To avoid missing important variables and their connections in networks, more and more variables are included in network analysis. Here we show that in a setting with many more parameters than observations (high-dimensional) it is possible to get a conservative (i.e., low false positive rate) estimate of the neighbourhood for each node (which connections are in the network). A neighbourhood is often estimated with a linear model, and this leads to two interesting cases: (i) If the true model is linear, then neighbourhood selection work reasonably well, and (ii) if the true model is nonlinear, then neighbourhood selection requires a penalty for the high dimensions. Here we show the impact of the ridge parameter on the mean squared error, and how this leads to low test variance and hence to neighbourhoods with large numbers of edges. We connect these insights with results from machine learning, where the so-called double descent (when more parameters are included than observations, the mean squared error goes down a second time) has put the traditional view on model selection upside down. Essentially, for adequate neighbourhood selection in models with a large number of parameters, the volume of the model space needs to be included in the penalty. Most neighbourhood selection methods (e.g., Lasso, AIC, BIC) lead to spurious edges (high false positive rate), but we prove that in the high-dimensional setting, minimum description length leads to correct neighbourhood selection or smaller (low false positive rates) in both cases when either the model is correctly or incorrectly assumed linear
Self-evolving agents accumulate reusable skills by appending successful procedures and failure fixes. Over time, the same requirement is often restated in several branches, examples, and warnings, while common action sequences are copied rather than reused. The resulting skill becomes expensive to inject and difficult to maintain. Generic prompt compression is ill-suited to this setting because a skill is not a flat passage: its name and description define when it applies, its workflow controls execution, its tool and output contracts constrain validity, and rare exceptions may remain essential even when no sampled task activates them. Evaluation-guided compression can test these behaviors, but it introduces rollouts, cost, and dependence on the compression-time evaluation set. We present SkillZip, an evaluation-free method that compresses a skill by finding its shortest faithful structural explanation. The intuition is explain once, reference many: state a repeated rule once at the scope where it applies, factor a repeated action sequence into a shared procedure, and keep only the differences as explicit exceptions. We formalize this intuition as a typed minimum description-length objective over a skill contract and a residual, subject to a hard coverage constraint for every extracted trigger, workflow edge, tool requirement, obligation, and output field. The formulation provides simple sharing thresholds, preserves unique rare rules by construction, and supports efficient local updates. SkillZip has a one-shot mode with one structured extraction call and deterministic optimization, and a continual Zip-on-Write mode that integrates each self-evolution patch without replaying tasks or reparsing the full history. Through comprehensive experimental evaluations, we demonstrate the effectiveness and superiority of SkillZip in compression performance, generalizability, and cost overhead.
We propose an information-theoretic framework for graph novelty generation, which aims to generate data that are distinct from existing patterns while preserving global structural consistency. Our approach embeds data into a latent space, models the latent distribution using finite mixture models, and generates novel samples by imposing explicit novelty and reliability conditions formulated in terms of description length. Specifically, novelty is enforced by requiring generated samples to be poorly explained by all existing mixture components, while reliability constrains their impact on the overall mixture structure under the Minimum Description Length (MDL) principle. We provide a theoretical analysis showing that, with appropriate threshold choices, the probabilities of misclassifying non-novel or unreliable samples converge to zero with explicit rates. Experiments on synthetic and benchmark graph datasets demonstrate that the proposed method enables principled novelty generation with quantifiable risk.
Minimum Description Length (MDL) formalizes the principle of Occam's razor by optimizing the total description length: $L(\mathrm{model})+L(\mathrm{data} \ | \ \mathrm{model})$. For sequential prediction, the MDL method repeatedly selects a model with a minimum objective score of the observed prefix for the next step prediction. Classical MDL prediction theory shows that exact optimization of the MDL objective indeed provides a strong compression guarantee that supports reliable prediction. However, practical machine learning usually can only find models by approximately optimizing the objective function. To bridge this gap, this paper addresses the following fundamental question: Under what forms of approximation and regularization does approximate MDL still guarantee reliable sequential prediction? This work offers a principled characterization. We prove that for any approximation with additive slack $C$ of the more general form of the balanced MDL objective: $λ\cdot L(\mathrm{model})+L(\mathrm{data} \ | \ \mathrm{model})$, the cumulative expected squared prediction error is finite for all $λ\ge1$. The case $λ>1$ is proved by an affinity-telescoping argument, while the boundary case $λ=1$ is proved by a likelihood-ratio stopping argument based on exact static MDL bounds. Our results establish that classical MDL regularization remains robust to any fixed additive optimization error. Furthermore, we establish that our characterization of the approximate MDL framework is sharp: When $0<λ<1$, overfits can happen to incur infinite cumulative expected error in the universal class of estimable measures, and hence a strong form of model-complexity regularization is necessary. In addition, model selection may fail in every regularized regime $λ>0$, under multiplicative approximation, and thus, additive approximation is both sufficient and essential.
Spectral clustering largely depends on the affinity graph, yet constructing a graph that preserves reliable local connectivity while adapting to heterogeneous data structures remains challenging. Existing granular-ball-based spectral clustering methods usually reduce graph complexity by using coarse-grained representatives. However, the learned local regions are often treated as graph nodes or anchors, and their structural information is not sufficiently used to regularize the original sample-level graph. To address this issue, this paper proposes a Minimum Description Length based Granular-Ball Tree-Regularized Spectral Clustering method, termed MDL-GBTRSC. The proposed method constructs a granular-ball tree through local MDL model selection, with reciprocal neighborhood continuity used to discourage splits that break reliable local connections. The stable leaf balls obtained from the tree provide coding-scale information for regularizing the sample-level affinity graph. In addition, a shared-neighbor bridge code is introduced to adjust weak local bridge relations without requiring an additional user-specified threshold. In this way, MDL-GBTRSC connects interpretable local representation learning with affinity graph construction in a unified spectral clustering framework. Experiments on real and synthetic datasets show that MDL-GBTRSC achieves the best average ARI and NMI under the adopted fixed-configuration protocol compared with classical spectral clustering baselines and representative granular-ball, micro-cluster, and anchor-based methods.
Regionalization aims to partition a spatial domain into contiguous regions that share similar characteristics, enabling more effective spatial analysis, policy making, and resource management. Existing approaches for spatial regionalization typically rely on static spatial snapshots rather than evolving time series. Meanwhile, most time series clustering methods ignore spatial structure or enforce spatial continuity through ad hoc regularization, constraining the number of inferred regions a priori either explicitly or implicitly. Utilizing the minimum description length principle from information theory, here we propose an efficient and fully nonparametric framework for the regionalization of spatial time series. Our method jointly infers a spatial partition along with a set of representative time series archetypes ("drivers") that best compress a spatiotemporal dataset, with a runtime log-linear in the number of time series. We demonstrate that this method can accurately recover planted regional structure and drivers in synthetic time series, and can extract meaningful structural regularities in large-scale empirical air quality and vegetation index records. Our method provides a principled and scalable framework for spatially contiguous partitioning, allowing interpretable temporal patterns and homogeneous regions to emerge directly from the data itself.