arXiv subjects

Haobo Yang

Publications and source records attributed to Haobo Yang.

17 recordsLinked to original sources

arXiv2026

Three Squares in a Rectangle

For $x\ge1$, let $G_3(x)$ be the maximum sum of the side lengths of three pairwise interior-disjoint, arbitrarily rotated squares contained in a $1\times x$ rectangle. We determine this function exactly: $G_3(x)=x+\tfrac12$ for $1\le x\le\tfrac32$, $G_3(x)=2$ for $\tfrac32\le x\le2$, $G_3(x)=x$ for $2\le x\le3$, and $G_3(x)=3$ for $x\ge3$. This completes the $n=3$ case of the rectangular square-packing question posed by Richard Stanley in a 2021 MathOverflow comment. The values for $\tfrac32\le x\le3$ follow from a strip theorem stating that three squares in $[0,1]\times[0,H]$, $H\ge2$, have total side length at most $H$. For $x\ge3$, the formula is immediate because each square has side length at most $1$. The range $1\le x\le\tfrac32$ is handled by combining the two-square theorem with an additional semi-perimeter estimate for a triangle whose two nonhorizontal sides have opposite slopes. In particular, the special case $x=2$ answers the question asked in the MathOverflow post. In connection with Erd\H{o}s problem #106, we also prove that every five-square packing in the unit square with an axis-parallel guillotine cut has total side length at most $2$.

math.MG↗

arXiv2026

Using Large Language Models as Low-Cost Statistical Estimators for Human-Response Data

Quantitative research across the social and behavioral sciences depends on human subject experiments that are expensive, slow, and subject to sampling bias. Here we show that pretrained large language models induce risk-equivalent estimators of conditional expectations under squared loss, establishing restricted functional risk equivalence: under squared loss, the LLM induces an estimator whose risk matches the Bayes optimal risk for squared-loss prediction of conditional expectations for any inference that depends on the data only through the conditional mean. We formalize the LLM as a misspecified functional estimator $T(\hat{P}_n)$ trained on i.i.d.\ data, decompose the estimation error into representation bias $\epsilon_{\mathrm{rep}}$ and optimization error, and prove that under mild regularity conditions the LLM's expected error converges to the irreducible population variance plus the squared representation bias, with the representation bias bounded by the Pinsker inequality. The identifiability error $\delta$ propagates into the effective bias, inflating the asymptotic risk floor. We establish restricted functional risk equivalence via a bidirectional Le Cam deficiency analysis: the forward deficiency vanishes asymptotically while the reverse deficiency is exactly zero. We provide finite-sample concentration bounds and a calibration protocol with explicit decision rules. The result is a precise, provable statement: a well-calibrated LLM achieves the Bayes-optimal risk for conditional-mean-dependent inference, bounded by explicit scope conditions. In practical applications, this means that under satisfied conditions and well-calibrated models, large language models can be used in many prediction and decision-making tasks that originally relied on human experiments, approximating near-optimal statistical inference at lower cost.

cs.AI↗

arXiv2026

Transformer Architectures as Complete Bayes Processes: A Formal Proof in the Measure-Theoretic Kernel Framework

We present a complete formal proof that transformer architectures, when their internal update mechanisms satisfy a Bayes joint-distribution condition, implement exact Bayesian posterior inference. Working within the measure-theoretic kernel framework, we define a hierarchy of abstractions -- from the core Bayesian transformer, through semantic transformers with explicit update kernels, to full transformer blocks with QKV/attention/residual/MLP pipelines, and finally multilayer stacks -- and prove at each level that the Bayes joint semantics implies the update kernel equals the posterior almost everywhere. For the block-level architecture, we derive the explicit Bayes formula through Radon-Nikodym differentiation and prove its normalization. We additionally prove that the softmax attention mechanism induces a valid probability distribution over keys, establishing the bridge between the abstract kernel framework and concrete attention implementations. The framework makes no architectural assumptions beyond the Markov kernel structure and exposes explicit conditions under which a transformer block is provably Bayesian. In essence, when this joint distribution condition is satisfied, the forward computation of a Transformer is formally equivalent to a rigorous Bayesian posterior update.

cs.LG↗

arXiv2026

Two-Way Feedback Mechanisms between the Madden-Julian Oscillation and Mesoscale Convective Systems

The Madden-Julian Oscillation (MJO) is a planetary-scale convective system characterized by large-scale envelopes of enhanced and suppressed convection that contain numerous mesoscale convective systems (MCSs). While MCSs are widely recognized as the fundamental convective elements embedded within the MJO, their relationship with the MJO is intrinsically two-way: the MJO modulates the large-scale dynamical and thermodynamic environment that organizes MCS activity, while the collective upscale impacts of MCSs feed back onto the MJO through the transport of momentum and heat. However, the nature of this bidirectional interaction remains insufficiently quantified from an observational perspective. In this study, we use satellite-based MJO indices together with a long-term, objectively tracked MCS dataset to investigate the two-way feedback mechanisms between the MJO and MCSs. By compositing MCS activity across different MJO phases and analyzing their environmental conditions, we quantify how the evolving MJO circulation regulates MCS frequency, intensity, and organization. At the same time, we diagnose the aggregate influence of MCS populations on the large-scale MJO circulation through their associated momentum and thermodynamic anomalies. Our results reveal a robust two-way coupling between the MJO and MCSs. Enhanced MCS activity preferentially occurs in specific MJO phases associated with favorable moisture, instability, and vertical shear, indicating strong MJO control on MCS organization. Conversely, periods of enhanced MCS activity are associated with coherent large-scale circulation anomalies consistent with upscale transport of momentum and moisture that reinforce the MJO convective envelope and support its eastward propagation. This feedback suggests that MCSs are not merely passive responses to the MJO environment, but actively contribute to its maintenance and evolution.

physics.comp-ph↗

arXiv2025

Leveraging Geometric Visual Illusions as Perceptual Inductive Biases for Vision Models

Contemporary deep learning models have achieved impressive performance in image classification by primarily leveraging statistical regularities within large datasets, but they rarely incorporate structured insights drawn directly from perceptual psychology. To explore the potential of perceptually motivated inductive biases, we propose integrating classic geometric visual illusions well-studied phenomena from human perception into standard image-classification training pipelines. Specifically, we introduce a synthetic, parametric geometric-illusion dataset and evaluate three multi-source learning strategies that combine illusion recognition tasks with ImageNet classification objectives. Our experiments reveal two key conceptual insights: (i) incorporating geometric illusions as auxiliary supervision systematically improves generalization, especially in visually challenging cases involving intricate contours and fine textures; and (ii) perceptually driven inductive biases, even when derived from synthetic stimuli traditionally considered unrelated to natural image recognition, can enhance the structural sensitivity of both CNN and transformer-based architectures. These results demonstrate a novel integration of perceptual science and machine learning and suggest new directions for embedding perceptual priors into vision model design.

cs.CV↗

arXiv2025

Stabilizing Information Flow Entropy: Regularization for Safe and Interpretable Autonomous Driving Perception

Deep perception networks in autonomous driving traditionally rely on data-intensive training regimes and post-hoc anomaly detection, often disregarding fundamental information-theoretic constraints governing stable information processing. We reconceptualize deep neural encoders as hierarchical communication chains that incrementally compress raw sensory inputs into task-relevant latent features. Within this framework, we establish two theoretically justified design principles for robust perception: (D1) smooth variation of mutual information between consecutive layers, and (D2) monotonic decay of latent entropy with network depth. Our analysis shows that, under realistic architectural assumptions, particularly blocks comprising repeated layers of similar capacity, enforcing smooth information flow (D1) naturally encourages entropy decay (D2), thus ensuring stable compression. Guided by these insights, we propose Eloss, a novel entropy-based regularizer designed as a lightweight, plug-and-play training objective. Rather than marginal accuracy improvements, this approach represents a conceptual shift: it unifies information-theoretic stability with standard perception tasks, enabling explicit, principled detection of anomalous sensor inputs through entropy deviations. Experimental validation on large-scale 3D object detection benchmarks (KITTI and nuScenes) demonstrates that incorporating Eloss consistently achieves competitive or improved accuracy while dramatically enhancing sensitivity to anomalies, amplifying distribution-shift signals by up to two orders of magnitude. This stable information-compression perspective not only improves interpretability but also establishes a solid theoretical foundation for safer, more robust autonomous driving perception systems.

cs.LG↗

arXiv2025

ILRe: Intermediate Layer Retrieval for Context Compression in Causal Language Models

Large Language Models (LLMs) have demonstrated success across many benchmarks. However, they still exhibit limitations in long-context scenarios, primarily due to their short effective context length, quadratic computational complexity, and high memory overhead when processing lengthy inputs. To mitigate these issues, we introduce a novel context compression pipeline, called Intermediate Layer Retrieval (ILRe), which determines one intermediate decoder layer offline, encodes context by streaming chunked prefill only up to that layer, and recalls tokens by the attention scores between the input query and full key cache in that specified layer. In particular, we propose a multi-pooling kernels allocating strategy in the token recalling process to maintain the completeness of semantics. Our approach not only reduces the prefilling complexity from $O(L^2)$ to $O(L)$ and trims the memory footprint to a few tenths of that required for the full context, but also delivers performance comparable to or superior to the full-context setup in long-context scenarios. Without additional post training or operator development, ILRe can process a single $1M$ tokens request in less than half a minute (speedup $\approx 180\times$) and scores RULER-$1M$ benchmark of $\approx 79.8$ with model Llama-3.1-UltraLong-8B-1M-Instruct on a Huawei Ascend 910B NPU.

cs.CL↗

arXiv2025

Thermal Property Microscopy with Compressive Sensing Frequency-Domain Thermoreflectance

Spatial mapping of thermal properties is critical for unveiling the structure-property relation of materials, heterogeneous interfaces, and devices. These property images can also serve as datasets for training artificial intelligence models for material discoveries and optimization. Here we introduce a high-throughput thermal property imaging method called compressive sensing frequency domain thermoreflectance (CS-FDTR), which can robustly profile thermal property distributions with micrometer resolutions while requiring only a random subset of pixels being experimentally measured. The high-resolution thermal property image is reconstructed from the raw down-sampled data through L_1-regularized minimization. The high-throughput imaging capability of CS-FDTR is validated using the following cases: (a) the thermal conductance of a patterned heterogeneous interface, (b) thermal conductivity variations of an annealed pyrolytic graphite sample, and (c) the sharp change in thermal conductivity across a vertical aluminum/graphite interface. With less than half of the pixels being experimentally sampled, the thermal property images measured using CS-FDTR show nice agreements with the ground truth (point-by-point scanning), with a relative deviation below 15%. This work opens the possibility of high-throughput thermal property imaging without sacrificing the data quality, which is critical for materials discovery and screening.

physics.app-ph↗

arXiv2024

Gradient-Guided Parameter Mask for Multi-Scenario Image Restoration Under Adverse Weather

Removing adverse weather conditions such as rain, raindrop, and snow from images is critical for various real-world applications, including autonomous driving, surveillance, and remote sensing. However, existing multi-task approaches typically rely on augmenting the model with additional parameters to handle multiple scenarios. While this enables the model to address diverse tasks, the introduction of extra parameters significantly complicates its practical deployment. In this paper, we propose a novel Gradient-Guided Parameter Mask for Multi-Scenario Image Restoration under adverse weather, designed to effectively handle image degradation under diverse weather conditions without additional parameters. Our method segments model parameters into common and specific components by evaluating the gradient variation intensity during training for each specific weather condition. This enables the model to precisely and adaptively learn relevant features for each weather scenario, improving both efficiency and effectiveness without compromising on performance. This method constructs specific masks based on gradient fluctuations to isolate parameters influenced by other tasks, ensuring that the model achieves strong performance across all scenarios without adding extra parameters. We demonstrate the state-of-the-art performance of our framework through extensive experiments on multiple benchmark datasets. Specifically, our method achieves PSNR scores of 29.22 on the Raindrop dataset, 30.76 on the Rain dataset, and 29.56 on the Snow100K dataset. Code is available at: \href{https://github.com/AierLab/MultiTask}{https://github.com/AierLab/MultiTask}.

cs.CV↗

arXiv2024

Comparison of Encryption Algorithms for Wearable Devices in IoT Systems

The Internet of Things (IoT) expansion has brought a new era of connected devices, including wearable devices like smartwatches and medical monitors, that are becoming integral parts of our daily lives. These devices not only offer innovative functionalities but also generate and transmit plenty of sensitive data, making their security and privacy the primary concerns. Given the unique challenges posed by wearable devices, such as limited computational resources and the need for real-time data processing, encryption stands as a cornerstone for safeguarding the integrity and confidentiality of the data they handle. Various encryption algorithms, each with its own set of advantages and limitations, are available to meet the diverse security and computational needs of wearable IoT devices. As we move into an age where quantum computing could potentially disrupt traditional encryption methods, choosing a suitable encryption algorithm becomes even more critical. This paper explores and evaluates the suitability of different encryption methods in the context of wearable IoT devices, considering current and future security challenges.

cs.CR↗

arXiv2024

Entropy Loss: An Interpretability Amplifier of 3D Object Detection Network for Intelligent Driving

With the increasing complexity of the traffic environment, the significance of safety perception in intelligent driving is intensifying. Traditional methods in the field of intelligent driving perception rely on deep learning, which suffers from limited interpretability, often described as a "black box." This paper introduces a novel type of loss function, termed "Entropy Loss," along with an innovative training strategy. Entropy Loss is formulated based on the functionality of feature compression networks within the perception model. Drawing inspiration from communication systems, the information transmission process in a feature compression network is expected to demonstrate steady changes in information volume and a continuous decrease in information entropy. By modeling network layer outputs as continuous random variables, we construct a probabilistic model that quantifies changes in information volume. Entropy Loss is then derived based on these expectations, guiding the update of network parameters to enhance network interpretability. Our experiments indicate that the Entropy Loss training strategy accelerates the training process. Utilizing the same 60 training epochs, the accuracy of 3D object detection models using Entropy Loss on the KITTI test set improved by up to 4.47\% compared to models without Entropy Loss, underscoring the method's efficacy. The implementation code is available at https://github.com/yhbcode000/Eloss-Interpretability.

cs.CV↗

arXiv2024

Enhancing Terrestrial Net Primary Productivity Estimation with EXP-CASA: A Novel Light Use Efficiency Model Approach

The Light Use Efficiency model, epitomized by the CASA model, is extensively applied in the quantitative estimation of vegetation Net Primary Productivity. However, the classic CASA model is marked by significant complexity: the estimation of environmental stress parameters, in particular, necessitates multi-source observation data, adding to the complexity and uncertainty of the model's operation. Additionally, the saturation effect of the Normalized Difference Vegetation Index (NDVI), a key variable in the CASA model, weakened the accuracy of CASA's NPP predictions in densely vegetated areas. To address these limitations, this study introduces the Exponential-CASA (EXP-CASA) model. The EXP-CASA model effectively improves the CASA model by using novel functions for estimating the fraction of absorbed photosynthetically active radiation (FPAR) and environmental stress, by utilizing long-term observational data from FLUXNET and MODIS surface reflectance data. In a comparative analysis of NPP estimation accuracy among four different NPP products, EXP-CASA ($R^2 = 0.68, RMSE= 1.1gC\cdot m^{-2} \cdot d^{-1}$) outperforms others, followed by GLASS-NPP, and lastly MODIS-NPP and classic CASA. Additionally, this research assesses the EXP-CASA model's adaptability to various vegetation indices, evaluates the sensitivity and stability of its parameters over time, and compares its accuracy against other leading NPP estimation products. The findings reveal that the EXP-CASA model exhibits strong adaptability to diverse vegetation indices and stability of model parameters over time series. By introducing a novel estimation approach that optimizes model construction, the EXP-CASA model remarkably improves the accuracy of NPP estimations and paves the way for global-scale, consistent, and continuous assessment of vegetation NPP.

q-bio.QM↗

arXiv2024

Utilizing (Al, Ga)2O3/Ga2O3 superlattices to measure cation vacancy diffusion and vacancy-concentration-dependent diffusion of Al, Sn, and Fe in \b{eta} -Ga2O3

Diffusion of native defects such as vacancies and their interactions with impurities are fundamental in semiconductor crystal growth, device processing, and long-term aging of equilibration and transient diffusion of vacancies are rarely investigated. We used aluminum-gallium oxide/gallium oxide superlattices (SLs) to detect and analyze transient diffusion of cation vacancies during annealing in O2 at 1000-1100 C. Using a novel finite difference scheme for the diffusion equation with time- and space-varying diffusion constant, we extract diffusion constants for Al, Fe, and cation vacancies under the given conditions, including the vacancy concentration dependence for Al. indicate that vacancies present in the substrate transiently diffuse through the SLs, interacting with Sn as it also diffuses. In the case of SLs grown on Sn-doped beta-gallium oxide substrates, gradients observed in the extent of Al diffusion indicate that vacancies present in the substrate transiently diffuse through the SLs, interacting with Sn as it also diffuses. In the case of SLs grown on (010) Fe-doped substrates, the Al diffusion is uniform through the SLs, indicating a depth-uniform concentration of vacancies. We find no evidence in either case for the introduction of gallium vacancies from the free surface at rates sufficient to affect Al diffusion down to ppm concentrations, which has important bearing on the validity of typically-made assumptions of vacancy equilibration. Additionally, we show that unintentional impurities in Sn-doped gallium oxide such as Fe, Ni, Mn, Cu, and Li also diffuse towards the surface and accumulate. Many of these likely have fast interstitial diffusion modes capable of destabilizing devices over time, thus highlighting the importance of controlling unintentional impurities in beta-gallium oxide wafers.

cond-mat.mtrl-sci↗

arXiv2023

InDL: A New Dataset and Benchmark for In-Diagram Logic Interpretation based on Visual Illusion

This paper introduces a novel approach to evaluating deep learning models' capacity for in-diagram logic interpretation. Leveraging the intriguing realm of visual illusions, we establish a unique dataset, InDL, designed to rigorously test and benchmark these models. Deep learning has witnessed remarkable progress in domains such as computer vision and natural language processing. However, models often stumble in tasks requiring logical reasoning due to their inherent 'black box' characteristics, which obscure the decision-making process. Our work presents a new lens to understand these models better by focusing on their handling of visual illusions -- a complex interplay of perception and logic. We utilize six classic geometric optical illusions to create a comparative framework between human and machine visual perception. This methodology offers a quantifiable measure to rank models, elucidating potential weaknesses and providing actionable insights for model improvements. Our experimental results affirm the efficacy of our benchmarking strategy, demonstrating its ability to effectively rank models based on their logic interpretation ability. As part of our commitment to reproducible research, the source code and datasets will be made publicly available at https://github.com/rabbit-magic-wh/InDL

cs.CV↗

arXiv2023

Eloss in the way: A Sensitive Input Quality Metrics for Intelligent Driving

With the increasing complexity of the traffic environment, the importance of safety perception in intelligent driving is growing. Conventional methods in the robust perception of intelligent driving focus on training models with anomalous data, letting the deep neural network decide how to tackle anomalies. However, these models cannot adapt smoothly to the diverse and complex real-world environment. This paper proposes a new type of metric known as Eloss and offers a novel training strategy to empower perception models from the aspect of anomaly detection. Eloss is designed based on an explanation of the perception model's information compression layers. Specifically, taking inspiration from the design of a communication system, the information transmission process of an information compression network has two expectations: the amount of information changes steadily, and the information entropy continues to decrease. Then Eloss can be obtained according to the above expectations, guiding the update of related network parameters and producing a sensitive metric to identify anomalies while maintaining the model performance. Our experiments demonstrate that Eloss can deviate from the standard value by a factor over 100 with anomalous data and produce distinctive values for similar but different types of anomalies, showing the effectiveness of the proposed method. Our code is available at: (code available after paper accepted).

cs.AI↗

arXiv2023

Thermo-optic phase shifter based on hydrogen-doped indium oxide microheater

Thermo-optic (TO) phase shifters are very fundamental units in large-scale active silicon photonic integrated circuits (PICs). However, due to the limitation of microheater materials with a trade-off between heating efficiency and absorption loss, designs reported so far typically suffer from slow response time, high power consumption, low yields, and so on. Here, we demonstrate an energy-efficient, fast-response, and low-loss TO phase shifter by introducing hydrogen-doped indium oxide (IHO) films as microheater, and the optimized electron concentration with enhanced mobility endows the IHO high conductivity as well as high near-infrared (NIR) transparency, which allow it to directly contact the silicon waveguide without any insulating layer for efficient tuning and fast response. The TO phase shifter achieves a sub-microsecond response time (970 ns/980 ns) with a {\pi} phase shift power consumption of 9.6 mW. And the insertion loss introduced by the IHO microheater is ~ 0.5 dB. The proposed IHO-based microheaters with compatible processing technology illustrate the great potential of such material in the application of large-scale silicon PICs.

physics.optics↗

arXiv2017

Fractional Path Integral Monte Carlo

Fractional derivatives are nonlocal differential operators of real order that often appear in models of anomalous diffusion and a variety of nonlocal phenomena. Recently, a version of the Schrödinger Equation containing a fractional Laplacian has been proposed. In this work, we develop a Fractional Path Integral Monte Carlo algorithm that can be used to study the finite temperature behavior of the time-independent Fractional Schrödinger Equation for a variety of potentials. In so doing, we derive an analytic form for the finite temperature fractional free particle density matrix and demonstrate how it can be sampled to acquire new sets of particle positions. We employ this algorithm to simulate both the free particle and $^{4}$He (Aziz) Hamiltonians. We find that the fractional Laplacian strongly encourages particle delocalization, even in the presence of interactions, suggesting that fractional Hamiltonians may manifest atypical forms of condensation. Our work opens the door to studying fractional Hamiltonians with arbitrarily complex potentials that escape analytical solutions.

cond-mat.stat-mech↗