Shoaib Jameel & Ubaid Azam
University of Southampton
Phase I Results & Phase II Vision | Grant KGaO-100018
Why AI needs to know what it doesn't know
Probability clouds & geometry
SOTA performance & uncertainty
Temporal, multi-source, inductive
Why defence intelligence needs uncertainty-aware AI
Intelligence analysts deal with vast, messy, conflicting information every day.
Thousands of reports from multiple sources daily
"An armoured vehicle near the border" — what kind? whose?
Source A says "Country X", Source B says "border of Y"
Click to toggle: Pins (old) vs. Clouds (PICASO)
Current view: Fixed Pins — every entity is a single point, no uncertainty
Current AI systems treat every fact as 100% certain. PICASO replaces rigid pins with probability clouds — capturing both what we know and how sure we are.
A Knowledge Graph stores facts as triples: (Subject, Relation, Object). Click the nodes!
Our dataset: 41,425 entities and 143,532 relations across 355 relation types
In 2000, cognitive scientist Peter Gärdenfors proposed that concepts live in geometric spaces — not as symbols or logic rules, but as regions in multi-dimensional quality spaces.
A conceptual space is built from quality dimensions (colour, size, temperature…). Concepts are convex regions in this space.
Similarity = distance. Categories = regions. "Between" has literal geometric meaning. A point between "red" and "yellow" is "orange".
Sub-conceptual (dimensions) → Conceptual (geometric regions) → Symbolic (language/logic). PICASO operates at the conceptual level.
Conceptual space: concepts as geometric regions with quality dimensions
Key insight: If concepts are inherently geometric, then the right AI framework should reason geometrically — exactly what PICASO does with entities and relations in knowledge graphs.
Gärdenfors' theory gives us a principled bridge between human-like concepts and mathematical representations:
Natural concepts form convex sets: any point between two members also belongs to that category.
"How alike are two entities?" becomes how close are their points? Distance captures graded similarity.
Relations like "part of" or "located in" are geometric operations: rotations, translations, scalings.
Arbitrary vector spaces with no cognitive grounding. Entities are meaningless points.
Geometry is the meaning. Distances, regions, and transformations have cognitive interpretations.
Conceptual spaces tell us what to represent. Bayesian geometry tells us how to learn it under uncertainty:
We never observe the full conceptual space — only sparse facts. We need to represent what we know and what we don't.
A Gaussian N(μ, Σ) has high density at the prototype, fading outward — exactly how Gärdenfors describes concepts.
New evidence sharpens the Gaussian (more certain) or shifts it (revised belief). Naturally handles evolving knowledge.
Entities = Gaussian regions in conceptual space
μ = prototype, σ² = boundary sharpness
Relations = Geometric transformations between regions
Rotation + scaling + translation with own uncertainty
Scoring = Geometric overlap of predicted & actual regions
KL divergence, Mahalanobis distance — conceptual space interpretations
Uncertainty = Intrinsic to the representation
Not bolted on afterwards — emerges from Gaussian geometry
PICASO is not just another embedding model — it is a cognitively grounded framework where Bayesian geometry meets conceptual space theory, giving us uncertainty-aware reasoning with a principled foundation.
Three key ideas, explained simply
Traditional systems: fixed pin for every entity.
PICASO: a probability cloud — capturing both what we know and how sure we are.
"Challenger 2 Tank" → Small, tight cloud (certain)
"Armoured Vehicle" → Large, diffuse cloud (could be anything)
μ = "best guess" location | σ² = "how unsure" we are.
Small σ² = confident. Large σ² = uncertain.
Bayesian methods are powerful but normally too slow. PICASO solves this with closed-form geometry:
🎯🎯🎯
Throw thousands of random darts and count hits. Slow
📐
Use a formula to calculate the exact answer instantly. O(1) per triple
In plain English: To predict a missing fact, PICASO rotates, scales, and translates the head entity's cloud. The uncertainty from both entity and relation combine — all with a single formula, no simulations.
Not all relationships look the same. PICASO uses 5 geometric lenses simultaneously:
"Frigate is a type of naval vessel"
containment
"UK is ally of France"
equality
"General X commanded Unit Y"
direction
In plain English: PICASO combines 5 different "views" of how well a fact fits. The model learns the weights (w) to trust the right view for each relationship type. All computed in closed form.
State-of-the-art performance with intrinsic uncertainty
Phase I exceeded all original objectives in a rapid 3-month timeline (Dec 2025 – Mar 2026), delivering a fully validated prototype with an analyst GUI.
Covers: military units, battles, weapons systems, treaties, operations, intelligence agencies, personnel.
The automated pipeline is repeatable and can be adapted for future data sources and domains.
Mean Reciprocal Rank (MRR) measures how high the correct answer appears in a ranked list.
Question: (Battle of Stalingrad, part of, ??)
PICASO ranks 14,541 possible answers and produces:
| Rank | Answer | |
|---|---|---|
| #1 | World War II | Correct! |
| #2 | Eastern Front | |
| #3 | Operation Barbarossa | |
| ... | 14,538 more entities | |
Reciprocal Rank = 1/1 = 1.0 (perfect!)
| Rank | Answer | |
|---|---|---|
| #1 | Eastern Front | Wrong |
| #2 | Operation Barbarossa | Wrong |
| #3 | World War II | Correct |
Reciprocal Rank = 1/3 = 0.33 (ranked 3rd)
MRR = average of reciprocal ranks across all test queries.
Higher is better. A score of 0.417 means the correct answer is typically ranked around 2nd–3rd out of 14,541.
Hits@K asks: "Is the correct answer in the top K predictions?"
Correct answer is at #1 → Hits@1 = Yes, Hits@3 = Yes, Hits@10 = Yes
33.9%
Correct answer is the #1 prediction
out of 14,541 entities
45.7%
Correct answer in top 3
out of 14,541 entities
55.9%
Correct answer in top 10
out of 14,541 entities
Think of it like a search engine: Hits@10 = 55.9% means more than half the time, the right answer appears on the "first page" of results — out of 14,541 possibilities.
Validated against 12 established baselines on two international benchmarks:
| Model | FB15k-237 | WN18RR | ||||||
|---|---|---|---|---|---|---|---|---|
| MRR | H@1 | H@3 | H@10 | MRR | H@1 | H@3 | H@10 | |
| TransE | .294 | — | — | .465 | .226 | — | — | .501 |
| RotatE | .338 | .241 | .375 | .533 | .476 | .428 | .492 | .571 |
| TuckER | .358 | .266 | .394 | .544 | .470 | .443 | .482 | .526 |
| GIE (prev. best) | .362 | .271 | .401 | .552 | .491 | .452 | .505 | .575 |
| NBFNet (deep reasoning) | .415 | .321 | .454 | .599 | .551 | .497 | .573 | .666 |
| PICASO (ours) | .417 | .339 | .457 | .559 | .488 | .445 | .510 | .568 |
Given (NATO, instance of, Military Alliance) — can PICASO tell if it's true or false?
| Model | Accuracy | PR-AUC | ROC-AUC |
|---|---|---|---|
| TransE | 67.3% | 0.727 | 0.736 |
| DistMult | 73.9% | 0.780 | 0.803 |
| R2D2+ | 76.4% | 0.865 | 0.857 |
| PICASO | 89.0% | 0.951 | 0.949 |
Operational meaning: Nearly 90% accuracy in detecting logically inconsistent facts. Acts as an automated triage filter — instantly flagging potentially poisoned intelligence for human review.
NBFNet is a heavy deep reasoning model that traverses entire subgraphs. PICASO matches it using simple geometric operations:
MRR on FB15k-237
O(1) per triple
Instant lookup + uncertainty
MRR on FB15k-237
O(|E| · |R|) per query
Expensive subgraph traversal
| Model | MRR | Hits@1 | Hits@3 | Hits@10 | Uncertainty? |
|---|---|---|---|---|---|
| NBFNet | 0.415 | 0.321 | 0.454 | 0.599 | No |
| PICASO | 0.417 | 0.339 | 0.457 | 0.559 | Yes |
PICASO beats NBFNet on MRR and Hits@1 while being orders of magnitude faster and uniquely providing calibrated uncertainty for risk-aware decisions.
We removed each component one at a time to measure its contribution:
| Variant | MRR | Hits@1 | Hits@3 | Hits@10 |
|---|---|---|---|---|
| Full PICASO | .417 | .339 | .457 | .559 |
| w/o MGS (5 scoring functions) | .355 (-14.9%) | .272 (-19.7%) | .386 | .519 |
| w/o Rotation transforms | .379 (-9.2%) | .288 | .428 | .541 |
| w/o Semantic Types | .425 | .364 | .449 | .539 (-3.6%) |
Removing the 5 geometric scoring functions causes -14.9% MRR drop. This is the core engine.
Phase-based rotation captures directional relationships — -9.2% without it.
Replacing clouds with pins keeps accuracy but eliminates all uncertainty capabilities.
Critical for defence: when PICASO is confident, it's usually right. When uncertain, it warns you.
Query: (Battle of Stalingrad, part of, ??)
Prediction: World War II ✅
Confidence: 92%
Query: (Obscure Unit X, country, ??)
Prediction: Germany ⚠️
Confidence: 34% — verify!
In plain English: Uncertainty = how "spread out" both entity clouds are. If both are tight, we're confident. If either is diffuse, we flag it.
On WN18RR: confident predictions achieve 59% accuracy, uncertain ones drop to 15% — a 4x difference. No post-hoc calibration needed.
Applied PICASO to our custom Defence-Wikidata knowledge graph:
Decision-makers can act on confident predictions and defer uncertain ones for human review — critical in defence where false positives are unacceptable.
20,808 entities from Wikipedia | 20,607 generated by Llama 3.2 (3B, local)
"The Treaty of Cherasco was a peace treaty that ended the War of the Mantuan Succession. It involved the Duchy of Savoy..."
Replaces random init with semantically meaningful Gaussian mean embeddings.
Improved uncertainty calibration — almost no hallucination. All processing runs locally.
We built a fully operational GUI and packaged the model as a reusable library:
GUI Demo: Interactive query interface with uncertainty dashboard
Library Demo: PICASO as an easy-to-use Python package
A tangible interface brings PICASO from theory to a working applied prototype. The packaged library enables defence SMEs and researchers to integrate uncertainty-aware KG reasoning directly.
We did not expect a closed-form geometric model to match NBFNet on FB15k-237. MGS alone accounts for 14.9% MRR contribution.
We expected to need post-hoc calibration (Platt scaling). Instead, PICASO's confidence is naturally calibrated. No post-processing needed.
The 12.6-point accuracy gap was unexpected. Distributional overlap provides a fundamentally richer signal than point-based scoring.
Llama 3.2 descriptions didn't just improve accuracy — they notably improved uncertainty calibration, with almost no hallucination.
Bottom line: Probabilistic geometry is not just theoretically elegant — it is a practically superior paradigm for knowledge representation in high-stakes settings.
Lightweight Cross-Lingual Federated Prompt Tuning for Low-Resource Languages
Privacy-preserving models for defence data. 90% GPU memory reduction.
Long Context Modeling with Ranked Memory-Augmented Retrieval
ERMAR framework — dynamic relevance scoring & pointwise re-ranking. SOTA on long-context benchmarks.
PROCS: Uncertainty-Aware Knowledge Representation via Conceptual Spaces
Core PICASO engine — strengthened with peer review feedback for resubmission.
Apr 2026: Cardiff University Invited Talk | May 2026: LREC 2026 Presentation
Full codebase + docs on GitHub
41K entities, 143K triples, 160M chars
Interactive prototype + demo videos
pip-installable for integration
ubaidazam.github.io/PICASO
School research presentation
All outputs freely available for the community to use and extend.
From static uncertainty to living intelligence
Building on the PICASO foundation to address three critical limitations:
Facts change over time. "Country X is led by Person Y" has a validity period.
Goal: Time-conditioned Gaussian distributions that evolve
Text-init showed value of text. Now fuse structured + textual evidence end-to-end.
Goal: Text-to-distribution encoders + Bayesian fusion
New entities appear constantly in intelligence. Can't retrain every time.
Goal: Infer about unseen entities from neighbourhood structure
Together, these advance PICASO from a static, transductive system to a temporally-aware, text-grounded, and inductive reasoning framework — addressing real operational needs in defence intelligence.
A military alliance in 1940 differs from 2024. Temporal distributions let us ask: "Was this true at time T?"
Analysts read reports, cables, news — not triples. End-to-end fusion lets the model absorb textual evidence continuously.
New entities appear constantly. Inductive reasoning enables instant inference without retraining.
| Capability | Delivered | Extension Adds |
|---|---|---|
| Temporal reasoning | Snapshot-based | → Time-aware distributions |
| Text integration | Entity initialisation | → End-to-end fusion |
| New entities | Transductive | → Inductive (zero-shot) |
| Evidence fusion | Structure + text-init | → Multi-source joint |
| Operational use | Working GUI | → Production-ready |
• AAAI / NeurIPS 2027 (full paper)
• EMNLP 2026 (text fusion)
• Open-source framework release
State-of-the-art on FB15k-237 (MRR 0.417). Matches NBFNet at fraction of cost. 89% triple classification.
Natively calibrated without post-hoc adjustment. 1.7x accuracy gap between confident and uncertain predictions.
LLM-generated descriptions improve uncertainty calibration. Almost no hallucination in generated text.
Full GUI with file upload, manual query, and uncertainty dashboard. Ready for analyst evaluation.
Questions & Discussion
Shoaib Jameel — M.S.Jameel@southampton.ac.uk
Ubaid Azam — u.azam@soton.ac.uk