arXiv subjects

Lizhong Chen

Publications and source records attributed to Lizhong Chen.

At least 19 recordsLinked to original sources

arXiv2026

Fixed-Defect Inverse Theorems for Subset Sums

Let $A$ be an $n$-element set of positive real numbers, let $FS(A)$ be its set of subset sums, and put $T_n=\binom{n+1}{2}$. For every fixed integer $C\geq-1$ and all sufficiently large $n$, we classify the sets satisfying $$ |FS(A)|\leq T_n+n+C+1. $$ Each such set is commensurable. Its unique primitive integer normalisation $B$ either satisfies $\sum B\leq T_n+n+C$ or belongs to an explicit exceptional family specified by a missing element $m\in\{1,2\}$ and an integer partition of $C+m$ or $C+m+1$. If $P$ denotes the partition function, the exceptional family has exactly $$ P(C+1)+2P(C+2)+P(C+3) $$ primitive dilation classes. We also prove a local inverse theorem for bounded increment excess. If, for sufficiently large $i$, adjoining the largest element to the preceding $i-1$ elements creates only $i+e$ new subset sums, where $e$ is bounded, then the $i$-element set is a dilation of $[1,i+e]_{\mathbb{Z}}$ with exactly $e$ elements deleted. Conversely, every such deletion pattern has increment excess $e$. The proof combines a stabiliser argument in $\mathbb{R}/x\mathbb{Z}$, Kneser's theorem, a quadratic subset-sum bound, and endpoint propagation. These arguments also give effective commensurability and a finite-state encoding. Together with earlier results for $C\leq-2$, this completes the eventual fixed-defect classification for every integer $C$.

math.CO↗

arXiv2026

Explicit and logarithmically improved chromatic bounds for $(P_2\cup P_3)$-free graphs

We prove that every $(P_2\cup P_3)$-free graph $G$, with $k=ω(G)$, satisfies \[ χ(G)=O\!\left(k^3\frac{\ln\ln k}{\ln k}\right). \] Thus the class admits an $o(k^3)$ binding function. We also prove the explicit bound \[ χ(G)\le \frac{k^3}{8}+\frac{5k^2}{4}-4k+8 \qquad(k\ge8), \] with a sharper formula for odd $k$. A further refinement gives an explicit cubic bound with leading coefficient $104/837<1/8$.

math.CO↗

arXiv2026

Exact Periodicity, Surjectivity, and a Haar Limit Law for a Restarting Josephus Process

We study a restarting Josephus process in which the participants retain their linear order and counting restarts at the current leftmost survivor after every deletion. For step size $m$, put $q=m-1$, and let $F_n(q)$ denote the initial position of the survivor. Reverse insertion gives $F_1(q)=1$ and $F_k(q)=F_{k-1}(q)+\mathbf{1}_{\{q\bmod k<F_{k-1}(q)\}}$. Writing $L_n=\operatorname{lcm}(1,\ldots,n)$, we establish three results for the compatible residue system in this recurrence. First, the full period group of $F_n$ is exactly $L_n\mathbb{Z}$. Second, $F_n$ is surjective onto $\{1,\ldots,n\}$. The proof is constructive and unconditional but computer-assisted: a Chinese-remainder construction and explicit prime estimates reduce it to a finite exact certificate. Third, if $\widetilde Q_n$ is uniform modulo $L_n$, then $(F_n(\widetilde Q_n)-1)/(n-1)$ converges to a symmetric, nondegenerate law on $[0,1]$. A common Haar coupling yields almost-sure and $L^r$ convergence for every $1\le r<\infty$, together with an $O(n^{-1/4})$ bound in $W_1$. Logarithmic boundary-mass estimates rule out every symmetric beta law. We also formulate endpoint dominance as an open problem, prove strict dominance over the two nearest internal positions for every $n\ge4$, exclude prime levels as minimal counterexamples, and verify the claim exactly through $n=49$.

math.CO↗

arXiv2026

An infinite family of minimally nonperfectly divisible graphs with a bisimplicial vertex

We disprove Hoàng's conjecture that a minimally nonperfectly divisible graph cannot contain a bisimplicial vertex by constructing an explicit infinite family. For every integer $t\geq1$, the graph $G_t$ in this family has clique number three, contains a bisimplicial vertex of degree four, and satisfies \[ |V(G_t)|=93+30(t-1),\qquad |E(G_t)|=320+104(t-1). \] In particular, the members are pairwise nonisomorphic. The construction uses a fixed 15-vertex rooted graph and a variable auxiliary graph. Every copy of the rooted graph forces its identified root into the perfect part of every perfect division. Three induced odd holes in the auxiliary graph then force a triangle into the other part. A uniform assignment lemma and a rooted product lemma show symbolically that every proper induced subgraph of every $G_t$ is perfectly divisible. The finite properties of the fixed rooted graph are verified by exact exhaustive computation, with an independent implementation providing a cross-check. The construction also gives an infinite family of negative examples to a prescribed-vertex problem of Hu, Xu and Zhuang.

math.CO↗

arXiv2026

BiKAN: Restoring Collapsed Basis of Binary Kolmogorov--Arnold Networks

Binarizing a polynomial Kolmogorov--Arnold Network (KAN) not only changes parameter precision, but also alters the function space available to each layer. When activations are restricted to ${-1,+1}$, all even powers reduce to $1$ and all odd powers reduce to $x$, causing the elementwise polynomial basis to collapse to constant and first-order responses. We refer to this structural failure as Spatial Orthogonality Collapse. Our proposed BiKAN addresses this critical issue by augmenting each binary KAN layer with selected degree-2 Walsh characters. Fixed circular channel rolls generate pairwise parities, and learned binary projections mix them using the same XNOR--popcount operations as the remaining W1A1 paths. This restores explicit pairwise coordinates without learned routing or multiplier-based feature generation. Experiments on CIFAR-10 confirms that removing parity reduces accuracy by $1.23$ points over five paired seeds ($p=0.003$), the gain increases as width decreases, and accuracy improves monotonically as more parity planes are added. At an equal $\sim$11.9M-parameter budget, parity outperforms conventional widening by $3.09$ points ($p<10^{-4}$). At W1A1, BiKAN reaches $99.48\%$, $84.38\%$, and $55.81\%$ on MNIST, CIFAR-10, and CIFAR-100, respectively. Post-route Zynq-7020 FPGA results show that the repair remains hardware-efficient; the convolutional design cuts DSP usage from 164 to 72 and estimated compute-core latency from 401 to 54.8 ms, while the power-of-two-aware dense design achieves zero-DSP inference with a 0.03-point accuracy loss. The BiKAN implementation is available at https://github.com/OSU-STARLAB/BiKAN.

cs.LG↗

arXiv2026

SparseKAN: Compressing Kolmogorov--Arnold Networks Across Basis Functions, Neurons, and Bits

Kolmogorov--Arnold Networks (KANs) replace scalar edge weights with learnable univariate functions parameterized by multiple basis coefficients. This introduces a source of redundancy that conventional neural-network compression does not directly expose. We present \textbf{SparseKAN}, a unified approach that compresses KANs along three complementary axes: basis functions, neurons/channels, and numerical precision. SparseKAN equips the base branch, nonlinear basis branch, and individual basis terms with hierarchical learnable gates trained under a differentiable active-cost objective. The learned importance structure is subsequently hardened under explicit basis and width budgets, recovered in full or low precision, and physically compacted into smaller dense tensors rather than retained as sparse masks. Experiments on MNIST, CIFAR-10, and CIFAR-100 across spline, polynomial, RBF, wavelet, and convolutional KAN variants show that the structural axes compose predictably in cost. We also find strong basis-dependent differences in term importance: coefficient-based selection outperforms matched low-order truncation by up to 15.25 accuracy points in the evaluated Gram-polynomial settings. Eight-bit quantization is broadly robust, whereas 4-bit convolutional KANs require quantization-aware adaptation. Physical compaction removes up to 73.0\% of parameters without accuracy loss on MNIST and reduces large-batch CUDA latency to as little as $0.51\times$ dense execution. On a ZCU104 FPGA, the resulting sparse low-bit models achieve up to $23.63\times$ lower inference latency, demonstrating that SparseKAN converts functional redundancy into measurable software and hardware efficiency. The SparseKAN implementation is available at https://github.com/OSU-STARLAB/SparseKAN.

cs.LG↗

arXiv2026

QuantKAN: A Unified Quantization Framework for Kolmogorov Arnold Networks

Kolmogorov--Arnold Networks (KANs) replace linear weights with spline-based functions, offering strong expressivity but posing challenges for low-precision deployment due to heterogeneous parameter distributions. We introduce QuantKAN, the first unified framework for quantization-aware training (QAT) and post-training quantization (PTQ) of KANs. The framework employs branch-aware quantizers for base and spline parameters and extends modern QAT and PTQ methods to spline-based layers across EfficientKAN, FastKAN, PyKAN, and KAGN. Experiments on MNIST, CIFAR-10/100, TinyImageNet, and ImageNet provide the first unified QAT/PTQ KAN benchmarks and show that DSQ is the most robust QAT method at aggressive low-bit settings, while GPTQ is the strongest PTQ method at moderate precision. Sensitivity analyses reveal architecture-specific failure modes: spline/basis parameters dominate in FastKAN, while base or scaling parameters dominate in EfficientKAN, GRAM, and PyKAN. Vivado HLS estimates on a Xilinx UltraScale+ device further suggest up to 3.32$\times$ throughput and 7.7$\times$ lower estimated dynamic energy per inference under W4A4, exposing a residual \emph{basis-evaluation tax} that motivates basis-aware microarchitecture. QuantKAN is available at https://github.com/OSU-STARLAB/QuantKAN/.

cs.LG↗

arXiv2026

PhysioSeq2Seq: A Hybrid Physiological Digital Twin and Sequence-to-Sequence LSTM for Long-Horizon Glucose Forecasting in Type 1 Diabetes

Accurate long-horizon glucose forecasting is critical for automated insulin delivery systems, which help people with type 1 diabetes (T1D) manage their glucose and avoid dangerous hypoglycemia. However, standard recursive long short-term memory (LSTM) networks suffer from systematic negative bias at longer horizons due to error compounding, while purely mechanistic ordinary differential equation (ODE) models fail to generalize across individuals when parameterized at the population level. We propose PhysioSeq2Seq, a hybrid architecture that combines patient-specific physiological modeling with a sequence-to-sequence (Seq2Seq) LSTM. For each glucose segment, twin matching searches a population of 300 parameterized digital twins to identify the best-fitting physiological match from a 3-hour continuous glucose monitoring (CGM) history. The 10 internal ODE state variables of the matched twin are injected as exogenous covariates into both the encoder and decoder of the Seq2Seq LSTM. This simultaneous 48-step prediction strategy eliminates recursive error compounding, while the ODE features provide a physics-grounded constraint that bounds long-horizon drift within physiologically plausible ranges. PhysioSeq2Seq was trained on CGM and insulin data from 348 participants in the Type 1 Diabetes Exercise Initiative (T1DEXI) dataset and evaluated on 74 held-out participants. At the 240-minute horizon, PhysioSeq2Seq achieves a mean absolute error of 39.28 mg/dL and a mean error of -10.62 mg/dL, reducing bias by 13.89 mg/dL over the recursive LSTM and reducing mean absolute error by 28.62 mg/dL over the ODE-based digital twin. These results show that eliminating architectural feedback and injecting patient-matched physiological states is an effective and clinically meaningful strategy for long-horizon glucose forecasting in T1D.

cs.LG↗

arXiv2026

FlashKAT: Understanding and Addressing Performance Bottlenecks in the Kolmogorov-Arnold Transformer

The Kolmogorov-Arnold Network (KAN) has been gaining popularity as an alternative to the multilayer perceptron (MLP) due to its greater expressiveness and interpretability. Even so, KAN suffers from training instability and being orders of magnitude slower due to its increased computational cost, limiting its applicability to large-scale tasks. Recently, the Kolmogorov-Arnold Transformer (KAT) has been proposed, achieving FLOPs comparable to traditional Transformer models with MLPs by leveraging Group-Rational KAN (GR-KAN). Unfortunately, despite the comparable FLOPs, our testing shows that KAT remains 123x slower during training, indicating that there are other performance bottlenecks beyond FLOPs. In this paper, we conduct a series of experiments to understand the root cause of the slowdown in KAT. We uncover that the slowdown can be isolated to memory stalls, linked more specifically to inefficient gradient accumulations in the backward pass of GR-KAN. To address this memory bottleneck, we propose FlashKAT, which minimizes accesses to slow memory and the usage of atomic adds through a restructured kernel. Evaluations show that FlashKAT achieves up to an 86.5x training speedup over state-of-the-art KAT while reducing rounding errors in gradient computation.

cs.LG↗

arXiv2026

MetaCluster: Enabling Deep Compression of Kolmogorov-Arnold Network

Kolmogorov-Arnold Networks (KANs) replace scalar weights with per-edge vectors of basis coefficients, thereby increasing expressivity and accuracy while also resulting in a multiplicative increase in parameters and memory. We propose MetaCluster, a framework that makes KANs highly compressible without sacrificing accuracy. Specifically, a lightweight meta-learner, trained jointly with the KAN, maps low-dimensional embeddings to coefficient vectors, thereby shaping them to lie on a low-dimensional manifold that is amenable to clustering. We then run K-means in coefficient space and replace per-edge vectors with shared centroids. Afterwards, the meta-learner can be discarded, and a brief fine-tuning of the centroid codebook recovers any residual accuracy loss. The resulting model stores only a small codebook and per-edge indices, exploiting the vector nature of KAN parameters to amortize storage across multiple coefficients. On MNIST, CIFAR-10, and CIFAR-100, across standard KANs and ConvKANs using multiple basis functions, MetaCluster achieves a reduction of up to $80\times$ in parameter storage, with no loss in accuracy. Similarly, on high-dimensional equation modeling tasks, MetaCluster achieves a parameter reduction of $124.1\times$, without impacting performance. Code will be released upon publication.

cs.LG↗

arXiv2025

Optimal chromatic bound for ($P_2\cup P_4$, HVN)-free graphs

The HVN is a graph formed by removing two edges incident to the same vertex from the complete graph $K_5$. In this paper, we prove that every ($P_2\cup P_4$, HVN)-free graph $G$ satisfies $χ(G)\leq\lceil\frac{4}{3}ω(G)\rceil$ when $ω(G)\ge4$, where $χ(G)$ and $ω(G)$ denote the chromatic number and clique number of $G$, respectively. Furthermore, this bound is optimal for every $ω(G)\ge4$. Constructions demonstrating the optimality of the bound are provided. Our work unifies several previously known results on $χ$-binding functions for several graph classes.

math.CO↗

arXiv2025

Perfect divisions in ($P_2 \cup P_4$, bull)-free graphs

A graph $G$ has a perfect division if its vertex set can be partitioned into two sets $A$, $B$ such that $G[A]$ is perfect and $ω(G[B]) < ω(G)$. We call $G$ perfectly divisible if every induced subgraph of $G$ admits a perfect division. We prove that every ($P_2 \cup P_4$, bull)-free graph $G$ with $ω(G) \geq 3$ has a perfect division if $G$ contains no homogeneous set. The clique-number condition is tight: a counterexample exists for $ω(G) = 2$. Additionally, we present a short proof of the perfect divisibility of ($P_5$, bull)-free graphs, originally established by Chudnovsky and Sivaraman [J. Graph Theory 90 (2019), 54-60.].

math.CO↗

arXiv2025

Towards Universal Semantics With Large Language Models

The Natural Semantic Metalanguage (NSM) is a linguistic theory based on a universal set of semantic primes: simple, primitive word-meanings that have been shown to exist in most, if not all, languages of the world. According to this framework, any word, regardless of complexity, can be paraphrased using these primes, revealing a clear and universally translatable meaning. These paraphrases, known as explications, can offer valuable applications for many natural language processing (NLP) tasks, but producing them has traditionally been a slow, manual process. In this work, we present the first study of using large language models (LLMs) to generate NSM explications. We introduce automatic evaluation methods, a tailored dataset for training and evaluation, and fine-tuned models for this task. Our 1B and 8B models outperform GPT-4o in producing accurate, cross-translatable explications, marking a significant step toward universal semantic representation with LLMs and opening up new possibilities for applications in semantic analysis, translation, and beyond. Our code is available at https://github.com/OSU-STARLAB/DeepNSM.

cs.CL↗

arXiv2025

BeaverTalk: Oregon State University's IWSLT 2025 Simultaneous Speech Translation System

This paper discusses the construction, fine-tuning, and deployment of BeaverTalk, a cascaded system for speech-to-text translation as part of the IWSLT 2025 simultaneous translation task. The system architecture employs a VAD segmenter for breaking a speech stream into segments, Whisper Large V2 for automatic speech recognition (ASR), and Gemma 3 12B for simultaneous translation. Regarding the simultaneous translation LLM, it is fine-tuned via low-rank adaptors (LoRAs) for a conversational prompting strategy that leverages a single prior-sentence memory bank from the source language as context. The cascaded system participated in the English$\rightarrow$German and English$\rightarrow$Chinese language directions for both the low and high latency regimes. In particular, on the English$\rightarrow$German task, the system achieves a BLEU of 24.64 and 27.83 at a StreamLAAL of 1837.86 and 3343.73, respectively. Then, on the English$\rightarrow$Chinese task, the system achieves a BLEU of 34.07 and 37.23 at a StreamLAAL of 2216.99 and 3521.35, respectively.

cs.CL↗

arXiv2025

ML For Hardware Design Interpretability: Challenges and Opportunities

The increasing size and complexity of machine learning (ML) models have driven the growing need for custom hardware accelerators capable of efficiently supporting ML workloads. However, the design of such accelerators remains a time-consuming process, heavily relying on engineers to manually ensure design interpretability through clear documentation and effective communication. Recent advances in large language models (LLMs) offer a promising opportunity to automate these design interpretability tasks, particularly the generation of natural language descriptions for register-transfer level (RTL) code, what we refer to as "RTL-to-NL tasks." In this paper, we examine how design interpretability, particularly in RTL-to-NL tasks, influences the efficiency of the hardware design process. We review existing work adapting LLMs for these tasks, highlight key challenges that remain unaddressed, including those related to data, computation, and model development, and identify opportunities to address them. By doing so, we aim to guide future research in leveraging ML to automate RTL-to-NL tasks and improve hardware design interpretability, thereby accelerating the hardware design process and meeting the increasing demand for custom hardware accelerators in machine learning and beyond.

cs.LG↗

arXiv2025

Hessian-aware Training for Enhancing DNNs Resilience to Parameter Corruptions

Deep neural networks are not resilient to parameter corruptions: even a single-bitwise error in their parameters in memory can cause an accuracy drop of over 10%, and in the worst cases, up to 99%. This susceptibility poses great challenges in deploying models on computing platforms, where adversaries can induce bit-flips through software or bitwise corruptions may occur naturally. Most prior work addresses this issue with hardware or system-level approaches, such as integrating additional hardware components to verify a model's integrity at inference. However, these methods have not been widely deployed as they require infrastructure or platform-wide modifications. In this paper, we propose a new approach to addressing this issue: training models to be more resilient to bitwise corruptions to their parameters. Our approach, Hessian-aware training, promotes models with $flatter$ loss surfaces. We show that, while there have been training methods, designed to improve generalization through Hessian-based approaches, they do not enhance resilience to parameter corruptions. In contrast, models trained with our method demonstrate increased resilience to parameter corruptions, particularly with a 20$-$50% reduction in the number of bits whose individual flipping leads to a 90$-$100% accuracy drop. Moreover, we show the synergy between ours and existing hardware and system-level defenses.

cs.CR↗

arXiv2025

Neurons for Neutrons: A Transformer Model for Computation Load Estimation on Domain-Decomposed Neutron Transport Problems

Domain decomposition is a technique used to reduce memory overhead on large neutron transport problems. Currently, the optimal load-balanced processor allocation for these domains is typically determined through small-scale simulations of the problem, which can be time-consuming for researchers and must be repeated anytime a problem input is changed. We propose a Transformer model with a unique 3D input embedding, and input representations designed for domain-decomposed neutron transport problems, which can predict the subdomain computation loads generated by small-scale simulations. We demonstrate that such a model trained on domain-decomposed Small Modular Reactor (SMR) simulations achieves 98.2% accuracy while being able to skip the small-scale simulation step entirely. Tests of the model's robustness on variant fuel assemblies, other problem geometries, and changes in simulation parameters are also discussed.

physics.comp-ph↗

arXiv2025

MatrixKAN: Parallelized Kolmogorov-Arnold Network

Kolmogorov-Arnold Networks (KAN) are a new class of neural network architecture representing a promising alternative to the Multilayer Perceptron (MLP), demonstrating improved expressiveness and interpretability. However, KANs suffer from slow training and inference speeds relative to MLPs due in part to the recursive nature of the underlying B-spline calculations. This issue is particularly apparent with respect to KANs utilizing high-degree B-splines, as the number of required non-parallelizable recursions is proportional to B-spline degree. We solve this issue by proposing MatrixKAN, a novel optimization that parallelizes B-spline calculations with matrix representation and operations, thus significantly improving effective computation time for models utilizing high-degree B-splines. In this paper, we demonstrate the superior scaling of MatrixKAN's computation time relative to B-spline degree. Further, our experiments demonstrate speedups of approximately 40x relative to KAN, with significant additional speedup potential for larger datasets or higher spline degrees.

cs.LG↗