E2: Numeral-Base Arithmetic Controlled Study

Quantitative study varying representational familiarity via numeral bases B10/B8/B9 at fixed computational complexity

Neighborhood — ranked by edge-count

concept

Prior-Target Mismatch (dr)
studies
Measures how far the target PT is from the prior P_prior; increases anchoring difficulty
Representational familiarity
studies
How familiar a model is with a numeral system, manipulated via bases in Experiment 2.
Target Pattern Cohesion (ρd)
studies
Measures how tightly the target pattern PT clusters in representation space; one of three components of S

method

in-context k-shot prompting
uses
Use k examples as anchors with no parameter update.
Logistic Fit for Shot Transitions
uses
Phenomenological method for fitting accuracy-vs.-shot curves to extract k50, k90, phase width
LoRA SFT
uses
Light fine-tuning method used in E2 to reduce mismatch dr.
LoRA+CoT
uses
Fine-tuning with chain-of-thought rationales aiming to reduce dr via procedural alignment.

dataset

Base-10 Arithmetic Dataset (B10)
uses
Two-digit addition in base-10; highest pretraining exposure; used as high-density anchor baseline in E2
Base-8 Arithmetic Dataset (B8)
uses
Two-digit addition in base-8; moderate pretraining exposure; intermediate threshold condition in E2
Base-9 Arithmetic Dataset (B9)
uses
Two-digit addition in base-9; lowest pretraining exposure; highest threshold condition in E2

artifact

cosine ≥ 0.65 · no typed edge

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

AE-2: Embodiment: Modeling output-input contingencies and using the model in perception or controlconcept0.753
Indicator of embodiment requiring forward models used for perception or motor control.
baseline control experimentmethod0.744
Control using objectively-NO factual questions under identical injection to measure global logit shift vs. genuine detection signal
controlconcept0.738
The act of directing a system's behavior; the objective of a regulator.
Base-10 arithmeticconcept0.730
High pretraining exposure numeral system used in E2.
Base-9 arithmeticconcept0.719
Low pretraining exposure numeral system used in E2.
Base-8 arithmeticconcept0.719
Moderate pretraining exposure numeral system used in E2.
Control over one's environmentconcept0.701
The ability of individuals and communities to shape, own, and modify their living spaces; a prerequisite for belonging
Control task for causal evaluationmethod0.700
Adaptation of Hewitt and Liang control tasks to CausalGym: next-token labels replaced with arbitrary tokens to measure method expressivity