arXiv subjects

Mingyu Li

Publications and source records attributed to Mingyu Li.

At least 19 recordsLinked to original sources

arXiv2026

AEON-z5: A Candidate AGN-driven Outflow Enriching the Circumgalactic Medium at $z\simeq5.23$

The dispersal of chemically enriched gas from galaxies into their surroundings is a key process in galaxy evolution, yet direct observational evidence at z>5 remains scarce. We present AEON-z5, a galaxy at z~5.23 in the COSMOS field comprising a compact continuum-emitting core surrounded by an extended, line-dominated ionized nebula. JWST/NIRCam imaging shows that H$\alpha$+[N II] and H$\beta$+[O III] emission extends to projected radii of >4 kpc - 2-2.5 times the typical effective radius at the host stellar mass - reaching the outer ISM and the inner CGM. F444W grism data reveal a highly asymmetric H$\alpha$+[N II] profile, which we interpret as a bipolar outflow and decompose into three kinematic components. The dominant component has a flux-weighted velocity offset of ~+489 km/s and FWHM~630 km/s, with a wing reaching $v_{84}$~792 km/s. A tentative detached feature at $\Delta v_{LOS}$~2800 km/s, detected at 1.5$\sigma$ in the 1D spectrum (2.4$\sigma$ in the 2D fit), may trace an outflow clump. These kinematics are most coherently explained by an AGN in the core. For the extended nebula, we derive a velocity curve shifting redward with radius, reaching 200-400 km/s at $r_p$~1.3-2.5 kpc - a trend that may reflect an accelerating outflow, corotating gas, or recycled inflow viewed in projection. Crucially, the measured [N II]/H$\alpha$ ratios imply near-solar N2-based abundances (0.7-1.0 $Z_\odot$), remaining >0.37 $Z_\odot$ after allowing for AGN excitation and calibration systematics. The combination of large extent, enrichment, and extreme kinematics identifies AEON-z5 as a candidate snapshot of feedback-driven metal transport, offering a direct view of how early AGN activity may redistribute chemically processed gas into the CGM within the first ~1.1 billion years.

astro-ph.GA↗

arXiv2026

Pointing the Way, Hiding the Destination: Practical Private Dense Retrieval at Scale

Hosted retrieval-augmented generation (RAG) and semantic search allow users to query valuable provider-held corpora, raising two competing demands: to hide each query and chosen result, yet reveal only the documents that the user is authorized to receive. Existing cryptographic approaches either make this costly by processing the entire corpus for every query, or sacrifice quality for efficiency by scanning a few clusters. We repurpose learned deep hashing as a private filter: a randomized binary code points the provider to a short candidate list, while encrypted reranking and oblivious key transfer protect the precise query and final selection. This shortlist short-circuits full-corpus cryptographic search without sacrificing retrieval quality: with 200-500 candidates, it closely matches full-corpus retrieval across five zero-shot corpora spanning 25K to 5.4M documents. On the full 2.68M-passage NQ corpus over a 10-Gbps link, our protocol only adds 0.73 seconds, or 10 percent, to a 128-token Qwen3-32B RAG pipeline. The released code satisfies directional metric differential privacy (DP) and substantially reduces embedding-inversion and property-inference leakage, demonstrating that a carefully learned shortlist can make private dense retrieval both accurate and practical.

cs.CR↗

arXiv2026

Low Ly$\alpha$ Visibility in Galaxy Overdensities: Reionization Topology and Neutral-Fraction Ceilings from DIVER over $4.8<z<11$

Ly-alpha emission is widely used to trace cosmic reionization, but its interpretation depends on how Ly-alpha visibility varies with galaxy environment. We use deep JWST/NIRSpec observations from Deep Insights into UV Spectroscopy at the Epoch of Reionization (DIVER) in GOODS-N to measure Ly-alpha visibility for 250 galaxies at 4.8 25 A. We combine these measurements with H-alpha and [O III] emitters from JWST/NIRCam wide-field slitless spectroscopy to map the density field around each DIVER galaxy. Galaxies with high Ly-alpha equivalent widths (W_Lyalpha>25 A) or high effective Ly-alpha escape fractions (f_esc,Lyalpha^eff>0.05) tend to lie farther from nearby H-alpha and [O III] emitters than galaxies with lower Ly-alpha visibility. The clearest signal occurs near the prominent GOODS-N overdensity at z~5.2, where fewer than 15% of galaxies show strong Ly-alpha emission. This trend is opposite to the simplest inside-out reionization expectation that overdensities produce larger ionized regions and enhance Ly-alpha visibility. Possible explanations include circumgalactic and local intergalactic opacity, dense absorbers, and gas kinematics. We also derive an empirical upper envelope for f_esc,Lyalpha^eff and calibrate it with reionization simulations. Interpreting this envelope as a limiting IGM-attenuation signal gives neutral-fraction ceilings of _max=0.36, 0.76, 0.74, 0.84, and 1.0 at z~5.2, 5.8, 6.7, 7.7, and 9.8, respectively. The z~8 ceiling disfavors an almost completely neutral IGM at this epoch. These results support patchy reionization already underway by z~8 and show that galaxy Ly-alpha visibility encodes both large-scale ionization topology and near-source gas structure.

astro-ph.GA↗

arXiv2026

OraclePhys: A Systematic Framework for LLM Fine-Tuning on Structural Mechanics

What a language model internalizes from fine-tuning is usually diagnosed after the fact. We make it an experimental variable. OraclePhys is a systematic fine-tuning framework with three components: OraclePhys-Bench, an exactly-graded structural-mechanics benchmark whose finite-element oracle scores every answer and counterfactual edit -- no human labels, no LLM judging; OraclePhys-30K, a supervision dataset of seven answer forms over byte-identical structure descriptions; and a controlled training study across the seven forms and three verifier roles. The study yields two findings. First, the label's answer form -- not its bit count -- causally determines what fine-tuning teaches: a ranking objective installs an out-of-distribution forward model where the untrained base sits at the guessing prior, a scalar objective at best a partial one, a boolean nothing detectable; the vector-scalar gulf survives a second physics domain, a second model family, and a paraphrased evaluation surface. Second, written or score-filtered answers install this capability, while advantage-weighted scores (GRPO) raise reward yet leave the model statistically equivalent to its start on held-out physics -- within the recipes and budgets tested -- sufficing only for routing. The trained 8B -- the first LLM on spatial structural response -- reaches the task's data-precision frontier: above a frontier LLM at zero- and 32-shot, at a specialist's level. What the label spells out about the target computation is what fine-tuning teaches; what you train on is what you route.

cs.LG↗

arXiv2026

SimP: Unifying Syntax- and Semantic-Guided Techniques for Efficient Program Reduction

Compiler bugs are pervasive in modern compiler systems, but the test programs that trigger them are often too large for practical debugging. Program reduction addresses this by minimizing test program size while preserving the original bug-triggering behavior. Existing approaches mainly rely on syntax-guided, rule-based deletion strategies that iteratively remove parts of the program in a trial-and-error manner. While effective in reduction quality, these approaches suffer from slow reduction speed. This paper presents SimP, a program reduction framework that combines traditional reduction with LLM-based syntax- and semantic-guided reduction. SimP leverages customized prompt design to guide the reduction process. SimP synergistically combines rule-based and LLM-based reduction stages to optimize the reduction performance. The results show that SimP improves reduction efficiency while achieving comparable reduction quality, with negligible LLM monetary cost.

cs.PL↗

arXiv2026

CV-DCLR: Causal-Visual Dynamic Label Refinement for Robust Zero-Shot Learning

Zero-Shot Learning (ZSL) facilitates knowledge transfer via shared semantic spaces. However, a critical bottleneck in this paradigm is Semantic Entanglement, where visual representations are inevitably conflated with visually similar semantic concepts, such as distinguishing the intrinsic traits of a Wolf from the shared features of a Husky. Existing global alignment methods often indiscriminately maximize correlations between visual and semantic modalities, leading models to overfit spurious similarities rather than capturing distinctive class identities. To address this fundamental limitation, we propose the Causal-Visual Dynamic Label Refinement (CV-DCLR) framework. Unlike traditional approaches that rely on superficial visual statistics, CV-DCLR recalibrates visual-semantic associations via a Dual-Stream Mutual Correction Mechanism. This includes a Visual Likelihood Stream to model observational patterns and a Causal Importance Stream that verifies the structural necessity of candidate prototypes through Counterfactual Intervention. Acting as a logical filter, our adaptive gating mechanism dynamically modulates feature responses to amplify genuine causal traits while suppressing visually plausible but structurally irrelevant distractors. Extensive experiments on the CUB, SUN, and AWA2 benchmarks under a rigorous Semantic Entanglement Injection protocol demonstrate that CV-DCLR significantly outperforms state-of-the-art methods in high-ambiguity scenarios. Specifically, while existing models suffer catastrophic degradation under entanglement, our framework maintains robust performance, effectively disentangling true class identities from semantic confounders.

cs.CV↗

arXiv2026

First-star imprints in a metal-poor galaxy overdensity near the end of reionization

The first generation of stars, known as Population III (Pop III), formed from primordial gas consisting solely of hydrogen and helium and is believed to have emerged only a few hundred million years after the Big Bang. Detecting the chemical enrichment of metal-poor circumgalactic gas offers a promising way to trace the enrichment signature of Pop III stars. Along the sightline to the quasar SDSS J0100+2802, a metal absorber at $z = 5.945$, showing over-abundant carbon and silicon compared to solar, has been reported to be consistent with the enrichment pattern of Pop III stars. With the James Webb Space Telescope, we report the discovery of an unusually metal-poor galaxy overdensity of 17 members (mean metallicity $\approx 3\%$ solar) near this metal absorber, which is $\sim 0.4$ dex more metal-poor than coeval galaxies in similarly overdense environments. This less chemically evolved system may have provided favorable conditions for preserving the absorption signatures of Pop III enrichment. We infer a minimum dark matter halo of $\log(M_{\mathrm{h,min}}/M_{\odot})=10.68^{+0.93}_{-1.72}$, supporting late-time Pop III formation at the outskirts of atomic hydrogen cooling halos. Our findings open a promising observational pathway to identify the chemical imprints of the first stars and constrain the conditions for their formation.

astro-ph.GA↗

arXiv2026

PerturbCellRL: Verifier-Guided Reinforcement Learning for Single-Cell Perturbation Prediction

Single-cell perturbation models can reduce costly wet-lab screening by predicting how cells respond transcriptionally to interventions. While recent generative models improve population-level prediction, individual generated cells are not explicitly checked for biological consistency. We introduce PerturbCellRL, a reinforcement learning (RL) framework that post-trains a pretrained single-cell transcriptomic generator using a suite of cell-level verifiers as rewards. These verifiers define four rewards: Pearson top-k similarity, RMSE top-k proximity, DE Spearman, and Pathway activity. The Pathway activity verifier rewards cells whose pathway responses match known perturbation biology. We evaluate PerturbCellRL on multiple genetic and chemical perturbation benchmarks. Across these benchmarks, PerturbCellRL improves over the pretrained flow-matching generator on reward-aligned evaluation metrics and a held-out evaluation metric. Moreover, PerturbCellRL remains competitive with state-of-the-art methods on population-level metrics. Together, these results frame trustworthy single-cell prediction as verifier-guided generative alignment, moving beyond matching expression distributions toward predictions whose single-cell perturbation effects are explicitly checked for biological consistency.

cs.LG↗

arXiv2026

A massive barred spiral galaxy at z = 5.102 discovered by JWST

We report M1149-BSG-z5, a barred spiral galaxy at $z = 5.102$, identified in the parallel field of MACS J1149+2223 with JWST and HST. M1149-BSG-z5 is the highest redshift barred galaxy candidate to date. Both isophote ellipse fitting and structural modeling support a stellar bar of length $a_\mathrm{bar} \approx 4.5$ kpc, and extended spiral arms peaking at $r \approx 5.5$ kpc. M1149-BSG-z5 is a massive main sequence star-forming galaxy, with a stellar mass of $10^{10.45}\rm M_\odot$ and a star-formation rate of $144\,\rm M_\odot/yr$. A concentrated bulge is embedded in an extended disk with a global S\'ersic index $n = 2.37$. With an effective radius of $R_{e} = 2.61\rm \ kpc$, M1149-BSG-z5 is larger than typical galaxies at $z \sim 5$ and comparable to barred galaxies at $2 < z < 4$. M1149-BSG-z5 also hosts a broad-line AGN, with a relatively low black-hole-to-stellar mass ratio of $\rm M_{\rm BH}/M_\ast\sim10^{-3}$. Its metal-enriched emission-line properties indicate that it is already chemically evolved. These properties imply M1149-BSG-z5 as an early-assembled and structurally evolved galaxy. We also find that M1149-BSG-z5 resides in an overdense region with a nearby companion galaxy, suggesting an interaction-driven bar formation mechanism. Its concentrated light, early assembly and main-sequence star formation also suggest baryon-dominated, gas-rich conditions, where gravitational instability can further accelerate the bar formation.

astro-ph.GA↗

arXiv2026

A Strongly Lensed Ultra-faint Arc at $z \approx 10$ with an F200W excess in Abell S1063

Strong gravitational lensing provides a powerful route to probing intrinsically faint galaxies during the first few hundred million years of cosmic history. In this Letter, we report the identification of GAR10, a highly magnified F115W-dropout galaxy at $z\approx10$ in the Abell S1063 cluster field, using deep JWST/NIRCam imaging from the GLIMPSE and GO-1840 programs. The source shows an unusually blue ultraviolet (UV) continuum and a significant F200W excess relative to adjacent bands. Under our high-magnification lensing solution, we infer a median magnification of $\mu=43^{+78}_{-20}$, corresponding to an intrinsic UV magnitude of $M_{\rm UV}\approx-15.8$. We use exploratory Prospector SED modeling to examine two physically motivated interpretations of the observed photometry. In Case I, GAR10 is described by an extremely metal-poor, continuum-dominated stellar population at $z=10.75_{-0.34}^{+0.41}$, with a blue UV slope of $\beta=-2.92\pm0.12$ and a low metallicity of $\log(Z/Z_\odot)=-3.56_{-0.85}^{+0.65}$, consistent with an extremely metal-poor or Pop III-like continuum-dominated interpretation under the adopted priors. In Case II, GAR10 is interpreted as an extremely young (1--3 Myr), high-ionization galaxy at $z=10.45_{-0.21}^{+0.11}$, in which the F200W excess is produced by intense rest-frame UV emission lines, including CIV, HeII, and CIII]. Both cases can partially reproduce the current photometry within the adopted priors, but they imply distinct ionizing sources, enrichment histories, and possible contributions to cosmic reionization. GAR10 therefore represents a rare laboratory for studying ultra-faint galaxy formation at cosmic dawn. Future JWST/NIRSpec spectroscopy will be essential to distinguishing between the steep continuum and emission-line origins of the F200W excess.

astro-ph.GA↗

arXiv2026

Lagrange: An Open-Vocabulary, Energy-Based Sparse Framework for Generalized End-to-End Driving

Scaling end-to-end autonomous driving to complex, open-world environments requires perceptual models that generalize to anomalous scenarios and planners that produce kinematically valid trajectories. Existing paradigms face a distinct dichotomy between representational efficiency and generalization capacity. Dense models (e.g., occupancy networks), while geometrically robust, incur critical computational bottlenecks and struggle with high-level semantic reasoning. Conversely, sparse, query-based planners are efficient but reliant on closed-set definitions, rendering them vulnerable to out-of-distribution (OOD) events. Although recent Vision-Language-Action (VLA) models offer open-vocabulary reasoning, their autoregressive, discrete token generation fundamentally conflicts with the continuous, high-frequency control requirements of vehicle dynamics. To address this, we propose Lagrange, an open-vocabulary, computationally sparse driving framework based on Masked Latent Fields (MLF). Rather than relying on dense volumetric reconstructions or closed-set query mechanisms, Lagrange exploits Vision-Language Models (VLMs) to encode class-agnostic object proposals into continuous semantic visual tokens. We introduce an intent-driven masked cross-attention module that temporally filters irrelevant entities, decoding the attended tokens into an implicit continuous energy field defined over spatial coordinates. By framing decision-making as a Lagrangian action minimization problem spanning this energy field, we enforce strict compliance with vehicle kinematics while executing collision avoidance. Extensive offline evaluations on both standard (nuScenes) and long-tail (CODA) benchmarks demonstrate that Lagrange establishes a promising framework for robust, interpretable, and kinematically feasible open-world autonomy.

cs.AI↗

arXiv2026

Probing Direct Contributions of Galaxies and AGN to Cosmic Reionization in a Quasar Field J0226+0302 with JWST NIRCam and NIRSpec

We present JWST Cycle 2 NIRCam and NIRSpec observations in a quasar field J0226+0302 at z=6.5412 to probe the direct connections between the intergalactic medium (IGM), galaxies, and AGN during reionization. This field was previously observed by the JWST ASPIRE program and eight [OIII]-emitting galaxies were detected at 5.3<z<6.4 with a single NIRCam pointing. Using new NIRCam and NIRSpec observations, we identify 65 additional line-emitting galaxies at 5.3<z<6.4. The IGM-galaxy cross-correlation function shows a ~2 sigma excess IGM transmission at ~10-40 cMpc from galaxies when compared with the average IGM transmission, suggesting a significant contribution from regions traced by star-forming galaxies to the local ionizing background during reionization. The IGM-galaxy cross-correlation function is consistent with THESAN simulations with an IGM neutral fraction of 5%-7% and an average ionizing photon escape fraction f_esc of 6% from galaxies. Among 49 line-emitting galaxies observed by NIRSpec, we identify four AGN through detection of broad H-alpha emission lines with an AGN fraction of (8+/-4)%. By measuring the IGM effective optical depth around the AGN and the IGM-AGN cross-correlation function, we find that the IGM transmission is higher within 5 cMpc/h of the AGN than around the majority of [OIII] emitters. We interpret the excess IGM transmission as resulting from the local radiation enhancement by the AGN, and estimate f_esc of 50%-100% of the AGN from the IGM-AGN cross-correlation function. Future JWST NIRSpec observations in quasar fields will yield a more constraining IGM-AGN cross-correlation function, providing further insights into the roles of galaxies and AGN in reionization.

astro-ph.GA↗

arXiv2026

Low-Rank Decay for Grokking in Scale-Invariant Transformers: A Spectral-Geometric View

Modern Transformer architectures frequently employ normalization mechanisms such as RMSNorm and Query-Key Normalization, making parts of the model approximately scale-invariant with respect to weight magnitudes. In this regime, standard Frobenius-norm weight decay acts purely along the radial direction of the weight space and cannot directly simplify the function represented by the normalized layer. We study grokking in small algorithmic tasks through this lens and propose \emph{Low-Rank Decay} (LRD), a nuclear-norm-like spectral regularizer whose subgradient -- the polar factor $UV^\top$ -- retains a tangential component even in the scale-invariant setting. This distinction has a concrete dynamical consequence: after the model memorizes the training set and task gradients vanish, L2 decay can no longer reshape the weight spectrum, whereas LRD continues to compress singular values in an $\ell_1$-like fashion. On modular arithmetic tasks, we find that LRD induces rapid effective-rank collapse in Query/Key matrices and expands the data-fraction boundary at which delayed generalization (grokking) occurs. We further provide a spectral-geometric interpretation through the ``needle-to-fan'' expansion of the nuclear-norm subdifferential near low-rank strata.

cs.LG↗

arXiv2026

Little red dots as a cosmological probe: constraining $H_0$ with quasi-periodic pulsations

The James Webb Space Telescope (JWST) has uncovered a population of ``little red dots'' (LRDs) at $z \gtrsim 4$, potentially representing early supermassive black holes embedded in dense gaseous envelopes. The recent discovery of the lensed LRD RXJ2211-RX1 reveals significant variability on rest-frame timescales of decades, which may be interpreted as quasi-periodic variation that has a potential physical parallel to stellar pulsations. In this work, we derive an idealized, self-consistent period-luminosity-temperature ($P$-$L$-$T_{\rm eff}$) relation based on the hydrostatic envelope model. If this theoretical relation holds and can be empirically validated/calibrated, it would offer a novel framework for constraining the Hubble constant ($H_0$). The current sparse sampling of \tgta\ yields a preliminary $H_0 = 120.7_{-46.5}^{+47.0} \text{ km s}^{-1}\text{ Mpc}^{-1}$ as a proof-of-concept, with the error budget dominated by the uncertainty of the pulsation period. Our forecasting analysis shows that continuous monitoring over a 10-year baseline can reduce the $H_0$ uncertainty to 3-20\%, depending on the intrinsic pulsation period, while the systematic uncertainty floor remains to be fully characterized. This method offers a potential independent probe to measure luminosity distances in the early universe.

astro-ph.GA↗

arXiv2026

A Steep-Extinction Quasi-stellar Object at z=4.6: JWST Evidence for Abundant Small Dust Grains

The rapid accumulation of massive dust reservoirs in the early Universe remains a major challenge in astrophysics. While core-collapse supernovae can inject large dust grains ($a \gtrsim 0.1\,\mu{\rm m}$) on short timescales, explaining the total dust budgets in the early Universe likely requires efficient grain growth in the interstellar medium (ISM). Such growth depends critically on an abundant population of small grains, which maximize the surface area available for accretion and may be generated by rapid dust-processing or dust-formation channels. Here, we report the discovery of a QSO, UDS-27023, at $z=4.556\pm0.003$, identified using JWST/NIRSpec spectroscopy. By quantitatively comparing the spectra to QSO composite templates, we find that UDS-27023 displays an exceptionally steep far-UV extinction curve ($A_{1500}/A_V \approx 8$) but notably lacks the 2175 A bump ($A_\mathrm{bump}/A_V<0.34$ at $3\sigma$), indicating a dominance of small silicate dust grains. We interpret this phenomenology as evidence for active small-grain production and processing in the QSO environment. Mechanical shattering of pre-existing large grains by QSO-driven shocks and outflows provides one natural pathway, while in situ condensation of silicate grains inside dense QSO-driven winds may offer an additional route. Such a population of steep-extinction QSOs (SEQs) may therefore reveal a short-lived phase in which luminous active galactic nuclei generate, process, and redistribute small grains, potentially facilitating rapid ISM grain growth and enriching the circumgalactic medium.

astro-ph.GA↗

arXiv2026

Soft-NBCE: Entropy-Weighted Chunk Fusion for Long-Context

The quadratic complexity of self-attention remains a bottleneck for Large Language Models (LLMs) processing ultra-long contexts. The Naive Bayes Cognitive Engine (NBCE) parallelizes long-context inference by chunking documents and routing to the lowest-entropy chunk at each decoding step. This hard-selection strategy causes semantic fragmentation during cross-chunk reasoning, as abrupt routing changes between adjacent tokens disrupt the model's contextual grounding. We present Soft-NBCE, a lightweight extension that replaces discrete chunk selection with soft entropy-weighted chunk fusion. A temperature-scaled Softmax over predictive entropies assigns continuous weights to all chunks, enabling log-space aggregation across chunk-conditioned distributions. To partially compensate for the conditional independence assumption introduced by chunking, we propose Consistency Distillation, a LoRA-based self-distillation that constrains the chunked logit distribution toward a full-context teacher via KL-divergence. On LongBench multi-hop benchmarks, Soft-NBCE with Consistency Distillation improves consistently over NBCE-style baselines (MuSiQue F1: 0.310 vs.\ 0.275 for Vanilla NBCE; HotpotQA F1: 0.479 vs.\ 0.427) while maintaining retrieval accuracy (NIAH-32K: 0.909) at O(L^2/n) peak memory.

cs.LG↗

arXiv2026

Expected Value Alignment for Generative Reward Modeling in Formal Mathematics Verification

Large Language Models (LLMs) are increasingly used with formal interactive theorem provers such as Lean 4. Scaling these systems with reinforcement learning or search methods requires process reward models (PRMs) that can evaluate intermediate reasoning steps. Existing reward-model designs expose a practical trade-off. Value-head models provide continuous scores but modify the generative model interface, while generative reward models preserve textual rationales but are poorly matched to continuous floating-point regression because numeric values are split across tokens. We introduce Expected Value Alignment (EVA), a reward-modeling procedure that keeps the surface output discrete while extracting continuous scores from the model's token distribution. The model emits integer scores in a structured JSON format, and EVA computes a continuous score as the expectation over the logits of the corresponding anchor tokens. Training combines the causal language modeling objective with an auxiliary mean squared error loss on these expected values. We instantiate EVA in \textit{Leibniz}, a reward model for Lean 4 formal verification, and evaluate it against zero-shot and reward-modeling baselines. The evaluation demonstrates that continuous logit-based scoring significantly reduces discretization artifacts while retaining the interpretability of generative critiques.

cs.AI↗

arXiv2026

A Formal Kinetic Theory for Zeroth-Order Newton Dynamics:Stein-Corrected Hessian Estimation and Curvature--Variance Trade-offs

Zeroth-order Newton-type methods are useful when gradients and Hessians are unavailable, but they behave quite differently from first-order gradient-free methods. We develop a kinetic framework for algorithms that estimate both gradient and Hessian from black-box function values. The naive random-direction Hessian estimator turns out to be biased even on quadratics; a Gaussian--Stein correction is needed to estimate the Hessian of the Gaussian-smoothed objective. Linearizing the inverse Hessian exposes two noise channels: gradient noise preconditioned by the inverse Hessian, and Hessian noise transmitted through an inverse-Hessian sandwich. Under a noisy oracle the second channel carries the second-difference factor $\mu_H^{-4}$. A small-mass kinetic lift links the finite-step Newton update to an underdamped phase-space model; the overdamped spatial limit yields a Lyapunov bound that exposes the curvature--variance trade-off between step size, batch sizes, smoothing radii, and regularization. Numerical experiments confirm estimator identities, the gradient and Hessian variance laws, dimension scaling, inverse-perturbation accuracy, and optimization behavior under query-budget and regularization ablations.

math.OC↗