Daily Papers

Modern training on a new task often starts from a previously trained model rather than from scratch, raising the question of how this initialization affects the subsequent training trajectory. Classical implicit-bias results characterize the direction selected by prolonged training, but this direction alone does not provide information regarding the intermediate behavior. We address this question through a geometric approximation of full-batch logistic gradient descent (GD) trajectories on strictly linearly separable data, with large initialization of scale R motivated by prior training. From any limiting normalized initial position, we use minimum-norm projection rules to construct a unique continuous ideal path consisting of finitely many linear segments. The path has two stages: negative-margin correction followed by minimum-margin growth. We prove that, after an explicit two-stage time reparameterization, the fixed-step GD trajectory divided by R converges uniformly to this path on every fixed parameter interval as Rtoinfty. Further, our quantitative error bounds account for initialization perturbations and the transition between stages. This approximation provides asymptotic formulas for peak evaluation loss and cumulative training loss. In particular, peak evaluation loss can grow linearly in R even when both endpoint losses tend to zero. The cumulative losses in the correction and margin-growth stages, normalized by R^2 and R, respectively, converge to explicit limits. Experiments on controlled geometries and fixed image features complement our theoretical results.

The conventional wisdom behind learning deep classification models is to focus on bad-classified examples and ignore well-classified examples that are far from the decision boundary. For instance, when training with cross-entropy loss, examples with higher likelihoods (i.e., well-classified examples) contribute smaller gradients in back-propagation. However, we theoretically show that this common practice hinders representation learning, energy optimization, and margin growth. To counteract this deficiency, we propose to reward well-classified examples with additive bonuses to revive their contribution to the learning process. This counterexample theoretically addresses these three issues. We empirically support this claim by directly verifying the theoretical results or significant performance improvement with our counterexample on diverse tasks, including image classification, graph classification, and machine translation. Furthermore, this paper shows that we can deal with complex scenarios, such as imbalanced classification, OOD detection, and applications under adversarial attacks because our idea can solve these three issues. Code is available at: https://github.com/lancopku/well-classified-examples-are-underestimated.

Wheat management strategies play a critical role in determining yield. Traditional management decisions often rely on labour-intensive expert inspections, which are expensive, subjective and difficult to scale. Recently, Vision-Language Models (VLMs) have emerged as a promising solution to enable scalable, data-driven management support. However, due to a lack of domain-specific knowledge, directly applying VLMs to wheat management tasks results in poor quantification and reasoning capabilities, ultimately producing vague or even misleading management recommendations. In response, we propose WisWheat, a wheat-specific dataset with a three-layered design to enhance VLM performance on wheat management tasks: (1) a foundational pretraining dataset of 47,871 image-caption pairs for coarsely adapting VLMs to wheat morphology; (2) a quantitative dataset comprising 7,263 VQA-style image-question-answer triplets for quantitative trait measuring tasks; and (3) an Instruction Fine-tuning dataset with 4,888 samples targeting biotic and abiotic stress diagnosis and management plan for different phenological stages. Extensive experimental results demonstrate that fine-tuning open-source VLMs (e.g., Qwen2.5 7B) on our dataset leads to significant performance improvements. Specifically, the Qwen2.5 VL 7B fine-tuned on our wheat instruction dataset achieves accuracy scores of 79.2% and 84.6% on wheat stress and growth stage conversation tasks respectively, surpassing even general-purpose commercial models such as GPT-4o by a margin of 11.9% and 34.6%.

Brain tumor growth is unique to each glioma patient and extends beyond what is visible in imaging scans, infiltrating surrounding brain tissue. Understanding these hidden patient-specific progressions is essential for effective therapies. Current treatment plans for brain tumors, such as radiotherapy, typically involve delineating a uniform margin around the visible tumor on pre-treatment scans to target this invisible tumor growth. This "one size fits all" approach is derived from population studies and often fails to account for the nuances of individual patient conditions. We present the GliODIL framework, which infers the full spatial distribution of tumor cell concentration from available multi-modal imaging, leveraging a Fisher-Kolmogorov type physics model to describe tumor growth. This is achieved through the newly introduced method of Optimizing the Discrete Loss (ODIL), where both data and physics-based constraints are softly assimilated into the solution. Our test dataset comprises 152 glioblastoma patients with pre-treatment imaging and post-treatment follow-ups for tumor recurrence monitoring. By blending data-driven techniques with physics-based constraints, GliODIL enhances recurrence prediction in radiotherapy planning, challenging traditional uniform margins and strict adherence to the Fisher-Kolmogorov partial differential equation (PDE) model, which is adapted for complex cases.

Understanding generalization in deep neural networks is an active area of research. A promising avenue of exploration has been that of margin measurements: the shortest distance to the decision boundary for a given sample or its representation internal to the network. While margins have been shown to be correlated with the generalization ability of a model when measured at its hidden representations (hidden margins), no such link between large margins and generalization has been established for input margins. We show that while input margins are not generally predictive of generalization, they can be if the search space is appropriately constrained. We develop such a measure based on input margins, which we refer to as `constrained margins'. The predictive power of this new measure is demonstrated on the 'Predicting Generalization in Deep Learning' (PGDL) dataset and contrasted with hidden representation margins. We find that constrained margins achieve highly competitive scores and outperform other margin measurements in general. This provides a novel insight on the relationship between generalization and classification margins, and highlights the importance of considering the data manifold for investigations of generalization in DNNs.

The Growth-at-Risk (GaR) framework has garnered attention in recent econometric literature, yet current approaches implicitly assume a constant Pareto exponent. We introduce novel and robust econometrics to estimate the tails of GaR based on a rigorous theoretical framework and establish validity and effectiveness. Simulations demonstrate consistent outperformance relative to existing alternatives in terms of predictive accuracy. We perform a long-term GaR analysis that provides accurate and insightful predictions, effectively capturing financial anomalies better than current methods.

We propose a structural default model for portfolio-wide valuation adjustments (xVAs) and represent it as a system of coupled backward stochastic differential equations. The framework is divided into four layers, each capturing a key component: (i) clean values, (ii) initial margin and Collateral Valuation Adjustment (ColVA), (iii) Credit/Debit Valuation Adjustments (CVA/DVA) together with Margin Valuation Adjustment (MVA), and (iv) Funding Valuation Adjustment (FVA). Because these layers depend on one another through collateral and default effects, a naive Monte Carlo approach would require deeply nested simulations, making the problem computationally intractable. To address this challenge, we use an iterative deep BSDE approach, handling each layer sequentially so that earlier outputs serve as inputs to the subsequent layers. Initial margin is computed via deep quantile regression to reflect margin requirements over the Margin Period of Risk. We also adopt a change-of-measure method that highlights rare but significant defaults of the bank or counterparty, ensuring that these events are accurately captured in the training process. We further extend Han and Long's (2020) a posteriori error analysis to BSDEs on bounded domains. Due to the random exit from the domain, we obtain an order of convergence of O(h^{1/4-epsilon}) rather than the usual O(h^{1/2}). Numerical experiments illustrate that this method drastically reduces computational demands and successfully scales to high-dimensional, non-symmetric portfolios. The results confirm its effectiveness and accuracy, offering a practical alternative to nested Monte Carlo simulations in multi-counterparty xVA analyses.

It is widely believed that given the same labeling budget, active learning (AL) algorithms like margin-based active learning achieve better predictive performance than passive learning (PL), albeit at a higher computational cost. Recent empirical evidence suggests that this added cost might be in vain, as margin-based AL can sometimes perform even worse than PL. While existing works offer different explanations in the low-dimensional regime, this paper shows that the underlying mechanism is entirely different in high dimensions: we prove for logistic regression that PL outperforms margin-based AL even for noiseless data and when using the Bayes optimal decision boundary for sampling. Insights from our proof indicate that this high-dimensional phenomenon is exacerbated when the separation between the classes is small. We corroborate this intuition with experiments on 20 high-dimensional datasets spanning a diverse range of applications, from finance and histology to chemistry and computer vision.

A growing literature argues that progress in human longevity is slowing, and that this slowdown may signal an approaching biological limit to lifespan. The argument rests on visible flattening of cumulative life expectancy records, evaluated through linear regressions or through comparisons of average gains across decades. These summaries, however, provide only weak evidence for slowing improvements, because they cannot distinguish a true from an apparent slowdown. An apparent slowdown may arise due to periods of low variance around unchanged mean annual gains. Applying a Bayesian change-point framework to annual gains, both at the best-practice frontier and separately for each record-holding country, we find no evidence that the expected annual gain has changed across nearly two centuries, but strong evidence that its variance has moved through distinct historical regimes, with progress most regular in recent decades. The recent flattening is consistent with a low-variance regime and provides little evidence for a decline in the underlying mean pace of improvement. Claims that the best-practice frontier signals a biological ceiling should therefore not rest on the recent bend in the cumulative record alone. The frontier is better read as an empirical benchmark, the highest country-specific survival achieved under observed historical conditions.

Acceleration of large language model pre-training is a critical issue in present NLP research. In this paper, we focus on speeding up pre-training by progressively growing from a small Transformer structure to a large one. There are two main research problems related to progressive growth: growth schedule and growth operator. For growth schedule, existing work has explored multi-stage expansion of depth and feedforward layers. However, the impact of each dimension on the schedule's efficiency is still an open question. For growth operator, existing work relies on the initialization of new weights to inherit knowledge, and achieve only non-strict function preservation, limiting further optimization of training dynamics. To address these issues, we propose Masked Structural Growth (MSG), including growth schedules involving all possible dimensions and strictly function-preserving growth operators that is independent of the initialization of new weights. Experiments show that MSG is significantly faster than related work: we achieve a speed-up of 80% for Bert-base and 120% for Bert-large pre-training. Moreover, MSG is able to improve fine-tuning performances at the same time.

In ecology, psychometrics, and the analysis of social and financial networks, binary matrices are often analyzed conditional on their observed row and column sums, which restricts the problem to a finite sample space of matrices with the same margins. Two fundamental problems are to count this space and to sample uniformly from it. Sequential importance sampling (SIS) addresses both with independent weighted samples and an unbiased count estimator, but its efficiency depends critically on the proposal distribution. Existing proposals are analytically designed, and their accuracy can vary substantially with the margins. We show that the ideal SIS proposal, under which every weight equals the count and the variance vanishes, is exactly the policy of a generative flow network (GFlowNet) with unit reward on every matrix that has the given margins. We therefore propose MarginFlow, a framework that turns the design of the proposal into a learning problem and amortizes it across margins by exploiting their self-similarity. Every partial matrix is itself an instance with reduced margins, so one set transformer that reads the remaining margins serves every margin. We train MarginFlow on a pool of 1904 margins and evaluate it zero-shot on 1190 held-out margins, synthetic and real, from 3times3 to 870times6. On 1187 of the 1190 margins it matches or beats the best of 31 analytically designed configurations, chosen post hoc for each margin, and its median effective sample fraction is 99.8%. On the 56 margins where that best loses more than one nat of effective sample size, MarginFlow wins every one and raises the median effective sample fraction from 10.3% to 94.1%.

The performance of trend following strategies can be ascribed to the difference between long-term and short-term realized variance. We revisit this general result and show that it holds for various definitions of trend strategies. This explains the positive convexity of the aggregate performance of Commodity Trading Advisors (CTAs) which -- when adequately measured -- turns out to be much stronger than anticipated. We also highlight interesting connections with so-called Risk Parity portfolios. Finally, we propose a new portfolio of strangle options that provides a pure exposure to the long-term variance of the underlying, offering yet another viewpoint on the link between trend and volatility.

Deep learning (DL) creates impactful advances following a virtuous recipe: model architecture search, creating large training data sets, and scaling computation. It is widely believed that growing training sets and models should improve accuracy and result in better products. As DL application domains grow, we would like a deeper understanding of the relationships between training set size, computational scale, and model accuracy improvements to advance the state-of-the-art. This paper presents a large scale empirical characterization of generalization error and model size growth as training sets grow. We introduce a methodology for this measurement and test four machine learning domains: machine translation, language modeling, image processing, and speech recognition. Our empirical results show power-law generalization error scaling across a breadth of factors, resulting in power-law exponents---the "steepness" of the learning curve---yet to be explained by theoretical work. Further, model improvements only shift the error but do not appear to affect the power-law exponent. We also show that model size scales sublinearly with data size. These scaling relationships have significant implications on deep learning research, practice, and systems. They can assist model debugging, setting accuracy targets, and decisions about data set growth. They can also guide computing system design and underscore the importance of continued computational scaling.

The growth rate of Av(1324) is the last unknown Stanley-Wilf limit of a length-four pattern. Since 2020 the best rigorous lower bound has been the 10.271012 of Bevan, Brignall, Elvey Price and Pantone; we raise it to 10.412263. Their construction lays 1324-avoiders along an infinite staircase of two-cell blocks alternating with single connecting cells, and forbids a 1324 by a local condition on how the points of a block interleave with the components of the cell beside it. Certain points of a block, its leaves, may be exempted from that condition. They exempt them on one axis only, and report that they could not count the possibilities when both are exempted. This paper exempts them on both axes and counts the result. The second relaxation is their own argument read in the other axis, and the Harris correlation inequality bounds the joint count below by the product of the two counts taken separately, at the cost of one factor of the component generating function.

Why does the low dimensionality of representations, typically dapprox 1000, not prevent modern embedding-based retrieval models from scaling to billions, or even trillions, of data points? To answer this question, we study maximal-margin embeddings in the following retrieval model, classically studied in communication complexity [PS86] and more recently in embedding-based retrieval [WBNL26]. Let Ain {0,1}^{Ntimes n} be a matrix indicating whether each of N queries is relevant to each of n documents. We are interested in the largest margin m>0, denoted by m^{rd}(d, A), for which there exist unit norm embeddings of the queries and documents {U_j}_{j = 1}^N, {V_i}_{i = 1}^n with the following property. langle U_j, V_irangle ge m whenever A_{ji} = 1 and langle U_j, V_irangle le -m otherwise. A large margin is a key proxy for representation quality: it controls both robustness to perturbations and compositional generalization across queries. Our main theorem establishes that the best possible margin without a restriction on the dimension, m^{rd}(+infty, A), can be nearly achieved in dimension d = O(m^{rd}(+infty, A)^{-2}log n) which improves a theorem of [BDES02]. Together with a matching lower bound in Theorem 1.5, we conclude that when Ain {0,1}^{n{k}times n} is the matrix containing all possible k-sparse rows once, dimension d = O(klog (n/k)) is necessary and sufficient for the maximal possible margin m^{rd}(+infty, A) = Θ(k^{-1/2}) in this setting. This fully resolves the setup of [WBNL26]. We also give several constructions for large margins when d = o(klog (n/k)). Finally, we empirically test the InfoNCE and sigmoid losses for producing large margin embeddings and demonstrate a clear advantage of the sigmoid loss.

Scaling laws predict how loss decreases with increases in computation. We show, contrary to conventional wisdom, that architectural interventions can modify scaling exponents in pre-training, leading to power-law improvements in performance as computation increases. As an anchoring point, we consider the architectural formulation of looped transformers. Although not typically used in this way, looping, also known as recursive depth, provides a mechanism for model growth, by increasing the number of loops during training. Model growth, with and without shared weights, provides the biggest changes to the scaling exponents. In particular, a 7.4B model growth architecture matches GPT-3 13B on CORE with roughly 20times less compute, and has compute efficiency gains that increase with scale. Moreover, simply using a boundary operator in a vanilla transformer, which normalizes and injects an earlier block, also provides an exponent increase, although to a lesser extent. In the data-constrained, multi-epoch setting, standard looping has a useful regularizing effect, where we find it is compute-optimal to increase the number of loops with scale. These results can be understood through the lens of computational depth: for a given computational budget, we wish to increase the usable depth of the transformer, which can lead to efficiency gains that increase with scale.

In hybrid forecasting, a language model is often one of several available signals. A system may already have a market, crowd, or statistical forecast and must decide whether the model adds useful information or should be ignored. The relevant target is therefore not standalone model accuracy, but relative competence, defined as the model's marginal value beyond the available external forecast. Under Brier loss, we characterize when model disagreement can improve an external forecast and derive the gain from using domain-specific rather than global pooling weights. We then introduce a competence gate that estimates domain-level source weights from resolved outcomes, shrinks uncertain estimates toward a global weight, and recalibrates the pooled forecast. Across 2,357 resolved binary questions and five language models, the gate improves the main external baseline from 0.0771 to 0.0732 Brier and significantly outperforms global forecast combinations. The gain remains significant under leakage controls and against a leakage-safe time-series prior on the pooled structured set, with separate evidence on FRED. In contrast, the gate gives no significant improvement on the official ForecastBench market subset, where it largely defers to the market. Across four Qwen models, verbal confidence does not reliably identify when the model outperforms the external forecast, while outcome-estimated competence supports better abstention decisions. These results provide a practical approach for selective model use based on measured marginal value.

In continual learning (CL), model growth enhances adaptability to new data. However, when model growth is applied improperly, especially in task-agnostic CL, where the entire grown model is used for inference, it can lead to severe degradation of learned knowledge, a problem we term growth-induced forgetting. Most existing methods that adopt model growth to improve adaptability often overlook the forgetting issue, resulting in compromised knowledge retention, making them unsuitable for task-agnostic settings. To promote both adaptability and knowledge retention with model growth, we identify the key: gradient and parameter sparsity. Introducing SparseGrow, which increases gradient sparsity through layer expansion and gradient gating to enable focused updates on parameters while preserving critical parameters, thus inhibiting forgetting. Moreover, it promotes parameter sparsity with sparse initialization and training, aiming at better control of model plasticity, improving adaptability over new data. Extensive experiments across diverse datasets, task-agnostic settings, and a large number of tasks demonstrate the necessity of controlled layer expansion and validate the effectiveness of SparseGrow in achieving high adaptability while minimizing forgetting in continual learning. By enabling model growth with sparsified gradients and parameters, SparseGrow paves the way for building scalable lifelong learning systems capable of continual adaptation with better knowledge retention.

Self-evolving vision-language models train on questions they generate from unlabeled images. Since these questions have no gold answers, prior methods label them by majority vote over sampled answers or by a model judge. In a human evaluation, we find that 24\% of majority-vote labels and 18\% of model-judge labels produced during self-evolution are wrong. To address this problem, we present Verifiable QA Generation for Self-Evolving Models (VQS), which changes how the model judges answers. Instead of voting on an answer, the model parses each image into a structured record, such as a scene graph, a chart table, or a diagram graph. Fixed programs then write a question from the record and compute its answer. The model still acts as a visual checker, but it only confirms the individual facts the program reads, one short claim at a time. These claim-level checks select the parser's training targets, so the parser also improves without labels. Human raters find 94\% of VQS answers correct, against 76\% for majority voting. Across ten benchmarks, VQS improves Qwen3-VL by up to 3.18 points at the 2B, 4B, and 8B scales and outperforms the strongest self-evolving baseline at each. Gains keep growing over three training rounds, reaching 3.84 points at 2B. Code is released at https://github.com/ahmedheakl/VQS