arXiv subjects

Dechen Zhang

Publications and source records attributed to Dechen Zhang.

17 recordsLinked to original sources

arXiv2026

VALG: An Agentic System for ML Theory Research

Machine learning theory studies learning procedures through mathematical setups in which the data model, training protocol, oracle access, loss, metric, and randomness define the phenomenon that a theorem is meant to explain. Solving an open problem therefore requires the problem formulation, theorem target, and proof mechanism to be developed in concert. Researchers formulate hypotheses, test them through preliminary theoretical or empirical analysis, and refine both assumptions and proofs. We investigate whether this process can be organized as an autonomous agentic workflow for ML theory research. We develop VALG, an agentic system that combines multi-level Verification, Adaptive formulation of Learning-theory problems, and Graph-structured proof development. Within each source-relative theorem branch, VALG maintains a fixed mathematical specification, checks the theorem-level composition of a typed proof-dependency graph, and constructs and reviews local proofs in dependency order. When a proof attempt fails, VALG identifies whether the obstruction lies in a derivation, the proof structure, or the theorem formulation and routes the next attempt accordingly. Formulation-level obstructions initiate an explicitly related variant or relaxation, preserving the mathematical relation between the resulting theorem and the source problem. We evaluate VALG on nine subproblems from five COLT 2026 open problems. Two runs produce internally finalized theorem candidates that match the scope of their source briefs; the remaining seven yield restricted-method results, special cases, or conditional theorems. These case studies show how VALG keeps source-scope matches, relaxations, conditional results, and blocked attempts mathematically distinct. VALG is open source at https://github.com/DechenZhang/VALG-ML-Theory-Agent.

cs.AI↗

arXiv2026

Divergence Decoding: Training-Free Capability Fusion

While large language models excel in reasoning, these generalists often lack knowledge for specialized scientific domains. Conversely, domain models~(specialists), while knowledgeable, suffer from specialization side-effects including diminished logic and reduced robustness.To address this dilemma, we introduce Divergence Decoding, a training-free framework for capability fusion. It reconstructs the "draft-and-verify" skeleton of speculative decoding into an adaptive routing mechanism. The core is using Jensen-Shannon divergence to monitor the distributional disagreement between the two models at each token. When the specialist exhibits significant divergence, our method identifies it as a potential reasoning risk and instantaneously routes control to the generalist. This allows the dynamic injection of general reasoning while preserving domain expertise, achieving inference-time policy composition of the generalist and the specialist.We evaluate Divergence Decoding across diverse model families (Qwen and Llama series) on challenging scientific benchmarks (GPQA, ChemBench, and ChemCoTBench). Experimental results demonstrate that Divergence Decoding outperforms both the domain-specialized and general-purpose models, effectively surpassing the performance of most single-model baseline. This suggests that Divergence Decoding provides a general, training-free paradigm for fusing diverse LLM capabilities through adaptive inference-time collaboration.

cs.AI↗

arXiv2026

Non-local low energy neutral excitations in a strongly disordered triangular Mott magnet Cr$_3$Se$_2$Br$_5$

Understanding if low-energy excitations can remain itinerant in the presence of strong disorder remains a central challenge in frustrated quantum magnets, where disorder is generally expected to localize excitations through Anderson-like mechanisms. Here we report the emergence of charge-neutral itinerant excitations in a van der Waals compound Cr$_3$Se$_2$Br$_5$, a strongly disordered $S = 3/2$ Mott insulator with a frustrated triangular lattice. Structural analysis reveals substantial intrinsic disorder arising from Cr-site deficiency and Se/Br-site mixing, which appear to be fixed and cannot be readily tuned. No long-range magnetic order or conventional glassy behavior is observed. In addition to its highly insulating nature, the magnetic specific heat C_mag/T and thermal conductivity \k{appa}_xx/T both exhibit linear temperature dependencies with substantial finite intercepts. In particular, a sizeable field-independent residual term $\kappa/T \approx 0.03~\mathrm{W\,m^{-1}\,K^{-2}}$ is observed, providing compelling evidence of itinerant low-energy excitations that carry entropy without charge. These findings conceptually advance our understanding of quantum matter by demonstrating a rare regime where the interplay of disorder, frustration, and electronic correlations actively reshapes the nature of low-energy excitations, allowing itinerant neutral excitations to coexist with strong intrinsic disorder.

cond-mat.str-el↗

arXiv2026

Scaling Laws for Precision in High-Dimensional Linear Regression

Low-precision training is critical for optimizing the trade-off between model quality and training costs, necessitating the joint allocation of model size, dataset size, and numerical precision. While empirical scaling laws suggest that quantization impacts effective model and data capacities or acts as an additive error, the theoretical mechanisms governing these effects remain largely unexplored. In this work, we initiate a theoretical study of scaling laws for low-precision training within a high-dimensional sketched linear regression framework. By analyzing multiplicative (signal-dependent) and additive (signal-independent) quantization, we identify a critical dichotomy in their scaling behaviors. Our analysis reveals that while both schemes introduce an additive error and degrade the effective data size, they exhibit distinct effects on effective model size: multiplicative quantization maintains the full-precision model size, whereas additive quantization reduces the effective model size. Numerical experiments validate our theoretical findings. By rigorously characterizing the complex interplay among model scale, dataset size, and quantization error, our work provides a principled theoretical basis for optimizing training protocols under practical hardware constraints.

stat.ML↗

arXiv2025

Learning under Quantization for High-Dimensional Linear Regression

The use of low-bit quantization has emerged as an indispensable technique for enabling the efficient training of large-scale models. Despite its widespread empirical success, a rigorous theoretical understanding of its impact on learning performance remains notably absent, even in the simplest linear regression setting. We present the first systematic theoretical study of this fundamental question, analyzing finite-step stochastic gradient descent (SGD) for high-dimensional linear regression under a comprehensive range of quantization targets: data, label, parameter, activation, and gradient. Our novel analytical framework establishes precise algorithm-dependent and data-dependent excess risk bounds that characterize how different quantization affects learning: parameter, activation, and gradient quantization amplify noise during training; data quantization distorts the data spectrum and introduces additional approximation error. Crucially, we distinguish the effects of two quantization schemes: we prove that for additive quantization (with constant quantization steps), the noise amplification benefits from a suppression effect scaled by the batch size, while multiplicative quantization (with input-dependent quantization steps) largely preserves the spectral structure, thereby reducing the spectral distortion. Furthermore, under common polynomial-decay data spectra, we quantitatively compare the risks of multiplicative and additive quantization, drawing a parallel to the comparison between FP and integer quantization methods. Our theory provides a powerful lens to characterize how quantization shapes the learning dynamics of optimization algorithms, paving the way to further explore learning theory under practical hardware constraints.

stat.ML↗

arXiv2025

Kernel Regression in Structured Non-IID Settings: Theory and Implications for Denoising Score Learning

Kernel ridge regression (KRR) is a foundational tool in machine learning, with recent work emphasizing its connections to neural networks. However, existing theory primarily addresses the i.i.d. setting, while real-world data often exhibits structured dependencies - particularly in applications like denoising score learning where multiple noisy observations derive from shared underlying signals. We present the first systematic study of KRR generalization for non-i.i.d. data with signal-noise causal structure, where observations represent different noisy views of common signals. By developing a novel blockwise decomposition method that enables precise concentration analysis for dependent data, we derive excess risk bounds for KRR that explicitly depend on: (1) the kernel spectrum, (2) causal structure parameters, and (3) sampling mechanisms (including relative sample sizes for signals and noises). We further apply our results to denoising score learning, establishing generalization guarantees and providing principled guidance for sampling noisy data points. This work advances KRR theory while providing practical tools for analyzing dependent data in modern machine learning applications.

stat.ML↗

arXiv2025

Strain-tunability of the multipolar Berry curvature in altermagnet MnTe

The anomalous Hall effect describes the generation of a transverse voltage by a longitudinal current even in the absence of an external magnetic field. While typically observed in ferromagnets, it has also been predicted to arise in altermagnets, materials characterized by rotational symmetries that enable broken time reversal symmetry despite compensated collinear magnetic ordering. These symmetries enforce band (anti)crossings that can generate significant contributions to the Berry curvature that drives the anomalous Hall effect. This Berry curvature is predicted to exhibit a characteristic multipolar order, resulting in a symmetry-enforced distribution at or near net compensation which is highly sensitive to perturbations that distort this balance. However, exploring the predicted multipolar Berry curvature of altermagnets and its reversible manipulation remains challenging. Here, we demonstrate evidence for the multipolar nature of the altermagnetic Berry curvature in MnTe by tuning the anomalous Hall effect via uniaxial stress. Upon straining, the magnitude of the anomalous Hall conductivity changes and, at a critical strain of 0.14%, the sign is reversed. Symmetry analysis and density functional theory calculations reveal that this tunability is a direct consequence of the altermagnetic multipolar Berry curvature. Our results provide insight into the role of crystal and magnetic symmetries in the realization of higher-order Berry curvature distributions and their unique tunability.

cond-mat.mtrl-sci↗

arXiv2025

Thermoelectric evidence of the electronic structure changes from the charge-density-wave transition in FeGe

Kagome metals provide a material platform for probing new correlated quantum phenomena due to the naturally incorporated linear dispersions, flat bands, and Van Hove singularities in their electronic structures. Among these quantum phenomena is the charge density wave (CDW), or the distortion of the lattice structure due to the motion of correlated electrons through the material. CDWs lower the energy of the compound, creating an energy gap that facilitates behaviors akin to superconductivity, nonlinear transport, or other quantum correlated phenomena. The kagome metal FeGe has been shown to host a CDW transition at approximately 100 K, and its occurrence is strongly influenced by the sample annealing conditions. However, a notable gap in the literature is the lack of clear thermoelectric transport evidence for electronic structure changes associated with this CDW transition. Here we present evidence of electron behavior modification due to annealing disorder via thermoelectric measurements on FeGe crystals presenting a CDW transition and those without a CDW. The observed Nernst effect and Seebeck effect under sufficient annealing demonstrate modified electrical transport properties resulting from induced disorder, including a change in carrier sign and an enhancement of the Nernst effect due to the CDW. Our results provide evidence of multiple phase transitions, which confirms the influence of CDW on the thermal properties of FeGe and demonstrates the suppression of CDW with sufficient disordering.

cond-mat.str-el↗

arXiv2025

Quantum oscillations in the heat capacity of Kondo insulator YbB12

We observe the magnetic quantum oscillation in the heat capacity of the Kondo insulator YbB$_{12}$. The frequency of these oscillations $F = 670$ T, aligns with findings from magnetoresistance and torque magnetometry experiments for $\mu_0 H > 35$ T in the Kondo insulating phase. Remarkably, the quantum oscillation amplitudes in the heat capacity are substantial, with $\Delta \tilde{C}/T \approx$ 0.5 $\rm{mJ}$ $\rm{mol^{-1}K^{-2}}$ at 0.8 K, accounting for 13$\%$ of the known linear heat capacity coefficient $\gamma$. Double-peak structures of quantum-oscillation amplitudes due to the distribution function of fermions were identified and used to determine the value of the effective mass from the heat capacity, which agrees well with that from torque magnetometry. These observations support charge-neutral fermions contributing to the quantum oscillations in YbB$_{12}$.

cond-mat.str-el↗

arXiv2024

Field tunable BKT and quantum phase transitions in spin-1/2 triangular lattice antiferromagnet

Quantum magnetism is one of the most active fields for exploring exotic phases and phase transitions. The recently synthesized Na2BaCo(PO4)2 (NBCP) is an ideal material incarnation of the spin-1/2 easy axis triangular lattice antiferromagnet (TLAF). Experimental evidence shows that NBCP hosts the spin supersolid state with a giant magnetocaloric effect. It was also proposed that the applied magnetic field B can drive the system through Berezinskii-Kosterlitz-Thouless (BKT) and other richer quantum phase transitions. However, the detection of these transitions is challenging because they onset at extremely low temperature T at around 60 mK, and the measurement of the magnetic susceptibility of these transitions requires high sensitivity. With the help of our newly developed gradient force magnetometer in a dilution refrigerator, we constructed the contour diagram of the magnetic susceptibility in the B-T phase diagram in T as cold as 30 mK. These results provide a more comprehensive and accurate understanding of the several field-tunable quantum phase transitions and BKT melting of the spin supersolidity, which are especially significant when their giant magnetocaloric effects highlight potential applications for sub-Kelvin refrigeration under concerns about global helium shortages.

cond-mat.str-el↗

arXiv2024

Large Oscillatory Thermal Hall Effect in Kagome Metals

The thermal Hall effect recently provided intriguing probes to the ground state of exotic quantum matters. These observations of transverse thermal Hall signals lead to the debate on the fermionic versus bosonic origins of these phenomena. The recent report of quantum oscillations (QOs) in Kitaev spin liquid points to a possible resolution. The Landau level quantization would most likely capture only the fermionic thermal transport effect. However, the QOs in the thermal Hall effect are generally hard to detect. In this work, we report the observation of a large oscillatory thermal Hall effect of correlated Kagome metals. We detect a 180-degree phase change of the oscillation and demonstrate the phase flip as an essential feature for QOs in the thermal transport properties. More importantly, the QOs in the thermal Hall channel are more profound than those in the electrical Hall channel, which strongly violates the Wiedemann Franz (WF) law for QOs. This result presents the oscillatory thermal Hall effect as a powerful probe to the correlated quantum materials.

cond-mat.str-el↗

arXiv2024

Quantum Oscillations Evidence for Topological Bands in Kagome Metal ScV6Sn6

Metals with kagome lattice provide bulk materials to host both the flat-band and Dirac electronic dispersions. A new family of kagome metals is recently discovered in AV6Sn6. The Dirac electronic structures of this material need more experimental evidence to confirm. In the manuscript, we investigate this problem by resolving the quantum oscillations in both electrical transport and magnetization in ScV6Sn6. The revealed orbits are consistent with the electronic band structure models. Furthermore, the Berry phase of a dominating orbit is revealed to be around $\pi$, providing direct evidence for the topological band structure, which is consistent with calculations. Our results demonstrate a rich physics and shed light on the correlated topological ground state of this kagome metal.

cond-mat.str-el↗

arXiv2024

Thermodynamic evidence of fermionic behavior in the vicinity of one-ninth plateau in a kagome antiferromagnet

The spin-1/2 kagome Heisenberg antiferromagnets are believed to host exotic quantum entangled states. Recently, the report of 1/9 magnetization plateau and magnetic oscillations in a kagome antiferromagnet YCu$_3$(OH)$_6$Br$_2$[Br$_x$(OH)$_{1-x}$] (YCOB) have made this material a promising candidate for experimentally realizing quantum spin liquid states. Here we present measurements of the specific heat $C_p$ in YCOB in high magnetic fields (up to 41.5 Tesla) down to 0.46 Kelvin, and the 1/9 plateau feature has been confirmed. Moreover, the temperature dependence of $C_p/T$ in the vicinity of 1/9 plateau region can be fitted by a linear in $T$ term which indicates the presence of a Dirac spectrum, together with a constant term, which indicates a finite density of states (DOS) contributed by other Fermi surfaces. Surprisingly the constant term is highly anisotropic in the direction of the magnetic field. Additionally, we observe a double-peak feature near $30$~T above the 1/9 plateau which is another hallmark of fermionic excitations in the specific heat.

cond-mat.str-el↗

arXiv2023

Unconventional Magnetic Oscillations in Kagome Mott Insulators

In metals, electrons in a magnetic field undergo cyclotron motion, leading to oscillations in physical properties called quantum oscillations. This phenomenon has never been seen in a robust insulator because there are no mobile electrons. We report the first exception to this rule. We study a Mott insulator on a kagome lattice which does not order magnetically down to milli-Kelvin temperatures despite antiferromagnetic interactions. We observe a plateau at magnetization equal to 1/9 Bohr magneton per magnetic ion, accompanied by oscillations in the magnetic torque, reminiscent of quantum oscillations in metals. The temperature dependence obeys Fermi distribution. These phenomena are consistent with a quantum spin liquid state whose excitations are fermionic spinons with a Dirac-like spectrum coupled to an emergent gauge field.

cond-mat.str-el↗

arXiv2023

"Extraordinary" Phase Transition Revealed in a van der Waals Antiferromagnet

While the surface-bulk correspondence has been ubiquitously shown in topological phases, the relationship between surface and bulk in Landau-like phases is much less explored. Theoretical investigations since 1970s for semi-infinite systems have predicted the possibility of the surface order emerging at a higher temperature than the bulk, clearly illustrating a counterintuitive situation and greatly enriching phase transitions. But experimental realizations of this prediction remain missing. Here, we demonstrate the higher-temperature surface and lower-temperature bulk phase transitions in CrSBr, a van der Waals (vdW) layered antiferromagnet. We leverage the surface sensitivity of electric dipole second harmonic generation (SHG) to resolve surface magnetism, the bulk nature of electric quadrupole SHG to probe bulk spin correlations, and their interference to capture the two magnetic domain states. Our density functional theory calculations show the suppression of ferromagnetic-antiferromagnetic competition at the surface responsible for this enhanced surface magnetism. Our results not only show unexpected, richer phase transitions in vdW magnets, but also provide viable ways to enhance magnetism in their 2D form.

cond-mat.mtrl-sci↗

arXiv2023

Universal sublinear resistivity in vanadium kagome materials hosting charge density waves

The recent discovery of a charge density (CDW) state in ScV$_6$Sn$_6$ at $T_{\textrm{CDW}}$ = 91 K offers new opportunities to understand the origins of electronic instabilities in topological kagome systems. By comparing to the isostructural non-CDW compound LuV$_6$Sn$_6$, we unravel interesting electrical transport properties in ScV$_6$Sn$_6$, above and below the charge ordering temperature. We observed that by applying a magnetic field along the $a$ axis, the temperature behavior of the longitudinal resistivity in ScV$_6$Sn$_6$ changes from metal-like to insulator-like above the CDW transition. We show that in the charge ordered state ScV$_6$Sn$_6$ follows the Fermi liquid behavior while above that, it transforms into a non-Fermi liquid phase in which the resistivity varies sublinearly over a broad temperature range. The sublinear resistivity, which scales by $T^{3/5}$ is a common feature among other vanadium-containing kagome compounds exhibiting CDW states such as KV$_3$Sb$_5$, RbV$_3$Sb$_5$, and CsV$_3$Sb$_5$. By contrast, the non-Fermi liquid behavior does not occur in LuV$_6$Sn$_6$. We explain the $T^{3/5}$ universal scaling behavior from the Coulomb scattering between Dirac electrons and Van Hove singularities; common features in the electronic structure of kagome materials. Finally, we show anomalous Hall-like behavior in ScV$_6$Sn$_6$ below $T_{\textrm{CDW}}$, which is absent in the Lu compound. Comparing the transport properties of ScV$_6$Sn$_6$ and LuV$_6$Sn$_6$ is valuable to highlight the impacts of the unusual CDW in the Sc compound.

cond-mat.str-el↗

arXiv2021

Hall anomaly, Quantum Oscillations and Possible Lifshitz Transitions in Kondo Insulator YbB$_{12}$: Evidence for Unconventional Charge Transport

In correlated electronic systems, strong interactions and the interplay between different degrees of freedom may give rise to anomalous charge transport properties, which can be tuned by external parameters like temperature and magnetic field. Recently, magnetic quantum oscillations and metallic low-temperature thermal conductivity have been observed in the Kondo insulator YbB$_{12}$, whose resistivity is a few orders of magnitude higher than those of conventional metals. As yet, these unusual observations are not fully understood. Here we present a detailed investigation of the behavior of YbB$_{12}$ under intense magnetic fields using both transport and torque magnetometry measurements. A low-field Hall anomaly, reminiscent of the Hall response associated with "strange-metal" physics, develops at $T < 1.5$ K. At two characteristic magnetic fields ($\mu_0H_1= 19.6$ T and $\mu_0H_2 \sim 31$ T), signatures appear in the Hall coefficient, magnetic torque, and magnetoresistance. We suggest that they are likely to be field-induced Lifshitz transitions. Moreover, above 35 T, the background resistivity displays an unusual, nonmetallic $T^{\alpha}$-behavior, with $\alpha$ being field-dependent and varying between -1.5 and -2. By normalizing the Shubnikov-de Haas oscillation amplitude to this $T^{\alpha}$-dependence, the calculated cyclotron mass becomes more consistent with that deduced from de Haas-van Alphen oscillations. Our results support a novel two-fluid scenario in YbB$_{12}$: a Fermi-liquid-like fluid of charge-neutral quasiparticles coexists with charge carriers that remain in a nonmetallic state. The former experience successive Lifshitz transitions and develop Landau quantization in applied magnetic fields, whilst scattering between both fluids allows the Shubnikov-de Haas effect to be observed in the electrical transport.

cond-mat.str-el↗