Daily Papers

Single-optimizer training is a poor fit for the distinct phases of deep network optimization: adaptive methods handle noisy early gradients well but overshoot flat minima, while SGD with momentum generalizes better in the late phase but converges slowly early on. We introduce AOS-R (Adaptive Optimizer Switching, Rule-Based), a lightweight controller that monitors six online gradient-space signals -- gradient noise scale (GNS), Hutchinson curvature trace, loss stagnation, update stability ratio, gradient stability index (GSI), and loss improvement ratio (LIR) -- and switches among AdamW, SGD-M, and Lion as the optimization landscape evolves. State-preserving momentum transfer and a 400-step learning-rate bridge prevent accuracy degradation at every transition point. On CIFAR-100/WRN-28x10, AOS-R reaches 78% top-1 in 81 epochs -- 26% fewer than AdamW (109), 43% fewer than SGD-M (143), and 16% fewer than Lion (96). Across eight model-dataset benchmarks, AOS-R achieves best accuracy on 6 of 8 combinations with a mean +0.4 pp gain and 0.80x convergence speedup over AdamW under a single shared hyperparameter configuration.

We present SmolTulu-1.7b-Instruct, referenced in this report as SmolTulu-DPO-1130, an instruction-tuned language model that adapts AllenAI's Tulu 3 post-training pipeline to enhance Huggingface's SmolLM2-1.7B base model. Through comprehensive empirical analysis using a 135M parameter model, we demonstrate that the relationship between learning rate and batch size significantly impacts model performance in a task-dependent manner. Our findings reveal a clear split: reasoning tasks like ARC and GSM8K benefit from higher learning rate to batch size ratios, while pattern recognition tasks such as HellaSwag and IFEval show optimal performance with lower ratios. These insights informed the development of SmolTulu, which achieves state-of-the-art performance among sub-2B parameter models on instruction following, scoring 67.7% on IFEval (Delta11%), and mathematical reasoning with 51.6% on GSM8K (Delta3.4%), with an alternate version achieving scoring 57.1% on ARC (Delta5.4%). We release our model, training recipes, and ablation studies to facilitate further research in efficient model alignment, demonstrating that careful adaptation of optimization dynamics can help bridge the capability gap between small and large language models.

The expanding computational costs and limited resources underscore the critical need for budgeted-iteration training, which aims to achieve optimal learning within predetermined iteration budgets.While learning rate schedules fundamentally govern the performance of different networks and tasks, particularly in budgeted-iteration scenarios, their design remains largely heuristic, lacking theoretical foundations.In addition, the optimal learning rate schedule requires extensive trial-and-error selection, making the training process inefficient.In this work, we propose the Unified Budget-Aware (UBA) schedule, a theoretically grounded learning rate schedule that consistently outperforms commonly-used schedules among diverse architectures and tasks under different constrained training budgets.First, we bridge the gap by constructing a novel training budget-aware optimization framework, which explicitly accounts for the robustness to landscape curvature variations.From this framework, we derive the UBA schedule, controlled by a single hyper-parameter varphi that provides a trade-off between flexibility and simplicity, eliminating the need for per-network numerical optimization. Moreover, we establish a theoretical connection between varphi and the condition number, adding interpretation and justification to our approach. Besides, we prove the convergence for different values of varphi.We offer practical guidelines for its selection via theoretical analysis and empirical results.xtensive experimental results show that UBA consistently surpasses the commonly-used schedules across diverse vision and language tasks, spanning network architectures (e.g., ResNet, OLMo) and scales, under different training-iteration budgets.

Post-training processes are essential phases in grounding pre-trained language models to real-world tasks, with learning from demonstrations or preference signals playing a crucial role in this adaptation. We present a unified theoretical framework bridging Supervised Fine-Tuning (SFT) and preference learning in Large Language Model (LLM) post-training. Through rigorous mathematical derivation, we demonstrate that both SFT and preference learning methods like Direct Preference Optimization (DPO) operate within the same optimal policy-reward subspace, with SFT representing a special case of implicit reward learning. Our analysis reveals a critical limitation in conventional SFT: the KL divergence term in distribution matching becomes constant with respect to the policy during optimization, failing to constrain model updates. To address this, we propose a simple yet effective learning rate reduction approach that yields significant performance improvements (up to 25\% relative gain and 6\% absolute win rate increase in instruction following tasks. Additionally, we derive alternative SFT objectives from various f-divergence functions that preserve the KL term during optimization, further enhancing post-DPO model performance. Finally, we extend the theoretical relationship between LLM logits and Q-functions from preference learning to the SFT context, providing mathematical derivations and experimental validation.

Recently, leveraging pre-trained vision-language models (VLMs) for building vision-language-action (VLA) models has emerged as a promising approach to effective robot manipulation learning. However, only few methods incorporate 3D signals into VLMs for action prediction, and they do not fully leverage the spatial structure inherent in 3D data, leading to low sample efficiency. In this paper, we introduce BridgeVLA, a novel 3D VLA model that (1) projects 3D inputs to multiple 2D images, ensuring input alignment with the VLM backbone, and (2) utilizes 2D heatmaps for action prediction, unifying the input and output spaces within a consistent 2D image space. In addition, we propose a scalable pre-training method that equips the VLM backbone with the capability to predict 2D heatmaps before downstream policy learning. Extensive experiments show the proposed method is able to learn 3D manipulation efficiently and effectively. BridgeVLA outperforms state-of-the-art baseline methods across three simulation benchmarks. In RLBench, it improves the average success rate from 81.4% to 88.2%. In COLOSSEUM, it demonstrates significantly better performance in challenging generalization settings, boosting the average success rate from 56.7% to 64.0%. In GemBench, it surpasses all the comparing baseline methods in terms of average success rate. In real-robot experiments, BridgeVLA outperforms a state-of-the-art baseline method by 32% on average. It generalizes robustly in multiple out-of-distribution settings, including visual disturbances and unseen instructions. Remarkably, it is able to achieve a success rate of 96.8% on 10+ tasks with only 3 trajectories per task, highlighting its extraordinary sample efficiency. Project Website:https://bridgevla.github.io/

We present ViP-VL, an efficient Vietnamese Self-supervised speech Pretraining model leveraging Vector-quantization Learning. To bridge the gap between high-resolution audio and efficient processing, ViP-VL incorporates Acoustic Stacking and Receptive Field Alignment to enable a synchronized 8x subsampling rate within the ChunkFormer architecture, while further enhancing representation robustness through a specialized Mask Selection Strategy during pretraining on the BEST-RQ framework. Pretrained on 17,000 hours of unlabeled Vietnamese speech, our model establishes new state-of-the-art results across four major downstream tasks: Automatic Speech Recognition, Speech Emotion Recognition, Dialect Classification, and Speaker Verification. To facilitate future research and the development of high-performance Vietnamese speech technologies, we publicly release our pretrained weights and implementation at github.com/khanld/chunkformer.

Large language models have achieved remarkable success, but their extensive parameter size necessitates substantial memory for training, thereby setting a high threshold. While the recently proposed low-memory optimization (LOMO) reduces memory footprint, its optimization technique, akin to stochastic gradient descent, is sensitive to hyper-parameters and exhibits suboptimal convergence, failing to match the performance of the prevailing optimizer for large language models, AdamW. Through empirical analysis of the Adam optimizer, we found that, compared to momentum, the adaptive learning rate is more critical for bridging the gap. Building on this insight, we introduce the low-memory optimization with adaptive learning rate (AdaLomo), which offers an adaptive learning rate for each parameter. To maintain memory efficiency, we employ non-negative matrix factorization for the second-order moment estimation in the optimizer state. Additionally, we suggest the use of a grouped update normalization to stabilize convergence. Our experiments with instruction-tuning and further pre-training demonstrate that AdaLomo achieves results on par with AdamW, while significantly reducing memory requirements, thereby lowering the hardware barrier to training large language models.

Parallel LLM inference scaling involves sampling a set of N>1 responses for a single input prompt. However, these N parallel responses tend to be generated independently from each other, partitioning compute resources and leaving potentially useful information in one generation untapped by others. This is in contrast to response length scaling where past computation is used in all future steps. For higher quality responses and response sets, we propose Bridge to generate interdependent responses in parallel by rethinking batched LLM hidden states as holistic tensors rather than independent slices. With only a small amount (2.8%-5.1%) of new parameters, Bridge improves the relative mean accuracy gains from reinforcement learning with verifiable rewards by up to 50% and boosts consistency of correct responses. Trained once, Bridge scales to any generation width, all with greater performance than independent generations, unlocking a more general mode of parallel scaling that effectively leverages information between sequences, compatible with any post-generation aggregation technique.

We study optimal learning-rate selection in two-layer and three-layer linear neural networks trained to learn linear target functions. In particular, we derive the exact closed-form expressions for the gradients and test loss after one and two steps of gradient descent, enabling a precise characterization of early training dynamics. We characterize how learning rates should scale under the gradient approximation in the first two steps, and prove that performing updates with this approximation yields a tractable surrogate loss with a tight, small approximation error. This formulation enables the theoretical analysis of layer-wise learning rates and reveals a distinct early-training regime: test loss can be minimized by unequal learning rates at the initial step, while equal learning rates become optimal in subsequent steps. Our numerical experiments validate the theory and demonstrate the importance of balancing layer-wise learning rates early during training. The code is available at: https://github.com/TDCSZ327/Layer-Balancing.

We provide the first proof of learning rate transfer with width in a linear multi-layer perceptron (MLP) parametrized with muP, a neural network parameterization designed to ``maximize'' feature learning in the infinite-width limit. We show that under mu P, the optimal learning rate converges to a non-zero constant as width goes to infinity, providing a theoretical explanation to learning rate transfer. In contrast, we show that this property fails to hold under alternative parametrizations such as Standard Parametrization (SP) and Neural Tangent Parametrization (NTP). We provide intuitive proofs and support the theoretical findings with extensive empirical results.

Modern one-step diffusion models achieve impressive quality through distribution-based timestep distillation. Yet, they rely on a critical assumption: Teacher and Student must inhabit the same latent space. This Shared-Space constraint prevents knowledge transfer from modern high-capacity Teachers (e.g., SD 3.5 and Flux) into compact, deployment-friendly Students such as SD 1.5, whose latent resolution and VAE parameterization differ from the Teacher. We formalize this overlooked regime as Cross-Space Distillation, where Teacher and Student differ in both latent resolution and VAE space. To enable distillation under this mismatch, we introduce the Bridge, a lightweight latent interface that maps Student latents into the Teacher space without modifying the Student backbone. Bridge combines a frozen Student VAE decoder as a spatial prior with a compact learnable projector, and is trained with latent reconstruction and attention fidelity objectives for stable Teacher-space alignment. Across diverse modern Teachers, Bridge enables substantial gains for compact one-step Students; for example, it improves SD 1.5 from 5.4 to 9.4 HPSv3 while preserving one-step inference, low latency, and broad ecosystem compatibility. These results show that heterogeneous large Teachers can be distilled into efficient, deployable backbones through a lightweight latent-space interface.

This paper aims to extend the Structured Knowledge Accumulation (SKA) framework recently proposed by mahi2025ska. We introduce two core concepts: the Tensor Net function and the characteristic time property of neural learning. First, we reinterpret the learning rate as a time step in a continuous system. This transforms neural learning from discrete optimization into continuous-time evolution. We show that learning dynamics remain consistent when the product of learning rate and iteration steps stays constant. This reveals a time-invariant behavior and identifies an intrinsic timescale of the network. Second, we define the Tensor Net function as a measure that captures the relationship between decision probabilities, entropy gradients, and knowledge change. Additionally, we define its zero-crossing as the equilibrium state between decision probabilities and entropy gradients. We show that the convergence of entropy and knowledge flow provides a natural stopping condition, replacing arbitrary thresholds with an information-theoretic criterion. We also establish that SKA dynamics satisfy a variational principle based on the Euler-Lagrange equation. These findings extend SKA into a continuous and self-organizing learning model. The framework links computational learning with physical systems that evolve by natural laws. By understanding learning as a time-based process, we open new directions for building efficient, robust, and biologically-inspired AI systems.

Memory-Mediated Learning Architecture (MMLA) separates slow base parameters theta, a bounded numerical policy carrier Phi, and a bounded authoritative memory M. Predictive Dual-State Adaptation (PDSA) lets feedback update Phi while one problem remains active and lets a trusted lifecycle atomically commit one typed row or exact NULL. Later reasoning may read both states, but their writers, resets, rollback domains, and ledgers remain distinct. Realized futures supervise values only during training; deployment is causal and future-blind. We give conditional theory and falsifiable contracts for reasoning-time updates, completed-segment consolidation, predictive admission, authoritative memory, and dual-state attribution. Assumptions, counterexamples, capacity and cost ledgers, recovery duties, and identifying experiments are explicit; these are not implementation guarantees. Controlled studies show exact lifecycle execution on 300/300 held-out records for each of three seeds, calibrated retrieval gains over frozen-hidden dense and BM25 baselines, and exact typed anchor-filler transport on 240/240 held-out records per seed. These validate restricted components, not natural-language memory management or complete PDSA. Post-training studies retain positive and negative evidence. Later protocols obtain restricted readout progress, but a nine-trajectory comparison finds that matched latent readout, a full-width bridge, and bridge plus frozen text-teacher alignment all fail continuous-event qualification across both task families. A separately adapted text reference and restoration checks pass. At the September 13, 2026 evidence cutoff, no strict policy-only reasoning-time-training effect, predictive-admission oracle margin, learned future-blind admission policy, or policy-by-memory factorial advantage is established.

In settings where labeled verifiable training data is the binding constraint, each checked example should be allocated carefully. The standard practice is to use this data directly on the model that will be deployed, for example by running GRPO on the deployment student. We argue that this is often an inefficient allocation because it overlooks a reward-density principle: sparse sequence-level reward should train models where exploration is productive, while dense token-level teacher reward should be used where the aim is to compress behavior into a smaller model. In this view, GRPO-style sparse RL and OPD-style dense teacher supervision are not separate recipes; they are different reward-density regimes. The allocation rule is simple: use scarce labeled training data upstream on the strongest model that can turn it into reward-shaped behavior, then transfer that behavior downstream as dense supervision. We evaluate this rule on verifiable math with Qwen3 and Llama models. At fixed Qwen3-1.7B deployment-student size, an RL-improved 8B teacher distilled through the dense bridge outperforms direct GRPO on the same student, while transfer from the same teacher before RL underperforms. The bridge is important: a forward-KL warmup on teacher rollouts followed by OPD on student rollouts is consistently strongest on MATH before any post-bridge student-side sparse RL, and also gives the best pre-Stage~3 AIME endpoints for the canonical 8B/14B teachers. The bridge also makes later student-side sparse RL effective: GRPO that is weak on a cold student lifts MATH from 75.4% to 78.5% after the bridge and outperforms a matched replay control by 2.8 points. The operational principal is to avoid using scarce labeled data on the least prepared policy: use sparse reward for teacher-side discovery, dense transfer for student compression, and student-side sparse reward only after the bridge.

Offline (or batch) reinforcement learning (RL) algorithms seek to learn an optimal policy from a fixed dataset without active data collection. Based on the composition of the offline dataset, two main categories of methods are used: imitation learning which is suitable for expert datasets and vanilla offline RL which often requires uniform coverage datasets. From a practical standpoint, datasets often deviate from these two extremes and the exact data composition is usually unknown a priori. To bridge this gap, we present a new offline RL framework that smoothly interpolates between the two extremes of data composition, hence unifying imitation learning and vanilla offline RL. The new framework is centered around a weak version of the concentrability coefficient that measures the deviation from the behavior policy to the expert policy alone. Under this new framework, we further investigate the question on algorithm design: can one develop an algorithm that achieves a minimax optimal rate and also adapts to unknown data composition? To address this question, we consider a lower confidence bound (LCB) algorithm developed based on pessimism in the face of uncertainty in offline RL. We study finite-sample properties of LCB as well as information-theoretic limits in multi-armed bandits, contextual bandits, and Markov decision processes (MDPs). Our analysis reveals surprising facts about optimality rates. In particular, in all three settings, LCB achieves a faster rate of 1/N for nearly-expert datasets compared to the usual rate of 1/N in offline RL, where N is the number of samples in the batch dataset. In the case of contextual bandits with at least two contexts, we prove that LCB is adaptively optimal for the entire data composition range, achieving a smooth transition from imitation learning to offline RL. We further show that LCB is almost adaptively optimal in MDPs.

Controllable human voice generation, particularly for expressive domains like singing, remains a significant challenge. This paper introduces Vevo2, a unified framework for controllable speech and singing voice generation. To tackle issues like the scarcity of annotated singing data and to enable flexible controllability, Vevo2 introduces two audio tokenizers: (1) a music-notation-free prosody tokenizer that captures prosody and melody from speech, singing, and even instrumental sounds, and (2) a low-frame-rate (12.5 Hz) content-style tokenizer that encodes linguistic content, prosody, and style for both speech and singing, while enabling timbre disentanglement. Vevo2 consists of an auto-regressive (AR) content-style modeling stage, which aims to enable controllability over text, prosody, and style, as well as a flow-matching acoustic modeling stage that allows for timbre control. Particularly, during pre-training of the AR model, we propose both explicit and implicit prosody learning strategies to bridge speech and singing voice. Moreover, to further enhance the AR model's ability to follow text and prosody, we design a multi-objective post-training task that integrates both intelligibility and prosody similarity alignment. Experimental results show that the unified modeling in Vevo2 brings mutual benefits to both speech and singing voice generation. Additionally, Vevo2's effectiveness across a wide range of synthesis, conversion, and editing tasks for both speech and singing further demonstrates its strong generalization ability and versatility. Audio samples are are available at https://versasinger.github.io/.

Learning-rate transfer can reduce the cost of training large language models: instead of sweeping learning rates at target scale, practitioners extrapolate from smaller runs. Existing approaches often assume that the optimal learning rate follows a log-linear scaling law in data scale and model size. We carefully examine and evaluate this scaling law. In our empirical study of GPT-2--style models from 22M to 707M parameters trained on 5B to 100B tokens, the optimal learning rate develops upward curvature at larger scales, leading to inaccurate extrapolation. We find that this curvature largely disappears when learning rates are replaced by effective learning rate (the step size in normalized weight space), and when data D extrapolation is used instead of model size N extrapolation. Next, we explain nonlinearity in scaling: weight-norm converges to equilibrium slower when optimal learning is small, requiring a larger step size to reduce the transient phase. Experiments with AdamH, which directly controls the effective learning rate, further support this explanation.

Large Language Models (LLMs) represent the recent success of deep learning in achieving remarkable human-like predictive performance. It has become a mainstream strategy to leverage fine-tuning to adapt LLMs for various real-world applications due to the prohibitive expenses associated with LLM training. The learning rate is one of the most important hyperparameters in LLM fine-tuning with direct impacts on both fine-tuning efficiency and fine-tuned LLM quality. Existing learning rate policies are primarily designed for training traditional deep neural networks (DNNs), which may not work well for LLM fine-tuning. We reassess the research challenges and opportunities of learning rate tuning in the coming era of Large Language Models. This paper makes three original contributions. First, we revisit existing learning rate policies to analyze the critical challenges of learning rate tuning in the era of LLMs. Second, we present LRBench++ to benchmark learning rate policies and facilitate learning rate tuning for both traditional DNNs and LLMs. Third, our experimental analysis with LRBench++ demonstrates the key differences between LLM fine-tuning and traditional DNN training and validates our analysis.

It is known that the learning rate is the most important hyper-parameter to tune for training deep neural networks. This paper describes a new method for setting the learning rate, named cyclical learning rates, which practically eliminates the need to experimentally find the best values and schedule for the global learning rates. Instead of monotonically decreasing the learning rate, this method lets the learning rate cyclically vary between reasonable boundary values. Training with cyclical learning rates instead of fixed values achieves improved classification accuracy without a need to tune and often in fewer iterations. This paper also describes a simple way to estimate "reasonable bounds" -- linearly increasing the learning rate of the network for a few epochs. In addition, cyclical learning rates are demonstrated on the CIFAR-10 and CIFAR-100 datasets with ResNets, Stochastic Depth networks, and DenseNets, and the ImageNet dataset with the AlexNet and GoogLeNet architectures. These are practical tools for everyone who trains neural networks.

Evaluating the real-world capabilities of AI systems requires grounding benchmark performance in human-interpretable measures of task difficulty. Existing approaches that rely on direct human task completion time annotations are costly, noisy, and difficult to scale across benchmarks. In this work, we propose BRIDGE, a unified psychometric framework that learns the latent difficulty scale from model responses and anchors it to human task completion time. Using a two-parameter logistic Item Response Theory model, we jointly estimate latent task difficulty and model capability from model performance data across multiple benchmarks. We demonstrate that latent task difficulty varies linearly with the logarithm of human completion time, allowing human task completion time to be inferred for new benchmarks from model performance alone. Leveraging this alignment, we forecast frontier model capabilities in terms of human task length and independently reproduce METR's exponential scaling results, with the 50% solvable task horizon doubling approximately every 6 months.

Long-form and real-time talking-head generation remains challenging due to a latency-quality trade-off: inefficient multi-step diffusion prohibits streaming generation, whereas real-time autoregressive approaches suffer from error accumulation and identity drift. To address this drawback, we propose LeapTalk, a novel framework that achieves stable and real-time talking-head generation with a single forward step, scaling to arbitrarily long videos. At the heart of our approach lies a single-step bridge distillation scheme. On the one hand, departing from the conventional noise-to-data paradigm, we introduce a data-to-data transport formulation based on a Brownian bridge. Anchored by a persistent reference, this strategy effectively mitigates identity drift and enhances long-term temporal stability. On the other hand, to enable smooth knowledge transfer from a pre-trained diffusion teacher to the student bridge model, we explore a heterogeneous distillation framework with an SNR-aligned time transformation Φ(τ), which bridges the functional discrepancy between the two models. Moreover, we propose an audio-driven classifier-free guidance mechanism to maintain fine-grained lip synchronization under extreme step reduction. Extensive experiments demonstrate that our method achieves high-fidelity and temporally consistent video generation with only 1 step at up to 200 FPS, significantly outperforming existing approaches in both efficiency and stability. Project Page: https://zhangrongxiang.github.io/leaptalk-page/

We show that learning-rate schedules for large model training behave surprisingly similar to a performance bound from non-smooth convex optimization theory. We provide a bound for the constant schedule with linear cooldown; in particular, the practical benefit of cooldown is reflected in the bound due to the absence of logarithmic terms. Further, we show that this surprisingly close match between optimization theory and practice can be exploited for learning-rate tuning: we achieve noticeable improvements for training 124M and 210M Llama-type models by (i) extending the schedule for continued training with optimal learning-rate, and (ii) transferring the optimal learning-rate across schedules.

Deep ensemble is a simple yet powerful way to improve the performance of deep neural networks. Under this motivation, recent works on mode connectivity have shown that parameters of ensembles are connected by low-loss subspaces, and one can efficiently collect ensemble parameters in those subspaces. While this provides a way to efficiently train ensembles, for inference, multiple forward passes should still be executed using all the ensemble parameters, which often becomes a serious bottleneck for real-world deployment. In this work, we propose a novel framework to reduce such costs. Given a low-loss subspace connecting two modes of a neural network, we build an additional neural network that predicts the output of the original neural network evaluated at a certain point in the low-loss subspace. The additional neural network, which we call a "bridge", is a lightweight network that takes minimal features from the original network and predicts outputs for the low-loss subspace without forward passes through the original network. We empirically demonstrate that we can indeed train such bridge networks and significantly reduce inference costs with the help of bridge networks.

In this paper, we contend that a natural objective of representation learning is to compress and transform the distribution of the data, say sets of tokens, towards a low-dimensional Gaussian mixture supported on incoherent subspaces. The goodness of such a representation can be evaluated by a principled measure, called sparse rate reduction, that simultaneously maximizes the intrinsic information gain and extrinsic sparsity of the learned representation. From this perspective, popular deep network architectures, including transformers, can be viewed as realizing iterative schemes to optimize this measure. Particularly, we derive a transformer block from alternating optimization on parts of this objective: the multi-head self-attention operator compresses the representation by implementing an approximate gradient descent step on the coding rate of the features, and the subsequent multi-layer perceptron sparsifies the features. This leads to a family of white-box transformer-like deep network architectures, named CRATE, which are mathematically fully interpretable. We show, by way of a novel connection between denoising and compression, that the inverse to the aforementioned compressive encoding can be realized by the same class of CRATE architectures. Thus, the so-derived white-box architectures are universal to both encoders and decoders. Experiments show that these networks, despite their simplicity, indeed learn to compress and sparsify representations of large-scale real-world image and text datasets, and achieve performance very close to highly engineered transformer-based models: ViT, MAE, DINO, BERT, and GPT2. We believe the proposed computational framework demonstrates great potential in bridging the gap between theory and practice of deep learning, from a unified perspective of data compression. Code is available at: https://ma-lab-berkeley.github.io/CRATE .

Embodied scene understanding requires not only comprehending visual-spatial information that has been observed but also determining where to explore next in the 3D physical world. Existing 3D Vision-Language (3D-VL) models primarily focus on grounding objects in static observations from 3D reconstruction, such as meshes and point clouds, but lack the ability to actively perceive and explore their environment. To address this limitation, we introduce \textbf{M}ove \textbf{t}o \textbf{U}nderstand (\model), a unified framework that integrates active perception with \textbf{3D} vision-language learning, enabling embodied agents to effectively explore and understand their environment. This is achieved by three key innovations: 1) Online query-based representation learning, enabling direct spatial memory construction from RGB-D frames, eliminating the need for explicit 3D reconstruction. 2) A unified objective for grounding and exploring, which represents unexplored locations as frontier queries and jointly optimizes object grounding and frontier selection. 3) End-to-end trajectory learning that combines Vision-Language-Exploration pre-training over a million diverse trajectories collected from both simulated and real-world RGB-D sequences. Extensive evaluations across various embodied navigation and question-answering benchmarks show that MTU3D outperforms state-of-the-art reinforcement learning and modular navigation approaches by 14\%, 23\%, 9\%, and 2\% in success rate on HM3D-OVON, GOAT-Bench, SG3D, and A-EQA, respectively. \model's versatility enables navigation using diverse input modalities, including categories, language descriptions, and reference images. These findings highlight the importance of bridging visual grounding and exploration for embodied intelligence.

Existing benchmarks and training pipelines for industrial intelligent customer service (ICS) remain misaligned with real-world dialogue requirements, overemphasizing verifiable task success while under-measuring subjective service quality and realistic failure modes, leaving a gap between offline gains and deployable dialogue behavior. We close this gap with a benchmark-to-optimization loop: we first introduce OlaBench, an ICS benchmark spanning retrieval-augmented generation, workflow-based systems, and agentic settings, which evaluates service capability, safety, and latency sensitivity; moreover, motivated by OlaBench results showing state-of-the-art LLMs still fall short, we propose OlaMind, which distills reusable reasoning patterns and service strategies from expert dialogues and applies rubric-aware staged exploration--exploitation reinforcement learning to improve model capability. OlaMind surpasses GPT-5.2 and Gemini 3 Pro on OlaBench (78.72 vs. 70.58/70.84) and, in online A/B tests, delivers an average +23.67% issue resolution and -6.6% human transfer rate versus the baseline, bridging offline gains to deployment. Together, OlaBench and OlaMind advance ICS systems toward more anthropomorphic, professional, and reliable deployment.

On-policy distillation (OPD) provides teacher supervision on states visited by the student, reducing the distribution gap between training and inference. However, in multi-turn agentic tasks, student deviations may accumulate over time, gradually moving the trajectory away from states where teacher guidance remains effective. Our quantitative analysis further shows that high-disagreement states offer promising opportunities for teacher guidance, but determining whether such guidance is beneficial requires examining its effect on subsequent student trajectories. We propose FutureBridge-OPD (FTB), which executes a short teacher bridge at a high disagreement state and uses the resulting student continuation to assess whether the bridge increases the density of positive distillation signals relative to the teacher. On ALFWorld, WebShop, and ScienceWorld, under the main Qwen3-32B teacher to Qwen3-1.7B student setting, FTB outperforms vanilla OPD and TCOD by an average of 16.6 and 7.6 points, respectively, and remains effective across student scales and teacher settings. Our code is publicly available at https://github.com/ChenChiShui/FutureBridge-OPD.

A fundamental question in modern machine learning is why large, over-parameterized models, such as deep neural networks and transformers, tend to generalize well, even when their number of parameters far exceeds the number of training samples. We investigate this phenomenon through the lens of information theory, grounded in universal learning theory. Specifically, we study a Bayesian mixture learner with log-loss and (almost) uniform prior over an expansive hypothesis class. Our key result shows that the learner's regret is not determined by the overall size of the hypothesis class, but rather by the cumulative probability of all models that are close, in Kullback-Leibler divergence distance, to the true data-generating process. We refer to this cumulative probability as the weight of the hypothesis. This leads to a natural notion of model simplicity: simple models are those with large weight and thus require fewer samples to generalize, while complex models have small weight and need more data. This perspective provides a rigorous and intuitive explanation for why over-parameterized models often avoid overfitting: the presence of simple hypotheses allows the posterior to concentrate on them when supported by the data. We further bridge theory and practice by recalling that stochastic gradient descent with Langevin dynamics samples from the correct posterior distribution, enabling our theoretical learner to be approximated using standard machine learning methods combined with ensemble learning. Our analysis yields non-uniform regret bounds and aligns with key practical concepts such as flat minima and model distillation. The results apply broadly across online, batch, and supervised learning settings, offering a unified and principled understanding of the generalization behavior of modern AI systems.

We introduce a general method for improving the convergence rate of gradient-based optimizers that is easy to implement and works well in practice. We demonstrate the effectiveness of the method in a range of optimization problems by applying it to stochastic gradient descent, stochastic gradient descent with Nesterov momentum, and Adam, showing that it significantly reduces the need for the manual tuning of the initial learning rate for these commonly used algorithms. Our method works by dynamically updating the learning rate during optimization using the gradient with respect to the learning rate of the update rule itself. Computing this "hypergradient" needs little additional computation, requires only one extra copy of the original gradient to be stored in memory, and relies upon nothing more than what is provided by reverse-mode automatic differentiation.

Training a neural network requires choosing a suitable learning rate, which involves a trade-off between speed and effectiveness of convergence. While there has been considerable theoretical and empirical analysis of how large the learning rate can be, most prior work focuses only on late-stage training. In this work, we introduce the maximal initial learning rate eta^{ast} - the largest learning rate at which a randomly initialized neural network can successfully begin training and achieve (at least) a given threshold accuracy. Using a simple approach to estimate eta^{ast}, we observe that in constant-width fully-connected ReLU networks, eta^{ast} behaves differently from the maximum learning rate later in training. Specifically, we find that eta^{ast} is well predicted as a power of depth times width, provided that (i) the width of the network is sufficiently large compared to the depth, and (ii) the input layer is trained at a relatively small learning rate. We further analyze the relationship between eta^{ast} and the sharpness lambda_{1} of the network at initialization, indicating they are closely though not inversely related. We formally prove bounds for lambda_{1} in terms of depth times width that align with our empirical results.

This paper studies the black-box optimization task which aims to find the maxima of a black-box function using a static set of its observed input-output pairs. This is often achieved via learning and optimizing a surrogate function with that offline data. Alternatively, it can also be framed as an inverse modeling task that maps a desired performance to potential input candidates that achieve it. Both approaches are constrained by the limited amount of offline data. To mitigate this limitation, we introduce a new perspective that casts offline optimization as a distributional translation task. This is formulated as learning a probabilistic bridge transforming an implicit distribution of low-value inputs (i.e., offline data) into another distribution of high-value inputs (i.e., solution candidates). Such probabilistic bridge can be learned using low- and high-value inputs sampled from synthetic functions that resemble the target function. These synthetic functions are constructed as the mean posterior of multiple Gaussian processes fitted with different parameterizations on the offline data, alleviating the data bottleneck. The proposed approach is evaluated on an extensive benchmark comprising most recent methods, demonstrating significant improvement and establishing a new state-of-the-art performance. Our code is publicly available at https://github.com/cuong-dm/ROOT.

Recent work on distillation transfers the capabilities of large models to smaller ones often by updating the latter's parameters, through teacher forcing, on-policy distillation, and related training-time methods. In this paper, we ask whether such transfer can instead occur at test time. We study strong-to-weak scaffolding: whether a stronger builder model can construct inference-time harnesses that help a weaker target model solve tasks more reliably without any parameter updates. Using four representative Theory-of-Mind benchmarks, each builder model uses 5% of the data as a validation set to iteratively refine its harness over multiple rounds, after which the finalized harness is evaluated on the full test set. Empirically, this form of test-time capability transfer is highly effective, nearly doubling average target-model performance from 0.49 to 0.91. Our analysis shows that the gains come primarily from offloading unstable model reasoning into deterministic code, benchmark-specific routing, and strict answer-format enforcement, rather than from encouraging the target model to reason more extensively or sample more broadly. We further find that builder-model reasoning effort improves harness quality monotonically, platform effects are modest relative to the builder model's own capability, and weaker target models receive the largest gains. These results suggest that inference-time harness design is an important complement to conventional training-time distillation, enabling strong models to transfer cognitive structure to weaker models without retraining.

We introduce Vision Bridge Transformer (ViBT), a large-scale instantiation of Brownian Bridge Models designed for conditional generation. Unlike traditional diffusion models that transform noise into data, Bridge Models directly model the trajectory between inputs and outputs, creating an efficient data-to-data translation paradigm. By scaling these models to 20B and 1.3B parameters, we demonstrate their effectiveness for image and video translation tasks. To support this scale, we adopt a Transformer architecture and propose a variance-stabilized velocity-matching objective for robust training. Together, these advances highlight the power of scaling Bridge Models for instruction-based image editing and complex video translation.

Autonomous AI agents tackling Long Horizon Tasks depend on marketplace skills that are certified one at a time: a scanner returns a safety verdict for each skill and declares the ecosystem safe if every package passes. We show that this assumption fails under skill composition. A skill may pass the per-skill scanner individually yet participate in a risky composition when an agent connects its outputs, capabilities, or side effects with those of other scanner-passing skills. This makes skill composition risk a path level property rather than a node level property, explaining why existing skill scanners that inspect individual packages achieve limited interception. To study this threat, we present CompoSkill, a framework that constructs skill composition attacks through a dual attacker system. The white-box attacker knows the victim's installed skill pool and directly injects explicit skill-id sequences; the black-box attacker knows only a role profile, downloads the top marketplace skills for that scenario, builds a Skill Composition Graph, and searches for high risk chains whose implicit lures never name skill identifiers. We further construct CompoSkill-Bench, a benchmark of 1,140 records built from long-horizon professional workflows across five threats and six scenarios on OpenClaw and Nanobot. CompoSkill achieves risk Chain Formation Rates (CFR) up to 83.3% in the white box setting and 80.6% in the black box setting, while existing skill scanners block only a limited fraction of the risky compositions. Finally, we observe a bridge-bonus-then-hop-decay pattern: a bridge skill can increase attack success, but Attack Success Rate (ASR) decreases once additional hops make the risk chain longer than three skills. These results expose a systematic gap in single skill certification for autonomous AI agents.

Expressive generative policies such as diffusion and flow models are appealing for MaxEnt online reinforcement learning because of their ability to model multimodal and highly non-Gaussian action distributions. However, training effective soft generative policies faces two obstacles that often arise together. First, marginal action densities are often unavailable, so existing methods typically rely on entropy bounds, heuristic proxies or approximations. Second, iterative shared-parameter samplers raise inference cost and require backpropagation through time over repeated network evaluations, increasing memory cost and destabilizing policy optimization. These obstacles motivate us to seek a generative policy that exposes a tractable MaxEnt objective while requiring only a single sampled actor forward pass for action generation. To this end, we propose soft generative actor-critic (SoftGAC), whose actor defines a stochastic bridge from a fixed base latent to a terminal action latent in pre-tanh space. This structured bridge allows us to lift the MaxEnt objective as an analytically tractable path-wise relative-entropy objective against a high-entropy reference process. In practical finite-step implementation, this relative entropy reduces exactly to sampled transition control energy and thus provides principled soft regularization. Moreover, we keep the single-pass actor lightweight by using small step-specific bridge transitions, each evaluated only once per sampled action, while maintaining a parameter budget comparable to strong actor baselines. Extensive experiments on challenging continuous-control benchmarks show that SoftGAC attains higher or competitive returns than strong generative policy baselines, including diffusion and flow-matching policies, while staying in the low-latency regime of one-pass actors and showing considerable improvements in the compute-return tradeoff.

Normalization layers have recently experienced a renaissance in the deep reinforcement learning and continual learning literature, with several works highlighting diverse benefits such as improving loss landscape conditioning and combatting overestimation bias. However, normalization brings with it a subtle but important side effect: an equivalence between growth in the norm of the network parameters and decay in the effective learning rate. This becomes problematic in continual learning settings, where the resulting effective learning rate schedule may decay to near zero too quickly relative to the timescale of the learning problem. We propose to make the learning rate schedule explicit with a simple re-parameterization which we call Normalize-and-Project (NaP), which couples the insertion of normalization layers with weight projection, ensuring that the effective learning rate remains constant throughout training. This technique reveals itself as a powerful analytical tool to better understand learning rate schedules in deep reinforcement learning, and as a means of improving robustness to nonstationarity in synthetic plasticity loss benchmarks along with both the single-task and sequential variants of the Arcade Learning Environment. We also show that our approach can be easily applied to popular architectures such as ResNets and transformers while recovering and in some cases even slightly improving the performance of the base model in common stationary benchmarks.

Bridge models have been investigated in speech enhancement but are mostly single-task, with constrained general speech restoration (GSR) capability. In this work, we propose VoiceBridge, a one-step latent bridge model (LBM) for GSR, capable of efficiently reconstructing 48 kHz fullband speech from diverse distortions. To inherit the advantages of data-domain bridge models, we design an energy-preserving variational autoencoder, enhancing the waveform-latent space alignment over varying energy levels. By compressing waveform into continuous latent representations, VoiceBridge models~various GSR tasks with a~single latent-to-latent generative process backed by a scalable transformer. To alleviate the challenge of reconstructing the high-quality target from distinctively different low-quality priors, we propose a joint neural prior for GSR, uniformly reducing the burden of the LBM in diverse tasks. Building upon these designs, we further investigate bridge training objective by jointly tuning LBM, decoder and discriminator together, transforming the model from a denoiser to generator and enabling one-step GSR without distillation. Extensive validation across in-domain (e.g., denoising and super-resolution) and out-of-domain tasks (e.g., refining synthesized speech) and datasets demonstrates the superior performance of VoiceBridge. Demos: https://VoiceBridgedemo.github.io/.

Diffusion models excel in noise-to-data generation tasks, providing a mapping from a Gaussian distribution to a more complex data distribution. However they struggle to model translations between complex distributions, limiting their effectiveness in data-to-data tasks. While Bridge Matching (BM) models address this by finding the translation between data distributions, their application to time-correlated data sequences remains unexplored. This is a critical limitation for video generation and manipulation tasks, where maintaining temporal coherence is particularly important. To address this gap, we propose Time-Correlated Video Bridge Matching (TCVBM), a framework that extends BM to time-correlated data sequences in the video domain. TCVBM explicitly models inter-sequence dependencies within the diffusion bridge, directly incorporating temporal correlations into the sampling process. We compare our approach to classical methods based on bridge matching and diffusion models for three video-related tasks: frame interpolation, image-to-video generation, and video super-resolution. TCVBM achieves superior performance across multiple quantitative metrics, demonstrating enhanced generation quality and reconstruction fidelity.

Sharing context between LLMs in a multi-model system requires the receiving model to prefill the shared prefix because KV caches are model-specific. Recent closed-form cross-model KV transfer, hereafter Full-Head Mapping, avoids this replay by fitting a training-free affine mapper from source to target caches. However, its full-head design maps each target KV head from every source KV head in the selected layers, making transfer quality sensitive to architectural differences and causing mapper storage and application cost to grow with layer support. To this end, we introduce CacheBridge, which co-designs architecture-indexed mapper support, attention-aligned calibration, and bounded mapper construction while retaining a closed-form affine interface for online deployment. CacheBridge restricts each target head to a matched source head, weights reconstruction errors by causal attention sensitivity, and uses a fused GPU kernel to construct weighted sufficient statistics without materializing full observation tensors. Across three transfer directions, CacheBridge recovers the two Ministral 3 transfer directions where Full-Head Mapping loses substantial accuracy while preserving 99.83\% mean target retention on Qwen3. On Qwen3 14Bto32B, it reduces mapper storage by 8times, accelerates application by up to 3.0times, matches \fullhead with one tenth of the calibration data, and reduces 500-sequence construction from 92.63 to 8.63 seconds (10.7times).

When an agent encounters a continual stream of new tasks in the lifelong learning setting, it leverages the knowledge it gained from the earlier tasks to help learn the new tasks better. In such a scenario, identifying an efficient knowledge representation becomes a challenging problem. Most research works propose to either store a subset of examples from the past tasks in a replay buffer, dedicate a separate set of parameters to each task or penalize excessive updates over parameters by introducing a regularization term. While existing methods employ the general task-agnostic stochastic gradient descent update rule, we propose a task-aware optimizer that adapts the learning rate based on the relatedness among tasks. We utilize the directions taken by the parameters during the updates by accumulating the gradients specific to each task. These task-based accumulated gradients act as a knowledge base that is maintained and updated throughout the stream. We empirically show that our proposed adaptive learning rate not only accounts for catastrophic forgetting but also allows positive backward transfer. We also show that our method performs better than several state-of-the-art methods in lifelong learning on complex datasets with a large number of tasks.

Schrödinger bridge (SB) learns stochastic transport between prescribed initial and target distributions. When the initial distribution shifts at test time, the learned dynamics can fail to recover the target distribution. We introduce the Distributionally Robust Schrödinger Bridge (DRSB), which learns a single controller that accounts for uncertainty in the initial distribution. The DRSB objective consists of control energy and a KL penalty between the resulting terminal distribution and the target distribution. DRSB seeks a single controller that minimizes the worst-case value of this objective as the initial distribution varies within an ambiguity set around the nominal distribution. We derive an exact variational formulation of this objective and connect its fixed-terminal-cost subproblem to stochastic optimal control and distributionally robust optimization. This formulation motivates an alternating algorithm that updates the adversarial initial distribution, estimates the terminal log-density ratio, and trains the controller. We develop Wasserstein and Sinkhorn variants using stochastic control optimality conditions to approximate the gradients required for adversarial updates. Experiments on two-dimensional transport tasks and image-to-image translation show improved robustness to input perturbations relative to standard SB, with a tradeoff in nominal performance. On Gaussian mixture transport, Sinkhorn DRSB also achieves lower mean sliced Wasserstein distance than fixed-level noise augmentation at both tested unseen noise levels.

In systems built on Robot Operating System 2 (ROS 2) and using Data Distribution Service (DDS), a single network-impaired or throttled subscriber on a RELIABLE topic can cause backpressure that degrades throughput and latency for all other subscribers, including safety-critical ones sharing the publisher, because the publisher's DDS writer can no longer accept new samples. We present Adaptive Bridge, a proxy-based layer that decouples critical subscribers from degraded or noncritical ones, thereby isolating the critical path through topic splitting and dynamic rate control. The proxy acts as a middleman and subscribes to the original topic and republishes the messages to two independent DDS writers: one RELIABLE writer for critical nodes and one BEST EFFORT writer for noncritical or degraded nodes, thus isolating the degraded nodes and safeguarding the publisher and critical nodes from backpressure. A probe-based classifier actively monitors subscriber health through sampling with hysteresis and adjusts subscriber rate limits in real time. We evaluate the system under a Gilbert-Elliott bursty wireless loss model using a reproducible Docker-based harness. The results show that using the Adaptive Bridge in our evaluation harness reduces the critical subscriber tail p95 latency from up to 15 s to 1.55 ms across all impairment severities while preserving the publisher's configured throughput.

Speech carries more information than just words: a child's voice, a fearful tone, or a noisy background should all lead a sufficiently competent spoken-dialogue assistant to different replies. Current Speech Language Models (SLMs) can recognize such paralinguistic cues but often ignore them in open-ended dialogue. We observe that a simple paralinguistic instruction scaffold at the inference stage narrows this perception-behavior gap, suggesting that the relevant cues are already latent in the model. Such scaffolds, however, remain brittle under multi-turn context and competing instructions. Therefore, we propose ParaBridge, an on-policy self-distillation method that turns a brittle inference-time scaffold into stable model behavior. During training, the scaffold serves only as a temporary privileged view; the scaffold-free model rolls out its own response, while the scaffolded view supplies dense, full-vocabulary next-token targets along its trajectory. This supervision teaches when non-lexical cues should affect the reply without the need for curated dialogues, human labels, or external reward models. On Qwen3-Omni-thinking, ParaBridge raises scaffold-free VoxSafeBench SAR from 14.6% to 40.3% and improves EchoMind average rating from 3.27 to 3.92. It also preserves general ability, with MMAU-Pro, VoiceBench, and GPQA all within 0.4 points of the original model. Beyond the training distribution, ParaBridge generalizes to unseen paralinguistic cues, transfers from safety-oriented training to empathy-oriented dialogue, and works on a different SLM backbone.

Diffusion models are a powerful class of generative models which simulate stochastic differential equations (SDEs) to generate data from noise. While diffusion models have achieved remarkable progress, they have limitations in unpaired image-to-image (I2I) translation tasks due to the Gaussian prior assumption. Schr\"{o}dinger Bridge (SB), which learns an SDE to translate between two arbitrary distributions, have risen as an attractive solution to this problem. Yet, to our best knowledge, none of SB models so far have been successful at unpaired translation between high-resolution images. In this work, we propose Unpaired Neural Schr\"{o}dinger Bridge (UNSB), which expresses the SB problem as a sequence of adversarial learning problems. This allows us to incorporate advanced discriminators and regularization to learn a SB between unpaired data. We show that UNSB is scalable and successfully solves various unpaired I2I translation tasks. Code: https://github.com/cyclomon/UNSB

We uncover ELR collapse in language model pretraining: learning rate (LR) and parameter norm govern loss dynamics primarily through their ratio, the effective learning rate (ELR). When ELR is matched across runs, their loss trajectories collapse throughout training despite substantially different LRs and parameter norms. Across optimizers, architectures, datasets, and model scales, mean collapse errors are typically a few x 10^-3, below the seed-to-seed variation measured in a representative configuration. Systematic ablations identify normalization design and the timescale of LR-norm variation as key determinants of collapse precision. Controlled interventions further show that weight decay and Hyperball shape loss dynamics primarily through the ELR schedules they induce. Replacing LR with ELR enables a fitted functional scaling law (FSL) to transfer across norm-control methods. The resulting ELR-based FSL also explains delayed acceleration, a recurring effect of norm control. Together, these results establish ELR as a common coordinate linking LR scheduling, norm control, and loss dynamics.

We establish a fundamental connection between score-based diffusion models and non-equilibrium thermodynamics by deriving performance limits based on entropy rates. Our main theoretical contribution is a lower bound on the negative log-likelihood of the data that relates model performance to entropy rates of diffusion processes. We numerically validate this bound on a synthetic dataset and investigate its tightness. By building a bridge to entropy rates - system, intrinsic, and exchange entropy - we provide new insights into the thermodynamic operation of these models, drawing parallels to Maxwell's demon and implications for thermodynamic computing hardware. Our framework connects generative modeling performance to fundamental physical principles through stochastic thermodynamics.

Scaling limits, such as infinite-width limits, serve as promising theoretical tools to study large-scale models. However, it is widely believed that existing infinite-width theory does not faithfully explain the behavior of practical networks, especially those trained in standard parameterization (SP) meaning He initialization with a global learning rate. For instance, existing theory for SP predicts instability at large learning rates and vanishing feature learning at stable ones. In practice, however, optimal learning rates decay slower than theoretically predicted and networks exhibit both stable training and non-trivial feature learning, even at very large widths. Here, we show that this discrepancy is not fully explained by finite-width phenomena. Instead, we find a resolution through a finer-grained analysis of the regime previously considered unstable and therefore uninteresting. In particular, we show that, under cross-entropy (CE) loss, the unstable regime comprises two distinct sub-regimes: a catastrophically unstable regime and a more benign controlled divergence regime, where logits diverge but gradients and activations remain stable. Moreover, under large learning rates at the edge of the controlled divergence regime, there exists a well-defined infinite width limit where features continue to evolve in all the hidden layers. In experiments across optimizers, architectures, and data modalities, we validate that neural networks operate in this controlled divergence regime under CE loss but not under MSE loss. Our empirical evidence suggests that width-scaling considerations are surprisingly useful for predicting empirically maximal stable learning rate exponents which provide useful guidance on optimal learning rate exponents. Finally, our analysis clarifies the effectiveness and limitations of recently proposed layerwise learning rate scaling for standard initialization.

Nearly all real world tasks are inherently partially observable, necessitating the use of memory in Reinforcement Learning (RL). Most model-free approaches summarize the trajectory into a latent Markov state using memory models borrowed from Supervised Learning (SL), even though RL tends to exhibit different training and efficiency characteristics. Addressing this discrepancy, we introduce Fast and Forgetful Memory, an algorithm-agnostic memory model designed specifically for RL. Our approach constrains the model search space via strong structural priors inspired by computational psychology. It is a drop-in replacement for recurrent neural networks (RNNs) in recurrent RL algorithms, achieving greater reward than RNNs across various recurrent benchmarks and algorithms without changing any hyperparameters. Moreover, Fast and Forgetful Memory exhibits training speeds two orders of magnitude faster than RNNs, attributed to its logarithmic time and linear space complexity. Our implementation is available at https://github.com/proroklab/ffm.

Large language models (LLMs) exhibit impressive capabilities across a wide range of tasks, yet the choice of which model to use often involves a trade-off between performance and cost. More powerful models, though effective, come with higher expenses, while less capable models are more cost-effective. To address this dilemma, we propose several efficient router models that dynamically select between a stronger and a weaker LLM during inference, aiming to optimize the balance between cost and response quality. We develop a training framework for these routers leveraging human preference data and data augmentation techniques to enhance performance. Our evaluation on widely-recognized benchmarks shows that our approach significantly reduces costs-by over 2 times in certain cases-without compromising the quality of responses. Interestingly, our router models also demonstrate significant transfer learning capabilities, maintaining their performance even when the strong and weak models are changed at test time. This highlights the potential of these routers to provide a cost-effective yet high-performance solution for deploying LLMs.

The theoretical landscape of federated learning (FL) undergoes rapid evolution, but its practical application encounters a series of intricate challenges, and hyperparameter optimization is one of these critical challenges. Amongst the diverse adjustments in hyperparameters, the adaptation of the learning rate emerges as a crucial component, holding the promise of significantly enhancing the efficacy of FL systems. In response to this critical need, this paper presents FedHyper, a novel hypergradient-based learning rate adaptation algorithm specifically designed for FL. FedHyper serves as a universal learning rate scheduler that can adapt both global and local rates as the training progresses. In addition, FedHyper not only showcases unparalleled robustness to a spectrum of initial learning rate configurations but also significantly alleviates the necessity for laborious empirical learning rate adjustments. We provide a comprehensive theoretical analysis of FedHyper's convergence rate and conduct extensive experiments on vision and language benchmark datasets. The results demonstrate that FEDHYPER consistently converges 1.1-3x faster than FedAvg and the competing baselines while achieving superior final accuracy. Moreover, FedHyper catalyzes a remarkable surge in accuracy, augmenting it by up to 15% compared to FedAvg under suboptimal initial learning rate settings.

Modern language models are likely to be updated throughout their lifetime rather than trained once and frozen. Each update therefore participates in a recurring cycle: decide which experience to learn from, understand what that update changes, and remain capable of learning from what comes next. We show that these challenges are governed by the same evolving update--behavior interaction. We derive a token- and layer-wise decomposition of how learning from one token changes another prediction. By separating the softmax force, shared readout geometry, and residual connections, it exposes two interaction channels and yields a forward-computable approximation. Following this interaction through time reveals a unified picture of continual adaptation. Positive interaction identifies useful experience; negative interaction produces either concentrated collision or accumulated erosion; over longer horizons, updates reshape the shared geometry mediating future learning signals, reducing their transmission. These predictions lead to effective data selection, mechanism-specific controls for interference, and a readout-based diagnostic of future learnability whose degradation predicts the benefit of restoring the readout. Across models and training regimes, the same local interaction thus explains both what an update changes now and how learning today changes what can be learned tomorrow. This view connects data attribution, forgetting, and plasticity loss as distinct regimes of the same evolving learning dynamics.

Multimodal large language models (MLLMs) extend the success of language models to visual understanding, and recent efforts have sought to build unified MLLMs that support both understanding and generation. However, constructing such models remains challenging: hybrid approaches combine continuous embeddings with diffusion or flow-based objectives, producing high-quality images but breaking the autoregressive paradigm, while pure autoregressive approaches unify text and image prediction over discrete visual tokens but often face trade-offs between semantic alignment and pixel-level fidelity. In this work, we present Bridge, a pure autoregressive unified MLLM that augments pre-trained visual understanding models with generative ability through a Mixture-of-Transformers architecture, enabling both image understanding and generation within a single next-token prediction framework. To further improve visual generation fidelity, we propose a semantic-to-pixel discrete representation that integrates compact semantic tokens with fine-grained pixel tokens, achieving strong language alignment and precise description of visual details with only a 7.9% increase in sequence length. Extensive experiments across diverse multimodal benchmarks demonstrate that Bridge achieves competitive or superior results in both understanding and generation benchmarks, while requiring less training data and reduced training time compared to prior unified MLLMs.

Reinforcement learning with verifiable rewards, and Group Relative Policy Optimization (GRPO) in particular, is now run routinely on a supervised checkpoint in the hope of producing a stronger agent. We ask whether it adds skill to a small language and vision-language model web agent at the 4B to 8B scale, or whether it mostly reshapes behavior the supervised model already has. Across a control grid of 18 runs that varies learning rate, KL weight, seed, initialization, and clipping, no configuration credibly improves the success rate of a strong supervised baseline on tasks the agent has largely mastered. On the text track, moderate to high learning rates make it credibly worse. The null holds under paired testing, 25 evaluation seeds, 6 training seeds, changes to the recipe, both text and Set-of-Marks screenshot observations, and scaling the backbone to 8B; the credible harm is a text-track finding and is only nominal under Set-of-Marks. To show that the null reflects the setting and not a broken pipeline, we run the identical harness, reward, and recipe on tasks whose reward is reachable by sampling, and there the success rate rises by 22 points with a paired interval that excludes zero. GRPO therefore helps only when there is headroom to climb, meaning the sampled policy already succeeds more often than the greedy one. We then explain the failure. A middle learning rate degrades the agent and a high one collapses it, and the two regimes form a double dissociation: grafting localizes the degrade regime to the attention and MLP blocks, while the collapse regime cannot be traced to any single group, and the embedding change that dominates the weight movement is causally inert. At 4B, effective rank in the late layers tracks capability in both directions; at 8B the two come apart. This coupling is specific to the smaller model, so we report it as scale-dependent.

Large language models (LLMs) are trained for downstream tasks by updating their parameters (e.g., via RL). However, updating parameters forces them to absorb task-specific information, which can result in catastrophic forgetting and loss of plasticity. In contrast, in-context learning with fixed LLM parameters can cheaply and rapidly adapt to task-specific requirements (e.g., prompt optimization), but cannot by itself typically match the performance gains available through updating LLM parameters. There is no good reason for restricting learning to being in-context or in-weights. Moreover, humans also likely learn at different time scales (e.g., System 1 vs 2). To this end, we introduce a fast-slow learning framework for LLMs, with model parameters as "slow" weights and optimized context as "fast" weights. These fast "weights" can learn from textual feedback to absorb the task-specific information, while allowing slow weights to stay closer to the base model and persist general reasoning behaviors. Fast-Slow Training (FST) is up to 3x more sample-efficient than only slow learning (RL) across reasoning tasks, while consistently reaching a higher performance asymptote. Moreover, FST-trained models remain closer to the base LLM (up to 70% less KL divergence), resulting in less catastrophic forgetting than RL-training. This reduced drift also preserves plasticity: after training on one task, FST trained models adapt more effectively to a subsequent task than parameter-only trained models. In continual learning scenarios, where task domains change on the fly, FST continues to acquire each new task while parameter-only RL stalls.

We show the formal equivalence of linearised self-attention mechanisms and fast weight controllers from the early '90s, where a ``slow" neural net learns by gradient descent to program the ``fast weights" of another net through sequences of elementary programming instructions which are additive outer products of self-invented activation patterns (today called keys and values). Such Fast Weight Programmers (FWPs) learn to manipulate the contents of a finite memory and dynamically interact with it. We infer a memory capacity limitation of recent linearised softmax attention variants, and replace the purely additive outer products by a delta rule-like programming instruction, such that the FWP can more easily learn to correct the current mapping from keys to values. The FWP also learns to compute dynamically changing learning rates. We also propose a new kernel function to linearise attention which balances simplicity and effectiveness. We conduct experiments on synthetic retrieval problems as well as standard machine translation and language modelling tasks which demonstrate the benefits of our methods.

As language models take a growing role in AI development, a natural aspiration is for them to reflect on their own learning process, as humans do, and use that reflection to improve themselves. At the same time, these models have an advantage that human learners lack, since training leaves parameter-level traces that can, in principle, be inspected directly. However, current models cannot decode these traces into an explicit account of what they have learned. To this end, we introduce the Imprint Reader, a model trained with Semantic Mount-and-Read Tuning (SaRT) to describe frozen weight updates. SMaRT mounts each update onto the Reader and uses an anchor-free meta-query to elicit a natural-language description, while no-change and random-perturbation controls discourage unsupported claims. On held-out updates, the joint Reader reaches judge-based Pass@100 of 2% for knowledge and 16% for behavior. These results demonstrate the feasibility of natural-language readout while pointing to reliability across updates as the next step. Beyond free-form generation, the Reader provides a differentiable proxy for the gap between a specified target behavior and a candidate weight update. Its coordinate-aligned gradients support intervention through MetaEdit. At a 0.5% pruning rate, Reader-guided selection raises measured harmful-prompt refusal from 57.9% to 64.1% under a safety-maintenance target. Using behavior descriptions without target-task training data, MetaEdit increases the frequency of backtracking and sub-goal expressions in mathematical reasoning traces and raises BFCL Overall from 41.69% to 44.60%.

Temporal context is essential for robotic manipulation because such tasks are inherently non-Markovian, yet mainstream VLA models typically overlook it and struggle with long-horizon, temporally dependent tasks. Cognitive science suggests that humans rely on working memory to buffer short-lived representations for immediate control, while the hippocampal system preserves verbatim episodic details and semantic gist of past experience for long-term memory. Inspired by these mechanisms, we propose MemoryVLA, a Cognition-Memory-Action framework for long-horizon robotic manipulation. A pretrained VLM encodes the observation into perceptual and cognitive tokens that form working memory, while a Perceptual-Cognitive Memory Bank stores low-level details and high-level semantics consolidated from it. Working memory retrieves decision-relevant entries from the bank, adaptively fuses them with current tokens, and updates the bank by merging redundancies. Using these tokens, a memory-conditioned diffusion action expert yields temporally aware action sequences. We evaluate MemoryVLA on 150+ simulation and real-world tasks across three robots. On SimplerEnv-Bridge, Fractal, and LIBERO-5 suites, it achieves 71.9%, 72.7%, and 96.5% success rates, respectively, all outperforming state-of-the-art baselines CogACT and pi-0, with a notable +14.6 gain on Bridge. On 12 real-world tasks spanning general skills and long-horizon temporal dependencies, MemoryVLA achieves 84.0% success rate, with long-horizon tasks showing a +26 improvement over state-of-the-art baseline. Project Page: https://shihao1895.github.io/MemoryVLA

We consider dense, associative neural-networks trained with no supervision and we investigate their computational capabilities analytically, via a statistical-mechanics approach, and numerically, via Monte Carlo simulations. In particular, we obtain a phase diagram summarizing their performance as a function of the control parameters such as the quality and quantity of the training dataset and the network storage, valid in the limit of large network size and structureless datasets. Moreover, we establish a bridge between macroscopic observables standardly used in statistical mechanics and loss functions typically used in the machine learning. As technical remarks, from the analytic side, we implement large deviations and stability analysis within Guerra's interpolation to tackle the not-Gaussian distributions involved in the post-synaptic potentials while, from the computational counterpart, we insert Plefka approximation in the Monte Carlo scheme, to speed up the evaluation of the synaptic tensors, overall obtaining a novel and broad approach to investigate neural networks in general.

Integrating image generation and understanding into a single framework has become a pivotal goal in the multimodal domain. However, how understanding can effectively assist generation has not been fully explored. Unlike previous works that focus on leveraging reasoning abilities and world knowledge from understanding models, this paper introduces a novel perspective: leveraging understanding to enhance the fidelity and detail richness of generated images. To this end, we propose Forge-and-Quench, a new unified framework that puts this principle into practice. In the generation process of our framework, an MLLM first reasons over the entire conversational context, including text instructions, to produce an enhanced text instruction. This refined instruction is then mapped to a virtual visual representation, termed the Bridge Feature, via a novel Bridge Adapter. This feature acts as a crucial link, forging insights from the understanding model to quench and refine the generation process. It is subsequently injected into the T2I backbone as a visual guidance signal, alongside the enhanced text instruction that replaces the original input. To validate this paradigm, we conduct comprehensive studies on the design of the Bridge Feature and Bridge Adapter. Our framework demonstrates exceptional extensibility and flexibility, enabling efficient migration across different MLLM and T2I models with significant savings in training overhead, all without compromising the MLLM's inherent multimodal understanding capabilities. Experiments show that Forge-and-Quench significantly improves image fidelity and detail across multiple models, while also maintaining instruction-following accuracy and enhancing world knowledge application. Models and codes are available at https://github.com/YanbingZeng/Forge-and-Quench.

Large language models (LLMs) have achieved remarkable progress on mathematical tasks through Chain-of-Thought (CoT) reasoning. However, existing mathematical CoT datasets often suffer from Thought Leaps due to experts omitting intermediate steps, which negatively impacts model learning and generalization. We propose the CoT Thought Leap Bridge Task, which aims to automatically detect leaps and generate missing intermediate reasoning steps to restore the completeness and coherence of CoT. To facilitate this, we constructed a specialized training dataset called ScaleQM+, based on the structured ScaleQuestMath dataset, and trained CoT-Bridge to bridge thought leaps. Through comprehensive experiments on mathematical reasoning benchmarks, we demonstrate that models fine-tuned on bridged datasets consistently outperform those trained on original datasets, with improvements of up to +5.87% on NuminaMath. Our approach effectively enhances distilled data (+3.02%) and provides better starting points for reinforcement learning (+3.1%), functioning as a plug-and-play module compatible with existing optimization techniques. Furthermore, CoT-Bridge demonstrate improved generalization to out-of-domain logical reasoning tasks, confirming that enhancing reasoning completeness yields broadly applicable benefits.

Low-Rank Adaptive Residual Connections (LARC) give a frozen model a compact numerical state that can learn from feedback. The map h+BAh adds a low-rank correction to a hidden representation. A slow state ρ learns starting factors across tasks; a private fast state Φ copies them, changes with feedback, and resets to the trained initialization. This report specifies an input-side realization of the numerical policy carrier in Memory-Mediated Learning Architecture and examines its factor-space dynamics and learning lifetime. We study a rank-4 input residual with 12,288 trainable parameters on a frozen MiniCPM5-1B-SFT substrate. In a four-candidate program-selection task, two feedback-gradient steps reduce expected query execution error by 24.65 and 36.65 percentage points relative to resetting to the respective trained static and post-adaptation initializations. These development results cover 16 parameter groups and three paired training seeds. A direct support-loss selection rule is much more accurate, reaching 0.78125% error. In a repository-balanced chronological replay of public continuous-integration jobs, retaining online updates raises half-Brier loss from 0.1274 to 0.1808. A fixed follow-up intervention records same-batch non-descent and inconsistent future benefit from shrinking updates. Together, the algebra and measurements distinguish residual capacity, adaptation relative to a starting point, and usefulness on later decisions.

Recent advancements in diffusion-based imitation learning, which show impressive performance in modeling multimodal distributions and training stability, have led to substantial progress in various robot learning tasks. In visual navigation, previous diffusion-based policies typically generate action sequences by initiating from denoising Gaussian noise. However, the target action distribution often diverges significantly from Gaussian noise, leading to redundant denoising steps and increased learning complexity. Additionally, the sparsity of effective action distributions makes it challenging for the policy to generate accurate actions without guidance. To address these issues, we propose a novel, unified visual navigation framework leveraging the denoising diffusion bridge models named NaviBridger. This approach enables action generation by initiating from any informative prior actions, enhancing guidance and efficiency in the denoising process. We explore how diffusion bridges can enhance imitation learning in visual navigation tasks and further examine three source policies for generating prior actions. Extensive experiments in both simulated and real-world indoor and outdoor scenarios demonstrate that NaviBridger accelerates policy inference and outperforms the baselines in generating target action sequences. Code is available at https://github.com/hren20/NaiviBridger.

The learning rate (LR) schedule is one of the most important hyper-parameters needing careful tuning in training DNNs. However, it is also one of the least automated parts of machine learning systems and usually costs significant manual effort and computing. Though there are pre-defined LR schedules and optimizers with adaptive LR, they introduce new hyperparameters that need to be tuned separately for different tasks/datasets. In this paper, we consider the question: Can we automatically tune the LR over the course of training without human involvement? We propose an efficient method, AutoLRS, which automatically optimizes the LR for each training stage by modeling training dynamics. AutoLRS aims to find an LR applied to every tau steps that minimizes the resulted validation loss. We solve this black-box optimization on the fly by Bayesian optimization (BO). However, collecting training instances for BO requires a system to evaluate each LR queried by BO's acquisition function for tau steps, which is prohibitively expensive in practice. Instead, we apply each candidate LR for only tau'lltau steps and train an exponential model to predict the validation loss after tau steps. This mutual-training process between BO and the loss-prediction model allows us to limit the training steps invested in the BO search. We demonstrate the advantages and the generality of AutoLRS through extensive experiments of training DNNs for tasks from diverse domains using different optimizers. The LR schedules auto-generated by AutoLRS lead to a speedup of 1.22times, 1.43times, and 1.5times when training ResNet-50, Transformer, and BERT, respectively, compared to the LR schedules in their original papers, and an average speedup of 1.31times over state-of-the-art heavily-tuned LR schedules.

Deep learning practitioners often operate on a computational and monetary budget. Thus, it is critical to design optimization algorithms that perform well under any budget. The linear learning rate schedule is considered the best budget-aware schedule, as it outperforms most other schedules in the low budget regime. On the other hand, learning rate schedules -- such as the 30-60-90 step schedule -- are known to achieve high performance when the model can be trained for many epochs. Yet, it is often not known a priori whether one's budget will be large or small; thus, the optimal choice of learning rate schedule is made on a case-by-case basis. In this paper, we frame the learning rate schedule selection problem as a combination of i) selecting a profile (i.e., the continuous function that models the learning rate schedule), and ii) choosing a sampling rate (i.e., how frequently the learning rate is updated/sampled from this profile). We propose a novel profile and sampling rate combination called the Reflected Exponential (REX) schedule, which we evaluate across seven different experimental settings with both SGD and Adam optimizers. REX outperforms the linear schedule in the low budget regime, while matching or exceeding the performance of several state-of-the-art learning rate schedules (linear, step, exponential, cosine, step decay on plateau, and OneCycle) in both high and low budget regimes. Furthermore, REX requires no added computation, storage, or hyperparameters.

We explore catastrophic forgetting in the context of large pre-trained models. By considering forgetting as a geometric problem in the input space of each weight matrix, we uncover a natural retention objective under which updates produced by gradient-based optimizers are suboptimal. Following this observation, we propose Local Support Learning (LSL), a general-purpose framework that augments gradient-based training for retention of prior capabilities without access to prior data. During a new learning phase, LSL pairs two components with distinct roles: a standard weight adapter, trained as usual to minimize the loss, and a gating function that enables the adapter only on input activations from its own training distribution, making the update local to that distribution. The key challenge is that this gate must route data from all learning phases while training only on data from the current one. We address this with a gate based on a Gaussian Mixture Model (GMM), whose likelihood decays rapidly away from its training data, giving it a natural tendency to stay closed on data from prior phases. We show that this post-training approach can resolve forgetting in LLMs of up to 7 billion parameters, retaining both pretrained and finetuned capabilities across multiple training phases, while being efficient in memory and compute, robust to hyperparameter choice, and showing scaling potential.

Scaling high-quality tutoring remains a major challenge in education. Due to growing demand, many platforms employ novice tutors who, unlike experienced educators, struggle to address student mistakes and thus fail to seize prime learning opportunities. Our work explores the potential of large language models (LLMs) to close the novice-expert knowledge gap in remediating math mistakes. We contribute Bridge, a method that uses cognitive task analysis to translate an expert's latent thought process into a decision-making model for remediation. This involves an expert identifying (A) the student's error, (B) a remediation strategy, and (C) their intention before generating a response. We construct a dataset of 700 real tutoring conversations, annotated by experts with their decisions. We evaluate state-of-the-art LLMs on our dataset and find that the expert's decision-making model is critical for LLMs to close the gap: responses from GPT4 with expert decisions (e.g., "simplify the problem") are +76% more preferred than without. Additionally, context-sensitive decisions are critical to closing pedagogical gaps: random decisions decrease GPT4's response quality by -97% than expert decisions. Our work shows the potential of embedding expert thought processes in LLM generations to enhance their capability to bridge novice-expert knowledge gaps. Our dataset and code can be found at: https://github.com/rosewang2008/bridge.

While Multimodal Large Language Models (MLLMs) excel on benchmarks, their processing paradigm differs from the human ability to integrate visual information. Unlike humans who naturally bridge details and high-level concepts, models tend to treat these elements in isolation. Prevailing evaluation protocols often decouple low-level perception from high-level reasoning, overlooking their semantic and causal dependencies, which yields non-diagnostic results and obscures performance bottlenecks. We present VCU-Bridge, a framework that operationalizes a human-like hierarchy of visual connotation understanding: multi-level reasoning that advances from foundational perception through semantic bridging to abstract connotation, with an explicit evidence-to-inference trace from concrete cues to abstract conclusions. Building on this framework, we construct HVCU-Bench, a benchmark for hierarchical visual connotation understanding with explicit, level-wise diagnostics. Comprehensive experiments demonstrate a consistent decline in performance as reasoning progresses to higher levels. We further develop a data generation pipeline for instruction tuning guided by Monte Carlo Tree Search (MCTS) and show that strengthening low-level capabilities yields measurable gains at higher levels. Interestingly, it not only improves on HVCU-Bench but also brings benefits on general benchmarks (average +2.53%), especially with substantial gains on MMStar (+7.26%), demonstrating the significance of the hierarchical thinking pattern and its effectiveness in enhancing MLLM capabilities. The project page is at https://vcu-bridge.github.io .

Diffusion bridges have shown potential in paired image-to-image (I2I) translation tasks. However, existing methods are limited by their unidirectional nature, requiring separate models for forward and reverse translations. This not only doubles the computational cost but also restricts their practicality. In this work, we introduce the Bidirectional Diffusion Bridge Model (BDBM), a scalable approach that facilitates bidirectional translation between two coupled distributions using a single network. BDBM leverages the Chapman-Kolmogorov Equation for bridges, enabling it to model data distribution shifts across timesteps in both forward and backward directions by exploiting the interchangeability of the initial and target timesteps within this framework. Notably, when the marginal distribution given endpoints is Gaussian, BDBM's transition kernels in both directions possess analytical forms, allowing for efficient learning with a single network. We demonstrate the connection between BDBM and existing bridge methods, such as Doob's h-transform and variational approaches, and highlight its advantages. Extensive experiments on high-resolution I2I translation tasks demonstrate that BDBM not only enables bidirectional translation with minimal additional cost but also outperforms state-of-the-art bridge models. Our source code is available at [https://github.com/kvmduc/BDBM||https://github.com/kvmduc/BDBM].

Fine-tuning LLMs to inject new knowledge faces a critical challenge: LLMs can quickly memorize new facts, yet fail to use them for downstream reasoning tasks. We formalize this failure as the \textbf{Knowing--Using Gap}, characterized by an accuracy gap and a temporal lag between memorization and generalization. To understand this phenomenon, we fine-tune LLMs with unseen knowledge and monitor the spatial permeation dynamics of the knowledge internally using a novel intervention technique called self-patching. Self-patching identifies activation locations where relocating representations substantially improves failed generalization cases. These results are consistent with a knowledge-circuit misalignment hypothesis: memorized representations can exist internally but may not be routed to computation-effective layers. To demonstrate the practicality of this diagnostic finding, we design a simple heuristic strategy which recovers 58--75\% of the oracle headroom in generalization failure. Experiments are done cross-domain for the robustness of this finding.

Training large neural networks with data-parallel stochastic gradient descent allocates N GPU replicas to compute effectively identical updates -- a practice that leaves the rich space of learning rate configurations entirely unexplored during training. We propose Hyperparameter-Divergent Ensemble Training (HDET), a method that repurposes these replicas for simultaneous learning rate exploration at negligible communication overhead. HDET operates in alternating phases: a fan-out stage in which replicas train independently under a structured, symmetric spread of learning rates, and a converge stage in which parameters are averaged across all replicas via AllReduce every T steps. Building on this ensemble substrate, we further propose an automatic learning rate (auto-LR) controller that treats the relative training loss across replicas as a performance signal, updating the shared base schedule toward higher-performing configurations via a momentum-based gradient-free meta-update. The combined method produces a self-adapting learning rate schedule that improves both optimization quality and generalization without additional hyperparameter sweeps or training budget. Crucially, the framework generalizes beyond learning rate: any scalar hyperparameter that does not alter model architecture -- such as dropout rate, attention scale temperature, or weight-decay coefficient -- can be explored across replicas using the same fan-out/converge protocol, with inter-replica loss differences serving as zero-order hypergradients that guide the search direction. HDET is implemented as a drop-in replacement for PyTorch's OneCycleLR scheduler, requiring no changes to model architecture, optimizer, or data pipeline.

Discrete diffusion has recently emerged as a promising paradigm in discrete data modeling. However, existing methods typically rely on a fixed rate transition matrix during training, which not only limits the expressiveness of latent representations, a fundamental strength of variational methods, but also constrains the overall design space. To address these limitations, we propose Discrete Markov Bridge, a novel framework specifically designed for discrete representation learning. Our approach is built upon two key components: Matrix Learning and Score Learning. We conduct a rigorous theoretical analysis, establishing formal performance guarantees for Matrix Learning and proving the convergence of the overall framework. Furthermore, we analyze the space complexity of our method, addressing practical constraints identified in prior studies. Extensive empirical evaluations validate the effectiveness of the proposed Discrete Markov Bridge, which achieves an Evidence Lower Bound (ELBO) of 1.38 on the Text8 dataset, outperforming established baselines. Moreover, the proposed model demonstrates competitive performance on the CIFAR-10 dataset, achieving results comparable to those obtained by image-specific generation approaches.

Vision-Language Models (VLMs) are a new family of models that align image content with natural language. Existing approaches typically fuse either (a) early: by mixing tokens/features inside the encoders, or (b) late: by comparing pooled embeddings. Many methods also tie fusion to an autoregressive decoder. However, the hidden states of both modalities already carry rich, modality-specific structure (spatial layout in vision; syntax and semantics in text), so directly aligning these states is a natural way to match what the two modalities "think". We propose a lightweight fusion module: a few cross-only, bidirectional attention layers placed near the top of both encoders. Each layer projects the vision and text encoder hidden-state sequences into a shared space, attends across modalities, and sends gated residual updates back, with simple stabilizers to improve alignment. The encoders remain non-causal and strong for understanding, while generation stays cleanly decoupled via an optional decoder. Across standard retrieval, VQA, and visual reasoning benchmarks, BRIDGE outperforms comparable VLMs while preserving the bi-encoder efficiency of contrastive models. We make our code publicly available at https://github.com/jfeinashley/BRIDGE.

Heterogeneous multi-agent LLM systems, where agents are powered by different model families, can outperform homogeneous configurations by reducing redundant reasoning patterns. Yet existing communication protocols either operate through text, discarding the sender's internal representations, or require architectural homogeneity for latent-level transfer. We identify the entity grounding problem in cross-architecture communication: cross-attention bridges that transfer continuous representations across different LLM families suffer from rare-token compression collapse, where entity identity is lost in the continuous bottleneck (bridge-only F1 ~30%). We propose XBRIDGE, a decode-free communication protocol that addresses this through two mechanisms. Lexical Anchor Mapping (LAM) maps the sender's original context tokens to the receiver's vocabulary, providing discrete entity anchors. A Latent Enrichment Bridge (LEB) lets the receiver query the sender's hidden states for contextual enrichment. The entity anchors ground the bridge's contextual signals to specific entities through the receiver's own self-attention. Across three model families (Llama, Qwen, and Mistral), seven benchmarks, and both communication directions, XBRIDGE outperforms text-based communication on all seven tasks for each model pair while achieving 11x lower latency, and in a same-architecture setting it also exceeds a KV-sharing baseline on six of seven tasks. LEB requires only 264M trainable parameters (3.8% of the receiver), is trained on a small balanced sample set, and adds negligible inference overhead.

In recent times there has been a surge of multi-modal architectures based on Large Language Models, which leverage the zero shot generation capabilities of LLMs and project image embeddings into the text space and then use the auto-regressive capacity to solve tasks such as VQA, captioning, and image retrieval. We name these architectures as "bridge-architectures" as they project from the image space to the text space. These models deviate from the traditional recipe of training transformer based multi-modal models, which involve using large-scale pre-training and complex multi-modal interactions through co or cross attention. However, the capabilities of bridge architectures have not been tested on complex visual reasoning tasks which require fine grained analysis about the image. In this project, we investigate the performance of these bridge-architectures on the NLVR2 dataset, and compare it to state-of-the-art transformer based architectures. We first extend the traditional bridge architectures for the NLVR2 dataset, by adding object level features to faciliate fine-grained object reasoning. Our analysis shows that adding object level features to bridge architectures does not help, and that pre-training on multi-modal data is key for good performance on complex reasoning tasks such as NLVR2. We also demonstrate some initial results on a recently bridge-architecture, LLaVA, in the zero shot setting and analyze its performance.

Creative capabilities of MLLMs matter in design, communication, education, and human--AI collaboration, yet remain difficult to evaluate because explicit targets and reward signals are scarce compared with accuracy-oriented tasks. Cross-concept understanding is a core cognitive capacity underlying receptive creativity. It enables a perceiver to recover intended meaning from non-obvious but meaningful conceptual relations. We operationalize item construction as cross-concept encoding and model inference as cross-concept decoding. We introduce C4, a cognition-inspired evaluation framework for Chengyu (Chinese idiom)-based Cross-Concept Creativity. Its encoding component maps target slots to imageable substitute concepts along bridge paths in a manually annotated and third-party-reviewed cross-concept network, enabling batch generation with explicit structure, difficulty indexed by bridge count and depth, and exact answers. Using this framework, we instantiate the C4 Evaluation Set (C4-Eval), comprising 184 synthetic items and 37 human-created cross-concept chengyu figures collected from online sources. We manually construct and review cross-concept relations, bridge paths, and reasoning processes for the collected figures. Each C4-Eval item is instantiated in five task settings, yielding 884 primary answer-recovery cases. Across ten evaluated MLLMs, the strongest closed models reach 50.7% and 48.0% primary accuracy, while open-source models remain substantially lower. Candidate constraints improve accuracy sharply, but bridge hints and explanation requests provide only modest gains. These results expose a substantial gap in how current MLLMs decode creatively encoded meaning through cross-concept relations. The code is in the supplementary material.

Large Language Models (LLMs), built on Transformer architectures, exhibit remarkable generalization across a wide range of tasks. However, fine-tuning these models for specific tasks remains resource-intensive due to their extensive parameterization. In this paper, we explore two remarkable phenomena related to the attention mechanism during the fine-tuning of LLMs (where W_q, W_k, and W_v denote the weights of the query, key, and value layers, respectively). The first phenomenon, termed "Unequal Importance of Attention Matrices", highlights the impact of fine-tuning different weight matrices. It shows that optimizing the W_v matrix yields significantly better performance than optimizing the W_k matrix. Fine-tuning only the W_q and W_v matrices is computationally efficient while delivering results comparable to, or even better than fine-tuning all three matrices (W_q, W_k, and W_v). The second phenomenon,"Attention Matrices with Customized Learning Rate Lead to Better Convergence", emphasizes the importance of assigning distinct learning rates to these matrices. Specifically, a higher learning rate for the W_v matrix compared to W_q and W_k accelerates convergence and improves performance. Building on these insights, we propose a new strategy that improves fine-tuning efficiency in terms of both storage and time. Experimental results on benchmark datasets validate the effectiveness of this approach, supporting our theoretical findings. Our analysis lays the theoretical groundwork for configuring and improving algorithms in LLMs fine-tuning.

Learning diffusion bridge models is easy; making them fast and practical is an art. Diffusion bridge models (DBMs) are a promising extension of diffusion models for applications in image-to-image translation. However, like many modern diffusion and flow models, DBMs suffer from the problem of slow inference. To address it, we propose a novel distillation technique based on the inverse bridge matching formulation and derive the tractable objective to solve it in practice. Unlike previously developed DBM distillation techniques, the proposed method can distill both conditional and unconditional types of DBMs, distill models in a one-step generator, and use only the corrupted images for training. We evaluate our approach for both conditional and unconditional types of bridge matching on a wide set of setups, including super-resolution, JPEG restoration, sketch-to-image, and other tasks, and show that our distillation technique allows us to accelerate the inference of DBMs from 4x to 100x and even provide better generation quality than used teacher model depending on particular setup.

We analyze the convergence of (stochastic) gradient descent algorithm for learning a convolutional filter with Rectified Linear Unit (ReLU) activation function. Our analysis does not rely on any specific form of the input distribution and our proofs only use the definition of ReLU, in contrast with previous works that are restricted to standard Gaussian input. We show that (stochastic) gradient descent with random initialization can learn the convolutional filter in polynomial time and the convergence rate depends on the smoothness of the input distribution and the closeness of patches. To the best of our knowledge, this is the first recovery guarantee of gradient-based algorithms for convolutional filter on non-Gaussian input distributions. Our theory also justifies the two-stage learning rate strategy in deep neural networks. While our focus is theoretical, we also present experiments that illustrate our theoretical findings.

How can we build agents that keep learning from experience, quickly and efficiently, after their initial training? Here we take inspiration from the main mechanism of learning in biological brains: synaptic plasticity, carefully tuned by evolution to produce efficient lifelong learning. We show that plasticity, just like connection weights, can be optimized by gradient descent in large (millions of parameters) recurrent networks with Hebbian plastic connections. First, recurrent plastic networks with more than two million parameters can be trained to memorize and reconstruct sets of novel, high-dimensional 1000+ pixels natural images not seen during training. Crucially, traditional non-plastic recurrent networks fail to solve this task. Furthermore, trained plastic networks can also solve generic meta-learning tasks such as the Omniglot task, with competitive results and little parameter overhead. Finally, in reinforcement learning settings, plastic networks outperform a non-plastic equivalent in a maze exploration task. We conclude that differentiable plasticity may provide a powerful novel approach to the learning-to-learn problem.

Message passing neural networks have shown a lot of success on graph-structured data. However, there are many instances where message passing can lead to over-smoothing or fail when neighboring nodes belong to different classes. In this work, we introduce a simple yet general framework for improving learning in message passing neural networks. Our approach essentially upsamples edges in the original graph by adding "slow nodes" at each edge that can mediate communication between a source and a target node. Our method only modifies the input graph, making it plug-and-play and easy to use with existing models. To understand the benefits of slowing down message passing, we provide theoretical and empirical analyses. We report results on several supervised and self-supervised benchmarks, and show improvements across the board, notably in heterophilic conditions where adjacent nodes are more likely to have different labels. Finally, we show how our approach can be used to generate augmentations for self-supervised learning, where slow nodes are randomly introduced into different edges in the graph to generate multi-scale views with variable path lengths.

Chain-of-Thought (CoT) prompting improves LLM accuracy on complex tasks but often increases token usage and inference cost. Existing "Budget Forcing" methods reducing cost via fine-tuning with heuristic length penalties, suppress both essential reasoning and redundant filler. We recast efficient reasoning as a lossy compression problem under the Information Bottleneck (IB) principle, and identify a key theoretical gap when applying naive IB to transformers: attention violates the Markov property between prompt, reasoning trace, and response. To resolve this issue, we model CoT generation under the Conditional Information Bottleneck (CIB) principle, where the reasoning trace Z acts as a computational bridge that contains only the information about the response Y that is not directly accessible from the prompt X. This yields a general Reinforcement Learning objective: maximize task reward while compressing completions under a prior over reasoning traces, subsuming common heuristics (e.g., length penalties) as special cases (e.g., uniform priors). In contrast to naive token-counting-based approaches, we introduce a semantic prior that measures token cost by surprisal under a language model prior. Empirically, our CIB objective prunes cognitive bloat while preserving fluency and logic, improving accuracy at moderate compression and enabling aggressive compression with minimal accuracy drop.

Models trained on a new task typically degrade on prior tasks, a phenomenon known as forgetting. Traditionally, mitigating forgetting has required replaying stored exemplars from prior tasks, which is often impractical. By contrast, language models can sample from their own training distribution, and we show that these self-generated samples serve as effective replay data, nearly eliminating forgetting. We find that forgetting nonetheless persists when the model has little remaining capacity: models pretrained close to saturation cannot absorb new information without overwriting prior knowledge. When capacity is not the limiting factor, low learning rates reduce forgetting but require substantially more training steps. Replay breaks this tradeoff, enabling fast, high-learning-rate finetuning without forgetting.

Gradient-based algorithms are a cornerstone of artificial neural network training, yet it remains unclear whether biological neural networks use similar gradient-based strategies during learning. Experiments often discover a diversity of synaptic plasticity rules, but whether these amount to an approximation to gradient descent is unclear. Here we investigate a previously overlooked possibility: that learning dynamics may include fundamentally non-gradient "curl"-like components while still being able to effectively optimize a loss function. Curl terms naturally emerge in networks with inhibitory-excitatory connectivity or Hebbian/anti-Hebbian plasticity, resulting in learning dynamics that cannot be framed as gradient descent on any objective. To investigate the impact of these curl terms, we analyze feedforward networks within an analytically tractable student-teacher framework, systematically introducing non-gradient dynamics through neurons exhibiting rule-flipped plasticity. Small curl terms preserve the stability of the original solution manifold, resulting in learning dynamics similar to gradient descent. Beyond a critical value, strong curl terms destabilize the solution manifold. Depending on the network architecture, this loss of stability can lead to chaotic learning dynamics that destroy performance. In other cases, the curl terms can counterintuitively speed learning compared to gradient descent by allowing the weight dynamics to escape saddles by temporarily ascending the loss. Our results identify specific architectures capable of supporting robust learning via diverse learning rules, providing an important counterpoint to normative theories of gradient-based learning in neural networks.

Learning rate schedules used in practice bear little resemblance to those recommended by theory. We close much of this theory/practice gap, and as a consequence are able to derive new problem-adaptive learning rate schedules. Our key technical contribution is a refined analysis of learning rate schedules for a wide class of optimization algorithms (including SGD). In contrast to most prior works that study the convergence of the average iterate, we study the last iterate, which is what most people use in practice. When considering only worst-case analysis, our theory predicts that the best choice is the linear decay schedule: a popular choice in practice that sets the stepsize proportionally to 1 - t/T, where t is the current iteration and T is the total number of steps. To go beyond this worst-case analysis, we use the observed gradient norms to derive schedules refined for any particular task. These refined schedules exhibit learning rate warm-up and rapid learning rate annealing near the end of training. Ours is the first systematic approach to automatically yield both of these properties. We perform the most comprehensive evaluation of learning rate schedules to date, evaluating across 10 diverse deep learning problems, a series of LLMs, and a suite of logistic regression problems. We validate that overall, the linear-decay schedule matches or outperforms all commonly used default schedules including cosine annealing, and that our schedule refinement method gives further improvements.

Robots that learn from a few demonstrations often require two forms of generalization. Compositional generalization recombines skills to solve new tasks, and skill generalization lets the learned policy behind each skill work in new situations. The two depend on each other, yet information is lost between composition and the skills it calls. Where a skill works is determined by the structure its policy is trained with, while composition sees the skill only through a separate description, such as a name, an instruction, or a symbolic operator, that omits this structure. Our key idea is to use each policy's structural prior as part of the interface between composition and the skill. A structural prior states what a behavior depends on, for example that a grasp depends only on the gripper's pose relative to the object. Built into training, it shapes where the policy generalizes; stated in language, it tells composition where the policy applies. We instantiate this idea in Agent Priors-guided Policy Learning (APPL). A construction agent segments complete demonstrations into reusable skills, proposes several structural priors for each skill, and trains and verifies one policy per prior. A runtime agent then selects among these prior-specific policies and composes them toward new task goals using their interfaces. Across MetaWorld and long-horizon ManiSkill tasks, APPL improves out-of-distribution skill generalization and enables previously unseen skill compositions; ablating the interface information substantially reduces performance. These results support the use of training-time structural assumptions as a bridge between skill learning and skill composition.

Large language model (LLM) agents operate over long, multi-session interactions in which facts change: a user moves, a price updates, a plan is revised. Acting correctly requires using the current value of a fact and discarding values that have been superseded. We isolate this ability on real conversational data and show that it is a distinct, unsolved failure. On the knowledge-update subset of LongMemEval, replacing an agent's full context with a bounded, self-maintained memory drops accuracy from 92% to 77% even on a frontier model (gpt-5.4), a gap that is statistically significant (paired McNemar p<0.005) and persists across model scale while full-context accuracy saturates near 92%. The bottleneck is therefore memory maintenance, not comprehension, and is not closed by a stronger model. We then ask whether this is merely an undersized memory, and find it is not: as the conversation grows 24x, accuracy falls further (from 68% to 28%), and granting the agent proportionally more memory yields no detectable recovery (28% to 28%, n=25). The failure scales with the length of the conversation, not the compression ratio. We release Supersede, an open reinforcement-learning environment (on the verifiers / prime-rl stack) that turns this measurement into a training signal: agents are rewarded for answering from the current value and penalized for stale ones. Finally, we close the loop and show the gap is trainable: GRPO fine-tuning a small open model (Qwen2.5-3B) on this environment nearly doubles its held-out supersession accuracy on real, unseen conversations (9.0% to 16.7%, a single run), along a monotonic checkpoint curve indicating the learned policy, not the harness, carries the gain. To our knowledge this is the first trainable environment whose reward targets temporal fact-currency, and the first evidence the supersession gap can be trained down, not only measured.

We rethink test-time scaling laws from a practical efficiency perspective, revealing that the effectiveness of smaller models is significantly overestimated. Prior work, grounded in compute-optimality, overlooks critical memory access bottlenecks introduced by inference-time strategies (e.g., Best-of-N, long CoTs). Our holistic analysis, spanning models from 0.6B to 32B parameters, reveals a new Kinetics Scaling Law that better guides resource allocation by incorporating both computation and memory access costs. Kinetics Scaling Law suggests that test-time compute is more effective when used on models above a threshold than smaller ones. A key reason is that in TTS, attention, rather than parameter count, emerges as the dominant cost factor. Motivated by this, we propose a new scaling paradigm centered on sparse attention, which lowers per-token cost and enables longer generations and more parallel samples within the same resource budget. Empirically, we show that sparse attention models consistently outperform dense counterparts, achieving over 60 points gains in low-cost regimes and over 5 points gains in high-cost regimes for problem-solving accuracy on AIME, encompassing evaluations on state-of-the-art MoEs. These results suggest that sparse attention is essential for realizing the full potential of test-time scaling because, unlike training, where parameter scaling saturates, test-time accuracy continues to improve through increased generation. The code is available at https://github.com/Infini-AI-Lab/Kinetics.

Learning rate configuration is a fundamental aspect of modern deep learning. The prevailing practice of applying a uniform learning rate across all layers overlooks the structural heterogeneity of Transformers, potentially limiting their effectiveness as the backbone of Large Language Models (LLMs). In this paper, we introduce Layerwise Learning Rate (LLR), an adaptive scheme that assigns distinct learning rates to individual Transformer layers. Our method is grounded in Heavy-Tailed Self-Regularization (HT-SR) theory, which characterizes the empirical spectral density (ESD) of weight correlation matrices to quantify heavy-tailedness. Layers with weaker heavy-tailedness are assigned larger learning rates to accelerate training, while layers with stronger heavy-tailedness receive smaller learning rates. By tailoring learning rates in this manner, LLR promotes more balanced training across layers, leading to faster convergence and improved generalization. Extensive experiments across architectures ranging from LLaMA to GPT-nano, optimizers including AdamW and Muon, and model scales from 60M to 3B parameters with up to 100B training tokens demonstrate the effectiveness of LLR. LLR achieves up to 1.5x training speedup and consistently outperforms uniform-learning-rate baselines. In particular, it improves the average zero-shot accuracy of 1B models from 47.09% to 49.02%, and that of 3B models from 48.58% to 50.61%. A key advantage of LLR is its low tuning overhead: it can transfer nearly optimal learning-rate settings directly from the uniform baseline. Code is available at https://github.com/hed-ucas/Layer-wise-Learning-Rate.

Knowledge distillation (KD) is a widely adopted technique for transferring knowledge from large language models to smaller student models; however, conventional supervised KD often suffers from a distribution mismatch between training and inference. While on-policy KD approaches attempt to mitigate this issue by learning directly from student-generated outputs, they frequently encounter training instabilities because the distributional gap between the novice student and the expert teacher is often too wide to bridge directly. These challenges manifest as pathological gradients in forward KL objectives or diversity collapse in reverse KL regimes. To address these limitations, we propose Veto, an objective-level reformulation that constructs a geometric bridge in the logit space. Unlike prior methods that mix data samples, Veto creates an intermediate target distribution that promotes alignment between the teacher and the student. By introducing a tunable parameter beta, Veto serves as an Adaptive Gradient Veto that stabilizes optimization by suppressing harmful gradients on low-confidence tokens, while simultaneously acting as a Decisiveness Knob to balance reward-driven performance with output diversity. Extensive experiments across various reasoning and generation tasks demonstrate that Veto consistently outperforms supervised fine-tuning and existing on-policy baselines.

In this paper, we make the case that a scientific theory of deep learning is emerging. By this we mean a theory which characterizes important properties and statistics of the training process, hidden representations, final weights, and performance of neural networks. We pull together major strands of ongoing research in deep learning theory and identify five growing bodies of work that point toward such a theory: (a) solvable idealized settings that provide intuition for learning dynamics in realistic systems; (b) tractable limits that reveal insights into fundamental learning phenomena; (c) simple mathematical laws that capture important macroscopic observables; (d) theories of hyperparameters that disentangle them from the rest of the training process, leaving simpler systems behind; and (e) universal behaviors shared across systems and settings which clarify which phenomena call for explanation. Taken together, these bodies of work share certain broad traits: they are concerned with the dynamics of the training process; they primarily seek to describe coarse aggregate statistics; and they emphasize falsifiable quantitative predictions. We argue that the emerging theory is best thought of as a mechanics of the learning process, and suggest the name learning mechanics. We discuss the relationship between this mechanics perspective and other approaches for building a theory of deep learning, including the statistical and information-theoretic perspectives. In particular, we anticipate a symbiotic relationship between learning mechanics and mechanistic interpretability. We also review and address common arguments that fundamental theory will not be possible or is not important. We conclude with a portrait of important open directions in learning mechanics and advice for beginners. We host further introductory materials, perspectives, and open questions at learningmechanics.pub.

Machine learning (ML) is increasingly used in structural engineering and design, yet its broader adoption is hampered by the lack of openly accessible datasets of structural systems. We introduce BridgeNet, a publicly available graph-based dataset of 20,000 form-found bridge structures aimed at enabling Graph ML and multi-modal learning in the context of conceptual structural design. Each datapoint consists of (i) a pin-jointed equilibrium wireframe model generated with the Combinatorial Equilibrium Modeling (CEM) form-finding method, (ii) a volumetric 3D mesh obtained through force-informed materialization, and (iii) rendered images from two canonical camera angles. The resulting dataset is modality-rich and application-agnostic, supporting tasks such as CEM-specific edge classification and parameter inference, surrogate modeling of form-finding, cross-modal reconstruction between graphs, meshes and images, and generative structural design. BridgeNet addresses a key bottleneck in data-driven applications for structural engineering and design by providing a dataset that facilitates the development of new ML-based approaches for equilibrium bridge structures.

On-policy distillation transfers reasoning capabilities by training a student model on its own generated trajectories using token-level feedback from a teacher. However, we identify a critical bottleneck, Supervision Fidelity Decay (SFD): as student-generated prefixes lengthen, the teacher's next-token distribution becomes less confident and less discriminative. Consequently, the teacher-dependent corrective signal in reverse-KL distillation weakens, causing student drift to compound across long reasoning chains. To mitigate SFD, we introduce Lookahead Group Reward (\ours{)}. Building on the insight that next-step teacher confidence reflects the discriminative strength of future reverse-KL supervision, evaluates the student's top-K candidate tokens by the teacher confidence they induce at the subsequent step and assigns a group-normalized reward. To maintain computational efficiency, we further design an entropy-triggered tree-attention mechanism. Across six math and code benchmarks, improves mean@8 by 2.57 points over OPD for a 7B student, with gains increasing in longer-generation and reaching +4.92 points on AIME-26 at 39k tokens.

Recent work has begun to equip vision-language-action (VLA) policies with explicit intermediate reasoning. In embodied control, however, textual chain-of-thought is a poor fit: irrelevant or weakly textual information can interfere with action prediction, while autoregressive text decoding adds too much latency for real-time closed-loop execution. We present VISUALTHINK-VLA, a visual intermediate-reasoning framework for accurate, low-latency VLA policies. Our bootstrapping philosophy is to guide action with effective visual thinking: VISUALTHINK-VLA bootstraps action prediction through a compact visual-evidence interface that preserves spatial precision while avoiding decoding overhead. Besides, to further improve performance and efficiency, VISUALTHINK-VLA adopts a tailored selective routing mechanism to learn the visual evidence tokens, enabling low-latency inference while preserving high-capacity specialization. We also introduce VisualEvidence-Kit, a supervision-and-audit resource centered on a VisualEvidence-Agent that constructs a 754.7k VLA instructions VisualEvidence-Set for route supervision and counterfactual faithfulness tests. Across multiple benchmarks and real-robot evaluation, VISUALTHINK-VLA achieves the highest success rate on most benchmarks while reducing the multi-second latency of reasoning-augmented baselines to the sub-second regime. For example, on BridgeData V2, it reduces step latency from 8.377,s with ECoT to 0.367,s, achieving a 22.8 times speedup.

Learning Rate Rewinding (LRR) has been established as a strong variant of Iterative Magnitude Pruning (IMP) to find lottery tickets in deep overparameterized neural networks. While both iterative pruning schemes couple structure and parameter learning, understanding how LRR excels in both aspects can bring us closer to the design of more flexible deep learning algorithms that can optimize diverse sets of sparse architectures. To this end, we conduct experiments that disentangle the effect of mask learning and parameter optimization and how both benefit from overparameterization. The ability of LRR to flip parameter signs early and stay robust to sign perturbations seems to make it not only more effective in mask identification but also in optimizing diverse sets of masks, including random ones. In support of this hypothesis, we prove in a simplified single hidden neuron setting that LRR succeeds in more cases than IMP, as it can escape initially problematic sign configurations.

Neural Memory Networks (NMNs) have received increased attention in recent years compared to deep architectures that use a constrained memory. Despite their new appeal, the success of NMNs hinges on the ability of the gradient-based optimiser to perform incremental training of the NMN controllers, determining how to leverage their high capacity for knowledge retrieval. This means that while excellent performance can be achieved when the training data is consistent and well distributed, rare data samples are hard to learn from as the controllers fail to incorporate them effectively during model training. Drawing inspiration from the human cognition process, in particular the utilisation of neuromodulators in the human brain, we propose to decouple the learning process of the NMN controllers to allow them to achieve flexible, rapid adaptation in the presence of new information. This trait is highly beneficial for meta-learning tasks where the memory controllers must quickly grasp abstract concepts in the target domain, and adapt stored knowledge. This allows the NMN controllers to quickly determine which memories are to be retained and which are to be erased, and swiftly adapt their strategy to the new task at hand. Through both quantitative and qualitative evaluations on multiple public benchmarks, including classification and regression tasks, we demonstrate the utility of the proposed approach. Our evaluations not only highlight the ability of the proposed NMN architecture to outperform the current state-of-the-art methods, but also provide insights on how the proposed augmentations help achieve such superior results. In addition, we demonstrate the practical implications of the proposed learning strategy, where the feedback path can be shared among multiple neural memory networks as a mechanism for knowledge sharing.

Training deep neural networks requires intricate initialization and careful selection of learning rates. The emergence of stochastic gradient optimization methods that use adaptive learning rates based on squared past gradients, e.g., AdaGrad, AdaDelta, and Adam, eases the job slightly. However, such methods have also been proven problematic in recent studies with their own pitfalls including non-convergence issues and so on. Alternative variants have been proposed for enhancement, such as AMSGrad, AdaShift and AdaBound. In this work, we identify a new problem of adaptive learning rate methods that exhibits at the beginning of learning where Adam produces extremely large learning rates that inhibit the start of learning. We propose the Adaptive and Momental Bound (AdaMod) method to restrict the adaptive learning rates with adaptive and momental upper bounds. The dynamic learning rate bounds are based on the exponential moving averages of the adaptive learning rates themselves, which smooth out unexpected large learning rates and stabilize the training of deep neural networks. Our experiments verify that AdaMod eliminates the extremely large learning rates throughout the training and brings significant improvements especially on complex networks such as DenseNet and Transformer, compared to Adam. Our implementation is available at: https://github.com/lancopku/AdaMod

Recent unified models integrate understanding experts (e.g., LLMs) with generative experts (e.g., diffusion models), achieving strong multimodal performance. However, recent advanced methods such as BAGEL and LMFusion follow the Mixture-of-Transformers (MoT) paradigm, adopting a symmetric design that mirrors one expert to another for convenient initialization and fusion, which remains suboptimal due to inherent modality discrepancies. In this work, we propose HBridge, an asymmetric H-shaped architecture that enables heterogeneous experts to optimally leverage pretrained priors from their respective modality domains. Unlike prior dense fusion strategies that straightforwardly connect all layers between experts via shared attention, HBridge selectively bridges intermediate layers, reducing over 40% attention sharing, which improves efficiency and enhances generation quality. Shallow and deep layers, which capture modality-specific representations, are decoupled, while mid-layer bridging promotes semantic alignment. To further strengthen cross-modal coherence, we introduce semantic reconstruction tokens that explicitly guide the generative expert to reconstruct visual semantic tokens of the target image. Extensive experiments across multiple benchmarks demonstrate the effectiveness and superior performance of HBridge, establishing a new paradigm for unified multimodal generation.

Aligning text-to-image flow matching models with human preferences via direct reward backpropagation is sample-efficient but hampered by two well-known pathologies: activations cannot be stored across the full sampling trajectory at modern model scale, and chained Jacobian products across steps inflate the reward gradient as it travels back to early indices. Connector-based methods, such as LeapAlign, address these issues by replacing the full backward trajectory with a short pinned path, highlighting a useful decoupling between sampling and optimization. However, the quality of the resulting gradient depends on how accurately this short path approximates the full rollout, especially over long intervals. We propose FlowBP, a unified surrogate-trajectory framework that treats the backward trajectory itself as the design object. FlowBP keeps a no-gradient cached rollout for sampling, then builds a lightweight backward surrogate from cached and selectively re-forwarded velocities. This view separates four choices: the reward-model input, active set, integration weights, and bridge coupling, and recovers prior direct-gradient methods as particular settings. Within this framework, we instantiate three variants: FlowBP-Sparse uses sparse Euler reconstruction, FlowBP-Bridge adds controlled bridge coupling, and FlowBP-Lagrange raises the order of leap quadrature. All three bound memory by the active-set size and limit gradient chaining to at most one Jacobian factor. Across SD3.5-M, FLUX.1-dev, and FLUX.2-Klein-base on preference, quality, and compositional metrics, the three variants improve over direct-gradient baselines on most metrics.

The widespread use of neural networks across different scientific domains often involves constraining them to satisfy certain symmetries, conservation laws, or other domain knowledge. Such constraints are often imposed as soft penalties during model training and effectively act as domain-specific regularizers of the empirical risk loss. Physics-informed neural networks is an example of this philosophy in which the outputs of deep neural networks are constrained to approximately satisfy a given set of partial differential equations. In this work we review recent advances in scientific machine learning with a specific focus on the effectiveness of physics-informed neural networks in predicting outcomes of physical systems and discovering hidden physics from noisy data. We will also identify and analyze a fundamental mode of failure of such approaches that is related to numerical stiffness leading to unbalanced back-propagated gradients during model training. To address this limitation we present a learning rate annealing algorithm that utilizes gradient statistics during model training to balance the interplay between different terms in composite loss functions. We also propose a novel neural network architecture that is more resilient to such gradient pathologies. Taken together, our developments provide new insights into the training of constrained neural networks and consistently improve the predictive accuracy of physics-informed neural networks by a factor of 50-100x across a range of problems in computational physics. All code and data accompanying this manuscript are publicly available at https://github.com/PredictiveIntelligenceLab/GradientPathologiesPINNs.

Federated learning is an emerging distributed machine learning framework which jointly trains a global model via a large number of local devices with data privacy protections. Its performance suffers from the non-vanishing biases introduced by the local inconsistent optimal and the rugged client-drifts by the local over-fitting. In this paper, we propose a novel and practical method, FedSpeed, to alleviate the negative impacts posed by these problems. Concretely, FedSpeed applies the prox-correction term on the current local updates to efficiently reduce the biases introduced by the prox-term, a necessary regularizer to maintain the strong local consistency. Furthermore, FedSpeed merges the vanilla stochastic gradient with a perturbation computed from an extra gradient ascent step in the neighborhood, thereby alleviating the issue of local over-fitting. Our theoretical analysis indicates that the convergence rate is related to both the communication rounds T and local intervals K with a upper bound small O(1/T) if setting a proper local interval. Moreover, we conduct extensive experiments on the real-world dataset to demonstrate the efficiency of our proposed FedSpeed, which performs significantly faster and achieves the state-of-the-art (SOTA) performance on the general FL experimental settings than several baselines. Our code is available at https://github.com/woodenchild95/FL-Simulator.git.

Diffusion models are powerful generative models that map noise to data using stochastic processes. However, for many applications such as image editing, the model input comes from a distribution that is not random noise. As such, diffusion models must rely on cumbersome methods like guidance or projected sampling to incorporate this information in the generative process. In our work, we propose Denoising Diffusion Bridge Models (DDBMs), a natural alternative to this paradigm based on diffusion bridges, a family of processes that interpolate between two paired distributions given as endpoints. Our method learns the score of the diffusion bridge from data and maps from one endpoint distribution to the other by solving a (stochastic) differential equation based on the learned score. Our method naturally unifies several classes of generative models, such as score-based diffusion models and OT-Flow-Matching, allowing us to adapt existing design and architectural choices to our more general problem. Empirically, we apply DDBMs to challenging image datasets in both pixel and latent space. On standard image translation problems, DDBMs achieve significant improvement over baseline methods, and, when we reduce the problem to image generation by setting the source distribution to random noise, DDBMs achieve comparable FID scores to state-of-the-art methods despite being built for a more general task.

We consider the problem of estimating the learning rate in adaptive methods, such as AdaGrad and Adam. We propose Prodigy, an algorithm that provably estimates the distance to the solution D, which is needed to set the learning rate optimally. At its core, Prodigy is a modification of the D-Adaptation method for learning-rate-free learning. It improves upon the convergence rate of D-Adaptation by a factor of O(log(D/d_0)), where d_0 is the initial estimate of D. We test Prodigy on 12 common logistic-regression benchmark datasets, VGG11 and ResNet-50 training on CIFAR10, ViT training on Imagenet, LSTM training on IWSLT14, DLRM training on Criteo dataset, VarNet on Knee MRI dataset, as well as RoBERTa and GPT transformer training on BookWiki. Our experimental results show that our approach consistently outperforms D-Adaptation and reaches test accuracy values close to that of hand-tuned Adam.

In this paper, we describe a phenomenon, which we named "super-convergence", where neural networks can be trained an order of magnitude faster than with standard training methods. The existence of super-convergence is relevant to understanding why deep networks generalize well. One of the key elements of super-convergence is training with one learning rate cycle and a large maximum learning rate. A primary insight that allows super-convergence training is that large learning rates regularize the training, hence requiring a reduction of all other forms of regularization in order to preserve an optimal regularization balance. We also derive a simplification of the Hessian Free optimization method to compute an estimate of the optimal learning rate. Experiments demonstrate super-convergence for Cifar-10/100, MNIST and Imagenet datasets, and resnet, wide-resnet, densenet, and inception architectures. In addition, we show that super-convergence provides a greater boost in performance relative to standard training when the amount of labeled training data is limited. The architectures and code to replicate the figures in this paper are available at github.com/lnsmith54/super-convergence. See http://www.fast.ai/2018/04/30/dawnbench-fastai/ for an application of super-convergence to win the DAWNBench challenge (see https://dawn.cs.stanford.edu/benchmark/).

Generative speech enhancement has recently shown promising advancements in improving speech quality in noisy environments. Multiple diffusion-based frameworks exist, each employing distinct training objectives and learning techniques. This paper aims at explaining the differences between these frameworks by focusing our investigation on score-based generative models and Schr\"odinger bridge. We conduct a series of comprehensive experiments to compare their performance and highlight differing training behaviors. Furthermore, we propose a novel perceptual loss function tailored for the Schr\"odinger bridge framework, demonstrating enhanced performance and improved perceptual quality of the enhanced speech signals. All experimental code and pre-trained models are publicly available to facilitate further research and development in this.

Bandwidth-constrained distributed reinforcement learning (RL) post-training of large language models is bottlenecked by two channels: weight synchronization from trainers to inference workers, and gradient or pseudo-gradient synchronization across trainers. We find that approximately 99% of per-step weight updates are invisible after the BF16 cast used by standard training and inference forward passes. We explain this sparsity by showing that, at typical RL post-training learning rates, Adam updates often fall below the local BF16 rounding threshold. We turn this observation into an algorithmic principle called compute-visible sparsification: transmit only updates that would change the next forward pass. PULSE (Precision-gated Updates for Low-precision Sparse Exchange) turns this principle into two communication algorithms: PULSESync sends lossless sparse BF16 weight patches from trainers to inference workers, and PULSELoCo sparsifies DiLoCo-style FP32 pseudo-gradient synchronization with error feedback. Over bandwidth-constrained commodity networks, PULSESync cuts weight-synchronization communication by over 100x while reconstructing trainer weights bit-identically. PULSELoCo matches DiLoCo across four models while reducing trainer-to-trainer communication by over 17x versus DiLoCo and over 100x versus DDP in the largest evaluated setting.

Image-to-video (I2V) generation is gaining increasing attention with its wide application in video synthesis. Recently, diffusion-based I2V models have achieved remarkable progress given their novel design on network architecture, cascaded framework, and motion representation. However, restricted by their noise-to-data generation process, diffusion-based methods inevitably suffer the difficulty to generate video samples with both appearance consistency and temporal coherence from an uninformative Gaussian noise, which may limit their synthesis quality. In this work, we present FrameBridge, taking the given static image as the prior of video target and establishing a tractable bridge model between them. By formulating I2V synthesis as a frames-to-frames generation task and modelling it with a data-to-data process, we fully exploit the information in input image and facilitate the generative model to learn the image animation process. In two popular settings of training I2V models, namely fine-tuning a pre-trained text-to-video (T2V) model or training from scratch, we further propose two techniques, SNR-Aligned Fine-tuning (SAF) and neural prior, which improve the fine-tuning efficiency of diffusion-based T2V models to FrameBridge and the synthesis quality of bridge-based I2V models respectively. Experiments conducted on WebVid-2M and UCF-101 demonstrate that: (1) our FrameBridge achieves superior I2V quality in comparison with the diffusion counterpart (zero-shot FVD 83 vs. 176 on MSR-VTT and non-zero-shot FVD 122 vs. 171 on UCF-101); (2) our proposed SAF and neural prior effectively enhance the ability of bridge-based I2V models in the scenarios of fine-tuning and training from scratch. Demo samples can be visited at: https://framebridge-demo.github.io/.

Having the ability to acquire inherent skills from environments without any external rewards or supervision like humans is an important problem. We propose a novel unsupervised skill discovery method named Information Bottleneck Option Learning (IBOL). On top of the linearization of environments that promotes more various and distant state transitions, IBOL enables the discovery of diverse skills. It provides the abstraction of the skills learned with the information bottleneck framework for the options with improved stability and encouraged disentanglement. We empirically demonstrate that IBOL outperforms multiple state-of-the-art unsupervised skill discovery methods on the information-theoretic evaluations and downstream tasks in MuJoCo environments, including Ant, HalfCheetah, Hopper and D'Kitty.

Multi-task learning has the potential to improve generalization by maximizing positive transfer between tasks while reducing task interference. Fully achieving this potential is hindered by manually designed architectures that remain static throughout training. On the contrary, learning in the brain occurs through structural changes that are in tandem with changes in synaptic strength. Thus, we propose Multi-Task Structural Learning (MTSL) that simultaneously learns the multi-task architecture and its parameters. MTSL begins with an identical single-task network for each task and alternates between a task-learning phase and a structural-learning phase. In the task learning phase, each network specializes in the corresponding task. In each of the structural learning phases, starting from the earliest layer, locally similar task layers first transfer their knowledge to a newly created group layer before being removed. MTSL then uses the group layer in place of the corresponding removed task layers and moves on to the next layers. Our empirical results show that MTSL achieves competitive generalization with various baselines and improves robustness to out-of-distribution data.

Humans continuously learn from experience, whereas conventional large language model (LLM) evaluations ignore the models' ability to improve through inference-time interaction. In this paper, we study how LLMs learn from iterative experience at test time, a setting we refer to as Chain-of-Experience (CoE), where models accumulate experiential traces through iterative interactions with self or environmental feedback to form a continual improvement loop beyond zero-shot inference. We instantiate CoE with diverse feedback mechanisms, including model self-feedback and environmental signals such as correctness or public coding test pass rates, and evaluate across math, coding, and knowledge domains using 8 LLMs, including GPT-5, Gemini-2.5 Pro, Claude-4.5 Sonnet. Our study shows that leveraging iterative experience consistently outperforms feedback-free baselines, achieving substantial gains with self feedback alone, alongside a 5.6% overall improvement and 19% lower API cost across tasks and models. We further show that combining complementary feedback channels (e.g., model and correctness signals) yields additional gains, and that CoE delivers higher accuracy per token than existing test-time strategies. We observe a positive correlation between LLM base ability and improvement capacity, and show that models remain robust under weak or spurious feedback, with different feedback contributing to distinct improvement aspects and most gains emerging early in the iterations.

Distribution shift (e.g., task or domain shift) in continual learning (CL) usually results in catastrophic forgetting of neural networks. Although it can be alleviated by repeatedly replaying buffered data, the every-step replay is time-consuming. In this paper, we study which modules in neural networks are more prone to forgetting by investigating their training dynamics during CL. Our proposed metrics show that only a few modules are more task-specific and sensitively alter between tasks, while others can be shared across tasks as common knowledge. Hence, we attribute forgetting mainly to the former and find that finetuning them only on a small buffer at the end of any CL method can bring non-trivial improvement. Due to the small number of finetuned parameters, such ``Forgetting Prioritized Finetuning (FPF)'' is efficient in computation. We further propose a more efficient and simpler method that entirely removes the every-step replay and replaces them by only k-times of FPF periodically triggered during CL. Surprisingly, this ``k-FPF'' performs comparably to FPF and outperforms the SOTA CL methods but significantly reduces their computational overhead and cost. In experiments on several benchmarks of class- and domain-incremental CL, FPF consistently improves existing CL methods by a large margin, and k-FPF further excels in efficiency without degrading the accuracy. We also empirically studied the impact of buffer size, epochs per task, and finetuning modules on the cost and accuracy of our methods.

We introduce the Dual-View Pheromone Pathway Network (DPPN), an architecture that routes sparse attention through a persistent pheromone field over latent slot transitions, and use it to discover two independent requirements for persistent structural memory in neural networks. Through five progressively refined experiments using up to 10 seeds per condition across 5 model variants and 4 transfer targets, we identify a core principle: persistent memory requires a stable coordinate system, and any coordinate system learned jointly with the model is inherently unstable. We characterize three obstacles -- pheromone saturation, surface-structure entanglement, and coordinate incompatibility -- and show that neither contrastive updates, multi-source distillation, Hungarian alignment, nor semantic decomposition resolves the instability when embeddings are learned from scratch. Fixed random Fourier features provide extrinsic coordinates that are stable, structure-blind, and informative, but coordinate stability alone is insufficient: routing-bias pheromone does not transfer (10 seeds, p>0.05). DPPN outperforms transformer and random sparse baselines for within-task learning (AULC 0.700 vs 0.680 vs 0.670). Replacing routing bias with learning-rate modulation eliminates negative transfer: warm pheromone as a learning-rate prior achieves +0.003 on same-family tasks (17 seeds, p<0.05) while never reducing performance. A structure completion function over extrinsic coordinates produces +0.006 same-family bonus beyond regularization, showing the catch-22 between stability and informativeness is partially permeable to learned functions. The contribution is two independent requirements for persistent structural memory: (a) coordinate stability and (b) graceful transfer mechanism.

Optimal configuration of the learning rate (LR) is a fundamental yet formidable challenge in large-scale pre-training. Given the stringent trade-off between training costs and model performance, the pivotal question is whether the optimal LR can be accurately extrapolated from low-cost experiments. In this paper, we formalize this investigation into two distinct research paradigms: Fitting and Transfer. Within the Fitting Paradigm, we innovatively introduce a Scaling Law for search factor, effectively reducing the search complexity from O(n^3) to O(n*C_D*C_η) via predictive modeling. Within the Transfer Paradigm, we extend the principles of μTransfer to the Mixture of Experts (MoE) architecture, broadening its applicability to encompass model depth, weight decay, and token horizons. By pushing the boundaries of existing hyperparameter research in terms of scale, we conduct a comprehensive comparison between these two paradigms. Our empirical results challenge the scalability of the widely adopted μ Transfer in large-scale pre-training scenarios. Furthermore, we provide a rigorous analysis through the dual lenses of training stability and feature learning to elucidate the underlying reasons why module-wise parameter tuning underperforms in large-scale settings. This work offers systematic practical guidelines and a fresh theoretical perspective for optimizing industrial-level pre-training.

We characterize the statistical efficiency of knowledge transfer through n samples from a teacher to a probabilistic student classifier with input space mathcal S over labels mathcal A. We show that privileged information at three progressive levels accelerates the transfer. At the first level, only samples with hard labels are known, via which the maximum likelihood estimator attains the minimax rate {|{mathcal S||{mathcal A}|}/{n}}. The second level has the teacher probabilities of sampled labels available in addition, which turns out to boost the convergence rate lower bound to {{|{mathcal S}||{mathcal A}|}/{n}}. However, under this second data acquisition protocol, minimizing a naive adaptation of the cross-entropy loss results in an asymptotically biased student. We overcome this limitation and achieve the fundamental limit by using a novel empirical variant of the squared error logit loss. The third level further equips the student with the soft labels (complete logits) on {mathcal A} given every sampled input, thereby provably enables the student to enjoy a rate {|{mathcal S}|}/{n} free of |{mathcal A}|. We find any Kullback-Leibler divergence minimizer to be optimal in the last case. Numerical simulations distinguish the four learners and corroborate our theory.

Denoising diffusion bridge models (DDBMs) are a powerful variant of diffusion models for interpolating between two arbitrary paired distributions given as endpoints. Despite their promising performance in tasks like image translation, DDBMs require a computationally intensive sampling process that involves the simulation of a (stochastic) differential equation through hundreds of network evaluations. In this work, we take the first step in fast sampling of DDBMs without extra training, motivated by the well-established recipes in diffusion models. We generalize DDBMs via a class of non-Markovian diffusion bridges defined on the discretized timesteps concerning sampling, which share the same marginal distributions and training objectives, give rise to generative processes ranging from stochastic to deterministic, and result in diffusion bridge implicit models (DBIMs). DBIMs are not only up to 25times faster than the vanilla sampler of DDBMs but also induce a novel, simple, and insightful form of ordinary differential equation (ODE) which inspires high-order numerical solvers. Moreover, DBIMs maintain the generation diversity in a distinguished way, by using a booting noise in the initial sampling step, which enables faithful encoding, reconstruction, and semantic interpolation in image translation tasks. Code is available at https://github.com/thu-ml/DiffusionBridge.

We document empirical capability ceilings in decoder-only autoregressive language models across knowledge-intensive tasks. Systematic evaluation of OPT and Pythia model families (70M-30B parameters, spanning 240 times scaling) reveals that knowledge retrieval tasks show negligible accuracy improvement despite smooth loss reduction. On MMLU mathematics benchmarks, accuracy remains flat at 19-20% (below 25% random chance) across all scales while cross-entropy loss decreases by 31%. In contrast, procedural tasks like arithmetic show conventional scaling where both metrics improve together. Attention intervention experiments reveal high sensitivity to perturbation: swapping attention patterns between models causes catastrophic performance collapse (complete accuracy loss) rather than graceful degradation. These measurements have immediate engineering implications: for knowledge-intensive applications using OPT and Pythia architectures, parameter scaling beyond 1-2B offers minimal accuracy gains despite continued loss improvement. Our findings quantify capability-specific scaling failures in these model families to inform resource allocation decisions. Whether these patterns reflect fundamental constraints of decoder-only architectures or implementation-specific limitations remains an open question requiring investigation across diverse architectural approaches.

Training large models is both resource-intensive and time-consuming, making it crucial to understand the quantitative relationship between model performance and hyperparameters. In this paper, we present an empirical law that describes how the pretraining loss of large language models evolves under different learning rate schedules, such as constant, cosine, and step decay schedules. Our proposed law takes a multi-power form, combining a power law based on the sum of learning rates and additional power laws to account for a loss reduction effect induced by learning rate decay. We extensively validate this law on various model sizes and architectures, and demonstrate that after fitting on a few learning rate schedules, the law accurately predicts the loss curves for unseen schedules of different shapes and horizons. Moreover, by minimizing the predicted final pretraining loss across learning rate schedules, we are able to find a schedule that outperforms the widely used cosine learning rate schedule. Interestingly, this automatically discovered schedule bears some resemblance to the recently proposed Warmup-Stable-Decay (WSD) schedule (Hu et al, 2024) but achieves a slightly lower final loss. We believe these results could offer valuable insights for understanding the dynamics of pretraining and designing learning rate schedules to improve efficiency.

Recent progress in large language models (LLMs) highlights the power of scaling test-time compute to achieve strong performance on complex tasks, such as mathematical reasoning and code generation. This raises a critical question: how should model training be modified to optimize performance under a subsequent test-time compute strategy and budget? To explore this, we focus on pass@N, a simple test-time strategy that searches for a correct answer in N independent samples. We show, surprisingly, that training with cross-entropy (CE) loss can be {it misaligned} with pass@N in that pass@N accuracy {it decreases} with longer training. We explain the origins of this misalignment in terms of model overconfidence induced by CE, and experimentally verify our prediction of overconfidence as an impediment to scaling test-time compute via pass@N. Furthermore we suggest a principled, modified training loss that is better aligned to pass@N by limiting model confidence and rescuing pass@N test performance. Our algorithm demonstrates improved mathematical reasoning on MATH and MiniF2F benchmarks under several scenarios: (1) providing answers to math questions; and (2) proving theorems by searching over proof trees of varying shapes. Overall our work underscores the importance of co-designing two traditionally separate phases of LLM development: training-time protocols and test-time search and reasoning strategies.

Large language models (LLMs) underpin applications in code generation, mathematical reasoning, and agent-based workflows. In practice, systems access LLMs via commercial APIs or open-source deployments, and the model landscape (e.g., GPT, Claude, Llama) evolves rapidly. This rapid evolution forces frequent model switches driven by capability, cost, deployment constraints, and privacy. Yet prompts are highly model-sensitive: reusing a prompt engineered for one model on another often yields substantially worse performance than a prompt optimized for the target model. We term this phenomenon Model Drifting. Through extensive empirical analysis across diverse LLM configurations, we show that model drifting is both common and severe. To address this challenge, we introduce PromptBridge, a training-free framework that preserves prompt effectiveness under model switches, enabling cross-model prompt transfer without costly per-task or per-model re-optimization. PromptBridge requires only a small set of alignment tasks for calibration. It first applies Model-Adaptive Reflective Prompt Evolution (MAP-RPE) to obtain task- and model-specific optimal prompts via iterative reflective refinement and quantitative evaluation. Using the resulting calibrated prompt pairs for the source and target models, PromptBridge learns a cross-model prompt mapping. At test time, i.e., for an unseen task, given a source-model prompt, this mapping directly produces an optimized prompt for the target model. Experiments in single-agent and multi-agent settings show that PromptBridge consistently improves downstream accuracy while reducing migration effort. The code will be available soon.

Rate control algorithms are at the heart of video conferencing platforms, determining target bitrates that match dynamic network characteristics for high quality. Recent data-driven strategies have shown promise for this challenging task, but the performance degradation they introduce during training has been a nonstarter for many production services, precluding adoption. This paper aims to bolster the practicality of data-driven rate control by presenting an alternative avenue for experiential learning: leveraging purely existing telemetry logs produced by the incumbent algorithm in production. We observe that these logs contain effective decisions, although often at the wrong times or in the wrong order. To realize this approach despite the inherent uncertainty that log-based learning brings (i.e., lack of feedback for new decisions), our system, Mowgli, combines a variety of robust learning techniques (i.e., conservatively reasoning about alternate behavior to minimize risk and using a richer model formulation to account for environmental noise). Across diverse networks (emulated and real-world), Mowgli outperforms the widely deployed GCC algorithm, increasing average video bitrates by 15-39% while reducing freeze rates by 60-100%.

Benchmarking the tradeoff between neural network accuracy and training time is computationally expensive. Here we show how a multiplicative cyclic learning rate schedule can be used to construct a tradeoff curve in a single training run. We generate cyclic tradeoff curves for combinations of training methods such as Blurpool, Channels Last, Label Smoothing and MixUp, and highlight how these cyclic tradeoff curves can be used to evaluate the effects of algorithmic choices on network training efficiency.