Designing, implementing, and comparing interpretable architectures requires a formal language to represent them. The most common representations fall short in one of two ways. Symbolic equations give no global view of an architecture at a glance. Probabilistic graphical models and flowcharts do not describe actual tensor manipulations, thus hiding key insights and limiting reproducibility. To close this gap, we introduce a graphical notation for designing interpretable AI architectures, adapted from Penrose tensor notation. This graphical notation gives a global view of an architecture and maps one to one onto PyTorch einsum code. We first use this notation to describe architectures that are interpretable by construction, including concept bottlenecks, sparse probes, prototype networks, neural additive models, and mixtures of linear models. We then diagram the key architectural components of Steerling-8B, a frontier interpretable language model. The diagram yields global insights into the architecture (e.g., showing that Steerling is a residual model), a geometric interpretation of each individual operation, and a direct translation into 33 lines of PyTorch code.
Johannes Fankhauser, Lukas J. Fiderer, Hans J. Briegelquant-ph cs.LG
Quantum machine learning models define probabilistic input--output maps through coherent quantum evolution and measurement. While such models can exhibit computational advantages, their internal functioning and decision making generally resists interpretation in terms of stochastic trajectories through intermediate configurations. In contrast to classical (Markovian) stochastic processes, quantum dynamics generically violates the Chapman--Kolmogorov divisibility condition, preventing a decomposition into probabilistically meaningful intermediate transitions. We develop a probabilistic framework for representing quantum learning models as stochastic processes over configuration spaces where the dynamics are modeled as linear maps on probability distributions. Starting from a fixed POVM, arbitrary quantum channels induce transition kernels on the associated probability representation. For informationally complete POVMs, and in particular SIC-POVMs, these kernels are Markovian but generally quasi-stochastic, with non-classicality appearing as negativity. By contrast, projective spaces admit positive stochastic kernels but generally require non-Markovian dynamics due to the failure of Chapman--Kolmogorov divisibility. This yields a trade-off between negativity and dependence on past configurations, i.e. quantum dynamics can be represented either by Markovian quasi-stochastic maps or by positive stochastic processes with higher Markov order. We discuss how such representations of quantum dynamics can be interpreted as stochastic walks through a memory space in the spirit of Projective Simulation, a model of learning and agency in which decisions arise from random walks over an episodic memory network. We further outline how finite-order stochastic kernels can approximate such quantum deliberation processes and show in what regimes the classical machine learning model is recovered.
Efficient tactical knowledge extraction and analysis in real-time strategy (RTS) games micromanagement are constrained by the high-dimensional coupled state-action sequential data and the black-box decision-making process. Current research rarely provides a hierarchical visualization-based attribution analysis from the perspective of data decoupling and abstraction. To facilitate interpretable tactical knowledge extraction and visualization-based analysis in RTS games, a systematic framework named state-action-tactic analysis pipeline (SAT-RTS) is proposed. To decipher the deep-seated drivers of critical decisions in RTS learning systems, this work integrates interpretable visualization with the automated extraction of latent tactical patterns from high-dimensional sequence data. By adapting a cluster-centric BK-tree algorithm and incorporating specialized distance metrics designed to quantify multi-aspect similarities, the proposed framework facilitates robust state-stream abstraction. Furthermore, a rule-based multi-label extraction method is developed to transform unstructured state-action sequences into discrete and interpretable tactical labels, effectively bridging the gap between raw behavioral data and high-level tactical insights. By holistically integrating these computational methods into a hierarchical visualization-based pipeline, the proposed framework effectively addresses the challenges of processing massive real-time data streams while providing fitness landscape visualizations and analytical insights to decipher deep-seated tactical drivers. Comprehensive experiments demonstrate that the proposed SAT-RTS significantly enhances the interpretability and efficiency of tactical analysis in complex RTS environments.
Contemporary artificial intelligence systems achieve strong performance through large-scale parameterization, retrieval augmentation, and training on extensive static corpora. Despite these advances, they continue to face limitations in persistent memory, temporal grounding, provenance, and interpretability. These challenges are especially pronounced in large language models, where experience is encoded implicitly in fixed parameters, limiting the ability to preserve, inspect, and reinterpret past interactions over time. This paper establishes a memory-centric architectural foundation for artificial intelligence in which experience is represented explicitly and persistently to support temporal grounding, provenance, and interpretability. It proposes an alternative to parameter-centric approaches by treating memory as a first-class, structured substrate for reasoning. We introduce the Dynamic Gist-Based Memory Model (DGMM), an architecture in which experience is represented as an evolving, graph-structured episodic-semantic memory. DGMM encodes experience as interconnected conceptual structures grounded in time, source, and interaction context, and defines selective, cue-conditioned recall as the mechanism for constructing working memory. A formal schema and architectural invariants are provided based on additive memory growth and recall-conditioned interpretation. The results specify properties of DGMM, including episodic persistence, locality of cue-conditioned surprise, and contextual variability without structural modification of stored memory. DGMM provides a coherent architectural theory in which memory is explicit and persistent, supporting evolving interpretation without retraining and enabling interpretable, context-aware, and temporally grounded AI systems.