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Inhibitory Cross-Talk Enables Functional Lateralization in Attention-Coupled Latent Memory
Hong Jeong
Intelligence
Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 94%
Last extracted: 7/20/2026, 7:29:33 AM
Summary
The paper introduces a memory-augmented transformer architecture featuring lateralized left and right memory banks coupled via a sign-controlled cross-talk mechanism. The core innovation is an attention-coupled update operator ($A^\top A V W$) that enables retrieval, consolidation, and write-back. The study demonstrates that inhibitory cross-talk ($s=-1$), inspired by callosal inhibition in the human brain, prevents bank-dominance collapse and achieves saturated functional specialization, significantly reducing loss on episodic recall tasks compared to excitatory or split-brain baselines.
Entities (9)
Relation Signals (7)
Left Memory Bank → iscoupledwith → Right Memory Bank
confidence 96% · partition the memory into lateralized left and right banks coupled through a sign-controlled cross-talk matrix
Inhibitory Cross-Talk → enables → Functional Lateralization
confidence 95% · Inhibitory cross-talk (s=-1)... actively suppresses contralateral bank activation and achieves saturated specialization
Attention-Coupled Latent Memory → outperforms → Standard Transformer
confidence 95% · the inhibitory model reduces cipher-domain loss by 124x over the baseline
Excitatory Cross-Talk → causes → Bank-Dominance Collapse
confidence 94% · Excitatory cross-talk (s=+1) causes bank-dominance collapse: one bank monopolises all inputs
Inhibitory Cross-Talk → improvesperformanceon → Episodic Bijection Cipher
confidence 94% · the inhibitory model reduces cipher-domain loss by 124x over the baseline
Attention-Coupled Latent Memory → uses → Tripartite Projection
confidence 93% · providing a principled tripartite projection: observation space -> latent memory -> supervised transformation
Inhibitory Cross-Talk → inspiredby → Callosal Projections
confidence 92% · motivated by the net inhibitory effect of callosal projections in human cortex
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Abstract
Abstract: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.
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- Source: https://arxiv.org/abs/2603.03355v1
- Canonical: https://arxiv.org/abs/2603.03355v1
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Inhibitory Cross-Talk Enables Functional Lateralization in Attention-Coupled Latent Memory Hong Jeong Department of Computer Information Engineering Inha University in Tashkent Uzbekistan h.jeong@inha.uz Abstract We present a memory-augmented transformer in which attention serves simultaneously as a retrieval, consolidation, and write-back operator. The core update, A⊤AVWA AVW, re-grounds retrieved values into persistent memory slots via the Gram matrix A⊤A A, providing a principled tripartite projection: observation space → latent memory → supervised transformation. We partition the memory into lateralized left and right banks coupled through a sign-controlled cross-talk matrix WsW_s, and show that the sign of this coupling is decisive for specialization. Excitatory cross-talk (s=+1s=+1) causes bank-dominance collapse: one bank monopolises all inputs and ct→0.5P_ct→ 0.5, despite lowering task loss. Inhibitory cross-talk (s=−1s=-1), motivated by the net inhibitory effect of callosal projections in human cortex, actively suppresses contralateral bank activation and achieves saturated specialization (sep=±1.00D_sep=± 1.00, ct≈0P_ct≈ 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 124×124× 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. 1 Introduction Memory-augmented neural networks extend attention-based models with persistent state, enabling long-horizon reasoning and structured retrieval (Weston et al., 2014; Graves et al., 2016; Vaswani et al., 2017). We study a memory-augmented architecture where attention is treated as a latent-space operator for retrieval and consolidation. Instead of using attention solely for lookup, we apply it to update persistent memories through structured write-backs. This view connects similarity-based retrieval with grouping and abstraction by composing attention weights with write transformations. The key distinction is the explicit, bank-wise memory geometry: we separate left and right memory banks and couple them through a sign-controlled cross-talk term. The sign of this coupling encodes a fundamental architectural choice. When cross-talk is excitatory (s=+1s=+1), contralateral values are added to each bank’s update, providing a gradient pathway along which one bank can absorb the other’s function. We show empirically that this causes bank-dominance collapse: the model routes all domains through a single bank, achieving lower raw task loss by abandoning specialization entirely. When cross-talk is inhibitory (s=−1s=-1), motivated by the net inhibitory effect of callosal projections onto cortical interneurons (Innocenti, 1986; Bloom and Hynd, 2005), the contralateral term is subtracted, so the dominant bank actively suppresses the non-dominant one. This sharpens bank boundaries rather than blurring them, achieving saturated specialization (sep=±1.00D_sep=± 1.00, ct≈0P_ct≈ 0). We view attention as an operator that shapes the geometry of memory. The same attention map serves multiple roles simultaneously: retrieval, grouping, differentiation, and consolidation. Applying A⊤A A emphasizes co-activation structure, while value and write transforms dictate how the memory evolves. The lateralized formulation exposes an additional degree of freedom — the sign of inter-bank coupling — that prior memory-augmented attention models have not studied. The remainder of the paper formalizes the A⊤AVWA AVW update, analyzes the three-way cross-talk ablation, and connects the inhibitory design to callosal physiology. 2 Related Work Memory-augmented neural networks. Classical gated recurrent models (LSTM, GRU) maintain implicit hidden state but lack explicit, addressable slots (Hochreiter and Schmidhuber, 1997; Cho et al., 2014). Memory Networks (Weston et al., 2014) and Differentiable Neural Computers (Graves et al., 2016) introduced addressable external memory with content-based read heads, but their write mechanisms are not attention-coupled in the A⊤A A sense we propose. Recent structured-state-space models (S4, Mamba, Jamba) compress long-range history into implicit state parameters via selective scans (Gu et al., 2022; Dao and Gu, 2023; Lieber et al., 2024), forgoing the explicit, inspectable slot structure central to our approach. Lateralization and inter-bank coupling. Functional specialization across anatomically distinct memory stores is well-documented in neuroscience (Innocenti, 1986; Bloom and Hynd, 2005), but it has not been treated as an explicit architectural degree of freedom in differentiable memory models. Multi-head attention (Vaswani et al., 2017) distributes computation across heads but treats all inter-head interactions symmetrically and shares a single key-value space. Mixture-of-experts routing encourages load-balanced specialization but does not model the sign of inter-expert coupling. To our knowledge, no prior work examines sign-controlled cross-bank coupling in a persistent memory architecture, nor connects this design choice to callosal physiology. 3 Attention Operations for Persistent Memory Let Zt∈ℝn×dzZ_t ^n× d_z denote the encoder output, representing a sequence of n latent token vectors. We maintain a hierarchical memory structure consisting of a shared proposal state Pt∈ℝp×dpP_t ^p× d_p and a lateralized semantic memory StS_t (see Figures 1 and 2). Given the current input ZtZ_t and the previous proposal Pt−1P_t-1, we first compute the cross-attention for the proposal state: Qp Q_p =ZtWQ∈ℝn×dk,Kp=Pt−1WK∈ℝp×dk,Vp=Pt−1WV∈ℝp×dv, =Z_tW_Q ^n× d_k, K_p=P_t-1W_K ^p× d_k, V_p=P_t-1W_V ^p× d_v, Ap A_p =softmax(QpKp⊤dk)∈ℝn×p,Cp=ApVp∈ℝn×dv. =softmax\! ( Q_pK_p d_k ) ^n× p, C_p=A_pV_p ^n× d_v. (1) Here, CpC_p is the retrieved context for each token, parameterized by the projection matrices WQ∈ℝdz×dkW_Q ^d_z× d_k, WK∈ℝdp×dkW_K ^d_p× d_k, and WV∈ℝdp×dvW_V ^d_p× d_v. The proposal state is then updated via an attention-coupled write operation, where γ∈(0,1]γ∈(0,1] is a temporal leak factor: Pt P_t =γPt−1+Ap⊤ApVpWp. =γ P_t-1+A_p A_pV_pW_p. (2) 4 Lateralization of Latent Spaces Driven by the updated proposal state PtP_t, we define the lateralized memory StS_t, which is updated via a hierarchical associative mechanism. To model functional lateralization, we physically partition StS_t into two specialized banks, LtL_t and RtR_t, corresponding to the left and right memory pathways. The queries for these lateral banks originate from the newly consolidated proposal state PtP_t, establishing a strict hierarchical information flow Z→Pt→(Lt,Rt)Z→ P_t→(L_t,R_t). Crucially, to allow the model to choose which bank to route each proposal slot to, we form a single joint attention over the concatenated left and right keys: Qlr Q_lr =PtWQ∈ℝp×dk,Klr=[Lt−1WKlRt−1WKr]∈ℝ2m×dk, =P_tW_Q ^p× d_k, K_lr= bmatrixL_t-1W_K_l\\ R_t-1W_K_r bmatrix ^2m× d_k, Alr A_lr =softmax(QlrKlr⊤dk)∈ℝp×2m. =softmax\! ( Q_lrK_lr d_k ) ^p× 2m. (3) The joint softmax ensures the total attention mass sums to one across both banks per proposal slot, so specialization naturally drives the mass for a given slot toward a single bank. We partition AlrA_lr to obtain Al=Alr[:,:m]∈ℝp×mA_l=A_lr[:,\,:m] ^p× m and Ar=Alr[:,m:]∈ℝp×mA_r=A_lr[:,\,m:] ^p× m, with values Vl=Lt−1WVlV_l=L_t-1W_V_l and Vr=Rt−1WVrV_r=R_t-1W_V_r. To permit controlled cross-talk and conceptual abstraction between the lateral banks during consolidation, we define a block-structured write projection: Ws W_s =[WllWlrWrlWrr]. = bmatrixW_l&W_lr\\ W_rl&W_r bmatrix. (4) Assuming the attention overlap between the left and right banks is minimal (i.e., the off-diagonal blocks of the Gram matrix vanish, Al⊤Ar≈0A_l A_r≈ 0), the monolithic update cleanly decouples into bank-specific update equations. We write the general form with a sign parameter s∈+1,−1s∈\+1,-1\ controlling the cross-talk mode: Lt L_t =γLt−1+Al⊤Al(VlWll+sVrWrl), =γ L_t-1+A_l A_l (V_lW_l+s\,V_rW_rl ), (5) Rt R_t =γRt−1+Ar⊤Ar(VrWrr+sVlWlr). =γ R_t-1+A_r A_r (V_rW_r+s\,V_lW_lr ). (6) When s=+1s=+1 (excitatory cross-talk), contralateral values reinforce the ipsilateral bank’s update, encouraging shared representations. When s=−1s=-1 (inhibitory cross-talk), contralateral activity subtracts from the ipsilateral update, actively suppressing contamination from the non-matched bank. Setting Wrl=Wlr=0W_rl=W_lr=0 (frozen) recovers a split-brain baseline with no cross-talk at all. We propose and evaluate the inhibitory variant, motivated by callosal physiology (Section 6.6). This formulation ensures that while each bank predominantly consolidates its own associative history (via WllW_l and WrrW_r), the inhibitory cross-talk actively sharpens the boundary between the specialised banks. 5 Geometric Interpretation of the Attention-Coupled Write The core structural innovation of Attention-Coupled Latent Memory lies in the update operator A⊤AVWA AVW. This mechanism can be systematically decomposed into a sequence of three geometric projections. We first analyze this for the shared proposal state P, and then extend the interpretation to the lateralized semantic banks L and R. 5.1 The Tripartite Projection for a Single Memory State For a generic memory state (such as the proposal P), the update Ap⊤ApVpWpA_p A_pV_pW_p represents a tripartite journey of the memory representations: 1. Observation Projection (V→ZV AZ-space): The value matrix Vp∈ℝp×dvV_p ^p× d_v residing in the latent memory space is projected into the observation space of the encoder Z∈ℝn×dzZ ^n× d_z. The attention map ApA_p acts as the projection operator, yielding Cp=ApVp∈ℝn×dvC_p=A_pV_p ^n× d_v. This extracts the memory content specifically retrieved by the current sequence of n tokens. 2. Re-grounding Projection (Z-space→A⊤LZ-space A L-space): The token-level context CpC_p is then projected back into the latent memory space via the transpose of the attention map, Ap⊤A_p . The operation Ap⊤Cp=Ap⊤ApVp∈ℝp×dvA_p C_p=A_p A_pV_p ^p× d_v functions as an evidence-pooling mechanism. The resulting Gram matrix Ap⊤ApA_p A_p acts as a data-dependent routing grid that binds information back to the specific memory slots that were activated. 3. Supervised Feature Transformation (L-space→UpdateL-space WUpdate): Finally, the re-grounded evidence is linearly transformed by the parameter matrix Wp∈ℝdv×dpW_p ^d_v× d_p. This step molds the raw pooled evidence into the optimal geometric subspace for the memory update. Because WpW_p is a learnable parameter, this final projection is directly shaped by the external influence of supervised learning (the task loss) during backpropagation. Latent Memory Vp∈ℝp×dvV_p ^p× d_vProposal Update Ap⊤ApVpWp∈ℝp×dpA_p A_pV_pW_p ^p× d_pZtZ_tRead (VpV_p)Write-back (Ap⊤A_p )InferenceTraining Figure 1: The tripartite projection sequence mapping latent values to the observation space and back, before applying the supervised transformation. 5.2 Bidirectional Projections for Abstractive Cross-Talk When this mechanism is partitioned into the lateralized banks L and R, the projection pathway becomes uniquely bidirectional. Under the inhibitory cross-talk variant (s=−1s=-1, proposed), the update equations are: Lt L_t =γLt−1+Al⊤AlVlWll−Al⊤AlVrWrl, =γ L_t-1+A_l A_lV_lW_l-A_l A_lV_rW_rl, Rt R_t =γRt−1+Ar⊤ArVrWrr−Ar⊤ArVlWlr. =γ R_t-1+A_r A_rV_rW_r-A_r A_rV_lW_lr. Geometrically, the term Al⊤AlVrWrlA_l A_lV_rW_rl projects right-bank values VrV_r upward into the shared proposal space using the left bank’s attention footprint, then re-grounds them into the left latent space via Al⊤A_l . The supervised cross-parameter WrlW_rl shapes this contralateral evidence into a format compatible with the left bank. Under inhibitory mode, this term is subtracted from the left-bank update: the more strongly the right bank is represented in the shared proposal space, the more it suppresses left-bank consolidation. This is the latent-space analogue of callosal inhibition (Section 6.6): the dominant bank actively silences the non-dominant one, preventing interference rather than absorbing it. Latent Memory Vl∈ℝm×dvV_l ^m× d_vLeft Bank Update Al⊤Al(VlWll+sVrWrl)∈ℝm×dvA_l A_l(V_lW_l+s\,V_rW_rl) ^m× d_vPtP_tRead (VlV_l)Write-back (Al⊤A_l )InferenceTrainingLatent Memory Vr∈ℝm×dvV_r ^m× d_vRight Bank Update Ar⊤Ar(VrWrr+sVlWlr)∈ℝm×dvA_r A_r(V_rW_r+s\,V_lW_lr) ^m× d_vPtP_tRead (VrV_r)Write-back (Ar⊤A_r )InferenceTrainingRead (VlV_l)Read (VrV_r) Figure 2: Bidirectional cross-talk pathways for lateralized memory (inhibitory mode, s=−1s=-1, proposed). The dashed red lines show the paths where one bank’s values reach the contralateral update. Under inhibitory cross-talk, these paths carry a negative coefficient: the right bank’s values VrV_r suppress the left bank’s update (and vice versa), sharpening bank separation rather than sharing representations. Setting s=+1s=+1 reverses these signs to excitatory; setting the cross-weights to zero gives the split-brain baseline. 6 Experiments We evaluate whether bank-wise persistence yields specialized responses and controlled cross-talk. We instantiate the model with a standard Transformer backbone and our lateralized memory update, and train on three splits: a left-only dataset (DatasetlDataset_l), a right-only dataset (DatasetrDataset_r), and a mixed dataset (DatasetlrDataset_lr) that interleaves both types. The expected behavior is specialization with selective activation: • For inputs from DatasetlDataset_l, the left bank should dominate the response while the right bank remains suppressed. • For inputs from DatasetrDataset_r, the right bank should dominate the response while the left bank remains suppressed. • For mixed inputs in DatasetlrDataset_lr, each bank should respond primarily to its own type, with limited cross-talk. 6.1 Synthetic Dataset Design To rigorously probe memory consolidation and routing without the confounding variables of natural language, we construct a controlled symbolic pilot dataset. We define a unified vocabulary of 40 tokens, comprising 26 letters, 10 digits, and standard control tokens. The datasets are generated as follows: • Left Domain (DatasetlDataset_l): Sequences over the 26-letter alphabet constructed by following a fixed random bijection σ:Σ→Σσ: → — a secret cipher chosen once at initialization. Given the current letter xtx_t, the next token is always σ(xt)σ(x_t), and each sequence starts from a random letter. Because σ is an arbitrary permutation with no algebraic structure, next-token prediction is impossible without memorizing all 26 mappings; no computable rule shortens the task. This requires the model to build an episodic, associative key-value store. • Right Domain (DatasetrDataset_r): Sequences of decimal digits following a strict +1+1 arithmetic progression (modulo 10). Given any recent token xtx_t, the next token is always xt+1(mod10)x_t+1 10. Prediction is possible from a single observation, so the model need only extract and apply a universal integer-addition rule. This requires pure rule extraction with no memorization. • Mixed Domain (DatasetlrDataset_lr): Interleaved sequences where the left and right rules unfold simultaneously but independently across alternating time steps (e.g., a 2 b 4 c 6). The model must predict the correct subsequent tokens (d followed by 8) without temporal interference. 6.2 Evaluation Metrics We quantify specialization using a separation degree that compares bank-specific activations and outputs (e.g., relative attention mass or contribution norms). Higher separation indicates stronger lateralization without sacrificing overall task performance. To formalize this, we define the Separation Degree (sepD_sep) based on the relative contribution norms of the left and right memory banks. Because the lateral banks are consolidated at the proposal level (Al,Ar∈ℝp×mA_l,A_r ^p× m, Cl=AlVl∈ℝp×dvC_l=A_lV_l ^p× d_v), we first back-project to token space using the proposal attention map Ap∈ℝn×pA_p ^n× p: C^l=ApCl∈ℝn×dv,C^r=ApCr∈ℝn×dv. C_l=A_pC_l ^n× d_v, C_r=A_pC_r ^n× d_v. (7) The sequence-level activation magnitude μb(X) _b(X) for each bank b∈l,rb∈\l,r\ is then the Frobenius norm of the back-projected context: μb(X)=1n‖C^b‖F=1n∑i=1n∑j=1dv|(C^b)i,j|2. _b(X)= 1n\| C_b\|_F= 1n _i=1^n _j=1^d_v|( C_b)_i,j|^2. (8) For inputs originating from a domain-specific dataset, such as DatasetlDataset_l, the separation degree measures the normalized dominance of the target bank over the contralateral bank: sep(Datasetl)=X∼Datasetl[μl(X)−μr(X)μl(X)+μr(X)]. _sep(Dataset_l)=E_X Dataset_l [ _l(X)- _r(X) _l(X)+ _r(X) ]. (9) A value of sep→+1D_sep→+1 indicates ideal left-bank dominance, sep→−1D_sep→-1 indicates right-bank dominance, and sep≈0D_sep≈ 0 implies a collapsed, non-lateralized state. An analogous metric sep(Datasetr)D_sep(Dataset_r) is computed to verify the right bank specializes symmetrically. Furthermore, for the mixed dataset DatasetlrDataset_lr, we must quantify the network’s ability to maintain boundaries during rapid context switching. We define the Cross-Talk Penalty (ctP_ct) to measure the attention mass inappropriately allocated to the mismatched bank. Because the lateral attention maps Al,Ar∈ℝp×mA_l,A_r ^p× m live in the proposal space, we compose them with the proposal attention to obtain effective token-level routing maps: A^l=ApAl∈ℝn×m,A^r=ApAr∈ℝn×m. A_l=A_pA_l ^n× m, A_r=A_pA_r ^n× m. (10) Note that A^l+A^r A_l+ A_r sums to one per token (inheriting the joint softmax), so mass concentrated on the wrong bank is genuinely misrouted. Given the ground-truth domain label yi∈l,ry_i∈\l,r\ for each token xix_i, the penalty is: ct=X∼Datasetlr[1n∑i=1n∑j=1m(yi=l(A^r)i,j+yi=r(A^l)i,j)], _ct=E_X Dataset_lr [ 1n _i=1^n _j=1^m (I_y_i=l\,( A_r)_i,j+I_y_i=r\,( A_l)_i,j ) ], (11) where I is the indicator function. A perfectly lateralized model achieves ct→0P_ct→ 0, while a uniform (unspecialized) model gives ct=0.5P_ct=0.5. 6.3 Baselines and Implementation Details We compare our Attention-Coupled Latent Memory model against a standard autoregressive Transformer baseline. Both models share an identical embedding layer and a base architecture of 4 layers, a hidden dimension of dmodel=128d_model=128, and 4 attention heads. For our model, we introduce the persistent memory state StS_t, physically partitioned into Lt∈ℝm×dmodelL_t ^m× d_model and Rt∈ℝm×dmodelR_t ^m× d_model, with m=16m=16 lateral memory slots per bank and p=32p=32 proposal slots. The proposal attention Ap∈ℝn×pA_p ^n× p drives information into P, which in turn routes it to L and R via the joint lateral attention Alr∈ℝp×2mA_lr ^p× 2m. We evaluate three cross-talk regimes as an ablation: none (Wlr=Wrl=0W_lr=W_rl=0, frozen, split-brain), excitatory (s=+1s=+1, contralateral values cooperate), and inhibitory (s=−1s=-1, contralateral values suppress, proposed). All three variants share the same routing auxiliary loss ℒroute=−λlat[(Al⋅l)mean+(Ar⋅r)mean]L_route=- _lat [(A_l·m_l)_mean+(A_r·m_r)_mean ] with λlat=2.0 _lat=2.0, where lm_l and rm_r are binary domain masks over the batch. The lateralized model has 2,534,440 trainable parameters versus 2,395,176 for the baseline, a parameter overhead of only ∼ 5.1%. 6.4 Results and Analysis Task Performance and Interference Mitigation. Table 1 reports the next-token prediction accuracy and cross-entropy loss across the three datasets. Both models achieve perfect or near-perfect accuracy on the homogeneous splits (DatasetlDataset_l, DatasetrDataset_r). However, the loss values reveal a qualitative difference between domains: on the cipher dataset (DatasetlDataset_l) the lateralized model achieves 0.0006 versus 0.0747 for the baseline — a 124×124× reduction, confirming that persistent associative memory is decisive for episodic key-value recall. On the arithmetic dataset (DatasetrDataset_r) both models achieve essentially the same loss (0.0002 vs. 0.0002), as expected: arithmetic requires only rule extraction, which the feed-forward backbone handles equally well without persistent storage. On the mixed dataset DatasetlrDataset_lr, the contrast is most pronounced. The standard Transformer accuracy drops to 93.8% with a high cross-entropy of 0.1692, symptomatic of catastrophic interference: the model’s shared hidden state conflates the cipher and arithmetic rules, losing predictive coherence on both simultaneously. The lateralized model holds at 94.4% with loss 0.1452, a 14%14\% reduction in loss, demonstrating that physically partitioning the latent space reduces cross-domain interference on the mixed task. Table 1: Next-token prediction accuracy and cross-entropy loss on homogeneous and interleaved symbolic sequences. The lateralized memory prevents the performance collapse seen in the baseline on mixed tasks. Model Accuracy Loss DatasetlDataset_l DatasetrDataset_r DatasetlrDataset_lr DatasetlDataset_l DatasetrDataset_r DatasetlrDataset_lr Standard Transformer 100.0% 100.0% 93.8% 0.0747 0.0002 0.1692 Attention-Coupled Lateral (Ours) 100.0% 100.0% 94.4% 0.0006 0.0002 0.1452 Emergence of Functional Lateralization. To confirm that the performance gains on DatasetlrDataset_lr stem from actual physical segregation in the memory banks, we measure the Separation Degree (sepD_sep) and the Cross-Talk Penalty (ctP_ct). Table 2 reports the results. On DatasetlDataset_l (episodic bijection sequences), we observe sep(L)=D_sep(L)=+1.001.00, indicating that 100%100\% of the effective attention mass is routed to the left bank. Symmetrically, DatasetrDataset_r (arithmetic sequences) yields sep(L)=D_sep(L)=-1.001.00, confirming that the right bank fully dominates arithmetic prediction. These boundary values (±1± 1) indicate saturated, non-overlapping specialization: every proposal slot has locked onto a single bank for its designated domain. The Cross-Talk Penalty on both pure datasets is ct=0.00=0.00P_ct=0.00=0.00, meaning zero attention mass is misrouted. On the mixed dataset, ct=0.03P_ct=0.03, confirming near-perfect routing across domain boundaries. The aggregate sepD_sep on DatasetlrDataset_lr (-0.420.42 and +0.420.42) reflects an asymmetry in bank activation magnitudes — the right/arithmetic bank generates slightly stronger norms overall — rather than misrouting; the low ctP_ct confirms that token-level routing is clean. Training Convergence. Figure 3 shows four panels tracking the evolution of the task loss, total (task + routing) loss, sepD_sep, and ctP_ct over 50 epochs. The task loss drops from 1.12 to 0.03, while the routing auxiliary loss drives the total loss slightly negative in later epochs as the routing signal saturates. ctP_ct collapses from 0.5 to near 0 within the first 4 epochs, demonstrating that bank assignment is resolved early in training. sepD_sep exhibits characteristic instability near epochs 15 and 33 (brief reversals as large gradient steps temporarily disrupt routing) before converging to a stable value, illustrating the interplay between task and routing objectives during consolidation. Figure 3: Training convergence of the Attention-Coupled Lateral model over 50 epochs. Panel 1 (task loss): cross-entropy drops from 1.12 to 0.03. Panel 2 (total loss): routing auxiliary term drives total loss slightly negative once routing saturates. Panel 3 (sepD_sep): Separation Degree converges after brief instabilities at epochs 15 and 33. Panel 4 (ctP_ct): Cross-Talk Penalty collapses to ≈0≈ 0 within 4 epochs and stays there, confirming stable lateralized routing throughout training. Table 2: Lateralization metrics demonstrating the emergence of specialized memory banks. Higher sepD_sep indicates strong routing to the correct hemisphere, while low ctP_ct indicates minimal inappropriate attention cross-talk. Metric Dataset_l Dataset_r Dataset_lr Left Separation Degree sep(L)D_sep(L) ++1.00 −-1.00 −-0.42 Right Separation Degree sep(R)D_sep(R) −-1.00 ++1.00 ++0.42 Cross-Talk Penalty ctP_ct 0.00 0.00 0.03 6.5 Analysis: Justification of the Memory Model Why persistent memory helps. The standard Transformer stores all contextual information in its final hidden state Z∈ℝn×dmodelZ ^n× d_model, which must simultaneously encode all sequential patterns encountered during training. When two structurally independent rule systems — a fixed-key bijection cipher (left domain) and a strict arithmetic progression (right domain) — are interleaved, the single shared state undergoes gradient-driven interference: updates that reinforce one rule partially overwrite representations for the other. The result is the 0.16920.1692 loss on DatasetlrDataset_lr, indicating the model has settled into a compromise representation that is suboptimal for both. The lateralized memory bypasses this bottleneck through explicit state partitioning. By maintaining separate LtL_t and RtR_t banks, the architecture provides dedicated storage for each cognitive mode: episodic/associative recall for the cipher and rule extraction for arithmetic. The attention-coupled write Ab⊤AbVbWbbA_b A_bV_bW_b consolidates domain-specific patterns within a bank without disturbing the contralateral bank, and the decay factor γ provides a natural forgetting mechanism that prevents stale information from accumulating across sequences. The role of the A⊤AVWA AVW update. The tripartite projection described in Section 5 directly explains the 35×35× loss reduction on homogeneous splits (e.g. 0.00060.0006 vs. 0.07470.0747 on DatasetlDataset_l). The Gram matrix Ab⊤AbA_b A_b acts as a co-activation router: slots that jointly attend to the same token cluster are reinforced together, implementing a form of Hebbian binding in latent space. The supervised write matrix WbbW_b then shapes this pooled evidence into a representation aligned with the task loss, enabling the memory to store predictive features rather than raw observations. Because the cipher domain has no computable rule (the bijection keys must be memorized), this persistent associative store provides a qualitative computational advantage that a purely feed-forward state cannot replicate. Two distinct cognitive modes necessitate two banks. The cipher task requires episodic/associative memory: given token x, retrieve the stored mapping σ(x)σ(x) from a fixed random bijection that cannot be inferred from local context. The arithmetic task requires rule extraction: infer the constant step size from the recent sequence and apply it. These are fundamentally different computational primitives. Routing them to separate persistent banks is not merely a convenience; it reflects a genuine architectural match between the structure of the task and the structure of the memory. The sep=±1.00D_sep=± 1.00 boundary values confirm that the training dynamics discovered this alignment and exploited it fully. The routing auxiliary loss as a symmetry-breaking signal. Without an explicit signal, both banks are symmetric at initialization, and gradient descent may settle into a collapsed fixed point where both banks process all inputs equally. The routing auxiliary loss ℒrouteL_route breaks this symmetry by rewarding attention mass concentrated on the domain-matched bank, providing a direct gradient toward specialization. The rapid collapse of ctP_ct within 4 epochs (Figure 3) demonstrates that once the symmetry is broken, the joint softmax mechanism reinforces specialization autonomously: routing mass to one bank suppresses the other, which in turn frees the dominant bank to further specialize, forming a positive feedback loop. Limitations and scope. The experiment operates at small scale on synthetic symbolic data with explicit domain labels. Validating the lateralization hypothesis on natural language corpora — where domain boundaries are implicit and routing supervision is unavailable — remains an important open direction. A domain-agnostic specialization metric (e.g., normalized mutual information between token domain labels and bank attention argmaxes) would provide a more robust quantification and is left for future work. Summary. The lateralized model achieves a 124×124× lower loss on the cipher domain (0.00060.0006 vs. 0.07470.0747) where persistent associative memory is decisive, while matching the baseline on the arithmetic domain (0.00020.0002 vs. 0.00020.0002). On the mixed dataset it reduces loss by 14%14\% (0.14520.1452 vs. 0.16920.1692) with only ∼ 5.1% additional parameters. The saturated sep=±1.00D_sep=± 1.00 and ct≈0P_ct≈ 0 on pure-domain data confirm clean functional lateralization. The ablation (Table 3) confirms that excitatory cross-talk destroys specialization — despite yielding lower task loss via bank-collapse — while inhibitory cross-talk preserves it, directly paralleling the function of callosal inhibition. 6.6 The Corpus Callosum as an Inhibitory Highway Neuroscientific motivation. The sign of the cross-talk matrices encodes a fundamental architectural choice about how the two banks interact during consolidation. This choice is directly analogous to the function of the corpus callosum in human neuroscience. Callosal axons are predominantly glutamatergic (excitatory) but their primary cortical targets are inhibitory interneurons, producing a net inhibitory effect on the contralateral hemisphere (Innocenti, 1986; Bloom and Hynd, 2005). During language production, for example, the left hemisphere actively suppresses homologous right-hemisphere areas via this callosal inhibition, creating sharp functional dominance rather than shared processing. Split-brain prediction. This predicts a three-way ordering: (1) excitatory cross-talk blurs bank boundaries because contralateral values are added to both banks simultaneously, providing a gradient shortcut that discourages specialization; (2) no cross-talk (split-brain) allows each bank to specialize independently but provides no active mechanism to suppress contralateral contamination; (3) inhibitory cross-talk maximally sharpens boundaries by making the dominant bank actively subtract the non-dominant bank’s influence. The split-brain condition also matches the historical observation that, after callosotomy, each hemisphere functions adequately for its own domain while cross-domain tasks requiring inter-hemispheric coordination become impaired. Ablation evidence. Table 3 confirms the three-way prediction. The excitatory condition produces total lateralization collapse: sep(L)|Datasetl=D_sep(L) |_Dataset_l=-0.820.82 (the right bank monopolises the left domain), sep(L)|Datasetr=D_sep(L) |_Dataset_r=-0.930.93 (right bank also dominates right domain), and ct=0.46P_ct=0.46 — essentially random routing. The right bank becomes the sole dominant processor for all inputs. Notably, this collapse yields a lower task loss (0.1017) than the lateralized conditions: the model takes a “free-ride” shortcut, concentrating all capacity in one bank at the cost of all specialization. This mirrors a neural architecture where an excitatory callosal projection allows one hemisphere to process both domains — reducing apparent workload at the expense of functional division. The split-brain and inhibitory conditions both achieve clean lateralization (sep(L)|Datasetl=D_sep(L) |_Dataset_l=+1.00=1.00=+1.001.00, ct=0.00P_ct=0.00 and 0.030.03 respectively). The slight residual in the inhibitory condition (0.030.03 vs. 0.000.00) is attributable to the trainable WlrW_lr/WrlW_rl matrices introducing intermittent gradient pathways, whereas the split-brain condition eliminates this source by construction. Table 3: Cross-talk mode ablation on the mixed dataset DatasetlrDataset_lr, evaluated with sep(L)D_sep(L) (measured on DatasetlDataset_l and DatasetrDataset_r separately), ctP_ct (on DatasetlrDataset_lr), and accuracy/loss on DatasetlrDataset_lr. All conditions share the same architecture, training procedure, and routing auxiliary loss. Cross-talk Mode sep(L)|l↑D_sep(L)|_l\! sep(L)|r↓D_sep(L)|_r\! ct↓P_ct\! Acc↑lr_lr\! Loss↓lr_lr\! None (split-brain) ++1.00 −-1.00 0.00 94.4% 0.1456 Excitatory (s=+1s=+1) −-0.82 −-0.93 0.46 95.8% 0.1017 Inhibitory (s=−1s=-1, ours) ++1.00 −-1.00 0.03 94.4% 0.1454 7 Conclusion We presented Attention-Coupled Latent Memory, a memory-augmented architecture in which attention serves simultaneously as a retrieval, consolidation, and write-back operator. The core A⊤AVWA AVW update provides a principled tripartite projection: values are lifted from latent memory into observation space, re-grounded via the Gram matrix, and transformed by a supervised write projection. Extending this to a bank-wise formulation with a block-structured write matrix WsW_s yields lateralized left and right memory pathways. We propose inhibitory cross-talk (s=−1s=-1) as the coupling mode, motivated by callosal physiology: the term −Ab⊤AbVb¯Wbb¯-A_b A_bV_ bW_b b actively subtracts the contralateral bank’s content from each ipsilateral update, sharpening bank boundaries rather than blurring them. Experiments on a controlled symbolic dataset confirm the architecture’s two central claims. First, persistent associative memory provides a 124×124× loss reduction on the episodic cipher task (0.00060.0006 vs. 0.07470.0747) — where no computable rule shortens the problem — while leaving the rule-extraction arithmetic task unchanged. Second, the three-condition ablation (Table 3) confirms the corpus callosum prediction: excitatory cross-talk causes complete lateralization collapse (sep(L)|Datasetl=D_sep(L) |_Dataset_l=-0.820.82, ct=0.46≈0.5P_ct=0.46≈ 0.5, the right bank monopolises all inputs) despite yielding a lower raw task loss, while inhibitory cross-talk achieves clean lateralization matching the split-brain baseline (sep(L)|Datasetl=D_sep(L) |_Dataset_l=+1.001.00, ct=0.03P_ct=0.03). The task design exposing a fundamental cognitive dichotomy — episodic recall versus rule extraction — is a necessary condition: without structurally distinct computational demands, bank specialization does not emerge. Together, the architecture, inhibitory coupling, routing auxiliary loss, and task structure form a mutually reinforcing system that produces reliable, measurable specialization. Future work will scale this architecture to natural language benchmarks, investigate multi-level memory hierarchies beyond the two-bank formulation, explore learned γ schedules for adaptive memory decay, and study whether the inhibitory cross-talk advantage over split-brain modes persists at larger scales where passive isolation is insufficient to prevent bank collapse. Acknowledgements The author thanks Inha University in Tashkent for research support. This work reflects the author’s ongoing inquiry into nature and human cognition. References [1] Weston, J., Chopra, S. & Bordes, A. 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