BACE: Behavior-Adaptive Connectivity Estimation for Interpretable Graphs of Neural Dynamics

## Abstract

Abstract Understanding how distributed brain regions coordinate to produce behavior requires models that are both predictive and interpretable. We introduce Behavior-Adaptive Connectivity Estimation (BACE), an end-to-end framework that learns phase-specific, directed inter-regional connectivity directly from multi-region intracranial local field potentials (LFP). BACE aggregates many micro-contacts within each anatomical region via per-region temporal encoders, applies a learnable adjacency specific to each behavioral phase, and is trained on a forecasting objective. On synthetic multivariate time series with known graphs, BACE accurately recovers ground-truth directed interactions while achieving forecasting performance comparable to state-of-the-art baselines. Applied to human subcortical LFP recorded simultaneously from eight regions during a cued reaching task, BACE yields an explicit 8 × 8 8{\times}8 connectivity matrix for each within-trial behavioral phase. The resulting behavioral phase-specific graphs reveal behavior-aligned reconfiguration of inter-regional influence and provide compact, interpretable adjacency matrices for comparing network organization across behavioral phases. By linking predictive success to explicit connectivity estimates, BACE offers a practical tool for generating data-driven hypotheses about the dynamic coordination of subcortical regions during behavior.

## 1 Introduction

Understanding how patterns of interaction between neural populations reorganize with behavior is central to systems neuroscience and to applications that decode or modulate brain activity. These interactions are often framed under the umbrella of brain connectivity, distinguished as structural (anatomical pathways), functional (statistical dependencies), and effective (directed influence)—complementary lenses on how distributed circuits communicate and adapt to task demands [1, 2]. Reviews emphasize both the promise and the challenges of connectivity-centric approaches, particularly the need to capture short-timescale dynamics while maintaining interpretability [3, 4].

Graph-based formulations make this agenda concrete: representing brain regions as nodes and their relationships as edges enables quantitative analysis of modularity, hubs, and task-dependent reconfiguration [5, 6]. Such network perspectives motivate methods that go beyond static, correlation-only descriptions toward dynamic, directed estimates that better align with mechanistic questions.

We focus on intracranial local field potentials (LFPs), a high-temporal-resolution measure of population activity recorded simultaneously from multiple deep-brain regions [7, 8, 9, 10]. Multi-region LFP imposes unique modeling requirements: (i) many micro-contacts per region must be consolidated into coherent region-level trajectories; (ii) neural activity reconfigures across well-defined behavioral phases; and (iii) the spatial layout of contacts is high-dimensional and non-Euclidean [11]. Existing pipelines often average across behavior with a single correlation-based graph [2] or impose hard-coded anatomical connectivity [12, 13], limiting their ability to capture phase-specific, directed interactions.

Recent machine learning advances in graph learning from neural time series highlight the opportunity but do not yet fill this gap. Models such as GraphS4mer couple sequence modeling with learned graphs but are primarily evaluated on decoding tasks without exposing directed region-level connectivity [14]. In fMRI, architectures like STAGIN improve classification via spatio-temporal attention but operate on undirected functional connectivity [15]. Forecasting-based models such as AMAG learn adaptive graphs from cortical LFP, yet they focus on channel-level grids and are not designed for multi-region, behavior-conditioned settings [16]. A framework that yields compact, directed, phase-specific connectivity estimates for invasive multi-region recordings remains lacking.

We introduce BACE (Behavior-Adaptive Connectivity Estimation), an encoder–projector–decoder framework that learns directed, behavioral phase-specific effective connectivity from multi-region LFP. BACE (i) aggregates many contacts within each anatomical region via per-region temporal encoders; (ii) learns a distinct adjacency for each behavioral phase, with a parameterization that separates edge pattern (“who influences whom”) from broadcast strength (per-row gains); and (iii) couples the learned graphs to signal dynamics through a forecasting objective with continuity and smoothness priors.

On synthetic multivariate time series with known ground-truth graphs, BACE accurately recovers directed interactions. Applied to human subcortical LFPs recorded from eight regions during a cued reaching task, BACE produces explicit $8{\times}8$ connectivity matrices for each behavioral segment. Beyond predictive accuracy, we assess reproducibility, quantify uncertainty, and test across-phase differences, turning learned adjacencies into auditable scientific objects rather than opaque model internals. We summarize the main contributions of our work below:

- •
A region-level graph model for neural forecasting. BACE couples per-region temporal encoders with a learnable adjacency to capture directed inter-regional influence.
- •
Recovery of interaction structure. On synthetic datasets with known ground truth, BACE reliably reconstructs directed connectivity using only a forecasting signal.
- •
Behavior-conditioned graphs. BACE yields compact, signed inter-regional adjacencies aligned to behavioral phases, enabling direct comparison of task-specific network organization.
- •
Interpretability. An adjacency parameterization decouples edge pattern from transmission strength, producing small, explicit matrices suitable for neuroscientific analysis.

## 2 Related Works

Our work is situated at the intersection of four key areas: (i) forecasting-based modeling of neural dynamics, (ii) dynamic brain-graph learning, (iii) graph-structure learning from time series, and (iv) interpretability in graph-based neuroscience. While these fields have advanced rapidly, methods that learn compact, directed, and behavior-specific inter-regional graphs remain underexplored.

#### Modeling neural dynamics with forecasting.

Modeling neural dynamics has evolved from linear state–space and Gaussian process factor models [17, 18, 19] to modern deep learning approaches. To capture complex nonlinearities, the field has widely adopted recurrent networks [20, 21], variational autoencoders [22], neural ODEs [23], and Transformers adapted to neural time series [24, 25]. A common thread across these modern approaches is the use of predictive objectives, which have proven effective for learning latent representations aligned with behavior [26]. Despite their success in uncovering latent dynamics, these methods are generally not designed to yield the explicit, interpretable, and behavior-conditioned connectivity graphs that are the primary focus of this work

#### Dynamic brain-graph learning.

Graph neural networks have emerged as a powerful framework for modeling time-resolved brain activity. In fMRI, spatiotemporal attention and Transformer-based architectures such as STAGIN [15] learn dynamic embeddings of functional connectivity for tasks like cognitive-state or demographic classification. Structured state-space hybrids, including GraphS4mer [14] and more recent Mamba-based variants [27], further extend this direction by coupling long-range temporal encoders with adaptive graph learners. Collectively, these works demonstrate the utility of spatiotemporal GNNs across neuroimaging modalities. However, they are generally evaluated on EEG or fMRI classification benchmarks and yield latent embeddings or undirected functional connectivity, rather than compact, directed adjacency matrices explicitly conditioned on behavioral phases.

#### Graph-structure learning from time series.

A distinct but related line of work, Graph-Structure Learning (GSL), aims to infer latent edges jointly with temporal dynamics [28]. This is particularly relevant for neuroscience, where the true underlying graph is unknown. AMAG exemplifies this direction by introducing additive and multiplicative message passing and, importantly, learning a trainable channel-level adjacency jointly with forecasting on cortical LFP and synthetic benchmarks [16]. The broader GSL literature includes variational models for discovering latent graphs [29] and bilinear graph learners for edge inference [30]. These studies validate the principle that predictive objectives can successfully uncover interaction structures from time-series data. However, they typically operate at the fine-grained channel level and do not explicitly model how such structure reconfigures with behavior. BACE addresses this gap by learning *directed, region-level* graphs explicitly conditioned on behavioral phases, enabling direct and interpretable comparisons of network organization across moments within a trial.

#### Interpretability in graph-based neuroscience.

Interpretability efforts in brain GNNs span ROI saliency and causal subgraph discovery. For example, BrainGNN highlights salient regions through ROI-aware pooling and regularizers, but it does not produce an explicit connectivity matrix [31]. CI-GNN learns sparse, causally-relevant subgraph masks from static, undirected fMRI connectivity graphs, linking them to diagnostic predictions [32]. Post-hoc explainers such as GNNExplainer [33] and domain-specific extensions like BrainNNExplainer target edge-level saliency, but again operate in settings focused on classification. Benchmarking and survey efforts such as NeuroGraph [34] and recent reviews of brain GNNs [35] confirm that most interpretability work remains tied to fMRI decoding tasks and post-hoc analysis. In contrast, BACE directly learns inter-regional graphs from invasive LFP dynamics and conditions them on behavioral phase, producing compact, directed adjacency matrices at the region level designed as primary scientific objects for comparing network structure across behavioral phases.

Figure: Figure 1: BACE architecture. Per-region temporal encoders (independent GRUs) extract local dynamics from raw neural windows. A behavioral-specific graph learner produces one directed adjacency $\mathbf{A}_{\phi}$ for each behavioral segment, which the graph projector applies to mix regional features. The forecaster head then predicts the unobserved future window using a residual objective. This end-to-end design links forecasting directly to explicit, behavioral-specific connectivity estimates.
Refer to caption: x1.png

## 3 Methods

We aim to learn dynamic effective connectivity between neural regions from multivariate time series.
Formally, let $\mathbf{X}_{t-T_{\text{in}}+1:t}\in\mathbb{R}^{N\times C\times T_{\text{in}}}$ denote neural activity from $N$ regions, each with $C$ channels, over a past window of length $T_{\text{in}}$.
Our objective is to learn a function

$$ $f_{\theta}:\big(\mathbf{X}_{t-T_{\text{in}}+1:t},\;k\big)\;\mapsto\;\big(\hat{\mathbf{Y}}_{t+1:t+T_{\text{out}}},\;\mathbf{A}^{(k)}\big).$ $$

that predicts the next $T_{\text{out}}$ time steps while simultaneously identifying a directed connectivity matrix
$\mathbf{A}^{(k)}\in\mathbb{R}^{N\times N}$ associated with behavioral context $k$.

The problem is thus framed as joint forecasting and connectivity estimation.
The key principle is that if a connectivity pattern is explanatory, it is expected to improve prediction of future neural dynamics.
This allows us to cast connectivity estimation as a supervised learning problem grounded in predictive modeling.

Our model comprises four components:

#### Regional Encoder.

In our dataset, each region contains multiple channels of neural recordings that capture locally correlated activity.
To encode these within-region dynamics, we employ a set of regional Gated Recurrent Unit (GRU) encoders [36], one per region:

$$ $\mathbf{H}_{r}=\text{GRU}_{r}(\mathbf{X}_{r}),\quad r=1,\dots,N,$ $$

where $\mathbf{X}_{r}\in\mathbb{R}^{C\times T_{\text{in}}}$ is the multichannel input for region $r$.

This design models local dynamics independently, preserving regional separation before cross-regional interactions are introduced.
This is essential, as inter-regional influences are explicitly represented in the learned connectivity matrix later in the model.
Encodings are further stabilized with layer normalization.
After encoding, a lightweight positional embedding is concatenated to each timestep to provide explicit information about relative time within the input window.

#### Context-Specific Graph Learner.

Our Context-Specific Graph Learner produces a directed graph per behavioral context. For each behavioral context $k$, we represent the system as a directed graph $G^{(k)}=(V,E^{(k)},A^{(k)})$, where $V=\{1,\dots,N\}$ denotes the set of regions, $E^{(k)}$ the set of directed edges, and $A^{(k)}\in\mathbb{R}^{N\times N}$ the weighted adjacency matrix. An entry $A^{(k)}_{ij}$ encodes the directed influence from region $j$ to region $i$.

For each behavioral context $k$, we learn a separate adjacency $A^{(k)}$. Rows are normalized to have unit $\ell_{1}$ norm, i.e. $\sum_{j}|A^{(k)}_{ij}|=1\ \forall i$, ensuring stable and interpretable graphs where each row can be read as a distribution of incoming influences to region $i$. During training, the context label of each trial acts as a selector, routing the input to the corresponding adjacency $A^{(k)}$.

#### Graph Projector.

Having defined a context-specific adjacency $A^{(k)}$, the next step is to propagate information between regions. Each region’s output from the encoder is a sequence of temporal embeddings $\mathbf{H}_{i}\in\mathbb{R}^{T\times d}$. To incorporate inter-regional influences, we update these embeddings with two components: (i) a self-update that preserves the region’s own trajectory, and (ii) a neighbor-mixing term that aggregates activity from other regions according to $A^{(k)}$.

Formally, for region $i$ and time $t$,

$$ $\mathbf{Z}_{i,t}\;=\;W_{\text{self}}\,\mathbf{H}_{i,t}\;+\;\sum_{j}A^{(k)}_{ij}\,W_{\text{neigh}}\,\mathbf{H}_{j,t},$ $$

where $W_{\text{self}}$ and $W_{\text{neigh}}$ are learnable linear maps. The first term retains the region’s own dynamics, while the second injects information from neighbors in proportion to the directed influences encoded in $A^{(k)}$. To ensure stability, the neighbor transformation is spectrally normalized.

This projection can be viewed as a single message-passing layer: each region maintains its encoded dynamics while receiving context-dependent inputs from other regions. The resulting sequence $\mathbf{Z}\in\mathbb{R}^{N\times T\times d}$ forms the input to the forecasting head.

#### Autoregressive forecasting head.

The final stage generates future trajectories autoregressively.
Given graph-projected embeddings $\mathbf{Z}\in\mathbb{R}^{N\times T_{\text{in}}\times d}$,
the decoder produces a sequence of length $T_{\text{out}}$.
The decoder attends to the full encoder sequence of past inputs, with attention weights that adapt across forecast steps to provide context for prediction.

At each forecast step $t$, the most recent prediction $\hat{\mathbf{y}}_{t-1}$ (initialized with the last observed sample) is refined through adjacency mixing:

$$ $\tilde{\mathbf{y}}_{t-1}=\hat{\mathbf{y}}_{t-1}+\alpha\,A^{(k)}\hat{\mathbf{y}}_{t-1}.$ $$

This step reintroduces the learned connectivity into the forecasting loop, ensuring that predictions remain explicitly shaped by inter-regional influences rather than relying only on the earlier graph-projected encoder states.
The refined feedback $\tilde{\mathbf{y}}_{t-1}$ is then combined with the context vector $\mathbf{c}_{t}$ from attention to update the decoder state and produce an increment $\Delta\hat{\mathbf{y}}_{t}$.

Absolute forecasts are recovered recursively as

$$ $\hat{\mathbf{y}}_{t}=\hat{\mathbf{y}}_{t-1}+\Delta\hat{\mathbf{y}}_{t},$ $$

a residual formulation that stabilizes training and mitigates drift in multi-step prediction.
A linear readout maps regional hidden states back to the original channel space, yielding predictions $\hat{\mathbf{Y}}\in\mathbb{R}^{N\times C\times T_{\text{out}}}$ aligned with the ground-truth future window.

#### Training and Optimization

The model is trained end-to-end to minimize forecasting error over the next
$T_{\text{out}}$ samples, with lightweight regularizers that encourage sparsity in the learned graphs and stabilize short-horizon predictions.
Optimization is performed with Adam and early stopping based on validation loss.
Full loss definitions, initialization, and optimization details are provided in the Appendix.

## 4 Experiments and Results

### 4.1 Synthetic Data: Recovery of Ground-Truth Connectivity

We first evaluated BACE on synthetic multivariate time series with known ground–truth connectivity to test whether it can recover the known interaction structure. These datasets were designed only to mimic the organization of our neural recordings (8 regions, hundreds of trials segmented into short windows); details of the real dataset follow in the next section.

#### Dataset design.

We generated two suites of datasets, each containing four regimes $\mathcal{D}_{1}$–$\mathcal{D}_{4}$.
In the *structured suite*, each regime is governed by a sparse adjacency matrix with identical row degree but differing placement of nonzeros, yielding multiple shifted but visually structured connectivity patterns.
In the *stochastic non–Gaussian suite*, datasets were generated using linear non–Gaussian dynamical systems, following prior work on learning structure from dynamics [16, 37, 38, 39].
The governing dynamics take the form $\mathbf{X}_{t}=\mathbf{X}_{t-1}+G(\mathbf{X}_{t-1},\mathbf{A})+\bm{\mu}_{t},$
where $G(\mathbf{X}_{t-1},\mathbf{A})=(-\lambda\mathbf{I}+\gamma\mathbf{A})\,\mathbf{X}_{t-1}$ encodes a linear leak term $\lambda>0$ and adjacency–mediated coupling $\gamma\mathbf{A}$.
The noise process $\bm{\mu}_{t}$ is autoregressive with uniform innovations, making it colored and non–Gaussian.

Figure: Figure 2: Adjacency recovery on synthetic datasets. (A) Stochastic non-Gaussian suite; (B) structured suite. Columns correspond to the four datasets $\mathcal{D}_{1}$–$\mathcal{D}_{4}$. Rows: (*top*) ground-truth adjacency $\mathbf{A}$; (*middle*) BACE’s learned adjacency $\hat{\mathbf{A}}$ (row-normalized at inference); (*bottom*) top-$k$ binarization of $\hat{\mathbf{A}}$ with $k$ equal to the ground-truth row degree (here $k{=}2$). Numbers above each panel indicate F1@$k_{\text{row}}$. Quantitatively, BACE achieves mean correlation $0.89$ and mean F1@$k_{\text{row}}{=}1.00$ on the structured suite, and $0.90$ / $0.98$ on the stochastic suite.
Refer to caption: x2.png

#### Synthetic validation.

For synthetic validation we applied the same BACE architecture described in Methods, with no supervision of spatial connectivity. Recovery was assessed with two metrics: (i) F1@$k_{\text{row}}$, which tests whether the top-$k$ entries in each row match the ground-truth nonzeros (with k=2 set to row degree), and (ii) Pearson correlation between learned and ground-truth weights. On the structured suite, BACE attained perfect edge recovery (F1@$k_{\text{row}}{=}1.0$ for all $\mathcal{D}_{1}$–$\mathcal{D}4$) with correlations 0.84/0.93/0.89/0.89 (mean 0.89). On the stochastic non-Gaussian suite, recovery remained strong with F1@$k{\text{row}}$ = 0.94/1.00/1.00/1.00 (mean 0.98) and correlations 0.88/0.94/0.88/0.90 (mean 0.90). Figure [2](https://arxiv.org/html/2510.20831v1#S4.F2) illustrates representative cases: strong edges align with ground truth, and weaker off-diagonal influences are captured with appropriate magnitude. These results show that BACE reliably reconstructs directed adjacency structure while being trained solely for forecasting, supporting its use for effective connectivity estimation.

### 4.2 Evaluation on Human LFP data

#### Dataset and Preprocessing.

We analyzed intracranial local field potentials (LFP) from a pediatric participant with dyskinetic cerebral palsy undergoing deep brain stimulation (DBS) [40, 9, 41, 42, 43] as part of clinical treatment. Neural data were recorded during a cued reaching task. The dataset contained 326 valid trials, each segmented into four behavioral segments: Wait (pre-go cue baseline), React (post-go cue, pre-movement), Reach (forward reach toward target), and Return (movement back to the home button). Each segment was represented by a 400 ms window (400 samples at 1 kHz), yielding consistent trial segments across conditions.

Recordings were obtained from 80 micro-contact channels across eight subcortical regions: internal globus pallidus anterior (GPi-anterior), internal globus pallidus posterior (GPi-posterior), ventral intermediate nucleus of the thalamus (VIM), and subthalamic nucleus (STN) in both hemispheres (10 channels from each region). Preprocessing included a 50 Hz low-pass filter, common average referencing, and downsampling to 1 kHz. For forecasting, each 400-sample segment was further split into sliding windows of 100-sample input ($T_{\text{in}}$) and 20-sample prediction ($T_{\text{out}}$) with stride 20. To prevent leakage, train/validation/test splits were made at the trial level, and all normalization statistics were computed on the training set. Task schematic and behavioral segments are illustrated in Fig. [3](https://arxiv.org/html/2510.20831v1#S4.F3); full details of task design and segmentation criteria are provided in the Appendix.

#### Benchmark Methods.

To contextualize BACE’s performance, we compare against representative models spanning recurrent, Transformer, and graph-based approaches. As a recurrent baseline we include a standard LSTM[20], a canonical gated architecture widely used for sequential modeling. From the Transformer family, we evaluate the Neural Data Transformer (NDT)[24], designed for neural sequence modeling with masked reconstruction objectives. Among graph-based methods, we consider three widely used variants: (i) DCRNN[44], a diffusion convolutional recurrent network that integrates graph diffusion into GRU updates over a fixed adjacency; (ii) GWNet[45], a spatio-temporal graph convolutional model that combines dilated causal convolutions with adaptive graph learning for spatial mixing; and (iii) AMAG[16], a GNN framework that adaptively learns dynamic channel-level graphs for neural forecasting.

Figure: Figure 3: (A) Task schematic and behavioral segmentation timeline. Each trial comprised four stages with a 400 ms analysis window: Wait ($-400$ ms to Go cue onset), React (0–400 ms after Go cue onset), Reach (0–400 ms after forward reach onset), and Return (0–400 ms after return onset). (B) behavioral-specific $8\times 8$ effective connectivity matrices estimated by BACE across eight subcortical regions (GPi1, GPi2, VIM, STN; left and right hemispheres). Matrix entry $A_{\phi}[i,j]$ denotes directed influence from source region $j$ (column) to target region $i$ (row).
Refer to caption: x3.png

#### Experimental Setup.

All models, including BACE and the five baselines, were trained and evaluated on the same intracranial LFP dataset described above. Each trial was segmented into four behavioral segments of 400 samples, further divided into sliding windows of $T_{\text{in}}{=}100$ input steps and $T_{\text{out}}{=}20$ forecast steps. Models were optimized with the Adam optimizer under their standard hyperparameters (details in Appendix). Training was performed with early stopping on validation loss, and the best checkpoint was used for reporting. Performance was assessed on the held-out test set using three metrics: mean squared error (MSE), coefficient of determination ($R^{2}$), and Pearson correlation (Corr). MSE measures absolute deviation, $R^{2}$ quantifies explained variance, and Corr evaluates trend alignment between predicted and ground-truth signals.

#### Model Performance.

We evaluate the ability of BACE and other models to forecast future neural activity, with multi-step results summarized in Table [1](https://arxiv.org/html/2510.20831v1#S4.T1). Each model was trained and tested on identical splits, and reported values reflect the mean with standard deviation over three runs. Among non-graph methods, LSTM and NDT achieved reasonable accuracy but lagged behind graph-based models, explaining less than 75% of the variance on average, consistent with their limited ability to capture structured inter-regional dependencies. Graph-based methods performed substantially better. DCRNN reached $R^{2}$ of $0.79$ confirming the benefit of incorporating graph priors, but reflecting the limitation that its adjacency is pre-computed and fixed during training. GWNet improved further with adaptive graph learning, and AMAG provided a modest additional gain, validating the utility of dynamic spatial structure. BACE consistently achieved the best performance across all metrics, with an $R^{2}$ of 0.884 and correlation of 0.94, reflecting both lower forecast error and tighter alignment with the true trajectories. By combining strong predictive accuracy with behavioral-specific graph estimation, BACE offers not only numerical improvement but also interpretable connectivity estimates among brain regions.

**Table 1: Multistep forecasting results on the LFP dataset with benchmark methods and BACE. $\uparrow$ indicates higher is better, $\downarrow$ indicates lower is better.**
| Model | R^2 $\uparrow$ | Corr $\uparrow$ | MSE $\downarrow$ |
| --- | --- | --- | --- |
| LSTM | 0.7271 $\pm$ 2$\mathrm{e}^{-3}$ | 0.8353 $\pm$ 4$\mathrm{e}^{-3}$ | 0.2690 $\pm$ 3$\mathrm{e}^{-4}$ |
| NDT | 0.7336 $\pm$ 3$\mathrm{e}^{-3}$ | 0.8610 $\pm$ 3$\mathrm{e}^{-3}$ | 0.2370 $\pm$ 3$\mathrm{e}^{-4}$ |
| DCRNN | 0.7895 $\pm$ 2$\mathrm{e}^{-3}$ | 0.8892 $\pm$ 4$\mathrm{e}^{-3}$ | 0.1822 $\pm$ 6$\mathrm{e}^{-4}$ |
| GWNet | 0.8632 $\pm$ 3$\mathrm{e}^{-3}$ | 0.9296 $\pm$ 4$\mathrm{e}^{-3}$ | 0.1184 $\pm$ 7$\mathrm{e}^{-4}$ |
| AMAG | 0.8676 $\pm$ 4$\mathrm{e}^{-3}$ | 0.9315 $\pm$ 4$\mathrm{e}^{-4}$ | 0.1146 $\pm$ 4$\mathrm{e}^{-4}$ |
| BACE | 0.8836 $\pm$ 3$\mathrm{e}^{-3}$ | 0.9400 $\pm$ 3$\mathrm{e}^{-4}$ | 0.1008 $\pm$ 2$\mathrm{e}^{-4}$ |

#### Computation complexity.

We compare the number of trainable parameters #P(M) and peak GPU memory $M(GB)$ in Table [2](https://arxiv.org/html/2510.20831v1#S4.T2). Parameter counts are determined by the model architecture and thus provide a stable point of comparison, whereas memory usage and runtime are more sensitive to implementation and hardware. BACE has the smallest footprint overall (0.13M parameters, 0.20 GB memory) while training in $\sim$9.8s per epoch. LSTM and NDT require substantially more parameters (0.45M and 0.63M, respectively). GWNet, DCRNN, and AMAG all introduce graph operators that increase both parameter counts and memory consumption, with GWNet the heaviest in terms of parameters. In particular, DCRNN and AMAG have parameter sizes close to BACE but still incur memory cost due to the overhead of diffusion and adaptive graph operators. These results indicate that BACE’s gains arise from its architectural design rather than increased capacity, combining efficiency with interpretability. Compute specifications are provided in Appendix [B.3](https://arxiv.org/html/2510.20831v1#A2.SS3).

**Table 2: Computation complexity for multi-step forecasting. BACE values are in bold; values better than BACE are also highlighted.**
|  | LSTM | NDT | GWNet | DCRNN | AMAG | BACE |
| --- | --- | --- | --- | --- | --- | --- |
| #P (M) | 0.45 | 0.63 | 0.48 | 0.30 | 0.26 | 0.13 |
| $M$ (GB) | 0.15 | 0.84 | 5.54 | 5.22 | 3.30 | 0.20 |

### 4.3 Analysis of Learned Connectivity

#### Reproducibility.

We first asked whether BACE’s learned connectivity graphs are stable across resampled subsets of trials. Split–half analysis showed high reproducibility, with correlations of absolute adjacency magnitudes $|\mathbf{A}^{(k)}|$ exceeding $r{>}0.8$ for all behavioral segments, corresponding to Spearman–Brown corrected [46, 47] full–data repeatability above $0.9$. These results indicate that BACE yields reliable, segment–specific connectivity estimates suitable for scientific interpretation (see Appendix [C](https://arxiv.org/html/2510.20831v1#A3) for full details).

#### Edge reliability and reconfiguration.

We next tested whether directed connectivity patterns reorganize with behavioral context. For each adjacency $\mathbf{A}^{(k)}$, we performed nonparametric bootstrap resampling to estimate confidence intervals and assessed across-context differences with FDR control [48]. Several edges exhibited significant changes between contexts, as illustrated in Fig. [4](https://arxiv.org/html/2510.20831v1#S4.F4)A. These findings suggest that subcortical networks are not strictly static but can flexibly adjust their directed interactions in relation to task demands [6]. Full bootstrap procedures and edgewise statistics are reported in Appendix [C](https://arxiv.org/html/2510.20831v1#A3).

#### Spatial organization.

We next examined whether the learned graphs reflect known spatial regularities of brain connectivity. First, consistent with the principle that networks favor short-range, intra-hemispheric coupling [49, 50], BACE estimated stronger ipsilateral than contralateral connections across all contexts. On average, the mean magnitude of ipsilateral effective connectivity was 9–16% greater than that of contralateral connections (Fig. [4](https://arxiv.org/html/2510.20831v1#S4.F4)C), with statistical testing reported in Appendix [C](https://arxiv.org/html/2510.20831v1#A3). Second, we assessed hemispheric asymmetry expected from contralateral motor organization: because subject performed the task with the left hand, greater outgoing influence from the right hemisphere was anticipated during movement [51, 52]. In result, hemisphere-of-origin analysis showed right side-dominant connectivity in React, Reach, and Return, whereas Wait remained balanced (Fig. [4](https://arxiv.org/html/2510.20831v1#S4.F4)B). Together, these spatial patterns highlight that BACE not only achieves strong predictive accuracy but also produces interpretable connectivity estimates that align with some established organizational principles of brain networks.

Figure: Figure 4: Group-level analyses of behaviorally-specific connectivity. (A) Edges showing significant differences across behavioral conditions, based on bootstrap CIs and Benjamini–Hochberg false discovery rate (FDR) correction. (B) Average outgoing connectivity strength from left vs. right hemisphere sources. (C) Average ipsilateral vs. contralateral connectivity strength.
Refer to caption: x4.png

## 5 Discussion

This work introduced BACE, a framework for estimating behavior-adapted connectivity from multi-region neural recordings. BACE couples forecasting with graph estimation, learning compact, directed inter-regional graphs whose parameters encode predictive interactions. By operating at the region level, the model consolidates many micro-contacts into interpretable embeddings and then estimates connectivity among regions. The resulting adjacency matrices are behavior-specific, and interpretable, supporting network analyses that can be inspected by domain experts.

In synthetic experiments, BACE recovered ground-truth connectivity through forecasting, indicating that dynamics-driven objectives can surface interaction structure in multivariate time series. Applied to human subcortical LFPs during a cued reaching task, the model produced one connectivity matrix per behavioral segment. Comparisons revealed segment-dependent reconfiguration of inter-regional influence, suggesting that deep-brain networks adapt their directed connectivity in a behavior-selective manner. The organization also reflected established principles: stronger ipsilateral than contralateral connections, consistent with wiring-cost and modularity constraints [49, 50], and right-hemisphere dominance during left-hand movement, in line with contralateral motor organization [51, 52]. Methodologically, several design choices contribute to interpretability. Independent regional encoders prevent cross-region leakage prior to graph mixing, adjacency parameterization separates relative edge patterns from broadcast strength, and lightweight temporal regularizers stabilize short-horizon predictions.

While this study provides a proof of concept, it remains limited to a single participant and should be viewed as a case study rather than a population-level analysis. The formulation also assumes labeled behavioral segments, which constrains applicability to datasets without clear trial structure, and the estimated graphs capture effective, predictive influence rather than causal interactions. Nonetheless, these choices allow us to focus on a well-controlled setting and demonstrate feasibility. Future directions, generalization across participants and tasks, integration of anatomical priors (e.g., diffusion tractography) or multimodal signals (EMG, video), and extensions toward continuously time-varying or weakly supervised contexts would broaden applicability. Incorporating causal discovery objectives could further enhance interpretability, and the framework is not specific to LFP: the same region-level design could be adapted to EEG, ECoG, or other neural modalities. Clinically, if replicated across patients and disorders, behavior-adapted connectivity estimates may offer a foundation for hypothesis generation and, in the longer term, inform exploratory simulation studies of deep-brain stimulation strategies, though any translational use will require substantial validation.

## References

- Friston [2011]
Karl J. Friston.
Functional and effective connectivity: A review.
*Brain Connectivity*, 1(1):13–36, 2011.
doi: 10.1089/brain.2011.0008.
- Fornito et al. [2016]
Alex Fornito, Andrew Zalesky, and Edward T. Bullmore.
*Fundamentals of Brain Network Analysis*.
Academic Press, San Diego, CA, 2016.
ISBN 978-0-12-407908-3.
- Mohammadi and Karwowski [2025]
Hamed Mohammadi and Waldemar Karwowski.
Brain connectivity research: Advances, applications, and emerging challenges.
*Neuroscience & Biobehavioral Reviews*, 2025.
In press.
- Srivastava et al. [2022]
Pragya Srivastava, Panagiotis Fotiadis, Linden Parkes, and Dani S. Bassett.
Dynamic reconfiguration of functional brain networks: From description to prediction and control.
*Progress in Neurobiology*, 208:102183, 2022.
doi: 10.1016/j.pneurobio.2021.102183.
- Bassett and Sporns [2017]
Danielle S. Bassett and Olaf Sporns.
Network neuroscience.
*Nature Neuroscience*, 20(3):353–364, 2017.
doi: 10.1038/nn.4502.
- Cole et al. [2013]
Michael W Cole, Jeremy R Reynolds, Jonathan D Power, Grega Repovs, Alan Anticevic, and Todd S Braver.
Multi-task connectivity reveals flexible hubs for adaptive task control.
*Nature neuroscience*, 16(9):1348–1355, 2013.
- Buzsáki et al. [2012]
György Buzsáki, Costas A Anastassiou, and Christof Koch.
The origin of extracellular fields and currents—eeg, ecog, lfp and spikes.
*Nature reviews neuroscience*, 13(6):407–420, 2012.
- Einevoll et al. [2013]
Gaute T Einevoll, Christoph Kayser, Nikos K Logothetis, and Stefano Panzeri.
Modelling and analysis of local field potentials for studying the function of cortical circuits.
*Nature Reviews Neuroscience*, 14(11):770–785, 2013.
- Kasiri et al. [2025a]
Maral Kasiri, Mehrnaz Asadi, Jaya Nataraj, Sumiko Abe, and Terence Sanger.
Optimized dbs in pediatric dystonia restores balance in transmission of signals within pallidothalamic network by modulating neural oscillations in deep brain regions.
*medRxiv*, 2025a.
- Kasiri et al. [2025b]
Maral Kasiri, Jessica Vidmark, Estefania Hernandez-Martin, S Alireza Seyyed Mousavi, and Terence David Sanger.
Deep brain stimulation in globus pallidus internus travels to thalamus and subthalamic nuclei along physiological pathways.
*Frontiers in Neuroscience*, 19:1592689, 2025b.
- Bronstein et al. [2021]
Michael M Bronstein, Joan Bruna, Taco Cohen, and Petar Veličković.
Geometric deep learning: Grids, groups, graphs, geodesics, and gauges.
*arXiv preprint arXiv:2104.13478*, 2021.
- Hutchison et al. [2013]
R Matthew Hutchison, Thilo Womelsdorf, Elena A Allen, Peter A Bandettini, Vince D Calhoun, Maurizio Corbetta, Stefania Della Penna, Jeff H Duyn, Gary H Glover, Javier Gonzalez-Castillo, et al.
Dynamic functional connectivity: promise, issues, and interpretations.
*Neuroimage*, 80:360–378, 2013.
- Preti et al. [2017]
Maria Giulia Preti, Thomas AW Bolton, and Dimitri Van De Ville.
The dynamic functional connectome: State-of-the-art and perspectives.
*Neuroimage*, 160:41–54, 2017.
- Tang et al. [2023]
Siyi Tang, Jared A Dunnmon, Qu Liangqiong, Khaled K Saab, Tina Baykaner, Christopher Lee-Messer, and Daniel L Rubin.
Modeling multivariate biosignals with graph neural networks and structured state space models.
In *Conference on health, inference, and learning*, pages 50–71. PMLR, 2023.
- Kim et al. [2021a]
Byung-Hoon Kim, Jong Chul Ye, and Jae-Jin Kim.
Learning dynamic graph representation of brain connectome with spatio-temporal attention.
*Advances in Neural Information Processing Systems*, 34:4314–4327, 2021a.
- Li et al. [2023]
Jingyuan Li, Leo Scholl, Trung Le, Pavithra Rajeswaran, Amy Orsborn, and Eli Shlizerman.
Amag: Additive, multiplicative and adaptive graph neural network for forecasting neuron activity.
In *Advances in Neural Information Processing Systems*, volume 36, pages 8988–9014, 2023.
- Dahlhaus [2000]
Rainer Dahlhaus.
Graphical interaction models for multivariate time series1.
*Metrika*, 51(2):157–172, 2000.
- Yu et al. [2008]
Byron M Yu, John P Cunningham, Gopal Santhanam, Stephen Ryu, Krishna V Shenoy, and Maneesh Sahani.
Gaussian-process factor analysis for low-dimensional single-trial analysis of neural population activity.
*Advances in neural information processing systems*, 21, 2008.
- Gao et al. [2016]
Yuanjun Gao, Evan W Archer, Liam Paninski, and John P Cunningham.
Linear dynamical neural population models through nonlinear embeddings.
*Advances in neural information processing systems*, 29, 2016.
- Hochreiter and Schmidhuber [1997]
Sepp Hochreiter and Jürgen Schmidhuber.
Long short-term memory.
*Neural computation*, 9(8):1735–1780, 1997.
- Pandarinath et al. [2018]
Chethan Pandarinath, Daniel J O’Shea, Jasmine Collins, Rafal Jozefowicz, Sergey D Stavisky, Jonathan C Kao, Eric M Trautmann, Matthew T Kaufman, Stephen I Ryu, Leigh R Hochberg, et al.
Inferring single-trial neural population dynamics using sequential auto-encoders.
*Nature methods*, 15(10):805–815, 2018.
- Zhou and Wei [2020]
Ding Zhou and Xue-Xin Wei.
Learning identifiable and interpretable latent models of high-dimensional neural activity using pi-vae.
*Advances in neural information processing systems*, 33:7234–7247, 2020.
- Kim et al. [2021b]
Timothy D Kim, Thomas Z Luo, Jonathan W Pillow, and Carlos D Brody.
Inferring latent dynamics underlying neural population activity via neural differential equations.
In *International Conference on Machine Learning*, pages 5551–5561. PMLR, 2021b.
- Ye and Pandarinath [2021]
Joel Ye and Chethan Pandarinath.
Representation learning for neural population activity with neural data transformers.
*arXiv preprint arXiv:2108.01210*, 2021.
- Le and Shlizerman [2022]
Trung Le and Eli Shlizerman.
Stndt: Modeling neural population activity with spatiotemporal transformers.
*Advances in Neural Information Processing Systems*, 35:17926–17939, 2022.
- Sani et al. [2021]
Omid G Sani, Hamidreza Abbaspourazad, Yan T Wong, Bijan Pesaran, and Maryam M Shanechi.
Modeling behaviorally relevant neural dynamics enabled by preferential subspace identification.
*Nature neuroscience*, 24(1):140–149, 2021.
- Behrouz and Hashemi [2024]
Ali Behrouz and Farnoosh Hashemi.
Brain-mamba: Encoding brain activity via selective state space models.
In *Conference on Health, Inference, and Learning*, pages 233–250. PMLR, 2024.
- Jin et al. [2020]
Wei Jin, Yao Ma, Xiaorui Liu, Xianfeng Tang, Suhang Wang, and Jiliang Tang.
Graph structure learning for robust graph neural networks.
In *Proceedings of the 26th ACM SIGKDD international conference on knowledge discovery & data mining*, pages 66–74, 2020.
- Huang and Yu [2022]
Yicong Huang and Zhuliang Yu.
Representation learning for dynamic functional connectivities via variational dynamic graph latent variable models.
*Entropy*, 24(2):152, 2022.
- Zhu et al. [2020]
Hongmin Zhu, Fuli Feng, Xiangnan He, Xiang Wang, Yan Li, Kai Zheng, and Yongdong Zhang.
Bilinear graph neural network with neighbor interactions.
*arXiv preprint arXiv:2002.03575*, 2020.
- Li et al. [2021]
Xiaoxiao Li, Yuan Zhou, Nicha Dvornek, Muhan Zhang, Siyuan Gao, Juntang Zhuang, Dustin Scheinost, Lawrence H Staib, Pamela Ventola, and James S Duncan.
Braingnn: Interpretable brain graph neural network for fmri analysis.
*Medical Image Analysis*, 74:102233, 2021.
doi: 10.1016/j.media.2021.102233.
- Zheng et al. [2024]
Kai Zheng, Song Yu, and Bo Chen.
Ci-gnn: A granger causality-inspired graph neural network for interpretable brain network-based psychiatric diagnosis.
*Neural Networks*, 172:106147, 2024.
ISSN 0893-6080.
doi: 10.1016/j.neunet.2024.106147.
- Ying et al. [2019]
Zhitao Ying, Dylan Bourgeois, Jiaxuan You, Marinka Zitnik, and Jure Leskovec.
Gnnexplainer: Generating explanations for graph neural networks.
*Advances in neural information processing systems*, 32, 2019.
- Said et al. [2023]
Anwar Said, Roza Bayrak, Tyler Derr, Mudassir Shabbir, Daniel Moyer, Catie Chang, and Xenofon Koutsoukos.
Neurograph: Benchmarks for graph machine learning in brain connectomics.
*Advances in Neural Information Processing Systems*, 36:6509–6531, 2023.
- Bessadok et al. [2022]
Alaa Bessadok, Mohamed Ali Mahjoub, and Islem Rekik.
Graph neural networks in network neuroscience.
*IEEE Transactions on Pattern Analysis and Machine Intelligence*, 45(5):5833–5848, 2022.
- Cho et al. [2014]
Kyunghyun Cho, Bart Van Merriënboer, Caglar Gulcehre, Dzmitry Bahdanau, Fethi Bougares, Holger Schwenk, and Yoshua Bengio.
Learning phrase representations using rnn encoder-decoder for statistical machine translation.
*arXiv preprint arXiv:1406.1078*, 2014.
- Biswas and Shlizerman [2022a]
Rahul Biswas and Eli Shlizerman.
Statistical perspective on functional and causal neural connectomics: The time-aware pc algorithm.
*PLOS Computational Biology*, 18(11):e1010653, 2022a.
- Biswas and Shlizerman [2022b]
Rahul Biswas and Eli Shlizerman.
Statistical perspective on functional and causal neural connectomics: A comparative study.
*Frontiers in Systems Neuroscience*, 16:817962, 2022b.
- Song et al. [2009]
Le Song, Mladen Kolar, and Eric P. Xing.
Time-varying dynamic Bayesian networks.
In *Advances in Neural Information Processing Systems*, volume 22, 2009.
- Sanger et al. [2018]
Terence D Sanger, Aaron Robison, Enrique Arguelles, Diana Ferman, and Mark Liker.
Case report: targeting for deep brain stimulation surgery using chronic recording and stimulation in an inpatient neuromodulation monitoring unit, with implantation of electrodes in gpi and vim in a 7-year-old child with progressive generalized dystonia.
*Journal of child neurology*, 33(12):776–783, 2018.
- Kasiri et al. [2023]
Maral Kasiri, Sina Javadzadeh, Jaya Nataraj, Seyyed Alireza Seyyed Mousavi, and Terence Sanger.
Correlated activity in globus pallidus and thalamus during voluntary reaching movement in three children with primary dystonia.
*Dystonia*, 2:11117, 2023.
- Kasiri et al. [2024]
M Kasiri, S Abe, R Soroushmojdehi, E Hernandez-Martin, SA Seyyed Mousavi, and T Sanger.
Local field potential signal transmission is correlated with the anatomical connectivity measured by diffusion tractography.
2024.
- Soroushmojdehi et al. [2025]
Rahil Soroushmojdehi, Jessica SL Vidmark, S Alireza Seyyed Mousavi, Sumiko Abe, and Terence D Sanger.
Frequency-dependent modulation of evoked potentials during gpi-dbs in pediatric dystonia.
*Scientific Reports*, 15(1):33551, 2025.
- Li et al. [2017]
Yaguang Li, Rose Yu, Cyrus Shahabi, and Yan Liu.
Diffusion convolutional recurrent neural network: Data-driven traffic forecasting.
*arXiv preprint arXiv:1707.01926*, 2017.
- Wu et al. [2019]
Zonghan Wu, Shirui Pan, Guodong Long, Jing Jiang, and Chengqi Zhang.
Graph wavenet for deep spatial-temporal graph modeling.
*arXiv preprint arXiv:1906.00121*, 2019.
- Spearman [1910]
Charles Spearman.
Correlation calculated from faulty data.
*British journal of psychology*, 3(3):271, 1910.
- Brown [1910]
William Brown.
Some experimental results in the correlation of mental abilities 1.
*British Journal of Psychology, 1904-1920*, 3(3):296–322, 1910.
- Bradley and Tibshirani [1993]
Efron Bradley and Robert J Tibshirani.
An introduction to the bootstrap.
*Monographs on statistics and applied probability*, 57:158, 1993.
- Bullmore and Sporns [2012]
Ed Bullmore and Olaf Sporns.
The economy of brain network organization.
*Nature reviews neuroscience*, 13(5):336–349, 2012.
- Sporns and Betzel [2016]
Olaf Sporns and Richard F Betzel.
Modular brain networks.
*Annual review of psychology*, 67(1):613–640, 2016.
- Shibasaki and Hallett [2006]
Hiroshi Shibasaki and Mark Hallett.
What is the bereitschaftspotential?
*Clinical neurophysiology*, 117(11):2341–2356, 2006.
- Vingerhoets [2014]
Guy Vingerhoets.
Contribution of the posterior parietal cortex in reaching, grasping, and using objects and tools.
*Frontiers in psychology*, 5:151, 2014.

## Appendix A Method Details

In the main text we denoted the context-specific adjacency by $\mathbf{A}^{(k)}$, a directed
$N\times N$ matrix. Concretely, we parameterize it as

$$ $\mathbf{A}^{(k)}=\mathrm{Diag}(\mathbf{g}^{(k)})\,\bar{\mathbf{S}}^{(k)},$ $$

where $\bar{\mathbf{S}}^{(k)}$ is a signed pattern matrix with zero diagonal and rows normalized
to unit $\ell_{1}$ norm ($\sum_{j}|\bar{S}^{(k)}_{ij}|=1$), and
$\mathbf{g}^{(k)}\in\mathbb{R}_{\geq 0}^{N}$ is a vector of non-negative row gains.
Row normalization of $\bar{\mathbf{S}}^{(k)}$ ensures stability and makes each row interpretable
as a distribution of relative influences onto region $i$, while the row gains $\mathbf{g}^{(k)}$
restore the ability of different regions to vary in their overall incoming strength.
Sparsity is encouraged through an $\ell_{1}$ penalty on the off-diagonal entries of
$\bar{\mathbf{S}}^{(k)}$.

### A.1 Forecasting Head: Implementation Details

#### Attention context.

At each forecast step $t$, the decoder forms a query from its hidden state $\mathbf{h}_{t-1}$
and computes attention weights over the encoder sequence $\mathbf{Z}$ of length $T_{\text{in}}$:

$$ $\mathbf{c}_{t}=\sum_{\tau=1}^{T_{\text{in}}}\alpha_{t,\tau}\,\mathbf{Z}_{\tau},\quad\alpha_{t,\tau}=\frac{\exp(\mathbf{q}_{t}^{\top}\mathbf{k}_{\tau})}{\sum_{\tau^{\prime}}\exp(\mathbf{q}_{t}^{\top}\mathbf{k}_{\tau^{\prime}})}.$ $$

#### Adjacency feedback.

The previous prediction is refined by adjacency mixing:

$$ $\tilde{\mathbf{y}}_{t-1,i}=\hat{\mathbf{y}}_{t-1,i}+\alpha\sum_{j}A^{(k)}_{ij}\,\hat{\mathbf{y}}_{t-1,j},$ $$

where $\alpha$ is a small damping coefficient.
This step enforces that autoregressive forecasts remain connectivity-aware.

#### GRU update.

The decoder state is updated as

$$ $\mathbf{h}_{t}=\text{GRUCell}\big([\mathbf{c}_{t},\tilde{\mathbf{y}}_{t-1}],\mathbf{h}_{t-1}\big),$ $$

where $[\cdot,\cdot]$ denotes concatenation.

#### Residual decoding.

The output increment is computed as

$$ $\Delta\hat{\mathbf{y}}_{t}=W_{o}\mathbf{h}_{t},$ $$

and absolute forecasts are recovered recursively:

$$ $\hat{\mathbf{y}}_{t}=\hat{\mathbf{y}}_{t-1}+\Delta\hat{\mathbf{y}}_{t},\quad\hat{\mathbf{y}}_{0}=\mathbf{x}_{\text{last}}.$ $$

#### Final readout.

Regional predictions are mapped back to the channel level by a linear projection, yielding

$$ $\hat{\mathbf{Y}}\in\mathbb{R}^{N\times C\times T_{\text{out}}}.$ $$

### A.2 Training Objective and Optimization

#### Forecasting objective.

Given past window $\mathbf{X}\in\mathbb{R}^{N\times C\times T_{\text{in}}}$ and future target
$\mathbf{Y}\in\mathbb{R}^{N\times C\times T_{\text{out}}}$, the decoder outputs increments
$\Delta\hat{\mathbf{Y}}$ which are accumulated to produce forecasts

$$ $\hat{\mathbf{Y}}_{t}=\mathbf{X}_{\text{last}}+\sum_{\tau=1}^{t}\Delta\hat{\mathbf{Y}}_{\tau},$ $$

where $\mathbf{X}_{\text{last}}$ is the final observed input sample.
This residual formulation mitigates drift in multi-step prediction.

#### Loss function.

The full training loss is

$$ $\displaystyle\mathcal{L}={}$ $\displaystyle\underbrace{\frac{1}{T_{\text{out}}}\sum_{t=1}^{T_{\text{out}}}w_{t}\big\|\hat{\mathbf{Y}}_{t}-\mathbf{Y}_{t}\big\|_{2}^{2}}_{\text{forecasting MSE}}+\lambda_{S}\,\|\bar{\mathbf{S}}^{(k)}\|_{1,\mathrm{off}}$ (A.1) $\displaystyle+\lambda_{\mathrm{cont}}\,\|\hat{\mathbf{Y}}_{1}-\mathbf{X}_{\text{last}}\|_{2}^{2}+\lambda_{\mathrm{vel}}\,\|\Delta\hat{\mathbf{Y}}_{1}-\Delta\mathbf{Y}_{1}\|_{2}^{2}+\lambda_{\mathrm{curv}}\,\|\Delta^{2}\hat{\mathbf{Y}}-\Delta^{2}\mathbf{Y}\|_{2}^{2}.$ $$

- •
The first term is the mean squared error across the horizon, with log-spaced weights $w_{t}$
emphasizing later steps.
- •
$\|\bar{\mathbf{S}}^{(k)}\|_{1,\mathrm{off}}$ applies an $\ell_{1}$ penalty on the off-diagonal
entries of the normalized pattern matrix, promoting sparse graphs while leaving row gains
$\mathbf{g}^{(k)}$ unconstrained.
- •
Continuity, velocity, and curvature penalties regularize short-term rollouts by aligning the
first prediction with the last input, matching the initial slope, and constraining higher-order
differences.

#### Optimization.

We use Adam (learning rate $10^{-3}$, weight decay $10^{-4}$), gradient clipping at $1.0$,
and early stopping with patience $10$. Graph parameters are initialized from train-only
regionwise correlations (diagonal zeroed), and row gains initialized near one to preserve scale.

## Appendix B Additional Details on Experiments

### B.1 Appendix: Dataset and Preprocessing

#### Participant and Experimental Protocol.

Data were recorded from an 11-year-old male with dyskinetic cerebral palsy approximately five days after temporary deep brain stimulation (DBS) lead implantation surgery. The diagnosis of dystonia was confirmed by a pediatric movement disorder specialist using standard criteria [40]. The study was approved by the local Institutional Review Boards, with informed consent obtained from the patient’s legal guardians.

During the experiment, the subject performed a cued reaching task. At the beginning of each trial, the subject held a “home” button. After a random interval (500–1500 ms), a green “go” cue was presented, prompting the subject to release the home button and reach forward to press a target button. After pressing the target, the subject was instructed to release it and return the hand to the home button to prepare for the next trial. Of 350 attempted trials, 326 valid trials were retained for analysis after exclusion based on task compliance (Fig. [3](https://arxiv.org/html/2510.20831v1#S4.F3)).

#### Recording Electrodes and Acquisition.

Recordings were obtained from up to eight temporary stereoelectroencephalography (sEEG) depth leads (AdTech MM16C), implanted into candidate DBS targets using standard stereotactic procedures. Each lead included six low-impedance macro-contacts (not used in this study) and ten high-impedance micro-contacts (50 $\mu$m, 70–90 k$\Omega$). Signals were digitized at 24,414 Hz with a PZ5M 256-channel digitizer and RZ2 processor, and stored on an RS4 system (Tucker-Davis Technologies). Only local field potentials (LFP) from the micro-contacts were analyzed.

#### Preprocessing.

All signals were low-pass filtered at 50 Hz, re-referenced to the common average, and downsampled to 1 kHz to yield LFP time series suitable for analysis.

#### Trial Segmentation.

Each trial was segmented into four behavioral segments of equal length (400 ms):

- •
Wait: 400 ms preceding the go cue onset.
- •
React: 0–400 ms following cue onset, prior to movement initiation.
- •
Reach: from reach onset to 400 ms after.
- •
Return: from return onset to 400 ms after.

This segmentation ensured consistent windows across trials aligned to behavioral events.

#### Sliding Windowing and Data Splitting.

Within each behavioral segment, data were divided into overlapping windows of length $T_{\text{in}}=100$ samples for input and $T_{\text{out}}=20$ samples for forecasting, with stride 20. The dataset was split into training, validation, and test sets at the *trial* level (not at the window level) to prevent data leakage. Normalization parameters (mean and standard deviation) were computed on the training set and applied consistently across validation and test sets.

### B.2 Additional model details

#### Details of Comparison Models.

#### LSTM.

We build a two-layer LSTM forecaster with hidden dimension $128$. The model takes past windows of length $100$ across all $80$ channels and predicts the next $20$ steps jointly for every channel. Training is performed with mean squared error loss using the Adam optimizer, with learning rate $10^{-3}$, weight decay $10^{-4}$, and gradient clipping at $1.0$. Models are trained for up to $100$ epochs with early stopping (patience of $10$, minimum delta $10^{-4}$), and the best checkpoint is selected based on validation loss. Evaluation reports mean squared error on the test set.

#### NDT.

We implement a Neural Data Transformer (NDT) baseline under a masked-forecasting setup. While NDT is typically used to reconstruct randomly masked neural activity, we adapt it for forecasting by designating the final $20$ steps of each window as the masked segment. The model is a three-layer Transformer with attention dimension $128$, applied over windows of length $100{+}20$ across all channels. During training, the past $100$ bins are provided while the last $20$ bins are zero-masked, and the model is optimized to reconstruct only this masked future segment. Training uses the Adam optimizer with learning rate $10^{-4}$, weight decay $10^{-5}$, and early stopping based on validation loss.

#### Graph WaveNet.

We implement Graph WaveNet (GWNet) to benchmark forecasting performance on the Button Task LFP dataset. The architecture consists of three layers, each composed of two spatio-temporal blocks (six blocks in total). Each block integrates (i) a gated dilated temporal convolution, (ii) a graph convolutional module for spatial mixing, and (iii) residual and skip connections. All temporal convolutions use kernel size $2$, with $64$ channels in the residual and dilated paths and $128$ channels in the skip path. The skip outputs are aggregated and passed through a two-stage output head consisting of a $1\times 1$ convolution with $64$ channels followed by a read-out convolution mapping to the $20$-step forecasting horizon. Training is performed using the Adam optimizer with an initial learning rate of $5\times 10^{-4}$, decayed by $0.95$ every $50$ epochs, and no weight decay. Static graph supports are constructed from training data via correlation-based $k$-nearest neighbors, and an adaptive adjacency matrix is learned jointly during training.

#### DCRNN.

We implement the Diffusion Convolutional Recurrent Neural Network (DCRNN) using a sequence-to-sequence architecture with diffusion convolutional GRU (DCGRU) cells. Both encoder and decoder consist of two stacked DCGRU layers with hidden dimension $64$. Each DCGRU layer performs diffusion convolution with $K{=}2$ steps. The model is trained with the Adam optimizer (learning rate $5\times 10^{-4}$, decayed by $0.95$ every $50$ epochs), no weight decay, and scheduled sampling (inverse-sigmoid with $\tau{=}3000$).

#### AMAG.

For multi-step forecasting, we implement AMAG with a single-layer Transformer encoder and decoder, each with hidden size $64$ and two attention heads. Both encoder and decoder operate on $80$-channel inputs with positional encodings. The sample-dependent adaptor MLP takes concatenated hidden features from node pairs and applies four sequential fully connected layers of sizes $64\times t$, $64\times 2$, $64\times 4$, and $64$, followed by a scalar output with sigmoid activation. Training uses the Adam optimizer with an initial learning rate of $5\times 10^{-4}$, decaying by $0.95$ every $50$ epochs, with early stopping based on validation loss.

### B.3 Compute Resources

All models were trained on a single workstation equipped with an AMD Ryzen Threadripper PRO 7955WX CPU (16 cores), 128 GiB RAM, and one NVIDIA RTX 4500 Ada GPU (24 GiB VRAM). Training was performed using PyTorch 2.2 with CUDA 12.2.

Table [2](https://arxiv.org/html/2510.20831v1#S4.T2) in the main text summarizes the parameter counts and peak memory usage for each model. Average epoch training times are reported alongside in the results section.

## Appendix C Statistical Inference of Connectivity

While forecasting accuracy serves as the primary training signal, we further evaluate the stability and significance of the learned graphs.

#### Split–half reproducibility.

For each behavioral context $k$, we performed $K{=}50$ random half–splits of trials. Graph parameters $(\mathbf{S}^{(k)},\mathbf{g}^{(k)})$ were re–estimated on each half, and Pearson correlations of $|\mathbf{A}^{(k)}|$ were computed. Spearman–Brown correction extrapolated full–data repeatability. Mean split–half correlations (95% confidence intervals) were:
Wait $r{=}0.90$ [0.83, 0.94],
React $r{=}0.88$ [0.82, 0.93],
Reach $r{=}0.91$ [0.86, 0.94],
Return $r{=}0.83$ [0.75, 0.89].
The corresponding Spearman–Brown coefficients were 0.95, 0.94, 0.95, and 0.91, respectively. These values indicate that context-specific graphs are highly reproducible across independent subsets.

#### Bootstrap resampling.

For precision of individual edges, we performed $B{=}1000$ nonparametric bootstrap resamples per context, refitting only graph parameters while holding encoder/decoder weights fixed. For each edge $(i,j)$, we computed percentile 95% confidence intervals of $|A^{(k)}_{ij}|$. An edge was considered reliable if its CI excluded zero and its sign was consistent in at least 80% of resamples.

#### Edgewise precision.

Absolute CI widths were narrow and consistent across contexts (medians $\approx 0.05$–$0.07$; few edges $>0.10$). To provide a scale–free summary, we report the relative half–width

$$ $\mathrm{rHW}=\frac{\mathrm{hi}-\mathrm{lo}}{2\,|\mathrm{median}|},$ $$

evaluated on edges whose median magnitude exceeded a threshold $\tau$ (66th percentile). Median rHW values were $\approx 0.12$–$0.20$, meaning nontrivial edges had 95% intervals of about $\pm$12–20% of their estimate.

#### Across–context differences.

To detect reconfiguration, we computed bootstrap distributions of edgewise differences

$$ $\Delta_{ij}=|A^{(k_{1})}_{ij}|-|A^{(k_{2})}_{ij}|,$ $$

applied two–sided sign tests, and corrected using Benjamini–Hochberg FDR ($\alpha{=}0.05$). Fig. [4](https://arxiv.org/html/2510.20831v1#S4.F4)A displays only those edges whose CIs excluded zero and survived correction. Complete edgewise statistics (median $\Delta$, CI, $p$, $q$) are reported in the supplement.

#### Ipsilateral vs. contralateral.

We quantified lateral organization by comparing average magnitudes of ipsilateral and contralateral connections. A one–sided paired bootstrap test ($B{=}1000$) on the log–ratio confirmed stronger ipsilateral connectivity in three of four contexts (Wait $p{<}0.05$, React $p{<}0.001$, Reach $p{<}0.01$).

#### Hemisphere dominance.

For lateralized motor organization, we averaged outgoing effective connectivity $\overline{|A^{(k)}_{\mathrm{eff}}|}$ from each hemisphere. Right–hemisphere dominance emerged during movement contexts (React, Reach, Return) but not Wait. A complementary bootstrap test on the log–ratio is reported in the supplement.

#### The Use of Large Language Models (LLMs).

LLMs were used as a general-purpose tool for editing, code debugging, and literature organization. Their role was limited to improving clarity of writing, drafting boilerplate sections, and suggesting implementation fixes. All research questions, methods, analyses, and conclusions were developed by the authors, and the LLM is not considered a scientific contributor.

## Peer Reviews

confidence: 3
contribution: 1
initial_rating: 2
presentation: 2
questions: ### General
- Methodological rigor and contribution seem to be limited compared to the value of the real-world human data. The work may be of more interest to the readers from other conferences or journals.

### Major
- Please add explanations and/or experiments on current and other architectural choices.
- Please consider adding more recent baseline methods in the main comparative experiment.
soundness: 2
strengths: - The method is validated on real-world human data, which is extremely difficult to acquire.
- The work addresses an important topic in the field of neuroimaging: the discovery of effective connectivity with interpretability.
summary: This paper proposes behavior-adaptive connectivity estimation (BACE) to approximate the effective connectivity of brain signals recorded via electrodes using a neural network. On a synthetic dataset, the model successfully reconstructs matrices similar to the true effective connectivity. Application to real-world human data also suggests that the estimated effective connectivity captures clinically meaningful information.
weaknesses: - The choice of the modules within the architecture is rather simple. The paper would benefit from further explanations and comparative experiments on the architectural choice.
- More recent baseline methods can be included in the comparative experiments.
- The study remains proof-of-concept, with a single-subject data.

---

confidence: 3
contribution: 3
initial_rating: 4
presentation: 3
questions: 1. Limited and Non-Generalizable Experimental Validation

Although the authors release the code, the real dataset used in experiments is private and single-subject, consisting of intracranial LFP recordings from one clinical patient. This makes it impossible to reproduce the reported results or assess how well the model generalizes to other participants, tasks, or data modalities. The empirical evaluation is therefore too narrow to support strong claims about the model’s general effectiveness.

2. Dependence on Predefined Behavioral Phase Labels

The framework requires explicit behavioral phase annotations (“Wait”, “React”, “Reach”, “Return”) as inputs to learn phase-specific connectivity. This reliance on manually segmented data limits its applicability to real-world, continuous, or unlabeled neural recordings, where such phase labels are unavailable.

3. Limited Causal and Biological Interpretability

The model estimates effective (predictive) connectivity, not true causal interactions. The learned directed edges capture statistical dependencies that may not reflect actual neural influence. Without causal modeling or multimodal validation (e.g., cortical or anatomical data), the biological interpretability and neuroscientific conclusions remain tentative.
soundness: 3
strengths: The paper introduces a novel and conceptually well-motivated framework, BACE, that jointly performs neural time-series forecasting and interpretable, behavior-adaptive connectivity estimation. Its main strength lies in combining predictive modeling with explicit, directed graph structures that reveal how neural interactions change across behavioral phases. The approach offers clear interpretability, allowing neuroscientific insights into dynamic brain networks, and demonstrates competitive forecasting accuracy compared to baselines such as DCRNN, GWNet, and AMAG.
summary: This paper presents BACE (Behavior-Adaptive Connectivity Estimation), a method that learns phase-specific directed graphs representing inter-regional neural connectivity from time-series data. The idea of behavior-adaptive, interpretable connectivity estimation is novel and well-motivated, and the paper is clearly written. However, the empirical validation is too limited: all real-data experiments use a single-subject, non-public intracranial LFP dataset, preventing reproducibility and generalization. The method also depends on manually defined behavioral phases and models effective rather than causal connectivity.
weaknesses: The main weaknesses of the paper lie in its limited empirical validation and lack of reproducibility. All real-data experiments are conducted on a single-subject, private intracranial LFP dataset, which cannot be shared due to clinical restrictions, making it impossible for others to reproduce or verify the results. The method also depends on manually defined behavioral phase labels, restricting its applicability to structured experimental settings rather than continuous or naturalistic data. Moreover, the inferred graphs capture effective (predictive) rather than causal connectivity, so the biological interpretability of the results remains limited. Finally, the learned connectivity is static within each phase and has not been tested across multiple subjects, modalities, or tasks, which weakens the generalizability and robustness of the proposed framework.

---

confidence: 4
contribution: 2
initial_rating: 2
presentation: 3
questions: -
soundness: 2
strengths: The methods' results on the simulation set are encouraging and look quite good. Moreover, I believe the authors are working on an interesting problem, and that although this paper has a lot of potential, it needs more work before I can recommend it for publication. I commend the authors on their work, and encourage them to continue improving it.
summary: The authors propose a model that infers effective connectivity between multiple brain regions from local field potentials (LFP) by modeling the signal in each region as a combination of dynamics from other brain regions, and an internal regional generator. The authors describe their method from a graph neural network perspective, and use this framework to propose a model that achieves good reconstruction and simulation results.
weaknesses: Major weaknesses:
1) Baselines and missing related work. Given the interest in this field, I believe the authors are missing a large amount of relevant previous work and baselines. First, the authors do not compare any baselines on their simulation experiments, so it is unclear whether their proposed method uniquely can perform well on the simulation. Second, although the authors refer to their connectivity as 'effective', which I agree with, they do not compare to any commonly used effective connectivity measures such as Granger causality, dynamic causal modeling, transfer entropy, etc. Third, the authors do not compare or discuss any of the methods from a rich field of multi-region communication inference. Just to name a few papers that the authors should compare against or at the very least discuss are CURBD [1], DLAG [2], and MR-SDS [3], among others. All of these works are very closely related to the authors' work, but none are cited nor compared against. 
2) Predictive behavior can be due to the capacity of the single-region encoder/decoder. Given the use of recurrent neural networks and the specific formulation the authors' use, it is unclear to me how the authors ensure that most of the variance in a region is not just captured by a region's specific neural network. More specifically: the authors describe that their GRU creates embeddings for each region $\mathbf{H_r} \in \mathbb{R}^{T \times d}$, where T and d are the number of input temporal steps, and the number of latent dimensions for region r. This embedding is then multiplied by $W_{\text{self}}$ (which has no restrictions it seems as opposed to $A$) plus a region-interaction term involving A to obtain $\mathbf{Z_{i,t}}$. Subsequently, $\mathbf{Z}$ is used to forecast new time steps. How do the authors avoid that the GRU just learns to forecast the next timesteps without much influence from the interactions? If values in A are restricted to be between -1 and 1, then $W_{\text{self}}$ can just learn to have large values and become the dominant force in forecasting. Although the authors try to reduce this issue with what they call adjacency mixing, they use a (presumably) learnable factor $\alpha$, which could reasonably lead to a small impact of A on the forecasted time steps $y_{t-1}$. Moreover, in the LFP data the authors use, they do not use their model to generalize to unseen contexts/tasks, so the GRU can reasonably learn the temporal shape of the time series for each task. Moreso, the authors split based on each trial, so it is not unreasonable that the GRU can explicitly learn the temporal shape for each trial in the training set and that this shape is quite similar to the temporal shapes in the test set.
3) The method requires the model to know the context. This reduces the generalizability of the method.

Minor weaknesses:
- It is unclear to me what makes the method phase-specific. In fact the authors refer to the graph learner as phase-specific both in the text and Figure 1, but in Section 3 the paragraph heading is 'Context-specific graph learner'. I do not see how the method computes the phase of the signal (i.e. through a Fourier transform), or does phase here refer to context as in 'a different phase of experiment'? The authors should clear up their use of language, especially because there are many phase-based connectivity measures [4].
- Generally it is unclear to me exactly what the context-specific graph learner does or how it produces each A, are the A matrices just learnable parameters?
- The authors do not address the issue of scaling, specifically because they use a separate GRU for each region, the number of parameters would quickly grow with a larger number of brain areas under consideration.
- The authors provide limited neuroscientific grounding for their claim that the directed region-level graph should be different for different task contexts. The authors claim in the discussion that '... the model produced one connectivity matrix per behavioral segment.' but this is a design choice. There is some neuroscientific discussion in the sentences after this statement, but it lacks depth and a firm grounding of the results.
- The authors place a lot of focus on computation complexity, even though each of the methods they compare against is quite low in computational complexity, instead the authors should focus on better baselines and a broader discussion of the implications of their results.
- L116-117 The authors should introduce AMAG before using it in the text, a previous reference to AMAG on L59 is too far back for comfortable reading
- L308-309 The authors mention the Appendix, but not the exact section.

[1] Perich, M. G., Arlt, C., Soares, S., Young, M. E., Mosher, C. P., Minxha, J., ... & Rajan, K. (2020). Inferring brain-wide interactions using data-constrained recurrent neural network models. BioRxiv, 2020-12. \
[2] Gokcen, E., Jasper, A. I., Semedo, J. D., Zandvakili, A., Kohn, A., Machens, C. K., & Yu, B. M. (2022). Disentangling the flow of signals between populations of neurons. Nature Computational Science, 2(8), 512-525. \
[3] Karniol-Tambour, O., Zoltowski, D. M., Diamanti, E. M., Pinto, L., Brody, C. D., Tank, D. W., & Pillow, J. W. (2024). Modeling state-dependent communication between brain regions with switching nonlinear dynamical systems. In The Twelfth International Conference on Learning Representations. \
[4] https://direct.mit.edu/books/monograph/4013/chapter/167048/Phase-Based-Connectivity \

---

confidence: 4
contribution: 3
initial_rating: 4
presentation: 2
questions: I believe I don't have any further questions beyond what I mention in the Weaknesses section. I'll reconsider only my score if the authors successfully tackle the main weakness I've identified, but a productive rebuttal would touch in all the points I've highlighted in Weaknesses except points (3) and (4).
soundness: 2
strengths: I don't have experience with the specific applied area, but assuming that the Introduction and Related Work sections are a good depiction of the field, this is indeed a very interesting work, and what a good domain-informed ML work should look like: there are domain-specific challenges and a new methodology is developed to tackle those challenges by creatively combining existing ideas. The experiments seem to show reasonable support that this method works, showing good performance across a synthetic and real-world dataset, across different baselines at a reduced computational cost. I should also comment that the Reproducibility analysis on section 4.3 is a really good one (ie, to check consistency of the model across different subsets of training data), as in my experience many deep learning models suffer from an annoying big lack of consistency when different seeds or training folds are used, and so I'd like to commend the authors for this specific experiment.

Despite these strengths, I have important concerns about the fairness of the comparisons used in this paper, and so for now I'm leaning towards rejection; hopefully this could change during the rebuttal period)
summary: This paper introduces BACE, a graph-learning framework that estimates directed, behaviour-specific brain connectivity from multi-region time series. BACE uses per-region GRU encoders and a learned adjacency matrix specific to each behavioural phase to forecast future neural signals while revealing interpretable regional interactions. BACE accurately recovers synthetic graphs, and real intracranial LFP recordings, with better performance when compared to a series of different baselines.
weaknesses: # Main Weakness
I have a main/key concern with this work, related to the fact that it seems that BACE's ability to learn "phase-specific" graphs depends on manually provided phase information. The model does not seem to infer the behaviour intervals; rather, it requires the trial data to be split by known behavioural phases (ie, phases seem to have been defined by marked events, I'm guessing done by doctors). This manual definition of contexts gives BACE additional information that baseline models did not have access to, raising fairness issues in the comparisons. If BACE knows the current phase (and uses a dedicated adjacency for that phase), it effectively has an "oracle" guiding it on when network changes can occur, whereas baselines had to model the entire sequence without such information. This could partly explain BACE’s superior performance. The paper should clarify whether phase indicators were indeed provided as inputs or used to select adjacency matrices during training. If so, the authors should justify whether the comparisons are fair, for instance could the baselines be extended with the same phase information? As it stands, it seems that none of the baseline models were given information about phase intervals or allowed to have different dynamics per phase. This means BACE had an advantage by effectively training a model with different parameters in each phase while others had to use one set of parameters across the whole trial.

To fairly assess the benefit of BACE, it would help to compare against at least one baseline that also leverages phase information. For instance, one could train separate baselines for each phase, or provide a one-hot phase indicator to a baseline as input. Without such comparisons, it’s unclear how much of BACE’s success comes from its novel architecture or just from privileged information. This issue needs clarification and possibly further experiments.


# Other Weaknesses

2. The paper makes a lot of bold claims in Introduction that I don't think are actually defended in the paper, and thus it would be good to get a clarification during the rebuttal period, specifically:
   1. proving/defending why contacts are high-dimensional and non-Euclidean (given we are talking I believe of only 8 such contacts, this claim seems difficult to defend?)
   2. Quantifying uncertainty
   3. Decoupling edge pattern from transmission strength
3. I think the paper can be improved with regards to clarity. 
   1. Firstly, I was only finally able to understand what these "behaviours" are in section 4.2. Up until then, the paper keeps mentioning behaviours (sometimes using other adjacent/related words like phase and context as if they were the same, adding to the confusion) as the key important part of this paper without any basic explanation to at least have an idea of what we are talking about.    
   2. Introduction mentions a "cued reaching task" which, given the broad computational background of ICLR, would require a brief explanation of what that is for better readability.
   3. Figure 1's caption mentions an adjacency $A_\phi$ that doesn't exist in the figure itself, while also saying "behavioral segment" in the caption while the figure instead uses the concept "Phase-specific".
   4. In the Methods section, regions are sometimes referred with letter "r" and other times with letter "i".
   5. What are the "contacts" mentioned on the the 3rd paragraph of Introduction which seem to be central to the motivation of this work?
   6. Figure 3, pane A, has some wiggly red lines under "ms"
4. I know this is mentioned in the Discussion section, but I have to highlight that the fact that only one participant was used means that we have no evidence that BACE could work for other individuals. Given this, one would expect more extensive comparisons to be more sure about the strengths of this work (as I'm detailing in this section)
5. A bit related to my main concern to this paper, I'm also concerned about how the baselines were trained. In the text it is said that models were optimised "under their standard hyperparameters", but that is not fair as it is well known how hyperparameters can be widely different for different datasets. Furthermore, given the strong claims on computational comparison, this is even more important; for example some of the models seem to have several hidden layers, and it is not clear whether a simpler structure would achieve similar results and thus making the claim of computational efficiency weaker.
6. A bit related to the previous point, it's unclear how much tuning of hyperparameters (e.g., GRU lengths, learning rate, etc.) was needed for this dataset. For example, the sliding windows and forecast steps were presumably chosen based on the task's timing, and the reliance on specific timings suggests the model might need careful setup for each new dataset. This isn't necessarily a flaw, but it means the method might require domain knowledge to deploy, and the paper doesn't discuss sensitivity to these choices, which in my opinion is an oversight given the reliance on a single dataset. Some justification of these design decisions and impact on interpretability would improve clarity and confidence that the approach can be adapted beyond the exact scenario presented.
7. No ablation study was done on the different components of the model to understand impact in performance. This ablation could be done in many different ways, but one that I think could be useful would be to use a single adjacency (ie, no phase differentiation), which would directly test how much benefit the behaviour conditioning provides in terms of forecasting accuracy.


Decision: Reject