Training Time

In gradual adaptation, how should the training time on each task change as the number of intermediate tasks increases? We study this question for overparameterized linear regression tasks that change smoothly and share a zero-loss solution. With $N$ tasks and training time $s_N$ on each, the final learning progress converges to a continuum curve when $Ns_N\toτ$. The limiting progress is $Θ(τ)$ for small $τ$ and $Θ(τ^{-1})$ for large $τ$, so both very short and very long training produce little progress. It follows that optimal per-task training times scale as $s_N^\star=Θ(N^{-1})$, equivalently $Ns_N^\star=Θ(1)$. Experiments on gradually rotated MNIST and a natural Yearbook time shift are consistent with less per-task training as the path is divided more finely.

Machine-learning benchmarks often pair a label that aggregates a long temporal horizon with input observed through one or a few short windows. Their apparent performance ceiling may therefore be an acquisition-protocol ceiling rather than a model-capacity ceiling. We study labels of the form $Θ_{g,T}=T^{-1}\int_0^T g\{Z(t)\}\,\mathrm{d}t$ when the latent Gaussian process contains both a stable individual trait and a correlated within-individual state. An exact protocol-conditioned Bayes-risk identity provides a common tool. First, we decompose label variance into an $O(1)$ trait component and an $O(T^{-1})$ state component, explaining why a snapshot can retain cross-sectional predictability while poorly tracking within-person change. Second, we derive task-dependent effective temporal spans: mean labels depend on the ordinary correlation time, whereas occupation-time labels depend on an entire spectrum of higher-order correlation times. Third, state-driven occupation-label variance is maximal when the stable trait lies at the threshold; window efficiency decays much more slowly away from that boundary. Under an equal segment budget, exact risks and Monte Carlo experiments show that repeated segments at one time rapidly saturate, whereas temporally dispersed observations continue to increase state explainability. The trait ceiling uses quantities available from ordinary test-retest data; only the state ceiling requires short-lag temporal calibration. The results distinguish architectural limits from protocol limits and show that the label, rather than duration or segment count alone, defines the relevant timescale.

Injecting factual knowledge into large language models (LLMs) reliably and at scale remains an open challenge. Hypernetworks provide a promising solution to large-scale knowledge injection. Although hypernetworks are typically applied for test-time adaptation, we explore their use in train-time knowledge injection, where, given a large corpus of facts, we train a hypernetwork to generate a fixed LoRA adapter that, when inserted into the target model, enable the model to answer questions about those facts. In this work, we investigate whether hypernetworks can be used to perform train-time knowledge injection and how this ability varies with scale. The scaling behavior of hypernetworks remains largely unstudied. Our design decouples the hypernetwork's injection capacity from the target model's general capability, enabling, for the first time, a rigorous study of scaling laws for hypernetwork architectures. We characterize how loss, reasoning accuracy, and out-of-distribution (OOD) generalization vary with hypernetwork depth, width, and target network size. We construct a large-scale dataset, called MegaWikiQA, containing tens of millions of multi-hop question-answer examples across 39 domains constructed from examples in Wikidata5M. Our results reveal: (i) hypernetwork-based injection exhibits broadly predictive power law scaling along all architecture axes; and (ii) hypernetworks are capable of reliable OOD generalization at increasing scales, suggesting that hypernetwork provides a promising alternative to other train-time adaptation methods such as LoRA finetuning and full fine-tuning, exhibiting steeper scaling exponents in all OOD evaluations. Together, these results establish hypernetworks as a principled and scalable substrate for train-time adaptation, and provide the first empirically grounded scaling laws to guide hypernetworks for factual reasoning in large language models.

In recent years Flow Matching has become a prominent method for generative modeling robot motion generation. In its generic form Flow Matching is an ODE-based neural sampler that is trained by regressing empirical flow fields associated with motion samples as data. However, in robot motion generation we often have additional constraints that might not be present in the collected data. The majority of current approaches train the flow on the available data and use inference-time guidance to enforce task-specific constraints. To address this mismatch, we propose \textbf{ConFlow}, a constraint-guided flow matching framework that incorporates constraint information directly into the training objective via differentiable barrier or cost functions. To address design specifications such as smoothness and boundary conditions, we propose replacing the standard Gaussian source distribution used in flow matching training with a conditional Gaussian Process. Our approach also uses infeasible demonstrations as negative supervision, improving constraint satisfaction without requiring additional expert data. Experiments on a two-robot navigation task demonstrate that ConFlow achieves lower collision rates and higher trajectory quality than standard flow matching baselines, with or without inference-time guidance. These results validate training-time constraint integration as an effective approach to closing the training--inference gap in generative motion models.

Constrained generative models aim to produce samples that satisfy complex feasibility constraints while remaining faithful to the data distribution. Existing constrained generation methods typically enforce constraints either through training-time optimization or sampling-time correction. Training-time optimization approaches optimize on states induced by the training distribution, which can differ substantially from those encountered during sampling. Sampling-time correction methods instead modify the sampling process at inference, introducing distribution shift and requiring expensive tuning, particularly for few-step sampling. We propose a fine-tuning framework that incorporates constraint guidance obtained through online rollout into the training process, which aligns training with sampling by differentiating through the fixed noise schedule used to numerically integrate the denoising process. This exposes the model to violations that arise along the denoising trajectory and aligns diffusion learning with the sampling process. Experiments across multiple tasks show that our method improves constraint satisfaction while maintaining competitive sampling quality compared to prior methods.

Training reinforcement-learning agents directly on physical robots makes every fall costly, since a fall can damage the platform and cannot be undone like a simulator reset; the goal is therefore to minimize falls during training rather than trade them off against return, as constrained Markov decision process (MDP) formulations do. A standard mitigation hands control to a separate recovery policy whenever the agent leaves a designer-specified safe region (a subset of state space it should stay within), but the resulting mixed-policy rollouts silently bias every on-policy update, and the importance-sampling correction that would remove this bias is ill-defined whenever the recovery policy is deterministic. We address this bias with a drop-in modification of proximal policy optimization (PPO). Its core is an unbiased policy-gradient estimator that uses the score function only at safe timesteps and never evaluates the recovery policy's density, so it stays valid even when the recovery policy is deterministic, exactly where importance sampling breaks, and it empirically dominates importance sampling even when the recovery policy is stochastic. Because the recovery policy still makes credit assignment slow near the safe-region boundary, two further components accelerate learning: a closed-form value for recovery-triggering states when dynamics and recovery are deterministic, and an imitation loss that copies recovery actions only when recovery succeeds. On a three-environment, five-seed benchmark, the resulting algorithm reduces training-time falls by factors of 233x, 48x, and 26x on HalfCheetah, Ant, and Unitree Go1 over standard PPO, while matching or exceeding PPO's final reward, and on Ant, where the recovery policy is unreliable, it is the only method that reaches 80% of the best final reward.

Few-step diffusion and flow-matching text-to-speech (TTS) models are usually trained with local objectives, such as conditional flow matching, reconstruction, and stop prediction. These losses provide stable optimization, but they never ask whether sampled speech follows the distribution of high-quality speech. We propose Speech Representation Fr'echet Distance loss (SR-FD), a training-time distributional regularizer for tokenizer-free flow-matching autoregressive TTS. During fine-tuning, the model synthesizes speech with the same few-step sampler used at deployment, and SR-FD matches the mean and covariance of frozen Whisper and CTC features of this speech to reference statistics computed offline from three complementary content targets. The loss requires no discriminator and no inference-time computation. On Seed-TTS English, four-step SR-FD fine-tuning reduces WER from the original four-step VoxCPM2 baseline's 2.2279% to 1.4147%, a 36.5% relative reduction, and also surpasses the original ten-step baseline at 1.7366%; both gains are significant under an utterance-level paired bootstrap. Speaker similarity and objective quality proxies are preserved at the ten-step level, and an error analysis shows the gain comes from content substitutions across all prompt lengths. SR-FD is thus an intelligibility-improving distributional regularizer for few-step TTS.

Large Language Models (LLMs) offer a natural interface for translating human objectives into reward signals for cooperative multi-agent reinforcement learning (MARL), yet the training-time dynamics of this integration remain poorly understood. We show that dynamically updating LLM-generated reward weights during off-policy MARL violates the stationarity assumption of Potential-Based Reward Shaping (PBRS) and contaminates the experience replay buffer, whose stored transitions carry reward labels computed under stale shaping weights. We characterise the result as a regime-dependent failure whose severity depends on how competent the unshaped baseline already is. To control it we propose two stabilisation strategies: a Phase-Based Freeze Schedule that enforces strict stationarity within training phases, and Exponential Moving Average (EMA) smoothing that bounds per-episode weight drift. We evaluate across three cooperative environments and five random seeds with QMIX, complemented by an exploratory VDN extension, yielding a three-regime taxonomy. In the augmentative regime (Simple Spread), where the baseline is functional (74.4 %), EMA significantly improves success to 86.7 % ($+12.3$ pp, $p<0.01$) while naive dynamic updates collapse it to 15.2 %. In the essential regime (Level-Based Foraging), where the baseline is broken (0.1 %), any shaping unlocks the task (95.9 % under EMA). In the supplementary regime (SMAC 3m), where the baseline is near-saturated (98.8 %), stabilised shaping preserves performance (99.9 %) while unstabilised shaping adds variance without gain. These findings establish reward-signal stationarity as a necessary design constraint and indicate that regime placement is a practical predictor of whether dynamic LLM shaping helps or harms.

Medical time series (MedTS) signals such as electroencephalography (EEG) and electrocardiography (ECG) support many clinical applications. However, substantial subject-level heterogeneity often induces subject-level distribution shift, causing a fixed parameter set to generalize poorly to unseen individuals. Compared with domain adaptation methods that often depend on extra adaptation components or target-batch statistics, Test-Time Training (TTT) provides a more practical solution for sequential clinical data by enabling online adaptation from unlabeled test samples. However, many representative TTT methods require iterative inner-loop optimization, increasing test-time overhead. In this paper, we propose MedTS-TTT, a test-time training framework for medical time series modeling. MedTS-TTT is built upon Closed-Loop Self-Alignment Test-Time Training (CLSA-TTT) and a Gated Convolutional Backbone (GCB). CLSA-TTT constructs a token-level self-supervised target and performs a single-step fast-weight update for intra-layer closed-loop alignment, enabling rapid sample-wise adaptation without iterative inner-loop optimization. GCB combines CLSA-TTT-based fast adaptation and token-level fusion with a gated convolutional branch to balance local dynamic modeling and information-flow control. On 4 public datasets (2 EEG and 2 ECG) with subject-independent splits, MedTS-TTT achieves 11 top-1 rankings out of 12 evaluations across 9 baselines and 3 metrics. The code is publicly available at https://github.com/mingzhi-c/MedTS-TTT.

World action models (WAMs) have recently shown promise in jointly modeling future observations and executable robot actions. However, most existing WAMs still operate in 2D video or latent spaces, where visually plausible rollouts miss the 3D spatial constraints and occluded contact geometry required for precise manipulation. While geometric foundation models offer strong priors for recovering dense 3D structure and motion from visual observations, forcing WAMs to predict the dense 4D representation introduces costly geometric decoding and slows down causal action generation. To address the trade-off, we present WAM4D, a fast 4D world action model that uses lightweight spatial register tokens as training-time future-depth readouts to transfer pretrained geometric priors into a causal video-action transformer, then removes the register branch for lightweight action inference. To prevent non-causal shortcuts, we further design causal mixture attention for the Mixture-of-Transformers (MoT) WAM backbone, defining modality-specific visibility among video, action, and geometry tokens. Comprehensive experiments on RoboTwin 2.0 and challenging real-world manipulation tasks show that WAM4D improves spatial consistency and achieves competitive action prediction while maintaining efficient inference.

Grokking is the delayed onset of generalization in neural networks, arising long after they fit the training data. Whether the weight norm causes this delay is disputed: some studies report a critical norm at the transition, others observe grokking with no fixed norm at all. We settle this by intervening on the norm during training rather than only observing it. Under free training with weight decay, networks grok when the weight norm reaches a value Wc that varies little across seeds and learning rates (CV 1 to 2 percent) and grows with the modular base as a power law. When we instead clamp the norm to a fixed multiple rho of Wc and hold it there, the network still groks, but the delay follows T_grok proportional to exp(alpha rho). One exponent, alpha near 7.5, fits this delay across four moduli (R^2 = 0.996). Over the swept ranges the held norm moves the delay by about 19x and the learning rate by only about 2x, and holding the norm above Wc slows grokking rather than preventing it. A final LayerNorm removes the dependence by decoupling weight scale from the network function; without it the exponential law returns. This pinned-norm delay is the exponential counterpart to the logarithmic delay predicted for a freely contracting norm.

Modern LLM training pipelines increasingly rely on other models to generate data, filter corpora, judge outputs, and guide development decisions. These dependencies are recursive: a model may depend on an upstream artifact whose own dependencies are documented only in separate releases and artifacts. As a result, the full dependency structure is fragmented across heterogeneous public artifacts, with complexity and recursive depth far outpacing humans' ability to trace. We introduce ModSleuth, an agentic system that recursively reconstructs LLM dependency graphs from public artifacts with source-grounded evidence. We find that the primary challenge is no longer information extraction, but defining what constitutes a dependency and reconciling artifact references across inconsistent documentation. We address these challenges through a formalization that distinguishes direct and indirect dependencies, represents heterogeneous pipeline roles through operation-centered relationships, and resolves artifact identities across names, versions, and repositories. Applying ModSleuth to four public-artifact-rich LLM releases, we recover 1,060 source-verified dependencies and construct large-scale dependency graphs of modern LLM development. These graphs reveal multi-hop license obligations, train-evaluation coupling, discrepancies between released and training-time artifacts, and documentation inconsistencies that would otherwise be difficult to uncover. We release ModSleuth and the resulting dependency graphs to support transparent analysis of the increasingly complex ecosystems underlying modern LLMs.

Training deep neural networks for clinical time-series analysis is computationally demanding, yet many healthcare settings lack the resources required for repeated model development and deployment. This challenge is particularly evident in electrocardiogram classification, where large datasets and long training schedules make efficiency practically important. Progressive Data Dropout reduces training cost by excluding samples from gradient updates once they are learned, but it relies on model confidence and may retain samples that are difficult due to noise or ambiguity rather than useful signal. In this work, we introduce ERTS, an explainability-based reliability training signal for efficient ECG classification. ERTS uses explanation quality during training to distinguish between informative and unreliable uncertainty. Building on progressive data selection, we compute Grad-CAM attention maps for candidate samples and derive a focus score that measures whether model predictions are supported by coherent and localised patterns. Samples with low focus are filtered out, while those with meaningful attention are prioritised for gradient updates. We evaluate ERTS across three ECG datasets and multiple backbone architectures, showing consistent improvements in macro-F1 alongside reduced effective training cost. These results suggest that explanation quality can serve as a practical signal for improving both efficiency and reliability in clinical time-series learning. Code will be released.

Large language models (LLMs) have made remarkable progress in reasoning tasks, largely driven by post-training paradigms, especially reinforcement learning with verifiable rewards (RLVR). However, a critical bottleneck persists: RLVR fails on highly challenging zero-reward problems, where all sampled reasoning trajectories yield uniformly failed outcomes, providing no optimization signal to drive model improvement. Prior efforts to address this limitation, such as dense process supervision, partial reward assignment, or prefix-guided exploration, suffer from inherent task constraints or do not fully equip the policy model with the capabilities necessary to solve the original intractable problems. To address this, we propose TD-Grokking, a training-time decomposition framework for zero-reward problems. It recursively decomposes intractable root problems into self-contained, verifiable subproblems, forming hierarchical trees where solvable leaves provide non-zero rewards. Evaluations on mathematical and medical tasks show that TD-Grokking outperforms vanilla GRPO as well as all baseline approaches. Together with detailed analysis, these results confirm that training-time decomposition effectively converts zero-reward examples into usable training signals, enabling consistent performance gains. Our code and datasets are available at https://anonymous.4open.science/r/TD-Grokking-6567/.

We study the log-alignment ratio (LAR), a measure of parameter-activation alignment, introduced in parameterization theory. We reformulate it as the overlap between a weight spectrum $p$ of the normalized squared singular values of a matrix and an activation spectrum $q$ of the normalized squared projections of inputs onto its singular directions. We show that unembedding LAR tracks the transition between memorization and generalization in two different settings by capturing the spread of $p$ and $q$ during training. In grokking, LAR predicts the effective dimension of the learned function: $k \approx n^{2(1-\text{LAR})}$, where $n$ is the input dimension of the matrix. In 3B-parameter language model pre-training, its deviation from a non-overfitting baseline tracks the generalization gap, and its rate of decline increases as overfitting approaches. LAR is computable from quantities available during the forward pass with negligible computational overhead, and requires no held-out validation data.

End-to-end training with full-depth backpropagation remains the dominant paradigm for optimizing deep neural networks, but its efficiency deteriorates as models grow deeper. Since every block must be executed and differentiated under a single global objective, full-depth BP introduces substantial parameter redundancy, activation-memory cost, and training latency, especially when neighboring layers exhibit highly correlated learning patterns. Directly skipping or removing layers can reduce cost, but often weakens representation capacity or requires architecture-specific reuse designs. In this paper, we propose Replacement Learning (RepL), a training-time paradigm that reduces full-depth redundancy by replacing selected blocks rather than simply discarding them. For each removed block, RepL inserts a lightweight computing layer that synthesizes a surrogate operator from the parameters of its adjacent preceding and succeeding blocks through a learnable transformation, and applies the synthesized operator to the preceding activation. In this way, RepL preserves local contextual continuity while avoiding unnecessary full-layer computation. We instantiate RepL for CNNs and ViTs with tailored parameter-fusion blocks that handle convolutional channels, feature resolutions, and transformer submodules. Extensive experiments on CIFAR-10, SVHN, STL-10, ImageNet, COCO, and CityScapes show that RepL reduces trainable parameters, GPU memory usage, and training time while matching or surpassing standard end-to-end training across classification, detection, and segmentation. Additional results on WikiText-2, transfer learning, inference throughput, checkpointing, stochastic depth, and INT8 quantization further demonstrate its generality and compatibility.

Existing accounts of grokking explain the phenomena in terms of mechanistic frameworks such as circuit efficiency or lazy-to-rich transitions. However, despite a known dependence between grokking and model size, how model capacity shapes grokking remains an open question. We give an information-theoretic account of this relationship on the task of modular arithmetic, showing that grokking does not immediately occur when a model becomes large enough to memorise the training set, but rather emerges as the outcome of a competition between two measurable timescales: a memorisation speed $T_{\text{mem}}(P)$ and a generalisation speed $T_{\text{gen}}(P)$, both of which are functions of model parameter count $P$. Adapting the information capacity framework of Morris et al. (2025), we estimate $T_{\text{mem}}(P)$ on random-label data of equivalent complexity and $T_{\text{gen}}(P)$ on the modular task itself, and show that grokking emerges close to the parameter scale where these timescales intersect. The framework also suggests an empirical model for predicting memorisation speed given model capacity and dataset complexity, recovering the previously reported empirical observation that larger models memorise faster. Overall, we motivate the formalisation of different learning timescales as important abstractions to study when explaining how model capacity shapes grokking on algorithmic tasks.

Large reasoning models (LRMs) achieve strong performance via extended chain-of-thought (CoT) reasoning, yet suffer from excessive token consumption and high inference latency. Existing reinforcement learning (RL) approaches for CoT compression rely on uniform, static length penalties that neglect model capability dynamics and problem-level difficulty variation. We propose \textbf{ExpThink}\xspace, an RL framework that addresses both dimensions through two complementary mechanisms. First, \emph{experience-guided reward shaping} tracks the shortest correct solution found so far for each problem and applies a three-tier reward: full credit for concise correct responses, discounted credit for verbose correct ones, and zero for incorrect ones. The threshold tightens automatically with model improvement, forming a self-evolving curriculum that requires no manual scheduling. Second, \emph{difficulty-adaptive advantage} replaces standard deviation normalization with correct-count normalization, yielding monotonically difficulty-scaled gradients that amplify learning on hard problems to preserve accuracy while suppressing gradients on easy ones to encourage brevity. Together, these mechanisms enforce an accuracy-first, compression-second training objective. Experiments on multiple mathematical reasoning benchmarks demonstrate that \textbf{ExpThink}\xspace reduces average response length by up to 77% while simultaneously improving accuracy, achieving up to $3\times$ higher accuracy-efficiency ratio (accuracy divided by average token count) than the vanilla baseline and outperforming existing RL-based compression methods on both metrics.

Autoregressive transformers make confident errors that output-confidence monitoring cannot catch. Activation monitors catch them only when training leaves a decision-quality signal beyond what the output already exposes. This signal is an architectural property of the trained model, fixed upstream of any monitor. Controlling for output confidence removes 60.3% of the raw activation-probe signal on average across 14 models. Raw probe signal is mostly output confidence, and output-side readouts cannot recover the residual. What remains depends on architecture and training. In Pythia's controlled training, both matched-width configurations form the signal early. One preserves it through convergence while another erases it as perplexity continues to improve. Capability and observability are not inherently in tension. Across independently trained families this pattern persists, even as the collapse point shifts. Where the signal survives, monitoring catches what confidence cannot. On downstream QA, a WikiText-trained probe with no task-specific tuning catches about one in eight confident errors that output-confidence monitoring misses, at a 20% flag rate. These results establish signal engineering as a training-time design axis alongside loss and capability. Architecture sets the conditions for observability, and training determines what remains readable.

Accurate prediction of training time in distributed deep learning is crucial for resource allocation, cost estimation, and job scheduling. We observe that the floating-point precision setting is a key determinant of training time, leading to training time variations of ~2.4x over its minimum. However, existing studies on distributed training time prediction rely on static model computation graphs that do not capture precision variations, including mixed precision. According to our experiments, training time prediction without considering precision results in significant prediction errors - reaching up to 147.85% in mean absolute percentage error (MAPE). To address this issue, we propose a precision-aware distributed training time predictor that achieves robust accuracy across diverse precision settings, including mixed precision, with 9.8% MAPE.

Deep learning (DL) has transformed neuroimaging by delivering state-of-the-art performance with reduced computation times. Yet, the numerical uncertainty inherent to DL training remains largely underexplored despite its potential to significantly impact the reliability of model outcomes. We show that training the FastSurfer segmentation model introduces substantial numerical uncertainty that exceeds its non-DL counterpart (FreeSurfer 7.3.2) in cortical regions, potentially impacting downstream clinical results. We also characterize this training-time uncertainty using random seed perturbations and demonstrate that seed-induced variability is structurally comparable to numerical variability. We then show that seed variability can be leveraged as a data augmentation technique through ensembling to improve downstream brain age regression performance. These findings position numerical uncertainty during DL training as a substantive factor in neuroimaging reliability, with measurable consequences for downstream tasks, and demonstrate that it can simultaneously be harnessed as a data augmentation technique.