Theoretical Architecture, Mathematical Formulation, and Empirical Framework for Edge-Partitioned Lifelogging Systems
Vinayak Sharma
ByteBastion Engineering Laboratory
Divison:Agent.exe + Mecha.exe
Preprint Specification • Theoretical Computer Science & Embedded Systems
Notice: This repository serves as the official academic pre-print companion, theoretical architectural specification, and empirical analysis repository for the SAGE Cognitive Co-Processor research paper. Per open-science publication guidelines, all raw hardware firmware, mobile applications, and backend implementations are partitioned into private evaluation environments to maintain double-blind review integrity and protect patent-pending architectural formulations.
Human episodic memory is susceptible to progressive decay, cognitive overload, and attentional omissions. While continuous lifelogging offers a theoretical pathway toward cognitive augmentation, deploying continuous audiovisual capture on sub-100mW wearable edge devices encounters a catastrophic hardware bottleneck: on-chip memory exhaustion and DMA bus contention.
When acquiring continuous video (
In this work, we present SAGE (Synchronized Agentic Guided Environment), a novel theoretical architecture and edge-cloud partitioning framework for continuous wearable memory capture and retrieval. SAGE introduces the Decoupled Dual-Buffer Asynchronous Pipeline (
- Visual and auditory streams are captured independently into non-contiguous, dedicated circular memory partitions on an asymmetric dual-core microcontroller, entirely bypassing in-flight container multiplexing.
- Uncompressed audiovisual buffers are offloaded over an ad-hoc high-throughput burst link to a local mobile host during deterministic idle intervals.
- Temporal synchronization is reconstructed downstream using microsecond header interpolation and container muxing.
- Synthesized episodes are mapped into a dense multimodal semantic vector space (
$\mathbb{R}^d$ ) governed by a temporal-decay Retrieval-Augmented Generation (RAG) kernel, enabling natural-language conversational queries over episodic autobiographical memories.
Empirical modeling demonstrates that
The ambition to augment human intellect through passive, ubiquitous recording traces its intellectual heritage to Vannevar Bush's seminal Memex concept (1945) and Steve Mann's pioneering work in Wearable Computing (1997). Despite decades of progress, real-world deployment of personal cognitive memory aids has faced three fundamental dilemmas:
┌────────────────────────────────────────────────────────┐
│ The Trilemma of Wearable Cognition │
└────────────────────────────────────────────────────────┘
▲
/ \
/ \
/ \
/ \
[Low-Power Wearability] ───────── [Continuous Fidelity]
\ /
\ /
\ /
\ /
▼
[Zero-Friction Recall]
-
Bandwidth vs. Thermal / Power Budget: Continuously streaming uncompressed audiovisual sensor telemetry off a sub-$20\text{g}$ wearable device over Wi-Fi/Bluetooth rapidly depletes battery cells (
$<2\text{ hours}$ ) and generates excessive thermal dissipation ($>42^\circ\text{C}$ on-skin). -
Deterministic Sampling vs. Compression Jitter: Image sensors (e.g., OV2640) exhibit variable compression latency (
$t_{jpeg} \in [45\text{ ms}, 180\text{ ms}]$ ) contingent on scene entropy and ambient luminance. Conversely, digital microphones (I2S PDM) require strictly deterministic Direct Memory Access (DMA) servicing ($f_s = 16\text{ kHz}$ ). Scheduling both on a shared microcontroller bus induces sample dropping or frame freezing. - Information Overload vs. Cognitive Utility: Early systems like Microsoft SenseCam (Hodges et al., 2006) and Narrative Clip (2013) generated petabytes of unindexed chronological imagery, shifting the cognitive burden onto the user to locate specific autobiographical episodes manually.
SAGE resolves this trilemma through asymmetric edge-cloud co-processing, mathematically separating real-time buffer capture, downstream container synthesis, and multimodal semantic projection.
Consider an edge node with total physical memory
In a traditional monolithic multiplexing pipeline (e.g., producing an in-flight .mp4 or .avi container with interleaved audio/video packets), the memory required at elapsed recording time
Where:
-
$R_v(t) = \text{FPS} \cdot S_{frame}(t)$ is the instantaneous visual bit rate. For VGA JPEG ($640 \times 480$ ) at$10\text{ fps}$ , average frame size$\bar{S}_{frame} \approx 35\text{ KB}$ , giving$\bar{R}_v \approx 350\text{ KB/s}$ . -
$R_a(t) = 2 \cdot f_s \cdot (\text{bit_depth} / 8)$ is the raw PCM audio rate. For$16\text{ kHz}$ , 16-bit mono:$R_a = 32\text{ KB/s}$ . -
$M_{mux_table}(T) = \mathcal{O}(T)$ is the index allocation table (e.g.,movi/idx1chunks in AVI, ormoov/stblatoms in MP4) that must reside in contiguous memory before file finalization. -
$M_{heap_frag}(T)$ represents non-contiguous heap allocation overhead from dynamic buffer reallocation.
Under standard FreeRTOS allocation policies, contiguous memory collapses when:
Empirically, for
SAGE resolves memory exhaustion by partitioning external PSRAM into two fixed, static, pre-allocated circular ring buffers:
$$\mathcal{B}{video} \in \mathbb{R}^{B_v}, \quad \mathcal{B}{audio} \in \mathbb{R}^{B_a}$$
Where buffer capacities are calculated strictly for a discrete capture epoch
Because buffers are pre-allocated at hardware boot, runtime allocation overhead is zero (
SAGE is organized into a four-tier hierarchical execution topology:
graph TD
subgraph Tier1["Tier 1: Micro-Sensor Edge Node (ESP32-S3)"]
Sensors[Sensors: OV2640 VGA + PDM Mic] --> DMA[Direct Memory Access Core 0]
DMA --> D2BAP["D²BAP: Isolated Ring Buffers (PSRAM)<br/>4.2MB Video Buffer | 480KB Audio Buffer"]
D2BAP --> HTTPServer["Local AP Binary Server Core 1<br/>Endpoints: /download_video, /download_audio"]
end
subgraph Tier2["Tier 2: Personal Gateway / Edge Intermediary (Mobile Client)"]
HTTPServer -->|Ad-Hoc Wi-Fi Burst Transfer| P2PReceiver[P2P Parallel Chunk Puller]
P2PReceiver --> DownstreamSync["Temporal Phase Muxer<br/>Header Interpolation + Audio-Visual Alignment"]
DownstreamSync --> LocalCache[Encrypted Local Episodic Cache]
end
subgraph Tier3["Tier 3: Multimodal Cognitive Reasoning Engine"]
LocalCache --> MultimodalProc["Multimodal AI Encoder<br/>Keyframe Extraction + Audio Transcription"]
MultimodalProc --> SemanticSynth["Episodic Narrative Synthesis<br/>Title • Context Summary • Prompt Reconstruction"]
SemanticSynth --> EmbeddingMap["Semantic Vector Space Mapping<br/>e_i in R^d Vector Space"]
end
subgraph Tier4["Tier 4: Sovereign Personal Vector & Cloud Vault"]
EmbeddingMap --> ChronoTimeline[Chronological Temporal Graph]
EmbeddingMap --> VectorStore[Dense Vector Memory Index]
LocalCache -->|Background OAuth2 Queue| CloudVault[User-Sovereign Private Cloud Storage]
UserQuery[User Conversational Query] --> RAGRetriever[Temporal-Decay RAG Retrieval Engine]
VectorStore --> RAGRetriever
ChronoTimeline --> RAGRetriever
RAGRetriever --> LLMResponse[Context-Aware Conversational Recall Response]
end
| Tier | Host Platform | Latency Profile | Primary Responsibility | Memory Boundary |
|---|---|---|---|---|
| Tier 1: Sensor Node | Dual-Core Tensilica LX7 | Hard Real-Time ( |
Asynchronous DMA buffer acquisition; Local AP serving |
|
| Tier 2: Gateway | Mobile Client (ARM64) | Soft Real-Time ( |
P2P burst transfer; temporal phase muxing; local caching | Host OS memory ( |
| Tier 3: Reasoning | Multimodal Cloud / Edge | High-Throughput ( |
Visual scene understanding; transcript fusion; dense vector embedding | Dynamic tensor compute |
| Tier 4: Storage Vault | Sovereign User Cloud | Asynchronous ( |
Cryptographically isolated archival; temporal graph indexing | User storage quota |
The lifecycle of each autobiographical episode on the wearable capture node is modeled as a deterministic finite state machine
┌────────────────────────────────────────────────────────┐
│ S_IDLE │
└────────────────────────────────────────────────────────┘
│
σ_start │ (Session Start Command)
▼
┌────────────────────────────────────────────────────────┐
│ S_CAPTURE │
│ Core 0: Concurrent DVP Frame Grab & I2S DMA │
└────────────────────────────────────────────────────────┘
│
t >= τ (15.0s) │ (Epoch Expiry)
▼
┌────────────────────────────────────────────────────────┐
│ S_FINALIZING │
│ Write AVI Header Index & RIFF Size Chunk │
└────────────────────────────────────────────────────────┘
│
δ_ready │
▼
┌────────────────────────────────────────────────────────┐
│ S_BURST_READY │
│ Pause Viewfinder; Switch to 802.11 AP │
└────────────────────────────────────────────────────────┘
│
σ_p2p_connect │ (Mobile Client Connected)
▼
┌────────────────────────────────────────────────────────┐
│ S_OFFLOADING │
│ Core 1: High-Speed TCP Binary Stream Transfers │
└────────────────────────────────────────────────────────┘
│
σ_xfer_done │ (MD5 Verified)
▼
┌────────────────────────────────────────────────────────┐
│ S_DECISION_WINDOW (30s) │
│ Awaiting Continuous Loop Confirmation │
└────────────────────────────────────────────────────────┘
│ │
σ_continue │ │ σ_terminate / timeout
▼ ▼
S_CAPTURE S_IDLE
Because the microcontroller lacks an atomic hardware multiplexer, the video frame rate fluctuates due to image compression complexity. Let
The accumulated phase disparity
In naive uncoordinated streaming,
SAGE solves synchronization downstream during Tier 2 ingestion through Proportional Timestamp Interpolation:
- At epoch termination
$T = \tau$ , the firmware embeds total acquired frames$N_v$ and precise elapsed microsecond duration$T_{\mu s} = t_{end} - t_0$ into the AVI stream header. - The effective visual frame rate is dynamically evaluated: $$\text{FPS}{effective} = \frac{N_v \times 10^6}{T{\mu s}}$$
- The audio duration is calculated from total bytes transferred
$S_a$ :$$T_a = \frac{S_a - \text{sizeof(RIFF_HEADER)}}{f_s \cdot 2} = \frac{S_a - 44}{32000}\text{ seconds}$$ - Downstream multiplexing maps visual presentation timestamps (
$PTS_v$ ) to audio presentation timestamps ($PTS_a$ ) via linear time rescaling:$$PTS_v(i) = i \cdot \left( \frac{T_a}{N_v} \right)$$
This guarantees strict phase alignment across the
Each episodic memory unit
A joint multimodal vision-language foundation model
The episodic embedding
When a user issues an autobiographical conversational query
The contextual relevance score
Where:
-
$\cos(\mathbf{e}_q, \mathbf{e}_i) = \mathbf{e}_q^\top \mathbf{e}_i$ represents pure semantic alignment. -
$\exp(-\lambda \frac{|t_q - t_i|}{\Delta T_{context}})$ represents recency bias (tunable via$\lambda \in [0, 1]$ ). -
$\alpha \in [0.6, 0.9]$ is the semantic dominance coefficient.
The top-$K$ scoring memory episodes
Generating an accurate, grounded autobiographical recall response citing direct video evidence timestamps without hallucination.
The following matrix compares SAGE against foundational and contemporary lifelogging / wearable AI systems:
| System / Feature | Microsoft SenseCam (2006) | Narrative Clip (2013) | Rewind Pendant (2023) | Limitless Pendant (2024) | Humane AI Pin (2024) | SAGE (This Work) |
|---|---|---|---|---|---|---|
| Primary Modality | Still Images | Still Images | Audio Only | Audio Only | Video + Audio + Projection | Synchronized Video + Audio |
| Wearable Compute Node | Custom 8-bit MCU | ARM9 Processor | Nordic BLE SoC | Nordic BLE SoC | Qualcomm Snapdragon 720G | ESP32-S3 Dual-Core SoC |
| Buffer Architecture | Flash Storage | Internal NAND Flash | Continuous BLE Stream | Continuous BLE Stream | Monolithic OS Heap | |
| Capture Mechanism | Sensor Triggered | Periodic (30s interval) | Continuous Passive | Continuous Passive | Intentional Tap Trigger | Periodic Epochs + Adaptive Loop |
| On-Chip Muxing | None (Unsynced) | None (Images only) | Raw Opus stream | Raw Opus stream | Monolithic Linux Mux | Downstream Phase Muxing |
| Indexing Paradigm | None (Folder view) | Chronological Cloud | Speech-to-Text / OCR | Cloud Speech-to-Text | Cloud Agent Dispatcher | Multimodal Temporal RAG ( |
| Conversational Recall | ❌ No | ❌ No | ✅ Full Audiovisual Epistemic RAG | |||
| Power Profile |
|
|||||
| Data Sovereignty | Local SD Card | Proprietary Cloud | Local Mac Storage | Proprietary Cloud | Proprietary Cloud | User-Owned Private Cloud Vault |
┌───────────────────────────────────────────────┐
│ SAGE Hardware Edge Node │
└───────────────────────────────────────────────┘
│
┌───────────────────────────────┴───────────────────────────────┐
▼ ▼
┌──────────────────────┐ ┌──────────────────────┐
│ OmniVision OV2640 │ │ MSM261S4030H0R │
│ VGA CMOS Sensor │ │ Digital PDM Mic │
└──────────────────────┘ └──────────────────────┘
│ (8-bit DVP Parallel Bus) │ (I2S DMA Bus)
▼ ▼
┌──────────────────────┐ ┌──────────────────────┐
│ Tensilica LX7 (C0) │ │ Tensilica LX7 (C0) │
│ Direct Memory Access│ │ I2S Controller │
└──────────────────────┘ └──────────────────────┘
│ │
└───────────────────────────────┬───────────────────────────────┘
▼
┌───────────────────────────────────┐
│ 8MB Octal-SPI PSRAM │
│ ┌───────────────┬───────────────┐ │
│ │ Video Buffer │ Audio Buffer │ │
│ │ (4.2 MB) │ (480 KB) │ │
│ └───────────────┴───────────────┘ │
└───────────────────────────────────┘
│
▼
┌───────────────────────────────────┐
│ Tensilica LX7 (Core 1) │
│ 802.11 b/g/n SoftAP Server │
└───────────────────────────────────┘
│
▼ (High-Speed Binary Bursts)
[To Mobile Gateway]
- Core Processor: Espressif Systems ESP32-S3 (Xtensa® Dual-Core 32-bit LX7, up to 240 MHz).
- Storage Interfaces: 8 MB Octal-SPI external PSRAM, 8 MB Quad-SPI Flash memory.
-
Camera Sensor Subsystem: OV2640 with DVP interface (YUV422/JPEG output), UXGA resolution native decimated to VGA (
$640 \times 480$ ). -
Audio Transducer: Omnidirectional digital PDM microphone, SNR
$64\text{ dBA}$ , sensitivity$-26\text{ dBFS}$ . -
RF Transceiver:
$2.4\text{ GHz}$ Wi-Fi ($802.11\text{ b/g/n}$ ), peaking at$+20.5\text{ dBm}$ output power in 802.11b mode. -
Operating Battery Budget: Single-cell LiPo (
$3.7\text{ V}$ ,$300\text{ mAh}$ nominal), delivering$\approx 4.5\text{ hours}$ operational capture life on$33%$ active duty cycle.
Continuous wearable recording raises profound privacy, consent, and societal considerations:
-
Bystander Privacy Paradigm: SAGE implements visible physical LED state indication during all active recording epochs (
$S_{CAPTURE}$ ). It strictly rejects hidden surveillance paradigms. - Local Credential Sovereignty: Authentication tokens (OAuth2) and private API keys remain strictly quarantined inside the personal mobile keychain. No intermediate telemetry broker, proxy server, or third-party logging platform intercepts episodic payloads.
- Right to Be Forgotten & Epistemic Audit: Users retain unmediated cryptographic ownership of their private storage vault. Deletion operations execute physical block-level purging rather than soft-delete flagging.
- Episodic Boundary Quarantine: The system enforces strict 15-second episodic chunking; continuous open-ended surveillance recording is structurally prohibited by the finite buffer topology.
The theoretical documentation in this repository is organized into the following specialized specifications:
SAGE-AI/
├── research/
│ ├── literature-review.md # Chronological survey of wearable lifelogging (1945–2026)
│ ├── gap-analysis.md # Mathematical memory modeling & DMA bus contention proofs
│ └── methodology.md # Formal algorithms for D²BAP, temporal phase muxing & RAG
│
├── hardware/
│ └── hardware-overview.md # Electrical specifications, timing models & pin mapping
│
└── docs/
├── architecture/
│ └── architecture-details.md # 4-tier execution topology & protocol definitions
├── gap-analysis/
│ └── gap-details.md # Empirical memory failure curves & comparative benchmarks
├── literature-review/
│ └── literature-details.md # Epistemic foundation & clinical memory rehabilitation
├── methodology/
│ └── methodology-details.md # Downstream reconstruction & alignment mathematics
├── objectives/
│ └── objectives-details.md # Theoretical milestones & engineering research metrics
├── use-cases/
│ └── use-cases-details.md # Naturalistic autobiographical recall experimental paradigms
└── ui-agent-framework.md # Multi-agent persona abstraction & cognitive UX theory
Vinayak Sharma
Lead Architect & Researcher