Intrinsic Knowledge Dependence (IKD)

• IKD is the reliance on internally encoded knowledge as opposed to information retrieved at inference, seen in contexts like ontology learning, search agents, and topological logic.
• Research quantifies IKD by comparing intrinsic-only versus combined intrinsic-extrinsic performance, with metrics such as a 12% F1 drop indicating model sensitivity to external grounding.
• The theory extends to topological frameworks where IKD is conceptualized as a continuous, invariant dependence between informational structures, informing design trade-offs in model evaluation.

Searching arXiv for papers on Intrinsic Knowledge Dependence and closely related uses of the term. Intrinsic Knowledge Dependence (IKD) denotes dependence on information internal to a system, but the term is used in multiple technical senses in recent literature. In work on ontology learning, search agents, and long-context LLMs, IKD concerns reliance on knowledge encoded in model parameters rather than on inference-time retrieval or other external evidence. In a topological-logical account, IKD is recast as a topology-invariant form of knowable dependence between empirical questions. These usages are not identical, but they converge on the distinction between what is internally available and what must be supplied or reconstructed externally (Akl, 2024, Fan et al., 27 May 2026, Fu et al., 11 Apr 2025, Baltag et al., 2024).

1. Terminological scope and principal formulations

Recent work uses IKD across several research programs with different formal objects, metrics, and failure modes.

Context	Internal object	External contrast
Ontology learning	fine-tuned LLM parameters	semantic tower retrieved at inference
Search agents	information encoded in the model before retrieval	search, browser, and code evidence
Long-context LLMs	intrinsic retrieval ability	extrinsic retrieval ability from supplied context
Topological logic	knowable dependence internal to questions	representation by topologies, metrics, or uniform structures

In the ontology-learning formulation, IKD is the degree to which a fine-tuned LLM relies on knowledge encoded in its parameters versus knowledge provided at inference time through an external semantic source. In search-agent evaluation, IKD is the failure mode in which a tool-using agent answers mainly from what it already “knows” and uses search chiefly as a confirmation channel. In long-context evaluation, IKD is formalized through the contrast between intrinsic and extrinsic retrieval ability as context length varies. In the topological account, IKD is identified with continuous or uniformly continuous dependence that is invariant under the appropriate structural isomorphisms (Akl, 2024, Fan et al., 27 May 2026, Fu et al., 11 Apr 2025, Baltag et al., 2024).

2. Ontology learning: intrinsic knowledge versus semantic towers

In “DSTI at LLMs4OL 2024 Task A: Intrinsic versus extrinsic knowledge for type classification,” intrinsic knowledge is what the model “already knows” after fine-tuning, whereas extrinsic knowledge is an explicit, external representation of domain semantics built separately from the LLM (Akl, 2024). The work operationalizes the contrast by fine-tuning flan-t5-small on term-typing subtasks and then toggling an external semantic source at inference time.

The external source is the semantic tower

$ST = \{s_1, s_2, \dots, s_n\},$

where each $s_i$ is a semantic primitive from a small, domain-specific set. For WordNet, the examples given are {subclass, instance, part, represents, description}. The construction pipeline is explicit: query Wikidata to collect the semantic set for each term type; tokenize, clean, and normalize by lowercasing and removing stop words; prune duplicates and empty items; embed each primitive $s_i \in ST$ into a 1024-dim vector $v_i$ using Google’s gte-large; and store the vectors in a MongoDB collection indexed for fast nearest-neighbor search. The tower can be viewed as a matrix $V \in \mathbb{R}^{n \times 1024}$, and inference embeds an input term $x$ to $e(x) \in \mathbb{R}^{1024}$, computes cosine similarity $\mathrm{sim}(e(x),V)$, retrieves the top-1 matching primitive $z$, and injects $z$ into the prompt.

The experimental setup fixes the task while varying whether the semantic tower is used. WordNet subtask A.1 contains 40 559 training terms and 9 470 test terms across the four classes {noun, verb, adjective, adverb}. GeoNames subtask A.2 contains 8 078 865 training and 702 510 test instances across 660 geographic categories, but because full fine-tuning on 8 M items was intractable, the study uses a curated 2 041-term balanced subset obtained by capping frequent categories at 25 examples. The model is flan-t5-small, fine-tuned separately on each subtask with identical hyperparameters: learning rate 1e-5, batch 4, epochs 5, optimizer Adam. Input text is term + sentence for WordNet and term alone for GeoNames, concatenated and embedded via gte-large before encoding by the T5.

Two inference regimes are compared. WN1/GN1 is intrinsic only: prompt the fine-tuned model directly with “Give the entity for term X. Select from list Y.” WN2/GN2 is intrinsic plus extrinsic: first retrieve the best primitive $s_i$0 from the semantic tower via $s_i$1, then prompt with “... Select from Y relying on the search result Z.” F1 is the primary metric. On the held-out WordNet test, WN1 attains F1 = 0.9820 and WN2 attains F1 = 0.8581. On the curated GeoNames test, GN1 = 0.6820 and GN2 = 0.5636. The paper therefore reports a roughly 10–12 point F1 drop when the tower is added. On the official WordNet leaderboard, WN1 scored 0.9716 and WN2 scored 0.8420, again showing a similar relative drop. No statistical significance tests are reported.

The paper does not introduce a closed-form IKD score, but it implicitly measures IKD by the relative gap between intrinsic-only and intrinsic-plus-extrinsic performance. The summary associated with the work states that one could define

$s_i$2

For WordNet this yields approximately $s_i$3, interpreted there as a 12.7% drop when reliance on extrinsic inputs is forced. The same study also reports qualitative counterexamples to a purely accuracy-centric reading: without the tower, the model overpredicts noun for “into the bargain,” whereas with the tower it corrects to adverb; on GeoNames, the tower helps distinguish plural versus singular categories and subtler subtype distinctions such as “stream” versus “section of stream.” The resulting picture is explicitly framed as a trade-off between performance and semantic grounding.

3. Search agents: IKD as guess-and-verify behavior

“LiveBrowseComp: Are Search Agents Searching, or Just Verifying What They Already Know?” defines IKD as the failure mode by which modern search agents, despite full tool access, answer benchmark questions primarily from what they already know in their parametric weights and then use the search interface largely as a confirmation channel rather than as a discovery mechanism (Fan et al., 27 May 2026). The paper further states that IKD is neither a fluke nor simple data contamination, but an intrinsic evaluation shortcut that becomes more pernicious as base models absorb more world knowledge during pre-training and fine-tuning.

The paper formalizes IKD through three binary quantities on a benchmark $s_i$4: closed-book correctness $s_i$5 with no tools, tool-augmented correctness $s_i$6 with full search, browser, and code access, and evidence-blocked correctness $s_i$7 when answer-supporting documents are removed from the index. Its IKD score is

$s_i$8

This measures the fraction of questions that a model can answer from memory but loses when confirmation is disallowed. A high value is presented as the signature of a guess-and-verify pattern.

To expose that pattern, the paper designs three diagnostics on BrowseComp. The first is closed-book coverage: tools are disabled and the agent answers from parametric memory, with pass@4 as the metric. The second is evidence-blocked search: a dense retrieval index is built over BrowseComp-Plus, all documents annotated as evidence or gold are removed, and the agent is evaluated again by pass@4; the absolute drop is $s_i$9. The third is search-trajectory grounding: each query in a multi-step browse trajectory is classified as model-originated or retrieval-originated, and the evidence-use rate records how often a retrieved answer-supporting document actually influences reasoning or the final answer within the next three turns.

The empirical magnitudes are large. Across four static benchmarks and 24 model–benchmark pairs, mean closed-book pass@4 is 38.9%, reaching 62.0% for Kimi K2.6 on BrowseComp-ZH and 44.5% for MiniMax M2.5 on BrowseComp. Under evidence blocking, average pass@4 drops from CB(M)=26.1% to EB(M)=6.2%, a net decline of 19.9 points. MiniMax M2.5 falls from 44.5% to 8.0%, and Kimi K2.6 from 25.5% to 2.3%. The search-trajectory analysis shows that more than half of all queries are model-originated, rising above 60% in later rounds, while the evidence-use rate remains below 33% for every evaluated agent. The paper’s interpretation is direct: agents guess from memory, then search for confirmation, and collapse when the confirming evidence is removed.

LiveBrowseComp is then introduced to neutralize IKD by placing questions beyond current intrinsic coverage. Its construction uses a 90-day temporal window, six updated sources—GDELT, TMDB, RAWG, CVE/NVD, SportsDB, and USGS—long-tail filtering, answer-stability constraints, and human-authored multi-step questions with multi-stage verification. The result is a 335-question benchmark. On LiveBrowseComp, closed-book accuracy falls below 2% for every model, search-augmented scores drop by 25–40 points relative to BrowseComp, and rankings become less stable: Spearman’s $s_i \in ST$0 is 0.87 between BrowseComp and BrowseComp-ZH but 0.74 between BrowseComp and LiveBrowseComp, while Pearson’s $s_i \in ST$1 drops from 0.79 to 0.53. Human searchers solve LiveBrowseComp at nearly the same rate as BrowseComp—31% versus 30%—which the paper uses to argue that the main change is the removal of the memory-verification shortcut rather than an intrinsic increase in question difficulty.

4. Long-context LLMs: dual retrieval and interference

“Harnessing the Unseen: The Hidden Influence of Intrinsic Knowledge in Long-Context LLMs” studies IKD in long-context models by explicitly distinguishing intrinsic and extrinsic retrieval ability (Fu et al., 11 Apr 2025). For a model $s_i \in ST$2 and context length $s_i \in ST$3, extrinsic retrieval ability $s_i \in ST$4 is the accuracy when the correct answer must be extracted from the supplied context, while intrinsic retrieval ability $s_i \in ST$5 is the accuracy when the correct answer resides only in parametric memory and the context is conflicting or irrelevant.

The paper defines two IKD summaries:

$s_i \in ST$6

It also proposes tracking the slope $s_i \in ST$7 as context grows and reports that this slope is strictly positive in its experiments. The operational instrument is the Hybrid Needle-in-a-Haystack (H-NiaH) test, which adds an intrinsic-retrieval stage before conventional context search. In the first stage, a question such as “Who wrote <book>?” must be answered purely from parametric memory; the correct target is never inserted into the context. In the second stage, that target becomes the key to a context-search question whose answer is hidden in a long haystack. To reduce pattern shortcuts, 0–3 random interference facts are added per example. Scoring uses token-level exact-match overlap:

$s_i \in ST$8

The evaluation covers Mistral-7B-Instruct (v0.2 & v0.3), Llama-3.1-8B-Instruct, Llama-3.1-70B-Instruct, and the [Qwen2.5](https://www.emergentmind.com/topics/qwen2-5) family (7B, 14B, 72B, plus a 7B variant trained for 1 M context). Context lengths reach 32 K for Mistral, 131 K for Llama-3.1 and Qwen2.5, and 1 M for the special Qwen2.5 model, with 40 insertion-depth intervals and averages over 5 or 2 random seeds or tasks. The benchmark suite includes I-WhoQA, HotpotQA-context, HotpotQA-internal, I-WhoQA-irrelevant, the original Needle-in-a-Haystack, and H-NiaH.

Several quantitative findings establish an IKD pattern. On I-WhoQA-Conflict, where context asserts a wrong answer, Mistral-7B’s reliance on intrinsic memory rises from approximately 15% to 45% as context length grows from 4 K to 32 K, while Llama-3.1-8B rises from approximately 20% to 60% over 8 K to 131 K. On I-WhoQA-Internal, where context matches memory, accuracy remains near 100% regardless of length. The paper therefore reports a steadily rising $s_i \in ST$9.

The same work also reports interference between retrieval modes. Using STRING positional encoding rather than baseline RoPE, Llama3.1-8B improves from 75% to 90% on HotpotQA-context at L=32 K, but drops from 92% to 83% on HotpotQA-internal; on I-WhoQA-irrelevant at L=32 K, Mistral-7B falls from 68% to 52%. The paper’s conclusion is that better extrinsic retrieval can interfere with intrinsic retrieval.

A representative H-NiaH excerpt at generation length 32 and 0 random facts further differentiates models: Mistral-7B-v0.2 = 89.3, Llama-3.1-8B = 93.0, Llama-3.1-70B = 95.7, Qwen2.5-7B = 86.4, Qwen2.5-14B = 54.5, Qwen2.5-72B = 64.0, Qwen2.5-7B-1M-128K = 97.7, and Qwen2.5-7B-1M (1 M context) = 60.1. The standard NIAH benchmark is reported as almost trivial at approximately 99–100% for all models, whereas H-NiaH reveals the need to chain intrinsic and extrinsic retrieval. The paper recommends dual-retrieval benchmarks, trade-off auditing, attention-context co-design, and reporting of $v_i$0, $v_i$1, and IKD curves over context length.

5. Topological and logical accounts of intrinsic dependence

“Knowability as continuity: a topological account of informational dependence” provides a mathematically distinct use of IKD, not as model-memory reliance, but as a topology-invariant form of knowable dependence between empirical questions (Baltag et al., 2024). The framework fixes a nonempty set $v_i$2 of states and represents an empirical variable as a surjection

$v_i$3

where $v_i$4 is a $v_i$5 topology on the value space. A propositional empirical question is simply a topology $v_i$6, with exact answer at $v_i$7 given by

$v_i$8

The framework moves freely between variables as topological maps and questions as topologies on $v_i$9.

Exact functional dependence is expressed by the local atom

$V \in \mathbb{R}^{n \times 1024}$0

with global dependence $V \in \mathbb{R}^{n \times 1024}$1. These satisfy Inclusion, Additivity, and Transitivity. The paper then replaces exactness by knowability through continuity. Global continuous dependence is

$V \in \mathbb{R}^{n \times 1024}$2

An equivalent formulation is

$V \in \mathbb{R}^{n \times 1024}$3

Its localized version is

$V \in \mathbb{R}^{n \times 1024}$4

The summary states that $V \in \mathbb{R}^{n \times 1024}$5 again enjoys Inclusion, Additivity, and Transitivity and fits an S4-style axiomatization.

A stronger notion is uniform dependence, written

$V \in \mathbb{R}^{n \times 1024}$6

now in a metric setting. Heine–Cantor is invoked to note that on compact or locally compact domains, continuity and uniform continuity coincide, and that in pseudo-locally Lipschitz settings one has $V \in \mathbb{R}^{n \times 1024}$7.

The same framework also studies independence. Exact independence is

$V \in \mathbb{R}^{n \times 1024}$8

while topological independence is

$V \in \mathbb{R}^{n \times 1024}$9

The summary emphasizes a striking possibility:

$x$0

Thus exact dependence and epistemic unlearnability from approximate data can coexist.

Within this framework, IKD is explicitly identified with knowable dependence itself. Local IKD is given by

$x$1

and global IKD by

$x$2

The summary further states that these operators are preserved under homeomorphisms or uniform equivalences, and that the completeness and representation theorems show invariance under refinements of topology and passage to discrete quotients. In this usage, IKD is therefore an internal property of the informational structure of questions rather than of a trained model’s weights.

6. Trade-offs, misconceptions, and disambiguation

Across the model-centric literature, the central empirical pattern is not that external evidence is useless, but that adding or emphasizing it does not automatically improve performance. In the ontology-learning experiments, the semantic tower reduces overall F1 even while correcting some systematic semantic errors and injecting finer grounding. In long-context models, improving extrinsic retrieval through STRING can reduce intrinsic retrieval. In search-agent evaluation, high tool-augmented scores on static benchmarks may largely reflect the ability to verify answers already present in parametric memory rather than to discover unknown facts (Akl, 2024, Fu et al., 11 Apr 2025, Fan et al., 27 May 2026).

Several specific recommendations follow directly from the cited works. The DSTI study suggests a hybrid regime in which intrinsic knowledge provides broad coverage while extrinsic grounding is activated selectively when subtle semantic distinctions matter. The LiveBrowseComp paper recommends time-sensitive, long-tail benchmark construction with clear temporal cutoffs, answer-stability filtering, and multi-stage human verification. The long-context study recommends dual-retrieval evaluation, trade-off awareness, attention-context co-design, and explicit reporting of both intrinsic and extrinsic retrieval curves. This suggests that IKD is best treated not as a scalar property of a model in isolation, but as a property of a model-task-evaluation configuration.

The literature also rejects several overly simple interpretations. The LiveBrowseComp paper explicitly argues that IKD is neither a fluke nor simple data contamination. The topological account shows that exact dependence and topological independence can coexist, so “dependence” need not imply learnability from approximate evidence. The ontology-learning experiments show that lower aggregate F1 under extrinsic augmentation does not preclude better behavior on semantically delicate cases. A plausible implication is that any single benchmark or single metric can obscure the distinction between raw task success and the source of the information used to obtain it.

Finally, the acronym “IKD” is not unique to Intrinsic Knowledge Dependence. “Intelligent Knowledge Distribution” is a CA-POMDP method for resource-aware multi-agent communication in which per-agent policies decide what information to send to whom and when under soft power and bandwidth constraints; in the reported UAV asset-tracking case, the intelligent policy satisfies both constraints 97% of the time, whereas greedy and naive baselines satisfy them far less often (Fowler et al., 2019). “IKD” is also used for “Imperfect Knowledge of Data” in Data Envelopment Analysis, where each observation is modeled as a convex uncertainty set $x$3 and sampled by Hit-and-Run to produce bootstrap distributions of efficiency scores (Ferreira et al., 2021). These are distinct topics, and the acronym overlap is purely terminological rather than conceptual.