F E Silva

Francisco Ferreira da Silva, Stefan Heimersheim

Neural networks are thought to represent concepts as directions in their activation space, and superposition lets them encode more concepts than they have dimensions. It is natural to ask whether they can also compute more functions than they have neurons, i.e., perform computation in superposition. In this regime many functions of sparse inputs are evaluated by a layer with fewer neurons than there are functions to compute. Representation in superposition is by now fairly well understood, but computation in superposition is not, and there are few toy models of it arising through training rather than being hand designed. As a toy model of computation in superposition we study the compressed-computation setup: a single-hidden-layer ReLU network with 50 neurons that must compute the ReLU of each of 100 sparse input features. We show that training it under an $L^4$ loss (the mean fourth power of the error), rather than the usual $L^2$, elicits a solution that appears to compute all features in superposition. We then reverse-engineer this solution. We find that the network assigns each feature a sparse binary codeword over neurons and decodes it with a pseudoinverse of the encoder. Given these codewords, a description with only three scalars recovers most of the network's performance, and we validate it by building equivalent networks from hand-designed codes.

Francisco Ferreira da Silva, Stefan Heimersheim

Understanding the features of large language models (LLMs) is a central goal of interpretability. LLMs are commonly assumed to use superposition to represent more features than they have dimensions. They may not only represent features in superposition but also perform computation in superposition. Theory predicts that computing in superposition requires error correction that privileges feature directions over generic ones, but this prediction has not been tested empirically. We propose an empirical test of error correction in LLMs based on activation perturbations. Perturbing residual-stream activations, we find that they are robust to small perturbations--forming activation plateaus consistent with error correction--but less robust along candidate feature directions ("pure" directions, constructed from contrastive prompt pairs) than along mixtures of two such directions, indicating that the pure directions are privileged. We quantify this privilegedness by modeling the perturbation effect as a function of the $L^p$-norm of its decomposition into feature components. For $p=2$ the response is a quadratic form with at most as many nonzero eigenvalues as the residual-stream dimension, which cannot privilege the many feature directions superposition requires. $p>2$ lifts this constraint and is consistent with feature-specific error correction. We find $p>2$ for contrastive, MELBO, and SAE-decoder directions, and $p\approx2$ for random and PCA directions (controls). These results replicate across Gemma-2-9B, Qwen3-1.7B, Llama-3.1-8B, Mistral-7B-v0.3, Aya-Expanse-8B, and Yi-1.5-9B. We further validate our method on a toy model of error correction with known ground-truth features, recovering $p>2$ for true feature directions, degrading toward $2$ as we rotate away from them.

Henrique Ferraz de Arruda, Andreia Sofia Teixeira, Pranay Gundala Reddy et al.

Despite raising concerns about the mental health effects associated with the usage of TikTok, little is known about how related content is framed by creators and received by audiences. We collect the content of 28,341 TikTok videos and 80,130 comments from Mental Health Awareness Month (May) in 2023 and 2024 via the TikTok Research API, and study how the tone of awareness varies across topics and years. We characterize "tone" as the emotional and interpersonal framing of mental health discourse, operationalized through sentiment and toxicity measures. We extract topics from video text using BERTopic and log-odds keywords, then quantify topic-conditioned sentiment (XLM-T) and toxicity (Detoxify) separately for video transcriptions and comments. Sentiment captures the affective valence of content, while toxicity reflects the presence of harmful or abusive language. We find a stable set of recurring themes across years, spanning clinical conditions, emotional disclosure, self-care, and campaign-oriented content, with engagement highly skewed toward a small subset of topics. All sentiment and toxicity analyses are computed separately for video content and comments, allowing us to distinguish between content production and audience reception. Sentiment in videos is often negative for emotionally charged topics, while comments tend to shift toward more mixed or positive polarity, especially for suicide prevention. Toxicity is low in median overall, but exhibits longer-tailed outliers in comments than in videos that are more pronounced in comments and concentrated in specific topics (e.g., "Duet", "Suicide Prevention", and "Psychisch"). Overall, our results provide a topic-level decomposition of mental health discourse on TikTok during awareness-month campaigns.