conservation_from_balance
Why this theorem is linked from Mobile-Agent: Autonomous Multi-Modal Mobile Device Agent with Visual Perception unclear
Pith linked this Lean declaration because the review connected a specific passage in the paper to this theorem. The relation tag says how strong that connection is; it is not a generic placeholder.
Different from previous solutions that rely on XML files of Apps or mobile system metadata, Mobile-Agent allows for greater adaptability across diverse mobile operating environments in a vision-centric way
Relation between the paper passage and the cited Recognition theorem.
plain-language theorem explainer
A balanced ledger of recognition events has zero net flow at every agent. Researchers deriving conservation laws from J-symmetry in discrete models cite this result. The proof rewrites net flow as a sum of flow contributions over events, switches to a multiset view invariant under the reciprocal map, and invokes the negation property of flow contributions under reciprocity to force the sum to zero.
Claim. If $L$ is a ledger whose events satisfy the balanced count condition and $a$ is an agent, then the net flow of $L$ at $a$ equals zero.
background
The LedgerForcing module shows that J-symmetry forces double-entry ledger structure. A Ledger consists of a list of RecognitionEvent together with the balanced_list predicate that enforces equal counts for each event and its reciprocal. Net flow at an agent sums the flow_contribution of each event, which adds or subtracts the logarithm of the event ratio according to whether the agent is source or target. The balanced hypothesis asserts that the multiset of events equals its image under the reciprocal automorphism. Upstream results supply the reciprocal definition from CostAlgebra and the add_assoc, add_comm lemmas used to manipulate the summation rewrites.
proof idea
The tactic proof first rewrites the foldl definition of net_flow into an explicit sum of flow_contribution terms via step_eq and two foldl lemmas. It then forms the multiset M of events and proves M equals M.map reciprocal by count equality from balanced_list together with injectivity of reciprocal. The relation flow_contribution_reciprocal supplies f(reciprocal e) = -f(e). The sum of f over M therefore equals its own negative, so the sum vanishes.
why it matters
This theorem supplies the conservation law used by finiteEulerLedger_net_flow_zero to conclude zero net flow for every finite Euler ledger. It realizes the double-entry invariance forced by J-symmetry, linking the Recognition Composition Law to ledger-level conservation. The result closes one step in the forcing chain from J-uniqueness to discrete accounting structure.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.
papers checked against this theorem (showing 30 of 35)
-
Fixed CO2 mix with oxygen keeps poultry water CO2 at 3-20 mg/L
"fixed percentage of CO2 to keep a constant level of dissolved CO2"
-
Counters compensate CAN delays to time spray valves precisely
"carrying out a synchronization between the main control unit, the local control unit, and the metering control unit for the activation, at the time, of the metering valve by starting a first counter in the main control unit, a second counter in the local control unit, and a third counter in the metering control unit, by a counter state of the first counter being recorded by the second and third counters, and a difference of the counter state of the first counter, a counter state of the second counter, and a counter state of the third counter being taken into account in the actuation of the m"
-
Tweezer array traps 6100 atoms with 12.6s coherence
"We present a plan for zone-based quantum computing and demonstrate necessary coherence-preserving qubit transport and pick-up/drop-off operations on large spatial scales, characterized through interleaved randomized benchmarking."
-
Duality defects forbid trivially gapped phases in 3+1D
"We focus on the case of a one-form symmetry in 3+1 dimensions, and determine the fusion rule... explicit realization of this duality defect in the free Maxwell theory... non-abelian gauge theories and the Z_N lattice gauge theory."
-
O-Voxel structure raises 3D generation quality
"the geometry and material quality of our generated assets far exceed those of existing models"
-
Black hole entanglement wedge loses info after scrambling time
"Turning on a coupling between one boundary and a further external auxiliary system which functions as a heat sink allows a two-sided otherwise-eternal black hole to evaporate on one side."
-
Agents evolve at runtime by reinforcing episodic memory strategies
"MEMRL organizes memory into a structured Intent-Experience-Utility triplet... Utility-Driven Update refines these Q-values through environmental feedback, applying Monte Carlo style updates"
-
Online RL boosts LLM self-correction up to 15.6% with self-generated data
"This regularization process includes an initial phase of multi-turn RL on a base model to generate a policy initialization that is less susceptible to collapse, followed by using a reward bonus to amplify self-correction."
-
Vision-based agent runs mobile apps without system metadata
"Different from previous solutions that rely on XML files of Apps or mobile system metadata, Mobile-Agent allows for greater adaptability across diverse mobile operating environments in a vision-centric way"
-
Black holes extract energy and trigger instabilities via superradiance
"In General Relativity, black-hole superradiance is permitted by the ergoregion, that allows for energy, charge and angular momentum extraction from the vacuum, even at the classical level."
-
Sigmoidal curves predict RL performance for LLMs at 100k GPU hours
"We propose a best-practice recipe, ScaleRL, and demonstrate its effectiveness by successfully scaling and predicting validation performance on a single RL run scaled up to 100,000 GPU-hours."
-
Large chunks unlock efficient test-time training for million-token sequences
"Test-Time Training (TTT) models context dependencies by adapting part of the model's weights (referred to as fast weights) during inference. This fast weight, akin to recurrent states in RNNs, stores temporary memories of past tokens"
-
Loudest black hole merger tests Kerr nature to few percent
"We probe the remnant’s Kerr nature by constraining the spectroscopic pattern of the dominant quadrupolar (ℓ = m = 2) mode and its first overtone to match the Kerr prediction to tens of percent at multiple post-peak times."
-
Text encoding lets one model handle planning, detection and maps from camera images
"This approach allows EMMA to jointly process various driving tasks in a unified language space"
-
MEMIT edits thousands of facts into large language models
"inspired by the ROME direct editing method... modify a sequence of layers and develop a way for thousands of modifications to be performed simultaneously"
-
Unique reciprocal cost on ratios forces balanced discrete ledgers
"Under deterministic update semantics and minimality (no intra-tick ordering metadata), we derive atomic ticks (at most one event per tick). Explicit structural assumptions (conservation, no sources/sinks, pairwise locality, quantization in δℤ) force balanced double-entry postings"
-
Trillion-parameter models scale recommendation quality with compute
"We reformulate recommendation problems as sequential transduction tasks within a generative modeling framework (Generative Recommenders), and propose a new architecture, HSTU, designed for high cardinality, non-stationary streaming recommendation data."
-
Gated DeltaNet beats Mamba2 on retrieval and long sequences
"the gated delta rule... combines both approaches... hardware-efficient chunkwise algorithm"
-
Sliding window halves GRPO training time for flow models
"the entire denoising process to be framed as a Markov Decision Process (MDP) in a stochastic environment, where GRPO is then applied to optimize the complete state-action sequence"
-
Blended diffusion sampling solves noisy nonlinear inverse problems
"we extend diffusion solvers to efficiently handle general noisy (non)linear inverse problems via approximation of the posterior sampling"
-
Hundreds of thousands of qubits needed for practical quantum advantage
"the overheads required to ensure fault-tolerant quantum computing will significantly outpace the resources required for fault-tolerant classical computing"
-
Paged KV cache lifts LLM serving throughput 2-4x
"we propose PagedAttention, an attention algorithm inspired by the classical virtual memory and paging techniques in operating systems. On top of it, we build vLLM, an LLM serving system that achieves (1) near-zero waste in KV cache memory and (2) flexible sharing of KV cache within and across requests"
-
RNNs learn to halt after variable steps
"the ponder cost ρt = N(t) + R(t) ... τP(x)"
-
Lightning attention scales test-time compute in 456B hybrid model
"we propose CISPO, a novel RL algorithm to further enhance RL efficiency. CISPO clips importance sampling weights rather than token updates"
-
LLM agents evolve memory skills from their own failures
"Experiments on LoCoMo, LongMemEval, HotpotQA, and ALFWorld demonstrate that MemSkill improves task performance over strong baselines and generalizes well across settings."
-
q-form global symmetries extend to higher-dimensional operators
"They can also have 't Hooft anomalies, which prevent us from gauging them, but lead to 't Hooft anomaly matching conditions. Such anomalies can also lead to anomaly inflow on various defects and exotic Symmetry Protected Topological phases."
-
Tiny changes fool neural networks and transfer across models
"the same perturbation can cause a different network, that was trained on a different subset of the dataset, to misclassify the same input."
-
GLM-4.5 Hits 91% on AIME and 64% on SWE-Bench
"Through multi-stage training on 23T tokens and comprehensive post-training with expert model iteration and reinforcement learning"
-
RL teaches LLMs to call search engines inside their reasoning
"SEARCH-R1 optimizes LLM reasoning trajectories with multi-turn search interactions, leveraging retrieved token masking for stable RL training"
-
67B DeepSeek LLM beats LLaMA-2 70B on code and math benchmarks
"To support the pre-training phase, we have developed a dataset that currently consists of 2 trillion tokens"