with matrix-valued hidden states and expressive non-linear state transitions. We demonstrate that the language modeling performance of non-linear RNNs is limited by their state size. We also demonstrate how the state size expansion mechanism enables efficient use of tensor cores. Empirically, M^2RNN achieves perfect state tracking generalization at sequence lengths not seen during training. These benefits also translate to large-scale language modeling. In hybrid settings that interleave recurrent layers with attention, Hybrid M^2RNN outperforms equivalent Gated DeltaNet hybrids by 0.4-0.5 perplexity points on a 7B MoE model, while using 3times smaller state sizes for the recurrent layers. Notably, replacing even a single recurrent layer with M^2RNN in an existing hybrid architecture yields accuracy gains comparable to Hybrid M^2RNN with minimal impact on training throughput. Further, the Hybrid Gated DeltaNet models with a single M^2RNN layer also achieve superior long-context generalization, outperforming state-of-the-art hybrid linear attention architectures by up to 8 points on LongBench. Together, these results establish non-linear RNN layers as a compelling building block for efficient and scalable language models.

Large Language Models (LLMs) have shown strong promise for mining Electronic Health Records (EHRs) by reasoning over longitudinal clinical information to capture context-rich patient trajectories. However, leveraging LLMs for structured EHRs (e.g., standardized diagnosis and medication codes) presents two key challenges. First, translating time-stamped EHR sequences into plain text can obscure both temporal structure and code identities, weakening the ability to capture code co-occurrence and longitudinal regularities. Second, unlike cohort-trained predictive models that learn a shared, task-aligned representation space across patients, LLMs are often applied in a case-isolated inference setting where each patient is processed independently without leveraging population-level patterns. To address these challenges, we introduce RePrompT, a time-aware LLM framework that integrates structured EHR encoders through prompt tuning, without modifying underlying architectures. Specifically, RePrompT recurrently incorporates latent states from prior visits to preserve longitudinal information, and injects population-level information through trainable prompt tokens derived from a cohort-trained, task-aligned EHR encoder. Experiments on MIMIC-III and MIMIC-IV demonstrate that RePrompT consistently outperforms both EHR-based and LLM-based baselines across multiple clinical prediction tasks.

We study Latent Recurrent Transformer (LRT), a lightweight augmentation of autoregressive transformers that reuses a high-level source-layer hidden state from the previous token as recurrent memory for the next token. Because this source state is already computed during ordinary decoding, LRT adds a cross-layer recurrent latent pathway across positions without inserting pause tokens or extra depth loops, and the standard attention mechanism and KV-cache interface are preserved. To pretrain this recurrence at scale without sequentially unrolling the transformer, we introduce interleaved parallel training: a single full-sequence initialization forward pass builds a shared buffer; then disjoint position subsets are refined in parallel and written back, so that all tokens receive recurrent-memory-aware supervision at roughly 2 times baseline compute. Across nanochat style backbones and a wide range of tokens-per-parameter budgets, LRT improves both language-modeling loss and in-context learning under matched effective compute while adding as little as 0.3% parameters.

Large language models achieve strong performance on many reasoning tasks when allowed to externalize intermediate steps as Chain-of-Thought (CoT). However, many questions require the model to internalize the multi-step reasoning within a single forward pass before generating the answer. We study this challenge through two-hop reasoning, a representative task where the model must compose multiple pieces of parametric knowledge within a single forward pass. Standard non-recurrent Transformers suffer from a depth-local storage problem: facts learned in earlier layers are unavailable where second-hop retrieval happens. We found that Looped Transformers mitigate this issue by reusing the same memory, but still generalize imperfectly. We show that the remaining bottleneck is representational. In the two-hop reasoning task, the first loop often makes the correct bridge entity nearly perfectly decodable, yet the corresponding hidden state remains poorly aligned with the bridge token embedding. Surprisingly, an easy training-free realignment intervention nearly closes the generalization gap. Building upon this insight, we propose DiscoLoop, a looping architecture whose recurrence carries both a discrete embedding channel and a continuous hidden-state channel. DiscoLoop achieves near-perfect accuracy with substantially fewer training steps across symbolic and synthetic-language multi-hop reasoning tasks. When applied to real-world pretraining, DiscoLoop attains lower training loss and stronger benchmark performance than looped-transformer baselines, suggesting that the mixed-channel design transfers to practical language modeling.

Universal multimodal embedding (UME) maps heterogeneous multimodal inputs into a shared embedding space. Existing UME models either form embeddings through single forward encoding or add computation through explicit rationale tokens and latent autoregressive states. Although token expansion can improve complex matching, serial generation increases retrieval latency and makes the final embedding depend on generated intermediate states. This raises a different question: can useful computation be expanded along model depth while keeping the token workspace fixed? We analyze positive-negative similarity separation at every layer of independently trained UME models and observe a shared progression: early layers contextualize multimodal inputs, a contiguous middle-to-late stage forms retrieval-discriminative features, and the final layers map them into the embedding space. Based on this finding, we propose ReLoop-UME, which executes the early layers once, recurrently reuses a parameter-shared retrieval-forming block, and applies the final mapping layers after the last loop. Learnable Retrieval Registers provide persistent retrieval-specific states that accumulate and exchange evidence across loops, with the final register serving as the embedding readout. On MMEB-V2 and MRMR, ReLoop-UME consistently improves retrieval across different backbones while running 44.9x faster than UME-R1 and 1.5x faster than PLUME.

Recurrent Transformers increase computational depth through temporal recurrence, feeding each token's high-level hidden state into the computation of the next. This raises a natural question: is additional computation better spent on more temporal steps or greater physical depth? We investigate this question using Latent Recurrent Transformers (LRTs), which retain one backbone forward pass per vocabulary token during decoding and provide a controlled setting for comparing these two ways of adding computation. Specifically, we insert a latent thought token between consecutive vocabulary tokens. Each thought token passes through the same L layers as a vocabulary token, sharing the backbone parameters and providing an additional stage of hidden-state refinement before predicting the next token. We compare this L-layer LRT against a 2L-layer LRT without thought tokens. Both execute 2L Transformer blocks per vocabulary token during decoding, but the thought-token model uses fewer parameters. On 16- and 20-layer mixture-of-experts NanoChat backbones, one thought token brings the shallower model within 0.006 and 0.004 bits per byte of its double-depth counterpart, recovering 67% and 81% of the improvement with approximately 48% fewer total parameters. These results suggest that temporal thinking offers a parameter-efficient alternative to increasing physical depth in recurrent Transformers.

Building interactive worlds that respond coherently to player actions has long been a shared goal of computer graphics, games, and artificial intelligence. Recent video generative models provide a data-driven route toward this goal by predicting future observations conditioned on user actions, and are increasingly regarded as potential next-generation game engines. Realizing a genuinely interactive game world, however, requires interaction outcomes that follow rules over evolving game conditions, consequences that persist over long horizons, and a generation loop that operates in real time. Conventional game engines realize these properties through a recurrent action-state-observation loop, in which player actions update an explicit game state according to predefined rules and observations are rendered from the resulting state. Taking this loop as an organizing lens, this paper examines interactive game world modeling along four dimensions: player action control, game state dynamics, state-observation persistence, and real-time interactive generation. For each dimension, we start from the capabilities required by an interactive game world, group existing approaches into representative families, and discuss the strengths and trade-offs of each family. Complementing this analysis, we present a scalable data engine for Black Myth: Wukong that collects over 90 hours of gameplay with frame-aligned player actions, ground-truth game states, and visual observations, together with structured and semantic annotations, as a resource for state-aware game world modeling. We hope this paper offers a clear picture of where the field stands and fosters progress toward interactive game worlds.

Data arrives at our senses as a continuous stream, smoothly transforming from one instant to the next. These smooth transformations can be viewed as continuous symmetries of the environment that we inhabit, defining equivalence relations between stimuli over time. In machine learning, neural network architectures that respect symmetries of their data are called equivariant and have provable benefits in terms of generalization ability and sample efficiency. To date, however, equivariance has been considered only for static transformations and feed-forward networks, limiting its applicability to sequence models, such as recurrent neural networks (RNNs), and corresponding time-parameterized sequence transformations. In this work, we extend equivariant network theory to this regime of `flows' -- one-parameter Lie subgroups capturing natural transformations over time, such as visual motion. We begin by showing that standard RNNs are generally not flow equivariant: their hidden states fail to transform in a geometrically structured manner for moving stimuli. We then show how flow equivariance can be introduced, and demonstrate that these models significantly outperform their non-equivariant counterparts in terms of training speed, length generalization, and velocity generalization, on both next step prediction and sequence classification. We present this work as a first step towards building sequence models that respect the time-parameterized symmetries which govern the world around us.

We introduce WARP (Weight-space Adaptive Recurrent Prediction), a simple yet powerful model that unifies weight-space learning with linear recurrence to redefine sequence modeling. Unlike conventional recurrent neural networks (RNNs) which collapse temporal dynamics into fixed-dimensional hidden states, WARP explicitly parametrizes its hidden state as the weights and biases of a distinct auxiliary neural network, and uses input differences to drive its recurrence. This brain-inspired formulation enables efficient gradient-free adaptation of the auxiliary network at test-time, in-context learning abilities, and seamless integration of domain-specific physical priors. Empirical validation shows that WARP matches or surpasses state-of-the-art baselines on diverse classification tasks, featuring in the top three in 5 out of 6 real-world challenging datasets. Furthermore, extensive experiments across sequential image completion, multivariate time series forecasting, and dynamical system reconstruction demonstrate its expressiveness and generalisation capabilities. Remarkably, a physics-informed variant of our model outperforms the next best model by more than 10x. Ablation studies confirm the architectural necessity of key components, solidifying weight-space linear RNNs as a transformative paradigm for adaptive machine intelligence.

We show that the MinMax algebra provides a form of recurrence that is expressively powerful, efficiently implementable, and most importantly it is not affected by vanishing or exploding gradient. We call MinMax Recurrent Neural Cascades (RNCs) the models obtained by cascading several layers of neurons that employ such recurrence. We show that MinMax RNCs enjoy many favourable theoretical properties. First, their formal expressivity includes all regular languages, arguably the maximal expressivity for a finite-memory system. Second, they can be evaluated in parallel with a runtime that is logarithmic in the input length given enough processors; and they can also be evaluated sequentially. Third, their state and activations are bounded uniformly for all input lengths. Fourth, at almost all points, their loss gradient exists and it is bounded. Fifth, they do not exhibit a vanishing state gradient: the gradient of a state w.r.t. a past state can have constant value one regardless of the time distance between the two states. Finally, we find empirical evidence that the favourable theoretical properties of MinMax RNCs are matched by their practical capabilities: they are able to perfectly solve a number of synthetic tasks, showing superior performance compared to the considered state-of-the-art recurrent neural networks; also, we train a MinMax RNC of 127M parameters on next-token prediction, and the obtained model shows competitive performance for its size, providing evidence of the potential of MinMax RNCs on real-world tasks.

Looped Language Models (LoopLMs) enable efficient latent reasoning through depth recurrence, yet exhibit unreliable test-time scaling behavior: performance often peaks at a certain iteration depth and then collapses with further recurrence. Through latent dynamics analysis, we find an inherent trade-off between stability and effectiveness in existing architectures and strategies. By conceptualizing reasoning as uncertainty reduction, we propose that convergence toward stable fixed points while preserving effectiveness represents a promising way. To this end, we propose STARS (STAbility-driven Recurrent Scaling), a training framework that constrains latent states to approach asymptotically stable fixed points. This is realized via efficient Jacobian Spectral Radius Regularization with random loop sampling, enabling STARS to maximize effectiveness while ensuring rigorous stability. Experiments on arithmetic tasks show that STARS achieves reliable test-time scaling, and on complex mathematical reasoning it substantially mitigates performance degradation as recurrence depth increases while also improving peak performance.

The human brain is autonomously active, being characterized by a self-sustained neural activity which would be present even in the absence of external sensory stimuli. Here we study the interrelation between the self-sustained activity in autonomously active recurrent neural nets and external sensory stimuli. There is no a priori semantical relation between the influx of external stimuli and the patterns generated internally by the autonomous and ongoing brain dynamics. The question then arises when and how are semantic correlations between internal and external dynamical processes learned and built up? We study this problem within the paradigm of transient state dynamics for the neural activity in recurrent neural nets, i.e. for an autonomous neural activity characterized by an infinite time-series of transiently stable attractor states. We propose that external stimuli will be relevant during the sensitive periods, {\it viz} the transition period between one transient state and the subsequent semi-stable attractor. A diffusive learning signal is generated unsupervised whenever the stimulus influences the internal dynamics qualitatively. For testing we have presented to the model system stimuli corresponding to the bars and stripes problem. We found that the system performs a non-linear independent component analysis on its own, being continuously and autonomously active. This emergent cognitive capability results here from a general principle for the neural dynamics, the competition between neural ensembles.

Biological neural networks can operate in qualitatively distinct dynamical regimes, and transitions between these regimes are thought to underlie changes in computation and behavior. The seminal work of Sompolinsky, Crisanti, and Sommers (SCS) showed that random recurrent networks undergo a transition from quiescence to asynchronous chaos, establishing a paradigmatic link between random connectivity, dynamical instability, and internally generated fluctuations in neural circuits. Here, we extend this framework to two-population firing-rate networks with segregated excitatory and inhibitory neurons and target-specific inhibitory couplings that break excitation--inhibition balance. Using dynamical mean-field theory, we derive self-consistent equations for the macroscopic mean activities and autocorrelations, together with stability criteria distinguishing mean-driven and fluctuation-driven instabilities. We show that target-specific inhibition organizes the phase diagram into three qualitative classes: inhibition-dominated or strictly balanced networks display only quiescent activity and asynchronous chaos; excitation-dominated networks display persistent activity together with either synchronous chaos with non-vanishing mean activity or coherent oscillations, depending on the stability-matrix eigenvalues. Crucially, coherent oscillations do not coexist with chaotic fluctuations around the periodic mean trajectory; rather, their onset suppresses the chaotic component, reminiscent of input-induced suppression of chaos. These results generalize SCS theory to recurrent networks with explicit excitatory--inhibitory structure and identify target-specific inhibition as a key control parameter for large-scale neural dynamics.

We introduce LoopVL to study whether Loop Transformers can be effectively extended to vision- language models. LoopVL combines Module-Loop and Model-Loop computation to iteratively update a unified vision-language state through shared modules. We train LoopVL from scratch through language pre-training, multimodal training, and post-training. LoopVL outperforms a range of similarly sized and larger non-recurrent models on multimodal understanding and visual reasoning benchmarks. We also observe Visual Aha Moments in LoopVL, characterized by pronounced shifts in visual attention across loops. LoopVL provides practical evidence for recurrent vision-language modeling and offers an intuitive perspective on how shared parameters can support deeper multimodal computation over continuously evolving visual-language states.

The role of hidden units in recurrent neural networks is typically seen as modeling memory, with research focusing on enhancing information retention through gating mechanisms. A less explored perspective views hidden units as active participants in the computation performed by the network, rather than passive memory stores. In this work, we revisit bi-linear operations, which involve multiplicative interactions between hidden units and input embeddings. We demonstrate theoretically and empirically that they constitute a natural inductive bias for representing the evolution of hidden states in state tracking tasks. These are the simplest type of task that require hidden units to actively contribute to the behavior of the network. We also show that bi-linear state updates form a natural hierarchy corresponding to state tracking tasks of increasing complexity, with popular linear recurrent networks such as Mamba residing at the lowest-complexity center of that hierarchy.

Language models with recurrent depth, also referred to as universal or looped when considering transformers, are defined by the capacity to increase their computation through the repetition of layers. Recent efforts in pretraining have demonstrated that these architectures can scale to modern language modeling tasks while exhibiting advantages in reasoning tasks. In this work, we examine the relationship between recurrent-depth models and diffusion language models. Building on their similarities, we develop a new diffusion forcing sampler for these models to accelerate generation. The sampler advances by decoding new tokens at every forward pass of the model, while the latent states of these tokens can be further refined in parallel through recurrence. Theoretically, generation with our sampler is strictly more expressive than the baseline autoregressive generation using the same time budget on modern hardware. Moreover, this sampler, based on principles from diffusion literature, can be directly applied to existing 3.5B recurrent-depth transformers without any tuning, leading to up to a 5x speedup. Consequently, our findings not only provide an efficient mechanism for parallelizing the extra computation in recurrent-depth models at inference, but also suggest that such models can be naturally viewed as strong continuous, though causal, diffusion language models.

Structured reasoning requires making and revising interdependent decisions to reach a globally consistent solution. Existing architectures struggle with this: autoregressive models commit sequentially and cannot revise earlier decisions, while masked diffusion models often require careful decoding schemes to coordinate interdependent predictions. We introduce Flow Reasoning Models (FRMs), a novel framework for structured reasoning that adapts continuous flows over discrete structured outputs with a simple recurrent refinement mechanism. By self-conditioning a flow model on its own past outputs, we turn one-shot denoising into iterative solution refinement. This lets FRMs make and revise decisions in parallel, efficiently coordinating interdependent choices across solutions. Yet conventional self-conditioning becomes unreliable at greater recurrent depth due to exposure bias between one-step training predictions and recursively generated inference states. We address this mismatch with Fixed-Point Forcing (FPF), which trains FRMs on states produced by their own inference dynamics while preserving the standard flow-matching objective. FRMs achieve solve rates of 99.5%, 100.0%, and 99.9% on Sudoku-Extreme, Zebra, and Maze-Unique, respectively. On Sudoku-Extreme, FRMs achieve higher peak accuracy than the evaluated masked-diffusion and specialized reasoning baselines while remaining highly compute-efficient, matching the next-best method's 98.7% peak solve rate with 44times fewer inference FLOPs.

Recurrent neural networks are a widely used class of neural architectures. They have, however, two shortcomings. First, they are often treated as black-box models and as such it is difficult to understand what exactly they learn as well as how they arrive at a particular prediction. Second, they tend to work poorly on sequences requiring long-term memorization, despite having this capacity in principle. We aim to address both shortcomings with a class of recurrent networks that use a stochastic state transition mechanism between cell applications. This mechanism, which we term state-regularization, makes RNNs transition between a finite set of learnable states. We evaluate state-regularized RNNs on (1) regular languages for the purpose of automata extraction; (2) non-regular languages such as balanced parentheses and palindromes where external memory is required; and (3) real-word sequence learning tasks for sentiment analysis, visual object recognition and text categorisation. We show that state-regularization (a) simplifies the extraction of finite state automata that display an RNN's state transition dynamic; (b) forces RNNs to operate more like automata with external memory and less like finite state machines, which potentiality leads to a more structural memory; (c) leads to better interpretability and explainability of RNNs by leveraging the probabilistic finite state transition mechanism over time steps.

The theory of state tracking in recurrent architectures has predominantly focused on expressive capacity: whether a fixed architecture can theoretically realize a set of symbolic transition rules. We argue that equally important is error control, the dynamics governing hidden-state drift along the directions that distinguish symbolic states. We prove that affine recurrent networks, a class of models encompassing State-Space Models and Linear Attention, cannot correct errors along state-separating subspaces once they preserve state representations. Consequently, practical affine trackers do not learn robust state tracking; rather, they learn finite horizon solutions governed by accumulated state-relevant error. We characterize the mechanics of this failure, showing that tracking remains readable only while the accumulating within-class spread remains small relative to the initial between-class separation. We demonstrate empirically on group state-tracking tasks that this breakdown is predictable: tracking collapses when the distinguishability ratio crosses the readability threshold of the trained decoder. Across trained models, the point of this crossing predicts the horizon at which downstream accuracy fails. These results establish that robust state tracking is determined not only by an architecture's theoretical expressivity but crucially by its error control.

Recurrent-depth language models, such as looped Transformers, repeatedly apply shared network blocks to refine latent representations without generating explicit intermediate reasoning tokens. However, each step recomputes full attention over the entire context, repeating costly global routing. We study how attention routing evolves across recurrent depth and find a consistent separation in convergence timescales: attention support and distributions stabilize substantially earlier than hidden states and attention outputs. This suggests two stages of recurrent inference: early discovery of a sparse working set, followed by representation refinement over largely stable routing support. Motivated by this finding, we introduce WISE (Working-set Inference with Support Exploitation), a training-free method that uses unrestricted attention during early recurrent steps to discover a block-structured working set, then reuses its support in later steps while keeping attention weights and recurrent refinement dynamic. Controlled interventions show that multi-step discovery yields more effective working sets than first-step selection, and that support reuse better preserves model behavior than more restrictive forms of attention reuse. Across multi-hop QA benchmarks, WISE largely preserves full-attention performance. Matched context-scaling experiments reveal an increasingly favorable quality-efficiency tradeoff as routing support becomes sparser with longer contexts. A sparse-attention implementation achieves up to a 1.76x late-step attention speedup over native FlashAttention at 4K context. Code: https://github.com/tbn5pj/WISE_code.

Symmetries such as gauge invariance and anyonic symmetry play a crucial role in quantum many-body physics. We develop a general approach to constructing gauge invariant or anyonic symmetric autoregressive neural network quantum states, including a wide range of architectures such as Transformer and recurrent neural network (RNN), for quantum lattice models. These networks can be efficiently sampled and explicitly obey gauge symmetries or anyonic constraint. We prove that our methods can provide exact representation for the ground and excited states of the 2D and 3D toric codes, and the X-cube fracton model. We variationally optimize our symmetry incorporated autoregressive neural networks for ground states as well as real-time dynamics for a variety of models. We simulate the dynamics and the ground states of the quantum link model of U(1) lattice gauge theory, obtain the phase diagram for the 2D Z_2 gauge theory, determine the phase transition and the central charge of the SU(2)_3 anyonic chain, and also compute the ground state energy of the SU(2) invariant Heisenberg spin chain. Our approach provides powerful tools for exploring condensed matter physics, high energy physics and quantum information science.

Chain-of-thought (CoT) reasoning has enabled transformer-based language models to excel at complex mathematics and multi-step planning. However, in standard decoder-only architectures, these reasoning steps are externalized in natural language, improving interpretability at the cost of efficiency. To capture reasoning that is not easily represented in words, many works have explored recurrent architectures that aim to internalize reasoning in latent space, potentially supporting latent CoT. In this paper, we investigate whether such reasoning structures emerge in Huginn-3.5B, a depth-recurrent Transformer that reuses layers at inference time without increasing parameter count. We examine the model's internal behavior on arithmetic tasks using a suite of probing techniques including the Logit Lens and Coda Lens. Our findings reveal limited evidence of interpretable latent CoT by tracking rank trajectories of final and intermediate result tokens. Furthermore, we uncover significant probing inconsistencies across recurrent blocks, where the interpretability of hidden states depends heavily on both the layer index and the decoding method. Finally, we empirically show that increasing recurrence depth yields only marginal gains and falls well short of models that explicitly externalize reasoning steps. The code is available at https://github.com/wenquanlu/huginn-latent-cot.

Standard Transformers have a fixed computational depth, fundamentally limiting their ability to generalize to tasks requiring variable-depth reasoning, such as multi-hop graph traversal or nested logic. We propose a depth-recurrent Transformer that decouples computational depth from parameter count by iteratively applying a shared-weight Transformer block in latent space -- enabling the model to trade recurrence steps for deeper reasoning at inference time. Our architecture incorporates three mechanisms to make deep recurrence (20+ steps) stable: (1) a silent thinking objective that supervises only the final output, forcing genuine multi-step reasoning rather than intermediate heuristic shortcuts; (2) LayerScale initialization to protect fragile reasoning states from untrained layer noise; and (3) an identity-biased recurrence that creates a gradient highway across many steps. We evaluate on three compositional reasoning domains with decreasing inductive biases: graph reachability (strict adjacency masking), nested boolean logic (relative positioning), and unstructured relational text (where sequence position provides no structural hints). Across all tasks, we observe a clear computational frontier -- a boundary where performance transitions from chance to near-perfect as thinking steps scale with task complexity. Moreover, these tasks reveal qualitatively different generalization behaviors: precise but brittle (graph), approximate but robust (logic), and autonomous latent routing without structural hints (text). This progression illuminates how the interplay between a task-invariant recurrent reasoning core and task-specific perceptual interfaces shapes out-of-distribution (OOD) generalization, offering a mechanistic perspective on vertical chain-of-thought that complements the prevailing horizontal token-generation paradigm.

The opioid epidemic, referring to the growing hospitalizations and deaths because of overdose of opioid usage and addiction, has become a severe health problem in the United States. Many strategies have been developed by the federal and local governments and health communities to combat this crisis. Among them, improving our understanding of the epidemic through better health surveillance is one of the top priorities. In addition to direct testing, machine learning approaches may also allow us to detect opioid users by analyzing data from social media because many opioid users may choose not to do the tests but may share their experiences on social media anonymously. In this paper, we take advantage of recent advances in machine learning, collect and analyze user posts from a popular social network Reddit with the goal to identify opioid users. Posts from more than 1,000 users who have posted on three sub-reddits over a period of one month have been collected. In addition to the ones that contain keywords such as opioid, opiate, or heroin, we have also collected posts that contain slang words of opioid such as black or chocolate. We apply an attention-based bidirectional long short memory model to identify opioid users. Experimental results show that the approaches significantly outperform competitive algorithms in terms of F1-score. Furthermore, the model allows us to extract most informative words, such as opiate, opioid, and black, from posts via the attention layer, which provides more insights on how the machine learning algorithm works in distinguishing drug users from non-drug users.

We propose a stronger formulation of RL on top of RWKV-style recurrent sequence models, in which the fixed-size recurrent state is explicitly interpreted as a belief state rather than an opaque hidden vector. Instead of conditioning policy and value on a single summary h_t, we maintain a compact uncertainty-aware state b_t = (μ_t, Σ_t) derived from RWKV-style recurrent statistics and let control depend on both memory and uncertainty. This design targets a key weakness of plain fixed-state policies in partially observed settings: they may store evidence, but not necessarily confidence. We present the method, a theoretical program, and a pilot RL experiment with hidden episode-level observation noise together with a test-time noise sweep. The pilot shows that belief-state policies nearly match the best recurrent baseline overall while slightly improving return on the hardest in-distribution regime and under a held-out noise shift. Additional ablations show that this simple belief readout is currently stronger than two more structured extensions, namely gated memory control and privileged belief targets, underscoring the need for richer benchmarks.

Inertial sensors play a pivotal role in indoor localization, which in turn lays the foundation for pervasive personal applications. However, low-cost inertial sensors, as commonly found in smartphones, are plagued by bias and noise, which leads to unbounded growth in error when accelerations are double integrated to obtain displacement. Small errors in state estimation propagate to make odometry virtually unusable in a matter of seconds. We propose to break the cycle of continuous integration, and instead segment inertial data into independent windows. The challenge becomes estimating the latent states of each window, such as velocity and orientation, as these are not directly observable from sensor data. We demonstrate how to formulate this as an optimization problem, and show how deep recurrent neural networks can yield highly accurate trajectories, outperforming state-of-the-art shallow techniques, on a wide range of tests and attachments. In particular, we demonstrate that IONet can generalize to estimate odometry for non-periodic motion, such as a shopping trolley or baby-stroller, an extremely challenging task for existing techniques.

Transformers achieve strong language modeling performance by providing direct token-to-token communication paths, but causal self-attention scales quadratically with context length. Recurrent and state-space models reduce this cost, yet compress history into sequentially updated fixed-size states. This paper studies a third primitive: a parallel content-addressed memory over causal successor records. The proposed Parallel Causal Associative Field (PCAF) writes local records from a context window into hash buckets, retrieves a bounded candidate set for the current query, forms a sparse cache distribution over successor tokens, and mixes that cache with a parametric local language model through a learned gate. The resulting model maintains sparse long-context access while avoiding a single fixed recurrent state bottleneck. We evaluate PCAF under full autoregressive pretraining on WikiText-103 and PG-19 using a distributed Google Cloud TPU v4-32 pod. At 303M parameters and context length T = 2048, PCAF-semantic reaches 36.31 perplexity on WikiText-103 and 52.45 perplexity on PG-19, compared with 47.49 and 53.84 for a matched dense Transformer. PCAF-semantic simultaneously processes 0.61-0.62M tokens/s across the TPU pod, versus 0.43M tokens/s for dense and local attention baselines. Supporting 41M-parameter multi-seed sweeps and single-GPU component ablations show that the associative cache, retrieval capacity, and learned gate materially affect the speed-quality trade-off.

Chain-of-thought prompting improves language-model reasoning by carrying intermediate states across successive computation steps. However, relying on natural language as the only recurrent interface is overly restrictive, since many transient computations do not need to be fully verbalized. Existing latent-reasoning methods remove this constraint by recurrently propagating continuous hidden states. However, these methods pass a dense hidden vector as a whole, without an explicit mechanism for selecting and organizing the information needed by the next reasoning step. This motivates an intermediate interface that remains linguistically grounded without requiring a decoded sentence. We introduce J-CoT, a recurrent reasoning framework built on J-space, a vocabulary-indexed coordinate system within the model's hidden representations. Within each cycle, the model computes in its full hidden space. At the cycle boundary, J-CoT expresses the intermediate state as vocabulary-indexed coefficients, carries these coefficients forward as a J-thought, and maps them back into the model's hidden representation for the next cycle. J-CoT therefore requires neither a fluent intermediate rationale nor recurrence over the complete hidden state. Under matched backbone and inference settings, J-CoT-Zero matches or exceeds the strongest evaluated latent-reasoning baseline on every benchmark, while J-CoT-Train obtains the highest score across the evaluated mathematical, scientific, coding, and structured path-reasoning tasks.

Recurrent reasoning models have attracted growing attention for scaling test-time computation, typically by iteratively refining latent states with shared parameters. However, these models apply each learned update with a fixed unit scale, which can be conservative when updates make persistent progress and overly aggressive when they fluctuate, limiting the benefit of additional loops. To understand how the scale should vary along the trajectory, we first analyze the sensitivity of terminal loss to recurrent update scale. We show that its temporal average admits an exact decomposition into persistent-progress and centered-fluctuation contributions. Based on this, we introduce the Trajectory Adaptive Progress-Fluctuation Scheduler (TAPS), which tracks their balance across recurrent updates and adapts the step size online. Theoretically, we establish sufficient conditions under which TAPS reduces expected terminal loss and reaches a target quality in fewer recurrent loops. Empirically, we show that TAPS improves terminal accuracy across structured reasoning tasks without retraining. By further incorporating the progress-fluctuation principle into training, TAPS yields additional accuracy gains with up to 1.56 times wall-clock speedup at matched baseline accuracy. The broad applicability of TAPS is supported by its effectiveness across diverse recurrent architectures and inference strategies. Together, these results establish update scale as complementary control axis of recurrent inference alongside architecture and depth.

Price responsiveness is a major feature of end use customers (EUCs) that participate in demand response (DR) programs, and has been conventionally modeled with static demand functions, which take the electricity price as the input and the aggregate energy consumption as the output. This, however, neglects the inherent temporal correlation of the EUC behaviors, and may result in large errors when predicting the actual responses of EUCs in real-time pricing (RTP) programs. In this paper, we propose a dynamical DR model so as to capture the temporal behavior of the EUCs. The states in the proposed dynamical DR model can be explicitly chosen, in which case the model can be represented by a linear function or a multi-layer feedforward neural network, or implicitly chosen, in which case the model can be represented by a recurrent neural network or a long short-term memory unit network. In both cases, the dynamical DR model can be learned from historical price and energy consumption data. Numerical simulation illustrated how the states are chosen and also showed the proposed dynamical DR model significantly outperforms the static ones.

Aerial grasp-and-lift tasks require whole-body coordination across approach, acquisition, and lifting under partial target observations. Early approach failures can limit exposure to later task stages during training, while changing visibility complicates alignment and closure timing during execution. We present a recurrent teacher-student framework that learns a single policy in simulation to jointly command flight, arm motion, and gripper closure without an explicit task-phase input. A privileged teacher learns through reinforcement learning with a critical-state curriculum that exposes acquisition and lifting states before connecting them to normal approach trajectories. Its behavior is distilled into a recurrent visual student that replaces privileged target states with dual-view point clouds and proprioception, integrating observation history for closed-loop control. A dedicated closure objective supervises closure timing from sustained model-defined readiness sequences. Training and primary evaluation use a simulated acquisition-and-payload model with condition-triggered latching, virtual attachment, and wrench-based payload loading for short-distance lifting. Across 8,996 completed simulation episodes under this model, the frozen student achieves full-task success rates of 99.97%, 97.14%, and 95.84% under nominal, physics/control-randomized, and additional camera-randomized conditions, respectively. The nominal latch-count-weighted mean of per-seed 90th-percentile alignment errors at acquisition is 8.12 mm.

Autoregressive (AR) video diffusion is a powerful paradigm for streaming and interactive video generation. However, its reliance on softmax self-attention leads to quadratic compute complexity in sequence length and memory usage due to key-value caching, which limits its scalability to long video horizons. Existing remedies (e.g., sparse attention and KV-cache compression) reduce per-step cost but still rely on a linearly growing cache or irreversibly discard past context, and thus fail to address linear memory growth and streaming context management. To address this scalability bottleneck, we propose ARL2 (Attend Locally, Remember Linearly), a hybrid attention module that replaces quadratic cross-frame attention with a fixed-size recurrent state. We decompose self-attention into two branches: an intra-frame softmax branch for spatial detail and local dependencies, and an inter-frame gated recurrent linear branch that maintains a fixed-size state for streaming context. Our key insight is that softmax attention captures fine-grained local interactions, while a recurrent state provides controllable long-range memory. This design achieves linear-time scaling with constant memory while improving temporal consistency over the full-softmax model. To prevent noisy intermediate states from corrupting memory, we update the recurrent state only after the denoised pass. To avoid within-frame information asymmetry, all tokens share the same pre-update state rather than sequential updates. To the best of our knowledge, this is the first work to convert a pretrained AR video diffusion model into a hybrid linear attention architecture, through an efficient two-stage training scheme for AR video. With 75% of layers replaced by hybrid linear attention, the model achieves up to 2.26 wall-clock speedup and 54% memory reduction, while maintaining comparable quality with improving temporal consistency.

We propose a simple technique for encouraging generative RNNs to plan ahead. We train a "backward" recurrent network to generate a given sequence in reverse order, and we encourage states of the forward model to predict cotemporal states of the backward model. The backward network is used only during training, and plays no role during sampling or inference. We hypothesize that our approach eases modeling of long-term dependencies by implicitly forcing the forward states to hold information about the longer-term future (as contained in the backward states). We show empirically that our approach achieves 9% relative improvement for a speech recognition task, and achieves significant improvement on a COCO caption generation task.

Tactile imaging seeks to reconstruct the internal structure of soft objects through touch sensing, with applications in medical diagnosis and robotic manipulation. Recent self-supervised learning approaches have shown promising results, but rely on global, unstructured representations and robot-controlled sensing, limiting generalization and practical use. We propose Local Encoder for Spatial Sensing (LESS), an object-centric tactile representation that exploits the local nature of touch. The tactile scene is modeled as a grid of recurrent encoders with local receptive fields, whose states are fused to reconstruct 2D or 3D images of internal structure. This compositional design enables strong generalization: models trained on single-inclusion phantoms accurately image objects with multiple inclusions and varying sizes. The local structure further supports spatial uncertainty estimation. In addition, we enable hand-held tactile imaging via external pose tracking and human-like palpation data, and extend tactile imaging to full 3D reconstruction.

Looped language models separate computational depth from parameter count by repeatedly applying the same transformer block. Adapting these models requires a shared update that remains effective as hidden states evolve throughout the recurrent computation. Our empirical analysis reveals a pronounced late-loop bias in standard low-rank adaptation (LoRA): the shared update is more effective at later loop positions. This imbalance motivates training shared updates under varying combinations of their applications. Randomly omitting adapter applications alone, however, does not improve task performance; it reduces expected update strength during training while leaving inference unchanged. We introduce Loop Dropout, which couples stochastic masking of adapter applications with inverse-survival rescaling to preserve expected update strength and promote effective adaptation across loops. Extensive experiments demonstrate improved mathematical reasoning across model sizes, adapter ranks and training recipes, with benefits extending to general instruction tuning and code generation. Loop Dropout outperforms existing LoRA variants and adapter regularizers, while further analysis shows stronger early-loop adaptation. Every backbone loop remains active, and inference applies the adapter at all loops using standard LoRA without additional trainable parameters or inference computation.

Machine-learning models trained directly on electronic spectra can predict spin--orbit-driven properties, yet models with comparable predictive accuracy may learn different electronic dependencies. We examine this problem using magnetic anisotropy in atomic-scale magnets and a validation strategy designed to assess the physical relevance of learned spectral relationships. We compare a bidirectional gated recurrent unit and a one-dimensional convolutional neural network, both trained to predict magnetic anisotropy energy (MAE) from spin- and orbital-resolved scalar-relativistic densities of states (SR-DOS). Despite comparable in-domain (ID) accuracy, the architectures learn only partly overlapping spectral dependencies. Shapley additive explanations identify spectral features shared between the two architectures that can be associated with plausible spin--orbit-coupling pathways consistent with second-order perturbation theory (PT2). Adding PT2-derived MAE contributions to the model inputs has little effect on ID performance but can improve transfer beyond the training domain, with gains differing between architectures. Controlled spectral perturbations further demonstrate that similar attribution patterns do not imply the same functional dependence of the predicted MAE on spectral weight. The contrasting responses provide a functional context for architecture-dependent out-of-domain transfer. End-to-end learning can identify candidate electronic signatures of magnetic anisotropy. Their credible microscopic interpretation, however, rests on convergent evidence from predictive performance, model comparison, physical theory, controlled spectral interventions, and evaluation under distribution shift.

Long-context training is increasingly important for large language models, and linear attention and state space models have become popular for improving long-context efficiency. However, efficiently parallelizing long-sequence training for recurrent and hybrid models remains challenging. We present StateFlow, a sequence pipeline parallelism system for models with linear recurrence. StateFlow partitions each sequence into chunks and schedules their execution while propagating boundary states and gradients across chunks, thereby reducing activation lifetimes and improving training throughput. StateFlow further uses profile-guided nonuniform chunking to balance recurrence and softmax attention computation in hybrid models, and overlaps state transitions that expose limited parallelism with surrounding computation. Applying StateFlow to models with up to 32B parameters and 256K context length, we achieve up to \(2.22\times\) throughput improvements and \(2.45\times\) memory reduction compared to conventional pipeline parallelism, enabling otherwise infeasible configurations.

Latent visual reasoning aims to perform multimodal reasoning through hidden-state computation rather than explicit textual chains of thought. However, visual information being present in a latent state does not imply that the model actually relies on that state when producing its answer, especially when alternative image-conditioned paths remain available. We introduce Causal Visual Recurrent Reasoning (CVRR), which preserves pretrained visual competence while making recurrent computation the required image-conditioned path to prediction. CVRR initializes recurrence from the question hidden state after the pretrained vision-language model has incorporated the image, then repeatedly updates this state while re-reading the same fixed visual evidence. Before decoding, visual states and the original multimodal KV cache are removed so that only the final recurrent state carries image-conditioned information to the answer. Across the V^*, MMVP, BLINK, and MME-RealWorld-Lite benchmarks, CVRR retains strong performance under this strict interface, while compatible latent reasoners fail to recover comparable visual competence even when retrained under the same constraint. Causal interventions further show that predictions remain sensitive to recurrent content when the question is held fixed, and that persistent visual evidence causally revises the recurrent trajectory. These results distinguish latent informativeness from latent computation that is actually used for prediction.

Modern sequence modeling is dominated by two families: Transformers, whose self-attention can access arbitrary elements of the visible sequence, and structured state-space models, which propagate information through an explicit recurrent state. These mechanisms face different limitations on long contexts: when attention is diffuse, the influence of individual tokens is diluted across the effective support, while recurrent state propagation can lose long-range sensitivity unless information is actively preserved. As a result, both mechanisms face challenges in preserving and selectively retrieving information over long contexts. We propose Sessa, a decoder that places attention inside a recurrent feedback path. This creates many attention-based paths through which past tokens can influence future states, rather than relying on a single attention read or a single recurrent chain. We prove that, under explicit assumptions and matched regimes, Sessa admits power-law memory tails O(ell^{-β}) for 0 < β< 1, with slower decay than in the corresponding Transformer and Mamba-style baselines. We further give an explicit construction that achieves this power-law rate. Under the same assumptions, Sessa is the only model class among those considered that realizes flexible selective retrieval, including profiles whose influence does not decay with distance. Consistent with this theoretical advantage, across matched experiments, Sessa achieves the strongest performance on long-context benchmarks while remaining competitive with Transformer and Mamba-style baselines on short-context language modeling.

Tactile feedback is critical for understanding the dynamics of both rigid and deformable objects in many manipulation tasks, such as non-prehensile manipulation and dense packing. We introduce an approach that combines visual and tactile sensing for robotic manipulation by learning a neural, tactile-informed dynamics model. Our proposed framework, RoboPack, employs a recurrent graph neural network to estimate object states, including particles and object-level latent physics information, from historical visuo-tactile observations and to perform future state predictions. Our tactile-informed dynamics model, learned from real-world data, can solve downstream robotics tasks with model-predictive control. We demonstrate our approach on a real robot equipped with a compliant Soft-Bubble tactile sensor on non-prehensile manipulation and dense packing tasks, where the robot must infer the physics properties of objects from direct and indirect interactions. Trained on only an average of 30 minutes of real-world interaction data per task, our model can perform online adaptation and make touch-informed predictions. Through extensive evaluations in both long-horizon dynamics prediction and real-world manipulation, our method demonstrates superior effectiveness compared to previous learning-based and physics-based simulation systems.

Vegetation monitoring under climate stress requires answering not only how it will evolve given the expected weather, but how it would respond to alternative meteorological conditions. Forecasting models return the expected vegetation state for the observed weather and cannot answer these scenario-conditioned questions, because future weather is fixed to the recorded trajectory. We present VegSim, a geospatial world model for scenario-conditioned vegetation simulation. VegSim infers a latent vegetation state from sparse satellite-derived NDVI histories, past meteorological covariates, and static spatial context, propagates it forward under future weather forcing through recurrent latent dynamics, and decodes predictive NDVI quantiles at each lead time. Because future forcing enters as a controllable input, the same trained model supports probabilistic forecasting under observed weather and conditional simulation under user-defined meteorological forcing, without supervision on scenario responses. We evaluate VegSim on GreenEarthNet across in-distribution data and spatial, temporal, and joint spatial-temporal shift, where it achieves strong point and probabilistic accuracy against time series and Earth observation forecasting baselines while using a compact architecture. We then simulate vegetation responses across Europe under four meteorological scenarios, and in a France summer 2022 case study, obtaining spatially coherent patterns consistent with known sensitivity to temperature and precipitation. The code is available at https://github.com/arco-group/vegsim.

Transformer-based architectures have dominated sequence modeling, largely due to the expressive power of attention mechanisms. However, for a class of deterministic state tracking tasks---such as parity checking, modular counting, and parenthesis matching---attention may be overkill. In this paper, we show that state propagation alone is sufficient. We propose the Complex State Propagator (CSP), a minimalistic recurrent architecture that only propagates hidden states across layers without output projections at intermediate steps. The state is represented as a complex-valued vector, updated via input-dependent rotations in the complex domain. To enable deep propagation without gradient vanishing or degradation, we introduce a block-level skip connection alongside element-wise complex normalization and SiLU activation at sequence boundaries. Applied with Focal Loss, CSP achieves 100\% accuracy with perfect F1 scores across canonical tasks.

Large Language Models (LLMs) achieve remarkable reasoning capabilities through transformer architectures with attention mechanisms. However, transformers suffer from quadratic time and memory complexity in the attention module (MHA) and require caching key-value states during inference, which severely limits throughput and scalability. High inference throughput is critical for agentic tasks, long-context reasoning, efficient deployment under high request loads, and more efficient test-time compute scaling. State Space Models (SSMs) such as Mamba offer a promising alternative with linear inference complexity and a constant memory footprint via recurrent computation with fixed-size hidden states. In this technical report we introduce the Apriel-H1 family of hybrid LLMs that combine transformer attention and SSM sequence mixers for efficient reasoning at 15B model size. These models are obtained through incremental distillation from a pretrained reasoning transformer, Apriel-Nemotron-15B-Thinker, progressively replacing less critical attention layers with linear Mamba blocks. We release multiple post-distillation variants of Apriel-H1-15B-Thinker with different SSM-to-MHA ratios and analyse how reasoning performance degrades as more Mamba layers replace MHA. Additionally, we release a 30/50 hybrid variant of Apriel-H1, further fine-tuned on a supervised dataset of reasoning traces, achieving over 2x higher inference throughput when deployed in the production-ready vLLM environment, with minimal degradation in reasoning performance. This shows that distilled hybrid SSM-Transformer architectures can deliver substantial efficiency gains over the pretrained transformer equivalent without substantially compromising the reasoning quality.

Recent advances in artificial neural networks for machine learning, and language modeling in particular, have established a family of recurrent neural network (RNN) architectures that, unlike conventional RNNs with vector-form hidden states, use two-dimensional (2D) matrix-form hidden states. Such 2D-state RNNs, known as Fast Weight Programmers (FWPs), can be interpreted as a neural network whose synaptic weights (called fast weights) dynamically change over time as a function of input observations, and serve as short-term memory storage; corresponding synaptic weight modifications are controlled or programmed by another network (the programmer) whose parameters are trained (e.g., by gradient descent). In this Primer, we review the technical foundations of FWPs, their computational characteristics, and their connections to transformers and state space models. We also discuss connections between FWPs and models of synaptic plasticity in the brain, suggesting a convergence of natural and artificial intelligence.

Transformers have been established as the de-facto backbones for most recent advances in sequence modeling, mainly due to their growing memory capacity that scales with the context length. While plausible for retrieval tasks, it causes quadratic complexity and so has motivated recent studies to explore viable subquadratic recurrent alternatives. Despite showing promising preliminary results in diverse domains, such recurrent architectures underperform Transformers in recall-intensive tasks, often attributed to their fixed-size memory. In this paper, we introduce Memory Caching (MC), a simple yet effective technique that enhances recurrent models by caching checkpoints of their memory states (a.k.a. hidden states). Memory Caching allows the effective memory capacity of RNNs to grow with sequence length, offering a flexible trade-off that interpolates between the fixed memory (i.e., O(L) complexity) of RNNs and the growing memory (i.e., O(L^2) complexity) of Transformers. We propose four variants of MC, including gated aggregation and sparse selective mechanisms, and discuss their implications on both linear and deep memory modules. Our experimental results on language modeling, and long-context understanding tasks show that MC enhances the performance of recurrent models, supporting its effectiveness. The results of in-context recall tasks indicate that while Transformers achieve the best accuracy, our MC variants show competitive performance, close the gap with Transformers, and performs better than state-of-the-art recurrent models.

Discrete diffusion language models (dLLMs) generate text by iteratively denoising a masked sequence. However, standard dLLMs condition each denoising step solely on the current hard-masked sequence, while intermediate continuous representations are discarded after sampling and remasking. We term this bottleneck the Information Island issue: continuous information remains isolated within individual denoising steps and fails to propagate across the trajectory. This bottleneck is especially harmful for reasoning, which requires intermediate reasoning state to be preserved and updated across many denoising steps. To address this limitation, we introduce MetaState, a lightweight recurrent augmentation that equips a frozen dLLM backbone with persistent, fixed-size working memory. MetaState comprises three modules with a shared time conditioner: a cross-attention Mixer that reads backbone activations into memory slots, a GRU-style Updater that integrates information across steps, and a cross-attention Injector that writes the updated memory back into the backbone. We train these modules with a dedicated K-step unrolling pipeline to learn multi-step dynamics. MetaState adds only {sim}0.6% trainable parameters while keeping the backbone frozen, and consistently improves reasoning performance over frozen baselines on mathematical reasoning and code generation benchmarks, with an average gain of 4.5% across all evaluations.

Looped language models repeatedly apply a weight-shared block to increase effective depth without increasing parameter count, but the resulting T sequential recurrent-block calls per generated token substantially increase decoding latency. To address the issue, we introduce Wavefront Decoding (WFD), a training-free self-speculative decoding framework designed for looped language models. WFD exploits two properties of these architectures: intermediate recurrence outputs provide effective draft predictions, and weight sharing allows token states at different positions and recurrence depths to be processed in one batched recurrent-block call. WFD organizes these mixed-depth states into a diagonal wavefront, continuously drafting new positions at shallow depth while advancing earlier positions toward full-depth verification. Unlike the phase-separated draft-then-verify schedule, WFD therefore concurrently batches drafting and verification within the same recurrent calls, while rejected drafts are corrected using full-depth predictions. Across six Spec-Bench task categories, WFD achieves 2.42x speedup on Ouro-2.6B and 3.54x on Huginn-3.5B over autoregressive decoding, consistently outperforming draft-then-verify. Cross-recurrence KV sharing further reduces wavefront KV traffic and increases WFD's speedup to 4.81x on Huginn-3.5B. The code is available at https://github.com/summerbro-hhj/wavefront-decoding.

Diffusion language models (DLMs) enable fast generation by predicting multiple tokens in parallel, but their practical adoption remains limited by a persistent quality gap relative to comparably sized autoregressive (AR) models. We attribute this gap to a computation-difficulty mismatch: within a partially observed sequence, some unknown tokens are easy to predict, while others require substantially more computation. Existing DLMs nevertheless apply uniform computational depth to all unknown positions at each denoising step. We introduce ALoDLM, which replaces uniform computation with token-adaptive latent recurrence. At each denoising step, ALoDLM iteratively refines latent representations and allocates computation according to token difficulty. Tokens ready to commit are fed back as discrete context, while unresolved tokens retain and further refine their latent states through additional recurrent passes. To learn token prediction and computation allocation jointly, we formulate token-wise computation schedules as latent variables and derive a conditional negative evidence lower bound (NELBO). We train ALoDLM at 1.7B and 8B parameter scales. Across eleven benchmarks, ALoDLM outperforms all evaluated DLMs and the corresponding AR baselines in average benchmark score at both scales. ALoDLM also retains fast parallel decoding, yielding a strong quality-efficiency trade-off among evaluated autoregressive and diffusion models under optimized inference engines.

Latent-reasoning looped language models (LoopLMs) offer a different scaling path for machine translation (MT): instead of increasing parameter count or emitting explicit chain-of-thought tokens, they spend additional recurrent computation inside hidden states. We introduce LatentMT, the first systematic study of latent-reasoning LoopLMs for machine translation. LatentMT adapts a small 2.6B-parameter backbone model with lightweight training. Across 32 translation directions spanning high-, mid-, and low-resource languages, LatentMT achieves performance comparable to models three to five times larger. It is competitive in a high-resource language and achieves state-of-the-art performance on both mid-resource and low-resource languages. Studying the behavior of scaling the number of recurrent reasoning steps, we find that recurrent computation consistently improves translation quality in early steps, then saturates quickly afterwards. Our mechanistic analysis shows that hidden-representation differences shrink along the recurrent reasoning-step axis, supporting the observed saturation in performance. Finally, our efficiency analysis shows that LatentMT requires lower training and inference compute than much larger non-latent-reasoning models with similar performance, making latent recurrent computation a promising path toward compact, efficient, and strong machine translation.

This paper examines memory mechanisms in Large Language Models (LLMs), emphasizing their importance for context-rich responses, reduced hallucinations, and improved efficiency. It categorizes memory into sensory, short-term, and long-term, with sensory memory corresponding to input prompts, short-term memory processing immediate context, and long-term memory implemented via external databases or structures. The text-based memory section covers acquisition (selection and summarization), management (updating, accessing, storing, and resolving conflicts), and utilization (full-text search, SQL queries, semantic search). The KV cache-based memory section discusses selection methods (regularity-based summarization, score-based approaches, special token embeddings) and compression techniques (low-rank compression, KV merging, multimodal compression), along with management strategies like offloading and shared attention mechanisms. Parameter-based memory methods (LoRA, TTT, MoE) transform memories into model parameters to enhance efficiency, while hidden-state-based memory approaches (chunk mechanisms, recurrent transformers, Mamba model) improve long-text processing by combining RNN hidden states with current methods. Overall, the paper offers a comprehensive analysis of LLM memory mechanisms, highlighting their significance and future research directions.

Quantization is widely used to reduce the computational and memory demands of neural-network inference. In recurrent networks, however, the quantized state is stored and returned at the next time step, so the rule used to store that state can alter subsequent computations. Here, we introduce recurrent-state write-back to denote this rule and isolate its effect in a compact GRU encoder--decoder for fluorescence lifetime imaging, a molecular imaging modality used in quantitative biological imaging. A central task is estimating two lifetime parameters, the short-lived component τ1 and the long-lived component τ2, from high-noise time-resolved fluorescence signals. Holding the trained model fixed, replacing continuous state propagation with deterministic 4-bit state storage increases estimation errors for τ1 and τ2 by approximately 70x and 300x, respectively. Failure occurs when repeated small updates remain below the write threshold, leaving the stored state nearly fixed while the network continues to propose change. Error feedback, residual memory, and direction memory carry information from these suppressed updates across time and recover accuracy without retraining. Precision sweeps show that increasing state precision can worsen a fixed recurrent solution, while matched training shows that compatibility with the state interface can be learned. To test whether this behavior extends beyond the GRU, we repeat the post-training intervention in an independently trained LSTM, where coarse write-back reproduces the failure, error feedback restores accuracy, and state-specific interventions reveal greater sensitivity of the cell state than the hidden state. Our results establish recurrent-state write-back as a key determinant of low-precision recurrent dynamics and identify the state-storage interface as a central design consideration for quantized recurrent inference.

We introduce WriteSAE, the first sparse autoencoder that decomposes and edits the matrix cache write of state-space and hybrid recurrent language models, where residual SAEs cannot reach. Existing SAEs read residual streams, but Gated DeltaNet, Mamba-2, and RWKV-7 write to a d_k times d_v cache through rank-1 updates k_t v_t^top that no vector atom can replace. WriteSAE factors each decoder atom into the native write shape, exposes a closed form for the per-token logit shift, and trains under matched Frobenius norm so atoms swap one cache slot at a time. Atom substitution beats matched-norm ablation on 92.4% of n=4{,}851 firings at Qwen3.5-0.8B L9 H4, the 87-atom population test holds at 89.8%, the closed form predicts measured effects at R^2=0.98, and Mamba-2-370M substitutes at 88.1% over 2,500 firings. Sustained three-position installs at 3times lift midrank target-in-continuation from 33.3% to 100% under greedy decoding, the first behavioral install at the matrix-recurrent write site.

Transformers owe much of their strong long-context retrieval capability to a token-level memory that grows with context length. This flexibility, however, incurs a quadratic computation complexity during training and a key--value cache that grows linearly during autoregressive inference. Recurrent alternatives offer efficient decoding by compressing the entire history into a fixed-size state, but often underperform on recall-intensive tasks since earlier associations usually get overwritten by subsequent updates, and only the most recent contextual information is retained. In this paper, we introduce Memory-Anchor Routing across Context History (MARCH), a network architecture that effectively scales state-space models beyond a fixed-size dimension, while maintaining computational efficiency over long-sequences. MARCH periodically caches cumulative recurrent-state checkpoints as state anchors and associates each anchor with a compact, content-conditioned anchor key. This lets MARCH maintain a memory bank, which can grow as context length increases, providing a controllable trade-off between historical resolution and memory cost. At each token, MARCH produces an anchor query to attend all causally available state anchors, and the output is calculated as an attention-style aggregation over all historical anchors along the current state. We show that after standard pretraining, MARCH consistently outperforms multiple linear attention variants across commonsense reasoning, LongBench, and in-context retrieval. These results demonstrate that content-routed state caching substantially strengthens recurrent long-range memory while preserving its native computation path.

Linear-attention and state-space language models compress the prefix into a fixed-size recurrent state, yielding O(1) memory at the cost of a lossy exact memory: when many key--value associations compete, earlier facts are overwritten and needle recall degrades. Inspired by Complementary Learning Systems, we give linear attention a hippocampal complement. HOLA (Hippocampal Linear Attention) keeps the usual delta-rule state as a compressive memory and adds a bounded exact KV cache, forming a semiparametric test-time memory: the state models linearly compressible structure, while the cache stores associations that should not be forced through that state. The cache writes without a learned eviction module, keeping tokens with large beta * ||e||, the prediction residual actually committed to the state; a decoupled RMSNorm-gamma cache read then turns these exact KV pairs into sharp retrieval rather than soft averaging. At 340M parameters trained on 15B SlimPajama tokens, HOLA lowers Wikitext perplexity from 27.32 to 22.92 (-16.1%), below a full-attention Transformer++ (26.88), and improves LAMBADA perplexity from 30.95 to 30.26. It also achieves the best linear in-context retrieval and remains much more robust than GDN or a matched HOLA+recency cache on RULER needle-in-a-haystack recall out to 32k tokens (16x its training length).

Recurrent neural networks (RNNs) provide a powerful approach in neuroscience to infer latent dynamics in neural populations and to generate hypotheses about the neural computations underlying behavior. However, past work has focused on relatively simple, input-driven, and largely deterministic behaviors - little is known about the mechanisms that would allow RNNs to generate the richer, spontaneous, and potentially stochastic behaviors observed in natural settings. Modeling with Hidden Markov Models (HMMs) has revealed a segmentation of natural behaviors into discrete latent states with stochastic transitions between them, a type of dynamics that may appear at odds with the continuous state spaces implemented by RNNs. Here we first show that RNNs can replicate HMM emission statistics and then reverse-engineer the trained networks to uncover the mechanisms they implement. In the absence of inputs, the activity of trained RNNs collapses towards a single fixed point. When driven by stochastic input, trajectories instead exhibit noise-sustained dynamics along closed orbits. Rotation along these orbits modulates the emission probabilities and is governed by transitions between regions of slow, noise-driven dynamics connected by fast, deterministic transitions. The trained RNNs develop highly structured connectivity, with a small set of "kick neurons" initiating transitions between these regions. This mechanism emerges during training as the network shifts into a regime of stochastic resonance, enabling it to perform probabilistic computations. Analyses across multiple HMM architectures - fully connected, cyclic, and linear-chain - reveal that this solution generalizes through the modular reuse of the same dynamical motif, suggesting a compositional principle by which RNNs can emulate complex discrete latent dynamics.

Recurrent neural networks (RNNs) are widely used throughout neuroscience as models of local neural activity. Many properties of single RNNs are well characterized theoretically, but experimental neuroscience has moved in the direction of studying multiple interacting areas, and RNN theory needs to be likewise extended. We take a constructive approach towards this problem, leveraging tools from nonlinear control theory and machine learning to characterize when combinations of stable RNNs will themselves be stable. Importantly, we derive conditions which allow for massive feedback connections between interacting RNNs. We parameterize these conditions for easy optimization using gradient-based techniques, and show that stability-constrained "networks of networks" can perform well on challenging sequential-processing benchmark tasks. Altogether, our results provide a principled approach towards understanding distributed, modular function in the brain.

Hybrid State-Space models combine Attention with recurrent State-Space Model (SSM) layers, balancing eidetic memory from Attention with compressed fading memory from SSMs. This yields smaller Key-Value caches and faster decoding than Transformers, along with a richer architectural design space. Exploring that design space at scale has so far required training from scratch, a barrier that has kept most large-model Hybrid research within a narrow range of architectures. We introduce Priming, a method that turns Hybrid architecture design from a pre-training problem into a knowledge transfer one. Priming initializes a Hybrid model from a pre-trained Transformer and, through short alignment and post-training phases, recovers downstream quality using less than 0.5% of the source model's pre-training token budget. Priming is agnostic to the source Transformer family (e.g., Qwen, Llama, Mistral), model class (dense or Mixture-of-Experts), and model scale. Priming enables us to run the first controlled comparison of SSM layer types at scale under identical conditions. We evaluate, Gated KalmaNet (GKA), Gated DeltaNet (GDN), and Mamba-2, and show that their expressiveness hierarchy, GKA>GDN>Mamba-2, directly predicts downstream performance on long-context reasoning tasks. We scale Priming to 8B/32B reasoning models with native 128K contexts. Our Hybrid GKA 32B improves over its source Qwen3-32B by +3.8 average reasoning points, while staying within 1% of a Transformer post-trained on the same data and enabling up to 2.3x higher decode throughput. To foster research on Hybrid architectures, we release a model zoo of primed Hybrid models for long-context reasoning and instruction following, together with the Priming training and inference code (Sequence Parallelism algorithms for long-context training, optimized GKA kernels, and vLLM serving plugin), all under Apache~2.0 License.

We study whether a structured recurrent state can serve as a compact associative backbone for language modeling while still supporting exact retrieval. We introduce UniMatrix, a Universal Transformer style family that reuses a shared recurrent block across depth and augments it with hybrid state updates, a ROSA-style residual path, and token-conditioned embedding modulation. We evaluate these models on byte-level WikiText-2, synthetic associative recall, throughput profiling on Apple MPS, and a corrected benchmark for triple-token interactions. At small scale, UniMatrix-Core and UniMatrix-ROSA slightly outperform a parameter-matched Transformer on WikiText-2 while using many fewer parameters, reaching 5.084 and 5.083 bits-per-byte versus 5.124. The main negative result is equally important: on associative recall, the original UniMatrix family remains near chance while the Transformer reaches 25.4 percent, showing that compressed recurrent state alone is not enough for exact lookup. A retrieval-oriented follow-up, UniMatrix-Assoc, helps only marginally. By contrast, UniMatrix-SparsePointer, which adds sparse slot routing and direct pointer-logit fusion, reaches 75.6 percent on the original pilot recipe and 99.2 percent on a no-dropout follow-up while using 53.8 percent fewer parameters than the Transformer baseline. Ablations show that the gain comes from sufficient slot capacity and exact pointer-level output routing. Overall, structured recurrent state is promising and parameter-efficient, but strong long-range behavior still requires explicit sparse retrieval and better kernels.

One essential advantage of recurrent neural networks (RNNs) over transformer-based language models is their linear computational complexity concerning the sequence length, which makes them much faster in handling long sequences during inference. However, most publicly available RNNs (e.g., Mamba and RWKV) are trained on sequences with less than 10K tokens, and their effectiveness in longer contexts remains largely unsatisfying so far. In this paper, we study the cause of the inability to process long context for RNNs and suggest critical mitigations. We examine two practical concerns when applying state-of-the-art RNNs to long contexts: (1) the inability to extrapolate to inputs longer than the training length and (2) the upper bound of memory capacity. Addressing the first concern, we first investigate *state collapse* (SC), a phenomenon that causes severe performance degradation on sequence lengths not encountered during training. With controlled experiments, we attribute this to overfitting due to the recurrent state being overparameterized for the training length. For the second concern, we train a series of Mamba-2 models on long documents to empirically estimate the recurrent state capacity in language modeling and passkey retrieval. Then, three SC mitigation methods are proposed to improve Mamba-2's length generalizability, allowing the model to process more than 1M tokens without SC. We also find that the recurrent state capacity in passkey retrieval scales exponentially to the state size, and we empirically train a Mamba-2 370M with near-perfect passkey retrieval accuracy on 256K context length. This suggests a promising future for RNN-based long-context modeling.

Using roughly 48 execution-verified HumanEval training solutions, tuning a single initial state matrix per recurrent layer, with zero inference overhead, outperforms LoRA by +10.8 pp (p < 0.001) on HumanEval. The method, which we call S0 tuning, optimizes one state matrix per recurrent layer while freezing all model weights. On Qwen3.5-4B (GatedDeltaNet hybrid), S0 tuning improves greedy pass@1 by +23.6 +/- 1.7 pp (10 seeds). On FalconH1-7B (Mamba-2 hybrid), S0 reaches 71.8% +/- 1.3 and LoRA reaches 71.4% +/- 2.4 (3 seeds), statistically indistinguishable at this sample size while requiring no weight merging. Cross-domain transfer is significant on MATH-500 (+4.8 pp, p = 0.00002, 8 seeds) and GSM8K (+2.8 pp, p = 0.0003, 10 seeds); a text-to-SQL benchmark (Spider) shows no transfer, consistent with the trajectory-steering mechanism. A prefix-tuning control on a pure Transformer (Qwen2.5-3B) degrades performance by -13.9 pp under all nine configurations tested. On Qwen3.5, a per-step state-offset variant reaches +27.1 pp, above both S0 and LoRA but with per-step inference cost. Taken together, the results show that recurrent state initialization is a strong zero-inference-overhead PEFT surface for hybrid language models when verified supervision is scarce. The tuned state is a ~48 MB file; task switching requires no weight merging or model reload. Code and library: https://github.com/jackyoung27/s0-tuning.

State Space Models (SSMs) compress sequence history into a bounded recurrent state, making the resulting memory law a central architectural choice for long-context performance. Most modern SSMs rely on ODE-based dynamics that lead to exponential forgetting, limiting their ability to retain information over broad temporal ranges. We introduce FRAC, a selective SSM architecture derived from fractional dynamics that replaces this exponential decay with power-law long memory. To make fractional dynamics practical, FRAC approximates the heavy-tailed target kernel with a finite-state, log-spaced sum of exponential modes. This construction turns fractional memory into an efficient recurrent module with parallel training and prefill, while retaining bounded-state autoregressive decoding. Extensive experiments, including 1.3B-parameter language modeling, demonstrate that FRAC consistently improves long-context performance over state-of-the-art SSM baselines while staying competitive on short-context. These results show that fractional dynamics provide a practical and effective prior for long-context SSMs.

Mainstream LLM serving systems reuse prefix work mainly through paged or radix key-value (KV) caches. This is highly effective for high-throughput, high-concurrency serving, but it manages only one positional fragment of execution state: the KV cache. We study the opposite regime: low-latency, small-batch, on-device physical-AI serving, where interactive LLM agents, speech systems, and robot policies repeatedly branch, reset, interrupt, and re-enter under tight responsiveness budgets. We introduce execution-state capsules, a graph-bound checkpoint and restore mechanism for the complete restorable state at a committed boundary. FlashRT is a white-box, backend-facing kernel runtime whose evaluated NVIDIA CUDA backend runs captured graph plans over contiguous static buffers with no block-table indirection. Because the live state is a closed set of named buffers, a capsule can snapshot, restore, fork, or roll back the whole execution boundary, including KV, recurrent state, convolution state, MTP state, and metadata. This moves reuse from token-addressed KV fragments to graph-bound execution-state boundaries. On an RTX 5090, capsule restore is byte-exact at the stored-state level and token-identical under greedy decode. A KV-only ablation diverges, showing that recurrent state is load-bearing. GPU-resident snapshot and restore are sub-millisecond, and TTFT speedup over cold prefill grows from 3.9x at 2k tokens to 27x at 16k tokens. On Jetson AGX Thor and DGX Spark, the same correctness and structural properties hold. Capsules are not a replacement for high-throughput KV-cache serving; they define a complementary latency-first serving point for explicit execution-state reuse.

State-space models (SSMs) maintain a fixed-size recurrent state, but reading and writing it at every decoding step can bottleneck hybrid models. This eager state management causes large state I/O with low arithmetic intensity, leaves speculative decoding no cheap rollback, and feeds state quantization error into subsequent recurrent updates. We introduce ReplaySSM, which unrolls the recurrence to represent the state as a checkpoint and a buffer of recent SSM inputs. This separates output computation from checkpoint updates. By updating the checkpoint periodically, ReplaySSM avoids state writes on most steps and roughly halves the dominant state memory traffic. Keeping recent inputs also makes speculative rollback a buffer-pointer operation and enables output-only verification without materializing intermediate states. The same separation allows a low-precision checkpoint to serve output computation on most steps while a higher-precision checkpoint serves recurrent updates, so rounding error in the low-precision copy never enters later updates. We implement ReplaySSM in vLLM for Mamba-2 and Gated DeltaNet. At serving batch size 256, it accelerates standard decoding by 1.20--1.47times over a tuned vLLM baseline across four hybrid models, and delivers about 1.8times the throughput of vLLM's speculative decoding on the two 120B-class models. Separate state precisions also reduce output KL divergence and downstream accuracy losses compared with a shared low-precision checkpoint.

Hierarchically gated linear RNN (HGRN,Qin et al. 2023) has demonstrated competitive training speed and performance in language modeling, while offering efficient inference. However, the recurrent state size of HGRN remains relatively small, which limits its expressiveness.To address this issue, inspired by linear attention, we introduce a simple outer-product-based state expansion mechanism so that the recurrent state size can be significantly enlarged without introducing any additional parameters. The linear attention form also allows for hardware-efficient training.Our extensive experiments verify the advantage of HGRN2 over HGRN1 in language modeling, image classification, and Long Range Arena.Our largest 3B HGRN2 model slightly outperforms Mamba and LLaMa Architecture Transformer for language modeling in a controlled experiment setting; and performs competitively with many open-source 3B models in downstream evaluation while using much fewer total training tokens.

Linear attention reformulates sequence modeling as recurrent state evolution, enabling efficient linear-time inference. Under the key-value associative paradigm, existing approaches restrict the role of the query to the readout operation, decoupling it from state evolution. We show that query-conditioned state readout induces a structured value prediction over accumulated memory that complements key-based retrieval. Based on this insight, we propose Q-Delta, a query-aware delta rule that integrates mixed key-query prediction errors into state evolution, enabling jointly corrective dynamics while preserving delta-rule efficiency. We establish stability guarantees for the resulting dynamics and derive a hardware-efficient chunkwise-parallel formulation with a custom Triton implementation. Empirical results demonstrate stable optimization, competitive throughput, and consistent improvements over strong baselines on language modeling and long-context retrieval tasks.

Long-sequence memory tracking places two opposing demands on a recurrent state: near-lossless retention of stored bindings over long horizons, and active overwriting of stale ones. In our diagnostic suite, the strongest efficient baselines tend to solve only one side well. Continuous-time-parameterized state-space models (SSMs) such as Mamba obtain their discrete recurrence by zero-order-hold discretization of a continuous-time system; we argue that this detour is unnecessary for memory tracking and parameterize the discrete transition directly. Naju (Native Adaptive Junction Unit) factorizes the recurrent update, schematically x_n = f_nodot x_{n-1} + i_nodot(B_n u_n), into an explicit discrete pole (a learned forget gate f_n), an independent write gain i_n, and input-dependent write/read maps. Since the sigmoid pole satisfies 0<f_n<1, each frozen local coordinate is Schur-stable by construction, and the full time-varying recurrence satisfies a fading-memory/BIBO bound under uniform boundedness assumptions, with no stability regularizer. We formalize the key structural limitation of coupled designs: any non-expansive complementary single-gate recurrence ties the effective retention r and write gain w through |r|+wle 1, so near-complete retention forces weak writing; decoupling f_n from i_n removes this constraint. Empirically, Naju is the only evaluated model that remains strong on both retention and overwriting at 4x the training length. Beyond the diagnostic suite, we evaluate Naju on WikiText-103 language modeling, Long Range Arena, and multi-query associative recall. Across these settings, Naju consistently combines strong long-range memory with competitive or superior performance, outperforming the Mamba baselines in the principal comparisons while remaining competitive with the Transformer and preserving linear-time, linear-memory scaling.

While Transformers have become the dominant architecture for visual generation, linear attention models, such as the state-space models (SSM), are increasingly recognized for their efficiency in processing long visual sequences. However, the essential efficiency of these models comes from formulating a limited recurrent state, enforcing causality among tokens that are prone to inconsistent modeling of N-dimensional visual data, leaving questions on their capacity to generate long non-causal sequences. In this paper, we explore the boundary of SSM on image and video generation by building the largest-scale diffusion SSM-Transformer hybrid model to date (5B parameters) based on the sub-quadratic bi-directional Hydra and self-attention, and generate up to 2K images and 360p 8 seconds (16 FPS) videos. Our results demonstrate that the model can produce faithful results aligned with complex text prompts and temporal consistent videos with high dynamics, suggesting the great potential of using SSMs for visual generation tasks.

Online surgical phase recognition (SPR) underpins context-aware operating-room systems and requires committing to a prediction at every frame from past context alone. Surgical video poses three demands that natural-video recognizers do not jointly address: procedures span tens of thousands of frames, time flows non-uniformly as long routine stretches are punctuated by brief phase-defining transitions, and the visual domain is narrow so backbone features are strongly correlated across channels. Existing recognizers either let per-frame cost grow with elapsed length, or hold cost bounded but advance state at a uniform rate with channel-independent dynamics, leaving the latter two demands unaddressed. We present SurgicalMamba, a causal SPR model built on Mamba2's structured state-space duality (SSD) that holds per-frame cost at O(d). It introduces three SSD-compatible components, each targeting one demand: a dual-path SSD block that separates long- and short-term regimes at the level of recurrent state; intensity-modulated stepping, a continuous-time time-warp that adapts the slow path's effective rate to phase-relevant information; and state regramming, a per-chunk Cayley rotation that opens cross-channel mixing in the otherwise axis-aligned SSM recurrence. The learned rotation planes inherit a phase-aligned structure without any direct supervision, offering an interpretable internal signature of surgical workflow. Across seven public SPR benchmarks, SurgicalMamba reaches state-of-the-art accuracy and phase-level Jaccard under strict online evaluation: 94.6%/82.7% on Cholec80 (+0.7 pp/+2.2 pp over the strongest prior) and 89.5%/68.9% on AutoLaparo (+1.7 pp/+2.0 pp), at 119 fps on a single GPU. Ablations isolate the contribution of each component. The code is publicly available at https://github.com/sukjuoh/Surgical-Mamba.

Hybrid-attention models replace most softmax attention layers with linear attention, reducing KV-cache growth and enabling larger decode batches where recurrent-state access becomes a major bottleneck. ReplaySSM amortizes state updates by buffering keys and values, but each new query still requires a full-state read even though the state remains unchanged between state updates. We observe that low-rank state-weighted query approximation accurately preserves state-read outputs. Although future queries are unknown, the basis vectors used to approximate them can be fixed offline. Based on this observation, we introduce SketchSSM, which preserves full-state updates while approximating reads. At each state update, SketchSSM reads the full state once to precompute outputs for these basis vectors, storing them in a compact sketch. Each subsequent decode step combines the sketch vectors with query-dependent coefficients to reconstruct the output without a full-state read. Across four Mamba-2-, GDN-, and KDA-based models, SketchSSM at a mean sketch rank of 8 reduces state-access traffic by approximately 10times while matching the average accuracy of the FP32 full-state baseline across four decode benchmarks, and preserves recall on four RULER retrieval tasks. At this rank on one NVIDIA B300, linear-attention kernel speedups over the Standard vLLM baseline reach 7.30times, 5.02times, and 5.24times for Mamba-2, GDN, and KDA, respectively, with up to 2.77times higher decode throughput on Nemotron 3 Super.

Hybrid LLMs pair softmax attention with linear-attention layers such as Gated DeltaNet (GDN), whose recurrent state summarizes the context in fixed size. Early community 4-bit quantizations of Qwen3.8-27B (48 GDN layers, 16 attention layers) left the GDN block in 8- or 16-bit precision -- especially its decay and write-strength gates -- on the intuition that errors in a recurrence accumulate over long contexts. We test that intuition by building Minima: NVFP4 W4A4 on all 496 linear layers, GDN included. Across perplexity at 4K/32K, MMLU-Pro, GSM8K, AIME'25, GPQA-Diamond, LiveCodeBench, and RULER retrieval to 64K, Minima matches BF16 within seed noise (5-task average -0.52) while being the smallest (17.5 GiB) and fastest-prefill (+14-19%) recipe we compare, and its 32K perplexity gap shrinks with position. A four-part mechanism study explains why: (i) NVFP4's 16-element block scaling localizes the residual stream's extreme outliers, equalizing activation error across layer roles; (ii) the supposedly fragile gate projections are the least sensitive -- softplus/exponential and sigmoid parameterizations compress ~11% GEMM error to ~2% output error; (iii) the delta-rule recurrence holds injected noise at a flat plateau over 32K tokens and forgets a state impulse within hundreds of steps, because each write overwrites the state along the current key direction; (iv) the per-token quantization cost washes out with context instead of compounding. We also repair a global-scale mismatch that arises when per-module-calibrated NVFP4 checkpoints are served by kernels that fuse those modules into one GEMM, and show calibrated FP8 KV-cache scales are performance-free. The result: a practical recipe -- quantize everything, ship KV scales -- and a mechanistic account of why the recurrent half of a hybrid LLM is the easy half to quantize. Checkpoint: https://huggingface.co/minima-ai/mnma_qwen3.8_27b_nvfp4

This paper addresses the general problem of reinforcement learning (RL) in partially observable environments. In 2013, our large RL recurrent neural networks (RNNs) learned from scratch to drive simulated cars from high-dimensional video input. However, real brains are more powerful in many ways. In particular, they learn a predictive model of their initially unknown environment, and somehow use it for abstract (e.g., hierarchical) planning and reasoning. Guided by algorithmic information theory, we describe RNN-based AIs (RNNAIs) designed to do the same. Such an RNNAI can be trained on never-ending sequences of tasks, some of them provided by the user, others invented by the RNNAI itself in a curious, playful fashion, to improve its RNN-based world model. Unlike our previous model-building RNN-based RL machines dating back to 1990, the RNNAI learns to actively query its model for abstract reasoning and planning and decision making, essentially "learning to think." The basic ideas of this report can be applied to many other cases where one RNN-like system exploits the algorithmic information content of another. They are taken from a grant proposal submitted in Fall 2014, and also explain concepts such as "mirror neurons." Experimental results will be described in separate papers.

Recurrent Neural Networks (RNNs) are popular models of brain function. The typical training strategy is to adjust their input-output behavior so that it matches that of the biological circuit of interest. Even though this strategy ensures that the biological and artificial networks perform the same computational task, it does not guarantee that their internal activity dynamics match. This suggests that the trained RNNs might end up performing the task employing a different internal computational mechanism, which would make them a suboptimal model of the biological circuit. In this work, we introduce a novel training strategy that allows learning not only the input-output behavior of an RNN but also its internal network dynamics, based on sparse neural recordings. We test the proposed method by training an RNN to simultaneously reproduce internal dynamics and output signals of a physiologically-inspired neural model. Specifically, this model generates the multiphasic muscle-like activity patterns typically observed during the execution of reaching movements, based on the oscillatory activation patterns concurrently observed in the motor cortex. Remarkably, we show that the reproduction of the internal dynamics is successful even when the training algorithm relies on the activities of a small subset of neurons sampled from the biological network. Furthermore, we show that training the RNNs with this method significantly improves their generalization performance. Overall, our results suggest that the proposed method is suitable for building powerful functional RNN models, which automatically capture important computational properties of the biological circuit of interest from sparse neural recordings.

Attention mechanisms have revolutionized sequence learning but suffer from quadratic computational complexity. This paper introduces Lattice, a novel recurrent neural network (RNN) mechanism that leverages the inherent low-rank structure of K-V matrices to efficiently compress the cache into a fixed number of memory slots, achieving sub-quadratic complexity. We formulate this compression as an online optimization problem and derive a dynamic memory update rule based on a single gradient descent step. The resulting recurrence features a state- and input-dependent gating mechanism, offering an interpretable memory update process. The core innovation is the orthogonal update: each memory slot is updated exclusively with information orthogonal to its current state hence incorporation of only novel, non-redundant data, which minimizes the interference with previously stored information. The experimental results show that Lattice achieves the best perplexity compared to all baselines across diverse context lengths, with performance improvement becoming more pronounced as the context length increases.

Countless learning tasks require dealing with sequential data. Image captioning, speech synthesis, and music generation all require that a model produce outputs that are sequences. In other domains, such as time series prediction, video analysis, and musical information retrieval, a model must learn from inputs that are sequences. Interactive tasks, such as translating natural language, engaging in dialogue, and controlling a robot, often demand both capabilities. Recurrent neural networks (RNNs) are connectionist models that capture the dynamics of sequences via cycles in the network of nodes. Unlike standard feedforward neural networks, recurrent networks retain a state that can represent information from an arbitrarily long context window. Although recurrent neural networks have traditionally been difficult to train, and often contain millions of parameters, recent advances in network architectures, optimization techniques, and parallel computation have enabled successful large-scale learning with them. In recent years, systems based on long short-term memory (LSTM) and bidirectional (BRNN) architectures have demonstrated ground-breaking performance on tasks as varied as image captioning, language translation, and handwriting recognition. In this survey, we review and synthesize the research that over the past three decades first yielded and then made practical these powerful learning models. When appropriate, we reconcile conflicting notation and nomenclature. Our goal is to provide a self-contained explication of the state of the art together with a historical perspective and references to primary research.

Recurrent Neural Networks (RNNs), and specifically a variant with Long Short-Term Memory (LSTM), are enjoying renewed interest as a result of successful applications in a wide range of machine learning problems that involve sequential data. However, while LSTMs provide exceptional results in practice, the source of their performance and their limitations remain rather poorly understood. Using character-level language models as an interpretable testbed, we aim to bridge this gap by providing an analysis of their representations, predictions and error types. In particular, our experiments reveal the existence of interpretable cells that keep track of long-range dependencies such as line lengths, quotes and brackets. Moreover, our comparative analysis with finite horizon n-gram models traces the source of the LSTM improvements to long-range structural dependencies. Finally, we provide analysis of the remaining errors and suggests areas for further study.

Recurrent neural networks are the foundation of many sequence-to-sequence models in machine learning, such as machine translation and speech synthesis. In contrast, applied quantum computing is in its infancy. Nevertheless there already exist quantum machine learning models such as variational quantum eigensolvers which have been used successfully e.g. in the context of energy minimization tasks. In this work we construct a quantum recurrent neural network (QRNN) with demonstrable performance on non-trivial tasks such as sequence learning and integer digit classification. The QRNN cell is built from parametrized quantum neurons, which, in conjunction with amplitude amplification, create a nonlinear activation of polynomials of its inputs and cell state, and allow the extraction of a probability distribution over predicted classes at each step. To study the model's performance, we provide an implementation in pytorch, which allows the relatively efficient optimization of parametrized quantum circuits with thousands of parameters. We establish a QRNN training setup by benchmarking optimization hyperparameters, and analyse suitable network topologies for simple memorisation and sequence prediction tasks from Elman's seminal paper (1990) on temporal structure learning. We then proceed to evaluate the QRNN on MNIST classification, both by feeding the QRNN each image pixel-by-pixel; and by utilising modern data augmentation as preprocessing step. Finally, we analyse to what extent the unitary nature of the network counteracts the vanishing gradient problem that plagues many existing quantum classifiers and classical RNNs.

Recurrent neural networks (RNNs) are a cornerstone of sequence modeling across various scientific and industrial applications. Owing to their versatility, numerous RNN variants have been proposed over the past decade, aiming to improve the modeling of long-term dependencies and to address challenges such as vanishing and exploding gradients. However, no central library is available to test these variations, and reimplementing diverse architectures can be time-consuming and error-prone, limiting reproducibility and exploration. Here, we introduce three open-source libraries in Julia and Python that centralize numerous recurrent cell implementations and higher-level recurrent architectures. torchrecurrent, RecurrentLayers.jl, and LuxRecurrentLayers.jl offer a consistent framework for constructing and extending RNN models, providing built-in mechanisms for customization and experimentation. All packages are available under the MIT license and actively maintained on GitHub.

Recurrent fast-weight memories and selective state-space models compress an expanding context into a fixed-size recurrent state, making the state transition an online learning rule. We study this rule under read-after-write autoregressive semantics. For the prefix-prediction objective considered here, the local fast-memory example revealed at step t is the prefix-aligned pair (x_t,y_t)=(ϕ(k_{t-1}),v_t). The common same-step association (ϕ(k_t),v_t) remains causal, but optimizes a different internal objective. We derive normalized first-order updates for squared-error regression and negative inner-product objectives. The regression family comprises Falcon-1 (a scalar NLMS update), Falcon-2 (its per-column extension), and Falcon-3 (a sliding-window mini-batch update); Falcon-1A/Falcon-2A/Falcon-3A are the corresponding inner-product variants. We provide recurrent, masked-parallel, and chunk-parallel forms, together with numerically stable positive-decay renormalization. Representative variants remain competitive in language modeling and improve length extrapolation on variable-digit addition. This framework separates temporal alignment, plasticity, forgetting, and bounded rehearsal in recurrent sequence models.

State Space Models (SSMs) are inherently recurrent along the sequence dimension, yet depth-recurrence - reusing the same block repeatedly across layers, as recently applied in looped transformers - has not been explored in this model family. We show that a looped SSM with k parameters iterated L times consistently closely matches or outperforms a standard SSM with k cdot L independent parameters across four architectures (LRU, S5, LinOSS, LrcSSM) and six time series classification benchmarks, despite operating within a strictly smaller hypothesis space, as we formally establish. Since the larger model contains the looped model as a special case, this dominance cannot be explained by expressivity and instead points to parameter sharing across depth as a beneficial inductive bias that simplifies optimization. These results demonstrate that depth-recurrence is orthogonal to sequence-recurrence and independently beneficial. We further show that input reshaping is an equally neglected design axis: concatenating timesteps for low-dimensional inputs, or flattening and rechunking the joint feature-time dimension for high-dimensional ones, yields accuracy gains of 1-6% across all models, confirmed over 5 random seeds. Both techniques provide standalone improvements that compound when combined, suggesting that depth and input reshaping are two independent and underexplored design axes for SSMs on time series.

Vision-Language-Action (VLA) models have shown remarkable progress in embodied tasks recently, but most methods process visual observations independently at each timestep. This history-agnostic design treats robot manipulation as a Markov Decision Process, even though real-world robotic control is inherently partially observable and requires reasoning over past interactions. To address this mismatch, we reformulate VLA policy learning from a Partially Observable Markov Decision Process perspective and propose AVA-VLA, a framework that conditions action generation on a recurrent state that serves as a neural approximation to the agent's belief over task history. Built on this recurrent state, we introduce Active Visual Attention (AVA), which dynamically reweights visual tokens in the current observation to focus on regions most relevant given both the instruction and execution history. Extensive experiments show that AVA-VLA achieves state-of-the-art performance on standard robotic benchmarks, including LIBERO and CALVIN, and transfers effectively to real-world dual-arm manipulation tasks. These results demonstrate the effectiveness of temporally grounded active visual processing for improving VLA performance in robotic sequential decision-making. The project page is available at https://liauto-dsr.github.io/AVA-VLA-Page.