Satchel Grant

Linas Nasvytis, Simon Jerome Han, Ben Prystawski et al.

Language models can use verifiable rewards to improve at a wide variety of reasoning tasks. However, both parametric (e.g. RLVR) and non-parametric (e.g. prompt optimization) approaches to doing so typically require hundreds of training samples and thousands of model rollouts, making them expensive in the best case and intractable in the worst. To address this challenge, we introduce Contrastive Reflection (CORE), a non-parametric learning algorithm that compares past reasoning traces to generate insights: short natural-language descriptions of reasoning strategies and constraints that capture differences between successful and unsuccessful problem attempts. Across four reasoning tasks, we demonstrate that CORE enables more rapid improvement than both parametric (GRPO) and non-parametric (GEPA, episodic RAG, and MemRL) methods, while using fewer rollouts. Under fixed rollout budgets with as few as five training samples, we then show that CORE also achieves comparable or greater performance gains than each baseline. Finally, we highlight how CORE is also substantially more context-efficient than non-parametric baselines, requiring fewer prompt tokens while storing learned knowledge as compact, interpretable natural-language insights. Our results therefore suggest that distilling contrasts between successful and unsuccessful reasoning traces into abstract and useful insights can provide a more efficient and interpretable route to model self-improvement than weight updates, prompt optimization, or direct reuse of stored reasoning traces.

Satchel Grant, Victor Gillioz, Jake Ward et al.

Defensive training methods such as positive preventative steering (PPS) and inoculation prompting (IP) offer surprising results through seemingly similar processes: both add trait-inducing objects to large language models (LLMs) during training, and both defend the LLM against acquiring the trait. The surprising success of these methods comes with the question: how do they work? Are PPS and IP doing the same thing? We provide behavioral and mechanistic comparisons of these two methods using "evilness" as a case-study trait. Our central finding is that PPS and IP achieve their defensive benefits through distinct mechanisms. Behaviorally, we show that neither PPS nor IP operates through a purely associative mechanism; and PPS can both defend against trait acquisition and actively reduce pre-existing expression, whereas IP is ineffective in models that were previously finetuned to express the trait. This behavioral divergence is reflected mechanistically: PPS shifts the activation gradient towards an attenuating direction along the PPS vector axis. When the PPS vector is aligned with a trait-expressing axis, it can reverse the gradient pressure, reducing rather than increasing activation along that axis. In contrast, IP continues to resist a precise mechanistic account. Direct cosine similarity analyses reveal that IP has a characteristically different gradient signature than PPS, and qualitative analyses reveal IP's gradient to be more diffuse. Furthermore, IP reduces the next-token prediction loss on trait-expressing data where PPS need not, consistent with the notion that IP "explains away" the trait-expression in the training data. Taken together, our analyses reveal distinct mechanisms by which each method operates and highlight open questions about IP's mechanistic picture.

Satchel Grant, Simon Jerome Han, Alexa R. Tartaglini et al.

A common approach to mechanistic interpretability is to causally manipulate model representations via targeted interventions in order to understand what those representations encode. Here we ask whether such interventions create out-of-distribution (divergent) representations, and whether this raises concerns about how faithful their resulting explanations are to the target model in its natural state. First, we demonstrate empirically that common causal intervention techniques often do shift internal representations away from the natural distribution of the target model. Then, we provide a theoretical analysis of two classes of such divergences: "harmless" divergences that occur in the null-space of the weights and from covariance within behavioral decision boundaries, and "pernicious" divergences that activate hidden network pathways and cause dormant behavioral changes. Finally, in an effort to mitigate the pernicious cases, we modify the Counterfactual Latent (CL) loss from Grant (2025) that regularizes interventions to remain closer to the natural distributions, reducing the likelihood of harmful divergences while preserving the interpretive power of interventions. Together, these results highlight a path towards more reliable interpretability methods.

Satchel Grant, Noah D. Goodman, James L. McClelland

What types of numeric representations emerge in neural systems, and what would a satisfying answer to this question look like? In this work, we interpret Neural Network (NN) solutions to sequence based number tasks using a variety of methods to understand how well we can interpret them through the lens of interpretable Symbolic Algorithms (SAs) -- precise programs describable by rules and typed, mutable variables. We use autoregressive GRUs, LSTMs, and Transformers trained on tasks where the correct tokens depend on numeric information only latent in the task structure. We show through multiple causal and theoretical methods that we can interpret raw NN activity through the lens of simplified SAs when we frame the activity in terms of neural subspaces rather than individual neurons. Using Distributed Alignment Search (DAS), we find that, depending on network architecture, dimensionality, and task specifications, alignments with SA's can be very high, or they can be only approximate, or fail altogether. We extend our analytic toolkit to address the failure cases by expanding the DAS framework to a broader class of alignment functions that more flexibly capture NN activity in terms of interpretable variables from SAs, and we provide theoretic and empirical explorations of Linear Alignment Functions (LAFs) in contrast to the preexisting Orthogonal Alignment Functions (OAFs). Through analyses of specific cases we confirm the usefulness of causal interventions on neural subspaces for NN interpretability, and we show that recurrent models can develop graded, symbol-like number variables in their neural activity. We further show that shallow Transformers learn very different solutions than recurrent networks, and we prove that such models must use anti-Markovian solutions -- solutions that do not rely on cumulative, Markovian hidden states -- in the absence of sufficient attention layers.

Satchel Grant

When can we say that two neural systems perform a task in the same way? What nuances do we miss when we fail to causally probe the representations of the systems, and how do we establish bidirectional causal relationships? In this work, we introduce a method that bidirectionally transfers neural activity between artificial neural networks and uses their resulting behavior as a measure of functional similarity. We first show that the method can be used to transfer the behavior from one frozen Neural Network (NN) to another in a manner similar to model stitching, and we show how the method can differ from correlative similarity measures like Representational Similarity Analysis. Next, we empirically and theoretically show how the method can be equivalent to model stitching when desired, or it can take a form that has a more restrictive focus to shared causal information; in both forms, it reduces the number of required matrices for a comparison of n models to be linear in n. We then present a case study on number-related tasks showing that the method can be used to examine specific subtypes of causal information demonstrating that numbers can be encoded differently in recurrent models depending on the task, and we present another case study showing that MAS can reveal misalignment in fine-tuned DeepSeek-r1-Qwen-1.5B models. Lastly, we augment the loss function with a counterfactual latent (CL) auxiliary objective to improve causal relevance when one of the two networks is causally inaccessible (as is often the case in comparisons with biological networks). We use our results to encourage the use of causal methods in neural similarity analyses and to suggest future explorations of network similarity methodology for model misalignment.

Alexa R. Tartaglini, Satchel Grant, Daniel Wurgaft et al.

Data visualizations are vital components of many scientific articles and news stories. Current vision-language models (VLMs) still struggle on basic data visualization understanding tasks, but the causes of failure remain unclear. Are VLM failures attributable to limitations in how visual information in the data visualization is encoded, how information is transferred between the vision and language modules, or how information is processed within the language module? We developed FUGU, a suite of data visualization understanding tasks, to precisely characterize potential sources of difficulty (e.g., extracting the position of data points, distances between them, and other summary statistics). We used FUGU to investigate three widely used VLMs. To diagnose the sources of errors produced by these models, we used activation patching and linear probes to trace information flow through models across a variety of prompting strategies. We found that some models fail to generate the coordinates of individual data points correctly, and these initial errors often lead to erroneous final responses. When these models are provided with the correct coordinates, performance improves substantially. Moreover, even when the model generates an incorrect response, the correct coordinates can be successfully read out from the latent representations in the vision encoder, suggesting that the source of these errors lies in the vision-language handoff. We further found that while providing correct coordinates helps with tasks involving one or a small number of data points, it generally worsens performance for tasks that require extracting statistical relationships across many data points. Fine-tuning models on FUGU also fails to yield ceiling performance. These findings point to architectural constraints in current VLMs that might pose significant challenges for reliable data visualization understanding.