Modelling Emotional Memory in Children with Tensor Networks

Linear attention and state-space models provide linear-time sequence modeling, but their recurrent memory remains a second-order tensor (a matrix), limiting the order of interactions that can be represented in the state. We introduce the RunningTensor, which generalizes this memory to an order-$o$ tensor, updated by a rank-1 outer product and read by contracting against $o-1$ vector queries. Order $2$ recovers linear attention; we study order $3$ as a proof of concept, retaining both recurrent and parallel forms while remaining linear in sequence length $T$ and improving working memory capacity from $\mathcal{O}(W^2)$ to $\mathcal{O}(W^o)$. On synthetic multi-query associative recall, RunningTensor outperforms linear-attention and SSM baselines. After pretraining, it also improves performance on language-understanding and non-synthetic retrieval tasks, suggesting that higher-order recurrent state can provide useful additional memory capacity beyond matrix-valued state.

Current language model memory systems store what happened but not how it felt. This distinction -- between semantic memory (knowing about a past event) and episodic memory (re-experiencing it) -- was identified by Tulving as the difference between noetic and autonoetic consciousness. Damasio demonstrated that humans with intact knowledge but absent emotional markers exhibit impaired decision-making. We bridge this gap for language models. Using Gemma 3 1B-IT with pretrained Gemma Scope 2 sparse autoencoders, we identify 310 emotion-exclusive features at layer 22 with psychologically valid geometry. We construct distinctive-feature emotion vectors during experience and partially re-inject them during recall, triggered by context similarity at layer 7. We test four conditions paralleling Damasio's framework: A (no memory), B (semantic labels), C (emotion echo), and BC (semantic + echo). For emotional orientation, the echo alone steepens the threat-safety gradient: the regression slope of threat rating on contextual similarity is 0.80 for C vs 0.56 for A ($p$=0.011, permutation test). For decisions, the echo amplifies knowledge into action: BC=80% good choices vs B=52% ($z$=+2.60, $p$<0.01), while the echo alone has no effect (C=22%, n.s.). The echo changes how the model feels independently, but changes what it does only when combined with knowledge -- replicating Damasio's core finding. The echo amplifies knowledge. It does not replace it.

Recent work identified emotion vectors in Claude Sonnet 4.5, which are internal representations that encode emotion concepts, causally influence behavior, and exhibit geometry mirroring human psychological structure. We test the generality of these findings in two open-weight models, Apertus-8B-Instruct-2509 and Gemma-4-E4B-it, extracting emotion contrast vectors across all layers, using two model-generated corpora. We recover valence geometry for both models, with peak PC1--valence correlations of $r = 0.76$ and $r = 0.83$, approaching the $r = 0.81$ reported for Claude.Beyond replication, we observe notable differences in how valence representations emerge across model depth. In Gemma-4-E4B-it, valence is strongly encoded in early layers but collapses towards later layers, whereas Apertus-8B-Instruct-2509 exhibits the opposite pattern, with valence representations absent in early layers, but emerging at mid depths. Arousal encoding, in contrast, is sensitive to the extraction corpus: both models show stronger PC2--arousal alignment with Gemma-generated stories ($r$ up to $0.45$) than Apertus-generated ones ($r \leq 0.21$), suggesting arousal-relevant cues are unevenly distributed across generated corpora. We open-source our experiment code and dataset for reproducible investigation of emotion representations across language model architectures.