Cognitive Trace Embeddings: Theory & Applications

• Cognitive trace embeddings are latent representations that capture temporal, multimodal, and memory-informed processes underlying human cognition.
• They utilize tensor memory frameworks and cross-modal perception-trace models to integrate semantic, episodic, and sensory data effectively.
• Dynamic knowledge tracing and alignment techniques using these embeddings enhance AI’s interpretability and clustering of complex, multimodal information.

Cognitive trace embeddings are latent vector representations that encode the temporal, multimodal, and memory-informed traces of human cognition as observed through experiments or computational modeling. These embeddings aim to capture not only the statistical regularities present in linguistic or perceptual corpora, but also the sequential, cross-modal, and attention-driven processes by which the human brain constructs meaning, forms concepts, and updates knowledge over time.

1. Foundational Concepts and Definitions

Cognitive trace embeddings originate from the hypothesis that the process of memory formation, retrieval, and conceptual association in humans can be usefully modeled by latent variable systems. Under the Unique-Representation Hypothesis, every entity—subject ($e_s$), predicate ($e_p$), object ($e_o$), and time index ($e_t$)—is assigned a single latent vector $\mathbf{a}_e \in \mathbb{R}^{\tilde r}$ (Tresp et al., 2015). These vectors are used to construct tensor memories (semantic, episodic, sensory, etc.) from which embeddings are derived, reflecting the brain’s organization of knowledge and experience.

In multimodal cognitive settings, such as reading or scene-inspection, cognitive trace embeddings are further enriched by perception traces: time-ordered records of human fixations, saccades, and revisits across text and image regions. This sequence embodies the real-world context in which meaning is constructed and subsequently encoded as embeddings (Rettinger et al., 2019).

2. Tensor Memory Frameworks and Semantic–Episodic Representations

The tensor memory paradigm expresses semantic memory as a three-way tensor $\mathcal{X} \in \mathbb{R}^{S \times P \times O}$, episodic memory as a four-way tensor $$\mathcal{Z} \in \mathbb{R}^{S \times P \times O \times T}$$, and sensory memory as $\mathcal{U}\in\mathbb{R}^{Q\times N\times T}$ (Tresp et al., 2015). The value in each tensor cell is derived via mapping functions:

• Semantic: $$\theta^{\mathrm{sem}}_{s,p,o} = f^{\mathrm{sem}}(\mathbf{a}_{e_s},\mathbf{a}_{e_p},\mathbf{a}_{e_o})$$
• Episodic: $$\theta^{\mathrm{epi}}_{s,p,o,t} = f^{\mathrm{epi}}(\mathbf{a}_{e_s},\mathbf{a}_{e_p},\mathbf{a}_{e_o},\mathbf{a}_{e_t})$$
• Sensory: $$\theta^{\mathrm{sens}}_{q,\gamma,t} = f^{\mathrm{sens}}(\mathbf{a}_{e_q},\mathbf{a}_{e_\gamma},\mathbf{a}_{e_t})$$

These latent mappings can be realized through PARAFAC, Tucker, or RESCAL-style tensor decompositions. Time evolution of traces can be handled by ARX, RNN, or symbolic-to-subsymbolic compression modules. This allows for rapid energy-based sampling during query-answering, semantic decoding of sensory scenes, and modeling of short-term and working memory processes.

The semantic–episodic interaction is grounded in marginalization (semantic memory as the marginal of episodic memory over time) and cross-access (episodic recall via semantic traces).

3. Perception-Trace–Driven Embeddings: CMPM and Cross-Modal Context

Standard distributional models define “context” by local word windows or graph walks; however, these are computational heuristics that contrast with genuine human perception, which is driven by selective attention, revisits, and multimodal integration. The Cross-Modal Perception-Trace Model (CMPM) utilizes eye-tracking data (fixation sequences across text and image AOIs, with revisits and cross-modal shifts) to define perception traces $S_d$ (Rettinger et al., 2019). Embedding training pairs are drawn from a window over these traces, fusing text and image information in accordance with human reading habits.

The skip-gram loss is maximized over $(e_c, e_o)$ pairs constituted from perception traces, with context windows spanning text and image entities:

$J = \sum_{(e_c, e_o) \in D} \log p(e_o | e_c)$

with $p(e_o | e_c)$ computed as a softmax over joint multimodal embeddings. Dimensionality reduction and auto-encoding produce a unified representation space ($d=100$), and final embeddings are fused elementwise across modalities.

Empirically, CMPM yields higher Spearman’s $\rho$ on semantic similarity benchmarks and superior clustering metrics compared to traditional word2vec and GloVe, reflecting better concordance with human semantic judgments and perceptual compactness.

4. Successor Representations, Cognitive Maps, and Multi-Scale Embedding

Cognitive trace embeddings are closely related to the successor representation (SR) framework for modeling cognitive maps in the entorhinal-hippocampal system. The SR matrix $M_\gamma = (I - \gamma T)^{-1}$ (or truncated recursion) aggregates long-run transition probabilities between states (concepts) under a range of discount factors ($\gamma$). Word embeddings define both inputs and transition probabilities $T(s, s') = \cos\theta$ (Stoewer et al., 2023).

Neural networks are trained (input embeddings, dropout, hidden layer, softmax) to approximate rows of the SR matrix, mapping each concept to its predictive successor distribution. The learned vectors, $\hat{y}(s',|s)$, encode how each concept “traces” its relationships to stored concepts at a given scale. Varying $\gamma$ modulates locality—and hence cluster formation—in the cognitive map. Higher $\gamma$ yields tighter, category-focused clusters.

Measured by Generalized Discrimination Value (GDV) and qualitative multidimensional scaling, multi-scale SR embeddings show that information disperses uniformly at low $\gamma$ but concentrates into distinct semantic clusters at high $\gamma$. These trace embeddings can be directly used by AI models, e.g., for multimodal context retrieval or abstraction-level adjustment.

5. Dynamic Knowledge Tracing and Latent Trajectories

Cognitive trace embeddings also arise in the context of student knowledge tracing via the DynEmb framework (Xu et al., 2020). Here, the trace is defined as the evolving RNN hidden state $h_t$ corresponding to a student’s sequential trajectory in a latent question embedding space:

• Static phase: matrix factorization yields question and student embeddings ($W$, $Z$, $b$, $c$)
• Dynamic phase: LSTM receives input $x_t = W_{q_{t-1}} \otimes [r_{t-1}, 1 - r_{t-1}]$, producing $h_t$ as the dynamic cognitive trace.

Predictions are made by combining $h_t$ with the corresponding question embedding to model student responses:

$$\hat{y}_t = \phi(\langle W_{q_t}, h_t \rangle + b_{q_t})$$

Exploratory MDS reveals that $W$ encodes cognitive latent space, while student trajectories $h_t$ reveal interpretable changes in proficiency or conceptual understanding. DynEmb yields AUC improvements (+1.65% to +5.43%) over previous models without explicit skill tagging.

A plausible implication is that learned traces serve not only individual-level diagnostics but also dataset-wide semantic organization, offering insights into learning processes and cross-student clusterings.

6. Alignment of Textual and Cognitive Representations: CogAlign Model

Robust cognitive trace embeddings for natural language can be achieved by jointly aligning textual representations and cognitive data (EEG, eye-tracking) via shared latent spaces. The CogAlign approach comprises private text and cognitive Bi-LSTM encoders, a shared encoder, and an adversarial modality discriminator (Ren et al., 2021).

A text-aware attention mechanism gates cognitive features via token-level compatibility:

$G = \tanh(H^{word^\top} U H^{cog})$

$q = \text{softmax}(\max_j G_{j, \cdot})$

$H^{cog'} = H^{cog} \odot q$

where $U$ is learned; $q$ up-weights cognitively salient features aligned to text. The shared encoder learns to produce modality-invariant hidden states through adversarial training.

The joint embedding space is evaluated by state-of-the-art gains (+0.5–2.2 F1) on benchmarks (NER, sentiment, relation extraction) and demonstrated transferability to datasets without cognitive signals (+1.5–2.0 F1). Ablation confirms the necessity of attention, modality discrimination, and dual-task predictors for robust trace alignment. t-SNE visualization supports the co-clustering of text and cognitive traces in shared latent space.

7. Contemporary Directions and Broad Implications

Cognitive trace embeddings unify distributional, sequential, multimodal, and neurocognitive perspectives on representation learning. Key empirical findings:

• Cross-modal, perception-trace–driven embeddings outperform heuristic context models on tasks closely tracking human semantics and perceptual organization (Rettinger et al., 2019).
• Successor representations capture flexible levels of abstraction and clustering, reflecting memory formation and rapid adaptation (Stoewer et al., 2023).
• Tensor-based frameworks link neural memory functions to explicit embedding spaces amenable to query-answering and simulation (Tresp et al., 2015).
• Dynamically evolving traces track both individual and collective knowledge across time, advancing analytic and diagnostic precision (Xu et al., 2020).
• Joint alignment models demonstrate transferability and noise mitigation, expanding the scope of cognitive signal utility (Ren et al., 2021).

A plausible implication is that further development of cognitive-trace embedding frameworks may bridge gaps between human and machine representations, improving interpretability, contextual adaptation, and functional competence in downstream AI systems.