Daily Papers

Looped Transformers have emerged as an efficient and powerful class of models for reasoning in the language domain. Recent studies show that these models achieve strong performance on algorithmic and reasoning tasks, suggesting that looped architectures possess an inductive bias toward latent reasoning. However, prior approaches fix the number of loop iterations during training and inference, leaving open the question of whether these models can flexibly adapt their computational depth under variable compute budgets. We introduce LoopFormer, a looped Transformer trained on variable-length trajectories to enable budget-conditioned reasoning. Our core contribution is a shortcut-consistency training scheme that aligns trajectories of different lengths, ensuring that shorter loops yield informative representations while longer loops continue to refine them. LoopFormer conditions each loop on the current time and step size, enabling representations to evolve consistently across trajectories of varying length rather than drifting or stagnating. Empirically, LoopFormer demonstrates robust performance on language modeling and reasoning benchmarks even under aggressive compute constraints, while scaling gracefully with additional budget. These results show that looped Transformers are inherently suited for adaptive language modeling, opening a path toward controllable and budget-aware large language models.

Large language models serve applications with diverse inference budgets, but training and maintaining separate models for each budget incurs substantial costs. Recent Looped Transformers enable flexible inference computation through parameter reuse, but maintaining strong performance across different inference budgets remains an open challenge. We introduce Accordion, a mixture-of-experts-based model that supports five inference budgets through fixed-prefix layer looping. Each budget follows a pre-defined execution path, while the minimum budget retains the unlooped model. Joint pretraining samples one budget per micro-batch and optimizes its next-token prediction loss without additional cross-budget consistency objectives. We further preserve these inference budgets through supervised fine-tuning and reinforcement learning, where parameter-group merging and budget-matched multi-teacher on-policy distillation integrate three domain experts into one model. After 3.6T tokens of pretraining, increasing inference depth improves Accordion-6B-A0.5B's five-category macro-average across 37 tasks by 3.01 percentage points, with the middle budget capturing 89% of this gain using half as many additional layer executions. The final model surpasses each domain expert on its corresponding task-and-budget average, while achieving strong instruction-following performance across all budgets and retaining depth-dependent gains in mathematical reasoning and code generation.

Looped Transformers have recently demonstrated strong performance in both reasoning and language tasks by reusing a shared set of parameters across multiple iterations, achieving parameter efficiency without sacrificing representational power. Besides, looped Transformers perform inference directly in the latent space (latent reasoning) to reduce the number of tokens consumed during inference, thereby achieving improved sample efficiency. However, these models typically apply a fixed recursion depth uniformly to every token, leading to suboptimal compute allocation and leaving significant efficiency gains on the table. In this work, we propose dynamic token-choice routing for looped transformers, enabling each token to adaptively determine its own number of loop iterations based on its hidden state, which can improve the token generation accuracy. Moreover, we further introduce recursion-wise KV cache, which maintains an independent key-value cache for each recursion loop, this design ensures that tokens at different depths only attend to their corresponding cached states, effectively enabling faster autoregressive decoding. Extensive experiments show that T-LoopFormer achieves robust performance on language modeling and zero-shot reasoning tasks and our model can reach the lowest decoding latency, which validate the effectiveness of token-choice router and recursion-wise KV cache. Code is available at https://github.com/YuMingQian1234/T-LoopFormer

In this work, we show that a single Transformer block, applied recurrently, can match the accuracy of a full-depth vision encoder at comparable inference FLOPs without intermediate feature distillation. reViT restores depth-specific transformations by representing the FFN at each recurrent depth as a convex combination of a small shared expert bank. A continuous normalized-depth coordinate programs this mixture, defining a resampleable trajectory through FFN parameter space. We evaluate this design in two regimes: supervised ImageNet-1k training and distillation from a DINOv2 teacher. Across both regimes, controlled adaptations identify weight-space merging as the strongest tested MoE family at a matching one-FFN budget, ahead of the token-dispatch and output-mixture alternatives. Trained from scratch, reViT-B/16 attains DeiT III accuracy with about 70\% fewer stored parameters. An 8-experts model distilled using only the teacher's output features retains nearly all of its DINOv2 teacher's linear-probe accuracy and transfers across classification, segmentation, and depth prediction. Elastic-depth training allows one checkpoint (trained model) to operate at multiple tested depths by resampling the same normalized coordinate interval. For fixed-depth deployment, the recurrent block can be materialized as a conventional dense graph, removing online routing and merging without changing the one-FFN-per-depth compute but expanding deployment storage.

We introduce Dory1.0-4B, a 4-billion-parameter looped (latent-recurrent) language model with elastic depth: a single checkpoint serves different inference compute budgets. Dory1.0-4B is built on a normalized Transformer (nGPT) backbone with interleaved sliding-window and full-attention layers, organized into an input block, a shared recurrent block, and an output block. At inference, the recurrent block can be applied a variable number of times. We pre-trained Dory1.0-4B on 6 trillion tokens. The first 4.5 trillion tokens were trained in NVFP4, and additional pre-training then extended the context length to 256K tokens. Next, we post-trained the model using Supervised Fine-Tuning (SFT) and Reinforcement Learning with Verifiable Rewards (RLVR), with a difficulty-aware loop curriculum that routes harder prompts to deeper loops. Increasing the loop count improves accuracy, with the largest gains on coding, agentic, and long-context benchmarks. With two or more loops, Dory1.0-4B outperforms larger models such as Qwen3.5-9B, Gemma 4 12B, and Gemma 4 26B-A4B on average across 12 benchmarks. Looping also makes Dory1.0-4B more token-efficient on agentic benchmarks: with four loops, it generates 1.3-2.5x fewer tokens than with one loop, as the extra computation is spent in latent space rather than on longer outputs. To reduce memory during looping, Dory1.0-4B caches keys and values only from the last loop, keeping its KV-cache footprint equal to that of a non-looped model at any loop count while retaining most of the accuracy gains. We open-source the BF16, MXFP8, NVFP4, and GGUF quantized checkpoints.

Monocular depth estimation (MDE) is a fundamental topic of geometric computer vision and a core technique for many downstream applications. Recently, several methods reframe the MDE as a classification-regression problem where a linear combination of probabilistic distribution and bin centers is used to predict depth. In this paper, we propose a novel concept of iterative elastic bins (IEBins) for the classification-regression-based MDE. The proposed IEBins aims to search for high-quality depth by progressively optimizing the search range, which involves multiple stages and each stage performs a finer-grained depth search in the target bin on top of its previous stage. To alleviate the possible error accumulation during the iterative process, we utilize a novel elastic target bin to replace the original target bin, the width of which is adjusted elastically based on the depth uncertainty. Furthermore, we develop a dedicated framework composed of a feature extractor and an iterative optimizer that has powerful temporal context modeling capabilities benefiting from the GRU-based architecture. Extensive experiments on the KITTI, NYU-Depth-v2 and SUN RGB-D datasets demonstrate that the proposed method surpasses prior state-of-the-art competitors. The source code is publicly available at https://github.com/ShuweiShao/IEBins.

A latent recurrent language model applies a shared block of layers repeatedly, so one checkpoint can trade inference compute for accuracy by changing the loop count. At one loop, however, such models typically fall well short of a non-recurrent model of the same size, a one-loop tax that makes a separate non-recurrent model the better choice whenever latency matters. We present Elastic Latent Recurrence (ELR), a recipe for training looped language models without this tax. At one loop, an ELR model costs the same to serve as a non-recurrent model of the same size and, trained on the same data, reaches similar accuracy. Each additional loop then buys more accuracy for more inference compute. Three choices make this work: a gated state update with a learned step size, loop counts mixed within each optimizer update, and conditioning each pass on its loop index and budget. The first two preserve one-loop accuracy, and the third lowers loss at every additional loop. Mixed depths can be introduced late in pretraining to limit the added training cost, and with zero-initialized conditioning added at the switch, this late schedule reaches lower loss than mixed-depth training from scratch. In MoE models, reusing first-loop expert routes on later loops cuts mixed-depth update time by 11.7% with no measurable change in accuracy. At inference, keeping only the last loop's attention KV cache holds attention KV memory at its one-loop level while retaining most of the gain from additional loops. On 4B dense and 30B-A3B MoE hybrid models, ELR at one loop is 0.52 points below and 1.04 points above its matched baseline on a ten-task average, and four loops add 7.25 and 4.75 points. Carried through post-training, the recipe yields Koi-4B, a single checkpoint that scores an estimated 18 on the Artificial Analysis Intelligence Index at one loop, matching Qwen3.5-4B, and 29 at four loops.

Large language models (LLMs) face inherent performance bottlenecks under parameter constraints, particularly in processing critical tokens that demand complex reasoning. Empirical analysis reveals challenging tokens induce abrupt gradient spikes across layers, exposing architectural stress points in standard Transformers. Building on this insight, we propose Inner Thinking Transformer (ITT), which reimagines layer computations as implicit thinking steps. ITT dynamically allocates computation through Adaptive Token Routing, iteratively refines representations via Residual Thinking Connections, and distinguishes reasoning phases using Thinking Step Encoding. ITT enables deeper processing of critical tokens without parameter expansion. Evaluations across 162M-466M parameter models show ITT achieves 96.5\% performance of a 466M Transformer using only 162M parameters, reduces training data by 43.2\%, and outperforms Transformer/Loop variants in 11 benchmarks. By enabling elastic computation allocation during inference, ITT balances performance and efficiency through architecture-aware optimization of implicit thinking pathways.

Modern sequence models are typically trained at a fixed computational capacity, while real-world applications require deployment across platforms with different resource constraints. Existing approaches either train or distill separate compact models for selected budgets, or use elastic architectures that shrink dimensions such as width, depth, Feed-Forward Network (FFN) size, or SSM state dimension. In this paper, we propose Elastic Spectral State Space Models (ES-SSM), a train-once, export-many sequence modeling framework that gains elasticity through spectral approximation of the SSM sequence operator. ES-SSM builds on Hankel spectral filtering for state space models, where long-range token mixing is represented through fixed Hankel spectral channels that define an operator-level approximation resolution. To make this spectral elasticity reliably deployable, ES-SSM combines input-adaptive channel-wise gates with budget dropout, training the same spectral prefixes that are used by compact models at inference time. This encourages low-index channels to become predictive on their own, while higher-index channels provide refinements for larger budgets. We evaluate ES-SSM across byte-level language modeling, Long Range Arena, Speech Commands V2, and offline reinforcement learning benchmarks. Across these settings, a single trained ES-SSM can be truncated to competitive compact models compared with modern Transformer and SSM baselines at similar parameter scales. Furthermore, by testing under various runtime budgets, we observe smooth and stable quality-cost curves over a wide range of truncation levels.

Training a family of large language models targeting multiple scales and deployment objectives is prohibitively expensive, requiring separate training runs for each different size. Recent work on model compression through pruning and knowledge distillation has reduced this cost; however, this process still incurs hundreds of billions of tokens worth of training cost per compressed model. In this paper, we present Nemotron Elastic, a framework for building reasoning-oriented LLMs, including hybrid Mamba-Attention architectures, that embed multiple nested submodels within a single parent model, each optimized for different deployment configurations and budgets. Each of these submodels shares weights with the parent model and can be extracted zero-shot during deployment without additional training or fine-tuning. We enable this functionality through an end-to-end trained router, tightly coupled to a two-stage training curriculum designed specifically for reasoning models. We additionally introduce group-aware SSM elastification that preserves Mamba's structural constraints, heterogeneous MLP elastification, normalized MSE-based layer importance for improved depth selection, and knowledge distillation enabling simultaneous multi-budget optimization. We apply Nemotron Elastic to the Nemotron Nano V2 12B model, simultaneously producing a 9B and a 6B model using only 110B training tokens; this results in over 360x cost reduction compared to training model families from scratch, and around 7x compared to SoTA compression techniques. Each of the nested models performs on par or better than the SoTA in accuracy. Moreover, unlike other compression methods, the nested capability of our approach allows having a many-in-one reasoning model that has constant deployment memory against the number of models in the family.

We introduce Elastic Looped Transformers (ELT), a highly parameter-efficient class of visual generative models based on a recurrent transformer architecture. While conventional generative models rely on deep stacks of unique transformer layers, our approach employs iterative, weight-shared transformer blocks to drastically reduce parameter counts while maintaining high synthesis quality. To effectively train these models for image and video generation, we propose the idea of Intra-Loop Self Distillation (ILSD), where student configurations (intermediate loops) are distilled from the teacher configuration (maximum training loops) to ensure consistency across the model's depth in a single training step. Our framework yields a family of elastic models from a single training run, enabling Any-Time inference capability with dynamic trade-offs between computational cost and generation quality, with the same parameter count. ELT significantly shifts the efficiency frontier for visual synthesis. With 4times reduction in parameter count under iso-inference-compute settings, ELT achieves a competitive FID of 2.0 on class-conditional ImageNet 256 times 256 and FVD of 72.8 on class-conditional UCF-101.

Multi-vector visual document retrievers achieve strong fine-grained matching by representing each page with multiple vectors from deep Vision-Language Models (VLMs), but this design makes deployment expensive in both storage and computational overhead. Existing efficiency techniques usually optimize only part of this budget, leaving multimodal retrievers without a unified way to trade accuracy for both vector width and encoder depth. Therefore, we propose MM-Matryoshka, a 2D Matryoshka training framework for budget-elastic Visual Document Retrieval (VDR), enabling ColPali-style multi-vector retrieval elastic along both dimension and layer. At inference time, a single retriever can select a 2D selectable budget without training separate models for different budgets. Through comprehensive experiments across multiple representative backbones, we demonstrate that by retaining significantly higher quality than direct truncation baselines while substantially reducing storage and computational overhead, MM-Matryoshka can offer robust budget elasticity for efficient VDR.

This work studies how to adaptively recompute key-value (KV) caches for diffusion large language models (DLMs) to maximize prediction accuracy while minimizing decoding latency. Prior methods' decoders recompute QKV for all tokens at every denoising step and layer, despite KV states changing little across most steps, especially in shallow layers, leading to substantial redundancy. We make three observations: (1) distant {bf MASK} tokens primarily act as a length-bias and can be cached block-wise beyond the active prediction window; (2) KV dynamics increase with depth, suggesting that selective refresh starting from deeper layers is sufficient; and (3) the most-attended token exhibits the smallest KV drift, providing a conservative lower bound on cache change for other tokens. Building on these, we propose {bf Elastic-Cache}, a training-free, architecture-agnostic strategy that jointly decides {when} to refresh (via an attention-aware drift test on the most-attended token) and {where} to refresh (via a depth-aware schedule that recomputes from a chosen layer onward while reusing shallow-layer caches and off-window MASK caches). Unlike fixed-period schemes, Elastic-Cache performs adaptive, layer-aware cache updates for diffusion LLMs, reducing redundant computation and accelerating decoding with negligible loss in generation quality. Experiments on LLaDA-Instruct, LLaDA-1.5, and LLaDA-V across mathematical reasoning and code generation tasks demonstrate consistent speedups: 8.7times on GSM8K (256 tokens), 45.1times on longer sequences, and 4.8times on HumanEval, while consistently maintaining higher accuracy than the baseline. Our method achieves significantly higher throughput (6.8times on GSM8K) than existing confidence-based approaches while preserving generation quality, enabling practical deployment of diffusion LLMs.

Training a family of large language models (LLMs), either from scratch or via iterative compression, is prohibitively expensive and inefficient, requiring separate training runs for each model in the family. In this paper, we introduce Star Elastic, a novel LLM post-training method that adds N nested submodels to a given parent reasoning model using the compute of one run (N-fold savings) via a single post-training job. Beyond reducing training costs, Star Elastic also addresses a fundamental limitation of efficient reasoning: the rigidity of static architectures, which forces the allocation of constant resources regardless of token difficulty. By unlocking elastic budget control, Star Elastic enables a novel inference scheme that uses different submodels for each reasoning phase (thinking and answering). Star Elastic supports (1) nesting along the SSM, embedding channel, MoE, and FFN axes, (2) learning nested submodels via an end-to-end trainable router, and (3) curriculum-based knowledge distillation. Building on the Nemotron Elastic framework, we apply Star Elastic to the NVIDIA Nemotron Nano models, with a particular focus on hybrid Mixture-of-Experts (MoE) architectures: from Nemotron Nano v3 (30B/3.6A), we generate 23B (2.8A) and 12B (2.0A) variants with 160B training tokens. All nested models match or outperform independently trained baselines of comparable size and achieve a 360x reduction versus pretraining from scratch and a 7x reduction over state-of-the-art compression. Crucially, elastic budget control advances the accuracy-latency Pareto frontier, achieving up to 16% higher accuracy and 1.9x lower latency via dynamic per-phase model selection. We further extend Star Elastic to quantized regimes via Quantization-Aware Distillation (QAD), producing nested NVFP4 and FP8 elastic checkpoints that preserve zero-shot slicing while delivering smaller deployment footprints.

Foundation models need to support diverse inference budgets, yet training a separate model for each budget duplicates pretraining effort. Elastic models train several nested sub-networks inside one weight-shared supernet, but existing recipes face three obstacles: variable per-step workloads that hinder distributed scaling, limited hyperparameter (HP) transfer across model sizes, and no guarantee that all sub-networks are maximally updated at once. We present \Ours, an elastic transformer that organizes hidden dimensions into a dense core and successive shells, so that every hidden matrix is block lower triangular. One full-width forward pass contains every sub-network's exact hidden states as prefixes, so joint training keeps a fixed computation graph and costs about as much per step as training the widest sub-network alone. We further introduce \muE, an extension of maximal update parameterization (\mup) to \Ours and other elastic architectures. Its scaling rules provably keep all sub-networks of a supernet maximally updated simultaneously (\muI), and keep doing so when the supernet is widened or given more shells; sweeps confirm that HPs tuned on a small non-elastic proxy stay near-optimal for elastic families and larger supernets (\muT). A single \Ours run produces sub-networks that outperform MatFormer and fully elastic baselines at matched parameter counts, and approach separately trained models that together take several times the steps.

Lowering costs by driving high utilization across deep learning workloads is a crucial lever for cloud providers. We present Singularity, Microsoft's globally distributed scheduling service for highly-efficient and reliable execution of deep learning training and inference workloads. At the heart of Singularity is a novel, workload-aware scheduler that can transparently preempt and elastically scale deep learning workloads to drive high utilization without impacting their correctness or performance, across a global fleet of AI accelerators (e.g., GPUs, FPGAs). All jobs in Singularity are preemptable, migratable, and dynamically resizable (elastic) by default: a live job can be dynamically and transparently (a) preempted and migrated to a different set of nodes, cluster, data center or a region and resumed exactly from the point where the execution was preempted, and (b) resized (i.e., elastically scaled-up/down) on a varying set of accelerators of a given type. Our mechanisms are transparent in that they do not require the user to make any changes to their code or require using any custom libraries that may limit flexibility. Additionally, our approach significantly improves the reliability of deep learning workloads. We show that the resulting efficiency and reliability gains with Singularity are achieved with negligible impact on the steady-state performance. Finally, our design approach is agnostic of DNN architectures and handles a variety of parallelism strategies (e.g., data/pipeline/model parallelism).

Scaling up transformers has produced models with broad capabilities, deployed across heterogeneous hardware and fluctuating workloads. Yet, model families offer only a few fixed sizes (e.g., S, B, L), forcing users to commit to a model based on hardware and latency constraints. This rigidity is often suboptimal under varying query loads. We introduce a retraining-free method that elastifies pre-trained transformers into a single model that adapts on-the-fly across a continuum of computational budgets. Our key contribution is a differentiable relaxation of the functional unit-ranking problem: unlike prior work, which optimizes a single importance weight per MLP block or attention head, we rank every individual MLP neuron and attention head jointly, on a common scale, by minimizing the model's loss under soft pruning across many sparsity targets, all at once. Across 27 vision and text transformer encoders ranging from 22M to 8B parameters, our method yields smooth degradation up to 60% sparsity and outperforms one-shot baselines under deep pruning. For example, pruning DINOv3 ViT-H+/16 to 50% sparsity removes 427M parameters while reducing ImageNet-1k linear-probing accuracy by only 0.8%, without the need for weight correction or retraining. At 60% sparsity, a pruned AugReg ViT-B/16 model achieves up to 1.80times higher throughput and 1.26times lower single-query latency on an A100 GPU. Elastic models are produced in minutes, with construction time scaling sub-linearly with parameter count.

This work puts forth a new optimal design formulation for planar elastic membranes. The goal is to minimize the membrane's compliance through choosing the material distribution described by a positive Radon measure. The deformation of the membrane itself is governed by the convexified F\"{o}ppl's model. The uniqueness of this model lies in the convexity of its variational formulation despite the inherent nonlinearity of the strain-displacement relation. It makes it possible to rewrite the optimization problem as a pair of mutually dual convex variational problems. In the primal problem a linear functional is maximized with respect to displacement functions while enforcing that point-wisely the strain lies in an unbounded closed convex set. The dual problem consists in finding equilibrated stresses that are to minimize a convex integral functional of linear growth defined on the space of Radon measures. The pair of problems is analysed: existence and regularity results are provided, together with the system of optimality criteria. To demonstrate the computational potential of the pair, a finite element scheme is developed around it. Upon reformulation to a conic-quadratic & semi-definite programming problem, the method is employed to produce numerical simulations for several load case scenarios.

Elastic geophysical properties (such as P- and S-wave velocities) are of great importance to various subsurface applications like CO_2 sequestration and energy exploration (e.g., hydrogen and geothermal). Elastic full waveform inversion (FWI) is widely applied for characterizing reservoir properties. In this paper, we introduce mathbb{E^{FWI}}, a comprehensive benchmark dataset that is specifically designed for elastic FWI. mathbb{E^{FWI}} encompasses 8 distinct datasets that cover diverse subsurface geologic structures (flat, curve, faults, etc). The benchmark results produced by three different deep learning methods are provided. In contrast to our previously presented dataset (pressure recordings) for acoustic FWI (referred to as OpenFWI), the seismic dataset in mathbb{E^{FWI}} has both vertical and horizontal components. Moreover, the velocity maps in mathbb{E^{FWI}} incorporate both P- and S-wave velocities. While the multicomponent data and the added S-wave velocity make the data more realistic, more challenges are introduced regarding the convergence and computational cost of the inversion. We conduct comprehensive numerical experiments to explore the relationship between P-wave and S-wave velocities in seismic data. The relation between P- and S-wave velocities provides crucial insights into the subsurface properties such as lithology, porosity, fluid content, etc. We anticipate that mathbb{E^{FWI}} will facilitate future research on multiparameter inversions and stimulate endeavors in several critical research topics of carbon-zero and new energy exploration. All datasets, codes and relevant information can be accessed through our website at https://efwi-lanl.github.io/

Layered viscoelastic interiors control the frequency dependence of planetary tidal dissipation, but repeated layered Love-number calculations are expensive in long-term orbital and spin integrations. Equivalent homogeneous rheologies provide a cheaper representation of the same response, but their effective parameters do not by themselves identify the interior layers they represent. We develop a local interpretation of such parameters by differentiating the layered-to-homogeneous construction about a fixed-geometry baseline, perturbing only selected layer rigidities and viscosities. We use the pole-residue representation of the degree-two Love number to construct a physical-to-effective transfer matrix. We then use its singular values, resolution matrix, and mode-dominance matrix to determine which physical perturbations are visible in the Love-number response and how they appear in effective-rheology coordinates. Applied to a five-layer lunar model, the full degree-two response is sensitive to seven of eight solid-layer rheological parameters. The single near-null direction is the inner-core rigidity, consistent with shielding by the fluid outer core and with the weak dependence of Love numbers on core elastic structure. Over the LLR frequency interval, fewer physical directions are visible. To first order, the elastic spring, isolated dashpot, and two Voigt elements reproduce the nine-pole response over this interval. Finite perturbations confirm the tangent prediction to within a few percent, with the validity radius limited by a nearly degenerate pair of long-timescale modes.