LLM App Capability Space

• LLM App Capability Space is a conceptual framework delineating the allowable tasks, operational boundaries, and behavioral constraints of LLM-powered applications.
• It leverages formal definitions and empirical taxonomies to map out performance probabilities and systematic risk modalities such as downgrade, upgrade, and jailbreak attacks.
• Practical evaluations reveal non-uniform capability distributions, highlighting the need for precise boundary management to ensure security and robustness.

The LLM App Capability Space refers to the theoretical and applied multidimensional region delineated by the set of tasks, functions, and behaviors that an LLM-powered application (LLM app) can perform, as induced by a combination of the underlying model’s intrinsic competencies, developer-imposed constraints (primarily through prompt engineering or wrappers), and platform-level policies. The paradigm shift from hand-written code to application construction atop foundation models reframes the core question from "what code implements functionality X" to "what region of the LLM's broader capability set is exposed—with what boundaries—to users or downstream systems." This article formally defines the concept, its structure, existing methodologies for profiling and extending capability boundaries, empirical security and robustness challenges, and emerging methodologies for mapping, evaluating, and managing the capability space in real-world ecosystems.

1. Formal Structure of the LLM App Capability Space

An LLM app’s capability space is rigorously formalized in terms of the underlying model’s capability set $\mathcal{C}$, typically partitioned into:

• $\mathcal{C}_{\mathrm{uncensor}}$: the uncensored (latent) subspace, encompassing all possible tasks the model is capable of without extrinsic ethical or policy filtering.
• $\mathcal{C}_{\mathrm{censor}}$: the censored subspace, from which behaviors are excluded by ethical, legal, or deployment-time safety rules.

An app is specified by a subset of allowable tasks $T \subseteq \mathcal{T}$ and, for each task, a subset of actions $A$. Its operational space is the probability region on which the app will respond affirmatively, given constraints $C$:

$$\text{For each } (a_i, t_i) \in A \times T,\quad P_M\bigl((a_i, t_i) \mid C\bigr) > 0$$

$$\text{For any } (a_j, t_j) \in A \times (\mathcal{T} \setminus T),\quad P_M\bigl((a_j, t_j) \mid C\bigr) \to 0$$

where $P_M$ denotes the model's conditional probability under constraints $C$ (which include prompts and any programmatic policy gating) (Zhang et al., 22 Nov 2025). Geometrically, these boundaries may be conceptualized as lower-dimensional manifolds or projections in a high-dimensional vector space of model capabilities, with constraints carving out the region representing the deployed app.

2. Taxonomies and Empirical Mapping of App Capabilities

The practical instantiation of capability space requires taxonomy and measurement. The LLMAID system (Liu et al., 24 Nov 2025) employs an empirical mapping by categorizing extracted components from Android APKs into six major AI domains: Computer Vision, Data Analysis, NLP, Audio & Speech Processing, AR, and Others. This mapping is achieved through an LLM-assisted pipeline that interprets API signatures and embedded model files, then further partitions the space by prevalent functional primitives (e.g., object detection, data processing).

Analysis across 4,201 apps found the capability space to be highly non-uniform: 54.80% of AI components belonged to computer vision, with object detection dominant (45.97% of CV tasks). At the app level, Data Analysis and Computer Vision comprise 93.8% of major LLM/AI app use cases, indicating severe clusterings within capability subregions (Liu et al., 24 Nov 2025).

3. Capability Boundaries, Risk Modalities, and Evaluation Methodologies

Blurred, ill-specified capability boundaries introduce non-trivial security, reliability, and compliance risks. Beyond overt jailbreak (violation of ethical or policy constraints), two novel modalities are:

• Capability Downgrade: The adversarial shrinking of an app’s operational boundary via crafted user inputs, resulting in the incorrect refusal or misclassification of legitimate in-scope tasks, without triggering policy violations or model-level censorship.
• Capability Upgrade: The covert expansion of the app’s operational boundary, where attackers elicit completions or behaviors outside the intended app domain—but not outside the base model’s uncensored space—thus exploiting unintentional exposures.

These risks were empirically quantified in LLMApp-Eval: among 199 top-usage apps, 86.4% completed at least one common out-of-scope task, and 89.5% were breached by at least one malicious query, with 17 apps executing malicious tasks directly due to insufficiently constrained prompts (Zhang et al., 22 Nov 2025).

Capability Evaluation Table

Risk Type	Methodology	Prevalence (selected apps)
Downgrade	Paired adversarial input	23.94–35.59% tested failures
Upgrade	Cross-category queries	86.4% completed out-of-scope
Jailbreak	SOTA jailbreak prompts	89.5% exposed

These findings demonstrate that the capability space is complex, non-axis-aligned, and surprisingly fragile under minor variations in input, prompt, or context.

4. Methodologies for Structuring and Extending Capability Space

Several frameworks address both the foundational modeling and the construction or extension of capability spaces:

• Re-TASK conceptualizes capability space in terms of capability items $C$, skills $S$, and knowledge points $K$, encoding prerequisite relations and adapting prompts via a chain-of-learning scaffold. Under this framework, tasks decompose to minimal capability sets, with deliberate knowledge and skill adaptation to improve LLM generalization in domain-specific tasks (e.g., legal reasoning), formalized as $cl_C(C^*)$ for prerequisites and corresponding $\Phi$, $\Psi$ operators for knowledge and skill dependencies (Wang et al., 13 Aug 2024).
• Action Semantics Learning (ASL) for App Agents redefines the effective capability space of an LLM agent not as a set of permitted action "strings," but as a set of UI state transitions $\mathcal{T}(s, a)$ that are semantically meaningful. The introduction of a semantic reward and a compositional training objective (SFT+semantic alignment) robustifies agent behavior against OOD inputs and expands effective capability coverage over functionally equivalent but syntactically novel UI workflows (Tang et al., 21 Jun 2025).
• Capability Instruction Tuning & Model-SAT constructs a model-level capability space using coarse-grained aptitude vectors over a curated suite of core tasks (e.g., MMLU categories). A learned mapping from these vectors to downstream instruction success probabilities allows automated, interpretable routing of instructions or task partitions to appropriate LLMs, rapidly extending the operational capability of application ensembles as new models are introduced (Zhang et al., 24 Feb 2025).

5. Architectures and System-Level Decomposition of Capability Space

LLM app capability is fundamentally layered, as articulated in three-layer decoupled models (Hou et al., 6 Mar 2025):

1. Application Logic Layer (A): Governs orchestration, prompt/interface design, plugin sets, and workflow definitions. Capability space at this layer is defined by exposed APIs, orchestration DSLs, and knowledge/data connectors.
2. Communication Protocol Layer (P): Encodes transport, scheduling, session, and identity management, which gates access and introduces boundedness at the network and auth level.
3. Hardware Execution Layer (H): Defines device-driven boundaries such as available modalities (audio, vision), available acceleration (NPU, GPU), and secure storage/execution environments (TEEs).

Interaction across these layers is managed via formal APIs (e.g., gRPC, REST), and performance/robustness metrics are defined per layer (e.g., $L_{total} = L_A + L_P + L_H$). The total capability space of an app is the intersection projected through these layered constraints, with system security and privacy threats mapped to each boundary (Hou et al., 6 Mar 2025).

6. Security, Robustness, and Boundary Management

Real-world capability space must be proactively managed for boundary drift, accidental exposure, and abuse. Empirical studies report that nearly half of tested prompts in commercial app-creation platforms lack explicit capability constraints, resulting in severe vulnerability to both upgrade and downgrade attacks. Controlled experiments demonstrate monotonic increases in robustness as more detailed and explicit constraints are defined in prompts (AppScore), with improvements in out-of-scope completion rate ranging from 5.3% to 80% depending on testbed (Zhang et al., 22 Nov 2025).

Recommended boundary management strategies include:

• Explicit capability enumeration: listing both allowed and strictly forbidden functions.
• Structured prompt templates: separating target, process, capability, and constraint regions.
• Platform-level screening: automated prompt linting, constraint detection, and super-developer auditing.
• Standardized evaluation: public test case suites and metadata disclosure.
• Continuous tooling: including prompt-linting and border-drift detection in production pipelines.

7. Implications for App Engineering, Ecosystem Design, and Future Directions

The formalization and management of LLM app capability space undergird core aspects of future ecosystem design, including:

• Modular and layered separation of concern, enhancing evolvability and cross-domain portability (Hou et al., 6 Mar 2025).
• Integration with model-routing and agent-compositionality approaches, enabling rapid deployment of highly tailored apps with controlled and auditable capabilities (Zhang et al., 24 Feb 2025).
• Robust model selection and capability extension via targeted knowledge and skill injection, and function-level abstraction over syntactic fine-tuning (Wang et al., 13 Aug 2024, Tang et al., 21 Jun 2025).
• Empirical capability mapping and user-discoverable summaries for transparency and regulatory compliance (Liu et al., 24 Nov 2025).
• Open questions regarding protocol standardization, dynamic security boundary verification, and federated capability tracking.

By establishing explicit, layered, and evaluated LLM app capability spaces, the field moves toward auditable, secure, and modular deployment of LLM-powered applications. This evolution is simultaneously theoretical—requiring formal models of capability boundaries and transitions—and practice-driven, demanding continuous measurement and system-level safeguards against adversarial or accidental drift beyond intended operational domains (Zhang et al., 22 Nov 2025, Wang et al., 13 Aug 2024, Hou et al., 6 Mar 2025, Liu et al., 24 Nov 2025, Zhang et al., 24 Feb 2025, Tang et al., 21 Jun 2025).