Machine Learning · Cross-listed from cs.CV
Is Complex Training Necessary for Long-Tailed OOD Detection? A Re-think from Feature Geometry
Ningkang Peng, Xuanming Chen and Yanhui Gu
Long-tailed out-of-distribution (LT-OOD) detection is often addressed with specialized training, including auxiliary out-of-distribution (OOD) data, abstention heads, contrastive objectives, energy losses, or gradient-conflict control. We show that these training mechanisms can obscure a simpler issue: frozen long-tailed representations may already contain useful OOD evidence, but raw Mahalanobis distance is distorted by frequency-coupled feature radius and poorly supported tail covariance. We propose Hyperspherical Pooled Mahalanobis (HPM), a post-hoc detector that normalizes features onto the unit sphere and replaces class-specific covariance with a pooled, ridge-regularized metric while keeping class means as semantic anchors. In CIFAR-LT experiments and an ImageNet-100-LT near-OOD boundary analysis, HPM improves raw Mahalanobis scoring; for Prior-Calibrated ERM (PC-ERM), it raises AUROC from 46.49 to 85.67 on CIFAR-10-LT and from 50.40 to 78.35 on CIFAR-100-LT. This simple PC-ERM+HPM pipeline also achieves the best Log Efficiency Score (LES; 3.08) on CIFAR-100-LT, retaining roughly 95% of the best CIFAR-100-LT AUROC observed among the compared post-hoc scores at substantially lower training-time cost. These results argue for evaluating representation quality, detector geometry, and training complexity as separate factors in LT-OOD detection.
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Machine Learning
When Accuracy Is Not Enough: Uncertainty Collapse between Noisy Label Learning and Out-of-Distribution Detection
Ningkang Peng, Jingyang Mao, Runhan Zhou et al. (+2 more)
Learning with noisy labels (LNL) is typically benchmarked by closed-set classification accuracy, yet deployment often requires classifiers to reject out-of-distribution (OOD) inputs. We present a learner-agnostic ACC-OOD
benchmark that freezes LNL checkpoints and evaluates them with standardized near-/far-OOD routing and post-hoc scores across synthetic and real label noise. The
benchmark reveals a recurring failure mode: high closed-set accuracy does not ensure OOD reliability, because low-confidence, misclassified in-distribution samples can overlap the score and feature regions occupied by OOD inputs under noisy training. We term this pathology uncertainty collapse. This structural overlap can make high-accuracy LNL methods lose separability at the ID-error/OOD interface under standard OOD scores. As an intervention, we study Virtual Margin Regularization (VMR), a lightweight repair probe demonstrated mainly with PSSCL that synthesizes boundary virtual outliers on trusted ID batches and widens the energy margin. VMR partially reduces the collapse-induced far-OOD failure without replacing the host objective or sacrificing closed-set accuracy in the tested settings. These results support LNL
benchmarks that co-report closed-set generalization, open-world reliability, and structural overlap diagnostics.
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All authors Ningkang Peng, Jingyang Mao, Runhan Zhou, Peirong Ma, Yanhui Gu
Machine Learning
HydroAgent: Closing the Gap Between Frontier LLMs and Human Experts in Hydrologic Model Calibration via Simulator-Grounded RL
Zhi Li, Songkun Yan, Jie Cao et al. (+4 more)
Calibrating distributed hydrologic models is a critical bottleneck across operational water resources management - streamflow prediction, reservoir operation, drought monitoring, infrastructure design, and flood
forecasting all depend on it. Each basin demands an expert to translate hydrograph signatures into adjustments of a high-dimensional parameter vector, and the resulting workflow does not transfer between watersheds. We ask: can frontier large
language model (LLM)
agents replace the human hydrologic modeler, and if not, what would it take? We
benchmark nine frontier LLM
agents - Claude Opus 4.6/4.7, Sonnet 4.6, GPT-5/5.4/5.4-pro, and Gemini 2.5-pro/3.1-pro/3-flash - on the operational CREST distributed hydrologic model used by the U.S. National Weather Service for flash-flood
forecasting. Best-of-twenty-rounds Nash-Sutcliffe Efficiency (NSE) across four held-out gauges spanning 329-40,792 km2 ranges from -0.16 (GPT-5.4) to 0.75 (Sonnet 4.6); the ceiling reproduces across all three vendors and capability tiers, with the strongest models concentrating in the 0.65-0.75 band, and no model reaches the human-expert reference except Opus-4.7 on one gauge. We argue this gap is not a parameter-count problem but a domain-grounding problem. We then propose HYDROAGENT, fine-tuning open-weight Qwen3-4B with supervised fine-tuning on 2,576 expert calibration trajectories and Group-Relative Policy Optimization using NSE as a verifiable reward from online CREST simulations - reinforcement learning with simulation feedback (RLSF). For Earth system science, a small domain-tuned policy with simulator-in-the-loop RL is a more compute-efficient and physically faithful path than scaling generic frontier models, and the multi-modal richness of Earth data - remote sensing, in-situ time series, and forecaster narrative - makes domain
agents a leveraged direction for AI in physical science.
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All authors Zhi Li, Songkun Yan, Jie Cao, Mofan Zhang, Anjiang Wei, Jinwoong Yoo, Yang Hong
Machine Learning · Cross-listed from cs.IR
Uncertainty-Calibrated Recommendations for Low-Active Users
Bob Junyi Zou, Sai Li, Tianyun Sun et al. (+2 more)
A fundamental challenge in recommender systems is balancing reliability for Low-Active Users (LAUs) with diversity for High-Active Users (HAUs). The key to this balance lies in quantifying model uncertainty, which approximates the risk of prediction errors and reveals the limits of the model's current knowledge. On large-scale short-
video and livestream platforms, model uncertainty can warn of low-quality recommendations that may lead to disengagement of LAUs and at the same time identify opportunities to diversify content recommendation for HAUs. To leverage this dichotomy, we introduce a unified, production-ready framework that calibrates uncertainty to drive differentiated strategies. Specifically, we implement a model-uncertainty-based risk-averse deboosting policy for LAUs to suppress unreliable recommendations, while employing a risk-seeking Upper Confidence Bound (UCB) strategy for HAUs to encourage exploration. Validated on a major livestream platform, our framework demonstrates significant improvements in retention (active hours) and satisfaction (quality watch time ratio) for LAUs as well as remarkable increases in interest diversity and category coverage for HAUs, proving the value of uncertainty-aware recommendation in industrial settings.
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All authors Bob Junyi Zou, Sai Li, Tianyun Sun, Wentao Guo, Qinglei Wang
Machine Learning
Revisiting the Adam-SGD Gap in LLM Pre-Training: The Role of Large Effective Learning Rates
Athanasios Glentis, Dawei Li, Chung-Yiu Yau et al. (+1 more)
It is widely believed that
stochastic gradient descent (SGD) performs significantly worse than adaptive optimizers such as Adam in pre-training Large
Language Models (LLMs). Yet the underlying reason for this gap remains unclear. In this work, we attribute a large part of the discrepancy to SGD's inability to sustain learning rates comparable to Adam's much larger effective learning rates. Through empirical and theoretical analysis of LLM pre-training dynamics, we identify that training is characterized by small gradient norms and large weight-to-gradient ratios, an effect that becomes more pronounced with larger batch sizes typical in pre-training, necessitating such large effective learning rates. However, we find that output-layer gradient magnitudes become highly uneven across
token classes, and that large gradient spikes frequently occur during training. Together, these effects severely restrict the admissible learning rate of SGD. Guided by this understanding, we show that simple clipping mechanisms that stabilize SGD at large learning rates enable it to recover most of Adam's performance. In our large-scale experiments, the validation loss gap between large-learning-rate SGD and Adam shrinks from more than 50% to only about 3.5% when pre-training a 1B-parameter LLaMA model with a 1M-
token batch size.
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All authors Athanasios Glentis, Dawei Li, Chung-Yiu Yau, Mingyi Hong
Machine Learning
Learning Variable-Length Tokenization for Generative Recommendation
Minhao Wang, Bowen Wu and Wei Zhang
Generative recommendation reformulates recommendation as next-
token prediction over discrete semantic identifiers (IDs). A fundamental yet unexplored design choice is that existing methods employ fixed-length tokenization for all items, implicitly assuming uniform encoding capacity regardless of item characteristics. Through systematic experiments across four
datasets, we discover the Popularity-Length Paradox: popular items achieve optimal performance with short IDs, while tail items require substantially longer codes to capture discriminative semantics. This reveals a critical mismatch where popular items benefit from abundant collaborative signals and require minimal semantic detail, whereas tail items must rely on fine-grained content features due to sparse interaction data. To address this, we propose VarLenRec, a framework for learning variable-length tokenization. We develop Popularity-Weighted Information Budget Allocation (PIBA), an information-theoretic framework proving that optimal ID length should scale as a negative power of popularity. Directly implementing variable-length allocation faces two technical challenges: standard Euclidean residual quantization lacks
geometric capacity to support diverse code lengths without distortion, and discrete length decisions are non-differentiable. We address these through
Hyperbolic Residual Quantization, which leverages the exponential volume growth of the Poincaré ball to naturally stratify encoding capacity, and a Soft Length Controller, which enables differentiable length prediction via continuous layer retention probabilities regularized by PIBA-derived priors. Extensive experiments demonstrate that VarLenRec achieves significant improvements over state-of-the-art methods in recommendation accuracy and training/inference efficiency, revealing the importance of adaptive encoding capacity in generative recommendation.
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Machine Learning · Cross-listed from math.ST
Radu Lecoiu, Debarghya Mukherjee and Pragya Sur
Self-
distillation has emerged as a promising technique for improving model performance in modern machine learning systems. We develop the statistical foundations of self-
distillation in high-dimensional linear regression by introducing and analyzing a broad class of
estimators, namely spectral shrinkage
estimators. We consider both spiked and general covariance
matrices. For the former, we establish that when the covariance has $s$ distinct spikes, $s$-step self-
distillation achieves optimal prediction among spectral shrinkage
estimators, outperforming well-known
estimators in statistics and machine learning. Moreover, we show that $s$ steps are necessary for optimality: any $(s-k)$-step distilled
estimator is strictly suboptimal for $1 \leq k \leq s$. For general covariance
matrices, we show that self-
distillation approaches the optimal limiting prediction risk among continuous spectral shrinkage
estimators as the number of
distillation steps increases. We further develop a generalized cross-validation procedure for selecting the
distillation parameters from data and establish an asymptotic oracle guarantee for the resulting
estimator. We also study a
federated approach where multiple data centers share spectral shrinkage
estimators and a common server seeks to aggregate them to achieve optimal performance. In this case, we find that the best local rule again takes the form of self-
distillation, though it differs from the optimal rule when data are hosted centrally on a single server. Together, our results explain why self-
distillation improves predictive performance and provide a broader statistical framework that connects it to classical shrinkage-based methods.
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Machine Learning · Cross-listed from stat.ML
Feature Learning in Linear-Width Two-Layer Networks: Two vs. One Step of Gradient Descent
Behrad Moniri and Hamed Hassani
We study feature learning in two-layer neural networks within the linear-width regime, where the number of hidden
neurons, sample size, and input dimension scale proportionally. While recent work has analyzed feature learning via a single step of gradient descent on the first layer weights in this regime, such one-step update schemes are fundamentally limited: the update to the weights is approximately rank-one, captures only a single direction, and requires the target function to have an information exponent of one. In this paper, we go beyond one-step updates to provide a full characterization of the features learned during the second step of gradient descent with step-sizes $\eta_1\asymp N^{\alpha_1}$ and $\eta_2 \asymp N^{\alpha_2}$ for $\alpha_1, \alpha_2 \in [0,0.5)$, where $N$ is the number of hidden
neurons. We derive a spectral characterization of the updated weights, demonstrating they behave as a spiked random
matrix with multiple outliers, each corresponding to a learned direction. We show that the number of the outliers is determined by the parameters $\alpha_1, \alpha_2$ through $\lfloor \frac{\alpha_2}{1/2 - \alpha_1} \rfloor$. Furthermore, by analyzing the
alignment between the learned directions and the target function, we identify a gap between training with independent versus reused batches. While independent batches restrict learning to directions with an information exponent of one, batch reuse enables the second update to capture directions even when the information exponent exceeds one, provided that $\alpha_1, \alpha_2$ are chosen properly. This shows that the benefits of batch reuse, previously observed in narrow-width regimes, persist in the linear-width limit as well. By characterizing these early-phase evolutions, our work proposes a tractable framework for studying optimization and feature learning phenomenology in modern overparameterized networks.
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Machine Learning
AURORA: Contextual Orthogonalization for Geometric Representation Learning in Healthcare Foundation Models
Yuanyun Zhang and Shi Li
Recent healthcare foundation models have achieved strong predictive performance through large scale self supervised learning, yet their latent representations frequently entangle physiologic severity, intervention intensity, observational structure, and institutional workflow into shared
embedding directions. While effective for downstream prediction, such representations remain semantically opaque and unstable under contextual shift. We introduce AURORA, Adaptive Uncertainty aware Representations through Orthogonalized Relational
Alignment, a new framework for healthcare representation learning based on contextual latent geometry. Rather than optimizing a single unified
embedding manifold, AURORA decomposes representations into orthogonal semantic subspaces corresponding to distinct contextual factors and learns relational consistency objectives within each subspace. This induces latent spaces that are both semantically disentangled and geometrically interpretable. Across multiple clinical prediction and
retrieval tasks, AURORA consistently outperforms reconstruction, contrastive, and self
distillation baselines while substantially improving contextual disentanglement, neighborhood purity, and robustness under institutional distribution shift. Our results suggest that latent geometry itself constitutes an important axis of healthcare foundation model design and that explicitly structuring representation space according to contextual semantics provides a complementary direction beyond conventional predictive compression objectives.
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Machine Learning · Cross-listed from cs.SI
MV-Gate: Insider Threat Detection via Multi-View Behavioral Statistics and Semantic Modeling
Kaichuan Kong, Dongjie Liu, Xiaobo Jin et al. (+1 more)
Insider threats often reveal early anomalies through disruptions in behavioral statistics-such as altered recurrence patterns or short-versus long-term frequency shifts-rather than changes in event semantics. Yet, as the field has shifted from statistical modeling to log tokenization and deep sequential encoders, these statistical cues are weakened or lost, leaving current models insensitive to gradual and low-visibility insider behaviors.We propose MV-Gate, a multi-view behavior modeling framework that explicitly integrates statistical regularities with sequence semantics. MV-Gate constructs three aligned behavioral sequences: activity
tokens, multi-scale status signals capturing recurrence patterns, and frequency-deviation signals describing short- vs long-term intensity differences. An anomaly-aware gating mechanism injects these statistical views into the
attention computation, guiding the encoder to emphasize statistically irregular events. Experiments on CERT r4.2, CERT r5.2, and ADFA-LD show that MV-Gate achieves notable gains over classical, deep-learning, and domain-specific baselines, particularly for progressive, weak-signal threats. These results highlight the necessity of jointly modeling statistical and sequential evidence for robust insider-threat detection.
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All authors Kaichuan Kong, Dongjie Liu, Xiaobo Jin, Guanggang Geng
Machine Learning
Memisis: Orchestrating and Evaluating Synthetic Data for Tabular Health Datasets
Nitish Nagesh, Pengbao Zhou, Atchuth Naveen Chilaparasetti et al. (+8 more)
Synthetic data is widely used in healthcare to create
datasets that preserve statistical properties of real data without exposing sensitive patient information. Generating and evaluating synthetic data across
privacy, utility, and
fairness dimensions is crucial for enabling high-quality data availability in downstream prediction tasks and clinical decision making. We present Memisis, a tool that orchestrates and evaluates synthetic data by leveraging existing synthesis libraries, large
language models (LLMs), and state-of-the-art evaluation metrics. Our tool creates a unified workflow for data generation, validation, and evaluation. Users can control training size, training epochs, and the number of synthetic rows to sample. Beyond manual configuration, an interactive
agent mode allows users to specify data generation goals in natural
language, and the tool orchestrates the full pipeline by invoking existing synthesizers while performing the requisite evaluation. For the demo, we use an open-source schizophrenia
dataset with protected attributes related to race and gender, evaluate six synthesizers spanning GANs, VAEs,
diffusion models, and normalizing flows, and use a local LLM to orchestrate the workflow. The system affords users flexibility and control over the data generation and evaluation process.
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All authors Nitish Nagesh, Pengbao Zhou, Atchuth Naveen Chilaparasetti, Yajat Nagaraj Kiran, Tu Nguyen, Arshia Harish Puthran, Muhjaazee Love, Aadi Sharma, Mahdi Bagheri, Ian Harris, Amir M. Rahmani
Machine Learning
OSCAR: Offline Spectral Covariance-Aware Rotation for 2-bit KV Cache Quantization
Zhongzhu Zhou, Donglin Zhuang, Jisen Li et al. (+4 more)
INT2 KV-cache quantization is attractive for long-context LLM serving, but it remains difficult to make both accurate and deployable. Simple rotations such as Hadamard transforms reduce outliers, but still degrade at INT2 because they are not aligned with downstream
attention. We propose OSCAR, an Ultra-low-bit KV Cache quantization method that estimates
attention-aware covariance structures offline and uses them to derive fixed rotations and clipping thresholds for quantization. In this way, it aligns KV quantization with the covariance structures that
attention actually consumes. More importantly, we not only provide theoretical justification but also develop a fully deployable OSCAR system with a custom INT2
attention kernel that remains compatible with paged KV-cache serving and fused kernel pipelines, enabling seamless integration into modern LLM serving frameworks such as SGLang and vLLM. We evaluate our methods on recent
reasoning models with
reasoning traces of up to 32k
tokens across 5 tasks. On Qwen3-4B-Thinking-2507 and Qwen3-8B, OSCAR reduces the BF16 accuracy gap to 3.78 and 1.42 points, respectively, while naive rotation INT2 collapses to nearly zero. We further scale OSCAR to Qwen3-32B and GLM-4.7 (358B params), where it remains effectively on par with BF16. On long context - RULER-NIAH up to 128K, OSCAR remains robust on both Qwen3 models, while naive rotation INT2 collapses. System-wise, OSCAR reduces KV-cache
memory by approximately 8x, improves throughput by up to 7x at large batch sizes under the same
memory budget, and accelerates batch-size-1 decoding by up to 3x over BF16 due to reduced
memory bandwidth overhead.
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All authors Zhongzhu Zhou, Donglin Zhuang, Jisen Li, Ziyan Chen, Shuaiwen Leon Song, Ben Athiwaratkun, Xiaoxia Wu
Machine Learning
Testable and Actionable Calibration for Full Swap Regret
Konstantina Bairaktari, Lunjia Hu, Huy L. Nguyen et al. (+1 more)
AI generated predictions increasingly inform decision making in critical tasks, and therefore must be trustworthy. One widely used measure of trustworthiness is calibration, which requires that the predictions match the true frequencies and can be treated like real probabilities of a given outcome. However, defining calibration is subtle, and designing good measures of calibration error has been an active topic of recent research. The first goal is to find calibration measures that are actionable, meaning they can inform decision makers about their utility loss when predictions are treated as true probabilities, which is known as swap regret. The second goal is to find calibration measures that are testable, meaning that calibration error can be measured from a small sample of predictions and outcomes. Although these are very basic requirements, there is no existing calibration measure that fully satisfies both properties, and all existing measures relax actionability by bounding a weaker notion of swap regret, or relax testability by having suboptimal estimation error. We introduce a new calibration measure, Soft-Binned Calibration Decision Loss (SCDL), which we prove is fully actionable without weakening either requirement, and testable with nearly optimal error rate. In addition, SCDL satisfies other desired properties such as continuity and consistency. We also provide a set of experiments confirming that the theoretical advantages of SCDL compared to other measures lead to better performance in practice.
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All authors Konstantina Bairaktari, Lunjia Hu, Huy L. Nguyen, Jonathan Ullman
Machine Learning · Cross-listed from stat.ML
StatQAT: Statistical Quantizer Optimization for Deep Networks
Mehmet Aktukmak, Daniel Huang and Ke Ding
Quantization is essential for reducing the computational cost and
memory usage of deep neural networks, enabling efficient inference on low-precision hardware. Despite the growing adoption of uniform and floating-point quantization schemes, selecting optimal quantization parameters remains a key challenge, particularly for diverse data distributions encountered during training and inference. This work presents a novel statistical error analysis framework for uniform and floating-point quantization, providing theoretical insight into error behavior across quantization configurations. Building on this analysis, we propose iterative quantizers designed for arbitrary data distributions and analytic quantizers tailored for Gaussian-like weight distributions. These methods enable efficient, low-error quantization suitable for both activations and weights. We incorporate our quantizers into quantization-aware training and evaluate them across integer and floating-point formats. Experiments demonstrate improved accuracy and stability, highlighting the effectiveness of our approach for training low-precision neural networks.
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Machine Learning · Cross-listed from cs.AI
Divergence-Suppressing Couplings for Rectified Flow
Yimeng Min and Carla P. Gomes
The promise of Rectified Flow rests on producing self-generated couplings whose trajectories are straight, or nearly so. In practice, trajectories generated by the base flow model can bend and intertwine, and the resulting coupling inherits this distortion. In this paper, we identify that such trajectory
entanglement is often associated with regions of nonzero divergence in the learned velocity field, where local expansion or contraction distorts trajectories and steers particles away from their ideal endpoints. We then propose divergence-suppressing couplings for Rectified Flow, an offline correction that attenuate the divergent component of the learned velocity during coupling generation. The correction is paid only once per coupling pair and amortized over training, so deployment runs plain Euler at identical wall-clock cost to standard Rectified Flow. Empirically, this offline modification yields consistent improvements on 2D synthetic
benchmarks and on image generation.
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Machine Learning
L-Drive: Beyond a Single Mapping-Latent Context Drives Time Series Forecasting
Fan Zhang, Shijun Chen and Hua Wang
Mainstream methods for multivariate time-series
forecasting largely follow the Direct-Mapping paradigm. They learn a unified mapping from history to the future in the observation space to fit value-level dependencies. However, real-world systems often undergo distribution shifts and regime changes. In such cases, a unified mapping can exhibit response lag around turning points, causing error accumulation within the switching window and reducing
forecasting reliability. To address this issue, we propose L-Drive, a change-aware
forecasting framework. L-Drive introduces a Latent-Context, to explicitly characterize high-level dynamics evolving over time, and uses gating to modulate increment representations. This provides more timely change cues and improves adaptation to changing segments. In addition, it incorporates patch-shared relative positional basis functions to strengthen intra-segment structural modeling and reduce overfitting caused by absolute-position memorization. Extensive experiments validate the effectiveness of L-Drive and show a better overall trade-off between
forecasting accuracy and computational efficiency.
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Machine Learning · Cross-listed from cs.CV
Domain Incremental Learning for Pandemic-Resilient Chest X-Ray Analysis
Danu Kim
Deep learning models achieved high accuracy in pneumonia detection from chest X-rays. However, their generalization across clinical domains remains limited due to variations in imaging devices, acquisition protocols, and institutional conditions. This study introduces a replay-based domain-incremental continual learning designed to enable continual adaptation to cross-domain variations without catastrophic forgetting. The proposed method incorporates a class-aware balanced replay to maintain balanced class representation within a constrained
memory and a class-aware loss to dynamically reweight class imbalance during training. Experiments conducted on a domain-shifted PneumoniaMNIST
dataset consisting of five simulated domains demonstrate that the proposed method achieves an average accuracy of 88.66%, outperforming Experience Replay, Fine-Tuning, and Joint Training baselines. These findings highlight the efficacy of the proposed approach in achieving robust and consistent pneumonia detection across clinical environment variations.
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Machine Learning · Cross-listed from q-fin.TR
Sequential Structure in Intraday Futures Data: LSTM vs Gradient Boosting on MNQ
Mathias Mesfin
This paper compares gradient boosting and long short-term
memory (LSTM) architectures for intraday directional prediction in Micro E-Mini Nasdaq 100 futures (MNQ). Motivated by recent foundation-model research on financial candlestick data, including the Kronos architecture, we test whether five-minute OHLCV bar sequences contain exploitable sequential predictive structure at the scale of a single instrument
dataset. Using 944 trading days from 2021-2025, four model configurations are evaluated under strict expanding-window walk-forward validation across three out-of-sample periods. The target variable is whether the session close exceeds the 10:30 AM open by more than ten points. No configuration produces statistically significant out-of-sample accuracy above the 51.8% base rate. Combined OOS accuracies range from 50.00% to 50.89% across gradient boosting variants, while the LSTM achieves 50.59%. Permutation tests yield p-values of 0.135 for the best gradient boosting model and 0.515 for the LSTM, indicating no statistically significant predictive edge. Feature importance instability across walk-forward folds suggests noise fitting rather than stable structural signal capture. The results indicate that four years of single-instrument five-minute OHLCV data are insufficient for reliable sequential ML-based intraday
forecasting. The primary contribution is a documented evaluation of a Kronos-inspired architecture on a constrained real-world
dataset, providing an empirical lower bound on data scale requirements for sequential financial ML.
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Machine Learning · Cross-listed from stat.ML
How does feature learning reshape the function space?
João Lobo, Bruno Loureiro, Long Tran-Than et al. (+1 more)
Feature learning is widely regarded as the key mechanism distinguishing neural networks from fixed-kernel methods, yet its impact on the induced function space remains poorly understood. In this work, we precisely characterize how the function space spanned by the features of a two-layer neural network evolves during gradient descent training. We prove that, in the high-dimensional proportional regime, after a large gradient step the post-update feature distribution is well approximated by a target-dependent spiked Gaussian covariance. This induces a data-adaptive kernel that reshapes the function space and modifies its spectral structure. Our analysis reveals that feature learning can be interpreted as a distributional transformation in either parameter space or input space, equivalently as the introduction of a target-dependent kernel. In particular, it selectively amplifies
eigenvalues aligned with the target direction and mixes leading eigenfunctions, coupling the top radial mode with a target-aligned quadratic harmonic. Overall, our results provide a precise function-space perspective on early-stage feature learning: rather than just rescaling a fixed kernel, gradient descent induces a data-adaptive deformation that preferentially enhances directions aligned with the signal in the data.
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All authors João Lobo, Bruno Loureiro, Long Tran-Than, Fanghui Liu
Machine Learning · Cross-listed from stat.ML
Online Conformal Prediction for Non-Exchangeable Panel Data
Daohong Tu and Kay Giesecke
We study online conformal prediction in a partially observed panel: a new cross-section of peer outcomes is observed before each target outcome, target feedback may be intermittent or absent, and neither units nor rounds need be exchangeable. We propose Weighted Temporal
Quantile Adjustment (W-TQA), which combines similarity weights learned from unit histories with an adaptive target-specific miscoverage level. We prove that neither target-peer mismatch nor coverage on unrevealed rounds is identifiable, so assumptions on cross-unit similarity and on the feedback mechanism cannot be avoided. We bound the past-conditional miscoverage in terms of this mismatch, quantify the cost of learning the weights under a profile-similarity assumption, and show that the implemented procedure, which falls back on the largest peer score, attains long-run average coverage under missing-completely-at-random feedback and a feasibility condition on the calibration panel. On synthetic panels and four real panels, including a genuinely asynchronous U.S.-to-Tokyo equity panel, W-TQA attains the highest coverage on the worst-covered target units on every panel; similarity weighting contributes most when target feedback is scarce, and temporal adaptation more as feedback accumulates.
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Machine Learning
Toy Combinatorial Interpretability Models Reveal Lottery Tickets in Early Feature Space
Alon Bebchuk and Nir Shavit
The lottery ticket hypothesis posits that dense networks contain sparse subnetworks, “winning tickets,” that, when rewound to their initial weights and retrained in isolation, match the performance of the full model. We ask a more mechanistic question: what internal object does a winning ticket preserve? We work in a combinatorial, clause-structured toy setting that admits an interpretable feature-space representation with well-defined combinatorial distances between features. We show that winning tickets in weight space correspond to precursor locations in feature space that are already near, at initialization, to the final feature-channel codes. Dense SGD resolves these locations through structured selection: proximal locations either converge to final codes or are rejected, with rejection concentrated at more crowded
neurons, implicating competition under superposition. A winning ticket is thus a family of compatible code locations that jointly balance proximity to final codes with low inter-feature interference. Sparse retraining often re-expresses the same clause/template family on a different row, so the preserved object is family-level rather than microscopic row identity. We validate this account with lightweight probes based on feature-space distance and motion; in our setting, these probes frequently outperform established weight-based ticket discovery methods in both accuracy and exact code recovery. Although these findings are grounded in a toy setting, they suggest that the lottery ticket structure is governed by hidden feature-space geometry rather than weight-space subnetwork identity.
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