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This module re-expresses the visited state-action exploration graph as dense
``torch`` tensors so the frontier / UCB / entropy / merge queries become single
vectorized kernel launches instead of Python loops over ``dict`` state nodes.
Layout
------
Visit counts and outcome sums live in two dense ``[table_size, num_actions]``
float tensors, indexed by a stable SHA-256 hash of the string state key:
index = int.from_bytes(sha256(state_key).digest()[:8], 'little') % table_size
Collisions are acceptable (hash-bucketed, like a hash table) -- two keys landing
in the same bucket simply share a row, exactly as they would share a dict slot.
The hash is identical to the one used by the other ``*_tensor.py`` companions so
a state addressed in :mod:`value_function_tensor` resolves to the same row here.
The ``TensorExplorationGraph`` is a :class:`torch.nn.Module`:
* It carries a *learnable* state-value embedding ``state_value`` of shape
``[table_size]`` (``requires_grad=True``) used by the UCB exploit term and the
optional value-prior blend. Gradients flow through ``recommend_next_scores`` /
``ucb_scores`` / ``state_value``.
* Visit counts / outcome sums are buffers (``register_buffer``) -- they are
exploration statistics, not learned parameters, so they do not take gradients
but they DO move with ``.to(device)`` / ``.cuda()`` and serialize in
``state_dict()``.
* All computation is tensor ops -- no Python loops over states/actions in the
hot path. ``index_add_`` / masked select / ``torch.where`` replace the dict
walks of the Python reference.
The original :mod:`resynthesis.causal_exploration` module is preserved as the
torch-free reference; this companion is additive and importable independently.
"""
from __future__ import annotations
import hashlib
import math
from collections.abc import Sequence
import torch
from torch import Tensor, nn
CAUSAL_EXPLORATION_TENSOR_SCHEMA = "nnf.resynthesis.causal_exploration_tensor.v1"
# Strategy names mirror the Python reference module.
STRATEGY_SHORTEST_TO_UNTESTED = "shortest_to_untested"
STRATEGY_LEAST_SAMPLED = "least_sampled"
STRATEGY_BEST_OUTCOME = "best_outcome"
STRATEGY_UCB = "ucb"
STRATEGY_HYPOTHESIS_DRIVEN = "hypothesis_driven"
UCB_DEFAULT_EXPLORATION = math.sqrt(2.0)
RHAE_DEFAULT_CAP = 1.15
DEFAULT_TABLE_SIZE = 4096
DEFAULT_NUM_ACTIONS = 8
def state_hash_index(
state_key: str,
*,
table_size: int = DEFAULT_TABLE_SIZE,
) -> int:
"""Stable SHA-256 -> integer table row index.
Same formula across every ``*_tensor.py`` companion so a state addressed in
one module resolves to the same row in the others.
"""
if table_size <= 0:
raise ValueError("table_size must be positive")
digest = hashlib.sha256(state_key.encode("utf-8")).digest()[:8]
return int.from_bytes(digest, "little") % table_size
def state_hash_indices(
state_keys: Sequence[str],
*,
table_size: int = DEFAULT_TABLE_SIZE,
) -> Tensor:
"""Vectorized :func:`state_hash_index` over a batch of keys -> ``int64[N]``."""
if table_size <= 0:
raise ValueError("table_size must be positive")
return torch.tensor(
[state_hash_index(k, table_size=table_size) for k in state_keys],
dtype=torch.long,
)
class TensorExplorationGraph(nn.Module):
"""Dense tensor representation of the visited ``(state, action)`` graph.
Visit statistics live in two ``[table_size, num_actions]`` float tensors
(counts and outcome sums); a learned per-state value embedding of shape
``[table_size]`` provides the UCB exploit term / value-prior seam. All
hot-path queries are single tensor ops.
"""
# Class-level annotations make mypy strict happy (register_buffer /
# nn.Parameter assignments are otherwise typed as Tensor | Module).
visit_counts: Tensor
outcome_sums: Tensor
state_value: Tensor
def __init__(
self,
*,
table_size: int = DEFAULT_TABLE_SIZE,
num_actions: int = DEFAULT_NUM_ACTIONS,
device: str | torch.device | None = None,
dtype: torch.dtype = torch.float32,
) -> None:
super().__init__()
if table_size <= 0:
raise ValueError("table_size must be positive")
if num_actions <= 0:
raise ValueError("num_actions must be positive")
self.table_size = int(table_size)
self.num_actions = int(num_actions)
self.dtype = dtype
# Exploration statistics (NOT learned): buffers move with .to(device).
self.register_buffer(
"visit_counts",
torch.zeros((self.table_size, self.num_actions), dtype=dtype, device=device),
)
self.register_buffer(
"outcome_sums",
torch.zeros((self.table_size, self.num_actions), dtype=dtype, device=device),
)
# Learned per-state value embedding (gradients flow).
self.state_value = nn.Parameter(
torch.zeros(self.table_size, dtype=dtype, device=device)
)
# ------------------------------------------------------------------
# device / dtype helpers
# ------------------------------------------------------------------
@property
def device(self) -> torch.device:
return self.visit_counts.device
# ------------------------------------------------------------------
# indexing
# ------------------------------------------------------------------
def _row(self, state_key: str) -> int:
return state_hash_index(state_key, table_size=self.table_size)
def _rows(self, state_keys: Sequence[str]) -> Tensor:
return state_hash_indices(state_keys, table_size=self.table_size).to(self.device)
# ------------------------------------------------------------------
# core mutation (tensor in-place ops; no Python loop over actions)
# ------------------------------------------------------------------
def record(
self,
*,
state_key: str,
action_index: int,
outcome: float,
) -> None:
"""Record one ``(state, action_index, outcome)`` visit tensorially.
``action_index`` is the integer column in ``[0, num_actions)`` (the
tensor module addresses actions by index, unlike the dict-keyed Python
reference). Visit counts and outcome sums accumulate in place.
"""
if not 0 <= action_index < self.num_actions:
raise ValueError(
f"action_index must be in [0, {self.num_actions}), got {action_index}"
)
row = self._row(state_key)
# In-place tensor updates on a single cell -- still a tensor op.
self.visit_counts[row, action_index] += 1.0
self.outcome_sums[row, action_index] += float(outcome)
def record_batch(
self,
*,
state_keys: Sequence[str],
action_indices: Tensor,
outcomes: Tensor,
) -> None:
"""Vectorized batch record via :func:`index_add_`.
``action_indices`` and ``outcomes`` are 1-D tensors of length ``N``;
``state_keys`` is the matching length-``N`` sequence of state strings
(hashed to row indices). All ``N`` updates happen in one kernel.
"""
if len(state_keys) != int(action_indices.shape[0]):
raise ValueError("state_keys and action_indices length mismatch")
if int(action_indices.shape[0]) != int(outcomes.shape[0]):
raise ValueError("action_indices and outcomes length mismatch")
rows = self._rows(state_keys)
actions = action_indices.to(self.device).to(torch.long)
outs = outcomes.to(self.device).to(self.dtype)
flat_index = rows * self.num_actions + actions
ones = torch.ones_like(outs)
self.visit_counts.view(-1).index_add_(0, flat_index, ones)
self.outcome_sums.view(-1).index_add_(0, flat_index, outs)
# ------------------------------------------------------------------
# queries
# ------------------------------------------------------------------
def visit_count(self, state_key: str, action_index: int) -> Tensor:
"""Scalar tensor visit count for one ``(state, action)`` pair."""
return self.visit_counts[self._row(state_key), action_index]
def mean_outcome(self, state_key: str, action_index: int) -> Tensor:
"""Scalar tensor mean outcome (0 where unvisited)."""
count = self.visit_count(state_key, action_index)
total = self.outcome_sums[self._row(state_key), action_index]
return torch.where(count > 0, total / count, torch.zeros_like(total))
def row_visits(self, state_key: str) -> Tensor:
"""Per-action visit counts ``[num_actions]`` for ``state_key``."""
return self.visit_counts[self._row(state_key)]
def row_mean_outcomes(self, state_key: str) -> Tensor:
"""Per-action mean outcomes ``[num_actions]`` (0 where unvisited)."""
row = self._row(state_key)
counts = self.visit_counts[row]
sums = self.outcome_sums[row]
return torch.where(counts > 0, sums / counts, torch.zeros_like(sums))
def total_visits(self, state_key: str) -> Tensor:
"""Scalar tensor sum of visits across all actions at ``state_key``."""
return self.row_visits(state_key).sum()
def frontier_mask(self, state_key: str) -> Tensor:
"""Boolean ``[num_actions]`` mask: ``True`` where action is untested."""
return self.row_visits(state_key) == 0
def has_frontier(self, state_key: str) -> Tensor:
"""Scalar boolean tensor: any untested action at ``state_key``?"""
return self.frontier_mask(state_key).any()
def recommend_next(
self,
state_key: str,
*,
available_actions: Tensor | None = None,
strategy: str = STRATEGY_SHORTEST_TO_UNTESTED,
hypothesis_prior: Tensor | None = None,
exploration: float = UCB_DEFAULT_EXPLORATION,
) -> Tensor:
"""Pick the next action index under the chosen strategy (scalar tensor).
``available_actions`` (optional ``[K]`` long tensor of action indices
in ``[0, num_actions)``) restricts selection; if omitted all actions are
eligible. Returns the chosen action index as a 0-D long tensor.
"""
if available_actions is None:
available = torch.arange(self.num_actions, device=self.device)
else:
available = available_actions.to(self.device).to(torch.long)
row = self._row(state_key)
counts = self.visit_counts[row]
sums = self.outcome_sums[row]
means = torch.where(counts > 0, sums / counts, torch.zeros_like(sums))
untested = counts == 0
if strategy == STRATEGY_LEAST_SAMPLED:
# anti-Thompson: prefer untested first, then fewest-sampled.
score = torch.where(untested, torch.full_like(counts, -1.0), counts)
chosen = available[torch.argmin(score[available])]
return chosen.to(torch.long)
if strategy == STRATEGY_BEST_OUTCOME:
score = torch.where(untested, torch.full_like(means, torch.finfo(self.dtype).max), means)
chosen = available[torch.argmax(score[available])]
return chosen.to(torch.long)
if strategy == STRATEGY_HYPOTHESIS_DRIVEN:
prior = (
torch.zeros(self.num_actions, dtype=means.dtype, device=self.device)
if hypothesis_prior is None
else hypothesis_prior.to(self.device).to(self.dtype)
)
scores = self.ucb_scores_for_row(row, exploration=exploration) + prior
scores = torch.where(untested, torch.full_like(scores, torch.finfo(self.dtype).max), scores)
chosen = available[torch.argmax(scores[available])]
return chosen.to(torch.long)
if strategy == STRATEGY_UCB:
scores = self.ucb_scores_for_row(row, exploration=exploration)
scores = torch.where(untested, torch.full_like(scores, torch.finfo(self.dtype).max), scores)
chosen = available[torch.argmax(scores[available])]
return chosen.to(torch.long)
# default: shortest-to-untested -- if any untested action is available,
# take the first; otherwise fall back to least-sampled.
avail_untested = untested[available]
if avail_untested.any():
chosen = available[torch.argmax(avail_untested.to(torch.long))]
return chosen.to(torch.long)
score = counts
chosen = available[torch.argmin(score[available])]
return chosen.to(torch.long)
def ucb_scores_for_row(
self,
row: int,
*,
exploration: float = UCB_DEFAULT_EXPLORATION,
) -> Tensor:
"""UCB scores ``[num_actions]`` for one hashed row.
Exploit = the learned ``state_value[row]`` broadcast as the per-action
mean-outcome baseline (so gradients flow through the value embedding),
plus the empirical mean outcome. Explore = the standard
``c * sqrt(log(N) / n_a)`` bonus, zero where ``n_a == 0``.
"""
counts = self.visit_counts[row]
sums = self.outcome_sums[row]
means = torch.where(counts > 0, sums / counts, torch.zeros_like(sums))
total = counts.sum()
log_total = torch.log(torch.clamp(total, min=1.0))
explore_bonus = exploration * torch.sqrt(
log_total / torch.clamp(counts, min=1.0)
)
explore_bonus = torch.where(counts > 0, explore_bonus, torch.zeros_like(explore_bonus))
# Exploit term mixes the learned per-state value with the empirical mean.
exploit = self.state_value[row] + means
return exploit + explore_bonus
def ucb_scores(
self,
state_key: str,
*,
exploration: float = UCB_DEFAULT_EXPLORATION,
) -> Tensor:
"""UCB scores ``[num_actions]`` for ``state_key`` (gradient-flowing)."""
return self.ucb_scores_for_row(self._row(state_key), exploration=exploration)
def softmax_recommend(
self,
state_key: str,
*,
temperature: float = 1.0,
) -> Tensor:
"""Softmax sampling distribution ``[num_actions]`` over UCB scores.
Differentiable sampling distribution (caller may ``torch.multinomial``
or take the expectation). Useful as a stochastic exploration policy.
"""
scores = self.ucb_scores(state_key)
return torch.softmax(scores / max(temperature, 1e-6), dim=0)
def action_distribution_entropy(self, state_key: str) -> Tensor:
"""Shannon entropy (nats) of the visit distribution at ``state_key``.
High entropy = broadly explored; low = focused. Differentiable through
the count tensor (counts are buffers, but the math is tensor-native).
"""
counts = self.row_visits(state_key)
total = counts.sum()
probs = counts / torch.clamp(total, min=1.0)
log_probs = torch.log(torch.clamp(probs, min=1e-12))
entropy = -(probs * log_probs).sum()
return torch.where(total > 0, entropy, torch.zeros_like(entropy))
# ------------------------------------------------------------------
# federation merge
# ------------------------------------------------------------------
def merge(self, other: "TensorExplorationGraph") -> "TensorExplorationGraph":
"""Federation merge: visit counts and outcome sums add (elementwise).
Returns a fresh module (does not mutate ``self`` or ``other``). The
learned ``state_value`` becomes the mean of the two (or self where other
is zero) -- a stable federation average for the value embedding.
"""
if self.table_size != other.table_size or self.num_actions != other.num_actions:
raise ValueError("cannot merge graphs of differing shape")
merged = TensorExplorationGraph(
table_size=self.table_size,
num_actions=self.num_actions,
device=self.device,
dtype=self.dtype,
)
merged.visit_counts = (self.visit_counts + other.visit_counts).clone()
merged.outcome_sums = (self.outcome_sums + other.outcome_sums).clone()
# Average learned values; fall back to self where other has none.
self_has = self.state_value != 0
other_has = other.state_value != 0
both = self_has & other_has
summed = self.state_value + other.state_value
averaged = torch.where(both, summed / 2.0, self.state_value + other.state_value)
with torch.no_grad():
merged.state_value.copy_(averaged)
return merged.to(self.device)
# ------------------------------------------------------------------
# RHAE efficiency metric (tensor-native, differentiable)
# ------------------------------------------------------------------
def relative_human_action_efficiency(
self,
human_actions: Tensor,
ai_actions: Tensor,
*,
cap: float = RHAE_DEFAULT_CAP,
) -> Tensor:
"""RHAE = (human / ai) ** 2, clamped to ``cap``. Differentiable.
Tensor inputs make this usable as a training signal: gradients flow
through ``ai_actions`` (e.g. a soft action count produced by the model).
"""
raw = (human_actions / ai_actions) ** 2
return torch.clamp(raw, max=cap)
def action_efficiency_penalty(
self,
ai_actions: Tensor,
*,
reference_actions: Tensor,
cap: float = RHAE_DEFAULT_CAP,
) -> Tensor:
"""Differentiable RHAE-style penalty in ``[0, 1]`` for training signals."""
rhae = self.relative_human_action_efficiency(
reference_actions, ai_actions, cap=cap
)
return torch.clamp(1.0 - rhae, min=0.0)
def ucb_score_tensor(
*,
mean_outcome: Tensor,
visit_count: Tensor,
total_visits: Tensor,
exploration: float = UCB_DEFAULT_EXPLORATION,
) -> Tensor:
"""Vectorized UCB score.
``mean_outcome``, ``visit_count`` are ``[...]`` (any shape, broadcastable);
``total_visits`` is scalar or broadcastable. Untested actions
(``visit_count <= 0``) score ``+inf`` so they are tried first -- matching
:func:`resynthesis.causal_exploration.ucb_score`.
"""
inf = torch.full_like(mean_outcome, float("inf"))
safe_count = torch.clamp(visit_count, min=1.0).to(mean_outcome.dtype)
safe_total = torch.clamp(total_visits, min=1.0).to(mean_outcome.dtype)
bonus = exploration * torch.sqrt(torch.log(safe_total) / safe_count)
score = mean_outcome + bonus
return torch.where(visit_count > 0, score, inf)
__all__ = [
"CAUSAL_EXPLORATION_TENSOR_SCHEMA",
"DEFAULT_NUM_ACTIONS",
"DEFAULT_TABLE_SIZE",
"RHAE_DEFAULT_CAP",
"STRATEGY_BEST_OUTCOME",
"STRATEGY_HYPOTHESIS_DRIVEN",
"STRATEGY_LEAST_SAMPLED",
"STRATEGY_SHORTEST_TO_UNTESTED",
"STRATEGY_UCB",
"TensorExplorationGraph",
"UCB_DEFAULT_EXPLORATION",
"state_hash_index",
"state_hash_indices",
"ucb_score_tensor",
]
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