arXiv:2610.12776v1 公告类型：新论文 摘要：自动微分（AD）是现代机器学习的基石。由于所有 AD 框架都隐式地固定了欧几里得空间的一组基来定义梯度和雅可比矩阵，因此它们原生处理的数学对象都是由一组固定坐标构成的数组。这使得旋转、体积形式和曲率等对象难以表达，而这些对象会出现在例如人工智能应用于科学的场景中。为特定问题定制的变通方案缺乏可复用性。我们证明：（i）单个与基无关的导数算子可以表示多种几何微分运算；（ii）该算子可以完全用现有的 AD 原语来表达。这种可复用的变换可以与 JAX 的批处理、编译和硬件加速功能组合使用。几何结构以代数数据的形式引入。我们通过实验展示了该变换在不同流形算子之间的复用、在时空逆问题处理流程中的组合，以及在不同旋转子子群上的优化中的应用。
arXiv:2610.12754v1 Announce Type: new Abstract: We propose NV-Tesseract-AD, a curriculum learning-enhanced conditional diffusion framework for multivariate time-series anomaly detection. Our central hypothesis is that reconstruction difficulty can be explicitly structured along two complementary axes, masking severity and diffusion noise level, and that training from easier to harder tasks along both axes simultaneously stabilizes optimization and improves residual discriminability. We integrate a Transformer-based diffusion backbone with a three-stage dual curriculum over masking ratios and diffusion timesteps, retaining anomalous samples throughout training and relying on structured corruption to drive self-supervised representation learning. We evaluate NV-Tesseract-AD under two regimes: in-distribution training on the TSB-UAD-M corpus and strict zero-shot transfer to ten EasyTSAD benchmark families without per-dataset tuning. The dual-axis curriculum produces masking-invariant reconstruction, confirmed by a near-zero loss gap between complementary masking strategies within the first training stage, and yields an approximately 3.7-fold improvement in F1 and a 56 percent reduction in MSE relative to a non-curriculum baseline. Zero-shot performance reaches F1 = 0.984 on NAB and F1 = 0.948 on NormA. Weaker results on heterogeneous families are traced to unsupervised threshold calibration rather than reconstruction quality, identifying calibration as the dominant remaining detection bottleneck. Accelerated inference via DPM-Solver++ reduces sampling cost by a factor of 3.5 to 5.7 at the dataset level but couples to thresholding behavior, establishing that the sampler and threshold must be validated jointly. Together, these findings demonstrate that aligning diffusion denoising difficulty with curriculum learning principles provides a principled and practical approach for robust anomaly detection in complex multivariate time series.
arXiv:2610.12744v1 Announce Type: new Abstract: Parameter-efficient continual learning updates a restricted subset of adapter parameters to incorporate sequential tasks while limiting catastrophic forgetting. Gradient attribution is a common rule for selecting that subset, but it requires an additional backward pass over calibration data. We identify a parameter-pool confound in comparisons between initialization-time gradient masks and unrestricted random masks under standard zero-initialized LoRA ($B=0$): the gradient with respect to $A$ is identically zero ($\partial\mathcal{L}/\partial A=0$), so gradient masks select strictly from the $B$ matrix whereas unrestricted random masks draw from both $A$ and $B$. Such a comparison changes both the selection rule and the candidate parameter pool. Isolating the selection criterion by restricting both approaches to the same parameter pool, we find a negative result: a uniform random mask consistently achieves lower loss-based backward transfer than gradient attribution across seven seeds on Qwen2.5-3B. The effect is concentrated on the medical task, which contributes 80\% of the aggregate; code and math move in the same direction, and legal shows no reliable difference. This advantage is consistent with a stability--plasticity trade-off under the tested task sequence, in which random masking slightly reduces single-task fitting. On the two discrete-option tasks (Medical and Legal), the mean accuracy-BWT difference is not statistically distinguishable from zero.
arXiv:2610.12741v1 Announce Type: new Abstract: We interpret Transformer networks as learned approximations to a hybrid probabilistic-inference procedure that combines max-product Loopy Belief Propagation (LBP) with Expectation--Maximization (EM). In this view, a Transformer performs inference in partially observed Markov Random Fields (MRFs) whose structure and parameters are not given a priori but are inferred from data. We show that self-attention implements a differentiable approximation to max-product LBP on an input-conditioned, dynamically structured MRF, with attention weights encoding learned structural affinities. We further establish an EM correspondence at the level of depth: each layer updates latent representations in an E-step-like forward pass, while the transition $\theta^{(l)} \to \theta^{(l+1)}$ across layers acts as an implicit M-step. Building on this interpretation, we introduce \emph{meta-models}, a design paradigm in which inputs generate instance-specific parameters, unifying mechanisms such as self-attention, mixture-of-experts, and gated units within a single framework. Empirical results support the proposed perspective.
arXiv:2610.12738v1 Announce Type: new Abstract: Forecasting rare, high-cost events in multivariate time-series systems is hard because their precursors are seldom observed, so a purely data-driven model has little to learn from. The engineers who run these systems, however, hold knowledge that precedes such events, information absent from the scarce labels. We call this a semantic prior and inject it into a self-supervised event forecaster through two switchable mechanisms, a covariate mechanism and an attention-bias mechanism, each the identity at its null, so one architecture serves every prior type with no per-dataset architecture search. A prior helps when it supplies information the observed window does not already contain: in a short context an informative prior beats no prior in-domain (pooled h-AUROC over the no-prior baseline: a periodicity clock +14%, p<0.001; a conservation residual +47% at a 0.25 label fraction), and a working prior transfers out-of-domain (+53%), substituting for feature transfer, while priors the window already recovers stay inert and the attention-bias mechanism shows no measurable gain. KITE is a switchable, attributable route to contextual conditioning, and a substrate for scaling toward cross-domain, pretrained time-series foundation world models that carry their governing structure explicitly.
arXiv:2610.12711v1 Announce Type: new Abstract: Federated Large Language Models (FedLLMs) are promising to deliver privacy-preserving, collaborative intelligence. The decentralized training process is vulnerable to Byzantine attacks that corrupt semantic consistency and factual resilience through malicious model updates. This paper presents a new resilience strategy that prevents semantically corrupted knowledge from propagating during federated aggregation. A defense problem is formulated to jointly maximize global accuracy and suppress manipulated model updates, enabling trustworthy knowledge aggregation without accessing private local data. To strengthen the resilience of FedLLMs, we develop a novel Hypergraph Message Passing Graph Autoencoder (HMP-GAE) framework, where low-rank model updates are represented as nodes in a hypergraph and high-order semantic relationships among multiple agents are exploited through iterative message passing. By leveraging historical checkpoints and cross-agent relational reasoning, HMP-GAE identifies and suppresses semantically inconsistent updates while preserving knowledge alignment among agents throughout federated training. HMP-GAE is implemented using Qwen-2.5 and Llama-3.2 as pretrained FedLLM backbones and evaluated on AG News and Yahoo! Answers datasets. Compared to existing defenses, HMP-GAE improves global accuracy by $1.21$\%, reduces final-model classification semantic entropy by $44.08$\%, and lowers perplexity by $13.34$\%. HMP-GAE outperforms the GAE-based defense by improving the accuracy $1.39$\%, reducing the semantic entropy by $54.5$\%, and lowering perplexity by $35.5$\%.
arXiv:2610.12679v1 Announce Type: new Abstract: Efficient sampling from Bayesian posterior distributions in high dimensions remains a hard problem, despite advances in theory and algorithms. Multiple steps are usually required to draw unbiased samples, for example, iterations of an MCMC algorithm or integration steps in a diffusion-based amortised sampler. However, scalable one-step amortised inference remains a challenging open problem. In this work, we build upon recent progress in data-driven generative modelling to offer a possible solution for one-step amortised sampling. Our one-step implicit sampler (OSIS) uses short-time MCMC dynamics to define a local target for the evolution of an implicitly modelled distribution. In the asymptotic limit, the modelled distribution is a fixed point of the MCMC kernel and thus samples from the target. We analyse the convergence properties of OSIS and show connections with other generative modelling and sampling algorithms. We study various design choices and show that OSIS performs well compared to multi-step amortised samplers and non-amortised MCMC baselines while being far more efficient at sampling time.
arXiv:2610.12658v1 Announce Type: new Abstract: We develop a data-driven sensor-placement framework and apply it to aerosol monitoring in the United Kingdom (UK). A trained convolutional Gaussian neural process is embedded within the DeepSensor optimisation framework. Genetic optimisation with lazy evaluation and caching reduces mean computational time by 60\% (10$\pm$3 versus 25$\pm$7 minutes) while producing sequential placement performance comparable to the greedy solver. Using the CAMS reference field to construct a retrospective oracle benchmark, Joint NLL improves by about 22\% for Joint-MI-driven genetic placement after five locations for aerosol stations are identified. Seasonal and wind-regime analyses show that agreement between model-based criteria and oracle benchmarks varies with meteorological transport conditions. These results show a computationally efficient approach for data-informed expansion of environmental observing systems.
arXiv:2610.12638v1 Announce Type: new Abstract: Day-ahead electricity forecasts can help building operators schedule heating, ventilation, and other services around anticipated demand. Choosing a forecasting model also requires balancing accuracy with its forecast-time inputs, local training, and computational requirements. We benchmark statistical, machine-learning, recurrent neural-network, and pretrained TimesFM models for a university building. We use chronological validation and evaluate all configurations on the same 57 test days, comparing accuracy across workdays, weekends, and holidays alongside local fitting and forecasting time. Weather covariates use retrospective observations. TimesFM 3.0 with covariates achieves the lowest overall errors, reducing mean absolute error by approximately 43\% relative to weekly seasonal-naive forecasting. XGBoost remains competitive, although paired daily comparisons do not establish a clear mean-absolute-error advantage for TimesFM. TimesFM also performs strongly using only past electricity consumption. Adding covariates improves its holiday forecasts but slightly worsens workday and weekend forecasts, leaving overall mean absolute error almost unchanged. TimesFM requires no building-specific weight training, while XGBoost offers rapid local fitting and inference. The evaluated LSTM takes longer to fit without outperforming either approach. An exploratory historical evaluation reveals seasonal variation, while a separate weather-source comparison produces only small changes in the selected TimesFM configuration's accuracy. These results support pretrained TimesFM as a strong initial forecasting baseline for this building, with XGBoost as a competitive locally fitted alternative. Covariates are particularly useful when improved holiday forecasts justify the additional input preparation.
arXiv:2610.12541v1 Announce Type: new Abstract: Boundary-value problems for the Laplace equation develop singular behaviour near corners, edges and junctions that smooth approximators resolve poorly. We combine holomorphic neural networks with singular functions derived from the local geometry and boundary conditions. The representation is harmonic by construction, so no interior residual is needed: the network fits the smooth remainder from boundary data alone, and the enrichment terms capture the singular behaviour. Singular exponents are trainable, so the construction also applies when the local expansion is not known in advance. We extend the approach to three dimensions using independent networks evaluated along complex null directions. The enriched model is the most accurate tested method on every problem. Its margin is several orders of magnitude where the enrichment captures the singularity exactly, and a factor of about 1.7-2.1 over the next-best method on a CdZnTe radiation detector with many singular sites, in both two and three dimensions.
arXiv:2610.12520v1 Announce Type: new Abstract: The goal of circuit discovery is to decompose a monolithic neural network into tiny modular subnetworks which are interpretable in the sense that each does an identifiable subtask. We develop a practical method for composing arbitrarily many circuits into a single model. We propose a greedy, density-scaled composition algorithm that overcomes limitations of previous attempts to compose circuits by naive union, then generalize it to $N$ circuits via CircuitTree, a new data structure built on a $\Theta(N\log N)$ tree-compose schedule. We compose circuits pruned from HuBERT for classifying individual phonemes into a syllable classifier, a capability none of the 39 phoneme circuits has individually. Chaining CircuitTrees into a hierarchy-of-circuits pipeline, we transcribe open syllables at 64.8\% accuracy, within 1.2 points of a 66.0\% ceiling that shares no circuitry at all, with 99.5\% of circuit components shared.
arXiv:2610.12496v1 Announce Type: new Abstract: Sequence models with a fixed-size state avoid the quadratic cost of attention, but face a design choice. An input-dependent state transition gives content-dependent memory at the cost of FFT-based training, while a fixed transition keeps the O(T log T) convolutional path but reads memory the same way for every input. ResonatorLM, a recent model of the second kind, reads a bank of damped complex oscillators through a fixed learned phase per head. We make that readout phase a function of the current token, which adds input dependence to the read only, keeps the convolution exact, and costs 0.2 percent more parameters. An analysis of the untrained bank shows that phase does encode elapsed time, but an ordinary token falls below the background within 2-8 steps and no choice of damping extends linear reconstruction beyond about 16 tokens. In 6M-parameter character-level models on WikiText-2, the input-dependent phase matches the original at the training length and removes its failure beyond it: trained on 256 tokens and tested on 1024, perplexity falls from 12.81 to 3.76. We trace the failure to long-memory heads that accumulate more history than training exposed them to. The learned phase tracks the current character rather than distance and does not improve retrieval.
arXiv:2610.12495v1 Announce Type: new Abstract: Small language models trained on a single local machine leave little room for architectural trial and error. Kairos combines bidirectional gated-DeltaNet linear attention and sliding-window attention over shared projections (LiZAttention2), block-wise Attention-Residual aggregation, a sparse Mixture-of-Experts (MoE) feed-forward layer and a multi-scale byte-level codec, trained with a uniform-noise denoising objective over one byte space shared by text, image, audio, video, lidar and control streams; this report asks whether the combination optimizes at all before asking whether it is useful. We give code-derived algorithms for each component, including a cross-session recurrent-state memory gate, then run convergence sanity checks: overfittinga single 440-byte sentence at 1--15M parameters, text only, with three seeds for codec and attention choices and single-run sweeps for seven further factors. The two attention variants tested at 3\,000 steps (LiZAttention2 and window attention alone) reach a minimum loss near $10^{-3}$. After 600 steps, the mean minimum loss ranges from 0.018 (patch codec) to 0.354 (depthwise convolutional codec) with an identical ranking on three seeds. An apparent advantage of shared over separate attention projections closes with more steps or more diverse data and reverses when the projections are frozen: it is a convergence-speed effect, not a capacity effect. These checks suggest that the implementation optimizes; they say nothing about generalization, multimodal training or comparison with existing models, which a planned pretraining run is meant to address. The Discussion sizes a 200M-total/25M-active target analytically; none of its throughput figures is measured. Code is available at https://github.com/fabienfrfr/Kairos . Python package at https://pypi.org/project/kairos-fm/ .