Papers

An approach to construct explicit integral representations for two-layer ReLU networks is presented, which provides relatively simple representations for any multivariate polynomial. Quantitative bounds are provided for a particular, sharpened ReLU integral representation, which involves a harmonic extension and a projection. The bounds demonstrate that functions can be approximated with $L^{2}(\mathcal{D})$ errors that do not depend explicitly on dimension or degree, but rather the coefficients of their monomial expansions and the distribution $\mathcal{D}$. We also present a connection to the RKHS of the exponential kernel $K(x,y)=\exp\left(\left\langle x,y\right\rangle \right)$, and a very simple integral representation involving additionally multiplication via a fixed function which has better quantitative bounds.

Symbolic regression aims to recover closed-form expressions from numerical data, but in differentiable symbolic regression the recovered expression depends not only on the grammar but also on the fixed architecture through which variables are routed during training. This is relevant to signal-processing settings in which closed-form models and interpretable nonlinear structure are useful. This architecture-specific effect has rarely been isolated directly, because existing comparisons often vary architecture together with operator family, grammar, or search procedure. Three depth-3 architectures are compared across twenty-four operator–shape–leaf combinations, holding operator family, grammar, and training protocol fixed as far as possible while varying the variable-routing architecture. Recovery changes from $0/64$ to $64/64$ trials on the same target under an architecture-plus-native-training-protocol comparison. The best architecture on one target is the worst on another, and trees with two equal-depth subtrees fail in every configuration tested ($0/3{,}776$). As a proof-of-concept mitigation, a small architecture set is trained and the hardened expression with the lowest held-out RMSE is selected. On the jointly-run subset, this improves recovery from $34.4\%$ for the only architecture present in all three configurations to $50.1\%$. On a Shockley diode target, the validation selector recovers cases missed by that baseline architecture, which by itself recovers $0/32$ seeds. Since the jointly-run subset contains only three configurations, the selector result is evidence that validation-based architecture selection is promising, not a complete benchmark. These results support treating architecture as a measurable design variable that should be reported, stress-tested, and selected using held-out validation rather than fixed a priori.

This paper investigates the deep learning optimization problem with softmax cross-entropy loss. We propose a layer separation strategy to alleviate the strong nonconvexity encountered during training deep networks. For cross-entropy models with fully connected and convolutional neural networks, we introduce auxiliary variables associated with hidden layer outputs and construct corresponding layer separation models, which decompose the original deeply nested optimization problem into a sequence of more manageable subproblems. We also conduct theoretical analyses, proving that the new layer separation loss provides an upper bound for the original cross-entropy loss. Moreover, we design alternating minimization algorithms and prove that, under appropriate conditions, these algorithms exhibit decreasing properties of the loss function. Numerical experiments validate the effectiveness of the proposed methods and indicate improved optimization behavior, especially for fully connected and convolutional neural networks.

Existing large-dimensional theory for spectral algorithms resolves either the optimally tuned point or the interpolation limit, but leaves the under-regularized regime unexplored. We study the learning curve and benign overfitting of spectral algorithms in the large-dimensional setting where the sample size and dimension are of comparable order, i.e., $n \asymp d^{\gamma}$ for some $\gamma>0$. We first consider inner-product kernels on the sphere $\mathbb{S}^{d-1}$ and establish a sharp asymptotic characterization of the excess risk across the full regularization path under various source conditions $s \geq 0$, where $s$ measures the relative smoothness of the regression function. Our results reveal that the learning curve is not simply U-shaped but instead consists of three distinct regimes: over-regularized, under-regularized, and interpolation regimes. This characterization allows us to fully capture the benign overfitting phenomenon, demonstrating that benign overfitting arises consistently across both the under-regularized and interpolation regimes whenever $s$ is positive but no larger than a critical threshold. We further show that, in the sufficiently regularized regime, the kernel learning curve is recovered by an associated sequence model. Finally, we extend the learning-curve analysis to large-dimensional KRR for a class of kernels on general domains in $\mathbb{R}^d$ whose low-degree eigenspaces satisfy spectral-scaling and hyper-contractivity conditions.

Deploying proprietary Deep Neural Networks (DNNs) on commodity edge devices demands hardware-backed Digital Rights Management (DRM) capable of withstanding both software-level and physical adversaries. In Unified Memory Architecture (UMA) systems, the host CPU and Neural Processing Unit (NPU) share physical DRAM, leaving plaintext model weights directly readable by a compromised OS kernel. Existing defenses fail in this constrained setting: trusted execution environments monopolize scarce memory with permanently reserved regions, while full-memory encryption operates at page granularity. This forces the system to fetch massive 4 KB memory pages for sub-page tensor tiles, severely crippling bandwidth. We present Tessera, a reference architecture for inline, cache-line granularity weight decryption on UMA edge accelerators. The design intercepts 64-byte AXI bursts, computing AES-256-CTR keystreams in parallel with DRAM fetches. This streams plaintext directly into isolated NPU SRAM, creating a transient memory footprint confined to the active tile and eliminating the need for permanent memory carve-outs. Measurements across three distinct SoC platforms demonstrate that this parallelization hides cryptographic latency behind standard DRAM fetch times, a condition that holds even under worst-case timing variations. Consequently, Tessera is projected to achieve 98.4% of the theoretical memory bandwidth ceiling (a mere 1.6% overhead). Across standard vision and language models, page-level memory encryption suffers up to a 32x bandwidth penalty, whereas Tessera maintains an optimal 1x footprint for all layer geometries. Finally, Tessera neutralizes major UMA-specific attack vectors – including physical DRAM extraction, rogue DMA, and compute hijacking – and formally prevents plaintext leakage across sparse tensors.

Delayed feedback poses a core challenge for online CVR prediction, forcing a trade-off between label accuracy and data freshness. Existing methods address this through delay modeling or sample reweighting, yet neglect how post-click behaviors evolve over the observation period. To overcome this limitation, we formalize this evolution as feedback trajectory and propose TRACE. Instead of forcing hard labels on unrevealed samples, our method evaluates how well the accumulated feedback status aligns with conversion versus non-conversion, dynamically refining posteriors without waiting for final outcomes. To counteract early-stage trajectory sparsity, we further design a reliability-gated retrospective completer that leverages full-lifecycle data to provide adaptive posterior guidance for unrevealed samples. Extensive experiments validate TRACE's superiority over state-of-the-art baselines and confirm the retrospective completion module as a model-agnostic enhancer for existing systems. Our code is available at https://github.com/LunaZhangxy/TRACE.

Perturbing a deterministic $n$-dimensional matrix with small Gaussian noise is a cornerstone of smoothed analysis of algorithms [Spielman and Teng, JACM 2004], as it reduces the condition number of the input to $O(n)$, and with it the complexity of many matrix algorithms. However, when deployed algorithmically, these perturbations are expensive due to the cost of generating and storing $n^2$ Gaussian random variables. We propose a perturbation that requires generating and storing $O(n)$ random numbers in $O(\log n)$ bits of precision, and reduces the condition number of any deterministic matrix to $O(n)$, matching Gaussian perturbations. Our result in particular implies a better complexity for the perturbed conjugate gradient algorithm, showing that we can solve an $n\times n$ linear system in linear space to within an arbitrarily small constant backward error using $O(n)$ matrix-vector products. In our construction, we introduce the concept of a pattern matrix, which is a dense deterministic matrix that maps all sparse vectors into dense vectors, and we combine it with a sparse perturbation whose entries are dependent and located in a non-uniform fashion. In order to analyze this construction, we develop new techniques for lower bounding the smallest singular value of a random matrix with dependent entries.

We propose a unified fractional regularization framework for sparse signal recovery based on the $\ell_1/\ell_p^q$ model. This model generalizes several widely used sparsity-promoting regularizers and provides additional flexibility through the parameters $p$ and $q$. Our main theoretical contribution is the characterization of the equivalence between the first-order stationary points of the $\ell_1/\ell_p^q$ formulation and the subtractive $\ell_1-\alpha\ell_p$ model, thereby offering a unified perspective on these nonconvex regularizers. In addition, we establish a new sufficient recovery condition under the Restricted Isometry Property (RIP), which shows that the proposed framework can provide relaxed recovery guarantees and improved robustness. To solve the resulting nonconvex problem, we develop a majorization–minimization (MM) algorithm and prove its convergence by using the Kurdyka–Łojasiewicz (KL) property. Numerical experiments on sparse recovery problems with different sensing matrices and MRI reconstruction demonstrate that the proposed approach outperforms existing methods in recovery accuracy.

In this work, we developed and tested 3 techniques for vector quantization (VQ) based model weight compression. To mitigate codebook collapse and enable end-to-end training, we adopted cosine similarity-based assignment. Building on ideas from attention-based formulations in Differentiable K-Means (DKM), we further improved this approach by using cosine similarity for assignment combined with top-1 sampling and a straight-through estimator, thereby eliminating the need for weighted-average reconstruction. Finally, we investigated the use of differentiable neural architecture search (NAS) to adaptively select layer-wise quantization configurations, further optimizing the compression process. Although our method does not consistently outperform existing approaches across all quantization levels, it provides useful insights into the design trade-offs and behaviors of VQ-based model compression methods.

Most recent state-of-the-art (SOTA) large language models (LLMs) use Mixture-of-Experts (MoE) architectures to scale model capacity without proportional per-token compute, enabling higher-quality outputs at manageable serving costs. However, MoE inference at scale is fundamentally bottlenecked by expert load imbalance and inefficient token routing, especially in multi-node deployments where tokens are not guaranteed to be routed to local experts, resulting in significant inter-node all-to-all communication overhead. To systematically characterize these challenges, we profile SOTA open-source MoE models, including Llama 4 Maverick, DeepSeek V3-671B, and Qwen3-230B-A22B, on various datasets and collected over 100k real expert activation traces. Upon studying the expert activation patterns, we uncover various persistent properties across all the frontier MoE models: variable expert load imbalance, domain-specific expert activation where expert popularity shifts across task families (code, math, chat, general), and a strong correlation between prefill and decode expert activations. Motivated by these findings, we propose workload-aware micro-batch grouping and an expert placement strategy to maximize token locality to the destination expert, thereby reducing inter-node communication. Across models and datasets, these optimizations help reduce all2all communication data up to 20, resulting in lower MoE decode latency and better accelerator utilization.

Lean 4 autoformalization has become increasingly popular in recent years, with frontier language models and open-weight autoformalizers now producing valid formalizations of mathematical theorems. However, these evaluations often rely on single canonical phrasings of theorems and rarely probe whether outputs are robust to natural variation in inputs, while prior work has shown that semantically equivalent paraphrases often induce divergent formal outputs. We study the structure of these divergences in Lean 4 by applying deterministic paraphrase rules to datasets of undergraduate and Olympiad-level math problems. Across four frontier models and three open-weight autoformalizers, we find that paraphrase sensitivity is dominated by failures at the code-generation layer, and that these failures are typed differently by dataset. Furthermore, these patterns generalize to open-weight models, showing that state-of-the-art autoformalizers still struggle to generate valid Lean code. Our results provide a failure-mode taxonomy for autoformalization and motivate training-time interventions targeted at specific compilation failures.

Accurate molecular representations are critical for drug discovery, and a central challenge lies in capturing the chemical environment of molecular fragments, as key interactions, such as H-bond and {\pi} stacking, occur only under specific local conditions. Most existing approaches represent molecules as atom-level graphs; however, atom-level representations can hardly express higher-order chemical context (e.g., stereochemistry, lone pairs, conjugation). Fragment-based methods (e.g., principal subgraph, predefined functional groups) fail to preserve essential information such as chirality, aromaticity, and ionic states. This work addresses these limitations from two aspects. (i) OverlapBPE tokenization. We propose a novel data-driven molecule tokenization method. Unlike existing approaches, our method allows overlapping fragments, reflecting the inherently fuzzy boundaries of small-molecule substructures and, together with enriched chemical information at the token level, thereby preserving a more complete chemical context. (ii) h-MINT model. OverlapBPE induces many-to-many atom-fragment mappings, which necessitate a new hierarchical architecture. We therefore develop a hierarchical molecular interaction network capable of jointly modeling interactions at both atom and fragment levels. By supporting fragment overlaps, the model naturally accommodates the many-to-many atom-fragment mappings introduced by the OverlapBPE scheme. Extensive evaluation against state-of-the-art methods shows our method improves binding affinity prediction by 2-4% Pearson/Spearman correlation on PDBBind and LBA, enhances virtual screening by 1-3% in key metrics on DUD-E and LIT-PCBA, and achieves the best overall HTS performance on PubChem assays. Further analysis demonstrates that our method effectively captures interactive information while maintaining good generalization.

Soil salinity is a major environmental challenge in coastal Bangladesh, threatening agricultural productivity and local livelihoods. This study develops a machine-learning-based framework to predict and map soil salinity in Satkhira district by integrating field observations with Landsat-derived spectral indices. A total of 205 soil samples collected during 2024-2025 were used to train an Extreme Gradient Boosting (XGBoost) model, and predictions were further improved using a Generalized Additive Model (GAM). Spatial cross-validation was applied to reduce autocorrelation bias, and bootstrap resampling was used to quantify prediction uncertainty. The results show strong spatial variability of soil salinity, with higher concentrations in the southern and central coastal regions and lower levels in the northern inland areas. Vegetation indices, particularly NDVI, along with salinity-related spectral indicators, were identified as key predictors. 10-year-window peak-exposure maps generated for 2014-2023 reveal recurrent high-salinity zones and a persistent, expanding footprint of moderate-to-high salinity exposure across the central parts of the district. Uncertainty analysis indicates higher variability in coastal zones and improved prediction stability when multi-year datasets are combined. The proposed framework provides a robust and scalable approach for long-term monitoring of soil salinity. It supports climate-resilient agriculture, land-use planning, and evidence-based decision-making in coastal Bangladesh.

Real-world data often exhibit long-tailed distributions with numerous noisy labels, substantially degrading the performance of deep models. While prior research has made progress in addressing this combined challenge, it overlooks the severe label-image mismatch inherent to high-noise settings, thereby limiting their effectiveness. Given that observed labels, though mismatched with images, still retain category information, we propose employing auxiliary text information from labels to address label-image inconsistencies in long-tailed noisy data. Specifically, we leverage the intrinsic cross-modal alignment in pre-trained visual-language models to correct the label-image inconsistencies. This supervisory signal, referred to as Weak Teacher Supervision (WTS), is unaffected by label noise and data distribution biases, albeit exhibits limited accuracy. Therefore, the activation of WTS is determined by evaluating the discrepancy between text-predicted labels and observed labels. Extensive experiments demonstrate the superior performance of WTS across synthetic and real-world datasets, particularly under high-noise conditions. The source code is available at https://anonymous.4open.science/r/WTS-0F3C.

Accurate prediction of drug-target binding affinity accelerates drug discovery by prioritizing compounds for experimental validation. Current methods face three limitations: sequence-based approaches discard spatial geometric constraints, structure-based methods fail to exploit hydrogen bond features, and conventional loss functions neglect prediction-target correlation, a key factor for identifying high-affinity compounds in virtual screening. We developed HBGSA (Hydrogen Bond Graph with Self-Attention), a 3.06M-parameter model that encodes hydrogen bond spatial features. HBGSA uses graph neural networks to model hydrogen bond spatial topology with self-attention enhancement and Pearson correlation loss. Experimental results on PDBbind Core Set and CSAR-HiQ dataset demonstrate that HBGSA outperforms baseline methods with strong generalization capability. Ablation studies confirm the effectiveness of hydrogen bond modeling and Pearson correlation loss.

In limited-data settings, a single endpoint mean of an evaluation metric such as the Continuous Ranked Probability Score (CRPS) is itself a random variable, yet it is routinely reported as if it were a stable property of the method. We study when this practice fails. Using 50 independent repetitions across six regression datasets, we show that CRPS variance trajectories differ substantially across methods and are not always well described by a smooth power-law decay. Methods with a learned heteroscedastic variance head, namely MAP and Deep Ensembles, can develop pronounced, reproducible variance peaks at intermediate training sizes on real datasets, whereas MC Dropout and Bayes by Backprop typically show smooth variance contraction. These peaks have direct practical consequences: at the variance peak on Seoul Bike, the relative RMSE of a single-seed MAP estimate reaches 93.6%, and the probability of falling within \(\pm 10\%\) of the repeated-run mean drops to 5.9%. We show that local CRPS variance provides a direct signal of single-seed estimation error, with Spearman correlations above 0.96 on every real dataset. Power-law fit quality and monotonicity together provide compact method-level summaries of trajectory regularity. Finally, replacing the standard heteroscedastic objective with \(\beta\)-NLL substantially reduces the irregular behavior, consistent with the view that the heteroscedastic training objective contributes to the instability. Practitioners should report trajectory summaries alongside endpoint means and concentrate repeated evaluation in high-variance regions.

Multimodal Federated Learning (MMFL) enables privacy-preserving collaborative training, but real-world clinical applications often suffer from within-modality missingness caused by sensor intermittency or irregular sampling. Existing methods implicitly represent unobserved data via architectural alignment or missing embeddings, often failing to recover the true distribution and yielding sub-optimal performance. We propose CondI, a federated framework explicitly addressing this missingness using conditional diffusion models. CondI employs a two-phase training pipeline: first, imputing unobserved temporal components using available multimodal context and conditional embeddings; second, optimizing modality-specific extractors and joint embedding spaces. During inference, imputed raw data pass through trained extractors to generate robust features, providing a holistic representation for downstream tasks. Explicit data imputation ensures models operate on complete semantic structures, significantly enhancing resilience against severe data incompleteness. Experiments on three clinical datasets (PTB-XL, SLEEP-EDF, MIMIC-IV) demonstrate CondI achieves comparable results to state-of-the-art baselines. Code: https://github.com/ZhengWugeng/CondI

Large Language Models (LLMs) based on Mixture-of-Experts (MoE) are pivotal in industrial applications for their ability to scale performance efficiently. However, standard MoEs enforce uniform expert sizes,creating a rigidity that fails to align computational costs with varying token-level complexity. While heterogeneous expert architectures attempt to address this by diversifying expert sizes, they often suffer from significant system-level challenges, specifically unbalanced GPU utilization and inefficient parameter utilization, which hinder practical deployment. To bridge the gap between theoretical heterogeneity and robust industrial application, we propose Mixture of Heterogeneous Grouped Experts (MoHGE) which introduces a two-level routing mechanism to enable flexible, resource-aware expert combinations. To optimize inference efficiency, we propose a Group-Wise Auxiliary Loss, which dynamically steers tokens to the most parameter-efficient expert groups based on task difficulty. To address the critical deployment challenge of GPU load balancing, we introduce an All-size Group-decoupling Allocation strategy coupled with an Intra-Group Experts Auxiliary Loss. These mechanisms collectively ensure uniform computation distribution across GPUs. Extensive evaluations demonstrate that MoHGE matches the performance of MoE architectures while reducing the total parameters by approximately 20% and maintaining balanced GPU utilization. Our work establishes a scalable paradigm for resource-efficient MoE design, offering a practical solution for optimizing inference costs in real-world scenarios. The code is publicly available at https://github.com/UnicomAI/MoHGE.

Causal effect estimation from observational data requires careful adjustment for confounding. Classical estimators such as inverse probability weighting and augmented inverse probability weighting can perform well under favorable model specification but may become unstable in complex settings. Machine-learning and representation-learning methods provide greater flexibility, but joint optimization may allow outcome information to alter treatment representations and compromise the intended causal structure. We propose MOCA (Modular One-way Causal Attention), a transformer-based framework that separates treatment and outcome modeling through a modular architecture. This design preserves directional information flow while retaining the flexibility of transformer architectures. Using a Markov-kernel formulation, we show that MOCA learns an autonomous treatment representation and is predictively KL-optimal within its Gaussian model class. Under correct specification, MOCA recovers the true average treatment effect, while additional two-way feedback does not further reduce average treatment effect estimation error. We also propose a conformal inference procedure for individual treatment effects. Across multiple simulation scenarios, MOCA achieved competitive or improved average treatment effect estimation compared with IPW, AIPW, the X-learner, TARNet, DragonNet, BART, Causal Forest, and Do-PFN. Ablation studies supported the contributions of the proposed architectural components. We further evaluated MOCA on the Infant Health and Development Program benchmark and the observational Dehejia-Wahba dataset. Overall, modular attention with one-way information flow provides an effective and interpretable framework for causal inference using modern deep-learning models.

Standard evaluations of Bayesian deep learning methods assume that metric estimates are reliable, but we show this assumption fails under data scarcity. Method rankings are not only unreliable at small $n$, but also dataset-dependent in ways that point estimates cannot reveal: the same method comparison yields $P(\mathrm{MCD} \prec \mathrm{Ensemble}) = 1.000$ at $n = 50$ on one dataset and remains below $0.95$ even at $n = 500$ on another. Across the datasets we consider, no universal sample size threshold exists, which is precisely why dataset-specific posterior inference is necessary. To address this, we use a Bayesian hierarchical model with method-specific variances to treat evaluation metrics as random variables across data realizations, and we use a predictive Minimum Detectable Difference curve to assess whether an observed gap would be detectable at a given training size. Across six Bayesian deep learning methods and five regression datasets, our results show that uncertainty-aware evaluation is necessary in low-data settings, because current evidence for method superiority and predictive detectability at the same training size can diverge substantially. Our framework provides practitioners with principled tools to determine whether their evaluation data is sufficient before drawing conclusions about method superiority.

Evaluating generative AI models is increasingly resource-intensive due to slow inference, expensive raters, and a rapidly growing landscape of models and benchmarks. We propose ProEval, a proactive evaluation framework that leverages transfer learning to efficiently estimate performance and identify failure cases. ProEval employs pre-trained Gaussian Processes (GPs) as surrogates for the performance score function, mapping model inputs to metrics such as the severity of errors or safety violations. By framing performance estimation as Bayesian quadrature (BQ) and failure discovery as superlevel set sampling, we develop uncertainty-aware decision strategies that actively select or synthesize highly informative inputs for testing. Theoretically, we prove that our pre-trained GP-based BQ estimator is unbiased and bounded. Empirically, extensive experiments on reasoning, safety alignment, and classification benchmarks demonstrate that ProEval is significantly more efficient than competitive baselines. It requires 8-65x fewer samples to achieve estimates within 1% of the ground truth, while simultaneously revealing more diverse failure cases under a stricter evaluation budget.

Portrait relighting is a low-level vision problem in which physically plausible illumination transfer, identity preservation, and compact real-time inference must be considered together. Iterative diffusion-style methods can synthesize fine detail, but stochastic inference and cost complicate deterministic live video creation; physically grounded relighting preserves identity, but controlled synthetic or light-stage supervision transfers poorly to unconstrained cameras. We present Hybrid Domain Knowledge Fusion (HDKF), a relighting-specific training framework that learns complementary physics, reflectance, and realism priors from synthetic, One-Light-at-A-Time (OLAT), and in-the-wild data, then distills their source-routed supervision into a compact student with clean teacher labels and degraded student inputs. The framework is trained with pixel-aligned RGB, albedo, and normal supervision, providing a simulation substrate for physically grounded low-level relighting. On a held-out OLAT benchmark, HDKF obtains the best MSE, PSNR, and SSIM among evaluated methods while remaining competitive in LPIPS. The distilled model runs in real time at 512x512, reaching 11.89 ms on an RTX 2060 and 1.82 ms on an RTX 4090.

Scaling EEG foundation models requires pooling data across heterogeneous electrode montages, a prerequisite both for larger pretraining corpora and for downstream deployment. We present the first systematic comparison of four channel adaptation methods (Conv1d projection, spherical spline interpolation (SSI), source-space decomposition, and Riemannian re-centering) across five pretrained EEG foundation models (5M–157M parameters), five downstream tasks, and two training regimes with 10–15 random seeds each. We find that rigid-montage models (BENDR, Neuro-GPT) require external adaptation, while flexible models (EEGPT, CBraMod) match or exceed it natively when fine-tuned but benefit from external methods under frozen-encoder deployment. A probe-SFT asymmetry exists: external adaptation can cause severe negative transfer during fine-tuning of flexible models. The optimal method is architecture-dependent (Conv1d for BENDR, SSI/Riemannian for Neuro-GPT, source-space decomposition for depression detection), and 5M-parameter CBraMod outperforms models up to 31$\times$ larger on 4/5 datasets, consistent with independent findings that compact EEG-specific architectures can match larger models.

Generative approaches to clustering provide information on geometric properties of clusters, whereas discriminative approaches provide boundaries between clusters. Ideas from both approaches are incorporated to present a fully unsupervised, probabilistic, and discriminative clustering method via a regularized mutual information objective function, wherein a mixture of mixtures of Gaussian and uniform distributions is used for formulation of the conditional model. Overfitting is avoided by the introduction of a regularizing term and a cluster merge step, similar to those applied in reversible jump Markov chain Monte Carlo methods used in Bayesian clustering. Consequently, the turtle shell method – a fully unsupervised clustering method capable of estimating non-linear boundary lines, automatically selecting the number of components, and capturing intuitive clusters in the presence of data abnormalities such as noise and/or irregular cluster shapes – is introduced. We test this method on various simulated and real datasets commonly explored in clustering research, and extend the analysis to datasets arising from flow cytometry experiments and image analysis.

The ability of large language models (LLMs) to express calibrated uncertainty is important for safe deployment. Chain-of-thought (CoT) reasoning is widely used to improve accuracy and reliability, but its effect on calibration is not fully understood. We show that this picture is incomplete: in some settings, increasing the reasoning budget beyond a task-specific threshold can cause models to become systematically overconfident, assigning high confidence to incorrect answers. We call this phenomenon Calibration Drift Under Reasoning (CDUR) and study it both theoretically and empirically. We define reasoning budget B and analyze conditions under which Expected Calibration Error ECE(B) follows a non-monotonic pattern: it first decreases as reasoning corrects errors, then increases as longer reasoning produces internally consistent but incorrect explanations. We propose a Hypothesis Lock-In model based on autoregressive generation to explain this behavior. We evaluate Llama-3.1-8B and Llama-3.3-70B on 47 reasoning-trap questions across four reasoning budgets and three seeds (1,368 API calls; 574 valid responses). The 8B model shows non-monotonic calibration behavior, while results for the 70B model are limited to baseline evaluation and are inconclusive for budget-dependent effects. We introduce CABStop, a calibration-aware stopping rule that halts reasoning when confidence diverges from an auxiliary accuracy estimate. These results suggest that increasing reasoning depth does not always improve reliability and should be monitored carefully.

Chronic osteomyelitis presents substantial prognostic challenges due to its high recurrence risk and complex postoperative recovery trajectories. Traditional assessment often relies on manual scoring systems, which limit scalability, efficiency, and consistency in clinical practice. Furthermore, the heterogeneous nature of clinical data poses challenges for current multimodal learning approaches that require aligned inputs and large annotated datasets. In this work, we propose RAG4Outcome, a retrieval-augmented generation (RAG) framework for prognostic prediction in chronic osteomyelitis. Our method integrates multimodal clinical data, including PET-CT imaging reports, structured surgical and diagnostic records, and unstructured follow-up notes, into a unified prediction pipeline. By combining a domain-specific retrieval corpus with expert-guided prompting, the framework enables more interpretable, evidence-grounded, and clinically reliable prognosis. Preliminary results on real-world cases demonstrate promising effectiveness and clinical alignment, highlighting the potential of RAG4Outcome for AI-assisted infection management and postoperative decision support.

Transformer-based large language models are in some respects limited by the quadratic time and space computational complexity of attention. We introduce the Toeplitz MLP Mixer (TMM), a transformer-like architecture that swaps attention for triangular-masked Toeplitz matrix multiplication over the sequence dimension resulting in $\mathcal{O} (dn \log n)$ time and $\mathcal O(dn)$ space complexity during training and $\mathcal O(dn)$ time and space at inference prefill. Despite the lack of sophisticated input modulation or state maintenance present in other sub-quadratic architectures, TMMs yield greater training efficiency in terms of loss achieved per compute and device memory. We demonstrate that TMMs are capable of retaining more input information resulting in improved copying ability, which we argue results from a lack of architectural biases. Consistent with higher input information retention, TMMs exhibit superior information retrieval and in-context learning benchmark accuracy compared to comparable architectures. We conclude with an analysis from the perspective of operator index theory and show that, counterintuitively, trained Toeplitz layers of causal non-invertible models are more likely to be invertible or nearly so than models that are actually invertible over their inputs.

State space models (SSMs) achieve linear-time complexity but struggle with multi-channel physiological signals due to three limitations: fixed kernels cannot capture multi-scale temporal dynamics (motor preparation over hundreds of milliseconds vs. execution transients in tens of milliseconds), Markovian state updates restrict global context for periodic oscillations, and channel-independent processing ignores spatial electrode topology. We introduce NAKUL, extending SSMs for medical signal analysis through three contributions: (1) Dynamic Kernel Generation-parallel SSM branches with varying kernel sizes (3, 5, 7, 11 timesteps) are weighted by a meta-network that analyzes input statistics, enabling adaptive temporal scale selection; (2) Spectral Context Modeling-FFT-based operations with learnable Gaussian frequency band filters capture global periodic patterns in $O(N \log N)$ complexity; (3) Graph-Guided Spatial Attention-fixed electrode topology provides spatial biases to multi-head attention for principled cross-channel interaction. On BCI Competition IV-2a motor imagery (our primary benchmark), NAKUL achieves 91.7$\pm$0.6% accuracy, matching EEG-Conformer (92.1$\pm$0.7%) while using 28% fewer parameters (2.5M vs 3.5M) and 2.0$\times$ faster inference (4.3ms vs 8.7ms). The model generalizes to EEG emotion recognition (83.6%), multimodal EEG-fMRI (91.4%), and medical imaging (92.8% on ultrasound), demonstrating architectural versatility. Ablations show dynamic kernels contribute +2.6% and exhibit interpretable scale selection patterns correlated with known neural dynamics.

Wearable devices running Human Activity Recognition(HAR) on Inertial Measurement Units~(IMUs) waste energy by performing continuous classification for each window, even during long periods of unchanged activity. We address this with a lightweight change-detection gate: a non-parametric algorithm based on dynamic template matching that runs continuously at only approximately 16kFLOPs per step, requires no offline training, and does not need prior definition of target activity classes. The gate invokes the full HAR network only when it detects an activity change, reducing the computational load by over 67% in realistic monitoring settings. The algorithm is evaluated on smart glasses, smartwatch, and smartphone data, requiring only a brief device-specific calibration phase. The gate achieves 98% sensitivity on UCA-EHAR, ensuring no genuine activity transition is missed, while 75% specificity keeps unnecessary HAR invocations low. Results on WISDM are 97% sensitivity and 76% specificity, demonstrating robustness and flexibility to various settings.

This work presents ROSA, a microring-based optical neural network architecture that improves robustness and energy efficiency using an optical shift-and-add (OSA) module and a layer-wise hybrid mapping strategy. It introduces a noise-aware voltage-to-weight model considering DAC and thermal variations, and a workload-aware framework to co-optimize MRR array size and layer-wise dataflow. Optimized arrays reduce the aggregated relative energy-delay product (EDP) by 64% and 26% compared with DEAP-CNNs and a general compact array, respectively. OSA further contributes 29% EDP reduction. The proposed hybrid mapping strategy improves CIFAR-10 accuracy by 8.3% over weight-stationary mapping while achieving an average 54.7% lower EDP than DEAP-CNNs.