Papers

In this paper, we propose Complex Diffusion Maps (CDM), a novel diffusion mapping framework that aims to reveal the dominant complex harmonics of high-dimensional data. Inspired by the local Gaussian kernel relevant to the heat equation and the nonlocal Schrödinger kernel relevant to the Schrödinger equation, we propose a unified family of $\omega$-parameterized complex-valued kernels for the trade-off between local and nonlocal connections. We establish the theoretical foundation based on the operator spectrum theory, where the corresponding diffusion operator, diffusion distance, and complex harmonic maps are well-defined. An optimization-based interpretation of the maps is also developed, aiming to preserve angular structure in the complex diffusion space rather than relying solely on real-valued magnitude. We extensively evaluate CDM on both synthetic and real-world datasets. The complex-valued kernel amplifies differences among easily confusable samples, improving discriminative power over both linear and nonlinear methods based on real-valued kernels. CDM remains robust in high-noise settings, yielding a clearer eigengap that enhances spectral separation. For resting-state fMRI data, CDM captures more strongly correlated and nonlocal spatiotemporal dynamics. Without task-specific tuning, CDM achieves competitive performance on a public EEG sleep dataset, while maintaining high computational efficiency compared with both traditional machine learning and deep neural network approaches, highlighting its generality and practical value.

Virtual screening performance depends heavily on the chosen docking and scoring methods. Recent AI-based tools such as DiffDock and NMDN have reported strong benchmark results, but their practical utility on realistic, experimentally-derived datasets remains unclear. Here we perform a large-scale evaluation on the LIT-PCBA library (15 targets, 578,295 ligand-target pairs with experimentally confirmed actives and inactives). We compare AutoDock-GPU and DiffDock for pose generation, followed by rescoring with GNINA and NMDN. We further evaluate rank-based consensus strategies and supervised machine learning models trained on docking features. GNINA rescoring of AutoDock-GPU poses (AutoDock-GNINA) emerged as the strongest single method with a median EF1% of 2.14. DiffDock-based approaches underperformed relative to AutoDock-GNINA, particularly on challenging targets such as OPRK1. Carefully designed consensus ranking improved robustness but did not surpass the best single scorer. Supervised ML re-ranking delivered the largest gains, achieving a median EF1% of 4.49 (+110% over AutoDock-GNINA). Our results highlight that even the best classical+ML hybrid workflows provide only modest early enrichment on realistic benchmarks. We conclude that no single docking method dominates across targets and that rigorously validated, cost-effective combinations with supervised re-ranking currently offer the most practical value for virtual screening.

Fall detection is a critical task in healthcare, particularly for elderly people. Timely fall detection and treatment can prevent severe injuries. Sensor-based activity data can be used to detect fall. However, this data are highly sensitive and raises significant privacy concerns. Existing privacy approaches apply uniform noise across all training samples, which affects the prediction performance. To address this limitation, we propose a Class-Aware Adaptive Differential Privacy (CA-ADP) framework integrated with a hybrid 3D Convolutional Neural Network and Bidirectional Long Short-Term Memory (3D CNN-BiLSTM) architecture. The CA-ADP mechanism dynamically adjusts the magnitude of noise added to gradients based on the class composition of each mini-batch. This process ensures privacy while mitigates performance degradation. We formally analyze the $(\epsilon,\delta)$-Differential Privacy guarantee and provide a privacy-utility trade-off analysis. The proposed method is evaluated on three public benchmark datasets, namely SisFall, UP-Fall, and MobiAct. The experimental results show that the proposed privacy model achieves improvements of 3.3%, 8.5%, and 7.5% over the conventional privacy-based model in terms of F-score for the SisFall, UP-Fall, and MobiAct datasets, respectively. Comparisons with prior studies show that the CA-AD based framework achieves competitive performance and provides formal privacy guarantees, which are largely overlooked in existing studies. Wilcoxon signed-rank tests confirm that the proposed mechanism consistently outperforms conventional differential privacy. Those results establish the proposed CA-ADP framework as an effective approach to privacy-preserving fall detection in real-world healthcare settings.

Missing data imputation remains a fundamental challenge in modern data science, especially when uncertainty quantification is essential. In this work, we propose MissBGM, an AI-powered missing data imputation method via Bayesian generative modeling that bridges the expressive flexibility of neural networks with the statistical rigor of Bayesian inference. Unlike existing methods that often focus on point estimates or treat the missingness mechanism implicitly, MissBGM explicitly and jointly models the data-generating and missingness mechanisms, providing principled posterior uncertainty over imputations rather than a single point estimate. We develop a stochastic optimization framework with alternating updates among missing values, model parameters, and latent variables until convergence. Our theoretical analysis shows that estimates of missing values from MissBGM converge consistently under mild assumptions. Empirically, we demonstrate that MissBGM achieves superior performance over traditional imputers and recent neural network-based methods across extensive experimental settings. These results establish MissBGM as a principled and scalable solution for modern missing data imputation. The code for MissBGM is open sourced at https://github.com/liuq-lab/MissBGM.

External priors of unknown reliability create a brittle trade-off in causal discovery: blind trust amplifies errors, blind rejection wastes signal. Real priors are also heterogeneously reliable – physical laws are trustworthy, LLM-suggested edges are speculative – yet existing methods either ignore priors or impose them through globally uniform trust. We propose PRCD-MAP, a soft prior-consumption layer that assigns per-edge trust to an imperfect prior and uses it to modulate a prior-aware $\ell_1$ and prior-weighted $\ell_2$ regularizer in a MAP objective. Trust is calibrated by empirical Bayes on a Laplace-approximated marginal likelihood and propagated along the prior graph by an MLP, so data-confirmed neighborhoods boost trust and contradictions suppress it. PRCD-MAP enjoys a population-level safety guarantee: it is $\varepsilon$-safe in expectation over the prior-generation distribution, with $\varepsilon\leq C\cdot\mathrm{acc}(1{-}\mathrm{acc})\cdot d^2/T$ at the parametric $T^{-1}$ rate and vanishing at the prior-quality endpoints. When the prior is uninformative, learned trust provably collapses to its floor and the method recovers a no-prior baseline. Empirically, on real CausalTime data PRCD-MAP exploits informative LLM priors (LLM-prior gain $+0.067/+0.089$ AUROC on AQI/Medical over a no-prior PRCD-MAP backbone; combined backbone+prior lead $+0.123/+0.043$ over PCMCI+), auto-attenuates on the anonymous-variable Traffic stress test, and retains a lead at $d{=}300$; against BayesDAG, the closest soft-Bayesian baseline, PRCD-MAP wins on every CausalTime dataset under a matched $W_0$-only protocol. A four-way ablation isolates each component: EB calibration and MLP trust propagation jointly carry the plurality of the gain, with positive sign on every dataset. Extensions to nonlinear (NAM) and cross-sectional settings show the calibrated-trust principle is setting-agnostic.

We propose Flow-Anchored Noise-conditioned Q-Learning (FAN), a highly efficient and high-performing offline reinforcement learning (RL) algorithm. Recent work has shown that expressive flow policies and distributional critics improve offline RL performance, but at a high computational cost. Specifically, flow policies require iterative sampling to produce a single action, and distributional critics require computation over multiple samples (e.g., quantiles) to estimate value. To address these inefficiencies while maintaining high performance, we introduce FAN. Our method employs a behavior regularization technique that uses a single flow policy iteration and requires a single Gaussian noise sample for distributional critics. Our theoretical analysis of convergence and performance bounds demonstrates that these simplifications not only improve efficiency but also lead to superior task performance. Experiments on robotic manipulation and locomotion tasks demonstrate that FAN achieves state-of-the-art performance while significantly reducing both training and inference runtimes. We release our code at https://github.com/brianlsy98/FAN.

Human cognition emerges from coordinated spiking dynamics in distributed neural circuits, where information is encoded via both firing rates and precise spike timing determined by brain rhythms. Inspired by this notion, we propose a brain-inspired learning primitive in which cognition-level neural synchrony emerges through iterative bottom-up and top-down interactions between micro-scale dynamics of spiking neurons and a macro-scale mechanism of oscillatory synchronization. Specifically, we model each parcel (e.g., a cortical region or an image pixel) in the target system as a spiking neuron embedded in a predefined connectivity scaffold. Low-level information is encoded in a spatiotemporal domain, where neurons are selectively grouped and fire spontaneously over time through self-organized dynamics. In the bottom-up route, oscillatory synchronization is formed from past spiking activity accumulated over a finite memory window. Since brain dynamics operate in a regime of partial and transient synchronization rather than global phase locking, we model oscillatory coordination using a time-delayed synchronization formulation, which enables a top-down modulation of heterogeneous neural spiking for a large-scale distributed system. Together, we devise a spiking-by-synchronization neural network (S2-Net) that uses rhythmic timing as a control mechanism for efficient information processing. Promising results have been achieved across a broad range of tasks, including neural activity decoding, energy-efficient signal processing, temporal binding and semantic reasoning.

We study homogeneous refinement operators \((V\gamma)(t)=\sum_{j\in\mathbb Z}A_j\gamma(Mt-j)\), acting on compactly supported continuous piecewise linear curves \(\gamma:\mathbb R\to\mathbb R^p\), where \(M\ge2\) and only finitely many matrices \(A_j\in\mathbb R^{p\times p}\) are nonzero. We prove that the iterates \(V^n\gamma\) admit exact ReLU realizations of fixed width and depth \(O(n)\). The main new ingredient is an exact loop controller for the residual dynamics. Instead of propagating scalar residual surrogates, the construction transports the residual orbit by a forward-exact state on a polygonal loop. Scalar factors and digit selectors are then recovered from this loop state by complementary CPwL readouts. The loop seam is not removed, but its remaining ambiguity is confined to the final readout/selector stage, where it is harmless because the scalar atom is supported away from the seam. This gives a homogeneous \(M\)-ary vector-valued extension of the scalar binary refinable-function construction with a more geometric controller architecture. We also record crude exponential bounds on the network weights and biases. Affine forcing terms are handled by expanding affine iterates into finite sums of homogeneous iterates, giving exact fixed-width realizations with depth \(O(n^2)\), and anchored open curves reduce to compactly supported defects with affine anchor mismatch. We also describe homogeneous polygonal generators, including dragon-type examples and a self-intersecting Hilbert-type prototype in arbitrary dimension. The extended version includes stage-dependent forcing, finite-state stacking reductions, and further geometric constructions such as Koch-, Gosper-, Morton-, and connector-based Hilbert-type variants.

Reliable subnational population estimates are essential for applications, yet remain difficult where censuses are sparse, outdated or spatially coarse. Existing population-mapping workflows rely on hand-built geospatial covariates, such as settlement extent, night-time lights, and environmental conditions, which must be assembled and harmonised across scales and geographies. Geospatial foundation models offer an alternative by learning reusable representations of place from more multifaceted and heterogeneous data sources. Here, we benchmark Population Dynamics Foundation Model (PDFM) embeddings against the harmonised geospatial covariates for subnational population estimation in Brazil, Nigeria and the United States. Under geographically structured validation, PDFM increased predictive fit by a median of 20.1% (IQR: 10.0-33.2%, across country-model comparisons) reduction in unexplained variance, and reduced Kullback-Leibler divergence by 23.2% (9.2-26.2%). However, these gains were uneven. PDFM was most advantageous where the geospatial covariates weakly characterised settlement context, such as larger and less-developed subnational areas. Moreover, PDFM performance was scale-coupled with embeddings providing less flexible transfer across spatial aggregations than geospatial covariates. These findings showed that geospatial foundation-model representations of place can improve population estimation in data poor settings, but their benefits break down predictably under spatial scale mismatch, revealing a fundamental limitation of current geospatial AI.

Financial institutions face significant challenges in detecting sophisticated money laundering patterns, such as smurfing and layering, due to extreme data imbalance (0.13% fraud rate) and evolving adversarial evasion tactics. This paper proposes FraudShield AI, a hybrid framework that integrates Long Short-Term Memory (LSTM) networks with hand-crafted Graph Topological Features to capture both temporal sequences and structural relational context. By engineering network-centric features including PageRank Centrality, In-Degree dynamics, and a custom Flow Ratio, the system shifts the detection paradigm from isolated transaction analysis to network-level forensics. A Focal Loss objective is used to address class imbalance, and a dynamic thresholding mechanism is introduced to improve resilience against low-value smurfing attacks. Experimental evaluation on the PaySim dataset shows that the proposed hybrid model substantially outperforms Logistic Regression and XGBoost baselines in Precision, Recall, and F1-Score, particularly on hard-to-detect micro-transaction fraud patterns. An ablation study confirms the complementary contribution of both the temporal and topological components.

Prompt wrappers often differ only in formatting, yet they can change model scores enough to flip leaderboard conclusions. We study this variance under a token-controlled protocol and introduce two complementary metrics: the Format Sensitivity Index (FSI), the accuracy range induced by wrapper choice, and the Parseability Sensitivity Index (PSI), the corresponding range in answer parseability. Across 140,000 OpenRouter generations spanning 7 QA tasks, 5 wrapper families, and 4 instruct models from 7B to 72B parameters, we find that mean FSI varies by over 30x across models and is largely explained by compliance failures. A fixed-effects regression shows that parseability remains a strong predictor of accuracy even after controlling for task, model, and wrapper. We argue that reporting accuracy without wrapper variance and compliance is statistically fragile, and we give practical recommendations for both benchmarking and structured-output deployments.

Large Language Models are routinely compressed via post-training quantization to reduce inference costs and memory footprint for cloud and edge deployment, yet the impact of this compression on model quality remains poorly understood. Existing studies typically compare only two conditions (full-precision vs. a single quantized variant), rely on aggregate bias metrics, and evaluate a single model family, making it impossible to distinguish gradual degradation from threshold-dependent safety failures. We conduct a controlled empirical study of three instruction-tuned models (Qwen2.5-7B, Mistral-7B, Phi-3.5-mini) at five precision levels (BF16 through 3-bit) on 12,148 BBQ bias benchmark items across 5 random seeds, totaling 911,100 inference records. Our results reveal that 3-bit quantization causes 6-21% of previously unbiased items to develop new stereotypical behaviors, following a clear dose-response pattern confirmed via logistic regression, while models' willingness to select "unknown" answers declines by 17.4%. Crucially, these item-level changes are invisible to standard quality metrics: perplexity increases by less than 0.5% at 8-bit and under 3% at 4-bit across all three models, yet 2.5-5.6% of items already develop new biases at 4-bit. These findings demonstrate that aggregate evaluation metrics systematically miss fairness-critical degradation, underscoring the need for quality-aware compression protocols that explicitly test for bias emergence before deployment.

Most work in audio enhancement targets human speech, while bioacoustics is less studied due to noisy recordings and the distinct traits of animal sounds. To fill this gap, we adapt speech enhancement methods and build BioSEN, a model made for bioacoustic signals. BioSEN has three modules: a multi-scale dual-axis attention unit for time-frequency feature extraction, a bio-harmonic multi-scale enhancement unit for capturing harmonic structures, and an energy-adaptive gating connection unit that uses frequency weights to keep vocalizations from being removed as noise. Tests on three bioacoustic datasets show that BioSEN matches or exceeds state-of-the-art speech enhancement models while using far less computation. These results show BioSEN's strength for bioacoustic audio enhancement and its promise for biodiversity monitoring and conservation.

Training a diffusion model involves two sources of randomness for each data sample: the timestep and the Gaussian noise realization. The timestep has been studied extensively through scheduling and weighting, whereas the impact of the noise realization at a given timestep is still underexplored. In this work, we examine whether different noise instances are equally informative. We introduce NoiseRater, a network that scores an individual noise instance conditioned on the data sample and timestep. The rater is learned through bilevel optimization, where its scores reweight the diffusion loss in the inner loop, and it is updated to reduce validation loss after the inner-loop updates. Using the trained rater to select training noise, we observe three properties of training noise. First, noise realizations at the same timestep are not equally useful: the rater's top-scored noise improves performance over i.i.d.\ sampling, while its bottom-scored noise degrades it. Second, this utility is contextual, depending jointly on the image, the class, and the timestep. Third, noise selection is complementary to timestep-level design, retaining most of its gain when combined with existing scheduling and weighting schemes. These findings establish instance-level noise valuation as a new axis for understanding and improving diffusion training. Code is available at https://github.com/JoeZhao527/Noise-Rater.

Large language models encode vast factual knowledge that can become outdated or incorrect after deployment, yet retraining is prohibitively costly. This motivates lifelong model editing, which updates targeted behavior while preserving the rest of the model. Existing editors, both parameter-modifying and parameter-preserving, degrade severely as edits accumulate and struggle to generalize across paraphrases. We propose HoReN, a codebook-based parameter-preserving editor that wraps a single MLP layer with a discrete key-value memory. HoReN treats each codebook entry as both a knowledge key and a Hopfield stored pattern, retrieves edits by angular similarity on the unit hypersphere, and refines queries through damped Hopfield dynamics so paraphrases converge to the correct memory basin while unrelated inputs remain stable. HoReN achieves strong editing performance with consistent gains across diverse benchmarks spanning standard ZsRE, structured WikiBigEdit, and unstructured UnKE evaluations. Moreover, HoReN scales to 50K sequential edits on ZsRE with stable overall performance above 0.93, while prior editors collapse or degrade severely before reaching 10K. Our code is available at https://github.com/ha11ucin8/HoReN.

Reasoning in large language models is predominantly evaluated through labeled benchmarks, conflating task performance with the quality of internal inference. Here we study reasoning as an intrinsic dynamical process by examining the evolution of internal representations during inference. We find that inference-time dynamics consistently self-organize into low-dimensional manifolds embedded within high-dimensional representation spaces. we find that such geometric compression, although pervasive, is not sufficient for stable or reliable reasoning. Instead, effective reasoning dynamics emerge within a constrained structural regime characterized by three conditions: adequate representational expressivity, spontaneous manifold compression, and preservation of non-degenerate information volume within the compressed subspace. Models outside this regime exhibit characteristic pathological inference dynamics. Based on these insights, we introduce a unified, label-free diagnostic computed solely from internal dynamics. These findings suggest that reasoning in LLMs is fundamentally governed by geometric and informational constraints, offering a complementary framework to benchmark-centric assessment.

The Karlsruhe Tritium Neutrino Experiment (KATRIN) aims to measure the absolute neutrino mass with unprecedented sensitivity, requiring precise monitoring of the windowless gaseous tritium source, where tritium beta decay occurs. To track variations of the source activity, beta-induced X-ray spectroscopy provides real-time diagnostics. However, traditional drift detection methods struggle with the infrequent and transient nature of instability events in gaseous tritium. This study bridges the gap between state-of-the-art time-series forecasting models and real-world experimental applications by leveraging deep learning to predict the time to stability after instabilities. Unlike standard benchmarking approaches that emphasize algorithmic performance on fixed datasets, we apply forecasting models – including LSTM, N-BEATS, TFT, NHITS, DLinear, NLinear, TSMixer, and Chronos-LLM – to complex, large-scale experimental data. Our findings highlight two challenges: learning from sparse instability events and forecasting long time horizons (i.e., predicting hundreds of future points), both of which are ongoing challenges in time-series forecasting and remain active areas of research. This prediction task has direct experimental value by enabling better scheduling and maintenance planning. A reliable forecast of stability time allows for more efficient measurement and task management during stabilization periods. Through model selection, we identified N-BEATS as the top performer, excelling in accuracy and repeatability, demonstrating that deep learning can optimize large-scale physics experiments.

Synthetic data has emerged as a crucial solution to the data scarcity bottleneck in large language models (LLMs), particularly for specialized domains and low-resource languages. However, the broader adoption of existing synthetic data tools is severely hindered by convoluted workflows, fragmented data standards, and limited scalability across modalities. To address these limitations, we develop DataArc-SynData-Toolkit, an open-source framework featuring: (1) a configuration-driven, end-to-end pipeline equipped with an intuitive visual interface and simplified CLI for exceptional usability; (2) a unified, quality-controllable synthesis paradigm that standardizes multi-source data generation to ensure high reusability; and (3) a highly modular architecture designed for seamless multimodal, multilingual, and multi-task adaptation. We apply the toolkit in multiple application scenarios. Experimental results demonstrate that our toolkit achieves an optimal balance between generation efficiency and data quality. By offering an end-to-end and visually interactive pipeline, DataArc-SynData-Toolkit significantly lowers the technical barrier to synthetic data generation and subsequent model training, accelerating its practical deployment in real-world applications.

Weight pruning is widely advocated for deploying Large Language Models on resource-constrained IoT and edge devices, yet its impact on model fairness remains poorly understood. We conduct a controlled empirical study of three instruction-tuned models (Gemma-2-9b-it, Mistral-7B-Instruct-v0.3, Phi-3.5-mini-instruct) across three pruning methods (Random, Magnitude, Wanda) at four sparsity levels (10-70%) on 12,148 BBQ bias benchmark items with 5 random seeds, totaling 2,368,860 inference records. Our results reveal a Smart Pruning Paradox: activation-aware pruning (Wanda) preserves perplexity nearly perfectly (just 3.5% increase at 50% sparsity for Mistral-7B), yet produces the highest bias amplification, with Stereotype Reliance Score increasing 83.7% and 47-59% of previously unbiased items developing new stereotypical behaviors at 70% sparsity. Random pruning destroys language capability entirely (perplexity exceeding $10^4$ and reaching $10^8$) but produces only random-chance bias. We further show that unstructured pruning provides zero storage savings and zero inference latency reduction on real edge hardware, undermining the primary motivation for its use in IoT deployment. Of 180 dense-vs-pruned comparisons, 141 (78.3%) are significant ($p < 0.05$) with mean $|h| = 0.305$. Published quantization studies report up to 21% of responses flipping between biased and unbiased states; our pruning results show transition rates nearly three times higher (47-59%), suggesting pruning poses a categorically greater risk to alignment than quantization. These findings demonstrate that perplexity-based evaluation provides false assurance of behavioral equivalence, and that IoT deployment pipelines require bias-aware validation before deploying pruned models at the edge.

Recursive reasoning systems alternate between acquiring new evidence and refining an accumulated understanding. Two design choices are typically left implicit: how to represent the evolving reasoning state, and when to stop iterating. This paper addresses both. We represent the reasoning state as an epistemic state graph encoding extracted claims, evidential relations, open questions, and confidence weights. We define the order-gap as the distance between the states reached by expand-then-consolidate versus consolidate-then-expand; a small order-gap suggests that the two orderings agree and further iteration is unlikely to help. Our main result gives a necessary and sufficient condition for the linearised order-gap to be non-degenerate near the fixed point, showing when the criterion is informative rather than algebraically vacuous. This is a local condition, not a global convergence guarantee. We apply the framework to recursive reasoning systems and sketch its application to agent loops, tree-of-thought reasoning, theorem proving, and continual learning.

Recommender systems are essential components of modern online platforms which presents personalized content in various domain. The traditional collaborative filtering methods depends on static user-item interaction graphs and a limited subset of similarity measures which fail to capture the changing nature of preferences of an individual. Recent graph neural network (GNN) based approaches focus on user-item bipartite graphs which do not use explicit user-user relational modelling and dynamic graph evolution during training. To address these limitations, this paper proposes a Dynamic Graph SimilarityAware Attention Graph Neural Network (DG-SA-GNN) framework that integrates dynamic user similarity graph construction with multi-similarity propagation and attention-based aggregation. The proposed architecture constructs four parallel user similarity graphs using Cosine, Jaccard, Discounted Pearson Correlation Coefficient (Discount PCC), and IPIJ similarity functions, each processed by a dedicated UserGNN module. A Graph Transformer fuses the four graph views, and a CrossAttention module refines user embeddings through interaction with item embeddings. Crucially, the graphs are reconstructed at scheduled epochs during training, enabling the model to adapt to the learned embedding space constituting the dynamic graph component. Mini-batch training with hard negative sampling improves scalability and convergence. Experiments on the MovieLens100K benchmark demonstrate that DG-SA-GNN achieves a Recall@20 of 0.162 and NDCG@20 of 0.065 which is better than the LightGCN baseline in recall. The results validate that dynamic multi-similarity graph construction coupled with attention-based fusion which produce recommendation performance

Representation Engineering analyses often characterize refusal using static directions extracted from terminal or pooled representations. We ask whether this view misses how refusal is constructed across layer-token positions. Using causal tracing, we identify a Refusal Trajectory: a sparse upstream activation pattern that often persists even when attacks such as GCG suppress terminal refusal signals. Based on this observation, we propose SALO (Sparse Activation Localization Operator), a lightweight white-box detector that operates on raw hidden-state volumes from a selected layer window. Across Qwen, Llama, and Mistral models, SALO improves jailbreak detection on several attack families under a fixed XSTest-calibrated operating point. We further analyze static RepE-style baselines, ROI sensitivity, adaptive GCG attacks, and encoded-input boundary cases, clarifying both the promise and limitations of refusal-trajectory monitoring.

Predicting complex human traits from genetic data is challenging because different genetic, clinical, and molecular data sources often contain different parts of the signal. Here, we present EFGPP, a reproducible framework for generating, ranking, and combining multiple types of data for genotype-to-phenotype prediction. We applied EFGPP to migraine prediction using UK Biobank data from 733 individuals. The framework combined genotype-derived features, principal components, clinical and metabolomic covariates, and polygenic risk scores generated from migraine and depression GWAS using PLINK, PRSice-2, AnnoPred, and LDAK-GWAS. The best single data type achieved a test AUC of 0.644, while combining multiple data types improved performance to 0.688 using migraine-focused inputs and 0.663 using cross-trait depression-derived inputs. Genetic features alone did not outperform the covariates-only baseline, but genotype-derived features performed better than PRS alone, and depression-derived PRS showed useful predictive signal. Overall, EFGPP provides a practical proof-of-concept framework for prioritising and integrating heterogeneous genetic data sources for complex phenotype prediction.

We study AI alignment through the lens of law-and-economics models of deterrence and enforcement. In these models, misconduct is not treated as an external failure, but as a strategic response to incentives: an actor weighs the gain from violation against the probability of detection and the severity of punishment. We argue that the same logic arises naturally in agentic AI pipelines. A solver may benefit from producing a persuasive but incorrect answer, hiding uncertainty, or exploiting spurious shortcuts, while an auditor or verifier must decide whether costly monitoring is worthwhile. Alignment is therefore a fixed-point problem: stronger penalties may deter solver misbehavior, but they can also reduce the auditor's incentive to inspect, since auditing then mainly incurs cost on a population that appears increasingly aligned. This perspective also changes what should count as a post-training signal. Standard feedback often attaches reward to the final answer alone, but a solver-auditor pipeline exposes the full correction event: whether the solver erred, whether the auditor inspected, whether the error was caught, and whether oversight incentives remained active. We formalize this interaction in a two-agent model in which a principal chooses rewards over joint correction outcomes, inducing both solver behavior and auditor monitoring. Reward design is therefore a bilevel optimization problem: rewards are judged not by their immediate semantic meaning, but by the behavioral equilibrium they induce. We propose a bandit-based outer-loop procedure for searching over reward profiles using noisy interaction feedback. Experiments on an LLM coding pipeline show that adaptive reward profiles can maintain useful oversight pressure and improve principal-aligned outcomes relative to static hand-designed rewards, including a substantial reduction in hallucinated incorrect attempts.

Prevailing alignment methods target a fixed set of preferences and therefore risk forcing value lock-in as societal norms evolve over time. We introduce Adaptive Pluralistic Alignment (APA), a modular pipeline for updating pluralistically aligned AI systems to track evolving values and avoid value lock-in without repeating costly pretraining or large-scale data collection. APA has three stages: (1) learning compact personalized reward models via low-rank reward basis decomposition, (2) using these models as a jury that collectively selects among candidate outputs through social-choice-theoretic voting, and (3) efficiently adapting the jury over time by fitting new annotator weights over the fixed reward bases as values shift. The resulting system is efficient, explainable, steerable, and modular. We implement a proof-of-concept instantiation using simulated historical annotators, demonstrate how jury composition and the choice of voting rule can substantially affect outcomes, and bound value tracking error given a sliding-window jury. We provide full code at https://github.com/RachelFreedman/apa.

Training compute is increasingly outpacing the availability of high-quality data. This shifts the central challenge from optimal compute allocation to extracting maximum value from limited data. The widely adopted Chinchilla scaling law assumes every training token is unique. This limits its ability to guide pretraining decisions in data-constrained regimes. We model the excess loss under repetition with a simple additive overfitting penalty and find that it accurately describes model behavior. Our scaling law yields qualitatively new compute-optimal allocation advice. Beyond a point, further repetition is counterproductive and compute is better spent on model capacity. We show that following our law's recommended configuration improves performance in data-constrained regimes. Finally, because our one-parameter form isolates overfitting in a single coefficient, it enables direct comparison across training configurations. As a case study, we show that strong weight decay ($\lambda=1.0$) reduces this coefficient by approximately 70%, providing a scaling-law explanation for recent findings that optimal weight decay in data-constrained regimes is an order of magnitude larger than standard practice.

We introduce the Banach-Butterfly Invariant (BBT), an influence-adaptive Banach geometry on the Walsh-Hadamard butterfly factorization. For a Boolean function $f:\{-1,+1\}^n\to\{-1,+1\}$ with coordinate influences $\mathrm{Inf}_\ell(f)$, BBT assigns exponent $p_\ell = 1+\mathrm{Inf}_\ell(f)$ to butterfly layer $\ell$, yielding the contraction invariant $\mu(f)=\prod_\ell 2^{-\mathrm{Inf}_\ell/(1+\mathrm{Inf}_\ell)}$. We prove a Jensen lower bound $\log_2\mu(f) \ge -I(f)/(1+I(f)/n)$ and that $\mu$ is strictly Schur-convex in the influence vector (modulo permutation), giving scaling classes $\mu\sim 2^{-n/2}$ (parity), $2^{-\Theta(\sqrt{n})}$ (majority), $2^{-1/2}$ (dictators). $\log_2\mu$ is rational but not polynomial in the Fourier coefficients while $\mu$ is algebraic, and $\mu$ separates functions with identical total influence (122 pairs at $n=3$). Using the certified $n \le 4$ ternary Walsh-threshold universe from a companion synthesis manuscript as a finite testbed, we compute exact MILP minimum-support certificates for all 65,536 Boolean functions at $n=4$ (mean 6.42, max 9, all-odd by a parity argument) and on 10,000 of the 616,126 NPN-canonical representatives we enumerate at $n=5$ (matching OEIS A000370). Conditional Spearman $\rho(\mu,|\mathrm{supp}|)$ at fixed total influence is $+0.571$ in the largest stratum at $n=4$ but reverses to $-0.38$ at $n=5$ under both function-uniform and NPN-canonical sampling: $\mu$ is a valid Schur-convex concentration invariant, not a universal monotone predictor of minimum support across $n$. A companion application paper validates a real-valued WHT activation-energy proxy inspired by this theory on five pretrained LLMs at W2A16, cutting wikitext-2 perplexity by 15-58% versus vanilla auto-round; the transfer from Boolean theory to the real-valued proxy is qualitative, not formal.

Physics-Informed Neural Networks (PINNs) offer a flexible paradigm for solving differential equations by embedding governing laws into the training objective. A persistent limitation is instance specificity: standard PINNs typically require retraining for each new forcing term, boundary/initial condition, or parameter setting. One-shot transfer learning (OTL) addresses this bottleneck for linear operators by freezing a pretrained latent representation and computing optimal output weights in closed form, but for nonlinear problems closed-form adaptation is generally unavailable because the loss is nonconvex in the output layer. In this paper we substantially broaden the class of nonlinearities amenable to one-shot PINN transfer by combining OTL with Chebyshev polynomial surrogates. We approximate general smooth weakly nonlinear terms by truncated Chebyshev expansions over a prescribed solution range, yielding a polynomial nonlinearity that can be handled by a perturbative decomposition into linear subproblems. A multi-head PINN learns a reusable latent space associated with the dominant linear operator; at test time, solutions to new instances are obtained via a sequence of closed-form linear solves in the output layer, without retraining the network body. We provide a unified derivation of the framework for ODEs and PDEs and demonstrate accuracy and fast online adaptation on nonlinear benchmarks, including non-polynomial and singular ODE nonlinearities as well as a reaction-diffusion PDE with saturating kinetics, demonstrating the method's utility in many-query regimes.

Models that are nearly indistinguishable on in-distribution data can behave very differently under distribution shift. We introduce Perturb-and-Correct (P&C), a post-hoc method for constructing epistemically diverse predictors from a single pretrained network. P&C applies random hidden-layer perturbations with a least-squares correction in the following affine layer, producing predictors that agree on calibration data while remaining free to disagree away from it. We analyze this mechanism through the post-correction residual that remains in the activation of the layer corrected using calibration data, yielding a leverage-based preservation bound and a covariance interpretation of ensemble disagreement. Empirically, P&C achieves a strong ID/OOD tradeoff across MuJoCo dynamics prediction and CIFAR-10 OOD detection, and scales to a pretrained ViT-B/16 on ImageNet-1K. In matched comparisons with Deep Ensembles, P&C substantially reduces construction and storage cost. Our findings highlight the potential in further exploiting overparameterization as a strength of deep learning models.

Self-normalized martingale inequalities lie at the heart of confidence ellipsoids for online least squares and, more broadly, many bandit and reinforcement-learning results. Yet existing vector and scalar results typically rely on bounded covariates and an explicit regularization matrix, producing bounds that are not scale-invariant: although the self-normalized quantity is scale-invariant by definition, its standard upper bounds are not. We characterize when scale-invariant upper bounds on self-normalized martingales are possible. Without further assumptions, we prove that nontrivial scale-invariant bounds exist only in dimension $d=1$; moreover, in $d=1$ we obtain $O(\log T)$ scale-invariant self-normalized bounds without any assumptions on the covariates. In contrast, for $d>1$ we show that no nontrivial scale-invariant bound can hold in full generality. We then connect this dichotomy to doubly-uniform regret in online linear regression (i.e., regret bounds that are simultaneously independent of the covariate scale and the comparator norm) and use it to resolve the open question of Gaillard, Gerchinovitz, Huard, and Stoltz, \emph{“Uniform regret bounds over $\mathbb{R}^d$ for the sequential linear regression problem with the square loss”} (ALT 2019): in $d=1$ we give an explicit algorithm with $O(\log T)$ doubly-uniform regret, whereas for $d>1$ sublinear doubly-uniform regret is impossible. Finally, under a natural smoothness condition (bounded Radon–Nikodym derivatives of the conditional covariate laws with respect to a fixed base measure), we recover sublinear regret for $d>1$ without bounded covariates and derive a self-normalized concentration inequality free of the usual regularization penalties, yielding arguably a first natural scale-invariant bound for adaptive, non-i.i.d. vector martingales.