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At least 343 records · Page 19Linked to original sources

Fitting and Learning Basis-Restricted Propositional Formulas

For a finite set $O$ of Boolean functions, we consider the class of propositional formulas built using the functions in $O$ as connectives. We determine, for each possible choice of $O$, the complexity of various fitting and learning problems. These include: finding a formula that fits a given labeled sample, finding a small one (an Occam algorithm), minimizing the number of misclassified examples when the sample is not realizable (empirical risk minimization), and several forms of PAC learning. Our results apply both to formulas (represented as trees) and to circuits. We also briefly discuss the status of the same questions for other kinds of propositional fragments.

cs.LO↗

GraphFAS: A Distributed System for Automated Graph Feature Generation and Selection in Industrial Transaction Networks

Industrial fraud detection often relies on costly expert-crafted features that overlook graph-structured relational signals, while GNNs often do not meet the interpretability and deployment requirements of financial risk control. We propose GraphFAS (Graph Feature Automated Selection), a distributed feature selection procedure based on Boruta that bridges this gap through: (1) a non-parametric graph feature generation module that constructs explicit, interpretable structural features via multi-hop subgraph extraction and multi-scale aggregation without learned parameters; and (2) an automated distributed feature selection algorithm extending Boruta with median-based aggregation across partitions to robustly identify informative features at scale with minimal domain expertise. Compared with end-to-end GNN pipelines, GraphFAS decouples feature aggregation from model training, enabling direct integration with tabular models and direct compatibility with TreeSHAPbased explanations. Deployed in Alipay, GraphFAS delivers orderof-magnitude improvements in engineering efficiency while showing strong performance against expert-driven and graph-learning baselines on large-scale graphs.

cs.LG↗

Deposon: An Auditable, Conservation-Guaranteed, Game-Theoretically Tested Scattering Layer over LLM Reasoning Paths

Multi-step LLM reasoning lacks a machine-recheckable ledger: discarded reasoning paths leave no auditable record. We propose the Deposon scattering layer, which binds each node of an LLM-generated concept-decomposition graph to a two-parameter Deposon state; paths undergo three-channel scattering -- transmission, reflection, irreversible dissipation -- obeying T+R+A=1 for arbitrary parameters, with a maximum per-path energy-audit deviation of 2.2E-16 (machine epsilon). We report all three evidence tiers honestly. On synthetic trap benchmarks the path-filtering gain is closed (pre-registered): unified reaches 100% versus a decoy-capture baseline at 7%/10%. On real benchmarks the layer is indistinguishable from a trivial six-keyword rule filter (GSM8K 0.87 >= 0.85, McNemar p=0.5; StrategyQA 0.899 = 0.899); no difference is detected here, so we sharpen the claim to "the differential value lies solely in machine verifiability." Fusion yields a second negative result: convex combinations with a semantic prior never improve (physics 0.484 -> 0.452), and the apparent lambda=2 gain is an anti-field artifact; any fusion gain must be nonlinear. Modeling the reverse dynamics as a potential game on the graph, we evidence an auditable scalar's monotonicity and near-gradientness and quantify the empirical coordination ratio (ECR). The three formalized dynamical-equivalence propositions (P1a/P1b/T-P1c) are falsified under the pre-registered kill protocol, and the potential-game claim is downgraded to approximate (cyclic-graph median residual 0.669): only consistency-level evidence survives at the dynamical level. Code: github.com/zeroandcat/Deposon.

cs.AI↗

Evaluation of Contextual Understanding in Large Language Models

Large Language Models (LLMs) demonstrate impressive performance across diverse NLP tasks, yet their ability to exhibit genuine contextual understanding remains uncertain. Traditional evaluation metrics such as perplexity, BiLingual Evaluation Understudy (BLEU), or surface-level accuracy fail to reveal how well LLMs extract, integrate, and reason over contextual information--a gap particularly critical in question answering, where models must align responses with contextually grounded knowledge rather than memorized associations. We propose a novel knowledge graph-based evaluation framework introducing Semantic Structural Similarity for KGs (S3KG), a hybrid similarity measure integrating structural and semantic similarity into a continuous evaluation score, alongside a diagnostic framework for categorizing reasoning errors. To validate this pipeline, we evaluate S3KG against established metrics on a curated question-answer (QA) benchmark, demonstrating its effectiveness in measuring correctness, faithfulness, and interpretability in LLM-generated responses.

cs.CL↗

Let It Go or Learn to Self-Correct: Continuous Diffusion for Constrained Discrete Tasks

Denoising Diffusion Probabilistic Models (DDPMs) generate samples by starting from noise and repeatedly denoising while keeping each update close to the current noisy state. This behavior is effective in many continuous domains, but its role is less clear for globally constrained discrete tasks, such as Sudoku, graph connectivity, Latin squares, and N-queens. In such settings, early discrete errors can be difficult to undo. As a result, standard diffusion sampling may preserve early mistakes, even when the model's clean predictions are informative. We compare standard samplers to sampling directly from the model's clean prediction. Without retraining, this single change improves Sudoku validity from 31% to 95%, with consistent gains across the other discrete tasks. We hypothesize that staying close to the current noisy state is harmful because the reverse trajectory can drift off the forward noising distribution the model was trained on. To reduce this train-test mismatch, we further introduce self-correction training, which exposes the model to its own predictions, improving robustness to errors that arise during inference. This substantially improves the performance of standard samplers. Our results suggest that continuous diffusion models can learn nontrivial global constraints, but discrete reasoning tasks require better alignment between training and inference: either through samplers that reduce commitment to early decisions, or through training that teaches the model to correct its own inference-time errors.

cs.LG↗

Closed-Form of the Local Galactic Potential and Stellar Distribution Function from Gaia DR3

The local dark matter density determines the strength of the signal expected in direct-detection experiments, yet published estimates from stellar motions disagree by more than their errors, and the most recent machine-learning analysis of Gaia data finds a local density consistent with zero. According to Jeans' theorem, a distribution function built from integrals of motion satisfies the collisionless Boltzmann equation (CBE) trivially for any choice of potential, so a search that simultaneously fits the distribution function and the potential to the CBE identifies neither. Our pipeline instead estimates the distribution function in isolation, linearizing the equation in terms of accelerations and allowing for direct measurement of the local force field, and then fits closed forms to that field via symbolic regression. Throughout, we find that the usable information lies not in the CBE residual but in the stellar number counts, the observable most distorted by survey selection. Along the vertical profile, our recovered potential agrees with the classical self-gravitating isothermal disc.

astro-ph.GA↗

Do Reasoning Representations Help Humans Evaluate LLM Outputs?

Reasoning representations are increasingly used as explanations for large language model outputs. Yet they are typically evaluated with model-centric criteria, such as answer accuracy and faithfulness, leaving it unclear whether they help people evaluate model responses. In this work, we study reasoning representations as human-facing interfaces rather than proxies for model reasoning ability. We conduct a controlled human study of six reasoning formats across tasks of varying complexity, supported by a web-based framework that randomizes task domains, problem instances, and representation order. The study collects fine-grained judgments of structural understanding, error detection and localization, and trust calibration. Our study shows a mismatch between perceived preference and support for human evaluation. Participants prefer planning- and decomposition-based representations, but simpler chain-of-thought traces better support verification, trust, and interpretability. Preferred representations also introduce calibration risks, with more false alarms on correct traces and high trust despite low willingness to verify.

cs.LG↗

Curriculum Learning as Transport: Understanding Curricula with Wasserstein Geodesics

Curriculum learning is governed by several coupled design choices---how difficulty is defined, how examples are ordered, how much exposure each level receives, and how quickly training moves across levels---making it hard to isolate what actually helps. We present Wasserstein curriculum paths, a simple transport-based framework that decouples these factors by representing curricula as trajectories of training distributions over discrete difficulty levels. Across a calibrated synthetic suite with 12 tasks and 33 difficulty axes, we use this framework to isolate the effects of ordering, matched exposure, endpoint smoothness, and pacing under fixed training budgets. We find that curriculum effects are strongly context-dependent: no single strategy dominates across tasks, difficulty axes, and budgets, and curricula mainly change where a fixed budget is spent most effectively. Within this framework, easy-to-hard ordering improves hard-level performance relative to exposure-matched static sampling, showing that the benefit is not explained by cumulative exposure alone. We further show that endpoint smoothness and pacing substantially affect where along the difficulty spectrum a curriculum is effective. Finally, we show that the same transport view naturally supports extensions to learned pacing through geometry and to structured difficulty spaces beyond one-dimensional orderings.

cs.LG↗

When Does Scale-Invariant Optimization Become Unstable? An Exact Schedule Law with Weight Decay

Normalization renders large parts of neural networks effectively scale invariant, inducing a hidden feedback loop in which learning-rate schedules and weight decay interact through the parameter norm to control the effective step taken by the optimizer. We show that this interaction is governed by an exact discrete-time law: a single scalar quantity captures all schedule and decay forcing, while norm growth induces an opposing geometric self-quenching effect. This yields a sharp boundary that cleanly separates contraction- and expansion-dominated effective learning rate regimes. To understand the underlying mechanism, we provide exact analysis of a fully solved normalized regression model where the dynamics reduce to two dimensions and show that the balance point is intrinsically unstable, implying that constant learning rate with weight decay cannot stably maintain an interior equilibrium and instead produces recurrent behavior driven by discrete-time Jacobian structure. We further extend this perspective across optimizers through unified homogeneous-optimizer framework that reveals a structural dichotomy in self-quenching strength, providing a first-principles explanation for why adaptive methods exhibit systematically weaker stabilization under normalization. Across dynamical systems and neural networks (MLP, CNN, GPT2 / MNIST, CIFAR, wikiText, OpenWebText), the predicted law holds with high precision and enables direct control of training via the identified scalar, with performance peaking sharply at the predicted boundary. Together, these results isolate a single governing quantity for scale-invariant optimization, providing a precise and actionable lens on training dynamics, optimizer behavior, and schedule design in modern deep learning. Code is available in https://github.com/shasanamin/normalized-optimization-dynamics.

cs.LG↗

A Generalization of Amari's Bayesian Duality

Amari's contributions to information geometry and machine learning are well known. Here, we revisit Amari's work on Bayesian duality which has not received as much attention. We connect Amari's Bayesian duality to a convex duality of Bayes' rule. Using this connection, we present a generalization of Amari's Bayesian duality and discuss its relevance for modern artificial intelligence.

cs.AI↗

Nearly Tight Rademacher Bounds for Sparsely Activated Neural Networks

An input may activate few hidden units even when different inputs collectively use an entire network. We study the statistical complexity of this input-dependent sparsity in the one-hidden-layer ReLU model of Awasthi et al. (COLT 2024). For width $s$, at most $k$ active units per input, and effective weight and bias bounds $W,B$, every size-$m$ sample in the class's fixed radius-$R$ input domain satisfies $\mathcal{R}(S)\le CWR\min\{k,\sqrt{sk/m}\log^{3/2}(2m)\}+kB/\sqrt m$. A support-preserving cover and a single normalized chaining argument remove the previous explicit dimension factor, up to logarithms. Lower bounds on appropriate i.i.d. marginals match up to those logarithms, showing how changing active units across inputs retains a width dependence. The input domain matters: zero-bias networks sparse on the entire ball have at most $2k$ nonzero units and complexity $O(kWR/\sqrt m)$, whereas bias bounds comparable to $WR$ restore the worst-case rate on that same domain in only logarithmic dimension. A spherical-cap construction proves the latter claim without assuming sparsity merely on the sampling support. For a specified normalized bounded loss and biases comparable to $WR$, we also obtain agnostic minimax excess-risk bounds of order $\min\{1,\sqrt{s/(km)}\}$ up to logarithms.

cs.LG↗

Entropy-Regularized Rank-Masked Policy Optimization for Test-Time Reinforcement Learning in Code Generation

Existing methods for test-time reinforcement learning (TTRL) derive rewards from answer-level self-voting on unlabeled test-time tasks with canonical answers, but this breaks down for code generation because programs cannot be compared by surface form and therefore do not directly provide a usable training signal. To make TTRL applicable to code generation, we propose probe-driven TTRL, which constructs output-free probe inputs from the problem statement, executes candidate programs on these probes, and defines a Probe Consensus Reward (PCR) from the resulting behavioral agreement. PCR provides a behavioral training signal for open-vocabulary programs, but it is not a fully reliable verifier and remains susceptible to reward hacking through spurious consensus. We therefore introduce Entropy-Regularized Rank-Masked Policy Optimization (ERPO), which converts low PCR into conservative negative updates through rank masking and controls policy drift with an entropy ceiling. On coding benchmarks, ERPO substantially improves pass@1 and pass@k in both in-domain adaptation and zero-shot transfer.

cs.LG↗

NOAH: Learning the Full Patient Journey. A Longitudinal Multimodal Time-Aware Model for Representation and Forecasting

The digitization of healthcare has generated vast, longitudinal, and multimodal patient records over a lifetime, yet fully exploiting these data to represent and predict patient state trajectories remains a critical challenge. Current AI models often struggle to capture the complex, irregular temporal dynamics and inherent stochasticity of real-world multimodal patient data. Existing AI approaches for modeling longitudinal patient records are predominantly discriminative, limited to a few modalities, constrained by closed categorical vocabularies, treating time as a monotonic inductive bias, or they are limited in forecasting future patient states. We introduce NOAH, a time-aware, task-agnostic, generative transformer model representing and forecasting the full multimodal patient journey. NOAH features a novel bidirectional time integration and a variational latent space to capture the continuous evolution of patient states and the stochasticity of clinical trajectories. Built from over 559 million clinical events from 431,000 hospital visits of 299,000 patients across the MIMIC dataset family, NOAH natively processes medical images, time-series and numeric signals, categorical events, as well as structured and unstructured clinical records. NOAH is the first truly holistic generative model in its field, enabling autoregressive forecasting with optional time control, zero-shot classification, and counterfactual intervention simulation. It generates highly informative and predictive patient state representations that demonstrate strong performance in probing for clinical outcomes, 15 ICD chapters, and 29 comorbidities, as well as in time-to-event prediction. Seamlessly handling diverse modalities and complex temporal dynamics, NOAH provides a versatile, task-agnostic, scalable foundation for intelligent predictive systems in personalized clinical care and digital medicine.

cs.LG↗

Learning Length-Extrapolatable Recurrent Models

Recurrent models provide a natural path to long-context modeling, yet models trained with backpropagation through time (BPTT) often fail beyond their training horizon. Classical analyses emphasize gradients that vanish or explode along temporal paths. However, dense per-token losses can still train a shared recurrent rule despite severe decay, showing that decay alone does not determine whether learning fails. We instead study state credit: the signal through which future losses reach earlier recurrent states before contributing to parameter updates. Accordingly, we intervene directly on state credit and propose Credit Stabilization through Time (CST). During backward propagation, CST locally rescales the state-credit signal to stabilize its norm without rotating the component being corrected, while leaving the forward computation unchanged. Because controlled synthetic tasks and real data exhibit different credit dynamics, we specialize CST to each regime. In both settings, CST improves performance beyond the training horizon, with gains observed at up to 128x the training length.

cs.LG↗

Scaling Post-Training Ternarisation to Qwen3-8B Capability Retention, Reproduction, Lossless Packing, and Packed Execution

Ultra-low-bit language models promise reductions in storage and memory traffic, but a nominal "1.58-bit" label does not specify the deployed representation or its execution cost. We study a scale-up of an aggressive post-training conversion pipeline from Qwen3-4B to Qwen3-8B. The conversion uses KOTMS rotation, E2M-ATQ adaptive ternarisation, and GPTQ-style error compensation in a weight-only A16 configuration. We do not claim these algorithms as new. Our contribution is the end-to-end scale-up characterisation: an external reproduction gate, matched 4B/8B capability analysis, cross-corpus perplexity, effective-bit accounting, lossless lattice-aware packing, and direct packed execution. The 8B model reaches a three-corpus perplexity ratio of 1.361x, with WikiText-2, C4, and PTB ratios of 1.318x, 1.393x, and 1.371x. On eight zero-shot tasks at n = 500, mean accuracy is 64.6% versus 72.4% for FP16, corresponding to 78.5% chance-corrected retention and a 7.8-point absolute cost. The matched 4B run retains 69.6%, yielding an 8.9-point 8B advantage. The packed checkpoint is 8.24 GiB and preserves the recorded perplexity to measurement precision. Direct packed execution reaches 15.52 tokens/s in 7.35 GiB, while a preliminary packed GEMV remains slower than FP16 cuBLAS. The result is a validated scale-up baseline: model size improves robustness to aggressive post-training discretisation, actual serialisation is solved for the measured artefact, and direct execution is feasible, while broader seeds, calibration distributions, and kernel optimisation remain open.

cs.LG↗

Distribution-Consistent Inference for Dynamic Sparse Mixture-of-Experts

Mixture-of-Experts (MoE) architectures have emerged as a powerful paradigm for scaling model capacity while preserving efficient inference in large foundation models. However, most MoE models use a fixed top-$k$ expert selection policy, assigning the same expert budget to every token even when fewer experts may be sufficient. Inference-time dynamic top-$k$ routing can reduce computation without retraining, but existing methods often overlook the distributional shift caused by deviating from the training-time routing configuration. We show that reducing the number of activated experts consistently increases the RMS scale and variance of SMoE outputs, inducing a representation mismatch that contributes to downstream performance degradation in addition to the loss of expert capacity. To address this correctable component, we propose Layer-wise Distribution Alignment (LDA), a lightweight inference-time correction that uses layer-wise calibration statistics to align reduced-routing representations with the default configuration. Across multiple SMoE LLMs, benchmarks, and routing strategies, LDA recovers much of the performance lost induced by the distributional shift under reduced routing while preserving sparse-inference efficiency with negligible overhead.

cs.LG↗

Critical initialization destabilizes higher input derivatives in wide scalar-input networks

The edge-of-chaos condition preserves first-order input perturbations in wide randomly initialized networks, but physics-informed losses, score matching and derivative regularization depend on higher input derivatives. For smooth scalar-input fully connected networks, using a joint Gaussianity of the finite derivative jet that holds in the infinite-width limit at each fixed depth, we derive mean-field recursions through third order that are exact at the variance fixed point, with finite-depth corrections that decay geometrically. At criticality, the first-derivative variance is depth-invariant, whereas the second-derivative variance grows linearly whenever the activation has nonzero curvature. The resulting third-order system closes on mean-field susceptibilities. For residual networks with branch scale L^{-1/2}, we prove that every fixed finite derivative order has uniformly bounded variance under explicit regularity assumptions. Simulations verify the critical growth laws, the residual bound, and the closed recursion. The results concern initialization, not trained-network performance.

stat.ML↗

What Fixed-Rollout pass@k Evaluations Can Identify

Repeated-sampling evaluations increasingly extrapolate pass@k far beyond the number n of samples collected per problem. We show that, in the pooled/random-task conditional-Binomial model, fixed-n success counts identify only the n free moments of the latent per-task success distribution. Consequently, direct pass@k is identified for k <= n, but generic extrapolated pass@k, tail exponents, and tail constants are not identified for k > n, even with arbitrarily many exchangeable tasks at the same rollout budget. This is stronger than the observation that the usual estimator is undefined beyond n: it characterizes the information missing from the fixed-depth count-law experiment. We give exact count-law-preserving constructions with incompatible extrapolations, state the exceptional unique-extension case, and compute sharp population identified intervals through Hausdorff principal representations. On the public 10,000-rollout-per-problem release of Brown et al., counterfactual n = 16 evaluations leave failure at k = 1000 ambiguous by factors from 1.5 to over 2,600 across four MATH/GSM8K/CodeContests configurations. The calibration shows that intermediate-scale failure share alone does not determine width. Our result does not reject parametric inference-time scaling laws; it supplies the nonparametric baseline against which their assumptions can be evaluated. We give an exact, conservative one-coordinate finite-task confidence certificate and a reporting standard separating direct estimates, identified sets, and model-conditioned forecasts.

stat.ML↗