Subspace Intervention Framework

The deployment of a geoengineering program to cool Earth's climate may be imminent. It is crucial that tools be developed to ensure that such a program would achieve its objectives while minimizing disruption. Here we exploit recently developed differentiable atmospheric models to demonstrate a novel geoengineering control strategy. In the differentiable primitive-equation atmospheric model JAX-GCM we impose a uniform $+4$,K ocean warming and ask what pattern of sea-surface temperature cooling -- in five ocean-masked zonal bands of prescribed SST forcings whose amplitudes are free -- returns land near-surface air temperature closest to the model's own unwarmed climatology. This idealized set-up represents a cooling pattern that could be delivered physically either by marine cloud brightening or stratospheric aerosol injection. Gradients through chaotic dynamics decorrelate from the true sensitivity beyond the Lyapunov horizon, so we optimize greedily over segments of 8 to 14 days, following receding-horizon control. The learned strategy removes $92.3 \pm 0.4\%$ of the realized land warming across a ten-member ensemble of two-year rollouts, and a three-year run sustains it. If we use the spatial pattern of land temperature as the optimization objective, the distributions of precipitation, evaporation, and specific humidity over land are restored as well, even though they are not included in the objective function. The learned strategy from JAX-GCM replayed in the AI emulators LUCIE and NeuralGCM without re-optimization is successful, suggesting robustness. These promising results demonstrate a strategy for designing optimal climate interventions that can be applied broadly for geoengineering scenarios under consideration.

We ask whether a small, directly addressable hidden-state intervention can place a learned world model on an intended counterfactual future and then let the model's own dynamics carry that future forward. In a controlled two-object collision environment, we study a 192-dimensional recurrent model trained on factual and locally edited counterfactual trajectories. Candidate carriers are learned from training-only counterfactual-minus-factual hidden differences, and an affine map predicts carrier coordinates from the factual state and requested edit without access to the native counterfactual hidden state at test time. For bounded single-component velocity edits, rank 4 is the smallest tested rank on the preregistered grid that satisfies the development criteria. A one-shot rank-4 patch launches a 12-transition autonomous rollout without future observations, teacher forcing, repeated hidden-state correction, or physical-state clamping. The frozen procedure satisfies the preregistered 2-of-3 fresh-checkpoint replication rule and remains reusable at nearby anchors. The same Single-derived carrier and Single-only affine map also support bounded same-object two-component requests. Across the matched training regimes, broader counterfactual support was associated mainly with better Joint rollout accuracy and more additive Joint hidden responses. Composition-related structure is enriched in the rank-4 subspace but is not confined to it, and local recurrent diagnostics show strong one-step coupling from the carrier to the rest of the hidden state. A position-edit stress test fails the required specificity controls. Together, these results support a compact dynamics-effective intervention-entry interface, not a closed four-dimensional state or an intrinsic state dimension.

The wide-scale use of sparse autoencoders (SAEs) as interpretability tools is limited by inconsistent links between SAE features and model behavior. Features with clear activation descriptions may have weak or unexpected causal effects; steering can vary across prompts or oppose the intended direction; and activation-based feature selection can miss features that produce the desired output change. Prior work has studied feature geometry inside the model, where features are computed. We instead study the geometry of changes in model logits caused by feature interventions. We introduce Feature-Effect Geometry Analysis (FEGA), an unsupervised framework that removes the same active SAE feature across contexts and analyzes the resulting cloud of logit changes. Across SAE variants, consistent one-dimensional effects are rare: few features behave like reusable directions. To interpret this variation, we distinguish value-like features, tied to static information such as factual attributes, from pointer-like features, associated with context-dependent operations. Value-like features more often exhibit structured, low-dimensional effects, although these effects typically span several directions. Pointer-like features, by contrast, predominantly exhibit diffuse effects. Our results show that a feature can be interpretable and causally relevant without providing a stable direction for steering.

We evaluate when sparse autoencoder (SAE) features act as localized control handles for safety-relevant behavior. This question is difficult because apparent success can arise from weak interventions, mismatched baselines, model robustness, or degenerate outputs that automated safety judges mark as unsafe without representing meaningful harmful compliance. We introduce a matched coherence-gated evaluation protocol for runtime safety interventions: methods are compared at matched target-effect points, and the primary target metric counts harmful compliance only when an output is both judge-unsafe and coherent. Applying this protocol to three prompt splits on Gemma-2-9B-it with a Gemma Scope layer-20 residual SAE, we find that SAE feature ablation has a narrow useful regime. SAE top800 reaches a low-to-mid target effect with lower total perturbation and competitive utility, but SAE top1600 loses utility relative to a matched dense refusal-direction baseline, and SAE top3200 primarily induces coherence collapse. Human audit confirms that coherence gating removes unsafe-only artifacts, and feature diagnostics show that the useful regime is driven by a stable head of refusal-aligned features whose activation separation decays rapidly with rank. These results argue that SAE-based safety interventions should be evaluated as regime-dependent control mechanisms rather than assumed to be uniformly localized.

Language models perform a wide range of tasks at varying levels of abstraction with the capacity to flexibly infer tasks from context, execute multiple tasks simultaneously, and select among competing tasks. To study the role of model components in task behaviour, their causal influence can be investigated through interventions. Prior work on model steering has largely focused on interventions along global directions in activation space, modeling task representations as approximately linear and additive. By studying interventions at the neuron level, we find substantial, neuron-specific nonlinear effects on model outputs that are not captured by current steering approaches. We introduce Distributed Sparse Interventions (DSI), an intervention approach that considers nonlinearities and interactions between neurons across layers to identify sparse sets of neurons that elicit task-relevant computations. Across a range of tasks, we demonstrate that DSI can activate task behaviour in instruction-tuned language models by localising and intervening on as few as 0.01% of neurons, highlighting the effectiveness of sparse, distributed interventions in the neuron basis. Additionally, adopting a set-based perspective enables computations over the identified neuron sets, offering insights into the roles of individual neurons by analysing their effects across tasks. Through sparse interventions, DSI enables fine-grained control over model behaviour, localisation of task-relevant neuron sets, and furthers our understanding of task composition.

Diffusion architectures now encompass convolutional UNets as well as transformer-based designs such as Diffusion Transformers (DiTs), inspired by Vision Transformers (ViTs), yet the effects of structured geometric perturbations within these architectures remain poorly understood. We study this question through a unified framework that applies reflection-based elements of the dihedral group to intermediate hidden states as controlled internal interventions, contrasting geometrically consistent and inconsistent variants. Using activation-level diagnostics, including Self-Consistency Shift (SCS), Activation Mass Scatter (AMS), and Drift, we analyze feature stability and geometric drift. We find that consistent transformations improve stability, while inconsistent ones induce predictable, architecture-specific failures. In the main Stable Diffusion 2.1 U-Net study, we evaluate seven intervention modes over three seeds and complement the internal diagnostics with image-level FID, KID, CLIP score, and LPIPS diversity. Taken together with supporting ViT and controlled DiT analyses, these results establish geometric consistency as a key principle for stable hidden-state interventions in spatially structured vision and diffusion models.

We introduce a controlled subspace intervention framework to investigate how self-supervised Vision Transformers (ViTs) encode dense geometric information. While linear probing is widely used to assess geometric representations, it treats features as a black box, failing to disentangle the underlying topology. To address this issue, we decompose the weights of converged linear probes to isolate the low-rank subspaces containing explicit geometric signals using Singular Value Decomposition (SVD). Our perspective yields three key insights: (1) Pre-training objectives determine how features are encoded. DINOv2 aligns spatial features for efficient linear extraction, while Masked Autoencoders (MAE) tend to disperse these signals, requiring a broader spatial context. (2) Explicit geometric representations are highly compressible, suggesting dense predictive heads could potentially be constrained to low-rank subspaces with minimal performance loss. (3) The layer-wise task affinity suggests that geometric precision peaks at intermediate layers before yielding to semantic abstraction in the final layers. By connecting internal encoding mechanics with downstream performance, these findings provide a basis for effective feature selection and lightweight decoder design. The source code is available at https://github.com/Zhou-Weichen/Geosubprobe.

Sparse Autoencoders (SAEs) decompose residual-stream activations into interpretable features. Recent latent-space defenses increasingly rely on these decompositions, assuming that identified "unsafe" SAE features serve as actionable handles for monitoring and intervention. In this paradigm, clamping a specific harmful feature is expected to reliably prevent model misbehavior. However, we show that this success may hide a recoverable failure mode: the clamp may block one visible route to a behavior without eliminating the behavior itself. We formulate this vulnerability as post-intervention recovery, a constrained residual-space optimization problem. Starting from the post-intervention residual state, we optimize residual perturbations to recover the pre-intervention behavior while preserving the post-intervention values of the targeted SAE features. Even under a strong threat model where the intervention remains active throughout optimization and generation, recovery remains possible. To rule out that recovery simply undoes the intervention, we use encoder-orthogonal updates for single-layer interventions and the corresponding feature-map Jacobian in the cross-layer setting. Across TPP, unlearning, IOI, and refusal steering experiments, this stress test reveals recoverable behavior despite successful feature-level intervention. Especially in the safety-critical refusal-steering setting, we achieve a 95.8% recovery rate on valid samples while keeping defended-feature relative drift to 0.131, substantially below suffix-based baselines. A recovery-path attribution analysis further localizes this recovery to the SAE reconstruction residual, the component left unexplained by the SAE. These results expose a gap between feature-level control and behavioral completeness: SAE features can support causal intervention, but controlling them does not guarantee control over the underlying behavior.

Generative models for counterfactual outcomes have great potential to support decision-making under complex interventions, but existing approaches are limited by unstable estimation, poor generalization across environments, and bias from nuisance model misspecification. We introduce ADIGen, a framework for automatic, debiased, and invariant counterfactual generation under general interventions, including high-dimensional interventions and outcomes. ADIGen combines Riesz regression to avoid unstable density-ratio estimation, causal invariance to improve generalization under distribution shift, and orthogonal statistical learning to obtain doubly robust guarantees against nuisance model misspecification. We provide excess-risk bounds showing that ADIGen controls counterfactual risk under general interventions, with a product-bias nuisance remainder and an invariant risk bound across environments.

Causal representation learning aims to infer the high-level latent causal concepts that give rise to observed low-level measurements. This is particularly relevant for heterogeneous data from different environments or domains since distribution shifts often arise through sparse, localized changes in some of the underlying causal mechanisms, while other parts of the generative process remain unchanged. Whereas identifiability of causal representations has been studied extensively, practical uncertainty-aware methods and real-world use cases remain less explored. In this work, we propose a Bayesian approach to learning causal representations from multi-environment data, focusing on the case of discrete causal concepts and unknown multi-node soft interventions. To this end, we translate causal assumptions and interpretability desiderata into suitable priors and parametric choices within a hierarchical model. We then devise an inference scheme based on sequential Monte Carlo sampling to approximate the resulting multimodal posterior. We showcase our approach through case studies on social survey data, where latent causal concepts correspond to cultural values or political opinions, measurements to survey responses, and environments to different countries or states. Our model infers meaningful high-level concepts and plausible causal relations among them, demonstrating its utility for learning causal representations of complex real-world data.

As language models are increasingly deployed in real-world applications, the ability to erase specific knowledge from them becomes critical for safety and compliance. Prominent methods seek persistent removal by updating the model's parameters, yet the target knowledge often can be recovered through adversarial prompting or relearning. In this work, we hypothesize this limitation stems in part from existing methods overlooking the embedding layer. To address this, we introduce EMBedding ERasure (EMBER), a plug-n-play erasure module that leverages Sparse Matrix Factorization for precise erasure of concept-related features from token embeddings. Through comprehensive evaluations across diverse concepts on Gemma-2-2B-it and Llama-3.1-8B-Instruct, we find that augmenting existing methods with EMBER consistently improves erasure efficacy and specificity across task formats, with minimal coherence loss. Moreover, it dramatically improves robustness to relearning, reducing regained accuracy by up to 50%, limiting it to 35% on Llama compared to 70%-76% for prior methods. Further analysis shows that the coherence cost is localized, affecting only a small set of concept-exclusive tokens. Our work establishes that precise embedding-level intervention is necessary for robust concept erasure, and demonstrates that existing methods can benefit from such augmentation.

Driving a system from one state to another through targeted interventions is a fundamental challenge in science, yet most predictive models offer limited mechanistic insight and no principled framework for decision-making. Here we present COAST (Causally Optimal Actions for State Transitions), a causal-intelligence approach for the in-silico design of constrained interventions that induce user-defined state transitions. Given data characterizing source and target states, COAST learns context-specific causal graphs and structural causal models, attributes observed distributional shifts to mechanism-level causal drivers, and introduces a novel constraint-aware multi-objective optimization formulation that balances transition efficacy, intervention complexity, and target-state stability. The approach is modular and domain-agnostic, integrating feature selection, causal discovery, causal modeling, and intervention identification and evaluation through interchangeable components. Across synthetic benchmarks and real biological datasets, COAST recovers key causal drivers and identifies robust single- and multi-target intervention strategies that achieve desired state transitions, accompanied by transparent mechanistic rationales to guide experimental validation.

Distilling demonstration effects into hidden-space interventions offers a lightweight alternative to full finetuning. However, existing multimodal variants are mostly evaluated on short-form tasks, where outputs end after a few tokens. Extending these methods to long-form generation exposes a fundamental yet underexamined limitation: token-level distillation implicitly treats all output tokens as equally informative, but long-form outputs are dominated by high-frequency template and grammatical tokens, while the tokens that actually determine output quality are sparsely distributed. In medical report generation (MRG), two such decisive tokens stand out: pathology-related tokens that determine diagnostic content, and the end-of-sequence (EOS) event that determines termination. Both receive insufficient supervision under uniform cross-entropy, and autoregressive decoding further compounds the problem by drifting away from teacher-forced trajectories. We propose DIVE, a frozen-backbone distillation framework that addresses long-form report generation through two complementary mechanisms matched to these failures. Decisive-token supervision restores supervision balance by upweighting the cross-entropy contribution of pathology-related tokens and the EOS event, ensuring that content fidelity and termination are learned during training rather than imposed at decoding time. State-conditioned dynamic steering replaces fixed open-loop residuals with hidden-state-dependent adapters, allowing the injected signal to adapt as decoding drifts. Experiments on MIMIC-CXR and CheXpert Plus with two medical VLM backbones show that DIVE consistently ranks among the strongest methods across lexical and clinical-proxy metrics. Our method achieves the best BLEU-4, ROUGE-L, and RadGraph F1 in all dataset--backbone settings, while remaining competitive on coarse label-level CheXbert F1.

Intervention is one of the most representative and widely used methods for understanding the internal representations of large language models (LLMs). However, existing intervention methods are confined to linear interventions grounded in the Linear Representation Hypothesis, leaving features encoded along non-linear manifolds beyond their reach. In this work, we introduce a general formulation of intervention that extends naturally to non-linearly represented features, together with a learning procedure that further enables intervention on implicit features lacking a direct output signature. We validate our framework on refusal bypass steering, where it steers the model more precisely than linear baselines by intervening on a non-linear feature governing refusal.

Causal probing methods aim to test and control how internal representations influence the behavior of generative models. In causal probing, an intervention modifies hidden states so that a property takes on a different value. Most existing approaches define such interventions by training an auxiliary probe classifier, which ties the method to a specific task or model and risks misalignment with the model's predictive geometry. We propose Hidden-state Driven Margin Intervention (HDMI), a probe-free, gradient-based technique that directly steers hidden states using the model's native output. HDMI applies a margin objective that increases the probability of a target continuation while decreasing that of the source, without relying on probe classifiers. We further introduce a lookahead variant (LA-HDMI) for text editing that backpropagates through the softmax embeddings, modifying the current hidden state so that the likelihood of user-specified tokens increases in next token generations while preserving fluency. To evaluate interventions, we measure completeness (whether the targeted property changes as intended) and selectivity (whether unrelated properties are preserved), and report their harmonic mean as an overall measure of reliability. HDMI consistently achieves higher reliability than prior methods on the LGD agreement corpus and the CausalGym benchmark, across Meta-Llama-3-8B-Instruct, and Pythia-70M.

Causal abstraction offers a principled framework for mechanistic interpretability, aligning a high-level causal model with the low-level computation realized by a neural network through counterfactual intervention analysis. Existing methods such as distributed alignment search (DAS) learn expressive subspace interventions, but the relevant neural site is unknown a priori, so finding a handle requires a computationally burdensome search over candidate sites. We introduce PLOT (Progressive Localization via Optimal Transport), a transport-based framework that localizes causal variables from the output effect geometry of abstract and neural interventions. PLOT fits an optimal transport coupling between abstract variables and candidate neural sites, yielding a global soft correspondence that can be calibrated into intervention handles. In simple settings, a single coupling over individual neurons suffices. In larger models, PLOT is applied progressively, moving from coarse sites such as tokens, timesteps, or layers to finer supports such as coordinate groups or PCA spans, and optionally guiding DAS based on the localized signal. Across experiments of increasing complexity, transport-only PLOT handles are exceedingly fast and competitive on accuracy, while PLOT-guided DAS reaches DAS-level accuracy at a fraction of full DAS runtime, providing an efficient localization engine for causal abstraction research at scale.

Large language models (LLMs) can acquire new capabilities through fine-tuning, but continual adaptation often leads to catastrophic forgetting. We propose CRAFT, a continual learning framework that avoids updating model weights by instead learning low-rank interventions on hidden representations. CRAFT proceeds in three stages: it first routes each task to a group of similar tasks based on output-distribution divergence; it then fine-tunes the model using a Kullback-Leibler (KL) divergence against the group's prior state, which directly controls forgetting and determines convergence; finally, it merges interventions for the updated task into the shared representation using the same KL signal. This design unifies routing, regularization, and merging through a single KL-based objective. CRAFT improves overall performance and reduces forgetting compared to strong LoRA-based approaches across multiple benchmarks and model scales, while remaining robust to task ordering. These results suggest that controlling adaptation in representation space, guided by output-space divergence, provides a scalable and principled approach to continual learning in LLMs.

Transportation surveys are widely used to understand travel preferences and adoption barriers, yet most survey-based analyses remain descriptive or predictive and rarely provide sparse, policy-feasible intervention strategies. We study sparse counterfactual community intervention from survey responses, where the goal is to shift a target respondent group toward a desired reference group through controllable survey-variable adjustments. We formulate this task as a policy-feasible distributional alignment problem using a fixed-basis nonnegative latent representation that preserves pre/post comparability and provides a stable map from latent factors to original variables. To make latent movement actionable, target-relevant latent factors are identified through Shapley-guided attribution and transferred to controllable variables as intervention priorities. Feasible group-level adjustments are then learned by minimizing an entropy-regularized optimal-transport discrepancy between the post-intervention target distribution and the reference distribution, together with a weighted $\ell_{2,1}$ penalty that promotes shared policy-lever sparsity. Experiments on real-world transportation survey datasets show that the proposed framework produces compact and interpretable policy-feasible interventions with explicit adjustment magnitudes, improves population-level conversion, and preserves intervention sparsity. Code and datasets are publicly available at: https://github.com/pangjunbiao/latent-group-alignment.git

Causality is a central topic in scientific inquiry, yet for complex systems, the identification and analysis of synergistic causation remain a challenging and fundamental problem. In the context of causal relations among multivariate variables, a decomposition framework grounded in interventionist causation is still lacking. To address this gap, this paper proposes Partial Effective Information Decomposition (PEID), a framework that decomposes the influence of multiple source variables on a target variable under maximum-entropy interventions into unique and synergistic information, thereby providing a unified and computable characterization of synergistic causal relations. Theoretically, in the three-variable case, the proposed framework is compatible with the major axioms of Partial Information Decomposition (PID). Empirically, under maximum-entropy interventions, correlations among input variables are removed, causing redundancy to vanish and thereby enabling PEID to compute synergistic relations. Furthermore, based on this framework, it is possible to define causal graphs containing hyperedges as well as downward causation, thus offering a unified toolkit for analyzing cross-scale and multivariate causal mechanisms in complex systems. Finally, applying the framework to a machine-learning-based air quality forecasting task on KnowAir-V2, we demonstrate that PEID can extract interpretable inter-station causal structures from a learned dynamical model. These results suggest that PEID provides a general interventionist information-theoretic tool for analyzing multivariate and synergistic causal mechanisms in complex systems.

Most tabular-data generators match marginal statistics yet ignore causal structure, leading downstream models to learn spurious or unfair patterns. We present TabSCM, a mixed-type generator that preserves those causal dependencies. Starting from a Completed Partially Directed Acyclic Graph (CPDAG) found by any causal structure discovery algorithm, TabSCM (i) orients edges to a DAG, (ii) fits root-node marginals with KDE or categorical frequencies, and (iii) learns topologically ordered structural assignments. Such assignments are achieved using conditional diffusion models for continuous variables as child nodes and gradient-boosted trees for categorical ones. Ancestral sampling yields semantically valid records and enables exact counterfactual queries. On seven public datasets, encompassing healthcare, finance, housing, environment, TabSCM matches or surpasses state-of-the-art GAN, diffusion, and LLM baselines in statistical fidelity, downstream utility, and privacy risk, while also cutting rule-violation rates and providing causally meaningful and robust conditional interventions. Because generation is decomposed into explicit equations, it runs up to 583$\times$ faster than diffusion-only models and exposes interpretable knobs for fairness auditing and policy simulation, making TabSCM a practical choice for realism, explainability, and causal soundness.

Semi-supervised domain adaptation (SSDA) seeks to achieve accurate predictions in a target domain with limited labeled target data by exploiting abundant source and unlabeled target data. We study this problem under structural causal models (SCMs), which provide a statistical framework to describe distribution shifts between source and target domains as interventions in the data-generating process rather than ad hoc changes in model parameters. The central phenomenon is that, under low-dimensional interventions, source and unlabeled target data can help identify the high-dimensional shared structure, leaving only a low-dimensional target-specific correction to be learned from limited labeled target data. We formalize this principle for three canonical intervention models and propose the corresponding SSDA methods FT-DIP, FT-OLS-Src and FT-CIP. Under each intervention model, we demonstrate how extending an unsupervised domain adaptation (UDA) method to SSDA can achieve minimax-optimal target performance with limited target labels, with the labeled-target sample complexity scaling with the intervention dimension rather than the ambient dimension. When the distribution shift is underspecified, we propose the Multi-Adaptive-Start Fine-Tuning (MASFT) algorithm, which fine-tunes from multiple adaptive starts and selects among them using a small target validation set, incurring only logarithmic overhead in the number of starts. We validate the effectiveness of our proposed methods through simulated and real data experiments.