Representation Use and Usability Framework

What makes representations analytically tractable:

• Interpretability: Can we extract meaningful content from the representation?
• Generalizability: Do representations transfer across subjects/models/tasks?
• Stability: Are representations consistent across repetitions?
• Discriminability: Can representations distinguish between different stimuli/concepts?

Analysis Framework

Phase 1: Identify Representations

def identify_representations(activations, stimuli, model_type="neural"):
    """
    Identify candidate representations from system activations.
    
    Args:
        activations: numpy array of shape (n_trials, n_units)
        stimuli: list of stimulus descriptions/labels
        model_type: 'neural' for brain data, 'model' for AI activations
    """
    from sklearn.decomposition import PCA
    from sklearn.manifold import TSNE
    
    # Dimensionality reduction to find representational structure
    pca = PCA(n_components=0.95)
    reduced = pca.fit_transform(activations)
    
    # Check for clustering by stimulus type
    unique_stimuli = list(set(stimuli))
    clusters = {s: reduced[[i for i, stim in enumerate(stimuli) if stim == s]] 
                for s in unique_stimuli}
    
    return {
        'reduced': reduced,
        'clusters': clusters,
        'variance_explained': pca.explained_variance_ratio_,
        'n_components': pca.n_components_
    }

Phase 2: Evaluate Use (Functional Analysis)

def evaluate_representation_use(representations, behavior, task_structure):
    """
    Evaluate how representations are used by the system.
    
    Args:
        representations: output from identify_representations
        behavior: behavioral outputs or decisions
        task_structure: description of the task demands
    """
    from sklearn.linear_model import LogisticRegression
    from sklearn.model_selection import cross_val_score
    
    # Can representations predict behavior?
    clf = LogisticRegression(max_iter=1000)
    accuracy = cross_val_score(clf, representations['reduced'], behavior).mean()
    
    # Which dimensions are most predictive?
    clf.fit(representations['reduced'], behavior)
    importance = abs(clf.coef_).mean(axis=0)
    
    return {
        'predictive_accuracy': accuracy,
        'feature_importance': importance,
        'usage_pattern': 'distributed' if importance.max() < 0.5 else 'localized'
    }

Phase 3: Evaluate Usability (Analytical Assessment)

def evaluate_representation_usability(representations, conditions=None):
    """
    Assess usability of representations for analysis.
    
    Args:
        representations: output from identify_representations
        conditions: optional dict of experimental conditions for cross-condition analysis
    """
    from scipy.spatial.distance import cdist
    import numpy as np
    
    reduced = representations['reduced']
    
    # Stability: consistency within clusters
    stability_scores = []
    for stim, cluster_data in representations['clusters'].items():
        if len(cluster_data) > 1:
            centroid = cluster_data.mean(axis=0)
            distances = cdist(cluster_data, [centroid]).flatten()
            stability_scores.append(1 / (1 + distances.mean()))
    
    # Discriminability: separation between clusters
    centroids = np.array([v.mean(axis=0) for v in representations['clusters'].values()])
    inter_distances = cdist(centroids, centroids)
    np.fill_diagonal(inter_distances, np.inf)
    discriminability = 1 / (1 + inter_distances.min())
    
    return {
        'stability': np.mean(stability_scores),
        'discriminability': discriminability,
        'usability_score': np.mean([np.mean(stability_scores), discriminability])
    }

Philosophical Framework

Key Distinctions

1. Structural vs. Functional Representations

   • Structural: what the representation looks like (pattern of activation)
   • Functional: what the representation does (causal role in system)

2. Vehicle vs. Content

   • Vehicle: the physical/computational substrate
   • Content: what the representation is about

3. Intrinsic vs. Derived Content

   • Intrinsic: content from system's own organization
   • Derived: content assigned by external observer

Evaluation Criteria

Applications

• Analyzing neural population codes
• Interpreting deep learning representations
• Comparing brain and model representations
• Evaluating representational alignment in AI systems
• Building interpretable cognitive models

Pitfalls

1. Observer-relative content: Be careful not to project meaning onto patterns
2. Granularity mismatch: Different analysis levels reveal different representations
3. Task-dependence: Representations change with task demands
4. Cross-subject variability: Neural representations vary between individuals
5. Correlation ≠ representation: Neural correlation with stimulus doesn't imply representation

References

• Convergent representations of linguistic constructions in the brain and neural language models
• Related: [[computational-lesions-multilingual-language-models-separate]], [[theater-mind-llms-cognitive]]41:["$","$L47",null,{"content":"$48","frontMatter":{"name":"use-usability-concepts-representation","description":"Unified framework for representation use and usability across philosophy and neuroscience. Bridges philosophical analysis of mental representation with empirical neuroscience methods. Covers how representations function in cognitive systems and how to evaluate their explanatory value. Use when analyzing neural representations, building interpretable AI models, or studying representational content in brain/computation. Activation: representation use, representation usability, neural representation analysis, philosophy of representation, cognitive representation, representational content, brain representation\n","version":"1.0.0","metadata":{"hermes":{"source_paper":"Convergent representations of linguistic constructions in the brain and neural language models (arXiv)","tags":["representation","philosophy","neuroscience","interpretability","cognitive-science"]}}}}]