papers/emergent-planning-rl/sau.json

{
  "paper_id": "emergent-planning-rl",
  "paper_title": "Interpreting Emergent Planning in Model-Free RL",
  "D1": [
    {
      "id": "emergent-planning-rl-D1-001",
      "claim": "Agent architecture: The main DRC(3,3) agent uses 3 ConvLSTM layers (D=3), performs 3 internal computational ticks per timestep (N=3), and has 32 channels per layer (G_d=32).",
      "source": "Section 2.3, Appendix E.3"
    },
    {
      "id": "emergent-planning-rl-D1-002",
      "claim": "Sokoban environment configuration: an 8x8 grid world with 4 boxes and 4 targets. The agent observes a symbolic representation x_t in R^{8x8x7} and can move up/down/left/right or stay still.",
      "source": "Section 2.2, Appendix E.2"
    },
    {
      "id": "emergent-planning-rl-D1-003",
      "claim": "Concept definitions: Two square-level multi-class concepts (C_A for agent approach direction, C_B for box push direction), each mapping every grid square at every timestep to one of 5 classes: UP, DOWN, LEFT, RIGHT, NEVER.",
      "source": "Section 3.2"
    },
    {
      "id": "emergent-planning-rl-D1-004",
      "claim": "Agent training: DRC(3,3) agent trained via IMPALA actor-critic on 900,000 Boxoban unfiltered training levels for 250 million total transitions, with discount factor gamma=0.97.",
      "source": "Appendix E.4"
    },
    {
      "id": "emergent-planning-rl-D1-005",
      "claim": "Probe architecture and training: 1x1 probes have 160 parameters (single cell-state vector input); 3x3 probes have 1440 parameters (3x3 patch input). Larger probes (5x5, 7x7) are also evaluated in appendix experiments. All probes trained via logistic regression with AdamW optimizer and 5 independent initialization seeds.",
      "source": "Section 4.1, Appendix D.1"
    },
    {
      "id": "emergent-planning-rl-D1-006",
      "claim": "Probe datasets: Training set of approximately 106,600 transitions from 3,000 Boxoban training episodes; test set of transitions from 1,000 held-out Boxoban validation episodes.",
      "source": "Section 4.1, Appendix D.1"
    },
    {
      "id": "emergent-planning-rl-D1-007",
      "claim": "Intervention experiment setup: 200 levels per intervention type (Agent-Shortcut, Box-Shortcut), constructed from 25 handcrafted base levels multiplied by 8 geometric transformations (vertical reflection and 90/180/270-degree rotations).",
      "source": "Section 6.1"
    },
    {
      "id": "emergent-planning-rl-D1-008",
      "claim": "Intervention protocol: Short-route interventions (adding NEVER class vector) are repeated at every step; directional interventions repeat only until the agent steps onto (or pushes box off) the target square. Random-probe baseline interventions use norm-matched vectors for comparability with trained-probe interventions.",
      "source": "Section 6.1"
    },
    {
      "id": "emergent-planning-rl-D1-009",
      "claim": "Thinking steps configuration: 5 thinking steps at episode start (agent forced stationary before acting), yielding 15 extra internal ticks for the DRC(3,3) agent (3 ticks per step x 5 steps).",
      "source": "Section 5, Section 6.2, Appendix A.3"
    },
    {
      "id": "emergent-planning-rl-D1-010",
      "claim": "Training emergence analysis: 50 checkpoints collected at 1M-transition intervals over the first 50M transitions of training, with linear probes re-trained independently at each checkpoint to account for the agent's evolving behavior-dependent concept representations.",
      "source": "Section 6.2, Appendix C"
    },
    {
      "id": "emergent-planning-rl-D1-011",
      "claim": "Behavioral test-time compute: 1,000 medium-difficulty and 1,000 hard-difficulty Boxoban levels tested with the number of thinking steps ranging from 0 to 5 to evaluate planning-like behavioral benefit from extra compute.",
      "source": "Appendix E.5"
    },
    {
      "id": "emergent-planning-rl-D1-012",
      "claim": "Search evidence corridor levels: 8 handcrafted base levels each with a corridor whose entrance is blocked by a myopically pushable box, replicated at 4 corridor lengths (2, 6, 10, 14), with 8 geometric transformations applied per configuration.",
      "source": "Appendix A.3.2"
    },
    {
      "id": "emergent-planning-rl-D1-013",
      "claim": "Cutoff level intervention setup: 200 total Cutoff levels (levels where default agent solves 0% due to myopic box-pushing), constructed from 25 handcrafted base levels x 8 geometric transformations.",
      "source": "Appendix B.3"
    },
    {
      "id": "emergent-planning-rl-D1-014",
      "claim": "DRC(1,9) variant architecture and training: 1 ConvLSTM layer (D=1), 9 internal ticks per step (N=9), trained for 100 million transitions using the same IMPALA training scheme as the main DRC(3,3) agent.",
      "source": "Appendix F.1"
    },
    {
      "id": "emergent-planning-rl-D1-015",
      "claim": "DRC(9,1) variant architecture and training: 9 ConvLSTM layers (D=9), 1 internal tick per step (N=1), trained for 100 million transitions using the same IMPALA training scheme as the main DRC(3,3) agent.",
      "source": "Appendix F.2"
    },
    {
      "id": "emergent-planning-rl-D1-016",
      "claim": "ResNet agent architecture: 24 residual blocks with 32 channels per block and an MLP hidden dimension of 256. No recurrent connections; iterative computation occurs across depth rather than across ticks. Trained for 250M transitions in Sokoban.",
      "source": "Appendix G"
    },
    {
      "id": "emergent-planning-rl-D1-017",
      "claim": "Mini PacMan environment configuration: 13x13 mazes generated via Primm's algorithm with 4 pills per maze. Observation shape is 13x13x14. The DRC(3,3) agent is trained for 250M transitions in this environment to probe plan formation in a non-Sokoban domain.",
      "source": "Appendix H.1"
    },
    {
      "id": "emergent-planning-rl-D1-018",
      "claim": "Alternative concept probing: Binary concept variants tested include simplified binary concepts Agent_Approach and Box_Push (classes NEVER/AGAIN, no direction), and reversed asymmetry concepts Agent_Exit_Direction and Box_Approach_Direction (classes L/R/U/D/NEVER).",
      "source": "Appendix D.4"
    },
    {
      "id": "emergent-planning-rl-D1-019",
      "claim": "Global probe for future actions: Global linear probes (10,240 parameters) take the agent's entire cell state as input to predict the agent's action 1 to 10 steps into the future, evaluated by accuracy.",
      "source": "Appendix D.5"
    },
    {
      "id": "emergent-planning-rl-D1-020",
      "claim": "Intervention variation parameters: Directional squares p tested in range [0, 3]; short-route intervention tested both with and without; intervention types tested include full (short-route + directional) and directional-only. Intervention strength alpha varied to find optimal scaling.",
      "source": "Appendix B.2"
    }
  ],
  "D2": [
    {
      "id": "emergent-planning-rl-D2-001",
      "claim": "Concept Ground Truth Label Computation (C_A and C_B): For each square (x,y) at timestep t, scan remaining episode trajectory (t..T) to find the first interaction. C_A: find first t'>t where agent steps onto (x,y); record entry direction {UP/DOWN/LEFT/RIGHT}; if none, assign NEVER. C_B: find first t'>t where a box is pushed off (x,y); record push direction; else NEVER. Labels are behavior-dependent: computed from the agent's actual trajectory under its current parameters θ using the full episode replay. Formally: C_A(x_t, (x,y), θ) = DIR if agent enters (x,y) from DIR at future step, NEVER otherwise.",
      "source": "Section 3.2"
    },
    {
      "id": "emergent-planning-rl-D2-002",
      "claim": "Linear Probe Logit Computation: For each class k ∈ {UP, DOWN, LEFT, RIGHT, NEVER} at position (x,y), logit l_k = w_k^T g_{x,y} where w_k ∈ R^32 is the learned class-specific weight vector and g_{x,y} ∈ R^32 is the cell state at that spatial position. Predicted class = argmax_k l_k. Softmax probability: P(k|g_{x,y}) = exp(l_k) / Σ_j exp(l_j). Probes trained via logistic regression (cross-entropy loss) with AdamW optimizer, 5 independent seeds. The vector w_k is also the concept direction vector used for causal intervention.",
      "source": "Section 2.4"
    },
    {
      "id": "emergent-planning-rl-D2-003",
      "claim": "Causal Intervention on Agent Cell State: g'_{x,y} = g_{x,y} + w_k. Where g_{x,y} ∈ R^32 is the cell state at position (x,y), w_k ∈ R^32 is the 1x1 probe's learned class vector for concept class k (e.g., w_{NEVER}^{C_A} or w_{DOWN}^{C_A}). With scaling strength α: g'_{x,y} = g_{x,y} + α · w_k. Too low α fails to meaningfully change representations; too high α pushes activations off-distribution. This intervention adds concept class information directly into the agent's internal state at specific spatial positions to steer its planned behavior.",
      "source": "Section 6.1, Equation 1"
    },
    {
      "id": "emergent-planning-rl-D2-004",
      "claim": "Algorithm 1: Agent-Shortcut Intervention. Pseudocode: (1) ShortRouteSquares = all positions (x,y) on the short path. (2) (x_0,y_0) = first square of the long route. (3) LongRouteSquaresDirs = first p squares agent would step onto if following the longer route, and the direction DIR. (4) For each timestep t: for (x,y) in ShortRouteSquares do g_{x,y} += α × w_{NEVER}^{C_A}; if agent has not moved onto (x_0,y_0) this episode, for each ((x,y), DIR) in LongRouteSquaresDirs do g_{x,y} += α × w_{DIR}^{C_A}. Default α=1, p=1 from Section 6.1.",
      "source": "Section 6.1, Appendix B.2, Algorithm 1"
    },
    {
      "id": "emergent-planning-rl-D2-005",
      "claim": "Algorithm 2: Box-Shortcut Intervention. Pseudocode: (1) ShortRouteSquares = all positions (x,y) on the short box-push route. (2) (x_0,y_0) = initial position of the box not adjacent to any target. (3) LongRouteSquaresDirs = first p squares a box would be pushed off if pushed the longer route, and direction DIR. (4) For each timestep t: for (x,y) in ShortRouteSquares do g_{x,y} += α × w_{NEVER}^{C_B}; if box has not been pushed off (x_0,y_0) this episode, for each ((x,y), DIR) in LongRouteSquaresDirs do g_{x,y} += α × w_{DIR}^{C_B}. Default α=1, p=1 from Section 6.1.",
      "source": "Section 6.1, Appendix B.2, Algorithm 2"
    },
    {
      "id": "emergent-planning-rl-D2-006",
      "claim": "DRC Agent Recurrent Tick Equations: The stack of D ConvLSTM units performs N internal ticks per environment step. Let s_t^d = (h_t^d, g_t^d) where h_t^d, g_t^d ∈ R^{8×8×32} are the output and cell state of the d-th ConvLSTM. Recurrence: s_{t,0} = s_{t-1}; for n=1..N: s_{t,n} = f_θ(i_t, s_{t,n-1}); s_t = s_{t,N}. Each ConvLSTM uses 3×3 kernels with zero-padding, preserving 8×8 spatial dimensions. The function f_θ applies standard LSTM gating (input, forget, output, cell-update gates) using convolutional connections. i_t = e(x_t) ∈ R^{8×8×32} is the encoded observation.",
      "source": "Section 2.3, Appendix E.3"
    },
    {
      "id": "emergent-planning-rl-D2-007",
      "claim": "DRC Pool-and-Inject Mechanism: Enables rapid spatial information spread by feeding each ConvLSTM a spatially-pooled version of its own prior-tick output. Formula: m_{t,n-1}^d = [MeanPool(h_{t,n-1}^d), MaxPool(h_{t,n-1}^d)]^T ∈ R^{2G_d}; p̂ = W_{p_d} m + b_{p_d} ∈ R^{H_d W_d G_d} with W_{p_d} ∈ R^{H_d W_d G_d × 2G_d}; then reshape: p_{t,n-1}^d = Reshape(p̂) ∈ R^{H_d×W_d×G_d}. The pooled tensor p is provided as additional input to the ConvLSTM at tick n, injecting global spatial summary back into local computation.",
      "source": "Appendix E.3"
    },
    {
      "id": "emergent-planning-rl-D2-008",
      "claim": "DRC Output Head Computation: The output of the final (D-th) ConvLSTM at final tick N, denoted h_{t,N}^D ∈ R^{8×8×32}, is concatenated with the input encoding i_t ∈ R^{8×8×32} and passed through an affine transformation + ReLU: o_t = ReLU(W_o [h_{t,N}^D; i_t] + b_o) ∈ R^{d_o}. Policy head: logits_t = W_π o_t + b_π ∈ R^5, a_t ~ Categorical(softmax(logits_t)). Value head: v_t = W_v o_t + b_v ∈ R. At test time, the agent acts greedily: a_t = argmax(logits_t). Training uses sampled actions from the categorical distribution.",
      "source": "Appendix E.3"
    },
    {
      "id": "emergent-planning-rl-D2-009",
      "claim": "IMPALA Training Loss with Penalties: The agent is trained via IMPALA actor-critic with V-trace returns. Total loss: L = L_{V-trace}(γ=0.97, λ=0.97) + 10^{-3}·||logits_t||^2 + 10^{-5}·(||W_π||^2 + ||W_v||^2) + 10^{-2}·H(π). The L2 penalty on action logits (1e-3) prevents overconfident predictions; L2 regularization (1e-5) on policy/value head weights; entropy bonus H(π) (1e-2) encourages exploration. Optimization: BPTT with unroll length 20, Adam optimizer, batch size 16, learning rate decays linearly from 4e-4 to 0.",
      "source": "Appendix E.4"
    },
    {
      "id": "emergent-planning-rl-D2-010",
      "claim": "Full Experiment Pipeline: Six sequential phases: (1) Train DRC(3,3) agent on 900k Sokoban levels via IMPALA for 250M transitions, collecting checkpoints at 1M intervals. (2) Define square-level concepts C_A (agent approach direction) and C_B (box push direction) as {UP,DOWN,LEFT,RIGHT,NEVER}-valued mappings from grid squares. (3) Train 1x1/3x3 linear probes via logistic regression on cell state from 3000/1000 episodes to verify linear encoding. (4) Decode internal plans over entire boards at each tick; qualitatively analyze forward/backward/parallel search motifs; quantify plan refinement with 5 thinking steps. (5) Intervene via g'_{x,y} = g_{x,y} + w_k on Agent-Shortcut/Box-Shortcut/Cutoff levels. (6) Correlate emergence of concept representations, plan refinement, and behavioral benefit across 50 training checkpoints.",
      "source": "Section 3.1, Sections 4-6"
    },
    {
      "id": "emergent-planning-rl-D2-011",
      "claim": "DRC(3,3) Skip Connections: Two types of skip connections enhance information flow. Bottom-up: the input encoding i_t = e(x_t) ∈ R^{8×8×32} is provided as input to ALL D=3 ConvLSTM units (not just the bottom layer), allowing raw observation information to reach every layer directly. Top-down: the output h_{t,n-1}^D of the final (D-th) ConvLSTM on tick n-1 is provided as an additional input to the bottom (1st) ConvLSTM on tick n, enabling processed high-level representations to influence early processing on the next iteration. Together these form a bidirectional information pathway across the depth stack.",
      "source": "Appendix E.3"
    },
    {
      "id": "emergent-planning-rl-D2-012",
      "claim": "Intervention Success Criterion: In Agent-Shortcut levels (two paths to box/target region): success = agent solves the level by following the suboptimal LONG path instead of the default short path. In Box-Shortcut levels (box can be pushed short or long route): success = agent pushes box via the suboptimal LONG route. In Cutoff levels (default 0% solve rate due to myopic box-pushing blocking corridor): success = agent solves the level at all. All interventions repeated with 5 independently trained probes; compared against random-probe baseline with norm-matched vectors. Success rates reported as mean ±1 SD over seeds.",
      "source": "Section 6.1, Appendix B.2, Appendix B.3"
    },
    {
      "id": "emergent-planning-rl-D2-013",
      "claim": "Macro F1 Evaluation Metric for Probes: Macro_F1 = (1/K) · Σ_{k=1}^{K} F1_k, where F1_k = 2 · P_k · R_k / (P_k + R_k) for class k, with P_k = precision and R_k = recall. K = 5 classes {UP, DOWN, LEFT, RIGHT, NEVER}. Macro F1 is used instead of accuracy because the NEVER class dominates most Sokoban boards (>95% of squares), making accuracy misleading. Scores are computed per-square, averaged over all squares in each board, then averaged across all episodes in the test set (1000 episodes).",
      "source": "Section 4.1, Section 4.2"
    },
    {
      "id": "emergent-planning-rl-D2-014",
      "claim": "Grid-Level Internal Plan Decoding: For each square (x,y) of the 8×8 grid, at each internal tick n and layer d, compute class logits l_k^{(x,y)} = w_k^T g_{x,y}^{d,n} for all k. Assign predicted class = argmax_k l_k^{(x,y)}. Visualize: colored arrows for directional classes (UP/DOWN/LEFT/RIGHT), blank for NEVER. The collective arrow pattern across all 64 squares constitutes the agent's decoded internal plan at that tick. Plans are decoded at the final tick of each environment step for visual analysis, and at each internal tick during thinking steps for refinement measurement.",
      "source": "Section 5"
    },
    {
      "id": "emergent-planning-rl-D2-015",
      "claim": "Plan Refinement Quality Measurement: Force agent stationary for 5 thinking steps at episode start, yielding 15 internal ticks (3 ticks per step × 5 steps). At each tick n ∈ {1,...,15}, decode C_A and C_B for all squares via 1x1 probes on cell state at each layer. Compute macro F1 against ground-truth labels from the full episode replay. Plot macro_F1(n) vs. tick n → monotonic increase indicates iterative plan improvement. Compute plan refinement gain: ΔF1 = macro_F1(tick_15) - macro_F1(tick_1). Averaged over 1000 Boxoban episodes. Replicated across all checkpoints for training emergence analysis.",
      "source": "Section 5, Appendix A.3"
    },
    {
      "id": "emergent-planning-rl-D2-016",
      "claim": "Thinking Step Behavioral Evaluation: For T ∈ {0,1,...,5} thinking steps: force agent to remain stationary (action=NO-OP) for first T environment steps, then act normally. Measure percentage of 1000 Medium-difficulty and 1000 Hard-difficulty Boxoban levels solved. Behavioral planning benefit = %solved(T=5) - %solved(T=0). For corridor length experiment: test on corridor levels of lengths L ∈ {2,6,10,14} (8 base levels × 4 lengths × 8 transformations = 256 total). Measure min thinking steps needed to solve ≥50% of levels at each corridor length. Higher m_thinking needed for longer corridors = evidence of deeper search.",
      "source": "Appendix A.3.2, Appendix E.5"
    },
    {
      "id": "emergent-planning-rl-D2-017",
      "claim": "Convolutional Encoder for Symbolic Observations: Input x_t ∈ R^{8×8×7} where each of 64 squares is a 7-dim one-hot vector encoding {wall, empty, box, agent, box_on_target, agent_on_target, target}. Encoder e is a convolutional network: i_t = e(x_t) ∈ R^{8×8×32} (G_0=32 channels). Uses kernel size 3 with a single layer of zero-padding to preserve spatial dimensions H_0=W_0=8. The encoder output i_t is fed to all D ConvLSTM layers via bottom-up skip connections. Spatial alignment between encoder output and Sokoban grid enables the agent to learn a spatial bijection between cell state positions and board squares.",
      "source": "Section 2.3, Appendix E.3"
    }
  ],
  "D3": [
    {
      "id": "emergent-planning-rl-D3-001",
      "claim": "Train 1x1 (160-param) and 3x3 (1440-param) linear probes on DRC(3,3) cell state at each of 3 ConvLSTM layers (final tick) to predict per-square C_A (agent approach direction) and C_B (box push direction). Evaluate using macro F1 on 1000 held-out Boxoban episodes. Compare against observation-only baseline probes to verify that the agent linearly represents planning-relevant concepts internally rather than probes learning from raw input. Train with 5 independent probe seeds via logistic regression (AdamW).",
      "source": "Section 4"
    },
    {
      "id": "emergent-planning-rl-D3-002",
      "claim": "Internal Plan Formation Qualitative Analysis: Decode DRC(3,3) agent's internal plans from cell state via 1x1 probes predicting C_A and C_B over entire Sokoban boards at each internal tick. Examine plan formation motifs (evaluative planning, forward search from boxes, backward search from targets, parallel search) across handpicked Boxoban levels including out-of-distribution variants (blind, generalized, blocked-route, new-route levels). Compare decoded plans against ground-truth optimal paths.",
      "source": "Section 5, Appendix A.1, Appendix A.2"
    },
    {
      "id": "emergent-planning-rl-D3-003",
      "claim": "Test-Time Plan Refinement Quantification: Force DRC(3,3) agent stationary for 5 thinking steps (15 extra internal ticks) at start of 1000 Boxoban episodes. Decode C_A and C_B at each tick using 1x1 probes trained on final-layer cell state. Measure macro F1 improvement over ticks. Compare against plan quality at tick 0 (no extra compute). Show plan quality monotonically improves with additional ticks, consistent with iterative search.",
      "source": "Section 5 (Figure 6), Appendix A.3"
    },
    {
      "id": "emergent-planning-rl-D3-004",
      "claim": "Causal Intervention: Agent-Shortcut Experiment: Add C_A concept vectors (NEVER to short-route squares, directional vector to long-route entry square) to DRC(3,3) cell state at each of 3 layers. Evaluate on 200 Agent-Shortcut levels (25 base x 8 geometric transformations). Measure intervention success rate (% episodes where agent follows suboptimal long path instead of default short path). Compare success rates against random-probe interventions with norm-matched vectors, averaged over 5 independently trained probe seeds.",
      "source": "Section 6.1 (Table 1, Figure 7), Appendix B.1, Appendix B.2"
    },
    {
      "id": "emergent-planning-rl-D3-005",
      "claim": "Causal Intervention: Box-Shortcut Experiment: Add C_B concept vectors (NEVER to short-route squares, directional vector to box's long-route starting square) to DRC(3,3) cell state at each of 3 layers. Evaluate on 200 Box-Shortcut levels (25 base x 8 geometric transformations) where one box can be pushed via short or long route. Measure intervention success rate (% episodes where agent pushes box via suboptimal long route). Compare against random-probe interventions with norm-matched vectors, averaged over 5 independently trained probe seeds.",
      "source": "Section 6.1 (Table 1, Figure 8), Appendix B.1, Appendix B.2"
    },
    {
      "id": "emergent-planning-rl-D3-006",
      "claim": "Collect 50 training checkpoints at 1M-transition intervals over the first 50M transitions. At each checkpoint: (i) retrain 1x1 probes to predict C_A and C_B from agent cell state and measure macro F1, (ii) measure additional medium-difficulty Boxoban levels solved with 5 thinking steps vs. 0 thinking steps (behavioral planning benefit). Plot correlation between probe performance and behavioral benefit (Figure 9, Figure 38) to demonstrate concept representations and planning-like behavior co-emerge during training.",
      "source": "Section 6.2 (Figure 9), Appendix C.1, Appendix C.3"
    },
    {
      "id": "emergent-planning-rl-D3-007",
      "claim": "At each of 50 training checkpoints (1M-transition intervals), decode agent internal plans via 1x1 probes at the 1st and 15th extra tick during 5 thinking steps across 1000 episodes. Measure macro F1 increase from tick 1 to tick 15 for C_A and C_B at each layer. Correlate plan refinement gain per checkpoint with additional levels solved via thinking steps (Figure 39). Verify that test-time plan refinement ability co-emerges with planning-like behavioral benefit during training.",
      "source": "Appendix C.2, Appendix C.4 (Figure 39)"
    },
    {
      "id": "emergent-planning-rl-D3-008",
      "claim": "Vary intervention strength alpha and number p of directional intervention squares (0 to 3 along the long route) in Agent-Shortcut and Box-Shortcut levels. Test both full intervention (short-route + directional) and directional-only (no short-route) configurations. Measure intervention success rate across 5 trained and 5 random probe seeds per {alpha, p, layer} combination. Evaluate on all 3 ConvLSTM layers to characterize how scaling, directional square count, and short-route presence affect steering success.",
      "source": "Appendix B.2"
    },
    {
      "id": "emergent-planning-rl-D3-009",
      "claim": "Design 200 Cutoff levels (25 base x 8 geometric transformations) where entrance to a variable-length corridor is blocked by a box adjacent to a target. By default the agent solves 0% (myopically pushes the blocking box onto the target, irreversibly blocking the corridor). Perform three intervention types at varying strengths alpha on each ConvLSTM layer: Agent-Only (C_A directional to enter corridor), Box-Only (C_B directional to push blocking box aside), Agent-and-Box (both). Measure solve rate; compare trained-probe vs. random-probe baselines with 5 seeds each.",
      "source": "Appendix B.3"
    },
    {
      "id": "emergent-planning-rl-D3-010",
      "claim": "Search Evidence: Corridor Length Experiment: Handcraft 8 base levels each with a corridor (entrance blocked by myopically pushable box) replicated at 4 corridor lengths (2,6,10,14), yielding 80 levels after 8 geometric transformations each. Test DRC(3,3) agent with 0-5 thinking steps. Measure percentage of levels solved per corridor length and number of thinking steps required to solve >=50% of each set. Compare solve rates against 0 thinking steps (myopic default behavior).",
      "source": "Appendix A.3.2"
    },
    {
      "id": "emergent-planning-rl-D3-011",
      "claim": "Alternative Concept Probing: Train 1x1 and 3x3 probes on DRC(3,3) cell state to predict (a) simplified binary concepts Agent_Approach and Box_Push (classes NEVER/AGAIN, no direction), and (b) reversed asymmetry concepts Agent_Exit_Direction and Box_Approach_Direction (classes L/R/U/D/NEVER). Evaluate on 1000 held-out Boxoban episodes using macro F1. Compare against main C_A/C_B probe performance and observation-only baselines to verify the agent represents the directional, asymmetric concepts rather than simpler or reversed alternatives.",
      "source": "Appendix D.4"
    },
    {
      "id": "emergent-planning-rl-D3-012",
      "claim": "Larger Probe Size Experiment: Train 1x1, 3x3, 5x5, and 7x7 probes on DRC(3,3) cell state to predict C_A and C_B at each layer. Evaluate on 1000 Boxoban test episodes using macro F1. Compare performance gain from larger receptive fields against gain observed in observation-only baseline probes to distinguish spatially-localized representations (minimal improvement from larger probes) from distributed representations (large improvement). Averaged over 5 seeds per probe type and size.",
      "source": "Appendix D.3"
    },
    {
      "id": "emergent-planning-rl-D3-013",
      "claim": "Train global linear probes (10,240 parameters, taking the agent's entire cell state as input) on DRC(3,3) cell state at each layer to predict the agent's action 1 to 10 steps into the future. Evaluate accuracy on 1000 test episodes; compare against observation-only baseline global probes. Purpose: apply the 3-step methodology to falsify the hypothesis that the agent plans by forming explicit sequences of future actions (e.g., LEFT, LEFT, UP, RIGHT). Results show these global future-action concepts are not linearly represented, ruling out this planning mechanism.",
      "source": "Appendix D.5"
    },
    {
      "id": "emergent-planning-rl-D3-014",
      "claim": "DRC Variant Probing: DRC(1,9) and DRC(9,1): Apply full three-step methodology (concept probing, plan formation, behavioral intervention) to DRC(1,9) agent (1 layer x 9 ticks, 100M transitions) and DRC(9,1) agent (9 layers x 1 tick, 100M transitions). Train 1x1 and 3x3 probes on 500/250 train/test episodes per agent to predict C_A and C_B. Measure plan refinement macro F1 over extra internal ticks during 5 thinking steps. Evaluate intervention success rates on Agent-Shortcut and Box-Shortcut levels with scaling factor 4. Compare probe and intervention performance across layers against random-probe baselines.",
      "source": "Appendix F"
    },
    {
      "id": "emergent-planning-rl-D3-015",
      "claim": "ResNet Agent Planning Investigation: Train 1x1 and 3x3 probes on hidden states after each of 24 residual blocks of a ResNet agent (no recurrent connections, 250M transitions) to predict C_A and C_B. Evaluate on 3000/1000 train/test Boxoban episodes via macro F1, tracking per-layer accuracy trend to identify iterative planning across layers. Perform Agent-Shortcut and Box-Shortcut interventions with scaling factor 4 on 200 levels each. Compare intervention success rates against random-probe baselines. Visualize internal plans decoded by 1x1 probes across layers to assess plan formation motifs.",
      "source": "Appendix G"
    },
    {
      "id": "emergent-planning-rl-D3-016",
      "claim": "Mini PacMan Environment Probing: Train DRC(3,3) agent on 13x13 Mini PacMan mazes (randomly generated via Primm's algorithm, 4 pills, ghosts chasing via A*) for 250M transitions. Train 1x1 and 3x3 probes on 23k/6k train/test transitions to decode time-limited concepts Agent_Approach_Direction_16 (5-class directional, 16-step horizon) and Agent_Approach_16 (binary visit/no-visit, 16-step horizon) from cell state at each layer. Evaluate using macro F1 against observation-only baselines. Visualize decoded plans to assess whether agent forms connected navigational paths toward targets (pills, edible ghosts).",
      "source": "Appendix H"
    },
    {
      "id": "emergent-planning-rl-D3-017",
      "claim": "DRC Agent Training Protocol: Train DRC(3,3) agent on 900k Sokoban levels (Boxoban unfiltered training set) using IMPALA actor-critic for 250M transitions. DRC variants DRC(1,9) and DRC(9,1) trained for 100M transitions using same scheme.",
      "source": "Appendix E.4"
    }
  ],
  "D4": [
    {
      "id": "emergent-planning-rl-D4-001",
      "claim": "Phase 1: Agent Training. Train the DRC(3,3) agent on Sokoban to establish a candidate model-free agent for planning investigation. Sub-steps: (a) configure DRC architecture with D=3 ConvLSTM layers, N=3 internal ticks per step, G_d=32 channels, kernel size 3 with zero-padding; (b) train via IMPALA actor-critic on 900,000 Boxoban unfiltered training levels for 250 million transitions; (c) collect checkpoints at 1M-transition intervals for subsequent emergence analysis; (d) verify baseline planning-like behavior (performance improves with extra test-time compute).",
      "source": "Section 2.3, Section 3.1, Appendix E.3, Appendix E.4, Appendix E.5"
    },
    {
      "id": "emergent-planning-rl-D4-002",
      "claim": "Phase 2: Concept Selection. Define planning-relevant concepts whose internal representations would indicate the agent is planning. Sub-steps: (a) characterize planning as requiring plan formulation, consequence evaluation, and behavioral influence; (b) hypothesize square-level multi-class concepts C_A (agent approach direction) and C_B (box push direction), each mapping grid squares to {UP, DOWN, LEFT, RIGHT, NEVER}; (c) define ground-truth label computation algorithm that determines concept classes for every square at every timestep from full episode trajectories; (d) validate that these concepts are instrumentally useful for spatial planning in Sokoban's grid-based dynamics.",
      "source": "Section 3.1, Section 3.2, Section 2.1"
    },
    {
      "id": "emergent-planning-rl-D4-003",
      "claim": "Phase 3: Probe for Concept Representations. Use linear probes to determine whether the agent internally represents the planning-relevant concepts. Sub-steps: (a) run agent for 3000/1000 train/test Boxoban episodes to collect cell state activations and ground-truth concept labels; (b) train 1x1 (160-param) and 3x3 (1440-param) linear probes via logistic regression with AdamW (5 seeds each) to predict C_A and C_B from cell state at each of 3 layers after the final tick; (c) compare probe macro F1 against observation-only baseline probes to distinguish internal representation from bottom-up inference; (d) confirm minimal improvement from 1x1 to 3x3 probes vs. large baseline improvement, verifying spatially-localized linear representations.",
      "source": "Section 4, Appendix D.1, Appendix D.3"
    },
    {
      "id": "emergent-planning-rl-D4-004",
      "claim": "Phase 4: Investigate Plan Formation. Gather qualitative and quantitative evidence that the agent forms, evaluates, and refines plans using the probed concept representations. Sub-steps: (a) decode internal plans by applying 1x1 probes over entire Sokoban boards, visually analyzing plan formation motifs (forward search from boxes, backward search from targets, parallelized bidirectional search, evaluative replanning); (b) test on out-of-distribution levels (blind without agent, generalized with extra boxes/targets, blocked-route, new-route); (c) quantify plan refinement: force agent stationary for 5 thinking steps (15 extra ticks) in 1000 episodes, measure macro F1 improvement of decoded plans over ticks; (d) conduct corridor length experiment as behavioral search evidence: test on corridor levels of lengths 2-14 with 0-5 thinking steps, measuring solve rates.",
      "source": "Section 5, Appendix A.1, Appendix A.2, Appendix A.3"
    },
    {
      "id": "emergent-planning-rl-D4-005",
      "claim": "Phase 5: Causal Intervention Verification. Confirm that the agent's concept representations causally influence its behavior by intervening on cell state activations. Sub-steps: (a) design Agent-Shortcut levels (200 levels) and Box-Shortcut levels (200 levels) where agent defaults to optimal short path but can be steered to suboptimal long path; (b) intervene by adding learned concept vectors (w_k for NEVER/directional classes) to cell state at each layer following g'_{x,y} = g_{x,y} + w_k; (c) measure intervention success rate (% episodes agent follows steered path) against random-probe baselines with norm-matched vectors (5 seeds each); (d) vary intervention parameters: scaling strength alpha, number of directional squares p (0-3), with/without short-route component; (e) test complementary Cutoff level interventions (200 levels) to induce optimal behavior where agent defaults to 0% solve rate, using Agent-Only, Box-Only, and Agent-and-Box variants.",
      "source": "Section 6.1, Appendix B.1, Appendix B.2, Appendix B.3"
    },
    {
      "id": "emergent-planning-rl-D4-006",
      "claim": "Phase 6: Training Emergence Analysis. Demonstrate that concept representations and planning-like behavior co-emerge during training, providing convergent evidence for the planning hypothesis. Sub-steps: (a) at each of 50 checkpoints (1M-transition intervals over first 50M transitions), retrain 1x1 probes for C_A/C_B and measure macro F1; (b) at each checkpoint, measure behavioral planning benefit as additional medium Boxoban levels solved with 5 thinking steps vs. 0; (c) at each checkpoint, measure plan refinement capability as macro F1 gain from tick 1 to tick 15 during 5 thinking steps; (d) correlate all three metrics, confirming concept representation quality, plan refinement ability, and behavioral benefit co-emerge; (e) verify the relationship holds across all 3 ConvLSTM layers, not just the final layer.",
      "source": "Section 6.2, Appendix C.1, Appendix C.2, Appendix C.3, Appendix C.4"
    }
  ]
}