A Miniature Brain Transformer: Thalamic Gating, Hippocampal Lateralization, Amygdaloid Salience, and Prefrontal Working Memory in Attention-Coupled Latent Memory

We present a memory-augmented transformer in which attention serves simultaneously as a retrieval, consolidation, and write-back operator. The core update, $A^\top A V W$, re-grounds retrieved values into persistent memory slots via the Gram matrix $A^\top A$, providing a principled tripartite projection: observation space $\to$ latent memory $\to$ supervised transformation. We partition the memory into lateralized left and right banks coupled through a sign-controlled cross-talk matrix $W_s$, and show that the sign of this coupling is decisive for specialization. Excitatory cross-talk ($s=+1$) causes bank-dominance collapse: one bank monopolises all inputs and $\mathcal{P}_{ct} \to 0.5$, despite lowering task loss. Inhibitory cross-talk ($s=-1$), motivated by the net inhibitory effect of callosal projections in human cortex, actively suppresses contralateral bank activation and achieves saturated specialization ($\mathcal{D}_{sep} = \pm 1.00$, $\mathcal{P}_{ct} \approx 0$). On a controlled symbolic benchmark combining an episodic bijection cipher (requiring associative recall) with a strict arithmetic progression (requiring rule extraction), the inhibitory model reduces cipher-domain loss by $124{\times}$ over the baseline while matching it on the arithmetic domain, confirming that persistent lateralized memory is necessary for episodic recall but not for rule-based prediction.

We introduce the Preisach Attention Layer (PAL), a novel sequence modelling architecture grounded in the classical Preisach hysteresis operator from mathematical physics. PAL replaces the softmax attention mechanism with a binary relay operator parameterised by learned activation and deactivation thresholds, maintaining a stack of local extrema as its internal state. A single-layer PAL-Transformer with O(1) depth is Turing-complete under arbitrary precision arithmetic, achievable through simulation of a two-stack pushdown automaton -- in contrast to the O(log n) depth required by standard hard-attention transformers. Second, we prove that the function classes computable by PAL and by the transformer are incomparable: PAL computes historical range statistics in O(1) layers that require O(log n) layers for transformers, while transformers support random-access retrieval that PAL cannot perform without auxiliary state. The separating property is rate-independence -- PAL responds only to the sequence of local extrema, not to absolute token positions or temporal spacing. Third, we show that the extremum stack constitutes a minimal sufficient statistic of the input history for all rate-independent functionals, providing a formal analogue of the wiping property in classical hysteresis theory. PAL is thus an efficient architecture for tasks with long episodic memory and weak positional dependence, with O(n log n) total inference cost versus O(n^2) for standard attention.

Memory consolidation, the process by which transient experiences are transformed into stable, structured representations, is a foundational organizing principle in the human brain, yet it remains largely unexplored as a design principle for modern sequence models. In this work, we leverage established neuroscientific theories of memory consolidation and cross-frequency coupling to propose the Hierarchical Memory Module (HMM), a neural memory architecture composed of two functionally distinct sub-modules that operate at different update frequencies. Inspired by the transformation hypothesis, the low-frequency sub-module produces high-level representations that capture abstract, gist-level knowledge, while the high-frequency sub-module produces fine-grained representations that preserve richer episodic detail. The final memory output is dynamically reconstructed as a context-dependent combination of both representations, analogous to the reconstructive nature of human memory retrieval. We integrate HMM into a Transformer-based language decoder to form Mela, a family of memory-augmented language models that perform online memory consolidation at test time. To further exploit the multi-granularity memory representations produced by HMM, we introduce MemStack, a method that distributes different levels of memory features across the early layers of the decoder without introducing additional tokens. Experiments on language modeling demonstrate that Mela outperforms Transformer baselines across all the model sizes. Moreover, with the pretrained context length fixed at 4K, Mela maintains performance on significantly longer contexts, whereas Transformer baselines degrade rapidly beyond their training length. Extensive ablation studies validate the contribution of each component and provide guidance for practical configuration.