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Mechanistic Interpretability of Cognitive Complexity in LLMs via Linear Probing using Bloom's Taxonomy
Bianca Raimondi, Maurizio Gabbrielli
Intelligence
Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 93%
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Summary
This study investigates the mechanistic interpretability of Large Language Models (LLMs) by using Bloom's Taxonomy to analyze internal neural representations. Through linear probing of activation vectors from the residual streams of four LLMs, the authors demonstrate that cognitive complexity levels (from Remember to Create) are linearly separable within the model's latent space. Key findings include the identification of a Cognitive Separability Onset (CSO) around layer 5, where representations become highly separable, and evidence that these representations are causally active through steering experiments.
Entities (9)
Relation Signals (6)
Bloom's Taxonomy → defineslevels → Remember
confidence 95% · Bloom’s Taxonomy, a framework that categorizes educational objectives into six levels: Remember, Understand, Apply, Analyze, Evaluate, and Create
Bloom's Taxonomy → defineslevels → Create
confidence 95% · Bloom’s Taxonomy, a framework that categorizes educational objectives into six levels: Remember, Understand, Apply, Analyze, Evaluate, and Create
Bloom's Taxonomy → usedfor → Cognitive Complexity
confidence 95% · This study investigates the internal neural representations of cognitive complexity using Bloom's Taxonomy as a hierarchical lens.
Llama-3.1-8B-Instruct → exhibits → Cognitive Separability Onset
confidence 92% · Comparing the models from Figure 2, we notice that the CSO happens near layer 5 for most of the models... for the Llama-3.1-8B-Instruct model.
Residual Stream → contains → Cognitive Complexity Representations
confidence 90% · cognitive level is encoded in a linearly accessible subspace of the model’s representations... within the model’s residual streams.
Linear Probing → detects → Cognitive Separability Onset
confidence 90% · A key advancement of our study is the discovery of a structural Cognitive Separability Onset (CSO) within the model’s internal representations.
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Abstract
Abstract:The black-box nature of Large Language Models necessitates novel evaluation frameworks that transcend surface-level performance metrics. This study investigates the internal neural representations of cognitive complexity using Bloom's Taxonomy as a hierarchical lens. By analyzing high-dimensional activation vectors from different LLMs, we probe whether different cognitive levels, ranging from basic recall (Remember) to abstract synthesis (Create), are linearly separable within the model's residual streams. Our results demonstrate that linear classifiers achieve approximately 95% mean accuracy across all Bloom levels, providing strong evidence that cognitive level is encoded in a linearly accessible subspace of the model's representations. These findings provide evidence that the model resolves the cognitive difficulty of a prompt early in the forward pass, with representations becoming increasingly separable across layers.
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- Source: https://arxiv.org/abs/2602.17229v2
- Canonical: https://arxiv.org/abs/2602.17229v2
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Mechanistic Interpretability of Cognitive Complexity in LLMs via Linear Probing using Bloom’s Taxonomy Bianca Raimondi a,∗ , Maurizio Gabbrielli a a Department of Computer Science and Engineering, University of Bologna, Bologna, Italy A R T I C L E I N F O Keywords: Large Language Models Bloom’s Taxonomy Mechanistic Interpretability A B S T R A C T The black-box nature of Large Language Models necessitates novel evaluation frameworks that tran- scend surface-level performance metrics. This study investigates the internal neural representations of cognitive complexity using Bloom’s Taxonomy as a hierarchical lens. By analyzing high-dimensional activation vectors from different LLMs, we probe whether different cognitive levels, ranging from basic recall (Remember) to abstract synthesis (Create), are linearly separable within the model’s residual streams. Our results demonstrate that linear classifiers achieve high accuracy across all Bloom levels, providing evidence that cognitive level is encoded in a linearly accessible subspace of the model’s representations. These findings provide evidence that the model organizes representations according to cognitive difficulty early in the forward pass, with representations becoming increasingly separable across layers. 1. Introduction The rise of Transformer-based Large Language Models (LLMs) has fundamentally changed the field of Artificial Intelligence (AI), creating systems that exhibit behaviours once considered the sole preserve of human cognition [32, 5]. These models demonstrate a versatility that challenges our definitions of machine understanding, from generating coherent prose to solving complex mathematical theorems. However, this functional capability is essentially a black box: the specific internal mechanisms that enable such high-level reasoning remain unknown [25]. A critical, yet under-explored, dimension of this inter- pretability challenge is the assessment of cognitive depth. Current benchmarks typically evaluate models based on answer correctness [12]. While useful, these metrics fail to distinguish between correct answers derived from rote memorization and those resulting from complex, multi-step reasoning. In human cognition, this distinction is founda- tional. A student who correctly recites a historical date is ex- ercising a different cognitive faculty than one who analyzes the socio-political causes of a historical event. This hierarchy of cognitive skills is formalized in Bloom’s Taxonomy, a framework that categorizes educational objectives into six levels: Remember, Understand, Apply, Analyze, Evaluate, and Create [21]. If LLMs are approximating general intelligence, their internal architectures should, at least in part, reflect different degrees of cognitive demand. Distinct forms of neural ac- tivity are expected to emerge when a Transformer engages in higher-order operations such as analysis or evaluation, as opposed to lower-level processes like factual recall. The presence of specialized internal representations associated with different cognitive levels would suggest that the model ∗ Corresponding author bianca.raimondi3@unibo.it (B. Raimondi) ORCID(s): 0009-0002-1562-7722 (B. Raimondi); 0009-0002-1562-7722 (M. Gabbrielli) encodes information consistent with a notion of problem dif- ficulty and task type, abstracted away from specific domain content. This paper conducts a mechanistic investigation of LLM internal representations through the lens of Bloom’s Tax- onomy, addressing the following research questions and corresponding findings: • RQ1. Do LLMs exhibit differences in internal ac- tivations when processing prompts associated with different Bloom levels? • RQ2. At what depth do representations of cognitive complexity emerge within the network? • RQ3. Is Bloom-level information linearly recoverable from hidden states, and do the resulting classification errors reflect the ordinal and semantic structure of the taxonomy? • RQ4. Are the identified cognitive representations causally active, or merely correlational phenomena of the forward pass? To address these questions, we extract activation vec- tors from the residual stream of four state-of-the-art open- weights LLMs and train linear probes at each layer to classify Bloom levels. The main findings can be summarized as follows. First, linear classifiers achieve high accuracy, indicating that cog- nitive level is encoded in a linearly accessible subspace of the model’s internal representations. Second, cognitive complexity emerges during the early-to-mid stages of pro- cessing, rather than being deferred to the deepest layers of the network. Moreover, confusion matrix analysis shows that misclassifications occur predominantly between adja- cent Bloom levels. This structured error pattern suggests that the learned representations reflect the ordinal organization of human educational theory, rather than arbitrary label B. Raimondi et al.: Preprint submitted to ElsevierPage 1 of 11 arXiv:2602.17229v2 [cs.AI] 17 Jul 2026 Mechanistic Interpretability of Cognitive Complexity in LLMs via Linear Probing using Bloom’s Taxonomy Dataset 1,128 Questions (188 per level) Bloom's Taxonomy Levels: Level 0: Remember Define recursion Level 1: Understand Explain how recursion works Level 2: Apply Use recursion to compute factorial Level 3: Analyze Compare recursion vs iteration Level 4: Evaluate Justify when recursion is preferable Level 5: Create Design a recursive algorithm Large Language Model Layer 1 Layer 2 ⋮ Layer L Activation Extraction Layer-wise Activations: x l ∈ ℝ d_model Store as dataset: <x l , y i >, where y i ∈ 0..5 Probing Logistic Regression Classifier: P(y=k | x l ), where k ∈ 0..5 Forward PassProbing x 1 = x emb + Attn(x emb ) + MLP(x emb ) x 2 = x 1 + Attn(x 1 ) + MLP(x 1 ) x L = x L-1 + Attn(x L-1 ) + MLP(x L-1 ) Figure 1: Overview of the experimental pipeline, from dataset construction and activation extraction to layer-wise linear probing. boundaries. Finally, we establish the causal relevance of these internal representations through activation steering experiments, demonstrating that intervening on the identi- fied directions can systematically shift the model’s cognitive processing level along the Bloom’s Taxonomy hierarchy. 2. Related Work Despite their empirical success, Transformer-based LLMs [32, 5] remain difficult to interpret, particularly with respect to the internal mechanisms that support complex reasoning [25]. Understanding these internal mechanisms has become a central focus of Mechanistic Interpretability (MI), which aims to reverse-engineer neural networks by analyzing their internal representations and computational structures [8]. Recent comprehensive reviews [27, 4, 30, 35, 10] have estab- lished MI as a critical framework for AI safety, emphasizing the need to move beyond surface-level performance metrics toward understanding the actual computational processes underlying model behavior. Some studies have expanded the scope of MI to in- clude semantic concepts [7] and bias [28, 31]. These works establish that modern MI can meaningfully probe high- level cognitive constructs, supporting our approach of using Bloom’s Taxonomy as an evaluation framework. Prior evaluations of LLMs have largely relied on bench- mark accuracy, including datasets such as MMLU [12]. However, such benchmarks primarily assess task perfor- mance and do not directly probe the structure of underlying cognitive representations. This limitation has motivated re- searchers to adopt Bloom’s Taxonomy [21] as a hierarchical framework for assessing cognitive complexity in AI systems. Recent work has demonstrated the taxonomy’s utility in educational applications [13, 9, 22] and proposed extensions for the AI era [15, 23]. Most directly relevant are the works conducted on a systematic cognitive evaluation of LLMs through Bloom’s lens [16, 33], though focusing on behav- ioral output rather than internal representations. Our work advances this landscape by shifting from be- havioral output to internal mechanistic analysis. While linear probing has become foundational for investigating linearly decodable features [2, 20], recent advances have explored higher-level conceptual representations [19, 24]. Emerging evidence suggests that LLMs spontaneously organize repre- sentations to encode abstract task properties [17, 3, 18]. A key advancement of our study is the discovery of a structural Cognitive Separability Onset (CSO) within the model’s internal representations. Unlike prior output-centric evaluations [16, 6, 36], our approach provides direct mecha- nistic evidence of how cognitive complexity is encoded. By combining MI techniques [27, 4] with Bloom’s taxonomy, we demonstrate that models refine cognitive complexity far beyond surface-level lexical cues, achieving high probe accuracy early in the forward pass and revealing that LLMs spontaneously organize their latent space to encode hierar- chical cognitive demand [14]. 3. Methodology Our experimental framework is designed to systemat- ically extract and classify internal activations across four distinct LLMs as depicted in Figure 1. 3.1. Problem Formulation Let = (푞 푖 ,푦 푖 ) 푁 푖=1 be a dataset of natural language questions, where 푞 푖 denotes a prompt and 푦 푖 ∈ 0,...,5 its associated Bloom level. Given a model with 퐿 layers and hidden dimension 푑 푚 , we study whether the cognitive level 푦 푖 is linearly decodable from internal representations. 3.2. Models To ensure that the observed result is not specific to a single architecture, we evaluate a diverse set of open- weight LLMs available on HuggingFace 1 (see Figure 1). The selected models vary in parameter count, depth, architectural design, and training data scale. 1 https://huggingface.co B. Raimondi et al.: Preprint submitted to ElsevierPage 2 of 11 Mechanistic Interpretability of Cognitive Complexity in LLMs via Linear Probing using Bloom’s Taxonomy ModelL 푑 푚 Llama-3.1-8B-Instruct32 4096 Qwen3-4B-Instruct-250736 2560 gemma-3-4b-it35 2560 DeepSeek-R1-Distill-Llama-8B 32 4096 Table 1 Models used in our study. For each model, we extract residual stream activations at every transformer layer during the forward pass. All models are evaluated in inference mode, and no fine-tuning is performed. 3.3. Dataset The foundation of our analysis is a curated, balanced dataset of 1,128 questions annotated with Bloom’s Taxon- omy levels (188 per level). Each prompt corresponds to a defined level of cognitive complexity. The final corpus is obtained by aggregating two different educational datasets: • Computer Science Course Queries: the dataset pro- vided by Zaman et al. [34] contains student queries from Computer Science courses (Data Structures, Introduction to Computers, and Research). These queries are uniquely scored based on cognitive diffi- culty, providing a granular mapping to Bloom’s levels. • EduQG: To enhance the diversity of the tasks, we in- cluded samples from EduQG [11]. This dataset offers multi-format multiple-choice questions specifically designed for the educational domain, with expert- verified Bloom’s Taxonomy annotations. To prevent architectural biases in the linear probes due to class imbalance, we performed a controlled downsampling of the aggregated data. This ensures that the probe’s ac- curacy reflects the model’s representational capacity rather than a statistical prior on the label distribution. Furthermore, questions range from 3 to 39 words count (휇 = 12.95, 휎 = 5.52), ensuring diversity in linguistic complexity. 3.4. Activation Extraction and Residual Stream Analysis The core of our analysis involves the extraction of activation vectors 푥 푙 from the residual stream. For clarity, we present a simplified formulation that highlights the main computational components of layers. In a decoder-only Transformer with 퐿 layers, the state at layer 푙+1 is updated recursively as: 푥 푙+1 = 푥 푙 + Attn(푥 푙 ) + MLP(푥 푙 )(1) where 푥 푙 ∈ ℝ 푑 푚 represents the hidden state at layer 푙. For each sample in our dataset, we perform a forward pass and capture the activation vector at the final token position. We focus on the final token position as it aggregates the full contextual information before generation begins. For Bloom Level 푑 0 ... 푑 푚 00.0047 ... 0.0007 10.0055 ... 0.0029 50.0050 ... 0.0019 30.0015 ... 0.0075 Table 2 Example of stored activations at specific layer i. 024681012141618202224262830323436 Layer 0.6 0.7 0.8 0.9 Accuracy Qwen/Qwen3-4B-Instruct-2507 google/gemma-3-4b-it deepseek-ai/DeepSeek-R1-Distill-Llama-8B meta-llama/Llama-3.1-8B-Instruct Figure 2: Layer-wise probe accuracy across all evaluated models. decoder-only models, the final token’s hidden state is the only position that has attended over the entire prompt and therefore represents the model’s full encoding of the input before generation [8]. We leave mean-pooled representations as a comparison point for future work. The resulting data structure is a tensor containing the layer-wise hidden states for all samples in our dataset. Ta- ble 2 provides a small illustration of these activations for a few example questions from the dataset. Each row in the dataset corresponds to a unique activation vector extracted at a specific layer in the network. The columns are defined as follows: • Bloom Level: represents the cognitive complexity of the question according to Bloom’s Taxonomy. In our experimental setup, these are encoded as integer val- ues (e.g., 0 for Remember, 1 for Understand, etc.), allowing us to analyze how the model’s internal state varies across different levels of abstraction. • 푑 0 ...푑 푚 : represent the individual dimensions of the hidden state vector at a specific layer. If the model has a hidden dimension of 푑 푚 (e.g., 4096 for Llama models), each value 푑 푖 represents the activation level of the 푖-th dimension at a specific layer. 3.5. Linear Probing To determine if the Bloom level is linearly encoded, we employ a Logistic Regression (LR) probe for each layer. Given an activation vector 푥 푙 from layer 푙, the probe predicts the probability of the prompt belonging to a specific Bloom level 푘 ∈ 0,...,5. The success of this probe in a specific layer indicates that the cognitive signal is disentangled and readable by subsequent components of the network. B. Raimondi et al.: Preprint submitted to ElsevierPage 3 of 11 Mechanistic Interpretability of Cognitive Complexity in LLMs via Linear Probing using Bloom’s Taxonomy The linear probe is implemented as a multiclass LR model. This choice ensures that successful classification re- flects linearly accessible information in the representations, rather than the expressive capacity of a nonlinear classifier. The model is trained using the default퓁 2 regularization with feature normalization. The dataset is split into training and test sets using a stratified sampling strategy with an 80∕20 ratio, preserving the class distribution across Bloom levels. Model performance is evaluated using standard multiclass metrics, including accuracy, precision, and recall. This setup ensures that the probe remains strictly linear and capacity- limited, so that successful prediction can be attributed to linearly decodable information already present in the rep- resentations rather than to probe expressivity. 4. Results This section presents a comprehensive analysis of prob- ing results across layers for all evaluated models. Rather than focusing on a single representative model, we emphasize cross-model consistency to assess whether the emergence of cognitive depth representations is a robust architectural phenomenon. To analyze how representations of cognitive depth emerge across the network, we trained independent linear probes on the residual stream at each layer for all evaluated architec- tures. Figure 2 summarizes the resulting layer-wise accuracy trajectories. Despite architectural differences, several clear and con- sistent patterns emerge. First, probe accuracy is low in the earliest layers and increases as depth increases, indicating that cognitive depth is not linearly separable at the input or embedding level but becomes increasingly so across layers through computation. We refer to this phenomenon as the already mentioned CSO, marking the layer at which repre- sentations become rapidly and stably linearly separable by cognitive level. Second, once high separability is reached, probe accu- racy remains stable across subsequent layers. This persis- tence indicates that, after representations of cognitive level become linearly separable, the corresponding structure is preserved in the residual stream rather than being repeatedly recomputed. Deeper layers, therefore, appear to represent an already-established estimate of cognitive complexity. In section 5 we discuss whether this representation is causally used during generation, rather than being just correlational. The accuracy results of specific Bloom’s levels can be found in Appendix A. These findings support the view that cognitive depth corresponds to a linearly accessible and structurally stable feature of internal representations in LLMs, emerging early in the forward pass and remaining stable in subsequent layers [8]. High classification accuracy implies the existence of affine decision boundaries that separate Bloom levels in representation space. Formally, linear separability at a given layer means that the representations corresponding to different Bloom levels can be separated by a set of linear decision boundaries. In particular, for each Bloom level, there exists a hyperplane in the representation space such that the activation vectors associated with that level lie on the correct side of the hyperplane and are assigned a higher score than those associated with any other level. Equivalently, each prompt’s internal representation is closer to the region corresponding to its true cognitive level than to the regions associated with the remaining levels. Thus, successful probing indicates that cognitive complexity is encoded in a linearly accessible subspace of the residual stream, rather than being distributed in a highly entangled or nonlinear manner. 4.1. The Cognitive Separability Onset To understand the internal mechanisms of what we named the CSO, here we analyze the first layer that achieves convergence. Let 퐴 푙 denote the probe accuracy at layer 푙. We define the CSO layer 푙 ⋆ as: 푙 ⋆ = min푙 ∣ 퐴 푙 ≥ 휏(2) where 휏 is a high-accuracy threshold. We set 휏 = 0.90 as a conservative criterion that is substantially above the majority-class baseline for a balanced-class problem while remaining robust to minor variance across random seeds. The choice of this threshold is further justified by the empir- ical stability observed in Figure 2: across all models, once probe accuracy reaches 휏, it remains at or above that level for all subsequent layers without systematic decline. This plateau behavior indicates that 푙 ⋆ does not merely mark an arbitrary accuracy level, but corresponds to the onset of a sta- ble representational regime. The probe-independent centroid analysis in Section 4 corroborates this interpretation: inter- centroid distances increase sharply around 푙 ⋆ and continue to grow monotonically, confirming that the transition reflects a genuine geometric restructuring of the latent space rather than a threshold artifact. Comparing the models from Figure 2, we notice that the CSO happens near layer 5 for most of the models. To provide a comparative overview of performance across different cognitive levels, we visualize the classifi- cation accuracies of the probe for 푙 ⋆ = 5 using a radar chart (Figure 3). Each axis represents one of the six Bloom levels, and each line corresponds to the probe on a specific model. The radar chart thus provides a holistic view of how different architectures handle varying cognitive complexity. To further analyze the structure of probe errors, we ex- amine the confusion matrix. Figure 4 shows a representative confusion matrix obtained from the Llama-3.1-8B-Instruct model. The confusion matrices for all other architectures are reported in Appendix B. The confusion matrix reveals a highly structured error pattern. Let ̂푦 푖 be the predicted Bloom level. We analyze the distribution of error distances |̂푦 푖 − 푦 푖 |. We observe that: 피 [ |̂푦 − 푦| ] ≈ 1(3) B. Raimondi et al.: Preprint submitted to ElsevierPage 4 of 11 Mechanistic Interpretability of Cognitive Complexity in LLMs via Linear Probing using Bloom’s Taxonomy Figure 3: Probe accuracy at layer 5 across Bloom levels for four models. All architectures exhibit consistently high performance, with minor variations reflecting the cognitive difficulty. Remember Understand Apply Analyze Evaluate Create Predicted Label Remember Understand Apply Analyze Evaluate Create True Label 86.3010.961.371.370.000.00 2.7892.590.003.700.930.00 0.000.0096.000.000.004.00 1.680.840.0089.924.203.36 0.001.921.926.7389.420.00 0.000.003.304.401.1091.21 Llama-3.1-8B-Instruct - Layer 5 Figure 4: Representative confusion matrix of the linear probe for Llama-3.1-8B-Instruct at layer 5. indicating that misclassifications preserve ordinal prox- imity and occur between adjacent Bloom levels. This adja- cency effect indicates that the learned representations pre- serve the ordinal structure of cognitive complexity. Importantly, this pattern aligns with well-established ambiguities in human assessment. Boundaries between neigh- boring levels, such as Remember and Understand, or Ana- lyze and Evaluate, are known to be context-dependent and difficult to operationalize consistently, whereas distinctions 0 11 22 33 44 5 Adjacent Bloom Level Pairs 0.0 2.5 5.0 7.5 10.0 12.5 15.0 L2 Distance Between Centroids 0 5 10 15 20 25 30 Layer Depth Figure 5: Figure 5: Layer-wise Euclidean distances between adjacent Bloom-level centroids for the Llama-3.1-8B-Instruct model. Distances are small in early layers and increase monotonically with depth, indicating progressive geometric disentanglement of cognitive levels. The CSO layer 푙 ⋆ = 5 marks the onset of rapid separation. between distant cognitive levels are substantially more ro- bust [21, 1]. The fact that probe errors mirror this structure suggests that the model encodes cognitive depth as a continuous and geometrically structured manifold rather than as a set of arbitrary discrete classes. The consistency of this adjacency- biased error structure across all models (Appendix B) pro- vides further evidence that the observed behavior reflects a genuine property of internal representations, rather than an artifact of a specific architecture or probing setup. 4.1.1. Geometric Evidence of CSO. To complement the probe-based analysis, we examine the geometric organization of representations across layers. For each layer 푙 and Bloom level 푘, we compute the class centroid 휇 푙,푘 = 피[푥 푙 ∣ 푦 = 푘](4) where 푥 푙 denotes the residual stream activation at layer 푙. We then measure the Euclidean distance between adjacent centroids: 퐷 (푘) 푙 = ‖휇 푙,푘+1 − 휇 푙,푘 ‖ 2 (5) Figure 5 reveals a clear depth-dependent separation pat- tern for the Llama-3.1-8B-Instruct model (further analysis for the other models can be found in Appendix C). In early layers, centroid distances are small, indicating that represen- tations of different cognitive levels remain highly entangled. Starting from approximately layer푙 ⋆ = 5, distances increase sharply and continue to grow in deeper layers, demonstrating progressive geometric disentanglement of Bloom levels. Importantly, this analysis is entirely probe-independent. The emergence of large and systematically increasing inter- centroid distances shows that the CSO corresponds to a probe-independent geometric separation in the latent space rather than an artifact of the linear classifier. After the transi- tion layer, deeper layers do not merely preserve separability B. Raimondi et al.: Preprint submitted to ElsevierPage 5 of 11 Mechanistic Interpretability of Cognitive Complexity in LLMs via Linear Probing using Bloom’s Taxonomy Remember Understand Apply Analyze Evaluate Create Predicted Label Remember Understand Apply Analyze Evaluate Create True Label 78.950.005.260.0015.790.00 10.5373.685.2610.530.000.00 0.005.0080.005.000.0010.00 5.0010.0020.0060.000.005.00 15.000.0010.000.0075.000.00 0.0015.7915.790.000.0068.42 Remember Understand Apply Analyze Evaluate Create Predicted Label Remember Understand Apply Analyze Evaluate Create True Label 68.425.260.000.0026.320.00 0.0068.4210.535.265.2610.53 0.0010.0060.000.005.0025.00 0.0015.0010.0065.005.005.00 25.005.005.005.0055.005.00 0.0015.7926.325.260.0052.63 Figure 6: Confusion matrices for the control experiments: TF-IDF on the left, and Sentence Embeddings on the right. but further amplify it, suggesting that cognitive complexity is encoded as an increasingly expanded and ordered mani- fold within the representation space. 4.2. Control Experiments To verify that probe accuracy reflects genuinely cogni- tive representations rather than surface-level lexical patterns, we conduct control experiments. A key potential confound in our probing setup is that Bloom levels may be recoverable from surface-level prompt formulations rather than from in- ternally constructed representations of cognitive complexity. Questions at different Bloom levels tend to be introduced by characteristic verbs: define and list for Remember, explain for Understand, compare and analyze for Analyze, justify for Evaluate, and design for Create. If these lexical cues alone drove probe accuracy, the signal would reflect surface-level text classification rather than any deeper representational structure. The following control experiments are designed to directly test this alternative explanation. Length Analysis. We examine whether question length differs across Bloom levels and could act as a potential confound. Statistical testing shows no significant differences in length across levels (푝 = 0.053), and no pairwise compar- isons remain significant after Bonferroni correction. These results indicate that question length is approximately bal- anced across Bloom categories and is unlikely to drive probe classification performance. Shallow Text Baselines. We train logistic regression clas- sifiers on TF-IDF vectors [26] and sentence embeddings [29] of the question text alone, without accessing LLM internal states. TF-IDF achieves 73% accuracy and sentence embeddings achieves61% accuracy, both substantially lower than our probe accuracy (∼ 90%), indicating that simple lexical features do not fully explain the signal. The corresponding confusion matrices in Figure 6 dis- play substantially noisier and less structured error patterns compared to the residual-stream probes. Misclassifications are more dispersed and frequently occur across non-adjacent Bloom levels. This contrast indicates that shallow lexical features alone do not encode the ordinal structure of cognitive complexity with the same fidelity observed in internal LLM representa- tions. These results strengthen the interpretation that cogni- tive depth is not fully reducible to superficial textual cues, suggesting that LLM residual streams encode additional cognitive structure beyond what is recoverable from surface form alone. 5. Causal Validation via Activation Steering The probing results presented in Section 4 establish that Bloom-level information is linearly encoded in the residual stream. However, linear separability alone does not imply causal use: the model may organize representations accord- ing to cognitive demand without actively exploiting them during generation. To address this, we conduct activation steering experiments to test whether perturbations along the identified cognitive direction induce meaningful changes in model behavior. 5.1. Experimental Setup Steering Vector. For a given injection layer 푠, we define a cognitive steering vector as: 퐯 푠,퓁 = 피[푥 푠 ∣ 푦 = 5] − 피[푥 푠 ∣ 푦 = 퓁](6) where 푥 푠 denotes the residual stream activation at layer 푠 and 퓁 is the source Bloom level. This vector captures the direction of maximal transition toward higher cognitive complexity (Create). Intervention. At inference time, we inject the steering vector into the residual stream: ̃푥 푠 = 푥 푠 + 훼 ⋅퐯 푠,퓁 (7) B. Raimondi et al.: Preprint submitted to ElsevierPage 6 of 11 Mechanistic Interpretability of Cognitive Complexity in LLMs via Linear Probing using Bloom’s Taxonomy where 훼 controls the intervention strength. The modified ac- tivation ̃푥 푠 is then propagated through the remaining layers. Measurement. We evaluate the effect of the intervention using the probe-predicted Bloom level: ̂푦 푝 = argmax 푘 푃(푦 = 푘 ∣ ̃푥 푝 )(8) and compute the mean shift relative to the baseline: Δ̂푦 = 피[̂푦 steered 푝 ] − 피[̂푦 baseline 푝 ](9) 5.2. Quantitative and Qualitative Effects Across configurations, steering consistently produces an upward shift in the probe-predicted cognitive level. This effect is monotonic with respect to the intervention strength 훼 and is observed across all initial Bloom levels except the trivial boundary case of Create, where the steering vector is null by construction. On average, the intervention induces a shift of approximately +1 to +1.5 Bloom levels. We note that probe-predicted level shift is a necessary but not sufficient condition for causal validation: it confirms that the steered activations move along the identified cogni- tive direction in representation space, but does not directly assess whether the generated outputs reflect higher-order reasoning. A fully quantitative causal assessment would require an independent, automated classifier of Bloom level applied to the generated text. However, no such classifier exists with sufficient reliability for free-form generated out- puts: existing Bloom-level annotation tools are designed for human-authored educational questions and do not generalize to model-generated continuations in a controlled steering setting. For this reason, we complement the quantitative probe-shift measure with a qualitative analysis of generated outputs, which allows us to assess whether the representa- tional shift corresponds to observable changes in reasoning style. 5.3. Qualitative Differences Across Layers and Steering Strength To better understand the causal role of the identified cog- nitive direction, we analyze how generated outputs change as a function of both the injection layer 푠 and the intervention strength 훼. Rather than treating steering as a single interven- tion, we examine it as a two-dimensional control mechanism: where the representation is perturbed and how strongly it is modified. 5.3.1. Effect of Injection Layer A first clear distinction emerges between early/intermediate layers (e.g., 푠 ∈ 5,10) and deeper layers (e.g., 푠 ∈ 15,20). Early layers (small 푠). When steering is applied at early stages, the model’s outputs exhibit a coherent shift in cogni- tive processing. The baseline outputs typically remain close to the prompt surface form, often listing information or repeating question structures: Baseline: “Also, what are the key differences between a histogram and a bar graph? How do you determine the appropriate scale? ...” Under steering at early layers, the same prompt produces: Steered (푠 = 5, moderate 훼): “Also, what are the key features of the graph, and how can we interpret the data from it? ...” In this example, the change is not merely lexical: the output introduces procedural reasoning and reframes the task in terms of analysis and interpretation. This observation suggests that, at least in some cases, early-layer steering may modify the internal construction of the task representation. Deep layers (large 푠). In contrast, steering at deeper layers produces qualitatively different effects. While the probe still detects a shift toward higher cognitive levels, the generated text often becomes unstable: Steered (푠 = 20, same 훼): “Also also the graph graph interpretation interpretation is important important because because data data ...” Here, the intervention no longer results in meaningful reasoning changes, but rather in degradation of fluency and coherence. This indicates that late-stage representations are less robust to perturbations and that steering at this stage pushes activations outside the manifold of well-formed out- puts. 5.3.2. Effect of Steering Strength (훼) A second axis of variation is the magnitude of the intervention. Low to moderate 훼. At smaller values of 훼, steering pro- duces gradual and interpretable changes. The model begins to move from retrieval-like responses toward more struc- tured explanations. For example: Steered (훼 = 1): Response remains close to baseline, with minor elaboration. Steered (훼 = 3): “It is important to not only identify the differences, but also to explain why these differences matter in terms of how the data is interpreted ...” This regime corresponds to a smooth transition in cog- nitive framing, where the model increasingly emphasizes relationships and reasoning steps. High 훼. At higher values of 훼, the effect becomes more pronounced but less stable: Steered (훼 = 5): “It is important important to interpret interpret the data in a broader context context of understanding understanding ...” B. Raimondi et al.: Preprint submitted to ElsevierPage 7 of 11 Mechanistic Interpretability of Cognitive Complexity in LLMs via Linear Probing using Bloom’s Taxonomy While the probe-predicted level continues to increase, the output may exhibit repetition, redundancy, or loss of coherence. This suggests that strong interventions amplify the cognitive direction beyond the range supported by the model’s training distribution. 6. Discussion Our results show that Bloom-level information is linearly decodable from early layers of multiple LLMs, suggesting that prompts are rapidly organized according to features correlated with cognitive demand. The emergence of a con- sistent Cognitive Separability Onset across architectures fur- ther indicates that this organization is not model-specific but reflects a robust representational pattern. Together with the centroid analysis, these findings support the view that cog- nitive complexity is encoded as a progressively disentangled and ordered manifold within the residual stream. Importantly, the gap between residual-stream probe ac- curacy and shallow text baselines provides evidence against the hypothesis that probe performance is driven solely by lexical cues such as task-indicative verbs. While some lex- ical signal is present as the non-trivial TF-IDF baseline confirms, the structured, ordinal error patterns observed exclusively in residual-stream probes suggest that LLMs encode additional information beyond what is recoverable from surface form alone. At the same time, linear separability does not imply causal use: the model may cluster inputs by surface strategy or task type rather than by fully abstract cognitive depth. Although shallow baselines underperform, residual-stream separability could still partially reflect training-induced reg- ularities in prompt formulation. Nonetheless, the structured ordinal error patterns suggest that internal representations preserve meaningful hierarchical relationships rather than arbitrary label boundaries. We address this gap directly in Section 5, providing experimental evidence that the identi- fied cognitive subspace is causally implicated in generation. 7. Conclusion and Future Work Our work provides evidence that LLMs possess a mea- surable, linearly separable internal representation of cog- nitive complexity that aligns closely with Bloom’s Tax- onomy. By systematically extracting and analyzing high- dimensional activation vectors from the residual streams of various state-of-the-art models, we have shown evidence that the distinction between varying levels of cognitive de- mand is unlikely to be merely a linguistic artifact, suggesting it reflects a structural property of the model’s latent space. Our investigation into the layer-wise dynamics of these representations revealed a striking Cognitive Separability Onset occurring in the early-to-intermediate stages of the forward pass. This finding suggests that representations cor- related with the cognitive demands of a task emerge long before the final token generation, with representations be- coming differentiated in early layers according to cognitive level. Furthermore, the high classification accuracy achieved by our linear probe indicates that these internal representa- tions encode cognitive level in a coherent and geometrically structured manner that preserves the ordinal structure of human educational theory. The validity of these findings is further supported by our control experiments. Shallow text baselines achieve substan- tially lower accuracy than the residual-stream probes, and their confusion matrices show dispersed, non-ordinal error patterns. This contrast confirms that the cognitive structure identified by our probes is not reducible to surface-level lex- ical regularities, but reflects a genuine internal organization of the model’s representations. These results suggest that Bloom’s Taxonomy may serve not only as an instrument for human learners, but also as a useful lens for analyzing internal representations of cognitive complexity in LLMs. Several promising directions emerge from our findings. The causal intervention study presented in Section 5 pro- vides initial evidence that cognitive representations are func- tionally active; future work could extend this by selectively ablating individual dimensions most predictive of Bloom level, testing whether targeted feature suppression produces graded cognitive degradation consistent with the taxonomy’s ordinal structure. Moreover, cross-lingual and cross-domain analysis would establish the universality of the CSO by extending our methodology to non-English languages and specialized pro- fessional domains (e.g., medical diagnosis, legal reasoning). As the field moves toward increasingly autonomous and complex AI agents, the ability to monitor, interpret, and potentially regulate these cognitive settings via their neural correlates will be essential. Our work contributes toward the possibility of evaluating AI against the same sophisticated standards of understanding that we apply to human intelli- gence. Limitations Our analysis focuses exclusively on decoder-only trans- former architectures and English educational questions. The generalizability to other architectures (e.g., encoder-only or encoder-decoder models) and languages remains to be estab- lished. Finally, our methodology examines only the residual stream, leaving attention patterns and MLP internals as areas for future investigation. The causal steering experiments are conducted on a single model (Qwen3-4B-Instruct); multi- model validation remain open direction. A. Accuracy per Bloom’s Level Figure 7 reports the probe accuracy separately for each Bloom level across layers and models. A consistent pattern emerges across architectures: all levels converge to near- ceiling performance by the CSO layer 푙 ⋆ = 5. B. Raimondi et al.: Preprint submitted to ElsevierPage 8 of 11 Mechanistic Interpretability of Cognitive Complexity in LLMs via Linear Probing using Bloom’s Taxonomy 024681012141618202224262830323436 Layer 0.92 0.94 0.96 0.98 1.00 Accuracy Bloom Level: Remember meta-llama/Llama-3.1-8B-Instruct Qwen/Qwen3-4B-Instruct-2507 google/gemma-3-4b-it deepseek-ai/DeepSeek-R1-Distill-Llama-8B 024681012141618202224262830323436 Layer 0.875 0.900 0.925 0.950 0.975 1.000 Accuracy Bloom Level: Understand meta-llama/Llama-3.1-8B-Instruct Qwen/Qwen3-4B-Instruct-2507 google/gemma-3-4b-it deepseek-ai/DeepSeek-R1-Distill-Llama-8B 024681012141618202224262830323436 Layer 0.875 0.900 0.925 0.950 0.975 1.000 Accuracy Bloom Level: Apply meta-llama/Llama-3.1-8B-Instruct Qwen/Qwen3-4B-Instruct-2507 google/gemma-3-4b-it deepseek-ai/DeepSeek-R1-Distill-Llama-8B 024681012141618202224262830323436 Layer 0.850 0.875 0.900 0.925 0.950 0.975 1.000 Accuracy Bloom Level: Analyze meta-llama/Llama-3.1-8B-Instruct Qwen/Qwen3-4B-Instruct-2507 google/gemma-3-4b-it deepseek-ai/DeepSeek-R1-Distill-Llama-8B 024681012141618202224262830323436 Layer 0.85 0.90 0.95 1.00 Accuracy Bloom Level: Evaluate meta-llama/Llama-3.1-8B-Instruct Qwen/Qwen3-4B-Instruct-2507 google/gemma-3-4b-it deepseek-ai/DeepSeek-R1-Distill-Llama-8B 024681012141618202224262830323436 Layer 0.88 0.90 0.92 0.94 0.96 0.98 1.00 Accuracy Bloom Level: Create meta-llama/Llama-3.1-8B-Instruct Qwen/Qwen3-4B-Instruct-2507 google/gemma-3-4b-it deepseek-ai/DeepSeek-R1-Distill-Llama-8B Figure 7: Layer-wise linear probe accuracy for each Bloom level. Remember Understand Apply Analyze Evaluate Create Predicted Label Remember Understand Apply Analyze Evaluate Create True Label 98.671.330.000.000.000.00 6.6786.672.863.810.000.00 0.000.0096.090.780.003.12 0.001.673.3387.505.831.67 0.002.833.773.7789.620.00 0.000.0011.342.060.0086.60 gemma-3-4b-it - Layer 5 Remember Understand Apply Analyze Evaluate Create Predicted Label Remember Understand Apply Analyze Evaluate Create True Label 92.216.491.300.000.000.00 0.9197.270.910.000.000.91 0.000.0097.760.750.001.49 0.814.031.6191.131.610.81 0.000.000.890.8996.431.79 0.001.0012.004.000.0083.00 DeepSeek-R1-Distill-Llama-8B - Layer 5 Remember Understand Apply Analyze Evaluate Create Predicted Label Remember Understand Apply Analyze Evaluate Create True Label 98.630.001.370.000.000.00 0.00100.000.000.000.000.00 0.000.0096.000.000.004.00 0.840.841.6893.282.520.84 0.000.000.000.9699.040.00 0.000.003.300.001.1095.60 Qwen3-4B-Instruct-2507 - Layer 5 Figure 8: Confusion matrices of the linear probe for four representative models at the CSO layer 푙 ⋆ = 5: gemma-3-4b-it, DeepSeek-R1-Distill-Llama-8B, and Qwen3-4B-Instruct-2507. B. Confusion Matrix The confusion matrices in Figure 8 confirm that clas- sification errors are highly structured rather than random. Across all architectures, misclassifications predominantly occur between adjacent Bloom levels (e.g., Analyze vs. Evaluate), while long-range confusions (e.g., Remember vs. Create) are absent. This adjacency bias provides further evidence that cogni- tive complexity is encoded as an ordered manifold within the representation space. The ordinal structure of Bloom’s tax- onomy is therefore preserved geometrically: representations of neighboring levels remain closer to each other, while dis- tant levels are separated by larger margins. The consistency of this pattern across models suggests that it reflects a general property of Transformer-based representations rather than an artifact of a specific architecture. B. Raimondi et al.: Preprint submitted to ElsevierPage 9 of 11 Mechanistic Interpretability of Cognitive Complexity in LLMs via Linear Probing using Bloom’s Taxonomy 0 11 22 33 44 5 Adjacent Bloom Level Pairs 0 1000 2000 3000 4000 5000 6000 L2 Distance Between Centroids 5 10 15 20 25 30 Layer Depth 0 11 22 33 44 5 Adjacent Bloom Level Pairs 0 5 10 15 20 L2 Distance Between Centroids 5 10 15 20 25 30 Layer Depth 0 11 22 33 44 5 Adjacent Bloom Level Pairs 0 25 50 75 100 125 150 L2 Distance Between Centroids 5 10 15 20 25 30 35 Layer Depth Figure 9: Layer-wise Euclidean distances between adjacent Bloom-level centroids for all evaluated models: gemma-3-4b-it, DeepSeek-R1-Distill-Llama-8B, and Qwen3-4B-Instruct-2507. C. Centroids Figure 9 visualizes the Euclidean distance between ad- jacent Bloom-level centroids across layers for all evaluated models. In early layers, centroid distances are small, indi- cating that representations of different cognitive levels are highly entangled. Starting around the CSO layer, distances increase sharply and then continue to expand monotonically with depth. This progressive separation demonstrates that deeper layers do not merely preserve linear separability, but actively amplify geometric distinctions between cognitive categories. Importantly, this analysis is probe-independent and there- fore confirms that the Cognitive Separability Onset corre- sponds to an intrinsic restructuring of the latent space rather than an artifact of linear classification. Acknowledgements This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. The authors declare no competing interests. CRediT authorship contribution statement Bianca Raimondi: Conceptualization of this study, Methodology, Software. Maurizio Gabbrielli: Supervision. References [1] Anderson, L.W., Krathwohl, D.R., 2001. 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[34] Zaman, K.A.U., Islam, A., Islam, Y.M., Sayed, M.A., 2024. Dataset of computer science course queries from students: Categorized and scored according to bloom’s taxonomy. Data in Brief 53, 110109. [35] Zhao, H., Yang, F., Shen, B., Lakkaraju, H., Du, M., 2024. Towards uncovering how large language model works: An explainability per- spective. arXiv preprint arXiv:2402.10688 . [36] Zoumpoulidi, M.E., Paraskevopoulos, G., Potamianos, A., 2025. Bloomwise: enhancing problem-solving capabilities of large language models using bloom’s-taxonomy-inspired prompts, in: Proceedings of The 3rd Workshop on Mathematical Natural Language Processing (MathNLP 2025), p. 34–49. Bianca Raimondi holds a Master’s degree in Com- puter Science from the University of Bologna. She is currently a PhD student specialising in Data Science and Computation. Her research focuses on applying Large Language Models in education, particularly examining the biases of these models and how they represent information internally. Maurizio Gabbrielli is professor of Computer Sci- ence since 2001 at the Department of Computer Science and Engineering of the University of Bologna and Associate dean for AI at Bologna Business School. He has been Head of the Depart- ment of Computer Science and Engineering and member of the INRIA project team FOCUS. He received his Ph.d. in Computer Science in 1992 from the University of Pisa and has been em- ployed at Centrum Wiskunde & Informatica (CWI, Amsterdam), at the University of Pisa and at the University of Udine. B. Raimondi et al.: Preprint submitted to ElsevierPage 11 of 11