Spectroscopy infers the internal structure of physical systems by measuring their response to perturbations. We apply this principle to neural networks: perturbing the data distribution by upweighting a token $y$ in context $x$, we measure the model's response via susceptibilities $\chi_{xy}$, which are covariances between component-level observables and the perturbation computed over a localized Gibbs posterior via stochastic gradient Langevin dynamics (SGLD). Theoretically, we show that susceptibilities decompose as a sum over \emph{modes} of the data distribution, explaining why tokens that follow their contexts ``for similar reasons'' cluster together in susceptibility space. Empirically, we apply this methodology to Pythia-14M, developing a conductance-based clustering algorithm that identifies 510 interpretable clusters ranging from grammatical patterns to code structure to mathematical notation. Comparing to sparse autoencoders, 50\% of our clusters match SAE features, validating that both methods recover similar structure.
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Reinforcement Learning · Everything Else
The successor representation (SR) provides a powerful framework for decoupling predictive dynamics from rewards, enabling rapid generalisation across reward configurations. However, the classical SR is limited by its inherent policy dependence: policies change due to ongoing learning, environmental non-stationarities, and changes in task demands, making established predictive representations obsolete. Furthermore, in topologically complex environments, SRs suffer from spectral diffusion, leading to dense and overlapping features that scale poorly. Here we propose the Hierarchical Successor Representation (HSR) for overcoming these limitations. By incorporating temporal abstractions into the construction of predictive representations, HSR learns stable state features which are robust to task-induced policy changes. Applying non-negative matrix factorisation (NMF) to the HSR yields a sparse, low-rank state representation that facilitates highly sample-efficient transfer to novel tasks in multi-compartmental environments. Further analysis reveals that HSR-NMF discovers interpretable topological structures, providing a policy-agnostic hierarchical map that effectively bridges model-free optimality and model-based flexibility. Beyond providing a useful basis for task-transfer, we show that HSR's temporally extended predictive structure can also be leveraged to drive efficient exploration, effectively scaling to large, procedurally generated environments.
Probabilistic Methods · Structure Learning
Symmetry is central to modern machine learning and physics: invariances and equivariances improve sample efficiency, robustness, and out-of-distribution generalization, while symmetry principles guide scientific modeling. Yet for stochastic dynamical systems, the relevant continuous symmetries are rarely known, and symmetry discovery for SDEs has remained essentially unexplored. We introduce *LieStoNet*, an end-to-end, *prior-free* framework for discovering Lie-point symmetries of SDEs directly from spatiotemporal trajectories, without prespecifying symmetry groups, templates, or canonical coordinates. Building on the seminal SDE Lie-symmetry theory of Gaeta and Quintero (1999), which formalizes Lie-point SDE symmetries and their relation to Fokker-Planck symmetries, LieStoNet learns neural surrogates for drift and diffusion from increments, then learns projectable generators by enforcing the SDE determining equations, separately regularizing for closure under Lie brackets, adherence to the Lie algebra axioms (bilinearity, antisymmetry, Jacobi), and a non-redundant independent basis. The surrogate also defines an associated Fokker-Planck equation, enabling optional discovery of its Lie-point symmetries in parallel. Across multiple canonical SDEs with known analytic symmetries, LieStoNet recovers generators consistent with the ground-truth symmetry algebra, providing interpretable symmetry discovery for noisy dynamics.
Reinforcement Learning · Everything Else
Reinforcement learning is a powerful paradigm for training autonomous agents and has achieved impressive performance in complex environments. However, this success often comes at the cost of interpretability, diminishing trust and complicating efforts to debug and improve agent behavior. To address these challenges, we introduce CausalXRL, a novel framework for explainable reinforcement learning (XRL). A key feature of CausalXRL is its use of causal graph reasoning, which provides transparent, structured, multi-level explanations of agent decision-making. We validate CausalXRL through comprehensive case studies and a two-part evaluation: (1) a quantitative analysis of agent performance and explanation fidelity in benchmark RL environments, and (2) a qualitative expert study assessing interpretability in a real-time strategy (RTS) game. Results show that CausalXRL enhances human understanding and diagnostic insight in multi-agent scenarios, without compromising task performance. By enabling human operators to interrogate RL agents through causal models, CausalXRL supports alignment by making behavior transparent and auditable.
Social Aspects · Accountability, Transparency, and Interpretability
Multi-step prompt injection attacks on LLM agents present a fundamental detection challenge because malicious intent emerges only after workflows complete, while individual actions remain legitimate in isolation. Existing defenses, including input sanitization, output validation, and instruction hierarchy, operate on individual actions or content patterns and cannot capture this sequential structure. We present \texttt{CausalTrace}, a detection system that reframes prompt-injection defense as causal inference. It constructs Structural Causal Models from agent trajectories with typed edges capturing data dependency, trust transfer, and state enablement, then applies Pearl's do-calculus to answer a counterfactual question, namely whether the harmful outcome would have occurred if the injection had been blocked. This formalization enables a principled distinction between attacks that depend on injections and benign workflows that share surface-level features. Evaluation on a dataset spanning crowdsourced traces, LLM agent benchmarks, and semi-real and real scenarios demonstrates strong detection performance, outperforming content-based baselines while requiring minimal LLM inference cost. Bidirectional slicing recovers complete attack chains, providing interpretable explanations that trace exploitation to its causal origins.
General Machine Learning · Representation Learning
Information retrieval is a core component of many intelligent systems as it enables conditioning of outputs on new and large-scale datasets. While effective, the standard practice of encoding data into high-dimensional representations for similarity search entails large memory and compute footprints, and also makes it hard to inspect the inner workings of the system. Hierarchical retrieval methods offer an interpretable alternative by organizing data at multiple granular levels, yet do not match the efficiency and performance of flat retrieval approaches. In this paper, we propose Retreever, a tree-based method that makes hierarchical retrieval viable at scale by directly optimizing its structure for retrieval performance while naturally providing transparency through meaningful semantic groupings. Our method offers the flexibility to balance cost and utility by indexing data using representations from any tree level. We show that Retreever delivers strong coarse (intermediate levels) and fine representations (terminal level), while achieving the highest retrieval accuracy at the lowest latency among hierarchical methods. These results demonstrate that this family of techniques is viable in practical applications.
Applications · Chemistry, Physics, and Earth Sciences
High-fidelity solubility prediction is fundamental to pharmaceutical development and environmental partitioning, where accurate modeling must couple molecular structure with thermodynamic behavior across diverse chemical environments. However, recent advancements have been dominated by deep learning architectures that often sacrifice physical interpretability for predictive power. We challenge this trend by showing that state-of-the-art performance does not require such non-transparent architectures. To address this, we introduce $Dissolvr$, a transparent framework for molecular solubility prediction. In addition, we perform a comprehensive literature review and a benchmarking study against various methods. We show that $Dissolvr$ approaches the aleatoric limit of experimental uncertainty and achieves OOD generalization through structural invariance derived by mapping molecules to physically-grounded descriptors. Then, we present an LLM-assisted post-hoc explanation pipeline that bridges the gap between symbolic model artifacts and chemically grounded narratives. Finally, a comparative benchmark of a survey involving 22 expert chemists reveals that expert evaluators provide deep insights.
Applications · Health / Medicine
Protein language models (pLMs) have emerged as powerful predictors of protein structure and function. However, the computational circuits underlying their predictions remain poorly understood. Recent mechanistic interpretability methods decompose pLM representations into interpretable features, but they treat each layer independently and thus fail to capture cross-layer computation, limiting their ability to approximate the full model. We introduce ProtoMech, a framework for discovering computational circuits in pLMs using cross-layer transcoders that learn sparse latent representations jointly across layers to capture the model’s full computational circuitry. Applied to the pLM ESM2, ProtoMech recovers 82–89\% of the original performance on protein family classification and function prediction tasks. ProtoMech then identifies compressed circuits that use <1\% of the latent space while retaining up to 79\% of model accuracy, revealing correspondence with structural and functional motifs, including binding, signaling, and stability. Steering along these circuits enables high-fitness protein design, surpassing baseline methods in more than 70\% of cases. These results establish ProtoMech as a principled framework for protein circuit tracing.
General Machine Learning · Everything Else
Functional ANOVA offers a principled framework for interpretability by decomposing a model’s prediction into main effects and higher-order interactions. For independent features, this decomposition is well-defined, strongly linked with SHAP values, and serves as a cornerstone of additive explainability. However, the lack of an explicit closed-form expression for general dependent distributions has forced practitioners to rely on costly sampling-based approximations. We completely resolve this limitation for categorical inputs. By bridging functional analysis with the extension of discrete Fourier analysis, we derive a closed-form decomposition without any assumption. Our formulation is computationally very efficient. It seamlessly recovers the classical independent case and extends to arbitrary dependence structures, including distributions with non-rectangular support. Furthermore, leveraging the intrinsic link between SHAP and ANOVA under independence, our framework yields a natural generalization of SHAP values for the general categorical setting.
Deep Learning · Foundation Models
Recent advances in generative diffusion and flow-matching models have revolutionized molecular design, enabling the creation of novel proteins, small molecules, and RNA sequences with unprecedented fidelity. Yet, these models remain intuitive rather than intelligent—they generate without reasoning. \textbf{ThinkProteo} reimagines generative science by introducing reasoning-guided diffusion models that think step-by-step, akin to how a scientist hypothesizes, tests, and refines molecular ideas. By embedding chain-of-thought (CoT) reasoning into the continuous generative trajectory, ThinkProteo transforms diffusion into a process of thought: each denoising step becomes an interpretable act of molecular reasoning guided by structural, energetic, and functional objectives. This framework bridges symbolic reasoning and physical generation, yielding models that not only design molecules but also explain why they work. We envision ThinkProteo as a foundation for cognitive generative chemistry—uniting the creativity of diffusion models with the deliberation of human reasoning to accelerate the discovery of safe and effective therapeutics.
Applications · Language, Speech and Dialog
We study black-box detection of machine-generated text under practical constraints: the scoring model (proxy LM) may mismatch the unknown source model, and per-input contrastive generation is costly. We propose SurpMark, a reference-based detector that summarizes a passage by the dynamics of its token surprisals. SurpMark discretizes surprisals into interpretable states, estimates a state-transition matrix for the test text, and scores it via a generalized Jensen–Shannon (GJS) gap between the test transitions and two fixed references (human vs. machine) built once from existing corpora. Theoretically, we derive design guidance for how the discretization bins should scale with data and provide a principled justification for our test statistic. Empirically, across multiple datasets, source models, and scenarios, SurpMark consistently matches or surpasses baselines, demonstrating strong robustness across domains and generators; our experiments on hyperparameter sensitivity exhibit trends that our theoretical results help to explain.
General Machine Learning · Causality
Understanding climate dynamics requires going beyond correlations in observational data to uncover their underlying causal process. Latent drivers, such as atmospheric processes, play a critical role in temporal dynamics, while direct causal influences also exist among geographically proximate observed variables. Traditional Causal Representation Learning (CRL) typically focuses on latent factors but overlooks such observable-to-observable causal relations, limiting its applicability to climate analysis. In this paper, we introduce a unified framework that jointly uncovers (i) causal relations among observed variables and (ii) latent driving forces together with their interactions. We establish conditions under which both the hidden dynamic processes and the causal structure among observed variables are simultaneously identifiable from time-series data. Remarkably, our guarantees hold even in the nonparametric setting, leveraging contextual information to recover latent variables and observable relations. Building on these insights, we propose CaDRe (Causal Discovery and Representation learning), a time-series generative model with structural constraints that integrates CRL and causal discovery. Experiments on synthetic datasets validate our theoretical results. On real-world climate datasets, CaDRe not only delivers competitive forecasting accuracy but also recovers visualized causal graphs aligned with domain expertise, thereby offering interpretable insights into climate systems.
Applications · Robotics
Vision–Language–Action (VLA) policies often fail under distribution shift, suggesting that decisions may depend on spurious visual correlations rather than task-relevant causes. We formulate visual–action attribution as an interventional estimation problem. Accordingly, we introduce the **Interventional Significance Score (ISS)**, an interventional masking procedure for estimating the causal influence of visual regions on action predictions, and the **Nuisance Mass Ratio (NMR)**, a scalar measure of attribution to task-irrelevant features. We analyze the statistical properties of ISS and show that it admits unbiased estimation, and we characterize conditions under which action prediction error provides a valid proxy for causal influence. Experiments across diverse manipulation tasks indicate that NMR predicts generalization behavior and that ISS yields more faithful explanations than existing interpretability methods. These results suggest that interventional attribution provides a simple diagnostic approach for identifying causal misalignment in embodied policies.
Deep Learning · Large Language Models
Large Reasoning Models (LRMs) solve complex tasks by generating long Chain-of-Thought (CoT) sequences; however, the emergent dynamics governing reasoning trajectories are not well understood and can lead to inconsistencies and reasoning pathologies. In this work, we propose to approximate LRM's emerging hierarchical reasoning dynamics as a trajectory within a Finite State Machine (FSM) transitioning among six abstract cognitive states. We demonstrate that these states and transitions can be captured in the latent state of the model. We believe that this representation can have different applications in the interpretability and optimization of LRM models. For example, by analyzing the topology of these transitions, we identify statistical shifts in reasoning strategies that help identify effective reasoning chains from those that fail. To illustrate these potential advantages, we propose $Q$-Value guided steering, a training-free inference-time control method that treats reasoning as a planning problem. We estimate the long-horizon utility of state transitions and apply sparse, orthogonal activation steering at sentence boundaries to align the CoT generation with optimal reasoning policies. Experiments across four benchmarks (AIME25, MATH-500, GSM8k, and GPQA Diamond) using three state-of-the-art open reasoning models demonstrate that $Q$-Value steering policy achieves significant performance gains with "surgical'' efficiency, often requiring $25\times$ fewer interventions than greedy and weighted baselines, which suggests that reasoning can be effectively controlled by guiding high-level cognitive dynamics rather than micro-managing token generation.
Probabilistic Methods · Bayesian Models and Methods
Vanilla variational inference finds an optimal approximation to the Bayesian posterior distribution, but even the exact Bayesian posterior is often not meaningful under model misspecification. We propose predictive variational inference (PVI): a general inference framework that seeks and samples from an optimal posterior density such that the resulting posterior predictive distribution is as close to the true data generating process as possible, while this closeness is measured by multiple scoring rules. By optimizing the objective, the predictive variational inference is generally not the same as, or even attempting to approximate, the Bayesian posterior, even asymptotically. Rather, we interpret it as implicit hierarchical expansion. Further, the learned posterior uncertainty detects heterogeneity of parameters among the population, enabling automatic model diagnosis. This framework applies to both likelihood-exact and likelihood-free models. We demonstrate its application in real data examples.
Deep Learning · Large Language Models
In-context learning (ICL) adapts large language models (LLMs) to new tasks by conditioning on demonstrations in the prompt without parameter updates. With long-context models, many-shot ICL can use dozens to hundreds of examples and achieve performance comparable to fine-tuning, yet current understanding of its scaling behavior is largely derived from non-reasoning tasks. We study many-shot chain-of-thought in-context learning (CoT-ICL) for reasoning and show that standard many-shot rules do not transfer. Across non-reasoning and reasoning-oriented LLMs and across non-reasoning and reasoning tasks, we find: (i) a setting-dependent scaling effect, where increasing the number of CoT demonstrations is unstable for non-reasoning LLMs and benefits mainly reasoning-oriented LLMs; (ii) similarity-based retrieval helps on non-reasoning tasks but fails on reasoning, since semantic similarity poorly predicts procedural (i.e., CoT) compatibility; and (iii) an order-scaling effect, where performance variance grows with more CoT demonstrations. We interpret these behaviors by viewing many-shot CoT-ICL as in-context test-time learning rather than scaled pattern matching, and suggests two principles: (i) demonstrations should be easy for the target model to understand, and (ii) they should be ordered to support a smooth conceptual progression. Guided by the principle, we propose Curvilinear Demonstration Selection (CDS), a simple ordering method that yields an average 3.81\% gain across math and narrative reasoning tasks. Overall, our results reframe the long context window from a retrieval buffer into a structured curriculum for in-context test-time learning.
Deep Learning · Other Representation Learning
Deep neural networks learn representations where individual features often lack interpretable meaning; a single neuron may activate for scattered, unrelated inputs. We introduce coherence, a geometric property inspired by neural coding in the brain, where neurons like grid cells and head direction cells respond to contiguous regions of state space. A non-negative matrix is coherent if both each row (sample) attends to geometrically clustered columns (features) and, vice versa, each feature attends to clustered samples. We prove that coherent matrices induce a bounded interleaving between the Vietoris-Rips filtrations of samples and features, guaranteeing that both spaces share compatible topological structure. This geometric constraint facilitates interpretability. For example, if data lies on a circle, coherent features must tile that circle into contiguous arcs. We introduce COH, a differentiable regularizer based on Fréchet variance that enforces coherence during training. Unlike sparsity, which bounds how many samples a feature activates on, coherence bounds *which* samples, requiring geometric connectivity rather than only rarity. This yields not just interpretable features but an interpretable feature space. We validate COH using synthetic and rotated MNIST datasets.
Social Aspects · Accountability, Transparency, and Interpretability
LLM-based multi-agent systems can fail even when planned actions are executed correctly because agents may misjudge their knowledge when evaluating plan feasibility, a phenomenon we term epistemic miscalibration in planning. Unlike execution errors, epistemic miscalibration is latent during planning, as generated plans can remain self-consistent and executable without observable errors; the miscalibration is also dynamic, as new information can alter feasibility assessments, potentially obscuring past miscalibration signals and causing them to recur over time. To address this, we propose the Epistemic Planning Calibration Agentic Workflow (EPC-AW), which assesses whether plans remain supported under varying information conditions rather than directly verifying feasibility. EPC-AW employs Information-consistency-based Plan Selection, selecting plans whose evaluations are stable across agents, together with Consistency-guided Epistemic State Refinement to adapt calibration over time by leveraging past discrepancies to guide future planning. Experiments show that EPC-AW improves system-level success by an average of 9.75\%.
Social Aspects · Accountability, Transparency, and Interpretability
Feature attribution is central to diagnosing and trusting deep neural networks, and Integrated Gradients (IG) is widely used due to its axiomatic properties. However, IG can yield unreliable explanations when the integration path between a baseline and the input passes through regions with noisy gradients. While Guided Integrated Gradients reduces this sensitivity by adaptively updating low-gradient-magnitude features, input-space guidance still produces intermediate inputs that deviate from the data manifold. To address this limitation, we propose **Manifold-Aligned Guided Integrated Gradients** (MA-GIG), which constructs attribution paths in the latent space of a pre-trained variational autoencoder. By ensuring that decoded intermediate images remain aligned with the data manifold, MA-GIG constrains gradient evaluation to statistically valid regions. Through qualitative and quantitative evaluations, we demonstrate that MA-GIG produces faithful explanations by aggregating gradients on path features proximal to the input. Consequently, our method suppresses off-manifold noise and outperforms prior path-based attribution methods across multiple datasets and classifiers.
Applications · Computer Vision
3D Gaussian Splatting (3DGS) enables real-time, high-fidelity view synthesis via explicit scene representations and has recently been extended to dynamic scene modeling. In spite of excellent quality and interpretability, we find explicit Dynamic GS often exhibits generalization degradation in large-motion scenes. Motivated by generalization insights from deep learning and the characteristics of Gaussian primitive optimization, we propose an update mixture strategy. This work focuses on two representative open-source explicit Dynamic GS pipelines and our approach includes: (i) a space–time dependent Strictly Sparse Update with additional regularization to stabilize adaptive updates; (ii) a constant-corrected adaptive algorithm to attenuate the over-scaling of primitive gradients, yielding a stable mixture of adaptive and non-adaptive steps; and (iii) attributes mixture via Stochastic Attribute Averaging to mitigate frame-preference under motion disturbances. Experiments show consistent improvements and reduced generalization issues, highlighting the role of non-adaptive updates and the influence from frame-preference in explicit Dynamic GS optimization.