Artificial Immune Systems Explorer — interactive explainer

Application Domain

Feature Space · 2D Projection READY

feature dimension 1

feature dimension 2

self data self-tolerance zone candidate (evaluating) rejected (overlaps self) mature detector test point (color = zone)

Parameters

self points 8

self-tolerance radius r_s 0.070

detector radius min r_min 0.040

detector radius max r_max 0.120

max live detectors (drag to ∞) 25

lifespan (steps — drag to ∞) 250

Speed

Controls

Display

self-tolerance halos

detector age fade

axis labels

Status

Press ▶ Run to begin generating candidate detectors, or use Step to advance one at a time. Drag a test point onto the canvas to classify a new observation.

Live Detectors

Censored

Generated

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Non-Self Coverage

Detector Representation & Censoring Criterion

Like in the CLONALG demo, anomaly classifiers are modelled here as abstract circular detectors parameterised by a center b and a recognition radius r_B. However, NSA does not evolve these parameters: candidates are generated randomly and accepted or rejected by a binary censoring test. There is no affinity function, no selection pressure, and no hypermutation — only the constraint that a mature detector must not overlap any self-tolerance zone.

Censoring geometry

Censoring criterion

accept (b, r_B) if ∀ s ∈ S : dist(b, s) ≥ r_s + r_B

reject (b, r_B) if ∃ s ∈ S : dist(b, s) < r_s + r_B

r_s = self-tolerance radius (same for all self points in this demo) · r_B drawn from [r_min, r_max] uniformly at random

Relationship to Evolutionary Strategies (ES without positive selection)

Mutation-only ES under negative selection — each new candidate is a random draw (mutation without a parent), and the censoring test is a binary selection step. Over time, especially with long detector lifetimes, the surviving population reflects the selection pressure exerted by the self-string distribution — large r_B are penalised by their higher probability of hitting a self-tolerance zone; small and intermediate r_B are shaped by their local context near self clusters.

Negative selection, not positive — unlike CLONALG, there is no fitness gradient pulling detectors toward a target. The population structure emerges entirely from what survives censoring, not from what is rewarded. This is analogous to purifying selection in population genetics — variation is generated blindly; the environment removes the unfit.

Long lifetimes ≈ sessile clonal accumulation — with lifespan set to ∞ and max detectors set to ∞, detectors accumulate indefinitely without dispersal. The surviving population tiles the non-self space in a way shaped entirely by the geometry of the self distribution — a “mutation-only” process whose output distribution is carved by negative selection.

b and r_B are both constrained — centers b are sampled uniformly within the feature space bounds; r_B is drawn from [r_min, r_max]. These bounds are the only free parameters the user controls — everything else is determined by the censoring geometry.

Algorithm Reference — Negative Selection

Training (online/continuous form)

given self set S, tolerance radius r_s output detector set D, capacity N_d ▷ G = 1: classical offline NSA generate N_d detectors once, then deploy G = ∞: continuous form (implemented here) G > 1 forces turnover via the N_d cap → coverage shifts each iteration ("random patrol") no other finite G is typically useful repeat for G iterations : draw random candidate (c, r_B) if ∀ s ∈ S : dist(c, s) > r_s + r_B add (c, r_B) to D ← mature detector if |D| > N_d : evict oldest ← circular buffer else discard ← censored (overlaps self) optionally expire after τ steps ← additional turnover

Detection (online)

for new sample x : if ∃ d ∈ D : ‖x − d.c‖ < d.r flag x as NON-SELF / ANOMALY else accept x as SELF / NORMAL

Relationship to GAs & NSA

No fitness function — selection is binary (pass/fail censoring), not graded; there is no objective to optimize

No crossover, no population — detectors are generated independently; there is no recombination or generational loop

Negative selection — keeps what does not match a template, the inverse of GA positive/fitness-proportionate selection

One-class learning — trains only on normal (self) data; anomaly labels are never required

Application Domain

Feature Space · 2D Projection READY

feature dimension 1

feature dimension 2

Parameters

antibody population N_ab 20

antigens N_ag 4

selection size top-k 5

rank-proportional cloning β 0.50

replacements d 2

mutation scale σ₀ 0.08

recognition radius min r_min 0.025

recognition radius max r_max 0.230

Speed

Controls

Display

mutation σ-rings

clone cloud

axis labels

evolve r_B (vs. fixed)

Status

Press ▶ Run to begin evolving antibodies, or use Step to advance one generation at a time. Drag a test point onto the canvas to classify a new observation.

Generation

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Active Pass

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Best M Affinity

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Memory Filled

Affinity Function — f(b, ag)

A B cell represents a pattern classifier whose parameters are subject to hypermutation and selection. In this demonstration, an abstract circular detector with center position b and detection radius r_B is used as a model of such a B-cell classifier. Affinity quantifies how well that classifier recognises a specific antigen: it measures both how close the center is to the antigen pattern and how tight the recognition circle is. Affinity drives selection, cloning, and hypermutation — it is the immune analogue of fitness, but grounded in classification quality, not an optimization objective. Both the center b and the radius r_B are mutated during hypermutation; selection and cloning then propagate whichever combination best covers each antigen tightly.

covered f(b, ag) = 1 r_B ⋅ 1 D + ε when D < r_B

not covered f(b, ag) = 1 r_B ⋅ δ D + ε when D ≥ r_B

D ≜ dist(b, ag) — Euclidean distance between B-cell center and antigen in feature space
ε = 0.008 — prevents ÷0 when D = 0 · δ = 0.04 — non-coverage penalty (δ « 1)
r_B ∈ [r_min, r_max] — recognition radius, evolved jointly with center b by hypermutation

Classifier Geometry

f vs. D (for a given r_B)

The 1/r_B factor penalises oversized circles even when covered — driving maturation toward the tightest circle that still contains the antigen. Equilibrium: r_B → D from above.

Interpretation

Covered and close: high f — the (1/r_B) factor rewards a small radius, so affinity peaks when the center is near the antigen and the circle is tight. The cell reliably detects this pattern with few false positives (low Type I error).

Covered but loose: lower f — the antigen is inside the circle but the large r_B is penalised by (1/r_B). Evolution shrinks r_B toward D, tightening the classifier and reducing false positives at deployment.

Not covered: near-zero f (the δ « 1 factor applies to both cases for consistency) — the classifier misses this antigen entirely (Type II error). The cell is unlikely to be selected or enter the memory set.

Large-radius exploitation: the (1/r_B) factor in both cases prevents a degenerate solution where one enormous circle covers all antigens and dominates the population — a known weakness of basic CLONALG without this term.

More sophisticated variants (AIRS, aiNet) add a term penalising affinity to self strings, blending the NSA censoring concept directly into the affinity function. This reduces false positives on normal inputs and is the natural extension beyond what is shown here.

Algorithm Reference — Clonal Selection (CLONALG) — Pattern Recognition Form

Training loop

input S = antigen set output M = memory cells ▷ one slot in M per ag ∈ S (canonical CLONALG) generate random B-cell population ▷ one generation = one sweep over all ag ∈ S G = ∞ (runs continuously) here repeat for G generations : for all antigens ag ∈ S : ▷ Phase 1: evaluate, select, clone, mutate compute f(b, ag) ∀ b ∈ B uses evolved (b, r_B) — see affinity card Ab* ← top-k B cells by f(·, ag) ← k by user for rank i, parent b_i ∈ Ab* : n_i ← round(β × N_ab / i) ← rank-proportional cloning σ_i ← σ₀ · exp(−f(b_i, ag)) ← inv. proportional mutation σ_r,i ← σ₀ · r_B · exp(−f(b_i, ag)) ← scales with current r_B C_i ← n_i clones of b_i; for each clone : b ← b + N(0, σ_i²) ← additive zero-mean Gaussian r_B ← r_B + N(0, σ_r,i²) ← r_B mutated independently re-evaluate f(c, ag) ∀ c ∈ C_i ▷ Phase 2: update B, memory, and diversity B ∪ C (all clones) compete; top-N_ab survive B ← top-N_ab of (B ∪ C₁ ∪ … ∪ C_k) ← full affinity competition if f(best c, ag) > f(M[ag], ag) : M[ag] ← best c ← M only ever improves replace d lowest-f(B) cells with random ← d by user; diversity

Recognition (deployment)

for new sample x : m* ← argmax_{m ∈ M} f(x, m) s.t. dist(x, m) ≤ m.r_B if m* found label x as class(m*) else return NO MATCH

What this visualizer shows

Each generation sweeps through all antigens in sequence. Phase 1 (first Step click): the active antigen glows; top-k parents are selected and their clone cloud appears. Phase 2 (second Step click): best clones replace parents; memory M is updated; d lowest-affinity cells are replaced with randoms. B cells are coloured by nearest antigen during the pass only — at rest all cells render neutrally, since CLONALG tracks no ownership.

Relationship to GAs & ES — key similarities and differences

Affinity = fitness — same role, different name; both drive selection toward better solutions

Clonal expansion ≈ fitness-proportionate selection + replication — more clones for higher-affinity cells, analogous to roulette-wheel; unlike GA, clones are copies of a single parent (no crossover)

No crossover — purely mutation-driven; structurally similar to (μ+λ)-ES but run independently per antigen each generation

Hypermutation rate ∝ 1/f — mutation tightens as affinity grows, the inverse of early GA intuition; compare to self-adaptive ES where σ also shrinks near the optimum via a separate strategy parameter

Per-antigen loop = multi-modal structure — each antigen is a separate peak to cover; the outer loop over S is analogous to Unit 4 niching, maintaining diversity across multiple targets simultaneously

Memory set M = elitism per antigen — M is the output, not just the population; analogous to an archive in multi-objective EA (Unit 3) but indexed by class rather than by objective trade-off

Random replacement = diversity maintenance — prevents full convergence; analogous to random immigrants in GAs

Can follow NSA — NSA learns the self/non-self boundary (one-class); CLONALG then learns to distinguish which non-self class, using NSA’s rejected regions as the anomaly search space

Note on dimensionality: This 2D projection is a pedagogical simplification. In practice, feature spaces are high-dimensional (dozens to hundreds of features), and random detector coverage becomes exponentially sparse — a fundamental challenge for real-valued immune algorithms that motivates structured detector generation strategies.