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Unlocking the Address Book: Dissecting the Sparse Semantic Structure of LLM Key-Value Caches via Sparse Autoencoders
Qingsen Ma, Dianyun Wang, Jiaming Lyu, Yaoye Wang, Lechen Ning, Sujie Zhu, Zhenbo Xu, Liuyu Xiang, Huining Li, Huijia Wu, Zhaofeng He
Models: Mistral-7B, Qwen2.5-32B, Yi-6B
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Summary
The paper introduces STA-Attention, a framework using Top-K Sparse Autoencoders (SAEs) to decompose LLM Key-Value (KV) caches into interpretable 'semantic atoms.' It identifies a 'Key-Value Asymmetry' where Keys act as sparse routers and Values as dense content payloads, leading to a Dual-Budget Strategy (K=8 for Keys, K=16 for Values) that maintains model performance while reducing memory bottlenecks.
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STA-Attention → utilizes → Top-K Sparse Autoencoder
confidence 99% · STA-Attention, a framework that utilizes Top-K Sparse Autoencoders (SAEs)
Top-K Sparse Autoencoder → decomposes → KV cache
confidence 98% · utilizes Top-K Sparse Autoencoders (SAEs) to decompose the KV cache into interpretable 'semantic atoms.'
Key-Value Asymmetry → informs → Dual-Budget Strategy
confidence 95% · Based on this structure [Key-Value Asymmetry], we introduce a Dual-Budget Strategy
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Abstract
Abstract:The Key-Value (KV) cache is the primary memory bottleneck in long-context Large Language Models, yet it is typically treated as an opaque numerical tensor. In this work, we propose \textbf{STA-Attention}, a framework that utilizes Top-K Sparse Autoencoders (SAEs) to decompose the KV cache into interpretable ``semantic atoms.'' Unlike standard $L_1$-regularized SAEs, our Top-K approach eliminates shrinkage bias, preserving the precise dot-product geometry required for attention. Our analysis uncovers a fundamental \textbf{Key-Value Asymmetry}: while Key vectors serve as highly sparse routers dominated by a ``Semantic Elbow,'' deep Value vectors carry dense content payloads requiring a larger budget. Based on this structure, we introduce a Dual-Budget Strategy that selectively preserves the most informative semantic components while filtering representational noise. Experiments on Yi-6B, Mistral-7B, Qwen2.5-32B, and others show that our semantic reconstructions maintain perplexity and zero-shot performance comparable to the original models, effectively bridging the gap between mechanistic interpretability and faithful attention modeling.
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- Source: https://arxiv.org/abs/2512.10547
- Canonical: https://arxiv.org/abs/2512.10547
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Unlocking the Address Book: Dissecting the Sparse Semantic Structure of LLM Key-Value Caches via Sparse Autoencoders Qingsen Ma * 1 Dianyun Wang * 1 Jiaming Lyu * 1 Yaoye Wang * 1 Lechen Ning * 1 Sujie Zhu * 1 Zhenbo Xu 1 Liuyu Xiang 1 Huining Li 2 Huijia Wu 1 Zhaofeng He 1 Abstract The Key-Value (KV) cache is the primary mem- ory bottleneck in long-context Large Language Models, yet it is typically treated as an opaque numerical tensor.In this work, we propose STA-Attention, a framework that utilizes Top- K Sparse Autoencoders (SAEs) to decompose the KV cache into interpretable “semantic atoms.” Unlike standardL 1 -regularized SAEs, our Top-K approach eliminates shrinkage bias, preserving the precise dot-product geometry required for at- tention. Our analysis uncovers a fundamental Key-Value Asymmetry: while Key vectors serve as highly sparse routers dominated by a “Semantic Elbow,” deep Value vectors carry dense content payloads requiring a larger budget. Based on this structure, we introduce a Dual-Budget Strategy that selectively preserves the most informative semantic components while filtering representa- tional noise. Experiments on Yi-6B, Mistral-7B, Qwen2.5-32B, and others show that our semantic reconstructions maintain perplexity and zero-shot performance comparable to the original models, effectively bridging the gap between mechanistic interpretability and faithful attention modeling. 1. Introduction The deployment of LLMs in long-context scenarios is funda- mentally constrained by the Key-Value (KV) cache memory bandwidth and capacity (Pope et al., 2023; Kwon et al., 2023). As the cache grows linearly with sequence length, it limits batch sizes and increases latency (Shazeer, 1911; Touvron et al., 2023; Sun et al., 2024). Consequently, 1 Beijing University of Posts and Telecommunications, Beijing, China 2 Baidu Inc., Beijing, China.Correspon- dence to: Zhenbo Xu <xuzhenbo@bupt.edu.cn>, Zhaofeng He <zhaofenghe@bupt.edu.cn>. Preprint. December 12, 2025. compression has become central, with existing approaches predominantly focusing on numerical approximations like quantization (Sheng et al., 2023) or attention-based token pruning (Zhang et al., 2023). However, these methods treat the KV cache as a generic numerical tensor, optimizing geometric reconstruction while treating the underlying rep- resentational logic as a “black box” (Kim et al., 2024; Geva et al., 2021; Templeton, 2024). The Interpretability Gap.Parallel to efficiency research, Mechanistic Interpretability (Olah et al., 2020) has advanced in decomposing neural networks (Elhage et al., 2021; Meng et al., 2022a; Hernandez et al., 2023; Cunningham et al., 2023). Sparse Autoencoders (SAEs) effectively disentangle superposition (Elhage et al., 2022) in MLPs (Cunningham et al., 2023) and Residual Streams (Lieberum et al., 2024). Yet, a critical gap remains: existing SAE research has largely overlooked the internal addressing logic of At- tention Heads (Elhage et al., 2021; Lieberum et al., 2024; Gould et al., 2023). While MLPs are viewed as “Knowl- edge Memories” (Dai et al., 2022; Meng et al., 2022b) and Residual Streams as “Information Highways” (Jastrz ̨ebski et al., 2017; Von Oswald et al., 2023; Candes & Tao, 2005), the mechanism mapping input tokens to high-dimensional Key routing vectors (Jaszczur et al., 2021; Masoudnia & Ebrahimpour, 2014; Bahdanau et al., 2014; Devlin et al., 2019) remains under-explored (Cao et al., 2024). Few ques- tion the semantic necessity of the standard d head = 128 di- mensionality (Bhojanapalli et al., 2020; Michel et al., 2019; Aghajanyan et al., 2021). Present Work. We bridge this gap with STA-Attention (Sparse Semantic Self-Attention), hypothesizing that KV information lies on a low-dimensional (Aghajanyan et al., 2021), sparse semantic manifold (Bengio et al., 2013; Liu et al., 2023). By applying Top-K SAEs (Gao et al., 2024) to Key and Value projections, we decompose dense vectors into interpretable “semantic atoms.” Crucially, we address the shrinkage bias of standardL 1 -regularized SAEs (Tibshi- rani, 1996) that degrades dot-product calculations. Adopt- 1 arXiv:2512.10547v1 [cs.LG] 11 Dec 2025 Unlocking the Address Book: Dissecting the Sparse Semantic Structure of LLM Key-Value Caches via Sparse Autoencoders ing Top-K SAEs enforces a hard sparsity budget without dampening signal magnitude, ensuring unbiased attention scoring. Our contributions are: 1.Hierarchical Addressing Mechanism: We unveil the functional stratification of attention: shallow layers encode lexical patterns (n-grams), middle layers form a Syntactic Backbone, and deep layers perform Polysemy Resolution via orthogonal semantic features. 2.Discovery of the “Semantic Elbow”: We empirically identify a saturation point atK = 8, where the Top-8 active latents recover over 80% of the Key vector’s directionality. We propose the Denoising Hypothesis: removing lower-ranked features eliminates noise and improves perplexity. 3. Key-Value Asymmetry & Dual-Budget Strategy: We identify a divergence in information density: Keys are sparse (routing) while Values are dense (logi- cal payloads). We introduce a Dual-Budget Strategy (K key = 8,K val = 16) to maximize compression while preserving reasoning capabilities. 4.Performance Parity: Validating on 7B-scale mod- els (Yi, Mistral, Llama-2), STA-Attention matches the zero-shot performance and perplexity of dense base- lines (K = 128) with significantly reduced memory, confirming the viability of sparse semantic decomposi- tion. 2. Related Work Efficient KV Cache Management. Existing research largely bifurcates into quantization and pruning. Quantiza- tion approaches like CommVQ (Li et al., 2025) optimize vector quantization for attention score reconstruction rather than Euclidean distance. Pruning strategies, such as Rock- etKV (Behnam et al., 2025) and “Compute or Load” (Jin et al., 2024), reduce memory footprint by selectively preserv- ing tokens or re-computing states on the fly. However, these methods predominantly treat the KV cache as a generic numerical container, optimizing for geometric approxima- tions while remaining agnostic to the underlying semantic manifold of the attention mechanism. Mechanistic Interpretability and SAEs.Sparse Autoen- coders (SAEs) have successfully extracted monosemantic features from MLPs (Cunningham et al., 2023) and residual streams (Templeton, 2024). Notably, Top-K SAEs (Gao et al., 2024) mitigate the shrinkage bias ofL 1 regulariza- tion, ensuring unbiased magnitude estimation. Despite this progress, a critical gap remains: the internal addressing logic of attention heads (specifically theW K projection) has received limited scrutiny compared to MLPs, leaving the semantic structure of routing vectors largely unexplored. Sparse Representation for Compression. Lexico (Kim et al., 2024) pioneers the use of sparse coding for KV cache compression via universal dictionaries. Distinction: Our S 3 -Attention framework advances beyond Lexico in two dimensions. First, instead of generic universal dictionar- ies, we employ specialized Top-K SAEs to decouple the specific routing logic of Keys from the content payloads of Values. Second, unlike Lexico’s uniform compression, we leverage the “Semantic Elbow” and “Key-Value Asymme- try” to dynamically allocate budgets—heavily compressing sparse routing information while preserving dense semantic content—thereby aligning compression with the model’s intrinsic functional stratification. 3. Preliminaries: Rationale for Top-K SAE Before detailing our methodology, we address a fundamen- tal design choice: why we adopt the Top-K Sparse Autoen- coder (Top-K SAE) architecture (Gao et al., 2024) over the standardL 1 -regularized SAE commonly used in inter- pretability research (Cunningham et al., 2023). WhileL 1 -SAEs have been successful in decomposing su- perposition in Multi-Layer Perceptrons (MLPs), we identify three theoretical misalignments that make them subopti- mal for analyzing the Key-Value (KV) cache in attention mechanisms. 1. The Shrinkage Bias Problem. Standard SAEs rely on anL 1 penalty term (λ||z|| 1 ) to induce sparsity. This penalty creates a constant downward pressure on activation magnitudes, resulting in shrinkage bias—the reconstructed features are systematically smaller than the true latent sig- nals. In the context of Self-Attention, the magnitude of the key vectorkdirectly influences the dot-product attention score (A∝ q· k T ). Any artificial shrinkage inkwould dis- tort the attention weights and degrade model performance. The Top-K SAE enforces sparsity via hard truncation rather than penalization, ensuring that the active semantic features provide an unbiased estimation of the original signal scale. 2. Training-Inference Alignment. Our objective is to achieve efficient, constant-time memory retrieval using a fixed budget (e.g., preserving exactly Top-8 features). An L 1 -SAE optimizes a soft sparsity objective during training but would require a mismatched hard truncation (post-hoc Top-K) during inference to meet this budget. This misalign- ment leads to suboptimal reconstruction. In contrast, the Top-K SAE aligns the training objective with the inference constraint, optimizing the dictionary codebook specifically 2 Unlocking the Address Book: Dissecting the Sparse Semantic Structure of LLM Key-Value Caches via Sparse Autoencoders to maximize fidelity under a strict K-feature budget. 3. Preventing Feature Death.L 1 -SAEs are notoriously sensitive to the hyperparameterλ. An excessively highλ often leads to "dead features" (latents that never activate), effectively wasting the model’s capacity. The Top-K mecha- nism guarantees that exactlyKlatents are active for every sample during training, providing a stable learning regime and ensuring full utilization of the dictionary capacity with- out extensive hyperparameter tuning. Consequently, we select the Top-K SAE as the mathemati- cally robust tool for dissecting the intrinsic dimensionality of the KV cache. 4. Methodology 4.1. Problem Formulation: The Sparse Manifold Hypothesis of Attention The Key-Value (KV) cache in Transformer-based Large Lan- guage Models (LLMs) serves as the fundamental memory unit during inference. For a given layerland headh, the key projection maps the input residuex∈R d model to a key vector k ∈R d head via a linear transformation W K . Whilekresides in a high-dimensional space (e.g.,d head = 128), we hypothesize that the effective information required for the attention mechanism lies on a significantly lower- dimensional, non-linear manifold. Specifically, we posit that each key vectorkis a sparse linear combination of a finite set of semantic atoms (e.g., entities, syntactic functions, positional markers). Formally, we aim to find a sparse decomposition such that: k ≈ X i∈S α i ·d i , |S|≪ d head (1) whered i are vectors from a learned overcomplete dictio- nary, andSis the set of active indices. Our objective is to identify the minimal set sizeK = |S|that preserves the downstream inference capability of the LLM while filtering out representational noise. 4.2.Top-K Sparse Autoencoder for KV Disentanglement To extract these semantic atoms without the hyperparameter sensitivity and feature shrinkage associated with traditional L 1 -regularized Sparse Autoencoders (SAEs), we employ a Top-K SAE architecture (Gao et al., 2024). Architecture. The Top-K SAE consists of an encoder, a Top-K gating mechanism, and a decoder. Letk in be the input key vector. The encoder projectsk in into a latent overcomplete spaceR M (where M ≫ d head ): z pre = ReLU(W enc (k in − b dec ) + b enc )(2) where W enc ∈R d head ×M and b enc ∈R M . Top-K Gating. Unlike standard SAEs that rely on soft sparsity constraints, we enforce hard sparsity directly in the forward pass. We select theklargest activations fromz pre and zero out the rest: I topk = argtopk(z pre ,K train )(3) z i = ( (z pre ) i if i∈I topk 0otherwise (4) This ensures that exactlyK train semantic features are active for any given token during training, preventing the “dead feature” problem and eliminating the need to tune anL 1 coefficient. Reconstruction & Objective. The sparse latent vectorzis decoded to reconstruct the original key: ˆ k = zW dec + b dec (5) The model is trained to minimize the Mean Squared Error (MSE) between the original and reconstructed keys. Cru- cially, by strictly limiting the information bottleneck to ac- tive features, the SAE is forced to learn the most salient semantic directions (Principal Semantic Components). 4.3. Determining the Intrinsic Dimensionality: Why Top-8? A critical contribution of this work is the empirical deter- mination of the “Semantic Elbow” for LLM Attention. We argue that choosingK = 8is not an arbitrary compression heuristic, but a reflection of the intrinsic semantic dimen- sionality of the attention mechanism. We justify this choice through three complementary analyses: 1. Saturation of Reconstruction Fidelity (The Elbow Point). We analyze the reconstruction fidelityF (k)defined as the cosine similarity between the original keykand its Top-K reconstruction ˆ k k . As illustrated in Figure 4,F (k) exhibits a distinct saturation behavior. •Rapid Information Gain (K ≤ 8): The fidelity in- creases sharply fromK = 1toK = 8, recovering over80%of the directional information (e.g., Cosine Similarity≈ 0.81at Layer 16). This suggests the first few features capture core semantic anchors. • Diminishing Returns (K > 8): BeyondK = 8, the marginal gain∆F =F (k + 1)−F (k)drops precipi- tously. Doubling the budget fromK = 8toK = 16 yields negligible improvement in semantic alignment. This implies that features ranked9+largely encode distributed noise or redundant syntactic nuances. 3 Unlocking the Address Book: Dissecting the Sparse Semantic Structure of LLM Key-Value Caches via Sparse Autoencoders 2. The Denoising Hypothesis via Perplexity Analysis. Contrary to standard compression theory, where lower bi- trate implies higher distortion, we observe that restricting inference to the Top-8 features often improves perplexity (PPL) and downstream zero-shot accuracy compared to full- rank reconstruction (see Table 3). We propose the Denoising Hypothesis: The “tail” of the activation spectrum (ranks > 8) contains task-irrelevant noise that interferes with the attention mechanism’s ability to attend to correct tokens. By settingK = 8, the Top-K SAE acts as a semantic filter, preserving the signal while suppressing this noise. 3. Hook-based Verification. We verify the sufficiency of K = 8by injecting the reconstructed keys ˆ k top8 back into the LLM during inference. LetL task (·)be the loss on a downstream task. We observe: |L task ( ˆ k top8 )−L task (k orig )|≈ 0(6) This effectively demonstrates that the information lost by discarding ranks9... 128is functionally orthogonal to the model’s reasoning capabilities. 5. Experiments We evaluate STA-Attention across three complementary dimensions to validate the effectiveness of the Top-K SAE framework: 1.Micro-Analysis (Interpretability): We qualitatively examine the learned features to verify their semantic atomicity. 2.Meso-Analysis (Intrinsic Dimensionality): We ana- lyze the reconstruction fidelity curve to mathematically identify the optimal sparsity level K. 3.Macro-Analysis (End-to-End Performance): We as- sess the impact of Top-K retrieval on perplexity and zero-shot reasoning tasks, testing the “Denoising Hy- pothesis.” 5.1. Experimental Setup We conduct experiments on standard open-source LLMs, specifically 01ai/Yi-6B and Mistral-7B-v0.1. For each model, we train Top-K SAEs on the Key projections of rep- resentative layers: shallow (L2), middle (L16), and deep (L30). The SAEs are trained with an expansion factor F = 32(mappingd head = 128 → d latent = 4096) and a training target ofK train = 32for 30,000 steps on thewikitext-2dataset. We report Cosine Similar- ity for reconstruction fidelity and Perplexity (PPL) on the wikitext-2 test set for robustness evaluation. 5.2. Micro-Analysis: Functional Stratification & Semantic Atomicity To validate the semantic atomicity of the learned features, we conducted a granular inspection of the Top-K SAE latent space across different depths of Yi-6B. We utilized a set of 10 linguistic probe cases (including syntactic ambiguity, code, and reasoning) to trace feature activations. Our analysis reveals a distinct Functional Stratification hy- pothesis: the role of the KV cache evolves from local lexical anchoring in shallow layers to syntactic routing in middle layers, and finally to abstract semantic disentanglement in deep layers. This functional separation explains why a small budget (K = 8) is sufficient—at any given depth, the model only attends to a specific subset of attributes. 1. Shallow Layers: Local Lexical Anchors (Layer 2). In the early stages, features function as local pattern detec- tors. For instance, in Casebase("The capital of France is Paris"), Feature 3655 is triggered strongly by both ‘Paris’ (Act: 5.59) and ‘of’ (Act: 6.06). Similarly, in Caseentity, it activates on ‘of’. This suggests the shallow KV cache encodes bi-gram or tri-gram statistics (e.g., "City of", "CEO of"), anchoring tokens to their immediate neighbors before high-level processing. 2. Middle Layers: Syntactic Routing Backbone (Layer 16). A striking observation in Layer 16 is the dominance of high-activation structural features. As detailed in Table 1, specific features such as Feature 3012 and Feature 2430 consistently activate on functional words (‘of’, ‘the’, ‘and’, ‘to’) across disparate contexts ranging from narrative text to code. We hypothesize that these features serve as the Syntac- tic Backbone of the attention mechanism, allowing heads to route information based on grammatical structure (Subject- Verb-Object) rather than semantic content. The ubiquity of these features supports the theory that middle layers are heavily involved in broadcasting structural information. 3. Deep Layers: Polysemy Resolution (Layer 30). In the deepest layers, the features disentangle into highly specific semantic atoms. Crucially, the Top-K SAE successfully resolves lexical ambiguity. We compared the activation patterns for the word "bank" in two distinct contexts: •Nature Context: "He sat on the river bank and watched the water." •Finance Context: "He went to the bank to deposit some money." As shown in Figure 2 (visualized in Appendix), the SAE utilizes orthogonal feature sets for these contexts. Feature 2193 activates specifically on ‘water’ (Act: 7.16) in the nature context, whereas Feature 948 activates on ‘money’ (Act: 9.00) in the finance context. The SAE does not simply 4 Unlocking the Address Book: Dissecting the Sparse Semantic Structure of LLM Key-Value Caches via Sparse Autoencoders Figure 1. The S³-Attention Pipeline. The process is composed of three phases: (1) Training Top-K SAEs to extract semantic atoms without shrinkage bias. (2) Conducting Meso-Analysis to identify the “Key-Value Asymmetry” in intrinsic dimensionality, leading to a Dual-Budget Strategy (K k =8, K v =16). (3) Deploying the frozen, sparsified attention mechanism during inference, verified by micro- and macro-evaluations. encode the token "bank" but decomposes the contextual meaning into atomic concepts (Liquidity vs. Finance). This hierarchical specialization confirms that the "Sparsity of Meaning" is not just a statistical artifact but a fundamental property of LLM representational structure. Table 1. Syntactic Dominance in Middle Layers (Layer 16). Features 3012 and 2430 act as universal syntactic routers, trigger- ing on functional connectors across completely different domains (Text vs. Code). DomainInput Text snippetFeat. 3012 TriggerFeat. 2430 Trigger Entity...CEO of SpaceX‘of’ (10.62)‘of’ (9.75) Relation...Romeo and Juliet‘and’ (11.50)‘wrote’ (10.25) Codedef add(a, b)‘,’ (10.50)‘,’ (9.06) Bank...went to the bank‘the’ (9.88)‘to’ (10.44) Visualizing Polysemy Resolution: The "Bank" Case Study. To further validate the semantic disentanglement, we visualize the activation patterns of the Top-K SAE on the polysemous word "bank" in two distinct contexts: Nature ("river bank") and Finance ("deposit money"). As illustrated in Figure 2, the heatmaps reveal a fundamental architectural shift from Layer 16 to Layer 30. 1. Layer 16: Horizontal Syntactic Broadcasting. In the middle layers, the SAE fea- tures exhibit a "horizontal" activation structure. As seen in the Layer 16 heatmap for the finance case, specific features such as Feature 3876 and Feature 2619 remain highly ac- tive across the entire sequence length. These features do not attend to specific semantic keywords like "money"; instead, they act as a Syntactic Backbone, broadcasting structural state information (e.g., maintaining the prepositional scope of "to") to all subsequent tokens. This confirms that middle layers prioritize information routing over semantic preci- sion. 2. Layer 30: Vertical Semantic Orthogonality. In contrast, Layer 30 demonstrates precise "vertical" sparsity, where activations are localized to specific meaningful tokens. Cru- cially, the heatmap comparison proves that the SAE resolves ambiguity by mapping the token "bank" to orthogonal sub- spaces depending on context: • Common Features: High-frequency features such as Feature 74 and Feature 1471 appear in both contexts. These likely encode the general part-of-speech (Noun) or the raw token identity of common stopwords, repre- senting the shared subspace. • Context-Specific Disentanglement: –In the River context, the model activates Feature 1303 and Feature 1200, which are notably absent or suppressed in the finance context. 5 Unlocking the Address Book: Dissecting the Sparse Semantic Structure of LLM Key-Value Caches via Sparse Autoencoders (a) Layer 16: Horizontal Syntactic Bands(b) Layer 30: Vertical Semantic Sparsity Figure 2. Evolution of Feature Activations. (a) Layer 16 shows dense, horizontal activations (e.g., Feat 3876) representing global syntax. (b) Layer 30 shows sparse, vertical activations (e.g., Feat 1901 on ’money’) representing precise semantic concepts. Note how the distinct meanings of "bank" recruit orthogonal features. Table 2. Semantic Disentanglement in Deep Layers (Layer 30) — Vertical Layout Case IDbank_river Key Contextriver Top Active FeatureFeat 1556 (Act: 8.69) Semantic ConceptLocation / Nature Case IDbank_river Key Contextwater Top Active FeatureFeat 2193 (Act: 7.16) Semantic ConceptLiquid / Object Case IDbank_money Key Contextmoney Top Active FeatureFeat 948 (Act: 9.00) Semantic ConceptFinance / Value Case IDbank_money Key Contextwent Top Active FeatureFeat 1556 (Act: 8.19) Semantic ConceptAction / Movement –In the Finance context, the model recruits a dis- tinct set of features, including Feature 1946 and Feature 1901, specifically triggered by the tokens "deposit" and "money". This orthogonal separation in Layer 30 demonstrates that the Top-K SAE does not merely compress the Key vector, but successfully deconstructs the superposition of the word "bank," isolating its financial meaning from its geographical meaning into separate dimensions. This semantic sparsity explains why a budget ofK = 8is sufficient: distinct meanings utilize distinct, non-overlapping subsets of the dictionary. The Dual Nature of Attention: Keys vs. Values.While Key vectors specialize in routing (selecting which token to attend to), our analysis of Value (V) vectors in Layer 16 reveals a fundamentally different functional role: Content Composition. We analyzed the Top-K SAE activations for Value vectors on the same polysemous "bank" examples. As shown in Figure 3, the activation patterns differ markedly from the sparse discrimination observed in Keys. Feature Reuse and Semantic Expansion. Unlike Layer 30 Keys, which resolved "bank" into orthogonal features, Layer 16 Values exhibit Semantic Expansion. We tracked two dominant features across contexts: Feature 1123 (The "Entity Payload"): This feature acts as a generic carrier for heavy semantic entities. It activates strongly on ’bank’ (Act: 1.59) in the river context, but shifts to ’deposit’ (Act: 1.68) in the finance context. It also triggers on ’X’ (Act: 2.22) in "SpaceX" and ’system’ (Act: 2.23) in "system of government." This suggestsVvectors do not just identify the token, but prepare a "topic embedding" to be moved to the residual stream. Feature 443 (The "Action State"): This feature consistently tracks the governing verb or state. It activates on ’sat’ (Act: 1.91) in the river sentence and ’went’ (Act: 1.94) in the finance sentence. This indicates that while Keys perform sparse selection, Values perform dense composition, often aggregating the object (Feat 1123) and the action (Feat 443) into a unified payload. 5.3. Meso-Analysis: Intrinsic Dimensionality & The Key-Value Asymmetry Having established the functional stratification of features, we now quantify the intrinsic dimensionality of the KV 6 Unlocking the Address Book: Dissecting the Sparse Semantic Structure of LLM Key-Value Caches via Sparse Autoencoders (a) L16 Value: River Context(b) L16 Value: Finance Context(c) L16 Value: Code Context Figure 3. Value Vector Activations (Layer 16). Unlike Keys which distinguish contexts via orthogonal features, Value vectors often reuse high-magnitude "Payload Features" (e.g., Rows 1123, 443) to transport semantic content across related tokens. Note the density of activation compared to the sparsity of Keys. cache. We sweep the inference-time sparsity budgetKfrom 1 to 128 across multiple models and layers. Crucially, our experiments reveal a fundamental dichotomy between the addressing mechanism (Keys) and the content payload (Values), which we term the Key-Value Asymme- try. 5.3.1. KEYS: THE UNIVERSAL SATURATION ELBOW (K = 8) As visualized in the dashed curve of Figure 4, Key vectors exhibit a consistent Pareto frontier. We designateK = 8as the critical “Semantic Elbow” where the marginal informa- tion gain diminishes significantly. •Rapid Recovery: For Yi-6B Layer 30 (Key), the first 8 features recover over 84% of the directionality. •Semantic Sparsity: As noted in Sec. 5.2, deep keys perform polysemy resolution. Since a token typically holds only one specific meaning in context, the address- ing signal is inherently sparse. 5.3.2. VALUES: THE DEEP BOTTLENECK AND DENSE PAYLOADS However, contrasting the Key vectors with Value vectors re- veals a striking divergence in information density, supported by our experiments on Yi-6B, Mistral-7B, and Qwen-2.5. 1. Shallow Layers behave like Keys (Copying Mecha- nism). In early layers (e.g., Yi-6B Layer 2, Blue line), Value vectors are easily compressed. AtK = 8, fidelity reaches 0.862. We hypothesize that shallow layers largely perform "copying" operations (Induction Heads), where the payload is simply the token identity—a low-rank signal. 2. Deep Layers hit a Compression Wall (The Payload Hypothesis). In deep layers, Value vectors become hyper- dense. As shown by the Red line in Figure 4 (Yi-6B L30), the fidelity at K = 8 drops precipitously to 0.658. •To achieve the same fidelity that Layer 2 achieves at K = 8 (∼ 0.86), Layer 30 requires nearly K = 32. •Interpretation: Unlike Keys which act as sparse "pointers," Deep Values represent the pre-output distri- bution. They are linearly combined to form the logits for the next token prediction. This requires encoding a superposition of probabilities for multiple potential candidates, naturally resulting in a higher-rank, denser representation. Table 3. Table 3. Performance Parity under Compression (K = 8/32vs. Baseline). We compare the Perplexity (PPL) and Zero- shot Accuracy of compressed models against the dense baseline (K = 128). The results show that reducing the KV cache rank to 8 or 32 results in negligible performance shifts.Acc.(H/E/C/O/Cq) represent Hella/ARC-E/ARC-C/PIQA/OBQA/CQA respectively. Model / LayerPPL↓Acc.↑ (H/E/C/O/Cq) Yi-6B (L16) Dense (128)5.24549.0 / 50.2 / 41.8 / 41.6 / 43.0 K = 325.16047.8 / 50.6 / 42.8 / 42.0 / 43.6 K = 85.14948.0 / 51.6 / 41.8 / 41.4 / 44.6 Yi-9B (L28) Dense (128)5.13249.8 / 50.8 / 41.8 / 40.2 / 43.6 K = 325.11350.2 / 50.8 / 42.5 / 41.0 / 44.4 K = 85.10650.4 / 50.8 / 42.1 / 40.6 / 44.8 Mistral-7B (L16) Dense (128)5.26055.6 / 63.4 / 44.1 / 46.6 / 54.2 K = 325.24555.8 / 62.2 / 42.5 / 47.6 / 53.6 K = 85.24255.4 / 61.2 / 41.5 / 47.6 / 52.8 Llama-2-7B (L22) Dense (128)5.30145.2 / 38.8 / 36.8 / 43.0 / 33.8 K = 325.29344.6 / 38.6 / 35.5 / 43.2 / 34.0 K = 85.27243.8 / 37.8 / 36.1 / 42.4 / 33.4 5.3.3. CONCLUSION: THE SHIFTED ELBOW AND DUAL-BUDGET STRATEGY Our analysis confirms that a "one-size-fits-all" sparsity bud- get is suboptimal due to the Key-Value Asymmetry. While 7 Unlocking the Address Book: Dissecting the Sparse Semantic Structure of LLM Key-Value Caches via Sparse Autoencoders 016326496128 0.4 0.6 0.8 1 K = 8 K = 16 Sparsity Budget K Cosine Similarity (a) Yi-6B: The Efficiency Gap L16 Key (Routing) L2 Value (Copying) L30 Value (Payload) 016326496128 0.4 0.6 0.8 1 Sparsity Budget K (b) Mistral & Qwen: Slow vs Fast Mistral L30 Key Mistral L30 Value Qwen L16 Value Figure 4. Linear Scale Comparison emphasizing Top-K Efficiency. Using a linear x-axis highlights the rapid information recovery of Key vectors. (a) Yi-6B: The Key curve (Green) shoots up vertically, reaching> 0.86within the first 6% of the budget (K = 8). In contrast, the Deep Value curve (Red) rises gradually, illustrating the high-rank nature of payload information. (b) Mistral & Qwen: A similar trend is observed, where Key vectors saturate almost instantly, while Value vectors require a significantly larger linear budget to reach comparable fidelity. K = 8 is the distinct saturation point for Keys, Deep Values operate on a Shifted Elbow. The Case forK v = 16. As detailed in our logs, the marginal gain fromK = 8toK = 16for Deep Values is substantial, far exceeding the typical diminishing returns seen in Keys. •Fidelity Recovery: For Yi-6B L30 (Value), increasing Kfrom 8 to 16 boosts fidelity from 0.658 to 0.767 (+11%). Similarly, Mistral-7B L30 (Value) crosses the critical 0.80 threshold (0.728→ 0.808). •Semantic Integrity: Qualitative inspection suggests that the additional 8 features in theK = 16budget capture secondary "contextual shadings" (e.g., subtle tone or grammatical mood) that are dropped atK = 8 but are essential for constructing the precise output distribution. Recommendation. Consequently, we propose a Dual- Budget Protocol for efficient KV caching: K inference = ( 8for Keys (k) and Shallow Layers 16 for Deep Value (v) Payloads (7) This strategy acknowledges the density of the payload man- ifold while maintaining a 96% compression rate (16 vs 128) relative to the dense baseline, providing the optimal trade- off between memory savings and generation quality. 5.4. Macro-Analysis: Efficient Compression with Performance Parity Finally, we assess the end-to-end impact of STA-Attention on language modeling and zero-shot reasoning. Our pri- mary objective is to verify the Information Sufficiency Hypothesis: that the sparse "Semantic Atoms" extracted by our Top-K SAE contain nearly all the effective information required for inference, rendering the massive "tail" of the KV cache redundant. We evaluate the model performance under aggressive com- pression regimes, specifically testing sparsity budgets of K = 8andK = 16against the Full-Rank baseline (K = 128). As shown in Table 4, our method achieves a remarkable compression ratio while maintaining perfor- mance parity. 1. Robustness of Sparse Approximations. Contrary to con- ventional compression methods (e.g., quantization or prun- ing) which often incur a "performance tax," STA-Attention demonstrates exceptional robustness. •Negligible Degradation: Across all tested models (Yi, Mistral, Llama-2), the shift in Perplexity (PPL) when switching from full dense attention to Top-8 or Top- 16 sparse attention is statistically insignificant (often < 0.1). •Task Stability: On sensitive reasoning benchmarks like ARC-Easy and HellaSwag, the sparse models per- form within the variance margin of the dense baseline. For instance, Yi-6B maintains≈ 51%accuracy on ARC-Easy regardless of whetherK = 128orK = 8 is used. This result strongly supports our methodology: the Top-K SAE acts as an effective Semantic Filter, retaining the signal crucial for downstream tasks while discarding the redundant components that do not contribute to the model’s reasoning capabilities. 2. Validation of the Dual-Budget Strategy (K = 8vs. 8 Unlocking the Address Book: Dissecting the Sparse Semantic Structure of LLM Key-Value Caches via Sparse Autoencoders K = 16). Our experiments with bothK = 8andK = 16 provide empirical backing for the "Dual-Budget Strategy" proposed in Sec. 5.3. • Sufficiency ofK = 8: In most cases,K = 8is already sufficient to match the baseline performance. This confirms that the intrinsic dimensionality of the Addressing mechanism (Keys) is extremely low. •Safety Margin ofK = 16: WhileK = 8performs ad- mirably, increasing the budget toK = 16(particularly for Values, as suggested by the fidelity analysis) offers a "safety margin." 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