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arXiv

Neural Message Passing on Structural Interaction Graphs for Fully-Inductive Graph Neural Networks

Omer Yom-Tov, Avigdor Gal

A central obstacle in building graph foundation models is the input heterogeneity in terms of feature space dimensionality, semantics, and structure. Such heterogeneity limits the capability of graph neural networks to generalize to new graphs with unseen feature spaces. We address the transferability challenge with SIGIL, a framework that maps any attributed graph to a unified representation space of fixed dimension. Given a graph, SIGIL lifts it to a structural interaction graph, where nodes are the input feature dimensions and weighted, typed edges encode feature alignment across multiple orders of the graph's connectivity. A relational message-passing network embeds each feature dimension into a shared space, transforming the original node features, of arbitrary dimensionality, into representations transferable to any downstream graph. By construction, SIGIL is equivariant to permutations of nodes, feature dimensions, and labels. Additionally, when the input features are one-hot indicators of discrete relations, SIGIL recovers and strictly generalizes existing foundation models for knowledge graph reasoning. A single SIGIL model, pretrained on one graph, delivers strong fully-inductive link prediction. Also, SIGIL can be used to implement existing knowledge graph foundation models. As such, SIGIL unifies several existing regimes in graph foundation model design under a single framework

arXiv

Aftab: A Comprehensive Benchmark of CNN Encoders and Advanced Value Functions in Parallelized Q-Networks

Taha Shieenavaz, Shabnam Zareshahraki, Loris Nanni

Recent advancements in deep reinforcement learning have increasingly favored simplified, highly parallelized paradigms. Notably, the Parallelized Q-Network (PQN) algorithm enables off-policy value learning without relying on experience replay buffers or target networks. However, the representational capacity and computational efficiency of visual encoders operating in these buffer-free settings remain comparatively underexplored. In this work, we systematically investigate the architectural design space of Convolutional Neural Networks within PQN. We evaluate eight distinct CNN topologies while explicitly characterizing their parameter and computational requirements. We further study the effect of multiplicative representation learning and advanced value estimation by integrating the Hadamax encoding paradigm with categorical, ensemble, and dueling value heads. Extensive experiments on Atari-57 show that our final composite architecture, Aftab, achieves an Interquartile Mean (IQM) Human-Normalized Score of 6.592, compared with 2.715 for the standard PQN baseline, together with a 0.86 Probability of Improvement over PQN. We additionally evaluate Aftab on Procgen-Hard to assess performance under procedurally varying visual environments. Aftab achieves a normalized learning-curve Area Under the Curve (nAUC) of 0.541 compared with 0.216 for PQN. Overall, the results demonstrate that carefully designed encoder topology, multiplicative feature interactions, and advanced value-estimation heads can substantially improve performance within a parallelized, replay-free Q-learning framework while preserving its memory-efficient training paradigm. The complete Aftab framework, including model definitions, training configurations, reproducibility settings, and raw experimental logs, is open-sourced at https://github.com/tahashieenavaz/aftab

arXiv

Short-term load forecasting under EU-AI Act Requirements in Safety-Critical Environments: Results from a 41-day live challenge on the aggregated German transmission-grid load

Thomas Bartz-Beielstein, Inalbek Akiev, Lalo Mohamad

Short-term load forecasting (STLF) plays a vital role in the electric power industry. It is relevant for critical infrastructure. STLF is no longer purely a performance and accuracy problem, because determinism, fail-safe handling, minimal-attack surface, and no dead code are software-engineering requirements rather than optional extras. This report describes results from a 41-day live challenge that evaluated an STLF pipeline for the aggregated German transmission-grid load. The STLF pipeline predicts the 24 hourly load values of a target day from European Network of Transmission System Operators for Electricity (ENTSO-E) data. It is based on the open-source Python library spotforecast2-safe, which tries to implement the EU-AI Act Requirements in Safety-Critical Environments by design. The STLF pipeline includes gap- and anomaly-aware data preprocessing, calendar and weather covariates, and a forecasting algorithm. Forecast quality is compared to the official ENTSO-E day-ahead forecast. The spotforecast2-safe pipeline beats the ENTSO-E baseline. In-context models show competitive performance. Transparent, deterministic, low-cost, and auditable local models (referred to as macl2l in this report) are competitive with more than 100-million-parameter large, energy-intensive pre-trained foundation models such as chronos-2. The challenge implementation, the submission history of all teams, and the archived leaderboard are publicly available.

arXiv

Surrogate Substitution Preserves PHI Detectability: A Multi-Detector Equivalence Study

Qiming Bao, Sherry J. H. Feng, Kim Chester Eugenio, Meng Fon

Structure-preserving de-identification replaces protected health information (PHI) with realistic same-type surrogates -- "Anna S." becomes "Maria S.", not [NAME] -- so that clinical text stays fluent and downstream tools keep working. But this only helps if the substitution does not itself corrupt the signal those tools rely on. We ask a narrow, testable question: on the spans a de-identifier actually masks, can downstream PHI detectors still find the surrogate? We introduce a paired, multi-detector evaluation protocol that (i) scores utility only on masked spans, decoupling coverage from utility; (ii) uses equivalence testing (TOST) rather than null-hypothesis significance testing, which is uninformative at our sample size (57k paired spans); and (iii) builds a surrogate-failure typology separating fixable generator defects from intrinsic detector limits. Across 11 detectors, 7 benchmarks, and 7 languages (1,750 documents), recall on masked spans moves from 76.1% to 74.9% -- a change our equivalence test shows is statistically equivalent to zero within a +/-2-point margin (p ~ 3e-9), with detector ranking preserved. The residual loss does not reflect detectors getting worse at PHI: it concentrates in malformed and out-of-distribution surrogates (truncation Chicago -> Illino, salience loss Cedars-Sinai -> Vidant). A redaction floor and an open-source surrogate baseline indicate the effect is a property of well-formed substitution, not of one tool. We release the evaluation subsets, scoring code, and an interactive dashboard at https://custodianai.pages.dev so the protocol can audit any structure-preserving transform.

arXiv

Pseudorandom Streams within Diffusion Models Act as Learnable Inputs That Affect Generation Quality

Shengzhi Deng, Chenqi Ye, Yanze Guo

Digital learning systems consume concrete pseudorandom values rather than abstract random variables. These values enter the realized loss and its gradient during training. If a pseudorandom stream contains structure that is accessible to the model, this structure can therefore become part of what the learning system learns. We show that this effect can be strong enough to change generation quality in diffusion models. For diffusion noise prediction, there are two related routes by which the loss can be reduced. The model can learn regularities of the clean data and use them to infer the added noise. It can also exploit regularities of the noise source itself to recover the realized noise from the noisy input. Random-role ablation shows that the dominant source-dependent effect in our experiments is associated with the diffusion-noise roles. A diffusion probe that removes reusable real-image structure still shows clear source-dependent noise-prediction learning, and its source ordering closely matches that of real-data diffusion training. Different pseudorandom sources also produce large differences in generation quality on MNIST and CIFAR-10. Further experiments show that the same source structure can also be learned in an independent next-value prediction task, although this is not the learning mechanism used by the diffusion model. Changing the probe clean reference preserves much of the source ordering while changing the numerical response, producing clean-reference-dependent power-law relations. Overall, the results show that a pseudorandom stream is not only a source of stochastic variation: its concrete structure can act as a learnable input whose effect depends on the learning system.

arXiv

Beckmann Transport Models: From Autonomous Flows to One-Step Maps

Lee Cheuk Kit, Florentin Coeurdoux, Yuyuan Chen, Sophia Tang, Peter Potaptchik, Yilun Du, Michael Samuel Albergo, Eric Vanden-Eijnden

We propose an instantiation of flow matching that relies on a time-independent velocity field (an \emph{autonomous flow}) to exactly map between two distributions, so long as the target is singular, i.e.\ supported on a lower-dimensional data manifold. We also show that the one-step generative map associated with this flow is the unique solution of a simple conservation equation, which can be used to learn the map directly from samples. These autonomous flows and maps give a dynamical meaning to the flux constraint of Beckmann's transportation problem. Their construction provides a unifying framework that recovers, for instance, the closed-form Poisson-flow generative model and equilibrium matching with a quadratic flow-matching regression loss. We illustrate how this theory corrects inconsistencies in existing methods and demonstrate the effectiveness of the autonomous flow and the one-step map on ImageNet 256x256.

arXiv

Thermalizing Stochastic Programs

Mirko Amico, Andraž Jelinčič, Colin Oscar Nancarrow, Leo Tyrpak, David Roberts, Seth Morton, Dalton Sakthivadivel, Ashwin Gopal, Guillaume Verdon

We present a set of tools for mapping general stochastic programs to thermodynamic hardware designed for energy-efficient stochastic sampling. Given a target stochastic program expressed as a Directed Factor Graph (DFG) of stochastic channels, or equivalently as a Parametrized Stochastic Circuit (PSC), we first introduce a method to approximately compile each factor in the DFG to an Energy-Based Model (EBM) that is native to the hardware. We then analyze how the error of the compiled DFG accumulates from the per-factor errors, and introduce two training refinements, context matching and trajectory-level REINFORCE post-training, which can reduce the residual error left by training each factor in isolation. The \texttt{thermalizers} framework takes a stochastic program expressed in the \texttt{torx} library and replaces its factors with thermodynamic kernels implemented and sampled using the \texttt{thrml} library. We demonstrate it on several example applications, including a market simulator that learns the joint day-to-day dynamics of a panel of financial time series from recorded market history alone, a probabilistic model from mathematical ecology, Gibbs sampling of an EBM the hardware cannot natively express, and a sequential Bayesian design loop over a Gaussian stochastic circuit.

arXiv

Round-Trip Consistency: Bidirectional Diffusion Models Can Predict Their Own Rollout Errors

Alexander Scheinker

Autoregressive models accumulate error over long rollouts, yet at deployment there is no ground truth to measure it against. We train a single conditional latent diffusion model that steps a dynamical system forward or backward in time via a direction flag, and show that this bidirectionality supplies a measurement-free test-time error signal: rolling forward $i$ steps and then backward $i$ steps must return the model to its start, so the round-trip discrepancy $\mathcal{C}_i$ is a self-supervised proxy for the unobservable rollout error: no ensembles, no held-out data, no governing equations, for one extra rollout. We validate on compressible magnetohydrodynamics (MHD), an astrophysical turbulent radiative mixing layer, and natural face videos (CelebV-HQ). On held-out MHD trajectories, $\mathcal{C}_i$ ranks rollout error (Spearman $0.91$-$0.98$ at fixed depth; $0.69 \pm 0.16$ within trajectories), and a simple calibrator fit on training rollouts predicts its magnitude to within $1.14\times$ ($68\%$) and $1.29\times$ ($95\%$) with near-nominal coverage - one nat beyond a depth-only predictor, transferring to all six decoded physical fields. The same signal flags the out-of-distribution Orszag-Tang vortex (AUROC $0.98$; $1.0$ by depth $10$) exactly where sampling-dispersion baselines invert, and it cuts incurred error by $15\%$ at $80\%$ coverage - three times the depth-only baseline. Bidirectional training comes at negative cost, beating direction specialists in both directions, and the backward direction doubles as a fast inverse solver. On LE-PDE-UQ's turbulent Navier-Stokes benchmark, a single bidirectional model reaches accuracy within $1.3\times$ of their ten-model ensemble at a tenth of the training cost, with the best training-free pixel-level calibration. Round-trip consistency turns reversibility into a practical trust signal for generative models.

arXiv

LOCUS-DT: Localization via Observation-Conditioned Uncertainty Scoring with Digital Twins

Haozhe Lei, Roberto Bomfin, Marwa Chafii, Sundeep Rangan

Accurate indoor localization is essential for emerging applications in robotic navigation and search and rescue. While classical methods typically focus on single-point estimates, complex indoor environments with heavy blockage and multipath propagation often lead to multimodal likelihood surfaces where a single estimate is insufficient. This paper proposes LOCUS-DT (Localization via Observation-Conditioned Uncertainty Scoring with Digital Twins), a framework that treats snapshot localization as posterior inference over the transmitter location. By leveraging a ray-tracing-based digital twin (DT) of the known environment, LOCUS-DT generates synthetic multipath profiles for candidate locations and compares them against the measured channel profile. Central to our approach is a novel learned scoring function designed to compare a fixed number of dominant specular paths, providing robustness against errors in both the DT environment model and the physical channel estimation. Importantly, LOCUS-DT is trained over an ensemble of environments to ensure generalization to unseen layouts. We evaluate the system using a Sionna-based ray-tracing backend, demonstrating that LOCUS-DT captures the sharp, multimodal posterior structures inherent in indoor settings more accurately than standard Gaussian or Gaussian-mixture benchmarks.

arXiv

The Noise Premium in Adversarial Training for Kernel Regression

Yiling Xie, Xiaoming Huo

Adversarial training can improve the robustness of predictive models to bounded perturbations, often at the cost of statistical efficiency. We study this trade-off in kernel regression over a reproducing kernel Hilbert space (RKHS). It is shown that, under squared loss, adversarial training in RKHS introduces a term involving the product of the function norm with the mean absolute value of the response noise, which we call the \textit{noise premium}. Our analysis shows that the noise premium makes the prediction error of adversarial training converge strictly more slowly than the nonparametric minimax benchmark even after balancing approximation and estimation errors. Moreover, for a fixed perturbation budget, once the budget exceeds a certain threshold, the solution to adversarial training collapses to the zero function. To mitigate these effects of the noise premium, we propose noise-debiased adversarial training. The resulting noise-debiased estimator can attain the minimax optimal rate up to a logarithmic factor for the prediction error, raises the collapse threshold, and admits an explicit bound on the increase in adversarial loss. Numerical experiments on synthetic and real data support the theoretical findings and validate the effectiveness of the proposed noise-debiased method.

arXiv

Wrong Design Intent Is Worse Than Never Conditioning: A Derangement-Control Diagnosis of Header Conditioning in CAD Program Completion

Yang Xiao

Fine-tuned code LLMs are routinely conditioned on a design-intent specification, but the correctness axis of such a signal -- a wrong intent rather than an absent one -- has not been tested, and the benefit of conditioning is usually scored with the same detector that defines the signal. We study CADCON, a five-feature design-intent header prepended to CadQuery-style programs during LoRA fine-tuning of Qwen2.5-Coder-1.5B, scoring adherence with executable geometric assertions that share no code with the header-defining extractor. On a pre-registered sample of 400 deduplicated held-out programs stratified over eleven intent profiles, at 40% prefix and three seeds, a semantically wrong header degrades adherence below the never-header-trained baseline on 3/3 seeds under both tokenizations at the program level, and on 3/3 token and 2/3 text seeds at the 298 distinct model inputs they present. Wrong-header executability is not depressed relative to that baseline. A derangement control, retrained so every program receives another program's header -- holding the header marginal fixed while destroying its correlation with the program -- saw the same programs, indices and wrong headers. Its correct-to-wrong change is -0.006/+0.016/-0.003 against 0.124/0.241/0.230 for the standard model, and the interaction is significant on 3/3 seeds (p <= 5.9e-7), so the model's sensitivity to whether the header is right or wrong requires the learned mapping. The control sits below the baseline by the same margin under a correct as under a wrong header, so we claim that sensitivity and not the below-baseline level. On features the true intent lacks, the standard model realizes a feature far more often when the wrong header names it; the control does not. Ground truth itself scores only 0.567 here, the scale on which arm levels should be read. Wrong design intent is not inert: it actively misdirects generation.

arXiv

Where Should Optimizer State Live? Tiered State Allocation for Memory-Efficient Mixture-of-Experts Training

Nuemaan Malik

Optimizer state is the largest single line item in the memory budget of mixture-of-experts (MoE) training. On a 6.78B-parameter MoE language model AdamW keeps 50.6 GB of first and second moments to update 12.6 GB of bfloat16 weights. We study SkewAdam, an optimizer built on the observation that the three parameter populations of an MoE differ enough in size and gradient statistics that they should not receive the same state. Those populations are the dense backbone, the experts and the router. SkewAdam keeps float32 momentum plus a factored second moment for the backbone (5% of parameters), a factored second moment alone for the experts (95%) and an exact second moment for the router (<0.01%). The resulting state occupies 1.29 GB or 2.6% of AdamW's and peak training memory falls from 81.4 GB to 31.3 GB, within the budget of a 40 GB accelerator. In a controlled comparison from identical initializations over 82M tokens, SkewAdam reaches validation perplexity 108.4, ahead of AdamW (126.8), Muon (120.2) and Lion (393.7), and settles router load balance to within 1% of its uniform floor. The allocation is not what earns that perplexity. A tier ablation reaches the same value while carrying twenty times the state, so the tiers buy memory rather than accuracy. Same-platform runs separate what does earn it. Removing momentum costs 31 perplexity points (tuned Adafactor, 139.7) and replacing the factored second moment and its update clipping with a full second moment costs 10 (tuned AdamW, 118.5), so neither tuned baseline reaches the untuned tiered policy. Where optimizer state lives, these results suggest, matters at least as much as how much of it there is.

arXiv

Scaling Time Series Classification via XAI-Driven Data Reduction

Davide Italo Serramazza, Thach Le Nguyen, Georgiana Ifrim

Explainable AI (XAI) for time series has seen significant algorithmic growth, but its utility in providing measurable performance gains for downstream tasks remains under-explored. This paper bridges this gap by introducing drXAI, a novel methodology that repurposes XAI attribution methods for effective data reduction in Time Series Classification (TSC). The core challenge in modern TSC is scalability; state-of-the-art models, such as Transformers, exhibit quadratic complexity relative to sequence length and linear complexity relative to the number of channels. This renders them computationally prohibitive for massive datasets. drXAI addresses this by using a fast, GPU-accelerated classifier (Hydra) to generate local attributions. We aggregate these into global feature importance scores and employ an automated elbow-cut heuristic to select the most salient features without requiring manual thresholds. We evaluate our approach on both synthetic and real-world univariate and multivariate datasets. On synthetic benchmarks, drXAI successfully recovers ground-truth features where traditional baselines fail. On real-world data, drXAI achieves between 80% and 90% data reduction while maintaining classification accuracy comparable to models trained on the full dataset. Most importantly, we show that drXAI allows resource-intensive models like ConvTran to scale to datasets that were previously inaccessible due to memory constraints. Our results show the benefits of using XAI not just for interpretability, but as a robust tool for feature selection and scalability in time series analysis. All our code and data are openly available.

arXiv

Infrared Organization and Critical Cognitive Field Formation in Transformer Dynamics

Byung Gyu Chae

Large language models exhibit remarkable emergent behaviors, yet the physical mechanism governing their collective dynamics remains poorly understood. Cognitive Field Theory predicts that learning reorganizes the collective relaxation spectrum, thereby modifying memory self-energy, long-memory dynamics, and collective susceptibility through the infrared organization of slow relaxation modes. Here we test this framework directly in Transformer dynamics. Using publicly available Pythia language models, we extract relaxation spectra from layer Jacobians throughout training, prompt ensembles, network depth, and model scale, allowing the collective observables of Cognitive Field Theory to be measured quantitatively. The measurements reveal pronounced infrared reorganization of the relaxation spectrum. Learning substantially redistributes spectral weight while preserving a nearly flat but weakly infrared-enhanced time-scale density of states, \( ρ(λ)\simλ^β, \qquad β\simeq-0.1, \) with a corresponding memory kernel exhibiting robust long-memory scaling close to \( K(t)\sim\frac{1}{t}. \) The collective observables further reveal a critical formation process: the memory self-energy reaches a transient maximum during early training before relaxing toward a metastable near-critical regime. Prompt-resolved and token-subspace measurements show that distinct local Jacobians recover a common macroscopic TDOS with shared infrared scaling, consistent with infrared fixed-point organization under coarse graining. The reproducibility of this infrared organization across training, prompt ensembles, network depth, and Transformer model scales supports infrared slow-mode organization as a robust collective principle of Transformer dynamics, providing a quantitative experimental realization of the collective observables predicted by Cognitive Field Theory.

arXiv

Vanilla SGD with Momentum Survives Heavy-Tailed Noise: Convergence Analysis without Gradient Clipping or Normalization

Ryusei Yamada, Naoki Sato, Hideaki Iiduka

Stochastic gradient descent (SGD) is a cornerstone of modern optimization. While its performance under heavy-tailed noise is often addressed through specialized modifications such as gradient clipping or normalization, we investigate a more fundamental question: how does vanilla SGD, particularly with momentum, perform in the presence of heavy-tailed noise? In this paper, we refine existing convergence results for vanilla SGD and, more importantly, provide the first comprehensive convergence analysis of vanilla SGD with momentum for strongly convex, convex, and nonconvex objectives, without employing any gradient control mechanisms. Our results demonstrate that the obtained convergence rates are inferior to the optimal rates achieved by clipped or normalized variants of SGD, thereby revealing inherent limitations of vanilla methods under heavy-tailed noise. The theoretical findings are supported by experiments on synthetic functions.

arXiv

Liquidity-Based Audit of Algorithmic Trading Strategies

Irene Aldridge

We show that net demand for liquidity by algo strategies is identifiable from its trade and price history alone, with no knowledge of its signal or optimization problem. An exact multi-period regret decomposition implies that the sign of this statistic classifies a linear strategy as a net liquidity consumer or provider, recovering the Kyle (1985) informed-trader/market-maker dichotomy from observables alone. Under an AR(1) cost process, the same statistic equals the product of strategy size and the squared Roll (1984) implied spread, making the correction a direct proxy for prevailing illiquidity. Extending to endogenous price impact and aggregating across N correlated strategies yields a liquidity-balance condition whose violation produces welfare loss scaling as N squared, a closed-form fire-sale externality. We calibrate to CRSP equity data (2016-2025), tracking implied spreads through the COVID-19 and 2022 rate-shock episodes, with an estimator computable in O(Tnd) time.

arXiv

Gradient-Free Warm-Start Library Recovery: an Amortized-Regret Separation

Jianwei Lou

Continual learning that is gradient-free, local, online, and append-only is attractive for edge and streaming deployment, but its value is usually argued informally. We give a provable account on recurring-regime streams. Given segmentation, a warm-start library learner attains amortized recovery cost $O\!\big(KD/\varepsilon^2+(R-K)\logK/Δ^2\big)$ versus a memoryless re-estimator's $Θ(RD/\varepsilon^2)$, an advantage $(R-K)\,Θ(D/\varepsilon^2)$ growing with dimension $D$ and recurrence density. The mechanism is a decoupling: recognizing which of $K$ seen regimes is active costs $O(\log K/Δ^2)$, independent of $D$, whereas estimating a regime costs $Θ(D/\varepsilon^2)$. We prove this is tight: matching lower bounds give recognition $Θ(\log K/Δ^2)$ and a memoryless-class bound $Ω(RD/\varepsilon^2)$, so each term is individually minimax-tight (the joint statement is conditional). The separation is born-immune (a memoryless learner's advantage is identically zero) and paradigm-level: it matches, and does not beat, a fair spawn-capable Bayesian baseline; the contribution is attaining this cost structure without end-to-end backprop and with zero forgetting by construction. A count-calibrated variant ties the baseline's leading constant up to a bounded, never-negative per-recurrence overshoot, hyperparameter-free and with no per-step transcendentals. We bound the scope: recognizable regimes are capped by simplex packing (walls $e^{Θ(D)}$); autonomous segmentation is impossible at the packing wall (no detector escapes the false-alarm/delay frontier as regimes overlap); the advantage vanishes under overlap. The dimension-dependent separation is corroborated on synthetic streams and real $k$-mer genome distributions (memoryless cost $\propto D^{1.04}$, recognition $D$-independent); the one real sequential stream sits in the $D{=}1$ near-null corner.

arXiv

SDS-LoRA: Overcoming Anisotropic Gradient Scaling in Low-Rank Adaptation

Junghun Oh, Sungyong Baik, Kyoung Mu Lee

Low-Rank Adaptation (LoRA) enables efficient adaptation of large pretrained models to downstream tasks by parameterizing weight updates with low-rank matrices. In this paper, we investigate the limitations of the LoRA parameterization from a geometric perspective. Specifically, we show that when a full fine-tuning gradient is backpropagated to the low-rank matrices, it undergoes anisotropic scaling driven by their singular values. We argue that this phenomenon is undesirable because it distorts the full fine-tuning gradient by skewing it toward dominant singular directions while suppressing others. Our analyses demonstrate that anisotropic gradient scaling reduces the effective rank of the low-rank matrices' gradients and fails to provide the best possible alignment between the full fine-tuning gradient and its low-rank approximation in LoRA for arbitrary gradients, thereby exacerbating the gap to full fine-tuning. To address these limitations, we propose a new low-rank parameterization, SDS-LoRA, which Structurally Decouples Singular values from the backward pass. Our method ensures that the full fine-tuning gradient backpropagates only through the orthonormal bases of the low-rank matrices' subspaces, independent of their scales. Convergence analysis demonstrates that while LoRA's convergence rate degrades with the condition number of the low-rank matrices, that of SDS-LoRA remains independent of it. Experimental results across natural language and vision benchmarks show that SDS-LoRA improves loss convergence and reduces the gap to full fine-tuning, significantly enhancing adaptation performance.

arXiv

Identifiability and Estimation for Unlabeled Finite Mixtures under Marginal Independence

Takafumi Kanamori, Yushi Hirose, Shohei Yamamoto

We study component recovery and mixing-matrix estimation from unlabeled finite mixtures whose observable distributions share the same latent components but have unknown mixing weights. The main identifying signal is marginal independence: each component is assumed to be independent on at least one coordinate pair, but no labels, clean component samples, or mixing weights are observed. We first prove a structural result for product components: under a subset-rank condition on the spans of the univariate marginals, any independent affine combination of the components must coincide with a single component. We then extend this principle to observable mixtures and show that, under the corresponding subset-rank, full-rank, and no-cancellation conditions, marginally independent affine combinations recover the corresponding latent components. When every component is independent on some coordinate pair, all components are identifiable, and the mixing matrix is recoverable under the stated completion conditions. Finally, we propose a Product-Marginal Maximum Mean Discrepancy (PM-MMD) estimator over affine combinations of the observable mixtures and prove uniform convergence and stability under approximate marginal independence. This framework also separates the empirical roles of the assumptions: irreducibility is, in general, not directly testable from the unlabeled mixtures alone, whereas marginal independence yields a candidate-level diagnostic through held-out PM-MMD. Controlled and flow-cytometry experiments show when marginal independence provides a useful recovery signal. In the reported multi-component comparisons, condition-aware representative selection stabilizes PM-MMD and improves recovery relative to clustering, factorization, and pairwise mixture-proportion baselines using the same unlabeled mixtures.

arXiv

Constitutional On-Policy Safe Distillation

Ming Wen, Yuxuan Liu, Kun Yang, Yunhao Feng, Zhuoer Xu, Yuhao Sun, shiwen cui, Xiang Zheng, Yi Liu, Xingjun Ma, Yu-Gang Jiang

On-policy self-distillation (OPSD) has emerged as an efficient post-training paradigm by using a teacher conditioned on privileged information to provide dense token-level supervision. Prior work has shown that OPSD can collapse in verifiable reasoning tasks, while safety alignment differs in that it is guided by high-level constitutions rather than explicit target answers. However, pilot studies reveals that safety OPSD nonetheless suffers from severe collapse, where constitutional conditioning contracts the teacher distribution toward short and overly conservative responses and Reverse KL further amplifies this contraction into reduced expressiveness. We formalize this effect as geometric leakage under safety boundaries in a non-orthogonal semantic space, where safety pressure transfers into the expressiveness dimension. Based on this analysis, we propose Constitutional On-Policy Safety Distillation (COPSD), which first calibrates the teacher through a Cross-SFT cold-start and then performs constitution-conditioned on-policy distillation. Experiments across 3 multimodal large language models (MLLMs) on 12 safety and general benchmarks show that COPSD improves both safety and helpfulness over baselines while reducing the safety tax on general reasoning.

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