Humans naturally retain memories of permanent elements, while ephemeral moments often slip through the cracks of memory. This selective retention is crucial for robotic perception, localization, and mapping. To endow robots with this capability, we introduce 3D Gaussian Mapping (3DGM), a self-supervised, camera-only offline mapping framework grounded in 3D Gaussian Splatting.

Morespecifically,3DGM formulates multitraverse environmental mapping as a robust 3D representation learning problem, treating pixels of the environment and objects as inliers and outliers, respectively.

We build such explanations and counterfactuals iteratively using constraint solving techniques and a heuristic based on feature-level sensitivity ranking.

How should we assess this possibility?

Let's assume we apply a random CCW torsion rotation of angle We detail here the formulae used in section section 2.4. Similar to AlphaFold [Senior et al., 2020], we fit distances using normal distributions and angles Such cases require a special treatment. So far, we haven't tackled the following difficulty: Examples are hydrogen groups as in Figure 1. We propose a new loss function based on eq. The EMD computation cannot be parallelized in mini-batches in the current version of the library, but everything else is batch-parallelizable in our model (e.g., The training stage happens without assembling the full conformer.

Standard simulations of Turing machines suggest a linear relationship between the temporal duration $t$ of a run and the amount of information that must be stored by known simulations to certify, verify, or regenerate the configuration at time $t$. For deterministic multitape Turing machines over a fixed finite alphabet, this apparent linear dependence is not intrinsic: any length-$t$ run can be simulated using $O(\sqrt{t})$ work-tape cells via a Height Compression Theorem for succinct computation trees together with an Algebraic Replay Engine. In this paper we recast that construction in geometric and information-theoretic language. We interpret the execution trace as a spacetime DAG of local update events and exhibit a family of recursively defined holographic boundary summaries such that, along the square-root-space simulation, the total description length of all boundary data stored at any time is $O(\sqrt{t})$. Using Kolmogorov complexity, we prove that every internal configuration has constant conditional description complexity given the appropriate boundary summary and time index, establishing that the spacetime bulk carries no additional algorithmic information beyond its boundary. We express this as a one-dimensional computational area law: there exists a simulation in which the information capacity of the active "holographic screen'' needed to generate a spacetime region of volume proportional to $t$ is bounded by $O(\sqrt{t})$. In this precise sense, deterministic computation on a one-dimensional work tape admits a holographic representation, with the bulk history algebraically determined by data residing on a lower-dimensional boundary screen.

Graph representation learning seeks to transform complex, high-dimensional graph structures into compact vector spaces that preserve both topology and semantics. Among the various strategies, subgraph-based methods provide an interpretable bridge between symbolic pattern discovery and continuous embedding learning. Yet, existing frequent or discriminative subgraph mining approaches often suffer from redundant multi-phase pipelines, high computational cost, and weak coupling between mined structures and their discriminative relevance. We propose DS-Span, a single-phase discriminative subgraph mining framework that unifies pattern growth, pruning, and supervision-driven scoring within one traversal of the search space. DS-Span introduces a coverage-capped eligibility mechanism that dynamically limits exploration once a graph is sufficiently represented, and an information-gain-guided selection that promotes subgraphs with strong class-separating ability while minimizing redundancy. The resulting subgraph set serves as an efficient, interpretable basis for downstream graph embedding and classification. Extensive experiments across benchmarks demonstrate that DS-Span generates more compact and discriminative subgraph features than prior multi-stage methods, achieving higher or comparable accuracy with significantly reduced runtime.