arXiv subjects

Mingyu Li

Publications and source records attributed to Mingyu Li.

At least 19 recordsLinked to original sources

arXiv2026

EMBER: A Little Red Dot Candidate at $z_{\rm spec}=10.36$ in the Seed Black Hole Era

Little red dots (LRDs) are a newly discovered population that may trace rapidly growing black holes (BHs) and provide a link between seed BHs and luminous active galactic nuclei (AGNs). However, no LRD had previously been spectroscopically confirmed at $z>10$, leaving this earliest phase observationally unexplored. Using JWST/NIRSpec spectroscopy from the EMBER program, we measure a spectroscopic redshift of $z_{\rm spec}=10.361^{+0.003}_{-0.002}$ for \target, the highest-redshift LRD candidate known to date. The redshift is constrained by a prominent Ly$α$ break and multiple tentative emission lines, including C\,{\sc iv}\,$λ\lambda1549,1551$ and [O\,{\sc iii}]\,$\lambda4363$ detected at $S/N=3.9$ and $3.6$, respectively. Its extreme NIRCam-MIRI color of $m_{\rm F444W}-m_{\rm F770W}=1.82\pm0.1$, characteristic V-shaped continuum with a turnover near the Balmer limit, and continuum slopes of $β_{\rm UV}=-2.26^{+0.11}_{-0.11}$ and $β_{\rm opt}=1.17^{+0.74}_{-0.70}$ all support its LRD nature. A possible iron complex at $λ_{\rm rest}\sim0.24$--$0.25\,{\rm μm}$ and a possibly high $\log\left([{\rm O\,III]\,\lambda4363/\rm Hγ}\right)=0.17^{+0.24}_{-0.22}$ further support an AGN-like interpretation, as seen in previously known LRDs. Tentative detection of Ly$α$ emission may indicate enhanced Ly$α$ transmission at $z\sim10$. Our findings extend the observational frontier of BH growth into the seed-BH formation era, and upcoming MIRI spectroscopy will further establish the physical nature of the source.

astro-ph.GA↗

arXiv2026

(LRDs)$^2$: The Low-ReDshift Little Red Dots Survey. II. DESI DR1 Sample

JWST has revealed a substantial population of "Little Red Dots" (LRDs) at $z>4$, challenging conventional AGN frameworks. However, the low-redshift regime remains largely unexplored. In the second paper of the (LRDs)$^2$ series, we present a systematic selection from DESI DR1 and identify 27 LRDs at $z=0.2-0.9$, yielding a number density lower limit of $7.5\times10^{-10}$ cMpc$^{-3}$. We conducted near-IR spectroscopic follow-up observations for 21 of them, revealing their full SED shapes and emission lines. These low-$z$ LRDs share the hallmark properties of their high-$z$ counterparts: compact morphology, V-shaped UV-optical continua, broad Balmer emission with extreme decrements (median H$α$/H$β\sim15$), frequent Balmer absorption (70%), and blackbody-like optical-to-near-IR continua. All have low metallicity, occupy the same regions in the BPT diagram as high-$z$ LRDs, and have softer ionizing spectra than typical AGNs. The consistency between low-$z$ and high-$z$ LRD properties indicates the same physical processes at work. The correlation between broad-line Balmer luminosity and $L_{5100}$ deviates from that of local type-1 AGNs, limiting the direct application of local BH mass calibrations. Ionized [O III] outflows are ubiquitous (78%). One LRD at $z=0.196$, J1717+3807, shows robust long-term variability in $i$ and WISE bands. The optical-to-NIR continua of LRDs reveal a wide range of temperatures $\sim2000-4700$ K (peak $0.6-1.4$ $μ$m), with a subset showing cooler and larger envelopes than those at high $z$. Low-$z$ LRDs serve not only as proximate laboratories for probing the nature of LRDs, but also trace the cosmic evolution of this population from the cosmic dawn to the present day.

astro-ph.GA↗

arXiv2026

Can Blue UV-Bright Galaxies Drive Reionization at Cosmic Dawn? An $M_{\rm UV}=-19.6$ Galaxy with $f_{\rm esc}\approx0.85$ at $z=9.244$

We revisit EBG-1, a gravitationally lensed galaxy at $z = 9.244$, using newly obtained deep (14 hr) JWST/NIRSpec G235M ($R \sim 1000$) spectroscopy. EBG-1 is one of the bluest galaxies observed at $z > 9$. Along with its remarkably blue continuum of $β= -2.99 \pm 0.15$, we find very weak nebular emission from EBG-1. We obtain a $3σ$ upper limit of EW $< 8.4$ Angstrom for C III], a marginal H$β$ measurement (EW $= 256.2 \pm 122.2$ Angstrom), and a $5σ$ detection of [O III] $λ5007$ (EW $= 882.8 \pm 180.6$ Angstrom). These lines suggest an oxygen abundance of $12 + \log(\mathrm{O/H}) = 7.16 \pm 0.25$ ($\simeq 3\% Z_{\odot}$) and $\log(\mathrm{C/O}) < -0.88$ ($3σ$), placing EBG-1 on the C/O-metallicity sequence traced by lower-redshift galaxies. To constrain the escape fraction ($f_{\rm esc}$), we compare the observed UV slope and emission-line equivalent widths with synthetic spectra generated using BEAGLE. The models favor $f_{\rm esc} \gtrsim 0.75$, with $f_{\rm esc} \approx 0.85$ providing the best overall agreement with the observations. These results suggest that relatively UV-bright galaxies like EBG-1 can achieve the exceptionally high ionizing efficiencies supported by late reionization scenarios.

astro-ph.GA↗

arXiv2026

ObjDream: Guiding Vision-Language-Action Models with Object-Level Understanding and Future State Prediction

Vision-language-action (VLA) models have emerged as a powerful paradigm for robotic manipulation, enabling robots to generate actions from visual observations and language instructions. However, most existing VLA models still operate on image-level visual representations inherited from pretrained vision-language backbones, while lacking fine-grained object understanding for manipulation. As a result, their robustness can degrade under out-of-distribution object layouts, clutter, and background variations. To address these limitations, we introduce ObjDream, an object-centric VLA framework centered on object-level understanding and future object state prediction. ObjDream uses a spatio-temporal object encoder to organize visual observations into temporal object slots, where persistent object identity and dynamic object state are represented through separate channels. These structured object representations are inserted into the token sequence of the vision-language model (VLM), where identity-guided routing modulates VLM attention to the corresponding object tokens. In addition, an action-conditioned object dynamics module predicts compact future object states relevant to manipulation during training, explicitly supervising object state evolution under robot actions without requiring future prediction at inference. Experiments on LIBERO, LIBERO-Plus, and RoboTwin 2.0 show that ObjDream improves generalization under diverse distribution shifts and scene perturbations. Real-world robot experiments further demonstrate that ObjDream transfers to physical manipulation settings with novel object arrangements and background changes.

cs.RO↗

arXiv2026

Proactive Physical AI through Continuous Observation and Timely Intervention

Physical AI is commonly formulated around an explicitly specified task: given a goal or instruction, a system perceives, reasons, and acts. In many real-world settings, however, important tasks emerge from continuously changing world states before a person explicitly formulates them. We study this complementary problem as Proactive Physical AI, where an AI system continuously observes the physical world, identifies situations that warrant intervention, and initiates appropriate actions at the right time. We develop ProAgent, an end-to-end system built around two components: a Jev-style proactive timing model (dubbed StreamingJev) that determines whether and when intervention is needed, and a Response Model that generates responses for people or invokes available device capabilities for physical execution. To support learning at scale, we develop an automated data pipeline that converts videos into supervision for proactive timing. Experiments demonstrate strong proactive performance under both explicit objectives and standing roles, combining more accurate intervention timing with fewer false triggers than the source-backbone baseline. Real-robot evaluations further demonstrate ProAgent's ability to identify emerging needs and translate them into appropriate physical actions.

cs.CV↗

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, detecting eight [OIII]-emitting galaxies 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, suggesting a significant contribution from regions traced by star-forming galaxies to the local ionizing background. The IGM-galaxy cross-correlation function in this field is consistent with THESAN simulations for an IGM neutral fraction of 5%-7% and an average galaxy ionizing photon escape fraction f_esc of 6%, although a single field is subject to substantial cosmic variance and cannot constrain these quantities independently. Among 49 line-emitting galaxies observed by NIRSpec, we identify four AGN with broad H-alpha emission lines, resulting in an AGN fraction of (8+/-4)%. From the IGM effective optical depth and the IGM-AGN cross-correlation function, we find that the IGM transmission is higher within 5 cMpc/h of four AGN than around the majority of [OIII] emitters. We interpret the excess transmission as resulting from the local radiation enhancement by the AGN, and estimate f_esc~50%-100%, based on our illustrative model for 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

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

PerturbCellRL: Aligning Distributions and Grounding Biology via Post-Training Perturbation Generators

Single-cell perturbation models can reduce costly wet-lab screening by predicting how cells respond transcriptionally to interventions. Recent advances in flow-matching have enabled population-level prediction of cellular responses. However, flow-matching training can fail to recover certain target distributions even within the model family, limiting its ability to capture cellular heterogeneity. We first prove that post-training can recover these distributions, then introduce PerturbCellRL, a reinforcement learning framework that post-trains single-cell perturbation generators using per-cell rewards. The central component is a gene-expression energy witness that translates population-level discrepancies into per-cell feedback. We further prove that this reward's policy gradient points toward better distributional alignment. Two complementary rewards, calibrated on real cells, penalize atypical expression profiles and insufficient pathway-level responses to perturbations. Across genetic and chemical perturbation benchmarks, PerturbCellRL substantially improves distributional alignment and recovers pathway enrichment patterns more faithfully. These results establish reward-guided post-training as an effective strategy for improving both distributional accuracy and biological fidelity in perturbation prediction.

cs.LG↗

arXiv2026

Galaxies Below the Fundamental Metallicity Relation Are Morphologically Disturbed: Merian H$α$ Morphologies and DESI Metallicities

Empirical results have revealed a connection between a galaxy's metallicity, mass, and star formation rate, known as the fundamental metallicity relation (FMR), in which metallicity increases with stellar mass and decreases with SFR. Physical interpretations of the FMR suggest that actively star-forming galaxies are fueled by pristine gas, likely obtained via IGM accretion or minor mergers. Here we demonstrate the value of galaxy morphology as an additional axis in the FMR. Using medium-band imaging from the Merian Survey, we construct spatially resolved maps of stellar continuum and H$α$ emission for a large sample of galaxies with DESI DR1 spectra, reaching stellar masses down to $10^8$ M$_\odot$. We measure non-parametric morphological parameters from the emission maps and derive gas-phase oxygen abundances from the spectra using strong-line calibrations. We fit a series of simple linear models to explore correlations among the metallicity, stellar mass, sSFR, and morphological parameters. We find that galaxies that are more metal-poor than predicted by the FMR appear particularly disturbed. At fixed stellar mass and sSFR, metallicity is inversely correlated with the asymmetry of both the continuum and H$α$ morphology. The observed trends -- and the existence of particularly metal-poor, morphologically disturbed, highly star-forming galaxies -- are consistent with external burst triggering. Our results indicate that a galaxy's morphology is linked to its metallicity and star formation history, providing an additional observational probe of the physical drivers of elevated star-formation in low-mass galaxies.

astro-ph.GA↗

arXiv2026

LATED: Ly$α$-anchored photometric selection of candidate metal-free and extremely metal-poor star formation from the end of reionisation to cosmic noon

Cosmological simulations allow a low-level tail of Population III (Pop III) star formation to persist to $z=2-6$. Spectroscopic confirmation is expensive, so an efficient photometric pre-selection is needed. We present LATED (Lyman-Alpha Tomography of Extremely Metal-poor Domains), which selects metal-free and extremely metal-poor candidates from a Ly$α$-emitter parent sample using strong-line diagnostics. The method requires three bands and two colours, $x=m_{\rm OIII}-m_{{\rm H}α}$ and $y=m_{{\rm H}α}-m_{\rm cont}$, which trace oxygen abundance and the H$α$ equivalent width, respectively. Requiring that the filters simultaneously contain [O III]+H$β$ and H$α$, together with a Ly$α$ parent selection, defines five windows spanning $z=1.92-6.60$ (four JWST/NIRCam, one Roman/WFI). The criteria, $x\geq x_{\rm min}(z)$ and $y\leq y_{\rm max}(z)$, are set by the per-redshift extrema of a forward-modelled Pop III template locus. Ordinary metal-enriched star-forming and AGN templates fall outside the selection region, and possible contaminants such as little red dots are flagged by their multi-band colours. To check contamination empirically, we apply LATED to 1126 JADES spectroscopic galaxies, and no source is selected in the four NIRCam windows. We release a Python package which converts the same photometry into R3=[O III]/H$β$ as a measurement or upper limit, reproducing JADES spectroscopy with small 0.12 dex scatter. Applied to 85 archival MUSE Ly$α$ emitters in Abell 2744, LATED recovers the confirmed extremely metal-poor galaxy AMORE6 and reveals three new candidates at $z=3-5$. Photometry alone cannot establish a metal-free nature. LATED delivers prioritised candidates for spectroscopic follow-up, providing a scalable route toward a systematic census of late-time Pop III star formation.

astro-ph.GA↗

arXiv2026

LATED: JWST integral field spectroscopy of a galaxy caught in chemical infancy at $z=4.8$ behind Abell 2744

When Population III (Pop III) star formation ended remains an open question. LATED-1 is an intrinsically faint ($M_\mathrm{UV}=-16.15$) Ly$α$ emitter at $z=4.80$ revealed by VLT/MUSE behind the lensing cluster Abell 2744 ($z=0.308$). Before any spectroscopic metallicity constraints, it was identified as an extremely metal-poor or metal-free galaxy candidate from JWST imaging by LATED, our novel photometric selection framework. Here we present serendipitous JWST/NIRSpec PRISM integral-field spectroscopy of this target. The spectrum reveals Ly$α$, H$β$, and H$α$ at 7.0, 5.6, and 17.7$σ$, as well as tentative detections of [O III]$λ\lambda4959,5007$ at 2.9$σ$, and yields $R3=\mathrm{[O\,III]\lambda5007/Hβ}=0.59^{+0.27}_{-0.21}$, upholding the earlier LATED photometric prediction of $R3<1.54$ ($2σ$ limit). The canonical JWST-based strong-line calibration, extrapolated to low metallicity, implies $\log (O/H)=6.45^{+0.17}_{-0.19}$, or $Z/Z_\odot=0.58_{-0.20}^{+0.28}\%$, placing LATED-1 among the most metal-poor galaxies known. Its modest magnification ($μ=2.80$) leaves the intrinsic properties insensitive to the lens model. LATED-1 is therefore a dwarf galaxy caught in the earliest state of chemical enrichment, and a compelling target for testing whether Pop III star formation can persist to $z<5$. The result demonstrates that photometric selection, especially through the LATED methodology, can reach below one per cent solar metallicity to identify Pop III galaxy candidates for spectroscopic follow-up.

astro-ph.GA↗

arXiv2026

VibeAvatar: Aligning Phonetic Kinematics and Human Aesthetics for High-Fidelity Talking Avatar Synthesis

Multi-modal talking avatar synthesis aims to generate realistic talking videos from a reference portrait and speech. Despite rapid progress in diffusion-based methods, existing approaches still struggle to jointly achieve accurate lip articulation, human-preferred motion aesthetics, and efficient inference. We observe that phonetic accuracy and motion aesthetics arise from fundamentally different sources and should be addressed at complementary stages rather than learned implicitly by a single generator. Based on this insight, we propose VibeAvatar, which disentangles these two objectives through a Phonetic Kinematics Adapter (PKA) that converts recognition-oriented speech features into phonetic-kinematic conditions at the conditioning stage, and an Aesthetic Motion Policy (AMP) that optimizes a flow-consistent stochastic sampling policy via Group Relative Policy Optimization (GRPO) at the post-training stage. With a lightweight flow-based motion generator operating in a compact 1D warp-based latent motion space, VibeAvatar achieves state-of-the-art results in articulation, aesthetics, and efficiency on both objective metrics and user studies, while generating a 10-second 512px video in under 10 seconds with only $\sim$3GB VRAM.

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

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$α$+[N II] and H$β$+[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$α$+[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 $Δv_{LOS}$~2800 km/s, detected at 1.5$σ$ in the 1D spectrum (2.4$σ$ 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$α$ 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

Hidden in Pixels. I. Discovery of dual "little red dots" indicates excess clustering on kilo-parsec scales

``Little Red Dots'' (LRDs) are an abundant high-redshift population newly discovered by the James Webb Space Telescope (JWST) and considered to be an early growth phase of supermassive black holes (SMBHs). Using a method of pixel-by-pixel color selection and relaxing the compactness criteria, we identify four dual LRD candidates in the COSMOS-Web survey with projected separations of $0.\!\!^{\prime\prime}2$-$1.\!\!^{\prime\prime}2$. A comparison between existing LRD samples and mock data reveals that the projected separations of these dual LRD candidates are unlikely to result from chance projections of objects at different redshifts. Furthermore, two of the four systems are covered by COSMOS-3D slitless spectroscopy, and a single-line detection at the same observed wavelength for each LRD in a pair strongly supports that they are at identical redshifts. Assuming that the detected lines are H$α$ based on their high equivalent width and broad profile, the spectroscopic redshifts of $z=5.822$ and $5.464$ for the two pairs are consistent with their photometric redshifts, yielding projected separations of $1.64$ and $7.36\,{\rm kpc}$. These discoveries suggest that the angular auto-correlation function (ACF) of LRDs exhibits an excess ($\sim20$-$30$ times) on sub-arcsec (kilo-parsec) separations compared to an extrapolation of a power-law ACF of JWST-found AGNs measured over $10^{\prime\prime}$-$100^{\prime\prime}$. Our sample is likely to represent precursors of mergers between LRDs, and such mergers may be one of the mechanisms that can drive the rapid growth of SMBHs in their early evolutionary stages.

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 ($a \gtrsim 0.1\,μ{\rm m}$) 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 $3σ$), 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↗