Research directions opened by ICA lens.

Standard compact ICA returns at most d components for a d-dimensional activation space. One way around this hard limit is to fit ICA on different datasets or distributions, then compare the resulting bases in the same activation space. Different corpora may expose different non-Gaussian directions, giving a route toward a richer component inventory without relying on a single overcomplete fit. Another route is to test higher-capacity ICA variants such as overcomplete ICA, adaptive or deflationary FastICA, Infomax, JADE, and heavy-tail-aware objectives.

Once an ICA model is fit, the explorer already exposes top examples, opposite-side examples, signed scores, ERF, trace plots, and prompt tests. A natural next step is to use this evidence to propose component labels automatically, then hand the candidate labels to humans for verification.

The current Effective Receptive Field diagnostic asks how much left context is sufficient to recover a component response. Future work can make this more principled: test robustness, compare recovery criteria, connect ERF to annotation difficulty, and relate component scope to model computation.

The current pipeline loads activation matrices into memory, which becomes limiting for 27B-scale models and beyond. A scalable ICA Lens would need better memory management: distributed fitting, streaming or blockwise whitening, activation offloading, and algorithms that can move between CPU, disk, and GPU without treating the full dataset as one in-memory matrix.

ICA Lens currently focuses on embeddings and residual-stream states. A broader analysis could include attention outputs, MLP outputs, residual updates, shared bases across layers, or multiple sites at once. This would help study how directions emerge, transform, persist, or disappear through the forward pass.

SAEBench TPP suggests that zeroing a small number of ICA coordinates can selectively move probe-relevant behavior. A practical steering workflow would need to edit signed scores, reconstruct through the writing map, the pseudoinverse of the reading map R, patch back into the residual stream, and check whether pseudoinverse quality and conditioning are good enough for stable edits outside benchmark probes and against strong task-specific baselines.

ICA and SAEs expose related but non-redundant directions in activation space. A hybrid method could combine ICA's compact non-Gaussian basis with SAE-style overcomplete sparse reconstruction, using the strengths of both to improve component discovery, labeling, and intervention.

ICA can also be fit on image-text datasets rather than text-only corpora. For VLMs, including image-token activations in the decomposition could help reveal what visual token positions represent in deeper layers and how visual evidence mixes with text through the model.

Row normalization makes ICA fitting more stable and supports the idea that directions carry important structure even when raw activation norms are set aside. This opens a deeper question: how much of LLM representation geometry becomes simpler on the normalized sphere, and what does that reveal about features, contexts, and interventions?