Split Learning

Classification and regression trees are typically constructed using a greedy splitting rule that maximizes the immediate reduction in prediction error at each node. Although this strategy is computationally efficient, it can miss splits that yield small short-term gains but create substantial downstream improvements after further partitioning. We propose a look-ahead tree-building method that evaluates each candidate split by the prediction error reduction achieved after growing a conventional CART subtree below that split. Because the full look-ahead procedure can be computationally expensive, we also describe a smart look-ahead algorithm that learns downstream split values using node-level features. The proposed framework preserves the interpretability of recursive partitioning while improving split selection in hierarchical or interaction-driven settings. We conduct a simulation study comparing conventional, full look-ahead, and smart look-ahead methods under several settings and apply the proposed methods to analyze two real data examples demonstrating the merit of the new methods.

Rising societal and lifestyle complexity has been linked to a growing prevalence of mental distress worldwide. Educational institutions, workplaces, clinics, etc. collect large volumes of mental health survey data to understand and reduce this burden. Collaborative analysis of such data could yield effective generalizable predictive models. Privacy constraints and varied survey designs (i.e., different questions, scales, and formats) hinder direct integration. We propose a schema-aware split learning (SL) framework that preserves privacy, using a large language model (LLM) as a shared semantic encoder to harmonize heterogeneous survey schemas across institutions. We serialize each survey record into a natural-language description, unifying disparate survey schemas into a common format. The LLM is fine-tuned for mental distress assessment via Low-Rank Adaptation (LoRA) and partitioned across client and server. Clients retain the raw survey responses locally and run only a lightweight front-end, so original records never leave the institution that collected them. The resource-intensive backbone runs on the server, minimizing client-side computation. Using LLaMA-3.2-3B-Instruct, the framework attains an average ANLS of 0.708 with only 2,000 training samples, surpasses federated learning (FL) in eight of nine settings, and cuts per-client computation by three orders of magnitude, while generalizing to unseen datasets. Overall, it enables accurate, privacy-preserving, and resource-efficient collaborative learning from heterogeneous mental health survey data.

Fine-tuning large language models (LLMs) on domain-specific data is essential for downstream adaptation. In many deployments, a participant cannot hold the complete model locally. This happens because the model owner keeps the full model proprietary, or because the participant lacks sufficient compute resources. Split Learning (SL) addresses this by partitioning the model between the participant and a server so that only a small portion runs locally. When the underlying data is additionally distributed across multiple institutions with privacy requirements, Federated Learning (FL) further enables collaborative training across participants by sharing only model updates instead of raw data. In this combined setting, each client transmits intermediate activations to the server, and for LLM fine-tuning, this exchange poses an inherent privacy paradox. The autoregressive nature of LLMs causes the transmitted activations to leak the input, and existing perturbation-based defenses are fundamentally ineffective in this setting. We address this leakage through a learned obfuscate-and-recover scheme that protects participants' private datasets while still allowing an independently deployable model to be trained on the server side. Experiments demonstrate that our approach achieves strong privacy protection with modest utility loss and system overhead, making split-based federated LLM fine-tuning practically viable.

In online A/B tests for real-time bidding (RTB), control and treatment models are typically trained on a shared serving log that includes data generated by the counterpart model. This shared-log training biases each model's training data through two channels: the counterpart model may have selected a different ad from the ad-candidate pool (ad-ranking disagreement) and may have bid a different price (bid-pricing disagreement), potentially distorting the A/B test outcome. Log-splitting eliminates the bias but sacrifices training data; log-sharing retains all data but leaves the bias unaddressed. We formalize the Bid-Aware Filter Family (BAFF), a class of (k,l)-parameterized hard filters that controls tolerance to each channel independently, providing a structured search space between these two extremes. We further propose a three-stage online measurement protocol that enables evaluating data-sharing strategies by their deviation from an interference-free reference model in production. In offline simulation, a (k,l) sweep surfaces operating points with smaller deviation from the interference-free reference model than both log-sharing and log-splitting. In a live RTB deployment on a demand-side platform (DSP), filter-based variants preserve the reference model's business metrics (e.g., CPC, CTR) more closely than both baselines. The best operating point is setting-dependent, underscoring the practical value of the search space itself.

Connected robotics is an emerging 6G application where mobile robots follow natural-language instructions to manipulate physical objects. The Vision-Language-Action (VLA) models that enable this are too large to run on the robot; a common trend is to offload inference to the cloud. The wireless link, however, limits how much sensing data the edge can transmit per control step. Two recent lines address this constraint: semantic communication codecs compress sensor data but require channel-specific retraining, and VLA token pruners select tokens from image but ignore the channel. Our insight is that the dense semantic information contained in the language already indicates which visual tokens matter. We propose ComVLA, a framework that uses this language guidance to adapt the VLA token budget to the channel capacity. Transmitting 32 tokens instead of 512 on the LIBERO benchmark, ComVLA cuts inference compute by 74% and inference latency by 22% versus the original OpenVLA-OFT baseline, at a cost of 1.5 pp in average task success (95.4% vs. 96.9%), and it stays within the capacity budget under Rayleigh and Rician fading. These results demonstrate that co-designing VLA inference and wireless communication is a practical direction for 6G-connected robotics.

Diffusion language models (DLMs) offer a non-autoregressive alternative for mobile edge agentic artificial intelligence (AI) by refining tokens through iterative denoising rather than left-to-right decoding. Compared with autoregressive Transformer-based large language models (LLMs), DLMs can update multiple uncertain tokens in parallel and exploit bidirectional context throughout the generation process, enabling more flexible quality-latency trade-offs beyond fixed sequential decoding. These properties are particularly attractive for edge agents, where partial refinement, early exit, and constraint-guided correction can reduce response delay and communication overhead while improving robustness under noisy, incomplete, or dynamic contexts. This survey reviews DLM foundations and analyzes their suitability for edge settings under latency, memory, energy, bandwidth, privacy, and reliability constraints. We cover resource-efficient architectures, training and inference acceleration, compression, edge/cloud deployment, communication-aware serving, Internet of Things (IoT)/wireless applications, and evaluation of DLM-based agents. We further discuss open issues in long-context state management, split inference, trustworthy execution, multimodal grounding, and reproducible benchmarking. The goal is to connect DLM modeling properties, including bidirectionality, parallel refinement, controllability, and quality-latency elasticity, with system-level requirements of future mobile edge intelligence.

Multimodal models are increasingly the default option for perception at the network edge, yet they are trained almost entirely in the datacenter, because a client holding several sensor streams cannot host an encoder per modality. Split Learning makes such training feasible by keeping only the first layers on the device, at the cost of an uplink that must carry smashed activations for every modality at every step. Existing compression schemes give each modality the same keep-ratio, so the shared budget is divided in proportion to smashed-activation dimension, a quantity unrelated to how much each modality contributes to the fused prediction. We make that division an explicit decision and call it inter-modality allocation: under a fixed uplink budget, every policy transmits the same expected payload and differs only in how that payload is split across modalities. Our allocator, ModalShare, sets each modality's keep-ratio from a Shapley contribution score that the server computes over coalitions of activations it has already received. Measuring this score adds no uplink traffic and no client-side computation, and needs no prior knowledge of which stream is which. ModalShare improves accuracy over equal keep-ratios by 15.4 and 12.4 percentage points on CREMA-D and MVSA at matched payload in 5x compression, with strong performance across three compressors, three datasets, and four budgets. We show that existing compressors underperform in multimodal settings, with ModalShare recovering what gains are left behind.

Crowd counting must recover reliable local density under severe variations in perspective, head scale, occlusion, and background clutter. Although modern counting objectives provide strong spatial supervision, many multi-level decoders still use spatially invariant feature fusion and apply one receptive-field pattern to every location. We propose DCA-MoE, a framework that makes both decisions content dependent while retaining a frozen DINOv3 encoder. Spatially Adaptive Layer Fusion (SALF) predicts position-wise weights over four aligned backbone features, and Density-Routed Multi-Receptive-Field Experts (DR-MoE) assigns each location a soft mixture of local, mid-range, and large-context residual experts. An EBC-style head reconstructs block density, while DMCount supervision and an auxiliary routing-balance term train the decoder without updating the backbone. On the NWPU-Crowd validation split, the strongest paired configuration, based on DINOv3 ViT-L/16, obtains 31.7 MAE and 72.2 RMSE; the matched ViT-B/16 full model obtains a paired 32.2/75.9. Cross-dataset results remain mixed, and several component baselines currently report independently selected minima from a single seed. The evidence therefore supports the feasibility of spatially adaptive fusion and routing, while broader paired and multi-seed evaluation remains necessary for causal attribution.

Large language models often fail when answer options require combining atomic judgments under explicit logical operators, even when they judge the individual atoms correctly. We study compound options connected by AND, OR, and NEITHER/NOR, introducing a framework that decomposes each option into atomic answers and scores contrastive hypotheses about each one, so the model never sees a compound option. An operator-constrained integer linear program then composes the calibrated scores into a single prediction. We evaluate on LOGICAL-COMMONSENSEQA and introduce LOGICAL-SATA, a reading-comprehension benchmark derived from SATA-Bench. Our framework improves Macro-F1 from 48.3 to 77.0 on the human-validated LOGICAL-COMMONSENSEQA split and from 47.0 to 75.6 on LOGICAL-SATA, with the largest gains on NEITHER/NOR.

This paper presents an interpretable machine-learning framework for predicting the splitting strength (ST) of asphalt concrete and supporting data-driven mixture design. A database consisting of 296 samples was established, and 14 input variables related to asphalt properties, aggregate gradation, and fiber characteristics were selected for modeling. Six machine-learning models, namely TabPFN, ANN, SVR, RF, XGBoost, and LightGBM, were developed and compared. Hyperparameter optimization was performed for five models using NSGA-II, while TabPFN was directly applied with its default configuration. The results show that all six models achieved satisfactory predictive capability, whereas TabPFN delivered the best overall performance on the testing set, with the lowest RMSE of 0.28, MAE of 0.21, MAPE of 18.01%, MAD of 0.14, the highest R^2 of 0.88, and the highest composite score of 0.91. SHAP analysis further revealed that nine dominant variables accounted for 92.0% of the total average contribution, among which Ag9.5, FT, Ag4.75, AC, and Du were the most influential. In addition, favorable parameter ranges for improving ST were quantified, such as Ag9.5 < 66.8%, Ag4.75 < 45.0%, AC < 5.4 wt.%, AV < 3.6%, and Du > 134.7 cm. Finally, a GUI platform integrating prediction and SHAP-based explanation was developed to improve the accessibility and practical applicability of the proposed framework.

Deploying state-of-the-art deep neural networks (DNNs) at the wireless edge is severely bottlenecked by the strict energy and resource constraints of mobile devices. While federated split learning (FSL) mitigates on-device computation by offloading workloads to an edge server, this may introduce systemic overheads, while the continuous exchange of cut-layer data, and submodels still incurs significant energy consumption (EC). To address this, we propose a green quantized FSL (GQ-FSL) framework that incorporates stochastic quantization for both local collaborative training and wireless transmissions. Notably, GQ-FSL supports asymmetric precision levels for the client- and server-side submodels, effectively decoupling device energy constraints from global convergence degradation. To quantify these tradeoffs, we develop parameterized energy models for the split architecture and derive a theoretical convergence bound under statistically heterogeneous data. Building on that, we formulate a joint optimization problem to configure the DNN split point and precision levels, minimizing the total system EC while satisfying a strict target accuracy constraint. Ultimately, we demonstrate that GQ-FSL enables large-scale DNN deployment on resource-constrained devices, achieving superior energy efficiency compared to quantized federated learning and full-precision FSL.

Branch and Bound (BaB) aims to achieve complete verification of neural networks by adaptively partitioning the problem and applying off-the-shelf verifiers to subproblems. Its problem-splitting history can be represented as a tree, where each subproblem corresponds to a child node. A key problem of BaB lies in searching for the verdict boundaries across all the paths that divide the verified and unverified subproblems. We observe that the existing BaB approach tackles this problem by solving each expensive subproblem sequentially along the tree path as its depth increases, requiring costly bounds propagation at every visited BaB tree node (i.e., subproblem), which is inefficient. To address this issue, we propose effective search approaches that leverage the monotonicity of each path to efficiently and precisely locate the verdict boundary by simultaneously splitting multiple activation functions (e.g., ReLU), rather than processing them one at a time as in the classical approach. Our approach performs an effective exponential search along each path, allowing us to skip many boundary-unrelated subproblems when identifying the verdict boundary. The enhanced version further improves this process by estimating the boundary's position using quantitative information obtained from subproblem solving. We perform experimental evaluation on commonly-used benchmarks to assess our proposed techniques, and compare them with recent BaB-based approaches.

We present PixCell, a neurosymbolic system in which multimodal agents convert a visually presented photonic component into a parametric program over a small domain-specific language (DSL) of geometric primitives. A system enabling deterministic visual verification renders evaluation asymmetrically cheaper than the generation attempt. While models using multi-seed sampling and iterative revision reach a mean best-turn IoU of only 0.416, multimodal agents through PixCell's interface and verifier consistently exceed 0.9 mean IoU, with scores reaching 0.974 and 0.955 across eight component targets while also satisfying source contracts. These results demonstrate that frontier multimodal agents can reliably understand and render executable parametric representations from visual targets. Using these live parameters, cross-stack studies on an interferometer reconstruct primitive programs that satisfy an 8.0 nm free spectral range target and the original footprint constraint on modeled 220-nm SOI, 400-nm SiN, and 400-nm TFLN stacks. PixCell further carries a paper-derived splitter from visual reconstruction through SOI full-wave simulation, producing symmetric propagation and balanced outputs. Finally, the same executable verifier supplies a training reward and dataset used to train a Qwen3.6-35B-A3B model with LoRA and GRPO without supervised demonstrations. On eight training-excluded paper figures, its mean champion IoU rises from 0.422 after eight initial attempts to 0.491 after three verifier-guided revision rounds. These results therefore establish a controlled framework for measuring, retargeting, and improving visual-to-parametric photonic component design.

Accurate model evaluation in machine learning depends critically on how datasets are split into training and testing subsets. Standard random splitting assumes that both partitions share the same underlying distribution, an assumption often violated in datasets with class imbalance, natural clustering, or spatial autocorrelation. This paper investigates the role of statistical similarity in train-test splitting and its consequences for AutoML model evaluation. Five established strategies are compared across fifteen UCI benchmark datasets: random splitting, stratified sampling, Kennard-Stone, Duplex, and SPXY. Similarity is assessed using chi-square, Kolmogorov-Smirnov, and Maximum Mean Discrepancy (MMD) tests. Geometry-based methods consistently produce near-zero MMD scores, introducing instability into downstream performance estimates. The proposed Optimised-Distribution method treats similarity as an explicit optimisation objective and achieves the highest mean MMD similarity, 89.0%, across all strategies evaluated.

Swarm Learning is a decentralized collaborative learning mechanism that allows multiple organizations to train a shared model without central coordination or direct data sharing. In typical horizontal Swarm Learning, datasets across sites are usually assumed to share the same feature set. However, in real-world applications, sites often have partially overlapping features because measurements, protocols, and available covariates differ across sites. This feature heterogeneity creates a practical issue for machine learning algorithms such as Random Forests. Specifically, when decision trees are pooled into a global Random Forest, inference at a given site can become ill-defined if a traversal encounters a split on a feature that is not available locally, often forcing organizations to discard site-specific variables upfront. In this paper, we address feature heterogeneity in Swarm Learning with Random Forests under partially overlapping feature spaces. We propose several deterministic and probabilistic inference-time strategies that resolve such missing splits without restricting training to the intersection of features. We evaluate the methods on nine datasets and demonstrate that they outperform both the intersection baseline and locally trained models across a broad range of scenarios.

Split learning enables collaborative model training by partitioning neural networks across clients and servers. However, improper split placement can lead to severe privacy leakage through intermediate representations. In this work, we propose a topology-guided framework for privacy-aware split learning based on the persistent Betti complexity of smashed activations. Through comprehensive layer-wise analysis, we show that privacy risk in split learning is highly non-uniform across layers and exhibits sharp transition regions that are not captured by architectural depth alone. In particular, feature inversion fidelity increases from negligible reconstruction to as high as 0.98 SSIM at deeper, privacy-critical split points. We further demonstrate that Betti complexity consistently identifies representation regimes associated with elevated feature-space privacy leakage across architectures and datasets. Leveraging this observation, we introduce BettiSafe, a topology-guided split selection strategy that identifies privacy-sensitive layers without requiring explicit attack execution. BettiSafe improves resistance to feature inversion by 2 to 5 times compared to depth-based heuristics while preserving classification accuracy. In addition, Betti-based regularisation increases inversion difficulty by nearly 5 x without degrading model utility, enabling a favourable privacy utility tradeoff. Overall, our results highlight topological complexity as a promising structural descriptor for secure, adaptive, and representation-aware split learning in real-world collaborative systems

Distributional random forests replace mean-based CART splitting with criteria that compare the full conditional response distribution in candidate children. We implement and systematically study a family of such criteria inside a single honest-forest implementation: isotropic random-Fourier-feature maximum mean discrepancy (MMD), an anisotropic diagonal-bandwidth variant, an adaptive per-split frequency-selection variant, and a non-kernel sliced-Wasserstein criterion, together with post-hoc kernel-mean shrinkage of the forest weights. Using paired-seed comparisons across synthetic quantile mechanisms, real univariate benchmarks, a California-housing subsample curve, and multivariate synthetic and real responses, we characterize where each extension pays. Three findings recur. First, among distributional criteria ordinary isotropic MMD is already close to best in class: the anisotropic, adaptive-frequency, and sliced-Wasserstein extensions, and post-hoc shrinkage, do not systematically improve on it. Second, on scalar tabular regression mean-based CART splitting remains the robust default and wins many cells. Third, multivariate responses are the regime where distributional splitting clearly earns its keep, most sharply on a pure-dependence copula where the energy score separates the criteria even though marginal CRPS does not. The evidence supports a simple allocation story: distributional splitting helps only when non-location structure is both present and estimable; otherwise it dilutes split-selection power away from the mean. All criteria, the honest forest, and the paired-comparison harness are implemented in the open-source \texttt{drforest} library, whose Rust-backed split search makes broad criterion sweeps inexpensive.

Discrete optimization algorithms are often analyzed through continuous-time limiting ODEs, but a convergence certificate for the ODE is not automatically one for the discrete algorithm. We develop contact Hamiltonian systems as a setting where the transfer can be made precise. A contact Hamiltonian $H$ on $J^1(\mathbb{R}^n)$ obeys the intrinsic decay identity $\dot H = -H\,\partial_s H$, so an augmented energy $\mathcal{E}$ built from $H$, together with the conformal rate $\partial_s H$, is a continuous-time rate certificate whenever $\mathcal{E}$ controls the objective gap. Our main theorem states, under three named and independently checkable hypotheses, that an order-$r$ contact splitting with step $h$ transfers this certificate over the finite horizon set by backward error analysis. The discrete decay envelope is governed by the modified conformal factor up to $O(h^r)$ perturbations plus a backward-error shadowing defect, and the mechanism is inherited exactly because the modified Hamiltonian is itself a contact Hamiltonian. Quadratic heavy ball is a fully solvable example: its projected dissipative-leapfrog spectrum agrees with established conformal-symplectic optimization theory, while the augmented contact Hamiltonian yields a sharp objective-to-certificate comparison that verifies the transfer hypotheses. For strongly convex objectives with state-dependent damping, an explicit Bregman-type Lyapunov certificate instead transfers by an auxiliary-shadowing corollary. The decomposition $H=K+V+D$ into kinetic, objective-encoding potential, and dissipation terms serves as a design template, with a catalogue of closed-form sub-flows including contact-specific damping families. Numerical experiments confirm the predicted conformal-factor tracking orders and show competitive performance on ill-conditioned benchmarks and deep-learning tasks.

Lean 4's grind tactic combines congruence closure, E-matching, and case-splitting into a single automated solver, and like any such solver, it relies on hand-tuned heuristics to decide what to instantiate and where to case-split. These heuristics are tempting targets for learning, but there is a catch: because grind's search is non-monotone, a learned heuristic that helps one proof can break another, and an always-on replacement usually nets out near zero. We avoid this by invoking a learned intervention only after stock grind has already failed: a failure-triggered cascade that, by construction, cannot lose a proof grind already had. We apply it to two of grind's internal decisions. A cost-aware E-matching filter solves slightly more problems and runs about 5% faster. A lookahead step proves five theorems it otherwise times out on. We also report the negative result that motivated the design: across four feature-based models, statically predicting the correct case split is no better than random, because whether a split explodes is a runtime property that the features do not capture. Our results suggest that learning within theorem-proving tactics is most effective as a mechanism for deciding when and how to spend bounded search, backed by a reliable symbolic fallback.

Document packets, multiple documents concatenated into a single file, are common in government and administrative workflows, yet splitting them into their constituent documents is difficult, especially for low-resource languages. We introduce Khondo (Bangla for split/segment), the first benchmark for document packet splitting on Bangladeshi government forms. Unlike prior English and OCR-text-based datasets, Khondo is bilingual (Bangla--English) and vision-native; where models operate directly on page images. It spans five concatenation schemes, from sequential to fully shuffled, across 14 administrative domains, with ground-truth boundaries, domain types, and page order. Zero-shot evaluation of MLLMs shows they cluster pages into their source documents fairly well but struggle in restoring the original page order once shuffled. To isolate what drives this difficulty, we run two controlled analyses, varying the prompt instruction and then the packet language. Both primarily affect ordering rather than clustering: (a) explicit page-order instructions are necessary but insufficient, and (b) English packets are ordered more reliably than Bangla, making page arrangement the dominant challenge and language a secondary but consistent factor. Khondo establishes page-order reconstruction as a key open problem in vision-based, low-resource document understanding, and provides a controlled benchmark for measuring progress toward solving it. Our dataset and code is available at https://huggingface.co/datasets/Mausul/khondo

Ordinal Classification (OC) deals with classification tasks where the classes follow a natural order. Despite the progress in OC, many existing approaches fail to fully leverage the ordinal information, treating the problem as nominal classification and thereby losing performance potential. In this work, ADABORD, an AdaBoost framework specifically designed for ordinal classification problems, is introduced. The ordinal nature of the classes is incorporated into two key components of the well-known AdaBoost algorithm: 1) the base estimator, where decision trees with the ordinal Gini splitting criterion are proposed; 2) the error function used to update sample weights at each stage and the weights of the classifier in the final ensemble model, given by the absolute ranked probability score, a measure that accounts for both the ordering and the distance between classes. ADABORD is extensively compared against seven state-of-the-art methods on the TOC-UCO repository, the largest benchmark collection for OC to date. The experimental results, supported by statistical analysis, show that ADABORD significantly outperforms competing methods, particularly on datasets with five or more classes, where the ordinal structure becomes more pronounced. Source code, along with all experimental protocols, is publicly available to ensure reproducibility and facilitate future research in OC.

This paper introduces Sentence Splitter, a self-supervised framework built upon a T5-based encoder--decoder architecture for uncovering the latent factual structure of natural language sentences. The proposed method identifies the semantic boundary between a descriptive prefix (head) and its factual completion (tail) by formulating sentence splitting as a discrete segmentation problem, where a sentence of length $N$ admits $N$ possible split points but only one recovers the intended head--tail structure. Rather than explicitly searching over all candidate boundaries, the model learns to recover the factual completion through probabilistic sequence generation. To eliminate the need for manual annotation, symbolic head--tail pairs are first verbalized into natural-language templates that provide supervision for training the Sentence Splitter. The trained splitter is then applied to raw text to extract aligned prefix--tail pairs, which are subsequently used to train a generative model that proposes additional plausible completions through a lightweight bootstrapping process. This unified pipeline provides a scalable and structure-aware approach to constructing self-supervised training data while bridging symbolic knowledge and natural language. Experiments on both structured and naturally occurring text demonstrate that the proposed splitter generalizes beyond synthetic templates and that the resulting structure-aware supervision consistently improves downstream performance on knowledge graph completion and commonsense question answering, highlighting the effectiveness of recovering latent factual structure for knowledge-centric NLP.

Multi-step enterprise agent tasks fail in a characteristic way: single-pass inference has no checkpoint between deciding an answer and committing to it. We study one production system (Leni) whose architecture installs such checkpoints: verification loops (execute, observe, compare, correct) staffed by lightweight task-specialized post-trained models. We evaluate the unmodified production configuration on three public benchmarks stressing distinct failure modes: SpreadsheetBench Verified (silent computation error), BullshitBench v2 (premise confabulation), and the GAIA validation split (cascade error over long tool chains). The full system improves over its frontier base model by +11.0 percentage points on SpreadsheetBench (91.25% vs 80.25%, n=400, p<0.001), +7 to +10 percentage points on BullshitBench (98% vs 91%, n=100), and roughly +15 points on GAIA validation (75.2% pass@1, n=165; 83.0% best-of-k). Our central contribution is a decomposition of that uplift: most of it comes from scaffolding, routing, and specialist models rather than from the verification step itself, whose isolated contribution is small (+1.5 points) but concentrated at the top of the score distribution, where it converts otherwise-failing tasks. We instrument the loop end-to-end, yielding an empirical verifier confusion matrix (catch rate about 0.20, fix rate 0.75, no false-alarm regressions) that grounds a compounding-reliability model. Specialist-swap ablations suggest that the loop's value depends on who observes it: replacing the small trained verifier with the generating frontier model eliminates most rescues. A valid-premise control shows zero over-rejections in 100 expert-level questions.

Molecular property models are commonly evaluated by holding out Bemis--Murcko scaffolds, yet a scaffold identifier is only one notion of chemical unfamiliarity. We introduce a label-free structural-frontier split that reserves the sparsest and most physicochemically remote scaffold groups, and evaluate it on six public experimental or curated ADMET tasks. Against a 70/10/20 scaffold control with identical acyclic grouping, the frontier inflates equally weighted primary error with a taskwise median of 87.0% and a skew-sensitive mean of 130.3% (descriptive task/seed bootstrap interval, 52.1--246.0%). The mean falls to 75.9% once BBB is removed; that endpoint is the one whose score ranking inverts at the frontier. A message-passing graph-network control still shows a large gap (mean 82.8% over four tasks) and does not invert, so a low-capacity head does not explain the effect. We also test Multi-View Frontier Risk Extrapolation (\method), a count-adjusted tail-risk penalty over four molecular views, and treat it as a falsifiable probe. It changes normalized frontier error by only 0.16% relative to empirical risk minimization for the perceptron head (interval, $-0.43$--0.84%) and by $-1.9$% for the graph network; three fixed robust-penalty controls are likewise inconclusive. Against the published Lo-Hi and DataSAIL splitters the frontier inflates error more on average, though no split is uniformly hardest. An audit of 31,561 marine natural products further shows that OOD status and agreement with legacy ADMET predictions depend on the molecular view, endpoint and teacher coverage. Split construction and label provenance are important evaluation constraints in their own right, and the tested training penalties do not resolve the frontier failures we observe.

The Prasthanatrayi -- the ten principal Upanisads, the Brahmasutra, and the Bhagavadgita, with Sankara's commentaries (bhasya) -- is the foundational corpus of Advaita Vedanta. Continuous euphonic combination (sandhi), long compounds (samasa), and dense scholastic prose make it hard to read at the word level: where one word ends, and what each word means grammatically, are both obscured. We present an open, fully offline, word-level digital reader of the entire Prasthanatrayi with Sankara's bhasya. Every word -- of both the root text (mula) and the commentary -- is clickable and resolves to a pop-up giving its split (padaccheda), morphological analysis, and gloss. Because every word carries a lemma, the reader also acts as a concordance: a search on a dictionary headword retrieves all of that word's inflected and sandhi-hidden occurrences, and its occurrences inside compounds, across both layers. The resource covers thirteen commentarial units (2,971 verses, sutras, and prose sections; 36,881 analysed word-occurrences of root text) and a global dictionary of 95,587 distinct commentarial surface forms. We describe the corpus, the hybrid pipeline -- a rule-based sandhi splitter over an inflected-form lexicon and attested-corpus look-ups, with LLM-assisted analysis under an adversarial two-pass verification protocol -- and a durable human-review loop whose corrections survive every regeneration. An intrinsic evaluation against independent Sanskrit resources finds high-confidence analyses agree with an authoritative inflectional lexicon on over 99% of attested forms, and a band-blind adjudication confirms that quality degrades predictably across confidence bands, with errors concentrated in the low-confidence tier the review loop targets. The reader is a single self-contained HTML file needing no server or network, offered as a freely redistributable teaching and reading aid.

Estimating heterogeneous treatment effects (CATE) requires simultaneously detecting effect modification and quantifying estimation uncertainty. Existing tree-based methods make an uneasy trade-off: significance-based approaches (Radcliffe and Surry 2011) identify subgroup interactions directly but lack valid inference; honest causal trees (Athey and Imbens 2016) deliver nominal confidence interval coverage but use outcome-agnostic splitting criteria that sacrifice interaction sensitivity. We introduce a hybrid algorithm that fuses significance-based splitting with honest sample-splitting and cross-validation. Our splitting criterion uses the squared $t$-statistic for the treatment $\times$ side interaction ($t^2$), which is shown to be directly aligned with the honest $\text{EMSE}_τ$ criterion when the interaction is strong. Post-hoc honest cross-validation selects the cost-complexity penalty, giving a single principled estimator with nominal CI coverage at the leaf level. For forests, we retain bootstrap count vectors to enable an infinitesimal jackknife (IJ) variance estimate of Monte-Carlo convergence rather than formal pointwise inference. On the three synthetic designs from (Athey and Imbens 2016) the single tree achieves approximately 90% leaf-average CI coverage at the 90% nominal level across all three designs (200 replications each); on the Criteo, Hillstrom and Starbucks uplift datasets we match Qini coefficient performance of S-, T-learner and GRF baselines. An open-source Python package with reproducible seeds, sklearn-compatible API, and full test coverage accompanies this work (https://codeberg.org/hadjipantelis/rattus).

We release \textsc{JavaVulBench}, a benchmark dataset and evaluation harness for Java vulnerability detection. The dataset contains $\sim$30{,}600 Java methods spanning 1{,}740 CVEs and 700+ projects, labelled at both method and line granularity, with per-CVE publication dates and five realistic split strategies: random, project-disjoint, temporal, deduplicated, and unseen CWE-family. The harness provides a single \texttt{LlmPrediction} schema across three backend families (encoder classifiers, local generative models served by Ollama, and API-served LLMs routed through OpenRouter) so that twelve reference detectors CodeBERT, GraphCodeBERT, UniXcoder, DeepSeek-Coder-1.3B, and eight API/open-weight LLMs (GPT-4o, GPT-4.1-mini, Claude Sonnet~4, DeepSeek-v3, DeepSeek-Coder-v2, Qwen-2.5-Coder-14B/7B, CodeLlama-13B) are evaluated under identical conditions from a single command. A pre-training contamination audit is shipped alongside every model so users can separate genuinely unseen test CVEs from potentially memorised ones. Data, code, and fine-tuned checkpoints are archived on Zenodo [31] and short demonstration video is available on YouTube (https://www.youtube.com/watch?v=nMTX\_hqkuoM) https://www.youtube.com/watch?v=nMTX_hqkuoM.

Recent generative models can produce high-quality synthetic images, offering scalable training training data for data-hungry models. Existing approaches to exploiting this potential typically involve 1) training or fine-tuning generators, or 2) using lightweight post-hoc adaptation like prompt engineering or inference-time guidance, making them generator-specific and expertise-intensive. We study a complementary question: given a fixed pool of generated images, can downstream utility be improved purely by selecting an informative subset? The answer is yes. We show that effective selection must counter a structural bias of modern generators: they tend to over-produce canonical modes of each class while underrepresenting intra-class variation. Building on this insight, we split each real class into a canonical Homogeneous (HO) subset and a non-redundant Heterogeneous (HE) subset, then score synthetic images by a fidelity-diversity criterion that rewards semantic alignment while penalizing canonical redundancy. The method is generator-agnostic and requires no retraining. Across multiple benchmarks, it consistently outperforms state-of-the-art data selection baselines and matches the real-data performance with up to 40% fewer synthetic samples. The same criterion remains effective when applied on top of stronger task-tuned generators, with gains on both classification and segmentation tasks. Post-generation selection is therefore not a substitute for better generators, but a complementary mechanism for improving the utility of synthetic data.

Performance evaluation in AI systems commonly assumes that random dataset splits produce independent and identically distributed (i.i.d.) subsets. We show that this assumption often breaks down in spatiotemporally correlated domains such as aerial surveillance, precision agriculture, and medical imaging, leading to two systematic failures: data leakage, where correlated samples span training and validation splits and inflate performance estimates, and hidden stratification, where errors on minority subpopulations are obscured by aggregate metrics. To address these issues, we propose a unified evaluation and training framework for spatially correlated data. We introduce Structure-Aware Stratified Partitioning (SASP), which constructs validation splits that reduce spatiotemporal leakage while preserving meaningful class balance, and Curriculum Distributionally Robust Optimization (CDRO), a curriculum-based relaxation of distributionally robust training that stabilizes optimization under these stricter splits. Across multiple benchmarks, this combination yields consistently improved generalization, more reliable confidence calibration, and exposes failure modes that remain hidden under conventional random-split evaluation.

Large Language Models are increasingly deployed in emotional-support contexts and crisis-related situations. Nevertheless, their cross-lingual abilities in these circumstances remain underexplored. Existing benchmarks emphasize multilingual performance but rarely examine crisis-related empathy and cultural grounding in low-to-mid-resource languages. We introduce SPLIT, a 500-prompt benchmark designed to evaluate LLM consistency in generating emotionally grounded responses across five categories: Stress, Panic, Loneliness, Internal Displacement, and Tension. We evaluate three technically diverse LLMs across three dimensions: Empathetic Accuracy, Linguistic Naturalness, and Contextual & Cultural Grounding. The framework aims to assess and compare the quality of LLM responses in both English and Ukrainian languages, as well as to explore the reliability of the LLM-as-a-jury paradigm. Our findings reveal that Gemini-2.5-Flash and LLaMA-3.3-70B-Instruct degrade when transitioning to Ukrainian, while DeepSeek-V3 remains comparatively stable within our benchmark. We additionally find that human and AI evaluators agree weakly on empathy and naturalness but diverge on cultural grounding. We further argue that producing Ukrainian text is not equivalent to producing Ukrainian emotional support. Our findings may assist in the future development of more culturally tailored benchmark designs, as well as encourage a stronger emphasis on human-centered evaluation.

Conformal prediction and its variants, including the split conformal prediction, provide a distribution-free framework for uncertainty quantification by constructing prediction intervals or sets with finite-sample coverage guarantees. The statistical efficiency of these intervals depends critically on how the data are split into training and calibration samples. Despite its practical importance, a principled characterization of the training-calibration split that minimizes prediction interval length while maintaining coverage has remained largely unresolved. In this paper, we develop a theoretical framework for optimal data splitting in split conformal prediction. We first analyze the problem in a general setting and derive analytical characterizations of the length-optimal split ratio under both symmetric and asymmetric regimes. We then show how the general results specialize to several commonly used regression settings, including linear regression, nonparametric regression, and neural networks, thereby demonstrating the scope of the framework. We also describe a data-based method for selecting the optimal proportion. Our analysis clarifies how model-related features govern the optimal allocation of samples between training and calibration and provides principled guidance for constructing shorter prediction intervals. Experiments on both synthetic and real-world datasets demonstrate the applicability of the proposed methodology across a variety of practical scenarios.

Sparse Autoencoders (SAEs) are widely used to interpret large language models by decomposing activations into sparse, human-understandable features, but scaling to large dictionaries exposes fundamental challenges. Systematic studies reveal pervasive feature splitting that fragments coherent concepts into non-atomic latents and widespread feature absorption that creates arbitrary exceptions in general features, severely compromising latent reliability. These issues stem from inconsistent latent assignment across samples: without cross-sample constraints, per-sample optimization often allows a single underlying concept to be inconsistently distributed across multiple redundant or interfering latents. To address this, we introduce C$^2$R (\underline{\textbf{C}}ross-sample \underline{\textbf{C}}onsistency \underline{\textbf{R}}egularization). C$^2$R explicitly encourages that each semantic feature is consistently represented by a unified latent across the batch by penalizing the co-activation of directionally similar latents. Comprehensive evaluation demonstrates that C$^2$R effectively mitigates both splitting and absorption while, crucially, preserving reconstruction fidelity, providing a principled solution that enhances latent interpretability without degrading model performance. Source code is available at https://github.com/hr-jin/Cross-sample-Consistency-Regularization.

Knowledge Distillation (KD) enables training smaller student models under the guidance of larger teacher models, and the widely adopted TRL library implements it. Yet, TRL treats both models symmetrically, missing opportunities to exploit their pronounced asymmetry in memory footprint, and communication requirements. This paper presents an HPC-aware methodology for KD that decouples teacher and student partitioning efficiently. Our approach achieves up to 67% higher samples-per-second than TRL by avoiding unnecessary teacher-model data structures and selecting the best split strategy. We combine vertical and horizontal partitioning of models, deriving an analytical expression that identifies the existence of inflection points between splitting regimes. These results showed that exploiting teacher--student asymmetry through topology-aware parallelism notably accelerated GKD training on production HPC clusters at our company

Distributed intelligent systems increasingly need to train across data silos without centralizing raw data. Federated learning keeps data local but can suffer under heterogeneous partitions and requires repeated full-model exchange. Split learning reduces communication through cut-layer activations, but standard protocols generally do not recover centralized mini-batch gradient behavior and may expose activations and gradients in plaintext. We present TL++, a two-mode traversal-learning framework that constructs virtual batches across nodes to recover centralized mini-batch gradient behavior under explicit synchronization assumptions. Base mode exchanges cut-layer activations and gradients rather than full models. Secure mode secret-shares each cut-layer activation and gradient between an orchestrator and a non-colluding helper, preventing either server from observing plaintext cut-layer tensors. This protection is limited to a semi-honest two-server setting; labels and loss-related outputs remain visible to the orchestrator. In the lightweight secure path evaluated here, exactness requires a linear or affine server path, while nonlinear operations require nonlinear MPC or approximation. We formalize TL++, analyze communication and computation costs, and evaluate it against federated and split-learning baselines on CIFAR-10 and BioGPT/PubMedQA using full fine-tuning and LoRA. On CIFAR-10, TL++ base cut 1 and exact secure cut 3 achieve accuracies of 91.41% (SD 0.19) and 90.93% (SD 0.17), respectively, exceeding the strongest measured non-TL++ baseline by more than 12 percentage points. TL++ base cut 1 also reduces per-step communication by 13.1-fold relative to full-model synchronization. PubMedQA results similarly favor TL++. Overall, TL++ approaches centralized-training performance while reducing communication and providing activation-level secret sharing.

Enzyme substrate interaction (ESI) prediction is a fundamental computational task for biocatalyst discovery and reaction screening in large biochemical spaces. In practical settings, ESI prediction is challenged by sparse positive supervision and low-homology distribution shift, where test enzymes share limited sequence identity with those observed during training. To address these challenges, we propose RAMMESI, a retrieval-augmented multimodal framework for robust ESI prediction. RAMMESI learns explicit pairwise enzyme-substrate representations through directional cross-modal interaction modeling and adaptive fusion. To enhance robustness, RAMMESI retrieves neighboring enzymes at inference time, recombines them with the query substrate, and aggregates the resulting pairwise predictions as contextual evidence. To improve learning under sparse positive supervision, we further adopt an imbalance-aware weighted-BCE objective. Experiments on two ESI benchmarks under sequence-identity-aware splits demonstrate that RAMMESI achieves consistently strong performance, with particular advantages in more challenging low-identity regimes. In addition, the retrieval module improves multiple ESI backbones in a plug-and-play manner, suggesting that retrieval provides a general mechanism for improving robustness under homology shift.

Split learning provides a practical paradigm for resource-constrained users to train Large Language Models (LLMs) by offloading computation-intensive layers to a server while keeping raw data local. However, existing privacy-preserving split learning methods still face a difficult trade-off among utility, privacy, efficiency, and stability. Specifically, these methods often suffer from substantial utility degradation, remain vulnerable to advanced data reconstruction attacks, incur prohibitive computational and communication overhead, or exhibit unstable performance across different tasks. In this paper, we propose MIXGUARD, a novel mixup-based privacy-preserving split learning framework for LLMs. MIXGUARD introduces token-level obfuscation, representation-level obfuscation, and adaptive gradient perturbation mechanisms, which operate jointly to preserve useful learning signals while preventing privacy leakage to the server. Technically, MIXGUARD first constructs a lightweight calibration model on a public dataset to refine the approximated target representation, and then applies this model during privacy-preserving fine-tuning on private data. We conduct extensive experiments on four classification tasks and four text generation tasks across multiple LLM families, model sizes, architectures, and fine-tuning strategies. The results show that MIXGUARD preserves model utility comparable to non-split training baselines, consistently achieves stronger privacy protection than existing split learning defense methods against state-of-the-art data reconstruction attacks, and remains robust under adaptive attack settings.

Running large language models locally is often impractical, pushing inference on sensitive text to third-party providers. Split inference partially mitigates this by keeping tokens on the client and sending only hidden representations, but these representations can still be recovered via nearest-neighbor search against the public embedding table. We propose an orthogonal obfuscation procedure in which the client multiplies embeddings by a secret orthogonal matrix before transmission. To enable correct inference under arbitrary rotations, we introduce ConjFormer, a transformer variant that is exactly $\mathrm{O}(d)$-equivariant via a lightweight normalization change (scalar RMSNorm) together with blockwise orthogonal conjugation of all linear weights. As a result, the server performs the full forward pass entirely in the rotated basis and never observes unrotated hidden states. Experiments on GPT-2 and Llama 3.2 1B models fine-tuned on PubMed show that orthogonal obfuscation eliminates direct cosine nearest-neighbor inversion and reduces token recovery from over 35% top-10 to at most 1.3%, while increasing perplexity by only 0.4% after fine-tuning. These results indicate that enforcing symmetry at the architectural level can provide a practical defense for privacy-preserving LLM inference without noise injection or heavy cryptographic machinery.

Large language models (LLMs) are increasingly deployed in privacy-sensitive domains, where users must balance the risk of data exposure through external APIs against the high computational cost of local deployment. Split learning has therefore emerged as a promising paradigm for LLM fine-tuning and inference under limited local resources. However, it introduces new privacy risks. Prior work primarily studies leakage of private input prompts, typically via inversion attacks on intermediate representations, while the potential for sensitive information leakage through generative response outputs remains largely unexplored. In this work, we unveil novel vulnerabilities of Split-LLM by presenting Patched Model Inversion with Dual-Sided Initialization (PIDI), a two-stage attack that simultaneously targets both private input prompts and output responses in Split-LLM settings. It combines dual-sided initialization with a patched inversion strategy to tackle long sequences, substantially outperforming prior inversion methods. To counter threats from both sides, we further propose the Adapter-based DualGuard with Mutual Information Defense (ADMI), which integrates an adapter-based local warmup strategy and mutual information regularization to provide a strong empirical privacy protection with minimal impact on task performance. Extensive experiments across diverse tasks and models demonstrate that ADMI effectively defends against PIDI and other state-of-the-art inversion attacks. Our code is publicly available at https://github.com/FLAIR-THU/VFLAIR-LLM.

In the era of Explainable Artificial Intelligence, there is a renewed focus on single trees for their ease of interpretation. This paper introduces Simultaneous Latent Budget Trees, a probabilistic machine learning framework for classification trees in the presence of a stratification factor such as a temporal, spatial, or demographic variable, acting as a control variable or potential confounder. Standard tree growth procedures are not designed to optimize a conditional split rule. A model-based split rule is proposed in which child nodes are interpreted as latent components of a simultaneous mixture model, such as the Simultaneous Latent Budget Model and its constrained versions, fitted to the parent node. Mixing parameters drive the observations, differently for each group, to the child nodes whereas latent budgets parameters update the response classes profile of each level of the control variable. Parameters are estimated by least squares considering a neural network perspective of the model. An informative tree structure can be interactively visualized with interpretation aids on the node and the paths, including visual pruning and decision tree selection procedure. Suitable measures are proposed to handle an unbalanced response class distribution. The proposed methodology is applied to investigate gender-related differences in disease progression of Amyotrophic Lateral Sclerosis. The SLBT library with the various tree-based algorithms is available in the linked GitHub repository.

String constraint solvers are crucial for reasoning about string-manipulating programs. However, many practical string constraints are undecidable, and real-world applications often present complex constraints that challenge current solvers. The rise of multi-core architectures offers an opportunity for parallel solving. A key parallel solving method is \emph{cube-and-conquer}, in which the quality of splitting heuristics is critical to effectively dividing the search space. Unfortunately, manually designing the heuristics is labor-intensive, and handcrafted heuristics are often sub-optimal. This paper introduces a data-driven approach to automatically generating splitting heuristics. We frame the problem of selecting a splitting atom as a learning task, using features from input formulas and dynamic data from solver execution. We implement this approach in two popular string solvers, Z3seq and Z3str4, demonstrating that the learned heuristics outperform manually designed ones in the number of solved formulas and the average solving time.

AI-generated music detectors can appear robust on standard benchmark splits, yet their deployments require transfer to generator sources absent during training. We study this problem with source-restricted evaluation on \textsc{MoM-open}, an open reconstruction of MoM-CLAM that replaces the non-redistributable real corpus with FMA and MTG-Jamendo while preserving the fake-generator protocol. To isolate the role of representation, we introduce \textsc{CoMoE}, a compact fixed classifier for comparing heterogeneous audio token spaces while keeping the downstream architecture and training recipe unchanged. Experiments show that standard and real-source-restricted splits are nearly saturated, whereas fake-source restriction exposes large differences between token spaces: X-Codec tokens are strongest when training on Udio alone, while MERT-derived tokens are stronger when training on Suno-v3.5 alone. These results suggest that codec-style discrete token spaces should be treated as a primary experimental axis under generator shift in AI-generated music detection. Our code and data are available at https://github.com/MAAP-LAB/CoMoE.

Standard continuous-time generative models rely on monolithic architectures that must navigate vastly different signal regimes, from isotropic noise to intricate data distributions. While scaling model capacity improves performance, deploying a massive network uniformly across the entire generative timeline is inherently inefficient. In this work, we propose Complexity-Balanced Splitting (CBS), a principled framework for temporal capacity allocation that distributes the generative workload across multiple specialized sub-networks. Grounded in function approximation theory and de Boor's equidistribution principle, CBS partitions the diffusion timeline into segments of equal approximation burden, allocating more representational capacity to regions where the generative dynamics are more difficult to model. To estimate this local complexity, we introduce two complementary and tractable monitor functions: a spatial measure based on the flow's Dirichlet energy, and a geometric measure based on the acceleration of the sampling trajectories. Using a lightweight auxiliary model to estimate these complexity profiles, our approach eliminates the need for heuristic temporal splits or computationally expensive search procedures. Extensive evaluation across multiple architectures (SiT, JiT, and UNet) and datasets demonstrates that CBS consistently improves synthesis quality without increasing per-step inference cost. In particular, CBS improves FID by ~35% on SiT-XL with CFG relative to naive temporal partitioning. Project page is available at https://noamissachar.github.io/CBS/.

Sparse Autoencoders (SAEs) are widely used for mechanistic interpretability in large language models, yet their formulation assigns each latent feature a single decoder direction, implicitly assuming features to be one-dimensional. We show that this assumption mismatches with the multi-dimensional structure of model features, provably inducing feature splitting through two distinct mechanisms. Geometrically, reconstructing a feature of intrinsic dimension $d_i \ge 2$ to error $\varepsilon$ with single-direction decoders forces a number of atoms that is exponential in $d_i$. From an end-to-end optimization perspective, this splitting is not merely possible but actively preferred. We prove that there exists a continuous path from the true $d_i$-dimensional basis to a strictly lower risk of the $\ell_1$-regularized SAE objective, whose descent directions drive any trained dictionary into that exponential regime. A single coherent feature is therefore fragmented across many near-collinear latents, producing spurious multiplicity and obscuring the intrinsic geometry. Motivated by this, we introduce Subspace-Aware Sparse Autoencoders (SASA), which replace single-vector decoders with learned decoder subspaces, enforce block sparsity via Top-$s$ group gating, and adapt each group's effective rank with a nuclear-norm regularizer. We then show that once the block size satisfies $r \ge d_i$, a single group not only can represent the entire feature slice but is the global minimizer of the SASA objective. This consolidation yields a sample complexity polynomial in $d_i$ rather than exponential -- a decisive advantage given that every training activation costs an LLM forward pass. Empirically, on GPT-2 and Mistral-7B, SASA reduces feature splitting and absorption, improves monosemanticity and interpretability, and matches or exceeds standard SAEs while training on roughly half the token budget.

Humanoid loco-manipulation requires stable whole-body control under varying object masses and pickup/placement heights. This becomes particularly challenging in sim-to-real transfer, where object-induced load variation and robot-side dynamics mismatch interact during physical contact. Existing history-based adapters often compress these factors into a single latent representation, which can weaken robustness under heavy-load manipulation. We propose \textbf{SplitAdapter: Load-Aware Humanoid Loco-Manipulation via Factorized Adaptation}, which freezes a pretrained box manipulation policy and extends it with object/load and dynamics-aware context encoders trained with split world-model objectives, GRL-based cross-adversarial regularization, and hierarchical Feature-wise Linear Modulation (FiLM). In sim-to-sim experiments and real-world deployment, SplitAdapter improves Full-task success over the base policy and world-model FiLM baselines across object masses of $2$, $4$, and $6$ kg and pickup/placement heights of $0$, $30$, and $60$ cm, with the largest improvements under heavy-load conditions.

Neural field surrogates can accelerate photonic design loops, but a surrogate that looks accurate in global field error can still mis-rank candidate devices when the final decision depends on localized output-port readouts. This risk is acute in propagation-dominated MMI splitters and couplers, where port power, splitting, phase, and coupling are determined by accumulated modal interference and output-window aggregation rather than by average field similarity alone. We study this field-to-design mismatch through a Field/Mediator/Readout view that separates dense complex-field error from propagation-profile and output-window errors before port aggregation. To align the surrogate with this chain, we propose PaNO, a propagation-aligned neural operator that keeps the full-field prediction interface while organizing latent states around local boundary structure, transverse modal content, axial propagation, and cross-mode interaction. We also evaluate PaNO-R2, an output-aware feedback variant for residual field components near the port region. On a 15-wavelength tunable $3{\times}3$ MMI benchmark with 4608 held-out fields, PaNO lowers NeurOLight's port-power error from 0.2018 to 0.0739 despite slightly higher cMAE, showing that global field accuracy alone is not sufficient for design-relevant readout fidelity. PaNO-R2 attains the best cMAE, propagation-profile error, output-profile error, and port-power error, reducing NeurOLight's port-power and output-profile errors by 72.7% and 72.5%.

Instruction tuning aligns large language models, including multimodal ones, with diverse user intents, but scaling to heterogeneous mixtures is hindered by gradient interference and bandwidth-heavy synchronization. We ask whether these two bottlenecks can be addressed jointly by training parts of the mixture independently and reconciling them once in parameter space. We develop a local quadratic theory inside a shared flat basin that yields three results: weight merging produces a curvature-weighted variance reduction; PCA-aligned conflict splitting maximizes this gain along high-curvature directions; and merging additionally acts as spectral filtering with implicit norm regularization. These results directly motivate MERIT, a decentralized merge-ready instruction-tuning pipeline that estimates dataset-level gradient conflicts, partitions the mixture along the top PCA conflict axes, fine-tunes each partition independently with no inter-partition communication, and merges once via token-weighted averaging. On Qwen2.5-VL-3B with 136 Vision-FLAN tasks, MERIT improves the 8-benchmark average from 54.3 (joint training) to 57.0. The same recipe scales to a 7B model on a 1.6M-example, 176-source mixture -- matching or exceeding centralized joint training with minimal cost overhead -- and transfers to text-only FLAN. Our code is available at https://github.com/naver-ai/merit.

Federated Learning (FL) combined with Split Learning (SL) is a privacy preserving paradigm that enables training deep neural networks (DNNs) on resource constrained devices while reducing overall training cost. However, determining the optimal split point, meaning the layer where the model is divided still remains a critical challenge, especially when clients have heterogeneous hardware capabilities. Fixed split points can overload weak devices and increase the communication and server load, which slows convergence and reduces stability. This paper introduces QSplitFL, a novel capability-aware Deep Q-Network (DQN) framework for optimal split point selection in Split learning based Federated Learning (SFL) environments. Unlike existing approaches that rely on high-dimensional model weight representations, QSplitFL employs a lightweight state representation derived directly from client hardware metrics, including CPU utilization, memory, battery level, and network latency. The proposed framework incorporates a decayed loss-drop reward function that prioritizes early convergence, and a committee-based DQN architecture with majority voting to mitigate reward hacking. Extensive experiments on MNIST, Fashion-MNIST, CIFAR-10, and CIFAR-100 datasets using CNN, ResNet50, MobileNetV4, and ConvNeXt architectures demonstrate that our approach achieves better convergence and higher accuracy compared to existing methods, while effectively adapting to heterogeneous device resources. The source code is publicly available at https://github.com/AIPO-Lab/QSplitFL.

Bagging-based ensembles, most notably Adaptive Random Forests, are among the strongest performers for learning from data streams. A common denominator across these methods is their reliance on Hoeffding Trees as base learners, which grow decision trees incrementally by testing whether a candidate split is significantly better than its alternatives using concentration inequalities. Despite their empirical success, existing variants lack valid statistical guarantees. Current analyses rely on fixed-sample concentration bounds, while split decisions are made using data-dependent stopping rules, which invalidates their guarantees and can drive the probabilty of incorrect splits to one. We introduce a principled alternative based on anytime-valid inference. Our method provides: (i) anytime-valid control of false splits under arbitrary data streams, including non-stationary settings; (ii) finite commitment time under a predictive advantage; and (iii) under stationary i.i.d. data, risk is monotone decreasing and strictly improves at every split. Empirically, we evaluate both standalone trees and their use within Adaptive Random Forests on non-stationary streams. Our method improves performance while producing substantially smaller trees.

Conformal prediction methods enjoy strong theoretical and empirical predictive inference performance, provided the data is exchangeable and is treated symmetrically during training. However, these assumptions are impractical in many settings, such as time series, where temporal dependence violates exchangeability and it is preferable to use predictors that leverage dependence by treating data asymmetrically. Recent work shows that split conformal prediction is robust to these issues, but sample splitting can reduce accuracy, motivating the study of methods that do not rely on data splitting in the time series setting. In this work, we show that the vanilla leave-one-out jackknife can suffer arbitrary loss of coverage even in canonical time series models with mild temporal dependence. As a remedy, we propose a modification tailored to such settings, which we term the leave-a-window-out (LWO) method, and show that it can achieve valid coverage provided that the model-fitting procedure satisfies mild stability properties. Our proofs are based on quantifying the degree to which the data departs from cyclic exchangeability, which we introduce new coefficients to measure. Experiments on time series demonstrate that our method often enjoys valid coverage when the vanilla jackknife fails to cover, while producing much narrower intervals than split conformal prediction.

Federated learning enables collaborative model training without sharing raw data, but its performance can degrade substantially under heterogeneous client data distributions. A single global model often cannot satisfy diverse client requirements, so personalized federated learning has therefore been explored to improve client specific performance while preserving global generalization. Existing PFL methods often face a fundamental tradeoff in which stronger global sharing can undermine local specialization, whereas stronger local adaptation can lead to overfitting under limited data, label imbalance, and missing class scenarios. In this work, we propose PGFedSplit, a personalized federated learning framework that improves both personalization and global generalization under severe client heterogeneity. PGFedSplit adopts a split architecture and performs adaptive aggregation scheduling tailored to the roles of different model components, enabling stable knowledge sharing while maintaining client specific adaptation. Each client further leverages a mixture of locally extracted representations and synthetic representations generated from server side Gaussian statistics, improving robustness under label imbalance and missing class conditions. Extensive experiments on Fashion MNIST, CIFAR 10, CIFAR 100, and Tiny ImageNet demonstrate consistent improvements over state of the art PFL methods, with stable convergence and superior personalization in highly heterogeneous settings.

Large-batch Contrastive Learning (CL), the foundation of modern representation learning, is fundamentally incompatible with the volatile resource constraints of edge devices. This conflict creates a dilemma: small on-device batches degrade model fidelity, while offloading to the cloud incurs unacceptable latency and bandwidth costs. Existing solutions often resort to static model compression, which fails to adapt to the runtime volatility of edge environments. To bridge this gap, we present StreamSplit, a novel framework that makes streaming CL practical across heterogeneous ARM client platforms. StreamSplit resolves the conflict between the continuous nature of ambient audio and the discrete batch requirements of models like CLAP and COLA. We introduce: (1) A distribution-based streaming framework that decouples representation quality from local batch size, using a tractable Hybrid Loss to maintain fidelity despite sparse updates; and (2) An Uncertainty-Guided Adaptive Splitter that uses a lightweight Reinforcement Learning (RL) policy to dynamically partition computation. Uniquely, this policy integrates real-time resource monitoring with embedding ambiguity to optimize the accuracy-latency trade-off on the fly. We evaluate StreamSplit on diverse hardware, from the resource-constrained Raspberry Pi 4 to the high-performance Apple M2. Results demonstrate that StreamSplit reduces per-sample latency by up to 4.7x and cuts bandwidth by 77.1% and energy by 52.3% compared to server-centric baselines. Crucially, it maintains accuracy within 2.2% of server-centric models, proving that adaptive, distributed learning is a viable path for the modern edge ecosystem.

3D Gaussian Splatting (3DGS) provides an efficient method for high-quality scene reconstruction using anisotropic Gaussians. Recently, 3DGS-based methods have significantly improved the rendering quality of human avatars while enabling real-time performance. However, existing methods suffer from a magnitude mismatch in the number of Gaussians generated by image-based and 3DMM-based approaches. This discrepancy results in reconstructed expressions that lack fine-grained detail. In this paper, we introduce a novel method for reconstructing an animatable head avatar from a single image. We propose a Graph splitting network to progressively generate Gaussians from coarse to fine using an autoregressive architecture. To address the graph inconsistency caused by split Gaussians, we employ a mesh topology extension method to align the GNN's connectivity with the increased Gaussian count. Furthermore, we introduce a novel density control method that includes a gating mechanism that generates soft masks for Gaussians, preventing over-densification after the splitting operation. This allows for dynamic control over Gaussian density across different facial regions. For smooth and rapid training, we employ a delayed filtering strategy to avoid re-computing the graph topology during training. Experimental results demonstrate that our autoregressive structure effectively improves expression representation ability by progressively splitting Gaussians. This process, enabled by the GNN-guided splitting, synthesizes more precise facial details and achieves higher reconstruction quality.

Dimensionality Reduction (DR) methods are widely used to visualize high-dimensional data. One key task in DR-based analysis is discovering neighborhoods, which relies on analyzing the fine-grained local structure of a projection. However, DR is an inherently lossy process; no technique can perfectly preserve the high-dimensional relationships, and projections therefore contain visual artifacts. In this paper, we highlight a typically overlooked source of visual artifacts: ambiguous instances. These are instances that are highly similar to multiple mutually dissimilar neighborhoods in the high-dimensional space. Standard DR methods cannot faithfully project such instances, since each data instance is mapped to a single point in the visual space. As a result, such an instance is placed in only one of its neighborhoods (or in none at all), so only part of its neighborhood structure is represented. We call this distortion partial neighborhood embedding. In this paper, we introduce a graph-based approach that identifies ambiguous instances and replicates them as multiple points in the projection, placing each copy within its respective neighborhood. We use UMAP for our results, but our approach also generalizes to other local graph-based DR techniques, and we show that our approach reveals previously hidden neighborhood memberships in projections and reduces partial neighborhood embedding across multiple examples, and is further supported by quantitative analyses.

Learning high-quality oblique decision trees remains a significant challenge due to the discrete and non-convex nature of split optimization. We present the Hinge Regression Tree (HRT) framework, which reframes each oblique split as a nonlinear least-squares problem over two linear predictors whose max/min envelope induces ReLU-like representation capacity. We show that the resulting node-level optimization can be interpreted as a damped Newton method, and we establish the monotonic decrease of the node objective for its backtracking line-search variant. We establish, theoretically, that HRT is a universal approximator with an explicit $O(δ^2)$ approximation rate. Building upon this base learner, we propose HRT-Boost, a mathematically synergistic ensemble extension that couples node-level Newton updates with stage-wise functional gradient descent. We show that this ensemble construction admits a stage-wise empirical risk reduction guarantee under the squared loss. Empirical evaluations on synthetic and real-world benchmarks show that HRT is highly competitive with established single-tree baselines, and HRT-Boost compares favorably with strong ensemble baselines and often yields substantially more compact models. The code is publicly available at https://github.com/Hongyi-Li-sz/HRT-Boost.

The deployment of large language models (LLMs) on resource-constrained devices remains challenging, spurring interest in split inference, where models are partitioned between client and server to reduce computational burden and enhance privacy by transmitting only intermediate activations. However, the privacy-preserving capabilities of split inference, particularly in the context of LLMs, have not been exhaustively investigated. To fill this gap, we introduce ActInv, which solves an intermediate activation matching problem to reconstruct the client's input. Extensive evaluations demonstrate that ActInv achieves high-fidelity reconstructions, even in the presence of common perturbation-based defenses such as Gaussian noise injection and activation sparsification. To systematically understand this vulnerability, we develop Perturbation Amplification Factor (PAF), a metric for quantifying a layer's inherent resistance to reconstruction. Our analysis reveals that privacy vulnerability is not uniform across layers, with some layers being highly susceptible to leakage while others offer natural resistance. Furthermore, we demonstrate that defense effectiveness can be significantly improved by calibrating perturbation directions to maximize reconstruction error during backpropagation. Building on these insights, we design PriPert and conduct comprehensive evaluations, covering privacy, utility, and computational overhead, to demonstrate its effectiveness.

Decision trees assign identical confidence to instances near and far from each split threshold. We introduce ternary decision trees, which augment each split node with an uncertainty zone of half-width delta. A decision-theoretic framework characterises the optimal zone width delta* as the solution to a node-local cost-minimisation problem; four formal properties are established: accuracy decomposition, a sufficiency condition for decided accuracy improvement, an exact efficiency characterisation (eta = Dec-Acc minus Acc_u, the accuracy gap between decided and boundary-uncertain predictions), and asymptotic consistency of the margin method. Instances within the zone receive predictions by weighted blending of both child subtrees and are flagged as boundary-uncertain. We propose and evaluate five delta-estimation methods: quality-plateau (plateau width of the split criterion curve), class-overlap (empirical class-distribution overlap), gain-ratio (split quality relative to split entropy), node-bootstrap (threshold variance under node-level resampling), and margin (SVM-inspired distance to the nearest cross-class training example). All methods reuse statistics already computed during standard CART split finding, requiring no external noise specification. Evaluated across 71 of the 72 OpenML-CC18 datasets with 5-fold cross-validation, all five methods with probabilistic routing significantly outperform standard CART on decided accuracy (Wilcoxon signed-rank, p < 0.001). The margin method achieves the best efficiency (0.104 accuracy gain per unit flagging rate), wins on 42 of 72 datasets, and requires zero hyperparameters. Analysis on Breiman synthetic benchmarks confirms margin is self-calibrating on clean data. On mammography, node-bootstrap achieves +0.71% decided accuracy by flagging 10.8% of cases as boundary-uncertain.

We introduce Tokenization with Split Trees (ToaST), a subword tokenization method that directly optimizes compression under a new recursive inference procedure. ToaST greedily splits each pretoken into a full binary tree using precomputed byte n-gram counts, independent of any vocabulary. Given a vocabulary, inference recursively descends each split tree and emits the first in-vocabulary node reached on each path. Vocabulary selection is formulated as an Integer Program (IP) that minimizes the total token count over all split trees under this inference procedure. The Linear Programming (LP) relaxation is near-integral in practice, yielding provably near-optimal vocabularies, with training time empirically scaling quadratically in the number of split trees. On English text, ToaST reduces token counts by more than 11% compared to BPE, WordPiece, and UnigramLM at vocabulary sizes of 40,960 and above, reducing the number of inference tokens for models using this tokenizer, thus extending the effective context length. ToaST also uses common single-byte tokens less frequently than these baselines, leading to a substantial improvement in Renyi efficiency. In experiments training 1.5B parameter language models, ToaST achieves the highest CORE score, outperforming baselines by 2.6%--7.6%, with significance for two of three, and scoring best on 13 of 22 individual tasks.

Large models have delivered remarkable performance across a wide range of perception and generation tasks, yet practical deployment is increasingly constrained by computational and memory budgets, as well as privacy requirements. Split execution alleviates these constraints by partitioning computation across devices, but it inevitably introduces intensive transmission and storage of intermediate features. Unlike conventional feature coding for CNNs that typically targets homogeneous spatial activation maps, modern large models generate heterogeneous features with varying statistical distributions and compression tolerances, e.g., multi-level/multi-modal representations and autoregressive context caches. These characteristics necessitate treating large model feature coding (LaMoFC) as a fundamental system component and call for a systematic evaluation framework. In this paper, we present a comprehensive benchmark and evaluation framework for LaMoFC. We first build the feature dataset LaMoFCBench, covering diverse task requirements across 4 categories and 16 scenarios while integrating widelyadopted architectures and various split-computing settings. We then specify representative split points according to practical application scenarios to extract intermediate features, establishing a unified pipeline for fair and reproducible comparisons. Finally, we benchmark mainstream universal feature codecs, exposing the profound misalignment between existing coding paradigms and the heterogeneous nature of large model features. These findings reveal that LaMoFC demands a fundamental departure from existing paradigms, and LaMoFCBench provides the shared empirical foundation to drive this transition. The data and code will be available at https://github.com/lartpang/LaMoFCBench.

Low-bit post-training quantization (PTQ) is a pivotal technique for deploying Vision-Language Models (VLMs) on resource-constrained devices. However, existing PTQ methods often degrade VLMs' accuracy due to the heterogeneous activation distributions of text and vision modalities during quantization. We find that this cross-modal heterogeneity is distributed unevenly across channels: a small subset of channels contains most modality-specific outliers, and these outliers typically reside in different channels for each modality. Motivated by this, we propose SplitQ, a channel-Splitting-driven post-training Quantization framework. At its core, SplitQ introduces a novel Modality-specific Outlier Channel Decoupling (MOCD) module that effectively isolates salient modality-specific outlier channels with minimal overhead. To further address the remaining cross-modal distribution discrepancies, we design an Adaptive Cross-Modal Calibration (ACC) module that employs dual lightweight learnable branches to dynamically mitigate modality-induced quantization errors. Extensive experiments on popular VLMs demonstrate that SplitQ significantly outperforms existing approaches across 6 popular multi-modal datasets under all evaluated quantization settings, including W4A8, W4A4, W3A3, and W3A2. Notably, SplitQ preserves 93.5% of FP16 performance under the challenging W3A3 setting (69.5 vs. 74.3), pushing the efficiency frontier for deploying advanced VLMs. Our code is available at https://github.com/EMVision-NK/SplitQ

We address the open problem of training hypernetworks for Controllable Pareto Front Learning (CPFL) under split feasibility conditions with rigorous theoretical guarantees. We reformulate the constrained Pareto problem as a Bi-Level Scalarized Split Problem (BSSP) and propose the Adaptive Balanced Penalty (ABP) algorithm, whose three gradient components -- optimality, set feasibility, and image feasibility -- are blended through an adaptive indicator driven by a computable lower bound. Using a novel convex surrogate technique, we prove full-sequence convergence under standard convexity and Robbins-Monro step-size assumptions. The ABP penalty structure is then translated into a two-phase, feasibility-first training strategy for Hyper-MLP and HyperTrans architectures (ABP-HyperNet). To evaluate constrained CPFL, we introduce the Expected Feasible Hypervolume (EFHV), which jointly captures solution quality and constraint satisfaction. Experiments on five multi-objective benchmarks validate the ABP solver against ground truth, while three multi-task learning datasets demonstrate that ABP-HyperNet achieves up to 2.3x higher EFHV than unconstrained baselines by raising feasibility from 36-49% to 87-100%.